LMFDB - Embedded newform 630.2.u.b.109.2

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			109.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	630.109
Dual form			630.2.u.b.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(1.86603 - 1.23205i) q^{10} -2.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(1.00000 - 2.00000i) q^{20} +(0.866025 - 0.500000i) q^{23} +(4.96410 - 0.598076i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(-2.59808 - 0.500000i) q^{28} -1.00000 q^{29} +(-5.00000 + 8.66025i) q^{31} +(-0.866025 - 0.500000i) q^{32} +2.00000 q^{34} +(-2.26795 - 5.46410i) q^{35} +(6.92820 - 4.00000i) q^{37} +(-1.73205 - 1.00000i) q^{38} +(-0.133975 - 2.23205i) q^{40} +3.00000 q^{41} +5.00000i q^{43} +(0.500000 - 0.866025i) q^{46} +(6.92820 - 4.00000i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(4.00000 - 3.00000i) q^{50} +(-1.73205 - 1.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(-2.50000 + 0.866025i) q^{56} +(-0.866025 + 0.500000i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(4.50000 + 7.79423i) q^{61} +10.0000i q^{62} -1.00000 q^{64} +(-0.267949 - 4.46410i) q^{65} +(-6.06218 - 3.50000i) q^{67} +(1.73205 - 1.00000i) q^{68} +(-4.69615 - 3.59808i) q^{70} -6.00000 q^{71} +(8.66025 + 5.00000i) q^{73} +(4.00000 - 6.92820i) q^{74} -2.00000 q^{76} +(-5.00000 - 8.66025i) q^{79} +(-1.23205 - 1.86603i) q^{80} +(2.59808 - 1.50000i) q^{82} +9.00000i q^{83} +(4.00000 + 2.00000i) q^{85} +(2.50000 + 4.33013i) q^{86} +(3.50000 + 6.06218i) q^{89} +(-5.00000 + 1.73205i) q^{91} -1.00000i q^{92} +(4.00000 - 6.92820i) q^{94} +(-2.46410 - 3.73205i) q^{95} +(-2.59808 + 6.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.866025	−	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
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$6$		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
$10$	1.86603	−	1.23205i	0.590089	−	0.389609i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		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	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$		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	−	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	$-0.633420\pi$
$23$	0.866025	−	0.500000i	0.180579	−	0.104257i	0.587565	+	0.809177i	$0.300087\pi$
$24$		0			0
$25$	4.96410	−	0.598076i	0.992820	−	0.119615i
$26$	−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	−0.0680129	+	0.997684i	$0.521666\pi$
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.830014	+	0.557743i	$0.811667\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	2.00000			0.342997
$35$	−2.26795	−	5.46410i	−0.383353	−	0.923602i
$36$		0			0
$37$	6.92820	−	4.00000i	1.13899	−	0.657596i	0.192809	−	0.981236i	$-0.438240\pi$
$37$	6.92820	−	4.00000i	1.13899	−	0.657596i	0.946180	+	0.323640i	$0.104907\pi$
$38$	−1.73205	−	1.00000i	−0.280976	−	0.162221i
$39$		0			0
$40$	−0.133975	−	2.23205i	−0.0211832	−	0.352918i
$41$	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	$-0.468365\pi$
$47$	6.92820	−	4.00000i	1.01058	−	0.583460i	0.911362	+	0.411606i	$0.135032\pi$
$48$		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	$-0.468532\pi$
$53$	−5.19615	−	3.00000i	−0.713746	−	0.412082i	−0.812447	+	0.583036i	$0.801865\pi$
$54$		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	−0.923749	−	0.382998i	$-0.874892\pi$
$59$	−1.00000	+	1.73205i	−0.130189	+	0.225494i	0.793560	+	0.608492i	$0.208225\pi$
$60$		0			0
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	0.995914	+	0.0903080i	$0.0287851\pi$
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	−0.419748	+	0.907641i	$0.637882\pi$
$62$			10.0000i			1.27000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.267949	−	4.46410i	−0.0332350	−	0.553704i
$66$		0			0
$67$	−6.06218	−	3.50000i	−0.740613	−	0.427593i	0.0816792	−	0.996659i	$-0.473972\pi$
$67$	−6.06218	−	3.50000i	−0.740613	−	0.427593i	−0.822292	+	0.569066i	$0.807305\pi$
$68$	1.73205	−	1.00000i	0.210042	−	0.121268i
$69$		0			0
$70$	−4.69615	−	3.59808i	−0.561298	−	0.430052i
