LMFDB - Embedded newform 1008.2.cc.a.209.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(209,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("1008.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cc (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:	$8.04892052375$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.3
Root			$1.82904 - 1.05600i$ of defining polynomial
Character	$\chi$	$=$	1008.209
Dual form			1008.2.cc.a.545.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.410052 - 1.68281i) q^{3} +(-1.41899 - 2.45776i) q^{5} +(0.387972 - 2.61715i) q^{7} +(-2.66372 + 1.38008i) q^{9} +O(q^{10})$	\(q+(-0.410052 - 1.68281i) q^{3} +(-1.41899 - 2.45776i) q^{5} +(0.387972 - 2.61715i) q^{7} +(-2.66372 + 1.38008i) q^{9} +(-0.136673 - 0.0789082i) q^{11} +(3.41468 - 1.97146i) q^{13} +(-3.55408 + 3.39569i) q^{15} -4.14487 q^{17} -6.33597i q^{19} +(-4.56326 + 0.420284i) q^{21} +(-0.472958 + 0.273062i) q^{23} +(-1.52704 + 2.64491i) q^{25} +(3.41468 + 3.91663i) q^{27} +(4.02704 + 2.32501i) q^{29} +(0.112086 - 0.0647129i) q^{31} +(-0.0767447 + 0.262352i) q^{33} +(-6.98284 + 2.76016i) q^{35} -2.46050 q^{37} +(-4.71780 - 4.93786i) q^{39} +(1.99569 + 3.45664i) q^{41} +(-3.28434 + 5.68864i) q^{43} +(7.17167 + 4.58845i) q^{45} +(-4.33370 + 7.50619i) q^{47} +(-6.69896 - 2.03076i) q^{49} +(1.69961 + 6.97504i) q^{51} +2.60234i q^{53} +0.447879i q^{55} +(-10.6623 + 2.59808i) q^{57} +(1.80686 + 3.12957i) q^{59} +(2.91472 + 1.68281i) q^{61} +(2.57843 + 7.50678i) q^{63} +(-9.69076 - 5.59496i) q^{65} +(0.663715 + 1.14959i) q^{67} +(0.653450 + 0.683930i) q^{69} -0.409310i q^{71} -15.0124i q^{73} +(5.07706 + 1.48517i) q^{75} +(-0.259540 + 0.327080i) q^{77} +(2.16372 - 3.74766i) q^{79} +(5.19076 - 7.35228i) q^{81} +(3.22585 - 5.58733i) q^{83} +(5.88151 + 10.1871i) q^{85} +(2.26127 - 7.73013i) q^{87} -5.05368 q^{89} +(-3.83482 - 9.70160i) q^{91} +(-0.154861 - 0.162084i) q^{93} +(-15.5723 + 8.99066i) q^{95} +(2.18452 + 1.26123i) q^{97} +(0.472958 + 0.0215693i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q + 2 * q^7 - 12 * q^9	$ 12 q + 2 q^{7} - 12 q^{9} - 6 q^{15} - 24 q^{21} - 24 q^{23} + 30 q^{29} - 4 q^{37} + 10 q^{43} + 6 q^{49} + 42 q^{51} - 18 q^{57} - 24 q^{63} - 78 q^{65} - 12 q^{67} - 24 q^{77} + 6 q^{79} + 24 q^{81} - 6 q^{85} + 24 q^{91} + 78 q^{93} - 72 q^{95} + 24 q^{99}+O(q^{100}) $ 12 * q + 2 * q^7 - 12 * q^9 - 6 * q^15 - 24 * q^21 - 24 * q^23 + 30 * q^29 - 4 * q^37 + 10 * q^43 + 6 * q^49 + 42 * q^51 - 18 * q^57 - 24 * q^63 - 78 * q^65 - 12 * q^67 - 24 * q^77 + 6 * q^79 + 24 * q^81 - 6 * q^85 + 24 * q^91 + 78 * q^93 - 72 * q^95 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.410052	−	1.68281i	−0.236743	−	0.971572i
$3$	−0.410052	−	1.68281i	−0.236743	−	0.971572i
$4$		0			0
$5$	−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
$7$	0.387972	−	2.61715i	0.146640	−	0.989190i
$7$	0.387972	−	2.61715i	0.146640	−	0.989190i
$8$		0			0
$9$	−2.66372	+	1.38008i	−0.887905	+	0.460027i
$10$		0			0
$11$	−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	0.0548943	−	0.998492i	$-0.482518\pi$
$13$	3.41468	−	1.97146i	0.947061	−	0.546786i	0.892167	+	0.451706i	$0.149184\pi$
$14$		0			0
$15$	−3.55408	+	3.39569i	−0.917661	+	0.876764i
$16$		0			0
$17$	−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			0
$21$	−4.56326	+	0.420284i	−0.995785	+	0.0917134i
$22$		0			0
$23$	−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
$26$		0			0
$27$	3.41468	+	3.91663i	0.657155	+	0.753756i
$28$		0			0
$29$	4.02704	+	2.32501i	0.747803	+	0.431744i	0.824900	−	0.565279i	$-0.191232\pi$
$29$	4.02704	+	2.32501i	0.747803	+	0.431744i	−0.0770966	+	0.997024i	$0.524565\pi$
$30$		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	$0.329634\pi$
$32$		0			0
$33$	−0.0767447	+	0.262352i	−0.0133595	+	0.0456696i
$34$		0			0
$35$	−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	$0.564826\pi$
$38$		0			0
$39$	−4.71780	−	4.93786i	−0.755453	−	0.790690i
$40$		0			0
$41$	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	$0.333648\pi$
$43$	−3.28434	+	5.68864i	−0.500857	+	0.867509i	−1.00000		0.000989450i	$0.999685\pi$
$44$		0			0
$45$	7.17167	+	4.58845i	1.06909	+	0.684005i
$46$		0			0
$47$	−4.33370	+	7.50619i	−0.632135	+	1.09489i	0.354979	+	0.934874i	$0.384488\pi$
$47$	−4.33370	+	7.50619i	−0.632135	+	1.09489i	−0.987114	+	0.160016i	$0.948845\pi$
$48$		0			0
$49$	−6.69896	−	2.03076i	−0.956994	−	0.290109i
$50$		0			0
$51$	1.69961	+	6.97504i	0.237993	+	0.976701i
$52$		0			0
$53$			2.60234i			0.357459i	0.983898	+	0.178730i	$0.0571988\pi$
$53$			2.60234i			0.357459i	−0.983898	+	0.178730i	$0.942801\pi$
$54$		0			0
$55$			0.447879i			0.0603920i
