LMFDB - Embedded newform 630.2.u.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(109,630)]

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, 3, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("630.109");

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.u (of order $6$, 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:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	630.289
Dual form			630.2.u.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +(0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +(0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.133975 + 2.23205i) q^{10} -2.00000i q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(1.00000 - 2.00000i) q^{20} +(-0.866025 - 0.500000i) q^{23} +(-1.96410 + 4.59808i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(2.59808 - 0.500000i) q^{28} -1.00000 q^{29} +(-5.00000 - 8.66025i) q^{31} +(0.866025 - 0.500000i) q^{32} +2.00000 q^{34} +(-5.73205 + 1.46410i) q^{35} +(-6.92820 - 4.00000i) q^{37} +(1.73205 - 1.00000i) q^{38} +(-1.86603 + 1.23205i) q^{40} +3.00000 q^{41} +5.00000i q^{43} +(0.500000 + 0.866025i) q^{46} +(-6.92820 - 4.00000i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(4.00000 - 3.00000i) q^{50} +(1.73205 - 1.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-2.50000 - 0.866025i) q^{56} +(0.866025 + 0.500000i) q^{58} +(-1.00000 - 1.73205i) q^{59} +(4.50000 - 7.79423i) q^{61} +10.0000i q^{62} -1.00000 q^{64} +(-3.73205 + 2.46410i) q^{65} +(6.06218 - 3.50000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +(5.69615 + 1.59808i) q^{70} -6.00000 q^{71} +(-8.66025 + 5.00000i) q^{73} +(4.00000 + 6.92820i) q^{74} -2.00000 q^{76} +(-5.00000 + 8.66025i) q^{79} +(2.23205 - 0.133975i) q^{80} +(-2.59808 - 1.50000i) q^{82} +9.00000i q^{83} +(4.00000 + 2.00000i) q^{85} +(2.50000 - 4.33013i) q^{86} +(3.50000 - 6.06218i) q^{89} +(-5.00000 - 1.73205i) q^{91} -1.00000i q^{92} +(4.00000 + 6.92820i) q^{94} +(4.46410 - 0.267949i) q^{95} +(2.59808 + 6.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{5}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^5	$ 4 q + 2 q^{4} + 2 q^{5} + 4 q^{10} - 8 q^{14} - 2 q^{16} - 4 q^{19} + 4 q^{20} + 6 q^{25} - 4 q^{26} - 4 q^{29} - 20 q^{31} + 8 q^{34} - 16 q^{35} - 4 q^{40} + 12 q^{41} + 2 q^{46} - 22 q^{49} + 16 q^{50} - 10 q^{56} - 4 q^{59} + 18 q^{61} - 4 q^{64} - 8 q^{65} + 2 q^{70} - 24 q^{71} + 16 q^{74} - 8 q^{76} - 20 q^{79} + 2 q^{80} + 16 q^{85} + 10 q^{86} + 14 q^{89} - 20 q^{91} + 16 q^{94} + 4 q^{95}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^5 + 4 * q^10 - 8 * q^14 - 2 * q^16 - 4 * q^19 + 4 * q^20 + 6 * q^25 - 4 * q^26 - 4 * q^29 - 20 * q^31 + 8 * q^34 - 16 * q^35 - 4 * q^40 + 12 * q^41 + 2 * q^46 - 22 * q^49 + 16 * q^50 - 10 * q^56 - 4 * q^59 + 18 * q^61 - 4 * q^64 - 8 * q^65 + 2 * q^70 - 24 * q^71 + 16 * q^74 - 8 * q^76 - 20 * q^79 + 2 * q^80 + 16 * q^85 + 10 * q^86 + 14 * q^89 - 20 * q^91 + 16 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$6$		0			0
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.133975	+	2.23205i	0.0423665	+	0.705836i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	0.275029	+	0.961436i	$0.411312\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	1.00000	−	2.00000i	0.223607	−	0.447214i
$21$		0			0
$22$		0			0
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	0.406986	−	0.913434i	$-0.366580\pi$
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	−0.587565	+	0.809177i	$0.699913\pi$
$24$		0			0
$25$	−1.96410	+	4.59808i	−0.392820	+	0.919615i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$		0			0
$28$	2.59808	−	0.500000i	0.490990	−	0.0944911i
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$		0			0
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.0680129	−	0.997684i	$-0.521666\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	2.00000			0.342997
$35$	−5.73205	+	1.46410i	−0.968893	+	0.247478i
$36$		0			0
$37$	−6.92820	−	4.00000i	−1.13899	−	0.657596i	−0.192809	−	0.981236i	$-0.561760\pi$
$37$	−6.92820	−	4.00000i	−1.13899	−	0.657596i	−0.946180	+	0.323640i	$0.895093\pi$
$38$	1.73205	−	1.00000i	0.280976	−	0.162221i
$39$		0			0
$40$	−1.86603	+	1.23205i	−0.295045	+	0.194804i
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$		0			0
$43$			5.00000i			0.762493i	0.924473	+	0.381246i	$0.124505\pi$
$43$			5.00000i			0.762493i	−0.924473	+	0.381246i	$0.875495\pi$
$44$		0			0
$45$		0			0
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.0992202	−	0.995066i	$-0.531635\pi$
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.911362	+	0.411606i	$0.864968\pi$
$48$		0			0
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$		0			0
$52$	1.73205	−	1.00000i	0.240192	−	0.138675i
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	−0.0987002	−	0.995117i	$-0.531468\pi$
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	0.812447	+	0.583036i	$0.198135\pi$
$54$		0			0
$55$		0			0
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$		0			0
$58$	0.866025	+	0.500000i	0.113715	+	0.0656532i
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	0.793560	−	0.608492i	$-0.208225\pi$
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	−0.923749	+	0.382998i	$0.874892\pi$
$60$		0			0
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	−0.419748	−	0.907641i	$-0.637882\pi$
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	0.995914	−	0.0903080i	$-0.0287851\pi$
$62$			10.0000i			1.27000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.73205	+	2.46410i	−0.462904	+	0.305634i
$66$		0			0
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	−0.0816792	−	0.996659i	$-0.526028\pi$
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	0.822292	+	0.569066i	$0.192695\pi$
$68$	−1.73205	−	1.00000i	−0.210042	−	0.121268i
$69$		0			0
$70$	5.69615	+	1.59808i	0.680820	+	0.191007i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−8.66025	+	5.00000i	−1.01361	+	0.585206i	−0.912245	−	0.409644i	$-0.865653\pi$
$73$	−8.66025	+	5.00000i	−1.01361	+	0.585206i	−0.101361	+	0.994850i	$0.532320\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$		0			0
$76$	−2.00000			−0.229416
$77$		0			0
$78$		0			0
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$	2.23205	−	0.133975i	0.249551	−	0.0149788i
$81$		0			0
$82$	−2.59808	−	1.50000i	−0.286910	−	0.165647i
$83$			9.00000i			0.987878i	0.869496	+	0.493939i	$0.164443\pi$
$83$			9.00000i			0.987878i	−0.869496	+	0.493939i	$0.835557\pi$
$84$		0			0
$85$	4.00000	+	2.00000i	0.433861	+	0.216930i
$86$	2.50000	−	4.33013i	0.269582	−	0.466930i
$87$		0			0
$88$		0			0
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	−0.618720	−	0.785611i	$-0.712349\pi$
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	0.989720	+	0.143022i	$0.0456819\pi$
