LMFDB - Embedded newform 342.2.g.f.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(163,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("342.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.g (of order $3$, degree $2$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	342.235
Dual form			342.2.g.f.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} +3.64575 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} +3.64575 q^{7} -1.00000 q^{8} +(0.822876 - 1.42526i) q^{10} +4.64575 q^{11} +(-1.00000 + 1.73205i) q^{13} +(1.82288 + 3.15731i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.67712 + 4.02334i) q^{19} +1.64575 q^{20} +(2.32288 + 4.02334i) q^{22} +(-0.822876 + 1.42526i) q^{23} +(1.14575 - 1.98450i) q^{25} -2.00000 q^{26} +(-1.82288 + 3.15731i) q^{28} +(0.822876 - 1.42526i) q^{29} -5.64575 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{35} +0.354249 q^{37} +(-2.64575 + 3.46410i) q^{38} +(0.822876 + 1.42526i) q^{40} +(-0.145751 - 0.252449i) q^{41} +(-5.64575 - 9.77873i) q^{43} +(-2.32288 + 4.02334i) q^{44} -1.64575 q^{46} +(2.17712 - 3.77089i) q^{47} +6.29150 q^{49} +2.29150 q^{50} +(-1.00000 - 1.73205i) q^{52} +(-6.29150 + 10.8972i) q^{53} +(-3.82288 - 6.62141i) q^{55} -3.64575 q^{56} +1.64575 q^{58} +(-3.96863 - 6.87386i) q^{59} +(-0.468627 + 0.811686i) q^{61} +(-2.82288 - 4.88936i) q^{62} +1.00000 q^{64} +3.29150 q^{65} +(-0.322876 + 0.559237i) q^{67} +(3.00000 - 5.19615i) q^{70} +(-1.35425 - 2.34563i) q^{71} +(-0.854249 - 1.47960i) q^{73} +(0.177124 + 0.306788i) q^{74} +(-4.32288 - 0.559237i) q^{76} +16.9373 q^{77} +(2.00000 + 3.46410i) q^{79} +(-0.822876 + 1.42526i) q^{80} +(0.145751 - 0.252449i) q^{82} -7.93725 q^{83} +(5.64575 - 9.77873i) q^{86} -4.64575 q^{88} +(-3.64575 + 6.31463i) q^{91} +(-0.822876 - 1.42526i) q^{92} +4.35425 q^{94} +(4.35425 - 5.70105i) q^{95} +(1.85425 + 3.21165i) q^{97} +(3.14575 + 5.44860i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8} - 2 q^{10} + 8 q^{11} - 4 q^{13} + 2 q^{14} - 2 q^{16} + 12 q^{19} - 4 q^{20} + 4 q^{22} + 2 q^{23} - 6 q^{25} - 8 q^{26} - 2 q^{28} - 2 q^{29} - 12 q^{31} + 2 q^{32} - 12 q^{35} + 12 q^{37} - 2 q^{40} + 10 q^{41} - 12 q^{43} - 4 q^{44} + 4 q^{46} + 14 q^{47} + 4 q^{49} - 12 q^{50} - 4 q^{52} - 4 q^{53} - 10 q^{55} - 4 q^{56} - 4 q^{58} + 14 q^{61} - 6 q^{62} + 4 q^{64} - 8 q^{65} + 4 q^{67} + 12 q^{70} - 16 q^{71} - 14 q^{73} + 6 q^{74} - 12 q^{76} + 36 q^{77} + 8 q^{79} + 2 q^{80} - 10 q^{82} + 12 q^{86} - 8 q^{88} - 4 q^{91} + 2 q^{92} + 28 q^{94} + 28 q^{95} + 18 q^{97} + 2 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8 - 2 * q^10 + 8 * q^11 - 4 * q^13 + 2 * q^14 - 2 * q^16 + 12 * q^19 - 4 * q^20 + 4 * q^22 + 2 * q^23 - 6 * q^25 - 8 * q^26 - 2 * q^28 - 2 * q^29 - 12 * q^31 + 2 * q^32 - 12 * q^35 + 12 * q^37 - 2 * q^40 + 10 * q^41 - 12 * q^43 - 4 * q^44 + 4 * q^46 + 14 * q^47 + 4 * q^49 - 12 * q^50 - 4 * q^52 - 4 * q^53 - 10 * q^55 - 4 * q^56 - 4 * q^58 + 14 * q^61 - 6 * q^62 + 4 * q^64 - 8 * q^65 + 4 * q^67 + 12 * q^70 - 16 * q^71 - 14 * q^73 + 6 * q^74 - 12 * q^76 + 36 * q^77 + 8 * q^79 + 2 * q^80 - 10 * q^82 + 12 * q^86 - 8 * q^88 - 4 * q^91 + 2 * q^92 + 28 * q^94 + 28 * q^95 + 18 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	0.621252	−	0.783611i	$-0.286624\pi$
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	−0.989253	+	0.146214i	$0.953291\pi$
$6$		0			0
$7$	3.64575			1.37796			0.688982	−	0.724778i	$-0.258058\pi$
$7$	3.64575			1.37796			0.688982	+	0.724778i	$0.258058\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.822876	−	1.42526i	0.260216	−	0.450708i
$11$	4.64575			1.40075			0.700373	−	0.713777i	$-0.253017\pi$
$11$	4.64575			1.40075			0.700373	+	0.713777i	$0.253017\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	1.82288	+	3.15731i	0.487184	+	0.843827i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	1.67712	+	4.02334i	0.384759	+	0.923017i
$19$	1.67712	+	4.02334i	0.384759	+	0.923017i
$20$	1.64575			0.368001
$21$		0			0
$22$	2.32288	+	4.02334i	0.495239	+	0.857779i
$23$	−0.822876	+	1.42526i	−0.171581	+	0.297188i	−0.938973	−	0.343991i	$-0.888221\pi$
$23$	−0.822876	+	1.42526i	−0.171581	+	0.297188i	0.767391	+	0.641179i	$0.221554\pi$
$24$		0			0
$25$	1.14575	−	1.98450i	0.229150	−	0.396900i
$26$	−2.00000			−0.392232
$27$		0			0
$28$	−1.82288	+	3.15731i	−0.344491	+	0.596676i
$29$	0.822876	−	1.42526i	0.152804	−	0.264665i	−0.779453	−	0.626461i	$-0.784503\pi$
$29$	0.822876	−	1.42526i	0.152804	−	0.264665i	0.932257	+	0.361796i	$0.117836\pi$
$30$		0			0
$31$	−5.64575			−1.01401			−0.507003	−	0.861944i	$-0.669247\pi$
$31$	−5.64575			−1.01401			−0.507003	+	0.861944i	$0.669247\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$	−3.00000	−	5.19615i	−0.507093	−	0.878310i
$36$		0			0
$37$	0.354249			0.0582381			0.0291191	−	0.999576i	$-0.490730\pi$
$37$	0.354249			0.0582381			0.0291191	+	0.999576i	$0.490730\pi$
$38$	−2.64575	+	3.46410i	−0.429198	+	0.561951i
$39$		0			0
$40$	0.822876	+	1.42526i	0.130108	+	0.225354i
$41$	−0.145751	−	0.252449i	−0.0227625	−	0.0394259i	0.854420	−	0.519583i	$-0.173913\pi$
$41$	−0.145751	−	0.252449i	−0.0227625	−	0.0394259i	−0.877182	+	0.480158i	$0.840579\pi$
$42$		0			0
$43$	−5.64575	−	9.77873i	−0.860969	−	1.49124i	−0.870995	−	0.491292i	$-0.836525\pi$
$43$	−5.64575	−	9.77873i	−0.860969	−	1.49124i	0.0100257	−	0.999950i	$-0.496809\pi$
$44$	−2.32288	+	4.02334i	−0.350187	+	0.606541i
$45$		0			0
$46$	−1.64575			−0.242653
$47$	2.17712	−	3.77089i	0.317566	−	0.550041i	−0.662413	−	0.749138i	$-0.730468\pi$
$47$	2.17712	−	3.77089i	0.317566	−	0.550041i	0.979980	+	0.199098i	$0.0638011\pi$
$48$		0			0
$49$	6.29150			0.898786
$50$	2.29150			0.324067
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−6.29150	+	10.8972i	−0.864204	+	1.49685i	0.00363070	+	0.999993i	$0.498844\pi$
$53$	−6.29150	+	10.8972i	−0.864204	+	1.49685i	−0.867835	+	0.496852i	$0.834489\pi$
$54$		0			0
$55$	−3.82288	−	6.62141i	−0.515476	−	0.892831i
$56$	−3.64575			−0.487184
$57$		0			0
$58$	1.64575			0.216098
$59$	−3.96863	−	6.87386i	−0.516671	−	0.894901i	−0.999813	−	0.0193585i	$-0.993838\pi$
$59$	−3.96863	−	6.87386i	−0.516671	−	0.894901i	0.483141	−	0.875542i	$-0.339496\pi$
$60$		0			0
$61$	−0.468627	+	0.811686i	−0.0600015	+	0.103926i	−0.894466	−	0.447136i	$-0.852444\pi$
$61$	−0.468627	+	0.811686i	−0.0600015	+	0.103926i	0.834464	+	0.551062i	$0.185777\pi$
$62$	−2.82288	−	4.88936i	−0.358506	−	0.620950i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.29150			0.408261
$66$		0			0
$67$	−0.322876	+	0.559237i	−0.0394455	+	0.0683217i	−0.885074	−	0.465450i	$-0.845892\pi$
$67$	−0.322876	+	0.559237i	−0.0394455	+	0.0683217i	0.845629	+	0.533772i	$0.179226\pi$
$68$		0			0
$69$		0			0
$70$	3.00000	−	5.19615i	0.358569	−	0.621059i
$71$	−1.35425	−	2.34563i	−0.160720	−	0.278375i	0.774407	−	0.632687i	$-0.218048\pi$
$71$	−1.35425	−	2.34563i	−0.160720	−	0.278375i	−0.935127	+	0.354313i	$0.884715\pi$
$72$		0			0
$73$	−0.854249	−	1.47960i	−0.0999822	−	0.173174i	0.811695	−	0.584082i	$-0.198545\pi$
