LMFDB - Embedded newform 560.2.q.b.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.q (of order $3$, degree $2$, not 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:	$4.47162251319$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	560.81
Dual form			560.2.q.b.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +2.00000 q^{15} +(3.00000 - 5.19615i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(1.00000 + 5.19615i) q^{21} +(4.50000 + 7.79423i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{27} +6.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(3.00000 + 5.19615i) q^{33} +(-2.50000 - 0.866025i) q^{35} +(3.50000 + 6.06218i) q^{37} +(1.00000 - 1.73205i) q^{39} +3.00000 q^{41} -2.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(4.50000 + 7.79423i) q^{47} +(1.00000 - 6.92820i) q^{49} +(6.00000 + 10.3923i) q^{51} +(-4.50000 + 7.79423i) q^{53} -3.00000 q^{55} +2.00000 q^{57} +(-4.00000 - 6.92820i) q^{61} +(-2.50000 - 0.866025i) q^{63} +(0.500000 + 0.866025i) q^{65} +(4.00000 - 6.92820i) q^{67} -18.0000 q^{69} +(2.00000 - 3.46410i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(-1.50000 - 7.79423i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(5.50000 - 9.52628i) q^{81} -6.00000 q^{85} +(-6.00000 + 10.3923i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-2.00000 + 1.73205i) q^{91} +(8.00000 + 13.8564i) q^{93} +(-0.500000 + 0.866025i) q^{95} -10.0000 q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - q^{5} + 4 q^{7} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - q^5 + 4 * q^7 - q^9	$ 2 q - 2 q^{3} - q^{5} + 4 q^{7} - q^{9} + 3 q^{11} - 2 q^{13} + 4 q^{15} + 6 q^{17} - q^{19} + 2 q^{21} + 9 q^{23} - q^{25} - 8 q^{27} + 12 q^{29} + 8 q^{31} + 6 q^{33} - 5 q^{35} + 7 q^{37} + 2 q^{39} + 6 q^{41} - 4 q^{43} - q^{45} + 9 q^{47} + 2 q^{49} + 12 q^{51} - 9 q^{53} - 6 q^{55} + 4 q^{57} - 8 q^{61} - 5 q^{63} + q^{65} + 8 q^{67} - 36 q^{69} + 4 q^{73} - 2 q^{75} - 3 q^{77} - 10 q^{79} + 11 q^{81} - 12 q^{85} - 12 q^{87} - 6 q^{89} - 4 q^{91} + 16 q^{93} - q^{95} - 20 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - q^5 + 4 * q^7 - q^9 + 3 * q^11 - 2 * q^13 + 4 * q^15 + 6 * q^17 - q^19 + 2 * q^21 + 9 * q^23 - q^25 - 8 * q^27 + 12 * q^29 + 8 * q^31 + 6 * q^33 - 5 * q^35 + 7 * q^37 + 2 * q^39 + 6 * q^41 - 4 * q^43 - q^45 + 9 * q^47 + 2 * q^49 + 12 * q^51 - 9 * q^53 - 6 * q^55 + 4 * q^57 - 8 * q^61 - 5 * q^63 + q^65 + 8 * q^67 - 36 * q^69 + 4 * q^73 - 2 * q^75 - 3 * q^77 - 10 * q^79 + 11 * q^81 - 12 * q^85 - 12 * q^87 - 6 * q^89 - 4 * q^91 + 16 * q^93 - q^95 - 20 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$		0			0
$5$	−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
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$		0			0
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	1.00000	+	5.19615i	0.218218	+	1.13389i
$22$		0			0
$23$	4.50000	+	7.79423i	0.938315	+	1.62521i	0.768613	+	0.639713i	$0.220947\pi$
$23$	4.50000	+	7.79423i	0.938315	+	1.62521i	0.169701	+	0.985496i	$0.445720\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$		0			0
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$		0			0
$35$	−2.50000	−	0.866025i	−0.422577	−	0.146385i
$36$		0			0
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$		0			0
$39$	1.00000	−	1.73205i	0.160128	−	0.277350i
$40$		0			0
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$		0			0
$43$	−2.00000			−0.304997			−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	6.00000	+	10.3923i	0.840168	+	1.45521i
$52$		0			0
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	0.371706	+	0.928351i	$0.378773\pi$
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	−0.989828	+	0.142269i	$0.954560\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$		0			0
$63$	−2.50000	−	0.866025i	−0.314970	−	0.109109i
$64$		0			0
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$		0			0
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	−0.511237	−	0.859440i	$-0.670813\pi$
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	0.999915	+	0.0130248i	$0.00414604\pi$
$68$		0			0
$69$	−18.0000			−2.16695
$70$		0			0
$71$		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	−0.724923	−	0.688830i	$-0.758125\pi$
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	0.959006	+	0.283387i	$0.0914581\pi$
$74$		0			0
$75$	−1.00000	−	1.73205i	−0.115470	−	0.200000i
$76$		0			0
$77$	−1.50000	−	7.79423i	−0.170941	−	0.888235i
$78$		0			0
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−6.00000			−0.650791
$86$		0			0
$87$	−6.00000	+	10.3923i	−0.643268	+	1.11417i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	−2.00000	+	1.73205i	−0.209657	+	0.181568i
$92$		0			0
$93$	8.00000	+	13.8564i	0.829561	+	1.43684i
$94$		0			0
$95$	−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	$0.669494\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$		0			0
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$		0			0
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	0.750510	−	0.660859i	$-0.229808\pi$
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	−0.947576	+	0.319531i	$0.896475\pi$
