LMFDB - Embedded newform 2646.2.h.p.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(361,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	2646.361
Dual form			2646.2.h.p.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -0.460505 q^{5} -1.00000 q^{8} +(-0.230252 + 0.398809i) q^{10} +3.64766 q^{11} +(-0.730252 + 1.26483i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.86693 + 3.23361i) q^{17} +(2.02704 + 3.51094i) q^{19} +(0.230252 + 0.398809i) q^{20} +(1.82383 - 3.15897i) q^{22} -1.13307 q^{23} -4.78794 q^{25} +(0.730252 + 1.26483i) q^{26} +(4.48755 + 7.77266i) q^{29} +(-0.257295 - 0.445647i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.86693 + 3.23361i) q^{34} +(-4.55408 - 7.88791i) q^{37} +4.05408 q^{38} +0.460505 q^{40} +(-0.472958 + 0.819187i) q^{41} +(4.66372 + 8.07779i) q^{43} +(-1.82383 - 3.15897i) q^{44} +(-0.566537 + 0.981271i) q^{46} +(-1.16372 + 2.01561i) q^{47} +(-2.39397 + 4.14647i) q^{50} +1.46050 q^{52} +(-6.21780 + 10.7695i) q^{53} -1.67977 q^{55} +8.97509 q^{58} +(6.44805 + 11.1684i) q^{59} +(6.04163 - 10.4644i) q^{61} -0.514589 q^{62} +1.00000 q^{64} +(0.336285 - 0.582462i) q^{65} +(1.16012 + 2.00938i) q^{67} +3.73385 q^{68} -1.67977 q^{71} +(6.62062 - 11.4673i) q^{73} -9.10817 q^{74} +(2.02704 - 3.51094i) q^{76} +(2.50360 - 4.33636i) q^{79} +(0.230252 - 0.398809i) q^{80} +(0.472958 + 0.819187i) q^{82} +(3.32383 + 5.75705i) q^{83} +(0.859728 - 1.48909i) q^{85} +9.32743 q^{86} -3.64766 q^{88} +(-1.36333 - 2.36135i) q^{89} +(0.566537 + 0.981271i) q^{92} +(1.16372 + 2.01561i) q^{94} +(-0.933463 - 1.61680i) q^{95} +(5.59358 + 9.68836i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8} + 5 q^{10} - 2 q^{11} + 2 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} - 5 q^{20} - q^{22} - 14 q^{23} + 4 q^{25} - 2 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34}+ \cdots + 28 q^{97}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 10 * q^5 - 6 * q^8 + 5 * q^10 - 2 * q^11 + 2 * q^13 - 3 * q^16 - 4 * q^17 + 3 * q^19 - 5 * q^20 - q^22 - 14 * q^23 + 4 * q^25 - 2 * q^26 + 5 * q^29 + 14 * q^31 + 3 * q^32 + 4 * q^34 - 9 * q^37 + 6 * q^38 - 10 * q^40 - 12 * q^41 + 18 * q^43 + q^44 - 7 * q^46 + 3 * q^47 + 2 * q^50 - 4 * q^52 - 9 * q^53 - 14 * q^55 + 10 * q^58 + 4 * q^59 - 4 * q^61 + 28 * q^62 + 6 * q^64 + 12 * q^65 + 5 * q^67 + 8 * q^68 - 14 * q^71 + 25 * q^73 - 18 * q^74 + 3 * q^76 + 7 * q^79 - 5 * q^80 + 12 * q^82 + 8 * q^83 + 14 * q^85 + 36 * q^86 + 2 * q^88 - 9 * q^89 + 7 * q^92 - 3 * q^94 - 2 * q^95 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.460505			−0.205944			−0.102972	−	0.994684i	$-0.532835\pi$
$5$	−0.460505			−0.205944			−0.102972	+	0.994684i	$0.532835\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.230252	+	0.398809i	−0.0728122	+	0.126114i
$11$	3.64766			1.09981			0.549906	−	0.835227i	$-0.314664\pi$
$11$	3.64766			1.09981			0.549906	+	0.835227i	$0.314664\pi$
$12$		0			0
$13$	−0.730252	+	1.26483i	−0.202536	+	0.350802i	−0.949345	−	0.314236i	$-0.898252\pi$
$13$	−0.730252	+	1.26483i	−0.202536	+	0.350802i	0.746809	+	0.665038i	$0.231585\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.86693	+	3.23361i	−0.452796	+	0.784266i	−0.998558	−	0.0536743i	$-0.982907\pi$
$17$	−1.86693	+	3.23361i	−0.452796	+	0.784266i	0.545763	+	0.837940i	$0.316240\pi$
$18$		0			0
$19$	2.02704	+	3.51094i	0.465035	+	0.805465i	0.999203	−	0.0399136i	$-0.0127083\pi$
$19$	2.02704	+	3.51094i	0.465035	+	0.805465i	−0.534168	+	0.845378i	$0.679375\pi$
$20$	0.230252	+	0.398809i	0.0514860	+	0.0891764i
$21$		0			0
$22$	1.82383	−	3.15897i	0.388842	−	0.673495i
$23$	−1.13307			−0.236262			−0.118131	−	0.992998i	$-0.537690\pi$
$23$	−1.13307			−0.236262			−0.118131	+	0.992998i	$0.537690\pi$
$24$		0			0
$25$	−4.78794			−0.957587
$26$	0.730252	+	1.26483i	0.143214	+	0.248054i
$27$		0			0
$28$		0			0
$29$	4.48755	+	7.77266i	0.833317	+	1.44335i	0.895394	+	0.445275i	$0.146894\pi$
$29$	4.48755	+	7.77266i	0.833317	+	1.44335i	−0.0620772	+	0.998071i	$0.519772\pi$
$30$		0			0
$31$	−0.257295	−	0.445647i	−0.0462115	−	0.0800406i	0.841994	−	0.539486i	$-0.181381\pi$
$31$	−0.257295	−	0.445647i	−0.0462115	−	0.0800406i	−0.888206	+	0.459446i	$0.848048\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	1.86693	+	3.23361i	0.320175	+	0.554560i
$35$		0			0
$36$		0			0
$37$	−4.55408	−	7.88791i	−0.748687	−	1.29676i	−0.948452	−	0.316920i	$-0.897351\pi$
$37$	−4.55408	−	7.88791i	−0.748687	−	1.29676i	0.199765	−	0.979844i	$-0.435982\pi$
$38$	4.05408			0.657659
$39$		0			0
$40$	0.460505			0.0728122
$41$	−0.472958	+	0.819187i	−0.0738636	+	0.127936i	−0.900592	−	0.434666i	$-0.856866\pi$
$41$	−0.472958	+	0.819187i	−0.0738636	+	0.127936i	0.826728	+	0.562602i	$0.190200\pi$
$42$		0			0
$43$	4.66372	+	8.07779i	0.711210	+	1.23185i	0.964403	+	0.264436i	$0.0851858\pi$
$43$	4.66372	+	8.07779i	0.711210	+	1.23185i	−0.253193	+	0.967416i	$0.581481\pi$
$44$	−1.82383	−	3.15897i	−0.274953	−	0.476233i
$45$		0			0
$46$	−0.566537	+	0.981271i	−0.0835314	+	0.144681i
$47$	−1.16372	+	2.01561i	−0.169745	+	0.294007i	−0.938330	−	0.345740i	$-0.887628\pi$
$47$	−1.16372	+	2.01561i	−0.169745	+	0.294007i	0.768585	+	0.639748i	$0.220961\pi$
$48$		0			0
$49$		0			0
$50$	−2.39397	+	4.14647i	−0.338558	+	0.586400i
$51$		0			0
$52$	1.46050			0.202536
$53$	−6.21780	+	10.7695i	−0.854080	+	1.47931i	0.0234151	+	0.999726i	$0.492546\pi$
$53$	−6.21780	+	10.7695i	−0.854080	+	1.47931i	−0.877495	+	0.479585i	$0.840787\pi$
$54$		0			0
$55$	−1.67977			−0.226500
$56$		0			0
$57$		0			0
$58$	8.97509			1.17849
$59$	6.44805	+	11.1684i	0.839465	+	1.45400i	0.890343	+	0.455291i	$0.150465\pi$
$59$	6.44805	+	11.1684i	0.839465	+	1.45400i	−0.0508779	+	0.998705i	$0.516202\pi$
$60$		0			0
$61$	6.04163	−	10.4644i	0.773552	−	1.33983i	−0.162053	−	0.986782i	$-0.551812\pi$
$61$	6.04163	−	10.4644i	0.773552	−	1.33983i	0.935605	−	0.353049i	$-0.114855\pi$
$62$	−0.514589			−0.0653529
$63$		0			0
$64$	1.00000			0.125000
$65$	0.336285	−	0.582462i	0.0417110	−	0.0722456i
$66$		0			0
$67$	1.16012	+	2.00938i	0.141731	+	0.245485i	0.928148	−	0.372210i	$-0.121400\pi$
$67$	1.16012	+	2.00938i	0.141731	+	0.245485i	−0.786418	+	0.617695i	$0.788067\pi$
$68$	3.73385			0.452796
$69$		0			0
$70$		0			0
$71$	−1.67977			−0.199352			−0.0996758	−	0.995020i	$-0.531781\pi$
$71$	−1.67977			−0.199352			−0.0996758	+	0.995020i	$0.531781\pi$
$72$		0			0
$73$	6.62062	−	11.4673i	0.774885	−	1.34214i	−0.159974	−	0.987121i	$-0.551141\pi$
$73$	6.62062	−	11.4673i	0.774885	−	1.34214i	0.934859	−	0.355019i	$-0.115526\pi$
$74$	−9.10817			−1.05880
$75$		0			0
$76$	2.02704	−	3.51094i	0.232518	−	0.402732i
$77$		0			0
$78$		0			0
$79$	2.50360	−	4.33636i	0.281677	−	0.487879i	−0.690121	−	0.723694i	$-0.742443\pi$
$79$	2.50360	−	4.33636i	0.281677	−	0.487879i	0.971798	+	0.235815i	$0.0757761\pi$
$80$	0.230252	−	0.398809i	0.0257430	−	0.0445882i
$81$		0			0
$82$	0.472958	+	0.819187i	0.0522295	+	0.0904641i
$83$	3.32383	+	5.75705i	0.364838	+	0.631918i	0.988750	−	0.149577i	$-0.0477911\pi$
