LMFDB - Embedded newform 630.2.u.c.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 210)
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.c.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(1.23205 + 1.86603i) q^{10} +(-2.50000 + 4.33013i) q^{11} -1.00000i q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(3.50000 + 6.06218i) q^{19} +(2.00000 + 1.00000i) q^{20} +5.00000i q^{22} +(2.59808 - 1.50000i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(2.59808 - 0.500000i) q^{28} +(3.00000 - 5.19615i) q^{31} +(-0.866025 - 0.500000i) q^{32} -2.00000 q^{34} +(-4.23205 + 4.13397i) q^{35} +(-4.33013 + 2.50000i) q^{37} +(6.06218 + 3.50000i) q^{38} +(2.23205 - 0.133975i) q^{40} +9.00000 q^{41} -10.0000i q^{43} +(2.50000 + 4.33013i) q^{44} +(1.50000 - 2.59808i) q^{46} +(11.2583 - 6.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-4.00000 + 3.00000i) q^{50} +(-0.866025 - 0.500000i) q^{52} +(0.866025 + 0.500000i) q^{53} +(-10.0000 - 5.00000i) q^{55} +(2.00000 - 1.73205i) q^{56} +(-2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} -6.00000i q^{62} -1.00000 q^{64} +(2.23205 - 0.133975i) q^{65} +(-5.19615 - 3.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(-1.59808 + 5.69615i) q^{70} +2.00000 q^{71} +(3.46410 + 2.00000i) q^{73} +(-2.50000 + 4.33013i) q^{74} +7.00000 q^{76} +(-12.9904 + 2.50000i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(1.86603 - 1.23205i) q^{80} +(7.79423 - 4.50000i) q^{82} -10.0000i q^{83} +(2.00000 - 4.00000i) q^{85} +(-5.00000 - 8.66025i) q^{86} +(4.33013 + 2.50000i) q^{88} +(-5.00000 - 8.66025i) q^{89} +(2.00000 - 1.73205i) q^{91} -3.00000i q^{92} +(6.50000 - 11.2583i) q^{94} +(-13.0622 + 8.62436i) q^{95} +8.00000i q^{97} +(2.59808 + 6.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{5}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^5	$ 4 q + 2 q^{4} + 4 q^{5} - 2 q^{10} - 10 q^{11} + 10 q^{14} - 2 q^{16} + 14 q^{19} + 8 q^{20} - 6 q^{25} - 2 q^{26} + 12 q^{31} - 8 q^{34} - 10 q^{35} + 2 q^{40} + 36 q^{41} + 10 q^{44} + 6 q^{46} - 4 q^{49} - 16 q^{50} - 40 q^{55} + 8 q^{56} - 8 q^{59} + 4 q^{61} - 4 q^{64} + 2 q^{65} + 4 q^{70} + 8 q^{71} - 10 q^{74} + 28 q^{76} - 28 q^{79} + 4 q^{80} + 8 q^{85} - 20 q^{86} - 20 q^{89} + 8 q^{91} + 26 q^{94} - 28 q^{95}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^5 - 2 * q^10 - 10 * q^11 + 10 * q^14 - 2 * q^16 + 14 * q^19 + 8 * q^20 - 6 * q^25 - 2 * q^26 + 12 * q^31 - 8 * q^34 - 10 * q^35 + 2 * q^40 + 36 * q^41 + 10 * q^44 + 6 * q^46 - 4 * q^49 - 16 * q^50 - 40 * q^55 + 8 * q^56 - 8 * q^59 + 4 * q^61 - 4 * q^64 + 2 * q^65 + 4 * q^70 + 8 * q^71 - 10 * q^74 + 28 * q^76 - 28 * q^79 + 4 * q^80 + 8 * q^85 - 20 * q^86 - 20 * q^89 + 8 * q^91 + 26 * q^94 - 28 * 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
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$		0			0
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.23205	+	1.86603i	0.389609	+	0.590089i
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$		−	1.00000i		−	0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$	2.50000	+	0.866025i	0.668153	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$		0			0
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	0.917663	+	0.397360i	$0.130073\pi$
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	−0.114708	+	0.993399i	$0.536593\pi$
$20$	2.00000	+	1.00000i	0.447214	+	0.223607i
$21$		0			0
$22$			5.00000i			1.06600i
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	−0.204046	−	0.978961i	$-0.565409\pi$
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	0.745782	+	0.666190i	$0.232076\pi$
$24$		0			0
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$		0			0
$28$	2.59808	−	0.500000i	0.490990	−	0.0944911i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	−0.460152	−	0.887840i	$-0.652205\pi$
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	0.998968	−	0.0454165i	$-0.0144615\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	−4.23205	+	4.13397i	−0.715347	+	0.698769i
$36$		0			0
$37$	−4.33013	+	2.50000i	−0.711868	+	0.410997i	−0.811752	−	0.584002i	$-0.801486\pi$
$37$	−4.33013	+	2.50000i	−0.711868	+	0.410997i	0.0998840	+	0.994999i	$0.468153\pi$
$38$	6.06218	+	3.50000i	0.983415	+	0.567775i
$39$		0			0
$40$	2.23205	−	0.133975i	0.352918	−	0.0211832i
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$		0			0
$43$		−	10.0000i		−	1.52499i	−0.646997	−	0.762493i	$-0.723975\pi$
$43$		−	10.0000i		−	1.52499i	0.646997	−	0.762493i	$-0.276025\pi$
$44$	2.50000	+	4.33013i	0.376889	+	0.652791i
$45$		0			0
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	11.2583	−	6.50000i	1.64220	−	0.948122i	0.662145	−	0.749375i	$-0.269646\pi$
$47$	11.2583	−	6.50000i	1.64220	−	0.948122i	0.980051	−	0.198747i	$-0.0636872\pi$
$48$		0			0
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$		0			0
$52$	−0.866025	−	0.500000i	−0.120096	−	0.0693375i
$53$	0.866025	+	0.500000i	0.118958	+	0.0686803i	0.558298	−	0.829640i	$-0.311454\pi$
$53$	0.866025	+	0.500000i	0.118958	+	0.0686803i	−0.439340	+	0.898321i	$0.644788\pi$
$54$		0			0
$55$	−10.0000	−	5.00000i	−1.34840	−	0.674200i
$56$	2.00000	−	1.73205i	0.267261	−	0.231455i
$57$		0			0
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$		−	6.00000i		−	0.762001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.23205	−	0.133975i	0.276852	−	0.0166175i
$66$		0			0
$67$	−5.19615	−	3.00000i	−0.634811	−	0.366508i	0.147802	−	0.989017i	$-0.452780\pi$
$67$	−5.19615	−	3.00000i	−0.634811	−	0.366508i	−0.782613	+	0.622509i	$0.786114\pi$
$68$	−1.73205	+	1.00000i	−0.210042	+	0.121268i
$69$		0			0
$70$	−1.59808	+	5.69615i	−0.191007	+	0.680820i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	3.46410	+	2.00000i	0.405442	+	0.234082i	0.688830	−	0.724923i	$-0.258125\pi$
$73$	3.46410	+	2.00000i	0.405442	+	0.234082i	−0.283387	+	0.959006i	$0.591458\pi$
$74$	−2.50000	+	4.33013i	−0.290619	+	0.503367i
$75$		0			0
$76$	7.00000			0.802955
$77$	−12.9904	+	2.50000i	−1.48039	+	0.284901i
$78$		0			0
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	−0.927457	−	0.373930i	$-0.878010\pi$
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	0.139895	−	0.990166i	$-0.455323\pi$
$80$	1.86603	−	1.23205i	0.208628	−	0.137747i
$81$		0			0
$82$	7.79423	−	4.50000i	0.860729	−	0.496942i
$83$		−	10.0000i		−	1.09764i	−0.835940	−	0.548821i	$-0.815077\pi$
$83$		−	10.0000i		−	1.09764i	0.835940	−	0.548821i	$-0.184923\pi$
$84$		0			0
$85$	2.00000	−	4.00000i	0.216930	−	0.433861i
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$		0			0
$88$	4.33013	+	2.50000i	0.461593	+	0.266501i
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$		0			0
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$		−	3.00000i		−	0.312772i
$93$		0			0
$94$	6.50000	−	11.2583i	0.670424	−	1.16121i
