LMFDB - Embedded newform 1323.2.i.c.1097.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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, 1]))

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (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			1097.1
Root			$1.82904 - 1.05600i$ of defining polynomial
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.c.521.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.18593i q^{2} +0.593579 q^{4} +(-1.41899 - 2.45776i) q^{5} -3.07579i q^{8} +O(q^{10})$	\(q-1.18593i q^{2} +0.593579 q^{4} +(-1.41899 - 2.45776i) q^{5} -3.07579i q^{8} +(-2.91472 + 1.68281i) q^{10} +(0.136673 + 0.0789082i) q^{11} +(-3.41468 - 1.97146i) q^{13} -2.46050 q^{16} +(2.07244 + 3.58956i) q^{17} +(-5.48711 - 3.16799i) q^{19} +(-0.842281 - 1.45887i) q^{20} +(0.0935793 - 0.162084i) q^{22} +(0.472958 - 0.273062i) q^{23} +(-1.52704 + 2.64491i) q^{25} +(-2.33801 + 4.04955i) q^{26} +(-4.02704 + 2.32501i) q^{29} -0.129426i q^{31} -3.23361i q^{32} +(4.25696 - 2.45776i) q^{34} +(1.23025 - 2.13086i) q^{37} +(-3.75700 + 6.50731i) q^{38} +(-7.55955 + 4.36451i) q^{40} +(1.99569 - 3.45664i) q^{41} +(3.28434 + 5.68864i) q^{43} +(0.0811263 + 0.0468383i) q^{44} +(-0.323832 - 0.560893i) q^{46} -8.66741 q^{47} +(3.13667 + 1.81096i) q^{50} +(-2.02688 - 1.17022i) q^{52} +(2.25370 - 1.30117i) q^{53} -0.447879i q^{55} +(2.75729 + 4.77577i) q^{58} +3.61372 q^{59} -3.36562i q^{61} -0.153489 q^{62} -8.75583 q^{64} +11.1899i q^{65} +1.32743 q^{67} +(1.23016 + 2.13069i) q^{68} +0.409310i q^{71} +(-13.0011 + 7.50619i) q^{73} +(-2.52704 - 1.45899i) q^{74} +(-3.25704 - 1.88045i) q^{76} +4.32743 q^{79} +(3.49142 + 6.04732i) q^{80} +(-4.09932 - 2.36674i) q^{82} +(-3.22585 - 5.58733i) q^{83} +(5.88151 - 10.1871i) q^{85} +(6.74630 - 3.89498i) q^{86} +(0.242705 - 0.420378i) q^{88} +(2.52684 - 4.37662i) q^{89} +(0.280738 - 0.162084i) q^{92} +10.2789i q^{94} +17.9813i q^{95} +(-2.18452 + 1.26123i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4}+O(q^{10}) $ 12 * q - 4 * q^4	$ 12 q - 4 q^{4} - 4 q^{16} - 10 q^{22} + 24 q^{23} - 30 q^{29} + 2 q^{37} - 10 q^{43} - 54 q^{44} + 20 q^{46} + 36 q^{50} + 12 q^{53} + 2 q^{58} + 16 q^{64} - 24 q^{67} - 12 q^{74} + 12 q^{79} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 30 q^{92}+O(q^{100}) $ 12 * q - 4 * q^4 - 4 * q^16 - 10 * q^22 + 24 * q^23 - 30 * q^29 + 2 * q^37 - 10 * q^43 - 54 * q^44 + 20 * q^46 + 36 * q^50 + 12 * q^53 + 2 * q^58 + 16 * q^64 - 24 * q^67 - 12 * q^74 + 12 * q^79 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 30 * q^92

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.18593i		−	0.838576i	−0.907853	−	0.419288i	$-0.862280\pi$
$2$		−	1.18593i		−	0.838576i	0.907853	−	0.419288i	$-0.137720\pi$
$3$		0			0
$3$		0			0
$4$	0.593579			0.296790
$5$	−1.41899	−	2.45776i	−0.634590	−	1.09914i	−0.986602	−	0.163146i	$-0.947836\pi$
$5$	−1.41899	−	2.45776i	−0.634590	−	1.09914i	0.352012	−	0.935995i	$-0.385498\pi$
$6$		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
$11$	0.136673	+	0.0789082i	0.0412085	+	0.0237917i	0.520463	−	0.853884i	$-0.325759\pi$
$11$	0.136673	+	0.0789082i	0.0412085	+	0.0237917i	−0.479254	+	0.877676i	$0.659093\pi$
$12$		0			0
$13$	−3.41468	−	1.97146i	−0.947061	−	0.546786i	−0.0548943	−	0.998492i	$-0.517482\pi$
$13$	−3.41468	−	1.97146i	−0.947061	−	0.546786i	−0.892167	+	0.451706i	$0.850816\pi$
$14$		0			0
$15$		0			0
$16$	−2.46050			−0.615126
$17$	2.07244	+	3.58956i	0.502640	+	0.870597i	0.999995	+	0.00305055i	$0.000971021\pi$
$17$	2.07244	+	3.58956i	0.502640	+	0.870597i	−0.497356	+	0.867547i	$0.665696\pi$
$18$		0			0
$19$	−5.48711	−	3.16799i	−1.25883	−	0.726786i	−0.285983	−	0.958235i	$-0.592320\pi$
$19$	−5.48711	−	3.16799i	−1.25883	−	0.726786i	−0.972847	+	0.231449i	$0.925653\pi$
$20$	−0.842281	−	1.45887i	−0.188340	−	0.326214i
$21$		0			0
$22$	0.0935793	−	0.162084i	0.0199512	−	0.0345565i
$23$	0.472958	−	0.273062i	0.0986185	−	0.0569374i	−0.449880	−	0.893089i	$-0.648533\pi$
$23$	0.472958	−	0.273062i	0.0986185	−	0.0569374i	0.548498	+	0.836152i	$0.315200\pi$
$24$		0			0
$25$	−1.52704	+	2.64491i	−0.305408	+	0.528983i
$26$	−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
$31$		−	0.129426i		−	0.0232456i	−0.999932	−	0.0116228i	$-0.996300\pi$
$31$		−	0.129426i		−	0.0232456i	0.999932	−	0.0116228i	$-0.00369973\pi$
$32$		−	3.23361i		−	0.571627i
$33$		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	−0.747002	−	0.664822i	$-0.768507\pi$
$37$	1.23025	−	2.13086i	0.202252	−	0.350311i	0.949254	+	0.314511i	$0.101841\pi$
$38$	−3.75700	+	6.50731i	−0.609465	+	1.05563i
$39$		0			0
$40$	−7.55955	+	4.36451i	−1.19527	+	0.690089i
$41$	1.99569	−	3.45664i	0.311675	−	0.539836i	−0.667050	−	0.745013i	$-0.732443\pi$
$41$	1.99569	−	3.45664i	0.311675	−	0.539836i	0.978725	+	0.205176i	$0.0657768\pi$
$42$		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
$47$	−8.66741			−1.26427			−0.632135	−	0.774858i	$-0.717821\pi$
$47$	−8.66741			−1.26427			−0.632135	+	0.774858i	$0.717821\pi$
$48$		0			0
$49$		0			0
$50$	3.13667	+	1.81096i	0.443593	+	0.256108i
$51$		0			0
$52$	−2.02688	−	1.17022i	−0.281078	−	0.162280i
$53$	2.25370	−	1.30117i	0.309569	−	0.178730i	−0.337165	−	0.941446i	$-0.609468\pi$
$53$	2.25370	−	1.30117i	0.309569	−	0.178730i	0.646734	+	0.762716i	$0.276135\pi$
$54$		0			0
$55$		−	0.447879i		−	0.0603920i
$56$		0			0
$57$		0			0
$58$	2.75729	+	4.77577i	0.362051	+	0.627090i
$59$	3.61372			0.470466			0.235233	−	0.971939i	$-0.424415\pi$
$59$	3.61372			0.470466			0.235233	+	0.971939i	$0.424415\pi$
$60$		0			0
$61$		−	3.36562i		−	0.430924i	−0.976512	−	0.215462i	$-0.930874\pi$
$61$		−	3.36562i		−	0.430924i	0.976512	−	0.215462i	$-0.0691258\pi$
$62$	−0.153489			−0.0194932
$63$		0			0
$64$	−8.75583			−1.09448
$65$			11.1899i			1.38794i
$66$		0			0
$67$	1.32743			0.162171			0.0810857	−	0.996707i	$-0.474161\pi$
$67$	1.32743			0.162171			0.0810857	+	0.996707i	$0.474161\pi$
