LMFDB - Embedded newform 189.2.o.a.62.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(62,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("189.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.o (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:	$1.50917259820$
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:	$\Z[a_1, \ldots, a_{7}]$
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			62.1
Root			$-1.82904 + 1.05600i$ of defining polynomial
Character	$\chi$	$=$	189.62
Dual form			189.2.o.a.125.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02704 - 0.592963i) q^{2} +(-0.296790 - 0.514055i) q^{4} +(-1.41899 - 2.45776i) q^{5} +(-2.07253 + 1.64457i) q^{7} +3.07579i q^{8} +O(q^{10})$	\(q+(-1.02704 - 0.592963i) q^{2} +(-0.296790 - 0.514055i) q^{4} +(-1.41899 - 2.45776i) q^{5} +(-2.07253 + 1.64457i) q^{7} +3.07579i q^{8} +3.36562i q^{10} +(-0.136673 - 0.0789082i) q^{11} +(-3.41468 + 1.97146i) q^{13} +(3.10375 - 0.460106i) q^{14} +(1.23025 - 2.13086i) q^{16} -4.14487 q^{17} -6.33597i q^{19} +(-0.842281 + 1.45887i) q^{20} +(0.0935793 + 0.162084i) q^{22} +(-0.472958 + 0.273062i) q^{23} +(-1.52704 + 2.64491i) q^{25} +4.67602 q^{26} +(1.46050 + 0.577305i) q^{28} +(-4.02704 - 2.32501i) q^{29} +(0.112086 - 0.0647129i) q^{31} +(2.80039 - 1.61680i) q^{32} +(4.25696 + 2.45776i) q^{34} +(6.98284 + 2.76016i) q^{35} -2.46050 q^{37} +(-3.75700 + 6.50731i) q^{38} +(7.55955 - 4.36451i) q^{40} +(1.99569 + 3.45664i) q^{41} +(3.28434 - 5.68864i) q^{43} +0.0936766i q^{44} +0.647664 q^{46} +(4.33370 - 7.50619i) q^{47} +(1.59079 - 6.81685i) q^{49} +(3.13667 - 1.81096i) q^{50} +(2.02688 + 1.17022i) q^{52} -2.60234i q^{53} +0.447879i q^{55} +(-5.05835 - 6.37468i) q^{56} +(2.75729 + 4.77577i) q^{58} +(-1.80686 - 3.12957i) q^{59} +(-2.91472 - 1.68281i) q^{61} -0.153489 q^{62} -8.75583 q^{64} +(9.69076 + 5.59496i) q^{65} +(-0.663715 - 1.14959i) q^{67} +(1.23016 + 2.13069i) q^{68} +(-5.53500 - 6.97537i) q^{70} -0.409310i q^{71} +15.0124i q^{73} +(2.52704 + 1.45899i) q^{74} +(-3.25704 + 1.88045i) q^{76} +(0.413030 - 0.0612283i) q^{77} +(-2.16372 + 3.74766i) q^{79} -6.98284 q^{80} -4.73348i q^{82} +(-3.22585 + 5.58733i) q^{83} +(5.88151 + 10.1871i) q^{85} +(-6.74630 + 3.89498i) q^{86} +(0.242705 - 0.420378i) q^{88} -5.05368 q^{89} +(3.83482 - 9.70160i) q^{91} +(0.280738 + 0.162084i) q^{92} +(-8.90179 + 5.13945i) q^{94} +(-15.5723 + 8.99066i) q^{95} +(-2.18452 - 1.26123i) q^{97} +(-5.67594 + 6.05791i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7}+O(q^{10}) $ 12 * q + 6 * q^2 + 2 * q^4 - 2 * q^7	$ 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7} + 12 q^{14} + 2 q^{16} - 10 q^{22} - 24 q^{23} - 8 q^{28} - 30 q^{29} + 12 q^{32} - 4 q^{37} - 10 q^{43} - 40 q^{46} + 6 q^{49} + 36 q^{50} - 42 q^{56} + 2 q^{58} + 16 q^{64} + 78 q^{65} + 12 q^{67} + 18 q^{70} + 12 q^{74} + 24 q^{77} - 6 q^{79} - 6 q^{85} - 96 q^{86} + 34 q^{88} - 24 q^{91} - 30 q^{92} - 72 q^{95}+O(q^{100}) $ 12 * q + 6 * q^2 + 2 * q^4 - 2 * q^7 + 12 * q^14 + 2 * q^16 - 10 * q^22 - 24 * q^23 - 8 * q^28 - 30 * q^29 + 12 * q^32 - 4 * q^37 - 10 * q^43 - 40 * q^46 + 6 * q^49 + 36 * q^50 - 42 * q^56 + 2 * q^58 + 16 * q^64 + 78 * q^65 + 12 * q^67 + 18 * q^70 + 12 * q^74 + 24 * q^77 - 6 * q^79 - 6 * q^85 - 96 * q^86 + 34 * q^88 - 24 * q^91 - 30 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.02704	−	0.592963i	−0.726228	−	0.419288i	0.0908124	−	0.995868i	$-0.471054\pi$
$2$	−1.02704	−	0.592963i	−0.726228	−	0.419288i	−0.817041	+	0.576580i	$0.804387\pi$
$3$		0			0
$3$		0			0
$4$	−0.296790	−	0.514055i	−0.148395	−	0.257027i
$5$	−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
$7$	−2.07253	+	1.64457i	−0.783344	+	0.621589i
$7$	−2.07253	+	1.64457i	−0.783344	+	0.621589i
$8$			3.07579i			1.08746i
$9$		0			0
$10$			3.36562i			1.06430i
$11$	−0.136673	−	0.0789082i	−0.0412085	−	0.0237917i	0.479254	−	0.877676i	$-0.340907\pi$
$11$	−0.136673	−	0.0789082i	−0.0412085	−	0.0237917i	−0.520463	+	0.853884i	$0.674241\pi$
$12$		0			0
$13$	−3.41468	+	1.97146i	−0.947061	+	0.546786i	−0.892167	−	0.451706i	$-0.850816\pi$
$13$	−3.41468	+	1.97146i	−0.947061	+	0.546786i	−0.0548943	+	0.998492i	$0.517482\pi$
$14$	3.10375	−	0.460106i	0.829511	−	0.122968i
$15$		0			0
$16$	1.23025	−	2.13086i	0.307563	−	0.532715i
$17$	−4.14487			−1.00528			−0.502640	−	0.864496i	$-0.667638\pi$
$17$	−4.14487			−1.00528			−0.502640	+	0.864496i	$0.667638\pi$
$18$		0			0
$19$		−	6.33597i		−	1.45357i	−0.686864	−	0.726786i	$-0.741013\pi$
$19$		−	6.33597i		−	1.45357i	0.686864	−	0.726786i	$-0.258987\pi$
$20$	−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	−0.548498	−	0.836152i	$-0.684800\pi$
$23$	−0.472958	+	0.273062i	−0.0986185	+	0.0569374i	0.449880	+	0.893089i	$0.351467\pi$
$24$		0			0
$25$	−1.52704	+	2.64491i	−0.305408	+	0.528983i
$26$	4.67602			0.917044
$27$		0			0
$28$	1.46050	+	0.577305i	0.276009	+	0.109100i
$29$	−4.02704	−	2.32501i	−0.747803	−	0.431744i	0.0770966	−	0.997024i	$-0.475435\pi$
$29$	−4.02704	−	2.32501i	−0.747803	−	0.431744i	−0.824900	+	0.565279i	$0.808768\pi$
$30$		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
$35$	6.98284	+	2.76016i	1.18032	+	0.466552i
$36$		0			0
$37$	−2.46050			−0.404505			−0.202252	−	0.979333i	$-0.564826\pi$
$37$	−2.46050			−0.404505			−0.202252	+	0.979333i	$0.564826\pi$
$38$	−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	0.978725	−	0.205176i	$-0.0657768\pi$
$41$	1.99569	+	3.45664i	0.311675	+	0.539836i	−0.667050	+	0.745013i	$0.732443\pi$
$42$		0			0
$43$	3.28434	−	5.68864i	0.500857	−	0.867509i	−0.499143	−	0.866520i	$-0.666352\pi$
$43$	3.28434	−	5.68864i	0.500857	−	0.867509i	1.00000		0.000989450i	$-0.000314952\pi$
$44$			0.0936766i			0.0141223i
$45$		0			0
$46$	0.647664			0.0954928
$47$	4.33370	−	7.50619i	0.632135	−	1.09489i	−0.354979	−	0.934874i	$-0.615512\pi$
$47$	4.33370	−	7.50619i	0.632135	−	1.09489i	0.987114	−	0.160016i	$-0.0511547\pi$
$48$		0			0
$49$	1.59079	−	6.81685i	0.227255	−	0.973835i