$95$	−13.0622	+	8.62436i	−1.34015	+	0.884840i
$96$		0			0
$97$			8.00000i			0.812277i	0.913812	+	0.406138i	$0.133125\pi$
$97$			8.00000i			0.812277i	−0.913812	+	0.406138i	$0.866875\pi$
$98$	2.59808	+	6.50000i	0.262445	+	0.656599i
$99$		0			0
$100$	−1.96410	+	4.59808i	−0.196410	+	0.459808i
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	−0.595466	−	0.803380i	$-0.703033\pi$
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	0.993481	+	0.113998i	$0.0363659\pi$
$102$		0			0
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	1.00000			0.0971286
$107$	−10.3923	+	6.00000i	−1.00466	+	0.580042i	−0.909624	−	0.415432i	$-0.863630\pi$
$107$	−10.3923	+	6.00000i	−1.00466	+	0.580042i	−0.0950377	+	0.995474i	$0.530297\pi$
$108$		0			0
$109$	−9.00000	+	15.5885i	−0.862044	+	1.49310i	0.00790932	+	0.999969i	$0.497482\pi$
$109$	−9.00000	+	15.5885i	−0.862044	+	1.49310i	−0.869953	+	0.493135i	$0.835851\pi$
$110$	−11.1603	+	0.669873i	−1.06409	+	0.0638699i
$111$		0			0
$112$	0.866025	−	2.50000i	0.0818317	−	0.236228i
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$		0			0
$115$	3.69615	+	5.59808i	0.344668	+	0.522023i
$116$		0			0
$117$		0			0
$118$			4.00000i			0.368230i
$119$	−1.00000	−	5.19615i	−0.0916698	−	0.476331i
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	1.73205	+	1.00000i	0.156813	+	0.0905357i
$123$		0			0
$124$	−3.00000	−	5.19615i	−0.269408	−	0.466628i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$			9.00000i			0.798621i	0.916816	+	0.399310i	$0.130750\pi$
$127$			9.00000i			0.798621i	−0.916816	+	0.399310i	$0.869250\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	1.86603	−	1.23205i	0.163661	−	0.108058i
$131$	−8.50000	−	14.7224i	−0.742648	−	1.28630i	−0.951285	−	0.308312i	$-0.900236\pi$
$131$	−8.50000	−	14.7224i	−0.742648	−	1.28630i	0.208637	−	0.977993i	$-0.433097\pi$
$132$		0			0
$133$	−6.06218	+	17.5000i	−0.525657	+	1.51744i
$134$	−6.00000			−0.518321
$135$		0			0
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	0.344668	−	0.938725i	$-0.387992\pi$
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	−0.640626	+	0.767853i	$0.721325\pi$
$138$		0			0
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	1.46410	+	5.73205i	0.123739	+	0.484447i
$141$		0			0
$142$	1.73205	−	1.00000i	0.145350	−	0.0839181i
$143$	4.33013	+	2.50000i	0.362103	+	0.209061i
$144$		0			0
$145$		0			0
$146$	4.00000			0.331042
$147$		0			0
$148$			5.00000i			0.410997i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.0615699	−	0.998103i	$-0.480389\pi$
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.833597	−	0.552372i	$-0.186277\pi$
$152$	6.06218	−	3.50000i	0.491708	−	0.283887i
$153$		0			0
$154$	−10.0000	+	8.66025i	−0.805823	+	0.697863i
$155$	12.0000	+	6.00000i	0.963863	+	0.481932i
$156$		0			0
$157$	−11.2583	−	6.50000i	−0.898513	−	0.518756i	−0.0217953	−	0.999762i	$-0.506938\pi$
$157$	−11.2583	−	6.50000i	−0.898513	−	0.518756i	−0.876717	+	0.481006i	$0.840272\pi$
$158$	−12.1244	−	7.00000i	−0.964562	−	0.556890i
$159$		0			0
$160$	1.00000	−	2.00000i	0.0790569	−	0.158114i
$161$	7.50000	+	2.59808i	0.591083	+	0.204757i
$162$		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	$0.177603\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	−5.00000	−	8.66025i	−0.388075	−	0.672166i
$167$			19.0000i			1.47026i	0.677924	+	0.735132i	$0.262880\pi$
$167$			19.0000i			1.47026i	−0.677924	+	0.735132i	$0.737120\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	−0.267949	−	4.46410i	−0.0205508	−	0.342381i
$171$		0			0
$172$	−8.66025	−	5.00000i	−0.660338	−	0.381246i
$173$	6.06218	−	3.50000i	0.460899	−	0.266100i	−0.251523	−	0.967851i	$-0.580932\pi$
$173$	6.06218	−	3.50000i	0.460899	−	0.266100i	0.712422	+	0.701751i	$0.247598\pi$
$174$		0			0
$175$	−9.79423	−	8.89230i	−0.740374	−	0.672195i
$176$	5.00000			0.376889
$177$		0			0
$178$	−8.66025	−	5.00000i	−0.649113	−	0.374766i
$179$	5.50000	−	9.52628i	0.411089	−	0.712028i	−0.583920	−	0.811811i	$-0.698482\pi$
$179$	5.50000	−	9.52628i	0.411089	−	0.712028i	0.995009	+	0.0997838i	$0.0318151\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0.866025	−	2.50000i	0.0641941	−	0.185312i
$183$		0			0
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	−6.16025	−	9.33013i	−0.452911	−	0.685965i
$186$		0			0
$187$	8.66025	−	5.00000i	0.633300	−	0.365636i
$188$		−	13.0000i		−	0.948122i
$189$		0			0
$190$	−7.00000	+	14.0000i	−0.507833	+	1.01567i
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	−0.995610	−	0.0935936i	$-0.970165\pi$
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	0.416751	−	0.909021i	$-0.363169\pi$
$192$		0			0
$193$	−15.5885	−	9.00000i	−1.12208	−	0.647834i	−0.180150	−	0.983639i	$-0.557658\pi$
$193$	−15.5885	−	9.00000i	−1.12208	−	0.647834i	−0.941932	+	0.335805i	$0.890992\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$			27.0000i			1.92367i	0.273629	+	0.961835i	$0.411776\pi$
$197$			27.0000i			1.92367i	−0.273629	+	0.961835i	$0.588224\pi$
$198$		0			0
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	−0.999990	−	0.00436292i	$-0.998611\pi$
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	0.503774	+	0.863836i	$0.331945\pi$
$200$	0.598076	+	4.96410i	0.0422904	+	0.351015i
$201$		0			0
$202$		−	8.00000i		−	0.562878i
$203$		0			0
$204$		0			0
$205$	1.20577	+	20.0885i	0.0842147	+	1.40304i
$206$		0			0
$207$		0			0
$208$	−0.866025	+	0.500000i	−0.0600481	+	0.0346688i
$209$	−35.0000			−2.42100
$210$		0			0
$211$	19.0000			1.30801			0.654007	−	0.756489i	$-0.273087\pi$
$211$	19.0000			1.30801			0.654007	+	0.756489i	$0.273087\pi$
$212$	0.866025	−	0.500000i	0.0594789	−	0.0343401i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	22.3205	−	1.33975i	1.52225	−	0.0913699i
$216$		0			0
$217$	15.5885	−	3.00000i	1.05821	−	0.203653i
$218$			18.0000i			1.21911i
$219$		0			0
$220$	−9.33013	+	6.16025i	−0.629037	+	0.415324i
$221$	−1.00000	+	1.73205i	−0.0672673	+	0.116510i
$222$		0			0
$223$		−	16.0000i		−	1.07144i	−0.844396	−	0.535720i	$-0.820040\pi$
$223$		−	16.0000i		−	1.07144i	0.844396	−	0.535720i	$-0.179960\pi$
$224$	−0.500000	−	2.59808i	−0.0334077	−	0.173591i
$225$		0			0
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	12.1244	+	7.00000i	0.804722	+	0.464606i	0.845120	−	0.534577i	$-0.179529\pi$
$227$	12.1244	+	7.00000i	0.804722	+	0.464606i	−0.0403978	+	0.999184i	$0.512863\pi$
$228$		0			0
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	0.792347	−	0.610071i	$-0.208859\pi$
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	−0.924510	+	0.381157i	$0.875526\pi$
$230$	6.00000	+	3.00000i	0.395628	+	0.197814i
$231$		0			0
$232$		0			0
$233$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$233$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$234$		0			0
$235$	16.0167	+	24.2583i	1.04481	+	1.58244i
