LMFDB - Embedded newform 630.2.k.d.541.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.541
Dual form			630.2.k.d.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} -1.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -3.00000 q^{22} +(4.50000 - 7.79423i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-0.500000 + 2.59808i) q^{28} -6.00000 q^{29} +(-4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(-2.50000 + 0.866025i) q^{35} +(3.50000 - 6.06218i) q^{37} +(0.500000 + 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{40} -3.00000 q^{41} +2.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(4.50000 + 7.79423i) q^{46} +(4.50000 - 7.79423i) q^{47} +(1.00000 + 6.92820i) q^{49} +1.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(4.50000 + 7.79423i) q^{53} +3.00000 q^{55} +(-2.00000 - 1.73205i) q^{56} +(3.00000 - 5.19615i) q^{58} +(-4.00000 + 6.92820i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(0.500000 - 2.59808i) q^{70} +(2.00000 + 3.46410i) q^{73} +(3.50000 + 6.06218i) q^{74} -1.00000 q^{76} +(1.50000 - 7.79423i) q^{77} +(5.00000 - 8.66025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(1.50000 - 2.59808i) q^{82} -6.00000 q^{85} +(-1.00000 + 1.73205i) q^{86} +(1.50000 + 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(2.00000 + 1.73205i) q^{91} -9.00000 q^{92} +(4.50000 + 7.79423i) q^{94} +(-0.500000 - 0.866025i) q^{95} -10.0000 q^{97} +(-6.50000 - 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + q^{5} - 4 q^{7} + 2 q^{8} + q^{10} + 3 q^{11} - 2 q^{13} + 5 q^{14} - q^{16} - 6 q^{17} + q^{19} - 2 q^{20} - 6 q^{22} + 9 q^{23} - q^{25} + q^{26} - q^{28} - 12 q^{29} - 8 q^{31}+ \cdots - 13 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + q^5 - 4 * q^7 + 2 * q^8 + q^10 + 3 * q^11 - 2 * q^13 + 5 * q^14 - q^16 - 6 * q^17 + q^19 - 2 * q^20 - 6 * q^22 + 9 * q^23 - q^25 + q^26 - q^28 - 12 * q^29 - 8 * q^31 - q^32 + 12 * q^34 - 5 * q^35 + 7 * q^37 + q^38 + q^40 - 6 * q^41 + 4 * q^43 + 3 * q^44 + 9 * q^46 + 9 * q^47 + 2 * q^49 + 2 * q^50 + q^52 + 9 * q^53 + 6 * q^55 - 4 * q^56 + 6 * q^58 - 8 * q^61 + 16 * q^62 + 2 * q^64 - q^65 - 8 * q^67 - 6 * q^68 + q^70 + 4 * q^73 + 7 * q^74 - 2 * q^76 + 3 * q^77 + 10 * q^79 + q^80 + 3 * q^82 - 12 * q^85 - 2 * q^86 + 3 * q^88 + 6 * q^89 + 4 * q^91 - 18 * q^92 + 9 * q^94 - q^95 - 20 * q^97 - 13 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	1.00000			0.353553
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−3.00000			−0.639602
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.169701	−	0.985496i	$-0.445720\pi$
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.768613	−	0.639713i	$-0.220947\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$		0			0
$28$	−0.500000	+	2.59808i	−0.0944911	+	0.490990i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	6.00000			1.02899
$35$	−2.50000	+	0.866025i	−0.422577	+	0.146385i
$36$		0			0
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$		0			0
$46$	4.50000	+	7.79423i	0.663489	+	1.14920i
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	−0.325150	−	0.945662i	$-0.605415\pi$
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	0.981543	−	0.191243i	$-0.0612518\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	1.00000			0.141421
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$		0			0
$55$	3.00000			0.404520
$56$	−2.00000	−	1.73205i	−0.267261	−	0.231455i
$57$		0			0
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	8.00000			1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		0			0
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$	0.500000	−	2.59808i	0.0597614	−	0.310530i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	0.959006	−	0.283387i	$-0.0914581\pi$
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	−0.724923	+	0.688830i	$0.758125\pi$
$74$	3.50000	+	6.06218i	0.406867	+	0.704714i
$75$		0			0
$76$	−1.00000			−0.114708
$77$	1.50000	−	7.79423i	0.170941	−	0.888235i
$78$		0			0
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−6.00000			−0.650791
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	2.00000	+	1.73205i	0.209657	+	0.181568i
$92$	−9.00000			−0.938315
$93$		0			0
$94$	4.50000	+	7.79423i	0.464140	+	0.803913i
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$		0			0
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$	−6.50000	−	2.59808i	−0.656599	−	0.262445i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	−9.00000			−0.874157
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$		0			0
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111218\pi$
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$110$	−1.50000	+	2.59808i	−0.143019	+	0.247717i
$111$		0			0
$112$	2.50000	−	0.866025i	0.236228	−	0.0818317i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$		0			0
$118$		0			0
$119$	−3.00000	+	15.5885i	−0.275010	+	1.42899i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$		0			0
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.500000	−	0.866025i	−0.0438529	−	0.0759555i
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	−0.793028	−	0.609185i	$-0.791497\pi$
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	0.924084	+	0.382190i	$0.124830\pi$
$132$		0			0
$133$	−2.50000	+	0.866025i	−0.216777	+	0.0750939i
$134$	8.00000			0.691095
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	2.00000	+	1.73205i	0.169031	+	0.146385i
$141$		0			0
$142$		0			0
$143$	−1.50000	−	2.59808i	−0.125436	−	0.217262i
$144$		0			0
