LMFDB - Embedded newform 560.2.bw.d.529.2

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			529.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	560.529
Dual form			560.2.bw.d.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86603 + 1.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	$q+(1.86603 + 1.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} -5.00000i q^{13} +(-1.73205 - 1.00000i) q^{17} +(2.50000 + 4.33013i) q^{19} +(6.06218 - 3.50000i) q^{23} +(1.96410 + 4.59808i) q^{25} +4.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-0.767949 - 5.86603i) q^{35} +(-0.866025 + 0.500000i) q^{37} +3.00000 q^{41} -2.00000i q^{43} +(0.401924 - 6.69615i) q^{45} +(-6.06218 + 3.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-7.79423 - 4.50000i) q^{53} +(6.00000 - 3.00000i) q^{55} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(-2.59808 + 7.50000i) q^{63} +(6.16025 - 9.33013i) q^{65} +(-1.73205 - 1.00000i) q^{67} +6.00000 q^{71} +(13.8564 + 8.00000i) q^{73} +(-7.79423 + 1.50000i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(-4.50000 + 7.79423i) q^{81} +6.00000i q^{83} +(-2.00000 - 4.00000i) q^{85} +(1.00000 + 1.73205i) q^{89} +(-10.0000 + 8.66025i) q^{91} +(-0.669873 + 11.1603i) q^{95} +12.0000i q^{97} -9.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$6$		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	$-0.756123\pi$
$13$		−	5.00000i		−	1.38675i	0.720577	−	0.693375i	$-0.243877\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$		0			0
$19$	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	0.290196	−	0.956967i	$-0.406280\pi$
$23$	6.06218	−	3.50000i	1.26405	−	0.729800i	0.973856	+	0.227167i	$0.0729463\pi$
$24$		0			0
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$		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
$35$	−0.767949	−	5.86603i	−0.129807	−	0.991539i
$36$		0			0
$37$	−0.866025	+	0.500000i	−0.142374	+	0.0821995i	−0.569495	−	0.821995i	$-0.692861\pi$
$37$	−0.866025	+	0.500000i	−0.142374	+	0.0821995i	0.427121	+	0.904194i	$0.359528\pi$
$38$		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	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$		0			0
$45$	0.401924	−	6.69615i	0.0599153	−	0.998203i
$46$		0			0
$47$	−6.06218	+	3.50000i	−0.884260	+	0.510527i	−0.872060	−	0.489398i	$-0.837217\pi$
$47$	−6.06218	+	3.50000i	−0.884260	+	0.510527i	−0.0121990	+	0.999926i	$0.503883\pi$
$48$		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	−0.142269	−	0.989828i	$-0.545440\pi$
$53$	−7.79423	−	4.50000i	−1.07062	−	0.618123i	−0.928351	+	0.371706i	$0.878773\pi$
$54$		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
$65$	6.16025	−	9.33013i	0.764085	−	1.15726i
$66$		0			0
$67$	−1.73205	−	1.00000i	−0.211604	−	0.122169i	0.390453	−	0.920623i	$-0.372318\pi$
$67$	−1.73205	−	1.00000i	−0.211604	−	0.122169i	−0.602056	+	0.798454i	$0.705652\pi$
$68$		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	$0.0524664\pi$
$73$	13.8564	+	8.00000i	1.62177	+	0.936329i	0.635323	+	0.772246i	$0.280867\pi$
$74$		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	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		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
$95$	−0.669873	+	11.1603i	−0.0687275	+	1.14502i
$96$		0			0
$97$			12.0000i			1.21842i	0.793011	+	0.609208i	$0.208512\pi$
$97$			12.0000i			1.21842i	−0.793011	+	0.609208i	$0.791488\pi$
$98$		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	−0.118199	−	0.992990i	$-0.537712\pi$
$103$	6.92820	−	4.00000i	0.682656	−	0.394132i	0.800855	+	0.598858i	$0.204379\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.8564	+	8.00000i	−1.33955	+	0.773389i	−0.986740	−	0.162306i	$-0.948107\pi$
$107$	−13.8564	+	8.00000i	−1.33955	+	0.773389i	−0.352809	+	0.935695i	$0.614773\pi$