$90$		0			0
$91$	−5.00000	−	1.73205i	−0.524142	−	0.181568i
$92$		−	1.00000i		−	0.104257i
$93$		0			0
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$	4.46410	−	0.267949i	0.458007	−	0.0274910i
$96$		0			0
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	2.59808	+	6.50000i	0.262445	+	0.656599i
$99$		0			0
$100$	−4.96410	+	0.598076i	−0.496410	+	0.0598076i
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$		0			0
$103$	9.52628	+	5.50000i	0.938652	+	0.541931i	0.889538	−	0.456862i	$-0.151027\pi$
$103$	9.52628	+	5.50000i	0.938652	+	0.541931i	0.0491146	+	0.998793i	$0.484360\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	−6.00000			−0.582772
$107$	6.06218	+	3.50000i	0.586053	+	0.338358i	0.763535	−	0.645766i	$-0.223462\pi$
$107$	6.06218	+	3.50000i	0.586053	+	0.338358i	−0.177482	+	0.984124i	$0.556795\pi$
$108$		0			0
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	0.960558	−	0.278078i	$-0.0896974\pi$
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	−0.721102	+	0.692829i	$0.756364\pi$
$110$		0			0
$111$		0			0
$112$	1.73205	+	2.00000i	0.163663	+	0.188982i
$113$			10.0000i			0.940721i	0.882474	+	0.470360i	$0.155876\pi$
$113$			10.0000i			0.940721i	−0.882474	+	0.470360i	$0.844124\pi$
$114$		0			0
$115$	0.133975	+	2.23205i	0.0124932	+	0.208140i
$116$	−0.500000	−	0.866025i	−0.0464238	−	0.0804084i
$117$		0			0
$118$			2.00000i			0.184115i
$119$	1.00000	+	5.19615i	0.0916698	+	0.476331i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−7.79423	+	4.50000i	−0.705656	+	0.407411i
$123$		0			0
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	4.46410	−	0.267949i	0.391528	−	0.0235007i
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.0155672	−	0.999879i	$-0.495045\pi$
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.858137	−	0.513421i	$-0.171622\pi$
$132$		0			0
$133$	3.46410	+	4.00000i	0.300376	+	0.346844i
$134$	−7.00000			−0.604708
$135$		0			0
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	13.8564	−	8.00000i	1.18383	−	0.683486i	0.226935	−	0.973910i	$-0.427130\pi$
$137$	13.8564	−	8.00000i	1.18383	−	0.683486i	0.956898	+	0.290424i	$0.0937963\pi$
$138$		0			0
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	−4.13397	−	4.23205i	−0.349385	−	0.357674i
$141$		0			0
$142$	5.19615	+	3.00000i	0.436051	+	0.251754i
$143$		0			0
$144$		0			0
$145$	1.23205	+	1.86603i	0.102316	+	0.154965i
$146$	10.0000			0.827606
$147$		0			0
$148$		−	8.00000i		−	0.657596i
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	−0.376061	−	0.926595i	$-0.622722\pi$
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	0.990485	−	0.137619i	$-0.0439449\pi$
$150$		0			0
$151$	−3.00000	−	5.19615i	−0.244137	−	0.422857i	0.717752	−	0.696299i	$-0.245171\pi$
$151$	−3.00000	−	5.19615i	−0.244137	−	0.422857i	−0.961888	+	0.273442i	$0.911838\pi$
$152$	1.73205	+	1.00000i	0.140488	+	0.0811107i
$153$		0			0
$154$		0			0
$155$	−10.0000	+	20.0000i	−0.803219	+	1.60644i
$156$		0			0
$157$	10.3923	−	6.00000i	0.829396	−	0.478852i	−0.0242497	−	0.999706i	$-0.507720\pi$
$157$	10.3923	−	6.00000i	0.829396	−	0.478852i	0.853646	+	0.520854i	$0.174386\pi$
$158$	8.66025	−	5.00000i	0.688973	−	0.397779i
$159$		0			0
$160$	−2.00000	−	1.00000i	−0.158114	−	0.0790569i
$161$	−2.00000	+	1.73205i	−0.157622	+	0.136505i
$162$		0			0
$163$	−10.3923	−	6.00000i	−0.813988	−	0.469956i	0.0343508	−	0.999410i	$-0.489064\pi$
$163$	−10.3923	−	6.00000i	−0.813988	−	0.469956i	−0.848339	+	0.529454i	$0.822397\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$		−	9.00000i		−	0.696441i	−0.937413	−	0.348220i	$-0.886786\pi$
$167$		−	9.00000i		−	0.696441i	0.937413	−	0.348220i	$-0.113214\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	−2.46410	−	3.73205i	−0.188988	−	0.286235i
$171$		0			0
$172$	−4.33013	+	2.50000i	−0.330169	+	0.190623i
$173$	10.3923	+	6.00000i	0.790112	+	0.456172i	0.840002	−	0.542583i	$-0.182554\pi$
$173$	10.3923	+	6.00000i	0.790112	+	0.456172i	−0.0498898	+	0.998755i	$0.515887\pi$
$174$		0			0
$175$	9.79423	+	8.89230i	0.740374	+	0.672195i
$176$		0			0
$177$		0			0
$178$	−6.06218	+	3.50000i	−0.454379	+	0.262336i
$179$	13.0000	+	22.5167i	0.971666	+	1.68297i	0.690526	+	0.723307i	$0.257379\pi$
$179$	13.0000	+	22.5167i	0.971666	+	1.68297i	0.281139	+	0.959667i	$0.409288\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	3.46410	+	4.00000i	0.256776	+	0.296500i
$183$		0			0
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	1.07180	+	17.8564i	0.0788001	+	1.31283i
$186$		0			0
$187$		0			0
$188$		−	8.00000i		−	0.583460i
$189$		0			0
$190$	−4.00000	−	2.00000i	−0.290191	−	0.145095i
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	0.235983	+	0.971757i	$0.424169\pi$
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	−0.959558	+	0.281511i	$0.909164\pi$
$192$		0			0
$193$	17.3205	−	10.0000i	1.24676	−	0.719816i	0.276296	−	0.961073i	$-0.410893\pi$
$193$	17.3205	−	10.0000i	1.24676	−	0.719816i	0.970461	+	0.241257i	$0.0775596\pi$
$194$		0			0
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$		0			0
$199$	6.00000	+	10.3923i	0.425329	+	0.736691i	0.996451	−	0.0841740i	$-0.0268252\pi$
$199$	6.00000	+	10.3923i	0.425329	+	0.736691i	−0.571122	+	0.820865i	$0.693492\pi$
$200$	4.59808	+	1.96410i	0.325133	+	0.138883i
$201$		0			0
$202$			15.0000i			1.05540i
$203$	−0.866025	+	2.50000i	−0.0607831	+	0.175466i
$204$		0			0
$205$	−3.69615	−	5.59808i	−0.258150	−	0.390987i
$206$	−5.50000	−	9.52628i	−0.383203	−	0.663727i
$207$		0			0
$208$	1.73205	+	1.00000i	0.120096	+	0.0693375i
$209$		0			0
$210$		0			0
$211$	−18.0000			−1.23917			−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000			−1.23917			−0.619586	+	0.784929i	$0.712699\pi$
$212$	5.19615	+	3.00000i	0.356873	+	0.206041i
$213$		0			0
$214$	−3.50000	−	6.06218i	−0.239255	−	0.414402i
$215$	9.33013	−	6.16025i	0.636309	−	0.420126i
$216$		0			0
$217$	−25.9808	+	5.00000i	−1.76369	+	0.339422i
$218$		−	5.00000i		−	0.338643i
$219$		0			0
$220$		0			0
$221$	2.00000	+	3.46410i	0.134535	+	0.233021i
$222$		0			0
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$	−0.500000	−	2.59808i	−0.0334077	−	0.173591i
$225$		0			0
$226$	5.00000	−	8.66025i	0.332595	−	0.576072i
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	−0.113761	−	0.993508i	$-0.536290\pi$
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	0.803523	+	0.595274i	$0.202957\pi$
$228$		0			0
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$	1.00000	−	2.00000i	0.0659380	−	0.131876i
$231$		0			0
$232$			1.00000i			0.0656532i
$233$	−12.1244	−	7.00000i	−0.794293	−	0.458585i	0.0471787	−	0.998886i	$-0.484977\pi$
$233$	−12.1244	−	7.00000i	−0.794293	−	0.458585i	−0.841472	+	0.540301i	$0.818310\pi$
$234$		0			0
$235$	1.07180	+	17.8564i	0.0699163	+	1.16482i
$236$	1.00000	−	1.73205i	0.0650945	−	0.112747i
