LMFDB - Embedded newform 560.2.bw.d.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(289,560)]

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, 3, 2]))

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

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

chi := DirichletCharacter("560.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bw (of order $6$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	560.529
Dual form			560.2.bw.d.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	$q+(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} +5.00000i q^{13} +(1.73205 + 1.00000i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-6.06218 + 3.50000i) q^{23} +(-4.96410 + 0.598076i) q^{25} +4.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-4.23205 + 4.13397i) q^{35} +(0.866025 - 0.500000i) q^{37} +3.00000 q^{41} +2.00000i q^{43} +(5.59808 - 3.69615i) q^{45} +(6.06218 - 3.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(7.79423 + 4.50000i) q^{53} +(6.00000 + 3.00000i) q^{55} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(2.59808 - 7.50000i) q^{63} +(-11.1603 + 0.669873i) q^{65} +(1.73205 + 1.00000i) q^{67} +6.00000 q^{71} +(-13.8564 - 8.00000i) q^{73} +(7.79423 - 1.50000i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(-4.50000 + 7.79423i) q^{81} -6.00000i q^{83} +(-2.00000 + 4.00000i) q^{85} +(1.00000 + 1.73205i) q^{89} +(-10.0000 + 8.66025i) q^{91} +(-9.33013 + 6.16025i) q^{95} -12.0000i q^{97} -9.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5} - 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^5 - 6 * q^9	$ 4 q + 4 q^{5} - 6 q^{9} + 6 q^{11} + 10 q^{19} - 6 q^{25} + 16 q^{29} - 4 q^{31} - 10 q^{35} + 12 q^{41} + 12 q^{45} - 4 q^{49} + 24 q^{55} + 8 q^{59} - 12 q^{61} - 10 q^{65} + 24 q^{71} - 28 q^{79} - 18 q^{81} - 8 q^{85} + 4 q^{89} - 40 q^{91} - 20 q^{95} - 36 q^{99}+O(q^{100}) $ 4 * q + 4 * q^5 - 6 * q^9 + 6 * q^11 + 10 * q^19 - 6 * q^25 + 16 * q^29 - 4 * q^31 - 10 * q^35 + 12 * q^41 + 12 * q^45 - 4 * q^49 + 24 * q^55 + 8 * q^59 - 12 * q^61 - 10 * q^65 + 24 * q^71 - 28 * q^79 - 18 * q^81 - 8 * q^85 + 4 * q^89 - 40 * q^91 - 20 * q^95 - 36 * 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
$3$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$3$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$4$		0			0
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$		0			0
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$8$		0			0
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		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
$13$			5.00000i			1.38675i	0.720577	+	0.693375i	$0.243877\pi$
$13$			5.00000i			1.38675i	−0.720577	+	0.693375i	$0.756123\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.06218	+	3.50000i	−1.26405	+	0.729800i	−0.973856	−	0.227167i	$-0.927054\pi$
$23$	−6.06218	+	3.50000i	−1.26405	+	0.729800i	−0.290196	+	0.956967i	$0.593720\pi$
$24$		0			0
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.23205	+	4.13397i	−0.715347	+	0.698769i
$36$		0			0
$37$	0.866025	−	0.500000i	0.142374	−	0.0821995i	−0.427121	−	0.904194i	$-0.640472\pi$
$37$	0.866025	−	0.500000i	0.142374	−	0.0821995i	0.569495	+	0.821995i	$0.307139\pi$
$38$		0			0
$39$		0			0
$40$		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
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$		0			0
$45$	5.59808	−	3.69615i	0.834512	−	0.550990i
$46$		0			0
$47$	6.06218	−	3.50000i	0.884260	−	0.510527i	0.0121990	−	0.999926i	$-0.496117\pi$
$47$	6.06218	−	3.50000i	0.884260	−	0.510527i	0.872060	+	0.489398i	$0.162783\pi$
$48$		0			0
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.79423	+	4.50000i	1.07062	+	0.618123i	0.928351	−	0.371706i	$-0.121227\pi$
$53$	7.79423	+	4.50000i	1.07062	+	0.618123i	0.142269	+	0.989828i	$0.454560\pi$
$54$		0			0
$55$	6.00000	+	3.00000i	0.809040	+	0.404520i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	0.607535	−	0.794293i	$-0.292159\pi$
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	−0.991645	+	0.128994i	$0.958825\pi$
$62$		0			0
$63$	2.59808	−	7.50000i	0.327327	−	0.944911i
$64$		0			0
$65$	−11.1603	+	0.669873i	−1.38426	+	0.0830875i
$66$		0			0
$67$	1.73205	+	1.00000i	0.211604	+	0.122169i	0.602056	−	0.798454i	$-0.294348\pi$
$67$	1.73205	+	1.00000i	0.211604	+	0.122169i	−0.390453	+	0.920623i	$0.627682\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−13.8564	−	8.00000i	−1.62177	−	0.936329i	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−13.8564	−	8.00000i	−1.62177	−	0.936329i	−0.635323	−	0.772246i	$-0.719133\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.79423	−	1.50000i	0.888235	−	0.170941i
$78$		0			0
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	−0.927457	−	0.373930i	$-0.878010\pi$
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	0.139895	−	0.990166i	$-0.455323\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$		0			0
$85$	−2.00000	+	4.00000i	−0.216930	+	0.433861i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	0.914146	−	0.405385i	$-0.132862\pi$
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	−0.808146	+	0.588982i	$0.799529\pi$
$90$		0			0
$91$	−10.0000	+	8.66025i	−1.04828	+	0.907841i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−9.33013	+	6.16025i	−0.957251	+	0.632029i
$96$		0			0
$97$		−	12.0000i		−	1.21842i	−0.793011	−	0.609208i	$-0.791488\pi$
$97$		−	12.0000i		−	1.21842i	0.793011	−	0.609208i	$-0.208512\pi$
$98$		0			0
$99$	−9.00000			−0.904534
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−6.92820	+	4.00000i	−0.682656	+	0.394132i	−0.800855	−	0.598858i	$-0.795621\pi$