$56$		0			0
$57$	−10.6623	+	2.59808i	−1.41225	+	0.344124i
$58$		0			0
$59$	1.80686	+	3.12957i	0.235233	+	0.407436i	0.959340	−	0.282252i	$-0.0910813\pi$
$59$	1.80686	+	3.12957i	0.235233	+	0.407436i	−0.724107	+	0.689687i	$0.757748\pi$
$60$		0			0
$61$	2.91472	+	1.68281i	0.373191	+	0.215462i	0.674852	−	0.737953i	$-0.264208\pi$
$61$	2.91472	+	1.68281i	0.373191	+	0.215462i	−0.301660	+	0.953415i	$0.597541\pi$
$62$		0			0
$63$	2.57843	+	7.50678i	0.324852	+	0.945765i
$64$		0			0
$65$	−9.69076	−	5.59496i	−1.20199	−	0.693970i
$66$		0			0
$67$	0.663715	+	1.14959i	0.0810857	+	0.140445i	0.903717	−	0.428131i	$-0.140828\pi$
$67$	0.663715	+	1.14959i	0.0810857	+	0.140445i	−0.822631	+	0.568576i	$0.807495\pi$
$68$		0			0
$69$	0.653450	+	0.683930i	0.0786661	+	0.0823355i
$70$		0			0
$71$		−	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	$-0.658522\pi$
$73$		−	15.0124i		−	1.75707i	0.477681	−	0.878533i	$-0.341478\pi$
$74$		0			0
$75$	5.07706	+	1.48517i	0.586249	+	0.171493i
$76$		0			0
$77$	−0.259540	+	0.327080i	−0.0295773	+	0.0372742i
$78$		0			0
$79$	2.16372	−	3.74766i	0.243437	−	0.421645i	−0.718254	−	0.695781i	$-0.755058\pi$
$79$	2.16372	−	3.74766i	0.243437	−	0.421645i	0.961691	+	0.274136i	$0.0883918\pi$
$80$		0			0
$81$	5.19076	−	7.35228i	0.576751	−	0.816920i
$82$		0			0
$83$	3.22585	−	5.58733i	0.354083	−	0.613289i	−0.632878	−	0.774252i	$-0.718126\pi$
$83$	3.22585	−	5.58733i	0.354083	−	0.613289i	0.986961	+	0.160963i	$0.0514598\pi$
$84$		0			0
$85$	5.88151	+	10.1871i	0.637940	+	1.10494i
$86$		0			0
$87$	2.26127	−	7.73013i	0.242433	−	0.828757i
$88$		0			0
$89$	−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			0
$93$	−0.154861	−	0.162084i	−0.0160583	−	0.0168073i
$94$		0			0
$95$	−15.5723	+	8.99066i	−1.59768	+	0.922422i
$96$		0			0
$97$	2.18452	+	1.26123i	0.221805	+	0.128059i	0.606786	−	0.794866i	$-0.292459\pi$
$97$	2.18452	+	1.26123i	0.221805	+	0.128059i	−0.384981	+	0.922925i	$0.625792\pi$
$98$		0			0
$99$	0.472958	+	0.0215693i	0.0475341	+	0.00216779i
$100$		0			0
$101$	−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	$0.558628\pi$
$104$		0			0
$105$	7.50816	+	10.6190i	0.732721	+	1.03631i
$106$		0			0
$107$		−	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			0
$111$	1.00893	+	4.14057i	0.0957638	+	0.393005i
$112$		0			0
$113$	−8.72665	+	5.03834i	−0.820935	+	0.473967i	−0.850739	−	0.525589i	$-0.823845\pi$
$113$	−8.72665	+	5.03834i	−0.820935	+	0.473967i	0.0298041	+	0.999556i	$0.490512\pi$
$114$		0			0
$115$	1.34224	+	0.774943i	0.125165	+	0.0722638i
$116$		0			0
$117$	−6.37495	+	9.96395i	−0.589364	+	0.921167i
$118$		0			0
$119$	−1.60809	+	10.8478i	−0.147414	+	0.994412i
$120$		0			0
$121$	−5.48755	−	9.50471i	−0.498868	−	0.864065i
$122$		0			0
$123$	4.99854	−	4.77577i	0.450703	−	0.430617i
$124$		0			0
$125$	−5.52245			−0.493943
$126$		0			0
$127$	12.4897			1.10828			0.554140	−	0.832423i	$-0.313047\pi$
$127$	12.4897			1.10828			0.554140	+	0.832423i	$0.313047\pi$
$128$		0			0
$129$	10.9197	+	3.19429i	0.961422	+	0.281241i
$130$		0			0
$131$	−5.02249	−	8.69921i	−0.438817	−	0.760054i	0.558781	−	0.829315i	$-0.311269\pi$
$131$	−5.02249	−	8.69921i	−0.438817	−	0.760054i	−0.997599	+	0.0692612i	$0.977936\pi$
$132$		0			0
$133$	−16.5822	−	2.45818i	−1.43786	−	0.213151i
$134$		0			0
$135$	4.78074	−	13.9501i	0.411460	−	1.20063i
$136$		0			0
$137$	−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	0.395358	−	0.918527i	$-0.370621\pi$
$139$	16.3702	−	9.45136i	1.38850	−	0.801654i	0.993147	+	0.116873i	$0.0372872\pi$
$140$		0			0
$141$	14.4086	+	4.21488i	1.21342	+	0.354957i
$142$		0			0
$143$	−0.622259			−0.0520359
$144$		0			0
$145$		−	13.1966i		−	1.09592i
$146$		0			0
$147$	−0.670471	+	12.1058i	−0.0552995	+	0.998470i
$148$		0			0
$149$	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	−0.900106	−	0.435672i	$-0.856511\pi$
$151$	−0.893968	+	1.54840i	−0.0727501	+	0.126007i	0.827356	+	0.561678i	$0.189844\pi$
$152$		0			0
$153$	11.0408	−	5.72026i	0.892592	−	0.462455i
$154$		0			0
$155$	−0.318097	−	0.183653i	−0.0255502	−	0.0147514i
$156$		0			0
$157$	−3.80255	+	2.19540i	−0.303477	+	0.175212i	−0.644004	−	0.765022i	$-0.722728\pi$
$157$	−3.80255	+	2.19540i	−0.303477	+	0.175212i	0.340527	+	0.940235i	$0.389395\pi$
$158$		0			0
$159$	4.37926	−	1.06710i	0.347298	−	0.0846262i
$160$		0			0
$161$	0.531151	+	1.34374i	0.0418606	+	0.105902i
$162$		0			0
$163$	−5.43560			−0.425749			−0.212874	−	0.977080i	$-0.568283\pi$
$163$	−5.43560			−0.425749			−0.212874	+	0.977080i	$0.568283\pi$
$164$		0			0
$165$	0.753696	−	0.183653i	0.0586751	−	0.0142974i
$166$		0			0
$167$	−5.25273	−	9.09799i	−0.406468	−	0.704024i	0.588023	−	0.808844i	$-0.299907\pi$
