LMFDB - Embedded newform 1323.2.s.c.962.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			962.5
Root			$-1.82904 + 1.05600i$ of defining polynomial
Character	$\chi$	$=$	1323.962
Dual form			1323.2.s.c.656.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02704 + 0.592963i) q^{2} +(-0.296790 - 0.514055i) q^{4} -2.83797 q^{5} -3.07579i q^{8} +O(q^{10})$	\(q+(1.02704 + 0.592963i) q^{2} +(-0.296790 - 0.514055i) q^{4} -2.83797 q^{5} -3.07579i q^{8} +(-2.91472 - 1.68281i) q^{10} -0.157816i q^{11} +(3.41468 + 1.97146i) q^{13} +(1.23025 - 2.13086i) q^{16} +(-2.07244 + 3.58956i) q^{17} +(-5.48711 + 3.16799i) q^{19} +(0.842281 + 1.45887i) q^{20} +(0.0935793 - 0.162084i) q^{22} +0.546125i q^{23} +3.05408 q^{25} +(2.33801 + 4.04955i) q^{26} +(-4.02704 + 2.32501i) q^{29} +(0.112086 - 0.0647129i) q^{31} +(-2.80039 + 1.61680i) q^{32} +(-4.25696 + 2.45776i) q^{34} +(1.23025 + 2.13086i) q^{37} -7.51399 q^{38} +8.72902i q^{40} +(-1.99569 + 3.45664i) q^{41} +(3.28434 + 5.68864i) q^{43} +(-0.0811263 + 0.0468383i) q^{44} +(-0.323832 + 0.560893i) q^{46} +(-4.33370 + 7.50619i) q^{47} +(3.13667 + 1.81096i) q^{50} -2.34044i q^{52} +(-2.25370 - 1.30117i) q^{53} +0.447879i q^{55} -5.51459 q^{58} +(1.80686 + 3.12957i) q^{59} +(-2.91472 - 1.68281i) q^{61} +0.153489 q^{62} -8.75583 q^{64} +(-9.69076 - 5.59496i) q^{65} +(-0.663715 - 1.14959i) q^{67} +2.46031 q^{68} +0.409310i q^{71} +(-13.0011 - 7.50619i) q^{73} +2.91798i q^{74} +(3.25704 + 1.88045i) q^{76} +(-2.16372 + 3.74766i) q^{79} +(-3.49142 + 6.04732i) q^{80} +(-4.09932 + 2.36674i) q^{82} +(3.22585 + 5.58733i) q^{83} +(5.88151 - 10.1871i) q^{85} +7.78996i q^{86} -0.485411 q^{88} +(-2.52684 - 4.37662i) q^{89} +(0.280738 - 0.162084i) q^{92} +(-8.90179 + 5.13945i) q^{94} +(15.5723 - 8.99066i) q^{95} +(2.18452 - 1.26123i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 2 q^{4}+O(q^{10}) $ 12 * q - 6 * q^2 + 2 * q^4	$ 12 q - 6 q^{2} + 2 q^{4} + 2 q^{16} - 10 q^{22} - 30 q^{29} - 12 q^{32} + 2 q^{37} - 10 q^{43} + 54 q^{44} + 20 q^{46} + 36 q^{50} - 12 q^{53} - 4 q^{58} + 16 q^{64} - 78 q^{65} + 12 q^{67} - 6 q^{79} - 6 q^{85} - 68 q^{88} - 30 q^{92} + 72 q^{95}+O(q^{100}) $ 12 * q - 6 * q^2 + 2 * q^4 + 2 * q^16 - 10 * q^22 - 30 * q^29 - 12 * q^32 + 2 * q^37 - 10 * q^43 + 54 * q^44 + 20 * q^46 + 36 * q^50 - 12 * q^53 - 4 * q^58 + 16 * q^64 - 78 * q^65 + 12 * q^67 - 6 * q^79 - 6 * q^85 - 68 * q^88 - 30 * q^92 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.02704	+	0.592963i	0.726228	+	0.419288i	0.817041	−	0.576580i	$-0.195613\pi$
$2$	1.02704	+	0.592963i	0.726228	+	0.419288i	−0.0908124	+	0.995868i	$0.528946\pi$
$3$		0			0
$3$		0			0
$4$	−0.296790	−	0.514055i	−0.148395	−	0.257027i
$5$	−2.83797			−1.26918			−0.634590	−	0.772849i	$-0.718831\pi$
$5$	−2.83797			−1.26918			−0.634590	+	0.772849i	$0.718831\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	3.07579i		−	1.08746i
$9$		0			0
$10$	−2.91472	−	1.68281i	−0.921714	−	0.532152i
$11$		−	0.157816i		−	0.0475835i	−0.999717	−	0.0237917i	$-0.992426\pi$
$11$		−	0.157816i		−	0.0475835i	0.999717	−	0.0237917i	$-0.00757386\pi$
$12$		0			0
$13$	3.41468	+	1.97146i	0.947061	+	0.546786i	0.892167	−	0.451706i	$-0.149184\pi$
$13$	3.41468	+	1.97146i	0.947061	+	0.546786i	0.0548943	+	0.998492i	$0.482518\pi$
$14$		0			0
$15$		0			0
$16$	1.23025	−	2.13086i	0.307563	−	0.532715i
$17$	−2.07244	+	3.58956i	−0.502640	+	0.870597i	0.497356	+	0.867547i	$0.334304\pi$
$17$	−2.07244	+	3.58956i	−0.502640	+	0.870597i	−0.999995	+	0.00305055i	$0.999029\pi$
$18$		0			0
$19$	−5.48711	+	3.16799i	−1.25883	+	0.726786i	−0.972847	−	0.231449i	$-0.925653\pi$
$19$	−5.48711	+	3.16799i	−1.25883	+	0.726786i	−0.285983	+	0.958235i	$0.592320\pi$
$20$	0.842281	+	1.45887i	0.188340	+	0.326214i
$21$		0			0
$22$	0.0935793	−	0.162084i	0.0199512	−	0.0345565i
$23$			0.546125i			0.113875i	0.998378	+	0.0569374i	$0.0181336\pi$
$23$			0.546125i			0.113875i	−0.998378	+	0.0569374i	$0.981866\pi$
$24$		0			0
$25$	3.05408			0.610817
$26$	2.33801	+	4.04955i	0.458522	+	0.794183i
$27$		0			0
$28$		0			0
$29$	−4.02704	+	2.32501i	−0.747803	+	0.431744i	−0.824900	−	0.565279i	$-0.808768\pi$
$29$	−4.02704	+	2.32501i	−0.747803	+	0.431744i	0.0770966	+	0.997024i	$0.475435\pi$
$30$		0			0
$31$	0.112086	−	0.0647129i	0.0201313	−	0.0116228i	−0.489901	−	0.871778i	$-0.662967\pi$
$31$	0.112086	−	0.0647129i	0.0201313	−	0.0116228i	0.510032	+	0.860156i	$0.329634\pi$
$32$	−2.80039	+	1.61680i	−0.495043	+	0.285813i
$33$		0			0
$34$	−4.25696	+	2.45776i	−0.730062	+	0.421502i
$35$		0			0
$36$		0			0
$37$	1.23025	+	2.13086i	0.202252	+	0.350311i	0.949254	−	0.314511i	$-0.101841\pi$
$37$	1.23025	+	2.13086i	0.202252	+	0.350311i	−0.747002	+	0.664822i	$0.768507\pi$
$38$	−7.51399			−1.21893
$39$		0			0
$40$			8.72902i			1.38018i
$41$	−1.99569	+	3.45664i	−0.311675	+	0.539836i	−0.978725	−	0.205176i	$-0.934223\pi$
$41$	−1.99569	+	3.45664i	−0.311675	+	0.539836i	0.667050	+	0.745013i	$0.267557\pi$
$42$		0			0
$43$	3.28434	+	5.68864i	0.500857	+	0.867509i	1.00000		0.000989450i	$0.000314952\pi$
$43$	3.28434	+	5.68864i	0.500857	+	0.867509i	−0.499143	+	0.866520i	$0.666352\pi$
$44$	−0.0811263	+	0.0468383i	−0.0122303	+	0.00706114i
$45$		0			0
$46$	−0.323832	+	0.560893i	−0.0477464	+	0.0826992i
$47$	−4.33370	+	7.50619i	−0.632135	+	1.09489i	0.354979	+	0.934874i	$0.384488\pi$
$47$	−4.33370	+	7.50619i	−0.632135	+	1.09489i	−0.987114	+	0.160016i	$0.948845\pi$
$48$		0			0
$49$		0			0
$50$	3.13667	+	1.81096i	0.443593	+	0.256108i
$51$		0			0
$52$		−	2.34044i		−	0.324561i
$53$	−2.25370	−	1.30117i	−0.309569	−	0.178730i	0.337165	−	0.941446i	$-0.390532\pi$
$53$	−2.25370	−	1.30117i	−0.309569	−	0.178730i	−0.646734	+	0.762716i	$0.723865\pi$
$54$		0			0
$55$			0.447879i			0.0603920i
$56$		0			0
$57$		0			0
$58$	−5.51459			−0.724101
$59$	1.80686	+	3.12957i	0.235233	+	0.407436i	0.959340	−	0.282252i	$-0.0910813\pi$
$59$	1.80686	+	3.12957i	0.235233	+	0.407436i	−0.724107	+	0.689687i	$0.757748\pi$
$60$		0			0
$61$	−2.91472	−	1.68281i	−0.373191	−	0.215462i	0.301660	−	0.953415i	$-0.402459\pi$
$61$	−2.91472	−	1.68281i	−0.373191	−	0.215462i	−0.674852	+	0.737953i	$0.735792\pi$
$62$	0.153489			0.0194932
$63$		0			0
$64$	−8.75583			−1.09448
$65$	−9.69076	−	5.59496i	−1.20199	−	0.693970i
$66$		0			0
$67$	−0.663715	−	1.14959i	−0.0810857	−	0.140445i	0.822631	−	0.568576i	$-0.192505\pi$
$67$	−0.663715	−	1.14959i	−0.0810857	−	0.140445i	−0.903717	+	0.428131i	$0.859172\pi$
$68$	2.46031			0.298356
$69$		0			0
$70$		0			0
$71$			0.409310i			0.0485761i	0.999705	+	0.0242881i	$0.00773189\pi$
$71$			0.409310i			0.0485761i	−0.999705	+	0.0242881i	$0.992268\pi$
$72$		0			0
$73$	−13.0011	−	7.50619i	−1.52166	−	0.878533i	−0.999673	−	0.0255830i	$-0.991856\pi$
$73$	−13.0011	−	7.50619i	−1.52166	−	0.878533i	−0.521992	−	0.852950i	$-0.674811\pi$
$74$			2.91798i			0.339208i
$75$		0			0
$76$	3.25704	+	1.88045i	0.373608	+	0.215703i
$77$		0			0
$78$		0			0
$79$	−2.16372	+	3.74766i	−0.243437	+	0.421645i	−0.961691	−	0.274136i	$-0.911608\pi$