$237$		0			0
$238$	1.73205	−	5.00000i	0.112272	−	0.324102i
$239$	−10.0000			−0.646846			−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000			−0.646846			−0.323423	+	0.946254i	$0.604834\pi$
$240$		0			0
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	−0.995509	−	0.0946700i	$-0.969820\pi$
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	0.415768	−	0.909471i	$-0.363513\pi$
$242$	−9.52628	+	5.50000i	−0.612372	+	0.353553i
$243$		0			0
$244$	9.00000			0.576166
$245$	−1.30385	+	15.5981i	−0.0832998	+	0.996525i
$246$		0			0
$247$	3.46410	+	2.00000i	0.220416	+	0.127257i
$248$	−8.66025	+	5.00000i	−0.549927	+	0.317500i
$249$		0			0
$250$	−10.5263	−	3.76795i	−0.665740	−	0.238306i
$251$	10.0000			0.631194			0.315597	−	0.948893i	$-0.397795\pi$
$251$	10.0000			0.631194			0.315597	+	0.948893i	$0.397795\pi$
$252$		0			0
$253$		0			0
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	0.139533	−	0.990217i	$-0.455440\pi$
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	−0.787787	+	0.615948i	$0.788773\pi$
$258$		0			0
$259$	−16.0000	+	13.8564i	−0.994192	+	0.860995i
$260$	−4.00000	−	2.00000i	−0.248069	−	0.124035i
$261$		0			0
$262$	−17.3205	+	10.0000i	−1.07006	+	0.617802i
$263$	−18.1865	+	10.5000i	−1.12143	+	0.647458i	−0.941766	−	0.336270i	$-0.890834\pi$
$263$	−18.1865	+	10.5000i	−1.12143	+	0.647458i	−0.179664	+	0.983728i	$0.557501\pi$
$264$		0			0
$265$	−12.0000	−	6.00000i	−0.737154	−	0.368577i
$266$	−1.00000	−	5.19615i	−0.0613139	−	0.318597i
$267$		0			0
$268$	6.06218	+	3.50000i	0.370306	+	0.213797i
$269$	−2.50000	−	4.33013i	−0.152428	−	0.264013i	0.779692	−	0.626164i	$-0.215376\pi$
$269$	−2.50000	−	4.33013i	−0.152428	−	0.264013i	−0.932119	+	0.362151i	$0.882042\pi$
$270$		0			0
$271$	−3.00000	+	5.19615i	−0.182237	+	0.315644i	−0.942642	−	0.333805i	$-0.891667\pi$
$271$	−3.00000	+	5.19615i	−0.182237	+	0.315644i	0.760405	+	0.649449i	$0.225000\pi$
$272$		−	2.00000i		−	0.121268i
$273$		0			0
$274$	−16.0000			−0.966595
$275$		0			0
$276$		0			0
$277$	22.5167	−	13.0000i	1.35290	−	0.781094i	0.364241	−	0.931305i	$-0.381328\pi$
$277$	22.5167	−	13.0000i	1.35290	−	0.781094i	0.988654	+	0.150210i	$0.0479951\pi$
$278$	−6.92820	−	4.00000i	−0.415526	−	0.239904i
$279$		0			0
$280$	1.46410	+	5.73205i	0.0874968	+	0.342556i
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$		0			0
$283$	6.92820	−	4.00000i	0.411839	−	0.237775i	−0.279741	−	0.960076i	$-0.590248\pi$
$283$	6.92820	−	4.00000i	0.411839	−	0.237775i	0.691580	+	0.722300i	$0.256915\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$		0			0
$287$	2.59808	−	7.50000i	0.153360	−	0.442711i
$288$		0			0
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$	−0.133975	−	2.23205i	−0.00786726	−	0.131071i
$291$		0			0
$292$	−8.66025	−	5.00000i	−0.506803	−	0.292603i
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$		0			0
$295$	−2.00000	+	4.00000i	−0.116445	+	0.232889i
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$		0			0
$298$	−12.9904	+	7.50000i	−0.752513	+	0.434463i
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$		0			0
$301$	12.5000	+	4.33013i	0.720488	+	0.249584i
$302$			6.00000i			0.345261i
$303$		0			0
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$	−20.0885	+	1.20577i	−1.15026	+	0.0690423i
$306$		0			0
$307$			19.0000i			1.08439i	0.840254	+	0.542194i	$0.182406\pi$
$307$			19.0000i			1.08439i	−0.840254	+	0.542194i	$0.817594\pi$
$308$		0			0
$309$		0			0
$310$	18.6603	−	12.3205i	1.05983	−	0.699758i
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	0.938460	−	0.345389i	$-0.112253\pi$
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	−0.768345	+	0.640036i	$0.778920\pi$
$312$		0			0
$313$	−6.92820	−	4.00000i	−0.391605	−	0.226093i	0.291250	−	0.956647i	$-0.405929\pi$
$313$	−6.92820	−	4.00000i	−0.391605	−	0.226093i	−0.682855	+	0.730554i	$0.739262\pi$
$314$	−12.0000			−0.677199
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−19.0526	−	11.0000i	−1.07010	−	0.617822i	−0.141890	−	0.989882i	$-0.545318\pi$
$317$	−19.0526	−	11.0000i	−1.07010	−	0.617822i	−0.928208	+	0.372061i	$0.878651\pi$
$318$		0			0
$319$		0			0
$320$	1.23205	+	1.86603i	0.0688737	+	0.104314i
$321$		0			0
$322$	2.59808	−	0.500000i	0.144785	−	0.0278639i
$323$		−	4.00000i		−	0.222566i
$324$		0			0
$325$	9.19615	+	3.92820i	0.510111	+	0.217898i
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$		0			0
$328$		−	3.00000i		−	0.165647i
$329$	−16.0000	+	13.8564i	−0.882109	+	0.763928i
$330$		0			0
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	−0.991735	−	0.128302i	$-0.959047\pi$
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	0.606980	+	0.794717i	$0.292381\pi$
$332$	−7.79423	+	4.50000i	−0.427764	+	0.246970i
$333$		0			0
$334$	−4.50000	+	7.79423i	−0.246229	+	0.426481i
$335$	−14.0000	−	7.00000i	−0.764902	−	0.382451i
$336$		0			0
$337$			2.00000i			0.108947i	0.998515	+	0.0544735i	$0.0173480\pi$
$337$			2.00000i			0.108947i	−0.998515	+	0.0544735i	$0.982652\pi$
$338$	−7.79423	−	4.50000i	−0.423950	−	0.244768i
$339$		0			0
$340$	0.267949	+	4.46410i	0.0145316	+	0.242100i
$341$		0			0
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	5.00000			0.269582
$345$		0			0
$346$	−6.00000	−	10.3923i	−0.322562	−	0.558694i
$347$	18.1865	−	10.5000i	0.976304	−	0.563670i	0.0751519	−	0.997172i	$-0.476056\pi$
$347$	18.1865	−	10.5000i	0.976304	−	0.563670i	0.901152	+	0.433503i	$0.142722\pi$
$348$		0			0
$349$	9.00000			0.481759			0.240879	−	0.970555i	$-0.422564\pi$
$349$	9.00000			0.481759			0.240879	+	0.970555i	$0.422564\pi$
$350$	−4.03590	−	12.5981i	−0.215728	−	0.673395i
$351$		0			0
$352$		0			0
$353$	5.19615	−	3.00000i	0.276563	−	0.159674i	−0.355303	−	0.934751i	$-0.615622\pi$
$353$	5.19615	−	3.00000i	0.276563	−	0.159674i	0.631867	+	0.775077i	$0.282289\pi$
$354$		0			0
$355$	7.39230	+	11.1962i	0.392343	+	0.594230i
$356$	7.00000			0.370999
$357$		0			0
$358$		−	26.0000i		−	1.37414i
$359$	7.00000	−	12.1244i	0.369446	−	0.639899i	−0.620033	−	0.784576i	$-0.712881\pi$
$359$	7.00000	−	12.1244i	0.369446	−	0.639899i	0.989479	+	0.144677i	$0.0462142\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−4.33013	−	2.50000i	−0.227586	−	0.131397i
$363$		0			0
$364$	−1.00000	−	5.19615i	−0.0524142	−	0.272352i
$365$	20.0000	+	10.0000i	1.04685	+	0.523424i
$366$		0			0
$367$	19.9186	−	11.5000i	1.03974	−	0.600295i	0.119982	−	0.992776i	$-0.461716\pi$
$367$	19.9186	−	11.5000i	1.03974	−	0.600295i	0.919760	+	0.392481i	$0.128383\pi$
$368$	0.866025	−	0.500000i	0.0451447	−	0.0260643i
$369$		0			0
$370$	8.00000	−	16.0000i	0.415900	−	0.831800i
$371$	−3.00000	−	15.5885i	−0.155752	−	0.809312i
$372$		0			0
$373$	−6.92820	−	4.00000i	−0.358729	−	0.207112i	0.309794	−	0.950804i	$-0.399740\pi$
$373$	−6.92820	−	4.00000i	−0.358729	−	0.207112i	−0.668523	+	0.743691i	$0.733073\pi$