$50$	3.13667	−	1.81096i	0.443593	−	0.256108i
$51$		0			0
$52$	2.02688	+	1.17022i	0.281078	+	0.162280i
$53$		−	2.60234i		−	0.357459i	−0.983898	−	0.178730i	$-0.942801\pi$
$53$		−	2.60234i		−	0.357459i	0.983898	−	0.178730i	$-0.0571988\pi$
$54$		0			0
$55$			0.447879i			0.0603920i
$56$	−5.05835	−	6.37468i	−0.675951	−	0.851853i
$57$		0			0
$58$	2.75729	+	4.77577i	0.362051	+	0.627090i
$59$	−1.80686	−	3.12957i	−0.235233	−	0.407436i	0.724107	−	0.689687i	$-0.242252\pi$
$59$	−1.80686	−	3.12957i	−0.235233	−	0.407436i	−0.959340	+	0.282252i	$0.908919\pi$
$60$		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	$0.859172\pi$
$68$	1.23016	+	2.13069i	0.149178	+	0.258384i
$69$		0			0
$70$	−5.53500	−	6.97537i	−0.661559	−	0.833716i
$71$		−	0.409310i		−	0.0485761i	−0.999705	−	0.0242881i	$-0.992268\pi$
$71$		−	0.409310i		−	0.0485761i	0.999705	−	0.0242881i	$-0.00773189\pi$
$72$		0			0
$73$			15.0124i			1.75707i	0.477681	+	0.878533i	$0.341478\pi$
$73$			15.0124i			1.75707i	−0.477681	+	0.878533i	$0.658522\pi$
$74$	2.52704	+	1.45899i	0.293763	+	0.169604i
$75$		0			0
$76$	−3.25704	+	1.88045i	−0.373608	+	0.215703i
$77$	0.413030	−	0.0612283i	0.0470691	−	0.00697762i
$78$		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	$0.244942\pi$
$80$	−6.98284			−0.780706
$81$		0			0
$82$		−	4.73348i		−	0.522726i
$83$	−3.22585	+	5.58733i	−0.354083	+	0.613289i	−0.986961	−	0.160963i	$-0.948540\pi$
$83$	−3.22585	+	5.58733i	−0.354083	+	0.613289i	0.632878	+	0.774252i	$0.281874\pi$
$84$		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
$89$	−5.05368			−0.535689			−0.267845	−	0.963462i	$-0.586311\pi$
$89$	−5.05368			−0.535689			−0.267845	+	0.963462i	$0.586311\pi$
$90$		0			0
$91$	3.83482	−	9.70160i	0.401999	−	1.01700i
$92$	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	$-0.374208\pi$
$97$	−2.18452	−	1.26123i	−0.221805	−	0.128059i	−0.606786	+	0.794866i	$0.707541\pi$
$98$	−5.67594	+	6.05791i	−0.573357	+	0.611941i
$99$		0			0
$100$	1.81284			0.181284
$101$	−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	−0.942950	−	0.332934i	$-0.891962\pi$
$103$	−11.4286	+	6.59832i	−1.12610	+	0.650152i	−0.183146	+	0.983086i	$0.558628\pi$
$104$	−6.06382	−	10.5028i	−0.594606	−	1.02989i
$105$		0			0
$106$	−1.54309	+	2.67272i	−0.149879	+	0.259597i
$107$		−	19.5555i		−	1.89051i	−0.326339	−	0.945253i	$-0.605815\pi$
$107$		−	19.5555i		−	1.89051i	0.326339	−	0.945253i	$-0.394185\pi$
$108$		0			0
$109$	13.2484			1.26897			0.634485	−	0.772935i	$-0.281212\pi$
$109$	13.2484			1.26897			0.634485	+	0.772935i	$0.281212\pi$
$110$	0.265576	−	0.459990i	0.0253216	−	0.0438584i
$111$		0			0
$112$	0.954606	+	6.43951i	0.0902018	+	0.608477i
$113$	8.72665	−	5.03834i	0.820935	−	0.473967i	−0.0298041	−	0.999556i	$-0.509488\pi$
$113$	8.72665	−	5.03834i	0.820935	−	0.473967i	0.850739	+	0.525589i	$0.176155\pi$
$114$		0			0
$115$	1.34224	+	0.774943i	0.125165	+	0.0722638i
$116$			2.76016i			0.256274i
$117$		0			0
$118$			4.28561i			0.394522i
$119$	8.59038	−	6.81653i	0.787479	−	0.624870i
$120$		0			0
$121$	−5.48755	−	9.50471i	−0.498868	−	0.864065i
$122$	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
$131$	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
$133$	10.4199	+	13.1315i	0.903524	+	1.13865i
$134$			1.57423i			0.135993i
$135$		0			0
$136$		−	12.7488i		−	1.09320i
$137$	6.96410	+	4.02073i	0.594984	+	0.343514i	0.767066	−	0.641569i	$-0.221716\pi$
$137$	6.96410	+	4.02073i	0.594984	+	0.343514i	−0.172082	+	0.985083i	$0.555049\pi$
$138$		0			0
$139$	16.3702	−	9.45136i	1.38850	−	0.801654i	0.395358	−	0.918527i	$-0.370621\pi$
$139$	16.3702	−	9.45136i	1.38850	−	0.801654i	0.993147	+	0.116873i	$0.0372872\pi$
$140$	−0.653562	−	4.40875i	−0.0552361	−	0.372607i
$141$		0			0
$142$	−0.242705	+	0.420378i	−0.0203674	+	0.0352774i
$143$	0.622259			0.0520359
$144$		0			0
$145$			13.1966i			1.09592i
$146$	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	−0.991776	−	0.127984i	$-0.959149\pi$
$149$	−16.8063	+	9.70313i	−1.37683	+	0.794912i	−0.385051	+	0.922895i	$0.625816\pi$
$150$		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	$0.143489\pi$
$152$	19.4881			1.58070
$153$		0			0
$154$	−0.460505	−	0.182027i	−0.0371085	−	0.0146682i
$155$	−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
$161$	0.531151	−	1.34374i	0.0418606	−	0.105902i
$162$		0			0
$163$	5.43560			0.425749			0.212874	−	0.977080i	$-0.431717\pi$
$163$	5.43560			0.425749			0.212874	+	0.977080i	$0.431717\pi$
$164$	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	0.994491	−	0.104821i	$-0.0334268\pi$
$167$	5.25273	+	9.09799i	0.406468	+	0.704024i	−0.588023	+	0.808844i	$0.700093\pi$
$168$		0			0
$169$	1.27335	−	2.20550i	0.0979497	−	0.169654i
$170$		−	13.9501i		−	1.06992i
$171$		0			0
$172$	−3.89903			−0.297298
$173$	−8.77949	+	15.2065i	−0.667492	+	1.15613i	0.311111	+	0.950374i	$0.399299\pi$
$173$	−8.77949	+	15.2065i	−0.667492	+	1.15613i	−0.978603	+	0.205757i	$0.934034\pi$
$174$		0			0
$175$	−1.18490	−	7.99300i	−0.0895699	−	0.604214i
$176$	−0.336285	+	0.194154i	−0.0253484	+	0.0146349i
$177$		0			0
$178$	5.19035	+	2.99665i	0.389033	+	0.224608i
$179$		−	18.2033i		−	1.36058i	−0.732945	−	0.680288i	$-0.761855\pi$
$179$		−	18.2033i		−	1.36058i	0.732945	−	0.680288i	$-0.238145\pi$
$180$		0			0
$181$		−	6.60182i		−	0.490710i	−0.969433	−	0.245355i	$-0.921096\pi$
$181$		−	6.60182i		−	0.490710i	0.969433	−	0.245355i	$-0.0789045\pi$
$182$	−9.69121	+	7.69004i	−0.718360	+	0.570024i
$183$		0			0
$184$	−0.839883	−	1.45472i	−0.0619170	−	0.107243i
$185$	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	0.874091	−	0.485762i	$-0.161458\pi$
$191$	12.3063	+	7.10506i	0.890454	+	0.514104i	0.0163630	+	0.999866i	$0.494791\pi$
$192$		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	$0.716089\pi$
$194$	1.49573	+	2.59068i	0.107387	+	0.186000i
$195$		0			0
$196$	−3.97636	+	1.20542i	−0.284026	+	0.0861013i
$197$			20.1017i			1.43218i	0.698006	+	0.716092i	$0.254071\pi$
$197$			20.1017i			1.43218i	−0.698006	+	0.716092i	$0.745929\pi$