$79$	−2.16372	+	3.74766i	−0.243437	+	0.421645i	0.718254	+	0.695781i	$0.244942\pi$
$80$	−3.49142	+	6.04732i	−0.390353	+	0.676111i
$81$		0			0
$82$	−4.09932	+	2.36674i	−0.452694	+	0.261363i
$83$	3.22585	+	5.58733i	0.354083	+	0.613289i	0.986961	−	0.160963i	$-0.0514598\pi$
$83$	3.22585	+	5.58733i	0.354083	+	0.613289i	−0.632878	+	0.774252i	$0.718126\pi$
$84$		0			0
$85$	5.88151	−	10.1871i	0.637940	−	1.10494i
$86$			7.78996i			0.840013i
$87$		0			0
$88$	−0.485411			−0.0517450
$89$	−2.52684	−	4.37662i	−0.267845	−	0.463921i	0.700460	−	0.713691i	$-0.252978\pi$
$89$	−2.52684	−	4.37662i	−0.267845	−	0.463921i	−0.968305	+	0.249771i	$0.919645\pi$
$90$		0			0
$91$		0			0
$92$	0.280738	−	0.162084i	0.0292690	−	0.0168984i
$93$		0			0
$94$	−8.90179	+	5.13945i	−0.918150	+	0.530094i
$95$	15.5723	−	8.99066i	1.59768	−	0.922422i
$96$		0			0
$97$	2.18452	−	1.26123i	0.221805	−	0.128059i	−0.384981	−	0.922925i	$-0.625792\pi$
$97$	2.18452	−	1.26123i	0.221805	−	0.128059i	0.606786	+	0.794866i	$0.292459\pi$
$98$		0			0
$99$		0			0
$100$	−0.906421	−	1.56997i	−0.0906421	−	0.156997i
$101$	−2.99146			−0.297662			−0.148831	−	0.988863i	$-0.547551\pi$
$101$	−2.99146			−0.297662			−0.148831	+	0.988863i	$0.547551\pi$
$102$		0			0
$103$		−	13.1966i		−	1.30030i	−0.759804	−	0.650152i	$-0.774705\pi$
$103$		−	13.1966i		−	1.30030i	0.759804	−	0.650152i	$-0.225295\pi$
$104$	6.06382	−	10.5028i	0.594606	−	1.02989i
$105$		0			0
$106$	−1.54309	−	2.67272i	−0.149879	−	0.259597i
$107$	16.9356	−	9.77777i	1.63723	−	0.945253i	0.655444	−	0.755244i	$-0.272482\pi$
$107$	16.9356	−	9.77777i	1.63723	−	0.945253i	0.981782	−	0.190009i	$-0.0608517\pi$
$108$		0			0
$109$	−6.62422	+	11.4735i	−0.634485	+	1.09896i	0.352139	+	0.935948i	$0.385455\pi$
$109$	−6.62422	+	11.4735i	−0.634485	+	1.09896i	−0.986624	+	0.163013i	$0.947879\pi$
$110$	−0.265576	+	0.459990i	−0.0253216	+	0.0438584i
$111$		0			0
$112$		0			0
$113$	8.72665	+	5.03834i	0.820935	+	0.473967i	0.850739	−	0.525589i	$-0.176155\pi$
$113$	8.72665	+	5.03834i	0.820935	+	0.473967i	−0.0298041	+	0.999556i	$0.509488\pi$
$114$		0			0
$115$		−	1.54989i		−	0.144528i
$116$	2.39037	+	1.38008i	0.221940	+	0.128137i
$117$		0			0
$118$			4.28561i			0.394522i
$119$		0			0
$120$		0			0
$121$	10.9751			0.997736
$122$	−1.99569	−	3.45664i	−0.180681	−	0.312949i
$123$		0			0
$124$	−0.0665320	−	0.0384123i	−0.00597475	−	0.00344952i
$125$	5.52245			0.493943
$126$		0			0
$127$	−12.4897			−1.10828			−0.554140	−	0.832423i	$-0.686953\pi$
$127$	−12.4897			−1.10828			−0.554140	+	0.832423i	$0.686953\pi$
$128$	−3.39183	−	1.95827i	−0.299798	−	0.173089i
$129$		0			0
$130$	−6.63521	−	11.4925i	−0.581946	−	1.00796i
$131$	10.0450			0.877635			0.438817	−	0.898576i	$-0.355398\pi$
$131$	10.0450			0.877635			0.438817	+	0.898576i	$0.355398\pi$
$132$		0			0
$133$		0			0
$134$		−	1.57423i		−	0.135993i
$135$		0			0
$136$	11.0408	+	6.37438i	0.946737	+	0.546599i
$137$			8.04145i			0.687028i	0.939148	+	0.343514i	$0.111617\pi$
$137$			8.04145i			0.687028i	−0.939148	+	0.343514i	$0.888383\pi$
$138$		0			0
$139$	−16.3702	−	9.45136i	−1.38850	−	0.801654i	−0.395358	−	0.918527i	$-0.629379\pi$
$139$	−16.3702	−	9.45136i	−1.38850	−	0.801654i	−0.993147	+	0.116873i	$0.962713\pi$
$140$		0			0
$141$		0			0
$142$	−0.242705	+	0.420378i	−0.0203674	+	0.0352774i
$143$	0.311130	−	0.538892i	0.0260180	−	0.0450644i
$144$		0			0
$145$	11.4286	−	6.59832i	0.949096	−	0.547961i
$146$	−8.90179	−	15.4184i	−0.736717	−	1.27603i
$147$		0			0
$148$	0.730252	−	1.26483i	0.0600264	−	0.103969i
$149$			19.4063i			1.58982i	0.606725	+	0.794912i	$0.292483\pi$
$149$			19.4063i			1.58982i	−0.606725	+	0.794912i	$0.707517\pi$
$150$		0			0
$151$	−1.78794			−0.145500			−0.0727501	−	0.997350i	$-0.523178\pi$
$151$	−1.78794			−0.145500			−0.0727501	+	0.997350i	$0.523178\pi$
$152$	9.74407	+	16.8772i	0.790348	+	1.36892i
$153$		0			0
$154$		0			0
$155$	−0.318097	+	0.183653i	−0.0255502	+	0.0147514i
$156$		0			0
$157$	3.80255	−	2.19540i	0.303477	−	0.175212i	−0.340527	−	0.940235i	$-0.610605\pi$
$157$	3.80255	−	2.19540i	0.303477	−	0.175212i	0.644004	+	0.765022i	$0.277272\pi$
$158$	−4.44445	+	2.56601i	−0.353582	+	0.204140i
$159$		0			0
$160$	7.94742	−	4.58845i	0.628299	−	0.362749i
$161$		0			0
$162$		0			0
$163$	−2.71780	−	4.70737i	−0.212874	−	0.368709i	0.739738	−	0.672894i	$-0.234949\pi$
$163$	−2.71780	−	4.70737i	−0.212874	−	0.368709i	−0.952613	+	0.304185i	$0.901616\pi$
$164$	2.36920			0.185004
$165$		0			0
$166$			7.65123i			0.593851i
$167$	−5.25273	+	9.09799i	−0.406468	+	0.704024i	−0.994491	−	0.104821i	$-0.966573\pi$
$167$	−5.25273	+	9.09799i	−0.406468	+	0.704024i	0.588023	+	0.808844i	$0.299907\pi$
$168$		0			0
$169$	1.27335	+	2.20550i	0.0979497	+	0.169654i
$170$	12.0811	−	6.97504i	0.926580	−	0.534961i
$171$		0			0
$172$	1.94951	−	3.37666i	0.148649	−	0.257468i
$173$	8.77949	−	15.2065i	0.667492	−	1.15613i	−0.311111	−	0.950374i	$-0.600701\pi$
$173$	8.77949	−	15.2065i	0.667492	−	1.15613i	0.978603	−	0.205757i	$-0.0659656\pi$
$174$		0			0
$175$		0			0
$176$	−0.336285	−	0.194154i	−0.0253484	−	0.0146349i
$177$		0			0
$178$		−	5.99330i		−	0.449217i
$179$	−15.7645	−	9.10163i	−1.17829	−	0.680288i	−0.222674	−	0.974893i	$-0.571479\pi$
$179$	−15.7645	−	9.10163i	−1.17829	−	0.680288i	−0.955619	+	0.294605i	$0.904812\pi$
$180$		0			0
$181$		−	6.60182i		−	0.490710i	−0.969433	−	0.245355i	$-0.921096\pi$
$181$		−	6.60182i		−	0.490710i	0.969433	−	0.245355i	$-0.0789045\pi$
$182$		0			0
$183$		0			0
$184$	1.67977			0.123834
$185$	−3.49142	−	6.04732i	−0.256694	−	0.444608i
$186$		0			0
$187$	0.566492	+	0.327065i	0.0414260	+	0.0239173i
$188$	5.14479			0.375223
$189$		0			0
$190$	21.3245			1.54704
$191$	−12.3063	−	7.10506i	−0.890454	−	0.514104i	−0.0163630	−	0.999866i	$-0.505209\pi$
$191$	−12.3063	−	7.10506i	−0.890454	−	0.514104i	−0.874091	+	0.485762i	$0.838542\pi$
$192$		0			0
$193$	5.00214	+	8.66395i	0.360062	+	0.623645i	0.987971	−	0.154642i	$-0.0494223\pi$
$193$	5.00214	+	8.66395i	0.360062	+	0.623645i	−0.627909	+	0.778287i	$0.716089\pi$
$194$	2.99146			0.214774
$195$		0			0
$196$		0			0
$197$		−	20.1017i		−	1.43218i	−0.698006	−	0.716092i	$-0.745929\pi$
$197$		−	20.1017i		−	1.43218i	0.698006	−	0.716092i	$-0.254071\pi$
$198$		0			0
$199$	11.2045	+	6.46890i	0.794263	+	0.458568i	0.841461	−	0.540318i	$-0.181696\pi$
$199$	11.2045	+	6.46890i	0.794263	+	0.458568i	−0.0471981	+	0.998886i	$0.515029\pi$
$200$		−	9.39373i		−	0.664237i
$201$		0			0
$202$	−3.07236	−	1.77383i	−0.216170	−	0.124806i
$203$		0			0
$204$		0			0
$205$	5.66372	−	9.80984i	0.395571	−	0.685149i
$206$	7.82512	−	13.5535i	0.545202	−	0.944318i
$207$		0			0
$208$	8.40183	−	4.85080i	0.582562	−	0.336342i
$209$	0.499960	+	0.865957i	0.0345830	+	0.0598995i
$210$		0			0
$211$	−4.50720	+	7.80669i	−0.310288	+	0.537435i	−0.978425	−	0.206604i	$-0.933759\pi$
$211$	−4.50720	+	7.80669i	−0.310288	+	0.537435i	0.668136	+	0.744039i	$0.267092\pi$
$212$			1.54470i			0.106090i
$213$		0			0
$214$	23.1914			1.58533
$215$	−9.32085	−	16.1442i	−0.635677	−	1.10102i
$216$		0			0
$217$		0			0