$374$		0			0
$375$		0			0
$376$	−4.00000	+	6.92820i	−0.206284	+	0.357295i
$377$			2.00000i			0.103005i
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$	2.46410	+	3.73205i	0.126406	+	0.191450i
$381$		0			0
$382$	17.3205	−	10.0000i	0.886194	−	0.511645i
$383$	−7.79423	−	4.50000i	−0.398266	−	0.229939i	0.287469	−	0.957790i	$-0.407186\pi$
$383$	−7.79423	−	4.50000i	−0.398266	−	0.229939i	−0.685736	+	0.727851i	$0.740519\pi$
$384$		0			0
$385$		0			0
$386$	−20.0000			−1.01797
$387$		0			0
$388$		0			0
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	0.998763	−	0.0497253i	$-0.0158346\pi$
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	−0.542445	+	0.840091i	$0.682501\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$	−4.33013	+	5.50000i	−0.218704	+	0.277792i
$393$		0			0
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$	22.3205	−	1.33975i	1.12307	−	0.0674099i
$396$		0			0
$397$	−27.7128	−	16.0000i	−1.39087	−	0.803017i	−0.397455	−	0.917622i	$-0.630107\pi$
$397$	−27.7128	−	16.0000i	−1.39087	−	0.803017i	−0.993411	+	0.114605i	$0.963440\pi$
$398$		−	12.0000i		−	0.601506i
$399$		0			0
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		0			0
$403$	−17.3205	+	10.0000i	−0.862796	+	0.498135i
$404$	7.50000	−	12.9904i	0.373139	−	0.646296i
$405$		0			0
$406$	2.00000	−	1.73205i	0.0992583	−	0.0859602i
$407$		0			0
$408$		0			0
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	0.575670	−	0.817682i	$-0.304741\pi$
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	−0.995968	+	0.0897044i	$0.971408\pi$
$410$	0.401924	+	6.69615i	0.0198496	+	0.330699i
$411$		0			0
$412$			11.0000i			0.541931i
$413$	−5.19615	+	1.00000i	−0.255686	+	0.0492068i
$414$		0			0
$415$	16.7942	−	11.0885i	0.824396	−	0.544311i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		0			0
$418$		0			0
$419$	−40.0000			−1.95413			−0.977064	−	0.212946i	$-0.931694\pi$
$419$	−40.0000			−1.95413			−0.977064	+	0.212946i	$0.931694\pi$
$420$		0			0
$421$	31.0000			1.51085			0.755424	−	0.655237i	$-0.227431\pi$
$421$	31.0000			1.51085			0.755424	+	0.655237i	$0.227431\pi$
$422$	15.5885	+	9.00000i	0.758834	+	0.438113i
$423$		0			0
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	−1.19615	−	9.92820i	−0.0580219	−	0.481589i
$426$		0			0
$427$	−15.5885	−	18.0000i	−0.754378	−	0.871081i
$428$			7.00000i			0.338358i
$429$		0			0
$430$	−11.1603	+	0.669873i	−0.538195	+	0.0323041i
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	0.937184	+	0.348836i	$0.113423\pi$
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	−0.166491	+	0.986043i	$0.553244\pi$
$432$		0			0
$433$		−	14.0000i		−	0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$		−	14.0000i		−	0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$	25.0000	+	8.66025i	1.20004	+	0.415705i
$435$		0			0
$436$	−2.50000	+	4.33013i	−0.119728	+	0.207375i
$437$	1.73205	−	1.00000i	0.0828552	−	0.0478365i
$438$		0			0
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$		0			0
$441$		0			0
$442$		−	4.00000i		−	0.190261i
$443$	−2.59808	−	1.50000i	−0.123438	−	0.0712672i	0.437009	−	0.899457i	$-0.356038\pi$
$443$	−2.59808	−	1.50000i	−0.123438	−	0.0712672i	−0.560448	+	0.828190i	$0.689371\pi$
$444$		0			0
$445$	−15.6244	+	0.937822i	−0.740665	+	0.0444570i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$		0			0
$448$	−0.866025	+	2.50000i	−0.0409159	+	0.118114i
$449$	23.0000			1.08544			0.542719	−	0.839915i	$-0.317395\pi$
$449$	23.0000			1.08544			0.542719	+	0.839915i	$0.317395\pi$
$450$		0			0
$451$		0			0
$452$	−8.66025	+	5.00000i	−0.407344	+	0.235180i
$453$		0			0
$454$	−12.0000			−0.563188
$455$	2.92820	+	11.4641i	0.137276	+	0.537445i
$456$		0			0
$457$	27.7128	+	16.0000i	1.29635	+	0.748448i	0.979772	−	0.200118i	$-0.0641325\pi$
$457$	27.7128	+	16.0000i	1.29635	+	0.748448i	0.316579	+	0.948566i	$0.397466\pi$
$458$	−8.66025	+	5.00000i	−0.404667	+	0.233635i
$459$		0			0
$460$	−1.86603	+	1.23205i	−0.0870039	+	0.0574447i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$			25.0000i			1.16185i	0.813958	+	0.580924i	$0.197309\pi$
$463$			25.0000i			1.16185i	−0.813958	+	0.580924i	$0.802691\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$		0			0
$466$	7.00000	+	12.1244i	0.324269	+	0.561650i
$467$	−0.866025	−	0.500000i	−0.0400749	−	0.0231372i	0.479829	−	0.877362i	$-0.340699\pi$
$467$	−0.866025	−	0.500000i	−0.0400749	−	0.0231372i	−0.519904	+	0.854225i	$0.674032\pi$
$468$		0			0
$469$	−3.50000	−	18.1865i	−0.161615	−	0.839776i
$470$	8.00000	−	16.0000i	0.369012	−	0.738025i
$471$		0			0
$472$	−1.73205	+	1.00000i	−0.0797241	+	0.0460287i
$473$		0			0
$474$		0			0
$475$	−6.00000	−	8.00000i	−0.275299	−	0.367065i
$476$	−4.00000	+	3.46410i	−0.183340	+	0.158777i
$477$		0			0
$478$	8.66025	+	5.00000i	0.396111	+	0.228695i
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$			18.0000i			0.819878i
$483$		0			0
$484$	11.0000			0.500000
$485$		0			0
$486$		0			0
$487$	−3.46410	+	2.00000i	−0.156973	+	0.0906287i	−0.576429	−	0.817147i	$-0.695554\pi$
$487$	−3.46410	+	2.00000i	−0.156973	+	0.0906287i	0.419456	+	0.907776i	$0.362221\pi$
$488$	−7.79423	−	4.50000i	−0.352828	−	0.203705i
$489$		0			0
$490$	8.92820	−	12.8564i	0.403335	−	0.580793i
$491$	18.0000			0.812329			0.406164	−	0.913800i	$-0.366866\pi$
$491$	18.0000			0.812329			0.406164	+	0.913800i	$0.366866\pi$
$492$		0			0
$493$	1.73205	−	1.00000i	0.0780076	−	0.0450377i
$494$	−2.00000	−	3.46410i	−0.0899843	−	0.155857i
$495$		0			0
$496$	10.0000			0.449013
$497$	−5.19615	+	15.0000i	−0.233079	+	0.672842i
$498$		0			0
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	−0.629519	−	0.776985i	$-0.716748\pi$
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	0.987648	+	0.156687i	$0.0500814\pi$
$500$	7.23205	+	8.52628i	0.323427	+	0.381307i
$501$		0			0
$502$	−8.66025	−	5.00000i	−0.386526	−	0.223161i
$503$			5.00000i			0.222939i	0.993768	+	0.111469i	$0.0355557\pi$
$503$			5.00000i			0.222939i	−0.993768	+	0.111469i	$0.964444\pi$
$504$		0			0
$505$	−15.0000	+	30.0000i	−0.667491	+	1.33498i
$506$		0			0
$507$		0			0
$508$	−6.92820	+	4.00000i	−0.307389	+	0.177471i
$509$	−17.5000	+	30.3109i	−0.775674	+	1.34351i	0.158741	+	0.987320i	$0.449256\pi$
$509$	−17.5000	+	30.3109i	−0.775674	+	1.34351i	−0.934415	+	0.356186i	$0.884077\pi$
$510$		0			0
$511$	5.00000	+	25.9808i	0.221187	+	1.14932i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	6.00000	+	10.3923i	0.264649	+	0.458385i
$515$	−1.47372	−	24.5526i	−0.0649399	−	1.08192i
$516$		0			0
$517$		0			0
$518$	20.7846	−	4.00000i	0.913223	−	0.175750i
$519$		0			0
$520$	2.46410	+	3.73205i	0.108058	+	0.163661i
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$		0			0
$523$	−3.46410	−	2.00000i	−0.151475	−	0.0874539i	0.422347	−	0.906434i	$-0.361206\pi$