$73$	−0.854249	−	1.47960i	−0.0999822	−	0.173174i	−0.911677	+	0.410907i	$0.865212\pi$
$74$	0.177124	+	0.306788i	0.0205903	+	0.0356634i
$75$		0			0
$76$	−4.32288	−	0.559237i	−0.495868	−	0.0641489i
$77$	16.9373			1.93018
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−0.822876	+	1.42526i	−0.0920003	+	0.159349i
$81$		0			0
$82$	0.145751	−	0.252449i	0.0160955	−	0.0278783i
$83$	−7.93725			−0.871227			−0.435613	−	0.900134i	$-0.643469\pi$
$83$	−7.93725			−0.871227			−0.435613	+	0.900134i	$0.643469\pi$
$84$		0			0
$85$		0			0
$86$	5.64575	−	9.77873i	0.608797	−	1.05447i
$87$		0			0
$88$	−4.64575			−0.495239
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	−3.64575	+	6.31463i	−0.382179	+	0.661953i
$92$	−0.822876	−	1.42526i	−0.0857907	−	0.148594i
$93$		0			0
$94$	4.35425			0.449106
$95$	4.35425	−	5.70105i	0.446736	−	0.584915i
$96$		0			0
$97$	1.85425	+	3.21165i	0.188270	+	0.326094i	0.944674	−	0.328012i	$-0.106379\pi$
$97$	1.85425	+	3.21165i	0.188270	+	0.326094i	−0.756403	+	0.654106i	$0.773045\pi$
$98$	3.14575	+	5.44860i	0.317769	+	0.550392i
$99$		0			0
$100$	1.14575	+	1.98450i	0.114575	+	0.198450i
$101$	−6.82288	+	11.8176i	−0.678902	+	1.17589i	0.296411	+	0.955061i	$0.404210\pi$
$101$	−6.82288	+	11.8176i	−0.678902	+	1.17589i	−0.975312	+	0.220831i	$0.929123\pi$
$102$		0			0
$103$	−13.2915			−1.30965			−0.654825	−	0.755780i	$-0.727258\pi$
$103$	−13.2915			−1.30965			−0.654825	+	0.755780i	$0.727258\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	−12.5830			−1.22217
$107$	−15.2915			−1.47829			−0.739143	−	0.673549i	$-0.764769\pi$
$107$	−15.2915			−1.47829			−0.739143	+	0.673549i	$0.764769\pi$
$108$		0			0
$109$	−7.29150	−	12.6293i	−0.698399	−	1.20966i	−0.969021	−	0.246977i	$-0.920563\pi$
$109$	−7.29150	−	12.6293i	−0.698399	−	1.20966i	0.270622	−	0.962686i	$-0.412771\pi$
$110$	3.82288	−	6.62141i	0.364497	−	0.631327i
$111$		0			0
$112$	−1.82288	−	3.15731i	−0.172246	−	0.298338i
$113$	15.5830			1.46593			0.732963	−	0.680269i	$-0.238137\pi$
$113$	15.5830			1.46593			0.732963	+	0.680269i	$0.238137\pi$
$114$		0			0
$115$	2.70850			0.252569
$116$	0.822876	+	1.42526i	0.0764021	+	0.132332i
$117$		0			0
$118$	3.96863	−	6.87386i	0.365342	−	0.632790i
$119$		0			0
$120$		0			0
$121$	10.5830			0.962091
$122$	−0.937254			−0.0848550
$123$		0			0
$124$	2.82288	−	4.88936i	0.253502	−	0.439078i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	6.64575	−	11.5108i	0.589715	−	1.02142i	−0.404554	−	0.914514i	$-0.632573\pi$
$127$	6.64575	−	11.5108i	0.589715	−	1.02142i	0.994270	−	0.106903i	$-0.0340933\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	1.64575	+	2.85052i	0.144342	+	0.250008i
$131$	0.968627	+	1.67771i	0.0846293	+	0.146582i	0.905233	−	0.424915i	$-0.139696\pi$
$131$	0.968627	+	1.67771i	0.0846293	+	0.146582i	−0.820604	+	0.571497i	$0.806363\pi$
$132$		0			0
$133$	6.11438	+	14.6681i	0.530184	+	1.27188i
$134$	−0.645751			−0.0557844
$135$		0			0
$136$		0			0
$137$	7.79150	−	13.4953i	0.665673	−	1.15298i	−0.313429	−	0.949612i	$-0.601478\pi$
$137$	7.79150	−	13.4953i	0.665673	−	1.15298i	0.979102	−	0.203368i	$-0.0651888\pi$
$138$		0			0
$139$	−9.32288	+	16.1477i	−0.790756	+	1.36963i	0.134743	+	0.990881i	$0.456979\pi$
$139$	−9.32288	+	16.1477i	−0.790756	+	1.36963i	−0.925499	+	0.378749i	$0.876354\pi$
$140$	6.00000			0.507093
$141$		0			0
$142$	1.35425	−	2.34563i	0.113646	−	0.196841i
$143$	−4.64575	+	8.04668i	−0.388497	+	0.672897i
$144$		0			0
$145$	−2.70850			−0.224928
$146$	0.854249	−	1.47960i	0.0706981	−	0.122453i
$147$		0			0
$148$	−0.177124	+	0.306788i	−0.0145595	+	0.0252178i
$149$	5.46863	+	9.47194i	0.448007	+	0.775972i	0.998256	−	0.0590292i	$-0.0188005\pi$
$149$	5.46863	+	9.47194i	0.448007	+	0.775972i	−0.550249	+	0.835001i	$0.685467\pi$
$150$		0			0
$151$	12.9373			1.05282			0.526409	−	0.850231i	$-0.323538\pi$
$151$	12.9373			1.05282			0.526409	+	0.850231i	$0.323538\pi$
$152$	−1.67712	−	4.02334i	−0.136033	−	0.326336i
$153$		0			0
$154$	8.46863	+	14.6681i	0.682421	+	1.18199i
$155$	4.64575	+	8.04668i	0.373156	+	0.646325i
$156$		0			0
$157$	5.29150	+	9.16515i	0.422308	+	0.731459i	0.996165	−	0.0874969i	$-0.0278868\pi$
$157$	5.29150	+	9.16515i	0.422308	+	0.731459i	−0.573857	+	0.818956i	$0.694553\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$		0			0
$160$	−1.64575			−0.130108
$161$	−3.00000	+	5.19615i	−0.236433	+	0.409514i
$162$		0			0
$163$	3.93725			0.308390			0.154195	−	0.988040i	$-0.450722\pi$
$163$	3.93725			0.308390			0.154195	+	0.988040i	$0.450722\pi$
$164$	0.291503			0.0227625
$165$		0			0
$166$	−3.96863	−	6.87386i	−0.308025	−	0.533515i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$		0			0
$172$	11.2915			0.860969
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	4.17712	−	7.23499i	0.315761	−	0.546914i
$176$	−2.32288	−	4.02334i	−0.175093	−	0.303271i
$177$		0			0
$178$		0			0
$179$	−4.06275			−0.303664			−0.151832	−	0.988406i	$-0.548517\pi$
$179$	−4.06275			−0.303664			−0.151832	+	0.988406i	$0.548517\pi$
$180$		0			0
$181$	−11.1144	+	19.2507i	−0.826125	+	1.43089i	0.0749311	+	0.997189i	$0.476126\pi$
$181$	−11.1144	+	19.2507i	−0.826125	+	1.43089i	−0.901056	+	0.433702i	$0.857207\pi$
$182$	−7.29150			−0.540482
$183$		0			0
$184$	0.822876	−	1.42526i	0.0606632	−	0.105072i
$185$	−0.291503	−	0.504897i	−0.0214317	−	0.0371208i
$186$		0			0
$187$		0			0
$188$	2.17712	+	3.77089i	0.158783	+	0.275020i
$189$		0			0
$190$	7.11438	+	0.920365i	0.516131	+	0.0667703i
$191$	−6.58301			−0.476330			−0.238165	−	0.971225i	$-0.576546\pi$
$191$	−6.58301			−0.476330			−0.238165	+	0.971225i	$0.576546\pi$
$192$		0			0
$193$	−7.29150	−	12.6293i	−0.524854	−	0.909074i	−0.999581	−	0.0289406i	$-0.990787\pi$
$193$	−7.29150	−	12.6293i	−0.524854	−	0.909074i	0.474727	−	0.880133i	$-0.342547\pi$
$194$	−1.85425	+	3.21165i	−0.133127	+	0.230583i
$195$		0			0
$196$	−3.14575	+	5.44860i	−0.224697	+	0.389186i
$197$	7.64575			0.544737			0.272369	−	0.962193i	$-0.412193\pi$
$197$	7.64575			0.544737			0.272369	+	0.962193i	$0.412193\pi$
$198$		0			0
$199$	9.93725	−	17.2118i	0.704433	−	1.22011i	−0.262462	−	0.964942i	$-0.584535\pi$
$199$	9.93725	−	17.2118i	0.704433	−	1.22011i	0.966896	−	0.255172i	$-0.0821321\pi$
$200$	−1.14575	+	1.98450i	−0.0810169	+	0.140325i
$201$		0			0
$202$	−13.6458			−0.960112
$203$	3.00000	−	5.19615i	0.210559	−	0.364698i
$204$		0			0
$205$	−0.239870	+	0.415468i	−0.0167533	+	0.0290175i
$206$	−6.64575	−	11.5108i	−0.463031	−	0.801994i
$207$		0			0
$208$	2.00000			0.138675
$209$	7.79150	+	18.6914i	0.538950	+	1.29291i
$210$		0			0
$211$	6.64575	+	11.5108i	0.457512	+	0.792435i	0.998829	−	0.0483843i	$-0.0154072\pi$
$211$	6.64575	+	11.5108i	0.457512	+	0.792435i	−0.541316	+	0.840819i	$0.682074\pi$
$212$	−6.29150	−	10.8972i	−0.432102	−	0.748423i
$213$		0			0
$214$	−7.64575	−	13.2428i	−0.522653	−	0.905261i
$215$	−9.29150	+	16.0934i	−0.633675	+	1.09756i
$216$		0			0
$217$	−20.5830			−1.39727
$218$	7.29150	−	12.6293i	0.493843	−	0.855361i
$219$		0			0
$220$	7.64575			0.515476
$221$		0			0
$222$		0			0
$223$	9.40588	+	16.2915i	0.629864	+	1.09096i	0.987579	+	0.157126i	$0.0502229\pi$