$218$	−13.6067	+	7.85584i	−0.921562	+	0.532064i
$219$		0			0
$220$	0.230234	−	0.132926i	0.0155224	−	0.00896185i
$221$	−14.1534	+	8.17147i	−0.952061	+	0.549672i
$222$		0			0
$223$	1.95429	−	1.12831i	0.130869	−	0.0755571i	−0.433136	−	0.901328i	$-0.642593\pi$
$223$	1.95429	−	1.12831i	0.130869	−	0.0755571i	0.564005	+	0.825771i	$0.309260\pi$
$224$		0			0
$225$		0			0
$226$	5.97509	+	10.3492i	0.397457	+	0.688416i
$227$	18.6417			1.23729			0.618647	−	0.785669i	$-0.287681\pi$
$227$	18.6417			1.23729			0.618647	+	0.785669i	$0.287681\pi$
$228$		0			0
$229$		−	14.3057i		−	0.945344i	−0.881238	−	0.472672i	$-0.843289\pi$
$229$		−	14.3057i		−	0.945344i	0.881238	−	0.472672i	$-0.156711\pi$
$230$	0.919025	−	1.59180i	0.0605987	−	0.104960i
$231$		0			0
$232$	7.15126	+	12.3863i	0.469503	+	0.813204i
$233$	−14.7812	+	8.53394i	−0.968350	+	0.559077i	−0.898733	−	0.438497i	$-0.855511\pi$
$233$	−14.7812	+	8.53394i	−0.968350	+	0.559077i	−0.0696170	+	0.997574i	$0.522178\pi$
$234$		0			0
$235$	12.2989	−	21.3024i	0.802293	−	1.38961i
$236$	1.07251	−	1.85765i	0.0698148	−	0.120923i
$237$		0			0
$238$		0			0
$239$	−1.93560	−	1.11752i	−0.125203	−	0.0722863i	0.436090	−	0.899903i	$-0.356363\pi$
$239$	−1.93560	−	1.11752i	−0.125203	−	0.0722863i	−0.561294	+	0.827617i	$0.689696\pi$
$240$		0			0
$241$			4.52023i			0.291174i	0.989345	+	0.145587i	$0.0465070\pi$
$241$			4.52023i			0.291174i	−0.989345	+	0.145587i	$0.953493\pi$
$242$	11.2719	+	6.50783i	0.724584	+	0.418339i
$243$		0			0
$244$			1.99777i			0.127894i
$245$		0			0
$246$		0			0
$247$	−24.9823			−1.58959
$248$	−0.199044	−	0.344754i	−0.0126393	−	0.0218919i
$249$		0			0
$250$	5.67179	+	3.27461i	0.358716	+	0.207105i
$251$	−21.1727			−1.33641			−0.668205	−	0.743978i	$-0.732937\pi$
$251$	−21.1727			−1.33641			−0.668205	+	0.743978i	$0.732937\pi$
$252$		0			0
$253$	0.0861875			0.00541856
$254$	−12.8274	−	7.40592i	−0.804865	−	0.464689i
$255$		0			0
$256$	6.43346	+	11.1431i	0.402091	+	0.696443i
$257$	−31.3005			−1.95247			−0.976236	−	0.216712i	$-0.930467\pi$
$257$	−31.3005			−1.95247			−0.976236	+	0.216712i	$0.930467\pi$
$258$		0			0
$259$		0			0
$260$			6.64211i			0.411926i
$261$		0			0
$262$	10.3166	+	5.95631i	0.637363	+	0.367982i
$263$			6.67671i			0.411704i	0.978583	+	0.205852i	$0.0659965\pi$
$263$			6.67671i			0.411704i	−0.978583	+	0.205852i	$0.934004\pi$
$264$		0			0
$265$	6.39593	+	3.69269i	0.392899	+	0.226840i
$266$		0			0
$267$		0			0
$268$	−0.393968	+	0.682372i	−0.0240654	+	0.0416825i
$269$	5.32947	−	9.23092i	0.324944	−	0.562819i	−0.656557	−	0.754276i	$-0.727988\pi$
$269$	5.32947	−	9.23092i	0.324944	−	0.562819i	0.981501	+	0.191457i	$0.0613213\pi$
$270$		0			0
$271$	6.44754	−	3.72249i	0.391660	−	0.226125i	−0.291219	−	0.956656i	$-0.594061\pi$
$271$	6.44754	−	3.72249i	0.391660	−	0.226125i	0.682879	+	0.730531i	$0.260727\pi$
$272$	5.09924	+	8.83214i	0.309187	+	0.535527i
$273$		0			0
$274$	−4.76829	+	8.25891i	−0.288063	+	0.498939i
$275$		−	0.481985i		−	0.0290648i
$276$		0			0
$277$	−26.5586			−1.59575			−0.797874	−	0.602824i	$-0.794042\pi$
$277$	−26.5586			−1.59575			−0.797874	+	0.602824i	$0.794042\pi$
$278$	−11.2086	−	19.4139i	−0.672248	−	1.16437i
$279$		0			0
$280$		0			0
$281$	−21.0993	+	12.1817i	−1.25868	+	0.726699i	−0.972818	−	0.231572i	$-0.925613\pi$
$281$	−21.0993	+	12.1817i	−1.25868	+	0.726699i	−0.285862	+	0.958271i	$0.592280\pi$
$282$		0			0
$283$	7.49302	−	4.32610i	0.445414	−	0.257160i	−0.260478	−	0.965480i	$-0.583880\pi$
$283$	7.49302	−	4.32610i	0.445414	−	0.257160i	0.705891	+	0.708320i	$0.250547\pi$
$284$	0.210408	−	0.121479i	0.0124854	−	0.00720844i
$285$		0			0
$286$	0.639086	−	0.368977i	0.0377900	−	0.0218181i
$287$		0			0
$288$		0			0
$289$	−0.0899807	−	0.155851i	−0.00529298	−	0.00916772i
$290$	15.6502			0.919014
$291$		0			0
$292$			8.91104i			0.521479i
$293$	4.40023	−	7.62143i	0.257064	−	0.445249i	−0.708390	−	0.705821i	$-0.750578\pi$
$293$	4.40023	−	7.62143i	0.257064	−	0.445249i	0.965454	+	0.260573i	$0.0839114\pi$
$294$		0			0
$295$	−5.12782	−	8.88164i	−0.298553	−	0.517109i
$296$	6.55408	−	3.78400i	0.380948	−	0.219941i
$297$		0			0
$298$	−11.5072	+	19.9311i	−0.666594	+	1.15457i
$299$	−1.07667	+	1.86484i	−0.0622652	+	0.107846i
$300$		0			0
$301$		0			0
$302$	−1.83628	−	1.06018i	−0.105666	−	0.0610065i
$303$		0			0
$304$			15.5897i			0.894130i
$305$	8.27188	+	4.77577i	0.473647	+	0.273460i
$306$		0			0
$307$			11.1747i			0.637771i	0.947793	+	0.318886i	$0.103309\pi$
$307$			11.1747i			0.637771i	−0.947793	+	0.318886i	$0.896691\pi$
$308$		0			0
$309$		0			0
$310$	−0.435599			−0.0247404
$311$	8.20279	+	14.2076i	0.465137	+	0.805641i	0.999208	−	0.0397985i	$-0.0126716\pi$
$311$	8.20279	+	14.2076i	0.465137	+	0.805641i	−0.534070	+	0.845440i	$0.679338\pi$
$312$		0			0
$313$	−7.10514	−	4.10216i	−0.401606	−	0.231868i	0.285570	−	0.958358i	$-0.407817\pi$
$313$	−7.10514	−	4.10216i	−0.401606	−	0.231868i	−0.687177	+	0.726490i	$0.741150\pi$
$314$	5.20717			0.293858
$315$		0			0
$316$	2.56867			0.144499
$317$	19.8427	+	11.4562i	1.11448	+	0.643443i	0.939985	−	0.341215i	$-0.110839\pi$
$317$	19.8427	+	11.4562i	1.11448	+	0.643443i	0.174491	+	0.984659i	$0.444172\pi$
$318$		0			0
$319$	0.366926	+	0.635534i	0.0205439	+	0.0355831i
$320$	24.8488			1.38909
$321$		0			0
$322$		0			0
$323$		−	26.2618i		−	1.46125i
$324$		0			0
$325$	10.4287	+	6.02102i	0.578481	+	0.333986i
$326$		−	6.44622i		−	0.357023i
$327$		0			0
$328$	10.6319	+	6.13833i	0.587049	+	0.338933i
$329$		0			0
$330$		0			0
$331$	−9.63161	+	16.6824i	−0.529401	+	0.916950i	0.470011	+	0.882661i	$0.344250\pi$
$331$	−9.63161	+	16.6824i	−0.529401	+	0.916950i	−0.999412	+	0.0342892i	$0.989083\pi$
$332$	1.91480	−	3.31652i	0.105088	−	0.182018i
$333$		0			0
$334$	−10.7895	+	6.22935i	−0.590378	+	0.340855i
$335$	1.88361	+	3.26250i	0.102912	+	0.178249i
$336$		0			0
$337$	−2.26829	+	3.92878i	−0.123561	+	0.214015i	−0.921170	−	0.389161i	$-0.872765\pi$
$337$	−2.26829	+	3.92878i	−0.123561	+	0.214015i	0.797608	+	0.603176i	$0.206098\pi$
$338$			3.02019i			0.164277i
$339$		0			0
$340$	−6.98229			−0.378668
$341$	−0.0102128	−	0.0176890i	−0.000553052	−	0.000957915i
$342$		0			0
$343$		0			0
$344$	17.4971	−	10.1019i	0.943379	−	0.544660i
$345$		0			0
$346$	18.0338	−	10.4118i	0.969504	−	0.559743i
$347$	7.56294	−	4.36646i	0.406000	−	0.234404i	−0.283070	−	0.959099i	$-0.591353\pi$
$347$	7.56294	−	4.36646i	0.406000	−	0.234404i	0.689070	+	0.724695i	$0.258019\pi$
$348$		0			0
$349$	−7.82927	+	4.52023i	−0.419091	+	0.241963i	−0.694689	−	0.719311i	$-0.744458\pi$
$349$	−7.82927	+	4.52023i	−0.419091	+	0.241963i	0.275597	+	0.961273i	$0.411124\pi$
$350$		0			0
$351$		0			0
$352$	0.255158	+	0.441947i	0.0136000	+	0.0235559i
$353$	−1.21579			−0.0647101			−0.0323550	−	0.999476i	$-0.510301\pi$
$353$	−1.21579			−0.0647101			−0.0323550	+	0.999476i	$0.510301\pi$
$354$		0			0
$355$		−	1.16161i		−	0.0616518i
$356$	−1.49988	+	2.59787i	−0.0794936	+	0.137687i
$357$		0			0
$358$	−10.7939	−	18.6955i	−0.570473	−	0.988089i
$359$	14.9882	−	8.65345i	0.791048	−	0.456712i	−0.0492833	−	0.998785i	$-0.515694\pi$