$68$	1.23016	+	2.13069i	0.149178	+	0.258384i
$69$		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	−0.521992	+	0.852950i	$0.674811\pi$
$73$	−13.0011	+	7.50619i	−1.52166	+	0.878533i	−0.999673	+	0.0255830i	$0.991856\pi$
$74$	−2.52704	−	1.45899i	−0.293763	−	0.169604i
$75$		0			0
$76$	−3.25704	−	1.88045i	−0.373608	−	0.215703i
$77$		0			0
$78$		0			0
$79$	4.32743			0.486874			0.243437	−	0.969917i	$-0.421725\pi$
$79$	4.32743			0.486874			0.243437	+	0.969917i	$0.421725\pi$
$80$	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	0.632878	−	0.774252i	$-0.281874\pi$
$83$	−3.22585	−	5.58733i	−0.354083	−	0.613289i	−0.986961	+	0.160963i	$0.948540\pi$
$84$		0			0
$85$	5.88151	−	10.1871i	0.637940	−	1.10494i
$86$	6.74630	−	3.89498i	0.727473	−	0.420007i
$87$		0			0
$88$	0.242705	−	0.420378i	0.0258725	−	0.0448125i
$89$	2.52684	−	4.37662i	0.267845	−	0.463921i	−0.700460	−	0.713691i	$-0.747022\pi$
$89$	2.52684	−	4.37662i	0.267845	−	0.463921i	0.968305	+	0.249771i	$0.0803552\pi$
$90$		0			0
$91$		0			0
$92$	0.280738	−	0.162084i	0.0292690	−	0.0168984i
$93$		0			0
$94$			10.2789i			1.06019i
$95$			17.9813i			1.84484i
$96$		0			0
$97$	−2.18452	+	1.26123i	−0.221805	+	0.128059i	−0.606786	−	0.794866i	$-0.707541\pi$
$97$	−2.18452	+	1.26123i	−0.221805	+	0.128059i	0.384981	+	0.922925i	$0.374208\pi$
$98$		0			0
$99$		0			0
$100$	−0.906421	+	1.56997i	−0.0906421	+	0.156997i
$101$	−1.49573	+	2.59068i	−0.148831	+	0.257782i	−0.930796	−	0.365540i	$-0.880884\pi$
$101$	−1.49573	+	2.59068i	−0.148831	+	0.257782i	0.781965	+	0.623323i	$0.214218\pi$
$102$		0			0
$103$	11.4286	−	6.59832i	1.12610	−	0.650152i	0.183146	−	0.983086i	$-0.441372\pi$
$103$	11.4286	−	6.59832i	1.12610	−	0.650152i	0.942950	+	0.332934i	$0.108038\pi$
$104$	−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	−0.981782	−	0.190009i	$-0.939148\pi$
$107$	−16.9356	−	9.77777i	−1.63723	−	0.945253i	−0.655444	−	0.755244i	$-0.727518\pi$
$108$		0			0
$109$	−6.62422	−	11.4735i	−0.634485	−	1.09896i	−0.986624	−	0.163013i	$-0.947879\pi$
$109$	−6.62422	−	11.4735i	−0.634485	−	1.09896i	0.352139	−	0.935948i	$-0.385455\pi$
$110$	−0.531151			−0.0506433
$111$		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
$115$	−1.34224	−	0.774943i	−0.125165	−	0.0722638i
$116$	−2.39037	+	1.38008i	−0.221940	+	0.128137i
$117$		0			0
$118$		−	4.28561i		−	0.394522i
$119$		0			0
$120$		0			0
$121$	−5.48755	−	9.50471i	−0.498868	−	0.864065i
$122$	−3.99138			−0.361363
$123$		0			0
$124$		−	0.0768245i		−	0.00689904i
$125$	−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	$0.686953\pi$
$128$			3.91655i			0.346177i
$129$		0			0
$130$	13.2704			1.16389
$131$	5.02249	+	8.69921i	0.438817	+	0.760054i	0.997599	−	0.0692612i	$-0.0220642\pi$
$131$	5.02249	+	8.69921i	0.438817	+	0.760054i	−0.558781	+	0.829315i	$0.688731\pi$
$132$		0			0
$133$		0			0
$134$		−	1.57423i		−	0.135993i
$135$		0			0
$136$	11.0408	−	6.37438i	0.946737	−	0.546599i
$137$	−6.96410	−	4.02073i	−0.594984	−	0.343514i	0.172082	−	0.985083i	$-0.444951\pi$
$137$	−6.96410	−	4.02073i	−0.594984	−	0.343514i	−0.767066	+	0.641569i	$0.778284\pi$
$138$		0			0
$139$	16.3702	+	9.45136i	1.38850	+	0.801654i	0.993147	−	0.116873i	$-0.0372872\pi$
$139$	16.3702	+	9.45136i	1.38850	+	0.801654i	0.395358	+	0.918527i	$0.370621\pi$
$140$		0			0
$141$		0			0
$142$	0.485411			0.0407348
$143$	−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
$149$	16.8063	−	9.70313i	1.37683	−	0.794912i	0.385051	−	0.922895i	$-0.374184\pi$
$149$	16.8063	−	9.70313i	1.37683	−	0.794912i	0.991776	+	0.127984i	$0.0408505\pi$
$150$		0			0
$151$	0.893968	−	1.54840i	0.0727501	−	0.126007i	−0.827356	−	0.561678i	$-0.810156\pi$
$151$	0.893968	−	1.54840i	0.0727501	−	0.126007i	0.900106	+	0.435672i	$0.143489\pi$
$152$	−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
$157$		−	4.39081i		−	0.350425i	−0.984531	−	0.175212i	$-0.943939\pi$
$157$		−	4.39081i		−	0.350425i	0.984531	−	0.175212i	$-0.0560612\pi$
$158$		−	5.13201i		−	0.408281i
$159$		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	−0.952613	−	0.304185i	$-0.901616\pi$
$163$	−2.71780	+	4.70737i	−0.212874	+	0.368709i	0.739738	+	0.672894i	$0.234949\pi$
$164$	1.18460	−	2.05179i	0.0925018	−	0.160218i
$165$		0			0
$166$	−6.62616	+	3.82562i	−0.514290	+	0.296925i
$167$	5.25273	−	9.09799i	0.406468	−	0.704024i	−0.588023	−	0.808844i	$-0.700093\pi$
$167$	5.25273	−	9.09799i	0.406468	−	0.704024i	0.994491	+	0.104821i	$0.0334268\pi$
$168$		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
$173$	17.5590			1.33498			0.667492	−	0.744617i	$-0.267368\pi$
$173$	17.5590			1.33498			0.667492	+	0.744617i	$0.267368\pi$
$174$		0			0
$175$		0			0
$176$	−0.336285	−	0.194154i	−0.0253484	−	0.0146349i
$177$		0			0
$178$	−5.19035	−	2.99665i	−0.389033	−	0.224608i
$179$	15.7645	−	9.10163i	1.17829	−	0.680288i	0.222674	−	0.974893i	$-0.428521\pi$
$179$	15.7645	−	9.10163i	1.17829	−	0.680288i	0.955619	+	0.294605i	$0.0951880\pi$
$180$		0			0
$181$			6.60182i			0.490710i	0.969433	+	0.245355i	$0.0789045\pi$
$181$			6.60182i			0.490710i	−0.969433	+	0.245355i	$0.921096\pi$
$182$		0			0
$183$		0			0
$184$	−0.839883	−	1.45472i	−0.0619170	−	0.107243i
$185$	−6.98284			−0.513389
$186$		0			0
$187$			0.654129i			0.0478347i
$188$	−5.14479			−0.375223
$189$		0			0
$190$	21.3245			1.54704
$191$			14.2101i			1.02821i	0.857728	+	0.514104i	$0.171875\pi$
$191$			14.2101i			1.02821i	−0.857728	+	0.514104i	$0.828125\pi$
$192$		0			0
$193$	−10.0043			−0.720123			−0.360062	−	0.932929i	$-0.617244\pi$
$193$	−10.0043			−0.720123			−0.360062	+	0.932929i	$0.617244\pi$
$194$	1.49573	+	2.59068i	0.107387	+	0.186000i
$195$		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	−0.0471981	−	0.998886i	$-0.515029\pi$
$199$	11.2045	−	6.46890i	0.794263	−	0.458568i	0.841461	+	0.540318i	$0.181696\pi$
$200$	8.13521	+	4.69687i	0.575246	+	0.332119i
$201$		0			0