$104$		0			0
$105$	4.00000	−	3.46410i	0.390360	−	0.338062i
$106$		0			0
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$		0			0
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	−0.173316	−	0.984866i	$-0.555448\pi$
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	0.939577	−	0.342337i	$-0.111218\pi$
$110$		0			0
$111$	−14.0000			−1.32882
$112$		0			0
$113$		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
$116$		0			0
$117$	0.500000	+	0.866025i	0.0462250	+	0.0800641i
$118$		0			0
$119$	−3.00000	−	15.5885i	−0.275010	−	1.42899i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	1.00000			0.0887357			0.0443678	−	0.999015i	$-0.485873\pi$
$127$	1.00000			0.0887357			0.0443678	+	0.999015i	$0.485873\pi$
$128$		0			0
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$		0			0
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	0.924084	−	0.382190i	$-0.124830\pi$
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	−0.793028	+	0.609185i	$0.791497\pi$
$132$		0			0
$133$	−2.50000	−	0.866025i	−0.216777	−	0.0750939i
$134$		0			0
$135$	2.00000	+	3.46410i	0.172133	+	0.298142i
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−18.0000			−1.51587
$142$		0			0
$143$	−1.50000	+	2.59808i	−0.125436	+	0.217262i
$144$		0			0
$145$	−3.00000	−	5.19615i	−0.249136	−	0.431517i
$146$		0			0
$147$	11.0000	+	8.66025i	0.907265	+	0.714286i
$148$		0			0
$149$	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
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$	−8.00000			−0.642575
$156$		0			0
$157$	−11.5000	+	19.9186i	−0.917800	+	1.58968i	−0.115050	+	0.993360i	$0.536703\pi$
$157$	−11.5000	+	19.9186i	−0.917800	+	1.58968i	−0.802749	+	0.596316i	$0.796630\pi$
$158$		0			0
$159$	−9.00000	−	15.5885i	−0.713746	−	1.23625i
$160$		0			0
$161$	22.5000	+	7.79423i	1.77325	+	0.614271i
$162$		0			0
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	0.930033	+	0.367477i	$0.119778\pi$
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	−0.146772	+	0.989170i	$0.546888\pi$
$164$		0			0
$165$	3.00000	−	5.19615i	0.233550	−	0.404520i
$166$		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
$170$		0			0
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$		0			0
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	0.642699	−	0.766119i	$-0.277815\pi$
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	−0.984828	+	0.173534i	$0.944481\pi$
$174$		0			0
$175$	0.500000	+	2.59808i	0.0377964	+	0.196396i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	−0.916623	−	0.399753i	$-0.869096\pi$
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	0.804508	+	0.593942i	$0.202429\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	16.0000			1.18275
$184$		0			0
$185$	3.50000	−	6.06218i	0.257325	−	0.445700i
$186$		0			0
$187$	−9.00000	−	15.5885i	−0.658145	−	1.13994i
$188$		0			0
$189$	−8.00000	+	6.92820i	−0.581914	+	0.503953i
$190$		0			0
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	−0.420096	−	0.907480i	$-0.638004\pi$
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	0.995948	−	0.0899262i	$-0.0286631\pi$
$194$		0			0
$195$	−2.00000			−0.143223
$196$		0			0
$197$	15.0000			1.06871			0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000			1.06871			0.534353	+	0.845262i	$0.320555\pi$
$198$		0			0
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$		0			0
$201$	8.00000	+	13.8564i	0.564276	+	0.977356i
$202$		0			0
$203$	12.0000	−	10.3923i	0.842235	−	0.729397i
$204$		0			0
$205$	−1.50000	−	2.59808i	−0.104765	−	0.181458i
$206$		0			0
$207$	4.50000	−	7.79423i	0.312772	−	0.541736i
$208$		0			0
$209$	−3.00000			−0.207514
$210$		0			0
$211$	−23.0000			−1.58339			−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000			−1.58339			−0.791693	+	0.610920i	$0.790800\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.00000	+	1.73205i	0.0681994	+	0.118125i
$216$		0			0
$217$	−4.00000	−	20.7846i	−0.271538	−	1.41095i
$218$		0			0
$219$	4.00000	+	6.92820i	0.270295	+	0.468165i
$220$		0			0
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$		0			0
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$		0			0
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$		0			0
$231$	15.0000	+	5.19615i	0.986928	+	0.341882i
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$		0			0
$237$	20.0000			1.29914
$238$		0			0
$239$	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	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$		0			0
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$		0			0
$245$	−6.50000	+	2.59808i	−0.415270	+	0.165985i
$246$		0			0
$247$	0.500000	+	0.866025i	0.0318142	+	0.0551039i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	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			0
$255$	6.00000	−	10.3923i	0.375735	−	0.650791i
$256$		0			0
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$	17.5000	+	6.06218i	1.08740	+	0.376685i
$260$		0			0
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$		0			0
$267$	12.0000			0.734388
$268$		0			0
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$		0			0