$359$	14.9882	−	8.65345i	0.791048	−	0.456712i	0.840331	+	0.542073i	$0.182360\pi$
$360$		0			0
$361$	10.5723	−	18.3117i	0.556435	−	0.963774i
$362$	3.91464	−	6.78035i	0.205749	−	0.356367i
$363$		0			0
$364$		0			0
$365$	36.8968	+	21.3024i	1.93127	+	1.11502i
$366$		0			0
$367$			28.2090i			1.47250i	0.676710	+	0.736250i	$0.263405\pi$
$367$			28.2090i			1.47250i	−0.676710	+	0.736250i	$0.736595\pi$
$368$	1.16372	+	0.671871i	0.0606628	+	0.0350237i
$369$		0			0
$370$		−	8.28114i		−	0.430516i
$371$		0			0
$372$		0			0
$373$	28.2527			1.46287			0.731435	−	0.681911i	$-0.238851\pi$
$373$	28.2527			1.46287			0.731435	+	0.681911i	$0.238851\pi$
$374$	0.387874	+	0.671818i	0.0200565	+	0.0347389i
$375$		0			0
$376$	23.0875	+	13.3296i	1.19065	+	0.687420i
$377$	−18.3347			−0.944287
$378$		0			0
$379$	14.6447			0.752250			0.376125	−	0.926569i	$-0.377256\pi$
$379$	14.6447			0.752250			0.376125	+	0.926569i	$0.377256\pi$
$380$	−9.24338	−	5.33667i	−0.474175	−	0.273765i
$381$		0			0
$382$	−8.42607	−	14.5944i	−0.431115	−	0.746714i
$383$	−24.7864			−1.26653			−0.633264	−	0.773936i	$-0.718285\pi$
$383$	−24.7864			−1.26653			−0.633264	+	0.773936i	$0.718285\pi$
$384$		0			0
$385$		0			0
$386$			11.8643i			0.603878i
$387$		0			0
$388$	−1.29669	−	0.748643i	−0.0658293	−	0.0380066i
$389$		−	5.12348i		−	0.259771i	−0.991529	−	0.129885i	$-0.958539\pi$
$389$		−	5.12348i		−	0.259771i	0.991529	−	0.129885i	$-0.0414609\pi$
$390$		0			0
$391$	−1.96035	−	1.13181i	−0.0991391	−	0.0572380i
$392$		0			0
$393$		0			0
$394$	11.9195	−	20.6453i	0.600498	−	1.04009i
$395$	6.14056	−	10.6358i	0.308965	−	0.535144i
$396$		0			0
$397$	−1.66358	+	0.960470i	−0.0834929	+	0.0482046i	−0.541165	−	0.840916i	$-0.682017\pi$
$397$	−1.66358	+	0.960470i	−0.0834929	+	0.0482046i	0.457672	+	0.889121i	$0.348683\pi$
$398$	7.67163	+	13.2877i	0.384544	+	0.666050i
$399$		0			0
$400$	3.75729	−	6.50783i	0.187865	−	0.325391i
$401$		−	14.3889i		−	0.718549i	−0.933232	−	0.359274i	$-0.883024\pi$
$401$		−	14.3889i		−	0.718549i	0.933232	−	0.359274i	$-0.116976\pi$
$402$		0			0
$403$	0.510317			0.0254207
$404$	0.887835	+	1.53778i	0.0441714	+	0.0765072i
$405$		0			0
$406$		0			0
$407$	0.336285	−	0.194154i	0.0166690	−	0.00962386i
$408$		0			0
$409$	8.42281	−	4.86291i	0.416481	−	0.240455i	−0.277090	−	0.960844i	$-0.589370\pi$
$409$	8.42281	−	4.86291i	0.416481	−	0.240455i	0.693571	+	0.720389i	$0.256037\pi$
$410$	11.6337	−	6.71675i	0.574550	−	0.331717i
$411$		0			0
$412$	−6.78380	+	3.91663i	−0.334214	+	0.192958i
$413$		0			0
$414$		0			0
$415$	−9.15486	−	15.8567i	−0.449394	−	0.778374i
$416$	−12.7499			−0.625115
$417$		0			0
$418$			1.18583i			0.0580010i
$419$	−14.9512	+	25.8963i	−0.730416	+	1.26512i	0.226289	+	0.974060i	$0.427340\pi$
$419$	−14.9512	+	25.8963i	−0.730416	+	1.26512i	−0.956706	+	0.291058i	$0.905993\pi$
$420$		0			0
$421$	−12.5452	−	21.7290i	−0.611417	−	1.05901i	−0.991002	−	0.133848i	$-0.957266\pi$
$421$	−12.5452	−	21.7290i	−0.611417	−	1.05901i	0.379585	−	0.925157i	$-0.376067\pi$
$422$	−9.25816	+	5.34520i	−0.450680	+	0.260200i
$423$		0			0
$424$	−4.00214	+	6.93190i	−0.194361	+	0.336643i
$425$	−6.32939	+	10.9628i	−0.307021	+	0.531775i
$426$		0			0
$427$		0			0
$428$	−10.0526	−	5.80388i	−0.485912	−	0.280541i
$429$		0			0
$430$		−	22.1077i		−	1.06613i
$431$	−5.53443	−	3.19531i	−0.266584	−	0.153913i	0.360750	−	0.932663i	$-0.382521\pi$
$431$	−5.53443	−	3.19531i	−0.266584	−	0.153913i	−0.627334	+	0.778750i	$0.715854\pi$
$432$		0			0
$433$		−	33.1771i		−	1.59439i	−0.603721	−	0.797196i	$-0.706316\pi$
$433$		−	33.1771i		−	1.59439i	0.603721	−	0.797196i	$-0.293684\pi$
$434$		0			0
$435$		0			0
$436$	7.86400			0.376617
$437$	−1.73012	−	2.99665i	−0.0827627	−	0.143349i
$438$		0			0
$439$	7.32931	+	4.23158i	0.349809	+	0.201962i	0.664601	−	0.747198i	$-0.268601\pi$
$439$	7.32931	+	4.23158i	0.349809	+	0.201962i	−0.314792	+	0.949161i	$0.601935\pi$
$440$	1.37758			0.0656737
$441$		0			0
$442$	−19.3815			−0.921885
$443$	16.1082	+	9.30006i	0.765322	+	0.441859i	0.831203	−	0.555969i	$-0.187652\pi$
$443$	16.1082	+	9.30006i	0.765322	+	0.441859i	−0.0658812	+	0.997827i	$0.520986\pi$
$444$		0			0
$445$	7.17111	+	12.4207i	0.339943	+	0.588799i
$446$	2.67618			0.126721
$447$		0			0
$448$		0			0
$449$			20.3100i			0.958489i	0.877681	+	0.479245i	$0.159089\pi$
$449$			20.3100i			0.958489i	−0.877681	+	0.479245i	$0.840911\pi$
$450$		0			0
$451$	0.545515	+	0.314953i	0.0256873	+	0.0148306i
$452$		−	5.98130i		−	0.281337i
$453$		0			0
$454$	19.1458	+	11.0538i	0.898558	+	0.518783i
$455$		0			0
$456$		0			0
$457$	−5.67830	+	9.83511i	−0.265620	+	0.460067i	−0.967726	−	0.252005i	$-0.918910\pi$
$457$	−5.67830	+	9.83511i	−0.265620	+	0.460067i	0.702106	+	0.712072i	$0.252243\pi$
$458$	8.48272	−	14.6925i	0.396372	−	0.686536i
$459$		0			0
$460$	−0.796727	+	0.459990i	−0.0371476	+	0.0214472i
$461$	−19.4984	−	33.7721i	−0.908129	−	1.57293i	−0.816661	−	0.577117i	$-0.804178\pi$
$461$	−19.4984	−	33.7721i	−0.908129	−	1.57293i	−0.0914676	−	0.995808i	$-0.529156\pi$
$462$		0			0
$463$	−5.03443	+	8.71990i	−0.233970	+	0.405248i	−0.958973	−	0.283498i	$-0.908505\pi$
$463$	−5.03443	+	8.71990i	−0.233970	+	0.405248i	0.725003	+	0.688746i	$0.241838\pi$
$464$			11.4414i			0.531154i
$465$		0			0
$466$	−20.2412			−0.937657
$467$	−1.79665	−	3.11188i	−0.0831389	−	0.144001i	0.821458	−	0.570269i	$-0.193161\pi$
$467$	−1.79665	−	3.11188i	−0.0831389	−	0.144001i	−0.904597	+	0.426269i	$0.859828\pi$
$468$		0			0
$469$		0			0
$470$	25.2630	−	14.5856i	1.16530	−	0.672784i
$471$		0			0
$472$	9.62592	−	5.55753i	0.443069	−	0.255806i
$473$	0.897761	−	0.518322i	0.0412791	−	0.0238325i
$474$		0			0
$475$	−16.7581	+	9.67530i	−0.768915	+	0.443933i
$476$		0			0
$477$		0			0
$478$	−1.32529	−	2.29548i	−0.0606176	−	0.104993i
$479$	−1.62218			−0.0741193			−0.0370597	−	0.999313i	$-0.511799\pi$
$479$	−1.62218			−0.0741193			−0.0370597	+	0.999313i	$0.511799\pi$
$480$		0			0
$481$			9.70160i			0.442355i
$482$	−2.68033	+	4.64247i	−0.122086	+	0.211459i
$483$		0			0
$484$	−3.25729	−	5.64180i	−0.148059	−	0.256445i
$485$	−6.19961	+	3.57935i	−0.281510	+	0.162530i
$486$		0			0
$487$	−3.99786	+	6.92450i	−0.181161	+	0.313779i	−0.942276	−	0.334837i	$-0.891319\pi$
$487$	−3.99786	+	6.92450i	−0.181161	+	0.313779i	0.761115	+	0.648616i	$0.224652\pi$
$488$	−5.17598	+	8.96507i	−0.234306	+	0.405829i
$489$		0			0
$490$		0			0
$491$	−9.30632	−	5.37300i	−0.419988	−	0.242480i	0.275084	−	0.961420i	$-0.411294\pi$
$491$	−9.30632	−	5.37300i	−0.419988	−	0.242480i	−0.695072	+	0.718940i	$0.744628\pi$
$492$		0			0
$493$		−	19.2738i		−	0.868047i
$494$	−25.6579	−	14.8136i	−1.15440	−	0.666494i
$495$		0			0
$496$		−	0.318453i		−	0.0142990i
$497$		0			0
$498$		0			0
$499$	16.9210			0.757488			0.378744	−	0.925501i	$-0.376356\pi$
$499$	16.9210			0.757488			0.378744	+	0.925501i	$0.376356\pi$
$500$	−1.63901	−	2.83884i	−0.0732986	−	0.126957i
$501$		0			0
$502$	−21.7453	−	12.5546i	−0.970538	−	0.560341i
$503$	33.9226			1.51253			0.756267	−	0.654263i	$-0.227021\pi$