$167$	−5.25273	−	9.09799i	−0.406468	−	0.704024i	−0.994491	+	0.104821i	$0.966573\pi$
$168$		0			0
$169$	1.27335	−	2.20550i	0.0979497	−	0.169654i
$170$		0			0
$171$	8.74415	+	16.8772i	0.668682	+	1.29063i
$172$		0			0
$173$	−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
$175$	6.32969	+	5.02265i	0.478480	+	0.379677i
$176$		0			0
$177$	4.52558	−	4.32389i	0.340163	−	0.325004i
$178$		0			0
$179$		−	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	$0.0789045\pi$
$181$			6.60182i			0.490710i	−0.969433	+	0.245355i	$0.921096\pi$
$182$		0			0
$183$	1.63667	−	5.59496i	0.120986	−	0.413591i
$184$		0			0
$185$	3.49142	+	6.04732i	0.256694	+	0.444608i
$186$		0			0
$187$	0.566492	+	0.327065i	0.0414260	+	0.0239173i
$188$		0			0
$189$	11.5752	−	7.41718i	0.841972	−	0.539521i
$190$		0			0
$191$	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	$0.716089\pi$
$194$		0			0
$195$	−5.44156	+	18.6020i	−0.389678	+	1.33211i
$196$		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
$199$		−	12.9378i		−	0.917136i	−0.888659	−	0.458568i	$-0.848363\pi$
$199$		−	12.9378i		−	0.917136i	0.888659	−	0.458568i	$-0.151637\pi$
$200$		0			0
$201$	1.66238	−	1.58830i	0.117256	−	0.112030i
$202$		0			0
$203$	7.64729	−	9.63734i	0.536735	−	0.676408i
$204$		0			0
$205$	5.66372	−	9.80984i	0.395571	−	0.685149i
$206$		0			0
$207$	0.882977	−	1.38008i	0.0613712	−	0.0959222i
$208$		0			0
$209$	−0.499960	+	0.865957i	−0.0345830	+	0.0598995i
$210$		0			0
$211$	4.50720	+	7.80669i	0.310288	+	0.537435i	0.978425	−	0.206604i	$-0.0662411\pi$
$211$	4.50720	+	7.80669i	0.310288	+	0.537435i	−0.668136	+	0.744039i	$0.732908\pi$
$212$		0			0
$213$	−0.688791	+	0.167838i	−0.0471952	+	0.0115001i
$214$		0			0
$215$	18.6417			1.27135
$216$		0			0
$217$	−0.125877	−	0.318453i	−0.00854510	−	0.0216180i
$218$		0			0
$219$	−25.2630	+	6.15585i	−1.70712	+	0.415974i
$220$		0			0
$221$	−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	$0.690740\pi$
$224$		0			0
$225$	0.417411	−	9.15274i	0.0278274	−	0.610183i
$226$		0			0
$227$	−9.32085	+	16.1442i	−0.618647	+	1.07153i	0.371086	+	0.928598i	$0.378985\pi$
$227$	−9.32085	+	16.1442i	−0.618647	+	1.07153i	−0.989733	+	0.142929i	$0.954348\pi$
$228$		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			0
$231$	0.656839	+	0.302638i	0.0432168	+	0.0199121i
$232$		0			0
$233$		−	17.0679i		−	1.11815i	−0.829116	−	0.559077i	$-0.811156\pi$
$233$		−	17.0679i		−	1.11815i	0.829116	−	0.559077i	$-0.188844\pi$
$234$		0			0
$235$	24.5979			1.60459
$236$		0			0
$237$	−7.19385	−	2.10439i	−0.467291	−	0.136695i
$238$		0			0
$239$	−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	0.620755	−	0.784005i	$-0.286826\pi$
$241$	3.91464	+	2.26012i	0.252164	+	0.145587i	−0.368591	+	0.929592i	$0.620160\pi$
$242$		0			0
$243$	−14.5010	−	5.72026i	−0.930239	−	0.366955i
$244$		0			0
$245$	4.51461	+	19.3460i	0.288428	+	1.23597i
$246$		0			0
$247$	−12.4911	−	21.6353i	−0.794793	−	1.37662i
$248$		0			0
$249$	−10.7252	−	3.13740i	−0.679681	−	0.198825i
$250$		0			0
$251$	−21.1727			−1.33641			−0.668205	−	0.743978i	$-0.732937\pi$
$251$	−21.1727			−1.33641			−0.668205	+	0.743978i	$0.732937\pi$
$252$		0			0
$253$	0.0861875			0.00541856
$254$		0			0
$255$	14.7312	−	14.0747i	0.922505	−	0.881393i
$256$		0			0
$257$	−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
$259$	−0.954606	+	6.43951i	−0.0593163	+	0.400132i
$260$		0			0
$261$	−13.9356	−	0.635534i	−0.862592	−	0.0393385i
$262$		0			0
$263$	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
$266$		0			0
$267$	2.07227	+	8.50440i	0.126821	+	0.520461i
$268$		0			0
$269$	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	$0.927394\pi$
$272$		0			0
$273$	−14.7535	+	10.4314i	−0.892922	+	0.631340i
$274$		0			0
$275$	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	$-0.127376\pi$
$278$		0			0
$279$	−0.209256	+	0.327065i	−0.0125278	+	0.0195808i
$280$		0			0
$281$	21.0993	+	12.1817i	1.25868	+	0.726699i	0.972818	−	0.231572i	$-0.0743869\pi$
$281$	21.0993	+	12.1817i	1.25868	+	0.726699i	0.285862	+	0.958271i	$0.407720\pi$
$282$		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			0
$285$	21.5150	+	22.5186i	1.27444	+	1.33389i
$286$		0			0
$287$	9.82082	−	3.88195i	0.579704	−	0.229144i
$288$		0			0
$289$	0.179961			0.0105860
$290$		0			0
$291$	1.22665	−	4.19331i	0.0719077	−	0.245816i
$292$		0			0
$293$	−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
$296$		0			0
$297$	−0.157640	−	0.804744i	−0.00914721	−	0.0466960i
$298$		0			0
$299$	−1.07667	+	1.86484i	−0.0622652	+	0.107846i
$300$		0			0
$301$	13.6138	+	10.8026i	0.784686	+	0.622654i
$302$		0			0
$303$	4.97296	+	1.45472i	0.285689	+	0.0835715i
$304$		0			0