$202$	3.07236	+	1.77383i	0.216170	+	0.124806i
$203$		0			0
$204$		0			0
$205$	−11.3274			−0.791142
$206$	−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	$0.267092\pi$
$212$	1.33775	−	0.772349i	0.0918769	−	0.0530451i
$213$		0			0
$214$	−11.5957	+	20.0844i	−0.792667	+	1.37294i
$215$	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
$220$		−	0.265852i		−	0.0179237i
$221$		−	16.3429i		−	1.09934i
$222$		0			0
$223$	−1.95429	+	1.12831i	−0.130869	+	0.0755571i	−0.564005	−	0.825771i	$-0.690740\pi$
$223$	−1.95429	+	1.12831i	−0.130869	+	0.0755571i	0.433136	+	0.901328i	$0.357407\pi$
$224$		0			0
$225$		0			0
$226$	5.97509	−	10.3492i	0.397457	−	0.688416i
$227$	9.32085	−	16.1442i	0.618647	−	1.07153i	−0.371086	−	0.928598i	$-0.621015\pi$
$227$	9.32085	−	16.1442i	0.618647	−	1.07153i	0.989733	−	0.142929i	$-0.0456522\pi$
$228$		0			0
$229$	12.3891	−	7.15283i	0.818692	−	0.472672i	−0.0312731	−	0.999511i	$-0.509956\pi$
$229$	12.3891	−	7.15283i	0.818692	−	0.472672i	0.849965	+	0.526839i	$0.176623\pi$
$230$	−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	$-0.144489\pi$
$233$	14.7812	+	8.53394i	0.968350	+	0.559077i	0.0696170	+	0.997574i	$0.477822\pi$
$234$		0			0
$235$	12.2989	+	21.3024i	0.802293	+	1.38961i
$236$	2.14503			0.139630
$237$		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
$241$	3.91464	+	2.26012i	0.252164	+	0.145587i	0.620755	−	0.784005i	$-0.286826\pi$
$241$	3.91464	+	2.26012i	0.252164	+	0.145587i	−0.368591	+	0.929592i	$0.620160\pi$
$242$	−11.2719	+	6.50783i	−0.724584	+	0.418339i
$243$		0			0
$244$		−	1.99777i		−	0.127894i
$245$		0			0
$246$		0			0
$247$	12.4911	+	21.6353i	0.794793	+	1.37662i
$248$	−0.398087			−0.0252786
$249$		0			0
$250$			6.54922i			0.414209i
$251$	21.1727			1.33641			0.668205	−	0.743978i	$-0.267063\pi$
$251$	21.1727			1.33641			0.668205	+	0.743978i	$0.267063\pi$
$252$		0			0
$253$	0.0861875			0.00541856
$254$			14.8118i			0.929378i
$255$		0			0
$256$	−12.8669			−0.804183
$257$	−15.6502	−	27.1070i	−0.976236	−	1.69089i	−0.675796	−	0.737089i	$-0.736200\pi$
$257$	−15.6502	−	27.1070i	−0.976236	−	1.69089i	−0.300440	−	0.953801i	$-0.597134\pi$
$258$		0			0
$259$		0			0
$260$			6.64211i			0.411926i
$261$		0			0
$262$	10.3166	−	5.95631i	0.637363	−	0.367982i
$263$	−5.78220	−	3.33836i	−0.356546	−	0.205852i	0.311019	−	0.950404i	$-0.399330\pi$
$263$	−5.78220	−	3.33836i	−0.356546	−	0.205852i	−0.667564	+	0.744552i	$0.732663\pi$
$264$		0			0
$265$	−6.39593	−	3.69269i	−0.392899	−	0.226840i
$266$		0			0
$267$		0			0
$268$	0.787935			0.0481308
$269$	−5.32947	−	9.23092i	−0.324944	−	0.562819i	0.656557	−	0.754276i	$-0.272012\pi$
$269$	−5.32947	−	9.23092i	−0.324944	−	0.562819i	−0.981501	+	0.191457i	$0.938679\pi$
$270$		0			0
$271$	6.44754	+	3.72249i	0.391660	+	0.226125i	0.682879	−	0.730531i	$-0.260727\pi$
$271$	6.44754	+	3.72249i	0.391660	+	0.226125i	−0.291219	+	0.956656i	$0.594061\pi$
$272$	−5.09924	−	8.83214i	−0.309187	−	0.535527i
$273$		0			0
$274$	−4.76829	+	8.25891i	−0.288063	+	0.498939i
$275$	−0.417411	+	0.240992i	−0.0251708	+	0.0145324i
$276$		0			0
$277$	13.2793	−	23.0004i	0.797874	−	1.38196i	−0.123124	−	0.992391i	$-0.539291\pi$
$277$	13.2793	−	23.0004i	0.797874	−	1.38196i	0.920998	−	0.389568i	$-0.127376\pi$
$278$	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
$283$		−	8.65219i		−	0.514319i	−0.966369	−	0.257160i	$-0.917213\pi$
$283$		−	8.65219i		−	0.514319i	0.966369	−	0.257160i	$-0.0827866\pi$
$284$			0.242958i			0.0144169i
$285$		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
$290$	7.82512	−	13.5535i	0.459507	−	0.795890i
$291$		0			0
$292$	−7.71719	+	4.45552i	−0.451614	+	0.260740i
$293$	−4.40023	+	7.62143i	−0.257064	+	0.445249i	−0.965454	−	0.260573i	$-0.916089\pi$
$293$	−4.40023	+	7.62143i	−0.257064	+	0.445249i	0.708390	+	0.705821i	$0.249422\pi$
$294$		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
$299$	−2.15333			−0.124530
$300$		0			0
$301$		0			0
$302$	−1.83628	−	1.06018i	−0.105666	−	0.0610065i
$303$		0			0
$304$	13.5011	+	7.79485i	0.774339	+	0.447065i
$305$	−8.27188	+	4.77577i	−0.473647	+	0.273460i
$306$		0			0
$307$		−	11.1747i		−	0.637771i	−0.947793	−	0.318886i	$-0.896691\pi$
$307$		−	11.1747i		−	0.637771i	0.947793	−	0.318886i	$-0.103309\pi$
$308$		0			0
$309$		0			0
$310$	0.217799	+	0.377240i	0.0123702	+	0.0214258i
$311$	16.4056			0.930275			0.465137	−	0.885239i	$-0.346005\pi$
$311$	16.4056			0.930275			0.465137	+	0.885239i	$0.346005\pi$
$312$		0			0
$313$		−	8.20431i		−	0.463735i	−0.972747	−	0.231868i	$-0.925516\pi$
$313$		−	8.20431i		−	0.463735i	0.972747	−	0.231868i	$-0.0744836\pi$
$314$	−5.20717			−0.293858
$315$		0			0
$316$	2.56867			0.144499
$317$		−	22.9124i		−	1.28689i	−0.765494	−	0.643443i	$-0.777505\pi$
$317$		−	22.9124i		−	1.28689i	0.765494	−	0.643443i	$-0.222495\pi$
$318$		0			0
$319$	−0.733851			−0.0410878
$320$	12.4244	+	21.5197i	0.694545	+	1.20299i
$321$		0			0
$322$		0			0
$323$		−	26.2618i		−	1.46125i
$324$		0			0
$325$	10.4287	−	6.02102i	0.578481	−	0.333986i
$326$	5.58259	+	3.22311i	0.309191	+	0.178512i
$327$		0			0
$328$	−10.6319	−	6.13833i	−0.587049	−	0.338933i
$329$		0			0
$330$		0			0
$331$	19.2632			1.05880			0.529401	−	0.848372i	$-0.322417\pi$
$331$	19.2632			1.05880			0.529401	+	0.848372i	$0.322417\pi$
$332$	−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	$0.206098\pi$
$338$	2.61556	−	1.51009i	0.142268	−	0.0821383i
$339$		0			0
$340$	3.49115	−	6.04684i	0.189334	−	0.327936i
$341$	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
$346$		−	20.8237i		−	1.11949i
$347$			8.73293i			0.468808i	0.972139	+	0.234404i	$0.0753139\pi$
$347$			8.73293i			0.468808i	−0.972139	+	0.234404i	$0.924686\pi$
$348$		0			0
$349$	7.82927	−	4.52023i	0.419091	−	0.241963i	−0.275597	−	0.961273i	$-0.588876\pi$
$349$	7.82927	−	4.52023i	0.419091	−	0.241963i	0.694689	+	0.719311i	$0.255542\pi$
$350$		0			0
$351$		0			0
$352$	0.255158	−	0.441947i	0.0136000	−	0.0235559i