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$		0			0
$238$	−3.46410	−	4.00000i	−0.224544	−	0.259281i
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	−12.1244	−	7.00000i	−0.779383	−	0.449977i
$243$		0			0
$244$	2.00000			0.128037
$245$	−15.5981	−	1.30385i	−0.996525	−	0.0832998i
$246$		0			0
$247$	6.06218	−	3.50000i	0.385727	−	0.222700i
$248$	−5.19615	−	3.00000i	−0.329956	−	0.190500i
$249$		0			0
$250$	−7.23205	−	8.52628i	−0.457395	−	0.539249i
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$		0			0
$253$			15.0000i			0.943042i
$254$	4.50000	+	7.79423i	0.282355	+	0.489053i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.66025	−	5.00000i	0.540212	−	0.311891i	−0.204953	−	0.978772i	$-0.565704\pi$
$257$	8.66025	−	5.00000i	0.540212	−	0.311891i	0.745165	+	0.666880i	$0.232371\pi$
$258$		0			0
$259$	−12.5000	−	4.33013i	−0.776712	−	0.269061i
$260$	1.00000	−	2.00000i	0.0620174	−	0.124035i
$261$		0			0
$262$	−14.7224	−	8.50000i	−0.909555	−	0.525132i
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.304487	−	0.952517i	$-0.598485\pi$
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.977147	+	0.212565i	$0.931818\pi$
$264$		0			0
$265$	−1.00000	+	2.00000i	−0.0614295	+	0.122859i
$266$	3.50000	+	18.1865i	0.214599	+	1.11509i
$267$		0			0
$268$	−5.19615	+	3.00000i	−0.317406	+	0.183254i
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	−0.996586	−	0.0825561i	$-0.973692\pi$
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	0.569789	+	0.821791i	$0.307025\pi$
$270$		0			0
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	0.718580	−	0.695444i	$-0.244792\pi$
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	−0.961563	+	0.274586i	$0.911459\pi$
$272$			2.00000i			0.121268i
$273$		0			0
$274$	−4.00000			−0.241649
$275$	9.82051	−	22.9904i	0.592199	−	1.38637i
$276$		0			0
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	0.447062	−	0.894503i	$-0.352470\pi$
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	−0.551131	+	0.834419i	$0.685804\pi$
$278$	6.92820	−	4.00000i	0.415526	−	0.239904i
$279$		0			0
$280$	4.13397	+	4.23205i	0.247052	+	0.252913i
$281$	11.0000			0.656205			0.328102	−	0.944642i	$-0.393591\pi$
$281$	11.0000			0.656205			0.328102	+	0.944642i	$0.393591\pi$
$282$		0			0
$283$	22.5167	+	13.0000i	1.33848	+	0.772770i	0.986581	−	0.163270i	$-0.0522041\pi$
$283$	22.5167	+	13.0000i	1.33848	+	0.772770i	0.351895	+	0.936039i	$0.385537\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$		0			0
$286$	5.00000			0.295656
$287$	15.5885	+	18.0000i	0.920158	+	1.06251i
$288$		0			0
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$		0			0
$291$		0			0
$292$	3.46410	−	2.00000i	0.202721	−	0.117041i
$293$			1.00000i			0.0584206i	0.999573	+	0.0292103i	$0.00929925\pi$
$293$			1.00000i			0.0584206i	−0.999573	+	0.0292103i	$0.990701\pi$
$294$		0			0
$295$	−8.00000	−	4.00000i	−0.465778	−	0.232889i
$296$	2.50000	+	4.33013i	0.145310	+	0.251684i
$297$		0			0
$298$	5.19615	+	3.00000i	0.301005	+	0.173785i
$299$	−1.50000	−	2.59808i	−0.0867472	−	0.150251i
$300$		0			0
$301$	20.0000	−	17.3205i	1.15278	−	0.998337i
$302$		−	22.0000i		−	1.26596i
$303$		0			0
$304$	3.50000	−	6.06218i	0.200739	−	0.347690i
$305$	−3.73205	+	2.46410i	−0.213697	+	0.141094i
$306$		0			0
$307$			2.00000i			0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$			2.00000i			0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$	−4.33013	+	12.5000i	−0.246732	+	0.712254i
$309$		0			0
$310$	13.3923	−	0.803848i	0.760632	−	0.0456555i
$311$	−13.0000	+	22.5167i	−0.737162	+	1.27680i	0.216606	+	0.976259i	$0.430501\pi$
$311$	−13.0000	+	22.5167i	−0.737162	+	1.27680i	−0.953768	+	0.300544i	$0.902832\pi$
$312$		0			0
$313$	8.66025	−	5.00000i	0.489506	−	0.282617i	−0.234863	−	0.972028i	$-0.575464\pi$
$313$	8.66025	−	5.00000i	0.489506	−	0.282617i	0.724370	+	0.689412i	$0.242131\pi$
$314$	−13.0000			−0.733632
$315$		0			0
$316$	−14.0000			−0.787562
$317$	−1.73205	+	1.00000i	−0.0972817	+	0.0561656i	−0.547852	−	0.836576i	$-0.684554\pi$
$317$	−1.73205	+	1.00000i	−0.0972817	+	0.0561656i	0.450570	+	0.892741i	$0.351221\pi$
$318$		0			0
$319$		0			0
$320$	−0.133975	−	2.23205i	−0.00748941	−	0.124775i
$321$		0			0
$322$	7.79423	−	1.50000i	0.434355	−	0.0835917i
$323$		−	14.0000i		−	0.778981i
$324$		0			0
$325$	0.598076	+	4.96410i	0.0331753	+	0.275359i
$326$	6.00000	−	10.3923i	0.332309	−	0.575577i
$327$		0			0
$328$		−	9.00000i		−	0.496942i
$329$	32.5000	+	11.2583i	1.79178	+	0.620692i
$330$		0			0
$331$	7.50000	+	12.9904i	0.412237	+	0.714016i	0.995134	−	0.0985303i	$-0.0314141\pi$
$331$	7.50000	+	12.9904i	0.412237	+	0.714016i	−0.582897	+	0.812546i	$0.698081\pi$
$332$	−8.66025	−	5.00000i	−0.475293	−	0.274411i
$333$		0			0
$334$	9.50000	+	16.4545i	0.519817	+	0.900349i
$335$	6.00000	−	12.0000i	0.327815	−	0.655630i
$336$		0			0
$337$		−	14.0000i		−	0.762629i	−0.924445	−	0.381314i	$-0.875472\pi$
$337$		−	14.0000i		−	0.762629i	0.924445	−	0.381314i	$-0.124528\pi$
$338$	10.3923	−	6.00000i	0.565267	−	0.326357i
$339$		0			0
$340$	−2.46410	−	3.73205i	−0.133635	−	0.202399i
$341$	15.0000	+	25.9808i	0.812296	+	1.40694i
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	−10.0000			−0.539164
$345$		0			0
$346$	3.50000	−	6.06218i	0.188161	−	0.325905i
$347$	−13.8564	−	8.00000i	−0.743851	−	0.429463i	0.0796169	−	0.996826i	$-0.474630\pi$
$347$	−13.8564	−	8.00000i	−0.743851	−	0.429463i	−0.823468	+	0.567363i	$0.807964\pi$
$348$		0			0
$349$	24.0000			1.28469			0.642345	−	0.766415i	$-0.277962\pi$
$349$	24.0000			1.28469			0.642345	+	0.766415i	$0.277962\pi$
$350$	−12.9282	−	2.80385i	−0.691042	−	0.149872i
$351$		0			0
$352$	4.33013	−	2.50000i	0.230797	−	0.133250i
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$	0.267949	+	4.46410i	0.0142213	+	0.236930i
$356$	−10.0000			−0.529999
$357$		0			0
$358$		−	11.0000i		−	0.581368i
$359$	14.0000	+	24.2487i	0.738892	+	1.27980i	0.952995	+	0.302987i	$0.0979839\pi$
$359$	14.0000	+	24.2487i	0.738892	+	1.27980i	−0.214103	+	0.976811i	$0.568683\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$	−1.73205	+	1.00000i	−0.0910346	+	0.0525588i
$363$		0			0
$364$	−0.500000	−	2.59808i	−0.0262071	−	0.136176i
$365$	−4.00000	+	8.00000i	−0.209370	+	0.418739i
$366$		0			0
$367$	32.0429	+	18.5000i	1.67263	+	0.965692i	0.966159	+	0.257948i	$0.0830464\pi$
$367$	32.0429	+	18.5000i	1.67263	+	0.965692i	0.706469	+	0.707744i	$0.250287\pi$
$368$	−2.59808	−	1.50000i	−0.135434	−	0.0781929i
$369$		0			0
$370$	−10.0000	−	5.00000i	−0.519875	−	0.259938i
$371$	0.500000	+	2.59808i	0.0259587	+	0.134885i
$372$		0			0
$373$	−5.19615	+	3.00000i	−0.269047	+	0.155334i	−0.628454	−	0.777847i	$-0.716312\pi$
$373$	−5.19615	+	3.00000i	−0.269047	+	0.155334i	0.359408	+	0.933181i	$0.382979\pi$
$374$	5.00000	−	8.66025i	0.258544	−	0.447811i