$305$		−	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			0
$309$	15.7901	+	16.5266i	0.898266	+	0.940165i
$310$		0			0
$311$	8.20279	+	14.2076i	0.465137	+	0.805641i	0.999208	−	0.0397985i	$-0.0126716\pi$
$311$	8.20279	+	14.2076i	0.465137	+	0.805641i	−0.534070	+	0.845440i	$0.679338\pi$
$312$		0			0
$313$	7.10514	+	4.10216i	0.401606	+	0.231868i	0.687177	−	0.726490i	$-0.258850\pi$
$313$	7.10514	+	4.10216i	0.401606	+	0.231868i	−0.285570	+	0.958358i	$0.592183\pi$
$314$		0			0
$315$	14.7911	−	16.9892i	0.833382	−	0.957231i
$316$		0			0
$317$	19.8427	+	11.4562i	1.11448	+	0.643443i	0.939985	−	0.341215i	$-0.110839\pi$
$317$	19.8427	+	11.4562i	1.11448	+	0.643443i	0.174491	+	0.984659i	$0.444172\pi$
$318$		0			0
$319$	−0.366926	−	0.635534i	−0.0205439	−	0.0355831i
$320$		0			0
$321$	−32.9083	+	8.01878i	−1.83676	+	0.447565i
$322$		0			0
$323$			26.2618i			1.46125i
$324$		0			0
$325$			12.0420i			0.667972i
$326$		0			0
$327$	−5.43255	−	22.2946i	−0.300420	−	1.23290i
$328$		0			0
$329$	17.9635	+	14.2541i	0.990359	+	0.785856i
$330$		0			0
$331$	9.63161	−	16.6824i	0.529401	−	0.916950i	−0.470011	−	0.882661i	$-0.655750\pi$
$331$	9.63161	−	16.6824i	0.529401	−	0.916950i	0.999412	−	0.0342892i	$-0.0109167\pi$
$332$		0			0
$333$	6.55408	−	3.39569i	0.359162	−	0.186083i
$334$		0			0
$335$	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	$0.872765\pi$
$338$		0			0
$339$	12.0570	+	12.6193i	0.654844	+	0.685389i
$340$		0			0
$341$	−0.0204255			−0.00110610
$342$		0			0
$343$	−7.91381	+	16.7443i	−0.427306	+	0.904107i
$344$		0			0
$345$	0.753696	−	2.57651i	0.0405776	−	0.138714i
$346$		0			0
$347$	−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	0.275597	−	0.961273i	$-0.411124\pi$
$349$	−7.82927	−	4.52023i	−0.419091	−	0.241963i	−0.694689	+	0.719311i	$0.744458\pi$
$350$		0			0
$351$	19.3815	+	6.64211i	1.03451	+	0.354529i
$352$		0			0
$353$	−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
$356$		0			0
$357$	18.9141	−	1.74202i	1.00104	−	0.0921975i
$358$		0			0
$359$		−	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
$362$		0			0
$363$	−13.7445	+	13.1319i	−0.721397	+	0.689248i
$364$		0			0
$365$	−36.8968	+	21.3024i	−1.93127	+	1.11502i
$366$		0			0
$367$	−24.4297	−	14.1045i	−1.27522	−	0.736250i	−0.299256	−	0.954173i	$-0.596738\pi$
$367$	−24.4297	−	14.1045i	−1.27522	−	0.736250i	−0.975966	+	0.217923i	$0.930072\pi$
$368$		0			0
$369$	−10.0864	−	6.45329i	−0.525077	−	0.335945i
$370$		0			0
$371$	6.81073	+	1.00964i	0.353595	+	0.0524177i
$372$		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			0
$375$	2.26449	+	9.29325i	0.116938	+	0.479902i
$376$		0			0
$377$	18.3347			0.944287
$378$		0			0
$379$	−14.6447			−0.752250			−0.376125	−	0.926569i	$-0.622744\pi$
$379$	−14.6447			−0.752250			−0.376125	+	0.926569i	$0.622744\pi$
$380$		0			0
$381$	−5.12142	−	21.0178i	−0.262378	−	1.07677i
$382$		0			0
$383$	12.3932	+	21.4657i	0.633264	+	1.09684i	0.986880	+	0.161454i	$0.0516184\pi$
$383$	12.3932	+	21.4657i	0.633264	+	1.09684i	−0.353617	+	0.935390i	$0.615048\pi$
$384$		0			0
$385$	1.17217	+	0.173764i	0.0597391	+	0.00885585i
$386$		0			0
$387$	0.897761	−	19.6856i	0.0456357	−	1.00067i
$388$		0			0
$389$	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
$393$	−12.5797	+	12.0190i	−0.634560	+	0.606280i
$394$		0			0
$395$	−12.2811			−0.617930
$396$		0			0
$397$			1.92094i			0.0964093i	0.998837	+	0.0482046i	$0.0153500\pi$
$397$			1.92094i			0.0964093i	−0.998837	+	0.0482046i	$0.984650\pi$
$398$		0			0
$399$	2.66290	+	28.9127i	0.133312	+	1.44745i
$400$		0			0
$401$	−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			0
$405$	−25.4357	−	2.32483i	−1.26391	−	0.115522i
$406$		0			0
$407$	0.336285	+	0.194154i	0.0166690	+	0.00962386i
$408$		0			0
$409$	−8.42281	+	4.86291i	−0.416481	+	0.240455i	−0.693571	−	0.720389i	$-0.743963\pi$
$409$	−8.42281	+	4.86291i	−0.416481	+	0.240455i	0.277090	+	0.960844i	$0.410630\pi$
$410$		0			0
$411$	−3.91049	+	13.3680i	−0.192890	+	0.659394i
$412$		0			0
$413$	8.89158	−	3.51464i	0.437526	−	0.172944i
$414$		0			0
$415$	−18.3097			−0.898789
$416$		0			0
$417$	−22.6175	−	23.6725i	−1.10758	−	1.15925i
$418$		0			0
$419$	−14.9512	−	25.8963i	−0.730416	−	1.26512i	−0.956706	−	0.291058i	$-0.905993\pi$
$419$	−14.9512	−	25.8963i	−0.730416	−	1.26512i	0.226289	−	0.974060i	$-0.427340\pi$
$420$		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	$0.957266\pi$
$422$		0			0
$423$	1.18460	−	25.9752i	0.0575973	−	1.26296i
$424$		0			0
$425$	6.32939	−	10.9628i	0.307021	−	0.531775i
$426$		0			0
$427$	5.53500	−	6.97537i	0.267857	−	0.337562i
$428$		0			0
$429$	0.255158	+	1.04715i	0.0123192	+	0.0505567i
$430$		0			0