$223$	9.40588	+	16.2915i	0.629864	+	1.09096i	−0.357714	+	0.933831i	$0.616444\pi$
$224$	1.82288	−	3.15731i	0.121796	−	0.210957i
$225$		0			0
$226$	7.79150	+	13.4953i	0.518283	+	0.897693i
$227$	7.35425			0.488119			0.244059	−	0.969760i	$-0.421521\pi$
$227$	7.35425			0.488119			0.244059	+	0.969760i	$0.421521\pi$
$228$		0			0
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$	1.35425	+	2.34563i	0.0892965	+	0.154666i
$231$		0			0
$232$	−0.822876	+	1.42526i	−0.0540244	+	0.0935731i
$233$	9.43725	+	16.3458i	0.618255	+	1.07085i	0.989804	+	0.142436i	$0.0454935\pi$
$233$	9.43725	+	16.3458i	0.618255	+	1.07085i	−0.371549	+	0.928413i	$0.621173\pi$
$234$		0			0
$235$	−7.16601			−0.467459
$236$	7.93725			0.516671
$237$		0			0
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	3.79150	−	6.56708i	0.244232	−	0.423022i	−0.717683	−	0.696370i	$-0.754797\pi$
$241$	3.79150	−	6.56708i	0.244232	−	0.423022i	0.961915	+	0.273347i	$0.0881308\pi$
$242$	5.29150	+	9.16515i	0.340151	+	0.589158i
$243$		0			0
$244$	−0.468627	−	0.811686i	−0.0300008	−	0.0519629i
$245$	−5.17712	−	8.96704i	−0.330754	−	0.572883i
$246$		0			0
$247$	−8.64575	−	1.11847i	−0.550116	−	0.0711668i
$248$	5.64575			0.358506
$249$		0			0
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	14.6144	−	25.3128i	0.922451	−	1.59773i	0.126842	−	0.991923i	$-0.459516\pi$
$251$	14.6144	−	25.3128i	0.922451	−	1.59773i	0.795610	−	0.605810i	$-0.207151\pi$
$252$		0			0
$253$	−3.82288	+	6.62141i	−0.240342	+	0.416285i
$254$	13.2915			0.833983
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.14575	−	10.6448i	0.383361	−	0.664001i	−0.608179	−	0.793800i	$-0.708100\pi$
$257$	6.14575	−	10.6448i	0.383361	−	0.664001i	0.991540	+	0.129798i	$0.0414330\pi$
$258$		0			0
$259$	1.29150			0.0802501
$260$	−1.64575	+	2.85052i	−0.102065	+	0.176782i
$261$		0			0
$262$	−0.968627	+	1.67771i	−0.0598420	+	0.103649i
$263$	−5.46863	−	9.47194i	−0.337210	−	0.584065i	0.646697	−	0.762747i	$-0.276150\pi$
$263$	−5.46863	−	9.47194i	−0.337210	−	0.584065i	−0.983907	+	0.178682i	$0.942817\pi$
$264$		0			0
$265$	20.7085			1.27211
$266$	−9.64575	+	12.6293i	−0.591419	+	0.774349i
$267$		0			0
$268$	−0.322876	−	0.559237i	−0.0197228	−	0.0341608i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	−6.17712	−	10.6991i	−0.375234	−	0.649924i	0.615128	−	0.788427i	$-0.289104\pi$
$271$	−6.17712	−	10.6991i	−0.375234	−	0.649924i	−0.990362	+	0.138503i	$0.955771\pi$
$272$		0			0
$273$		0			0
$274$	15.5830			0.941404
$275$	5.32288	−	9.21949i	0.320981	−	0.555956i
$276$		0			0
$277$	−27.5203			−1.65353			−0.826766	−	0.562546i	$-0.809822\pi$
$277$	−27.5203			−1.65353			−0.826766	+	0.562546i	$0.809822\pi$
$278$	−18.6458			−1.11830
$279$		0			0
$280$	3.00000	+	5.19615i	0.179284	+	0.310530i
$281$	12.7288	−	22.0469i	0.759334	−	1.31520i	−0.183857	−	0.982953i	$-0.558858\pi$
$281$	12.7288	−	22.0469i	0.759334	−	1.31520i	0.943191	−	0.332252i	$-0.107808\pi$
$282$		0			0
$283$	−15.3229	−	26.5400i	−0.910850	−	1.57764i	−0.812866	−	0.582451i	$-0.802094\pi$
$283$	−15.3229	−	26.5400i	−0.910850	−	1.57764i	−0.0979848	−	0.995188i	$-0.531240\pi$
$284$	2.70850			0.160720
$285$		0			0
$286$	−9.29150			−0.549418
$287$	−0.531373	−	0.920365i	−0.0313660	−	0.0543274i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−1.35425	−	2.34563i	−0.0795242	−	0.137740i
$291$		0			0
$292$	1.70850			0.0999822
$293$	−28.9373			−1.69053			−0.845266	−	0.534345i	$-0.820558\pi$
$293$	−28.9373			−1.69053			−0.845266	+	0.534345i	$0.820558\pi$
$294$		0			0
$295$	−6.53137	+	11.3127i	−0.380271	+	0.658649i
$296$	−0.354249			−0.0205903
$297$		0			0
$298$	−5.46863	+	9.47194i	−0.316789	+	0.548695i
$299$	−1.64575	−	2.85052i	−0.0951763	−	0.164850i
$300$		0			0
$301$	−20.5830	−	35.6508i	−1.18638	−	2.05488i
$302$	6.46863	+	11.2040i	0.372228	+	0.644717i
$303$		0			0
$304$	2.64575	−	3.46410i	0.151744	−	0.198680i
$305$	1.54249			0.0883225
$306$		0			0
$307$	−0.322876	−	0.559237i	−0.0184275	−	0.0319173i	0.856665	−	0.515874i	$-0.172533\pi$
$307$	−0.322876	−	0.559237i	−0.0184275	−	0.0319173i	−0.875092	+	0.483956i	$0.839199\pi$
$308$	−8.46863	+	14.6681i	−0.482545	+	0.835792i
$309$		0			0
$310$	−4.64575	+	8.04668i	−0.263861	+	0.457021i
$311$	−13.6458			−0.773780			−0.386890	−	0.922126i	$-0.626451\pi$
$311$	−13.6458			−0.773780			−0.386890	+	0.922126i	$0.626451\pi$
$312$		0			0
$313$	−4.43725	+	7.68555i	−0.250808	+	0.434413i	−0.963749	−	0.266812i	$-0.914030\pi$
$313$	−4.43725	+	7.68555i	−0.250808	+	0.434413i	0.712940	+	0.701225i	$0.247363\pi$
$314$	−5.29150	+	9.16515i	−0.298617	+	0.517219i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$		0			0
$319$	3.82288	−	6.62141i	0.214040	−	0.370728i
$320$	−0.822876	−	1.42526i	−0.0460001	−	0.0796746i
$321$		0			0
$322$	−6.00000			−0.334367
$323$		0			0
$324$		0			0
$325$	2.29150	+	3.96900i	0.127110	+	0.220160i
$326$	1.96863	+	3.40976i	0.109032	+	0.188849i
$327$		0			0
$328$	0.145751	+	0.252449i	0.00804777	+	0.0139391i
$329$	7.93725	−	13.7477i	0.437595	−	0.757937i
$330$		0			0
$331$	19.8118			1.08895			0.544476	−	0.838776i	$-0.316728\pi$
$331$	19.8118			1.08895			0.544476	+	0.838776i	$0.316728\pi$
$332$	3.96863	−	6.87386i	0.217807	−	0.377252i
$333$		0			0
$334$	−12.0000			−0.656611
$335$	1.06275			0.0580640
$336$		0			0
$337$	4.85425	+	8.40781i	0.264428	+	0.458002i	0.967414	−	0.253202i	$-0.0814836\pi$
$337$	4.85425	+	8.40781i	0.264428	+	0.458002i	−0.702986	+	0.711204i	$0.748150\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$		0			0
$340$		0			0
$341$	−26.2288			−1.42037
$342$		0			0
$343$	−2.58301			−0.139469
$344$	5.64575	+	9.77873i	0.304399	+	0.527234i
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	−11.6144	−	20.1167i	−0.623492	−	1.07992i	−0.988830	−	0.149046i	$-0.952380\pi$
$347$	−11.6144	−	20.1167i	−0.623492	−	1.07992i	0.365338	−	0.930875i	$-0.380953\pi$
$348$		0			0
$349$	21.1660			1.13299			0.566495	−	0.824065i	$-0.308299\pi$
$349$	21.1660			1.13299			0.566495	+	0.824065i	$0.308299\pi$
$350$	8.35425			0.446553
$351$		0			0
$352$	2.32288	−	4.02334i	0.123810	−	0.214445i
$353$	−12.8745			−0.685241			−0.342620	−	0.939474i	$-0.611314\pi$
$353$	−12.8745			−0.685241			−0.342620	+	0.939474i	$0.611314\pi$
$354$		0			0
$355$	−2.22876	+	3.86032i	−0.118290	+	0.204884i
$356$		0			0
$357$		0			0
$358$	−2.03137	−	3.51844i	−0.107361	−	0.185955i
$359$	−2.46863	−	4.27579i	−0.130289	−	0.225667i	0.793499	−	0.608572i	$-0.208257\pi$
$359$	−2.46863	−	4.27579i	−0.130289	−	0.225667i	−0.923788	+	0.382904i	$0.874924\pi$
$360$		0			0
$361$	−13.3745	+	13.4953i	−0.703921	+	0.710278i
$362$	−22.2288			−1.16832
$363$		0			0
$364$	−3.64575	−	6.31463i	−0.191089	−	0.330976i
$365$	−1.40588	+	2.43506i	−0.0735872	+	0.127457i
$366$		0			0
$367$	−8.11438	+	14.0545i	−0.423567	+	0.733640i	−0.996285	−	0.0861125i	$-0.972556\pi$
$367$	−8.11438	+	14.0545i	−0.423567	+	0.733640i	0.572718	+	0.819752i	$0.305889\pi$
$368$	1.64575			0.0857907
$369$		0			0
$370$	0.291503	−	0.504897i	0.0151545	−	0.0262484i