$198$		0			0
$199$		−	12.9378i		−	0.917136i	−0.888659	−	0.458568i	$-0.848363\pi$
$199$		−	12.9378i		−	0.917136i	0.888659	−	0.458568i	$-0.151637\pi$
$200$	−8.13521	−	4.69687i	−0.575246	−	0.332119i
$201$		0			0
$202$	3.07236	−	1.77383i	0.216170	−	0.124806i
$203$	12.1698	−	1.80408i	0.854154	−	0.126622i
$204$		0			0
$205$	5.66372	−	9.80984i	0.395571	−	0.685149i
$206$	15.6502			1.09040
$207$		0			0
$208$			9.70160i			0.672685i
$209$	−0.499960	+	0.865957i	−0.0345830	+	0.0598995i
$210$		0			0
$211$	−4.50720	−	7.80669i	−0.310288	−	0.537435i	0.668136	−	0.744039i	$-0.267092\pi$
$211$	−4.50720	−	7.80669i	−0.310288	−	0.537435i	−0.978425	+	0.206604i	$0.933759\pi$
$212$	−1.33775	+	0.772349i	−0.0918769	+	0.0530451i
$213$		0			0
$214$	−11.5957	+	20.0844i	−0.792667	+	1.37294i
$215$	−18.6417			−1.27135
$216$		0			0
$217$	−0.125877	+	0.318453i	−0.00854510	+	0.0216180i
$218$	−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	$-0.357407\pi$
$223$	−1.95429	−	1.12831i	−0.130869	−	0.0755571i	−0.564005	+	0.825771i	$0.690740\pi$
$224$	−3.14495	+	7.95631i	−0.210131	+	0.531604i
$225$		0			0
$226$	−11.9502			−0.794915
$227$	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	−0.849965	−	0.526839i	$-0.823377\pi$
$229$	−12.3891	+	7.15283i	−0.818692	+	0.472672i	0.0312731	+	0.999511i	$0.490044\pi$
$230$	−0.919025	−	1.59180i	−0.0605987	−	0.104960i
$231$		0			0
$232$	7.15126	−	12.3863i	0.469503	−	0.813204i
$233$			17.0679i			1.11815i	0.829116	+	0.559077i	$0.188844\pi$
$233$			17.0679i			1.11815i	−0.829116	+	0.559077i	$0.811156\pi$
$234$		0			0
$235$	−24.5979			−1.60459
$236$	−1.07251	+	1.85765i	−0.0698148	+	0.120923i
$237$		0			0
$238$	−12.8646	+	1.90708i	−0.833890	+	0.123618i
$239$	−1.93560	+	1.11752i	−0.125203	+	0.0722863i	−0.561294	−	0.827617i	$-0.689696\pi$
$239$	−1.93560	+	1.11752i	−0.125203	+	0.0722863i	0.436090	+	0.899903i	$0.356363\pi$
$240$		0			0
$241$	−3.91464	−	2.26012i	−0.252164	−	0.145587i	0.368591	−	0.929592i	$-0.379840\pi$
$241$	−3.91464	−	2.26012i	−0.252164	−	0.145587i	−0.620755	+	0.784005i	$0.713174\pi$
$242$			13.0157i			0.836678i
$243$		0			0
$244$			1.99777i			0.127894i
$245$	−19.0114	+	5.76324i	−1.21460	+	0.368200i
$246$		0			0
$247$	12.4911	+	21.6353i	0.794793	+	1.37662i
$248$	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	$-0.267063\pi$
$251$	21.1727			1.33641			0.668205	+	0.743978i	$0.267063\pi$
$252$		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
$257$	−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
$259$	5.09948	−	4.04647i	0.316866	−	0.251435i
$260$		−	6.64211i		−	0.411926i
$261$		0			0
$262$		−	11.9126i		−	0.735964i
$263$	5.78220	+	3.33836i	0.356546	+	0.205852i	0.667564	−	0.744552i	$-0.267337\pi$
$263$	5.78220	+	3.33836i	0.356546	+	0.205852i	−0.311019	+	0.950404i	$0.600670\pi$
$264$		0			0
$265$	−6.39593	+	3.69269i	−0.392899	+	0.226840i
$266$	−2.91522	−	19.6653i	−0.178743	−	1.20575i
$267$		0			0
$268$	−0.393968	+	0.682372i	−0.0240654	+	0.0416825i
$269$	10.6589			0.649887			0.324944	−	0.945733i	$-0.394655\pi$
$269$	10.6589			0.649887			0.324944	+	0.945733i	$0.394655\pi$
$270$		0			0
$271$			7.44498i			0.452250i	0.974098	+	0.226125i	$0.0726058\pi$
$271$			7.44498i			0.452250i	−0.974098	+	0.226125i	$0.927394\pi$
$272$	−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	$-0.127376\pi$
$278$	−22.4172			−1.34450
$279$		0			0
$280$	−8.48968	+	21.4778i	−0.507356	+	1.28354i
$281$	−21.0993	−	12.1817i	−1.25868	−	0.726699i	−0.285862	−	0.958271i	$-0.592280\pi$
$281$	−21.0993	−	12.1817i	−1.25868	−	0.726699i	−0.972818	+	0.231572i	$0.925613\pi$
$282$		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
$287$	−9.82082	−	3.88195i	−0.579704	−	0.229144i
$288$		0			0
$289$	0.179961			0.0105860
$290$	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	0.708390	−	0.705821i	$-0.249422\pi$
$293$	−4.40023	−	7.62143i	−0.257064	−	0.445249i	−0.965454	+	0.260573i	$0.916089\pi$
$294$		0			0
$295$	−5.12782	+	8.88164i	−0.298553	+	0.517109i
$296$		−	7.56800i		−	0.439881i
$297$		0			0
$298$	23.0144			1.33319
$299$	1.07667	−	1.86484i	0.0622652	−	0.107846i
$300$		0			0
$301$	2.54846	+	17.1912i	0.146891	+	0.990885i
$302$	−1.83628	+	1.06018i	−0.105666	+	0.0610065i
$303$		0			0
$304$	−13.5011	−	7.79485i	−0.774339	−	0.447065i
$305$			9.55155i			0.546920i
$306$		0			0
$307$			11.1747i			0.637771i	0.947793	+	0.318886i	$0.103309\pi$
$307$			11.1747i			0.637771i	−0.947793	+	0.318886i	$0.896691\pi$
$308$	−0.154058	−	0.194148i	−0.00877825	−	0.0110626i
$309$		0			0
$310$	0.217799	+	0.377240i	0.0123702	+	0.0214258i
$311$	−8.20279	−	14.2076i	−0.465137	−	0.805641i	0.534070	−	0.845440i	$-0.320662\pi$
$311$	−8.20279	−	14.2076i	−0.465137	−	0.805641i	−0.999208	+	0.0397985i	$0.987328\pi$
$312$		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	−0.174491	−	0.984659i	$-0.555828\pi$
$317$	−19.8427	−	11.4562i	−1.11448	−	0.643443i	−0.939985	+	0.341215i	$0.889161\pi$
$318$		0			0
$319$	0.366926	+	0.635534i	0.0205439	+	0.0355831i
$320$	12.4244	+	21.5197i	0.694545	+	1.20299i
$321$		0			0
$322$	−1.34230	+	1.06513i	−0.0748037	+	0.0593572i
$323$			26.2618i			1.46125i
$324$		0			0
$325$		−	12.0420i		−	0.667972i
$326$	−5.58259	−	3.22311i	−0.309191	−	0.178512i
$327$		0			0
$328$	−10.6319	+	6.13833i	−0.587049	+	0.338933i
$329$	3.36271	+	22.6839i	0.185392	+	1.25060i
$330$		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	$0.989083\pi$
$332$	3.82959			0.210176
$333$		0			0
$334$		−	12.4587i		−	0.681709i
$335$	−1.88361	+	3.26250i	−0.102912	+	0.178249i
$336$		0			0
$337$	−2.26829	−	3.92878i	−0.123561	−	0.214015i	0.797608	−	0.603176i	$-0.206098\pi$
$337$	−2.26829	−	3.92878i	−0.123561	−	0.214015i	−0.921170	+	0.389161i	$0.872765\pi$
$338$	−2.61556	+	1.51009i	−0.142268	+	0.0821383i
$339$		0			0
$340$	3.49115	−	6.04684i	0.189334	−	0.327936i
$341$	−0.0204255			−0.00110610
$342$		0			0
$343$	7.91381	+	16.7443i	0.427306	+	0.904107i
$344$	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	−0.689070	−	0.724695i	$-0.741981\pi$