$375$		0			0
$376$	−6.50000	−	11.2583i	−0.335212	−	0.580604i
$377$		0			0
$378$		0			0
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$	0.937822	+	15.6244i	0.0481093	+	0.801513i
$381$		0			0
$382$	−13.8564	−	8.00000i	−0.708955	−	0.409316i
$383$	−7.79423	+	4.50000i	−0.398266	+	0.229939i	−0.685736	−	0.727851i	$-0.740519\pi$
$383$	−7.79423	+	4.50000i	−0.398266	+	0.229939i	0.287469	+	0.957790i	$0.407186\pi$
$384$		0			0
$385$	−7.32051	−	28.6603i	−0.373088	−	1.46066i
$386$	−18.0000			−0.916176
$387$		0			0
$388$	6.92820	+	4.00000i	0.351726	+	0.203069i
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$	−6.00000			−0.303433
$392$	6.92820	+	1.00000i	0.349927	+	0.0505076i
$393$		0			0
$394$	13.5000	+	23.3827i	0.680120	+	1.17800i
$395$	26.1244	−	17.2487i	1.31446	−	0.867877i
$396$		0			0
$397$	−1.73205	+	1.00000i	−0.0869291	+	0.0501886i	−0.542834	−	0.839840i	$-0.682649\pi$
$397$	−1.73205	+	1.00000i	−0.0869291	+	0.0501886i	0.455905	+	0.890028i	$0.349316\pi$
$398$			14.0000i			0.701757i
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	−0.976714	−	0.214544i	$-0.931173\pi$
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	0.302556	−	0.953131i	$-0.402160\pi$
$402$		0			0
$403$	−5.19615	−	3.00000i	−0.258839	−	0.149441i
$404$	−4.00000	−	6.92820i	−0.199007	−	0.344691i
$405$		0			0
$406$		0			0
$407$		−	25.0000i		−	1.23920i
$408$		0			0
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	−0.715523	−	0.698589i	$-0.753812\pi$
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	0.962757	+	0.270367i	$0.0871450\pi$
$410$	11.0885	+	16.7942i	0.547620	+	0.829408i
$411$		0			0
$412$		0			0
$413$	−10.3923	+	2.00000i	−0.511372	+	0.0984136i
$414$		0			0
$415$	22.3205	−	1.33975i	1.09567	−	0.0657655i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$		0			0
$418$	−30.3109	+	17.5000i	−1.48255	+	0.855953i
$419$	3.00000			0.146560			0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000			0.146560			0.0732798	+	0.997311i	$0.476653\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	16.4545	−	9.50000i	0.800992	−	0.462453i
$423$		0			0
$424$	0.500000	−	0.866025i	0.0242821	−	0.0420579i
$425$	9.19615	+	3.92820i	0.446079	+	0.190546i
$426$		0			0
$427$	−1.73205	+	5.00000i	−0.0838198	+	0.241967i
$428$			12.0000i			0.580042i
$429$		0			0
$430$	18.6603	−	12.3205i	0.899877	−	0.594148i
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	−0.563658	−	0.826008i	$-0.690607\pi$
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	0.997173	+	0.0751385i	$0.0239399\pi$
$432$		0			0
$433$		−	4.00000i		−	0.192228i	−0.995370	−	0.0961139i	$-0.969359\pi$
$433$		−	4.00000i		−	0.192228i	0.995370	−	0.0961139i	$-0.0306413\pi$
$434$	12.0000	−	10.3923i	0.576018	−	0.498847i
$435$		0			0
$436$	9.00000	+	15.5885i	0.431022	+	0.746552i
$437$	18.1865	+	10.5000i	0.869980	+	0.502283i
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	−5.00000	+	10.0000i	−0.238366	+	0.476731i
$441$		0			0
$442$			2.00000i			0.0951303i
$443$	−5.19615	+	3.00000i	−0.246877	+	0.142534i	−0.618333	−	0.785916i	$-0.712192\pi$
$443$	−5.19615	+	3.00000i	−0.246877	+	0.142534i	0.371457	+	0.928450i	$0.378858\pi$
$444$		0			0
$445$	18.6603	−	12.3205i	0.884581	−	0.584048i
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$		0			0
$448$	−1.73205	−	2.00000i	−0.0818317	−	0.0944911i
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	−22.5000	+	38.9711i	−1.05948	+	1.83508i
$452$	5.19615	+	3.00000i	0.244406	+	0.141108i
$453$		0			0
$454$	14.0000			0.657053
$455$	4.13397	+	4.23205i	0.193804	+	0.198402i
$456$		0			0
$457$	−32.9090	+	19.0000i	−1.53942	+	0.888783i	−0.540544	+	0.841316i	$0.681781\pi$
$457$	−32.9090	+	19.0000i	−1.53942	+	0.888783i	−0.998873	+	0.0474665i	$0.984885\pi$
$458$	−3.46410	−	2.00000i	−0.161867	−	0.0934539i
$459$		0			0
$460$	6.69615	−	0.401924i	0.312210	−	0.0187398i
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$			15.0000i			0.697109i	0.937288	+	0.348555i	$0.113327\pi$
$463$			15.0000i			0.697109i	−0.937288	+	0.348555i	$0.886673\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.73205	+	1.00000i	−0.0801498	+	0.0462745i	−0.539539	−	0.841960i	$-0.681402\pi$
$467$	−1.73205	+	1.00000i	−0.0801498	+	0.0462745i	0.459390	+	0.888235i	$0.348068\pi$
$468$		0			0
$469$	−3.00000	−	15.5885i	−0.138527	−	0.719808i
$470$	26.0000	+	13.0000i	1.19929	+	0.599645i
$471$		0			0
$472$	3.46410	+	2.00000i	0.159448	+	0.0920575i
$473$	43.3013	+	25.0000i	1.99099	+	1.14950i
$474$		0			0
$475$	−21.0000	−	28.0000i	−0.963546	−	1.28473i
$476$	−5.00000	−	1.73205i	−0.229175	−	0.0793884i
$477$		0			0
$478$	17.3205	−	10.0000i	0.792222	−	0.457389i
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	−0.942821	−	0.333300i	$-0.891838\pi$
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	0.760056	+	0.649857i	$0.225171\pi$
$480$		0			0
$481$	2.50000	+	4.33013i	0.113990	+	0.197437i
$482$		−	1.00000i		−	0.0455488i
$483$		0			0
$484$	−14.0000			−0.636364
$485$	−17.8564	+	1.07180i	−0.810818	+	0.0486678i
$486$		0			0
$487$	−20.7846	−	12.0000i	−0.941841	−	0.543772i	−0.0513038	−	0.998683i	$-0.516338\pi$
$487$	−20.7846	−	12.0000i	−0.941841	−	0.543772i	−0.890537	+	0.454911i	$0.849671\pi$
$488$	1.73205	−	1.00000i	0.0784063	−	0.0452679i
$489$		0			0
$490$	−14.1603	+	6.66987i	−0.639695	+	0.301314i
$491$	−24.0000			−1.08310			−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000			−1.08310			−0.541552	+	0.840667i	$0.682163\pi$
$492$		0			0
$493$		0			0
$494$	3.50000	−	6.06218i	0.157472	−	0.272750i
$495$		0			0
$496$	−6.00000			−0.269408
$497$	3.46410	+	4.00000i	0.155386	+	0.179425i
$498$		0			0
$499$	−14.0000	−	24.2487i	−0.626726	−	1.08552i	−0.988204	−	0.153141i	$-0.951061\pi$
$499$	−14.0000	−	24.2487i	−0.626726	−	1.08552i	0.361478	−	0.932381i	$-0.382272\pi$
$500$	−10.5263	−	3.76795i	−0.470750	−	0.168508i
$501$		0			0
$502$	2.59808	−	1.50000i	0.115958	−	0.0669483i
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$		0			0
$505$	16.0000	+	8.00000i	0.711991	+	0.355995i
$506$	7.50000	+	12.9904i	0.333416	+	0.577493i
$507$		0			0
$508$	7.79423	+	4.50000i	0.345813	+	0.199655i
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	0.668151	−	0.744026i	$-0.267086\pi$
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	−0.978421	+	0.206623i	$0.933753\pi$
$510$		0			0
$511$	2.00000	+	10.3923i	0.0884748	+	0.459728i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	5.00000	−	8.66025i	0.220541	−	0.381987i
$515$		0			0
$516$		0			0
$517$			65.0000i			2.85870i
$518$	−12.9904	+	2.50000i	−0.570765	+	0.109844i
$519$		0			0
$520$	−0.133975	−	2.23205i	−0.00587517	−	0.0978819i
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	−0.982231	−	0.187678i	$-0.939904\pi$
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	0.653650	+	0.756797i	$0.273237\pi$
$522$		0			0