$71$	−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	$-0.134347\pi$
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.101361	+	0.994850i	$0.467680\pi$
$74$	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	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$	−1.23205	−	1.86603i	−0.137747	−	0.208628i
$81$		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	0.989720	−	0.143022i	$-0.0456819\pi$
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	−0.618720	+	0.785611i	$0.712349\pi$
$90$		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
$95$	−2.46410	−	3.73205i	−0.252811	−	0.382900i
$96$		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
$100$	1.96410	−	4.59808i	0.196410	−	0.459808i
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$		0			0
$103$	−9.52628	+	5.50000i	−0.938652	+	0.541931i	−0.889538	−	0.456862i	$-0.848973\pi$
$103$	−9.52628	+	5.50000i	−0.938652	+	0.541931i	−0.0491146	+	0.998793i	$0.515640\pi$
$104$	−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	$-0.776538\pi$
$107$	−6.06218	+	3.50000i	−0.586053	+	0.338358i	0.177482	+	0.984124i	$0.443205\pi$
$108$		0			0
$109$	2.50000	−	4.33013i	0.239457	−	0.414751i	−0.721102	−	0.692829i	$-0.756364\pi$
$109$	2.50000	−	4.33013i	0.239457	−	0.414751i	0.960558	+	0.278078i	$0.0896974\pi$
$110$		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
$115$	1.86603	−	1.23205i	0.174008	−	0.114889i
$116$	−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
$130$	−2.46410	−	3.73205i	−0.216116	−	0.327323i
$131$	10.0000	+	17.3205i	0.873704	+	1.51330i	0.858137	+	0.513421i	$0.171622\pi$
$131$	10.0000	+	17.3205i	0.873704	+	1.51330i	0.0155672	+	0.999879i	$0.495045\pi$
$132$		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	$-0.572870\pi$
$137$	−13.8564	−	8.00000i	−1.18383	−	0.683486i	−0.956898	+	0.290424i	$0.906204\pi$
$138$		0			0
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	−5.86603	−	0.767949i	−0.495770	−	0.0649036i
$141$		0			0
$142$	−5.19615	+	3.00000i	−0.436051	+	0.251754i
$143$		0			0
$144$		0			0
$145$	−2.23205	+	0.133975i	−0.185362	+	0.0111260i
$146$	10.0000			0.827606
$147$		0			0
$148$		−	8.00000i		−	0.657596i
$149$	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
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	−0.961888	−	0.273442i	$-0.911838\pi$
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	0.717752	+	0.696299i	$0.245171\pi$
$152$	−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	$-0.492280\pi$
$157$	−10.3923	−	6.00000i	−0.829396	−	0.478852i	−0.853646	+	0.520854i	$0.825614\pi$
$158$	−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	$-0.510936\pi$
$163$	10.3923	−	6.00000i	0.813988	−	0.469956i	0.848339	+	0.529454i	$0.177603\pi$
$164$	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
$170$	4.46410	−	0.267949i	0.342381	−	0.0205508i
$171$		0			0
$172$	4.33013	+	2.50000i	0.330169	+	0.190623i
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	−0.840002	−	0.542583i	$-0.817446\pi$
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	0.0498898	+	0.998755i	$0.484113\pi$
$174$		0			0
$175$	−5.79423	−	11.8923i	−0.438003	−	0.898974i
$176$		0			0
$177$		0			0
$178$	6.06218	+	3.50000i	0.454379	+	0.262336i
$179$	13.0000	−	22.5167i	0.971666	−	1.68297i	0.281139	−	0.959667i	$-0.409288\pi$
$179$	13.0000	−	22.5167i	0.971666	−	1.68297i	0.690526	−	0.723307i	$-0.257379\pi$
$180$		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
$185$	14.9282	−	9.85641i	1.09754	−	0.724657i
$186$		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	−0.959558	−	0.281511i	$-0.909164\pi$
$191$	−10.0000	−	17.3205i	−0.723575	−	1.25327i	0.235983	−	0.971757i	$-0.424169\pi$
$192$		0			0
$193$	−17.3205	−	10.0000i	−1.24676	−	0.719816i	−0.276296	−	0.961073i	$-0.589107\pi$
$193$	−17.3205	−	10.0000i	−1.24676	−	0.719816i	−0.970461	+	0.241257i	$0.922440\pi$
$194$		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	−0.571122	−	0.820865i	$-0.693492\pi$
$199$	6.00000	−	10.3923i	0.425329	−	0.736691i	0.996451	+	0.0841740i	$0.0268252\pi$