$347$	−7.56294	+	4.36646i	−0.406000	+	0.234404i	0.283070	+	0.959099i	$0.408647\pi$
$348$		0			0
$349$	7.82927	+	4.52023i	0.419091	+	0.241963i	0.694689	−	0.719311i	$-0.255542\pi$
$349$	7.82927	+	4.52023i	0.419091	+	0.241963i	−0.275597	+	0.961273i	$0.588876\pi$
$350$	−3.52261	+	8.91175i	−0.188292	+	0.476353i
$351$		0			0
$352$	−0.510317			−0.0272000
$353$	−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
$359$		−	17.3069i		−	0.913424i	−0.889615	−	0.456712i	$-0.849027\pi$
$359$		−	17.3069i		−	0.913424i	0.889615	−	0.456712i	$-0.150973\pi$
$360$		0			0
$361$	−21.1445			−1.11287
$362$	−3.91464	+	6.78035i	−0.205749	+	0.356367i
$363$		0			0
$364$	−6.12529	+	0.908025i	−0.321052	+	0.0475934i
$365$	36.8968	−	21.3024i	1.93127	−	1.11502i
$366$		0			0
$367$	−24.4297	−	14.1045i	−1.27522	−	0.736250i	−0.299256	−	0.954173i	$-0.596738\pi$
$367$	−24.4297	−	14.1045i	−1.27522	−	0.736250i	−0.975966	+	0.217923i	$0.930072\pi$
$368$			1.34374i			0.0700474i
$369$		0			0
$370$		−	8.28114i		−	0.430516i
$371$	4.27973	+	5.39344i	0.222193	+	0.280014i
$372$		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	$-0.427816\pi$
$374$	−0.387874	−	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
$383$	−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
$385$	−0.736567	−	0.928244i	−0.0375390	−	0.0473077i
$386$		−	11.8643i		−	0.603878i
$387$		0			0
$388$			1.49729i			0.0760131i
$389$	−4.43706	−	2.56174i	−0.224968	−	0.129885i	0.383281	−	0.923632i	$-0.374794\pi$
$389$	−4.43706	−	2.56174i	−0.224968	−	0.129885i	−0.608248	+	0.793747i	$0.708128\pi$
$390$		0			0
$391$	1.96035	−	1.13181i	0.0991391	−	0.0572380i
$392$	20.9672	+	4.89293i	1.05900	+	0.247130i
$393$		0			0
$394$	11.9195	−	20.6453i	0.600498	−	1.04009i
$395$	12.2811			0.617930
$396$		0			0
$397$		−	1.92094i		−	0.0964093i	−0.998837	−	0.0482046i	$-0.984650\pi$
$397$		−	1.92094i		−	0.0964093i	0.998837	−	0.0482046i	$-0.0153500\pi$
$398$	−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	−0.155475	−	0.987840i	$-0.549691\pi$
$401$	12.4612	−	7.19446i	0.622282	−	0.359274i	0.777757	+	0.628565i	$0.216358\pi$
$402$		0			0
$403$	−0.255158	+	0.441947i	−0.0127103	+	0.0220150i
$404$	1.77567			0.0883429
$405$		0			0
$406$	−13.5687	−	5.36339i	−0.673402	−	0.266181i
$407$	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
$413$	8.89158	+	3.51464i	0.437526	+	0.172944i
$414$		0			0
$415$	18.3097			0.898789
$416$	−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	0.956706	+	0.291058i	$0.0940072\pi$
$419$	14.9512	+	25.8963i	0.730416	+	1.26512i	−0.226289	+	0.974060i	$0.572660\pi$
$420$		0			0
$421$	−12.5452	+	21.7290i	−0.611417	+	1.05901i	0.379585	+	0.925157i	$0.376067\pi$
$421$	−12.5452	+	21.7290i	−0.611417	+	1.05901i	−0.991002	+	0.133848i	$0.957266\pi$
$422$			10.6904i			0.520401i
$423$		0			0
$424$	8.00427			0.388722
$425$	6.32939	−	10.9628i	0.307021	−	0.531775i
$426$		0			0
$427$	8.80835	−	1.30577i	0.426266	−	0.0631905i
$428$	−10.0526	+	5.80388i	−0.485912	+	0.280541i
$429$		0			0
$430$	19.1458	+	11.0538i	0.923293	+	0.533064i
$431$		−	6.39061i		−	0.307825i	−0.988084	−	0.153913i	$-0.950813\pi$
$431$		−	6.39061i		−	0.307825i	0.988084	−	0.153913i	$-0.0491874\pi$
$432$		0			0
$433$		−	33.1771i		−	1.59439i	−0.603721	−	0.797196i	$-0.706316\pi$
$433$		−	33.1771i		−	1.59439i	0.603721	−	0.797196i	$-0.293684\pi$
$434$	0.318112	−	0.252424i	0.0152699	−	0.0121167i
$435$		0			0
$436$	−3.93200	−	6.81042i	−0.188309	−	0.326160i
$437$	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	0.0658812	−	0.997827i	$-0.479014\pi$
$443$	−16.1082	−	9.30006i	−0.765322	−	0.441859i	−0.831203	+	0.555969i	$0.812348\pi$
$444$		0			0
$445$	7.17111	+	12.4207i	0.339943	+	0.588799i
$446$	1.33809	+	2.31764i	0.0633604	+	0.109743i
$447$		0			0
$448$	18.1468	−	14.3996i	0.857353	−	0.680316i
$449$		−	20.3100i		−	0.958489i	−0.877681	−	0.479245i	$-0.840911\pi$
$449$		−	20.3100i		−	0.958489i	0.877681	−	0.479245i	$-0.159089\pi$
$450$		0			0
$451$		−	0.629906i		−	0.0296611i
$452$	−5.17996	−	2.99065i	−0.243645	−	0.140668i
$453$		0			0
$454$	−19.1458	+	11.0538i	−0.898558	+	0.518783i
$455$	−29.2857	+	4.34137i	−1.37294	+	0.203527i
$456$		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	$0.252243\pi$
$458$	16.9654			0.792743
$459$		0			0
$460$		−	0.919981i		−	0.0428943i
$461$	19.4984	−	33.7721i	0.908129	−	1.57293i	0.0914676	−	0.995808i	$-0.470844\pi$
$461$	19.4984	−	33.7721i	0.908129	−	1.57293i	0.816661	−	0.577117i	$-0.195822\pi$
$462$		0			0
$463$	−5.03443	−	8.71990i	−0.233970	−	0.405248i	0.725003	−	0.688746i	$-0.241838\pi$
$463$	−5.03443	−	8.71990i	−0.233970	−	0.405248i	−0.958973	+	0.283498i	$0.908505\pi$
$464$	−9.90856	+	5.72071i	−0.459993	+	0.265577i
$465$		0			0
$466$	10.1206	−	17.5294i	0.468829	−	0.812035i
$467$	−3.59330			−0.166278			−0.0831389	−	0.996538i	$-0.526495\pi$
$467$	−3.59330			−0.166278			−0.0831389	+	0.996538i	$0.526495\pi$
$468$		0			0
$469$	3.26615	+	1.29103i	0.150817	+	0.0596145i
$470$	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
$476$	−6.05361	−	2.39285i	−0.277467	−	0.109676i
$477$		0			0
$478$	2.65059			0.121235
$479$	−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
$485$			7.15869i			0.325060i
$486$		0			0
$487$	7.99573			0.362321			0.181161	−	0.983454i	$-0.442015\pi$
$487$	7.99573			0.362321			0.181161	+	0.983454i	$0.442015\pi$
$488$	5.17598	−	8.96507i	0.234306	−	0.405829i
$489$		0			0
$490$	22.9429	+	5.35399i	1.03646	+	0.241869i
$491$	−9.30632	+	5.37300i	−0.419988	+	0.242480i	−0.695072	−	0.718940i	$-0.744628\pi$
$491$	−9.30632	+	5.37300i	−0.419988	+	0.242480i	0.275084	+	0.961420i	$0.411294\pi$
$492$		0			0
$493$	16.6916	+	9.63688i	0.751751	+	0.434023i
$494$		−	29.6272i		−	1.33299i
$495$		0			0
$496$		−	0.318453i		−	0.0142990i
$497$	0.673138	+	0.848308i	0.0301944	+	0.0380518i
$498$		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	$0.956977\pi$
$500$	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	$-0.772979\pi$
$503$	−33.9226			−1.51253			−0.756267	+	0.654263i	$0.772979\pi$