$523$	−10.3923	+	6.00000i	−0.454424	+	0.262362i	−0.709697	−	0.704507i	$-0.751168\pi$
$523$	−10.3923	+	6.00000i	−0.454424	+	0.262362i	0.255273	+	0.966869i	$0.417835\pi$
$524$	−17.0000			−0.742648
$525$		0			0
$526$	−24.0000			−1.04645
$527$	−10.3923	+	6.00000i	−0.452696	+	0.261364i
$528$		0			0
$529$	−7.00000	+	12.1244i	−0.304348	+	0.527146i
$530$	0.133975	+	2.23205i	0.00581948	+	0.0969541i
$531$		0			0
$532$	12.1244	+	14.0000i	0.525657	+	0.606977i
$533$		−	9.00000i		−	0.389833i
$534$		0			0
$535$	−14.7846	−	22.3923i	−0.639194	−	0.968104i
$536$	−3.00000	+	5.19615i	−0.129580	+	0.224440i
$537$		0			0
$538$			14.0000i			0.603583i
$539$	−27.5000	−	21.6506i	−1.18451	−	0.932559i
$540$		0			0
$541$	−2.00000	−	3.46410i	−0.0859867	−	0.148933i	0.819825	−	0.572615i	$-0.194071\pi$
$541$	−2.00000	−	3.46410i	−0.0859867	−	0.148933i	−0.905811	+	0.423681i	$0.860738\pi$
$542$	−6.92820	−	4.00000i	−0.297592	−	0.171815i
$543$		0			0
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$	−36.0000	−	18.0000i	−1.54207	−	0.771035i
$546$		0			0
$547$		−	14.0000i		−	0.598597i	−0.954160	−	0.299298i	$-0.903247\pi$
$547$		−	14.0000i		−	0.598597i	0.954160	−	0.299298i	$-0.0967526\pi$
$548$	−3.46410	+	2.00000i	−0.147979	+	0.0854358i
$549$		0			0
$550$	−2.99038	−	24.8205i	−0.127510	−	1.05835i
$551$		0			0
$552$		0			0
$553$	12.1244	−	35.0000i	0.515580	−	1.48835i
$554$	−2.00000			−0.0849719
$555$		0			0
$556$	4.00000	−	6.92820i	0.169638	−	0.293821i
$557$	−33.7750	−	19.5000i	−1.43109	−	0.826242i	−0.433888	−	0.900967i	$-0.642859\pi$
$557$	−33.7750	−	19.5000i	−1.43109	−	0.826242i	−0.997204	+	0.0747252i	$0.976192\pi$
$558$		0			0
$559$	−10.0000			−0.422955
$560$	5.69615	+	1.59808i	0.240706	+	0.0675310i
$561$		0			0
$562$	9.52628	−	5.50000i	0.401842	−	0.232003i
$563$	−25.9808	−	15.0000i	−1.09496	−	0.632175i	−0.160066	−	0.987106i	$-0.551171\pi$
$563$	−25.9808	−	15.0000i	−1.09496	−	0.632175i	−0.934892	+	0.354932i	$0.884504\pi$
$564$		0			0
$565$	−13.3923	+	0.803848i	−0.563418	+	0.0338181i
$566$	26.0000			1.09286
$567$		0			0
$568$		−	2.00000i		−	0.0839181i
$569$	1.50000	+	2.59808i	0.0628833	+	0.108917i	0.895753	−	0.444552i	$-0.146637\pi$
$569$	1.50000	+	2.59808i	0.0628833	+	0.108917i	−0.832870	+	0.553469i	$0.813304\pi$
$570$		0			0
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	−0.770108	−	0.637913i	$-0.779798\pi$
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	0.937503	+	0.347977i	$0.113131\pi$
$572$	4.33013	−	2.50000i	0.181052	−	0.104530i
$573$		0			0
$574$	22.5000	+	7.79423i	0.939132	+	0.325325i
$575$	−12.0000	+	9.00000i	−0.500435	+	0.375326i
$576$		0			0
$577$	−20.7846	−	12.0000i	−0.865275	−	0.499567i	0.000500448	−	1.00000i	$-0.499841\pi$
$577$	−20.7846	−	12.0000i	−0.865275	−	0.499567i	−0.865775	+	0.500433i	$0.833174\pi$
$578$	−11.2583	−	6.50000i	−0.468285	−	0.270364i
$579$		0			0
$580$		0			0
$581$	20.0000	−	17.3205i	0.829740	−	0.718576i
$582$		0			0
$583$	−4.33013	+	2.50000i	−0.179336	+	0.103539i
$584$	2.00000	−	3.46410i	0.0827606	−	0.143346i
$585$		0			0
$586$	0.500000	+	0.866025i	0.0206548	+	0.0357752i
$587$		−	2.00000i		−	0.0825488i	−0.999148	−	0.0412744i	$-0.986858\pi$
$587$		−	2.00000i		−	0.0825488i	0.999148	−	0.0412744i	$-0.0131418\pi$
$588$		0			0
$589$	42.0000			1.73058
$590$	−8.92820	+	0.535898i	−0.367568	+	0.0220626i
$591$		0			0
$592$	4.33013	+	2.50000i	0.177967	+	0.102749i
$593$	−29.4449	+	17.0000i	−1.20916	+	0.698106i	−0.962575	−	0.271016i	$-0.912640\pi$
$593$	−29.4449	+	17.0000i	−1.20916	+	0.698106i	−0.246581	+	0.969122i	$0.579307\pi$
$594$		0			0
$595$	11.4641	−	2.92820i	0.469982	−	0.120045i
$596$	6.00000			0.245770
$597$		0			0
$598$	−2.59808	−	1.50000i	−0.106243	−	0.0613396i
$599$	14.0000	−	24.2487i	0.572024	−	0.990775i	−0.424333	−	0.905506i	$-0.639492\pi$
$599$	14.0000	−	24.2487i	0.572024	−	0.990775i	0.996358	−	0.0852695i	$-0.0271751\pi$
$600$		0			0
$601$	−30.0000			−1.22373			−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000			−1.22373			−0.611863	+	0.790964i	$0.709580\pi$
$602$	8.66025	−	25.0000i	0.352966	−	1.01892i
$603$		0			0
$604$	−11.0000	−	19.0526i	−0.447584	−	0.775238i
$605$	26.1244	−	17.2487i	1.06211	−	0.701260i
$606$		0			0
$607$	11.2583	−	6.50000i	0.456962	−	0.263827i	−0.253804	−	0.967256i	$-0.581682\pi$
$607$	11.2583	−	6.50000i	0.456962	−	0.263827i	0.710766	+	0.703429i	$0.248349\pi$
$608$		−	7.00000i		−	0.283887i
$609$		0			0
$610$	−2.00000	+	4.00000i	−0.0809776	+	0.161955i
$611$	−6.50000	−	11.2583i	−0.262962	−	0.455463i
$612$		0			0
$613$	16.4545	+	9.50000i	0.664590	+	0.383701i	0.794024	−	0.607887i	$-0.207983\pi$
$613$	16.4545	+	9.50000i	0.664590	+	0.383701i	−0.129433	+	0.991588i	$0.541316\pi$
$614$	1.00000	+	1.73205i	0.0403567	+	0.0698999i
$615$		0			0
$616$	2.50000	+	12.9904i	0.100728	+	0.523397i
$617$		−	30.0000i		−	1.20775i	−0.797077	−	0.603877i	$-0.793622\pi$
$617$		−	30.0000i		−	1.20775i	0.797077	−	0.603877i	$-0.206378\pi$
$618$		0			0
$619$	7.50000	−	12.9904i	0.301450	−	0.522127i	−0.675014	−	0.737805i	$-0.735863\pi$
$619$	7.50000	−	12.9904i	0.301450	−	0.522127i	0.976465	+	0.215677i	$0.0691959\pi$
$620$	11.1962	−	7.39230i	0.449648	−	0.296882i
$621$		0			0
$622$			26.0000i			1.04251i
$623$	8.66025	−	25.0000i	0.346966	−	1.00160i
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	5.00000	−	8.66025i	0.199840	−	0.346133i
$627$		0			0
$628$	−11.2583	+	6.50000i	−0.449256	+	0.259378i
$629$	10.0000			0.398726
$630$		0			0
$631$	18.0000			0.716569			0.358284	−	0.933613i	$-0.383362\pi$
$631$	18.0000			0.716569			0.358284	+	0.933613i	$0.383362\pi$
$632$	−12.1244	+	7.00000i	−0.482281	+	0.278445i
$633$		0			0
$634$	−1.00000	+	1.73205i	−0.0397151	+	0.0687885i
$635$	−20.0885	+	1.20577i	−0.797186	+	0.0478496i
$636$		0			0
$637$	6.92820	+	1.00000i	0.274505	+	0.0396214i
$638$		0			0
$639$		0			0
$640$	−1.23205	−	1.86603i	−0.0487011	−	0.0737611i
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$		0			0
$643$		−	38.0000i		−	1.49857i	−0.662246	−	0.749287i	$-0.730396\pi$
$643$		−	38.0000i		−	1.49857i	0.662246	−	0.749287i	$-0.269604\pi$
$644$	6.00000	−	5.19615i	0.236433	−	0.204757i
$645$		0			0
$646$	−7.00000	−	12.1244i	−0.275411	−	0.477026i
$647$	−0.866025	−	0.500000i	−0.0340470	−	0.0196570i	0.482880	−	0.875687i	$-0.339591\pi$
$647$	−0.866025	−	0.500000i	−0.0340470	−	0.0196570i	−0.516927	+	0.856030i	$0.672924\pi$
$648$		0			0
$649$	−10.0000	−	17.3205i	−0.392534	−	0.679889i
$650$	3.00000	+	4.00000i	0.117670	+	0.156893i
$651$		0			0
$652$		−	12.0000i		−	0.469956i
$653$	4.33013	−	2.50000i	0.169451	−	0.0978326i	−0.412876	−	0.910787i	$-0.635476\pi$
$653$	4.33013	−	2.50000i	0.169451	−	0.0978326i	0.582327	+	0.812955i	$0.302142\pi$
$654$		0			0
$655$	31.7224	−	20.9449i	1.23950	−	0.818384i
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$		0			0