$145$	−3.00000	+	5.19615i	−0.249136	+	0.431517i
$146$	−4.00000			−0.331042
$147$		0			0
$148$	−7.00000			−0.575396
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$	0.500000	−	0.866025i	0.0405554	−	0.0702439i
$153$		0			0
$154$	6.00000	+	5.19615i	0.483494	+	0.418718i
$155$	−8.00000			−0.642575
$156$		0			0
$157$	−11.5000	−	19.9186i	−0.917800	−	1.58968i	−0.802749	−	0.596316i	$-0.796630\pi$
$157$	−11.5000	−	19.9186i	−0.917800	−	1.58968i	−0.115050	−	0.993360i	$-0.536703\pi$
$158$	5.00000	+	8.66025i	0.397779	+	0.688973i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−22.5000	+	7.79423i	−1.77325	+	0.614271i
$162$		0			0
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$		0			0
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	3.00000	−	5.19615i	0.230089	−	0.398527i
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	−0.642699	−	0.766119i	$-0.722185\pi$
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	0.984828	+	0.173534i	$0.0555188\pi$
$174$		0			0
$175$	−0.500000	+	2.59808i	−0.0377964	+	0.196396i
$176$	−3.00000			−0.226134
$177$		0			0
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	0.804508	−	0.593942i	$-0.202429\pi$
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	−0.916623	+	0.399753i	$0.869096\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−2.50000	+	0.866025i	−0.185312	+	0.0641941i
$183$		0			0
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	−3.50000	−	6.06218i	−0.257325	−	0.445700i
$186$		0			0
$187$	9.00000	−	15.5885i	0.658145	−	1.13994i
$188$	−9.00000			−0.656392
$189$		0			0
$190$	1.00000			0.0725476
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	−0.563081	−	0.826402i	$-0.690384\pi$
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	0.997225	+	0.0744412i	$0.0237173\pi$
$192$		0			0
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	0.995948	+	0.0899262i	$0.0286631\pi$
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	−0.420096	+	0.907480i	$0.638004\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	−15.0000			−1.06871			−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000			−1.06871			−0.534353	+	0.845262i	$0.679445\pi$
$198$		0			0
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	−12.0000			−0.844317
$203$	12.0000	+	10.3923i	0.842235	+	0.729397i
$204$		0			0
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$	2.00000	+	3.46410i	0.139347	+	0.241355i
$207$		0			0
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	3.00000			0.207514
$210$		0			0
$211$	23.0000			1.58339			0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000			1.58339			0.791693	+	0.610920i	$0.209200\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$		0			0
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	1.00000	−	1.73205i	0.0681994	−	0.118125i
$216$		0			0
$217$	−4.00000	+	20.7846i	−0.271538	+	1.41095i
$218$	−16.0000			−1.08366
$219$		0			0
$220$	−1.50000	−	2.59808i	−0.101130	−	0.175162i
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$		0			0
$226$		0			0
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	−0.792347	−	0.610071i	$-0.791141\pi$
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	0.924510	+	0.381157i	$0.124474\pi$
$230$	9.00000			0.593442
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$		0			0
$235$	−4.50000	−	7.79423i	−0.293548	−	0.508439i
$236$		0			0
$237$		0			0
$238$	−12.0000	−	10.3923i	−0.777844	−	0.673633i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$		0			0
$244$	8.00000			0.512148
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$		0			0
$247$	−0.500000	+	0.866025i	−0.0318142	+	0.0551039i
$248$	−4.00000	−	6.92820i	−0.254000	−	0.439941i
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	15.0000			0.946792			0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000			0.946792			0.473396	+	0.880850i	$0.343028\pi$
$252$		0			0
$253$	27.0000			1.69748
$254$	0.500000	−	0.866025i	0.0313728	−	0.0543393i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$	−17.5000	+	6.06218i	−1.08740	+	0.376685i
$260$	1.00000			0.0620174
$261$		0			0
$262$	1.50000	+	2.59808i	0.0926703	+	0.160510i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	0.500000	−	2.59808i	0.0306570	−	0.159298i
$267$		0			0
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	−12.0000			−0.724947
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	2.00000	−	3.46410i	0.119952	−	0.207763i
$279$		0			0
$280$	−2.50000	+	0.866025i	−0.149404	+	0.0517549i
$281$	27.0000			1.61068			0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000			1.61068			0.805342	+	0.592810i	$0.201981\pi$
$282$		0			0
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	0.579437	−	0.815017i	$-0.303272\pi$
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	−0.995544	+	0.0942988i	$0.969939\pi$
$284$		0			0
$285$		0			0
$286$	3.00000			0.177394
$287$	6.00000	+	5.19615i	0.354169	+	0.306719i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	−3.00000	−	5.19615i	−0.176166	−	0.305129i
$291$		0			0
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$	9.00000			0.525786			0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000			0.525786			0.262893	+	0.964825i	$0.415323\pi$
$294$		0			0
$295$		0			0
$296$	3.50000	−	6.06218i	0.203433	−	0.352357i
$297$		0			0
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	−4.50000	+	7.79423i	−0.260242	+	0.450752i
$300$		0			0
$301$	−4.00000	−	3.46410i	−0.230556	−	0.199667i
$302$	−10.0000			−0.575435
$303$		0			0