$83$	3.32383	+	5.75705i	0.364838	+	0.631918i	−0.623912	+	0.781494i	$0.714458\pi$
$84$		0			0
$85$	0.859728	−	1.48909i	0.0932506	−	0.161515i
$86$	9.32743			1.00580
$87$		0			0
$88$	−3.64766			−0.388842
$89$	−1.36333	−	2.36135i	−0.144512	−	0.250303i	0.784679	−	0.619903i	$-0.212828\pi$
$89$	−1.36333	−	2.36135i	−0.144512	−	0.250303i	−0.929191	+	0.369600i	$0.879495\pi$
$90$		0			0
$91$		0			0
$92$	0.566537	+	0.981271i	0.0590656	+	0.102305i
$93$		0			0
$94$	1.16372	+	2.01561i	0.120028	+	0.207895i
$95$	−0.933463	−	1.61680i	−0.0957713	−	0.165881i
$96$		0			0
$97$	5.59358	+	9.68836i	0.567942	+	0.983704i	0.996769	+	0.0803178i	$0.0255935\pi$
$97$	5.59358	+	9.68836i	0.567942	+	0.983704i	−0.428827	+	0.903386i	$0.641073\pi$
$98$		0			0
$99$		0			0
$100$	2.39397	+	4.14647i	0.239397	+	0.414647i
$101$	13.7558			1.36876			0.684378	−	0.729127i	$-0.260074\pi$
$101$	13.7558			1.36876			0.684378	+	0.729127i	$0.260074\pi$
$102$		0			0
$103$	−11.1623			−1.09985			−0.549925	−	0.835214i	$-0.685344\pi$
$103$	−11.1623			−1.09985			−0.549925	+	0.835214i	$0.685344\pi$
$104$	0.730252	−	1.26483i	0.0716071	−	0.124027i
$105$		0			0
$106$	6.21780	+	10.7695i	0.603926	+	1.04603i
$107$	3.89037	+	6.73832i	0.376096	+	0.651418i	0.990490	−	0.137581i	$-0.0439329\pi$
$107$	3.89037	+	6.73832i	0.376096	+	0.651418i	−0.614394	+	0.788999i	$0.710600\pi$
$108$		0			0
$109$	−3.75729	+	6.50783i	−0.359884	+	0.623337i	−0.987941	−	0.154830i	$-0.950517\pi$
$109$	−3.75729	+	6.50783i	−0.359884	+	0.623337i	0.628058	+	0.778167i	$0.283850\pi$
$110$	−0.839883	+	1.45472i	−0.0800797	+	0.138702i
$111$		0			0
$112$		0			0
$113$	−3.03064	+	5.24922i	−0.285099	+	0.493805i	−0.972633	−	0.232346i	$-0.925360\pi$
$113$	−3.03064	+	5.24922i	−0.285099	+	0.493805i	0.687534	+	0.726152i	$0.258693\pi$
$114$		0			0
$115$	0.521786			0.0486568
$116$	4.48755	−	7.77266i	0.416658	−	0.721673i
$117$		0			0
$118$	12.8961			1.18718
$119$		0			0
$120$		0			0
$121$	2.30545			0.209586
$122$	−6.04163	−	10.4644i	−0.546984	−	0.947403i
$123$		0			0
$124$	−0.257295	+	0.445647i	−0.0231057	+	0.0400203i
$125$	4.50739			0.403153
$126$		0			0
$127$	8.80992			0.781754			0.390877	−	0.920443i	$-0.372172\pi$
$127$	8.80992			0.781754			0.390877	+	0.920443i	$0.372172\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.336285	−	0.582462i	−0.0294941	−	0.0510853i
$131$	21.1373			1.84678			0.923389	−	0.383865i	$-0.125407\pi$
$131$	21.1373			1.84678			0.923389	+	0.383865i	$0.125407\pi$
$132$		0			0
$133$		0			0
$134$	2.32023			0.200438
$135$		0			0
$136$	1.86693	−	3.23361i	0.160088	−	0.277280i
$137$	4.40642			0.376466			0.188233	−	0.982124i	$-0.439724\pi$
$137$	4.40642			0.376466			0.188233	+	0.982124i	$0.439724\pi$
$138$		0			0
$139$	1.01245	−	1.75362i	0.0858751	−	0.148740i	−0.819889	−	0.572523i	$-0.805965\pi$
$139$	1.01245	−	1.75362i	0.0858751	−	0.148740i	0.905764	+	0.423783i	$0.139298\pi$
$140$		0			0
$141$		0			0
$142$	−0.839883	+	1.45472i	−0.0704815	+	0.122077i
$143$	−2.66372	+	4.61369i	−0.222751	+	0.385816i
$144$		0			0
$145$	−2.06654	−	3.57935i	−0.171617	−	0.297249i
$146$	−6.62062	−	11.4673i	−0.547927	−	0.949037i
$147$		0			0
$148$	−4.55408	+	7.88791i	−0.374343	+	0.648382i
$149$	9.16225			0.750601			0.375300	−	0.926903i	$-0.377540\pi$
$149$	9.16225			0.750601			0.375300	+	0.926903i	$0.377540\pi$
$150$		0			0
$151$	−0.103896			−0.00845496			−0.00422748	−	0.999991i	$-0.501346\pi$
$151$	−0.103896			−0.00845496			−0.00422748	+	0.999991i	$0.501346\pi$
$152$	−2.02704	−	3.51094i	−0.164415	−	0.284775i
$153$		0			0
$154$		0			0
$155$	0.118485	+	0.205223i	0.00951698	+	0.0164839i
$156$		0			0
$157$	10.4911	+	18.1712i	0.837285	+	1.45022i	0.892157	+	0.451726i	$0.149192\pi$
$157$	10.4911	+	18.1712i	0.837285	+	1.45022i	−0.0548721	+	0.998493i	$0.517475\pi$
$158$	−2.50360	−	4.33636i	−0.199176	−	0.344982i
$159$		0			0
$160$	−0.230252	−	0.398809i	−0.0182031	−	0.0315286i
$161$		0			0
$162$		0			0
$163$	−11.5182	−	19.9501i	−0.902174	−	1.56261i	−0.824666	−	0.565620i	$-0.808637\pi$
$163$	−11.5182	−	19.9501i	−0.902174	−	1.56261i	−0.0775078	−	0.996992i	$-0.524696\pi$
$164$	0.945916			0.0738636
$165$		0			0
$166$	6.64766			0.515959
$167$	−5.31498	+	9.20581i	−0.411285	+	0.712367i	−0.995031	−	0.0995698i	$-0.968253\pi$
$167$	−5.31498	+	9.20581i	−0.411285	+	0.712367i	0.583745	+	0.811937i	$0.301587\pi$
$168$		0			0
$169$	5.43346	+	9.41103i	0.417959	+	0.723926i
$170$	−0.859728	−	1.48909i	−0.0659382	−	0.114208i
$171$		0			0
$172$	4.66372	−	8.07779i	0.355605	−	0.615926i
$173$	−1.46936	+	2.54500i	−0.111713	+	0.193493i	−0.916461	−	0.400124i	$-0.868967\pi$
$173$	−1.46936	+	2.54500i	−0.111713	+	0.193493i	0.804748	+	0.593617i	$0.202301\pi$
$174$		0			0
$175$		0			0
$176$	−1.82383	+	3.15897i	−0.137476	+	0.238116i
$177$		0			0
$178$	−2.72665			−0.204371
$179$	4.58113	−	7.93474i	0.342409	−	0.593071i	−0.642470	−	0.766311i	$-0.722090\pi$
$179$	4.58113	−	7.93474i	0.342409	−	0.593071i	0.984880	+	0.173240i	$0.0554237\pi$
$180$		0			0
$181$	−22.4284			−1.66709			−0.833545	−	0.552452i	$-0.813692\pi$
$181$	−22.4284			−1.66709			−0.833545	+	0.552452i	$0.813692\pi$
$182$		0			0
$183$		0			0
$184$	1.13307			0.0835314
$185$	2.09718	+	3.63242i	0.154188	+	0.267061i
$186$		0			0
$187$	−6.80992	+	11.7951i	−0.497990	+	0.862545i
$188$	2.32743			0.169745
$189$		0			0
$190$	−1.86693			−0.135441
$191$	1.24484	−	2.15613i	0.0900736	−	0.156012i	−0.817468	−	0.575974i	$-0.804623\pi$
$191$	1.24484	−	2.15613i	0.0900736	−	0.156012i	0.907542	+	0.419962i	$0.137956\pi$
$192$		0			0
$193$	−2.24484	−	3.88818i	−0.161587	−	0.279877i	0.773851	−	0.633368i	$-0.218328\pi$
$193$	−2.24484	−	3.88818i	−0.161587	−	0.279877i	−0.935438	+	0.353491i	$0.884995\pi$
$194$	11.1872			0.803191
$195$		0			0
$196$		0			0
$197$	−12.7339			−0.907249			−0.453625	−	0.891193i	$-0.649869\pi$
$197$	−12.7339			−0.907249			−0.453625	+	0.891193i	$0.649869\pi$
$198$		0			0
$199$	1.47296	−	2.55124i	0.104415	−	0.180852i	−0.809084	−	0.587693i	$-0.800036\pi$
$199$	1.47296	−	2.55124i	0.104415	−	0.180852i	0.913499	+	0.406841i	$0.133370\pi$
$200$	4.78794			0.338558
$201$		0			0
$202$	6.87792	−	11.9129i	0.483928	−	0.838189i
$203$		0			0
$204$		0			0
$205$	0.217799	−	0.377240i	0.0152118	−	0.0263476i
$206$	−5.58113	+	9.66679i	−0.388855	+	0.673517i
$207$		0			0
$208$	−0.730252	−	1.26483i	−0.0506339	−	0.0877005i
$209$	7.39397	+	12.8067i	0.511451	+	0.885860i
$210$		0			0
$211$	−0.608168	+	1.05338i	−0.0418680	+	0.0725176i	−0.886200	−	0.463303i	$-0.846664\pi$
$211$	−0.608168	+	1.05338i	−0.0418680	+	0.0725176i	0.844332	+	0.535820i	$0.179998\pi$
$212$	12.4356			0.854080
$213$		0			0
$214$	7.78074			0.531880
$215$	−2.14766	−	3.71986i	−0.146469	−	0.253693i
$216$		0			0
$217$		0			0
$218$	3.75729	+	6.50783i	0.254476	+	0.440766i
$219$		0			0
$220$	0.839883	+	1.45472i	0.0566249	+	0.0980773i
$221$	−2.72665	−	4.72270i	−0.183415	−	0.317683i
$222$		0			0
$223$	0.445916	+	0.772349i	0.0298607	+	0.0517203i	0.880570	−	0.473917i	$-0.157160\pi$