$523$	−3.46410	−	2.00000i	−0.151475	−	0.0874539i	−0.573822	+	0.818980i	$0.694540\pi$
$524$	20.0000			0.873704
$525$		0			0
$526$	21.0000			0.915644
$527$	17.3205	+	10.0000i	0.754493	+	0.435607i
$528$		0			0
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$	7.39230	+	11.1962i	0.321101	+	0.486330i
$531$		0			0
$532$	−1.73205	+	5.00000i	−0.0750939	+	0.216777i
$533$		−	6.00000i		−	0.259889i
$534$		0			0
$535$	−0.937822	−	15.6244i	−0.0405456	−	0.675500i
$536$	−3.50000	−	6.06218i	−0.151177	−	0.261846i
$537$		0			0
$538$			5.00000i			0.215565i
$539$		0			0
$540$		0			0
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	−0.914750	−	0.404020i	$-0.867613\pi$
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	0.807267	+	0.590187i	$0.200946\pi$
$542$	5.19615	−	3.00000i	0.223194	−	0.128861i
$543$		0			0
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	5.00000	−	10.0000i	0.214176	−	0.428353i
$546$		0			0
$547$		−	37.0000i		−	1.58201i	−0.611812	−	0.791003i	$-0.709559\pi$
$547$		−	37.0000i		−	1.58201i	0.611812	−	0.791003i	$-0.290441\pi$
$548$	13.8564	+	8.00000i	0.591916	+	0.341743i
$549$		0			0
$550$		0			0
$551$	1.00000	−	1.73205i	0.0426014	−	0.0737878i
$552$		0			0
$553$	17.3205	+	20.0000i	0.736543	+	0.850487i
$554$	−26.0000			−1.10463
$555$		0			0
$556$	4.00000	+	6.92820i	0.169638	+	0.293821i
$557$	−3.46410	+	2.00000i	−0.146779	+	0.0847427i	−0.571591	−	0.820539i	$-0.693674\pi$
$557$	−3.46410	+	2.00000i	−0.146779	+	0.0847427i	0.424812	+	0.905282i	$0.360340\pi$
$558$		0			0
$559$	10.0000			0.422955
$560$	1.59808	−	5.69615i	0.0675310	−	0.240706i
$561$		0			0
$562$	15.5885	+	9.00000i	0.657559	+	0.379642i
$563$	−9.52628	+	5.50000i	−0.401485	+	0.231797i	−0.687124	−	0.726540i	$-0.741127\pi$
$563$	−9.52628	+	5.50000i	−0.401485	+	0.231797i	0.285640	+	0.958337i	$0.407794\pi$
$564$		0			0
$565$	18.6603	−	12.3205i	0.785043	−	0.518328i
$566$	−8.00000			−0.336265
$567$		0			0
$568$			6.00000i			0.251754i
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$		0			0
$571$	5.00000	+	8.66025i	0.209243	+	0.362420i	0.951476	−	0.307722i	$-0.0995665\pi$
$571$	5.00000	+	8.66025i	0.209243	+	0.362420i	−0.742233	+	0.670142i	$0.766233\pi$
$572$		0			0
$573$		0			0
$574$	−6.00000	+	5.19615i	−0.250435	+	0.216883i
$575$	4.00000	−	3.00000i	0.166812	−	0.125109i
$576$		0			0
$577$	13.8564	−	8.00000i	0.576850	−	0.333044i	−0.183031	−	0.983107i	$-0.558591\pi$
$577$	13.8564	−	8.00000i	0.576850	−	0.333044i	0.759880	+	0.650063i	$0.225257\pi$
$578$	11.2583	−	6.50000i	0.468285	−	0.270364i
$579$		0			0
$580$	−1.00000	+	2.00000i	−0.0415227	+	0.0830455i
$581$	22.5000	+	7.79423i	0.933457	+	0.323359i
$582$		0			0
$583$		0			0
$584$	5.00000	+	8.66025i	0.206901	+	0.358364i
$585$		0			0
$586$	−12.0000	+	20.7846i	−0.495715	+	0.858604i
$587$			28.0000i			1.15568i	0.816149	+	0.577842i	$0.196105\pi$
$587$			28.0000i			1.15568i	−0.816149	+	0.577842i	$0.803895\pi$
$588$		0			0
$589$	20.0000			0.824086
$590$	3.73205	−	2.46410i	0.153646	−	0.101445i
$591$		0			0
$592$	6.92820	−	4.00000i	0.284747	−	0.164399i
$593$	36.3731	+	21.0000i	1.49366	+	0.862367i	0.999974	−	0.00727173i	$-0.00231468\pi$
$593$	36.3731	+	21.0000i	1.49366	+	0.862367i	0.493689	+	0.869638i	$0.335648\pi$
$594$		0			0
$595$	8.46410	−	8.26795i	0.346994	−	0.338953i
$596$	15.0000			0.614424
$597$		0			0
$598$	1.73205	−	1.00000i	0.0708288	−	0.0408930i
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	−0.954521	−	0.298143i	$-0.903633\pi$
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	0.219061	−	0.975711i	$-0.429701\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	−8.66025	−	10.0000i	−0.352966	−	0.407570i
$603$		0			0
$604$	3.00000	−	5.19615i	0.122068	−	0.211428i
$605$	−24.5526	+	1.47372i	−0.998203	+	0.0599153i
$606$		0			0
$607$	4.33013	+	2.50000i	0.175754	+	0.101472i	0.585296	−	0.810819i	$-0.300978\pi$
$607$	4.33013	+	2.50000i	0.175754	+	0.101472i	−0.409542	+	0.912291i	$0.634311\pi$
$608$			2.00000i			0.0811107i
$609$		0			0
$610$	18.0000	+	9.00000i	0.728799	+	0.364399i
$611$	−8.00000	+	13.8564i	−0.323645	+	0.560570i
$612$		0			0
$613$	15.5885	−	9.00000i	0.629612	−	0.363507i	−0.150990	−	0.988535i	$-0.548246\pi$
$613$	15.5885	−	9.00000i	0.629612	−	0.363507i	0.780602	+	0.625029i	$0.214913\pi$
$614$	9.50000	−	16.4545i	0.383389	−	0.664049i
$615$		0			0
$616$		0			0
$617$			20.0000i			0.805170i	0.915383	+	0.402585i	$0.131888\pi$
$617$			20.0000i			0.805170i	−0.915383	+	0.402585i	$0.868112\pi$
$618$		0			0
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$	−22.3205	+	1.33975i	−0.896413	+	0.0538055i
$621$		0			0
$622$		−	6.00000i		−	0.240578i
$623$	−12.1244	−	14.0000i	−0.485752	−	0.560898i
$624$		0			0
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	4.00000	+	6.92820i	0.159872	+	0.276907i
$627$		0			0
$628$	10.3923	+	6.00000i	0.414698	+	0.239426i
$629$	16.0000			0.637962
$630$		0			0
$631$	−24.0000			−0.955425			−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000			−0.955425			−0.477712	+	0.878516i	$0.658534\pi$
$632$	8.66025	+	5.00000i	0.344486	+	0.198889i
$633$		0			0
$634$	11.0000	+	19.0526i	0.436866	+	0.756674i
$635$	14.9282	−	9.85641i	0.592408	−	0.391140i
$636$		0			0
$637$	−8.66025	+	11.0000i	−0.343132	+	0.435836i
$638$		0			0
$639$		0			0
$640$	−0.133975	−	2.23205i	−0.00529581	−	0.0882296i
$641$	−17.5000	−	30.3109i	−0.691208	−	1.19721i	−0.971442	−	0.237276i	$-0.923745\pi$
$641$	−17.5000	−	30.3109i	−0.691208	−	1.19721i	0.280234	−	0.959932i	$-0.409588\pi$
$642$		0			0
$643$		−	20.0000i		−	0.788723i	−0.918955	−	0.394362i	$-0.870966\pi$
$643$		−	20.0000i		−	0.788723i	0.918955	−	0.394362i	$-0.129034\pi$
$644$	−2.50000	−	0.866025i	−0.0985138	−	0.0341262i
$645$		0			0
$646$	−2.00000	+	3.46410i	−0.0786889	+	0.136293i
$647$	18.1865	−	10.5000i	0.714986	−	0.412798i	−0.0979182	−	0.995194i	$-0.531218\pi$
$647$	18.1865	−	10.5000i	0.714986	−	0.412798i	0.812905	+	0.582397i	$0.197885\pi$
$648$		0			0
$649$		0			0
$650$	−6.00000	−	8.00000i	−0.235339	−	0.313786i
$651$		0			0
$652$		−	12.0000i		−	0.469956i
$653$	36.3731	+	21.0000i	1.42339	+	0.821794i	0.996587	−	0.0825519i	$-0.0263070\pi$
$653$	36.3731	+	21.0000i	1.42339	+	0.821794i	0.426801	+	0.904345i	$0.359640\pi$
$654$		0			0
$655$	−44.6410	+	2.67949i	−1.74427	+	0.104696i
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$		0			0
$658$	20.7846	−	4.00000i	0.810268	−	0.155936i
$659$	30.0000			1.16863			0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000			1.16863			0.584317	+	0.811525i	$0.301362\pi$
$660$		0			0
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	0.921331	+	0.388778i	$0.127103\pi$
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	−0.123974	+	0.992286i	$0.539564\pi$
$662$	12.1244	−	7.00000i	0.471226	−	0.272063i
$663$		0			0
$664$	9.00000			0.349268
$665$	3.19615	−	11.3923i	0.123941	−	0.441775i
$666$		0			0