$431$		−	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	$0.293684\pi$
$433$			33.1771i			1.59439i	−0.603721	+	0.797196i	$0.706316\pi$
$434$		0			0
$435$	−22.2075	+	5.41131i	−1.06477	+	0.259452i
$436$		0			0
$437$	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	$0.601935\pi$
$440$		0			0
$441$	20.6467	−	3.83573i	0.983177	−	0.182654i
$442$		0			0
$443$	−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
$446$		0			0
$447$	−23.2200	−	24.3031i	−1.09827	−	1.14950i
$448$		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
$451$		−	0.629906i		−	0.0296611i
$452$		0			0
$453$	2.97224	+	0.869457i	0.139648	+	0.0408506i
$454$		0			0
$455$	−18.4026	+	23.1915i	−0.862727	+	1.08723i
$456$		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	$0.252243\pi$
$458$		0			0
$459$	−14.1534	−	16.2339i	−0.660624	−	0.757735i
$460$		0			0
$461$	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	0.958973	−	0.283498i	$-0.0914949\pi$
$463$	5.03443	+	8.71990i	0.233970	+	0.405248i	−0.725003	+	0.688746i	$0.758162\pi$
$464$		0			0
$465$	−0.178618	+	0.610605i	−0.00828321	+	0.0283161i
$466$		0			0
$467$	3.59330			0.166278			0.0831389	−	0.996538i	$-0.473505\pi$
$467$	3.59330			0.166278			0.0831389	+	0.996538i	$0.473505\pi$
$468$		0			0
$469$	3.26615	−	1.29103i	0.150817	−	0.0596145i
$470$		0			0
$471$	5.25370	+	5.49875i	0.242078	+	0.253369i
$472$		0			0
$473$	0.897761	−	0.518322i	0.0412791	−	0.0238325i
$474$		0			0
$475$	16.7581	+	9.67530i	0.768915	+	0.443933i
$476$		0			0
$477$	−3.59144	−	6.93190i	−0.164441	−	0.317390i
$478$		0			0
$479$	0.811090	−	1.40485i	0.0370597	−	0.0641892i	−0.846901	−	0.531751i	$-0.821534\pi$
$479$	0.811090	−	1.40485i	0.0370597	−	0.0641892i	0.883960	+	0.467562i	$0.154868\pi$
$480$		0			0
$481$	−8.40183	+	4.85080i	−0.383090	+	0.221177i
$482$		0			0
$483$	2.04347	−	1.44483i	0.0929810	−	0.0657421i
$484$		0			0
$485$		−	7.15869i		−	0.325060i
$486$		0			0
$487$	−7.99573			−0.362321			−0.181161	−	0.983454i	$-0.557985\pi$
$487$	−7.99573			−0.362321			−0.181161	+	0.983454i	$0.557985\pi$
$488$		0			0
$489$	2.22888	+	9.14709i	0.100793	+	0.413646i
$490$		0			0
$491$	−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
$494$		0			0
$495$	−0.618109	−	1.19302i	−0.0277819	−	0.0536223i
$496$		0			0
$497$	−1.07122	−	0.158801i	−0.0480510	−	0.00712318i
$498$		0			0
$499$	8.46050	+	14.6540i	0.378744	+	0.656004i	0.990880	−	0.134749i	$-0.0430227\pi$
$499$	8.46050	+	14.6540i	0.378744	+	0.656004i	−0.612136	+	0.790753i	$0.709689\pi$
$500$		0			0
$501$	−13.1563	+	12.5700i	−0.587781	+	0.561586i
$502$		0			0
$503$	33.9226			1.51253			0.756267	−	0.654263i	$-0.227021\pi$
$503$	33.9226			1.51253			0.756267	+	0.654263i	$0.227021\pi$
$504$		0			0
$505$	8.48968			0.377786
$506$		0			0
$507$	−4.23358	−	1.23843i	−0.188020	−	0.0550008i
$508$		0			0
$509$	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
$511$	−39.2897	−	5.82438i	−1.73807	−	0.257655i
$512$		0			0
$513$	24.8157	−	21.6353i	1.09564	−	0.955222i
$514$		0			0
$515$	32.4341	+	18.7259i	1.42922	+	0.825160i
$516$		0			0
$517$	1.18460	−	0.683930i	0.0520987	−	0.0300792i
$518$		0			0
$519$	29.1898	+	8.53878i	1.28129	+	0.374811i
$520$		0			0
$521$	−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	$-0.0566634\pi$
$524$		0			0
$525$	5.85668	−	12.7112i	0.255606	−	0.554764i
$526$		0			0
$527$	−0.464582	+	0.268227i	−0.0202375	+	0.0116841i
$528$		0			0
$529$	−11.3509	+	19.6603i	−0.493516	+	0.854795i
$530$		0			0
$531$	−9.13202	−	5.84268i	−0.396296	−	0.253551i
$532$		0			0
$533$	13.6293	+	7.86887i	0.590350	+	0.340839i
$534$		0			0
$535$	−48.0628	+	27.7490i	−2.07793	+	1.19970i
$536$		0			0
$537$	−30.6327	+	7.46428i	−1.32190	+	0.322107i
$538$		0			0
$539$	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	$0.491676\pi$
$542$		0			0
$543$	11.1096	−	2.70709i	0.476760	−	0.116172i
$544$		0			0
$545$	−18.7994	−	32.5614i	−0.805276	−	1.39478i
$546$		0			0
$547$	−13.1278	+	22.7380i	−0.561305	+	0.972209i	0.436078	+	0.899909i	$0.356367\pi$
$547$	−13.1278	+	22.7380i	−0.561305	+	0.972209i	−0.997383	+	0.0722999i	$0.976966\pi$
$548$		0			0
$549$	−10.0864	−	0.459990i	−0.430477	−	0.0196319i
$550$		0			0
$551$	14.7312	−	25.5152i	0.627571	−	1.08699i
$552$		0			0
$553$	−8.96874	−	7.11676i	−0.381390	−	0.302635i
$554$		0			0
$555$	8.74484	−	8.35512i	0.371198	−	0.354655i
$556$		0			0
$557$		−	27.2172i		−	1.15323i	−0.817016	−	0.576615i	$-0.804373\pi$
$557$		−	27.2172i		−	1.15323i	0.817016	−	0.576615i	$-0.195627\pi$
$558$		0			0
$559$			25.8998i			1.09545i
$560$		0			0
$561$	0.318097	−	1.08741i	0.0134301	−	0.0459106i
$562$		0			0
$563$	−4.68017	−	8.10630i	−0.197246	−	0.341640i	0.750389	−	0.660997i	$-0.229866\pi$