$223$	0.445916	+	0.772349i	0.0298607	+	0.0517203i	−0.850709	+	0.525637i	$0.823827\pi$
$224$		0			0
$225$		0			0
$226$	3.03064	+	5.24922i	0.201595	+	0.349173i
$227$	−14.6519			−0.972483			−0.486242	−	0.873824i	$-0.661632\pi$
$227$	−14.6519			−0.972483			−0.486242	+	0.873824i	$0.661632\pi$
$228$		0			0
$229$	9.57587			0.632791			0.316396	−	0.948627i	$-0.397527\pi$
$229$	9.57587			0.632791			0.316396	+	0.948627i	$0.397527\pi$
$230$	0.260893	−	0.451880i	0.0172028	−	0.0297961i
$231$		0			0
$232$	−4.48755	−	7.77266i	−0.294622	−	0.510300i
$233$	−7.21420	−	12.4954i	−0.472618	−	0.818598i	0.526891	−	0.849933i	$-0.323358\pi$
$233$	−7.21420	−	12.4954i	−0.472618	−	0.818598i	−0.999509	+	0.0313345i	$0.990024\pi$
$234$		0			0
$235$	0.535897	−	0.928200i	0.0349580	−	0.0605491i
$236$	6.44805	−	11.1684i	0.419732	−	0.726998i
$237$		0			0
$238$		0			0
$239$	9.15486	−	15.8567i	0.592179	−	1.02568i	−0.401760	−	0.915745i	$-0.631601\pi$
$239$	9.15486	−	15.8567i	0.592179	−	1.02568i	0.993938	−	0.109938i	$-0.0350654\pi$
$240$		0			0
$241$	−0.0933847			−0.00601544			−0.00300772	−	0.999995i	$-0.500957\pi$
$241$	−0.0933847			−0.00601544			−0.00300772	+	0.999995i	$0.500957\pi$
$242$	1.15272	−	1.99658i	0.0741000	−	0.128345i
$243$		0			0
$244$	−12.0833			−0.773552
$245$		0			0
$246$		0			0
$247$	−5.92101			−0.376745
$248$	0.257295	+	0.445647i	0.0163382	+	0.0282986i
$249$		0			0
$250$	2.25370	−	3.90352i	0.142536	−	0.246880i
$251$	−18.2733			−1.15340			−0.576702	−	0.816955i	$-0.695661\pi$
$251$	−18.2733			−1.15340			−0.576702	+	0.816955i	$0.695661\pi$
$252$		0			0
$253$	−4.13307			−0.259844
$254$	4.40496	−	7.62961i	0.276392	−	0.478724i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−21.0512			−1.31314			−0.656568	−	0.754267i	$-0.727992\pi$
$257$	−21.0512			−1.31314			−0.656568	+	0.754267i	$0.727992\pi$
$258$		0			0
$259$		0			0
$260$	−0.672570			−0.0417110
$261$		0			0
$262$	10.5687	−	18.3055i	0.652935	−	1.13092i
$263$	5.16518			0.318499			0.159249	−	0.987238i	$-0.449093\pi$
$263$	5.16518			0.318499			0.159249	+	0.987238i	$0.449093\pi$
$264$		0			0
$265$	2.86333	−	4.95943i	0.175893	−	0.304655i
$266$		0			0
$267$		0			0
$268$	1.16012	−	2.00938i	0.0708654	−	0.122742i
$269$	8.42840	−	14.5984i	0.513889	−	0.890081i	−0.485981	−	0.873969i	$-0.661538\pi$
$269$	8.42840	−	14.5984i	0.513889	−	0.890081i	0.999870	−	0.0161123i	$-0.00512891\pi$
$270$		0			0
$271$	−12.5562	−	21.7480i	−0.762736	−	1.32110i	−0.941435	−	0.337194i	$-0.890522\pi$
$271$	−12.5562	−	21.7480i	−0.762736	−	1.32110i	0.178699	−	0.983904i	$-0.442811\pi$
$272$	−1.86693	−	3.23361i	−0.113199	−	0.196066i
$273$		0			0
$274$	2.20321	−	3.81607i	0.133101	−	0.230537i
$275$	−17.4648			−1.05317
$276$		0			0
$277$	3.38151			0.203176			0.101588	−	0.994827i	$-0.467608\pi$
$277$	3.38151			0.203176			0.101588	+	0.994827i	$0.467608\pi$
$278$	−1.01245	−	1.75362i	−0.0607229	−	0.105175i
$279$		0			0
$280$		0			0
$281$	10.1388	+	17.5609i	0.604831	+	1.04760i	0.992078	+	0.125622i	$0.0400925\pi$
$281$	10.1388	+	17.5609i	0.604831	+	1.04760i	−0.387248	+	0.921976i	$0.626574\pi$
$282$		0			0
$283$	8.67471	+	15.0250i	0.515658	+	0.893145i	0.999835	+	0.0181754i	$0.00578571\pi$
$283$	8.67471	+	15.0250i	0.515658	+	0.893145i	−0.484177	+	0.874970i	$0.660881\pi$
$284$	0.839883	+	1.45472i	0.0498379	+	0.0863218i
$285$		0			0
$286$	2.66372	+	4.61369i	0.157509	+	0.272813i
$287$		0			0
$288$		0			0
$289$	1.52918	+	2.64861i	0.0899517	+	0.155801i
$290$	−4.13307			−0.242702
$291$		0			0
$292$	−13.2412			−0.774885
$293$	−4.93560	+	8.54871i	−0.288341	+	0.499421i	−0.973414	−	0.229054i	$-0.926437\pi$
$293$	−4.93560	+	8.54871i	−0.288341	+	0.499421i	0.685073	+	0.728474i	$0.259770\pi$
$294$		0			0
$295$	−2.96936	−	5.14308i	−0.172883	−	0.299442i
$296$	4.55408	+	7.88791i	0.264701	+	0.458475i
$297$		0			0
$298$	4.58113	−	7.93474i	0.265378	−	0.459647i
$299$	0.827430	−	1.43315i	0.0478515	−	0.0828813i
$300$		0			0
$301$		0			0
$302$	−0.0519482	+	0.0899768i	−0.00298928	+	0.00517759i
$303$		0			0
$304$	−4.05408			−0.232518
$305$	−2.78220	+	4.81891i	−0.159308	+	0.275930i
$306$		0			0
$307$	−7.78794			−0.444481			−0.222240	−	0.974992i	$-0.571337\pi$
$307$	−7.78794			−0.444481			−0.222240	+	0.974992i	$0.571337\pi$
$308$		0			0
$309$		0			0
$310$	0.236971			0.0134590
$311$	−7.70535	−	13.3461i	−0.436930	−	0.756785i	0.560521	−	0.828140i	$-0.310601\pi$
$311$	−7.70535	−	13.3461i	−0.436930	−	0.756785i	−0.997451	+	0.0713552i	$0.977268\pi$
$312$		0			0
$313$	4.24844	−	7.35851i	0.240136	−	0.415928i	−0.720617	−	0.693334i	$-0.756141\pi$
$313$	4.24844	−	7.35851i	0.240136	−	0.415928i	0.960753	+	0.277406i	$0.0894746\pi$
$314$	20.9823			1.18410
$315$		0			0
$316$	−5.00720			−0.281677
$317$	−7.05262	+	12.2155i	−0.396115	+	0.686091i	−0.993243	−	0.116055i	$-0.962975\pi$
$317$	−7.05262	+	12.2155i	−0.396115	+	0.686091i	0.597128	+	0.802146i	$0.296308\pi$
$318$		0			0
$319$	16.3691	+	28.3520i	0.916491	+	1.58741i
$320$	−0.460505			−0.0257430
$321$		0			0
$322$		0			0
$323$	−15.1373			−0.842264
$324$		0			0
$325$	3.49640	−	6.05594i	0.193945	−	0.335923i
$326$	−23.0364			−1.27587
$327$		0			0
$328$	0.472958	−	0.819187i	0.0261147	−	0.0452320i
$329$		0			0
$330$		0			0
$331$	−13.7719	+	23.8536i	−0.756971	+	1.31111i	0.187417	+	0.982280i	$0.439988\pi$
$331$	−13.7719	+	23.8536i	−0.756971	+	1.31111i	−0.944388	+	0.328832i	$0.893345\pi$
$332$	3.32383	−	5.75705i	0.182419	−	0.315959i
$333$		0			0
$334$	5.31498	+	9.20581i	0.290823	+	0.503720i
$335$	−0.534239	−	0.925330i	−0.0291886	−	0.0505562i
$336$		0			0
$337$	0.748440	−	1.29634i	0.0407701	−	0.0706159i	−0.844920	−	0.534892i	$-0.820352\pi$
$337$	0.748440	−	1.29634i	0.0407701	−	0.0706159i	0.885690	+	0.464276i	$0.153686\pi$
$338$	10.8669			0.591083
$339$		0			0
$340$	−1.71946			−0.0932506
$341$	−0.938524	−	1.62557i	−0.0508239	−	0.0880296i
$342$		0			0
$343$		0			0
$344$	−4.66372	−	8.07779i	−0.251451	−	0.435525i
$345$		0			0
$346$	1.46936	+	2.54500i	0.0789932	+	0.136820i
$347$	−9.14406	−	15.8380i	−0.490879	−	0.850228i	0.509066	−	0.860728i	$-0.329991\pi$
$347$	−9.14406	−	15.8380i	−0.490879	−	0.850228i	−0.999945	+	0.0105001i	$0.996658\pi$
$348$		0			0
$349$	3.90136	+	6.75735i	0.208835	+	0.361713i	0.951348	−	0.308119i	$-0.0996995\pi$
$349$	3.90136	+	6.75735i	0.208835	+	0.361713i	−0.742513	+	0.669832i	$0.766366\pi$
$350$		0			0
$351$		0			0
$352$	1.82383	+	3.15897i	0.0972106	+	0.168374i
$353$	26.9253			1.43309			0.716544	−	0.697542i	$-0.245723\pi$
$353$	26.9253			1.43309			0.716544	+	0.697542i	$0.245723\pi$
$354$		0			0
$355$	0.773541			0.0410553
$356$	−1.36333	+	2.36135i	−0.0722562	+	0.125151i
$357$		0			0
$358$	−4.58113	−	7.93474i	−0.242120	−	0.419364i
$359$	3.13161	+	5.42411i	0.165280	+	0.286274i	0.936755	−	0.349987i	$-0.113814\pi$
$359$	3.13161	+	5.42411i	0.165280	+	0.286274i	−0.771475	+	0.636260i	$0.780481\pi$
$360$		0			0
$361$	1.28220	−	2.22084i	0.0674842	−	0.116886i
$362$	−11.2142	+	19.4236i	−0.589405	+	1.02088i
