LMFDB - Embedded newform 624.2.bv.d.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(49,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("624.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bv (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:	$4.98266508613$
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:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	624.49
Dual form			624.2.bv.d.433.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +1.73205i q^{5} +(4.09808 + 2.36603i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +1.73205i q^{5} +(4.09808 + 2.36603i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-4.09808 + 2.36603i) q^{11} +(-3.59808 - 0.232051i) q^{13} +(1.50000 - 0.866025i) q^{15} +(-2.59808 + 4.50000i) q^{17} +(-1.09808 - 0.633975i) q^{19} -4.73205i q^{21} +(-1.09808 - 1.90192i) q^{23} +2.00000 q^{25} +1.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +2.53590i q^{31} +(4.09808 + 2.36603i) q^{33} +(-4.09808 + 7.09808i) q^{35} +(2.59808 - 1.50000i) q^{37} +(1.59808 + 3.23205i) q^{39} +(0.401924 - 0.232051i) q^{41} +(-3.09808 + 5.36603i) q^{43} +(-1.50000 - 0.866025i) q^{45} +1.26795i q^{47} +(7.69615 + 13.3301i) q^{49} +5.19615 q^{51} +3.00000 q^{53} +(-4.09808 - 7.09808i) q^{55} +1.26795i q^{57} +(12.0000 + 6.92820i) q^{59} +(-2.40192 + 4.16025i) q^{61} +(-4.09808 + 2.36603i) q^{63} +(0.401924 - 6.23205i) q^{65} +(9.29423 - 5.36603i) q^{67} +(-1.09808 + 1.90192i) q^{69} +(-7.09808 - 4.09808i) q^{71} -12.1244i q^{73} +(-1.00000 - 1.73205i) q^{75} -22.3923 q^{77} +12.3923 q^{79} +(-0.500000 - 0.866025i) q^{81} -11.6603i q^{83} +(-7.79423 - 4.50000i) q^{85} +(1.50000 - 2.59808i) q^{87} +(2.19615 - 1.26795i) q^{89} +(-14.1962 - 9.46410i) q^{91} +(2.19615 - 1.26795i) q^{93} +(1.09808 - 1.90192i) q^{95} +(5.19615 + 3.00000i) q^{97} -4.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 6 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 6 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} + 6 q^{7} - 2 q^{9} - 6 q^{11} - 4 q^{13} + 6 q^{15} + 6 q^{19} + 6 q^{23} + 8 q^{25} + 4 q^{27} + 6 q^{29} + 6 q^{33} - 6 q^{35} - 4 q^{39} + 12 q^{41} - 2 q^{43} - 6 q^{45} + 10 q^{49} + 12 q^{53} - 6 q^{55} + 48 q^{59} - 20 q^{61} - 6 q^{63} + 12 q^{65} + 6 q^{67} + 6 q^{69} - 18 q^{71} - 4 q^{75} - 48 q^{77} + 8 q^{79} - 2 q^{81} + 6 q^{87} - 12 q^{89} - 36 q^{91} - 12 q^{93} - 6 q^{95}+O(q^{100}) $ 4 * q - 2 * q^3 + 6 * q^7 - 2 * q^9 - 6 * q^11 - 4 * q^13 + 6 * q^15 + 6 * q^19 + 6 * q^23 + 8 * q^25 + 4 * q^27 + 6 * q^29 + 6 * q^33 - 6 * q^35 - 4 * q^39 + 12 * q^41 - 2 * q^43 - 6 * q^45 + 10 * q^49 + 12 * q^53 - 6 * q^55 + 48 * q^59 - 20 * q^61 - 6 * q^63 + 12 * q^65 + 6 * q^67 + 6 * q^69 - 18 * q^71 - 4 * q^75 - 48 * q^77 + 8 * q^79 - 2 * q^81 + 6 * q^87 - 12 * q^89 - 36 * q^91 - 12 * q^93 - 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$			1.73205i			0.774597i	0.921954	+	0.387298i	$0.126592\pi$
$5$			1.73205i			0.774597i	−0.921954	+	0.387298i	$0.873408\pi$
$6$		0			0
$7$	4.09808	+	2.36603i	1.54893	+	0.894274i	0.998224	+	0.0595724i	$0.0189737\pi$
$7$	4.09808	+	2.36603i	1.54893	+	0.894274i	0.550703	+	0.834701i	$0.314360\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−4.09808	+	2.36603i	−1.23562	+	0.713384i	−0.968195	−	0.250196i	$-0.919505\pi$
$11$	−4.09808	+	2.36603i	−1.23562	+	0.713384i	−0.267421	+	0.963580i	$0.586172\pi$
$12$		0			0
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$14$		0			0
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$		0			0
$17$	−2.59808	+	4.50000i	−0.630126	+	1.09141i	0.357400	+	0.933952i	$0.383663\pi$
$17$	−2.59808	+	4.50000i	−0.630126	+	1.09141i	−0.987526	+	0.157459i	$0.949670\pi$
$18$		0			0
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	0.368725	−	0.929538i	$-0.379794\pi$
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	−0.620641	+	0.784095i	$0.713128\pi$
$20$		0			0
$21$		−	4.73205i		−	1.03262i
$22$		0			0
$23$	−1.09808	−	1.90192i	−0.228965	−	0.396579i	0.728537	−	0.685007i	$-0.240201\pi$
$23$	−1.09808	−	1.90192i	−0.228965	−	0.396579i	−0.957502	+	0.288428i	$0.906867\pi$
$24$		0			0
$25$	2.00000			0.400000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$			2.53590i			0.455461i	0.973724	+	0.227730i	$0.0731305\pi$
$31$			2.53590i			0.455461i	−0.973724	+	0.227730i	$0.926870\pi$
$32$		0			0
$33$	4.09808	+	2.36603i	0.713384	+	0.411872i
$34$		0			0
$35$	−4.09808	+	7.09808i	−0.692701	+	1.19979i
$36$		0			0
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	−0.270998	−	0.962580i	$-0.587354\pi$
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	0.698119	+	0.715981i	$0.254020\pi$
$38$		0			0
$39$	1.59808	+	3.23205i	0.255897	+	0.517542i
$40$		0			0
$41$	0.401924	−	0.232051i	0.0627700	−	0.0362402i	−0.468287	−	0.883577i	$-0.655129\pi$
$41$	0.401924	−	0.232051i	0.0627700	−	0.0362402i	0.531057	+	0.847336i	$0.321795\pi$
$42$		0			0
$43$	−3.09808	+	5.36603i	−0.472452	+	0.818311i	−0.999503	−	0.0315225i	$-0.989964\pi$
$43$	−3.09808	+	5.36603i	−0.472452	+	0.818311i	0.527051	+	0.849834i	$0.323298\pi$
$44$		0			0
$45$	−1.50000	−	0.866025i	−0.223607	−	0.129099i
$46$		0			0
$47$			1.26795i			0.184949i	0.995715	+	0.0924747i	$0.0294777\pi$
$47$			1.26795i			0.184949i	−0.995715	+	0.0924747i	$0.970522\pi$
$48$		0			0
$49$	7.69615	+	13.3301i	1.09945	+	1.90430i
$50$		0			0
$51$	5.19615			0.727607
$52$		0			0
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$		0			0
$55$	−4.09808	−	7.09808i	−0.552584	−	0.957104i
$56$		0			0
$57$			1.26795i			0.167944i
$58$		0			0
$59$	12.0000	+	6.92820i	1.56227	+	0.901975i	0.997027	+	0.0770484i	$0.0245496\pi$
$59$	12.0000	+	6.92820i	1.56227	+	0.901975i	0.565240	+	0.824927i	$0.308784\pi$
$60$		0			0
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	−0.977822	−	0.209435i	$-0.932837\pi$
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	0.670288	+	0.742101i	$0.266171\pi$
$62$		0			0
$63$	−4.09808	+	2.36603i	−0.516309	+	0.298091i
$64$		0			0
$65$	0.401924	−	6.23205i	0.0498525	−	0.772991i
$66$		0			0
$67$	9.29423	−	5.36603i	1.13547	−	0.655564i	0.190166	−	0.981752i	$-0.439097\pi$
$67$	9.29423	−	5.36603i	1.13547	−	0.655564i	0.945305	+	0.326188i	$0.105764\pi$
$68$		0			0
$69$	−1.09808	+	1.90192i	−0.132193	+	0.228965i
$70$		0			0
$71$	−7.09808	−	4.09808i	−0.842387	−	0.486352i	0.0156881	−	0.999877i	$-0.495006\pi$
$71$	−7.09808	−	4.09808i	−0.842387	−	0.486352i	−0.858075	+	0.513525i	$0.828339\pi$
$72$		0			0
$73$		−	12.1244i		−	1.41905i	−0.704681	−	0.709524i	$-0.748910\pi$
$73$		−	12.1244i		−	1.41905i	0.704681	−	0.709524i	$-0.251090\pi$
$74$		0			0