$504$		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
$509$	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
$511$	−24.6889	−	31.1137i	−1.09217	−	1.37639i
$512$		−	23.0923i		−	1.02055i
$513$		0			0
$514$			37.1201i			1.63730i
$515$	32.4341	+	18.7259i	1.42922	+	0.825160i
$516$		0			0
$517$	−1.18460	+	0.683930i	−0.0520987	+	0.0300792i
$518$	−7.63679	+	1.13209i	−0.335541	+	0.0497413i
$519$		0			0
$520$	−17.2089	+	29.8068i	−0.754662	+	1.30711i
$521$	−31.6986			−1.38874			−0.694370	−	0.719618i	$-0.744317\pi$
$521$	−31.6986			−1.38874			−0.694370	+	0.719618i	$0.744317\pi$
$522$		0			0
$523$		−	8.09911i		−	0.354149i	−0.984197	−	0.177075i	$-0.943337\pi$
$523$		−	8.09911i		−	0.354149i	0.984197	−	0.177075i	$-0.0566634\pi$
$524$	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
$530$	8.75851			0.380446
$531$		0			0
$532$	3.65779	−	9.25372i	0.158585	−	0.401200i
$533$	−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
$539$	−0.755323	+	0.806153i	−0.0325341	+	0.0347235i
$540$		0			0
$541$	1.21634			0.0522944			0.0261472	−	0.999658i	$-0.491676\pi$
$541$	1.21634			0.0522944			0.0261472	+	0.999658i	$0.491676\pi$
$542$	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	−0.436078	−	0.899909i	$-0.643633\pi$
$547$	13.1278	−	22.7380i	0.561305	−	0.972209i	0.997383	−	0.0722999i	$-0.0230339\pi$
$548$		−	4.77324i		−	0.203903i
$549$		0			0
$550$	−0.571598			−0.0243730
$551$	−14.7312	+	25.5152i	−0.627571	+	1.08699i
$552$		0			0
$553$	−1.67892	−	11.3255i	−0.0713950	−	0.481611i
$554$	−27.2768	+	15.7482i	−1.15888	+	0.669079i
$555$		0			0
$556$	−9.71703	−	5.61013i	−0.412094	−	0.237923i
$557$			27.2172i			1.15323i	0.817016	+	0.576615i	$0.195627\pi$
$557$			27.2172i			1.15323i	−0.817016	+	0.576615i	$0.804373\pi$
$558$		0			0
$559$			25.8998i			1.09545i
$560$	14.4722	−	11.4838i	0.611561	−	0.485278i
$561$		0			0
$562$	14.4466	+	25.0222i	0.609393	+	1.05550i
$563$	4.68017	+	8.10630i	0.197246	+	0.341640i	0.947634	−	0.319357i	$-0.103467\pi$
$563$	4.68017	+	8.10630i	0.197246	+	0.341640i	−0.750389	+	0.660997i	$0.770134\pi$
$564$		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	0.974576	−	0.224055i	$-0.0719296\pi$
$569$	30.2424	+	17.4605i	1.26783	+	0.731980i	0.293251	+	0.956036i	$0.405263\pi$
$570$		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	$0.823528\pi$
$572$	−0.184680	−	0.319875i	−0.00772186	−	0.0133747i
$573$		0			0
$574$	7.78454	+	9.81030i	0.324920	+	0.409474i
$575$		−	1.66791i		−	0.0695567i
$576$		0			0
$577$			18.6196i			0.775146i	0.921839	+	0.387573i	$0.126686\pi$
$577$			18.6196i			0.775146i	−0.921839	+	0.387573i	$0.873314\pi$
$578$	−0.184828	−	0.106710i	−0.00768783	−	0.00443857i
$579$		0			0
$580$	6.78380	−	3.91663i	0.281682	−	0.162629i
$581$	−2.50307	−	16.8851i	−0.103845	−	0.700510i
$582$		0			0
$583$	−0.205346	+	0.355670i	−0.00850458	+	0.0147304i
$584$	−46.1750			−1.91073
$585$		0			0
$586$			10.4367i			0.431136i
$587$	−9.28551	+	16.0830i	−0.383254	+	0.663816i	−0.991525	−	0.129914i	$-0.958530\pi$
$587$	−9.28551	+	16.0830i	−0.383254	+	0.663816i	0.608271	+	0.793729i	$0.291863\pi$
$588$		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
$593$	30.9228			1.26985			0.634924	−	0.772574i	$-0.281031\pi$
$593$	30.9228			1.26985			0.634924	+	0.772574i	$0.281031\pi$
$594$		0			0
$595$	−28.9430	−	11.4405i	−1.18655	−	0.469015i
$596$	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	−0.722566	−	0.691302i	$-0.757037\pi$
$599$	−11.8741	+	6.85553i	−0.485164	+	0.280109i	0.237402	+	0.971411i	$0.423704\pi$
$600$		0			0
$601$	−17.1065	−	9.87644i	−0.697788	−	0.402868i	0.108735	−	0.994071i	$-0.465320\pi$
$601$	−17.1065	−	9.87644i	−0.697788	−	0.402868i	−0.806523	+	0.591203i	$0.798653\pi$
$602$	7.57638	−	19.1672i	0.308790	−	0.781198i
$603$		0			0
$604$	−1.06128			−0.0431829
$605$	−15.5735	+	26.9741i	−0.633153	+	1.09665i
$606$		0			0
$607$	−15.5219	+	8.96157i	−0.630014	+	0.363739i	−0.780757	−	0.624834i	$-0.785167\pi$
$607$	−15.5219	+	8.96157i	−0.630014	+	0.363739i	0.150744	+	0.988573i	$0.451833\pi$
$608$	−10.2440	−	17.7432i	−0.415450	−	0.719581i
$609$		0			0
$610$	5.66372	−	9.80984i	0.229317	−	0.397189i
$611$			34.1750i			1.38257i
$612$		0			0
$613$	−41.4327			−1.67345			−0.836725	−	0.547623i	$-0.815533\pi$
$613$	−41.4327			−1.67345			−0.836725	+	0.547623i	$0.815533\pi$
$614$	6.62616	−	11.4768i	0.267410	−	0.463168i
$615$		0			0
$616$	0.188326	+	1.27039i	0.00758786	+	0.0511856i
$617$	−19.9686	+	11.5289i	−0.803904	+	0.464134i	−0.844835	−	0.535028i	$-0.820301\pi$
$617$	−19.9686	+	11.5289i	−0.803904	+	0.464134i	0.0409302	+	0.999162i	$0.486968\pi$
$618$		0			0
$619$	1.67850	+	0.969082i	0.0674646	+	0.0389507i	0.533353	−	0.845893i	$-0.320932\pi$
$619$	1.67850	+	0.969082i	0.0674646	+	0.0389507i	−0.465888	+	0.884844i	$0.654265\pi$
$620$			0.218026i			0.00875613i
$621$		0			0
$622$			19.4558i			0.780106i
$623$	10.4739	−	8.31113i	0.419629	−	0.332978i
$624$		0			0
$625$	15.4715	+	26.7974i	0.618860	+	1.07190i
$626$	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
$635$	17.7227	+	30.6966i	0.703303	+	1.21816i
$636$		0			0
$637$	8.00715	+	26.4135i	0.317255	+	1.04654i
$638$		−	0.870293i		−	0.0344552i
$639$		0			0
$640$		−	11.1151i		−	0.439361i
$641$	−21.5093	−	12.4184i	−0.849568	−	0.490498i	0.0109373	−	0.999940i	$-0.496518\pi$
$641$	−21.5093	−	12.4184i	−0.849568	−	0.490498i	−0.860505	+	0.509442i	$0.829852\pi$
$642$		0			0
$643$	37.9247	−	21.8959i	1.49561	−	0.863489i	0.495619	−	0.868540i	$-0.334941\pi$
$643$	37.9247	−	21.8959i	1.49561	−	0.863489i	0.999987	+	0.00505169i	$0.00160801\pi$
$644$	−0.848397	+	0.125768i	−0.0334315	+	0.00495596i
$645$		0			0
$646$	15.5723	−	26.9720i	0.612683	−	1.06120i
$647$	−29.3713			−1.15471			−0.577353	−	0.816494i	$-0.695914\pi$
$647$	−29.3713			−1.15471			−0.577353	+	0.816494i	$0.695914\pi$
$648$		0			0
$649$			0.570305i			0.0223864i
$650$	−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	0.162981	−	0.986629i	$-0.447889\pi$