$273$	−1.00000	−	5.19615i	−0.0605228	−	0.314485i
$274$		0			0
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$		0			0
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$		0			0
$279$	−8.00000			−0.478947
$280$		0			0
$281$	−27.0000			−1.61068			−0.805342	−	0.592810i	$-0.798019\pi$
$281$	−27.0000			−1.61068			−0.805342	+	0.592810i	$0.798019\pi$
$282$		0			0
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$		0			0
$285$	−1.00000	−	1.73205i	−0.0592349	−	0.102598i
$286$		0			0
$287$	6.00000	−	5.19615i	0.354169	−	0.306719i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$	10.0000	−	17.3205i	0.586210	−	1.01535i
$292$		0			0
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−6.00000	+	10.3923i	−0.348155	+	0.603023i
$298$		0			0
$299$	−4.50000	−	7.79423i	−0.260242	−	0.450752i
$300$		0			0
$301$	−4.00000	+	3.46410i	−0.230556	+	0.199667i
$302$		0			0
$303$	−12.0000	−	20.7846i	−0.689382	−	1.19404i
$304$		0			0
$305$	−4.00000	+	6.92820i	−0.229039	+	0.396708i
$306$		0			0
$307$	−14.0000			−0.799022			−0.399511	−	0.916728i	$-0.630820\pi$
$307$	−14.0000			−0.799022			−0.399511	+	0.916728i	$0.630820\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	14.0000	+	24.2487i	0.791327	+	1.37062i	0.925146	+	0.379612i	$0.123943\pi$
$313$	14.0000	+	24.2487i	0.791327	+	1.37062i	−0.133819	+	0.991006i	$0.542724\pi$
$314$		0			0
$315$	0.500000	+	2.59808i	0.0281718	+	0.146385i
$316$		0			0
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$	24.0000			1.33955
$322$		0			0
$323$	−6.00000			−0.333849
$324$		0			0
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$		0			0
$327$	16.0000	+	27.7128i	0.884802	+	1.53252i
$328$		0			0
$329$	22.5000	+	7.79423i	1.24047	+	0.429710i
$330$		0			0
$331$	−3.50000	−	6.06218i	−0.192377	−	0.333207i	0.753660	−	0.657264i	$-0.228286\pi$
$331$	−3.50000	−	6.06218i	−0.192377	−	0.333207i	−0.946038	+	0.324057i	$0.894953\pi$
$332$		0			0
$333$	3.50000	−	6.06218i	0.191799	−	0.332205i
$334$		0			0
$335$	−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	$0.704518\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.0000	−	20.7846i	−0.649836	−	1.12555i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$	9.00000	+	15.5885i	0.484544	+	0.839254i
$346$		0			0
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$		0			0
$351$	4.00000			0.213504
$352$		0			0
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	−0.980352	−	0.197256i	$-0.936797\pi$
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	0.661004	+	0.750382i	$0.270130\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	30.0000	+	10.3923i	1.58777	+	0.550019i
$358$		0			0
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	0.999590	−	0.0286287i	$-0.00911406\pi$
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	−0.524588	+	0.851356i	$0.675781\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	−4.00000			−0.209946
$364$		0			0
$365$	−4.00000			−0.209370
$366$		0			0
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	−0.999989	−	0.00473247i	$-0.998494\pi$
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	0.504093	+	0.863649i	$0.331827\pi$
$368$		0			0
$369$	−1.50000	−	2.59808i	−0.0780869	−	0.135250i
$370$		0			0
$371$	4.50000	+	23.3827i	0.233628	+	1.21397i
$372$		0			0
$373$	−1.00000	−	1.73205i	−0.0517780	−	0.0896822i	0.838975	−	0.544170i	$-0.183156\pi$
$373$	−1.00000	−	1.73205i	−0.0517780	−	0.0896822i	−0.890753	+	0.454488i	$0.849822\pi$
$374$		0			0
$375$	−1.00000	+	1.73205i	−0.0516398	+	0.0894427i
$376$		0			0
$377$	−6.00000			−0.309016
$378$		0			0
$379$	−23.0000			−1.18143			−0.590715	−	0.806880i	$-0.701154\pi$
$379$	−23.0000			−1.18143			−0.590715	+	0.806880i	$0.701154\pi$
$380$		0			0
$381$	−1.00000	+	1.73205i	−0.0512316	+	0.0887357i
$382$		0			0
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	0.999088	+	0.0427020i	$0.0135966\pi$
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	−0.462563	+	0.886586i	$0.653070\pi$
$384$		0			0
$385$	−6.00000	+	5.19615i	−0.305788	+	0.264820i
$386$		0			0
$387$	1.00000	+	1.73205i	0.0508329	+	0.0880451i
$388$		0			0
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	−0.672874	−	0.739758i	$-0.734940\pi$
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	0.977086	+	0.212847i	$0.0682735\pi$
$390$		0			0
$391$	54.0000			2.73090
$392$		0			0
$393$	−6.00000			−0.302660
$394$		0			0
$395$	−5.00000	+	8.66025i	−0.251577	+	0.435745i
$396$		0			0
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$		0			0
$399$	4.00000	−	3.46410i	0.200250	−	0.173422i
$400$		0			0
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$		0			0
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$		0			0
$405$	−11.0000			−0.546594
$406$		0			0
$407$	21.0000			1.04093
$408$		0			0
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	0.341994	+	0.939702i	$0.388898\pi$
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	−0.984803	+	0.173675i	$0.944436\pi$
$410$		0			0
$411$	−12.0000	−	20.7846i	−0.591916	−	1.02523i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−4.00000	+	6.92820i	−0.195881	+	0.339276i
$418$		0			0