$75$	−1.00000	−	1.73205i	−0.115470	−	0.200000i
$76$		0			0
$77$	−22.3923			−2.55184
$78$		0			0
$79$	12.3923			1.39424			0.697122	−	0.716953i	$-0.254464\pi$
$79$	12.3923			1.39424			0.697122	+	0.716953i	$0.254464\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	11.6603i		−	1.27988i	−0.768425	−	0.639940i	$-0.778959\pi$
$83$		−	11.6603i		−	1.27988i	0.768425	−	0.639940i	$-0.221041\pi$
$84$		0			0
$85$	−7.79423	−	4.50000i	−0.845403	−	0.488094i
$86$		0			0
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$		0			0
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	−0.379068	−	0.925369i	$-0.623755\pi$
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	0.611859	+	0.790967i	$0.290422\pi$
$90$		0			0
$91$	−14.1962	−	9.46410i	−1.48816	−	0.992107i
$92$		0			0
$93$	2.19615	−	1.26795i	0.227730	−	0.131480i
$94$		0			0
$95$	1.09808	−	1.90192i	0.112660	−	0.195133i
$96$		0			0
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	0.740034	−	0.672569i	$-0.234809\pi$
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	−0.212445	+	0.977173i	$0.568143\pi$
$98$		0			0
$99$		−	4.73205i		−	0.475589i
$100$		0			0
$101$	−0.696152	−	1.20577i	−0.0692698	−	0.119979i	0.829310	−	0.558788i	$-0.188734\pi$
$101$	−0.696152	−	1.20577i	−0.0692698	−	0.119979i	−0.898580	+	0.438810i	$0.855400\pi$
$102$		0			0
$103$	−4.19615			−0.413459			−0.206730	−	0.978398i	$-0.566282\pi$
$103$	−4.19615			−0.413459			−0.206730	+	0.978398i	$0.566282\pi$
$104$		0			0
$105$	8.19615			0.799863
$106$		0			0
$107$	4.09808	+	7.09808i	0.396176	+	0.686197i	0.993251	−	0.115989i	$-0.0370037\pi$
$107$	4.09808	+	7.09808i	0.396176	+	0.686197i	−0.597075	+	0.802186i	$0.703670\pi$
$108$		0			0
$109$		−	16.3923i		−	1.57010i	−0.619434	−	0.785049i	$-0.712638\pi$
$109$		−	16.3923i		−	1.57010i	0.619434	−	0.785049i	$-0.287362\pi$
$110$		0			0
$111$	−2.59808	−	1.50000i	−0.246598	−	0.142374i
$112$		0			0
$113$	−5.59808	+	9.69615i	−0.526623	+	0.912137i	0.472896	+	0.881118i	$0.343209\pi$
$113$	−5.59808	+	9.69615i	−0.526623	+	0.912137i	−0.999519	+	0.0310191i	$0.990125\pi$
$114$		0			0
$115$	3.29423	−	1.90192i	0.307188	−	0.177355i
$116$		0			0
$117$	2.00000	−	3.00000i	0.184900	−	0.277350i
$118$		0			0
$119$	−21.2942	+	12.2942i	−1.95204	+	1.12701i
$120$		0			0
$121$	5.69615	−	9.86603i	0.517832	−	0.896911i
$122$		0			0
$123$	−0.401924	−	0.232051i	−0.0362402	−	0.0209233i
$124$		0			0
$125$			12.1244i			1.08444i
$126$		0			0
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	0.941014	−	0.338368i	$-0.109875\pi$
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	−0.763542	+	0.645758i	$0.776542\pi$
$128$		0			0
$129$	6.19615			0.545541
$130$		0			0
$131$	−16.3923			−1.43220			−0.716101	−	0.697997i	$-0.754075\pi$
$131$	−16.3923			−1.43220			−0.716101	+	0.697997i	$0.754075\pi$
$132$		0			0
$133$	−3.00000	−	5.19615i	−0.260133	−	0.450564i
$134$		0			0
$135$			1.73205i			0.149071i
$136$		0			0
$137$	7.79423	+	4.50000i	0.665906	+	0.384461i	0.794524	−	0.607233i	$-0.207721\pi$
$137$	7.79423	+	4.50000i	0.665906	+	0.384461i	−0.128618	+	0.991694i	$0.541054\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$	1.09808	−	0.633975i	0.0924747	−	0.0533903i
$142$		0			0
$143$	15.2942	−	7.56218i	1.27897	−	0.632381i
$144$		0			0
$145$	−4.50000	+	2.59808i	−0.373705	+	0.215758i
$146$		0			0
$147$	7.69615	−	13.3301i	0.634768	−	1.09945i
$148$		0			0
$149$	−15.6962	−	9.06218i	−1.28588	−	0.742403i	−0.307962	−	0.951399i	$-0.599647\pi$
$149$	−15.6962	−	9.06218i	−1.28588	−	0.742403i	−0.977916	+	0.208996i	$0.932980\pi$
$150$		0			0
$151$		−	7.26795i		−	0.591457i	−0.955272	−	0.295729i	$-0.904438\pi$
$151$		−	7.26795i		−	0.591457i	0.955272	−	0.295729i	$-0.0955624\pi$
$152$		0			0
$153$	−2.59808	−	4.50000i	−0.210042	−	0.363803i
$154$		0			0
$155$	−4.39230			−0.352798
$156$		0			0
$157$	−3.19615			−0.255081			−0.127540	−	0.991833i	$-0.540708\pi$
$157$	−3.19615			−0.255081			−0.127540	+	0.991833i	$0.540708\pi$
$158$		0			0
$159$	−1.50000	−	2.59808i	−0.118958	−	0.206041i
$160$		0			0
$161$		−	10.3923i		−	0.819028i
$162$		0			0
$163$	8.19615	+	4.73205i	0.641972	+	0.370643i	0.785374	−	0.619022i	$-0.212471\pi$
$163$	8.19615	+	4.73205i	0.641972	+	0.370643i	−0.143402	+	0.989665i	$0.545804\pi$
$164$		0			0
$165$	−4.09808	+	7.09808i	−0.319035	+	0.552584i
$166$		0			0
$167$	2.19615	−	1.26795i	0.169943	−	0.0981169i	−0.412616	−	0.910905i	$-0.635385\pi$
$167$	2.19615	−	1.26795i	0.169943	−	0.0981169i	0.582559	+	0.812788i	$0.302051\pi$
$168$		0			0
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$		0			0
$171$	1.09808	−	0.633975i	0.0839720	−	0.0484812i
$172$		0			0
$173$	8.19615	−	14.1962i	0.623142	−	1.07931i	−0.365755	−	0.930711i	$-0.619189\pi$
$173$	8.19615	−	14.1962i	0.623142	−	1.07931i	0.988897	−	0.148602i	$-0.0474774\pi$
$174$		0			0
$175$	8.19615	+	4.73205i	0.619571	+	0.357709i
$176$		0			0
$177$		−	13.8564i		−	1.04151i
$178$		0			0
$179$	4.09808	+	7.09808i	0.306305	+	0.530535i	0.977551	−	0.210699i	$-0.0675741\pi$
$179$	4.09808	+	7.09808i	0.306305	+	0.530535i	−0.671246	+	0.741234i	$0.734241\pi$
$180$		0			0
$181$	11.5885			0.861363			0.430682	−	0.902504i	$-0.358273\pi$
$181$	11.5885			0.861363			0.430682	+	0.902504i	$0.358273\pi$
$182$		0			0
$183$	4.80385			0.355111
$184$		0			0
$185$	2.59808	+	4.50000i	0.191014	+	0.330847i
$186$		0			0
$187$		−	24.5885i		−	1.79809i
$188$		0			0
$189$	4.09808	+	2.36603i	0.298091	+	0.172103i
$190$		0			0
$191$	10.3923	−	18.0000i	0.751961	−	1.30243i	−0.194910	−	0.980821i	$-0.562442\pi$
$191$	10.3923	−	18.0000i	0.751961	−	1.30243i	0.946871	−	0.321613i	$-0.104225\pi$
$192$		0			0
$193$	−11.0885	+	6.40192i	−0.798165	+	0.460821i	−0.842829	−	0.538181i	$-0.819111\pi$
$193$	−11.0885	+	6.40192i	−0.798165	+	0.460821i	0.0446644	+	0.999002i	$0.485778\pi$
$194$		0			0
$195$	−5.59808	+	2.76795i	−0.400887	+	0.198217i
$196$		0			0
$197$	−6.00000	+	3.46410i	−0.427482	+	0.246807i	−0.698273	−	0.715831i	$-0.746048\pi$
$197$	−6.00000	+	3.46410i	−0.427482	+	0.246807i	0.270791	+	0.962638i	$0.412715\pi$
$198$		0			0
$199$	−4.29423	+	7.43782i	−0.304410	+	0.527253i	−0.977130	−	0.212644i	$-0.931793\pi$
$199$	−4.29423	+	7.43782i	−0.304410	+	0.527253i	0.672720	+	0.739897i	$0.265126\pi$
$200$		0			0
$201$	−9.29423	−	5.36603i	−0.655564	−	0.378490i
$202$		0			0
$203$			14.1962i			0.996375i
$204$		0			0
$205$	0.401924	+	0.696152i	0.0280716	+	0.0486214i
$206$		0			0
$207$	2.19615			0.152643
$208$		0			0
$209$	6.00000			0.415029
$210$		0			0
$211$	−1.80385	−	3.12436i	−0.124182	−	0.215090i	0.797231	−	0.603674i	$-0.206297\pi$
$211$	−1.80385	−	3.12436i	−0.124182	−	0.215090i	−0.921413	+	0.388585i	$0.872964\pi$