$363$		0			0
$364$		0			0
$365$	−3.04883	+	5.28073i	−0.159583	+	0.276406i
$366$		0			0
$367$	−29.2733			−1.52806			−0.764028	−	0.645183i	$-0.776781\pi$
$367$	−29.2733			−1.52806			−0.764028	+	0.645183i	$0.776781\pi$
$368$	0.566537	−	0.981271i	0.0295328	−	0.0511523i
$369$		0			0
$370$	4.19436			0.218054
$371$		0			0
$372$		0			0
$373$	17.8597			0.924742			0.462371	−	0.886687i	$-0.346999\pi$
$373$	17.8597			0.924742			0.462371	+	0.886687i	$0.346999\pi$
$374$	6.80992	+	11.7951i	0.352132	+	0.609911i
$375$		0			0
$376$	1.16372	−	2.01561i	0.0600140	−	0.103947i
$377$	−13.1082			−0.675105
$378$		0			0
$379$	−22.4255			−1.15192			−0.575960	−	0.817478i	$-0.695371\pi$
$379$	−22.4255			−1.15192			−0.575960	+	0.817478i	$0.695371\pi$
$380$	−0.933463	+	1.61680i	−0.0478856	+	0.0829403i
$381$		0			0
$382$	−1.24484	−	2.15613i	−0.0636916	−	0.110317i
$383$	−14.1403			−0.722534			−0.361267	−	0.932462i	$-0.617656\pi$
$383$	−14.1403			−0.722534			−0.361267	+	0.932462i	$0.617656\pi$
$384$		0			0
$385$		0			0
$386$	−4.48968			−0.228519
$387$		0			0
$388$	5.59358	−	9.68836i	0.283971	−	0.491852i
$389$	23.1301			1.17275			0.586373	−	0.810041i	$-0.300555\pi$
$389$	23.1301			1.17275			0.586373	+	0.810041i	$0.300555\pi$
$390$		0			0
$391$	2.11537	−	3.66392i	0.106979	−	0.185292i
$392$		0			0
$393$		0			0
$394$	−6.36693	+	11.0278i	−0.320761	+	0.555574i
$395$	−1.15292	+	1.99691i	−0.0580097	+	0.100476i
$396$		0			0
$397$	5.13307	+	8.89075i	0.257622	+	0.446214i	0.965604	−	0.260016i	$-0.0837279\pi$
$397$	5.13307	+	8.89075i	0.257622	+	0.446214i	−0.707983	+	0.706230i	$0.750395\pi$
$398$	−1.47296	−	2.55124i	−0.0738327	−	0.127882i
$399$		0			0
$400$	2.39397	−	4.14647i	0.119698	−	0.207324i
$401$	−34.0335			−1.69955			−0.849775	−	0.527146i	$-0.823262\pi$
$401$	−34.0335			−1.69955			−0.849775	+	0.527146i	$0.823262\pi$
$402$		0			0
$403$	0.751560			0.0374379
$404$	−6.87792	−	11.9129i	−0.342189	−	0.592689i
$405$		0			0
$406$		0			0
$407$	−16.6118	−	28.7724i	−0.823415	−	1.42620i
$408$		0			0
$409$	−1.74484	−	3.02215i	−0.0862769	−	0.149436i	0.819658	−	0.572854i	$-0.194164\pi$
$409$	−1.74484	−	3.02215i	−0.0862769	−	0.149436i	−0.905935	+	0.423418i	$0.860830\pi$
$410$	−0.217799	−	0.377240i	−0.0107563	−	0.0186305i
$411$		0			0
$412$	5.58113	+	9.66679i	0.274962	+	0.476249i
$413$		0			0
$414$		0			0
$415$	−1.53064	−	2.65115i	−0.0751362	−	0.130140i
$416$	−1.46050			−0.0716071
$417$		0			0
$418$	14.7879			0.723302
$419$	14.4897	−	25.0969i	0.707867	−	1.22606i	−0.257779	−	0.966204i	$-0.582991\pi$
$419$	14.4897	−	25.0969i	0.707867	−	1.22606i	0.965647	−	0.259858i	$-0.0836759\pi$
$420$		0			0
$421$	−1.06128	−	1.83819i	−0.0517237	−	0.0895881i	0.839004	−	0.544125i	$-0.183138\pi$
$421$	−1.06128	−	1.83819i	−0.0517237	−	0.0895881i	−0.890728	+	0.454537i	$0.849805\pi$
$422$	0.608168	+	1.05338i	0.0296052	+	0.0512777i
$423$		0			0
$424$	6.21780	−	10.7695i	0.301963	−	0.523015i
$425$	8.93872	−	15.4823i	0.433592	−	0.751003i
$426$		0			0
$427$		0			0
$428$	3.89037	−	6.73832i	0.188048	−	0.325709i
$429$		0			0
$430$	−4.29533			−0.207139
$431$	−10.9356	+	18.9410i	−0.526749	+	0.912356i	0.472765	+	0.881189i	$0.343256\pi$
$431$	−10.9356	+	18.9410i	−0.526749	+	0.912356i	−0.999514	+	0.0311679i	$0.990077\pi$
$432$		0			0
$433$	13.0512			0.627199			0.313599	−	0.949555i	$-0.398465\pi$
$433$	13.0512			0.627199			0.313599	+	0.949555i	$0.398465\pi$
$434$		0			0
$435$		0			0
$436$	7.51459			0.359884
$437$	−2.29679	−	3.97816i	−0.109870	−	0.190301i
$438$		0			0
$439$	2.43200	−	4.21235i	0.116073	−	0.201044i	−0.802135	−	0.597143i	$-0.796303\pi$
$439$	2.43200	−	4.21235i	0.116073	−	0.201044i	0.918208	+	0.396098i	$0.129636\pi$
$440$	1.67977			0.0800797
$441$		0			0
$442$	−5.45331			−0.259387
$443$	−5.76975	+	9.99350i	−0.274129	+	0.474805i	−0.969915	−	0.243444i	$-0.921723\pi$
$443$	−5.76975	+	9.99350i	−0.274129	+	0.474805i	0.695786	+	0.718249i	$0.255056\pi$
$444$		0			0
$445$	0.627819	+	1.08741i	0.0297615	+	0.0515484i
$446$	0.891832			0.0422294
$447$		0			0
$448$		0			0
$449$	26.4251			1.24708			0.623538	−	0.781793i	$-0.285694\pi$
$449$	26.4251			1.24708			0.623538	+	0.781793i	$0.285694\pi$
$450$		0			0
$451$	−1.72519	+	2.98812i	−0.0812361	+	0.140705i
$452$	6.06128			0.285099
$453$		0			0
$454$	−7.32597	+	12.6889i	−0.343825	+	0.595522i
$455$		0			0
$456$		0			0
$457$	1.86906	−	3.23731i	0.0874310	−	0.151435i	−0.818994	−	0.573803i	$-0.805468\pi$
$457$	1.86906	−	3.23731i	0.0874310	−	0.151435i	0.906425	+	0.422368i	$0.138801\pi$
$458$	4.78794	−	8.29295i	0.223726	−	0.387504i
$459$		0			0
$460$	−0.260893	−	0.451880i	−0.0121642	−	0.0210690i
$461$	−7.90496	−	13.6918i	−0.368171	−	0.637690i	0.621109	−	0.783724i	$-0.286682\pi$
$461$	−7.90496	−	13.6918i	−0.368171	−	0.637690i	−0.989280	+	0.146034i	$0.953349\pi$
$462$		0			0
$463$	19.1965	−	33.2493i	0.892137	−	1.54523i	0.0548278	−	0.998496i	$-0.482539\pi$
$463$	19.1965	−	33.2493i	0.892137	−	1.54523i	0.837309	−	0.546730i	$-0.184128\pi$
$464$	−8.97509			−0.416658
$465$		0			0
$466$	−14.4284			−0.668383
$467$	3.15652	+	5.46725i	0.146066	+	0.252994i	0.929770	−	0.368140i	$-0.120005\pi$
$467$	3.15652	+	5.46725i	0.146066	+	0.252994i	−0.783704	+	0.621134i	$0.786672\pi$
$468$		0			0
$469$		0			0
$470$	−0.535897	−	0.928200i	−0.0247191	−	0.0428147i
$471$		0			0
$472$	−6.44805	−	11.1684i	−0.296796	−	0.514065i
$473$	17.0117	+	29.4651i	0.782197	+	1.35481i
$474$		0			0
$475$	−9.70535	−	16.8102i	−0.445312	−	0.771303i
$476$		0			0
$477$		0			0
$478$	−9.15486	−	15.8567i	−0.418734	−	0.725268i
$479$	−20.4136			−0.932722			−0.466361	−	0.884594i	$-0.654435\pi$
$479$	−20.4136			−0.932722			−0.466361	+	0.884594i	$0.654435\pi$
$480$		0			0
$481$	13.3025			0.606543
$482$	−0.0466924	+	0.0808735i	−0.00212678	+	0.00368369i
$483$		0			0
$484$	−1.15272	−	1.99658i	−0.0523966	−	0.0907535i
$485$	−2.57587	−	4.46154i	−0.116964	−	0.202588i
$486$		0			0
$487$	6.18190	−	10.7074i	0.280129	−	0.485197i	−0.691287	−	0.722580i	$-0.742956\pi$
$487$	6.18190	−	10.7074i	0.280129	−	0.485197i	0.971416	+	0.237383i	$0.0762895\pi$
$488$	−6.04163	+	10.4644i	−0.273492	+	0.473702i
$489$		0			0
$490$		0			0
$491$	−0.207004	+	0.358541i	−0.00934194	+	0.0161807i	−0.870659	−	0.491888i	$-0.836307\pi$
$491$	−0.207004	+	0.358541i	−0.00934194	+	0.0161807i	0.861317	+	0.508069i	$0.169640\pi$
$492$		0			0
$493$	−33.5117			−1.50929
$494$	−2.96050	+	5.12774i	−0.133199	+	0.230708i
$495$		0			0
$496$	0.514589			0.0231057
$497$		0			0
$498$		0			0
$499$	−0.923935			−0.0413610			−0.0206805	−	0.999786i	$-0.506583\pi$
$499$	−0.923935			−0.0413610			−0.0206805	+	0.999786i	$0.506583\pi$
$500$	−2.25370	−	3.90352i	−0.100788	−	0.174571i
$501$		0			0
$502$	−9.13667	+	15.8252i	−0.407790	+	0.706312i
$503$	−23.8142			−1.06182			−0.530911	−	0.847428i	$-0.678150\pi$
$503$	−23.8142			−1.06182			−0.530911	+	0.847428i	$0.678150\pi$
$504$		0			0
$505$	−6.33463			−0.281887
$506$	−2.06654	+	3.57935i	−0.0918688	+	0.159121i
$507$		0			0
$508$	−4.40496	−	7.62961i	−0.195438	−	0.338509i