$371$	−22.9373	+	39.7285i	−1.19084	+	2.06260i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$		0			0
$376$	−2.17712	+	3.77089i	−0.112277	+	0.194469i
$377$	1.64575	+	2.85052i	0.0847605	+	0.146810i
$378$		0			0
$379$	10.7085			0.550059			0.275029	−	0.961436i	$-0.411312\pi$
$379$	10.7085			0.550059			0.275029	+	0.961436i	$0.411312\pi$
$380$	2.76013	+	6.62141i	0.141592	+	0.339671i
$381$		0			0
$382$	−3.29150	−	5.70105i	−0.168408	−	0.291691i
$383$	2.76013	+	4.78068i	0.141036	+	0.244282i	0.927887	−	0.372861i	$-0.121623\pi$
$383$	2.76013	+	4.78068i	0.141036	+	0.244282i	−0.786851	+	0.617143i	$0.788290\pi$
$384$		0			0
$385$	−13.9373	−	24.1400i	−0.710308	−	1.23029i
$386$	7.29150	−	12.6293i	0.371128	−	0.642812i
$387$		0			0
$388$	−3.70850			−0.188270
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	−0.672874	−	0.739758i	$-0.734940\pi$
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	0.977086	+	0.212847i	$0.0682735\pi$
$390$		0			0
$391$		0			0
$392$	−6.29150			−0.317769
$393$		0			0
$394$	3.82288	+	6.62141i	0.192594	+	0.333582i
$395$	3.29150	−	5.70105i	0.165613	−	0.286851i
$396$		0			0
$397$	−10.5314	−	18.2409i	−0.528554	−	0.915483i	−0.999446	−	0.0332919i	$-0.989401\pi$
$397$	−10.5314	−	18.2409i	−0.528554	−	0.915483i	0.470891	−	0.882191i	$-0.343932\pi$
$398$	19.8745			0.996219
$399$		0			0
$400$	−2.29150			−0.114575
$401$	13.7915	+	23.8876i	0.688715	+	1.19289i	0.972254	+	0.233928i	$0.0751581\pi$
$401$	13.7915	+	23.8876i	0.688715	+	1.19289i	−0.283539	+	0.958961i	$0.591509\pi$
$402$		0			0
$403$	5.64575	−	9.77873i	0.281235	−	0.487113i
$404$	−6.82288	−	11.8176i	−0.339451	−	0.587946i
$405$		0			0
$406$	6.00000			0.297775
$407$	1.64575			0.0815769
$408$		0			0
$409$	3.79150	−	6.56708i	0.187478	−	0.324721i	−0.756931	−	0.653495i	$-0.773302\pi$
$409$	3.79150	−	6.56708i	0.187478	−	0.324721i	0.944409	+	0.328774i	$0.106635\pi$
$410$	−0.479741			−0.0236927
$411$		0			0
$412$	6.64575	−	11.5108i	0.327413	−	0.567095i
$413$	−14.4686	−	25.0604i	−0.711955	−	1.23314i
$414$		0			0
$415$	6.53137	+	11.3127i	0.320612	+	0.555317i
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$		0			0
$418$	−12.2915	+	16.0934i	−0.601197	+	0.787152i
$419$	31.7490			1.55104			0.775520	−	0.631322i	$-0.217488\pi$
$419$	31.7490			1.55104			0.775520	+	0.631322i	$0.217488\pi$
$420$		0			0
$421$	12.4059	+	21.4876i	0.604626	+	1.04724i	0.992111	+	0.125366i	$0.0400106\pi$
$421$	12.4059	+	21.4876i	0.604626	+	1.04724i	−0.387485	+	0.921876i	$0.626656\pi$
$422$	−6.64575	+	11.5108i	−0.323510	+	0.560336i
$423$		0			0
$424$	6.29150	−	10.8972i	0.305542	−	0.529215i
$425$		0			0
$426$		0			0
$427$	−1.70850	+	2.95920i	−0.0826800	+	0.143206i
$428$	7.64575	−	13.2428i	0.369571	−	0.640116i
$429$		0			0
$430$	−18.5830			−0.896152
$431$	13.9373	−	24.1400i	0.671334	−	1.16278i	−0.306192	−	0.951970i	$-0.599055\pi$
$431$	13.9373	−	24.1400i	0.671334	−	1.16278i	0.977526	−	0.210815i	$-0.0676117\pi$
$432$		0			0
$433$	−8.93725	+	15.4798i	−0.429497	+	0.743911i	−0.996829	−	0.0795788i	$-0.974642\pi$
$433$	−8.93725	+	15.4798i	−0.429497	+	0.743911i	0.567332	+	0.823489i	$0.307976\pi$
$434$	−10.2915	−	17.8254i	−0.494008	−	0.855647i
$435$		0			0
$436$	14.5830			0.698399
$437$	−7.11438	−	0.920365i	−0.340327	−	0.0440270i
$438$		0			0
$439$	−5.40588	−	9.36326i	−0.258009	−	0.446884i	0.707700	−	0.706513i	$-0.249733\pi$
$439$	−5.40588	−	9.36326i	−0.258009	−	0.446884i	−0.965708	+	0.259629i	$0.916400\pi$
$440$	3.82288	+	6.62141i	0.182248	+	0.315664i
$441$		0			0
$442$		0			0
$443$	5.32288	−	9.21949i	0.252897	−	0.438031i	−0.711425	−	0.702762i	$-0.751950\pi$
$443$	5.32288	−	9.21949i	0.252897	−	0.438031i	0.964322	+	0.264731i	$0.0852831\pi$
$444$		0			0
$445$		0			0
$446$	−9.40588	+	16.2915i	−0.445381	+	0.771423i
$447$		0			0
$448$	3.64575			0.172246
$449$	24.2915			1.14639			0.573193	−	0.819420i	$-0.305704\pi$
$449$	24.2915			1.14639			0.573193	+	0.819420i	$0.305704\pi$
$450$		0			0
$451$	−0.677124	−	1.17281i	−0.0318845	−	0.0552256i
$452$	−7.79150	+	13.4953i	−0.366481	+	0.634765i
$453$		0			0
$454$	3.67712	+	6.36897i	0.172576	+	0.298910i
$455$	12.0000			0.562569
$456$		0			0
$457$	32.8745			1.53780			0.768902	−	0.639366i	$-0.220803\pi$
$457$	32.8745			1.53780			0.768902	+	0.639366i	$0.220803\pi$
$458$	10.0000	+	17.3205i	0.467269	+	0.809334i
$459$		0			0
$460$	−1.35425	+	2.34563i	−0.0631422	+	0.109365i
$461$	9.58301	+	16.5983i	0.446325	+	0.773058i	0.998143	−	0.0609066i	$-0.0193992\pi$
$461$	9.58301	+	16.5983i	0.446325	+	0.773058i	−0.551818	+	0.833964i	$0.686066\pi$
$462$		0			0
$463$	−38.4575			−1.78727			−0.893636	−	0.448792i	$-0.851854\pi$
$463$	−38.4575			−1.78727			−0.893636	+	0.448792i	$0.851854\pi$
$464$	−1.64575			−0.0764021
$465$		0			0
$466$	−9.43725	+	16.3458i	−0.437172	+	0.757205i
$467$	19.3542			0.895608			0.447804	−	0.894132i	$-0.352206\pi$
$467$	19.3542			0.895608			0.447804	+	0.894132i	$0.352206\pi$
$468$		0			0
$469$	−1.17712	+	2.03884i	−0.0543546	+	0.0941448i
$470$	−3.58301	−	6.20595i	−0.165272	−	0.286259i
$471$		0			0
$472$	3.96863	+	6.87386i	0.182671	+	0.316395i
$473$	−26.2288	−	45.4295i	−1.20600	−	2.08885i
$474$		0			0
$475$	9.90588	+	1.28149i	0.454513	+	0.0587989i
$476$		0			0
$477$		0			0
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	3.29150	−	5.70105i	0.150393	−	0.260488i	−0.780979	−	0.624557i	$-0.785280\pi$
$479$	3.29150	−	5.70105i	0.150393	−	0.260488i	0.931372	+	0.364069i	$0.118613\pi$
$480$		0			0
$481$	−0.354249	+	0.613577i	−0.0161523	+	0.0279767i
$482$	7.58301			0.345396
$483$		0			0
$484$	−5.29150	+	9.16515i	−0.240523	+	0.416598i
$485$	3.05163	−	5.28558i	0.138567	−	0.240006i
$486$		0			0
$487$	4.22876			0.191623			0.0958116	−	0.995399i	$-0.469455\pi$
$487$	4.22876			0.191623			0.0958116	+	0.995399i	$0.469455\pi$
$488$	0.468627	−	0.811686i	0.0212137	−	0.0367433i
$489$		0			0
$490$	5.17712	−	8.96704i	0.233879	−	0.405090i
$491$	19.6458	+	34.0274i	0.886600	+	1.53564i	0.843868	+	0.536550i	$0.180273\pi$
$491$	19.6458	+	34.0274i	0.886600	+	1.53564i	0.0427320	+	0.999087i	$0.486394\pi$
$492$		0			0
$493$		0			0
$494$	−3.35425	−	8.04668i	−0.150915	−	0.362037i
$495$		0			0
$496$	2.82288	+	4.88936i	0.126751	+	0.219539i
$497$	−4.93725	−	8.55157i	−0.221466	−	0.383591i
$498$		0			0
$499$	2.38562	+	4.13202i	0.106795	+	0.184975i	0.914470	−	0.404653i	$-0.132608\pi$
$499$	2.38562	+	4.13202i	0.106795	+	0.184975i	−0.807675	+	0.589628i	$0.799274\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$		0			0
$502$	29.2288			1.30454
$503$	−20.4686	+	35.4527i	−0.912651	+	1.58076i	−0.102346	+	0.994749i	$0.532635\pi$
$503$	−20.4686	+	35.4527i	−0.912651	+	1.58076i	−0.810305	+	0.586009i	$0.800698\pi$
$504$		0			0
$505$	22.4575			0.999346
$506$	−7.64575			−0.339895
$507$		0			0
$508$	6.64575	+	11.5108i	0.294858	+	0.510708i
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	0.263560	+	0.964643i	$0.415103\pi$
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	−0.967185	+	0.254072i	$0.918230\pi$
$510$		0			0
$511$	−3.11438	−	5.39426i	−0.137772	−	0.238628i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	12.2915			0.542155