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$	4.00000	+	6.92820i	0.229039	+	0.396708i
$306$		0			0
$307$	14.0000			0.799022			0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000			0.799022			0.399511	+	0.916728i	$0.369180\pi$
$308$	−7.50000	+	2.59808i	−0.427352	+	0.148039i
$309$		0			0
$310$	4.00000	−	6.92820i	0.227185	−	0.393496i
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	14.0000	−	24.2487i	0.791327	−	1.37062i	−0.133819	−	0.991006i	$-0.542724\pi$
$313$	14.0000	−	24.2487i	0.791327	−	1.37062i	0.925146	−	0.379612i	$-0.123943\pi$
$314$	23.0000			1.29797
$315$		0			0
$316$	−10.0000			−0.562544
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$		0			0
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	4.50000	−	23.3827i	0.250775	−	1.30307i
$323$	−6.00000			−0.333849
$324$		0			0
$325$	0.500000	+	0.866025i	0.0277350	+	0.0480384i
$326$	−10.0000	−	17.3205i	−0.553849	−	0.959294i
$327$		0			0
$328$	−3.00000			−0.165647
$329$	−22.5000	+	7.79423i	−1.24047	+	0.429710i
$330$		0			0
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	−0.753660	−	0.657264i	$-0.771714\pi$
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	0.946038	+	0.324057i	$0.105047\pi$
$332$		0			0
$333$		0			0
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$	−8.00000			−0.437087
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$	3.00000	+	5.19615i	0.162698	+	0.281801i
$341$	12.0000	−	20.7846i	0.649836	−	1.12555i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	2.00000			0.107833
$345$		0			0
$346$	4.50000	+	7.79423i	0.241921	+	0.419020i
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$		0			0
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$	−2.00000	−	1.73205i	−0.106904	−	0.0925820i
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	6.00000	+	10.3923i	0.319348	+	0.553127i	0.980352	−	0.197256i	$-0.0632029\pi$
$353$	6.00000	+	10.3923i	0.319348	+	0.553127i	−0.661004	+	0.750382i	$0.729870\pi$
$354$		0			0
$355$		0			0
$356$	−6.00000			−0.317999
$357$		0			0
$358$	3.00000			0.158555
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	−0.524588	−	0.851356i	$-0.675781\pi$
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	0.999590	+	0.0286287i	$0.00911406\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$		0			0
$364$	0.500000	−	2.59808i	0.0262071	−	0.136176i
$365$	4.00000			0.209370
$366$		0			0
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$	4.50000	+	7.79423i	0.234579	+	0.406302i
$369$		0			0
$370$	7.00000			0.363913
$371$	4.50000	−	23.3827i	0.233628	−	1.21397i
$372$		0			0
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	−0.890753	−	0.454488i	$-0.849822\pi$
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	0.838975	+	0.544170i	$0.183156\pi$
$374$	9.00000	+	15.5885i	0.465379	+	0.806060i
$375$		0			0
$376$	4.50000	−	7.79423i	0.232070	−	0.401957i
$377$	6.00000			0.309016
$378$		0			0
$379$	23.0000			1.18143			0.590715	−	0.806880i	$-0.298846\pi$
$379$	23.0000			1.18143			0.590715	+	0.806880i	$0.298846\pi$
$380$	−0.500000	+	0.866025i	−0.0256495	+	0.0444262i
$381$		0			0
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	−0.462563	−	0.886586i	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$		0			0
$385$	−6.00000	−	5.19615i	−0.305788	−	0.264820i
$386$	−16.0000			−0.814379
$387$		0			0
$388$	5.00000	+	8.66025i	0.253837	+	0.439658i
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	0.672874	−	0.739758i	$-0.265060\pi$
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	−0.977086	+	0.212847i	$0.931726\pi$
$390$		0			0
$391$	−54.0000			−2.73090
$392$	1.00000	+	6.92820i	0.0505076	+	0.349927i
$393$		0			0
$394$	7.50000	−	12.9904i	0.377845	−	0.654446i
$395$	−5.00000	−	8.66025i	−0.251577	−	0.435745i
$396$		0			0
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$	−16.0000			−0.802008
$399$		0			0
$400$	1.00000			0.0500000
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	0.302556	+	0.953131i	$0.402160\pi$
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	−0.976714	+	0.214544i	$0.931173\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	6.00000	−	10.3923i	0.298511	−	0.517036i
$405$		0			0
$406$	−15.0000	+	5.19615i	−0.744438	+	0.257881i
$407$	21.0000			1.04093
$408$		0			0
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	−0.984803	−	0.173675i	$-0.944436\pi$
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	0.341994	−	0.939702i	$-0.388898\pi$
$410$	−1.50000	−	2.59808i	−0.0740797	−	0.128310i
$411$		0			0
$412$	−4.00000			−0.197066
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$		0			0
$418$	−1.50000	+	2.59808i	−0.0733674	+	0.127076i
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	−11.5000	+	19.9186i	−0.559811	+	0.969622i
$423$		0			0
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$		0			0
$427$	20.0000	−	6.92820i	0.967868	−	0.335279i
$428$	12.0000			0.580042
$429$		0			0
$430$	1.00000	+	1.73205i	0.0482243	+	0.0835269i
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$		0			0
$433$	−40.0000			−1.92228			−0.961139	−	0.276066i	$-0.910969\pi$
$433$	−40.0000			−1.92228			−0.961139	+	0.276066i	$0.910969\pi$
$434$	−16.0000	−	13.8564i	−0.768025	−	0.665129i
$435$		0			0
$436$	8.00000	−	13.8564i	0.383131	−	0.663602i
$437$	−4.50000	−	7.79423i	−0.215264	−	0.372849i
$438$		0			0
$439$	−13.0000	+	22.5167i	−0.620456	+	1.07466i	0.368945	+	0.929451i	$0.379719\pi$
$439$	−13.0000	+	22.5167i	−0.620456	+	1.07466i	−0.989401	+	0.145210i	$0.953614\pi$
$440$	3.00000			0.143019
$441$		0			0