$509$	−30.6342			−1.35784			−0.678919	−	0.734213i	$-0.737551\pi$
$509$	−30.6342			−1.35784			−0.678919	+	0.734213i	$0.737551\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−10.5256	+	18.2308i	−0.464263	+	0.804128i
$515$	5.14027			0.226507
$516$		0			0
$517$	−4.24484	+	7.35228i	−0.186688	+	0.323353i
$518$		0			0
$519$		0			0
$520$	−0.336285	+	0.582462i	−0.0147471	+	0.0255427i
$521$	−13.4518	+	23.2993i	−0.589336	+	1.02076i	0.404984	+	0.914324i	$0.367277\pi$
$521$	−13.4518	+	23.2993i	−0.589336	+	1.02076i	−0.994320	+	0.106436i	$0.966056\pi$
$522$		0			0
$523$	7.85301	+	13.6018i	0.343388	+	0.594766i	0.985060	−	0.172214i	$-0.0550920\pi$
$523$	7.85301	+	13.6018i	0.343388	+	0.594766i	−0.641671	+	0.766980i	$0.721759\pi$
$524$	−10.5687	−	18.3055i	−0.461695	−	0.799679i
$525$		0			0
$526$	2.58259	−	4.47318i	0.112606	−	0.195040i
$527$	1.92140			0.0836975
$528$		0			0
$529$	−21.7161			−0.944180
$530$	−2.86333	−	4.95943i	−0.124375	−	0.215424i
$531$		0			0
$532$		0			0
$533$	−0.690757	−	1.19643i	−0.0299200	−	0.0518230i
$534$		0			0
$535$	−1.79153	−	3.10303i	−0.0774548	−	0.134156i
$536$	−1.16012	−	2.00938i	−0.0501094	−	0.0867920i
$537$		0			0
$538$	−8.42840	−	14.5984i	−0.363374	−	0.629383i
$539$		0			0
$540$		0			0
$541$	−2.05934	−	3.56688i	−0.0885379	−	0.153352i	0.818355	−	0.574713i	$-0.194886\pi$
$541$	−2.05934	−	3.56688i	−0.0885379	−	0.153352i	−0.906893	+	0.421360i	$0.861553\pi$
$542$	−25.1124			−1.07867
$543$		0			0
$544$	−3.73385			−0.160088
$545$	1.73025	−	2.99689i	0.0741159	−	0.128372i
$546$		0			0
$547$	−11.8602	−	20.5425i	−0.507106	−	0.878333i	−0.999966	−	0.00822465i	$-0.997382\pi$
$547$	−11.8602	−	20.5425i	−0.507106	−	0.878333i	0.492860	−	0.870108i	$-0.335951\pi$
$548$	−2.20321	−	3.81607i	−0.0941165	−	0.163015i
$549$		0			0
$550$	−8.73239	+	15.1249i	−0.372350	+	0.644930i
$551$	−18.1929	+	31.5110i	−0.775043	+	1.34241i
$552$		0			0
$553$		0			0
$554$	1.69076	−	2.92848i	0.0718334	−	0.124419i
$555$		0			0
$556$	−2.02491			−0.0858751
$557$	21.0313	−	36.4273i	0.891125	−	1.54347i	0.0525975	−	0.998616i	$-0.483250\pi$
$557$	21.0313	−	36.4273i	0.891125	−	1.54347i	0.838528	−	0.544859i	$-0.183417\pi$
$558$		0			0
$559$	−13.6228			−0.576181
$560$		0			0
$561$		0			0
$562$	20.2776			0.855360
$563$	−5.91216	−	10.2402i	−0.249168	−	0.431571i	0.714127	−	0.700016i	$-0.246824\pi$
$563$	−5.91216	−	10.2402i	−0.249168	−	0.431571i	−0.963295	+	0.268445i	$0.913490\pi$
$564$		0			0
$565$	1.39562	−	2.41729i	0.0587144	−	0.101696i
$566$	17.3494			0.729250
$567$		0			0
$568$	1.67977			0.0704815
$569$	7.10078	−	12.2989i	0.297680	−	0.515597i	−0.677925	−	0.735131i	$-0.737120\pi$
$569$	7.10078	−	12.2989i	0.297680	−	0.515597i	0.975605	+	0.219534i	$0.0704538\pi$
$570$		0			0
$571$	−5.97869	−	10.3554i	−0.250200	−	0.433360i	0.713380	−	0.700777i	$-0.247163\pi$
$571$	−5.97869	−	10.3554i	−0.250200	−	0.433360i	−0.963581	+	0.267417i	$0.913830\pi$
$572$	5.32743			0.222751
$573$		0			0
$574$		0			0
$575$	5.42509			0.226242
$576$		0			0
$577$	−21.3135	+	36.9161i	−0.887293	+	1.53684i	−0.0442307	+	0.999021i	$0.514084\pi$
$577$	−21.3135	+	36.9161i	−0.887293	+	1.53684i	−0.843062	+	0.537816i	$0.819250\pi$
$578$	3.05836			0.127211
$579$		0			0
$580$	−2.06654	+	3.57935i	−0.0858083	+	0.148624i
$581$		0			0
$582$		0			0
$583$	−22.6804	+	39.2837i	−0.939328	+	1.62696i
$584$	−6.62062	+	11.4673i	−0.273963	+	0.474518i
$585$		0			0
$586$	4.93560	+	8.54871i	0.203888	+	0.353144i
$587$	20.5328	+	35.5638i	0.847478	+	1.46788i	0.883451	+	0.468523i	$0.155214\pi$
$587$	20.5328	+	35.5638i	0.847478	+	1.46788i	−0.0359730	+	0.999353i	$0.511453\pi$
$588$		0			0
$589$	1.04309	−	1.80669i	0.0429799	−	0.0744434i
$590$	−5.93872			−0.244493
$591$		0			0
$592$	9.10817			0.374343
$593$	16.1008	+	27.8874i	0.661180	+	1.14520i	0.980306	+	0.197485i	$0.0632772\pi$
$593$	16.1008	+	27.8874i	0.661180	+	1.14520i	−0.319126	+	0.947712i	$0.603389\pi$
$594$		0			0
$595$		0			0
$596$	−4.58113	−	7.93474i	−0.187650	−	0.325020i
$597$		0			0
$598$	−0.827430	−	1.43315i	−0.0338361	−	0.0586059i
$599$	9.53590	+	16.5167i	0.389626	+	0.674852i	0.992399	−	0.123060i	$-0.0392709\pi$
$599$	9.53590	+	16.5167i	0.389626	+	0.674852i	−0.602773	+	0.797913i	$0.705938\pi$
$600$		0			0
$601$	−4.27188	−	7.39912i	−0.174254	−	0.301816i	0.765649	−	0.643259i	$-0.222418\pi$
$601$	−4.27188	−	7.39912i	−0.174254	−	0.301816i	−0.939903	+	0.341442i	$0.889085\pi$
$602$		0			0
$603$		0			0
$604$	0.0519482	+	0.0899768i	0.00211374	+	0.00366111i
$605$	−1.06167			−0.0431631
$606$		0			0
$607$	−38.0115			−1.54284			−0.771419	−	0.636328i	$-0.780453\pi$
$607$	−38.0115			−1.54284			−0.771419	+	0.636328i	$0.780453\pi$
$608$	−2.02704	+	3.51094i	−0.0822074	+	0.142387i
$609$		0			0
$610$	2.78220	+	4.81891i	0.112648	+	0.195112i
$611$	−1.69961	−	2.94381i	−0.0687589	−	0.119094i
$612$		0			0
$613$	11.3296	−	19.6234i	0.457597	−	0.792581i	−0.541237	−	0.840870i	$-0.682044\pi$
$613$	11.3296	−	19.6234i	0.457597	−	0.792581i	0.998833	+	0.0482894i	$0.0153770\pi$
$614$	−3.89397	+	6.74455i	−0.157148	+	0.272188i
$615$		0			0
$616$		0			0
$617$	10.1388	−	17.5609i	0.408173	−	0.706977i	−0.586512	−	0.809941i	$-0.699499\pi$
$617$	10.1388	−	17.5609i	0.408173	−	0.706977i	0.994685	+	0.102964i	$0.0328327\pi$
$618$		0			0
$619$	−2.06128			−0.0828499			−0.0414249	−	0.999142i	$-0.513190\pi$
$619$	−2.06128			−0.0828499			−0.0414249	+	0.999142i	$0.513190\pi$
$620$	0.118485	−	0.205223i	0.00475849	−	0.00824194i
$621$		0			0
$622$	−15.4107			−0.617912
$623$		0			0
$624$		0			0
$625$	21.8640			0.874560
$626$	−4.24844	−	7.35851i	−0.169802	−	0.294105i
$627$		0			0
$628$	10.4911	−	18.1712i	0.418642	−	0.725110i
$629$	34.0085			1.35601
$630$		0			0
$631$	1.63715			0.0651740			0.0325870	−	0.999469i	$-0.489625\pi$
$631$	1.63715			0.0651740			0.0325870	+	0.999469i	$0.489625\pi$
$632$	−2.50360	+	4.33636i	−0.0995878	+	0.172491i
$633$		0			0
$634$	7.05262	+	12.2155i	0.280095	+	0.485139i
$635$	−4.05701			−0.160998
$636$		0			0
$637$		0			0
$638$	32.7381			1.29611
$639$		0			0
$640$	−0.230252	+	0.398809i	−0.00910153	+	0.0157643i
$641$	−21.9325			−0.866281			−0.433140	−	0.901326i	$-0.642595\pi$
$641$	−21.9325			−0.866281			−0.433140	+	0.901326i	$0.642595\pi$
$642$		0			0
$643$	14.1819	−	24.5638i	0.559280	−	0.968701i	−0.438277	−	0.898840i	$-0.644411\pi$
$643$	14.1819	−	24.5638i	0.559280	−	0.968701i	0.997557	−	0.0698609i	$-0.0222555\pi$
$644$		0			0
$645$		0			0
$646$	−7.56867	+	13.1093i	−0.297785	+	0.515780i
$647$	17.3904	−	30.1210i	0.683686	−	1.18418i	−0.290162	−	0.956978i	$-0.593709\pi$
$647$	17.3904	−	30.1210i	0.683686	−	1.18418i	0.973848	−	0.227201i	$-0.0729575\pi$
$648$		0			0
$649$	23.5203	+	40.7384i	0.923253	+	1.59912i
$650$	−3.49640	−	6.05594i	−0.137140	−	0.237534i
$651$		0			0
$652$	−11.5182	+	19.9501i	−0.451087	+	0.781306i
$653$	3.19863			0.125172			0.0625860	−	0.998040i	$-0.480065\pi$
$653$	3.19863			0.125172			0.0625860	+	0.998040i	$0.480065\pi$
$654$		0			0
$655$	−9.73385			−0.380333