$653$	28.0816	−	16.2129i	1.09892	−	0.634461i	0.935937	+	0.352168i	$0.114556\pi$
$654$		0			0
$655$	14.2537	−	24.6881i	0.556938	−	0.964645i
$656$	9.82082			0.383438
$657$		0			0
$658$	9.99707	−	25.2913i	0.389727	−	0.985957i
$659$	0.203016	+	0.117211i	0.00790837	+	0.00456590i	0.503949	−	0.863733i	$-0.331880\pi$
$659$	0.203016	+	0.117211i	0.00790837	+	0.00456590i	−0.496041	+	0.868299i	$0.665213\pi$
$660$		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
$665$	17.4883	−	44.2431i	0.678167	−	1.71567i
$666$		0			0
$667$	2.53950			0.0983296
$668$	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	−0.633511	−	0.773734i	$-0.718387\pi$
$673$	9.16585	−	15.8757i	0.353318	−	0.611964i	0.986829	+	0.161770i	$0.0517202\pi$
$674$			5.38004i			0.207231i
$675$		0			0
$676$	−1.51166			−0.0581409
$677$	16.9260	−	29.3166i	0.650517	−	1.12673i	−0.332480	−	0.943110i	$-0.607885\pi$
$677$	16.9260	−	29.3166i	0.650517	−	1.12673i	0.982998	−	0.183619i	$-0.0587812\pi$
$678$		0			0
$679$	6.60168	−	0.978646i	0.253349	−	0.0375570i
$680$	−31.3334	+	18.0903i	−1.20158	+	0.693732i
$681$		0			0
$682$	0.0209779	+	0.0121116i	0.000803285	+	0.000463777i
$683$		−	28.0284i		−	1.07248i	−0.844066	−	0.536239i	$-0.819844\pi$
$683$		−	28.0284i		−	1.07248i	0.844066	−	0.536239i	$-0.180156\pi$
$684$		0			0
$685$		−	22.8214i		−	0.871962i
$686$	1.80093	−	21.8897i	0.0687599	−	0.835753i
$687$		0			0
$688$	−8.08113	−	13.9969i	−0.308090	−	0.533628i
$689$	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
$698$	−5.36066	−	9.28494i	−0.202904	−	0.351440i
$699$		0			0
$700$	−3.75717	+	2.98134i	−0.142008	+	0.112684i
$701$			26.3889i			0.996696i	0.866977	+	0.498348i	$0.166060\pi$
$701$			26.3889i			0.996696i	−0.866977	+	0.498348i	$0.833940\pi$
$702$		0			0
$703$			15.5897i			0.587976i
$704$	1.19669	+	0.690907i	0.0451018	+	0.0260396i
$705$		0			0
$706$	1.24867	−	0.720920i	0.0469943	−	0.0271322i
$707$	−1.16060	−	7.82911i	−0.0436489	−	0.294444i
$708$		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	$0.102192\pi$
$710$	1.37758			0.0516998
$711$		0			0
$712$		−	15.5441i		−	0.582539i
$713$	−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
$719$	17.5794			0.655601			0.327801	−	0.944747i	$-0.393693\pi$
$719$	17.5794			0.655601			0.327801	+	0.944747i	$0.393693\pi$
$720$		0			0
$721$	12.8348	−	32.4704i	0.477994	−	1.20926i
$722$	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	0.988860	+	0.148847i	$0.0475563\pi$
$727$	43.4695	+	25.0971i	1.61220	+	0.930802i	0.623336	+	0.781954i	$0.285777\pi$
$728$	29.8401	+	11.7951i	1.10595	+	0.437156i
$729$		0			0
$730$	−50.5261			−1.87005
$731$	−13.6132	+	23.5787i	−0.503501	+	0.872089i
$732$		0			0
$733$	34.5617	−	19.9542i	1.27656	−	0.737025i	0.300350	−	0.953829i	$-0.402897\pi$
$733$	34.5617	−	19.9542i	1.27656	−	0.737025i	0.976215	+	0.216804i	$0.0695633\pi$
$734$	16.7269	+	28.9719i	0.617402	+	1.06937i
$735$		0			0
$736$	−0.882977	+	1.52936i	−0.0325470	+	0.0563730i
$737$			0.209490i			0.00771668i
$738$		0			0
$739$	30.3432			1.11619			0.558096	−	0.829777i	$-0.311532\pi$
$739$	30.3432			1.11619			0.558096	+	0.829777i	$0.311532\pi$
$740$	2.07244	−	3.58956i	0.0761843	−	0.131955i
$741$		0			0
$742$	−1.19735	−	8.07702i	−0.0439562	−	0.296517i
$743$	39.5861	−	22.8550i	1.45227	−	0.838470i	0.453662	−	0.891174i	$-0.350117\pi$
$743$	39.5861	−	22.8550i	1.45227	−	0.838470i	0.998610	+	0.0527041i	$0.0167840\pi$
$744$		0			0
$745$	47.6959	+	27.5372i	1.74744	+	1.00889i
$746$			33.5056i			1.22673i
$747$		0			0
$748$		−	0.388278i		−	0.0141968i
$749$	32.1604	+	40.5295i	1.17512	+	1.48092i
$750$		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	$0.904517\pi$
$752$	−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
$761$	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
$763$	−27.4578	+	21.7880i	−0.994040	+	0.788777i
$764$		−	8.43483i		−	0.305161i
$765$		0			0
$766$			29.3949i			1.06208i
$767$	12.3397	+	7.12432i	0.445560	+	0.257244i
$768$		0			0
$769$	−9.42879	+	5.44371i	−0.340011	+	0.196305i	−0.660277	−	0.751022i	$-0.729561\pi$
$769$	−9.42879	+	5.44371i	−0.340011	+	0.196305i	0.320266	+	0.947328i	$0.396228\pi$
$770$	0.206072	+	1.39010i	0.00742630	+	0.0500958i
$771$		0			0
$772$	2.96916	−	5.14274i	0.106863	−	0.185091i
$773$	37.3337			1.34280			0.671400	−	0.741096i	$-0.265693\pi$
$773$	37.3337			1.34280			0.671400	+	0.741096i	$0.265693\pi$
$774$		0			0
$775$			0.395277i			0.0141988i
$776$	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
$782$	−2.68448			−0.0959969
$783$		0			0
$784$	−12.5687	−	11.7762i	−0.448881	−	0.420578i
$785$	−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
$791$	−9.80039	+	24.7937i	−0.348462	+	0.881562i
$792$		0			0
$793$	13.2704			0.471246
$794$	−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	0.746070	−	0.665868i	$-0.231939\pi$
$797$	−5.74854	−	9.95676i	−0.203624	−	0.352687i	−0.949693	+	0.313181i	$0.898605\pi$
$798$		0			0
$799$	−17.9626	+	31.1122i	−0.635473	+	1.10067i
$800$			9.87572i			0.349159i
$801$		0			0
$802$	−17.0642			−0.602558
$803$	1.18460	−	2.05179i	0.0418037	−	0.0724061i
$804$		0			0
$805$	−4.05629	+	0.601312i	−0.142965	+	0.0211935i
$806$	0.524117	−	0.302599i	0.0184612	−	0.0106586i
$807$		0			0
$808$	−7.96840	−	4.60056i	−0.280327	−	0.161847i
$809$		−	13.1945i		−	0.463893i	−0.972729	−	0.231946i	$-0.925491\pi$
$809$		−	13.1945i		−	0.463893i	0.972729	−	0.231946i	$-0.0745094\pi$
$810$		0			0
$811$			46.5800i			1.63565i	0.575469	+	0.817823i	$0.304819\pi$
$811$			46.5800i			1.63565i	−0.575469	+	0.817823i	$0.695181\pi$
$812$	−4.53927	−	5.72052i	−0.159297	−	0.200751i
$813$		0			0
$814$	−0.230252	−	0.398809i	−0.00807034	−	0.0139782i
$815$	−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	−0.238865	−	0.971053i	$-0.576775\pi$
$821$	−34.3623	−	19.8391i	−1.19925	−	0.692390i	−0.960389	+	0.278663i	$0.910109\pi$
$822$		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	$0.593679\pi$
$824$	−20.2951	−	35.1521i	−0.707013	−	1.22458i
$825$		0			0
$826$	−7.04797	−	8.88206i	−0.245230	−	0.309046i