$103$	−6.92820	+	4.00000i	−0.682656	+	0.394132i	0.118199	+	0.992990i	$0.462288\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	13.8564	−	8.00000i	1.33955	−	0.773389i	0.352809	−	0.935695i	$-0.385227\pi$
$107$	13.8564	−	8.00000i	1.33955	−	0.773389i	0.986740	+	0.162306i	$0.0518932\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	14.0000i		−	1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$		−	14.0000i		−	1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$		0			0
$115$	−8.62436	−	13.0622i	−0.804225	−	1.21805i
$116$		0			0
$117$	12.9904	−	7.50000i	1.20096	−	0.693375i
$118$		0			0
$119$	1.00000	+	5.19615i	0.0916698	+	0.476331i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$		−	7.00000i		−	0.621150i	−0.950549	−	0.310575i	$-0.899478\pi$
$127$		−	7.00000i		−	0.621150i	0.950549	−	0.310575i	$-0.100522\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	0.843356	−	0.537355i	$-0.180577\pi$
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	−0.887041	+	0.461690i	$0.847243\pi$
$132$		0			0
$133$	−4.33013	+	12.5000i	−0.375470	+	1.08389i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.92820	+	4.00000i	0.591916	+	0.341743i	0.765855	−	0.643013i	$-0.222316\pi$
$137$	6.92820	+	4.00000i	0.591916	+	0.341743i	−0.173939	+	0.984757i	$0.555649\pi$
$138$		0			0
$139$	16.0000			1.35710			0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000			1.35710			0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	12.9904	+	7.50000i	1.08631	+	0.627182i
$144$		0			0
$145$	0.535898	+	8.92820i	0.0445039	+	0.741447i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	−0.961888	−	0.273442i	$-0.911838\pi$
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	0.717752	+	0.696299i	$0.245171\pi$
$152$		0			0
$153$		−	6.00000i		−	0.485071i
$154$		0			0
$155$	−4.00000	−	2.00000i	−0.321288	−	0.160644i
$156$		0			0
$157$	7.79423	+	4.50000i	0.622047	+	0.359139i	0.777666	−	0.628678i	$-0.216404\pi$
$157$	7.79423	+	4.50000i	0.622047	+	0.359139i	−0.155618	+	0.987817i	$0.549737\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−17.5000	−	6.06218i	−1.37919	−	0.477767i
$162$		0			0
$163$	−10.3923	+	6.00000i	−0.813988	+	0.469956i	−0.848339	−	0.529454i	$-0.822397\pi$
$163$	−10.3923	+	6.00000i	−0.813988	+	0.469956i	0.0343508	+	0.999410i	$0.489064\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	15.0000i		−	1.16073i	−0.814355	−	0.580367i	$-0.802909\pi$
$167$		−	15.0000i		−	1.16073i	0.814355	−	0.580367i	$-0.197091\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	7.50000	−	12.9904i	0.573539	−	0.993399i
$172$		0			0
$173$	−7.79423	+	4.50000i	−0.592584	+	0.342129i	−0.766119	−	0.642699i	$-0.777815\pi$
$173$	−7.79423	+	4.50000i	−0.592584	+	0.342129i	0.173534	+	0.984828i	$0.444481\pi$
$174$		0			0
$175$	−9.79423	−	8.89230i	−0.740374	−	0.672195i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.50000	+	11.2583i	−0.485833	+	0.841487i	−0.999867	−	0.0162823i	$-0.994817\pi$
$179$	−6.50000	+	11.2583i	−0.485833	+	0.841487i	0.514035	+	0.857769i	$0.328150\pi$
$180$		0			0
$181$	26.0000			1.93256			0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000			1.93256			0.966282	+	0.257485i	$0.0828937\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.23205	+	1.86603i	0.0905822	+	0.137193i
$186$		0			0
$187$	5.19615	−	3.00000i	0.379980	−	0.219382i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.0000	−	17.3205i	−0.723575	−	1.25327i	−0.959558	−	0.281511i	$-0.909164\pi$
$191$	−10.0000	−	17.3205i	−0.723575	−	1.25327i	0.235983	−	0.971757i	$-0.424169\pi$
$192$		0			0
$193$	−8.66025	−	5.00000i	−0.623379	−	0.359908i	0.154805	−	0.987945i	$-0.450525\pi$
$193$	−8.66025	−	5.00000i	−0.623379	−	0.359908i	−0.778183	+	0.628037i	$0.783859\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.00000i		−	0.356235i	−0.984009	−	0.178118i	$-0.942999\pi$
$197$		−	5.00000i		−	0.356235i	0.984009	−	0.178118i	$-0.0570008\pi$
$198$		0			0
$199$	−9.00000	+	15.5885i	−0.637993	+	1.10504i	0.347879	+	0.937539i	$0.386902\pi$
$199$	−9.00000	+	15.5885i	−0.637993	+	1.10504i	−0.985873	+	0.167497i	$0.946431\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.92820	+	8.00000i	0.486265	+	0.561490i
$204$		0			0
$205$	0.401924	+	6.69615i	0.0280716	+	0.467680i
$206$		0			0
$207$	18.1865	+	10.5000i	1.26405	+	0.729800i
$208$		0			0
$209$	15.0000			1.03757
$210$		0			0
$211$	9.00000			0.619586			0.309793	−	0.950804i	$-0.399740\pi$
$211$	9.00000			0.619586			0.309793	+	0.950804i	$0.399740\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.46410	+	0.267949i	−0.304449	+	0.0182740i
$216$		0			0
$217$	−5.19615	+	1.00000i	−0.352738	+	0.0678844i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.00000	+	8.66025i	−0.336336	+	0.582552i
$222$		0			0
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$		0			0
$225$	9.00000	+	12.0000i	0.600000	+	0.800000i
$226$		0			0
$227$	−5.19615	−	3.00000i	−0.344881	−	0.199117i	0.317547	−	0.948242i	$-0.397141\pi$
$227$	−5.19615	−	3.00000i	−0.344881	−	0.199117i	−0.662428	+	0.749125i	$0.730474\pi$
$228$		0			0
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	0.999442	+	0.0334101i	$0.0106368\pi$
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	−0.470787	+	0.882247i	$0.656030\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.92820	−	4.00000i	0.453882	−	0.262049i	−0.255586	−	0.966786i	$-0.582269\pi$
$233$	6.92820	−	4.00000i	0.453882	−	0.262049i	0.709468	+	0.704737i	$0.248935\pi$
$234$		0			0
$235$	8.62436	+	13.0622i	0.562591	+	0.852083i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	4.50000	−	7.79423i	0.289870	−	0.502070i	−0.683908	−	0.729568i	$-0.739721\pi$