$419$	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	$0.484480\pi$
$422$		0			0
$423$	4.50000	−	7.79423i	0.218797	−	0.378968i
$424$		0			0
$425$	3.00000	+	5.19615i	0.145521	+	0.252050i
$426$		0			0
$427$	−20.0000	−	6.92820i	−0.967868	−	0.335279i
$428$		0			0
$429$	−3.00000	−	5.19615i	−0.144841	−	0.250873i
$430$		0			0
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	−40.0000			−1.92228			−0.961139	−	0.276066i	$-0.910969\pi$
$433$	−40.0000			−1.92228			−0.961139	+	0.276066i	$0.910969\pi$
$434$		0			0
$435$	12.0000			0.575356
$436$		0			0
$437$	4.50000	−	7.79423i	0.215264	−	0.372849i
$438$		0			0
$439$	13.0000	+	22.5167i	0.620456	+	1.07466i	0.989401	+	0.145210i	$0.0463858\pi$
$439$	13.0000	+	22.5167i	0.620456	+	1.07466i	−0.368945	+	0.929451i	$0.620281\pi$
$440$		0			0
$441$	−6.50000	+	2.59808i	−0.309524	+	0.123718i
$442$		0			0
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$		0			0
$445$	−3.00000	+	5.19615i	−0.142214	+	0.246321i
$446$		0			0
$447$	−12.0000			−0.567581
$448$		0			0
$449$	21.0000			0.991051			0.495526	−	0.868593i	$-0.334975\pi$
$449$	21.0000			0.991051			0.495526	+	0.868593i	$0.334975\pi$
$450$		0			0
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$		0			0
$453$	−10.0000	−	17.3205i	−0.469841	−	0.813788i
$454$		0			0
$455$	2.50000	+	0.866025i	0.117202	+	0.0405999i
$456$		0			0
$457$	−7.00000	−	12.1244i	−0.327446	−	0.567153i	0.654558	−	0.756012i	$-0.272855\pi$
$457$	−7.00000	−	12.1244i	−0.327446	−	0.567153i	−0.982004	+	0.188858i	$0.939521\pi$
$458$		0			0
$459$	−12.0000	+	20.7846i	−0.560112	+	0.970143i
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	1.00000			0.0464739			0.0232370	−	0.999730i	$-0.492603\pi$
$463$	1.00000			0.0464739			0.0232370	+	0.999730i	$0.492603\pi$
$464$		0			0
$465$	8.00000	−	13.8564i	0.370991	−	0.642575i
$466$		0			0
$467$	−3.00000	−	5.19615i	−0.138823	−	0.240449i	0.788228	−	0.615383i	$-0.210999\pi$
$467$	−3.00000	−	5.19615i	−0.138823	−	0.240449i	−0.927052	+	0.374934i	$0.877665\pi$
$468$		0			0
$469$	−4.00000	−	20.7846i	−0.184703	−	0.959744i
$470$		0			0
$471$	−23.0000	−	39.8372i	−1.05978	−	1.83560i
$472$		0			0
$473$	−3.00000	+	5.19615i	−0.137940	+	0.238919i
$474$		0			0
$475$	1.00000			0.0458831
$476$		0			0
$477$	9.00000			0.412082
$478$		0			0
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$	−3.50000	−	6.06218i	−0.159586	−	0.276412i
$482$		0			0
$483$	−36.0000	+	31.1769i	−1.63806	+	1.41860i
$484$		0			0
$485$	5.00000	+	8.66025i	0.227038	+	0.393242i
$486$		0			0
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$		0			0
$489$	−40.0000			−1.80886
$490$		0			0
$491$	−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			0
$495$	1.50000	+	2.59808i	0.0674200	+	0.116775i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$		0			0
$501$	3.00000	−	5.19615i	0.134030	−	0.232147i
$502$		0			0
$503$	−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
$506$		0			0
$507$	12.0000	−	20.7846i	0.532939	−	0.923077i
$508$		0			0
$509$	21.0000	+	36.3731i	0.930809	+	1.61221i	0.781943	+	0.623350i	$0.214229\pi$
$509$	21.0000	+	36.3731i	0.930809	+	1.61221i	0.148866	+	0.988857i	$0.452438\pi$
$510$		0			0
$511$	−2.00000	−	10.3923i	−0.0884748	−	0.459728i
$512$		0			0
$513$	2.00000	+	3.46410i	0.0883022	+	0.152944i
$514$		0			0
$515$	−2.00000	+	3.46410i	−0.0881305	+	0.152647i
$516$		0			0
$517$	27.0000			1.18746
$518$		0			0
$519$	18.0000			0.790112
$520$		0			0
$521$	7.50000	−	12.9904i	0.328581	−	0.569119i	−0.653650	−	0.756797i	$-0.726763\pi$
$521$	7.50000	−	12.9904i	0.328581	−	0.569119i	0.982231	+	0.187678i	$0.0600963\pi$
$522$		0			0
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	−0.990873	−	0.134801i	$-0.956961\pi$
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	0.378695	−	0.925521i	$-0.376373\pi$
$524$		0			0
$525$	−5.00000	−	1.73205i	−0.218218	−	0.0755929i
$526$		0			0
$527$	−24.0000	−	41.5692i	−1.04546	−	1.81078i
$528$		0			0
$529$	−29.0000	+	50.2295i	−1.26087	+	2.18389i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.00000			−0.129944
$534$		0			0
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$		0			0
$537$	−3.00000	−	5.19615i	−0.129460	−	0.224231i
$538$		0			0
$539$	−16.5000	−	12.9904i	−0.710705	−	0.559535i
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$		0			0
$543$	−2.00000	+	3.46410i	−0.0858282	+	0.148659i
$544$		0			0
$545$	−16.0000			−0.685365
$546$		0			0
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$		0			0
$549$	−4.00000	+	6.92820i	−0.170716	+	0.295689i
$550$		0			0
$551$	−3.00000	−	5.19615i	−0.127804	−	0.221364i
$552$		0			0
$553$	−25.0000	−	8.66025i	−1.06311	−	0.368271i
$554$		0			0
$555$	7.00000	+	12.1244i	0.297133	+	0.514650i
$556$		0			0
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	−0.754802	−	0.655953i	$-0.772267\pi$
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	0.945473	+	0.325701i	$0.105600\pi$
$558$		0			0
$559$	2.00000			0.0845910
$560$		0			0
$561$	36.0000			1.51992
$562$		0			0
$563$	21.0000	−	36.3731i	0.885044	−	1.53294i	0.0393818	−	0.999224i	$-0.487461\pi$