$442$	−6.00000			−0.285391
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$		0			0
$445$	−3.00000	−	5.19615i	−0.142214	−	0.246321i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$		0			0
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$	−21.0000			−0.991051			−0.495526	−	0.868593i	$-0.665025\pi$
$449$	−21.0000			−0.991051			−0.495526	+	0.868593i	$0.665025\pi$
$450$		0			0
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$		0			0
$453$		0			0
$454$	12.0000			0.563188
$455$	2.50000	−	0.866025i	0.117202	−	0.0405999i
$456$		0			0
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	−0.982004	−	0.188858i	$-0.939521\pi$
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	0.654558	+	0.756012i	$0.272855\pi$
$458$	2.00000	+	3.46410i	0.0934539	+	0.161867i
$459$		0			0
$460$	−4.50000	+	7.79423i	−0.209814	+	0.363408i
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	−1.00000			−0.0464739			−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000			−0.0464739			−0.0232370	+	0.999730i	$0.507397\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	−3.00000	+	5.19615i	−0.138823	+	0.240449i	−0.927052	−	0.374934i	$-0.877665\pi$
$467$	−3.00000	+	5.19615i	−0.138823	+	0.240449i	0.788228	+	0.615383i	$0.210999\pi$
$468$		0			0
$469$	−4.00000	+	20.7846i	−0.184703	+	0.959744i
$470$	9.00000			0.415139
$471$		0			0
$472$		0			0
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$		0			0
$475$	−1.00000			−0.0458831
$476$	15.0000	−	5.19615i	0.687524	−	0.238165i
$477$		0			0
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	−3.50000	+	6.06218i	−0.159586	+	0.276412i
$482$	−1.00000			−0.0455488
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−5.00000	+	8.66025i	−0.227038	+	0.393242i
$486$		0			0
$487$	8.00000	+	13.8564i	0.362515	+	0.627894i	0.988374	−	0.152042i	$-0.0485850\pi$
$487$	8.00000	+	13.8564i	0.362515	+	0.627894i	−0.625859	+	0.779936i	$0.715252\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$		0			0
$490$	−5.50000	+	4.33013i	−0.248465	+	0.195615i
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$		0			0
$493$	18.0000	+	31.1769i	0.810679	+	1.40414i
$494$	−0.500000	−	0.866025i	−0.0224961	−	0.0389643i
$495$		0			0
$496$	8.00000			0.359211
$497$		0			0
$498$		0			0
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−7.50000	+	12.9904i	−0.334741	+	0.579789i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$	−13.5000	+	23.3827i	−0.600148	+	1.03949i
$507$		0			0
$508$	0.500000	+	0.866025i	0.0221839	+	0.0384237i
$509$	−21.0000	+	36.3731i	−0.930809	+	1.61221i	−0.148866	+	0.988857i	$0.547562\pi$
$509$	−21.0000	+	36.3731i	−0.930809	+	1.61221i	−0.781943	+	0.623350i	$0.785771\pi$
$510$		0			0
$511$	2.00000	−	10.3923i	0.0884748	−	0.459728i
$512$	1.00000			0.0441942
$513$		0			0
$514$		0			0
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$		0			0
$517$	27.0000			1.18746
$518$	3.50000	−	18.1865i	0.153781	−	0.799070i
$519$		0			0
$520$	−0.500000	+	0.866025i	−0.0219265	+	0.0379777i
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	0.653650	−	0.756797i	$-0.273237\pi$
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	−0.982231	+	0.187678i	$0.939904\pi$
$522$		0			0
$523$	14.0000	−	24.2487i	0.612177	−	1.06032i	−0.378695	−	0.925521i	$-0.623627\pi$
$523$	14.0000	−	24.2487i	0.612177	−	1.06032i	0.990873	−	0.134801i	$-0.0430394\pi$
$524$	−3.00000			−0.131056
$525$		0			0
$526$		0			0
$527$	−24.0000	+	41.5692i	−1.04546	+	1.81078i
$528$		0			0
$529$	−29.0000	−	50.2295i	−1.26087	−	2.18389i
$530$	−4.50000	+	7.79423i	−0.195468	+	0.338560i
$531$		0			0
$532$	2.00000	+	1.73205i	0.0867110	+	0.0750939i
$533$	3.00000			0.129944
$534$		0			0
$535$	6.00000	+	10.3923i	0.259403	+	0.449299i
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$		0			0
$538$		0			0
$539$	−16.5000	+	12.9904i	−0.710705	+	0.559535i
$540$		0			0
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$	8.00000	+	13.8564i	0.343629	+	0.595184i
$543$		0			0
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$	16.0000			0.685365
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$		0			0
$550$	1.50000	+	2.59808i	0.0639602	+	0.110782i
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$		0			0
$553$	−25.0000	+	8.66025i	−1.06311	+	0.368271i
$554$	−10.0000			−0.424859
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	0.754802	−	0.655953i	$-0.227733\pi$
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	−0.945473	+	0.325701i	$0.894400\pi$
$558$		0			0
$559$	−2.00000			−0.0845910
$560$	0.500000	−	2.59808i	0.0211289	−	0.109789i
$561$		0			0
$562$	−13.5000	+	23.3827i	−0.569463	+	0.986339i
$563$	21.0000	+	36.3731i	0.885044	+	1.53294i	0.845663	+	0.533718i	$0.179206\pi$
$563$	21.0000	+	36.3731i	0.885044	+	1.53294i	0.0393818	+	0.999224i	$0.487461\pi$
$564$		0			0
$565$		0			0
$566$	14.0000			0.588464
$567$		0			0
$568$		0			0
$569$	10.5000	−	18.1865i	0.440183	−	0.762419i	−0.557520	−	0.830164i	$-0.688247\pi$
$569$	10.5000	−	18.1865i	0.440183	−	0.762419i	0.997703	+	0.0677445i	$0.0215803\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−1.50000	+	2.59808i	−0.0627182	+	0.108631i
$573$		0			0
$574$	−7.50000	+	2.59808i	−0.313044	+	0.108442i
$575$	−9.00000			−0.375326
$576$		0			0
$577$	−22.0000	−	38.1051i	−0.915872	−	1.58634i	−0.805620	−	0.592433i	$-0.798167\pi$
$577$	−22.0000	−	38.1051i	−0.915872	−	1.58634i	−0.110252	−	0.993904i	$-0.535166\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$		0			0
$580$	6.00000			0.249136
$581$		0			0
$582$		0			0