$658$	33.7750	−	6.50000i	1.31669	−	0.253396i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	−20.0000	+	34.6410i	−0.777910	+	1.34738i	0.155235	+	0.987878i	$0.450387\pi$
$661$	−20.0000	+	34.6410i	−0.777910	+	1.34738i	−0.933144	+	0.359502i	$0.882947\pi$
$662$	12.9904	+	7.50000i	0.504885	+	0.291496i
$663$		0			0
$664$	−10.0000			−0.388075
$665$	−39.8731	−	11.1865i	−1.54621	−	0.433795i
$666$		0			0
$667$		0			0
$668$	16.4545	+	9.50000i	0.636643	+	0.367566i
$669$		0			0
$670$	−0.803848	−	13.3923i	−0.0310553	−	0.517390i
$671$	−10.0000			−0.386046
$672$		0			0
$673$		−	36.0000i		−	1.38770i	−0.720121	−	0.693849i	$-0.755914\pi$
$673$		−	36.0000i		−	1.38770i	0.720121	−	0.693849i	$-0.244086\pi$
$674$	−7.00000	−	12.1244i	−0.269630	−	0.467013i
$675$		0			0
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−28.5788	+	16.5000i	−1.09837	+	0.634147i	−0.935793	−	0.352549i	$-0.885315\pi$
$677$	−28.5788	+	16.5000i	−1.09837	+	0.634147i	−0.162581	+	0.986695i	$0.551982\pi$
$678$		0			0
$679$	−16.0000	+	13.8564i	−0.614024	+	0.531760i
$680$	−4.00000	−	2.00000i	−0.153393	−	0.0766965i
$681$		0			0
$682$	25.9808	+	15.0000i	0.994855	+	0.574380i
$683$	3.46410	+	2.00000i	0.132550	+	0.0765279i	0.564809	−	0.825222i	$-0.308950\pi$
$683$	3.46410	+	2.00000i	0.132550	+	0.0765279i	−0.432259	+	0.901750i	$0.642283\pi$
$684$		0			0
$685$	4.00000	−	8.00000i	0.152832	−	0.305664i
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$		0			0
$688$	−8.66025	+	5.00000i	−0.330169	+	0.190623i
$689$	0.500000	−	0.866025i	0.0190485	−	0.0329929i
$690$		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	$0.709113\pi$
$692$		−	7.00000i		−	0.266100i
$693$		0			0
$694$	−16.0000			−0.607352
$695$	1.07180	+	17.8564i	0.0406556	+	0.677332i
$696$		0			0
$697$	−15.5885	−	9.00000i	−0.590455	−	0.340899i
$698$	20.7846	−	12.0000i	0.786709	−	0.454207i
$699$		0			0
$700$	−12.5981	+	4.03590i	−0.476163	+	0.152543i
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	−30.3109	−	17.5000i	−1.14320	−	0.660025i
$704$	2.50000	−	4.33013i	0.0942223	−	0.163198i
$705$		0			0
$706$		0			0
$707$	20.7846	−	4.00000i	0.781686	−	0.150435i
$708$		0			0
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	0.976237	−	0.216705i	$-0.0695310\pi$
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	−0.675791	+	0.737093i	$0.736198\pi$
$710$	2.46410	+	3.73205i	0.0924761	+	0.140061i
$711$		0			0
$712$	−8.66025	+	5.00000i	−0.324557	+	0.187383i
$713$		−	18.0000i		−	0.674105i
$714$		0			0
$715$	−5.00000	+	10.0000i	−0.186989	+	0.373979i
$716$	−5.50000	−	9.52628i	−0.205545	−	0.356014i
$717$		0			0
$718$	24.2487	+	14.0000i	0.904954	+	0.522475i
$719$	1.00000	+	1.73205i	0.0372937	+	0.0645946i	0.884070	−	0.467355i	$-0.154793\pi$
$719$	1.00000	+	1.73205i	0.0372937	+	0.0645946i	−0.846776	+	0.531949i	$0.821460\pi$
$720$		0			0
$721$		0			0
$722$			30.0000i			1.11648i
$723$		0			0
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$		0			0
$726$		0			0
$727$			53.0000i			1.96566i	0.184510	+	0.982831i	$0.440930\pi$
$727$			53.0000i			1.96566i	−0.184510	+	0.982831i	$0.559070\pi$
$728$	−1.73205	−	2.00000i	−0.0641941	−	0.0741249i
$729$		0			0
$730$	0.535898	+	8.92820i	0.0198345	+	0.330448i
$731$	−10.0000	+	17.3205i	−0.369863	+	0.640622i
$732$		0			0
$733$	18.1865	−	10.5000i	0.671735	−	0.387826i	−0.124999	−	0.992157i	$-0.539893\pi$
$733$	18.1865	−	10.5000i	0.671735	−	0.387826i	0.796734	+	0.604331i	$0.206559\pi$
$734$	37.0000			1.36569
$735$		0			0
$736$	−3.00000			−0.110581
$737$	25.9808	−	15.0000i	0.957014	−	0.552532i
$738$		0			0
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	−0.00311943	−	0.999995i	$-0.500993\pi$
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	0.867581	−	0.497296i	$-0.165674\pi$
$740$	−11.1603	+	0.669873i	−0.410259	+	0.0246250i
$741$		0			0
$742$	1.73205	+	2.00000i	0.0635856	+	0.0734223i
$743$		−	31.0000i		−	1.13728i	−0.822587	−	0.568640i	$-0.807470\pi$
$743$		−	31.0000i		−	1.13728i	0.822587	−	0.568640i	$-0.192530\pi$
$744$		0			0
$745$	−11.1962	+	7.39230i	−0.410195	+	0.270833i
$746$	−3.00000	+	5.19615i	−0.109838	+	0.190245i
$747$		0			0
$748$		−	10.0000i		−	0.365636i
$749$	−30.0000	−	10.3923i	−1.09618	−	0.379727i
$750$		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	$0.856585\pi$
$752$	−11.2583	−	6.50000i	−0.410549	−	0.237031i
$753$		0			0
$754$		0			0
$755$	44.0000	+	22.0000i	1.60132	+	0.800662i
$756$		0			0
$757$		−	26.0000i		−	0.944986i	−0.881334	−	0.472493i	$-0.843354\pi$
$757$		−	26.0000i		−	0.944986i	0.881334	−	0.472493i	$-0.156646\pi$
$758$	0.866025	−	0.500000i	0.0314555	−	0.0181608i
$759$		0			0
$760$	8.62436	+	13.0622i	0.312838	+	0.473815i
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	0.837557	−	0.546350i	$-0.183983\pi$
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	−0.891932	+	0.452170i	$0.850650\pi$
$762$		0			0
$763$	−46.7654	+	9.00000i	−1.69302	+	0.325822i
$764$	−16.0000			−0.578860
$765$		0			0
$766$	−4.50000	+	7.79423i	−0.162592	+	0.281617i
$767$	3.46410	+	2.00000i	0.125081	+	0.0722158i
$768$		0			0
$769$	−51.0000			−1.83911			−0.919554	−	0.392965i	$-0.871449\pi$
$769$	−51.0000			−1.83911			−0.919554	+	0.392965i	$0.871449\pi$
$770$	−20.6699	−	21.1603i	−0.744891	−	0.762563i
$771$		0			0
$772$	−15.5885	+	9.00000i	−0.561041	+	0.323917i
$773$	32.0429	+	18.5000i	1.15250	+	0.665399i	0.949496	−	0.313778i	$-0.101595\pi$
$773$	32.0429	+	18.5000i	1.15250	+	0.665399i	0.203008	+	0.979177i	$0.434928\pi$
$774$		0			0
$775$	−11.7846	+	27.5885i	−0.423316	+	0.991007i
$776$	8.00000			0.287183
$777$		0			0
$778$			6.00000i			0.215110i
$779$	31.5000	+	54.5596i	1.12860	+	1.95480i
$780$		0			0
$781$	−5.00000	+	8.66025i	−0.178914	+	0.309888i
$782$	−5.19615	+	3.00000i	−0.185814	+	0.107280i
$783$		0			0
$784$	6.50000	−	2.59808i	0.232143	−	0.0927884i
$785$	13.0000	−	26.0000i	0.463990	−	0.927980i
$786$		0			0
$787$	−32.9090	−	19.0000i	−1.17308	−	0.677277i	−0.218675	−	0.975798i	$-0.570173\pi$
$787$	−32.9090	−	19.0000i	−1.17308	−	0.677277i	−0.954403	+	0.298521i	$0.903507\pi$
$788$	23.3827	+	13.5000i	0.832974	+	0.480918i
$789$		0			0
$790$	14.0000	−	28.0000i	0.498098	−	0.996195i
$791$	−12.0000	+	10.3923i	−0.426671	+	0.369508i
$792$		0			0
$793$	1.73205	−	1.00000i	0.0615069	−	0.0355110i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$		0			0
$796$	7.00000	+	12.1244i	0.248108	+	0.429736i
$797$			30.0000i			1.06265i	0.847167	+	0.531327i	$0.178307\pi$
$797$			30.0000i			1.06265i	−0.847167	+	0.531327i	$0.821693\pi$
$798$		0			0
$799$	−26.0000			−0.919814
$800$	4.59808	+	1.96410i	0.162567	+	0.0694415i
$801$		0			0
$802$	−23.3827	−	13.5000i	−0.825671	−	0.476702i
$803$	−17.3205	+	10.0000i	−0.611227	+	0.352892i
$804$		0			0
$805$	−4.79423	+	17.0885i	−0.168974	+	0.602289i
$806$	−6.00000			−0.211341
$807$		0			0
$808$	−6.92820	−	4.00000i	−0.243733	−	0.140720i