$563$	−4.68017	−	8.10630i	−0.197246	−	0.341640i	−0.947634	+	0.319357i	$0.896533\pi$
$564$		0			0
$565$	24.7660	+	14.2987i	1.04191	+	0.601549i
$566$		0			0
$567$	−17.2282	−	16.4375i	−0.723515	−	0.690309i
$568$		0			0
$569$	−30.2424	−	17.4605i	−1.26783	−	0.731980i	−0.293251	−	0.956036i	$-0.594737\pi$
$569$	−30.2424	−	17.4605i	−1.26783	−	0.731980i	−0.974576	+	0.224055i	$0.928070\pi$
$570$		0			0
$571$	−0.735987	−	1.27477i	−0.0308001	−	0.0533473i	0.850214	−	0.526436i	$-0.176472\pi$
$571$	−0.735987	−	1.27477i	−0.0308001	−	0.0533473i	−0.881015	+	0.473089i	$0.843139\pi$
$572$		0			0
$573$	6.91025	−	23.6227i	0.288680	−	0.986851i
$574$		0			0
$575$		−	1.66791i		−	0.0695567i
$576$		0			0
$577$		−	18.6196i		−	0.775146i	−0.921839	−	0.387573i	$-0.873314\pi$
$577$		−	18.6196i		−	0.775146i	0.921839	−	0.387573i	$-0.126686\pi$
$578$		0			0
$579$	12.5287	−	11.9703i	0.520674	−	0.497470i
$580$		0			0
$581$	−13.3713	−	10.6103i	−0.554737	−	0.440187i
$582$		0			0
$583$	0.205346	−	0.355670i	0.00850458	−	0.0147304i
$584$		0			0
$585$	33.5349	+	1.52936i	1.38650	+	0.0632313i
$586$		0			0
$587$	9.28551	−	16.0830i	0.383254	−	0.663816i	−0.608271	−	0.793729i	$-0.708137\pi$
$587$	9.28551	−	16.0830i	0.383254	−	0.663816i	0.991525	+	0.129914i	$0.0414700\pi$
$588$		0			0
$589$	−0.410019	−	0.710174i	−0.0168945	−	0.0292622i
$590$		0			0
$591$	−33.8273	+	8.24272i	−1.39147	+	0.339060i
$592$		0			0
$593$	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
$596$		0			0
$597$	−21.7719	+	5.30517i	−0.891064	+	0.217126i
$598$		0			0
$599$	−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	0.806523	−	0.591203i	$-0.201347\pi$
$601$	17.1065	+	9.87644i	0.697788	+	0.402868i	−0.108735	+	0.994071i	$0.534680\pi$
$602$		0			0
$603$	−3.35447	−	2.14620i	−0.136605	−	0.0873999i
$604$		0			0
$605$	−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	$0.451833\pi$
$608$		0			0
$609$	−19.3536	−	8.91715i	−0.784248	−	0.361341i
$610$		0			0
$611$			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	$0.815533\pi$
$614$		0			0
$615$	−18.8305	−	5.50843i	−0.759321	−	0.222121i
$616$		0			0
$617$	19.9686	−	11.5289i	0.803904	−	0.464134i	−0.0409302	−	0.999162i	$-0.513032\pi$
$617$	19.9686	−	11.5289i	0.803904	−	0.464134i	0.844835	+	0.535028i	$0.179699\pi$
$618$		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			0
$621$	−2.68448	−	0.919981i	−0.107725	−	0.0369176i
$622$		0			0
$623$	−1.96069	+	13.2263i	−0.0785532	+	0.529899i
$624$		0			0
$625$	15.4715	+	26.7974i	0.618860	+	1.07190i
$626$		0			0
$627$	1.66225	+	0.486253i	0.0663840	+	0.0194191i
$628$		0			0
$629$	10.1985			0.406640
$630$		0			0
$631$	−23.5831			−0.938827			−0.469414	−	0.882978i	$-0.655535\pi$
$631$	−23.5831			−0.938827			−0.469414	+	0.882978i	$0.655535\pi$
$632$		0			0
$633$	11.2890	−	10.7859i	0.448698	−	0.428702i
$634$		0			0
$635$	−17.7227	−	30.6966i	−0.703303	−	1.21816i
$636$		0			0
$637$	−26.8783	+	6.27236i	−1.06496	+	0.248520i
$638$		0			0
$639$	0.564880	+	1.09028i	0.0223463	+	0.0431310i
$640$		0			0
$641$	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	0.495619	−	0.868540i	$-0.334941\pi$
$643$	37.9247	−	21.8959i	1.49561	−	0.863489i	0.999987	+	0.00505169i	$0.00160801\pi$
$644$		0			0
$645$	−7.64406	−	31.3705i	−0.300985	−	1.23521i
$646$		0			0
$647$	29.3713			1.15471			0.577353	−	0.816494i	$-0.304086\pi$
$647$	29.3713			1.15471			0.577353	+	0.816494i	$0.304086\pi$
$648$		0			0
$649$		−	0.570305i		−	0.0223864i
$650$		0			0
$651$	−0.484280	+	0.342410i	−0.0189804	+	0.0134201i
$652$		0			0
$653$	−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
$656$		0			0
$657$	20.7183	+	39.9887i	0.808298	+	1.56011i
$658$		0			0
$659$	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	−0.439482	−	0.898251i	$-0.644838\pi$
$661$	3.05138	−	1.76171i	0.118685	−	0.0685227i	0.558167	+	0.829728i	$0.311505\pi$
$662$		0			0
$663$	19.5547	+	20.4668i	0.759441	+	0.794864i
$664$		0			0
$665$	17.4883	+	44.2431i	0.678167	+	1.71567i
$666$		0			0
$667$	−2.53950			−0.0983296
$668$		0			0
$669$	−1.09737	+	3.75136i	−0.0424269	+	0.145036i
$670$		0			0
$671$	−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	$0.0517202\pi$
$674$		0			0
$675$	−15.5735	+	3.05067i	−0.599424	+	0.117420i
$676$		0			0
$677$	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
$679$	4.14837	−	5.22790i	0.159200	−	0.200628i
$680$		0			0
$681$	30.9897	+	9.06530i	1.18753	+	0.347383i
$682$		0			0
$683$		−	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
$686$		0			0
$687$	−17.1170	−	17.9154i	−0.653055	−	0.683517i
$688$		0			0
$689$	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	$0.278695\pi$
$692$		0			0
$693$	0.239944	−	1.22943i	0.00911473	−	0.0467023i