$241$	4.50000	−	7.79423i	0.289870	−	0.502070i	0.973779	+	0.227498i	$0.0730544\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−15.5981	−	1.30385i	−0.996525	−	0.0832998i
$246$		0			0
$247$	−21.6506	+	12.5000i	−1.37760	+	0.795356i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−5.00000			−0.315597			−0.157799	−	0.987471i	$-0.550440\pi$
$251$	−5.00000			−0.315597			−0.157799	+	0.987471i	$0.550440\pi$
$252$		0			0
$253$			21.0000i			1.32026i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.19615	+	3.00000i	−0.324127	+	0.187135i	−0.653231	−	0.757159i	$-0.726587\pi$
$257$	−5.19615	+	3.00000i	−0.324127	+	0.187135i	0.329104	+	0.944294i	$0.393253\pi$
$258$		0			0
$259$	2.50000	+	0.866025i	0.155342	+	0.0538122i
$260$		0			0
$261$	−6.00000	−	10.3923i	−0.371391	−	0.643268i
$262$		0			0
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$	−9.00000	+	18.0000i	−0.552866	+	1.10573i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.00000	+	8.66025i	−0.304855	+	0.528025i	−0.977229	−	0.212187i	$-0.931941\pi$
$269$	−5.00000	+	8.66025i	−0.304855	+	0.528025i	0.672374	+	0.740212i	$0.265275\pi$
$270$		0			0
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	0.957328	+	0.289003i	$0.0933238\pi$
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	−0.228380	+	0.973572i	$0.573343\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.89230	+	13.7942i	−0.355319	+	0.831823i
$276$		0			0
$277$	1.73205	+	1.00000i	0.104069	+	0.0600842i	0.551131	−	0.834419i	$-0.314196\pi$
$277$	1.73205	+	1.00000i	0.104069	+	0.0600842i	−0.447062	+	0.894503i	$0.647530\pi$
$278$		0			0
$279$	6.00000			0.359211
$280$		0			0
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$		0			0
$283$	−12.1244	−	7.00000i	−0.720718	−	0.416107i	0.0942988	−	0.995544i	$-0.469939\pi$
$283$	−12.1244	−	7.00000i	−0.720718	−	0.416107i	−0.815017	+	0.579437i	$0.803272\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.19615	+	6.00000i	0.306719	+	0.354169i
$288$		0			0
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			9.00000i			0.525786i	0.964825	+	0.262893i	$0.0846766\pi$
$293$			9.00000i			0.525786i	−0.964825	+	0.262893i	$0.915323\pi$
$294$		0			0
$295$	8.00000	+	4.00000i	0.465778	+	0.232889i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−17.5000	−	30.3109i	−1.01205	−	1.75292i
$300$		0			0
$301$	−4.00000	+	3.46410i	−0.230556	+	0.199667i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	11.1962	−	7.39230i	0.641090	−	0.423282i
$306$		0			0
$307$			22.0000i			1.25561i	0.778372	+	0.627803i	$0.216046\pi$
$307$			22.0000i			1.25561i	−0.778372	+	0.627803i	$0.783954\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	19.0526	−	11.0000i	1.07691	−	0.621757i	0.146852	−	0.989158i	$-0.453086\pi$
$313$	19.0526	−	11.0000i	1.07691	−	0.621757i	0.930062	+	0.367402i	$0.119753\pi$
$314$		0			0
$315$	17.0885	+	4.79423i	0.962825	+	0.270124i
$316$		0			0
$317$	−1.73205	+	1.00000i	−0.0972817	+	0.0561656i	−0.547852	−	0.836576i	$-0.684554\pi$
$317$	−1.73205	+	1.00000i	−0.0972817	+	0.0561656i	0.450570	+	0.892741i	$0.351221\pi$
$318$		0			0
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			10.0000i			0.556415i
$324$		0			0
$325$	−2.99038	−	24.8205i	−0.165876	−	1.37679i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	17.5000	+	6.06218i	0.964806	+	0.334219i
$330$		0			0
$331$	2.50000	+	4.33013i	0.137412	+	0.238005i	0.926516	−	0.376254i	$-0.122788\pi$
$331$	2.50000	+	4.33013i	0.137412	+	0.238005i	−0.789104	+	0.614260i	$0.789455\pi$
$332$		0			0
$333$	−2.59808	−	1.50000i	−0.142374	−	0.0821995i
$334$		0			0
$335$	−2.00000	+	4.00000i	−0.109272	+	0.218543i
$336$		0			0
$337$			10.0000i			0.544735i	0.962193	+	0.272367i	$0.0878066\pi$
$337$			10.0000i			0.544735i	−0.962193	+	0.272367i	$0.912193\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.00000	+	5.19615i	0.162459	+	0.281387i
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	0.194409	−	0.980921i	$-0.437721\pi$
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	−0.752297	+	0.658824i	$0.771054\pi$
$348$		0			0
$349$	12.0000			0.642345			0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000			0.642345			0.321173	+	0.947021i	$0.395923\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	20.7846	+	12.0000i	1.10625	+	0.638696i	0.937856	−	0.347024i	$-0.112808\pi$
$353$	20.7846	+	12.0000i	1.10625	+	0.638696i	0.168397	+	0.985719i	$0.446141\pi$
$354$		0			0
$355$	0.803848	+	13.3923i	0.0426638	+	0.710790i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.00000	−	13.8564i	−0.422224	−	0.731313i	0.573933	−	0.818902i	$-0.305417\pi$
$359$	−8.00000	−	13.8564i	−0.422224	−	0.731313i	−0.996157	+	0.0875892i	$0.972084\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	16.0000	−	32.0000i	0.837478	−	1.67496i
$366$		0			0
$367$	11.2583	+	6.50000i	0.587680	+	0.339297i	0.764180	−	0.645003i	$-0.223144\pi$
$367$	11.2583	+	6.50000i	0.587680	+	0.339297i	−0.176500	+	0.984301i	$0.556477\pi$
$368$		0			0
$369$	−4.50000	−	7.79423i	−0.234261	−	0.405751i
$370$		0			0
$371$	4.50000	+	23.3827i	0.233628	+	1.21397i
$372$		0			0
$373$	−22.5167	+	13.0000i	−1.16587	+	0.673114i	−0.952703	−	0.303902i	$-0.901711\pi$
$373$	−22.5167	+	13.0000i	−1.16587	+	0.673114i	−0.213165	+	0.977016i	$0.568377\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			20.0000i			1.03005i
$378$		0			0
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.0427020	−	0.999088i	$-0.486403\pi$
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.886586	+	0.462563i	$0.153070\pi$
$384$		0			0