$108$		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	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$	15.6244	+	0.937822i	1.45698	+	0.0874524i
$116$		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	$0.100522\pi$
$127$			7.00000i			0.621150i	−0.950549	+	0.310575i	$0.899478\pi$
$128$		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	0.173939	−	0.984757i	$-0.444351\pi$
$137$	−6.92820	−	4.00000i	−0.591916	−	0.341743i	−0.765855	+	0.643013i	$0.777684\pi$
$138$		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
$145$	7.46410	+	4.92820i	0.619860	+	0.409265i
$146$		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	0.155618	−	0.987817i	$-0.450263\pi$
$157$	−7.79423	−	4.50000i	−0.622047	−	0.359139i	−0.777666	+	0.628678i	$0.783596\pi$
$158$		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	−0.0343508	−	0.999410i	$-0.510936\pi$
$163$	10.3923	−	6.00000i	0.813988	−	0.469956i	0.848339	+	0.529454i	$0.177603\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			15.0000i			1.16073i	0.814355	+	0.580367i	$0.197091\pi$
$167$			15.0000i			1.16073i	−0.814355	+	0.580367i	$0.802909\pi$
$168$		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	−0.173534	−	0.984828i	$-0.555519\pi$
$173$	7.79423	−	4.50000i	0.592584	−	0.342129i	0.766119	+	0.642699i	$0.222185\pi$
$174$		0			0
$175$	5.79423	−	11.8923i	0.438003	−	0.898974i
$176$		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
$185$	−2.23205	−	0.133975i	−0.164104	−	0.00985001i
$186$		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	0.778183	−	0.628037i	$-0.216141\pi$
$193$	8.66025	+	5.00000i	0.623379	+	0.359908i	−0.154805	+	0.987945i	$0.549475\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			5.00000i			0.356235i	0.984009	+	0.178118i	$0.0570008\pi$
$197$			5.00000i			0.356235i	−0.984009	+	0.178118i	$0.942999\pi$
$198$		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
$205$	5.59808	+	3.69615i	0.390987	+	0.258150i
$206$		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
$215$	2.46410	−	3.73205i	0.168050	−	0.254524i
$216$		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	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$		0			0
$225$	9.00000	−	12.0000i	0.600000	−	0.800000i
$226$		0			0
$227$	5.19615	+	3.00000i	0.344881	+	0.199117i	0.662428	−	0.749125i	$-0.269526\pi$
$227$	5.19615	+	3.00000i	0.344881	+	0.199117i	−0.317547	+	0.948242i	$0.602859\pi$
$228$		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	−0.709468	−	0.704737i	$-0.751065\pi$
$233$	−6.92820	+	4.00000i	−0.453882	+	0.262049i	0.255586	+	0.966786i	$0.417731\pi$
$234$		0			0
$235$	−15.6244	−	0.937822i	−1.01922	−	0.0611768i
$236$		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
$245$	−10.4019	+	11.6962i	−0.664555	+	0.747240i
$246$		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	−0.329104	−	0.944294i	$-0.606747\pi$
$257$	5.19615	−	3.00000i	0.324127	−	0.187135i	0.653231	+	0.757159i	$0.273413\pi$
$258$		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
$275$	14.8923	+	1.79423i	0.898040	+	0.108196i
$276$		0			0
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	0.447062	−	0.894503i	$-0.352470\pi$
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	−0.551131	+	0.834419i	$0.685804\pi$
$278$		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	0.815017	−	0.579437i	$-0.196728\pi$
$283$	12.1244	+	7.00000i	0.720718	+	0.416107i	−0.0942988	+	0.995544i	$0.530061\pi$
$284$		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	$-0.915323\pi$
$293$		−	9.00000i		−	0.525786i	0.964825	−	0.262893i	$-0.0846766\pi$
$294$		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
$305$	0.803848	−	13.3923i	0.0460282	−	0.766841i
$306$		0			0
$307$		−	22.0000i		−	1.25561i	−0.778372	−	0.627803i	$-0.783954\pi$