$515$	10.9373	+	18.9439i	0.481953	+	0.834767i
$516$		0			0
$517$	10.1144	−	17.5186i	0.444830	−	0.770468i
$518$	0.645751	+	1.11847i	0.0283727	+	0.0491429i
$519$		0			0
$520$	−3.29150			−0.144342
$521$	11.7085			0.512959			0.256479	−	0.966550i	$-0.417437\pi$
$521$	11.7085			0.512959			0.256479	+	0.966550i	$0.417437\pi$
$522$		0			0
$523$	0.937254	−	1.62337i	0.0409833	−	0.0709851i	−0.844806	−	0.535072i	$-0.820284\pi$
$523$	0.937254	−	1.62337i	0.0409833	−	0.0709851i	0.885789	+	0.464087i	$0.153618\pi$
$524$	−1.93725			−0.0846293
$525$		0			0
$526$	5.46863	−	9.47194i	0.238443	−	0.412996i
$527$		0			0
$528$		0			0
$529$	10.1458	+	17.5730i	0.441120	+	0.764042i
$530$	10.3542	+	17.9341i	0.449760	+	0.779007i
$531$		0			0
$532$	−15.7601	−	2.03884i	−0.683288	−	0.0883949i
$533$	0.583005			0.0252528
$534$		0			0
$535$	12.5830	+	21.7944i	0.544011	+	0.942254i
$536$	0.322876	−	0.559237i	0.0139461	−	0.0241554i
$537$		0			0
$538$		0			0
$539$	29.2288			1.25897
$540$		0			0
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$	6.17712	−	10.6991i	0.265330	−	0.459565i
$543$		0			0
$544$		0			0
$545$	−12.0000	+	20.7846i	−0.514024	+	0.890315i
$546$		0			0
$547$	−5.64575	+	9.77873i	−0.241395	+	0.418108i	−0.961112	−	0.276159i	$-0.910938\pi$
$547$	−5.64575	+	9.77873i	−0.241395	+	0.418108i	0.719717	+	0.694268i	$0.244272\pi$
$548$	7.79150	+	13.4953i	0.332836	+	0.576490i
$549$		0			0
$550$	10.6458			0.453936
$551$	7.11438	+	0.920365i	0.303083	+	0.0392089i
$552$		0			0
$553$	7.29150	+	12.6293i	0.310066	+	0.537050i
$554$	−13.7601	−	23.8332i	−0.584612	−	1.01258i
$555$		0			0
$556$	−9.32288	−	16.1477i	−0.395378	−	0.684815i
$557$	−2.70850	+	4.69126i	−0.114763	+	0.198775i	−0.917685	−	0.397309i	$-0.869944\pi$
$557$	−2.70850	+	4.69126i	−0.114763	+	0.198775i	0.802922	+	0.596084i	$0.203277\pi$
$558$		0			0
$559$	22.5830			0.955159
$560$	−3.00000	+	5.19615i	−0.126773	+	0.219578i
$561$		0			0
$562$	25.4575			1.07386
$563$	−10.0627			−0.424094			−0.212047	−	0.977259i	$-0.568013\pi$
$563$	−10.0627			−0.424094			−0.212047	+	0.977259i	$0.568013\pi$
$564$		0			0
$565$	−12.8229	−	22.2099i	−0.539462	−	0.934376i
$566$	15.3229	−	26.5400i	0.644069	−	1.11556i
$567$		0			0
$568$	1.35425	+	2.34563i	0.0568230	+	0.0984203i
$569$	−6.58301			−0.275974			−0.137987	−	0.990434i	$-0.544063\pi$
$569$	−6.58301			−0.275974			−0.137987	+	0.990434i	$0.544063\pi$
$570$		0			0
$571$	7.81176			0.326912			0.163456	−	0.986551i	$-0.447736\pi$
$571$	7.81176			0.326912			0.163456	+	0.986551i	$0.447736\pi$
$572$	−4.64575	−	8.04668i	−0.194249	−	0.336448i
$573$		0			0
$574$	0.531373	−	0.920365i	0.0221791	−	0.0384153i
$575$	1.88562	+	3.26599i	0.0786359	+	0.136201i
$576$		0			0
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$	17.0000			0.707107
$579$		0			0
$580$	1.35425	−	2.34563i	0.0562321	−	0.0973969i
$581$	−28.9373			−1.20052
$582$		0			0
$583$	−29.2288	+	50.6257i	−1.21053	+	2.09670i
$584$	0.854249	+	1.47960i	0.0353491	+	0.0612264i
$585$		0			0
$586$	−14.4686	−	25.0604i	−0.597693	−	1.03524i
$587$	−7.06275	−	12.2330i	−0.291511	−	0.504911i	0.682656	−	0.730739i	$-0.260825\pi$
$587$	−7.06275	−	12.2330i	−0.291511	−	0.504911i	−0.974167	+	0.225828i	$0.927491\pi$
$588$		0			0
$589$	−9.46863	−	22.7148i	−0.390148	−	0.935946i
$590$	−13.0627			−0.537785
$591$		0			0
$592$	−0.177124	−	0.306788i	−0.00727977	−	0.0126089i
$593$	14.8542	−	25.7283i	0.609991	−	1.05654i	−0.381250	−	0.924472i	$-0.624506\pi$
$593$	14.8542	−	25.7283i	0.609991	−	1.05654i	0.991241	−	0.132063i	$-0.0421602\pi$
$594$		0			0
$595$		0			0
$596$	−10.9373			−0.448007
$597$		0			0
$598$	1.64575	−	2.85052i	0.0672998	−	0.116567i
$599$	−8.46863	+	14.6681i	−0.346019	+	0.599322i	−0.985538	−	0.169453i	$-0.945800\pi$
$599$	−8.46863	+	14.6681i	−0.346019	+	0.599322i	0.639520	+	0.768775i	$0.279133\pi$
$600$		0			0
$601$	10.4170			0.424918			0.212459	−	0.977170i	$-0.431853\pi$
$601$	10.4170			0.424918			0.212459	+	0.977170i	$0.431853\pi$
$602$	20.5830	−	35.6508i	0.838901	−	1.45302i
$603$		0			0
$604$	−6.46863	+	11.2040i	−0.263205	+	0.455884i
$605$	−8.70850	−	15.0836i	−0.354051	−	0.613234i
$606$		0			0
$607$	6.93725			0.281574			0.140787	−	0.990040i	$-0.455037\pi$
$607$	6.93725			0.281574			0.140787	+	0.990040i	$0.455037\pi$
$608$	4.32288	+	0.559237i	0.175316	+	0.0226801i
$609$		0			0
$610$	0.771243	+	1.33583i	0.0312267	+	0.0540863i
$611$	4.35425	+	7.54178i	0.176154	+	0.305108i
$612$		0			0
$613$	−3.70850	−	6.42331i	−0.149785	−	0.259435i	0.781363	−	0.624077i	$-0.214525\pi$
$613$	−3.70850	−	6.42331i	−0.149785	−	0.259435i	−0.931148	+	0.364642i	$0.881191\pi$
$614$	0.322876	−	0.559237i	0.0130302	−	0.0225690i
$615$		0			0
$616$	−16.9373			−0.682421
$617$	−15.4373	+	26.7381i	−0.621480	+	1.07644i	0.367730	+	0.929933i	$0.380135\pi$
$617$	−15.4373	+	26.7381i	−0.621480	+	1.07644i	−0.989210	+	0.146503i	$0.953198\pi$
$618$		0			0
$619$	−8.45751			−0.339936			−0.169968	−	0.985450i	$-0.554366\pi$
$619$	−8.45751			−0.339936			−0.169968	+	0.985450i	$0.554366\pi$
$620$	−9.29150			−0.373156
$621$		0			0
$622$	−6.82288	−	11.8176i	−0.273572	−	0.473841i
$623$		0			0
$624$		0			0
$625$	4.14575	+	7.18065i	0.165830	+	0.287226i
$626$	−8.87451			−0.354697
$627$		0			0
$628$	−10.5830			−0.422308
$629$		0			0
$630$		0			0
$631$	12.4059	−	21.4876i	0.493870	−	0.855408i	−0.506105	−	0.862472i	$-0.668915\pi$
$631$	12.4059	−	21.4876i	0.493870	−	0.855408i	0.999975	+	0.00706354i	$0.00224841\pi$
$632$	−2.00000	−	3.46410i	−0.0795557	−	0.137795i
$633$		0			0
$634$	−6.00000			−0.238290
$635$	−21.8745			−0.868063
$636$		0			0
$637$	−6.29150	+	10.8972i	−0.249278	+	0.431763i
$638$	7.64575			0.302698
$639$		0			0
$640$	0.822876	−	1.42526i	0.0325270	−	0.0563384i
$641$	6.43725	+	11.1497i	0.254256	+	0.440385i	0.964693	−	0.263376i	$-0.0848360\pi$
$641$	6.43725	+	11.1497i	0.254256	+	0.440385i	−0.710437	+	0.703761i	$0.751503\pi$
$642$		0			0
$643$	3.26013	+	5.64671i	0.128567	+	0.222685i	0.923122	−	0.384508i	$-0.125629\pi$
$643$	3.26013	+	5.64671i	0.128567	+	0.222685i	−0.794555	+	0.607193i	$0.792296\pi$
$644$	−3.00000	−	5.19615i	−0.118217	−	0.204757i
$645$		0			0
$646$		0			0
$647$	22.4575			0.882896			0.441448	−	0.897287i	$-0.354465\pi$
$647$	22.4575			0.882896			0.441448	+	0.897287i	$0.354465\pi$
$648$		0			0
$649$	−18.4373	−	31.9343i	−0.723726	−	1.25353i
$650$	−2.29150	+	3.96900i	−0.0898801	+	0.155677i
$651$		0			0
$652$	−1.96863	+	3.40976i	−0.0770974	+	0.133537i
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$		0			0
$655$	1.59412	−	2.76110i	0.0622874	−	0.107885i
$656$	−0.145751	+	0.252449i	−0.00569063	+	0.00985646i
$657$		0			0
$658$	15.8745			0.618853
$659$	−9.29150	+	16.0934i	−0.361946	+	0.626908i	−0.988281	−	0.152646i	$-0.951221\pi$
$659$	−9.29150	+	16.0934i	−0.361946	+	0.626908i	0.626335	+	0.779554i	$0.284554\pi$
$660$		0			0
$661$	−8.11438	+	14.0545i	−0.315613	+	0.546657i	−0.979568	−	0.201115i	$-0.935543\pi$
$661$	−8.11438	+	14.0545i	−0.315613	+	0.546657i	0.663955	+	0.747773i	$0.268877\pi$
$662$	9.90588	+	17.1575i	0.385003	+	0.666845i
$663$		0			0