$212$		0			0
$213$			8.19615i			0.561591i
$214$		0			0
$215$	−9.29423	−	5.36603i	−0.633861	−	0.365960i
$216$		0			0
$217$	−6.00000	+	10.3923i	−0.407307	+	0.705476i
$218$		0			0
$219$	−10.5000	+	6.06218i	−0.709524	+	0.409644i
$220$		0			0
$221$	10.3923	−	15.5885i	0.699062	−	1.04859i
$222$		0			0
$223$	−16.3923	+	9.46410i	−1.09771	+	0.633763i	−0.935619	−	0.353013i	$-0.885157\pi$
$223$	−16.3923	+	9.46410i	−1.09771	+	0.633763i	−0.162091	+	0.986776i	$0.551824\pi$
$224$		0			0
$225$	−1.00000	+	1.73205i	−0.0666667	+	0.115470i
$226$		0			0
$227$	8.49038	+	4.90192i	0.563526	+	0.325352i	0.754560	−	0.656231i	$-0.227851\pi$
$227$	8.49038	+	4.90192i	0.563526	+	0.325352i	−0.191033	+	0.981584i	$0.561184\pi$
$228$		0			0
$229$			19.8564i			1.31215i	0.754696	+	0.656074i	$0.227784\pi$
$229$			19.8564i			1.31215i	−0.754696	+	0.656074i	$0.772216\pi$
$230$		0			0
$231$	11.1962	+	19.3923i	0.736653	+	1.27592i
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$	−2.19615			−0.143261
$236$		0			0
$237$	−6.19615	−	10.7321i	−0.402483	−	0.697122i
$238$		0			0
$239$		−	24.5885i		−	1.59050i	−0.606285	−	0.795248i	$-0.707341\pi$
$239$		−	24.5885i		−	1.59050i	0.606285	−	0.795248i	$-0.292659\pi$
$240$		0			0
$241$	−0.696152	−	0.401924i	−0.0448431	−	0.0258902i	0.477411	−	0.878680i	$-0.341575\pi$
$241$	−0.696152	−	0.401924i	−0.0448431	−	0.0258902i	−0.522254	+	0.852790i	$0.674909\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−23.0885	+	13.3301i	−1.47507	+	0.851631i
$246$		0			0
$247$	3.80385	+	2.53590i	0.242033	+	0.161355i
$248$		0			0
$249$	−10.0981	+	5.83013i	−0.639940	+	0.369469i
$250$		0			0
$251$	2.19615	−	3.80385i	0.138620	−	0.240097i	−0.788355	−	0.615221i	$-0.789067\pi$
$251$	2.19615	−	3.80385i	0.138620	−	0.240097i	0.926974	+	0.375124i	$0.122400\pi$
$252$		0			0
$253$	9.00000	+	5.19615i	0.565825	+	0.326679i
$254$		0			0
$255$			9.00000i			0.563602i
$256$		0			0
$257$	6.40192	+	11.0885i	0.399341	+	0.691679i	0.993645	−	0.112562i	$-0.0359056\pi$
$257$	6.40192	+	11.0885i	0.399341	+	0.691679i	−0.594304	+	0.804241i	$0.702572\pi$
$258$		0			0
$259$	14.1962			0.882106
$260$		0			0
$261$	−3.00000			−0.185695
$262$		0			0
$263$	−1.09808	−	1.90192i	−0.0677103	−	0.117278i	0.830183	−	0.557491i	$-0.188236\pi$
$263$	−1.09808	−	1.90192i	−0.0677103	−	0.117278i	−0.897893	+	0.440214i	$0.854903\pi$
$264$		0			0
$265$			5.19615i			0.319197i
$266$		0			0
$267$	−2.19615	−	1.26795i	−0.134402	−	0.0775972i
$268$		0			0
$269$	14.1962	−	24.5885i	0.865555	−	1.49918i	−0.000940662	−	1.00000i	$-0.500299\pi$
$269$	14.1962	−	24.5885i	0.865555	−	1.49918i	0.866495	−	0.499185i	$-0.166367\pi$
$270$		0			0
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$		0			0
$273$	−1.09808	+	17.0263i	−0.0664586	+	1.03048i
$274$		0			0
$275$	−8.19615	+	4.73205i	−0.494247	+	0.285353i
$276$		0			0
$277$	7.59808	−	13.1603i	0.456524	−	0.790723i	−0.542250	−	0.840217i	$-0.682428\pi$
$277$	7.59808	−	13.1603i	0.456524	−	0.790723i	0.998774	+	0.0494940i	$0.0157609\pi$
$278$		0			0
$279$	−2.19615	−	1.26795i	−0.131480	−	0.0759101i
$280$		0			0
$281$			24.4641i			1.45941i	0.683764	+	0.729703i	$0.260342\pi$
$281$			24.4641i			1.45941i	−0.683764	+	0.729703i	$0.739658\pi$
$282$		0			0
$283$	15.0981	+	26.1506i	0.897487	+	1.55449i	0.830696	+	0.556727i	$0.187943\pi$
$283$	15.0981	+	26.1506i	0.897487	+	1.55449i	0.0667919	+	0.997767i	$0.478724\pi$
$284$		0			0
$285$	−2.19615			−0.130089
$286$		0			0
$287$	2.19615			0.129635
$288$		0			0
$289$	−5.00000	−	8.66025i	−0.294118	−	0.509427i
$290$		0			0
$291$		−	6.00000i		−	0.351726i
$292$		0			0
$293$	12.6962	+	7.33013i	0.741717	+	0.428231i	0.822693	−	0.568485i	$-0.192470\pi$
$293$	12.6962	+	7.33013i	0.741717	+	0.428231i	−0.0809762	+	0.996716i	$0.525804\pi$
$294$		0			0
$295$	−12.0000	+	20.7846i	−0.698667	+	1.21013i
$296$		0			0
$297$	−4.09808	+	2.36603i	−0.237795	+	0.137291i
$298$		0			0
$299$	3.50962	+	7.09808i	0.202967	+	0.410492i
$300$		0			0
$301$	−25.3923	+	14.6603i	−1.46359	+	0.845003i
$302$		0			0
$303$	−0.696152	+	1.20577i	−0.0399929	+	0.0692698i
$304$		0			0
$305$	−7.20577	−	4.16025i	−0.412601	−	0.238215i
$306$		0			0
$307$		−	10.7321i		−	0.612510i	−0.951949	−	0.306255i	$-0.900924\pi$
$307$		−	10.7321i		−	0.612510i	0.951949	−	0.306255i	$-0.0990761\pi$
$308$		0			0
$309$	2.09808	+	3.63397i	0.119355	+	0.206730i
$310$		0			0
$311$	2.19615			0.124532			0.0622662	−	0.998060i	$-0.480167\pi$
$311$	2.19615			0.124532			0.0622662	+	0.998060i	$0.480167\pi$
$312$		0			0
$313$	−24.3923			−1.37873			−0.689367	−	0.724412i	$-0.742111\pi$
$313$	−24.3923			−1.37873			−0.689367	+	0.724412i	$0.742111\pi$
$314$		0			0
$315$	−4.09808	−	7.09808i	−0.230900	−	0.399931i
$316$		0			0
$317$		−	6.12436i		−	0.343978i	−0.985099	−	0.171989i	$-0.944981\pi$
$317$		−	6.12436i		−	0.343978i	0.985099	−	0.171989i	$-0.0550194\pi$
$318$		0			0
$319$	−12.2942	−	7.09808i	−0.688345	−	0.397416i
$320$		0			0
$321$	4.09808	−	7.09808i	0.228732	−	0.396176i
$322$		0			0
$323$	5.70577	−	3.29423i	0.317478	−	0.183296i
$324$		0			0
$325$	−7.19615	−	0.464102i	−0.399171	−	0.0257437i
$326$		0			0
$327$	−14.1962	+	8.19615i	−0.785049	+	0.453248i
$328$		0			0
$329$	−3.00000	+	5.19615i	−0.165395	+	0.286473i
$330$		0			0
$331$	−10.3923	−	6.00000i	−0.571213	−	0.329790i	0.186421	−	0.982470i	$-0.440311\pi$
$331$	−10.3923	−	6.00000i	−0.571213	−	0.329790i	−0.757634	+	0.652680i	$0.773645\pi$
$332$		0			0
$333$			3.00000i			0.164399i
$334$		0			0
$335$	9.29423	+	16.0981i	0.507798	+	0.879532i
$336$		0			0
$337$	31.0000			1.68868			0.844339	−	0.535810i	$-0.179994\pi$
$337$	31.0000			1.68868			0.844339	+	0.535810i	$0.179994\pi$
$338$		0			0
$339$	11.1962			0.608092
$340$		0			0
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$		0			0
$343$			39.7128i			2.14429i
$344$		0			0
$345$	−3.29423	−	1.90192i	−0.177355	−	0.102396i
$346$		0			0
$347$	−6.29423	+	10.9019i	−0.337892	+	0.585246i	−0.984036	−	0.177969i	$-0.943047\pi$
$347$	−6.29423	+	10.9019i	−0.337892	+	0.585246i	0.646144	+	0.763215i	$0.276380\pi$
$348$		0			0
$349$	2.19615	−	1.26795i	0.117557	−	0.0678718i	−0.440068	−	0.897964i	$-0.645046\pi$
$349$	2.19615	−	1.26795i	0.117557	−	0.0678718i	0.557626	+	0.830093i	$0.311712\pi$
$350$		0			0
$351$	−3.59808	−	0.232051i	−0.192051	−	0.0123860i
$352$		0			0
$353$	−5.00962	+	2.89230i	−0.266635	+	0.153942i	−0.627358	−	0.778731i	$-0.715864\pi$
$353$	−5.00962	+	2.89230i	−0.266635	+	0.153942i	0.360722	+	0.932673i	$0.382530\pi$
$354$		0			0
$355$	7.09808	−	12.2942i	0.376727	−	0.652510i
$356$		0			0
$357$	21.2942	+	12.2942i	1.12701	+	0.650680i
$358$		0			0
$359$		−	22.0526i		−	1.16389i	−0.813228	−	0.581945i	$-0.802292\pi$