$563$	21.0000	−	36.3731i	0.885044	−	1.53294i	0.845663	−	0.533718i	$-0.179206\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−5.50000	−	28.5788i	−0.230978	−	1.20020i
$568$		0			0
$569$	−10.5000	−	18.1865i	−0.440183	−	0.762419i	0.557520	−	0.830164i	$-0.311753\pi$
$569$	−10.5000	−	18.1865i	−0.440183	−	0.762419i	−0.997703	+	0.0677445i	$0.978420\pi$
$570$		0			0
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	−0.577301	−	0.816532i	$-0.695894\pi$
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	0.995788	+	0.0916910i	$0.0292272\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$		0			0
$575$	−9.00000			−0.375326
$576$		0			0
$577$	−22.0000	+	38.1051i	−0.915872	+	1.58634i	−0.110252	+	0.993904i	$0.535166\pi$
$577$	−22.0000	+	38.1051i	−0.915872	+	1.58634i	−0.805620	+	0.592433i	$0.798167\pi$
$578$		0			0
$579$	16.0000	+	27.7128i	0.664937	+	1.15171i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	13.5000	+	23.3827i	0.559113	+	0.968412i
$584$		0			0
$585$	0.500000	−	0.866025i	0.0206725	−	0.0358057i
$586$		0			0
$587$	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
$591$	−15.0000	+	25.9808i	−0.617018	+	1.06871i
$592$		0			0
$593$	−12.0000	−	20.7846i	−0.492781	−	0.853522i	0.507184	−	0.861838i	$-0.330686\pi$
$593$	−12.0000	−	20.7846i	−0.492781	−	0.853522i	−0.999965	+	0.00831589i	$0.997353\pi$
$594$		0			0
$595$	−12.0000	+	10.3923i	−0.491952	+	0.426043i
$596$		0			0
$597$	−16.0000	−	27.7128i	−0.654836	−	1.13421i
$598$		0			0
$599$	−21.0000	+	36.3731i	−0.858037	+	1.48616i	0.0157622	+	0.999876i	$0.494983\pi$
$599$	−21.0000	+	36.3731i	−0.858037	+	1.48616i	−0.873799	+	0.486287i	$0.838351\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$		0			0
$603$	−8.00000			−0.325785
$604$		0			0
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	−0.500000	−	0.866025i	−0.0202944	−	0.0351509i	0.855700	−	0.517472i	$-0.173127\pi$
$607$	−0.500000	−	0.866025i	−0.0202944	−	0.0351509i	−0.875994	+	0.482322i	$0.839794\pi$
$608$		0			0
$609$	6.00000	+	31.1769i	0.243132	+	1.26335i
$610$		0			0
$611$	−4.50000	−	7.79423i	−0.182051	−	0.315321i
$612$		0			0
$613$	−14.5000	+	25.1147i	−0.585649	+	1.01437i	0.409145	+	0.912470i	$0.365827\pi$
$613$	−14.5000	+	25.1147i	−0.585649	+	1.01437i	−0.994794	+	0.101905i	$0.967506\pi$
$614$		0			0
$615$	6.00000			0.241943
$616$		0			0
$617$	−18.0000			−0.724653			−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000			−0.724653			−0.362326	+	0.932051i	$0.618017\pi$
$618$		0			0
$619$	11.5000	−	19.9186i	0.462224	−	0.800595i	−0.536847	−	0.843679i	$-0.680385\pi$
$619$	11.5000	−	19.9186i	0.462224	−	0.800595i	0.999071	+	0.0430838i	$0.0137183\pi$
$620$		0			0
$621$	−18.0000	−	31.1769i	−0.722315	−	1.25109i
$622$		0			0
$623$	−15.0000	−	5.19615i	−0.600962	−	0.208179i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$		0			0
$629$	42.0000			1.67465
$630$		0			0
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$		0			0
$633$	23.0000	−	39.8372i	0.914168	−	1.58339i
$634$		0			0
$635$	−0.500000	−	0.866025i	−0.0198419	−	0.0343672i
$636$		0			0
$637$	−1.00000	+	6.92820i	−0.0396214	+	0.274505i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	0.466029	+	0.884769i	$0.345684\pi$
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	−0.999247	+	0.0387913i	$0.987649\pi$
$642$		0			0
$643$	−2.00000			−0.0788723			−0.0394362	−	0.999222i	$-0.512556\pi$
$643$	−2.00000			−0.0788723			−0.0394362	+	0.999222i	$0.512556\pi$
$644$		0			0
$645$	−4.00000			−0.157500
$646$		0			0
$647$	16.5000	−	28.5788i	0.648682	−	1.12355i	−0.334756	−	0.942305i	$-0.608654\pi$
$647$	16.5000	−	28.5788i	0.648682	−	1.12355i	0.983438	−	0.181245i	$-0.0580128\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	40.0000	+	13.8564i	1.56772	+	0.543075i
$652$		0			0
$653$	4.50000	+	7.79423i	0.176099	+	0.305012i	0.940541	−	0.339680i	$-0.110319\pi$
$653$	4.50000	+	7.79423i	0.176099	+	0.305012i	−0.764442	+	0.644692i	$0.776986\pi$
$654$		0			0
$655$	1.50000	−	2.59808i	0.0586098	−	0.101515i
$656$		0			0
$657$	−4.00000			−0.156055
$658$		0			0
$659$	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	−0.454099	−	0.890951i	$-0.650039\pi$
$661$	14.0000	−	24.2487i	0.544537	−	0.943166i	0.998636	−	0.0522143i	$-0.0166279\pi$
$662$		0			0
$663$	−6.00000	−	10.3923i	−0.233021	−	0.403604i
$664$		0			0
$665$	0.500000	+	2.59808i	0.0193892	+	0.100749i
$666$		0			0
$667$	27.0000	+	46.7654i	1.04544	+	1.81076i
$668$		0			0
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$		0			0
$671$	−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	$0.727459\pi$
$674$		0			0
$675$	2.00000	−	3.46410i	0.0769800	−	0.133333i
$676$		0			0
$677$	4.50000	+	7.79423i	0.172949	+	0.299557i	0.939450	−	0.342687i	$-0.111337\pi$
$677$	4.50000	+	7.79423i	0.172949	+	0.299557i	−0.766501	+	0.642244i	$0.778004\pi$
$678$		0			0
$679$	−20.0000	+	17.3205i	−0.767530	+	0.664700i
$680$		0			0
$681$	−12.0000	−	20.7846i	−0.459841	−	0.796468i
$682$		0			0
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$	−8.00000			−0.305219
$688$		0			0
$689$	4.50000	−	7.79423i	0.171436	−	0.296936i
$690$		0			0
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	0.991460	+	0.130410i	$0.0416295\pi$