$583$	−13.5000	+	23.3827i	−0.559113	+	0.968412i
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$		0			0
$586$	−4.50000	+	7.79423i	−0.185893	+	0.321977i
$587$	24.0000			0.990586			0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000			0.990586			0.495293	+	0.868726i	$0.335061\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$		0			0
$591$		0			0
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	−0.507184	−	0.861838i	$-0.669314\pi$
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	0.999965	+	0.00831589i	$0.00264706\pi$
$594$		0			0
$595$	12.0000	+	10.3923i	0.491952	+	0.426043i
$596$	6.00000			0.245770
$597$		0			0
$598$	−4.50000	−	7.79423i	−0.184019	−	0.318730i
$599$	−21.0000	−	36.3731i	−0.858037	−	1.48616i	−0.873799	−	0.486287i	$-0.838351\pi$
$599$	−21.0000	−	36.3731i	−0.858037	−	1.48616i	0.0157622	−	0.999876i	$-0.494983\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	5.00000	−	1.73205i	0.203785	−	0.0705931i
$603$		0			0
$604$	5.00000	−	8.66025i	0.203447	−	0.352381i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$		0			0
$607$	0.500000	−	0.866025i	0.0202944	−	0.0351509i	−0.855700	−	0.517472i	$-0.826873\pi$
$607$	0.500000	−	0.866025i	0.0202944	−	0.0351509i	0.875994	+	0.482322i	$0.160206\pi$
$608$	−1.00000			−0.0405554
$609$		0			0
$610$	−8.00000			−0.323911
$611$	−4.50000	+	7.79423i	−0.182051	+	0.315321i
$612$		0			0
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	−0.994794	−	0.101905i	$-0.967506\pi$
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	0.409145	−	0.912470i	$-0.365827\pi$
$614$	−7.00000	+	12.1244i	−0.282497	+	0.489299i
$615$		0			0
$616$	1.50000	−	7.79423i	0.0604367	−	0.314038i
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$		0			0
$619$	−11.5000	−	19.9186i	−0.462224	−	0.800595i	0.536847	−	0.843679i	$-0.319615\pi$
$619$	−11.5000	−	19.9186i	−0.462224	−	0.800595i	−0.999071	+	0.0430838i	$0.986282\pi$
$620$	4.00000	+	6.92820i	0.160644	+	0.278243i
$621$		0			0
$622$	24.0000			0.962312
$623$	−15.0000	+	5.19615i	−0.600962	+	0.208179i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	14.0000	+	24.2487i	0.559553	+	0.969173i
$627$		0			0
$628$	−11.5000	+	19.9186i	−0.458900	+	0.794838i
$629$	−42.0000			−1.67465
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	5.00000	−	8.66025i	0.198889	−	0.344486i
$633$		0			0
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$	−0.500000	+	0.866025i	−0.0198419	+	0.0343672i
$636$		0			0
$637$	−1.00000	−	6.92820i	−0.0396214	−	0.274505i
$638$	18.0000			0.712627
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	0.999247	+	0.0387913i	$0.0123508\pi$
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	−0.466029	+	0.884769i	$0.654316\pi$
$642$		0			0
$643$	2.00000			0.0788723			0.0394362	−	0.999222i	$-0.487444\pi$
$643$	2.00000			0.0788723			0.0394362	+	0.999222i	$0.487444\pi$
$644$	18.0000	+	15.5885i	0.709299	+	0.614271i
$645$		0			0
$646$	3.00000	−	5.19615i	0.118033	−	0.204440i
$647$	16.5000	+	28.5788i	0.648682	+	1.12355i	0.983438	+	0.181245i	$0.0580128\pi$
$647$	16.5000	+	28.5788i	0.648682	+	1.12355i	−0.334756	+	0.942305i	$0.608654\pi$
$648$		0			0
$649$		0			0
$650$	−1.00000			−0.0392232
$651$		0			0
$652$	20.0000			0.783260
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	−0.940541	−	0.339680i	$-0.889681\pi$
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	0.764442	+	0.644692i	$0.223014\pi$
$654$		0			0
$655$	−1.50000	−	2.59808i	−0.0586098	−	0.101515i
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$		0			0
$658$	4.50000	−	23.3827i	0.175428	−	0.911552i
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	14.0000	+	24.2487i	0.544537	+	0.943166i	0.998636	+	0.0522143i	$0.0166279\pi$
$661$	14.0000	+	24.2487i	0.544537	+	0.943166i	−0.454099	+	0.890951i	$0.650039\pi$
$662$	3.50000	+	6.06218i	0.136031	+	0.235613i
$663$		0			0
$664$		0			0
$665$	−0.500000	+	2.59808i	−0.0193892	+	0.100749i
$666$		0			0
$667$	−27.0000	+	46.7654i	−1.04544	+	1.81076i
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$		0			0
$670$	4.00000	−	6.92820i	0.154533	−	0.267660i
$671$	−24.0000			−0.926510
$672$		0			0
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$	11.0000	−	19.0526i	0.423704	−	0.733877i
$675$		0			0
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	−0.939450	−	0.342687i	$-0.888663\pi$
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	0.766501	+	0.642244i	$0.221996\pi$
$678$		0			0
$679$	20.0000	+	17.3205i	0.767530	+	0.664700i
$680$	−6.00000			−0.230089
$681$		0			0
$682$	12.0000	+	20.7846i	0.459504	+	0.795884i
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$		0			0
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	−4.50000	−	7.79423i	−0.171436	−	0.296936i
$690$		0			0
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	0.382791	+	0.923835i	$0.374963\pi$
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	−0.991460	+	0.130410i	$0.958371\pi$
$692$	−9.00000			−0.342129
$693$		0			0
$694$		0			0
$695$	−2.00000	+	3.46410i	−0.0758643	+	0.131401i
$696$		0			0
$697$	9.00000	+	15.5885i	0.340899	+	0.590455i
$698$	−13.0000	+	22.5167i	−0.492057	+	0.852268i
$699$		0			0
$700$	2.50000	−	0.866025i	0.0944911	−	0.0327327i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$	−3.50000	−	6.06218i	−0.132005	−	0.228639i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	−12.0000			−0.451626
$707$	6.00000	−	31.1769i	0.225653	−	1.17253i
$708$		0			0
$709$	23.0000	−	39.8372i	0.863783	−	1.49612i	−0.00446726	−	0.999990i	$-0.501422\pi$