$664$	7.93725			0.308025
$665$	15.8745	−	20.7846i	0.615587	−	0.805993i
$666$		0			0
$667$	1.35425	+	2.34563i	0.0524367	+	0.0908231i
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$		0			0
$670$	0.531373	+	0.920365i	0.0205287	+	0.0355568i
$671$	−2.17712	+	3.77089i	−0.0840470	+	0.145574i
$672$		0			0
$673$	−13.8745			−0.534823			−0.267411	−	0.963582i	$-0.586168\pi$
$673$	−13.8745			−0.534823			−0.267411	+	0.963582i	$0.586168\pi$
$674$	−4.85425	+	8.40781i	−0.186979	+	0.323857i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	11.4170			0.438791			0.219395	−	0.975636i	$-0.429592\pi$
$677$	11.4170			0.438791			0.219395	+	0.975636i	$0.429592\pi$
$678$		0			0
$679$	6.76013	+	11.7089i	0.259430	+	0.449346i
$680$		0			0
$681$		0			0
$682$	−13.1144	−	22.7148i	−0.502175	−	0.869793i
$683$	5.41699			0.207276			0.103638	−	0.994615i	$-0.466952\pi$
$683$	5.41699			0.207276			0.103638	+	0.994615i	$0.466952\pi$
$684$		0			0
$685$	−25.6458			−0.979874
$686$	−1.29150	−	2.23695i	−0.0493098	−	0.0854071i
$687$		0			0
$688$	−5.64575	+	9.77873i	−0.215242	+	0.372811i
$689$	−12.5830	−	21.7944i	−0.479374	−	0.830301i
$690$		0			0
$691$	2.58301			0.0982622			0.0491311	−	0.998792i	$-0.484355\pi$
$691$	2.58301			0.0982622			0.0491311	+	0.998792i	$0.484355\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	11.6144	−	20.1167i	0.440876	−	0.763619i
$695$	30.6863			1.16400
$696$		0			0
$697$		0			0
$698$	10.5830	+	18.3303i	0.400573	+	0.693812i
$699$		0			0
$700$	4.17712	+	7.23499i	0.157880	+	0.273457i
$701$	5.17712	+	8.96704i	0.195537	+	0.338681i	0.947077	−	0.321008i	$-0.104022\pi$
$701$	5.17712	+	8.96704i	0.195537	+	0.338681i	−0.751539	+	0.659688i	$0.770688\pi$
$702$		0			0
$703$	0.594119	+	1.42526i	0.0224076	+	0.0537548i
$704$	4.64575			0.175093
$705$		0			0
$706$	−6.43725	−	11.1497i	−0.242269	−	0.419623i
$707$	−24.8745	+	43.0839i	−0.935502	+	1.62034i
$708$		0			0
$709$	−1.82288	+	3.15731i	−0.0684595	+	0.118575i	−0.898223	−	0.439539i	$-0.855142\pi$
$709$	−1.82288	+	3.15731i	−0.0684595	+	0.118575i	0.829764	+	0.558115i	$0.188475\pi$
$710$	−4.45751			−0.167287
$711$		0			0
$712$		0			0
$713$	4.64575	−	8.04668i	0.173985	−	0.301350i
$714$		0			0
$715$	15.2915			0.571870
$716$	2.03137	−	3.51844i	0.0759160	−	0.131490i
$717$		0			0
$718$	2.46863	−	4.27579i	0.0921283	−	0.159571i
$719$	1.35425	+	2.34563i	0.0505050	+	0.0874771i	0.890173	−	0.455623i	$-0.150584\pi$
$719$	1.35425	+	2.34563i	0.0505050	+	0.0874771i	−0.839668	+	0.543100i	$0.817250\pi$
$720$		0			0
$721$	−48.4575			−1.80465
$722$	−18.3745	−	4.83502i	−0.683828	−	0.179941i
$723$		0			0
$724$	−11.1144	−	19.2507i	−0.413063	−	0.715445i
$725$	−1.88562	−	3.26599i	−0.0700302	−	0.121296i
$726$		0			0
$727$	−0.708497	−	1.22715i	−0.0262767	−	0.0455126i	0.852588	−	0.522584i	$-0.175032\pi$
$727$	−0.708497	−	1.22715i	−0.0262767	−	0.0455126i	−0.878865	+	0.477071i	$0.841698\pi$
$728$	3.64575	−	6.31463i	0.135121	−	0.234036i
$729$		0			0
$730$	−2.81176			−0.104068
$731$		0			0
$732$		0			0
$733$	−16.1033			−0.594788			−0.297394	−	0.954755i	$-0.596117\pi$
$733$	−16.1033			−0.594788			−0.297394	+	0.954755i	$0.596117\pi$
$734$	−16.2288			−0.599014
$735$		0			0
$736$	0.822876	+	1.42526i	0.0303316	+	0.0525359i
$737$	−1.50000	+	2.59808i	−0.0552532	+	0.0957014i
$738$		0			0
$739$	16.9059	+	29.2818i	0.621893	+	1.07715i	0.989133	+	0.147024i	$0.0469694\pi$
$739$	16.9059	+	29.2818i	0.621893	+	1.07715i	−0.367240	+	0.930126i	$0.619697\pi$
$740$	0.583005			0.0214317
$741$		0			0
$742$	−45.8745			−1.68411
$743$	−23.7601	−	41.1538i	−0.871675	−	1.50978i	−0.860263	−	0.509850i	$-0.829701\pi$
$743$	−23.7601	−	41.1538i	−0.871675	−	1.50978i	−0.0114112	−	0.999935i	$-0.503632\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	−2.00000	−	3.46410i	−0.0732252	−	0.126830i
$747$		0			0
$748$		0			0
$749$	−55.7490			−2.03702
$750$		0			0
$751$	3.93725	−	6.81952i	0.143672	−	0.248848i	−0.785204	−	0.619237i	$-0.787442\pi$
$751$	3.93725	−	6.81952i	0.143672	−	0.248848i	0.928877	+	0.370389i	$0.120775\pi$
$752$	−4.35425			−0.158783
$753$		0			0
$754$	−1.64575	+	2.85052i	−0.0599347	+	0.103810i
$755$	−10.6458	−	18.4390i	−0.387439	−	0.671063i
$756$		0			0
$757$	2.29150	+	3.96900i	0.0832861	+	0.144256i	0.904660	−	0.426135i	$-0.140125\pi$
$757$	2.29150	+	3.96900i	0.0832861	+	0.144256i	−0.821374	+	0.570391i	$0.806792\pi$
$758$	5.35425	+	9.27383i	0.194475	+	0.336841i
$759$		0			0
$760$	−4.35425	+	5.70105i	−0.157945	+	0.206799i
$761$	−42.8745			−1.55420			−0.777100	−	0.629377i	$-0.783310\pi$
$761$	−42.8745			−1.55420			−0.777100	+	0.629377i	$0.783310\pi$
$762$		0			0
$763$	−26.5830	−	46.0431i	−0.962369	−	1.66687i
$764$	3.29150	−	5.70105i	0.119082	−	0.206257i
$765$		0			0
$766$	−2.76013	+	4.78068i	−0.0997275	+	0.172733i
$767$	15.8745			0.573195
$768$		0			0
$769$	−17.6458	+	30.5633i	−0.636322	+	1.10214i	0.349911	+	0.936783i	$0.386212\pi$
$769$	−17.6458	+	30.5633i	−0.636322	+	1.10214i	−0.986233	+	0.165359i	$0.947122\pi$
$770$	13.9373	−	24.1400i	0.502264	−	0.869946i
$771$		0			0
$772$	14.5830			0.524854
$773$	−2.46863	+	4.27579i	−0.0887903	+	0.153789i	−0.907000	−	0.421130i	$-0.861633\pi$
$773$	−2.46863	+	4.27579i	−0.0887903	+	0.153789i	0.818210	+	0.574920i	$0.194967\pi$
$774$		0			0
$775$	−6.46863	+	11.2040i	−0.232360	+	0.402459i
$776$	−1.85425	−	3.21165i	−0.0665636	−	0.115292i
$777$		0			0
$778$	12.0000			0.430221
$779$	0.771243	−	1.00979i	0.0276327	−	0.0361796i
$780$		0			0
$781$	−6.29150	−	10.8972i	−0.225128	−	0.389933i
$782$		0			0
$783$		0			0
$784$	−3.14575	−	5.44860i	−0.112348	−	0.194593i
$785$	8.70850	−	15.0836i	0.310820	−	0.538355i
$786$		0			0
$787$	−42.5203			−1.51568			−0.757842	−	0.652438i	$-0.773746\pi$
$787$	−42.5203			−1.51568			−0.757842	+	0.652438i	$0.773746\pi$
$788$	−3.82288	+	6.62141i	−0.136184	+	0.235878i
$789$		0			0
$790$	6.58301			0.234213
$791$	56.8118			2.01999
$792$		0			0
$793$	−0.937254	−	1.62337i	−0.0332829	−	0.0576476i
$794$	10.5314	−	18.2409i	0.373744	−	0.647344i
$795$		0			0
$796$	9.93725	+	17.2118i	0.352217	+	0.610057i
$797$	44.8118			1.58731			0.793657	−	0.608365i	$-0.208174\pi$
$797$	44.8118			1.58731			0.793657	+	0.608365i	$0.208174\pi$
$798$		0			0
$799$		0			0
$800$	−1.14575	−	1.98450i	−0.0405084	−	0.0701627i
$801$		0			0
$802$	−13.7915	+	23.8876i	−0.486995	+	0.843500i
$803$	−3.96863	−	6.87386i	−0.140050	−	0.242573i
$804$		0			0
$805$	9.87451			0.348031
$806$	11.2915			0.397726
$807$		0			0
$808$	6.82288	−	11.8176i	0.240028	−	0.415741i
$809$	9.00000			0.316423			0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000			0.316423			0.158212	+	0.987405i	$0.449427\pi$
$810$		0			0
$811$	15.6458	−	27.0992i	0.549397	−	0.951583i	−0.448919	−	0.893572i	$-0.648191\pi$
$811$	15.6458	−	27.0992i	0.549397	−	0.951583i	0.998316	−	0.0580106i	$-0.0184757\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$		0			0
$814$	0.822876	+	1.42526i	0.0288418	+	0.0499554i
$815$	−3.23987	−	5.61162i	−0.113488	−	0.196566i
$816$		0			0
$817$	29.8745	−	39.1149i	1.04518	−	1.36846i
$818$	7.58301			0.265134
$819$		0			0