$353$	−0.607896	+	1.05291i	−0.0323550	+	0.0560406i	−0.881750	−	0.471718i	$-0.843634\pi$
$353$	−0.607896	+	1.05291i	−0.0323550	+	0.0560406i	0.849394	+	0.527758i	$0.176967\pi$
$354$		0			0
$355$	1.00598	−	0.580805i	0.0533920	−	0.0308259i
$356$	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	$-0.484306\pi$
$359$	−14.9882	−	8.65345i	−0.791048	−	0.456712i	−0.840331	+	0.542073i	$0.817640\pi$
$360$		0			0
$361$	10.5723	+	18.3117i	0.556435	+	0.963774i
$362$	7.82927			0.411498
$363$		0			0
$364$		0			0
$365$	36.8968	+	21.3024i	1.93127	+	1.11502i
$366$		0			0
$367$	24.4297	+	14.1045i	1.27522	+	0.736250i	0.975966	−	0.217923i	$-0.0699282\pi$
$367$	24.4297	+	14.1045i	1.27522	+	0.736250i	0.299256	+	0.954173i	$0.403262\pi$
$368$	−1.16372	+	0.671871i	−0.0606628	+	0.0350237i
$369$		0			0
$370$			8.28114i			0.430516i
$371$		0			0
$372$		0			0
$373$	−14.1264	−	24.4676i	−0.731435	−	1.26688i	−0.956270	−	0.292486i	$-0.905518\pi$
$373$	−14.1264	−	24.4676i	−0.731435	−	1.26688i	0.224835	−	0.974397i	$-0.427816\pi$
$374$	0.775749			0.0401130
$375$		0			0
$376$			26.6591i			1.37484i
$377$	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	$0.377256\pi$
$380$			10.6733i			0.547531i
$381$		0			0
$382$	16.8521			0.862231
$383$	−12.3932	−	21.4657i	−0.633264	−	1.09684i	−0.986880	−	0.161454i	$-0.948382\pi$
$383$	−12.3932	−	21.4657i	−0.633264	−	1.09684i	0.353617	−	0.935390i	$-0.384952\pi$
$384$		0			0
$385$		0			0
$386$			11.8643i			0.603878i
$387$		0			0
$388$	−1.29669	+	0.748643i	−0.0658293	+	0.0380066i
$389$	4.43706	+	2.56174i	0.224968	+	0.129885i	0.608248	−	0.793747i	$-0.291872\pi$
$389$	4.43706	+	2.56174i	0.224968	+	0.129885i	−0.383281	+	0.923632i	$0.625206\pi$
$390$		0			0
$391$	1.96035	+	1.13181i	0.0991391	+	0.0572380i
$392$		0			0
$393$		0			0
$394$	−23.8391			−1.20100
$395$	−6.14056	−	10.6358i	−0.308965	−	0.535144i
$396$		0			0
$397$	−1.66358	−	0.960470i	−0.0834929	−	0.0482046i	0.457672	−	0.889121i	$-0.348683\pi$
$397$	−1.66358	−	0.960470i	−0.0834929	−	0.0482046i	−0.541165	+	0.840916i	$0.682017\pi$
$398$	−7.67163	−	13.2877i	−0.384544	−	0.666050i
$399$		0			0
$400$	3.75729	−	6.50783i	0.187865	−	0.325391i
$401$	−12.4612	+	7.19446i	−0.622282	+	0.359274i	−0.777757	−	0.628565i	$-0.783642\pi$
$401$	−12.4612	+	7.19446i	−0.622282	+	0.359274i	0.155475	+	0.987840i	$0.450309\pi$
$402$		0			0
$403$	−0.255158	+	0.441947i	−0.0127103	+	0.0220150i
$404$	−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
$409$		−	9.72582i		−	0.480911i	−0.970660	−	0.240455i	$-0.922703\pi$
$409$		−	9.72582i		−	0.480911i	0.970660	−	0.240455i	$-0.0772968\pi$
$410$			13.4335i			0.663433i
$411$		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
$416$	−6.37495	+	11.0417i	−0.312558	+	0.541366i
$417$		0			0
$418$	−1.02696	+	0.592916i	−0.0502303	+	0.0290005i
$419$	14.9512	−	25.8963i	0.730416	−	1.26512i	−0.226289	−	0.974060i	$-0.572660\pi$
$419$	14.9512	−	25.8963i	0.730416	−	1.26512i	0.956706	−	0.291058i	$-0.0940072\pi$
$420$		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
$425$	−12.6588			−0.614041
$426$		0			0
$427$		0			0
$428$	−10.0526	−	5.80388i	−0.485912	−	0.280541i
$429$		0			0
$430$	−19.1458	−	11.0538i	−0.923293	−	0.533064i
$431$	5.53443	−	3.19531i	0.266584	−	0.153913i	−0.360750	−	0.932663i	$-0.617479\pi$
$431$	5.53443	−	3.19531i	0.266584	−	0.153913i	0.627334	+	0.778750i	$0.284146\pi$
$432$		0			0
$433$			33.1771i			1.59439i	0.603721	+	0.797196i	$0.293684\pi$
$433$			33.1771i			1.59439i	−0.603721	+	0.797196i	$0.706316\pi$
$434$		0			0
$435$		0			0
$436$	−3.93200	−	6.81042i	−0.188309	−	0.326160i
$437$	−3.46023			−0.165525
$438$		0			0
$439$			8.46316i			0.403925i	0.979393	+	0.201962i	$0.0647319\pi$
$439$			8.46316i			0.403925i	−0.979393	+	0.201962i	$0.935268\pi$
$440$	−1.37758			−0.0656737
$441$		0			0
$442$	−19.3815			−0.921885
$443$		−	18.6001i		−	0.883718i	−0.897085	−	0.441859i	$-0.854319\pi$
$443$		−	18.6001i		−	0.883718i	0.897085	−	0.441859i	$-0.145681\pi$
$444$		0			0
$445$	−14.3422			−0.679886
$446$	1.33809	+	2.31764i	0.0633604	+	0.109743i
$447$		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
$452$	5.17996	+	2.99065i	0.243645	+	0.140668i
$453$		0			0
$454$	−19.1458	−	11.0538i	−0.898558	−	0.518783i
$455$		0			0
$456$		0			0
$457$	11.3566			0.531240			0.265620	−	0.964078i	$-0.414423\pi$
$457$	11.3566			0.531240			0.265620	+	0.964078i	$0.414423\pi$
$458$	−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	$0.195822\pi$
$461$	19.4984	+	33.7721i	0.908129	+	1.57293i	0.0914676	+	0.995808i	$0.470844\pi$
$462$		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	$0.241838\pi$
$464$	9.90856	−	5.72071i	0.459993	−	0.265577i
$465$		0			0
$466$	10.1206	−	17.5294i	0.468829	−	0.812035i
$467$	1.79665	−	3.11188i	0.0831389	−	0.144001i	−0.821458	−	0.570269i	$-0.806839\pi$
$467$	1.79665	−	3.11188i	0.0831389	−	0.144001i	0.904597	+	0.426269i	$0.140172\pi$
$468$		0			0
$469$		0			0
$470$	25.2630	−	14.5856i	1.16530	−	0.672784i
$471$		0			0
$472$		−	11.1151i		−	0.511612i
$473$			1.03664i			0.0476650i
$474$		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
$479$	−0.811090	+	1.40485i	−0.0370597	+	0.0641892i	−0.883960	−	0.467562i	$-0.845132\pi$
$479$	−0.811090	+	1.40485i	−0.0370597	+	0.0641892i	0.846901	+	0.531751i	$0.178466\pi$
$480$		0			0
$481$	−8.40183	+	4.85080i	−0.383090	+	0.221177i
$482$	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	0.761115	−	0.648616i	$-0.224652\pi$
$487$	−3.99786	−	6.92450i	−0.181161	−	0.313779i	−0.942276	+	0.334837i	$0.891319\pi$
$488$	−10.3520			−0.468612
$489$		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
$493$	−16.6916	−	9.63688i	−0.751751	−	0.434023i
$494$	25.6579	−	14.8136i	1.15440	−	0.666494i
$495$		0			0
$496$			0.318453i			0.0142990i
$497$		0			0
$498$		0			0
$499$	−8.46050	−	14.6540i	−0.378744	−	0.656004i	0.612136	−	0.790753i	$-0.290311\pi$
$499$	−8.46050	−	14.6540i	−0.378744	−	0.656004i	−0.990880	+	0.134749i	$0.956977\pi$