$307$		−	22.0000i		−	1.25561i	0.778372	−	0.627803i	$-0.216046\pi$
$308$		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	−0.930062	−	0.367402i	$-0.880247\pi$
$313$	−19.0526	+	11.0000i	−1.07691	+	0.621757i	−0.146852	+	0.989158i	$0.546914\pi$
$314$		0			0
$315$	−14.0885	+	10.7942i	−0.793795	+	0.608186i
$316$		0			0
$317$	1.73205	−	1.00000i	0.0972817	−	0.0561656i	−0.450570	−	0.892741i	$-0.648779\pi$
$317$	1.73205	−	1.00000i	0.0972817	−	0.0561656i	0.547852	+	0.836576i	$0.315446\pi$
$318$		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
$325$	22.9904	−	9.82051i	1.27528	−	0.544744i
$326$		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	$-0.912193\pi$
$337$		−	10.0000i		−	0.544735i	0.962193	−	0.272367i	$-0.0878066\pi$
$338$		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	0.752297	−	0.658824i	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$		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	−0.168397	−	0.985719i	$-0.553859\pi$
$353$	−20.7846	−	12.0000i	−1.10625	−	0.638696i	−0.937856	+	0.347024i	$0.887192\pi$
$354$		0			0
$355$	11.1962	+	7.39230i	0.594230	+	0.392343i
$356$		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	0.176500	−	0.984301i	$-0.443523\pi$
$367$	−11.2583	−	6.50000i	−0.587680	−	0.339297i	−0.764180	+	0.645003i	$0.776856\pi$
$368$		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	0.213165	−	0.977016i	$-0.431623\pi$
$373$	22.5167	−	13.0000i	1.16587	−	0.673114i	0.952703	+	0.303902i	$0.0982894\pi$
$374$		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	−0.886586	−	0.462563i	$-0.846930\pi$
$383$	−18.1865	+	10.5000i	−0.929288	+	0.536525i	−0.0427020	+	0.999088i	$0.513597\pi$
$384$		0			0
$385$	−16.3923	−	6.80385i	−0.835429	−	0.346756i
$386$		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
$395$	1.87564	−	31.2487i	0.0943739	−	1.57229i
$396$		0			0
$397$	12.1244	−	7.00000i	0.608504	−	0.351320i	−0.163876	−	0.986481i	$-0.552400\pi$
$397$	12.1244	−	7.00000i	0.608504	−	0.351320i	0.772380	+	0.635161i	$0.219066\pi$
$398$		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
$415$	−7.39230	+	11.1962i	−0.362874	+	0.549598i
$416$		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
$425$	1.19615	−	9.92820i	0.0580219	−	0.481589i
$426$		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	$0.234907\pi$
$433$			28.0000i			1.34559i	−0.739827	+	0.672797i	$0.765093\pi$
$434$		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	−0.967941	−	0.251179i	$-0.919182\pi$
$443$	−25.9808	+	15.0000i	−1.23438	+	0.712672i	−0.266443	+	0.963851i	$0.585848\pi$
$444$		0			0
$445$	−0.267949	+	4.46410i	−0.0127020	+	0.211619i
$446$		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
$455$	−29.3301	+	3.83975i	−1.37502	+	0.180010i
$456$		0			0
$457$	8.66025	−	5.00000i	0.405110	−	0.233890i	−0.283577	−	0.958950i	$-0.591521\pi$
$457$	8.66025	−	5.00000i	0.405110	−	0.233890i	0.688686	+	0.725059i	$0.258188\pi$
$458$		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	$0.129265\pi$
$463$			17.0000i			0.790057i	−0.918669	+	0.395029i	$0.870735\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	29.4449	−	17.0000i	1.36255	−	0.786666i	0.372584	−	0.927999i	$-0.378472\pi$
$467$	29.4449	−	17.0000i	1.36255	−	0.786666i	0.989962	+	0.141332i	$0.0451386\pi$
$468$		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
$485$	−14.7846	+	22.3923i	−0.671335	+	1.01678i
$486$		0			0
$487$	27.7128	+	16.0000i	1.25579	+	0.725029i	0.972253	−	0.233933i	$-0.0751596\pi$
$487$	27.7128	+	16.0000i	1.25579	+	0.725029i	0.283535	+	0.958962i	$0.408493\pi$
$488$		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
$495$	−16.7942	−	11.0885i	−0.754844	−	0.498389i
$496$		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	$-0.649474\pi$
$503$		−	40.0000i		−	1.78351i	0.452517	−	0.891756i	$-0.350526\pi$