$385$	4.39230	+	17.1962i	0.223853	+	0.876397i
$386$		0			0
$387$	5.19615	−	3.00000i	0.264135	−	0.152499i
$388$		0			0
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$	−14.0000			−0.708010
$392$		0			0
$393$		0			0
$394$		0			0
$395$	26.1244	−	17.2487i	1.31446	−	0.867877i
$396$		0			0
$397$	−12.1244	+	7.00000i	−0.608504	+	0.351320i	−0.772380	−	0.635161i	$-0.780934\pi$
$397$	−12.1244	+	7.00000i	−0.608504	+	0.351320i	0.163876	+	0.986481i	$0.447600\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		0			0
$403$	−8.66025	−	5.00000i	−0.431398	−	0.249068i
$404$		0			0
$405$	−18.0000	−	9.00000i	−0.894427	−	0.447214i
$406$		0			0
$407$		−	3.00000i		−	0.148704i
$408$		0			0
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.3923	−	2.00000i	0.511372	−	0.0984136i
$414$		0			0
$415$	13.3923	−	0.803848i	0.657402	−	0.0394593i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	35.0000			1.70986			0.854931	−	0.518742i	$-0.173599\pi$
$419$	35.0000			1.70986			0.854931	+	0.518742i	$0.173599\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$		0			0
$423$	−18.1865	−	10.5000i	−0.884260	−	0.510527i
$424$		0			0
$425$	−9.19615	−	3.92820i	−0.446079	−	0.190546i
$426$		0			0
$427$	5.19615	−	15.0000i	0.251459	−	0.725901i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.00000	−	1.73205i	0.0481683	−	0.0834300i	−0.840936	−	0.541135i	$-0.817995\pi$
$431$	1.00000	−	1.73205i	0.0481683	−	0.0834300i	0.889104	+	0.457705i	$0.151328\pi$
$432$		0			0
$433$		−	28.0000i		−	1.34559i	−0.739827	−	0.672797i	$-0.765093\pi$
$433$		−	28.0000i		−	1.34559i	0.739827	−	0.672797i	$-0.234907\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−30.3109	−	17.5000i	−1.44997	−	0.837139i
$438$		0			0
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$	19.5000	−	7.79423i	0.928571	−	0.371154i
$442$		0			0
$443$	25.9808	−	15.0000i	1.23438	−	0.712672i	0.266443	−	0.963851i	$-0.414152\pi$
$443$	25.9808	−	15.0000i	1.23438	−	0.712672i	0.967941	+	0.251179i	$0.0808184\pi$
$444$		0			0
$445$	−3.73205	+	2.46410i	−0.176916	+	0.116810i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−5.00000			−0.235965			−0.117982	−	0.993016i	$-0.537643\pi$
$449$	−5.00000			−0.235965			−0.117982	+	0.993016i	$0.537643\pi$
$450$		0			0
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−20.6699	−	21.1603i	−0.969019	−	0.992008i
$456$		0			0
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	−0.688686	−	0.725059i	$-0.741812\pi$
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	0.283577	+	0.958950i	$0.408479\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−32.0000			−1.49039			−0.745194	−	0.666847i	$-0.767643\pi$
$461$	−32.0000			−1.49039			−0.745194	+	0.666847i	$0.767643\pi$
$462$		0			0
$463$		−	17.0000i		−	0.790057i	−0.918669	−	0.395029i	$-0.870735\pi$
$463$		−	17.0000i		−	0.790057i	0.918669	−	0.395029i	$-0.129265\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−29.4449	+	17.0000i	−1.36255	+	0.786666i	−0.989962	−	0.141332i	$-0.954861\pi$
$467$	−29.4449	+	17.0000i	−1.36255	+	0.786666i	−0.372584	+	0.927999i	$0.621528\pi$
$468$		0			0
$469$	1.00000	+	5.19615i	0.0461757	+	0.239936i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.19615	+	3.00000i	0.238919	+	0.137940i
$474$		0			0
$475$	−15.0000	−	20.0000i	−0.688247	−	0.917663i
$476$		0			0
$477$		−	27.0000i		−	1.23625i
$478$		0			0
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	0.0814184	+	0.996680i	$0.474055\pi$
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	−0.903859	+	0.427830i	$0.859278\pi$
$480$		0			0
$481$	2.50000	+	4.33013i	0.113990	+	0.197437i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	26.7846	−	1.60770i	1.21623	−	0.0730017i
$486$		0			0
$487$	−27.7128	−	16.0000i	−1.25579	−	0.725029i	−0.283535	−	0.958962i	$-0.591507\pi$
$487$	−27.7128	−	16.0000i	−1.25579	−	0.725029i	−0.972253	+	0.233933i	$0.924840\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−24.0000			−1.08310			−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000			−1.08310			−0.541552	+	0.840667i	$0.682163\pi$
$492$		0			0
$493$	6.92820	+	4.00000i	0.312031	+	0.180151i
$494$		0			0
$495$	−1.20577	−	20.0885i	−0.0541954	−	0.902909i
$496$		0			0
$497$	10.3923	+	12.0000i	0.466159	+	0.538274i
$498$		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
$501$		0			0
$502$		0			0
$503$			40.0000i			1.78351i	0.452517	+	0.891756i	$0.350526\pi$
$503$			40.0000i			1.78351i	−0.452517	+	0.891756i	$0.649474\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−17.0000	−	29.4449i	−0.753512	−	1.30512i	−0.946111	−	0.323843i	$-0.895025\pi$
$509$	−17.0000	−	29.4449i	−0.753512	−	1.30512i	0.192599	−	0.981278i	$-0.438308\pi$
$510$		0			0
$511$	−8.00000	−	41.5692i	−0.353899	−	1.83891i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.85641	−	14.9282i	−0.434325	−	0.657815i
$516$		0			0
$517$		−	21.0000i		−	0.923579i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.5000	−	23.3827i	0.591446	−	1.02441i	−0.402592	−	0.915379i	$-0.631891\pi$
$521$	13.5000	−	23.3827i	0.591446	−	1.02441i	0.994038	−	0.109035i	$-0.0347759\pi$
$522$		0			0
$523$	13.8564	−	8.00000i	0.605898	−	0.349816i	−0.165460	−	0.986216i	$-0.552911\pi$
$523$	13.8564	−	8.00000i	0.605898	−	0.349816i	0.771358	+	0.636401i	$0.219578\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.46410	+	2.00000i	−0.150899	+	0.0871214i
$528$		0			0
$529$	13.0000	−	22.5167i	0.565217	−	0.978985i
$530$		0			0
$531$	−12.0000			−0.520756
$532$		0			0
$533$			15.0000i			0.649722i
$534$		0			0
$535$	19.7128	+	29.8564i	0.852259	+	1.29081i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	16.5000	+	12.9904i	0.710705	+	0.559535i