$200$	−0.598076	−	4.96410i	−0.0422904	−	0.351015i
$201$		0			0
$202$			15.0000i			1.05540i
$203$	0.866025	+	2.50000i	0.0607831	+	0.175466i
$204$		0			0
$205$	6.69615	−	0.401924i	0.467680	−	0.0280716i
$206$	−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
$215$	0.669873	+	11.1603i	0.0456850	+	0.761123i
$216$		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	$-0.463710\pi$
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	−0.803523	+	0.595274i	$0.797043\pi$
$228$		0			0
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$	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	$-0.515023\pi$
$233$	12.1244	−	7.00000i	0.794293	−	0.458585i	0.841472	+	0.540301i	$0.181690\pi$
$234$		0			0
$235$	14.9282	−	9.85641i	0.973809	−	0.642961i
$236$	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	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$	9.52628	+	5.50000i	0.612372	+	0.353553i
$243$		0			0
$244$	9.00000			0.576166
$245$	−11.6962	+	10.4019i	−0.747240	+	0.664555i
$246$		0			0
$247$	−3.46410	+	2.00000i	−0.220416	+	0.127257i
$248$	8.66025	+	5.00000i	0.549927	+	0.317500i
$249$		0			0
$250$	8.52628	−	7.23205i	0.539249	−	0.457395i
$251$	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	$-0.544560\pi$
$257$	10.3923	−	6.00000i	0.648254	−	0.374270i	0.787787	+	0.615948i	$0.211227\pi$
$258$		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	$-0.109166\pi$
$263$	18.1865	+	10.5000i	1.12143	+	0.647458i	0.179664	+	0.983728i	$0.442499\pi$
$264$		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	−0.932119	−	0.362151i	$-0.882042\pi$
$269$	−2.50000	+	4.33013i	−0.152428	+	0.264013i	0.779692	+	0.626164i	$0.215376\pi$
$270$		0			0
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	0.760405	−	0.649449i	$-0.225000\pi$
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	−0.942642	+	0.333805i	$0.891667\pi$
$272$		−	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	$-0.618672\pi$
$277$	−22.5167	−	13.0000i	−1.35290	−	0.781094i	−0.988654	+	0.150210i	$0.952005\pi$
$278$	6.92820	−	4.00000i	0.415526	−	0.239904i
$279$		0			0
$280$	−5.46410	+	2.26795i	−0.326543	+	0.135536i
$281$	−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	$-0.409752\pi$
$283$	−6.92820	−	4.00000i	−0.411839	−	0.237775i	−0.691580	+	0.722300i	$0.743085\pi$
$284$	−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
$290$	−1.86603	+	1.23205i	−0.109577	+	0.0723485i
$291$		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
$305$	11.0885	+	16.7942i	0.634923	+	0.961635i
$306$		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
$310$	1.33975	+	22.3205i	0.0760925	+	1.26772i
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	6.92820	−	4.00000i	0.391605	−	0.226093i	−0.291250	−	0.956647i	$-0.594071\pi$
$313$	6.92820	−	4.00000i	0.391605	−	0.226093i	0.682855	+	0.730554i	$0.260738\pi$
$314$	−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	$-0.454682\pi$
$317$	19.0526	−	11.0000i	1.07010	−	0.617822i	0.928208	+	0.372061i	$0.121349\pi$
$318$		0			0
$319$		0			0
$320$	−2.23205	+	0.133975i	−0.124775	+	0.00748941i
$321$		0			0
$322$	−2.59808	−	0.500000i	−0.144785	−	0.0278639i
$323$		−	4.00000i		−	0.222566i
$324$		0			0
$325$	−1.19615	−	9.92820i	−0.0663506	−	0.550718i
$326$	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	0.606980	−	0.794717i	$-0.292381\pi$
$331$	−7.00000	−	12.1244i	−0.384755	−	0.666415i	−0.991735	+	0.128302i	$0.959047\pi$
$332$	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
$340$	3.73205	−	2.46410i	0.202399	−	0.133635i
$341$		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	$-0.523944\pi$
$347$	−18.1865	−	10.5000i	−0.976304	−	0.563670i	−0.901152	+	0.433503i	$0.857278\pi$
$348$		0			0
$349$	9.00000			0.481759			0.240879	−	0.970555i	$-0.422564\pi$
$349$	9.00000			0.481759			0.240879	+	0.970555i	$0.422564\pi$
$350$	−10.9641	−	7.40192i	−0.586056	−	0.395649i
$351$		0			0
$352$		0			0
$353$	−5.19615	−	3.00000i	−0.276563	−	0.159674i	0.355303	−	0.934751i	$-0.384378\pi$