$709$	23.0000	−	39.8372i	0.863783	−	1.49612i	0.868250	−	0.496126i	$-0.165245\pi$
$710$		0			0
$711$		0			0
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	−72.0000			−2.69642
$714$		0			0
$715$	−3.00000			−0.112194
$716$	−1.50000	+	2.59808i	−0.0560576	+	0.0970947i
$717$		0			0
$718$	9.00000	+	15.5885i	0.335877	+	0.581756i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$	−10.0000	+	3.46410i	−0.372419	+	0.129010i
$722$	−18.0000			−0.669891
$723$		0			0
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$		0			0
$727$	−1.00000			−0.0370879			−0.0185440	−	0.999828i	$-0.505903\pi$
$727$	−1.00000			−0.0370879			−0.0185440	+	0.999828i	$0.505903\pi$
$728$	2.00000	+	1.73205i	0.0741249	+	0.0641941i
$729$		0			0
$730$	−2.00000	+	3.46410i	−0.0740233	+	0.128212i
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$		0			0
$733$	21.5000	−	37.2391i	0.794121	−	1.37546i	−0.129275	−	0.991609i	$-0.541265\pi$
$733$	21.5000	−	37.2391i	0.794121	−	1.37546i	0.923396	−	0.383849i	$-0.125402\pi$
$734$	−19.0000			−0.701303
$735$		0			0
$736$	−9.00000			−0.331744
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$		0			0
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	−0.984589	−	0.174883i	$-0.944045\pi$
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	0.340841	−	0.940121i	$-0.389288\pi$
$740$	−3.50000	+	6.06218i	−0.128663	+	0.222850i
$741$		0			0
$742$	18.0000	+	15.5885i	0.660801	+	0.572270i
$743$	45.0000			1.65089			0.825445	−	0.564483i	$-0.190924\pi$
$743$	45.0000			1.65089			0.825445	+	0.564483i	$0.190924\pi$
$744$		0			0
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$	−1.00000	−	1.73205i	−0.0366126	−	0.0634149i
$747$		0			0
$748$	−18.0000			−0.658145
$749$	30.0000	−	10.3923i	1.09618	−	0.379727i
$750$		0			0
$751$	5.00000	−	8.66025i	0.182453	−	0.316017i	−0.760263	−	0.649616i	$-0.774930\pi$
$751$	5.00000	−	8.66025i	0.182453	−	0.316017i	0.942715	+	0.333599i	$0.108263\pi$
$752$	4.50000	+	7.79423i	0.164098	+	0.284226i
$753$		0			0
$754$	−3.00000	+	5.19615i	−0.109254	+	0.189233i
$755$	10.0000			0.363937
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	−11.5000	+	19.9186i	−0.417699	+	0.723476i
$759$		0			0
$760$	−0.500000	−	0.866025i	−0.0181369	−	0.0314140i
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	−0.999925	−	0.0122260i	$-0.996108\pi$
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	0.510551	+	0.859848i	$0.329442\pi$
$762$		0			0
$763$	8.00000	−	41.5692i	0.289619	−	1.50491i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	10.5000	+	18.1865i	0.379380	+	0.657106i
$767$		0			0
$768$		0			0
$769$	23.0000			0.829401			0.414701	−	0.909958i	$-0.363886\pi$
$769$	23.0000			0.829401			0.414701	+	0.909958i	$0.363886\pi$
$770$	7.50000	−	2.59808i	0.270281	−	0.0936282i
$771$		0			0
$772$	8.00000	−	13.8564i	0.287926	−	0.498703i
$773$	−25.5000	−	44.1673i	−0.917171	−	1.58859i	−0.803691	−	0.595047i	$-0.797133\pi$
$773$	−25.5000	−	44.1673i	−0.917171	−	1.58859i	−0.113480	−	0.993540i	$-0.536200\pi$
$774$		0			0
$775$	−4.00000	+	6.92820i	−0.143684	+	0.248868i
$776$	−10.0000			−0.358979
$777$		0			0
$778$	12.0000			0.430221
$779$	−1.50000	+	2.59808i	−0.0537431	+	0.0930857i
$780$		0			0
$781$		0			0
$782$	27.0000	−	46.7654i	0.965518	−	1.67233i
$783$		0			0
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$	−23.0000			−0.820905
$786$		0			0
$787$	11.0000	+	19.0526i	0.392108	+	0.679150i	0.992727	−	0.120384i	$-0.0384127\pi$
$787$	11.0000	+	19.0526i	0.392108	+	0.679150i	−0.600620	+	0.799535i	$0.705079\pi$
$788$	7.50000	+	12.9904i	0.267176	+	0.462763i
$789$		0			0
$790$	10.0000			0.355784
$791$		0			0
$792$		0			0
$793$	4.00000	−	6.92820i	0.142044	−	0.246028i
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$		0			0
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	−6.00000			−0.212531			−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000			−0.212531			−0.106265	+	0.994338i	$0.533889\pi$
$798$		0			0
$799$	−54.0000			−1.91038
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	−13.5000	−	23.3827i	−0.476702	−	0.825671i
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$		0			0
$805$	−4.50000	+	23.3827i	−0.158604	+	0.824131i
$806$	−8.00000			−0.281788
$807$		0			0
$808$	6.00000	+	10.3923i	0.211079	+	0.365600i
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	0.776012	−	0.630718i	$-0.217239\pi$
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	−0.934224	+	0.356687i	$0.883906\pi$
$810$		0			0
$811$	−25.0000			−0.877869			−0.438934	−	0.898519i	$-0.644644\pi$
$811$	−25.0000			−0.877869			−0.438934	+	0.898519i	$0.644644\pi$
$812$	3.00000	−	15.5885i	0.105279	−	0.547048i
$813$		0			0
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$	10.0000	+	17.3205i	0.350285	+	0.606711i
$816$		0			0
$817$	1.00000	−	1.73205i	0.0349856	−	0.0605968i
$818$	26.0000			0.909069
$819$		0			0
$820$	3.00000			0.104765
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	−0.476122	−	0.879379i	$-0.657958\pi$
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	0.999626	−	0.0273557i	$-0.00870868\pi$
$822$		0			0
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	2.00000	−	3.46410i	0.0696733	−	0.120678i
$825$		0			0
$826$		0			0
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$		0			0
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	0.718481	−	0.695546i	$-0.244838\pi$
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	−0.961601	+	0.274450i	$0.911504\pi$
$830$		0			0
$831$		0			0