$820$	−0.239870	−	0.415468i	−0.00837664	−	0.0145088i
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$		0			0
$823$	15.9373	−	27.6041i	0.555538	−	0.962220i	−0.442324	−	0.896855i	$-0.645846\pi$
$823$	15.9373	−	27.6041i	0.555538	−	0.962220i	0.997861	−	0.0653641i	$-0.0208209\pi$
$824$	13.2915			0.463031
$825$		0			0
$826$	14.4686	−	25.0604i	0.503428	−	0.871963i
$827$	−26.3229	+	45.5926i	−0.915336	+	1.58541i	−0.108928	+	0.994050i	$0.534742\pi$
$827$	−26.3229	+	45.5926i	−0.915336	+	1.58541i	−0.806408	+	0.591359i	$0.798592\pi$
$828$		0			0
$829$	−17.1660			−0.596200			−0.298100	−	0.954535i	$-0.596353\pi$
$829$	−17.1660			−0.596200			−0.298100	+	0.954535i	$0.596353\pi$
$830$	−6.53137	+	11.3127i	−0.226707	+	0.392669i
$831$		0			0
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$		0			0
$834$		0			0
$835$	19.7490			0.683443
$836$	−20.0830	−	2.59808i	−0.694585	−	0.0898563i
$837$		0			0
$838$	15.8745	+	27.4955i	0.548376	+	0.949815i
$839$	−20.7601	−	35.9576i	−0.716719	−	1.24139i	−0.962293	−	0.272016i	$-0.912310\pi$
$839$	−20.7601	−	35.9576i	−0.716719	−	1.24139i	0.245573	−	0.969378i	$-0.421024\pi$
$840$		0			0
$841$	13.1458	+	22.7691i	0.453302	+	0.785142i
$842$	−12.4059	+	21.4876i	−0.427535	+	0.740512i
$843$		0			0
$844$	−13.2915			−0.457512
$845$	7.40588	−	12.8274i	0.254770	−	0.441275i
$846$		0			0
$847$	38.5830			1.32573
$848$	12.5830			0.432102
$849$		0			0
$850$		0			0
$851$	−0.291503	+	0.504897i	−0.00999258	+	0.0173077i
$852$		0			0
$853$	−4.29150	−	7.43310i	−0.146938	−	0.254505i	0.783156	−	0.621825i	$-0.213609\pi$
$853$	−4.29150	−	7.43310i	−0.146938	−	0.254505i	−0.930094	+	0.367321i	$0.880275\pi$
$854$	−3.41699			−0.116927
$855$		0			0
$856$	15.2915			0.522653
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	0.987739	−	0.156112i	$-0.0498959\pi$
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	−0.629066	+	0.777352i	$0.716563\pi$
$858$		0			0
$859$	−6.61438	+	11.4564i	−0.225680	+	0.390889i	−0.956523	−	0.291656i	$-0.905794\pi$
$859$	−6.61438	+	11.4564i	−0.225680	+	0.390889i	0.730843	+	0.682545i	$0.239127\pi$
$860$	−9.29150	−	16.0934i	−0.316838	−	0.548779i
$861$		0			0
$862$	27.8745			0.949410
$863$	31.0627			1.05739			0.528694	−	0.848812i	$-0.322682\pi$
$863$	31.0627			1.05739			0.528694	+	0.848812i	$0.322682\pi$
$864$		0			0
$865$	−4.93725	+	8.55157i	−0.167872	+	0.290762i
$866$	−17.8745			−0.607401
$867$		0			0
$868$	10.2915	−	17.8254i	0.349316	−	0.605034i
$869$	9.29150	+	16.0934i	0.315193	+	0.545930i
$870$		0			0
$871$	−0.645751	−	1.11847i	−0.0218804	−	0.0378980i
$872$	7.29150	+	12.6293i	0.246921	+	0.427680i
$873$		0			0
$874$	−2.76013	−	6.62141i	−0.0933628	−	0.223973i
$875$	−43.7490			−1.47899
$876$		0			0
$877$	20.8229	+	36.0663i	0.703139	+	1.21787i	0.967359	+	0.253409i	$0.0815520\pi$
$877$	20.8229	+	36.0663i	0.703139	+	1.21787i	−0.264221	+	0.964462i	$0.585115\pi$
$878$	5.40588	−	9.36326i	0.182440	−	0.315995i
$879$		0			0
$880$	−3.82288	+	6.62141i	−0.128869	+	0.223208i
$881$	36.8745			1.24233			0.621167	−	0.783678i	$-0.286659\pi$
$881$	36.8745			1.24233			0.621167	+	0.783678i	$0.286659\pi$
$882$		0			0
$883$	14.1974	−	24.5906i	0.477780	−	0.827539i	−0.521896	−	0.853009i	$-0.674775\pi$
$883$	14.1974	−	24.5906i	0.477780	−	0.827539i	0.999676	+	0.0254701i	$0.00810828\pi$
$884$		0			0
$885$		0			0
$886$	10.6458			0.357651
$887$	−8.70850	+	15.0836i	−0.292403	+	0.506456i	−0.974377	−	0.224919i	$-0.927788\pi$
$887$	−8.70850	+	15.0836i	−0.292403	+	0.506456i	0.681975	+	0.731376i	$0.261121\pi$
$888$		0			0
$889$	24.2288	−	41.9654i	0.812606	−	1.40748i
$890$		0			0
$891$		0			0
$892$	−18.8118			−0.629864
$893$	18.8229	+	2.43506i	0.629884	+	0.0814861i
$894$		0			0
$895$	3.34313	+	5.79048i	0.111749	+	0.193554i
$896$	1.82288	+	3.15731i	0.0608980	+	0.105478i
$897$		0			0
$898$	12.1458	+	21.0371i	0.405309	+	0.702016i
$899$	−4.64575	+	8.04668i	−0.154944	+	0.268372i
$900$		0			0
$901$		0			0
$902$	0.677124	−	1.17281i	0.0225458	−	0.0390504i
$903$		0			0
$904$	−15.5830			−0.518283
$905$	36.5830			1.21606
$906$		0			0
$907$	−19.9686	−	34.5867i	−0.663047	−	1.14843i	−0.979811	−	0.199927i	$-0.935929\pi$
$907$	−19.9686	−	34.5867i	−0.663047	−	1.14843i	0.316763	−	0.948505i	$-0.397404\pi$
$908$	−3.67712	+	6.36897i	−0.122030	+	0.211362i
$909$		0			0
$910$	6.00000	+	10.3923i	0.198898	+	0.344502i
$911$	−16.9373			−0.561156			−0.280578	−	0.959831i	$-0.590526\pi$
$911$	−16.9373			−0.561156			−0.280578	+	0.959831i	$0.590526\pi$
$912$		0			0
$913$	−36.8745			−1.22037
$914$	16.4373	+	28.4702i	0.543696	+	0.941709i
$915$		0			0
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$	3.53137	+	6.11652i	0.116616	+	0.201985i
$918$		0			0
$919$	−19.8745			−0.655600			−0.327800	−	0.944747i	$-0.606307\pi$
$919$	−19.8745			−0.655600			−0.327800	+	0.944747i	$0.606307\pi$
$920$	−2.70850			−0.0892965
$921$		0			0
$922$	−9.58301	+	16.5983i	−0.315599	+	0.546634i
$923$	5.41699			0.178303
$924$		0			0
$925$	0.405881	−	0.703006i	0.0133453	−	0.0231147i
$926$	−19.2288	−	33.3052i	−0.631896	−	1.09448i
$927$		0			0
$928$	−0.822876	−	1.42526i	−0.0270122	−	0.0467865i
$929$	−4.79150	−	8.29913i	−0.157204	−	0.272285i	0.776655	−	0.629926i	$-0.216915\pi$
$929$	−4.79150	−	8.29913i	−0.157204	−	0.272285i	−0.933859	+	0.357640i	$0.883581\pi$
$930$		0			0
$931$	10.5516	+	25.3128i	0.345816	+	0.829595i
$932$	−18.8745			−0.618255
$933$		0			0
$934$	9.67712	+	16.7613i	0.316645	+	0.548446i
$935$		0			0
$936$		0			0
$937$	−3.56275	+	6.17086i	−0.116390	+	0.201593i	−0.918334	−	0.395805i	$-0.870466\pi$
$937$	−3.56275	+	6.17086i	−0.116390	+	0.201593i	0.801945	+	0.597398i	$0.203799\pi$
$938$	−2.35425			−0.0768689
$939$		0			0
$940$	3.58301	−	6.20595i	0.116865	−	0.202416i
$941$	8.41699	−	14.5787i	0.274386	−	0.475251i	−0.695594	−	0.718435i	$-0.744859\pi$
$941$	8.41699	−	14.5787i	0.274386	−	0.475251i	0.969980	+	0.243184i	$0.0781920\pi$
$942$		0			0
$943$	0.479741			0.0156225
$944$	−3.96863	+	6.87386i	−0.129168	+	0.223725i
$945$		0			0
$946$	26.2288	−	45.4295i	0.852770	−	1.47704i
$947$	−3.87451	−	6.71084i	−0.125905	−	0.218073i	0.796182	−	0.605058i	$-0.206850\pi$
$947$	−3.87451	−	6.71084i	−0.125905	−	0.218073i	−0.922086	+	0.386985i	$0.873517\pi$
$948$		0			0
$949$	3.41699			0.110920
$950$	3.84313	+	9.21949i	0.124688	+	0.299120i
$951$		0			0
$952$		0			0
$953$	−6.72876	−	11.6545i	−0.217966	−	0.377528i	0.736220	−	0.676742i	$-0.236609\pi$
$953$	−6.72876	−	11.6545i	−0.217966	−	0.377528i	−0.954186	+	0.299214i	$0.903275\pi$
$954$		0			0
$955$	5.41699	+	9.38251i	0.175290	+	0.303611i
$956$	−6.00000	+	10.3923i	−0.194054	+	0.336111i
$957$		0			0
$958$	6.58301			0.212687
$959$	28.4059	−	49.2004i	0.917274	−	1.58876i
$960$		0			0
$961$	0.874508			0.0282099
$962$	−0.708497			−0.0228429
$963$		0			0
$964$	3.79150	+	6.56708i	0.122116	+	0.211511i
$965$	−12.0000	+	20.7846i	−0.386294	+	0.669080i
$966$		0			0
$967$	6.64575	+	11.5108i	0.213713	+	0.370162i	0.952874	−	0.303367i	$-0.0981109\pi$
$967$	6.64575	+	11.5108i	0.213713	+	0.370162i	−0.739161	+	0.673529i	$0.764778\pi$
$968$	−10.5830			−0.340151