$353$	−5.19615	−	3.00000i	−0.276563	−	0.159674i	−0.631867	+	0.775077i	$0.717711\pi$
$354$		0			0
$355$	−13.3923	+	0.803848i	−0.710790	+	0.0426638i
$356$	7.00000			0.370999
$357$		0			0
$358$		−	26.0000i		−	1.37414i
$359$	7.00000	+	12.1244i	0.369446	+	0.639899i	0.989479	−	0.144677i	$-0.0462142\pi$
$359$	7.00000	+	12.1244i	0.369446	+	0.639899i	−0.620033	+	0.784576i	$0.712881\pi$
$360$		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	$-0.538284\pi$
$367$	−19.9186	−	11.5000i	−1.03974	−	0.600295i	−0.919760	+	0.392481i	$0.871617\pi$
$368$	−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	$-0.600260\pi$
$373$	6.92820	−	4.00000i	0.358729	−	0.207112i	0.668523	+	0.743691i	$0.266927\pi$
$374$		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	$0.483642\pi$
$380$	−4.46410	+	0.267949i	−0.229004	+	0.0137455i
$381$		0			0
$382$	−17.3205	−	10.0000i	−0.886194	−	0.511645i
$383$	7.79423	−	4.50000i	0.398266	−	0.229939i	−0.287469	−	0.957790i	$-0.592814\pi$
$383$	7.79423	−	4.50000i	0.398266	−	0.229939i	0.685736	+	0.727851i	$0.259481\pi$
$384$		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	−0.542445	−	0.840091i	$-0.682501\pi$
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	0.998763	+	0.0497253i	$0.0158346\pi$
$390$		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
$395$	−12.3205	−	18.6603i	−0.619912	−	0.938899i
$396$		0			0
$397$	27.7128	−	16.0000i	1.39087	−	0.803017i	0.397455	−	0.917622i	$-0.369893\pi$
$397$	27.7128	−	16.0000i	1.39087	−	0.803017i	0.993411	+	0.114605i	$0.0365601\pi$
$398$		−	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	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		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	−0.995968	−	0.0897044i	$-0.971408\pi$
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	0.575670	+	0.817682i	$0.304741\pi$
$410$	5.59808	−	3.69615i	0.276469	−	0.182540i
$411$		0			0
$412$			11.0000i			0.541931i
$413$	5.19615	+	1.00000i	0.255686	+	0.0492068i
$414$		0			0
$415$	1.20577	+	20.0885i	0.0591890	+	0.986104i
$416$	−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
$425$	9.19615	+	3.92820i	0.446079	+	0.190546i
$426$		0			0
$427$	15.5885	−	18.0000i	0.754378	−	0.871081i
$428$			7.00000i			0.338358i
$429$		0			0
$430$	6.16025	+	9.33013i	0.297074	+	0.449939i
$431$	16.0000	−	27.7128i	0.770693	−	1.33488i	−0.166491	−	0.986043i	$-0.553244\pi$
$431$	16.0000	−	27.7128i	0.770693	−	1.33488i	0.937184	−	0.348836i	$-0.113423\pi$
$432$		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	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$		0			0
$442$		−	4.00000i		−	0.190261i
$443$	2.59808	−	1.50000i	0.123438	−	0.0712672i	−0.437009	−	0.899457i	$-0.643962\pi$
$443$	2.59808	−	1.50000i	0.123438	−	0.0712672i	0.560448	+	0.828190i	$0.310629\pi$
$444$		0			0
$445$	8.62436	+	13.0622i	0.408834	+	0.619207i
$446$	−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
$455$	−10.9282	+	4.53590i	−0.512322	+	0.212646i
$456$		0			0
$457$	−27.7128	+	16.0000i	−1.29635	+	0.748448i	−0.979772	−	0.200118i	$-0.935868\pi$
$457$	−27.7128	+	16.0000i	−1.29635	+	0.748448i	−0.316579	+	0.948566i	$0.602534\pi$
$458$	8.66025	+	5.00000i	0.404667	+	0.233635i
$459$		0			0
$460$	−0.133975	−	2.23205i	−0.00624660	−	0.104070i
$461$	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	$-0.659301\pi$
$467$	0.866025	−	0.500000i	0.0400749	−	0.0231372i	0.519904	+	0.854225i	$0.325968\pi$
$468$		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	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$	−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	$-0.304446\pi$
$487$	3.46410	+	2.00000i	0.156973	+	0.0906287i	−0.419456	+	0.907776i	$0.637779\pi$
$488$	7.79423	−	4.50000i	0.352828	−	0.203705i
$489$		0			0
$490$	−4.92820	+	14.8564i	−0.222634	+	0.671144i
$491$	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	0.987648	−	0.156687i	$-0.0500814\pi$
$499$	8.00000	+	13.8564i	0.358129	+	0.620298i	−0.629519	+	0.776985i	$0.716748\pi$
$500$	3.76795	−	10.5263i	0.168508	−	0.470750i
$501$		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	−0.934415	−	0.356186i	$-0.884077\pi$