$827$		−	21.0827i		−	0.733118i	−0.930395	−	0.366559i	$-0.880536\pi$
$827$		−	21.0827i		−	0.733118i	0.930395	−	0.366559i	$-0.119464\pi$
$828$		0			0
$829$		−	13.3261i		−	0.462834i	−0.972855	−	0.231417i	$-0.925664\pi$
$829$		−	13.3261i		−	0.462834i	0.972855	−	0.231417i	$-0.0743361\pi$
$830$	−18.8049	−	10.8570i	−0.652726	−	0.376852i
$831$		0			0
$832$	29.8983	−	17.2618i	1.03654	−	0.598446i
$833$	−6.59361	+	28.2550i	−0.228455	+	0.978976i
$834$		0			0
$835$	14.9071	−	25.8198i	0.515881	−	0.893533i
$836$	0.593532			0.0205277
$837$		0			0
$838$		−	35.4621i		−	1.22502i
$839$	−8.39768	+	14.5452i	−0.289920	+	0.502156i	−0.973790	−	0.227447i	$-0.926962\pi$
$839$	−8.39768	+	14.5452i	−0.289920	+	0.502156i	0.683870	+	0.729604i	$0.260295\pi$
$840$		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
$845$	−7.22744			−0.248632
$846$		0			0
$847$	27.0043	+	10.6742i	0.927878	+	0.366769i
$848$	−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	$-0.580949\pi$
$853$	−35.5011	−	20.4966i	−1.21554	−	0.701790i	−0.963960	+	0.266048i	$0.914282\pi$
$854$	−9.82082	−	3.88195i	−0.336061	−	0.132837i
$855$		0			0
$856$	60.1488			2.05584
$857$	−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	−0.0300858	−	0.999547i	$-0.509578\pi$
$859$	24.0479	−	13.8841i	0.820505	−	0.473719i	0.850590	+	0.525829i	$0.176245\pi$
$860$	5.53267	+	9.58286i	0.188662	+	0.326773i
$861$		0			0
$862$	−3.78940	+	6.56343i	−0.129067	+	0.223551i
$863$			45.6090i			1.55255i	0.630396	+	0.776274i	$0.282893\pi$
$863$			45.6090i			1.55255i	−0.630396	+	0.776274i	$0.717107\pi$
$864$		0			0
$865$	49.8319			1.69434
$866$	−19.6728	+	34.0743i	−0.668510	+	1.15789i
$867$		0			0
$868$	0.201061	−	0.0298057i	0.00682447	−	0.00101167i
$869$	0.591443	−	0.341470i	0.0200633	−	0.0115836i
$870$		0			0
$871$	4.53275	+	2.61698i	0.153586	+	0.0886731i
$872$			40.7495i			1.37995i
$873$		0			0
$874$		−	4.10358i		−	0.138806i
$875$	11.4455	−	9.08206i	0.386927	−	0.307030i
$876$		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	$0.929863\pi$
$878$	−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	$-0.437305\pi$
$881$	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	$0.704095\pi$
$884$	−8.40116	−	4.85041i	−0.282562	−	0.163137i
$885$		0			0
$886$	11.0292	+	19.1031i	0.370532	+	0.641781i
$887$	−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
$889$	25.8853	−	20.5401i	0.868165	−	0.688894i
$890$		−	17.0088i		−	0.570136i
$891$		0			0
$892$			1.33948i			0.0448492i
$893$	−47.5590	−	27.4582i	−1.59150	−	0.918854i
$894$		0			0
$895$	−44.7392	+	25.8302i	−1.49547	+	0.863408i
$896$	−10.2502	+	1.51951i	−0.342435	+	0.0507633i
$897$		0			0
$898$	−12.0431	+	20.8593i	−0.401883	+	0.696082i
$899$	−0.601834			−0.0200723
$900$		0			0
$901$			10.7864i			0.359346i
$902$	−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	$0.956779\pi$
$908$	−11.0653			−0.367216
$909$		0			0
$910$	32.6519	+	12.9066i	1.08240	+	0.427849i
$911$	34.4774	+	19.9056i	1.14229	+	0.659500i	0.946996	−	0.321245i	$-0.104101\pi$
$911$	34.4774	+	19.9056i	1.14229	+	0.659500i	0.195292	+	0.980745i	$0.437435\pi$
$912$		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
$917$	−24.7157	−	9.76957i	−0.816186	−	0.322620i
$918$		0			0
$919$	−56.8725			−1.87605			−0.938026	−	0.346565i	$-0.887348\pi$
$919$	−56.8725			−1.87605			−0.938026	+	0.346565i	$0.887348\pi$
$920$	−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
$926$			11.9409i			0.392403i
$927$		0			0
$928$	−15.0364			−0.493593
$929$	22.8885	−	39.6440i	0.750946	−	1.30068i	−0.196419	−	0.980520i	$-0.562931\pi$
$929$	22.8885	−	39.6440i	0.750946	−	1.30068i	0.947365	−	0.320156i	$-0.103735\pi$
$930$		0			0
$931$	−43.1913	−	10.0792i	−1.41554	−	0.330332i
$932$	8.77383	−	5.06557i	0.287396	−	0.165928i
$933$		0			0
$934$	3.69047	+	2.13069i	0.120756	+	0.0697183i
$935$		−	1.85640i		−	0.0607108i
$936$		0			0
$937$			24.0003i			0.784054i	0.919954	+	0.392027i	$0.128226\pi$
$937$			24.0003i			0.784054i	−0.919954	+	0.392027i	$0.871774\pi$
$938$	−2.58894	−	3.26265i	−0.0845318	−	0.106529i
$939$		0			0
$940$	7.30039	+	12.6446i	0.238112	+	0.412423i
$941$	−1.64316	−	2.84603i	−0.0535654	−	0.0927780i	0.837999	−	0.545671i	$-0.183725\pi$
$941$	−1.64316	−	2.84603i	−0.0535654	−	0.0927780i	−0.891565	+	0.452893i	$0.850392\pi$
$942$		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	0.858284	−	0.513176i	$-0.171531\pi$
$947$	25.9420	+	14.9776i	0.843002	+	0.486707i	−0.0152815	+	0.999883i	$0.504864\pi$
$948$		0			0
$949$	−29.5964	−	51.2624i	−0.960739	−	1.66405i
$950$	−11.4742	−	19.8739i	−0.372272	−	0.644794i
$951$		0			0
$952$	20.9662	+	26.4222i	0.679519	+	0.856350i
$953$			16.0580i			0.520169i	0.965586	+	0.260084i	$0.0837504\pi$
$953$			16.0580i			0.520169i	−0.965586	+	0.260084i	$0.916250\pi$
$954$		0			0
$955$		−	40.3279i		−	1.30498i
$956$	1.14893	+	0.663336i	0.0371591	+	0.0214538i
$957$		0			0
$958$	1.66605	−	0.961893i	0.0538275	−	0.0310773i
$959$	−21.0457	+	3.11986i	−0.679601	+	0.100745i
$960$		0			0
$961$	−15.4916	+	26.8323i	−0.499730	+	0.865557i
$962$	−11.5054			−0.370948
$963$		0			0
$964$			2.68312i			0.0864174i
$965$	14.1959	−	24.5881i	0.456983	−	0.791518i
$966$		0			0
$967$	25.0275	+	43.3489i	0.804831	+	1.39401i	0.916405	+	0.400252i	$0.131077\pi$
$967$	25.0275	+	43.3489i	0.804831	+	1.39401i	−0.111574	+	0.993756i	$0.535589\pi$
$968$	29.2345	−	16.8786i	0.939633	−	0.542497i
$969$		0			0
$970$	4.24484	−	7.35228i	0.136294	−	0.236068i
$971$	1.04188			0.0334354			0.0167177	−	0.999860i	$-0.494678\pi$
$971$	1.04188			0.0334354			0.0167177	+	0.999860i	$0.494678\pi$
$972$		0			0
$973$	−18.3844	+	46.5102i	−0.589378	+	1.49105i
$974$	−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	−0.798910	−	0.601450i	$-0.794590\pi$
$977$	−21.1765	+	12.2262i	−0.677495	+	0.391152i	0.121416	+	0.992602i	$0.461257\pi$
$978$		0			0
$979$	0.690703	+	0.398777i	0.0220750	+	0.0127450i
$980$	8.60502	+	8.06246i	0.274877	+	0.257546i
$981$		0			0
$982$	12.7440			0.406677