$503$	33.9226			1.51253			0.756267	+	0.654263i	$0.227021\pi$
$504$		0			0
$505$	8.48968			0.377786
$506$	0.0885182	+	0.0511060i	0.00393511	+	0.00227194i
$507$		0			0
$508$	3.70681	+	6.42038i	0.164463	+	0.284858i
$509$	10.1361			0.449275			0.224637	−	0.974442i	$-0.427880\pi$
$509$	10.1361			0.449275			0.224637	+	0.974442i	$0.427880\pi$
$510$		0			0
$511$		0			0
$512$			23.0923i			1.02055i
$513$		0			0
$514$	−32.1469	−	18.5600i	−1.41794	−	0.818648i
$515$			37.4517i			1.65032i
$516$		0			0
$517$	1.18460	+	0.683930i	0.0520987	+	0.0300792i
$518$		0			0
$519$		0			0
$520$	−17.2089	+	29.8068i	−0.754662	+	1.30711i
$521$	−15.8493	+	27.4518i	−0.694370	+	1.20268i	0.276022	+	0.961151i	$0.410984\pi$
$521$	−15.8493	+	27.4518i	−0.694370	+	1.20268i	−0.970393	+	0.241533i	$0.922350\pi$
$522$		0			0
$523$	−7.01403	+	4.04955i	−0.306702	+	0.177075i	−0.645450	−	0.763803i	$-0.723330\pi$
$523$	−7.01403	+	4.04955i	−0.306702	+	0.177075i	0.338748	+	0.940877i	$0.389997\pi$
$524$	−2.98125	−	5.16367i	−0.130236	−	0.225576i
$525$		0			0
$526$	−3.95904	+	6.85726i	−0.172622	+	0.298991i
$527$			0.536454i			0.0233683i
$528$		0			0
$529$	22.7017			0.987033
$530$	4.37926	+	7.58509i	0.190223	+	0.329475i
$531$		0			0
$532$		0			0
$533$	−13.6293	+	7.86887i	−0.590350	+	0.340839i
$534$		0			0
$535$	−48.0628	+	27.7490i	−2.07793	+	1.19970i
$536$	−3.53590	+	2.04145i	−0.152727	+	0.0881772i
$537$		0			0
$538$	10.9472	−	6.32036i	0.471967	−	0.272490i
$539$		0			0
$540$		0			0
$541$	−0.608168	−	1.05338i	−0.0261472	−	0.0452883i	0.852656	−	0.522473i	$-0.174991\pi$
$541$	−0.608168	−	1.05338i	−0.0261472	−	0.0452883i	−0.878803	+	0.477185i	$0.841657\pi$
$542$	8.82920			0.379246
$543$		0			0
$544$		−	13.4029i		−	0.574645i
$545$	18.7994	−	32.5614i	0.805276	−	1.39478i
$546$		0			0
$547$	13.1278	+	22.7380i	0.561305	+	0.972209i	0.997383	+	0.0722999i	$0.0230339\pi$
$547$	13.1278	+	22.7380i	0.561305	+	0.972209i	−0.436078	+	0.899909i	$0.643633\pi$
$548$	4.13375	−	2.38662i	0.176585	−	0.101951i
$549$		0			0
$550$	0.285799	−	0.495019i	0.0121865	−	0.0211077i
$551$	14.7312	−	25.5152i	0.627571	−	1.08699i
$552$		0			0
$553$		0			0
$554$	−27.2768	−	15.7482i	−1.15888	−	0.669079i
$555$		0			0
$556$			11.2203i			0.475845i
$557$	23.5708	+	13.6086i	0.998727	+	0.576615i	0.907871	−	0.419249i	$-0.137706\pi$
$557$	23.5708	+	13.6086i	0.998727	+	0.576615i	0.0908558	+	0.995864i	$0.471040\pi$
$558$		0			0
$559$			25.8998i			1.09545i
$560$		0			0
$561$		0			0
$562$	−28.8932			−1.21879
$563$	−4.68017	−	8.10630i	−0.197246	−	0.341640i	0.750389	−	0.660997i	$-0.229866\pi$
$563$	−4.68017	−	8.10630i	−0.197246	−	0.341640i	−0.947634	+	0.319357i	$0.896533\pi$
$564$		0			0
$565$	−24.7660	−	14.2987i	−1.04191	−	0.601549i
$566$	10.2609			0.431296
$567$		0			0
$568$	1.25895			0.0528244
$569$	−30.2424	−	17.4605i	−1.26783	−	0.731980i	−0.293251	−	0.956036i	$-0.594737\pi$
$569$	−30.2424	−	17.4605i	−1.26783	−	0.731980i	−0.974576	+	0.224055i	$0.928070\pi$
$570$		0			0
$571$	0.735987	+	1.27477i	0.0308001	+	0.0533473i	0.881015	−	0.473089i	$-0.156861\pi$
$571$	0.735987	+	1.27477i	0.0308001	+	0.0533473i	−0.850214	+	0.526436i	$0.823528\pi$
$572$	−0.369360			−0.0154437
$573$		0			0
$574$		0			0
$575$			1.66791i			0.0695567i
$576$		0			0
$577$	−16.1251	−	9.30982i	−0.671296	−	0.387573i	0.125272	−	0.992122i	$-0.460020\pi$
$577$	−16.1251	−	9.30982i	−0.671296	−	0.387573i	−0.796567	+	0.604550i	$0.793353\pi$
$578$		−	0.213421i		−	0.00887714i
$579$		0			0
$580$	−6.78380	−	3.91663i	−0.281682	−	0.162629i
$581$		0			0
$582$		0			0
$583$	−0.205346	+	0.355670i	−0.00850458	+	0.0147304i
$584$	−23.0875	+	39.9887i	−0.955367	+	1.65475i
$585$		0			0
$586$	9.03845	−	5.21835i	0.373375	−	0.215568i
$587$	9.28551	+	16.0830i	0.383254	+	0.663816i	0.991525	−	0.129914i	$-0.0414700\pi$
$587$	9.28551	+	16.0830i	0.383254	+	0.663816i	−0.608271	+	0.793729i	$0.708137\pi$
$588$		0			0
$589$	−0.410019	+	0.710174i	−0.0168945	+	0.0292622i
$590$		−	12.1624i		−	0.500719i
$591$		0			0
$592$	6.05408			0.248821
$593$	15.4614	+	26.7800i	0.634924	+	1.09972i	0.986531	+	0.163573i	$0.0523021\pi$
$593$	15.4614	+	26.7800i	0.634924	+	1.09972i	−0.351607	+	0.936148i	$0.614365\pi$
$594$		0			0
$595$		0			0
$596$	9.97588	−	5.75958i	0.408628	−	0.235922i
$597$		0			0
$598$	−2.21156	+	1.27685i	−0.0904375	+	0.0522141i
$599$	11.8741	−	6.85553i	0.485164	−	0.280109i	−0.237402	−	0.971411i	$-0.576296\pi$
$599$	11.8741	−	6.85553i	0.485164	−	0.280109i	0.722566	+	0.691302i	$0.242963\pi$
$600$		0			0
$601$	17.1065	−	9.87644i	0.697788	−	0.402868i	−0.108735	−	0.994071i	$-0.534680\pi$
$601$	17.1065	−	9.87644i	0.697788	−	0.402868i	0.806523	+	0.591203i	$0.201347\pi$
$602$		0			0
$603$		0			0
$604$	0.530641	+	0.919097i	0.0215915	+	0.0373975i
$605$	−31.1470			−1.26631
$606$		0			0
$607$		−	17.9231i		−	0.727477i	−0.931501	−	0.363739i	$-0.881500\pi$
$607$		−	17.9231i		−	0.727477i	0.931501	−	0.363739i	$-0.118500\pi$
$608$	10.2440	−	17.7432i	0.415450	−	0.719581i
$609$		0			0
$610$	5.66372	+	9.80984i	0.229317	+	0.397189i
$611$	−29.5964	+	17.0875i	−1.19734	+	0.691286i
$612$		0			0
$613$	20.7163	−	35.8817i	0.836725	−	1.44925i	−0.0558932	−	0.998437i	$-0.517801\pi$
$613$	20.7163	−	35.8817i	0.836725	−	1.44925i	0.892618	−	0.450813i	$-0.148866\pi$
$614$	−6.62616	+	11.4768i	−0.267410	+	0.463168i
$615$		0			0
$616$		0			0
$617$	−19.9686	−	11.5289i	−0.803904	−	0.464134i	0.0409302	−	0.999162i	$-0.486968\pi$
$617$	−19.9686	−	11.5289i	−0.803904	−	0.464134i	−0.844835	+	0.535028i	$0.820301\pi$
$618$		0			0
$619$		−	1.93816i		−	0.0779014i	−0.999241	−	0.0389507i	$-0.987598\pi$
$619$		−	1.93816i		−	0.0779014i	0.999241	−	0.0389507i	$-0.0124015\pi$
$620$	0.188816	+	0.109013i	0.00758303	+	0.00437806i
$621$		0			0
$622$			19.4558i			0.780106i
$623$		0			0
$624$		0			0
$625$	−30.9430			−1.23772
$626$	−4.86485	−	8.42617i	−0.194439	−	0.336778i
$627$		0			0
$628$	−2.25712	−	1.30315i	−0.0900687	−	0.0520012i
$629$	−10.1985			−0.406640
$630$		0			0
$631$	23.5831			0.938827			0.469414	−	0.882978i	$-0.344465\pi$
$631$	23.5831			0.938827			0.469414	+	0.882978i	$0.344465\pi$
$632$	11.5270	+	6.65514i	0.458521	+	0.264727i
$633$		0			0
$634$	13.5862	+	23.5320i	0.539576	+	0.934574i
$635$	35.4454			1.40661
$636$		0			0
$637$		0			0
$638$			0.870293i			0.0344552i
$639$		0			0
$640$	9.62592	+	5.55753i	0.380498	+	0.219681i
$641$		−	24.8368i		−	0.980996i	−0.871442	−	0.490498i	$-0.836815\pi$
$641$		−	24.8368i		−	0.980996i	0.871442	−	0.490498i	$-0.163185\pi$
$642$		0			0
$643$	−37.9247	−	21.8959i	−1.49561	−	0.863489i	−0.495619	−	0.868540i	$-0.665059\pi$
$643$	−37.9247	−	21.8959i	−1.49561	−	0.863489i	−0.999987	+	0.00505169i	$0.998392\pi$
$644$		0			0
$645$		0			0
$646$	15.5723	−	26.9720i	0.612683	−	1.06120i
$647$	−14.6857	+	25.4363i	−0.577353	+	1.00001i	0.418428	+	0.908250i	$0.362581\pi$
$647$	−14.6857	+	25.4363i	−0.577353	+	1.00001i	−0.995782	+	0.0917553i	$0.970752\pi$
$648$		0			0
$649$	0.493898	−	0.285152i	0.0193872	−	0.0111932i
$650$	7.14048	+	12.3677i	0.280073	+	0.485100i
$651$		0			0
$652$	−1.61323	+	2.79420i	−0.0631789	+	0.109429i