$504$		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
$515$	17.8564	+	1.07180i	0.786847	+	0.0472290i
$516$		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	−0.771358	−	0.636401i	$-0.780422\pi$
$523$	−13.8564	+	8.00000i	−0.605898	+	0.349816i	0.165460	+	0.986216i	$0.447089\pi$
$524$		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
$535$	−35.7128	−	2.14359i	−1.54400	−	0.0926756i
$536$		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	$-0.812397\pi$
$547$		−	26.0000i		−	1.11168i	0.831289	−	0.555840i	$-0.187603\pi$
$548$		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	0.858614	−	0.512622i	$-0.171326\pi$
$557$	19.9186	+	11.5000i	0.843978	+	0.487271i	−0.0146368	+	0.999893i	$0.504659\pi$
$558$		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	0.536054	−	0.844183i	$-0.319914\pi$
$563$	1.73205	+	1.00000i	0.0729972	+	0.0421450i	−0.463057	+	0.886328i	$0.653248\pi$
$564$		0			0
$565$	−17.2487	+	26.1244i	−0.725659	+	1.09906i
$566$		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	0.426158	−	0.904649i	$-0.359867\pi$
$577$	−3.46410	−	2.00000i	−0.144212	−	0.0832611i	−0.570370	+	0.821388i	$0.693200\pi$
$578$		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
$585$	−33.4808	−	2.00962i	−1.38426	−	0.0830875i
$586$		0			0
$587$			34.0000i			1.40333i	0.712507	+	0.701665i	$0.247560\pi$
$587$			34.0000i			1.40333i	−0.712507	+	0.701665i	$0.752440\pi$
$588$		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	−0.602881	−	0.797831i	$-0.705981\pi$
$593$	−5.19615	+	3.00000i	−0.213380	+	0.123195i	0.389501	+	0.921026i	$0.372647\pi$
$594$		0			0
$595$	−4.53590	+	10.9282i	−0.185954	+	0.448013i
$596$		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
$605$	−0.267949	+	4.46410i	−0.0108937	+	0.181492i
$606$		0			0
$607$	−11.2583	+	6.50000i	−0.456962	+	0.263827i	−0.710766	−	0.703429i	$-0.751651\pi$
$607$	−11.2583	+	6.50000i	−0.456962	+	0.263827i	0.253804	+	0.967256i	$0.418318\pi$
$608$		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	0.738846	−	0.673874i	$-0.235371\pi$
$613$	12.9904	+	7.50000i	0.524677	+	0.302922i	−0.214169	+	0.976797i	$0.568704\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	14.0000i		−	0.563619i	−0.959470	−	0.281809i	$-0.909065\pi$
$617$		−	14.0000i		−	0.563619i	0.959470	−	0.281809i	$-0.0909346\pi$
$618$		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
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$		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
$635$	−8.62436	+	13.0622i	−0.342247	+	0.518357i
$636$		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	$0.0890266\pi$
$643$			14.0000i			0.552106i	−0.961142	+	0.276053i	$0.910973\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	23.3827	+	13.5000i	0.919268	+	0.530740i	0.883402	−	0.468617i	$-0.155247\pi$
$647$	23.3827	+	13.5000i	0.919268	+	0.530740i	0.0358667	+	0.999357i	$0.488581\pi$
$648$		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	−0.448303	−	0.893882i	$-0.647971\pi$
$653$	2.59808	−	1.50000i	0.101671	−	0.0586995i	0.549973	+	0.835182i	$0.314638\pi$
$654$		0			0
$655$	0.133975	−	2.23205i	0.00523482	−	0.0872134i
$656$		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
$665$	23.4808	−	17.9904i	0.910545	−	0.697637i
$666$		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	$0.211553\pi$
$673$			32.0000i			1.23351i	−0.787155	+	0.616755i	$0.788447\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.7224	−	8.50000i	0.565829	−	0.326682i	−0.189653	−	0.981851i	$-0.560736\pi$
$677$	14.7224	−	8.50000i	0.565829	−	0.326682i	0.755482	+	0.655170i	$0.227403\pi$
$678$		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	−0.459136	−	0.888366i	$-0.651841\pi$
$683$	−38.1051	−	22.0000i	−1.45805	−	0.841807i	−0.998916	+	0.0465592i	$0.985174\pi$