$656$	−0.472958	−	0.819187i	−0.0184659	−	0.0319839i
$657$		0			0
$658$		0			0
$659$	−5.30418	−	9.18711i	−0.206622	−	0.357879i	0.744027	−	0.668150i	$-0.232914\pi$
$659$	−5.30418	−	9.18711i	−0.206622	−	0.357879i	−0.950648	+	0.310271i	$0.899580\pi$
$660$		0			0
$661$	5.06507	+	8.77297i	0.197009	+	0.341229i	0.947557	−	0.319586i	$-0.103544\pi$
$661$	5.06507	+	8.77297i	0.197009	+	0.341229i	−0.750549	+	0.660815i	$0.770211\pi$
$662$	13.7719	+	23.8536i	0.535259	+	0.927097i
$663$		0			0
$664$	−3.32383	−	5.75705i	−0.128990	−	0.223417i
$665$		0			0
$666$		0			0
$667$	−5.08472	−	8.80700i	−0.196881	−	0.341008i
$668$	10.6300			0.411285
$669$		0			0
$670$	−1.06848			−0.0412789
$671$	22.0378	−	38.1707i	0.850761	−	1.47356i
$672$		0			0
$673$	1.60817	+	2.78543i	0.0619903	+	0.107370i	0.895355	−	0.445353i	$-0.146922\pi$
$673$	1.60817	+	2.78543i	0.0619903	+	0.107370i	−0.833365	+	0.552724i	$0.813589\pi$
$674$	−0.748440	−	1.29634i	−0.0288288	−	0.0499330i
$675$		0			0
$676$	5.43346	−	9.41103i	0.208979	−	0.361963i
$677$	14.6819	−	25.4298i	0.564271	−	0.977347i	−0.432846	−	0.901468i	$-0.642491\pi$
$677$	14.6819	−	25.4298i	0.564271	−	0.977347i	0.997117	−	0.0758786i	$-0.0241762\pi$
$678$		0			0
$679$		0			0
$680$	−0.859728	+	1.48909i	−0.0329691	+	0.0571041i
$681$		0			0
$682$	−1.87705			−0.0718759
$683$	−12.6278	+	21.8720i	−0.483190	+	0.836910i	−0.999814	−	0.0193029i	$-0.993855\pi$
$683$	−12.6278	+	21.8720i	−0.483190	+	0.836910i	0.516624	+	0.856213i	$0.327189\pi$
$684$		0			0
$685$	−2.02918			−0.0775309
$686$		0			0
$687$		0			0
$688$	−9.32743			−0.355605
$689$	−9.08113	−	15.7290i	−0.345963	−	0.599226i
$690$		0			0
$691$	−7.68190	+	13.3054i	−0.292233	+	0.506163i	−0.974338	−	0.225092i	$-0.927732\pi$
$691$	−7.68190	+	13.3054i	−0.292233	+	0.506163i	0.682104	+	0.731255i	$0.261065\pi$
$692$	2.93872			0.111713
$693$		0			0
$694$	−18.2881			−0.694208
$695$	−0.466240	+	0.807551i	−0.0176855	+	0.0306321i
$696$		0			0
$697$	−1.76595	−	3.05872i	−0.0668903	−	0.115857i
$698$	7.80272			0.295337
$699$		0			0
$700$		0			0
$701$	13.3700			0.504980			0.252490	−	0.967600i	$-0.418751\pi$
$701$	13.3700			0.504980			0.252490	+	0.967600i	$0.418751\pi$
$702$		0			0
$703$	18.4626	−	31.9782i	0.696332	−	1.20608i
$704$	3.64766			0.137476
$705$		0			0
$706$	13.4626	−	23.3180i	0.506673	−	0.877584i
$707$		0			0
$708$		0			0
$709$	0.562939	−	0.975038i	0.0211416	−	0.0366183i	−0.855261	−	0.518197i	$-0.826603\pi$
$709$	0.562939	−	0.975038i	0.0211416	−	0.0366183i	0.876403	+	0.481579i	$0.159937\pi$
$710$	0.386770	−	0.669906i	0.0145152	−	0.0251411i
$711$		0			0
$712$	1.36333	+	2.36135i	0.0510928	+	0.0884954i
$713$	0.291534	+	0.504951i	0.0109180	+	0.0189106i
$714$		0			0
$715$	1.22665	−	2.12463i	0.0458743	−	0.0794565i
$716$	−9.16225			−0.342409
$717$		0			0
$718$	6.26322			0.233741
$719$	9.13667	+	15.8252i	0.340740	+	0.590180i	0.984570	−	0.174989i	$-0.0559889\pi$
$719$	9.13667	+	15.8252i	0.340740	+	0.590180i	−0.643830	+	0.765169i	$0.722656\pi$
$720$		0			0
$721$		0			0
$722$	−1.28220	−	2.22084i	−0.0477186	−	0.0826510i
$723$		0			0
$724$	11.2142	+	19.4236i	0.416772	+	0.721871i
$725$	−21.4861	−	37.2150i	−0.797973	−	1.38213i
$726$		0			0
$727$	14.8478	+	25.7171i	0.550673	+	0.953793i	0.998226	+	0.0595359i	$0.0189621\pi$
$727$	14.8478	+	25.7171i	0.550673	+	0.953793i	−0.447553	+	0.894257i	$0.647705\pi$
$728$		0			0
$729$		0			0
$730$	3.04883	+	5.28073i	0.112842	+	0.195448i
$731$	−34.8272			−1.28813
$732$		0			0
$733$	−19.2278			−0.710195			−0.355098	−	0.934829i	$-0.615552\pi$
$733$	−19.2278			−0.710195			−0.355098	+	0.934829i	$0.615552\pi$
$734$	−14.6367	+	25.3515i	−0.540249	+	0.935740i
$735$		0			0
$736$	−0.566537	−	0.981271i	−0.0208828	−	0.0361701i
$737$	4.23171	+	7.32955i	0.155877	+	0.269987i
$738$		0			0
$739$	−15.1336	+	26.2121i	−0.556697	+	0.964227i	0.441073	+	0.897471i	$0.354598\pi$
$739$	−15.1336	+	26.2121i	−0.556697	+	0.964227i	−0.997769	+	0.0667556i	$0.978735\pi$
$740$	2.09718	−	3.63242i	0.0770938	−	0.133530i
$741$		0			0
$742$		0			0
$743$	11.8815	−	20.5794i	0.435890	−	0.754984i	−0.561477	−	0.827492i	$-0.689767\pi$
$743$	11.8815	−	20.5794i	0.435890	−	0.754984i	0.997368	+	0.0725076i	$0.0231002\pi$
$744$		0			0
$745$	−4.21926			−0.154582
$746$	8.92986	−	15.4670i	0.326946	−	0.566286i
$747$		0			0
$748$	13.6198			0.497990
$749$		0			0
$750$		0			0
$751$	12.6683			0.462273			0.231136	−	0.972921i	$-0.425756\pi$
$751$	12.6683			0.462273			0.231136	+	0.972921i	$0.425756\pi$
$752$	−1.16372	−	2.01561i	−0.0424363	−	0.0735019i
$753$		0			0
$754$	−6.55408	+	11.3520i	−0.238686	+	0.413416i
$755$	0.0478448			0.00174125
$756$		0			0
$757$	−29.0799			−1.05693			−0.528464	−	0.848955i	$-0.677232\pi$
$757$	−29.0799			−1.05693			−0.528464	+	0.848955i	$0.677232\pi$
$758$	−11.2127	+	19.4210i	−0.407265	+	0.705404i
$759$		0			0
$760$	0.933463	+	1.61680i	0.0338603	+	0.0586477i
$761$	29.2029			1.05860			0.529302	−	0.848433i	$-0.322454\pi$
$761$	29.2029			1.05860			0.529302	+	0.848433i	$0.322454\pi$
$762$		0			0
$763$		0			0
$764$	−2.48968			−0.0900736
$765$		0			0
$766$	−7.07014	+	12.2458i	−0.255454	+	0.442460i
$767$	−18.8348			−0.680086
$768$		0			0
$769$	−12.5869	+	21.8011i	−0.453894	+	0.786167i	−0.998624	−	0.0524443i	$-0.983299\pi$
$769$	−12.5869	+	21.8011i	−0.453894	+	0.786167i	0.544730	+	0.838611i	$0.316632\pi$
$770$		0			0
$771$		0			0
$772$	−2.24484	+	3.88818i	−0.0807936	+	0.139939i
$773$	−0.752039	+	1.30257i	−0.0270490	+	0.0468502i	−0.879233	−	0.476392i	$-0.841944\pi$
$773$	−0.752039	+	1.30257i	−0.0270490	+	0.0468502i	0.852184	+	0.523242i	$0.175278\pi$
$774$		0			0
$775$	1.23191	+	2.13373i	0.0442515	+	0.0766458i
$776$	−5.59358	−	9.68836i	−0.200798	−	0.347792i
$777$		0			0
$778$	11.5651	−	20.0313i	0.414628	−	0.718157i
$779$	−3.83482			−0.137397
$780$		0			0
$781$	−6.12722			−0.219249
$782$	−2.11537	−	3.66392i	−0.0756453	−	0.131022i
$783$		0			0
$784$		0			0
$785$	−4.83122	−	8.36792i	−0.172434	−	0.298664i
$786$		0			0
$787$	−7.47656	−	12.9498i	−0.266510	−	0.461610i	0.701448	−	0.712721i	$-0.252537\pi$
$787$	−7.47656	−	12.9498i	−0.266510	−	0.461610i	−0.967958	+	0.251111i	$0.919204\pi$
$788$	6.36693	+	11.0278i	0.226812	+	0.392850i
$789$		0			0
$790$	1.15292	+	1.99691i	0.0410190	+	0.0710470i
$791$		0			0
$792$		0			0
$793$	8.82383	+	15.2833i	0.313343	+	0.542727i
$794$	10.2661			0.364332
$795$		0			0
$796$	−2.94592			−0.104415
$797$	−4.56294	+	7.90324i	−0.161628	+	0.279947i	−0.935453	−	0.353452i	$-0.885008\pi$
$797$	−4.56294	+	7.90324i	−0.161628	+	0.279947i	0.773825	+	0.633400i	$0.218341\pi$
$798$		0			0
$799$	−4.34514	−	7.52600i	−0.153720	−	0.266251i
$800$	−2.39397	−	4.14647i	−0.0846395	−	0.146600i
$801$		0			0
$802$	−17.0167	+	29.4738i	−0.600881	+	1.04076i
$803$	24.1498	−	41.8287i	0.852228	−	1.47610i
$804$		0			0
$805$		0			0
$806$	0.375780	−	0.650870i	0.0132363	−	0.0229259i
$807$		0			0
$808$	−13.7558			−0.483928
$809$	−17.7755	+	30.7880i	−0.624953	+	1.08245i	0.363597	+	0.931556i	$0.381548\pi$