$540$		0			0
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	0.985162	−	0.171628i	$-0.0549027\pi$
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	−0.641215	+	0.767361i	$0.721569\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.00000	+	2.00000i	0.171341	+	0.0856706i
$546$		0			0
$547$			26.0000i			1.11168i	0.831289	+	0.555840i	$0.187603\pi$
$547$			26.0000i			1.11168i	−0.831289	+	0.555840i	$0.812397\pi$
$548$		0			0
$549$	−9.00000	+	15.5885i	−0.384111	+	0.665299i
$550$		0			0
$551$	10.0000	+	17.3205i	0.426014	+	0.737878i
$552$		0			0
$553$	12.1244	−	35.0000i	0.515580	−	1.48835i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.9186	−	11.5000i	−0.843978	−	0.487271i	0.0146368	−	0.999893i	$-0.495341\pi$
$557$	−19.9186	−	11.5000i	−0.843978	−	0.487271i	−0.858614	+	0.512622i	$0.828674\pi$
$558$		0			0
$559$	−10.0000			−0.422955
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.73205	−	1.00000i	−0.0729972	−	0.0421450i	0.463057	−	0.886328i	$-0.346752\pi$
$563$	−1.73205	−	1.00000i	−0.0729972	−	0.0421450i	−0.536054	+	0.844183i	$0.680086\pi$
$564$		0			0
$565$	31.2487	−	1.87564i	1.31464	−	0.0789090i
$566$		0			0
$567$	−23.3827	+	4.50000i	−0.981981	+	0.188982i
$568$		0			0
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	0.664897	−	0.746935i	$-0.268475\pi$
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	−0.979313	+	0.202350i	$0.935142\pi$
$570$		0			0
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	−0.308443	−	0.951243i	$-0.599808\pi$
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	0.978022	−	0.208502i	$-0.0668588\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	28.0000	−	21.0000i	1.16768	−	0.875761i
$576$		0			0
$577$	3.46410	+	2.00000i	0.144212	+	0.0832611i	0.570370	−	0.821388i	$-0.306800\pi$
$577$	3.46410	+	2.00000i	0.144212	+	0.0832611i	−0.426158	+	0.904649i	$0.640133\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	12.0000	−	10.3923i	0.497844	−	0.431145i
$582$		0			0
$583$	23.3827	−	13.5000i	0.968412	−	0.559113i
$584$		0			0
$585$	18.4808	+	27.9904i	0.764085	+	1.15726i
$586$		0			0
$587$		−	34.0000i		−	1.40333i	−0.712507	−	0.701665i	$-0.752440\pi$
$587$		−	34.0000i		−	1.40333i	0.712507	−	0.701665i	$-0.247560\pi$
$588$		0			0
$589$	−10.0000			−0.412043
$590$		0			0
$591$		0			0
$592$		0			0
$593$	5.19615	−	3.00000i	0.213380	−	0.123195i	−0.389501	−	0.921026i	$-0.627353\pi$
$593$	5.19615	−	3.00000i	0.213380	−	0.123195i	0.602881	+	0.797831i	$0.294019\pi$
$594$		0			0
$595$	−11.4641	+	2.92820i	−0.469982	+	0.120045i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		0			0
$603$		−	6.00000i		−	0.244339i
$604$		0			0
$605$	−3.73205	+	2.46410i	−0.151729	+	0.100180i
$606$		0			0
$607$	11.2583	−	6.50000i	0.456962	−	0.263827i	−0.253804	−	0.967256i	$-0.581682\pi$
$607$	11.2583	−	6.50000i	0.456962	−	0.263827i	0.710766	+	0.703429i	$0.248349\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	17.5000	+	30.3109i	0.707974	+	1.22625i
$612$		0			0
$613$	−12.9904	−	7.50000i	−0.524677	−	0.302922i	0.214169	−	0.976797i	$-0.431296\pi$
$613$	−12.9904	−	7.50000i	−0.524677	−	0.302922i	−0.738846	+	0.673874i	$0.764629\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			14.0000i			0.563619i	0.959470	+	0.281809i	$0.0909346\pi$
$617$			14.0000i			0.563619i	−0.959470	+	0.281809i	$0.909065\pi$
$618$		0			0
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	−0.991325	−	0.131434i	$-0.958042\pi$
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	0.609488	+	0.792796i	$0.291375\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.73205	+	5.00000i	−0.0693932	+	0.200321i
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.00000			0.0797452
$630$		0			0
$631$	18.0000			0.716569			0.358284	−	0.933613i	$-0.383362\pi$
$631$	18.0000			0.716569			0.358284	+	0.933613i	$0.383362\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	15.6244	−	0.937822i	0.620034	−	0.0372163i
$636$		0			0
$637$	−34.6410	−	5.00000i	−1.37253	−	0.198107i
$638$		0			0
$639$	−9.00000	−	15.5885i	−0.356034	−	0.616670i
$640$		0			0
$641$	2.50000	−	4.33013i	0.0987441	−	0.171030i	−0.812421	−	0.583071i	$-0.801851\pi$
$641$	2.50000	−	4.33013i	0.0987441	−	0.171030i	0.911165	+	0.412042i	$0.135184\pi$
$642$		0			0
$643$		−	14.0000i		−	0.552106i	−0.961142	−	0.276053i	$-0.910973\pi$
$643$		−	14.0000i		−	0.552106i	0.961142	−	0.276053i	$-0.0890266\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−23.3827	−	13.5000i	−0.919268	−	0.530740i	−0.0358667	−	0.999357i	$-0.511419\pi$
$647$	−23.3827	−	13.5000i	−0.919268	−	0.530740i	−0.883402	+	0.468617i	$0.844753\pi$
$648$		0			0
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	−0.549973	−	0.835182i	$-0.685362\pi$
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	0.448303	+	0.893882i	$0.352029\pi$
$654$		0			0
$655$	1.86603	−	1.23205i	0.0729116	−	0.0481402i
$656$		0			0
$657$			48.0000i			1.87266i
$658$		0			0
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	−8.00000	+	13.8564i	−0.311164	+	0.538952i	−0.978615	−	0.205702i	$-0.934052\pi$
$661$	−8.00000	+	13.8564i	−0.311164	+	0.538952i	0.667451	+	0.744654i	$0.267385\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−28.4808	−	7.99038i	−1.10444	−	0.309854i
$666$		0			0
$667$	−24.2487	+	14.0000i	−0.938914	+	0.542082i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−18.0000			−0.694882
$672$		0			0
$673$		−	32.0000i		−	1.23351i	−0.787155	−	0.616755i	$-0.788447\pi$
$673$		−	32.0000i		−	1.23351i	0.787155	−	0.616755i	$-0.211553\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.7224	+	8.50000i	−0.565829	+	0.326682i	−0.755482	−	0.655170i	$-0.772597\pi$