$667$	0.866025	+	0.500000i	0.0335326	+	0.0193601i
$668$	7.79423	−	4.50000i	0.301568	−	0.174110i
$669$		0			0
$670$	8.62436	+	13.0622i	0.333188	+	0.504636i
$671$		0			0
$672$		0			0
$673$			20.0000i			0.770943i	0.922720	+	0.385472i	$0.125961\pi$
$673$			20.0000i			0.770943i	−0.922720	+	0.385472i	$0.874039\pi$
$674$	1.00000	−	1.73205i	0.0385186	−	0.0667161i
$675$		0			0
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	1.73205	+	1.00000i	0.0665681	+	0.0384331i	0.532915	−	0.846169i	$-0.321097\pi$
$677$	1.73205	+	1.00000i	0.0665681	+	0.0384331i	−0.466347	+	0.884602i	$0.654430\pi$
$678$		0			0
$679$		0			0
$680$	2.00000	−	4.00000i	0.0766965	−	0.153393i
$681$		0			0
$682$		0			0
$683$	−21.6506	+	12.5000i	−0.828439	+	0.478299i	−0.853318	−	0.521391i	$-0.825413\pi$
$683$	−21.6506	+	12.5000i	−0.828439	+	0.478299i	0.0248792	+	0.999690i	$0.492080\pi$
$684$		0			0
$685$	−32.0000	−	16.0000i	−1.22266	−	0.611329i
$686$	18.5000	−	0.866025i	0.706333	−	0.0330650i
$687$		0			0
$688$	−4.33013	−	2.50000i	−0.165085	−	0.0953116i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	−0.610704	−	0.791859i	$-0.709113\pi$
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	0.991122	+	0.132956i	$0.0424468\pi$
$692$			12.0000i			0.456172i
$693$		0			0
$694$	−21.0000			−0.797149
$695$	−9.85641	−	14.9282i	−0.373875	−	0.566259i
$696$		0			0
$697$	−5.19615	+	3.00000i	−0.196818	+	0.113633i
$698$	−7.79423	−	4.50000i	−0.295016	−	0.170328i
$699$		0			0
$700$	−2.80385	+	12.9282i	−0.105975	+	0.488640i
$701$	1.00000			0.0377695			0.0188847	−	0.999822i	$-0.493988\pi$
$701$	1.00000			0.0377695			0.0188847	+	0.999822i	$0.493988\pi$
$702$		0			0
$703$	13.8564	−	8.00000i	0.522604	−	0.301726i
$704$		0			0
$705$		0			0
$706$	−6.00000			−0.225813
$707$	−38.9711	+	7.50000i	−1.46566	+	0.282067i
$708$		0			0
$709$	−4.50000	+	7.79423i	−0.169001	+	0.292718i	−0.938069	−	0.346449i	$-0.887387\pi$
$709$	−4.50000	+	7.79423i	−0.169001	+	0.292718i	0.769068	+	0.639167i	$0.220721\pi$
$710$	−0.803848	−	13.3923i	−0.0301679	−	0.502604i
$711$		0			0
$712$	−6.06218	−	3.50000i	−0.227190	−	0.131168i
$713$			10.0000i			0.374503i
$714$		0			0
$715$		0			0
$716$	−13.0000	+	22.5167i	−0.485833	+	0.841487i
$717$		0			0
$718$	−12.1244	+	7.00000i	−0.452477	+	0.261238i
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	−0.990016	−	0.140955i	$-0.954983\pi$
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	0.617079	+	0.786901i	$0.288316\pi$
$720$		0			0
$721$	22.0000	−	19.0526i	0.819323	−	0.709554i
$722$		−	15.0000i		−	0.558242i
$723$		0			0
$724$	2.50000	+	4.33013i	0.0929118	+	0.160928i
$725$	1.96410	−	4.59808i	0.0729449	−	0.170768i
$726$		0			0
$727$			29.0000i			1.07555i	0.843088	+	0.537775i	$0.180735\pi$
$727$			29.0000i			1.07555i	−0.843088	+	0.537775i	$0.819265\pi$
$728$	−1.73205	+	5.00000i	−0.0641941	+	0.185312i
$729$		0			0
$730$	−12.3205	−	18.6603i	−0.456002	−	0.690647i
$731$	−5.00000	−	8.66025i	−0.184932	−	0.320311i
$732$		0			0
$733$	13.8564	+	8.00000i	0.511798	+	0.295487i	0.733572	−	0.679611i	$-0.237852\pi$
$733$	13.8564	+	8.00000i	0.511798	+	0.295487i	−0.221774	+	0.975098i	$0.571185\pi$
$734$	−23.0000			−0.848945
$735$		0			0
$736$	−1.00000			−0.0368605
$737$		0			0
$738$		0			0
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	−0.994420	−	0.105493i	$-0.966358\pi$
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	0.405851	−	0.913939i	$-0.366975\pi$
$740$	−14.9282	+	9.85641i	−0.548772	+	0.362329i
$741$		0			0
$742$	−5.19615	+	15.0000i	−0.190757	+	0.550667i
$743$			3.00000i			0.110059i	0.998485	+	0.0550297i	$0.0175253\pi$
$743$			3.00000i			0.110059i	−0.998485	+	0.0550297i	$0.982475\pi$
$744$		0			0
$745$	−33.4808	+	2.00962i	−1.22664	+	0.0736267i
$746$	4.00000	+	6.92820i	0.146450	+	0.253660i
$747$		0			0
$748$		0			0
$749$	14.0000	−	12.1244i	0.511549	−	0.443014i
$750$		0			0
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	−0.900207	−	0.435463i	$-0.856585\pi$
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	0.827225	+	0.561870i	$0.189918\pi$
$752$	6.92820	−	4.00000i	0.252646	−	0.145865i
$753$		0			0
$754$	1.00000	−	1.73205i	0.0364179	−	0.0630776i
$755$	−6.00000	+	12.0000i	−0.218362	+	0.436725i
$756$		0			0
$757$			6.00000i			0.218074i	0.994038	+	0.109037i	$0.0347767\pi$
$757$			6.00000i			0.218074i	−0.994038	+	0.109037i	$0.965223\pi$
$758$	−1.73205	−	1.00000i	−0.0629109	−	0.0363216i
$759$		0			0
$760$	−0.267949	−	4.46410i	−0.00971954	−	0.161930i
$761$	−25.0000	+	43.3013i	−0.906249	+	1.56967i	−0.0870179	+	0.996207i	$0.527734\pi$
$761$	−25.0000	+	43.3013i	−0.906249	+	1.56967i	−0.819231	+	0.573463i	$0.805600\pi$
$762$		0			0
$763$	12.9904	−	2.50000i	0.470283	−	0.0905061i
$764$	−20.0000			−0.723575
$765$		0			0
$766$	4.50000	+	7.79423i	0.162592	+	0.281617i
$767$	−3.46410	+	2.00000i	−0.125081	+	0.0722158i
$768$		0			0
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$		0			0
$772$	17.3205	+	10.0000i	0.623379	+	0.359908i
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	−0.192740	−	0.981250i	$-0.561737\pi$
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	0.753418	+	0.657542i	$0.228404\pi$
$774$		0			0
$775$	49.6410	−	5.98076i	1.78316	−	0.214835i
$776$		0			0
$777$		0			0
$778$		−	18.0000i		−	0.645331i
$779$	−3.00000	+	5.19615i	−0.107486	+	0.186171i
$780$		0			0
$781$		0			0
$782$	−1.73205	−	1.00000i	−0.0619380	−	0.0357599i
$783$		0			0
$784$	6.50000	−	2.59808i	0.232143	−	0.0927884i
$785$	−24.0000	−	12.0000i	−0.856597	−	0.428298i
$786$		0			0
$787$	−18.1865	+	10.5000i	−0.648280	+	0.374285i	−0.787797	−	0.615935i	$-0.788778\pi$
$787$	−18.1865	+	10.5000i	−0.648280	+	0.374285i	0.139517	+	0.990220i	$0.455445\pi$
$788$	6.92820	−	4.00000i	0.246807	−	0.142494i
$789$		0			0
$790$	−20.0000	−	10.0000i	−0.711568	−	0.355784i
$791$	25.0000	+	8.66025i	0.888898	+	0.307923i
$792$		0			0
$793$	−15.5885	−	9.00000i	−0.553562	−	0.319599i
$794$	16.0000	+	27.7128i	0.567819	+	0.983491i
$795$		0			0
$796$	−6.00000	+	10.3923i	−0.212664	+	0.368345i
$797$		−	8.00000i		−	0.283375i	−0.989911	−	0.141687i	$-0.954747\pi$
$797$		−	8.00000i		−	0.283375i	0.989911	−	0.141687i	$-0.0452527\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$	0.598076	+	4.96410i	0.0211452	+	0.175507i
$801$		0			0
$802$	−2.59808	+	1.50000i	−0.0917413	+	0.0529668i
$803$		0			0
$804$		0			0
$805$	5.69615	+	1.59808i	0.200763	+	0.0563248i
$806$	20.0000			0.704470
$807$		0			0
$808$	−12.9904	+	7.50000i	−0.457000	+	0.263849i
$809$	−12.5000	−	21.6506i	−0.439477	−	0.761196i	0.558173	−	0.829725i	$-0.311503\pi$
$809$	−12.5000	−	21.6506i	−0.439477	−	0.761196i	−0.997649	+	0.0685291i	$0.978169\pi$
$810$		0			0
$811$	6.00000			0.210688			0.105344	−	0.994436i	$-0.466406\pi$
$811$	6.00000			0.210688			0.105344	+	0.994436i	$0.466406\pi$
$812$	−2.59808	+	0.500000i	−0.0911746	+	0.0175466i