$509$	−17.5000	−	30.3109i	−0.775674	−	1.34351i	0.158741	−	0.987320i	$-0.449256\pi$
$510$		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
$515$	−20.5263	+	13.5526i	−0.904496	+	0.597197i
$516$		0			0
$517$		0			0
$518$	−20.7846	−	4.00000i	−0.913223	−	0.175750i
$519$		0			0
$520$	−4.46410	+	0.267949i	−0.195764	+	0.0117503i
$521$	−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
$523$	3.46410	−	2.00000i	0.151475	−	0.0874539i	−0.422347	−	0.906434i	$-0.638794\pi$
$523$	3.46410	−	2.00000i	0.151475	−	0.0874539i	0.573822	+	0.818980i	$0.305460\pi$
$524$	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
$530$	−13.3923	+	0.803848i	−0.581725	+	0.0349169i
$531$		0			0
$532$	1.73205	+	5.00000i	0.0750939	+	0.216777i
$533$		−	6.00000i		−	0.259889i
$534$		0			0
$535$	−13.0622	+	8.62436i	−0.564727	+	0.372863i
$536$	−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	0.807267	−	0.590187i	$-0.200946\pi$
$541$	−2.50000	−	4.33013i	−0.107483	−	0.186167i	−0.914750	+	0.404020i	$0.867613\pi$
$542$	−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	$-0.306326\pi$
$557$	3.46410	+	2.00000i	0.146779	+	0.0847427i	−0.424812	+	0.905282i	$0.639660\pi$
$558$		0			0
$559$	10.0000			0.422955
$560$	−3.59808	+	4.69615i	−0.152046	+	0.198449i
$561$		0			0
$562$	−15.5885	+	9.00000i	−0.657559	+	0.379642i
$563$	9.52628	+	5.50000i	0.401485	+	0.231797i	0.687124	−	0.726540i	$-0.258873\pi$
$563$	9.52628	+	5.50000i	0.401485	+	0.231797i	−0.285640	+	0.958337i	$0.592206\pi$
$564$		0			0
$565$	1.33975	+	22.3205i	0.0563635	+	0.939031i
$566$	−8.00000			−0.336265
$567$		0			0
$568$			6.00000i			0.251754i
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	5.00000	−	8.66025i	0.209243	−	0.362420i	−0.742233	−	0.670142i	$-0.766233\pi$
$571$	5.00000	−	8.66025i	0.209243	−	0.362420i	0.951476	+	0.307722i	$0.0995665\pi$
$572$		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	$-0.441409\pi$
$577$	−13.8564	−	8.00000i	−0.576850	−	0.333044i	−0.759880	+	0.650063i	$0.774743\pi$
$578$	−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
$590$	0.267949	+	4.46410i	0.0110313	+	0.183784i
$591$		0			0
$592$	−6.92820	−	4.00000i	−0.284747	−	0.164399i
$593$	−36.3731	+	21.0000i	−1.49366	+	0.862367i	−0.999974	−	0.00727173i	$-0.997685\pi$
$593$	−36.3731	+	21.0000i	−1.49366	+	0.862367i	−0.493689	+	0.869638i	$0.664352\pi$
$594$		0			0
$595$	1.53590	−	11.7321i	0.0629657	−	0.480967i
$596$	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	0.219061	+	0.975711i	$0.429701\pi$
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	−0.954521	+	0.298143i	$0.903633\pi$
$600$		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
$605$	13.5526	+	20.5263i	0.550990	+	0.834512i
$606$		0			0
$607$	−4.33013	+	2.50000i	−0.175754	+	0.101472i	−0.585296	−	0.810819i	$-0.699022\pi$
$607$	−4.33013	+	2.50000i	−0.175754	+	0.101472i	0.409542	+	0.912291i	$0.365689\pi$
$608$			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	$-0.451754\pi$
$613$	−15.5885	−	9.00000i	−0.629612	−	0.363507i	−0.780602	+	0.625029i	$0.785087\pi$
$614$	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	−0.993959	−	0.109749i	$-0.964995\pi$
$619$	−10.0000	+	17.3205i	−0.401934	+	0.696170i	0.592025	+	0.805919i	$0.298329\pi$
$620$	12.3205	+	18.6603i	0.494804	+	0.749414i
$621$		0			0
$622$		−	6.00000i		−	0.240578i
$623$	12.1244	−	14.0000i	0.485752	−	0.560898i
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	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
$635$	1.07180	+	17.8564i	0.0425330	+	0.708610i
$636$		0			0
$637$	8.66025	+	11.0000i	0.343132	+	0.435836i
$638$		0			0
$639$		0			0
$640$	−1.86603	+	1.23205i	−0.0737611	+	0.0487011i
$641$	−17.5000	+	30.3109i	−0.691208	+	1.19721i	0.280234	+	0.959932i	$0.409588\pi$
$641$	−17.5000	+	30.3109i	−0.691208	+	1.19721i	−0.971442	+	0.237276i	$0.923745\pi$
$642$		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	$-0.468782\pi$
$647$	−18.1865	−	10.5000i	−0.714986	−	0.412798i	−0.812905	+	0.582397i	$0.802115\pi$