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	−0.382791	+	0.923835i	$0.625037\pi$
$692$		0			0
$693$	−6.00000	+	5.19615i	−0.227921	+	0.197386i
$694$		0			0
$695$	−2.00000	−	3.46410i	−0.0758643	−	0.131401i
$696$		0			0
$697$	9.00000	−	15.5885i	0.340899	−	0.590455i
$698$		0			0
$699$	−12.0000			−0.453882
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	3.50000	−	6.06218i	0.132005	−	0.228639i
$704$		0			0
$705$	9.00000	+	15.5885i	0.338960	+	0.587095i
$706$		0			0
$707$	6.00000	+	31.1769i	0.225653	+	1.17253i
$708$		0			0
$709$	23.0000	+	39.8372i	0.863783	+	1.49612i	0.868250	+	0.496126i	$0.165245\pi$
$709$	23.0000	+	39.8372i	0.863783	+	1.49612i	−0.00446726	+	0.999990i	$0.501422\pi$
$710$		0			0
$711$	−5.00000	+	8.66025i	−0.187515	+	0.324785i
$712$		0			0
$713$	72.0000			2.69642
$714$		0			0
$715$	3.00000			0.112194
$716$		0			0
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	−10.0000	−	3.46410i	−0.372419	−	0.129010i
$722$		0			0
$723$	1.00000	+	1.73205i	0.0371904	+	0.0644157i
$724$		0			0
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		0			0
$727$	1.00000			0.0370879			0.0185440	−	0.999828i	$-0.494097\pi$
$727$	1.00000			0.0370879			0.0185440	+	0.999828i	$0.494097\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−6.00000	+	10.3923i	−0.221918	+	0.384373i
$732$		0			0
$733$	21.5000	+	37.2391i	0.794121	+	1.37546i	0.923396	+	0.383849i	$0.125402\pi$
$733$	21.5000	+	37.2391i	0.794121	+	1.37546i	−0.129275	+	0.991609i	$0.541265\pi$
$734$		0			0
$735$	2.00000	−	13.8564i	0.0737711	−	0.511101i
$736$		0			0
$737$	−12.0000	−	20.7846i	−0.442026	−	0.765611i
$738$		0			0
$739$	17.5000	−	30.3109i	0.643748	−	1.11500i	−0.340841	−	0.940121i	$-0.610712\pi$
$739$	17.5000	−	30.3109i	0.643748	−	1.11500i	0.984589	−	0.174883i	$-0.0559548\pi$
$740$		0			0
$741$	−2.00000			−0.0734718
$742$		0			0
$743$	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
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−30.0000	−	10.3923i	−1.09618	−	0.379727i
$750$		0			0
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	0.760263	−	0.649616i	$-0.225070\pi$
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	−0.942715	+	0.333599i	$0.891737\pi$
$752$		0			0
$753$	−15.0000	+	25.9808i	−0.546630	+	0.946792i
$754$		0			0
$755$	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	$0.257361\pi$
$758$		0			0
$759$	−27.0000	+	46.7654i	−0.980038	+	1.69748i
$760$		0			0
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	0.999925	−	0.0122260i	$-0.00389175\pi$
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	−0.510551	+	0.859848i	$0.670558\pi$
$762$		0			0
$763$	−8.00000	−	41.5692i	−0.289619	−	1.50491i
$764$		0			0
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$		0			0
$767$		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	$0.363886\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	25.5000	−	44.1673i	0.917171	−	1.58859i	0.113480	−	0.993540i	$-0.463800\pi$
$773$	25.5000	−	44.1673i	0.917171	−	1.58859i	0.803691	−	0.595047i	$-0.202867\pi$
$774$		0			0
$775$	4.00000	+	6.92820i	0.143684	+	0.248868i
$776$		0			0
$777$	−28.0000	+	24.2487i	−1.00449	+	0.869918i
$778$		0			0
$779$	−1.50000	−	2.59808i	−0.0537431	−	0.0930857i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−24.0000			−0.857690
$784$		0			0
$785$	23.0000			0.820905
$786$		0			0
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	−0.992727	−	0.120384i	$-0.961587\pi$
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	0.600620	+	0.799535i	$0.294921\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.00000	+	6.92820i	0.142044	+	0.246028i
$794$		0			0
$795$	−9.00000	+	15.5885i	−0.319197	+	0.552866i
$796$		0			0
$797$	6.00000			0.212531			0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000			0.212531			0.106265	+	0.994338i	$0.466111\pi$
$798$		0			0
$799$	54.0000			1.91038
$800$		0			0
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$		0			0
$803$	−6.00000	−	10.3923i	−0.211735	−	0.366736i
$804$		0			0
$805$	−4.50000	−	23.3827i	−0.158604	−	0.824131i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	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
$811$	25.0000			0.877869			0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000			0.877869			0.438934	+	0.898519i	$0.355356\pi$
$812$		0			0
$813$	32.0000			1.12229
$814$		0			0
$815$	10.0000	−	17.3205i	0.350285	−	0.606711i
$816$		0			0
$817$	1.00000	+	1.73205i	0.0349856	+	0.0605968i
$818$		0			0
$819$	2.50000	+	0.866025i	0.0873571	+	0.0302614i
$820$		0			0
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$		0			0
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	−0.898776	−	0.438408i	$-0.855543\pi$
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	0.829060	+	0.559159i	$0.188876\pi$
$824$		0			0
$825$	−6.00000			−0.208893
$826$		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	−0.961601	−	0.274450i	$-0.911504\pi$
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	0.718481	+	0.695546i	$0.244838\pi$
$830$		0			0
$831$	10.0000	+	17.3205i	0.346896	+	0.600842i
$832$		0			0
$833$	−33.0000	−	25.9808i	−1.14338	−	0.900180i