$813$		0			0
$814$		0			0
$815$	1.60770	+	26.7846i	0.0563151	+	0.938224i
$816$		0			0
$817$	−8.66025	−	5.00000i	−0.302984	−	0.174928i
$818$			17.0000i			0.594391i
$819$		0			0
$820$	3.00000	−	6.00000i	0.104765	−	0.209529i
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	0.222731	+	0.974880i	$0.428503\pi$
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	−0.955636	+	0.294549i	$0.904831\pi$
$822$		0			0
$823$	−38.9711	+	22.5000i	−1.35845	+	0.784301i	−0.989415	−	0.145115i	$-0.953645\pi$
$823$	−38.9711	+	22.5000i	−1.35845	+	0.784301i	−0.369034	+	0.929416i	$0.620311\pi$
$824$	5.50000	−	9.52628i	0.191602	−	0.331864i
$825$		0			0
$826$	5.00000	+	1.73205i	0.173972	+	0.0602658i
$827$		−	37.0000i		−	1.28662i	−0.765607	−	0.643308i	$-0.777561\pi$
$827$		−	37.0000i		−	1.28662i	0.765607	−	0.643308i	$-0.222439\pi$
$828$		0			0
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	0.994174	+	0.107788i	$0.0343769\pi$
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	−0.403739	+	0.914874i	$0.632290\pi$
$830$	−20.0885	+	1.20577i	−0.697281	+	0.0418529i
$831$		0			0
$832$			2.00000i			0.0693375i
$833$	13.8564	+	2.00000i	0.480096	+	0.0692959i
$834$		0			0
$835$	−16.7942	+	11.0885i	−0.581188	+	0.383732i
$836$		0			0
$837$		0			0
$838$	34.6410	+	20.0000i	1.19665	+	0.690889i
$839$	32.0000			1.10476			0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000			1.10476			0.552381	+	0.833592i	$0.313719\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	−26.8468	−	15.5000i	−0.925201	−	0.534165i
$843$		0			0
$844$	−9.00000	−	15.5885i	−0.309793	−	0.536577i
$845$	−11.0885	−	16.7942i	−0.381455	−	0.577739i
$846$		0			0
$847$	−19.0526	−	22.0000i	−0.654654	−	0.755929i
$848$			6.00000i			0.206041i
$849$		0			0
$850$	−3.92820	+	9.19615i	−0.134736	+	0.315425i
$851$	4.00000	+	6.92820i	0.137118	+	0.237496i
$852$		0			0
$853$		−	10.0000i		−	0.342393i	−0.985237	−	0.171197i	$-0.945237\pi$
$853$		−	10.0000i		−	0.342393i	0.985237	−	0.171197i	$-0.0547634\pi$
$854$	4.50000	+	23.3827i	0.153987	+	0.800139i
$855$		0			0
$856$	3.50000	−	6.06218i	0.119628	−	0.207201i
$857$	−3.46410	+	2.00000i	−0.118331	+	0.0683187i	−0.557998	−	0.829843i	$-0.688430\pi$
$857$	−3.46410	+	2.00000i	−0.118331	+	0.0683187i	0.439666	+	0.898161i	$0.355097\pi$
$858$		0			0
$859$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$859$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$860$	10.0000	+	5.00000i	0.340997	+	0.170499i
$861$		0			0
$862$		−	32.0000i		−	1.08992i
$863$	−9.52628	−	5.50000i	−0.324278	−	0.187222i	0.329020	−	0.944323i	$-0.393282\pi$
$863$	−9.52628	−	5.50000i	−0.324278	−	0.187222i	−0.653298	+	0.757101i	$0.726615\pi$
$864$		0			0
$865$	−1.60770	−	26.7846i	−0.0546633	−	0.910704i
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$		0			0
$868$	−17.3205	−	20.0000i	−0.587896	−	0.678844i
$869$		0			0
$870$		0			0
$871$	−7.00000	−	12.1244i	−0.237186	−	0.410818i
$872$	4.33013	−	2.50000i	0.146637	−	0.0846607i
$873$		0			0
$874$	−2.00000			−0.0676510
$875$	4.52628	−	29.2321i	0.153016	−	0.988224i
$876$		0			0
$877$	−12.1244	−	7.00000i	−0.409410	−	0.236373i	0.281126	−	0.959671i	$-0.409292\pi$
$877$	−12.1244	−	7.00000i	−0.409410	−	0.236373i	−0.690536	+	0.723298i	$0.742625\pi$
$878$	−6.92820	+	4.00000i	−0.233816	+	0.134993i
$879$		0			0
$880$		0			0
$881$	3.00000			0.101073			0.0505363	−	0.998722i	$-0.483907\pi$
$881$	3.00000			0.101073			0.0505363	+	0.998722i	$0.483907\pi$
$882$		0			0
$883$			4.00000i			0.134611i	0.997732	+	0.0673054i	$0.0214402\pi$
$883$			4.00000i			0.134611i	−0.997732	+	0.0673054i	$0.978560\pi$
$884$	−2.00000	+	3.46410i	−0.0672673	+	0.116510i
$885$		0			0
$886$	1.50000	+	2.59808i	0.0503935	+	0.0872841i
$887$	−7.79423	−	4.50000i	−0.261705	−	0.151095i	0.363407	−	0.931630i	$-0.381613\pi$
$887$	−7.79423	−	4.50000i	−0.261705	−	0.151095i	−0.625112	+	0.780535i	$0.714947\pi$
$888$		0			0
$889$	20.0000	+	6.92820i	0.670778	+	0.232364i
$890$	14.0000	+	7.00000i	0.469281	+	0.234641i
$891$		0			0
$892$	6.92820	−	4.00000i	0.231973	−	0.133930i
$893$	13.8564	−	8.00000i	0.463687	−	0.267710i
$894$		0			0
$895$	26.0000	−	52.0000i	0.869084	−	1.73817i
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$		0			0
$898$	−19.9186	−	11.5000i	−0.664692	−	0.383760i
$899$	5.00000	+	8.66025i	0.166759	+	0.288836i
$900$		0			0
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$		0			0
$903$		0			0
$904$	10.0000			0.332595
$905$	−6.16025	−	9.33013i	−0.204774	−	0.310144i
$906$		0			0
$907$	21.6506	−	12.5000i	0.718898	−	0.415056i	−0.0954492	−	0.995434i	$-0.530429\pi$
$907$	21.6506	−	12.5000i	0.718898	−	0.415056i	0.814347	+	0.580379i	$0.197095\pi$
$908$	10.3923	+	6.00000i	0.344881	+	0.199117i
$909$		0			0
$910$	3.19615	−	11.3923i	0.105951	−	0.377651i
$911$	−8.00000			−0.265052			−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000			−0.265052			−0.132526	+	0.991180i	$0.542309\pi$
$912$		0			0
$913$		0			0
$914$	−16.0000	−	27.7128i	−0.529233	−	0.916658i
$915$		0			0
$916$	10.0000			0.330409
$917$	−34.6410	−	40.0000i	−1.14395	−	1.32092i
$918$		0			0
$919$	13.0000	−	22.5167i	0.428830	−	0.742756i	−0.567939	−	0.823071i	$-0.692259\pi$
$919$	13.0000	−	22.5167i	0.428830	−	0.742756i	0.996770	+	0.0803145i	$0.0255924\pi$
$920$	2.23205	−	0.133975i	0.0735885	−	0.00441701i
$921$		0			0
$922$	−12.1244	−	7.00000i	−0.399294	−	0.230533i
$923$			12.0000i			0.394985i
$924$		0			0
$925$	32.0000	−	24.0000i	1.05215	−	0.789115i
$926$	12.5000	−	21.6506i	0.410775	−	0.711484i
$927$		0			0
$928$	−0.866025	+	0.500000i	−0.0284287	+	0.0164133i
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	−0.997905	−	0.0646999i	$-0.979391\pi$
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	0.554984	+	0.831861i	$0.312724\pi$
$930$		0			0
$931$	13.0000	−	5.19615i	0.426058	−	0.170297i
$932$		−	14.0000i		−	0.458585i
$933$		0			0
$934$	0.500000	+	0.866025i	0.0163605	+	0.0283372i
$935$		0			0
$936$		0			0
$937$			56.0000i			1.82944i	0.404088	+	0.914720i	$0.367589\pi$
$937$			56.0000i			1.82944i	−0.404088	+	0.914720i	$0.632411\pi$
$938$	−6.06218	+	17.5000i	−0.197937	+	0.571395i
$939$		0			0
$940$	−14.9282	+	9.85641i	−0.486904	+	0.321481i
$941$	7.00000	+	12.1244i	0.228193	+	0.395243i	0.957273	−	0.289187i	$-0.0933848\pi$
$941$	7.00000	+	12.1244i	0.228193	+	0.395243i	−0.729079	+	0.684429i	$0.760051\pi$
$942$		0			0
$943$	−2.59808	−	1.50000i	−0.0846050	−	0.0488467i
$944$	2.00000			0.0650945
$945$		0			0
$946$		0			0
$947$	2.59808	+	1.50000i	0.0844261	+	0.0487435i	0.541619	−	0.840624i	$-0.317812\pi$
$947$	2.59808	+	1.50000i	0.0844261	+	0.0487435i	−0.457193	+	0.889368i	$0.651145\pi$
$948$		0			0
$949$	10.0000	+	17.3205i	0.324614	+	0.562247i
$950$	1.19615	+	9.92820i	0.0388083	+	0.322113i
$951$		0			0
$952$	5.19615	−	1.00000i	0.168408	−	0.0324102i