$500$	−3.27801			−0.146597
$501$		0			0
$502$		−	25.1093i		−	1.12068i
$503$	−33.9226			−1.51253			−0.756267	−	0.654263i	$-0.772979\pi$
$503$	−33.9226			−1.51253			−0.756267	+	0.654263i	$0.772979\pi$
$504$		0			0
$505$	8.48968			0.377786
$506$		−	0.102212i		−	0.00454388i
$507$		0			0
$508$	−7.41362			−0.328926
$509$	5.06805	+	8.77812i	0.224637	+	0.389083i	0.956211	−	0.292680i	$-0.0945469\pi$
$509$	5.06805	+	8.77812i	0.224637	+	0.389083i	−0.731573	+	0.681763i	$0.761214\pi$
$510$		0			0
$511$		0			0
$512$			23.0923i			1.02055i
$513$		0			0
$514$	−32.1469	+	18.5600i	−1.41794	+	0.818648i
$515$	−32.4341	−	18.7259i	−1.42922	−	0.825160i
$516$		0			0
$517$	−1.18460	−	0.683930i	−0.0520987	−	0.0300792i
$518$		0			0
$519$		0			0
$520$	34.4179			1.50932
$521$	15.8493	+	27.4518i	0.694370	+	1.20268i	0.970393	+	0.241533i	$0.0776502\pi$
$521$	15.8493	+	27.4518i	0.694370	+	1.20268i	−0.276022	+	0.961151i	$0.589016\pi$
$522$		0			0
$523$	−7.01403	−	4.04955i	−0.306702	−	0.177075i	0.338748	−	0.940877i	$-0.389997\pi$
$523$	−7.01403	−	4.04955i	−0.306702	−	0.177075i	−0.645450	+	0.763803i	$0.723330\pi$
$524$	2.98125	+	5.16367i	0.130236	+	0.225576i
$525$		0			0
$526$	−3.95904	+	6.85726i	−0.172622	+	0.298991i
$527$	0.464582	−	0.268227i	0.0202375	−	0.0116841i
$528$		0			0
$529$	−11.3509	+	19.6603i	−0.493516	+	0.854795i
$530$	−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
$535$			55.4981i			2.39939i
$536$		−	4.08290i		−	0.176354i
$537$		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	−0.878803	−	0.477185i	$-0.841657\pi$
$541$	−0.608168	+	1.05338i	−0.0261472	+	0.0452883i	0.852656	+	0.522473i	$0.174991\pi$
$542$	4.41460	−	7.64631i	0.189623	−	0.328437i
$543$		0			0
$544$	11.6073	−	6.70145i	0.497657	−	0.287322i
$545$	−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
$551$	29.4624			1.25514
$552$		0			0
$553$		0			0
$554$	−27.2768	−	15.7482i	−1.15888	−	0.669079i
$555$		0			0
$556$	9.71703	+	5.61013i	0.412094	+	0.237923i
$557$	−23.5708	+	13.6086i	−0.998727	+	0.576615i	−0.907871	−	0.419249i	$-0.862294\pi$
$557$	−23.5708	+	13.6086i	−0.998727	+	0.576615i	−0.0908558	+	0.995864i	$0.528960\pi$
$558$		0			0
$559$		−	25.8998i		−	1.09545i
$560$		0			0
$561$		0			0
$562$	14.4466	+	25.0222i	0.609393	+	1.05550i
$563$	−9.36035			−0.394492			−0.197246	−	0.980354i	$-0.563200\pi$
$563$	−9.36035			−0.394492			−0.197246	+	0.980354i	$0.563200\pi$
$564$		0			0
$565$		−	28.5973i		−	1.20310i
$566$	−10.2609			−0.431296
$567$		0			0
$568$	1.25895			0.0528244
$569$			34.9209i			1.46396i	0.681326	+	0.731980i	$0.261404\pi$
$569$			34.9209i			1.46396i	−0.681326	+	0.731980i	$0.738596\pi$
$570$		0			0
$571$	−1.47197			−0.0616002			−0.0308001	−	0.999526i	$-0.509806\pi$
$571$	−1.47197			−0.0616002			−0.0308001	+	0.999526i	$0.509806\pi$
$572$	−0.184680	−	0.319875i	−0.00772186	−	0.0133747i
$573$		0			0
$574$		0			0
$575$			1.66791i			0.0695567i
$576$		0			0
$577$	−16.1251	+	9.30982i	−0.671296	+	0.387573i	−0.796567	−	0.604550i	$-0.793353\pi$
$577$	−16.1251	+	9.30982i	−0.671296	+	0.387573i	0.125272	+	0.992122i	$0.460020\pi$
$578$	0.184828	+	0.106710i	0.00768783	+	0.00443857i
$579$		0			0
$580$	6.78380	+	3.91663i	0.281682	+	0.162629i
$581$		0			0
$582$		0			0
$583$	0.410693			0.0170092
$584$	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	0.608271	−	0.793729i	$-0.291863\pi$
$587$	−9.28551	−	16.0830i	−0.383254	−	0.663816i	−0.991525	+	0.129914i	$0.958530\pi$
$588$		0			0
$589$	−0.410019	+	0.710174i	−0.0168945	+	0.0292622i
$590$	−10.5330	+	6.08121i	−0.433636	+	0.250360i
$591$		0			0
$592$	−3.02704	+	5.24299i	−0.124411	+	0.215486i
$593$	−15.4614	+	26.7800i	−0.634924	+	1.09972i	0.351607	+	0.936148i	$0.385635\pi$
$593$	−15.4614	+	26.7800i	−0.634924	+	1.09972i	−0.986531	+	0.163573i	$0.947698\pi$
$594$		0			0
$595$		0			0
$596$	9.97588	−	5.75958i	0.408628	−	0.235922i
$597$		0			0
$598$			2.55369i			0.104428i
$599$			13.7111i			0.560219i	0.959968	+	0.280109i	$0.0903707\pi$
$599$			13.7111i			0.560219i	−0.959968	+	0.280109i	$0.909629\pi$
$600$		0			0
$601$	−17.1065	+	9.87644i	−0.697788	+	0.402868i	−0.806523	−	0.591203i	$-0.798653\pi$
$601$	−17.1065	+	9.87644i	−0.697788	+	0.402868i	0.108735	+	0.994071i	$0.465320\pi$
$602$		0			0
$603$		0			0
$604$	0.530641	−	0.919097i	0.0215915	−	0.0373975i
$605$	−15.5735	+	26.9741i	−0.633153	+	1.09665i
$606$		0			0
$607$	15.5219	−	8.96157i	0.630014	−	0.363739i	−0.150744	−	0.988573i	$-0.548167\pi$
$607$	15.5219	−	8.96157i	0.630014	−	0.363739i	0.780757	+	0.624834i	$0.214833\pi$
$608$	−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	0.892618	+	0.450813i	$0.148866\pi$
$613$	20.7163	+	35.8817i	0.836725	+	1.44925i	−0.0558932	+	0.998437i	$0.517801\pi$
$614$	−13.2523			−0.534820
$615$		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
$619$	−1.67850	−	0.969082i	−0.0674646	−	0.0389507i	0.465888	−	0.884844i	$-0.345735\pi$
$619$	−1.67850	−	0.969082i	−0.0674646	−	0.0389507i	−0.533353	+	0.845893i	$0.679068\pi$
$620$	−0.188816	+	0.109013i	−0.00758303	+	0.00437806i
$621$		0			0
$622$		−	19.4558i		−	0.780106i
$623$		0			0
$624$		0			0
$625$	15.4715	+	26.7974i	0.618860	+	1.07190i
$626$	−9.72971			−0.388877
$627$		0			0
$628$		−	2.60629i		−	0.104002i
$629$	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	$0.344465\pi$
$632$		−	13.3103i		−	0.529455i
$633$		0			0
$634$	−27.1724			−1.07915
$635$	17.7227	+	30.6966i	0.703303	+	1.21816i
$636$		0			0
$637$		0			0
$638$			0.870293i			0.0344552i
$639$		0			0
$640$	9.62592	−	5.55753i	0.380498	−	0.219681i
$641$	21.5093	+	12.4184i	0.849568	+	0.490498i	0.860505	−	0.509442i	$-0.170148\pi$
$641$	21.5093	+	12.4184i	0.849568	+	0.490498i	−0.0109373	+	0.999940i	$0.503482\pi$
$642$		0			0
$643$	37.9247	+	21.8959i	1.49561	+	0.863489i	0.999987	−	0.00505169i	$-0.00160801\pi$
$643$	37.9247	+	21.8959i	1.49561	+	0.863489i	0.495619	+	0.868540i	$0.334941\pi$
$644$		0			0