$983$	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
$989$			3.58731i			0.114070i
$990$		0			0
$991$	18.2278			0.579025			0.289513	−	0.957174i	$-0.406507\pi$
$991$	18.2278			0.579025			0.289513	+	0.957174i	$0.406507\pi$
$992$	0.209256	−	0.362443i	0.00664390	−	0.0115076i
$993$		0			0
$994$	−0.188326	−	1.27039i	−0.00597333	−	0.0402944i
$995$	−31.7979	+	18.3586i	−1.00806	+	0.582005i
$996$		0			0
$997$	−29.8197	−	17.2164i	−0.944399	−	0.545249i	−0.0530623	−	0.998591i	$-0.516898\pi$
$997$	−29.8197	−	17.2164i	−0.944399	−	0.545249i	−0.891337	+	0.453342i	$0.850232\pi$
$998$			20.0671i			0.635212i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.o.a.62.1		12
3.2	odd	2		63.2.o.a.20.5	✓	12
4.3	odd	2		3024.2.cc.a.2897.1		12
7.2	even	3		1323.2.i.c.521.5		12
7.3	odd	6		1323.2.s.c.656.5		12
7.4	even	3		1323.2.s.c.656.6		12
7.5	odd	6		1323.2.i.c.521.6		12
7.6	odd	2	inner	189.2.o.a.62.2		12
9.2	odd	6		567.2.c.c.566.3		12
9.4	even	3		63.2.o.a.41.6	yes	12
9.5	odd	6	inner	189.2.o.a.125.2		12
9.7	even	3		567.2.c.c.566.10		12
12.11	even	2		1008.2.cc.a.209.4		12
21.2	odd	6		441.2.i.c.227.2		12
21.5	even	6		441.2.i.c.227.1		12
21.11	odd	6		441.2.s.c.362.1		12
21.17	even	6		441.2.s.c.362.2		12
21.20	even	2		63.2.o.a.20.6	yes	12
28.27	even	2		3024.2.cc.a.2897.6		12
36.23	even	6		3024.2.cc.a.881.6		12
36.31	odd	6		1008.2.cc.a.545.3		12
63.4	even	3		441.2.i.c.68.5		12
63.5	even	6		1323.2.s.c.962.6		12
63.13	odd	6		63.2.o.a.41.5	yes	12
63.20	even	6		567.2.c.c.566.4		12
63.23	odd	6		1323.2.s.c.962.5		12
63.31	odd	6		441.2.i.c.68.6		12
63.32	odd	6		1323.2.i.c.1097.2		12
63.34	odd	6		567.2.c.c.566.9		12
63.40	odd	6		441.2.s.c.374.1		12
63.41	even	6	inner	189.2.o.a.125.1		12
63.58	even	3		441.2.s.c.374.2		12
63.59	even	6		1323.2.i.c.1097.1		12
84.83	odd	2		1008.2.cc.a.209.3		12
252.139	even	6		1008.2.cc.a.545.4		12
252.167	odd	6		3024.2.cc.a.881.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.5	✓	12	3.2	odd	2
63.2.o.a.20.6	yes	12	21.20	even	2
63.2.o.a.41.5	yes	12	63.13	odd	6
63.2.o.a.41.6	yes	12	9.4	even	3
189.2.o.a.62.1		12	1.1	even	1	trivial
189.2.o.a.62.2		12	7.6	odd	2	inner
189.2.o.a.125.1		12	63.41	even	6	inner
189.2.o.a.125.2		12	9.5	odd	6	inner
441.2.i.c.68.5		12	63.4	even	3
441.2.i.c.68.6		12	63.31	odd	6
441.2.i.c.227.1		12	21.5	even	6
441.2.i.c.227.2		12	21.2	odd	6
441.2.s.c.362.1		12	21.11	odd	6
441.2.s.c.362.2		12	21.17	even	6
441.2.s.c.374.1		12	63.40	odd	6
441.2.s.c.374.2		12	63.58	even	3
567.2.c.c.566.3		12	9.2	odd	6
567.2.c.c.566.4		12	63.20	even	6
567.2.c.c.566.9		12	63.34	odd	6
567.2.c.c.566.10		12	9.7	even	3
1008.2.cc.a.209.3		12	84.83	odd	2
1008.2.cc.a.209.4		12	12.11	even	2
1008.2.cc.a.545.3		12	36.31	odd	6
1008.2.cc.a.545.4		12	252.139	even	6
1323.2.i.c.521.5		12	7.2	even	3
1323.2.i.c.521.6		12	7.5	odd	6
1323.2.i.c.1097.1		12	63.59	even	6
1323.2.i.c.1097.2		12	63.32	odd	6
1323.2.s.c.656.5		12	7.3	odd	6
1323.2.s.c.656.6		12	7.4	even	3
1323.2.s.c.962.5		12	63.23	odd	6
1323.2.s.c.962.6		12	63.5	even	6
3024.2.cc.a.881.1		12	252.167	odd	6
3024.2.cc.a.881.6		12	36.23	even	6
3024.2.cc.a.2897.1		12	4.3	odd	2
3024.2.cc.a.2897.6		12	28.27	even	2

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.02704 - 0.592963i) q^{2} +(-0.296790 - 0.514055i) q^{4} +(-1.41899 - 2.45776i) q^{5} +(-2.07253 + 1.64457i) q^{7} +3.07579i q^{8} +O(q^{10})\)	\(q+(-1.02704 - 0.592963i) q^{2} +(-0.296790 - 0.514055i) q^{4} +(-1.41899 - 2.45776i) q^{5} +(-2.07253 + 1.64457i) q^{7} +3.07579i q^{8} +3.36562i q^{10} +(-0.136673 - 0.0789082i) q^{11} +(-3.41468 + 1.97146i) q^{13} +(3.10375 - 0.460106i) q^{14} +(1.23025 - 2.13086i) q^{16} -4.14487 q^{17} -6.33597i q^{19} +(-0.842281 + 1.45887i) q^{20} +(0.0935793 + 0.162084i) q^{22} +(-0.472958 + 0.273062i) q^{23} +(-1.52704 + 2.64491i) q^{25} +4.67602 q^{26} +(1.46050 + 0.577305i) q^{28} +(-4.02704 - 2.32501i) q^{29} +(0.112086 - 0.0647129i) q^{31} +(2.80039 - 1.61680i) q^{32} +(4.25696 + 2.45776i) q^{34} +(6.98284 + 2.76016i) q^{35} -2.46050 q^{37} +(-3.75700 + 6.50731i) q^{38} +(7.55955 - 4.36451i) q^{40} +(1.99569 + 3.45664i) q^{41} +(3.28434 - 5.68864i) q^{43} +0.0936766i q^{44} +0.647664 q^{46} +(4.33370 - 7.50619i) q^{47} +(1.59079 - 6.81685i) q^{49} +(3.13667 - 1.81096i) q^{50} +(2.02688 + 1.17022i) q^{52} -2.60234i q^{53} +0.447879i q^{55} +(-5.05835 - 6.37468i) q^{56} +(2.75729 + 4.77577i) q^{58} +(-1.80686 - 3.12957i) q^{59} +(-2.91472 - 1.68281i) q^{61} -0.153489 q^{62} -8.75583 q^{64} +(9.69076 + 5.59496i) q^{65} +(-0.663715 - 1.14959i) q^{67} +(1.23016 + 2.13069i) q^{68} +(-5.53500 - 6.97537i) q^{70} -0.409310i q^{71} +15.0124i q^{73} +(2.52704 + 1.45899i) q^{74} +(-3.25704 + 1.88045i) q^{76} +(0.413030 - 0.0612283i) q^{77} +(-2.16372 + 3.74766i) q^{79} -6.98284 q^{80} -4.73348i q^{82} +(-3.22585 + 5.58733i) q^{83} +(5.88151 + 10.1871i) q^{85} +(-6.74630 + 3.89498i) q^{86} +(0.242705 - 0.420378i) q^{88} -5.05368 q^{89} +(3.83482 - 9.70160i) q^{91} +(0.280738 + 0.162084i) q^{92} +(-8.90179 + 5.13945i) q^{94} +(-15.5723 + 8.99066i) q^{95} +(-2.18452 - 1.26123i) q^{97} +(-5.67594 + 6.05791i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7}+O(q^{10}) \) 12 * q + 6 * q^2 + 2 * q^4 - 2 * q^7	\( 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7} + 12 q^{14} + 2 q^{16} - 10 q^{22} - 24 q^{23} - 8 q^{28} - 30 q^{29} + 12 q^{32} - 4 q^{37} - 10 q^{43} - 40 q^{46} + 6 q^{49} + 36 q^{50} - 42 q^{56} + 2 q^{58} + 16 q^{64} + 78 q^{65} + 12 q^{67} + 18 q^{70} + 12 q^{74} + 24 q^{77} - 6 q^{79} - 6 q^{85} - 96 q^{86} + 34 q^{88} - 24 q^{91} - 30 q^{92} - 72 q^{95}+O(q^{100}) \) 12 * q + 6 * q^2 + 2 * q^4 - 2 * q^7 + 12 * q^14 + 2 * q^16 - 10 * q^22 - 24 * q^23 - 8 * q^28 - 30 * q^29 + 12 * q^32 - 4 * q^37 - 10 * q^43 - 40 * q^46 + 6 * q^49 + 36 * q^50 - 42 * q^56 + 2 * q^58 + 16 * q^64 + 78 * q^65 + 12 * q^67 + 18 * q^70 + 12 * q^74 + 24 * q^77 - 6 * q^79 - 6 * q^85 - 96 * q^86 + 34 * q^88 - 24 * q^91 - 30 * q^92 - 72 * q^95

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