$809$	−17.7755	+	30.7880i	−0.624953	+	1.08245i	−0.988550	+	0.150894i	$0.951785\pi$
$810$		0			0
$811$	13.5070			0.474295			0.237148	−	0.971474i	$-0.423788\pi$
$811$	13.5070			0.474295			0.237148	+	0.971474i	$0.423788\pi$
$812$		0			0
$813$		0			0
$814$	−33.2235			−1.16448
$815$	5.30418	+	9.18711i	0.185797	+	0.321810i
$816$		0			0
$817$	−18.9071	+	32.7480i	−0.661475	+	1.14571i
$818$	−3.48968			−0.122014
$819$		0			0
$820$	−0.435599			−0.0152118
$821$	10.8114	−	18.7259i	0.377320	−	0.653537i	−0.613352	−	0.789810i	$-0.710179\pi$
$821$	10.8114	−	18.7259i	0.377320	−	0.653537i	0.990671	+	0.136273i	$0.0435125\pi$
$822$		0			0
$823$	0.753501	+	1.30510i	0.0262654	+	0.0454930i	0.878859	−	0.477081i	$-0.158305\pi$
$823$	0.753501	+	1.30510i	0.0262654	+	0.0454930i	−0.852594	+	0.522574i	$0.824972\pi$
$824$	11.1623			0.388855
$825$		0			0
$826$		0			0
$827$	−23.3786			−0.812953			−0.406477	−	0.913661i	$-0.633243\pi$
$827$	−23.3786			−0.812953			−0.406477	+	0.913661i	$0.633243\pi$
$828$		0			0
$829$	11.0095	−	19.0691i	0.382377	−	0.662296i	−0.609025	−	0.793151i	$-0.708439\pi$
$829$	11.0095	−	19.0691i	0.382377	−	0.662296i	0.991401	+	0.130855i	$0.0417723\pi$
$830$	−3.06128			−0.106259
$831$		0			0
$832$	−0.730252	+	1.26483i	−0.0253169	+	0.0438502i
$833$		0			0
$834$		0			0
$835$	2.44757	−	4.23932i	0.0847018	−	0.146708i
$836$	7.39397	−	12.8067i	0.255726	−	0.442930i
$837$		0			0
$838$	−14.4897	−	25.0969i	−0.500538	−	0.866957i
$839$	−1.06507	−	1.84476i	−0.0367705	−	0.0636883i	0.847055	−	0.531506i	$-0.178374\pi$
$839$	−1.06507	−	1.84476i	−0.0367705	−	0.0636883i	−0.883825	+	0.467818i	$0.845040\pi$
$840$		0			0
$841$	−25.7762	+	44.6456i	−0.888833	+	1.53950i
$842$	−2.12256			−0.0731483
$843$		0			0
$844$	1.21634			0.0418680
$845$	−2.50214	−	4.33383i	−0.0860761	−	0.149088i
$846$		0			0
$847$		0			0
$848$	−6.21780	−	10.7695i	−0.213520	−	0.369828i
$849$		0			0
$850$	−8.93872	−	15.4823i	−0.306596	−	0.531039i
$851$	5.16012	+	8.93758i	0.176887	+	0.306376i
$852$		0			0
$853$	3.50146	+	6.06471i	0.119888	+	0.207652i	0.919723	−	0.392568i	$-0.128413\pi$
$853$	3.50146	+	6.06471i	0.119888	+	0.207652i	−0.799835	+	0.600220i	$0.795080\pi$
$854$		0			0
$855$		0			0
$856$	−3.89037	−	6.73832i	−0.132970	−	0.230311i
$857$	10.9282			0.373300			0.186650	−	0.982426i	$-0.440237\pi$
$857$	10.9282			0.373300			0.186650	+	0.982426i	$0.440237\pi$
$858$		0			0
$859$	13.9076			0.474520			0.237260	−	0.971446i	$-0.423751\pi$
$859$	13.9076			0.474520			0.237260	+	0.971446i	$0.423751\pi$
$860$	−2.14766	+	3.71986i	−0.0732347	+	0.126846i
$861$		0			0
$862$	10.9356	+	18.9410i	0.372468	+	0.645133i
$863$	18.4231	+	31.9098i	0.627131	+	1.08622i	0.988125	+	0.153655i	$0.0491043\pi$
$863$	18.4231	+	31.9098i	0.627131	+	1.08622i	−0.360993	+	0.932568i	$0.617562\pi$
$864$		0			0
$865$	0.676647	−	1.17199i	0.0230067	−	0.0398488i
$866$	6.52558	−	11.3026i	0.221748	−	0.384079i
$867$		0			0
$868$		0			0
$869$	9.13229	−	15.8176i	0.309792	−	0.536575i
$870$		0			0
$871$	−3.38871			−0.114822
$872$	3.75729	−	6.50783i	0.127238	−	0.220383i
$873$		0			0
$874$	−4.59358			−0.155380
$875$		0			0
$876$		0			0
$877$	−10.3595			−0.349817			−0.174908	−	0.984585i	$-0.555963\pi$
$877$	−10.3595			−0.349817			−0.174908	+	0.984585i	$0.555963\pi$
$878$	−2.43200	−	4.21235i	−0.0820760	−	0.142160i
$879$		0			0
$880$	0.839883	−	1.45472i	0.0283125	−	0.0490386i
$881$	9.34806			0.314944			0.157472	−	0.987523i	$-0.449666\pi$
$881$	9.34806			0.314944			0.157472	+	0.987523i	$0.449666\pi$
$882$		0			0
$883$	2.29494			0.0772308			0.0386154	−	0.999254i	$-0.487705\pi$
$883$	2.29494			0.0772308			0.0386154	+	0.999254i	$0.487705\pi$
$884$	−2.72665	+	4.72270i	−0.0917073	+	0.158842i
$885$		0			0
$886$	5.76975	+	9.99350i	0.193838	+	0.335738i
$887$	−27.6726			−0.929154			−0.464577	−	0.885533i	$-0.653794\pi$
$887$	−27.6726			−0.929154			−0.464577	+	0.885533i	$0.653794\pi$
$888$		0			0
$889$		0			0
$890$	1.25564			0.0420891
$891$		0			0
$892$	0.445916	−	0.772349i	0.0149304	−	0.0258602i
$893$	−9.43560			−0.315750
$894$		0			0
$895$	−2.10963	+	3.65399i	−0.0705172	+	0.122139i
$896$		0			0
$897$		0			0
$898$	13.2125	−	22.8848i	0.440908	−	0.763676i
$899$	2.30924	−	3.99973i	0.0770176	−	0.133398i
$900$		0			0
$901$	−23.2163	−	40.2119i	−0.773448	−	1.33965i
$902$	1.72519	+	2.98812i	0.0574426	+	0.0994935i
$903$		0			0
$904$	3.03064	−	5.24922i	0.100798	−	0.174587i
$905$	10.3284			0.343327
$906$		0			0
$907$	−2.93152			−0.0973396			−0.0486698	−	0.998815i	$-0.515498\pi$
$907$	−2.93152			−0.0973396			−0.0486698	+	0.998815i	$0.515498\pi$
$908$	7.32597	+	12.6889i	0.243121	+	0.421098i
$909$		0			0
$910$		0			0
$911$	−15.3171	−	26.5300i	−0.507479	−	0.878979i	−0.999963	−	0.00865719i	$-0.997244\pi$
$911$	−15.3171	−	26.5300i	−0.507479	−	0.878979i	0.492484	−	0.870322i	$-0.336089\pi$
$912$		0			0
$913$	12.1242	+	20.9998i	0.401253	+	0.694991i
$914$	−1.86906	−	3.23731i	−0.0618231	−	0.107081i
$915$		0			0
$916$	−4.78794	−	8.29295i	−0.158198	−	0.274007i
$917$		0			0
$918$		0			0
$919$	13.1857	+	22.8383i	0.434956	+	0.753366i	0.997292	−	0.0735429i	$-0.0234306\pi$
$919$	13.1857	+	22.8383i	0.434956	+	0.753366i	−0.562336	+	0.826909i	$0.690097\pi$
$920$	−0.521786			−0.0172028
$921$		0			0
$922$	−15.8099			−0.520672
$923$	1.22665	−	2.12463i	0.0403758	−	0.0699329i
$924$		0			0
$925$	21.8047	+	37.7668i	0.716933	+	1.24176i
$926$	−19.1965	−	33.2493i	−0.630836	−	1.09264i
$927$		0			0
$928$	−4.48755	+	7.77266i	−0.147311	+	0.255150i
$929$	−8.93706	+	15.4794i	−0.293215	+	0.507864i	−0.974568	−	0.224091i	$-0.928059\pi$
$929$	−8.93706	+	15.4794i	−0.293215	+	0.507864i	0.681353	+	0.731955i	$0.261392\pi$
$930$		0			0
$931$		0			0
$932$	−7.21420	+	12.4954i	−0.236309	+	0.409299i
$933$		0			0
$934$	6.31304			0.206569
$935$	3.13600	−	5.43171i	0.102558	−	0.177636i
$936$		0			0
$937$	−15.9134			−0.519869			−0.259934	−	0.965626i	$-0.583701\pi$
$937$	−15.9134			−0.519869			−0.259934	+	0.965626i	$0.583701\pi$
$938$		0			0
$939$		0			0
$940$	−1.07179			−0.0349580
$941$	8.14027	+	14.0994i	0.265365	+	0.459626i	0.967659	−	0.252261i	$-0.0811741\pi$
$941$	8.14027	+	14.0994i	0.265365	+	0.459626i	−0.702294	+	0.711887i	$0.747841\pi$
$942$		0			0
$943$	0.535897	−	0.928200i	0.0174512	−	0.0302264i
$944$	−12.8961			−0.419732
$945$		0			0
$946$	34.0233			1.10619
$947$	−14.2951	+	24.7599i	−0.464529	+	0.804589i	−0.999180	−	0.0404846i	$-0.987110\pi$
$947$	−14.2951	+	24.7599i	−0.464529	+	0.804589i	0.534651	+	0.845073i	$0.320443\pi$
$948$		0			0
$949$	9.66945	+	16.7480i	0.313884	+	0.543662i
$950$	−19.4107			−0.629766
$951$		0			0
$952$		0			0
$953$	29.3537			0.950859			0.475430	−	0.879754i	$-0.342293\pi$
$953$	29.3537			0.950859			0.475430	+	0.879754i	$0.342293\pi$
$954$		0			0
$955$	−0.573256	+	0.992908i	−0.0185501	+	0.0321297i
$956$	−18.3097			−0.592179
$957$		0			0
$958$	−10.2068	+	17.6787i	−0.329767	+	0.571173i
$959$		0			0
$960$		0			0
$961$	15.3676	−	26.6175i	0.495729	−	0.858628i
$962$	6.65126	−	11.5203i	0.214445	−	0.371430i