$648$		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	$-0.973693\pi$
$653$	−36.3731	+	21.0000i	−1.42339	+	0.821794i	−0.426801	+	0.904345i	$0.640360\pi$
$654$		0			0
$655$	24.6410	+	37.3205i	0.962804	+	1.45823i
$656$	−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	−0.123974	−	0.992286i	$-0.539564\pi$
$661$	20.5000	−	35.5070i	0.797358	−	1.38106i	0.921331	−	0.388778i	$-0.127103\pi$
$662$	−12.1244	−	7.00000i	−0.471226	−	0.272063i
$663$		0			0
$664$	9.00000			0.349268
$665$	−7.19615	+	9.39230i	−0.279055	+	0.364218i
$666$		0			0
$667$	−0.866025	+	0.500000i	−0.0335326	+	0.0193601i
$668$	−7.79423	−	4.50000i	−0.301568	−	0.174110i
$669$		0			0
$670$	−15.6244	+	0.937822i	−0.603622	+	0.0362312i
$671$		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	$-0.678903\pi$
$677$	−1.73205	+	1.00000i	−0.0665681	+	0.0384331i	0.466347	+	0.884602i	$0.345570\pi$
$678$		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	$-0.174587\pi$
$683$	21.6506	+	12.5000i	0.828439	+	0.478299i	−0.0248792	+	0.999690i	$0.507920\pi$
$684$		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	0.991122	−	0.132956i	$-0.0424468\pi$
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	−0.610704	+	0.791859i	$0.709113\pi$
$692$			12.0000i			0.456172i
$693$		0			0
$694$	−21.0000			−0.797149
$695$	17.8564	−	1.07180i	0.677332	−	0.0406556i
$696$		0			0
$697$	5.19615	+	3.00000i	0.196818	+	0.113633i
$698$	7.79423	−	4.50000i	0.295016	−	0.170328i
$699$		0			0
$700$	−13.1962	−	0.928203i	−0.498768	−	0.0350828i
$701$	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	0.769068	−	0.639167i	$-0.220721\pi$
$709$	−4.50000	−	7.79423i	−0.169001	−	0.292718i	−0.938069	+	0.346449i	$0.887387\pi$
$710$	−11.1962	+	7.39230i	−0.420184	+	0.277428i
$711$		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	0.617079	−	0.786901i	$-0.288316\pi$
$719$	−10.0000	−	17.3205i	−0.372937	−	0.645946i	−0.990016	+	0.140955i	$0.954983\pi$
$720$		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
$725$	−4.96410	+	0.598076i	−0.184362	+	0.0222120i
$726$		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
$730$	22.3205	−	1.33975i	0.826119	−	0.0495862i
$731$	−5.00000	+	8.66025i	−0.184932	+	0.320311i
$732$		0			0
$733$	−13.8564	+	8.00000i	−0.511798	+	0.295487i	−0.733572	−	0.679611i	$-0.762148\pi$
$733$	−13.8564	+	8.00000i	−0.511798	+	0.295487i	0.221774	+	0.975098i	$0.428815\pi$
$734$	−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	0.405851	+	0.913939i	$0.366975\pi$
$739$	−16.0000	+	27.7128i	−0.588570	+	1.01943i	−0.994420	+	0.105493i	$0.966358\pi$
$740$	−1.07180	−	17.8564i	−0.0394000	−	0.656415i
$741$		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
$745$	18.4808	+	27.9904i	0.677083	+	1.02549i
$746$	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	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$	−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
$760$	−3.73205	+	2.46410i	−0.135376	+	0.0893824i
$761$	−25.0000	−	43.3013i	−0.906249	−	1.56967i	−0.819231	−	0.573463i	$-0.805600\pi$
$761$	−25.0000	−	43.3013i	−0.906249	−	1.56967i	−0.0870179	−	0.996207i	$-0.527734\pi$
$762$		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	$-0.438263\pi$
$773$	−15.5885	−	9.00000i	−0.560678	−	0.323708i	−0.753418	+	0.657542i	$0.771596\pi$
$774$		0			0
$775$	−19.6410	+	45.9808i	−0.705526	+	1.65168i
$776$		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	$-0.211222\pi$
$787$	18.1865	+	10.5000i	0.648280	+	0.374285i	−0.139517	+	0.990220i	$0.544555\pi$
$788$	−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
$800$	−4.59808	−	1.96410i	−0.162567	−	0.0694415i
$801$		0			0
$802$	2.59808	+	1.50000i	0.0917413	+	0.0529668i
$803$		0			0
$804$		0			0
$805$	−4.69615	−	3.59808i	−0.165518	−	0.126816i
$806$	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	−0.997649	−	0.0685291i	$-0.978169\pi$
$809$	−12.5000	+	21.6506i	−0.439477	+	0.761196i	0.558173	+	0.829725i	$0.311503\pi$
$810$		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
$815$	22.3923	−	14.7846i	0.784368	−	0.517882i