$832$	−1.00000			−0.0346688
$833$	33.0000	−	25.9808i	1.14338	−	0.900180i
$834$		0			0
$835$	−1.50000	+	2.59808i	−0.0519096	+	0.0899101i
$836$	−1.50000	−	2.59808i	−0.0518786	−	0.0898563i
$837$		0			0
$838$	−4.50000	+	7.79423i	−0.155450	+	0.269247i
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−1.00000	+	1.73205i	−0.0344623	+	0.0596904i
$843$		0			0
$844$	−11.5000	−	19.9186i	−0.395846	−	0.685626i
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$		0			0
$847$	−5.00000	+	1.73205i	−0.171802	+	0.0595140i
$848$	−9.00000			−0.309061
$849$		0			0
$850$	−3.00000	−	5.19615i	−0.102899	−	0.178227i
$851$	−31.5000	−	54.5596i	−1.07981	−	1.87028i
$852$		0			0
$853$	−19.0000			−0.650548			−0.325274	−	0.945620i	$-0.605456\pi$
$853$	−19.0000			−0.650548			−0.325274	+	0.945620i	$0.605456\pi$
$854$	−4.00000	+	20.7846i	−0.136877	+	0.711235i
$855$		0			0
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$		0			0
$859$	−16.0000	+	27.7128i	−0.545913	+	0.945549i	0.452636	+	0.891695i	$0.350484\pi$
$859$	−16.0000	+	27.7128i	−0.545913	+	0.945549i	−0.998549	+	0.0538535i	$0.982850\pi$
$860$	−2.00000			−0.0681994
$861$		0			0
$862$	−12.0000			−0.408722
$863$	−1.50000	+	2.59808i	−0.0510606	+	0.0884395i	−0.890426	−	0.455128i	$-0.849593\pi$
$863$	−1.50000	+	2.59808i	−0.0510606	+	0.0884395i	0.839365	+	0.543568i	$0.182927\pi$
$864$		0			0
$865$	−4.50000	−	7.79423i	−0.153005	−	0.265012i
$866$	20.0000	−	34.6410i	0.679628	−	1.17715i
$867$		0			0
$868$	20.0000	−	6.92820i	0.678844	−	0.235159i
$869$	30.0000			1.01768
$870$		0			0
$871$	4.00000	+	6.92820i	0.135535	+	0.234753i
$872$	8.00000	+	13.8564i	0.270914	+	0.469237i
$873$		0			0
$874$	9.00000			0.304430
$875$	2.00000	+	1.73205i	0.0676123	+	0.0585540i
$876$		0			0
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	−0.735163	−	0.677891i	$-0.762894\pi$
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	0.954652	+	0.297724i	$0.0962275\pi$
$878$	−13.0000	−	22.5167i	−0.438729	−	0.759900i
$879$		0			0
$880$	−1.50000	+	2.59808i	−0.0505650	+	0.0875811i
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$		0			0
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	3.00000	−	5.19615i	0.100901	−	0.174766i
$885$		0			0
$886$	6.00000	+	10.3923i	0.201574	+	0.349136i
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	0.109881	+	0.993945i	$0.464953\pi$
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	−0.915722	+	0.401813i	$0.868380\pi$
$888$		0			0
$889$	2.00000	+	1.73205i	0.0670778	+	0.0580911i
$890$	6.00000			0.201120
$891$		0			0
$892$	−4.00000	−	6.92820i	−0.133930	−	0.231973i
$893$	−4.50000	−	7.79423i	−0.150587	−	0.260824i
$894$		0			0
$895$	−3.00000			−0.100279
$896$	2.50000	−	0.866025i	0.0835191	−	0.0289319i
$897$		0			0
$898$	10.5000	−	18.1865i	0.350390	−	0.606892i
$899$	24.0000	+	41.5692i	0.800445	+	1.38641i
$900$		0			0
$901$	27.0000	−	46.7654i	0.899500	−	1.55798i
$902$	9.00000			0.299667
$903$		0			0
$904$		0			0
$905$	1.00000	−	1.73205i	0.0332411	−	0.0575753i
$906$		0			0
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$		0			0
$910$	−0.500000	+	2.59808i	−0.0165748	+	0.0861254i
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$		0			0
$913$		0			0
$914$	−7.00000	−	12.1244i	−0.231539	−	0.401038i
$915$		0			0
$916$	−4.00000			−0.132164
$917$	−7.50000	+	2.59808i	−0.247672	+	0.0857960i
$918$		0			0
$919$	11.0000	−	19.0526i	0.362857	−	0.628486i	−0.625573	−	0.780165i	$-0.715135\pi$
$919$	11.0000	−	19.0526i	0.362857	−	0.628486i	0.988430	+	0.151680i	$0.0484682\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$		0			0
$922$	−15.0000	+	25.9808i	−0.493999	+	0.855631i
$923$		0			0
$924$		0			0
$925$	−7.00000			−0.230159
$926$	0.500000	−	0.866025i	0.0164310	−	0.0284594i
$927$		0			0
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	28.5000	−	49.3634i	0.935055	−	1.61956i	0.160518	−	0.987033i	$-0.448683\pi$
$929$	28.5000	−	49.3634i	0.935055	−	1.61956i	0.774536	−	0.632529i	$-0.217983\pi$
$930$		0			0
$931$	6.50000	+	2.59808i	0.213029	+	0.0851485i
$932$	6.00000			0.196537
$933$		0			0
$934$	−3.00000	−	5.19615i	−0.0981630	−	0.170023i
$935$	−9.00000	−	15.5885i	−0.294331	−	0.509797i
$936$		0			0
$937$	−10.0000			−0.326686			−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000			−0.326686			−0.163343	+	0.986569i	$0.552228\pi$
$938$	−16.0000	−	13.8564i	−0.522419	−	0.452428i
$939$		0			0
$940$	−4.50000	+	7.79423i	−0.146774	+	0.254220i
$941$	24.0000	+	41.5692i	0.782378	+	1.35512i	0.930553	+	0.366157i	$0.119327\pi$
$941$	24.0000	+	41.5692i	0.782378	+	1.35512i	−0.148176	+	0.988961i	$0.547340\pi$
$942$		0			0
$943$	−13.5000	+	23.3827i	−0.439620	+	0.761445i
$944$		0			0
$945$		0			0
$946$	−6.00000			−0.195077
$947$	3.00000	−	5.19615i	0.0974869	−	0.168852i	−0.813157	−	0.582045i	$-0.802253\pi$
$947$	3.00000	−	5.19615i	0.0974869	−	0.168852i	0.910644	+	0.413192i	$0.135586\pi$
$948$		0			0
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$	0.500000	−	0.866025i	0.0162221	−	0.0280976i
$951$		0			0
$952$	−3.00000	+	15.5885i	−0.0972306	+	0.505225i
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$		0			0
$955$	−6.00000	−	10.3923i	−0.194155	−	0.336287i
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$		0			0
$958$		0			0
$959$	6.00000	−	31.1769i	0.193750	−	1.00676i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−3.50000	−	6.06218i	−0.112845	−	0.195452i
$963$		0			0
$964$	0.500000	−	0.866025i	0.0161039	−	0.0278928i
$965$	16.0000			0.515058
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$		0			0