$969$		0			0
$970$	6.10326			0.195964
$971$	−27.1974	−	47.1073i	−0.872806	−	1.51174i	−0.859082	−	0.511838i	$-0.828965\pi$
$971$	−27.1974	−	47.1073i	−0.872806	−	1.51174i	−0.0137234	−	0.999906i	$-0.504368\pi$
$972$		0			0
$973$	−33.9889	+	58.8705i	−1.08963	+	1.88730i
$974$	2.11438	+	3.66221i	0.0677491	+	0.117345i
$975$		0			0
$976$	0.937254			0.0300008
$977$	7.45751			0.238587			0.119293	−	0.992859i	$-0.461937\pi$
$977$	7.45751			0.238587			0.119293	+	0.992859i	$0.461937\pi$
$978$		0			0
$979$		0			0
$980$	10.3542			0.330754
$981$		0			0
$982$	−19.6458	+	34.0274i	−0.626921	+	1.08586i
$983$	15.8745	+	27.4955i	0.506318	+	0.876969i	0.999973	+	0.00731102i	$0.00232719\pi$
$983$	15.8745	+	27.4955i	0.506318	+	0.876969i	−0.493655	+	0.869658i	$0.664339\pi$
$984$		0			0
$985$	−6.29150	−	10.8972i	−0.200464	−	0.347214i
$986$		0			0
$987$		0			0
$988$	5.29150	−	6.92820i	0.168345	−	0.220416i
$989$	18.5830			0.590905
$990$		0			0
$991$	1.41699	+	2.45431i	0.0450123	+	0.0779636i	0.887654	−	0.460511i	$-0.152334\pi$
$991$	1.41699	+	2.45431i	0.0450123	+	0.0779636i	−0.842641	+	0.538475i	$0.819001\pi$
$992$	−2.82288	+	4.88936i	−0.0896264	+	0.155237i
$993$		0			0
$994$	4.93725	−	8.55157i	0.156600	−	0.271239i
$995$	−32.7085			−1.03693
$996$		0			0
$997$	−8.11438	+	14.0545i	−0.256985	+	0.445111i	−0.965433	−	0.260652i	$-0.916062\pi$
$997$	−8.11438	+	14.0545i	−0.256985	+	0.445111i	0.708448	+	0.705763i	$0.249396\pi$
$998$	−2.38562	+	4.13202i	−0.0755155	+	0.130797i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.g.f.235.1		4
3.2	odd	2		38.2.c.b.7.1	✓	4
4.3	odd	2		2736.2.s.v.577.1		4
12.11	even	2		304.2.i.e.273.2		4
15.2	even	4		950.2.j.g.349.3		8
15.8	even	4		950.2.j.g.349.2		8
15.14	odd	2		950.2.e.k.501.2		4
19.7	even	3		6498.2.a.ba.1.2		2
19.11	even	3	inner	342.2.g.f.163.1		4
19.12	odd	6		6498.2.a.bg.1.2		2
24.5	odd	2		1216.2.i.l.577.2		4
24.11	even	2		1216.2.i.k.577.1		4
57.2	even	18		722.2.e.o.389.1		12
57.5	odd	18		722.2.e.n.99.2		12
57.8	even	6		722.2.c.j.429.2		4
57.11	odd	6		38.2.c.b.11.1	yes	4
57.14	even	18		722.2.e.o.99.1		12
57.17	odd	18		722.2.e.n.389.2		12
57.23	odd	18		722.2.e.n.245.2		12
57.26	odd	6		722.2.a.j.1.2		2
57.29	even	18		722.2.e.o.415.2		12
57.32	even	18		722.2.e.o.423.1		12
57.35	odd	18		722.2.e.n.595.1		12
57.41	even	18		722.2.e.o.595.2		12
57.44	odd	18		722.2.e.n.423.2		12
57.47	odd	18		722.2.e.n.415.1		12
57.50	even	6		722.2.a.g.1.1		2
57.53	even	18		722.2.e.o.245.1		12
57.56	even	2		722.2.c.j.653.2		4
76.11	odd	6		2736.2.s.v.1873.1		4
228.11	even	6		304.2.i.e.49.2		4
228.83	even	6		5776.2.a.ba.1.1		2
228.107	odd	6		5776.2.a.z.1.2		2
285.68	even	12		950.2.j.g.49.3		8
285.182	even	12		950.2.j.g.49.2		8
285.239	odd	6		950.2.e.k.201.2		4
456.11	even	6		1216.2.i.k.961.1		4
456.125	odd	6		1216.2.i.l.961.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.1	✓	4	3.2	odd	2
38.2.c.b.11.1	yes	4	57.11	odd	6
304.2.i.e.49.2		4	228.11	even	6
304.2.i.e.273.2		4	12.11	even	2
342.2.g.f.163.1		4	19.11	even	3	inner
342.2.g.f.235.1		4	1.1	even	1	trivial
722.2.a.g.1.1		2	57.50	even	6
722.2.a.j.1.2		2	57.26	odd	6
722.2.c.j.429.2		4	57.8	even	6
722.2.c.j.653.2		4	57.56	even	2
722.2.e.n.99.2		12	57.5	odd	18
722.2.e.n.245.2		12	57.23	odd	18
722.2.e.n.389.2		12	57.17	odd	18
722.2.e.n.415.1		12	57.47	odd	18
722.2.e.n.423.2		12	57.44	odd	18
722.2.e.n.595.1		12	57.35	odd	18
722.2.e.o.99.1		12	57.14	even	18
722.2.e.o.245.1		12	57.53	even	18
722.2.e.o.389.1		12	57.2	even	18
722.2.e.o.415.2		12	57.29	even	18
722.2.e.o.423.1		12	57.32	even	18
722.2.e.o.595.2		12	57.41	even	18
950.2.e.k.201.2		4	285.239	odd	6
950.2.e.k.501.2		4	15.14	odd	2
950.2.j.g.49.2		8	285.182	even	12
950.2.j.g.49.3		8	285.68	even	12
950.2.j.g.349.2		8	15.8	even	4
950.2.j.g.349.3		8	15.2	even	4
1216.2.i.k.577.1		4	24.11	even	2
1216.2.i.k.961.1		4	456.11	even	6
1216.2.i.l.577.2		4	24.5	odd	2
1216.2.i.l.961.2		4	456.125	odd	6
2736.2.s.v.577.1		4	4.3	odd	2
2736.2.s.v.1873.1		4	76.11	odd	6
5776.2.a.z.1.2		2	228.107	odd	6
5776.2.a.ba.1.1		2	228.83	even	6
6498.2.a.ba.1.2		2	19.7	even	3
6498.2.a.bg.1.2		2	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} +3.64575 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} +3.64575 q^{7} -1.00000 q^{8} +(0.822876 - 1.42526i) q^{10} +4.64575 q^{11} +(-1.00000 + 1.73205i) q^{13} +(1.82288 + 3.15731i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.67712 + 4.02334i) q^{19} +1.64575 q^{20} +(2.32288 + 4.02334i) q^{22} +(-0.822876 + 1.42526i) q^{23} +(1.14575 - 1.98450i) q^{25} -2.00000 q^{26} +(-1.82288 + 3.15731i) q^{28} +(0.822876 - 1.42526i) q^{29} -5.64575 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{35} +0.354249 q^{37} +(-2.64575 + 3.46410i) q^{38} +(0.822876 + 1.42526i) q^{40} +(-0.145751 - 0.252449i) q^{41} +(-5.64575 - 9.77873i) q^{43} +(-2.32288 + 4.02334i) q^{44} -1.64575 q^{46} +(2.17712 - 3.77089i) q^{47} +6.29150 q^{49} +2.29150 q^{50} +(-1.00000 - 1.73205i) q^{52} +(-6.29150 + 10.8972i) q^{53} +(-3.82288 - 6.62141i) q^{55} -3.64575 q^{56} +1.64575 q^{58} +(-3.96863 - 6.87386i) q^{59} +(-0.468627 + 0.811686i) q^{61} +(-2.82288 - 4.88936i) q^{62} +1.00000 q^{64} +3.29150 q^{65} +(-0.322876 + 0.559237i) q^{67} +(3.00000 - 5.19615i) q^{70} +(-1.35425 - 2.34563i) q^{71} +(-0.854249 - 1.47960i) q^{73} +(0.177124 + 0.306788i) q^{74} +(-4.32288 - 0.559237i) q^{76} +16.9373 q^{77} +(2.00000 + 3.46410i) q^{79} +(-0.822876 + 1.42526i) q^{80} +(0.145751 - 0.252449i) q^{82} -7.93725 q^{83} +(5.64575 - 9.77873i) q^{86} -4.64575 q^{88} +(-3.64575 + 6.31463i) q^{91} +(-0.822876 - 1.42526i) q^{92} +4.35425 q^{94} +(4.35425 - 5.70105i) q^{95} +(1.85425 + 3.21165i) q^{97} +(3.14575 + 5.44860i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8} - 2 q^{10} + 8 q^{11} - 4 q^{13} + 2 q^{14} - 2 q^{16} + 12 q^{19} - 4 q^{20} + 4 q^{22} + 2 q^{23} - 6 q^{25} - 8 q^{26} - 2 q^{28} - 2 q^{29} - 12 q^{31} + 2 q^{32} - 12 q^{35} + 12 q^{37} - 2 q^{40} + 10 q^{41} - 12 q^{43} - 4 q^{44} + 4 q^{46} + 14 q^{47} + 4 q^{49} - 12 q^{50} - 4 q^{52} - 4 q^{53} - 10 q^{55} - 4 q^{56} - 4 q^{58} + 14 q^{61} - 6 q^{62} + 4 q^{64} - 8 q^{65} + 4 q^{67} + 12 q^{70} - 16 q^{71} - 14 q^{73} + 6 q^{74} - 12 q^{76} + 36 q^{77} + 8 q^{79} + 2 q^{80} - 10 q^{82} + 12 q^{86} - 8 q^{88} - 4 q^{91} + 2 q^{92} + 28 q^{94} + 28 q^{95} + 18 q^{97} + 2 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8 - 2 * q^10 + 8 * q^11 - 4 * q^13 + 2 * q^14 - 2 * q^16 + 12 * q^19 - 4 * q^20 + 4 * q^22 + 2 * q^23 - 6 * q^25 - 8 * q^26 - 2 * q^28 - 2 * q^29 - 12 * q^31 + 2 * q^32 - 12 * q^35 + 12 * q^37 - 2 * q^40 + 10 * q^41 - 12 * q^43 - 4 * q^44 + 4 * q^46 + 14 * q^47 + 4 * q^49 - 12 * q^50 - 4 * q^52 - 4 * q^53 - 10 * q^55 - 4 * q^56 - 4 * q^58 + 14 * q^61 - 6 * q^62 + 4 * q^64 - 8 * q^65 + 4 * q^67 + 12 * q^70 - 16 * q^71 - 14 * q^73 + 6 * q^74 - 12 * q^76 + 36 * q^77 + 8 * q^79 + 2 * q^80 - 10 * q^82 + 12 * q^86 - 8 * q^88 - 4 * q^91 + 2 * q^92 + 28 * q^94 + 28 * q^95 + 18 * q^97 + 2 * q^98

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