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$		0			0
$811$	11.0000			0.386262			0.193131	−	0.981173i	$-0.438136\pi$
$811$	11.0000			0.386262			0.193131	+	0.981173i	$0.438136\pi$
$812$		0			0
$813$		0			0
$814$	−12.5000	−	21.6506i	−0.438125	−	0.758854i
$815$	14.7846	+	22.3923i	0.517882	+	0.784368i
$816$		0			0
$817$	60.6218	−	35.0000i	2.12089	−	1.22449i
$818$		−	10.0000i		−	0.349642i
$819$		0			0
$820$	18.0000	+	9.00000i	0.628587	+	0.314294i
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$		0			0
$823$	−6.92820	−	4.00000i	−0.241502	−	0.139431i	0.374365	−	0.927281i	$-0.377861\pi$
$823$	−6.92820	−	4.00000i	−0.241502	−	0.139431i	−0.615867	+	0.787850i	$0.711194\pi$
$824$		0			0
$825$		0			0
$826$	−8.00000	+	6.92820i	−0.278356	+	0.241063i
$827$			42.0000i			1.46048i	0.683189	+	0.730242i	$0.260592\pi$
$827$			42.0000i			1.46048i	−0.683189	+	0.730242i	$0.739408\pi$
$828$		0			0
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	−0.848137	−	0.529777i	$-0.822276\pi$
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	0.882869	+	0.469620i	$0.155609\pi$
$830$	18.6603	−	12.3205i	0.647707	−	0.427651i
$831$		0			0
$832$			1.00000i			0.0346688i
$833$	8.66025	−	11.0000i	0.300060	−	0.381127i
$834$		0			0
$835$	−42.4090	+	2.54552i	−1.46762	+	0.0880913i
$836$	−17.5000	+	30.3109i	−0.605250	+	1.04832i
$837$		0			0
$838$	2.59808	−	1.50000i	0.0897491	−	0.0518166i
$839$	2.00000			0.0690477			0.0345238	−	0.999404i	$-0.489009\pi$
$839$	2.00000			0.0690477			0.0345238	+	0.999404i	$0.489009\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	−17.3205	+	10.0000i	−0.596904	+	0.344623i
$843$		0			0
$844$	9.50000	−	16.4545i	0.327003	−	0.566387i
$845$	1.60770	+	26.7846i	0.0553064	+	0.921419i
$846$		0			0
$847$	12.1244	−	35.0000i	0.416598	−	1.20261i
$848$		−	1.00000i		−	0.0343401i
$849$		0			0
$850$	9.92820	−	1.19615i	0.340535	−	0.0410277i
$851$	−7.50000	+	12.9904i	−0.257097	+	0.445305i
$852$		0			0
$853$			49.0000i			1.67773i	0.544341	+	0.838864i	$0.316780\pi$
$853$			49.0000i			1.67773i	−0.544341	+	0.838864i	$0.683220\pi$
$854$	1.00000	+	5.19615i	0.0342193	+	0.177809i
$855$		0			0
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	−48.4974	−	28.0000i	−1.65664	−	0.956462i	−0.974249	−	0.225475i	$-0.927607\pi$
$857$	−48.4974	−	28.0000i	−1.65664	−	0.956462i	−0.682391	−	0.730987i	$-0.739060\pi$
$858$		0			0
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	0.990533	+	0.137277i	$0.0438352\pi$
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	−0.376381	+	0.926465i	$0.622831\pi$
$860$	10.0000	−	20.0000i	0.340997	−	0.681994i
$861$		0			0
$862$		−	18.0000i		−	0.613082i
$863$	12.9904	−	7.50000i	0.442198	−	0.255303i	−0.262332	−	0.964978i	$-0.584491\pi$
$863$	12.9904	−	7.50000i	0.442198	−	0.255303i	0.704529	+	0.709675i	$0.251158\pi$
$864$		0			0
$865$	8.62436	+	13.0622i	0.293237	+	0.444127i
$866$	−2.00000	−	3.46410i	−0.0679628	−	0.117715i
$867$		0			0
$868$	5.19615	−	15.0000i	0.176369	−	0.509133i
$869$	70.0000			2.37459
$870$		0			0
$871$	−3.00000	+	5.19615i	−0.101651	+	0.176065i
$872$	15.5885	+	9.00000i	0.527892	+	0.304778i
$873$		0			0
$874$	21.0000			0.710336
$875$	18.5359	−	23.0526i	0.626628	−	0.779319i
$876$		0			0
$877$	−23.3827	+	13.5000i	−0.789577	+	0.455863i	−0.839814	−	0.542875i	$-0.817336\pi$
$877$	−23.3827	+	13.5000i	−0.789577	+	0.455863i	0.0502365	+	0.998737i	$0.484002\pi$
$878$		0			0
$879$		0			0
$880$	0.669873	+	11.1603i	0.0225814	+	0.376212i
$881$	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
$883$			52.0000i			1.74994i	0.484178	+	0.874970i	$0.339119\pi$
$883$			52.0000i			1.74994i	−0.484178	+	0.874970i	$0.660881\pi$
$884$	1.00000	+	1.73205i	0.0336336	+	0.0582552i
$885$		0			0
$886$	−3.00000	+	5.19615i	−0.100787	+	0.174568i
$887$	10.3923	−	6.00000i	0.348939	−	0.201460i	−0.315279	−	0.948999i	$-0.602098\pi$
$887$	10.3923	−	6.00000i	0.348939	−	0.201460i	0.664218	+	0.747539i	$0.268765\pi$
$888$		0			0
$889$	−18.0000	+	15.5885i	−0.603701	+	0.522820i
$890$	10.0000	−	20.0000i	0.335201	−	0.670402i
$891$		0			0
$892$	−13.8564	−	8.00000i	−0.463947	−	0.267860i
$893$	78.8083	+	45.5000i	2.63722	+	1.52260i
$894$		0			0
$895$	22.0000	+	11.0000i	0.735379	+	0.367689i
$896$	−2.50000	−	0.866025i	−0.0835191	−	0.0289319i
$897$		0			0
$898$	7.79423	−	4.50000i	0.260097	−	0.150167i
$899$		0			0
$900$		0			0
$901$	−1.00000	−	1.73205i	−0.0333148	−	0.0577030i
$902$			45.0000i			1.49834i
$903$		0			0
$904$	6.00000			0.199557
$905$	−0.267949	−	4.46410i	−0.00890693	−	0.148392i
$906$		0			0
$907$	13.8564	+	8.00000i	0.460094	+	0.265636i	0.712084	−	0.702094i	$-0.247752\pi$
$907$	13.8564	+	8.00000i	0.460094	+	0.265636i	−0.251990	+	0.967730i	$0.581085\pi$
$908$	12.1244	−	7.00000i	0.402361	−	0.232303i
$909$		0			0
$910$	5.69615	+	1.59808i	0.188826	+	0.0529757i
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$		0			0
$913$	43.3013	+	25.0000i	1.43306	+	0.827379i
$914$	−19.0000	+	32.9090i	−0.628464	+	1.08853i
$915$		0			0
$916$	−4.00000			−0.132164
$917$	14.7224	−	42.5000i	0.486178	−	1.40347i
$918$		0			0
$919$	28.0000	+	48.4974i	0.923635	+	1.59978i	0.793742	+	0.608254i	$0.208130\pi$
$919$	28.0000	+	48.4974i	0.923635	+	1.59978i	0.129893	+	0.991528i	$0.458537\pi$
$920$	5.59808	−	3.69615i	0.184563	−	0.121859i
$921$		0			0
$922$	10.3923	−	6.00000i	0.342252	−	0.197599i
$923$		−	2.00000i		−	0.0658308i
$924$		0			0
$925$	20.0000	−	15.0000i	0.657596	−	0.493197i
$926$	7.50000	+	12.9904i	0.246465	+	0.426890i
$927$		0			0
$928$		0			0
$929$	−16.5000	−	28.5788i	−0.541347	−	0.937641i	−0.998827	−	0.0484211i	$-0.984581\pi$
$929$	−16.5000	−	28.5788i	−0.541347	−	0.937641i	0.457480	−	0.889220i	$-0.348752\pi$
$930$		0			0
$931$	−45.5000	+	18.1865i	−1.49120	+	0.596040i
$932$		0			0
$933$		0			0
$934$	−1.00000	+	1.73205i	−0.0327210	+	0.0566744i
$935$	12.3205	+	18.6603i	0.402924	+	0.610256i
$936$		0			0
$937$		−	34.0000i		−	1.11073i	−0.831606	−	0.555366i	$-0.812578\pi$
$937$		−	34.0000i		−	1.11073i	0.831606	−	0.555366i	$-0.187422\pi$
$938$	−10.3923	−	12.0000i	−0.339321	−	0.391814i
$939$		0			0
$940$	29.0167	−	1.74167i	0.946419	−	0.0568070i
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$	23.3827	−	13.5000i	0.761445	−	0.439620i
$944$	4.00000			0.130189
$945$		0			0
$946$	50.0000			1.62564
$947$	−10.3923	+	6.00000i	−0.337705	+	0.194974i	−0.659256	−	0.751918i	$-0.729129\pi$
$947$	−10.3923	+	6.00000i	−0.337705	+	0.194974i	0.321552	+	0.946892i	$0.395796\pi$
$948$		0			0
$949$	2.00000	−	3.46410i	0.0649227	−	0.112449i
$950$	−32.1865	−	13.7487i	−1.04427	−	0.446067i
$951$		0			0
$952$	−5.19615	+	1.00000i	−0.168408	+	0.0324102i
$953$		−	24.0000i		−	0.777436i	−0.921357	−	0.388718i	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$		0			0
$955$	29.8564	−	19.7128i	0.966131	−	0.637892i