$677$	−14.7224	+	8.50000i	−0.565829	+	0.326682i	0.189653	+	0.981851i	$0.439264\pi$
$678$		0			0
$679$	24.0000	−	20.7846i	0.921035	−	0.797640i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	38.1051	+	22.0000i	1.45805	+	0.841807i	0.998916	−	0.0465592i	$-0.0148256\pi$
$683$	38.1051	+	22.0000i	1.45805	+	0.841807i	0.459136	+	0.888366i	$0.348159\pi$
$684$		0			0
$685$	−8.00000	+	16.0000i	−0.305664	+	0.611329i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−22.5000	+	38.9711i	−0.857182	+	1.48468i
$690$		0			0
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	0.0555386	−	0.998457i	$-0.482312\pi$
$692$		0			0
$693$	−15.5885	−	18.0000i	−0.592157	−	0.683763i
$694$		0			0
$695$	2.14359	+	35.7128i	0.0813111	+	1.35466i
$696$		0			0
$697$	5.19615	+	3.00000i	0.196818	+	0.113633i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	26.0000			0.982006			0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000			0.982006			0.491003	+	0.871158i	$0.336630\pi$
$702$		0			0
$703$	4.33013	+	2.50000i	0.163314	+	0.0942893i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	6.00000	+	10.3923i	0.225335	+	0.390291i	0.956420	−	0.291995i	$-0.0943191\pi$
$709$	6.00000	+	10.3923i	0.225335	+	0.390291i	−0.731085	+	0.682286i	$0.760986\pi$
$710$		0			0
$711$	−21.0000	+	36.3731i	−0.787562	+	1.36410i
$712$		0			0
$713$		−	14.0000i		−	0.524304i
$714$		0			0
$715$	−15.0000	+	30.0000i	−0.560968	+	1.12194i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−13.0000	−	22.5167i	−0.484818	−	0.839730i	0.515030	−	0.857172i	$-0.327781\pi$
$719$	−13.0000	−	22.5167i	−0.484818	−	0.839730i	−0.999848	+	0.0174426i	$0.994448\pi$
$720$		0			0
$721$	−20.0000	−	6.92820i	−0.744839	−	0.258020i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−19.8564	+	2.39230i	−0.737448	+	0.0888480i
$726$		0			0
$727$			29.0000i			1.07555i	0.843088	+	0.537775i	$0.180735\pi$
$727$			29.0000i			1.07555i	−0.843088	+	0.537775i	$0.819265\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−2.00000	+	3.46410i	−0.0739727	+	0.128124i
$732$		0			0
$733$	−35.5070	+	20.5000i	−1.31148	+	0.757185i	−0.982342	−	0.187096i	$-0.940092\pi$
$733$	−35.5070	+	20.5000i	−1.31148	+	0.757185i	−0.329141	+	0.944281i	$0.606759\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.19615	−	3.00000i	0.191403	−	0.110506i
$738$		0			0
$739$	14.5000	−	25.1147i	0.533391	−	0.923861i	−0.465848	−	0.884865i	$-0.654251\pi$
$739$	14.5000	−	25.1147i	0.533391	−	0.923861i	0.999239	−	0.0389959i	$-0.0124159\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	21.0000i		−	0.770415i	−0.922830	−	0.385208i	$-0.874130\pi$
$743$		−	21.0000i		−	0.770415i	0.922830	−	0.385208i	$-0.125870\pi$
$744$		0			0
$745$	33.5885	−	22.1769i	1.23059	−	0.812499i
$746$		0			0
$747$	−15.5885	+	9.00000i	−0.570352	+	0.329293i
$748$		0			0
$749$	40.0000	+	13.8564i	1.46157	+	0.506302i
$750$		0			0
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	0.999921	+	0.0125942i	$0.00400897\pi$
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	−0.489053	+	0.872254i	$0.662658\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−12.0000	−	6.00000i	−0.436725	−	0.218362i
$756$		0			0
$757$			42.0000i			1.52652i	0.646094	+	0.763258i	$0.276401\pi$
$757$			42.0000i			1.52652i	−0.646094	+	0.763258i	$0.723599\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.500000	−	0.866025i	−0.0181250	−	0.0313934i	0.856821	−	0.515615i	$-0.172436\pi$
$761$	−0.500000	−	0.866025i	−0.0181250	−	0.0313934i	−0.874946	+	0.484221i	$0.839103\pi$
$762$		0			0
$763$	5.19615	−	1.00000i	0.188113	−	0.0362024i
$764$		0			0
$765$	13.3923	−	0.803848i	0.484200	−	0.0290632i
$766$		0			0
$767$	17.3205	+	10.0000i	0.625407	+	0.361079i
$768$		0			0
$769$	29.0000			1.04577			0.522883	−	0.852404i	$-0.324856\pi$
$769$	29.0000			1.04577			0.522883	+	0.852404i	$0.324856\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	38.9711	+	22.5000i	1.40169	+	0.809269i	0.994567	−	0.104102i	$-0.0331970\pi$
$773$	38.9711	+	22.5000i	1.40169	+	0.809269i	0.407128	+	0.913371i	$0.366530\pi$
$774$		0			0
$775$	3.92820	−	9.19615i	0.141105	−	0.330336i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	7.50000	+	12.9904i	0.268715	+	0.465429i
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−9.00000	+	18.0000i	−0.321224	+	0.642448i
$786$		0			0
$787$	15.5885	+	9.00000i	0.555668	+	0.320815i	0.751405	−	0.659841i	$-0.229376\pi$
$787$	15.5885	+	9.00000i	0.555668	+	0.320815i	−0.195737	+	0.980656i	$0.562710\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	28.0000	−	24.2487i	0.995565	−	0.862185i
$792$		0			0
$793$	25.9808	−	15.0000i	0.922604	−	0.532666i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	2.00000i		−	0.0708436i	−0.999372	−	0.0354218i	$-0.988723\pi$
$797$		−	2.00000i		−	0.0708436i	0.999372	−	0.0354218i	$-0.0112775\pi$
$798$		0			0
$799$	14.0000			0.495284
$800$		0			0
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$		0			0
$803$	−41.5692	+	24.0000i	−1.46695	+	0.846942i
$804$		0			0
$805$	11.1865	−	39.8731i	0.394273	−	1.40534i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−2.50000	+	4.33013i	−0.0878953	+	0.152239i	−0.906621	−	0.421945i	$-0.861347\pi$
$809$	−2.50000	+	4.33013i	−0.0878953	+	0.152239i	0.818726	+	0.574184i	$0.194681\pi$
$810$		0			0
$811$	33.0000			1.15879			0.579393	−	0.815048i	$-0.303290\pi$
$811$	33.0000			1.15879			0.579393	+	0.815048i	$0.303290\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−14.7846	−	22.3923i	−0.517882	−	0.784368i
$816$		0			0