$359$		−	22.0526i		−	1.16389i	0.813228	−	0.581945i	$-0.197708\pi$
$360$		0			0
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$		0			0
$363$	−11.3923			−0.597941
$364$		0			0
$365$	21.0000			1.09919
$366$		0			0
$367$	−12.0981	−	20.9545i	−0.631514	−	1.09382i	−0.987242	−	0.159225i	$-0.949100\pi$
$367$	−12.0981	−	20.9545i	−0.631514	−	1.09382i	0.355728	−	0.934590i	$-0.384233\pi$
$368$		0			0
$369$			0.464102i			0.0241602i
$370$		0			0
$371$	12.2942	+	7.09808i	0.638285	+	0.368514i
$372$		0			0
$373$	−11.9904	+	20.7679i	−0.620838	+	1.07532i	0.368492	+	0.929631i	$0.379874\pi$
$373$	−11.9904	+	20.7679i	−0.620838	+	1.07532i	−0.989330	+	0.145693i	$0.953459\pi$
$374$		0			0
$375$	10.5000	−	6.06218i	0.542218	−	0.313050i
$376$		0			0
$377$	−4.79423	−	9.69615i	−0.246915	−	0.499377i
$378$		0			0
$379$	−15.8038	+	9.12436i	−0.811789	+	0.468687i	−0.847577	−	0.530673i	$-0.821939\pi$
$379$	−15.8038	+	9.12436i	−0.811789	+	0.468687i	0.0357877	+	0.999359i	$0.488606\pi$
$380$		0			0
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$		0			0
$383$	−9.80385	−	5.66025i	−0.500953	−	0.289225i	0.228154	−	0.973625i	$-0.426731\pi$
$383$	−9.80385	−	5.66025i	−0.500953	−	0.289225i	−0.729107	+	0.684400i	$0.760064\pi$
$384$		0			0
$385$		−	38.7846i		−	1.97665i
$386$		0			0
$387$	−3.09808	−	5.36603i	−0.157484	−	0.272770i
$388$		0			0
$389$	13.3923			0.679017			0.339508	−	0.940603i	$-0.389739\pi$
$389$	13.3923			0.679017			0.339508	+	0.940603i	$0.389739\pi$
$390$		0			0
$391$	11.4115			0.577107
$392$		0			0
$393$	8.19615	+	14.1962i	0.413441	+	0.716101i
$394$		0			0
$395$			21.4641i			1.07998i
$396$		0			0
$397$	14.1962	+	8.19615i	0.712484	+	0.411353i	0.811980	−	0.583685i	$-0.198390\pi$
$397$	14.1962	+	8.19615i	0.712484	+	0.411353i	−0.0994958	+	0.995038i	$0.531723\pi$
$398$		0			0
$399$	−3.00000	+	5.19615i	−0.150188	+	0.260133i
$400$		0			0
$401$	18.1865	−	10.5000i	0.908192	−	0.524345i	0.0283431	−	0.999598i	$-0.490977\pi$
$401$	18.1865	−	10.5000i	0.908192	−	0.524345i	0.879849	+	0.475253i	$0.157644\pi$
$402$		0			0
$403$	0.588457	−	9.12436i	0.0293131	−	0.454517i
$404$		0			0
$405$	1.50000	−	0.866025i	0.0745356	−	0.0430331i
$406$		0			0
$407$	−7.09808	+	12.2942i	−0.351839	+	0.609402i
$408$		0			0
$409$	−2.89230	−	1.66987i	−0.143015	−	0.0825699i	0.426785	−	0.904353i	$-0.359646\pi$
$409$	−2.89230	−	1.66987i	−0.143015	−	0.0825699i	−0.569800	+	0.821783i	$0.692979\pi$
$410$		0			0
$411$		−	9.00000i		−	0.443937i
$412$		0			0
$413$	32.7846	+	56.7846i	1.61323	+	2.79419i
$414$		0			0
$415$	20.1962			0.991390
$416$		0			0
$417$	4.00000			0.195881
$418$		0			0
$419$	8.19615	+	14.1962i	0.400408	+	0.693527i	0.993775	−	0.111405i	$-0.0355350\pi$
$419$	8.19615	+	14.1962i	0.400408	+	0.693527i	−0.593367	+	0.804932i	$0.702202\pi$
$420$		0			0
$421$		−	0.464102i		−	0.0226189i	−0.999936	−	0.0113095i	$-0.996400\pi$
$421$		−	0.464102i		−	0.0226189i	0.999936	−	0.0113095i	$-0.00359999\pi$
$422$		0			0
$423$	−1.09808	−	0.633975i	−0.0533903	−	0.0308249i
$424$		0			0
$425$	−5.19615	+	9.00000i	−0.252050	+	0.436564i
$426$		0			0
$427$	−19.6865	+	11.3660i	−0.952698	+	0.550041i
$428$		0			0
$429$	−14.1962	−	9.46410i	−0.685397	−	0.456931i
$430$		0			0
$431$	24.0788	−	13.9019i	1.15984	−	0.669632i	0.208572	−	0.978007i	$-0.433118\pi$
$431$	24.0788	−	13.9019i	1.15984	−	0.669632i	0.951265	+	0.308375i	$0.0997851\pi$
$432$		0			0
$433$	−16.8923	+	29.2583i	−0.811792	+	1.40607i	0.0998161	+	0.995006i	$0.468175\pi$
$433$	−16.8923	+	29.2583i	−0.811792	+	1.40607i	−0.911608	+	0.411060i	$0.865159\pi$
$434$		0			0
$435$	4.50000	+	2.59808i	0.215758	+	0.124568i
$436$		0			0
$437$			2.78461i			0.133206i
$438$		0			0
$439$	−8.29423	−	14.3660i	−0.395862	−	0.685653i	0.597349	−	0.801982i	$-0.296221\pi$
$439$	−8.29423	−	14.3660i	−0.395862	−	0.685653i	−0.993211	+	0.116329i	$0.962887\pi$
$440$		0			0
$441$	−15.3923			−0.732967
$442$		0			0
$443$	4.39230			0.208685			0.104342	−	0.994541i	$-0.466726\pi$
$443$	4.39230			0.208685			0.104342	+	0.994541i	$0.466726\pi$
$444$		0			0
$445$	2.19615	+	3.80385i	0.104108	+	0.180320i
$446$		0			0
$447$			18.1244i			0.857253i
$448$		0			0
$449$	−28.9808	−	16.7321i	−1.36769	−	0.789634i	−0.377054	−	0.926191i	$-0.623063\pi$
$449$	−28.9808	−	16.7321i	−1.36769	−	0.789634i	−0.990632	+	0.136557i	$0.956396\pi$
$450$		0			0
$451$	−1.09808	+	1.90192i	−0.0517064	+	0.0895581i
$452$		0			0
$453$	−6.29423	+	3.63397i	−0.295729	+	0.170739i
$454$		0			0
$455$	16.3923	−	24.5885i	0.768483	−	1.15272i
$456$		0			0
$457$	−17.3038	+	9.99038i	−0.809440	+	0.467330i	−0.846761	−	0.531973i	$-0.821451\pi$
$457$	−17.3038	+	9.99038i	−0.809440	+	0.467330i	0.0373215	+	0.999303i	$0.488117\pi$
$458$		0			0
$459$	−2.59808	+	4.50000i	−0.121268	+	0.210042i
$460$		0			0
$461$	−17.3038	−	9.99038i	−0.805921	−	0.465298i	0.0396167	−	0.999215i	$-0.487386\pi$
$461$	−17.3038	−	9.99038i	−0.805921	−	0.465298i	−0.845537	+	0.533917i	$0.820720\pi$
$462$		0			0
$463$			26.1962i			1.21744i	0.793386	+	0.608719i	$0.208316\pi$
$463$			26.1962i			1.21744i	−0.793386	+	0.608719i	$0.791684\pi$
$464$		0			0
$465$	2.19615	+	3.80385i	0.101844	+	0.176399i
$466$		0			0
$467$	36.5885			1.69311			0.846556	−	0.532300i	$-0.178672\pi$
$467$	36.5885			1.69311			0.846556	+	0.532300i	$0.178672\pi$
$468$		0			0
$469$	50.7846			2.34502
$470$		0			0
$471$	1.59808	+	2.76795i	0.0736355	+	0.127540i
$472$		0			0
$473$		−	29.3205i		−	1.34816i
$474$		0			0
$475$	−2.19615	−	1.26795i	−0.100766	−	0.0581775i
$476$		0			0
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$		0			0
$479$	30.5885	−	17.6603i	1.39762	−	0.806918i	0.403479	−	0.914989i	$-0.367801\pi$
$479$	30.5885	−	17.6603i	1.39762	−	0.806918i	0.994143	+	0.108071i	$0.0344675\pi$
$480$		0			0
$481$	−9.69615	+	4.79423i	−0.442106	+	0.218598i
$482$		0			0
$483$	−9.00000	+	5.19615i	−0.409514	+	0.236433i
$484$		0			0
$485$	−5.19615	+	9.00000i	−0.235945	+	0.408669i
$486$		0			0
$487$	−7.90192	−	4.56218i	−0.358070	−	0.206732i	0.310164	−	0.950683i	$-0.399616\pi$
$487$	−7.90192	−	4.56218i	−0.358070	−	0.206732i	−0.668234	+	0.743951i	$0.732949\pi$
$488$		0			0
$489$		−	9.46410i		−	0.427981i
$490$		0			0
$491$	−0.294229	−	0.509619i	−0.0132784	−	0.0229988i	0.859310	−	0.511455i	$-0.170893\pi$
$491$	−0.294229	−	0.509619i	−0.0132784	−	0.0229988i	−0.872588	+	0.488457i	$0.837560\pi$
$492$		0			0
$493$	−15.5885			−0.702069
$494$		0			0
$495$	8.19615			0.368390
$496$		0			0
$497$	−19.3923	−	33.5885i	−0.869864	−	1.50665i
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$	−2.19615	−	1.26795i	−0.0981169	−	0.0566478i
$502$		0			0
$503$	−9.29423	+	16.0981i	−0.414409	+	0.717778i	−0.995366	−	0.0961565i	$-0.969345\pi$