$684$		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
$695$	29.8564	+	19.7128i	1.13252	+	0.747750i
$696$		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
$725$	7.85641	+	18.3923i	0.291780	+	0.683073i
$726$		0			0
$727$		−	29.0000i		−	1.07555i	−0.843088	−	0.537775i	$-0.819265\pi$
$727$		−	29.0000i		−	1.07555i	0.843088	−	0.537775i	$-0.180735\pi$
$728$		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	0.329141	−	0.944281i	$-0.393241\pi$
$733$	35.5070	−	20.5000i	1.31148	−	0.757185i	0.982342	+	0.187096i	$0.0599076\pi$
$734$		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	$0.125870\pi$
$743$			21.0000i			0.770415i	−0.922830	+	0.385208i	$0.874130\pi$
$744$		0			0
$745$	2.41154	−	40.1769i	0.0883521	−	1.47197i
$746$		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	$-0.723599\pi$
$757$		−	42.0000i		−	1.52652i	0.646094	−	0.763258i	$-0.276401\pi$
$758$		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
$765$	−7.39230	+	11.1962i	−0.267269	+	0.404798i
$766$		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	−0.407128	−	0.913371i	$-0.633470\pi$
$773$	−38.9711	−	22.5000i	−1.40169	−	0.809269i	−0.994567	+	0.104102i	$0.966803\pi$
$774$		0			0
$775$	−9.92820	−	1.19615i	−0.356632	−	0.0429671i
$776$		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	0.195737	−	0.980656i	$-0.437290\pi$
$787$	−15.5885	−	9.00000i	−0.555668	−	0.320815i	−0.751405	+	0.659841i	$0.770624\pi$
$788$		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	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$		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
$805$	−25.1865	−	32.8731i	−0.887709	−	1.15862i
$806$		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
$815$	26.7846	+	1.60770i	0.938224	+	0.0563151i
$816$		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	0.0919029	−	0.995768i	$-0.470705\pi$
$823$	−20.7846	−	12.0000i	−0.724506	−	0.418294i	−0.816409	+	0.577474i	$0.804038\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	22.0000i		−	0.765015i	−0.923952	−	0.382507i	$-0.875061\pi$
$827$		−	22.0000i		−	0.765015i	0.923952	−	0.382507i	$-0.124939\pi$
$828$		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
$835$	−18.4808	+	27.9904i	−0.639553	+	0.968647i
$836$		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
$845$	−22.3923	−	14.7846i	−0.770319	−	0.508606i
$846$		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	$-0.736644\pi$
$853$		−	43.0000i		−	1.47229i	0.676823	−	0.736146i	$-0.263356\pi$
$854$		0			0
$855$	30.0000	−	15.0000i	1.02598	−	0.512989i
$856$		0			0
$857$	6.92820	+	4.00000i	0.236663	+	0.136637i	0.613642	−	0.789584i	$-0.289704\pi$
$857$	6.92820	+	4.00000i	0.236663	+	0.136637i	−0.376979	+	0.926222i	$0.623037\pi$
$858$		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	−0.329020	−	0.944323i	$-0.606718\pi$
$863$	9.52628	−	5.50000i	0.324278	−	0.187222i	0.653298	+	0.757101i	$0.273385\pi$
$864$		0			0
$865$	20.0885	+	1.20577i	0.683028	+	0.0409975i
$866$		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
$875$	25.4641	−	15.0526i	0.860844	−	0.508869i
$876$		0			0
$877$	−26.8468	+	15.5000i	−0.906552	+	0.523398i	−0.879320	−	0.476231i	$-0.842002\pi$
$877$	−26.8468	+	15.5000i	−0.906552	+	0.523398i	−0.0272316	+	0.999629i	$0.508669\pi$
$878$		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	$-0.913234\pi$
$883$		−	16.0000i		−	0.538443i	0.963078	−	0.269221i	$-0.0867663\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	31.1769	−	18.0000i	1.04682	−	0.604381i	0.125061	−	0.992149i	$-0.460087\pi$
$887$	31.1769	−	18.0000i	1.04682	−	0.604381i	0.921757	+	0.387768i	$0.126754\pi$
$888$		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
$905$	48.5167	+	32.0333i	1.61275	+	1.06482i
$906$		0			0