$694$		0			0
$695$	−46.4583	−	26.8227i	−1.76226	−	1.01744i
$696$		0			0
$697$	−8.27188	−	14.3273i	−0.313320	−	0.542686i
$698$		0			0
$699$	−28.7220	+	6.99871i	−1.08637	+	0.264716i
$700$		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
$703$			15.5897i			0.587976i
$704$		0			0
$705$	−10.0864	−	41.3936i	−0.379875	−	1.55897i
$706$		0			0
$707$	6.19990	+	4.91966i	0.233171	+	0.185023i
$708$		0			0
$709$	5.35661	−	9.27792i	0.201172	−	0.348440i	−0.747735	−	0.663998i	$-0.768858\pi$
$709$	5.35661	−	9.27792i	0.201172	−	0.348440i	0.948906	+	0.315558i	$0.102192\pi$
$710$		0			0
$711$	−0.591443	+	12.9688i	−0.0221809	+	0.486368i
$712$		0			0
$713$	−0.0353413	+	0.0612130i	−0.00132354	+	0.00229244i
$714$		0			0
$715$	0.882977	+	1.52936i	0.0330215	+	0.0571949i
$716$		0			0
$717$	2.67427	+	2.79901i	0.0998724	+	0.104531i
$718$		0			0
$719$	−17.5794			−0.655601			−0.327801	−	0.944747i	$-0.606307\pi$
$719$	−17.5794			−0.655601			−0.327801	+	0.944747i	$0.606307\pi$
$720$		0			0
$721$	12.8348	+	32.4704i	0.477994	+	1.20926i
$722$		0			0
$723$	2.19815	−	7.51437i	0.0817500	−	0.279462i
$724$		0			0
$725$	−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	$0.285777\pi$
$728$		0			0
$729$	−3.67996	+	26.7480i	−0.136295	+	0.990668i
$730$		0			0
$731$	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	$0.597103\pi$
$734$		0			0
$735$	30.7045	−	15.5301i	1.13255	−	0.572837i
$736$		0			0
$737$		−	0.209490i		−	0.00771668i
$738$		0			0
$739$	−30.3432			−1.11619			−0.558096	−	0.829777i	$-0.688468\pi$
$739$	−30.3432			−1.11619			−0.558096	+	0.829777i	$0.688468\pi$
$740$		0			0
$741$	−31.2861	+	29.8918i	−1.14932	+	1.09810i
$742$		0			0
$743$	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
$746$		0			0
$747$	−0.881773	+	19.3350i	−0.0322624	+	0.707430i
$748$		0			0
$749$	−51.1798	−	7.58700i	−1.87007	−	0.277223i
$750$		0			0
$751$	6.07753	+	10.5266i	0.221772	+	0.384121i	0.955346	−	0.295489i	$-0.0954826\pi$
$751$	6.07753	+	10.5266i	0.221772	+	0.384121i	−0.733574	+	0.679610i	$0.762149\pi$
$752$		0			0
$753$	8.68190	+	35.6297i	0.316386	+	1.29842i
$754$		0			0
$755$	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	$0.556500\pi$
$758$		0			0
$759$	−0.0353413	−	0.145037i	−0.00128281	−	0.00526452i
$760$		0			0
$761$	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
$763$	5.14002	−	34.6732i	0.186081	−	1.25525i
$764$		0			0
$765$	−29.7257	−	19.0185i	−1.07473	−	0.687616i
$766$		0			0
$767$	12.3397	+	7.12432i	0.445560	+	0.257244i
$768$		0			0
$769$	9.42879	−	5.44371i	0.340011	−	0.196305i	−0.320266	−	0.947328i	$-0.603772\pi$
$769$	9.42879	−	5.44371i	0.340011	−	0.196305i	0.660277	+	0.751022i	$0.270439\pi$
$770$		0			0
$771$	−39.1986	+	37.4517i	−1.41170	+	1.34879i
$772$		0			0
$773$	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
$776$		0			0
$777$	11.2279	−	1.03411i	0.402800	−	0.0370985i
$778$		0			0
$779$	21.9012	−	12.6446i	0.784691	−	0.453041i
$780$		0			0
$781$	−0.0322979	+	0.0559416i	−0.00115571	+	0.00200175i
$782$		0			0
$783$	4.64483	+	23.7116i	0.165993	+	0.847383i
$784$		0			0
$785$	10.7915	+	6.23049i	0.385166	+	0.222376i
$786$		0			0
$787$	−15.4554	+	8.92315i	−0.550924	+	0.318076i	−0.749495	−	0.662011i	$-0.769703\pi$
$787$	−15.4554	+	8.92315i	−0.550924	+	0.318076i	0.198571	+	0.980087i	$0.436370\pi$
$788$		0			0
$789$	3.24682	−	11.0993i	0.115590	−	0.395144i
$790$		0			0
$791$	9.80039	+	24.7937i	0.348462	+	0.881562i
$792$		0			0
$793$	13.2704			0.471246
$794$		0			0
$795$	−8.83676	−	9.24895i	−0.313408	−	0.328026i
$796$		0			0
$797$	−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
$800$		0			0
$801$	13.4616	−	6.97449i	0.475641	−	0.246431i
$802$		0			0
$803$	−1.18460	+	2.05179i	−0.0418037	+	0.0724061i
$804$		0			0
$805$	2.54890	−	3.21219i	0.0898367	−	0.113215i
$806$		0			0
$807$	−4.37072	−	17.9370i	−0.153857	−	0.631413i
$808$		0			0
$809$			13.1945i			0.463893i	0.972729	+	0.231946i	$0.0745094\pi$
$809$			13.1945i			0.463893i	−0.972729	+	0.231946i	$0.925491\pi$
$810$		0			0
$811$			46.5800i			1.63565i	0.575469	+	0.817823i	$0.304819\pi$
$811$			46.5800i			1.63565i	−0.575469	+	0.817823i	$0.695181\pi$
$812$		0			0
$813$	12.5285	−	3.05283i	0.439394	−	0.107067i
$814$		0			0
$815$	7.71304	+	13.3594i	0.270176	+	0.467958i
$816$		0			0
$817$	36.0431	+	20.8095i	1.26099	+	0.728031i
$818$		0			0
$819$	23.6039	+	20.5499i	0.824785	+	0.718073i
$820$		0			0
$821$	34.3623	+	19.8391i	1.19925	+	0.692390i	0.960389	−	0.278663i	$-0.0898913\pi$
$821$	34.3623	+	19.8391i	1.19925	+	0.692390i	0.238865	+	0.971053i	$0.423225\pi$
$822$		0			0
$823$	−19.6156	−	33.9751i	−0.683755	−	1.18430i	−0.973826	−	0.227294i	$-0.927012\pi$