$653$		−	32.4258i		−	1.26892i	−0.772955	−	0.634461i	$-0.781222\pi$
$653$		−	32.4258i		−	1.26892i	0.772955	−	0.634461i	$-0.218778\pi$
$654$		0			0
$655$	−28.5074			−1.11388
$656$	4.91041	+	8.50508i	0.191719	+	0.332067i
$657$		0			0
$658$		0			0
$659$	0.203016	−	0.117211i	0.00790837	−	0.00456590i	−0.496041	−	0.868299i	$-0.665213\pi$
$659$	0.203016	−	0.117211i	0.00790837	−	0.00456590i	0.503949	+	0.863733i	$0.331880\pi$
$660$		0			0
$661$	−3.05138	+	1.76171i	−0.118685	+	0.0685227i	−0.558167	−	0.829728i	$-0.688495\pi$
$661$	−3.05138	+	1.76171i	−0.118685	+	0.0685227i	0.439482	+	0.898251i	$0.355162\pi$
$662$	−19.7841	+	11.4224i	−0.768933	+	0.443943i
$663$		0			0
$664$	17.1855	−	9.92204i	0.666926	−	0.385050i
$665$		0			0
$666$		0			0
$667$	−1.26975	−	2.19927i	−0.0491648	−	0.0851560i
$668$	6.23582			0.241271
$669$		0			0
$670$			4.46763i			0.172600i
$671$	−0.265576	+	0.459990i	−0.0102524	+	0.0177577i
$672$		0			0
$673$	9.16585	+	15.8757i	0.353318	+	0.611964i	0.986829	−	0.161770i	$-0.0517202\pi$
$673$	9.16585	+	15.8757i	0.353318	+	0.611964i	−0.633511	+	0.773734i	$0.718387\pi$
$674$	−4.65925	+	2.69002i	−0.179468	+	0.103616i
$675$		0			0
$676$	0.755832	−	1.30914i	0.0290705	−	0.0503515i
$677$	−16.9260	+	29.3166i	−0.650517	+	1.12673i	0.332480	+	0.943110i	$0.392115\pi$
$677$	−16.9260	+	29.3166i	−0.650517	+	1.12673i	−0.982998	+	0.183619i	$0.941219\pi$
$678$		0			0
$679$		0			0
$680$	−31.3334	−	18.0903i	−1.20158	−	0.693732i
$681$		0			0
$682$		−	0.0242232i		−	0.000927553i
$683$	−24.2733	−	14.0142i	−0.928794	−	0.536239i	−0.0423639	−	0.999102i	$-0.513489\pi$
$683$	−24.2733	−	14.0142i	−0.928794	−	0.536239i	−0.886430	+	0.462863i	$0.846822\pi$
$684$		0			0
$685$		−	22.8214i		−	0.871962i
$686$		0			0
$687$		0			0
$688$	16.1623			0.616180
$689$	−5.13043	−	8.88616i	−0.195454	−	0.338536i
$690$		0			0
$691$	42.7393	+	24.6756i	1.62588	+	0.938703i	0.985304	+	0.170809i	$0.0546381\pi$
$691$	42.7393	+	24.6756i	1.62588	+	0.938703i	0.640577	+	0.767894i	$0.278695\pi$
$692$	−10.4226			−0.396210
$693$		0			0
$694$	10.3566			0.393131
$695$	46.4583	+	26.8227i	1.76226	+	1.01744i
$696$		0			0
$697$	−8.27188	−	14.3273i	−0.313320	−	0.542686i
$698$	−10.7213			−0.405808
$699$		0			0
$700$		0			0
$701$		−	26.3889i		−	0.996696i	−0.866977	−	0.498348i	$-0.833940\pi$
$701$		−	26.3889i		−	0.996696i	0.866977	−	0.498348i	$-0.166060\pi$
$702$		0			0
$703$	−13.5011	−	7.79485i	−0.509202	−	0.293988i
$704$			1.38181i			0.0520791i
$705$		0			0
$706$	−1.24867	−	0.720920i	−0.0469943	−	0.0271322i
$707$		0			0
$708$		0			0
$709$	5.35661	−	9.27792i	0.201172	−	0.348440i	−0.747735	−	0.663998i	$-0.768858\pi$
$709$	5.35661	−	9.27792i	0.201172	−	0.348440i	0.948906	+	0.315558i	$0.102192\pi$
$710$	0.688791	−	1.19302i	0.0258499	−	0.0447733i
$711$		0			0
$712$	−13.4616	+	7.77204i	−0.504494	+	0.291270i
$713$	0.0353413	+	0.0612130i	0.00132354	+	0.00229244i
$714$		0			0
$715$	−0.882977	+	1.52936i	−0.0330215	+	0.0571949i
$716$			10.8051i			0.403805i
$717$		0			0
$718$	20.5247			0.765975
$719$	8.78970	+	15.2242i	0.327801	+	0.567767i	0.982075	−	0.188490i	$-0.0603592\pi$
$719$	8.78970	+	15.2242i	0.327801	+	0.567767i	−0.654275	+	0.756257i	$0.727026\pi$
$720$		0			0
$721$		0			0
$722$	21.7163	−	12.5379i	0.808198	−	0.466614i
$723$		0			0
$724$	−3.39370	+	1.95935i	−0.126126	+	0.0728188i
$725$	−12.2989	+	7.10079i	−0.456771	+	0.263717i
$726$		0			0
$727$	−43.4695	+	25.0971i	−1.61220	+	0.930802i	−0.623336	+	0.781954i	$0.714223\pi$
$727$	−43.4695	+	25.0971i	−1.61220	+	0.930802i	−0.988860	+	0.148847i	$0.952444\pi$
$728$		0			0
$729$		0			0
$730$	25.2630	+	43.7569i	0.935027	+	1.61951i
$731$	−27.2263			−1.00700
$732$		0			0
$733$			39.9084i			1.47405i	0.675865	+	0.737025i	$0.263770\pi$
$733$			39.9084i			1.47405i	−0.675865	+	0.737025i	$0.736230\pi$
$734$	−16.7269	+	28.9719i	−0.617402	+	1.06937i
$735$		0			0
$736$	−0.882977	−	1.52936i	−0.0325470	−	0.0563730i
$737$	−0.181424	+	0.104745i	−0.00668284	+	0.00385834i
$738$		0			0
$739$	−15.1716	+	26.2780i	−0.558096	+	0.966650i	0.439560	+	0.898213i	$0.355135\pi$
$739$	−15.1716	+	26.2780i	−0.558096	+	0.966650i	−0.997655	+	0.0684369i	$0.978199\pi$
$740$	−2.07244	+	3.58956i	−0.0761843	+	0.131955i
$741$		0			0
$742$		0			0
$743$	39.5861	+	22.8550i	1.45227	+	0.838470i	0.998610	−	0.0527041i	$-0.0167840\pi$
$743$	39.5861	+	22.8550i	1.45227	+	0.838470i	0.453662	+	0.891174i	$0.350117\pi$
$744$		0			0
$745$		−	55.0744i		−	2.01777i
$746$	29.0167	+	16.7528i	1.06238	+	0.613364i
$747$		0			0
$748$		−	0.388278i		−	0.0141968i
$749$		0			0
$750$		0			0
$751$	12.1551			0.443544			0.221772	−	0.975099i	$-0.428816\pi$
$751$	12.1551			0.443544			0.221772	+	0.975099i	$0.428816\pi$
$752$	10.6631	+	18.4690i	0.388843	+	0.673496i
$753$		0			0
$754$	−18.8305	−	10.8718i	−0.685768	−	0.395928i
$755$	5.07411			0.184666
$756$		0			0
$757$	−9.71614			−0.353139			−0.176570	−	0.984288i	$-0.556500\pi$
$757$	−9.71614			−0.353139			−0.176570	+	0.984288i	$0.556500\pi$
$758$	15.0408	+	8.68379i	0.546305	+	0.315409i
$759$		0			0
$760$	−27.6534	−	47.8971i	−1.00309	−	1.73741i
$761$	38.8349			1.40776			0.703882	−	0.710317i	$-0.251448\pi$
$761$	38.8349			1.40776			0.703882	+	0.710317i	$0.251448\pi$
$762$		0			0
$763$		0			0
$764$			8.43483i			0.305161i
$765$		0			0
$766$	−25.4567	−	14.6974i	−0.919788	−	0.531040i
$767$			14.2486i			0.514489i
$768$		0			0
$769$	9.42879	+	5.44371i	0.340011	+	0.196305i	0.660277	−	0.751022i	$-0.270439\pi$
$769$	9.42879	+	5.44371i	0.340011	+	0.196305i	−0.320266	+	0.947328i	$0.603772\pi$
$770$		0			0
$771$		0			0
$772$	2.96916	−	5.14274i	0.106863	−	0.185091i
$773$	18.6668	−	32.3319i	0.671400	−	1.16290i	−0.306108	−	0.951997i	$-0.599027\pi$
$773$	18.6668	−	32.3319i	0.671400	−	1.16290i	0.977507	−	0.210901i	$-0.0676398\pi$
$774$		0			0
$775$	0.342320	−	0.197639i	0.0122965	−	0.00709939i
$776$	−3.87930	−	6.71914i	−0.139259	−	0.241203i
$777$		0			0
$778$	3.03803	−	5.26203i	0.108919	−	0.188653i
$779$		−	25.2893i		−	0.906083i
$780$		0			0
$781$	0.0645958			0.00231142
$782$	−1.34224	−	2.32483i	−0.0479984	−	0.0831357i
$783$		0			0
$784$		0			0
$785$	−10.7915	+	6.23049i	−0.385166	+	0.222376i
$786$		0			0
$787$	−15.4554	+	8.92315i	−0.550924	+	0.318076i	−0.749495	−	0.662011i	$-0.769703\pi$
$787$	−15.4554	+	8.92315i	−0.550924	+	0.318076i	0.198571	+	0.980087i	$0.436370\pi$
$788$	−10.3334	+	5.96597i	−0.368111	+	0.212529i
$789$		0			0
$790$	12.6132	−	7.28225i	0.448759	−	0.259091i
$791$		0			0
$792$		0			0
$793$	−6.63521	−	11.4925i	−0.235623	−	0.408111i
$794$	−2.27809			−0.0808465
$795$		0			0
$796$		−	7.67961i		−	0.272197i
$797$	5.74854	−	9.95676i	0.203624	−	0.352687i	−0.746070	−	0.665868i	$-0.768061\pi$
$797$	5.74854	−	9.95676i	0.203624	−	0.352687i	0.949693	+	0.313181i	$0.101395\pi$
$798$		0			0
$799$	−17.9626	−	31.1122i	−0.635473	−	1.10067i
$800$	−8.55262	+	4.93786i	−0.302381	+	0.174580i
$801$		0			0
$802$	8.53210	−	14.7780i	0.301279	−	0.521831i
$803$	−1.18460	+	2.05179i	−0.0418037	+	0.0724061i
$804$		0			0
$805$		0			0