$817$	−8.66025	+	5.00000i	−0.302984	+	0.174928i
$818$		0			0
$819$	37.5000	+	12.9904i	1.31036	+	0.453921i
$820$		0			0
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$		0			0
$823$	20.7846	+	12.0000i	0.724506	+	0.418294i	0.816409	−	0.577474i	$-0.195962\pi$
$823$	20.7846	+	12.0000i	0.724506	+	0.418294i	−0.0919029	+	0.995768i	$0.529295\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			22.0000i			0.765015i	0.923952	+	0.382507i	$0.124939\pi$
$827$			22.0000i			0.765015i	−0.923952	+	0.382507i	$0.875061\pi$
$828$		0			0
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	−0.998480	−	0.0551154i	$-0.982447\pi$
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	0.546971	+	0.837151i	$0.315781\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−8.66025	+	11.0000i	−0.300060	+	0.381127i
$834$		0			0
$835$	33.4808	−	2.00962i	1.15865	−	0.0695457i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−34.0000			−1.17381			−0.586905	−	0.809656i	$-0.699654\pi$
$839$	−34.0000			−1.17381			−0.586905	+	0.809656i	$0.699654\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.60770	−	26.7846i	−0.0553064	−	0.921419i
$846$		0			0
$847$	−1.73205	+	5.00000i	−0.0595140	+	0.171802i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.50000	+	6.06218i	−0.119978	+	0.207809i
$852$		0			0
$853$			43.0000i			1.47229i	0.676823	+	0.736146i	$0.263356\pi$
$853$			43.0000i			1.47229i	−0.676823	+	0.736146i	$0.736644\pi$
$854$		0			0
$855$	30.0000	+	15.0000i	1.02598	+	0.512989i
$856$		0			0
$857$	−6.92820	−	4.00000i	−0.236663	−	0.136637i	0.376979	−	0.926222i	$-0.376963\pi$
$857$	−6.92820	−	4.00000i	−0.236663	−	0.136637i	−0.613642	+	0.789584i	$0.710296\pi$
$858$		0			0
$859$	6.00000	+	10.3923i	0.204717	+	0.354581i	0.950043	−	0.312120i	$-0.101039\pi$
$859$	6.00000	+	10.3923i	0.204717	+	0.354581i	−0.745325	+	0.666701i	$0.767706\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.52628	+	5.50000i	−0.324278	+	0.187222i	−0.653298	−	0.757101i	$-0.726615\pi$
$863$	−9.52628	+	5.50000i	−0.324278	+	0.187222i	0.329020	+	0.944323i	$0.393282\pi$
$864$		0			0
$865$	−11.0885	−	16.7942i	−0.377019	−	0.571021i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−42.0000			−1.42475
$870$		0			0
$871$	−5.00000	+	8.66025i	−0.169419	+	0.293442i
$872$		0			0
$873$	−31.1769	+	18.0000i	−1.05518	+	0.609208i
$874$		0			0
$875$	18.5359	−	23.0526i	0.626628	−	0.779319i
$876$		0			0
$877$	26.8468	−	15.5000i	0.906552	−	0.523398i	0.0272316	−	0.999629i	$-0.491331\pi$
$877$	26.8468	−	15.5000i	0.906552	−	0.523398i	0.879320	+	0.476231i	$0.157998\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−15.0000			−0.505363			−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000			−0.505363			−0.252681	+	0.967550i	$0.581312\pi$
$882$		0			0
$883$			16.0000i			0.538443i	0.963078	+	0.269221i	$0.0867663\pi$
$883$			16.0000i			0.538443i	−0.963078	+	0.269221i	$0.913234\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−31.1769	+	18.0000i	−1.04682	+	0.604381i	−0.921757	−	0.387768i	$-0.873246\pi$
$887$	−31.1769	+	18.0000i	−1.04682	+	0.604381i	−0.125061	+	0.992149i	$0.539913\pi$
$888$		0			0
$889$	14.0000	−	12.1244i	0.469545	−	0.406638i
$890$		0			0
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$		0			0
$893$	30.3109	+	17.5000i	1.01432	+	0.585615i
$894$		0			0
$895$	−26.0000	−	13.0000i	−0.869084	−	0.434542i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.00000	+	6.92820i	−0.133407	+	0.231069i
$900$		0			0
$901$	9.00000	+	15.5885i	0.299833	+	0.519327i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.48334	+	58.0333i	0.115790	+	1.92909i
$906$		0			0
$907$	−34.6410	−	20.0000i	−1.15024	−	0.664089i	−0.201291	−	0.979531i	$-0.564514\pi$
$907$	−34.6410	−	20.0000i	−1.15024	−	0.664089i	−0.948945	+	0.315442i	$0.897847\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−2.00000			−0.0662630			−0.0331315	−	0.999451i	$-0.510548\pi$
$911$	−2.00000			−0.0662630			−0.0331315	+	0.999451i	$0.510548\pi$
$912$		0			0
$913$	−15.5885	−	9.00000i	−0.515903	−	0.297857i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.866025	−	2.50000i	0.0285987	−	0.0825573i
$918$		0			0
$919$	−10.0000	−	17.3205i	−0.329870	−	0.571351i	0.652616	−	0.757689i	$-0.273671\pi$
$919$	−10.0000	−	17.3205i	−0.329870	−	0.571351i	−0.982486	+	0.186338i	$0.940338\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			30.0000i			0.987462i
$924$		0			0
$925$	−4.00000	+	3.00000i	−0.131519	+	0.0986394i
$926$		0			0
$927$	20.7846	+	12.0000i	0.682656	+	0.394132i
$928$		0			0
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	0.985262	−	0.171054i	$-0.0547172\pi$
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	−0.640768	+	0.767735i	$0.721384\pi$
$930$		0			0
$931$	−32.5000	+	12.9904i	−1.06514	+	0.425743i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	7.39230	+	11.1962i	0.241754	+	0.366153i
$936$		0			0
$937$		−	26.0000i		−	0.849383i	−0.905338	−	0.424691i	$-0.860383\pi$
$937$		−	26.0000i		−	0.849383i	0.905338	−	0.424691i	$-0.139617\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	14.0000	−	24.2487i	0.456387	−	0.790485i	−0.542380	−	0.840133i	$-0.682477\pi$
$941$	14.0000	−	24.2487i	0.456387	−	0.790485i	0.998767	+	0.0496480i	$0.0158099\pi$
$942$		0			0
$943$	−18.1865	+	10.5000i	−0.592235	+	0.341927i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	−0.321552	−	0.946892i	$-0.604204\pi$
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	0.659256	+	0.751918i	$0.270871\pi$
$948$		0			0
$949$	40.0000	−	69.2820i	1.29845	−	2.24899i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			24.0000i			0.777436i	0.921357	+	0.388718i	$0.127082\pi$