$645$		0			0
$646$	−31.1445			−1.22537
$647$	14.6857	+	25.4363i	0.577353	+	1.00001i	0.995782	+	0.0917553i	$0.0292478\pi$
$647$	14.6857	+	25.4363i	0.577353	+	1.00001i	−0.418428	+	0.908250i	$0.637419\pi$
$648$		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
$653$	−28.0816	+	16.2129i	−1.09892	+	0.634461i	−0.935937	−	0.352168i	$-0.885444\pi$
$653$	−28.0816	+	16.2129i	−1.09892	+	0.634461i	−0.162981	+	0.986629i	$0.552111\pi$
$654$		0			0
$655$	14.2537	−	24.6881i	0.556938	−	0.964645i
$656$	−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
$661$			3.52343i			0.137045i	0.997650	+	0.0685227i	$0.0218286\pi$
$661$			3.52343i			0.137045i	−0.997650	+	0.0685227i	$0.978171\pi$
$662$		−	22.8448i		−	0.887887i
$663$		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
$668$	3.11791	−	5.40038i	0.120636	−	0.208947i
$669$		0			0
$670$	−3.86908	+	2.23382i	−0.149476	+	0.0862999i
$671$	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
$677$	−33.8519			−1.30103			−0.650517	−	0.759491i	$-0.725448\pi$
$677$	−33.8519			−1.30103			−0.650517	+	0.759491i	$0.725448\pi$
$678$		0			0
$679$		0			0
$680$	−31.3334	−	18.0903i	−1.20158	−	0.693732i
$681$		0			0
$682$	−0.0209779	−	0.0121116i	−0.000803285	−	0.000463777i
$683$	24.2733	−	14.0142i	0.928794	−	0.536239i	0.0423639	−	0.999102i	$-0.486511\pi$
$683$	24.2733	−	14.0142i	0.928794	−	0.536239i	0.886430	+	0.462863i	$0.153178\pi$
$684$		0			0
$685$			22.8214i			0.871962i
$686$		0			0
$687$		0			0
$688$	−8.08113	−	13.9969i	−0.308090	−	0.533628i
$689$	−10.2609			−0.390908
$690$		0			0
$691$			49.3511i			1.87741i	0.344727	+	0.938703i	$0.387971\pi$
$691$			49.3511i			1.87741i	−0.344727	+	0.938703i	$0.612029\pi$
$692$	10.4226			0.396210
$693$		0			0
$694$	10.3566			0.393131
$695$		−	53.6454i		−	2.03488i
$696$		0			0
$697$	16.5438			0.626640
$698$	−5.36066	−	9.28494i	−0.202904	−	0.351440i
$699$		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
$704$	−1.19669	−	0.690907i	−0.0451018	−	0.0260396i
$705$		0			0
$706$	1.24867	+	0.720920i	0.0469943	+	0.0271322i
$707$		0			0
$708$		0			0
$709$	−10.7132			−0.402343			−0.201172	−	0.979556i	$-0.564475\pi$
$709$	−10.7132			−0.402343			−0.201172	+	0.979556i	$0.564475\pi$
$710$	−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
$716$	9.35748	−	5.40254i	0.349705	−	0.201902i
$717$		0			0
$718$	−10.2624	+	17.7749i	−0.382988	+	0.663354i
$719$	−8.78970	+	15.2242i	−0.327801	+	0.567767i	−0.982075	−	0.188490i	$-0.939641\pi$
$719$	−8.78970	+	15.2242i	−0.327801	+	0.567767i	0.654275	+	0.756257i	$0.272974\pi$
$720$		0			0
$721$		0			0
$722$	21.7163	−	12.5379i	0.808198	−	0.466614i
$723$		0			0
$724$			3.91871i			0.145638i
$725$		−	14.2016i		−	0.527433i
$726$		0			0
$727$	43.4695	−	25.0971i	1.61220	−	0.930802i	0.623336	−	0.781954i	$-0.285777\pi$
$727$	43.4695	−	25.0971i	1.61220	−	0.930802i	0.988860	−	0.148847i	$-0.0475563\pi$
$728$		0			0
$729$		0			0
$730$	25.2630	−	43.7569i	0.935027	−	1.61951i
$731$	−13.6132	+	23.5787i	−0.503501	+	0.872089i
$732$		0			0
$733$	−34.5617	+	19.9542i	−1.27656	+	0.737025i	−0.976215	−	0.216804i	$-0.930437\pi$
$733$	−34.5617	+	19.9542i	−1.27656	+	0.737025i	−0.300350	+	0.953829i	$0.597103\pi$
$734$	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	−0.997655	−	0.0684369i	$-0.978199\pi$
$739$	−15.1716	−	26.2780i	−0.558096	−	0.966650i	0.439560	−	0.898213i	$-0.355135\pi$
$740$	−4.14487			−0.152369
$741$		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
$745$	−47.6959	−	27.5372i	−1.74744	−	1.00889i
$746$	−29.0167	+	16.7528i	−1.06238	+	0.613364i
$747$		0			0
$748$			0.388278i			0.0141968i
$749$		0			0
$750$		0			0
$751$	−6.07753	−	10.5266i	−0.221772	−	0.384121i	0.733574	−	0.679610i	$-0.237851\pi$
$751$	−6.07753	−	10.5266i	−0.221772	−	0.384121i	−0.955346	+	0.295489i	$0.904517\pi$
$752$	21.3262			0.777686
$753$		0			0
$754$		−	21.7436i		−	0.791857i
$755$	−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	$0.556500\pi$
$758$		−	17.3676i		−	0.630819i
$759$		0			0
$760$	55.3068			2.00619
$761$	19.4175	+	33.6320i	0.703882	+	1.21916i	0.967093	+	0.254422i	$0.0818851\pi$
$761$	19.4175	+	33.6320i	0.703882	+	1.21916i	−0.263211	+	0.964738i	$0.584782\pi$
$762$		0			0
$763$		0			0
$764$			8.43483i			0.305161i
$765$		0			0
$766$	−25.4567	+	14.6974i	−0.919788	+	0.531040i
$767$	−12.3397	−	7.12432i	−0.445560	−	0.257244i
$768$		0			0
$769$	−9.42879	−	5.44371i	−0.340011	−	0.196305i	0.320266	−	0.947328i	$-0.396228\pi$
$769$	−9.42879	−	5.44371i	−0.340011	−	0.196305i	−0.660277	+	0.751022i	$0.729561\pi$
$770$		0			0
$771$		0			0
$772$	−5.93833			−0.213725
$773$	−18.6668	−	32.3319i	−0.671400	−	1.16290i	−0.977507	−	0.210901i	$-0.932360\pi$
$773$	−18.6668	−	32.3319i	−0.671400	−	1.16290i	0.306108	−	0.951997i	$-0.400973\pi$
$774$		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
$779$	−21.9012	+	12.6446i	−0.784691	+	0.453041i
$780$		0			0
$781$	−0.0322979	+	0.0559416i	−0.00115571	+	0.00200175i
$782$	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
$787$			17.8463i			0.636152i	0.948065	+	0.318076i	$0.103037\pi$
$787$			17.8463i			0.636152i	−0.948065	+	0.318076i	$0.896963\pi$
$788$		−	11.9319i		−	0.425058i
$789$		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
$794$	−1.13905	+	1.97289i	−0.0404233	+	0.0700151i
$795$		0			0
$796$	6.65074	−	3.83980i	0.235729	−	0.136098i
$797$	−5.74854	+	9.95676i	−0.203624	+	0.352687i	−0.949693	−	0.313181i	$-0.898605\pi$
$797$	−5.74854	+	9.95676i	−0.203624	+	0.352687i	0.746070	+	0.665868i	$0.231939\pi$
$798$		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
$803$	−2.36920			−0.0836073
$804$		0			0
$805$		0			0
$806$	0.524117	+	0.302599i	0.0184612	+	0.0106586i
$807$		0			0
$808$	7.96840	+	4.60056i	0.280327	+	0.161847i
$809$	11.4267	−	6.59723i	0.401743	−	0.231946i	−0.285493	−	0.958381i	$-0.592157\pi$
$809$	11.4267	−	6.59723i	0.401743	−	0.231946i	0.687236	+	0.726434i	$0.258824\pi$
$810$		0			0