$953$		−	36.0000i		−	1.16615i	−0.812417	−	0.583077i	$-0.801849\pi$
$953$		−	36.0000i		−	1.16615i	0.812417	−	0.583077i	$-0.198151\pi$
$954$		0			0
$955$	44.6410	−	2.67949i	1.44455	−	0.0867063i
$956$	−5.00000	−	8.66025i	−0.161712	−	0.280093i
$957$		0			0
$958$			18.0000i			0.581554i
$959$	−8.00000	−	41.5692i	−0.258333	−	1.34234i
$960$		0			0
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$	13.8564	−	8.00000i	0.446748	−	0.257930i
$963$		0			0
$964$	9.00000	−	15.5885i	0.289870	−	0.502070i
$965$	−40.0000	−	20.0000i	−1.28765	−	0.643823i
$966$		0			0
$967$		−	17.0000i		−	0.546683i	−0.961917	−	0.273342i	$-0.911871\pi$
$967$		−	17.0000i		−	0.546683i	0.961917	−	0.273342i	$-0.0881289\pi$
$968$	−9.52628	−	5.50000i	−0.306186	−	0.176777i
$969$		0			0
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$	6.92820	−	20.0000i	0.222108	−	0.641171i
$974$	4.00000			0.128168
$975$		0			0
$976$	4.50000	+	7.79423i	0.144041	+	0.249487i
$977$	31.1769	−	18.0000i	0.997438	−	0.575871i	0.0899487	−	0.995946i	$-0.471330\pi$
$977$	31.1769	−	18.0000i	0.997438	−	0.575871i	0.907489	+	0.420075i	$0.137996\pi$
$978$		0			0
$979$		0			0
$980$	−14.1603	+	6.66987i	−0.452333	+	0.213061i
$981$		0			0
$982$	−15.5885	−	9.00000i	−0.497448	−	0.287202i
$983$	−21.6506	+	12.5000i	−0.690548	+	0.398688i	−0.803817	−	0.594876i	$-0.797201\pi$
$983$	−21.6506	+	12.5000i	−0.690548	+	0.398688i	0.113269	+	0.993564i	$0.463868\pi$
$984$		0			0
$985$	−14.9282	+	9.85641i	−0.475652	+	0.314051i
$986$	−2.00000			−0.0636930
$987$		0			0
$988$			4.00000i			0.127257i
$989$	2.50000	−	4.33013i	0.0794954	−	0.137690i
$990$		0			0
$991$	13.0000	+	22.5167i	0.412959	+	0.715265i	0.995212	−	0.0977423i	$-0.0311621\pi$
$991$	13.0000	+	22.5167i	0.412959	+	0.715265i	−0.582253	+	0.813008i	$0.697829\pi$
$992$	−8.66025	−	5.00000i	−0.274963	−	0.158750i
$993$		0			0
$994$	12.0000	−	10.3923i	0.380617	−	0.329624i
$995$	12.0000	−	24.0000i	0.380426	−	0.760851i
$996$		0			0
$997$	−29.4449	+	17.0000i	−0.932528	+	0.538395i	−0.887610	−	0.460595i	$-0.847636\pi$
$997$	−29.4449	+	17.0000i	−0.932528	+	0.538395i	−0.0449179	+	0.998991i	$0.514303\pi$
$998$	−13.8564	+	8.00000i	−0.438617	+	0.253236i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.u.b.289.1		4
3.2	odd	2		70.2.i.a.9.2	yes	4
5.4	even	2	inner	630.2.u.b.289.2		4
7.4	even	3	inner	630.2.u.b.109.2		4
12.11	even	2		560.2.bw.c.289.2		4
15.2	even	4		350.2.e.f.51.1		2
15.8	even	4		350.2.e.g.51.1		2
15.14	odd	2		70.2.i.a.9.1	✓	4
21.2	odd	6		490.2.c.c.99.1		2
21.5	even	6		490.2.c.b.99.1		2
21.11	odd	6		70.2.i.a.39.1	yes	4
21.17	even	6		490.2.i.b.459.1		4
21.20	even	2		490.2.i.b.79.2		4
35.4	even	6	inner	630.2.u.b.109.1		4
60.59	even	2		560.2.bw.c.289.1		4
84.11	even	6		560.2.bw.c.529.1		4
105.2	even	12		2450.2.a.s.1.1		1
105.23	even	12		2450.2.a.r.1.1		1
105.32	even	12		350.2.e.f.151.1		2
105.44	odd	6		490.2.c.c.99.2		2
105.47	odd	12		2450.2.a.bh.1.1		1
105.53	even	12		350.2.e.g.151.1		2
105.59	even	6		490.2.i.b.459.2		4
105.68	odd	12		2450.2.a.c.1.1		1
105.74	odd	6		70.2.i.a.39.2	yes	4
105.89	even	6		490.2.c.b.99.2		2
105.104	even	2		490.2.i.b.79.1		4
420.179	even	6		560.2.bw.c.529.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.a.9.1	✓	4	15.14	odd	2
70.2.i.a.9.2	yes	4	3.2	odd	2
70.2.i.a.39.1	yes	4	21.11	odd	6
70.2.i.a.39.2	yes	4	105.74	odd	6
350.2.e.f.51.1		2	15.2	even	4
350.2.e.f.151.1		2	105.32	even	12
350.2.e.g.51.1		2	15.8	even	4
350.2.e.g.151.1		2	105.53	even	12
490.2.c.b.99.1		2	21.5	even	6
490.2.c.b.99.2		2	105.89	even	6
490.2.c.c.99.1		2	21.2	odd	6
490.2.c.c.99.2		2	105.44	odd	6
490.2.i.b.79.1		4	105.104	even	2
490.2.i.b.79.2		4	21.20	even	2
490.2.i.b.459.1		4	21.17	even	6
490.2.i.b.459.2		4	105.59	even	6
560.2.bw.c.289.1		4	60.59	even	2
560.2.bw.c.289.2		4	12.11	even	2
560.2.bw.c.529.1		4	84.11	even	6
560.2.bw.c.529.2		4	420.179	even	6
630.2.u.b.109.1		4	35.4	even	6	inner
630.2.u.b.109.2		4	7.4	even	3	inner
630.2.u.b.289.1		4	1.1	even	1	trivial
630.2.u.b.289.2		4	5.4	even	2	inner
2450.2.a.c.1.1		1	105.68	odd	12
2450.2.a.r.1.1		1	105.23	even	12
2450.2.a.s.1.1		1	105.2	even	12
2450.2.a.bh.1.1		1	105.47	odd	12

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.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +(0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +(0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.133975 + 2.23205i) q^{10} -2.00000i q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(1.00000 - 2.00000i) q^{20} +(-0.866025 - 0.500000i) q^{23} +(-1.96410 + 4.59808i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(2.59808 - 0.500000i) q^{28} -1.00000 q^{29} +(-5.00000 - 8.66025i) q^{31} +(0.866025 - 0.500000i) q^{32} +2.00000 q^{34} +(-5.73205 + 1.46410i) q^{35} +(-6.92820 - 4.00000i) q^{37} +(1.73205 - 1.00000i) q^{38} +(-1.86603 + 1.23205i) q^{40} +3.00000 q^{41} +5.00000i q^{43} +(0.500000 + 0.866025i) q^{46} +(-6.92820 - 4.00000i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(4.00000 - 3.00000i) q^{50} +(1.73205 - 1.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-2.50000 - 0.866025i) q^{56} +(0.866025 + 0.500000i) q^{58} +(-1.00000 - 1.73205i) q^{59} +(4.50000 - 7.79423i) q^{61} +10.0000i q^{62} -1.00000 q^{64} +(-3.73205 + 2.46410i) q^{65} +(6.06218 - 3.50000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +(5.69615 + 1.59808i) q^{70} -6.00000 q^{71} +(-8.66025 + 5.00000i) q^{73} +(4.00000 + 6.92820i) q^{74} -2.00000 q^{76} +(-5.00000 + 8.66025i) q^{79} +(2.23205 - 0.133975i) q^{80} +(-2.59808 - 1.50000i) q^{82} +9.00000i q^{83} +(4.00000 + 2.00000i) q^{85} +(2.50000 - 4.33013i) q^{86} +(3.50000 - 6.06218i) q^{89} +(-5.00000 - 1.73205i) q^{91} -1.00000i q^{92} +(4.00000 + 6.92820i) q^{94} +(4.46410 - 0.267949i) q^{95} +(2.59808 + 6.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{5}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^5	\( 4 q + 2 q^{4} + 2 q^{5} + 4 q^{10} - 8 q^{14} - 2 q^{16} - 4 q^{19} + 4 q^{20} + 6 q^{25} - 4 q^{26} - 4 q^{29} - 20 q^{31} + 8 q^{34} - 16 q^{35} - 4 q^{40} + 12 q^{41} + 2 q^{46} - 22 q^{49} + 16 q^{50} - 10 q^{56} - 4 q^{59} + 18 q^{61} - 4 q^{64} - 8 q^{65} + 2 q^{70} - 24 q^{71} + 16 q^{74} - 8 q^{76} - 20 q^{79} + 2 q^{80} + 16 q^{85} + 10 q^{86} + 14 q^{89} - 20 q^{91} + 16 q^{94} + 4 q^{95}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^5 + 4 * q^10 - 8 * q^14 - 2 * q^16 - 4 * q^19 + 4 * q^20 + 6 * q^25 - 4 * q^26 - 4 * q^29 - 20 * q^31 + 8 * q^34 - 16 * q^35 - 4 * q^40 + 12 * q^41 + 2 * q^46 - 22 * q^49 + 16 * q^50 - 10 * q^56 - 4 * q^59 + 18 * q^61 - 4 * q^64 - 8 * q^65 + 2 * q^70 - 24 * q^71 + 16 * q^74 - 8 * q^76 - 20 * q^79 + 2 * q^80 + 16 * q^85 + 10 * q^86 + 14 * q^89 - 20 * q^91 + 16 * q^94 + 4 * q^95

Introduction

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