$834$		0			0
$835$	1.50000	+	2.59808i	0.0519096	+	0.0899101i
$836$		0			0
$837$	−16.0000	+	27.7128i	−0.553041	+	0.957895i
$838$		0			0
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	27.0000	−	46.7654i	0.929929	−	1.61068i
$844$		0			0
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$		0			0
$847$	5.00000	+	1.73205i	0.171802	+	0.0595140i
$848$		0			0
$849$	14.0000	+	24.2487i	0.480479	+	0.832214i
$850$		0			0
$851$	−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	$0.605456\pi$
$854$		0			0
$855$	1.00000			0.0341993
$856$		0			0
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	0.998549	+	0.0538535i	$0.0171504\pi$
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	−0.452636	+	0.891695i	$0.649516\pi$
$860$		0			0
$861$	3.00000	+	15.5885i	0.102240	+	0.531253i
$862$		0			0
$863$	−1.50000	−	2.59808i	−0.0510606	−	0.0884395i	0.839365	−	0.543568i	$-0.182927\pi$
$863$	−1.50000	−	2.59808i	−0.0510606	−	0.0884395i	−0.890426	+	0.455128i	$0.849593\pi$
$864$		0			0
$865$	−4.50000	+	7.79423i	−0.153005	+	0.265012i
$866$		0			0
$867$	38.0000			1.29055
$868$		0			0
$869$	−30.0000			−1.01768
$870$		0			0
$871$	−4.00000	+	6.92820i	−0.135535	+	0.234753i
$872$		0			0
$873$	5.00000	+	8.66025i	0.169224	+	0.293105i
$874$		0			0
$875$	2.00000	−	1.73205i	0.0676123	−	0.0585540i
$876$		0			0
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	0.954652	−	0.297724i	$-0.0962275\pi$
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	−0.735163	+	0.677891i	$0.762894\pi$
$878$		0			0
$879$	9.00000	−	15.5885i	0.303562	−	0.525786i
$880$		0			0
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$		0			0
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	−0.915722	−	0.401813i	$-0.868380\pi$
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	0.109881	−	0.993945i	$-0.464953\pi$
$888$		0			0
$889$	2.00000	−	1.73205i	0.0670778	−	0.0580911i
$890$		0			0
$891$	−16.5000	−	28.5788i	−0.552771	−	0.957427i
$892$		0			0
$893$	4.50000	−	7.79423i	0.150587	−	0.260824i
$894$		0			0
$895$	3.00000			0.100279
$896$		0			0
$897$	18.0000			0.601003
$898$		0			0
$899$	24.0000	−	41.5692i	0.800445	−	1.38641i
$900$		0			0
$901$	27.0000	+	46.7654i	0.899500	+	1.55798i
$902$		0			0
$903$	−2.00000	−	10.3923i	−0.0665558	−	0.345834i
$904$		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	$-0.886426\pi$
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	0.770996	+	0.636841i	$0.219759\pi$
$908$		0			0
$909$	12.0000			0.398015
$910$		0			0
$911$	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
$914$		0			0
$915$	−8.00000	−	13.8564i	−0.264472	−	0.458079i
$916$		0			0
$917$	7.50000	+	2.59808i	0.247672	+	0.0857960i
$918$		0			0
$919$	−11.0000	−	19.0526i	−0.362857	−	0.628486i	0.625573	−	0.780165i	$-0.284865\pi$
$919$	−11.0000	−	19.0526i	−0.362857	−	0.628486i	−0.988430	+	0.151680i	$0.951532\pi$
$920$		0			0
$921$	14.0000	−	24.2487i	0.461316	−	0.799022i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−7.00000			−0.230159
$926$		0			0
$927$	−2.00000	+	3.46410i	−0.0656886	+	0.113776i
$928$		0			0
$929$	−28.5000	−	49.3634i	−0.935055	−	1.61956i	−0.774536	−	0.632529i	$-0.782017\pi$
$929$	−28.5000	−	49.3634i	−0.935055	−	1.61956i	−0.160518	−	0.987033i	$-0.551317\pi$
$930$		0			0
$931$	−6.50000	+	2.59808i	−0.213029	+	0.0851485i
$932$		0			0
$933$	−24.0000	−	41.5692i	−0.785725	−	1.36092i
$934$		0			0
$935$	−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	$0.552228\pi$
$938$		0			0
$939$	−56.0000			−1.82749
$940$		0			0
$941$	−24.0000	+	41.5692i	−0.782378	+	1.35512i	0.148176	+	0.988961i	$0.452660\pi$
$941$	−24.0000	+	41.5692i	−0.782378	+	1.35512i	−0.930553	+	0.366157i	$0.880673\pi$
$942$		0			0
$943$	13.5000	+	23.3827i	0.439620	+	0.761445i
$944$		0			0
$945$	10.0000	+	3.46410i	0.325300	+	0.112687i
$946$		0			0
$947$	3.00000	+	5.19615i	0.0974869	+	0.168852i	0.910644	−	0.413192i	$-0.135586\pi$
$947$	3.00000	+	5.19615i	0.0974869	+	0.168852i	−0.813157	+	0.582045i	$0.802253\pi$
$948$		0			0
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$		0			0
$951$	12.0000			0.389127
$952$		0			0
$953$	36.0000			1.16615			0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000			1.16615			0.583077	+	0.812417i	$0.301849\pi$
$954$		0			0
$955$	6.00000	−	10.3923i	0.194155	−	0.336287i
$956$		0			0
$957$	18.0000	+	31.1769i	0.581857	+	1.00781i
$958$		0			0
$959$	6.00000	+	31.1769i	0.193750	+	1.00676i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$		0			0
$965$	−16.0000			−0.515058
$966$		0			0
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$		0			0
$969$	6.00000	−	10.3923i	0.192748	−	0.333849i
$970$		0			0
$971$	−22.5000	−	38.9711i	−0.722059	−	1.25064i	−0.960173	−	0.279406i	$-0.909862\pi$
$971$	−22.5000	−	38.9711i	−0.722059	−	1.25064i	0.238114	−	0.971237i	$-0.423471\pi$
$972$		0			0
$973$	8.00000	−	6.92820i	0.256468	−	0.222108i
$974$		0			0
$975$	1.00000	+	1.73205i	0.0320256	+	0.0554700i
$976$		0			0
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	−0.305530	−	0.952183i	$-0.598833\pi$
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	0.977379	−	0.211495i	$-0.0678332\pi$
$978$		0			0