$811$		−	46.5800i		−	1.63565i	−0.575469	−	0.817823i	$-0.695181\pi$
$811$		−	46.5800i		−	1.63565i	0.575469	−	0.817823i	$-0.304819\pi$
$812$		0			0
$813$		0			0
$814$	−0.230252	−	0.398809i	−0.00807034	−	0.0139782i
$815$	15.4261			0.540352
$816$		0			0
$817$		−	41.6189i		−	1.45606i
$818$	−11.5341			−0.403280
$819$		0			0
$820$	−6.72373			−0.234803
$821$		−	39.6782i		−	1.38478i	−0.721524	−	0.692390i	$-0.756558\pi$
$821$		−	39.6782i		−	1.38478i	0.721524	−	0.692390i	$-0.243442\pi$
$822$		0			0
$823$	−39.2311			−1.36751			−0.683755	−	0.729711i	$-0.739654\pi$
$823$	−39.2311			−1.36751			−0.683755	+	0.729711i	$0.739654\pi$
$824$	−20.2951	−	35.1521i	−0.707013	−	1.22458i
$825$		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	−0.286014	−	0.958225i	$-0.592331\pi$
$829$	11.5407	−	6.66304i	0.400826	−	0.231417i	0.686840	+	0.726808i	$0.258997\pi$
$830$	18.8049	+	10.8570i	0.652726	+	0.376852i
$831$		0			0
$832$	29.8983	+	17.2618i	1.03654	+	0.598446i
$833$		0			0
$834$		0			0
$835$	−29.8142			−1.03176
$836$	−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	0.683870	−	0.729604i	$-0.260295\pi$
$839$	−8.39768	−	14.5452i	−0.289920	−	0.502156i	−0.973790	+	0.227447i	$0.926962\pi$
$840$		0			0
$841$	−3.68862	+	6.38888i	−0.127194	+	0.220306i
$842$	−25.7690	+	14.8777i	−0.888057	+	0.512720i
$843$		0			0
$844$	−2.67538	+	4.63389i	−0.0920903	+	0.159505i
$845$	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
$850$			15.0124i			0.514921i
$851$		−	1.34374i		−	0.0460629i
$852$		0			0
$853$	−35.5011	+	20.4966i	−1.21554	+	0.701790i	−0.963960	−	0.266048i	$-0.914282\pi$
$853$	−35.5011	+	20.4966i	−1.21554	+	0.701790i	−0.251576	+	0.967838i	$0.580949\pi$
$854$		0			0
$855$		0			0
$856$	−30.0744	+	52.0904i	−1.02792	+	1.78041i
$857$	−20.8718	+	36.1510i	−0.712967	+	1.23489i	0.250772	+	0.968046i	$0.419316\pi$
$857$	−20.8718	+	36.1510i	−0.712967	+	1.23489i	−0.963739	+	0.266848i	$0.914018\pi$
$858$		0			0
$859$	−24.0479	+	13.8841i	−0.820505	+	0.473719i	−0.850590	−	0.525829i	$-0.823755\pi$
$859$	−24.0479	+	13.8841i	−0.820505	+	0.473719i	0.0300858	+	0.999547i	$0.490422\pi$
$860$	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	$-0.0504407\pi$
$863$	39.4985	+	22.8045i	1.34455	+	0.776274i	0.357075	+	0.934076i	$0.383774\pi$
$864$		0			0
$865$	−24.9159	−	43.1557i	−0.847168	−	1.46734i
$866$	39.3456			1.33702
$867$		0			0
$868$		0			0
$869$	0.591443	+	0.341470i	0.0200633	+	0.0115836i
$870$		0			0
$871$	−4.53275	−	2.61698i	−0.153586	−	0.0886731i
$872$	−35.2901	+	20.3747i	−1.19507	+	0.689975i
$873$		0			0
$874$			4.10358i			0.138806i
$875$		0			0
$876$		0			0
$877$	−8.84368	−	15.3177i	−0.298630	−	0.517242i	0.677193	−	0.735805i	$-0.263196\pi$
$877$	−8.84368	−	15.3177i	−0.298630	−	0.517242i	−0.975823	+	0.218564i	$0.929863\pi$
$878$	10.0367			0.338722
$879$		0			0
$880$			1.10201i			0.0371487i
$881$	11.6169			0.391384			0.195692	−	0.980665i	$-0.437305\pi$
$881$	11.6169			0.391384			0.195692	+	0.980665i	$0.437305\pi$
$882$		0			0
$883$	−35.5480			−1.19629			−0.598143	−	0.801389i	$-0.704095\pi$
$883$	−35.5480			−1.19629			−0.598143	+	0.801389i	$0.704095\pi$
$884$		−	9.70083i		−	0.326274i
$885$		0			0
$886$	−22.0584			−0.741065
$887$	−12.2751	−	21.2610i	−0.412156	−	0.713876i	0.582969	−	0.812494i	$-0.301891\pi$
$887$	−12.2751	−	21.2610i	−0.412156	−	0.713876i	−0.995125	+	0.0986188i	$0.968558\pi$
$888$		0			0
$889$		0			0
$890$			17.0088i			0.570136i
$891$		0			0
$892$	−1.16002	+	0.669741i	−0.0388405	+	0.0224246i
$893$	47.5590	+	27.4582i	1.59150	+	0.918854i
$894$		0			0
$895$	−44.7392	−	25.8302i	−1.49547	−	0.863408i
$896$		0			0
$897$		0			0
$898$	24.0862			0.803766
$899$	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
$905$	16.2257	−	9.36790i	0.539360	−	0.311399i
$906$		0			0
$907$	−18.4502	+	31.9567i	−0.612628	+	1.06110i	0.378167	+	0.925737i	$0.376554\pi$
$907$	−18.4502	+	31.9567i	−0.612628	+	1.06110i	−0.990796	+	0.135366i	$0.956779\pi$
$908$	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
$913$		−	1.01818i		−	0.0336970i
$914$		−	13.4681i		−	0.445485i
$915$		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	0.168879	−	0.985637i	$-0.445985\pi$
$919$	28.4363	−	49.2531i	0.938026	−	1.62471i	0.769147	−	0.639072i	$-0.220681\pi$
$920$	−2.38357	+	4.12846i	−0.0785838	+	0.136111i
$921$		0			0
$922$	40.0513	−	23.1236i	1.31902	−	0.761535i
$923$	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
$929$	−45.7769			−1.50189			−0.750946	−	0.660364i	$-0.770402\pi$
$929$	−45.7769			−1.50189			−0.750946	+	0.660364i	$0.770402\pi$
$930$		0			0
$931$		0			0
$932$	8.77383	+	5.06557i	0.287396	+	0.165928i
$933$		0			0
$934$	−3.69047	−	2.13069i	−0.120756	−	0.0697183i
$935$	1.60769	−	0.928200i	0.0525771	−	0.0303554i
$936$		0			0
$937$		−	24.0003i		−	0.784054i	−0.919954	−	0.392027i	$-0.871774\pi$
$937$		−	24.0003i		−	0.784054i	0.919954	−	0.392027i	$-0.128226\pi$
$938$		0			0
$939$		0			0
$940$	7.30039	+	12.6446i	0.238112	+	0.412423i
$941$	3.28632			0.107131			0.0535654	−	0.998564i	$-0.482941\pi$
$941$	3.28632			0.107131			0.0535654	+	0.998564i	$0.482941\pi$
$942$		0			0
$943$		−	2.17979i		−	0.0709838i
$944$	−8.89158			−0.289396
$945$		0			0
$946$	1.22938			0.0399707
$947$			29.9552i			0.973415i	0.873565	+	0.486707i	$0.161802\pi$
$947$			29.9552i			0.973415i	−0.873565	+	0.486707i	$0.838198\pi$
$948$		0			0
$949$	59.1928			1.92148
$950$	−11.4742	−	19.8739i	−0.372272	−	0.644794i
$951$		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
$956$	−1.14893	−	0.663336i	−0.0371591	−	0.0214538i
$957$		0			0
$958$	1.66605	+	0.961893i	0.0538275	+	0.0310773i
$959$		0			0
$960$		0			0
$961$	30.9832			0.999460
$962$	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	$-0.131077\pi$
$968$	−29.2345	+	16.8786i	−0.939633	+	0.542497i
$969$		0			0
$970$	4.24484	−	7.35228i	0.136294	−	0.236068i
$971$	−0.520938	+	0.902292i	−0.0167177	+	0.0289559i	−0.874263	−	0.485452i	$-0.838655\pi$