$970$	−5.00000	−	8.66025i	−0.160540	−	0.278064i
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	0.238114	+	0.971237i	$0.423471\pi$
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	−0.960173	+	0.279406i	$0.909862\pi$
$972$		0			0
$973$	8.00000	+	6.92820i	0.256468	+	0.222108i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	0.305530	−	0.952183i	$-0.401167\pi$
$978$		0			0
$979$	18.0000			0.575282
$980$	−1.00000	−	6.92820i	−0.0319438	−	0.221313i
$981$		0			0
$982$	18.0000	−	31.1769i	0.574403	−	0.994895i
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	0.888955	−	0.457995i	$-0.151432\pi$
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	−0.841112	+	0.540860i	$0.818099\pi$
$984$		0			0
$985$	−7.50000	+	12.9904i	−0.238970	+	0.413908i
$986$	−36.0000			−1.14647
$987$		0			0
$988$	1.00000			0.0318142
$989$	9.00000	−	15.5885i	0.286183	−	0.495684i
$990$		0			0
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	−0.968864	−	0.247592i	$-0.920361\pi$
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	0.270011	−	0.962857i	$-0.412973\pi$
$992$	−4.00000	+	6.92820i	−0.127000	+	0.219971i
$993$		0			0
$994$		0			0
$995$	16.0000			0.507234
$996$		0			0
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	0.985961	−	0.166978i	$-0.0534008\pi$
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	−0.637587	+	0.770378i	$0.720067\pi$
$998$	2.00000	+	3.46410i	0.0633089	+	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.k.d.541.1		2
3.2	odd	2		70.2.e.d.51.1	yes	2
7.2	even	3		4410.2.a.x.1.1		1
7.4	even	3	inner	630.2.k.d.361.1		2
7.5	odd	6		4410.2.a.bg.1.1		1
12.11	even	2		560.2.q.b.401.1		2
15.2	even	4		350.2.j.d.149.2		4
15.8	even	4		350.2.j.d.149.1		4
15.14	odd	2		350.2.e.b.51.1		2
21.2	odd	6		490.2.a.a.1.1		1
21.5	even	6		490.2.a.d.1.1		1
21.11	odd	6		70.2.e.d.11.1	✓	2
21.17	even	6		490.2.e.g.361.1		2
21.20	even	2		490.2.e.g.471.1		2
84.11	even	6		560.2.q.b.81.1		2
84.23	even	6		3920.2.a.bh.1.1		1
84.47	odd	6		3920.2.a.e.1.1		1
105.2	even	12		2450.2.c.q.99.1		2
105.23	even	12		2450.2.c.q.99.2		2
105.32	even	12		350.2.j.d.249.1		4
105.44	odd	6		2450.2.a.bf.1.1		1
105.47	odd	12		2450.2.c.e.99.1		2
105.53	even	12		350.2.j.d.249.2		4
105.68	odd	12		2450.2.c.e.99.2		2
105.74	odd	6		350.2.e.b.151.1		2
105.89	even	6		2450.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.d.11.1	✓	2	21.11	odd	6
70.2.e.d.51.1	yes	2	3.2	odd	2
350.2.e.b.51.1		2	15.14	odd	2
350.2.e.b.151.1		2	105.74	odd	6
350.2.j.d.149.1		4	15.8	even	4
350.2.j.d.149.2		4	15.2	even	4
350.2.j.d.249.1		4	105.32	even	12
350.2.j.d.249.2		4	105.53	even	12
490.2.a.a.1.1		1	21.2	odd	6
490.2.a.d.1.1		1	21.5	even	6
490.2.e.g.361.1		2	21.17	even	6
490.2.e.g.471.1		2	21.20	even	2
560.2.q.b.81.1		2	84.11	even	6
560.2.q.b.401.1		2	12.11	even	2
630.2.k.d.361.1		2	7.4	even	3	inner
630.2.k.d.541.1		2	1.1	even	1	trivial
2450.2.a.v.1.1		1	105.89	even	6
2450.2.a.bf.1.1		1	105.44	odd	6
2450.2.c.e.99.1		2	105.47	odd	12
2450.2.c.e.99.2		2	105.68	odd	12
2450.2.c.q.99.1		2	105.2	even	12
2450.2.c.q.99.2		2	105.23	even	12
3920.2.a.e.1.1		1	84.47	odd	6
3920.2.a.bh.1.1		1	84.23	even	6
4410.2.a.x.1.1		1	7.2	even	3
4410.2.a.bg.1.1		1	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} -1.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -3.00000 q^{22} +(4.50000 - 7.79423i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-0.500000 + 2.59808i) q^{28} -6.00000 q^{29} +(-4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(-2.50000 + 0.866025i) q^{35} +(3.50000 - 6.06218i) q^{37} +(0.500000 + 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{40} -3.00000 q^{41} +2.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(4.50000 + 7.79423i) q^{46} +(4.50000 - 7.79423i) q^{47} +(1.00000 + 6.92820i) q^{49} +1.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(4.50000 + 7.79423i) q^{53} +3.00000 q^{55} +(-2.00000 - 1.73205i) q^{56} +(3.00000 - 5.19615i) q^{58} +(-4.00000 + 6.92820i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(0.500000 - 2.59808i) q^{70} +(2.00000 + 3.46410i) q^{73} +(3.50000 + 6.06218i) q^{74} -1.00000 q^{76} +(1.50000 - 7.79423i) q^{77} +(5.00000 - 8.66025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(1.50000 - 2.59808i) q^{82} -6.00000 q^{85} +(-1.00000 + 1.73205i) q^{86} +(1.50000 + 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(2.00000 + 1.73205i) q^{91} -9.00000 q^{92} +(4.50000 + 7.79423i) q^{94} +(-0.500000 - 0.866025i) q^{95} -10.0000 q^{97} +(-6.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + q^{5} - 4 q^{7} + 2 q^{8} + q^{10} + 3 q^{11} - 2 q^{13} + 5 q^{14} - q^{16} - 6 q^{17} + q^{19} - 2 q^{20} - 6 q^{22} + 9 q^{23} - q^{25} + q^{26} - q^{28} - 12 q^{29} - 8 q^{31}+ \cdots - 13 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + q^5 - 4 * q^7 + 2 * q^8 + q^10 + 3 * q^11 - 2 * q^13 + 5 * q^14 - q^16 - 6 * q^17 + q^19 - 2 * q^20 - 6 * q^22 + 9 * q^23 - q^25 + q^26 - q^28 - 12 * q^29 - 8 * q^31 - q^32 + 12 * q^34 - 5 * q^35 + 7 * q^37 + q^38 + q^40 - 6 * q^41 + 4 * q^43 + 3 * q^44 + 9 * q^46 + 9 * q^47 + 2 * q^49 + 2 * q^50 + q^52 + 9 * q^53 + 6 * q^55 - 4 * q^56 + 6 * q^58 - 8 * q^61 + 16 * q^62 + 2 * q^64 - q^65 - 8 * q^67 - 6 * q^68 + q^70 + 4 * q^73 + 7 * q^74 - 2 * q^76 + 3 * q^77 + 10 * q^79 + q^80 + 3 * q^82 - 12 * q^85 - 2 * q^86 + 3 * q^88 + 6 * q^89 + 4 * q^91 - 18 * q^92 + 9 * q^94 - q^95 - 20 * q^97 - 13 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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