$806$	0.524117	+	0.302599i	0.0184612	+	0.0106586i
$807$		0			0
$808$			9.20112i			0.323694i
$809$	−11.4267	−	6.59723i	−0.401743	−	0.231946i	0.285493	−	0.958381i	$-0.407843\pi$
$809$	−11.4267	−	6.59723i	−0.401743	−	0.231946i	−0.687236	+	0.726434i	$0.741176\pi$
$810$		0			0
$811$			46.5800i			1.63565i	0.575469	+	0.817823i	$0.304819\pi$
$811$			46.5800i			1.63565i	−0.575469	+	0.817823i	$0.695181\pi$
$812$		0			0
$813$		0			0
$814$	0.460505			0.0161407
$815$	7.71304	+	13.3594i	0.270176	+	0.467958i
$816$		0			0
$817$	−36.0431	−	20.8095i	−1.26099	−	0.728031i
$818$	11.5341			0.403280
$819$		0			0
$820$	−6.72373			−0.234803
$821$	34.3623	+	19.8391i	1.19925	+	0.692390i	0.960389	−	0.278663i	$-0.0898913\pi$
$821$	34.3623	+	19.8391i	1.19925	+	0.692390i	0.238865	+	0.971053i	$0.423225\pi$
$822$		0			0
$823$	19.6156	+	33.9751i	0.683755	+	1.18430i	0.973826	+	0.227294i	$0.0729878\pi$
$823$	19.6156	+	33.9751i	0.683755	+	1.18430i	−0.290071	+	0.957005i	$0.593679\pi$
$824$	−40.5902			−1.41403
$825$		0			0
$826$		0			0
$827$			21.0827i			0.733118i	0.930395	+	0.366559i	$0.119464\pi$
$827$			21.0827i			0.733118i	−0.930395	+	0.366559i	$0.880536\pi$
$828$		0			0
$829$	11.5407	+	6.66304i	0.400826	+	0.231417i	0.686840	−	0.726808i	$-0.258997\pi$
$829$	11.5407	+	6.66304i	0.400826	+	0.231417i	−0.286014	+	0.958225i	$0.592331\pi$
$830$		−	21.7140i		−	0.753703i
$831$		0			0
$832$	−29.8983	−	17.2618i	−1.03654	−	0.598446i
$833$		0			0
$834$		0			0
$835$	14.9071	−	25.8198i	0.515881	−	0.893533i
$836$	0.296766	−	0.514014i	0.0102639	−	0.0177776i
$837$		0			0
$838$	−30.7111	+	17.7311i	−1.06090	+	0.612510i
$839$	8.39768	+	14.5452i	0.289920	+	0.502156i	0.973790	−	0.227447i	$-0.0730379\pi$
$839$	8.39768	+	14.5452i	0.289920	+	0.502156i	−0.683870	+	0.729604i	$0.739705\pi$
$840$		0			0
$841$	−3.68862	+	6.38888i	−0.127194	+	0.220306i
$842$		−	29.7554i		−	1.02544i
$843$		0			0
$844$	5.35076			0.184181
$845$	−3.61372	−	6.25915i	−0.124316	−	0.215321i
$846$		0			0
$847$		0			0
$848$	−5.54523	+	3.20154i	−0.190424	+	0.109941i
$849$		0			0
$850$	−13.0011	+	7.50619i	−0.445934	+	0.257460i
$851$	−1.16372	+	0.671871i	−0.0398916	+	0.0230315i
$852$		0			0
$853$	35.5011	−	20.4966i	1.21554	−	0.701790i	0.251576	−	0.967838i	$-0.419051\pi$
$853$	35.5011	−	20.4966i	1.21554	−	0.701790i	0.963960	+	0.266048i	$0.0857179\pi$
$854$		0			0
$855$		0			0
$856$	−30.0744	−	52.0904i	−1.02792	−	1.78041i
$857$	−41.7436			−1.42593			−0.712967	−	0.701198i	$-0.752649\pi$
$857$	−41.7436			−1.42593			−0.712967	+	0.701198i	$0.752649\pi$
$858$		0			0
$859$			27.7682i			0.947437i	0.880676	+	0.473719i	$0.157089\pi$
$859$			27.7682i			0.947437i	−0.880676	+	0.473719i	$0.842911\pi$
$860$	−5.53267	+	9.58286i	−0.188662	+	0.326773i
$861$		0			0
$862$	−3.78940	−	6.56343i	−0.129067	−	0.223551i
$863$	−39.4985	+	22.8045i	−1.34455	+	0.776274i	−0.987471	−	0.157802i	$-0.949559\pi$
$863$	−39.4985	+	22.8045i	−1.34455	+	0.776274i	−0.357075	+	0.934076i	$0.616226\pi$
$864$		0			0
$865$	−24.9159	+	43.1557i	−0.847168	+	1.46734i
$866$	19.6728	−	34.0743i	0.668510	−	1.15789i
$867$		0			0
$868$		0			0
$869$	0.591443	+	0.341470i	0.0200633	+	0.0115836i
$870$		0			0
$871$		−	5.23396i		−	0.177346i
$872$	35.2901	+	20.3747i	1.19507	+	0.689975i
$873$		0			0
$874$		−	4.10358i		−	0.138806i
$875$		0			0
$876$		0			0
$877$	17.6874			0.597259			0.298630	−	0.954369i	$-0.403470\pi$
$877$	17.6874			0.597259			0.298630	+	0.954369i	$0.403470\pi$
$878$	5.01834	+	8.69203i	0.169361	+	0.293342i
$879$		0			0
$880$	0.954367	+	0.551004i	0.0321717	+	0.0185743i
$881$	−11.6169			−0.391384			−0.195692	−	0.980665i	$-0.562695\pi$
$881$	−11.6169			−0.391384			−0.195692	+	0.980665i	$0.562695\pi$
$882$		0			0
$883$	−35.5480			−1.19629			−0.598143	−	0.801389i	$-0.704095\pi$
$883$	−35.5480			−1.19629			−0.598143	+	0.801389i	$0.704095\pi$
$884$	8.40116	+	4.85041i	0.282562	+	0.163137i
$885$		0			0
$886$	11.0292	+	19.1031i	0.370532	+	0.641781i
$887$	−24.5501			−0.824313			−0.412156	−	0.911113i	$-0.635224\pi$
$887$	−24.5501			−0.824313			−0.412156	+	0.911113i	$0.635224\pi$
$888$		0			0
$889$		0			0
$890$			17.0088i			0.570136i
$891$		0			0
$892$	−1.16002	−	0.669741i	−0.0388405	−	0.0224246i
$893$		−	54.9164i		−	1.83771i
$894$		0			0
$895$	44.7392	+	25.8302i	1.49547	+	0.863408i
$896$		0			0
$897$		0			0
$898$	−12.0431	+	20.8593i	−0.401883	+	0.696082i
$899$	−0.300917	+	0.521203i	−0.0100361	+	0.0173831i
$900$		0			0
$901$	9.34128	−	5.39319i	0.311203	−	0.179673i
$902$	0.373511	+	0.646940i	0.0124366	+	0.0215407i
$903$		0			0
$904$	15.4969	−	26.8414i	0.515419	−	0.892731i
$905$			18.7358i			0.622799i
$906$		0			0
$907$	36.9004			1.22526			0.612628	−	0.790371i	$-0.290112\pi$
$907$	36.9004			1.22526			0.612628	+	0.790371i	$0.290112\pi$
$908$	−5.53267	−	9.58286i	−0.183608	−	0.318018i
$909$		0			0
$910$		0			0
$911$	34.4774	−	19.9056i	1.14229	−	0.659500i	0.195292	−	0.980745i	$-0.437435\pi$
$911$	34.4774	−	19.9056i	1.14229	−	0.659500i	0.946996	+	0.321245i	$0.104101\pi$
$912$		0			0
$913$	0.881773	−	0.509092i	0.0291824	−	0.0168485i
$914$	−11.6637	+	6.73405i	−0.385801	+	0.222743i
$915$		0			0
$916$	−7.35389	+	4.24577i	−0.242979	+	0.140284i
$917$		0			0
$918$		0			0
$919$	28.4363	+	49.2531i	0.938026	+	1.62471i	0.769147	+	0.639072i	$0.220681\pi$
$919$	28.4363	+	49.2531i	0.938026	+	1.62471i	0.168879	+	0.985637i	$0.445985\pi$
$920$	−4.76713			−0.157168
$921$		0			0
$922$		−	46.2472i		−	1.52307i
$923$	−0.806939	+	1.39766i	−0.0265607	+	0.0460045i
$924$		0			0
$925$	3.75729	+	6.50783i	0.123539	+	0.213976i
$926$	−10.3412	+	5.97047i	−0.339831	+	0.196202i
$927$		0			0
$928$	7.51819	−	13.0219i	0.246797	−	0.427464i
$929$	−22.8885	+	39.6440i	−0.750946	+	1.30068i	0.196419	+	0.980520i	$0.437069\pi$
$929$	−22.8885	+	39.6440i	−0.750946	+	1.30068i	−0.947365	+	0.320156i	$0.896265\pi$
$930$		0			0
$931$		0			0
$932$	8.77383	+	5.06557i	0.287396	+	0.165928i
$933$		0			0
$934$		−	4.26138i		−	0.139437i
$935$	−1.60769	−	0.928200i	−0.0525771	−	0.0303554i
$936$		0			0
$937$			24.0003i			0.784054i	0.919954	+	0.392027i	$0.128226\pi$
$937$			24.0003i			0.784054i	−0.919954	+	0.392027i	$0.871774\pi$
$938$		0			0
$939$		0			0
$940$	−14.6008			−0.476225
$941$	1.64316	+	2.84603i	0.0535654	+	0.0927780i	0.891565	−	0.452893i	$-0.149608\pi$
$941$	1.64316	+	2.84603i	0.0535654	+	0.0927780i	−0.837999	+	0.545671i	$0.816275\pi$
$942$		0			0
$943$	−1.88776	−	1.08990i	−0.0614738	−	0.0354919i
$944$	8.89158			0.289396
$945$		0			0
$946$	1.22938			0.0399707
$947$	−25.9420	−	14.9776i	−0.843002	−	0.486707i	0.0152815	−	0.999883i	$-0.495136\pi$
$947$	−25.9420	−	14.9776i	−0.843002	−	0.486707i	−0.858284	+	0.513176i	$0.828469\pi$
$948$		0			0
$949$	−29.5964	−	51.2624i	−0.960739	−	1.66405i
$950$	−22.9484			−0.744544
$951$		0			0
$952$		0			0
$953$		−	16.0580i		−	0.520169i	−0.965586	−	0.260084i	$-0.916250\pi$
$953$		−	16.0580i		−	0.520169i	0.965586	−	0.260084i	$-0.0837504\pi$
$954$		0			0
$955$	34.9250	+	20.1639i	1.13015	+	0.652490i
$956$			1.32667i			0.0429076i
$957$		0			0