$971$	−0.520938	+	0.902292i	−0.0167177	+	0.0289559i	0.857546	+	0.514408i	$0.171988\pi$
$972$		0			0
$973$		0			0
$974$	−8.21195	+	4.74117i	−0.263128	+	0.151917i
$975$		0			0
$976$			8.28114i			0.265073i
$977$			24.4525i			0.782304i	0.920326	+	0.391152i	$0.127923\pi$
$977$			24.4525i			0.782304i	−0.920326	+	0.391152i	$0.872077\pi$
$978$		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
$983$	28.0788	−	48.6339i	0.895575	−	1.55118i	0.0624829	−	0.998046i	$-0.480098\pi$
$983$	28.0788	−	48.6339i	0.895575	−	1.55118i	0.833092	−	0.553135i	$-0.186569\pi$
$984$		0			0
$985$	−49.4050	+	28.5240i	−1.57417	+	0.908850i
$986$	−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	0.684181	−	0.729312i	$-0.260160\pi$
$991$	−9.11390	−	15.7857i	−0.289513	−	0.501451i	−0.973693	+	0.227862i	$0.926827\pi$
$992$	−0.418513			−0.0132878
$993$		0			0
$994$		0			0
$995$	−31.7979	−	18.3586i	−1.00806	−	0.582005i
$996$		0			0
$997$	29.8197	+	17.2164i	0.944399	+	0.545249i	0.891337	−	0.453342i	$-0.149768\pi$
$997$	29.8197	+	17.2164i	0.944399	+	0.545249i	0.0530623	+	0.998591i	$0.483102\pi$
$998$	−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.i.c.1097.1		12
3.2	odd	2		441.2.i.c.68.6		12
7.2	even	3		189.2.o.a.125.1		12
7.3	odd	6		1323.2.s.c.962.5		12
7.4	even	3		1323.2.s.c.962.6		12
7.5	odd	6		189.2.o.a.125.2		12
7.6	odd	2	inner	1323.2.i.c.1097.2		12
9.2	odd	6		1323.2.s.c.656.5		12
9.7	even	3		441.2.s.c.362.2		12
21.2	odd	6		63.2.o.a.41.5	yes	12
21.5	even	6		63.2.o.a.41.6	yes	12
21.11	odd	6		441.2.s.c.374.1		12
21.17	even	6		441.2.s.c.374.2		12
21.20	even	2		441.2.i.c.68.5		12
28.19	even	6		3024.2.cc.a.881.6		12
28.23	odd	6		3024.2.cc.a.881.1		12
63.2	odd	6		189.2.o.a.62.2		12
63.5	even	6		567.2.c.c.566.10		12
63.11	odd	6	inner	1323.2.i.c.521.6		12
63.16	even	3		63.2.o.a.20.6	yes	12
63.20	even	6		1323.2.s.c.656.6		12
63.23	odd	6		567.2.c.c.566.9		12
63.25	even	3		441.2.i.c.227.1		12
63.34	odd	6		441.2.s.c.362.1		12
63.38	even	6	inner	1323.2.i.c.521.5		12
63.40	odd	6		567.2.c.c.566.3		12
63.47	even	6		189.2.o.a.62.1		12
63.52	odd	6		441.2.i.c.227.2		12
63.58	even	3		567.2.c.c.566.4		12
63.61	odd	6		63.2.o.a.20.5	✓	12
84.23	even	6		1008.2.cc.a.545.4		12
84.47	odd	6		1008.2.cc.a.545.3		12
252.47	odd	6		3024.2.cc.a.2897.1		12
252.79	odd	6		1008.2.cc.a.209.3		12
252.187	even	6		1008.2.cc.a.209.4		12
252.191	even	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	63.61	odd	6
63.2.o.a.20.6	yes	12	63.16	even	3
63.2.o.a.41.5	yes	12	21.2	odd	6
63.2.o.a.41.6	yes	12	21.5	even	6
189.2.o.a.62.1		12	63.47	even	6
189.2.o.a.62.2		12	63.2	odd	6
189.2.o.a.125.1		12	7.2	even	3
189.2.o.a.125.2		12	7.5	odd	6
441.2.i.c.68.5		12	21.20	even	2
441.2.i.c.68.6		12	3.2	odd	2
441.2.i.c.227.1		12	63.25	even	3
441.2.i.c.227.2		12	63.52	odd	6
441.2.s.c.362.1		12	63.34	odd	6
441.2.s.c.362.2		12	9.7	even	3
441.2.s.c.374.1		12	21.11	odd	6
441.2.s.c.374.2		12	21.17	even	6
567.2.c.c.566.3		12	63.40	odd	6
567.2.c.c.566.4		12	63.58	even	3
567.2.c.c.566.9		12	63.23	odd	6
567.2.c.c.566.10		12	63.5	even	6
1008.2.cc.a.209.3		12	252.79	odd	6
1008.2.cc.a.209.4		12	252.187	even	6
1008.2.cc.a.545.3		12	84.47	odd	6
1008.2.cc.a.545.4		12	84.23	even	6
1323.2.i.c.521.5		12	63.38	even	6	inner
1323.2.i.c.521.6		12	63.11	odd	6	inner
1323.2.i.c.1097.1		12	1.1	even	1	trivial
1323.2.i.c.1097.2		12	7.6	odd	2	inner
1323.2.s.c.656.5		12	9.2	odd	6
1323.2.s.c.656.6		12	63.20	even	6
1323.2.s.c.962.5		12	7.3	odd	6
1323.2.s.c.962.6		12	7.4	even	3
3024.2.cc.a.881.1		12	28.23	odd	6
3024.2.cc.a.881.6		12	28.19	even	6
3024.2.cc.a.2897.1		12	252.47	odd	6
3024.2.cc.a.2897.6		12	252.191	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.18593i q^{2} +0.593579 q^{4} +(-1.41899 - 2.45776i) q^{5} -3.07579i q^{8} +O(q^{10})\)	\(q-1.18593i q^{2} +0.593579 q^{4} +(-1.41899 - 2.45776i) q^{5} -3.07579i q^{8} +(-2.91472 + 1.68281i) q^{10} +(0.136673 + 0.0789082i) q^{11} +(-3.41468 - 1.97146i) q^{13} -2.46050 q^{16} +(2.07244 + 3.58956i) q^{17} +(-5.48711 - 3.16799i) q^{19} +(-0.842281 - 1.45887i) q^{20} +(0.0935793 - 0.162084i) q^{22} +(0.472958 - 0.273062i) q^{23} +(-1.52704 + 2.64491i) q^{25} +(-2.33801 + 4.04955i) q^{26} +(-4.02704 + 2.32501i) q^{29} -0.129426i q^{31} -3.23361i q^{32} +(4.25696 - 2.45776i) q^{34} +(1.23025 - 2.13086i) q^{37} +(-3.75700 + 6.50731i) q^{38} +(-7.55955 + 4.36451i) q^{40} +(1.99569 - 3.45664i) q^{41} +(3.28434 + 5.68864i) q^{43} +(0.0811263 + 0.0468383i) q^{44} +(-0.323832 - 0.560893i) q^{46} -8.66741 q^{47} +(3.13667 + 1.81096i) q^{50} +(-2.02688 - 1.17022i) q^{52} +(2.25370 - 1.30117i) q^{53} -0.447879i q^{55} +(2.75729 + 4.77577i) q^{58} +3.61372 q^{59} -3.36562i q^{61} -0.153489 q^{62} -8.75583 q^{64} +11.1899i q^{65} +1.32743 q^{67} +(1.23016 + 2.13069i) q^{68} +0.409310i q^{71} +(-13.0011 + 7.50619i) q^{73} +(-2.52704 - 1.45899i) q^{74} +(-3.25704 - 1.88045i) q^{76} +4.32743 q^{79} +(3.49142 + 6.04732i) q^{80} +(-4.09932 - 2.36674i) q^{82} +(-3.22585 - 5.58733i) q^{83} +(5.88151 - 10.1871i) q^{85} +(6.74630 - 3.89498i) q^{86} +(0.242705 - 0.420378i) q^{88} +(2.52684 - 4.37662i) q^{89} +(0.280738 - 0.162084i) q^{92} +10.2789i q^{94} +17.9813i q^{95} +(-2.18452 + 1.26123i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4}+O(q^{10}) \) 12 * q - 4 * q^4	\( 12 q - 4 q^{4} - 4 q^{16} - 10 q^{22} + 24 q^{23} - 30 q^{29} + 2 q^{37} - 10 q^{43} - 54 q^{44} + 20 q^{46} + 36 q^{50} + 12 q^{53} + 2 q^{58} + 16 q^{64} - 24 q^{67} - 12 q^{74} + 12 q^{79} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 30 q^{92}+O(q^{100}) \) 12 * q - 4 * q^4 - 4 * q^16 - 10 * q^22 + 24 * q^23 - 30 * q^29 + 2 * q^37 - 10 * q^43 - 54 * q^44 + 20 * q^46 + 36 * q^50 + 12 * q^53 + 2 * q^58 + 16 * q^64 - 24 * q^67 - 12 * q^74 + 12 * q^79 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 30 * q^92

Introduction

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