$503$	−9.29423	+	16.0981i	−0.414409	+	0.717778i	0.580957	+	0.813934i	$0.302678\pi$
$504$		0			0
$505$	2.08846	−	1.20577i	0.0929351	−	0.0536561i
$506$		0			0
$507$	−5.00000	−	12.0000i	−0.222058	−	0.532939i
$508$		0			0
$509$	−8.08846	+	4.66987i	−0.358515	+	0.206988i	−0.668429	−	0.743776i	$-0.733033\pi$
$509$	−8.08846	+	4.66987i	−0.358515	+	0.206988i	0.309914	+	0.950764i	$0.399700\pi$
$510$		0			0
$511$	28.6865	−	49.6865i	1.26902	−	2.19800i
$512$		0			0
$513$	−1.09808	−	0.633975i	−0.0484812	−	0.0279907i
$514$		0			0
$515$		−	7.26795i		−	0.320264i
$516$		0			0
$517$	−3.00000	−	5.19615i	−0.131940	−	0.228527i
$518$		0			0
$519$	−16.3923			−0.719542
$520$		0			0
$521$	−18.8038			−0.823812			−0.411906	−	0.911226i	$-0.635137\pi$
$521$	−18.8038			−0.823812			−0.411906	+	0.911226i	$0.635137\pi$
$522$		0			0
$523$	0.705771	+	1.22243i	0.0308612	+	0.0534532i	0.881044	−	0.473035i	$-0.156842\pi$
$523$	0.705771	+	1.22243i	0.0308612	+	0.0534532i	−0.850182	+	0.526488i	$0.823508\pi$
$524$		0			0
$525$		−	9.46410i		−	0.413047i
$526$		0			0
$527$	−11.4115	−	6.58846i	−0.497095	−	0.286998i
$528$		0			0
$529$	9.08846	−	15.7417i	0.395150	−	0.684420i
$530$		0			0
$531$	−12.0000	+	6.92820i	−0.520756	+	0.300658i
$532$		0			0
$533$	−1.50000	+	0.741670i	−0.0649722	+	0.0321253i
$534$		0			0
$535$	−12.2942	+	7.09808i	−0.531526	+	0.306877i
$536$		0			0
$537$	4.09808	−	7.09808i	0.176845	−	0.306305i
$538$		0			0
$539$	−63.0788	−	36.4186i	−2.71700	−	1.56866i
$540$		0			0
$541$			16.8564i			0.724714i	0.932039	+	0.362357i	$0.118028\pi$
$541$			16.8564i			0.724714i	−0.932039	+	0.362357i	$0.881972\pi$
$542$		0			0
$543$	−5.79423	−	10.0359i	−0.248654	−	0.430682i
$544$		0			0
$545$	28.3923			1.21619
$546$		0			0
$547$	6.19615			0.264928			0.132464	−	0.991188i	$-0.457711\pi$
$547$	6.19615			0.264928			0.132464	+	0.991188i	$0.457711\pi$
$548$		0			0
$549$	−2.40192	−	4.16025i	−0.102512	−	0.177555i
$550$		0			0
$551$		−	3.80385i		−	0.162049i
$552$		0			0
$553$	50.7846	+	29.3205i	2.15958	+	1.24683i
$554$		0			0
$555$	2.59808	−	4.50000i	0.110282	−	0.191014i
$556$		0			0
$557$	19.2846	−	11.1340i	0.817115	−	0.471762i	−0.0323055	−	0.999478i	$-0.510285\pi$
$557$	19.2846	−	11.1340i	0.817115	−	0.471762i	0.849421	+	0.527716i	$0.176952\pi$
$558$		0			0
$559$	12.3923	−	18.5885i	0.524139	−	0.786208i
$560$		0			0
$561$	−21.2942	+	12.2942i	−0.899043	+	0.519063i
$562$		0			0
$563$	−4.39230	+	7.60770i	−0.185114	+	0.320626i	−0.943615	−	0.331046i	$-0.892599\pi$
$563$	−4.39230	+	7.60770i	−0.185114	+	0.320626i	0.758501	+	0.651672i	$0.225932\pi$
$564$		0			0
$565$	−16.7942	−	9.69615i	−0.706539	−	0.407920i
$566$		0			0
$567$		−	4.73205i		−	0.198727i
$568$		0			0
$569$	−16.3923	−	28.3923i	−0.687201	−	1.19027i	−0.972740	−	0.231900i	$-0.925506\pi$
$569$	−16.3923	−	28.3923i	−0.687201	−	1.19027i	0.285538	−	0.958367i	$-0.407828\pi$
$570$		0			0
$571$	−13.8038			−0.577673			−0.288837	−	0.957378i	$-0.593268\pi$
$571$	−13.8038			−0.577673			−0.288837	+	0.957378i	$0.593268\pi$
$572$		0			0
$573$	−20.7846			−0.868290
$574$		0			0
$575$	−2.19615	−	3.80385i	−0.0915859	−	0.158631i
$576$		0			0
$577$			16.2679i			0.677244i	0.940923	+	0.338622i	$0.109961\pi$
$577$			16.2679i			0.677244i	−0.940923	+	0.338622i	$0.890039\pi$
$578$		0			0
$579$	11.0885	+	6.40192i	0.460821	+	0.266055i
$580$		0			0
$581$	27.5885	−	47.7846i	1.14456	−	1.98244i
$582$		0			0
$583$	−12.2942	+	7.09808i	−0.509175	+	0.293972i
$584$		0			0
$585$	5.19615	+	3.46410i	0.214834	+	0.143223i
$586$		0			0
$587$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$587$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$588$		0			0
$589$	1.60770	−	2.78461i	0.0662439	−	0.114738i
$590$		0			0
$591$	6.00000	+	3.46410i	0.246807	+	0.142494i
$592$		0			0
$593$		−	46.8564i		−	1.92416i	−0.272764	−	0.962081i	$-0.587938\pi$
$593$		−	46.8564i		−	1.92416i	0.272764	−	0.962081i	$-0.412062\pi$
$594$		0			0
$595$	−21.2942	−	36.8827i	−0.872978	−	1.51204i
$596$		0			0
$597$	8.58846			0.351502
$598$		0			0
$599$	4.39230			0.179465			0.0897324	−	0.995966i	$-0.471399\pi$
$599$	4.39230			0.179465			0.0897324	+	0.995966i	$0.471399\pi$
$600$		0			0
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	0.553697	−	0.832718i	$-0.313216\pi$
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	−0.998004	+	0.0631568i	$0.979883\pi$
$602$		0			0
$603$			10.7321i			0.437043i
$604$		0			0
$605$	17.0885	+	9.86603i	0.694745	+	0.401111i
$606$		0			0
$607$	−24.3923	+	42.2487i	−0.990053	+	1.71482i	−0.373182	+	0.927758i	$0.621733\pi$
$607$	−24.3923	+	42.2487i	−0.990053	+	1.71482i	−0.616871	+	0.787064i	$0.711600\pi$
$608$		0			0
$609$	12.2942	−	7.09808i	0.498187	−	0.287629i
$610$		0			0
$611$	0.294229	−	4.56218i	0.0119032	−	0.184566i
$612$		0			0
$613$	35.3827	−	20.4282i	1.42909	−	0.825087i	0.432044	−	0.901853i	$-0.357793\pi$
$613$	35.3827	−	20.4282i	1.42909	−	0.825087i	0.997049	+	0.0767652i	$0.0244592\pi$
$614$		0			0
$615$	0.401924	−	0.696152i	0.0162071	−	0.0280716i
$616$		0			0
$617$	9.18653	+	5.30385i	0.369836	+	0.213525i	0.673387	−	0.739290i	$-0.264839\pi$
$617$	9.18653	+	5.30385i	0.369836	+	0.213525i	−0.303551	+	0.952815i	$0.598172\pi$
$618$		0			0
$619$			7.60770i			0.305779i	0.988243	+	0.152890i	$0.0488579\pi$
$619$			7.60770i			0.305779i	−0.988243	+	0.152890i	$0.951142\pi$
$620$		0			0
$621$	−1.09808	−	1.90192i	−0.0440643	−	0.0763216i
$622$		0			0
$623$	12.0000			0.480770
$624$		0			0
$625$	−11.0000			−0.440000
$626$		0			0
$627$	−3.00000	−	5.19615i	−0.119808	−	0.207514i
$628$		0			0
$629$			15.5885i			0.621552i
$630$		0			0
$631$	22.3923	+	12.9282i	0.891424	+	0.514664i	0.874408	−	0.485192i	$-0.161250\pi$
$631$	22.3923	+	12.9282i	0.891424	+	0.514664i	0.0170157	+	0.999855i	$0.494583\pi$
$632$		0			0
$633$	−1.80385	+	3.12436i	−0.0716965	+	0.124182i
$634$		0			0
$635$	−6.00000	+	3.46410i	−0.238103	+	0.137469i
$636$		0			0
$637$	−24.5981	−	49.7487i	−0.974611	−	1.97112i
$638$		0			0
$639$	7.09808	−	4.09808i	0.280796	−	0.162117i
$640$		0			0
$641$	−15.4019	+	26.6769i	−0.608339	+	1.05367i	0.383175	+	0.923676i	$0.374831\pi$
$641$	−15.4019	+	26.6769i	−0.608339	+	1.05367i	−0.991514	+	0.129999i	$0.958503\pi$
$642$		0			0
$643$	24.0000	+	13.8564i	0.946468	+	0.546443i	0.891982	−	0.452071i	$-0.149315\pi$
$643$	24.0000	+	13.8564i	0.946468	+	0.546443i	0.0544858	+	0.998515i	$0.482648\pi$
$644$		0			0
$645$			10.7321i			0.422574i
$646$		0			0
$647$	−6.58846	−	11.4115i	−0.259019	−	0.448634i	0.706960	−	0.707253i	$-0.250066\pi$
$647$	−6.58846	−	11.4115i	−0.259019	−	0.448634i	−0.965979	+	0.258619i	$0.916733\pi$
$648$		0			0