$816$		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	−0.955636	−	0.294549i	$-0.904831\pi$
$821$	−21.0000	−	36.3731i	−0.732905	−	1.26943i	0.222731	−	0.974880i	$-0.428503\pi$
$822$		0			0
$823$	38.9711	+	22.5000i	1.35845	+	0.784301i	0.989415	−	0.145115i	$-0.0463553\pi$
$823$	38.9711	+	22.5000i	1.35845	+	0.784301i	0.369034	+	0.929416i	$0.379689\pi$
$824$	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	−0.403739	−	0.914874i	$-0.632290\pi$
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	0.994174	−	0.107788i	$-0.0343769\pi$
$830$	11.0885	+	16.7942i	0.384886	+	0.582936i
$831$		0			0
$832$			2.00000i			0.0693375i
$833$	−13.8564	+	2.00000i	−0.480096	+	0.0692959i
$834$		0			0
$835$	−1.20577	−	20.0885i	−0.0417274	−	0.695190i
$836$		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
$845$	20.0885	−	1.20577i	0.691064	−	0.0414798i
$846$		0			0
$847$	19.0526	−	22.0000i	0.654654	−	0.755929i
$848$			6.00000i			0.206041i
$849$		0			0
$850$	9.92820	−	1.19615i	0.340535	−	0.0410277i
$851$	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	$-0.311570\pi$
$857$	3.46410	+	2.00000i	0.118331	+	0.0683187i	−0.439666	+	0.898161i	$0.644903\pi$
$858$		0			0
$859$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$859$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$860$	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	$-0.606718\pi$
$863$	9.52628	−	5.50000i	0.324278	−	0.187222i	0.653298	+	0.757101i	$0.273385\pi$
$864$		0			0
$865$	−22.3923	+	14.7846i	−0.761361	+	0.502692i
$866$	−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
$875$	−14.5263	−	25.7679i	−0.491078	−	0.871116i
$876$		0			0
$877$	12.1244	−	7.00000i	0.409410	−	0.236373i	−0.281126	−	0.959671i	$-0.590708\pi$
$877$	12.1244	−	7.00000i	0.409410	−	0.236373i	0.690536	+	0.723298i	$0.257375\pi$
$878$	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	$-0.618387\pi$
$887$	7.79423	−	4.50000i	0.261705	−	0.151095i	0.625112	+	0.780535i	$0.285053\pi$
$888$		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
$905$	11.1603	−	0.669873i	0.370979	−	0.0222673i
$906$		0			0
$907$	−21.6506	−	12.5000i	−0.718898	−	0.415056i	0.0954492	−	0.995434i	$-0.469571\pi$
$907$	−21.6506	−	12.5000i	−0.718898	−	0.415056i	−0.814347	+	0.580379i	$0.802905\pi$
$908$	−10.3923	+	6.00000i	−0.344881	+	0.199117i
$909$		0			0
$910$	−7.19615	+	9.39230i	−0.238550	+	0.311352i
$911$	−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	0.996770	−	0.0803145i	$-0.0255924\pi$
$919$	13.0000	+	22.5167i	0.428830	+	0.742756i	−0.567939	+	0.823071i	$0.692259\pi$
$920$	−1.23205	−	1.86603i	−0.0406195	−	0.0615210i
$921$		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	0.554984	−	0.831861i	$-0.312724\pi$
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	−0.997905	+	0.0646999i	$0.979391\pi$
$930$		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
$940$	−1.07180	−	17.8564i	−0.0349582	−	0.582412i
$941$	7.00000	−	12.1244i	0.228193	−	0.395243i	−0.729079	−	0.684429i	$-0.760051\pi$
$941$	7.00000	−	12.1244i	0.228193	−	0.395243i	0.957273	+	0.289187i	$0.0933848\pi$
$942$		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	$-0.682188\pi$
$947$	−2.59808	+	1.50000i	−0.0844261	+	0.0487435i	0.457193	+	0.889368i	$0.348855\pi$
$948$		0			0
$949$	10.0000	−	17.3205i	0.324614	−	0.562247i
$950$	−9.19615	−	3.92820i	−0.298363	−	0.127448i
$951$		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
$955$	−24.6410	−	37.3205i	−0.797365	−	1.20766i
$956$	−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	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$		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	$-0.528670\pi$
$977$	−31.1769	−	18.0000i	−0.997438	−	0.575871i	−0.907489	+	0.420075i	$0.862004\pi$
$978$		0			0
$979$		0			0
$980$	3.16025	+	15.3301i	0.100951	+	0.489703i
$981$		0			0
$982$	15.5885	−	9.00000i	0.497448	−	0.287202i
$983$	21.6506	+	12.5000i	0.690548	+	0.398688i	0.803817	−	0.594876i	$-0.202799\pi$
$983$	21.6506	+	12.5000i	0.690548	+	0.398688i	−0.113269	+	0.993564i	$0.536132\pi$
$984$		0			0