$958$	−1.66605	−	0.961893i	−0.0538275	−	0.0310773i
$959$		0			0
$960$		0			0
$961$	−15.4916	+	26.8323i	−0.499730	+	0.865557i
$962$	−5.75269	+	9.96395i	−0.185474	+	0.321251i
$963$		0			0
$964$	2.32365	−	1.34156i	0.0748397	−	0.0432087i
$965$	−14.1959	−	24.5881i	−0.456983	−	0.791518i
$966$		0			0
$967$	25.0275	−	43.3489i	0.804831	−	1.39401i	−0.111574	−	0.993756i	$-0.535589\pi$
$967$	25.0275	−	43.3489i	0.804831	−	1.39401i	0.916405	−	0.400252i	$-0.131077\pi$
$968$		−	33.7571i		−	1.08499i
$969$		0			0
$970$	−8.48968			−0.272587
$971$	0.520938	+	0.902292i	0.0167177	+	0.0289559i	0.874263	−	0.485452i	$-0.161345\pi$
$971$	0.520938	+	0.902292i	0.0167177	+	0.0289559i	−0.857546	+	0.514408i	$0.828012\pi$
$972$		0			0
$973$		0			0
$974$	−8.21195	+	4.74117i	−0.263128	+	0.151917i
$975$		0			0
$976$	−7.17167	+	4.14057i	−0.229560	+	0.132536i
$977$	21.1765	−	12.2262i	0.677495	−	0.391152i	−0.121416	−	0.992602i	$-0.538743\pi$
$977$	21.1765	−	12.2262i	0.677495	−	0.391152i	0.798910	+	0.601450i	$0.205410\pi$
$978$		0			0
$979$	−0.690703	+	0.398777i	−0.0220750	+	0.0127450i
$980$		0			0
$981$		0			0
$982$	−6.37199	−	11.0366i	−0.203338	−	0.352192i
$983$	56.1576			1.79115			0.895575	−	0.444911i	$-0.146765\pi$
$983$	56.1576			1.79115			0.895575	+	0.444911i	$0.146765\pi$
$984$		0			0
$985$			57.0480i			1.81770i
$986$	11.4286	−	19.7950i	0.363962	−	0.630400i
$987$		0			0
$988$	7.41449	+	12.8423i	0.235886	+	0.408567i
$989$	−3.10671	+	1.79366i	−0.0987875	+	0.0570350i
$990$		0			0
$991$	−9.11390	+	15.7857i	−0.289513	+	0.501451i	−0.973693	−	0.227862i	$-0.926827\pi$
$991$	−9.11390	+	15.7857i	−0.289513	+	0.501451i	0.684181	+	0.729312i	$0.260160\pi$
$992$	−0.209256	+	0.362443i	−0.00664390	+	0.0115076i
$993$		0			0
$994$		0			0
$995$	−31.7979	−	18.3586i	−1.00806	−	0.582005i
$996$		0			0
$997$			34.4328i			1.09050i	0.838274	+	0.545249i	$0.183565\pi$
$997$			34.4328i			1.09050i	−0.838274	+	0.545249i	$0.816435\pi$
$998$	17.3786	+	10.0335i	0.550110	+	0.317606i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.c.962.5		12
3.2	odd	2		441.2.s.c.374.2		12
7.2	even	3		1323.2.i.c.1097.2		12
7.3	odd	6		189.2.o.a.125.1		12
7.4	even	3		189.2.o.a.125.2		12
7.5	odd	6		1323.2.i.c.1097.1		12
7.6	odd	2	inner	1323.2.s.c.962.6		12
9.2	odd	6		1323.2.i.c.521.5		12
9.7	even	3		441.2.i.c.227.2		12
21.2	odd	6		441.2.i.c.68.5		12
21.5	even	6		441.2.i.c.68.6		12
21.11	odd	6		63.2.o.a.41.6	yes	12
21.17	even	6		63.2.o.a.41.5	yes	12
21.20	even	2		441.2.s.c.374.1		12
28.3	even	6		3024.2.cc.a.881.1		12
28.11	odd	6		3024.2.cc.a.881.6		12
63.2	odd	6	inner	1323.2.s.c.656.6		12
63.4	even	3		567.2.c.c.566.3		12
63.11	odd	6		189.2.o.a.62.1		12
63.16	even	3		441.2.s.c.362.1		12
63.20	even	6		1323.2.i.c.521.6		12
63.25	even	3		63.2.o.a.20.5	✓	12
63.31	odd	6		567.2.c.c.566.4		12
63.32	odd	6		567.2.c.c.566.10		12
63.34	odd	6		441.2.i.c.227.1		12
63.38	even	6		189.2.o.a.62.2		12
63.47	even	6	inner	1323.2.s.c.656.5		12
63.52	odd	6		63.2.o.a.20.6	yes	12
63.59	even	6		567.2.c.c.566.9		12
63.61	odd	6		441.2.s.c.362.2		12
84.11	even	6		1008.2.cc.a.545.3		12
84.59	odd	6		1008.2.cc.a.545.4		12
252.11	even	6		3024.2.cc.a.2897.1		12
252.115	even	6		1008.2.cc.a.209.3		12
252.151	odd	6		1008.2.cc.a.209.4		12
252.227	odd	6		3024.2.cc.a.2897.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.5	✓	12	63.25	even	3
63.2.o.a.20.6	yes	12	63.52	odd	6
63.2.o.a.41.5	yes	12	21.17	even	6
63.2.o.a.41.6	yes	12	21.11	odd	6
189.2.o.a.62.1		12	63.11	odd	6
189.2.o.a.62.2		12	63.38	even	6
189.2.o.a.125.1		12	7.3	odd	6
189.2.o.a.125.2		12	7.4	even	3
441.2.i.c.68.5		12	21.2	odd	6
441.2.i.c.68.6		12	21.5	even	6
441.2.i.c.227.1		12	63.34	odd	6
441.2.i.c.227.2		12	9.7	even	3
441.2.s.c.362.1		12	63.16	even	3
441.2.s.c.362.2		12	63.61	odd	6
441.2.s.c.374.1		12	21.20	even	2
441.2.s.c.374.2		12	3.2	odd	2
567.2.c.c.566.3		12	63.4	even	3
567.2.c.c.566.4		12	63.31	odd	6
567.2.c.c.566.9		12	63.59	even	6
567.2.c.c.566.10		12	63.32	odd	6
1008.2.cc.a.209.3		12	252.115	even	6
1008.2.cc.a.209.4		12	252.151	odd	6
1008.2.cc.a.545.3		12	84.11	even	6
1008.2.cc.a.545.4		12	84.59	odd	6
1323.2.i.c.521.5		12	9.2	odd	6
1323.2.i.c.521.6		12	63.20	even	6
1323.2.i.c.1097.1		12	7.5	odd	6
1323.2.i.c.1097.2		12	7.2	even	3
1323.2.s.c.656.5		12	63.47	even	6	inner
1323.2.s.c.656.6		12	63.2	odd	6	inner
1323.2.s.c.962.5		12	1.1	even	1	trivial
1323.2.s.c.962.6		12	7.6	odd	2	inner
3024.2.cc.a.881.1		12	28.3	even	6
3024.2.cc.a.881.6		12	28.11	odd	6
3024.2.cc.a.2897.1		12	252.11	even	6
3024.2.cc.a.2897.6		12	252.227	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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02704 + 0.592963i) q^{2} +(-0.296790 - 0.514055i) q^{4} -2.83797 q^{5} -3.07579i q^{8} +O(q^{10})\)	\(q+(1.02704 + 0.592963i) q^{2} +(-0.296790 - 0.514055i) q^{4} -2.83797 q^{5} -3.07579i q^{8} +(-2.91472 - 1.68281i) q^{10} -0.157816i q^{11} +(3.41468 + 1.97146i) q^{13} +(1.23025 - 2.13086i) q^{16} +(-2.07244 + 3.58956i) q^{17} +(-5.48711 + 3.16799i) q^{19} +(0.842281 + 1.45887i) q^{20} +(0.0935793 - 0.162084i) q^{22} +0.546125i q^{23} +3.05408 q^{25} +(2.33801 + 4.04955i) q^{26} +(-4.02704 + 2.32501i) q^{29} +(0.112086 - 0.0647129i) q^{31} +(-2.80039 + 1.61680i) q^{32} +(-4.25696 + 2.45776i) q^{34} +(1.23025 + 2.13086i) q^{37} -7.51399 q^{38} +8.72902i q^{40} +(-1.99569 + 3.45664i) q^{41} +(3.28434 + 5.68864i) q^{43} +(-0.0811263 + 0.0468383i) q^{44} +(-0.323832 + 0.560893i) q^{46} +(-4.33370 + 7.50619i) q^{47} +(3.13667 + 1.81096i) q^{50} -2.34044i q^{52} +(-2.25370 - 1.30117i) q^{53} +0.447879i q^{55} -5.51459 q^{58} +(1.80686 + 3.12957i) q^{59} +(-2.91472 - 1.68281i) q^{61} +0.153489 q^{62} -8.75583 q^{64} +(-9.69076 - 5.59496i) q^{65} +(-0.663715 - 1.14959i) q^{67} +2.46031 q^{68} +0.409310i q^{71} +(-13.0011 - 7.50619i) q^{73} +2.91798i q^{74} +(3.25704 + 1.88045i) q^{76} +(-2.16372 + 3.74766i) q^{79} +(-3.49142 + 6.04732i) q^{80} +(-4.09932 + 2.36674i) q^{82} +(3.22585 + 5.58733i) q^{83} +(5.88151 - 10.1871i) q^{85} +7.78996i q^{86} -0.485411 q^{88} +(-2.52684 - 4.37662i) q^{89} +(0.280738 - 0.162084i) q^{92} +(-8.90179 + 5.13945i) q^{94} +(15.5723 - 8.99066i) q^{95} +(2.18452 - 1.26123i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 2 q^{4}+O(q^{10}) \) 12 * q - 6 * q^2 + 2 * q^4	\( 12 q - 6 q^{2} + 2 q^{4} + 2 q^{16} - 10 q^{22} - 30 q^{29} - 12 q^{32} + 2 q^{37} - 10 q^{43} + 54 q^{44} + 20 q^{46} + 36 q^{50} - 12 q^{53} - 4 q^{58} + 16 q^{64} - 78 q^{65} + 12 q^{67} - 6 q^{79} - 6 q^{85} - 68 q^{88} - 30 q^{92} + 72 q^{95}+O(q^{100}) \) 12 * q - 6 * q^2 + 2 * q^4 + 2 * q^16 - 10 * q^22 - 30 * q^29 - 12 * q^32 + 2 * q^37 - 10 * q^43 + 54 * q^44 + 20 * q^46 + 36 * q^50 - 12 * q^53 - 4 * q^58 + 16 * q^64 - 78 * q^65 + 12 * q^67 - 6 * q^79 - 6 * q^85 - 68 * q^88 - 30 * q^92 + 72 * q^95

Introduction

L-functions

Modular forms

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Representations

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Database

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