$649$	−65.5692			−2.57382
$650$		0			0
$651$	12.0000			0.470317
$652$		0			0
$653$	24.5885	+	42.5885i	0.962221	+	1.66662i	0.716904	+	0.697172i	$0.245559\pi$
$653$	24.5885	+	42.5885i	0.962221	+	1.66662i	0.245317	+	0.969443i	$0.421108\pi$
$654$		0			0
$655$		−	28.3923i		−	1.10938i
$656$		0			0
$657$	10.5000	+	6.06218i	0.409644	+	0.236508i
$658$		0			0
$659$	12.5885	−	21.8038i	0.490377	−	0.849357i	−0.509562	−	0.860434i	$-0.670193\pi$
$659$	12.5885	−	21.8038i	0.490377	−	0.849357i	0.999939	+	0.0110766i	$0.00352588\pi$
$660$		0			0
$661$	7.79423	−	4.50000i	0.303160	−	0.175030i	−0.340701	−	0.940172i	$-0.610665\pi$
$661$	7.79423	−	4.50000i	0.303160	−	0.175030i	0.643862	+	0.765142i	$0.277331\pi$
$662$		0			0
$663$	−18.6962	−	1.20577i	−0.726098	−	0.0468283i
$664$		0			0
$665$	9.00000	−	5.19615i	0.349005	−	0.201498i
$666$		0			0
$667$	3.29423	−	5.70577i	0.127553	−	0.220928i
$668$		0			0
$669$	16.3923	+	9.46410i	0.633763	+	0.365903i
$670$		0			0
$671$		−	22.7321i		−	0.877561i
$672$		0			0
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$		0			0
$675$	2.00000			0.0769800
$676$		0			0
$677$	4.39230			0.168810			0.0844050	−	0.996432i	$-0.473101\pi$
$677$	4.39230			0.168810			0.0844050	+	0.996432i	$0.473101\pi$
$678$		0			0
$679$	14.1962	+	24.5885i	0.544798	+	0.943618i
$680$		0			0
$681$		−	9.80385i		−	0.375684i
$682$		0			0
$683$	24.0000	+	13.8564i	0.918334	+	0.530201i	0.883103	−	0.469179i	$-0.155450\pi$
$683$	24.0000	+	13.8564i	0.918334	+	0.530201i	0.0352311	+	0.999379i	$0.488783\pi$
$684$		0			0
$685$	−7.79423	+	13.5000i	−0.297802	+	0.515808i
$686$		0			0
$687$	17.1962	−	9.92820i	0.656074	−	0.378785i
$688$		0			0
$689$	−10.7942	−	0.696152i	−0.411227	−	0.0265213i
$690$		0			0
$691$	−16.9019	+	9.75833i	−0.642979	+	0.371224i	−0.785761	−	0.618530i	$-0.787729\pi$
$691$	−16.9019	+	9.75833i	−0.642979	+	0.371224i	0.142782	+	0.989754i	$0.454395\pi$
$692$		0			0
$693$	11.1962	−	19.3923i	0.425307	−	0.736653i
$694$		0			0
$695$	−6.00000	−	3.46410i	−0.227593	−	0.131401i
$696$		0			0
$697$			2.41154i			0.0913437i
$698$		0			0
$699$	−9.00000	−	15.5885i	−0.340411	−	0.589610i
$700$		0			0
$701$	−4.39230			−0.165895			−0.0829475	−	0.996554i	$-0.526433\pi$
$701$	−4.39230			−0.165895			−0.0829475	+	0.996554i	$0.526433\pi$
$702$		0			0
$703$	−3.80385			−0.143465
$704$		0			0
$705$	1.09808	+	1.90192i	0.0413559	+	0.0716306i
$706$		0			0
$707$		−	6.58846i		−	0.247784i
$708$		0			0
$709$	−2.81347	−	1.62436i	−0.105662	−	0.0610040i	0.446238	−	0.894914i	$-0.352764\pi$
$709$	−2.81347	−	1.62436i	−0.105662	−	0.0610040i	−0.551900	+	0.833910i	$0.686097\pi$
$710$		0			0
$711$	−6.19615	+	10.7321i	−0.232374	+	0.402483i
$712$		0			0
$713$	4.82309	−	2.78461i	0.180626	−	0.104284i
$714$		0			0
$715$	13.0981	+	26.4904i	0.489840	+	0.990684i
$716$		0			0
$717$	−21.2942	+	12.2942i	−0.795248	+	0.459136i
$718$		0			0
$719$	−26.1962	+	45.3731i	−0.976952	+	1.69213i	−0.303613	+	0.952795i	$0.598193\pi$
$719$	−26.1962	+	45.3731i	−0.976952	+	1.69213i	−0.673338	+	0.739335i	$0.735140\pi$
$720$		0			0
$721$	−17.1962	−	9.92820i	−0.640418	−	0.369746i
$722$		0			0
$723$			0.803848i			0.0298954i
$724$		0			0
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$		0			0
$727$	−24.1962			−0.897386			−0.448693	−	0.893686i	$-0.648110\pi$
$727$	−24.1962			−0.897386			−0.448693	+	0.893686i	$0.648110\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−16.0981	−	27.8827i	−0.595409	−	1.03128i
$732$		0			0
$733$			14.3205i			0.528940i	0.964394	+	0.264470i	$0.0851970\pi$
$733$			14.3205i			0.528940i	−0.964394	+	0.264470i	$0.914803\pi$
$734$		0			0
$735$	23.0885	+	13.3301i	0.851631	+	0.491689i
$736$		0			0
$737$	−25.3923	+	43.9808i	−0.935338	+	1.62005i
$738$		0			0
$739$	16.3923	−	9.46410i	0.603001	−	0.348143i	−0.167220	−	0.985920i	$-0.553479\pi$
$739$	16.3923	−	9.46410i	0.603001	−	0.348143i	0.770221	+	0.637777i	$0.220146\pi$
$740$		0			0
$741$	0.294229	−	4.56218i	0.0108088	−	0.167596i
$742$		0			0
$743$	3.80385	−	2.19615i	0.139550	−	0.0805690i	−0.428600	−	0.903494i	$-0.640993\pi$
$743$	3.80385	−	2.19615i	0.139550	−	0.0805690i	0.568149	+	0.822925i	$0.307660\pi$
$744$		0			0
$745$	15.6962	−	27.1865i	0.575063	−	0.996038i
$746$		0			0
$747$	10.0981	+	5.83013i	0.369469	+	0.213313i
$748$		0			0
$749$			38.7846i			1.41716i
$750$		0			0
$751$	12.4904	+	21.6340i	0.455780	+	0.789435i	0.998733	−	0.0503286i	$-0.0160269\pi$
$751$	12.4904	+	21.6340i	0.455780	+	0.789435i	−0.542952	+	0.839764i	$0.682694\pi$
$752$		0			0
$753$	−4.39230			−0.160064
$754$		0			0
$755$	12.5885			0.458141
$756$		0			0
$757$	−9.39230	−	16.2679i	−0.341369	−	0.591269i	0.643318	−	0.765599i	$-0.277557\pi$
$757$	−9.39230	−	16.2679i	−0.341369	−	0.591269i	−0.984687	+	0.174330i	$0.944224\pi$
$758$		0			0
$759$		−	10.3923i		−	0.377217i
$760$		0			0
$761$	3.80385	+	2.19615i	0.137889	+	0.0796105i	0.567358	−	0.823471i	$-0.307966\pi$
$761$	3.80385	+	2.19615i	0.137889	+	0.0796105i	−0.429468	+	0.903082i	$0.641299\pi$
$762$		0			0
$763$	38.7846	−	67.1769i	1.40410	−	2.43197i
$764$		0			0
$765$	7.79423	−	4.50000i	0.281801	−	0.162698i
$766$		0			0
$767$	−41.5692	−	27.7128i	−1.50098	−	1.00065i
$768$		0			0
$769$	−29.1962	+	16.8564i	−1.05284	+	0.607858i	−0.923443	−	0.383735i	$-0.874638\pi$
$769$	−29.1962	+	16.8564i	−1.05284	+	0.607858i	−0.129397	+	0.991593i	$0.541304\pi$
$770$		0			0
$771$	6.40192	−	11.0885i	0.230560	−	0.399341i
$772$		0			0
$773$	−43.9808	−	25.3923i	−1.58188	−	0.913298i	−0.994585	−	0.103923i	$-0.966860\pi$
$773$	−43.9808	−	25.3923i	−1.58188	−	0.913298i	−0.587293	−	0.809375i	$-0.699806\pi$
$774$		0			0
$775$			5.07180i			0.182184i
$776$		0			0
$777$	−7.09808	−	12.2942i	−0.254642	−	0.441053i
$778$		0			0
$779$	−0.588457			−0.0210837
$780$		0			0
$781$	38.7846			1.38782
$782$		0			0
$783$	1.50000	+	2.59808i	0.0536056	+	0.0928477i
$784$		0			0
$785$		−	5.53590i		−	0.197585i
$786$		0			0
$787$	−12.5885	−	7.26795i	−0.448730	−	0.259074i	0.258564	−	0.965994i	$-0.416751\pi$
$787$	−12.5885	−	7.26795i	−0.448730	−	0.259074i	−0.707294	+	0.706920i	$0.750084\pi$
$788$		0			0
$789$	−1.09808	+	1.90192i	−0.0390925	+	0.0677103i
$790$		0			0
$791$	−45.8827	+	26.4904i	−1.63140	+	0.941890i
$792$		0			0
$793$	9.60770	−	14.4115i	0.341179	−	0.511769i
$794$		0			0
$795$	4.50000	−	2.59808i	0.159599	−	0.0921443i
$796$		0			0
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	−0.807989	−	0.589197i	$-0.799444\pi$
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	0.914255	+	0.405140i	$0.132777\pi$
$798$		0			0
$799$	−5.70577	−	3.29423i	−0.201856	−	0.116541i
$800$		0			0
$801$			2.53590i			0.0896016i
$802$		0			0