$907$	34.6410	+	20.0000i	1.15024	+	0.664089i	0.948945	−	0.315442i	$-0.102153\pi$
$907$	34.6410	+	20.0000i	1.15024	+	0.664089i	0.201291	+	0.979531i	$0.435486\pi$
$908$		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
$935$	−13.3923	−	0.803848i	−0.437975	−	0.0262886i
$936$		0			0
$937$			26.0000i			0.849383i	0.905338	+	0.424691i	$0.139617\pi$
$937$			26.0000i			0.849383i	−0.905338	+	0.424691i	$0.860383\pi$
$938$		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	−0.659256	−	0.751918i	$-0.729129\pi$
$947$	−10.3923	+	6.00000i	−0.337705	+	0.194974i	0.321552	+	0.946892i	$0.395796\pi$
$948$		0			0
$949$	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	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$		0			0
$955$	2.67949	−	44.6410i	0.0867063	−	1.44455i
$956$		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	$0.172032\pi$
$967$			32.0000i			1.02905i	−0.857475	+	0.514525i	$0.827968\pi$
$968$		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	0.999990	−	0.00442082i	$-0.00140720\pi$
$977$	46.7654	+	27.0000i	1.49616	+	0.863807i	0.496167	+	0.868227i	$0.334741\pi$
$978$		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	0.0427975	−	0.999084i	$-0.486373\pi$
$983$	−25.1147	−	14.5000i	−0.801036	−	0.462478i	−0.843833	+	0.536606i	$0.819706\pi$
$984$		0			0
$985$	−6.16025	+	9.33013i	−0.196282	+	0.297283i
$986$		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	−0.121771	−	0.992558i	$-0.538857\pi$
$997$	−32.9090	−	19.0000i	−1.04224	−	0.601736i	−0.920466	+	0.390822i	$0.872191\pi$
$998$		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.529.2		4
4.3	odd	2		70.2.i.b.39.1	yes	4
5.4	even	2	inner	560.2.bw.d.529.1		4
7.2	even	3	inner	560.2.bw.d.289.1		4
12.11	even	2		630.2.u.a.109.2		4
20.3	even	4		350.2.e.j.151.1		2
20.7	even	4		350.2.e.c.151.1		2
20.19	odd	2		70.2.i.b.39.2	yes	4
28.3	even	6		490.2.c.d.99.1		2
28.11	odd	6		490.2.c.a.99.1		2
28.19	even	6		490.2.i.a.79.2		4
28.23	odd	6		70.2.i.b.9.2	yes	4
28.27	even	2		490.2.i.a.459.1		4
35.9	even	6	inner	560.2.bw.d.289.2		4
60.59	even	2		630.2.u.a.109.1		4
84.23	even	6		630.2.u.a.289.1		4
140.3	odd	12		2450.2.a.j.1.1		1
140.19	even	6		490.2.i.a.79.1		4
140.23	even	12		350.2.e.j.51.1		2
140.39	odd	6		490.2.c.a.99.2		2
140.59	even	6		490.2.c.d.99.2		2
140.67	even	12		2450.2.a.ba.1.1		1
140.79	odd	6		70.2.i.b.9.1	✓	4
140.87	odd	12		2450.2.a.bb.1.1		1
140.107	even	12		350.2.e.c.51.1		2
140.123	even	12		2450.2.a.k.1.1		1
140.139	even	2		490.2.i.a.459.2		4
420.359	even	6		630.2.u.a.289.2		4

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

\(f(q)\)	\(=\)	\(q+(1.86603 + 1.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.86603 + 1.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} -5.00000i q^{13} +(-1.73205 - 1.00000i) q^{17} +(2.50000 + 4.33013i) q^{19} +(6.06218 - 3.50000i) q^{23} +(1.96410 + 4.59808i) q^{25} +4.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-0.767949 - 5.86603i) q^{35} +(-0.866025 + 0.500000i) q^{37} +3.00000 q^{41} -2.00000i q^{43} +(0.401924 - 6.69615i) q^{45} +(-6.06218 + 3.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-7.79423 - 4.50000i) q^{53} +(6.00000 - 3.00000i) q^{55} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(-2.59808 + 7.50000i) q^{63} +(6.16025 - 9.33013i) q^{65} +(-1.73205 - 1.00000i) q^{67} +6.00000 q^{71} +(13.8564 + 8.00000i) q^{73} +(-7.79423 + 1.50000i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(-4.50000 + 7.79423i) q^{81} +6.00000i q^{83} +(-2.00000 - 4.00000i) q^{85} +(1.00000 + 1.73205i) q^{89} +(-10.0000 + 8.66025i) q^{91} +(-0.669873 + 11.1603i) q^{95} +12.0000i q^{97} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} - 6 q^{9}+O(q^{10}) \) 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

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