$956$	10.0000	−	17.3205i	0.323423	−	0.560185i
$957$		0			0
$958$			8.00000i			0.258468i
$959$	−2.00000	−	10.3923i	−0.0645834	−	0.335585i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$	4.33013	+	2.50000i	0.139609	+	0.0806032i
$963$		0			0
$964$	−0.500000	−	0.866025i	−0.0161039	−	0.0278928i
$965$	18.0000	−	36.0000i	0.579441	−	1.15888i
$966$		0			0
$967$		−	24.0000i		−	0.771788i	−0.922543	−	0.385894i	$-0.873893\pi$
$967$		−	24.0000i		−	0.771788i	0.922543	−	0.385894i	$-0.126107\pi$
$968$	−12.1244	+	7.00000i	−0.389692	+	0.224989i
$969$		0			0
$970$	−14.9282	+	9.85641i	−0.479316	+	0.316470i
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	0.988389	+	0.151948i	$0.0485545\pi$
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	−0.362604	+	0.931943i	$0.618112\pi$
$972$		0			0
$973$	13.8564	+	16.0000i	0.444216	+	0.512936i
$974$	−24.0000			−0.769010
$975$		0			0
$976$	1.00000	−	1.73205i	0.0320092	−	0.0554416i
$977$	36.3731	+	21.0000i	1.16368	+	0.671850i	0.952183	−	0.305530i	$-0.0988335\pi$
$977$	36.3731	+	21.0000i	1.16368	+	0.671850i	0.211495	+	0.977379i	$0.432167\pi$
$978$		0			0
$979$	50.0000			1.59801
$980$	−8.92820	+	12.8564i	−0.285201	+	0.410683i
$981$		0			0
$982$	−20.7846	+	12.0000i	−0.663264	+	0.382935i
$983$	−28.5788	−	16.5000i	−0.911523	−	0.526268i	−0.0306024	−	0.999532i	$-0.509743\pi$
$983$	−28.5788	−	16.5000i	−0.911523	−	0.526268i	−0.880921	+	0.473263i	$0.843076\pi$
$984$		0			0
$985$	−60.2654	+	3.61731i	−1.92021	+	0.115257i
$986$		0			0
$987$		0			0
$988$		−	7.00000i		−	0.222700i
$989$	−15.0000	−	25.9808i	−0.476972	−	0.826140i
$990$		0			0
$991$	18.0000	−	31.1769i	0.571789	−	0.990367i	−0.424594	−	0.905384i	$-0.639583\pi$
$991$	18.0000	−	31.1769i	0.571789	−	0.990367i	0.996382	−	0.0849833i	$-0.0270837\pi$
$992$	−5.19615	+	3.00000i	−0.164978	+	0.0952501i
$993$		0			0
$994$	5.00000	+	1.73205i	0.158590	+	0.0549373i
$995$	−28.0000	−	14.0000i	−0.887660	−	0.443830i
$996$		0			0
$997$	8.66025	+	5.00000i	0.274273	+	0.158352i	0.630828	−	0.775923i	$-0.282715\pi$
$997$	8.66025	+	5.00000i	0.274273	+	0.158352i	−0.356555	+	0.934274i	$0.616049\pi$
$998$	−24.2487	−	14.0000i	−0.767580	−	0.443162i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.u.c.109.2		4
3.2	odd	2		210.2.n.a.109.1	yes	4
5.4	even	2	inner	630.2.u.c.109.1		4
7.2	even	3	inner	630.2.u.c.289.1		4
12.11	even	2		1680.2.di.a.529.1		4
15.2	even	4		1050.2.i.f.151.1		2
15.8	even	4		1050.2.i.o.151.1		2
15.14	odd	2		210.2.n.a.109.2	yes	4
21.2	odd	6		210.2.n.a.79.2	yes	4
21.5	even	6		1470.2.n.i.79.2		4
21.11	odd	6		1470.2.g.f.589.1		2
21.17	even	6		1470.2.g.a.589.1		2
21.20	even	2		1470.2.n.i.949.1		4
35.9	even	6	inner	630.2.u.c.289.2		4
60.59	even	2		1680.2.di.a.529.2		4
84.23	even	6		1680.2.di.a.289.2		4
105.2	even	12		1050.2.i.f.751.1		2
105.17	odd	12		7350.2.a.ch.1.1		1
105.23	even	12		1050.2.i.o.751.1		2
105.32	even	12		7350.2.a.bn.1.1		1
105.38	odd	12		7350.2.a.b.1.1		1
105.44	odd	6		210.2.n.a.79.1	✓	4
105.53	even	12		7350.2.a.t.1.1		1
105.59	even	6		1470.2.g.a.589.2		2
105.74	odd	6		1470.2.g.f.589.2		2
105.89	even	6		1470.2.n.i.79.1		4
105.104	even	2		1470.2.n.i.949.2		4
420.359	even	6		1680.2.di.a.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.n.a.79.1	✓	4	105.44	odd	6
210.2.n.a.79.2	yes	4	21.2	odd	6
210.2.n.a.109.1	yes	4	3.2	odd	2
210.2.n.a.109.2	yes	4	15.14	odd	2
630.2.u.c.109.1		4	5.4	even	2	inner
630.2.u.c.109.2		4	1.1	even	1	trivial
630.2.u.c.289.1		4	7.2	even	3	inner
630.2.u.c.289.2		4	35.9	even	6	inner
1050.2.i.f.151.1		2	15.2	even	4
1050.2.i.f.751.1		2	105.2	even	12
1050.2.i.o.151.1		2	15.8	even	4
1050.2.i.o.751.1		2	105.23	even	12
1470.2.g.a.589.1		2	21.17	even	6
1470.2.g.a.589.2		2	105.59	even	6
1470.2.g.f.589.1		2	21.11	odd	6
1470.2.g.f.589.2		2	105.74	odd	6
1470.2.n.i.79.1		4	105.89	even	6
1470.2.n.i.79.2		4	21.5	even	6
1470.2.n.i.949.1		4	21.20	even	2
1470.2.n.i.949.2		4	105.104	even	2
1680.2.di.a.289.1		4	420.359	even	6
1680.2.di.a.289.2		4	84.23	even	6
1680.2.di.a.529.1		4	12.11	even	2
1680.2.di.a.529.2		4	60.59	even	2
7350.2.a.b.1.1		1	105.38	odd	12
7350.2.a.t.1.1		1	105.53	even	12
7350.2.a.bn.1.1		1	105.32	even	12
7350.2.a.ch.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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(1.23205 + 1.86603i) q^{10} +(-2.50000 + 4.33013i) q^{11} -1.00000i q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(3.50000 + 6.06218i) q^{19} +(2.00000 + 1.00000i) q^{20} +5.00000i q^{22} +(2.59808 - 1.50000i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(2.59808 - 0.500000i) q^{28} +(3.00000 - 5.19615i) q^{31} +(-0.866025 - 0.500000i) q^{32} -2.00000 q^{34} +(-4.23205 + 4.13397i) q^{35} +(-4.33013 + 2.50000i) q^{37} +(6.06218 + 3.50000i) q^{38} +(2.23205 - 0.133975i) q^{40} +9.00000 q^{41} -10.0000i q^{43} +(2.50000 + 4.33013i) q^{44} +(1.50000 - 2.59808i) q^{46} +(11.2583 - 6.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-4.00000 + 3.00000i) q^{50} +(-0.866025 - 0.500000i) q^{52} +(0.866025 + 0.500000i) q^{53} +(-10.0000 - 5.00000i) q^{55} +(2.00000 - 1.73205i) q^{56} +(-2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} -6.00000i q^{62} -1.00000 q^{64} +(2.23205 - 0.133975i) q^{65} +(-5.19615 - 3.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(-1.59808 + 5.69615i) q^{70} +2.00000 q^{71} +(3.46410 + 2.00000i) q^{73} +(-2.50000 + 4.33013i) q^{74} +7.00000 q^{76} +(-12.9904 + 2.50000i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(1.86603 - 1.23205i) q^{80} +(7.79423 - 4.50000i) q^{82} -10.0000i q^{83} +(2.00000 - 4.00000i) q^{85} +(-5.00000 - 8.66025i) q^{86} +(4.33013 + 2.50000i) q^{88} +(-5.00000 - 8.66025i) q^{89} +(2.00000 - 1.73205i) q^{91} -3.00000i q^{92} +(6.50000 - 11.2583i) q^{94} +(-13.0622 + 8.62436i) q^{95} +8.00000i q^{97} +(2.59808 + 6.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^5	\( 4 q + 2 q^{4} + 4 q^{5} - 2 q^{10} - 10 q^{11} + 10 q^{14} - 2 q^{16} + 14 q^{19} + 8 q^{20} - 6 q^{25} - 2 q^{26} + 12 q^{31} - 8 q^{34} - 10 q^{35} + 2 q^{40} + 36 q^{41} + 10 q^{44} + 6 q^{46} - 4 q^{49} - 16 q^{50} - 40 q^{55} + 8 q^{56} - 8 q^{59} + 4 q^{61} - 4 q^{64} + 2 q^{65} + 4 q^{70} + 8 q^{71} - 10 q^{74} + 28 q^{76} - 28 q^{79} + 4 q^{80} + 8 q^{85} - 20 q^{86} - 20 q^{89} + 8 q^{91} + 26 q^{94} - 28 q^{95}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^5 - 2 * q^10 - 10 * q^11 + 10 * q^14 - 2 * q^16 + 14 * q^19 + 8 * q^20 - 6 * q^25 - 2 * q^26 + 12 * q^31 - 8 * q^34 - 10 * q^35 + 2 * q^40 + 36 * q^41 + 10 * q^44 + 6 * q^46 - 4 * q^49 - 16 * q^50 - 40 * q^55 + 8 * q^56 - 8 * q^59 + 4 * q^61 - 4 * q^64 + 2 * q^65 + 4 * q^70 + 8 * q^71 - 10 * q^74 + 28 * q^76 - 28 * q^79 + 4 * q^80 + 8 * q^85 - 20 * q^86 - 20 * q^89 + 8 * q^91 + 26 * q^94 - 28 * q^95

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