$803$	28.6865	+	49.6865i	1.01233	+	1.75340i
$804$		0			0
$805$	18.0000			0.634417
$806$		0			0
$807$	−28.3923			−0.999456
$808$		0			0
$809$	23.5981	+	40.8731i	0.829664	+	1.43702i	0.898302	+	0.439379i	$0.144801\pi$
$809$	23.5981	+	40.8731i	0.829664	+	1.43702i	−0.0686377	+	0.997642i	$0.521865\pi$
$810$		0			0
$811$			4.39230i			0.154235i	0.997022	+	0.0771173i	$0.0245716\pi$
$811$			4.39230i			0.154235i	−0.997022	+	0.0771173i	$0.975428\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−8.19615	+	14.1962i	−0.287099	+	0.497270i
$816$		0			0
$817$	6.80385	−	3.92820i	0.238036	−	0.137430i
$818$		0			0
$819$	15.2942	−	7.56218i	0.534424	−	0.264244i
$820$		0			0
$821$	35.1962	−	20.3205i	1.22835	−	0.709191i	0.261669	−	0.965158i	$-0.415727\pi$
$821$	35.1962	−	20.3205i	1.22835	−	0.709191i	0.966685	+	0.255967i	$0.0823939\pi$
$822$		0			0
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	−0.439961	−	0.898017i	$-0.645008\pi$
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	0.997686	−	0.0679910i	$-0.0216589\pi$
$824$		0			0
$825$	8.19615	+	4.73205i	0.285353	+	0.164749i
$826$		0			0
$827$			32.1051i			1.11640i	0.829705	+	0.558202i	$0.188509\pi$
$827$			32.1051i			1.11640i	−0.829705	+	0.558202i	$0.811491\pi$
$828$		0			0
$829$	−5.99038	−	10.3756i	−0.208055	−	0.360361i	0.743047	−	0.669239i	$-0.233380\pi$
$829$	−5.99038	−	10.3756i	−0.208055	−	0.360361i	−0.951102	+	0.308878i	$0.900046\pi$
$830$		0			0
$831$	−15.1962			−0.527149
$832$		0			0
$833$	−79.9808			−2.77117
$834$		0			0
$835$	2.19615	+	3.80385i	0.0760010	+	0.131638i
$836$		0			0
$837$			2.53590i			0.0876535i
$838$		0			0
$839$	−10.3923	−	6.00000i	−0.358782	−	0.207143i	0.309764	−	0.950813i	$-0.399750\pi$
$839$	−10.3923	−	6.00000i	−0.358782	−	0.207143i	−0.668546	+	0.743670i	$0.733083\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	21.1865	−	12.2321i	0.729703	−	0.421294i
$844$		0			0
$845$	−2.89230	+	22.3301i	−0.0994983	+	0.768180i
$846$		0			0
$847$	46.6865	−	26.9545i	1.60417	−	0.926167i
$848$		0			0
$849$	15.0981	−	26.1506i	0.518165	−	0.897487i
$850$		0			0
$851$	−5.70577	−	3.29423i	−0.195591	−	0.112925i
$852$		0			0
$853$			9.00000i			0.308154i	0.988059	+	0.154077i	$0.0492404\pi$
$853$			9.00000i			0.308154i	−0.988059	+	0.154077i	$0.950760\pi$
$854$		0			0
$855$	1.09808	+	1.90192i	0.0375534	+	0.0650444i
$856$		0			0
$857$	54.3731			1.85735			0.928674	−	0.370896i	$-0.120949\pi$
$857$	54.3731			1.85735			0.928674	+	0.370896i	$0.120949\pi$
$858$		0			0
$859$	−10.5885			−0.361273			−0.180637	−	0.983550i	$-0.557816\pi$
$859$	−10.5885			−0.361273			−0.180637	+	0.983550i	$0.557816\pi$
$860$		0			0
$861$	−1.09808	−	1.90192i	−0.0374223	−	0.0648174i
$862$		0			0
$863$			4.48334i			0.152615i	0.997084	+	0.0763073i	$0.0243130\pi$
$863$			4.48334i			0.152615i	−0.997084	+	0.0763073i	$0.975687\pi$
$864$		0			0
$865$	24.5885	+	14.1962i	0.836033	+	0.482684i
$866$		0			0
$867$	−5.00000	+	8.66025i	−0.169809	+	0.294118i
$868$		0			0
$869$	−50.7846	+	29.3205i	−1.72275	+	0.994630i
$870$		0			0
$871$	−34.6865	+	17.1506i	−1.17531	+	0.581127i
$872$		0			0
$873$	−5.19615	+	3.00000i	−0.175863	+	0.101535i
$874$		0			0
$875$	−28.6865	+	49.6865i	−0.969782	+	1.67971i
$876$		0			0
$877$	37.5788	+	21.6962i	1.26895	+	0.732627i	0.974789	−	0.223130i	$-0.0716273\pi$
$877$	37.5788	+	21.6962i	1.26895	+	0.732627i	0.294158	+	0.955757i	$0.404961\pi$
$878$		0			0
$879$		−	14.6603i		−	0.494478i
$880$		0			0
$881$	18.9904	+	32.8923i	0.639802	+	1.10817i	0.985476	+	0.169815i	$0.0543171\pi$
$881$	18.9904	+	32.8923i	0.639802	+	1.10817i	−0.345674	+	0.938355i	$0.612350\pi$
$882$		0			0
$883$	−24.7846			−0.834069			−0.417034	−	0.908891i	$-0.636930\pi$
$883$	−24.7846			−0.834069			−0.417034	+	0.908891i	$0.636930\pi$
$884$		0			0
$885$	24.0000			0.806751
$886$		0			0
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	0.915722	+	0.401813i	$0.131620\pi$
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	−0.109881	+	0.993945i	$0.535047\pi$
$888$		0			0
$889$			18.9282i			0.634832i
$890$		0			0
$891$	4.09808	+	2.36603i	0.137291	+	0.0792648i
$892$		0			0
$893$	0.803848	−	1.39230i	0.0268997	−	0.0465917i
$894$		0			0
$895$	−12.2942	+	7.09808i	−0.410951	+	0.237263i
$896$		0			0
$897$	4.39230	−	6.58846i	0.146655	−	0.219982i
$898$		0			0
$899$	−6.58846	+	3.80385i	−0.219737	+	0.126865i
$900$		0			0
$901$	−7.79423	+	13.5000i	−0.259663	+	0.449750i
$902$		0			0
$903$	25.3923	+	14.6603i	0.845003	+	0.487863i
$904$		0			0
$905$			20.0718i			0.667209i
$906$		0			0
$907$	20.5885	+	35.6603i	0.683629	+	1.18408i	0.973866	+	0.227125i	$0.0729325\pi$
$907$	20.5885	+	35.6603i	0.683629	+	1.18408i	−0.290237	+	0.956955i	$0.593734\pi$
$908$		0			0
$909$	1.39230			0.0461798
$910$		0			0
$911$	−37.1769			−1.23173			−0.615863	−	0.787853i	$-0.711193\pi$
$911$	−37.1769			−1.23173			−0.615863	+	0.787853i	$0.711193\pi$
$912$		0			0
$913$	27.5885	+	47.7846i	0.913045	+	1.58144i
$914$		0			0
$915$			8.32051i			0.275068i
$916$		0			0
$917$	−67.1769	−	38.7846i	−2.21838	−	1.28078i
$918$		0			0
$919$	16.1962	−	28.0526i	0.534262	−	0.925369i	−0.464937	−	0.885344i	$-0.653923\pi$
$919$	16.1962	−	28.0526i	0.534262	−	0.925369i	0.999199	−	0.0400247i	$-0.0127437\pi$
$920$		0			0
$921$	−9.29423	+	5.36603i	−0.306255	+	0.176817i
$922$		0			0
$923$	24.5885	+	16.3923i	0.809339	+	0.539559i
$924$		0			0
$925$	5.19615	−	3.00000i	0.170848	−	0.0986394i
$926$		0			0
$927$	2.09808	−	3.63397i	0.0689099	−	0.119355i
$928$		0			0
$929$	−29.9711	−	17.3038i	−0.983321	−	0.567721i	−0.0800501	−	0.996791i	$-0.525508\pi$
$929$	−29.9711	−	17.3038i	−0.983321	−	0.567721i	−0.903271	+	0.429070i	$0.858841\pi$
$930$		0			0
$931$		−	19.5167i		−	0.639633i
$932$		0			0
$933$	−1.09808	−	1.90192i	−0.0359494	−	0.0622662i
$934$		0			0
$935$	42.5885			1.39279
$936$		0			0
$937$	5.39230			0.176159			0.0880795	−	0.996113i	$-0.471927\pi$
$937$	5.39230			0.176159			0.0880795	+	0.996113i	$0.471927\pi$
$938$		0			0
$939$	12.1962	+	21.1244i	0.398006	+	0.689367i
$940$		0			0
$941$		−	2.78461i		−	0.0907757i	−0.998969	−	0.0453878i	$-0.985548\pi$
$941$		−	2.78461i		−	0.0907757i	0.998969	−	0.0453878i	$-0.0144524\pi$
$942$		0			0
$943$	−0.882686	−	0.509619i	−0.0287442	−	0.0165955i
$944$		0			0
$945$	−4.09808	+	7.09808i	−0.133310	+	0.230900i
$946$		0			0
$947$	37.1769	−	21.4641i	1.20809	−	0.697490i	0.245746	−	0.969334i	$-0.420967\pi$
$947$	37.1769	−	21.4641i	1.20809	−	0.697490i	0.962341	+	0.271845i	$0.0876337\pi$
$948$		0			0
$949$	−2.81347	+	43.6244i	−0.0913290	+	1.41611i
$950$		0			0
$951$	−5.30385	+	3.06218i	−0.171989	+	0.0992979i
$952$		0			0
$953$	−12.0000	+	20.7846i	−0.388718	+	0.673280i	−0.992277	−	0.124039i	$-0.960415\pi$