$979$	−18.0000			−0.575282
$980$		0			0
$981$	−16.0000			−0.510841
$982$		0			0
$983$	1.50000	−	2.59808i	0.0478426	−	0.0828658i	−0.841112	−	0.540860i	$-0.818099\pi$
$983$	1.50000	−	2.59808i	0.0478426	−	0.0828658i	0.888955	+	0.457995i	$0.151432\pi$
$984$		0			0
$985$	−7.50000	−	12.9904i	−0.238970	−	0.413908i
$986$		0			0
$987$	−36.0000	+	31.1769i	−1.14589	+	0.992372i
$988$		0			0
$989$	−9.00000	−	15.5885i	−0.286183	−	0.495684i
$990$		0			0
$991$	22.0000	−	38.1051i	0.698853	−	1.21045i	−0.270011	−	0.962857i	$-0.587027\pi$
$991$	22.0000	−	38.1051i	0.698853	−	1.21045i	0.968864	−	0.247592i	$-0.0796392\pi$
$992$		0			0
$993$	14.0000			0.444277
$994$		0			0
$995$	16.0000			0.507234
$996$		0			0
$997$	11.0000	−	19.0526i	0.348373	−	0.603401i	−0.637587	−	0.770378i	$-0.720067\pi$
$997$	11.0000	−	19.0526i	0.348373	−	0.603401i	0.985961	+	0.166978i	$0.0534008\pi$
$998$		0			0
$999$	−14.0000	−	24.2487i	−0.442940	−	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.q.b.81.1		2
4.3	odd	2		70.2.e.d.11.1	✓	2
7.2	even	3	inner	560.2.q.b.401.1		2
7.3	odd	6		3920.2.a.e.1.1		1
7.4	even	3		3920.2.a.bh.1.1		1
12.11	even	2		630.2.k.d.361.1		2
20.3	even	4		350.2.j.d.249.2		4
20.7	even	4		350.2.j.d.249.1		4
20.19	odd	2		350.2.e.b.151.1		2
28.3	even	6		490.2.a.d.1.1		1
28.11	odd	6		490.2.a.a.1.1		1
28.19	even	6		490.2.e.g.471.1		2
28.23	odd	6		70.2.e.d.51.1	yes	2
28.27	even	2		490.2.e.g.361.1		2
84.11	even	6		4410.2.a.x.1.1		1
84.23	even	6		630.2.k.d.541.1		2
84.59	odd	6		4410.2.a.bg.1.1		1
140.3	odd	12		2450.2.c.e.99.2		2
140.23	even	12		350.2.j.d.149.1		4
140.39	odd	6		2450.2.a.bf.1.1		1
140.59	even	6		2450.2.a.v.1.1		1
140.67	even	12		2450.2.c.q.99.1		2
140.79	odd	6		350.2.e.b.51.1		2
140.87	odd	12		2450.2.c.e.99.1		2
140.107	even	12		350.2.j.d.149.2		4
140.123	even	12		2450.2.c.q.99.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.d.11.1	✓	2	4.3	odd	2
70.2.e.d.51.1	yes	2	28.23	odd	6
350.2.e.b.51.1		2	140.79	odd	6
350.2.e.b.151.1		2	20.19	odd	2
350.2.j.d.149.1		4	140.23	even	12
350.2.j.d.149.2		4	140.107	even	12
350.2.j.d.249.1		4	20.7	even	4
350.2.j.d.249.2		4	20.3	even	4
490.2.a.a.1.1		1	28.11	odd	6
490.2.a.d.1.1		1	28.3	even	6
490.2.e.g.361.1		2	28.27	even	2
490.2.e.g.471.1		2	28.19	even	6
560.2.q.b.81.1		2	1.1	even	1	trivial
560.2.q.b.401.1		2	7.2	even	3	inner
630.2.k.d.361.1		2	12.11	even	2
630.2.k.d.541.1		2	84.23	even	6
2450.2.a.v.1.1		1	140.59	even	6
2450.2.a.bf.1.1		1	140.39	odd	6
2450.2.c.e.99.1		2	140.87	odd	12
2450.2.c.e.99.2		2	140.3	odd	12
2450.2.c.q.99.1		2	140.67	even	12
2450.2.c.q.99.2		2	140.123	even	12
3920.2.a.e.1.1		1	7.3	odd	6
3920.2.a.bh.1.1		1	7.4	even	3
4410.2.a.x.1.1		1	84.11	even	6
4410.2.a.bg.1.1		1	84.59	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +2.00000 q^{15} +(3.00000 - 5.19615i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(1.00000 + 5.19615i) q^{21} +(4.50000 + 7.79423i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{27} +6.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(3.00000 + 5.19615i) q^{33} +(-2.50000 - 0.866025i) q^{35} +(3.50000 + 6.06218i) q^{37} +(1.00000 - 1.73205i) q^{39} +3.00000 q^{41} -2.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(4.50000 + 7.79423i) q^{47} +(1.00000 - 6.92820i) q^{49} +(6.00000 + 10.3923i) q^{51} +(-4.50000 + 7.79423i) q^{53} -3.00000 q^{55} +2.00000 q^{57} +(-4.00000 - 6.92820i) q^{61} +(-2.50000 - 0.866025i) q^{63} +(0.500000 + 0.866025i) q^{65} +(4.00000 - 6.92820i) q^{67} -18.0000 q^{69} +(2.00000 - 3.46410i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(-1.50000 - 7.79423i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(5.50000 - 9.52628i) q^{81} -6.00000 q^{85} +(-6.00000 + 10.3923i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-2.00000 + 1.73205i) q^{91} +(8.00000 + 13.8564i) q^{93} +(-0.500000 + 0.866025i) q^{95} -10.0000 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - q^{5} + 4 q^{7} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - q^5 + 4 * q^7 - q^9	\( 2 q - 2 q^{3} - q^{5} + 4 q^{7} - q^{9} + 3 q^{11} - 2 q^{13} + 4 q^{15} + 6 q^{17} - q^{19} + 2 q^{21} + 9 q^{23} - q^{25} - 8 q^{27} + 12 q^{29} + 8 q^{31} + 6 q^{33} - 5 q^{35} + 7 q^{37} + 2 q^{39} + 6 q^{41} - 4 q^{43} - q^{45} + 9 q^{47} + 2 q^{49} + 12 q^{51} - 9 q^{53} - 6 q^{55} + 4 q^{57} - 8 q^{61} - 5 q^{63} + q^{65} + 8 q^{67} - 36 q^{69} + 4 q^{73} - 2 q^{75} - 3 q^{77} - 10 q^{79} + 11 q^{81} - 12 q^{85} - 12 q^{87} - 6 q^{89} - 4 q^{91} + 16 q^{93} - q^{95} - 20 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - q^5 + 4 * q^7 - q^9 + 3 * q^11 - 2 * q^13 + 4 * q^15 + 6 * q^17 - q^19 + 2 * q^21 + 9 * q^23 - q^25 - 8 * q^27 + 12 * q^29 + 8 * q^31 + 6 * q^33 - 5 * q^35 + 7 * q^37 + 2 * q^39 + 6 * q^41 - 4 * q^43 - q^45 + 9 * q^47 + 2 * q^49 + 12 * q^51 - 9 * q^53 - 6 * q^55 + 4 * q^57 - 8 * q^61 - 5 * q^63 + q^65 + 8 * q^67 - 36 * q^69 + 4 * q^73 - 2 * q^75 - 3 * q^77 - 10 * q^79 + 11 * q^81 - 12 * q^85 - 12 * q^87 - 6 * q^89 - 4 * q^91 + 16 * q^93 - q^95 - 20 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

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