$963$		0			0
$964$	0.0466924	+	0.0808735i	0.00150386	+	0.00260476i
$965$	1.03376	+	1.79053i	0.0332779	+	0.0576391i
$966$		0			0
$967$	−4.69815	+	8.13743i	−0.151082	+	0.261682i	−0.931626	−	0.363419i	$-0.881609\pi$
$967$	−4.69815	+	8.13743i	−0.151082	+	0.261682i	0.780543	+	0.625102i	$0.214943\pi$
$968$	−2.30545			−0.0741000
$969$		0			0
$970$	−5.15174			−0.165412
$971$	7.77335	+	13.4638i	0.249459	+	0.432075i	0.963376	−	0.268155i	$-0.0864140\pi$
$971$	7.77335	+	13.4638i	0.249459	+	0.432075i	−0.713917	+	0.700230i	$0.753081\pi$
$972$		0			0
$973$		0			0
$974$	−6.18190	−	10.7074i	−0.198081	−	0.343086i
$975$		0			0
$976$	6.04163	+	10.4644i	0.193388	+	0.334958i
$977$	−4.79893	−	8.31198i	−0.153531	−	0.265924i	0.778992	−	0.627034i	$-0.215731\pi$
$977$	−4.79893	−	8.31198i	−0.153531	−	0.265924i	−0.932523	+	0.361110i	$0.882398\pi$
$978$		0			0
$979$	−4.97296	−	8.61342i	−0.158936	−	0.275286i
$980$		0			0
$981$		0			0
$982$	0.207004	+	0.358541i	0.00660575	+	0.0114415i
$983$	−46.8535			−1.49439			−0.747197	−	0.664603i	$-0.768601\pi$
$983$	−46.8535			−1.49439			−0.747197	+	0.664603i	$0.768601\pi$
$984$		0			0
$985$	5.86400			0.186843
$986$	−16.7558	+	29.0220i	−0.533614	+	0.924247i
$987$		0			0
$988$	2.96050	+	5.12774i	0.0941862	+	0.163135i
$989$	−5.28434	−	9.15274i	−0.168032	−	0.291040i
$990$		0			0
$991$	10.8260	−	18.7511i	0.343898	−	0.595649i	−0.641255	−	0.767328i	$-0.721586\pi$
$991$	10.8260	−	18.7511i	0.343898	−	0.595649i	0.985153	+	0.171679i	$0.0549192\pi$
$992$	0.257295	−	0.445647i	0.00816911	−	0.0141493i
$993$		0			0
$994$		0			0
$995$	−0.678304	+	1.17486i	−0.0215037	+	0.0372455i
$996$		0			0
$997$	57.2379			1.81274			0.906372	−	0.422481i	$-0.138841\pi$
$997$	57.2379			1.81274			0.906372	+	0.422481i	$0.138841\pi$
$998$	−0.461967	+	0.800151i	−0.0146233	+	0.0253283i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.p.361.1		6
3.2	odd	2		882.2.h.o.67.1		6
7.2	even	3		2646.2.e.o.1549.3		6
7.3	odd	6		2646.2.f.o.1765.1		6
7.4	even	3		2646.2.f.n.1765.3		6
7.5	odd	6		378.2.e.c.37.1		6
7.6	odd	2		378.2.h.d.361.3		6
9.2	odd	6		882.2.e.p.655.2		6
9.7	even	3		2646.2.e.o.2125.3		6
21.2	odd	6		882.2.e.p.373.2		6
21.5	even	6		126.2.e.d.121.2	yes	6
21.11	odd	6		882.2.f.m.589.2		6
21.17	even	6		882.2.f.l.589.2		6
21.20	even	2		126.2.h.c.67.3	yes	6
28.19	even	6		3024.2.q.h.2305.1		6
28.27	even	2		3024.2.t.g.1873.3		6
63.2	odd	6		882.2.h.o.79.1		6
63.4	even	3		7938.2.a.bx.1.1		3
63.5	even	6		1134.2.g.k.163.3		6
63.11	odd	6		882.2.f.m.295.2		6
63.13	odd	6		1134.2.g.n.487.1		6
63.16	even	3	inner	2646.2.h.p.667.1		6
63.20	even	6		126.2.e.d.25.2	✓	6
63.25	even	3		2646.2.f.n.883.3		6
63.31	odd	6		7938.2.a.bu.1.3		3
63.32	odd	6		7938.2.a.by.1.3		3
63.34	odd	6		378.2.e.c.235.1		6
63.38	even	6		882.2.f.l.295.2		6
63.40	odd	6		1134.2.g.n.163.1		6
63.41	even	6		1134.2.g.k.487.3		6
63.47	even	6		126.2.h.c.79.3	yes	6
63.52	odd	6		2646.2.f.o.883.1		6
63.59	even	6		7938.2.a.cb.1.1		3
63.61	odd	6		378.2.h.d.289.3		6
84.47	odd	6		1008.2.q.h.625.2		6
84.83	odd	2		1008.2.t.g.193.1		6
252.47	odd	6		1008.2.t.g.961.1		6
252.83	odd	6		1008.2.q.h.529.2		6
252.187	even	6		3024.2.t.g.289.3		6
252.223	even	6		3024.2.q.h.2881.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.2	✓	6	63.20	even	6
126.2.e.d.121.2	yes	6	21.5	even	6
126.2.h.c.67.3	yes	6	21.20	even	2
126.2.h.c.79.3	yes	6	63.47	even	6
378.2.e.c.37.1		6	7.5	odd	6
378.2.e.c.235.1		6	63.34	odd	6
378.2.h.d.289.3		6	63.61	odd	6
378.2.h.d.361.3		6	7.6	odd	2
882.2.e.p.373.2		6	21.2	odd	6
882.2.e.p.655.2		6	9.2	odd	6
882.2.f.l.295.2		6	63.38	even	6
882.2.f.l.589.2		6	21.17	even	6
882.2.f.m.295.2		6	63.11	odd	6
882.2.f.m.589.2		6	21.11	odd	6
882.2.h.o.67.1		6	3.2	odd	2
882.2.h.o.79.1		6	63.2	odd	6
1008.2.q.h.529.2		6	252.83	odd	6
1008.2.q.h.625.2		6	84.47	odd	6
1008.2.t.g.193.1		6	84.83	odd	2
1008.2.t.g.961.1		6	252.47	odd	6
1134.2.g.k.163.3		6	63.5	even	6
1134.2.g.k.487.3		6	63.41	even	6
1134.2.g.n.163.1		6	63.40	odd	6
1134.2.g.n.487.1		6	63.13	odd	6
2646.2.e.o.1549.3		6	7.2	even	3
2646.2.e.o.2125.3		6	9.7	even	3
2646.2.f.n.883.3		6	63.25	even	3
2646.2.f.n.1765.3		6	7.4	even	3
2646.2.f.o.883.1		6	63.52	odd	6
2646.2.f.o.1765.1		6	7.3	odd	6
2646.2.h.p.361.1		6	1.1	even	1	trivial
2646.2.h.p.667.1		6	63.16	even	3	inner
3024.2.q.h.2305.1		6	28.19	even	6
3024.2.q.h.2881.1		6	252.223	even	6
3024.2.t.g.289.3		6	252.187	even	6
3024.2.t.g.1873.3		6	28.27	even	2
7938.2.a.bu.1.3		3	63.31	odd	6
7938.2.a.bx.1.1		3	63.4	even	3
7938.2.a.by.1.3		3	63.32	odd	6
7938.2.a.cb.1.1		3	63.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -0.460505 q^{5} -1.00000 q^{8} +(-0.230252 + 0.398809i) q^{10} +3.64766 q^{11} +(-0.730252 + 1.26483i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.86693 + 3.23361i) q^{17} +(2.02704 + 3.51094i) q^{19} +(0.230252 + 0.398809i) q^{20} +(1.82383 - 3.15897i) q^{22} -1.13307 q^{23} -4.78794 q^{25} +(0.730252 + 1.26483i) q^{26} +(4.48755 + 7.77266i) q^{29} +(-0.257295 - 0.445647i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.86693 + 3.23361i) q^{34} +(-4.55408 - 7.88791i) q^{37} +4.05408 q^{38} +0.460505 q^{40} +(-0.472958 + 0.819187i) q^{41} +(4.66372 + 8.07779i) q^{43} +(-1.82383 - 3.15897i) q^{44} +(-0.566537 + 0.981271i) q^{46} +(-1.16372 + 2.01561i) q^{47} +(-2.39397 + 4.14647i) q^{50} +1.46050 q^{52} +(-6.21780 + 10.7695i) q^{53} -1.67977 q^{55} +8.97509 q^{58} +(6.44805 + 11.1684i) q^{59} +(6.04163 - 10.4644i) q^{61} -0.514589 q^{62} +1.00000 q^{64} +(0.336285 - 0.582462i) q^{65} +(1.16012 + 2.00938i) q^{67} +3.73385 q^{68} -1.67977 q^{71} +(6.62062 - 11.4673i) q^{73} -9.10817 q^{74} +(2.02704 - 3.51094i) q^{76} +(2.50360 - 4.33636i) q^{79} +(0.230252 - 0.398809i) q^{80} +(0.472958 + 0.819187i) q^{82} +(3.32383 + 5.75705i) q^{83} +(0.859728 - 1.48909i) q^{85} +9.32743 q^{86} -3.64766 q^{88} +(-1.36333 - 2.36135i) q^{89} +(0.566537 + 0.981271i) q^{92} +(1.16372 + 2.01561i) q^{94} +(-0.933463 - 1.61680i) q^{95} +(5.59358 + 9.68836i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8} + 5 q^{10} - 2 q^{11} + 2 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} - 5 q^{20} - q^{22} - 14 q^{23} + 4 q^{25} - 2 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34}+ \cdots + 28 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 10 * q^5 - 6 * q^8 + 5 * q^10 - 2 * q^11 + 2 * q^13 - 3 * q^16 - 4 * q^17 + 3 * q^19 - 5 * q^20 - q^22 - 14 * q^23 + 4 * q^25 - 2 * q^26 + 5 * q^29 + 14 * q^31 + 3 * q^32 + 4 * q^34 - 9 * q^37 + 6 * q^38 - 10 * q^40 - 12 * q^41 + 18 * q^43 + q^44 - 7 * q^46 + 3 * q^47 + 2 * q^50 - 4 * q^52 - 9 * q^53 - 14 * q^55 + 10 * q^58 + 4 * q^59 - 4 * q^61 + 28 * q^62 + 6 * q^64 + 12 * q^65 + 5 * q^67 + 8 * q^68 - 14 * q^71 + 25 * q^73 - 18 * q^74 + 3 * q^76 + 7 * q^79 - 5 * q^80 + 12 * q^82 + 8 * q^83 + 14 * q^85 + 36 * q^86 + 2 * q^88 - 9 * q^89 + 7 * q^92 - 3 * q^94 - 2 * q^95 + 28 * q^97

Introduction

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