$953$			24.0000i			0.777436i	−0.921357	+	0.388718i	$0.872918\pi$
$954$		0			0
$955$	37.3205	−	24.6410i	1.20766	−	0.797365i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.00000	+	20.7846i	0.129167	+	0.671170i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$		0			0
$963$	−41.5692	−	24.0000i	−1.33955	−	0.773389i
$964$		0			0
$965$	10.0000	−	20.0000i	0.321911	−	0.643823i
$966$		0			0
$967$		−	32.0000i		−	1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$967$		−	32.0000i		−	1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	−0.999408	−	0.0344175i	$-0.989042\pi$
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	0.469897	−	0.882721i	$-0.344291\pi$
$972$		0			0
$973$	27.7128	+	32.0000i	0.888432	+	1.02587i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−46.7654	−	27.0000i	−1.49616	−	0.863807i	−0.496167	−	0.868227i	$-0.665259\pi$
$977$	−46.7654	−	27.0000i	−1.49616	−	0.863807i	−0.999990	+	0.00442082i	$0.998593\pi$
$978$		0			0
$979$	6.00000			0.191761
$980$		0			0
$981$	−6.00000			−0.191565
$982$		0			0
$983$	25.1147	+	14.5000i	0.801036	+	0.462478i	0.843833	−	0.536606i	$-0.180294\pi$
$983$	25.1147	+	14.5000i	0.801036	+	0.462478i	−0.0427975	+	0.999084i	$0.513627\pi$
$984$		0			0
$985$	11.1603	−	0.669873i	0.355595	−	0.0213439i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.00000	−	12.1244i	−0.222587	−	0.385532i
$990$		0			0
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	−0.922538	−	0.385906i	$-0.873889\pi$
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	0.795474	+	0.605988i	$0.207222\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−36.0000	−	18.0000i	−1.14128	−	0.570638i
$996$		0			0
$997$	32.9090	+	19.0000i	1.04224	+	0.601736i	0.920466	−	0.390822i	$-0.127809\pi$
$997$	32.9090	+	19.0000i	1.04224	+	0.601736i	0.121771	+	0.992558i	$0.461143\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bw.d.529.1		4
4.3	odd	2		70.2.i.b.39.2	yes	4
5.4	even	2	inner	560.2.bw.d.529.2		4
7.2	even	3	inner	560.2.bw.d.289.2		4
12.11	even	2		630.2.u.a.109.1		4
20.3	even	4		350.2.e.c.151.1		2
20.7	even	4		350.2.e.j.151.1		2
20.19	odd	2		70.2.i.b.39.1	yes	4
28.3	even	6		490.2.c.d.99.2		2
28.11	odd	6		490.2.c.a.99.2		2
28.19	even	6		490.2.i.a.79.1		4
28.23	odd	6		70.2.i.b.9.1	✓	4
28.27	even	2		490.2.i.a.459.2		4
35.9	even	6	inner	560.2.bw.d.289.1		4
60.59	even	2		630.2.u.a.109.2		4
84.23	even	6		630.2.u.a.289.2		4
140.3	odd	12		2450.2.a.bb.1.1		1
140.19	even	6		490.2.i.a.79.2		4
140.23	even	12		350.2.e.c.51.1		2
140.39	odd	6		490.2.c.a.99.1		2
140.59	even	6		490.2.c.d.99.1		2
140.67	even	12		2450.2.a.k.1.1		1
140.79	odd	6		70.2.i.b.9.2	yes	4
140.87	odd	12		2450.2.a.j.1.1		1
140.107	even	12		350.2.e.j.51.1		2
140.123	even	12		2450.2.a.ba.1.1		1
140.139	even	2		490.2.i.a.459.1		4
420.359	even	6		630.2.u.a.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.b.9.1	✓	4	28.23	odd	6
70.2.i.b.9.2	yes	4	140.79	odd	6
70.2.i.b.39.1	yes	4	20.19	odd	2
70.2.i.b.39.2	yes	4	4.3	odd	2
350.2.e.c.51.1		2	140.23	even	12
350.2.e.c.151.1		2	20.3	even	4
350.2.e.j.51.1		2	140.107	even	12
350.2.e.j.151.1		2	20.7	even	4
490.2.c.a.99.1		2	140.39	odd	6
490.2.c.a.99.2		2	28.11	odd	6
490.2.c.d.99.1		2	140.59	even	6
490.2.c.d.99.2		2	28.3	even	6
490.2.i.a.79.1		4	28.19	even	6
490.2.i.a.79.2		4	140.19	even	6
490.2.i.a.459.1		4	140.139	even	2
490.2.i.a.459.2		4	28.27	even	2
560.2.bw.d.289.1		4	35.9	even	6	inner
560.2.bw.d.289.2		4	7.2	even	3	inner
560.2.bw.d.529.1		4	1.1	even	1	trivial
560.2.bw.d.529.2		4	5.4	even	2	inner
630.2.u.a.109.1		4	12.11	even	2
630.2.u.a.109.2		4	60.59	even	2
630.2.u.a.289.1		4	420.359	even	6
630.2.u.a.289.2		4	84.23	even	6
2450.2.a.j.1.1		1	140.87	odd	12
2450.2.a.k.1.1		1	140.67	even	12
2450.2.a.ba.1.1		1	140.123	even	12
2450.2.a.bb.1.1		1	140.3	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bw (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} +5.00000i q^{13} +(1.73205 + 1.00000i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-6.06218 + 3.50000i) q^{23} +(-4.96410 + 0.598076i) q^{25} +4.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-4.23205 + 4.13397i) q^{35} +(0.866025 - 0.500000i) q^{37} +3.00000 q^{41} +2.00000i q^{43} +(5.59808 - 3.69615i) q^{45} +(6.06218 - 3.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(7.79423 + 4.50000i) q^{53} +(6.00000 + 3.00000i) q^{55} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(2.59808 - 7.50000i) q^{63} +(-11.1603 + 0.669873i) q^{65} +(1.73205 + 1.00000i) q^{67} +6.00000 q^{71} +(-13.8564 - 8.00000i) q^{73} +(7.79423 - 1.50000i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(-4.50000 + 7.79423i) q^{81} -6.00000i q^{83} +(-2.00000 + 4.00000i) q^{85} +(1.00000 + 1.73205i) q^{89} +(-10.0000 + 8.66025i) q^{91} +(-9.33013 + 6.16025i) q^{95} -12.0000i q^{97} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} - 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^5 - 6 * q^9	\( 4 q + 4 q^{5} - 6 q^{9} + 6 q^{11} + 10 q^{19} - 6 q^{25} + 16 q^{29} - 4 q^{31} - 10 q^{35} + 12 q^{41} + 12 q^{45} - 4 q^{49} + 24 q^{55} + 8 q^{59} - 12 q^{61} - 10 q^{65} + 24 q^{71} - 28 q^{79} - 18 q^{81} - 8 q^{85} + 4 q^{89} - 40 q^{91} - 20 q^{95} - 36 q^{99}+O(q^{100}) \) 4 * q + 4 * q^5 - 6 * q^9 + 6 * q^11 + 10 * q^19 - 6 * q^25 + 16 * q^29 - 4 * q^31 - 10 * q^35 + 12 * q^41 + 12 * q^45 - 4 * q^49 + 24 * q^55 + 8 * q^59 - 12 * q^61 - 10 * q^65 + 24 * q^71 - 28 * q^79 - 18 * q^81 - 8 * q^85 + 4 * q^89 - 40 * q^91 - 20 * q^95 - 36 * q^99

Introduction

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