$953$	−12.0000	+	20.7846i	−0.388718	+	0.673280i	0.603559	+	0.797318i	$0.293749\pi$
$954$		0			0
$955$	31.1769	+	18.0000i	1.00886	+	0.582466i
$956$		0			0
$957$			14.1962i			0.458896i
$958$		0			0
$959$	21.2942	+	36.8827i	0.687627	+	1.19100i
$960$		0			0
$961$	24.5692			0.792555
$962$		0			0
$963$	−8.19615			−0.264117
$964$		0			0
$965$	−11.0885	−	19.2058i	−0.356950	−	0.618256i
$966$		0			0
$967$		−	14.8756i		−	0.478368i	−0.970974	−	0.239184i	$-0.923120\pi$
$967$		−	14.8756i		−	0.478368i	0.970974	−	0.239184i	$-0.0768800\pi$
$968$		0			0
$969$	−5.70577	−	3.29423i	−0.183296	−	0.105826i
$970$		0			0
$971$	−6.58846	+	11.4115i	−0.211434	+	0.366214i	−0.952163	−	0.305589i	$-0.901147\pi$
$971$	−6.58846	+	11.4115i	−0.211434	+	0.366214i	0.740730	+	0.671803i	$0.234480\pi$
$972$		0			0
$973$	−16.3923	+	9.46410i	−0.525513	+	0.303405i
$974$		0			0
$975$	3.19615	+	6.46410i	0.102359	+	0.207017i
$976$		0			0
$977$	14.5981	−	8.42820i	0.467034	−	0.269642i	−0.247963	−	0.968769i	$-0.579761\pi$
$977$	14.5981	−	8.42820i	0.467034	−	0.269642i	0.714997	+	0.699127i	$0.246428\pi$
$978$		0			0
$979$	−6.00000	+	10.3923i	−0.191761	+	0.332140i
$980$		0			0
$981$	14.1962	+	8.19615i	0.453248	+	0.261683i
$982$		0			0
$983$			20.7846i			0.662926i	0.943468	+	0.331463i	$0.107542\pi$
$983$			20.7846i			0.662926i	−0.943468	+	0.331463i	$0.892458\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$		0			0
$987$	6.00000			0.190982
$988$		0			0
$989$	13.6077			0.432700
$990$		0			0
$991$	14.6865	+	25.4378i	0.466533	+	0.808059i	0.999269	−	0.0382223i	$-0.0121695\pi$
$991$	14.6865	+	25.4378i	0.466533	+	0.808059i	−0.532736	+	0.846281i	$0.678836\pi$
$992$		0			0
$993$			12.0000i			0.380808i
$994$		0			0
$995$	−12.8827	−	7.43782i	−0.408409	−	0.235795i
$996$		0			0
$997$	−6.59808	+	11.4282i	−0.208963	+	0.361935i	−0.951388	−	0.307994i	$-0.900342\pi$
$997$	−6.59808	+	11.4282i	−0.208963	+	0.361935i	0.742425	+	0.669929i	$0.233676\pi$
$998$		0			0
$999$	2.59808	−	1.50000i	0.0821995	−	0.0474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bv.d.49.2		4
3.2	odd	2		1872.2.by.k.1297.2		4
4.3	odd	2		78.2.i.b.49.2	yes	4
12.11	even	2		234.2.l.a.127.1		4
13.2	odd	12		8112.2.a.bx.1.2		2
13.4	even	6	inner	624.2.bv.d.433.2		4
13.11	odd	12		8112.2.a.bq.1.1		2
20.3	even	4		1950.2.y.a.49.1		4
20.7	even	4		1950.2.y.h.49.2		4
20.19	odd	2		1950.2.bc.c.751.1		4
39.17	odd	6		1872.2.by.k.433.2		4
52.3	odd	6		1014.2.b.d.337.4		4
52.7	even	12		1014.2.e.j.529.1		4
52.11	even	12		1014.2.a.h.1.1		2
52.15	even	12		1014.2.a.j.1.2		2
52.19	even	12		1014.2.e.h.529.2		4
52.23	odd	6		1014.2.b.d.337.1		4
52.31	even	4		1014.2.e.h.991.2		4
52.35	odd	6		1014.2.i.f.823.1		4
52.43	odd	6		78.2.i.b.43.2	✓	4
52.47	even	4		1014.2.e.j.991.1		4
52.51	odd	2		1014.2.i.f.361.1		4
156.11	odd	12		3042.2.a.v.1.2		2
156.23	even	6		3042.2.b.l.1351.4		4
156.95	even	6		234.2.l.a.199.1		4
156.107	even	6		3042.2.b.l.1351.1		4
156.119	odd	12		3042.2.a.s.1.1		2
260.43	even	12		1950.2.y.h.199.2		4
260.147	even	12		1950.2.y.a.199.1		4
260.199	odd	6		1950.2.bc.c.901.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.b.43.2	✓	4	52.43	odd	6
78.2.i.b.49.2	yes	4	4.3	odd	2
234.2.l.a.127.1		4	12.11	even	2
234.2.l.a.199.1		4	156.95	even	6
624.2.bv.d.49.2		4	1.1	even	1	trivial
624.2.bv.d.433.2		4	13.4	even	6	inner
1014.2.a.h.1.1		2	52.11	even	12
1014.2.a.j.1.2		2	52.15	even	12
1014.2.b.d.337.1		4	52.23	odd	6
1014.2.b.d.337.4		4	52.3	odd	6
1014.2.e.h.529.2		4	52.19	even	12
1014.2.e.h.991.2		4	52.31	even	4
1014.2.e.j.529.1		4	52.7	even	12
1014.2.e.j.991.1		4	52.47	even	4
1014.2.i.f.361.1		4	52.51	odd	2
1014.2.i.f.823.1		4	52.35	odd	6
1872.2.by.k.433.2		4	39.17	odd	6
1872.2.by.k.1297.2		4	3.2	odd	2
1950.2.y.a.49.1		4	20.3	even	4
1950.2.y.a.199.1		4	260.147	even	12
1950.2.y.h.49.2		4	20.7	even	4
1950.2.y.h.199.2		4	260.43	even	12
1950.2.bc.c.751.1		4	20.19	odd	2
1950.2.bc.c.901.1		4	260.199	odd	6
3042.2.a.s.1.1		2	156.119	odd	12
3042.2.a.v.1.2		2	156.11	odd	12
3042.2.b.l.1351.1		4	156.107	even	6
3042.2.b.l.1351.4		4	156.23	even	6
8112.2.a.bq.1.1		2	13.11	odd	12
8112.2.a.bx.1.2		2	13.2	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +1.73205i q^{5} +(4.09808 + 2.36603i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +1.73205i q^{5} +(4.09808 + 2.36603i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-4.09808 + 2.36603i) q^{11} +(-3.59808 - 0.232051i) q^{13} +(1.50000 - 0.866025i) q^{15} +(-2.59808 + 4.50000i) q^{17} +(-1.09808 - 0.633975i) q^{19} -4.73205i q^{21} +(-1.09808 - 1.90192i) q^{23} +2.00000 q^{25} +1.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +2.53590i q^{31} +(4.09808 + 2.36603i) q^{33} +(-4.09808 + 7.09808i) q^{35} +(2.59808 - 1.50000i) q^{37} +(1.59808 + 3.23205i) q^{39} +(0.401924 - 0.232051i) q^{41} +(-3.09808 + 5.36603i) q^{43} +(-1.50000 - 0.866025i) q^{45} +1.26795i q^{47} +(7.69615 + 13.3301i) q^{49} +5.19615 q^{51} +3.00000 q^{53} +(-4.09808 - 7.09808i) q^{55} +1.26795i q^{57} +(12.0000 + 6.92820i) q^{59} +(-2.40192 + 4.16025i) q^{61} +(-4.09808 + 2.36603i) q^{63} +(0.401924 - 6.23205i) q^{65} +(9.29423 - 5.36603i) q^{67} +(-1.09808 + 1.90192i) q^{69} +(-7.09808 - 4.09808i) q^{71} -12.1244i q^{73} +(-1.00000 - 1.73205i) q^{75} -22.3923 q^{77} +12.3923 q^{79} +(-0.500000 - 0.866025i) q^{81} -11.6603i q^{83} +(-7.79423 - 4.50000i) q^{85} +(1.50000 - 2.59808i) q^{87} +(2.19615 - 1.26795i) q^{89} +(-14.1962 - 9.46410i) q^{91} +(2.19615 - 1.26795i) q^{93} +(1.09808 - 1.90192i) q^{95} +(5.19615 + 3.00000i) q^{97} -4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 6 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 6 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} + 6 q^{7} - 2 q^{9} - 6 q^{11} - 4 q^{13} + 6 q^{15} + 6 q^{19} + 6 q^{23} + 8 q^{25} + 4 q^{27} + 6 q^{29} + 6 q^{33} - 6 q^{35} - 4 q^{39} + 12 q^{41} - 2 q^{43} - 6 q^{45} + 10 q^{49} + 12 q^{53} - 6 q^{55} + 48 q^{59} - 20 q^{61} - 6 q^{63} + 12 q^{65} + 6 q^{67} + 6 q^{69} - 18 q^{71} - 4 q^{75} - 48 q^{77} + 8 q^{79} - 2 q^{81} + 6 q^{87} - 12 q^{89} - 36 q^{91} - 12 q^{93} - 6 q^{95}+O(q^{100}) \) 4 * q - 2 * q^3 + 6 * q^7 - 2 * q^9 - 6 * q^11 - 4 * q^13 + 6 * q^15 + 6 * q^19 + 6 * q^23 + 8 * q^25 + 4 * q^27 + 6 * q^29 + 6 * q^33 - 6 * q^35 - 4 * q^39 + 12 * q^41 - 2 * q^43 - 6 * q^45 + 10 * q^49 + 12 * q^53 - 6 * q^55 + 48 * q^59 - 20 * q^61 - 6 * q^63 + 12 * q^65 + 6 * q^67 + 6 * q^69 - 18 * q^71 - 4 * q^75 - 48 * q^77 + 8 * q^79 - 2 * q^81 + 6 * q^87 - 12 * q^89 - 36 * q^91 - 12 * q^93 - 6 * q^95

Introduction

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