$985$	−1.07180	−	17.8564i	−0.0341503	−	0.568952i
$986$	−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	−0.582253	−	0.813008i	$-0.697829\pi$
$991$	13.0000	−	22.5167i	0.412959	−	0.715265i	0.995212	+	0.0977423i	$0.0311621\pi$
$992$	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	$-0.152364\pi$
$997$	29.4449	+	17.0000i	0.932528	+	0.538395i	0.0449179	+	0.998991i	$0.485697\pi$
$998$	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.109.2		4
3.2	odd	2		70.2.i.a.39.1	yes	4
5.4	even	2	inner	630.2.u.b.109.1		4
7.2	even	3	inner	630.2.u.b.289.1		4
12.11	even	2		560.2.bw.c.529.1		4
15.2	even	4		350.2.e.f.151.1		2
15.8	even	4		350.2.e.g.151.1		2
15.14	odd	2		70.2.i.a.39.2	yes	4
21.2	odd	6		70.2.i.a.9.2	yes	4
21.5	even	6		490.2.i.b.79.2		4
21.11	odd	6		490.2.c.c.99.1		2
21.17	even	6		490.2.c.b.99.1		2
21.20	even	2		490.2.i.b.459.1		4
35.9	even	6	inner	630.2.u.b.289.2		4
60.59	even	2		560.2.bw.c.529.2		4
84.23	even	6		560.2.bw.c.289.2		4
105.2	even	12		350.2.e.f.51.1		2
105.17	odd	12		2450.2.a.bh.1.1		1
105.23	even	12		350.2.e.g.51.1		2
105.32	even	12		2450.2.a.s.1.1		1
105.38	odd	12		2450.2.a.c.1.1		1
105.44	odd	6		70.2.i.a.9.1	✓	4
105.53	even	12		2450.2.a.r.1.1		1
105.59	even	6		490.2.c.b.99.2		2
105.74	odd	6		490.2.c.c.99.2		2
105.89	even	6		490.2.i.b.79.1		4
105.104	even	2		490.2.i.b.459.2		4
420.359	even	6		560.2.bw.c.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.a.9.1	✓	4	105.44	odd	6
70.2.i.a.9.2	yes	4	21.2	odd	6
70.2.i.a.39.1	yes	4	3.2	odd	2
70.2.i.a.39.2	yes	4	15.14	odd	2
350.2.e.f.51.1		2	105.2	even	12
350.2.e.f.151.1		2	15.2	even	4
350.2.e.g.51.1		2	105.23	even	12
350.2.e.g.151.1		2	15.8	even	4
490.2.c.b.99.1		2	21.17	even	6
490.2.c.b.99.2		2	105.59	even	6
490.2.c.c.99.1		2	21.11	odd	6
490.2.c.c.99.2		2	105.74	odd	6
490.2.i.b.79.1		4	105.89	even	6
490.2.i.b.79.2		4	21.5	even	6
490.2.i.b.459.1		4	21.20	even	2
490.2.i.b.459.2		4	105.104	even	2
560.2.bw.c.289.1		4	420.359	even	6
560.2.bw.c.289.2		4	84.23	even	6
560.2.bw.c.529.1		4	12.11	even	2
560.2.bw.c.529.2		4	60.59	even	2
630.2.u.b.109.1		4	5.4	even	2	inner
630.2.u.b.109.2		4	1.1	even	1	trivial
630.2.u.b.289.1		4	7.2	even	3	inner
630.2.u.b.289.2		4	35.9	even	6	inner
2450.2.a.c.1.1		1	105.38	odd	12
2450.2.a.r.1.1		1	105.53	even	12
2450.2.a.s.1.1		1	105.32	even	12
2450.2.a.bh.1.1		1	105.17	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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(1.86603 - 1.23205i) q^{10} -2.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(1.00000 - 2.00000i) q^{20} +(0.866025 - 0.500000i) q^{23} +(4.96410 - 0.598076i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(-2.59808 - 0.500000i) q^{28} -1.00000 q^{29} +(-5.00000 + 8.66025i) q^{31} +(-0.866025 - 0.500000i) q^{32} +2.00000 q^{34} +(-2.26795 - 5.46410i) q^{35} +(6.92820 - 4.00000i) q^{37} +(-1.73205 - 1.00000i) q^{38} +(-0.133975 - 2.23205i) q^{40} +3.00000 q^{41} +5.00000i q^{43} +(0.500000 - 0.866025i) q^{46} +(6.92820 - 4.00000i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(4.00000 - 3.00000i) q^{50} +(-1.73205 - 1.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(-2.50000 + 0.866025i) q^{56} +(-0.866025 + 0.500000i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(4.50000 + 7.79423i) q^{61} +10.0000i q^{62} -1.00000 q^{64} +(-0.267949 - 4.46410i) q^{65} +(-6.06218 - 3.50000i) q^{67} +(1.73205 - 1.00000i) q^{68} +(-4.69615 - 3.59808i) q^{70} -6.00000 q^{71} +(8.66025 + 5.00000i) q^{73} +(4.00000 - 6.92820i) q^{74} -2.00000 q^{76} +(-5.00000 - 8.66025i) q^{79} +(-1.23205 - 1.86603i) q^{80} +(2.59808 - 1.50000i) q^{82} +9.00000i q^{83} +(4.00000 + 2.00000i) q^{85} +(2.50000 + 4.33013i) q^{86} +(3.50000 + 6.06218i) q^{89} +(-5.00000 + 1.73205i) q^{91} -1.00000i q^{92} +(4.00000 - 6.92820i) q^{94} +(-2.46410 - 3.73205i) q^{95} +(-2.59808 + 6.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{5}+O(q^{10}) \) 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

L-functions

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