$823$	−19.6156	−	33.9751i	−0.683755	−	1.18430i	0.290071	−	0.957005i	$-0.406321\pi$
$824$		0			0
$825$	−0.576705	−	0.603605i	−0.0200783	−	0.0210148i
$826$		0			0
$827$		−	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	$0.0743361\pi$
$829$			13.3261i			0.462834i	−0.972855	+	0.231417i	$0.925664\pi$
$830$		0			0
$831$	−44.1505	−	12.9152i	−1.53156	−	0.448023i
$832$		0			0
$833$	27.7663	+	8.41724i	0.962046	+	0.291640i
$834$		0			0
$835$	−14.9071	+	25.8198i	−0.515881	+	0.893533i
$836$		0			0
$837$	0.636194	+	0.218026i	0.0219901	+	0.00753607i
$838$		0			0
$839$	8.39768	−	14.5452i	0.289920	−	0.502156i	−0.683870	−	0.729604i	$-0.739705\pi$
$839$	8.39768	−	14.5452i	0.289920	−	0.502156i	0.973790	+	0.227447i	$0.0730379\pi$
$840$		0			0
$841$	−3.68862	−	6.38888i	−0.127194	−	0.220306i
$842$		0			0
$843$	11.8477	−	40.5013i	0.408056	−	1.39494i
$844$		0			0
$845$	−7.22744			−0.248632
$846$		0			0
$847$	−27.0043	+	10.6742i	−0.927878	+	0.366769i
$848$		0			0
$849$	−10.3525	−	10.8354i	−0.355298	−	0.371871i
$850$		0			0
$851$	1.16372	−	0.671871i	0.0398916	−	0.0230315i
$852$		0			0
$853$	35.5011	+	20.4966i	1.21554	+	0.701790i	0.963960	−	0.266048i	$-0.0857179\pi$
$853$	35.5011	+	20.4966i	1.21554	+	0.701790i	0.251576	+	0.967838i	$0.419051\pi$
$854$		0			0
$855$	29.0723	−	45.4395i	0.994251	−	1.55400i
$856$		0			0
$857$	−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	$0.176245\pi$
$860$		0			0
$861$	−10.5596	−	14.9348i	−0.359871	−	0.508976i
$862$		0			0
$863$			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
$866$		0			0
$867$	−0.0737935	−	0.302841i	−0.00250616	−	0.0102850i
$868$		0			0
$869$	−0.591443	+	0.341470i	−0.0200633	+	0.0115836i
$870$		0			0
$871$	4.53275	+	2.61698i	0.153586	+	0.0886731i
$872$		0			0
$873$	−7.55955	−	0.344754i	−0.255852	−	0.0116681i
$874$		0			0
$875$	−2.14256	+	14.4531i	−0.0724316	+	0.488604i
$876$		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	$0.929863\pi$
$878$		0			0
$879$	−11.0211	+	10.5299i	−0.371733	+	0.355166i
$880$		0			0
$881$	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	$-0.295905\pi$
$883$	35.5480			1.19629			0.598143	+	0.801389i	$0.295905\pi$
$884$		0			0
$885$	−17.0488	−	4.98722i	−0.573089	−	0.167644i
$886$		0			0
$887$	12.2751	+	21.2610i	0.412156	+	0.713876i	0.995125	−	0.0986188i	$-0.0314424\pi$
$887$	12.2751	+	21.2610i	0.412156	+	0.713876i	−0.582969	+	0.812494i	$0.698109\pi$
$888$		0			0
$889$	4.84564	−	32.6874i	0.162518	−	1.09630i
$890$		0			0
$891$	−1.28959	+	0.595265i	−0.0432030	+	0.0199421i
$892$		0			0
$893$	47.5590	+	27.4582i	1.59150	+	0.918854i
$894$		0			0
$895$	−44.7392	+	25.8302i	−1.49547	+	0.863408i
$896$		0			0
$897$	3.57966	+	1.04715i	0.119521	+	0.0349632i
$898$		0			0
$899$	0.601834			0.0200723
$900$		0			0
$901$		−	10.7864i		−	0.359346i
$902$		0			0
$903$	12.5964	−	27.3391i	0.419184	−	0.909788i
$904$		0			0
$905$	16.2257	−	9.36790i	0.539360	−	0.311399i
$906$		0			0
$907$	18.4502	−	31.9567i	0.612628	−	1.06110i	−0.378167	−	0.925737i	$-0.623446\pi$
$907$	18.4502	−	31.9567i	0.612628	−	1.06110i	0.990796	−	0.135366i	$-0.0432211\pi$
$908$		0			0
$909$	0.408852	−	8.96507i	0.0135608	−	0.297352i
$910$		0			0
$911$	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
$914$		0			0
$915$	−16.0735	+	3.91663i	−0.531372	+	0.129480i
$916$		0			0
$917$	−24.7157	+	9.76957i	−0.816186	+	0.322620i
$918$		0			0
$919$	56.8725			1.87605			0.938026	−	0.346565i	$-0.112652\pi$
$919$	56.8725			1.87605			0.938026	+	0.346565i	$0.112652\pi$
$920$		0			0
$921$	18.8049	−	4.58219i	0.619641	−	0.150988i
$922$		0			0
$923$	−0.806939	−	1.39766i	−0.0265607	−	0.0460045i
$924$		0			0
$925$	3.75729	−	6.50783i	0.123539	−	0.213976i
$926$		0			0
$927$	21.3364	−	33.3485i	0.700779	−	1.09531i
$928$		0			0
$929$	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
$931$	−12.8668	+	42.4444i	−0.421694	+	1.39106i
$932$		0			0
$933$	20.5452	−	19.6296i	0.672621	−	0.642645i
$934$		0			0
$935$		−	1.85640i		−	0.0607108i
$936$		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
$939$	3.98968	−	13.6387i	0.130198	−	0.445083i
$940$		0			0
$941$	−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
$944$		0			0
$945$	−34.6547	−	17.9241i	−1.12732	−	0.583073i
$946$		0			0
$947$	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
$950$		0			0
$951$	11.1421	−	38.0892i	0.361307	−	1.23513i
$952$		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
$955$		−	40.3279i		−	1.30498i
$956$		0			0
$957$	−0.919025	+	0.878068i	−0.0297079	+	0.0283839i
$958$		0			0
$959$	−13.2247	+	16.6662i	−0.427049	+	0.538179i
$960$		0			0
$961$	−15.4916	+	26.8323i	−0.499730	+	0.865557i
$962$		0			0
$963$	26.9882	+	52.0904i	0.869683	+	1.67859i
$964$		0			0
$965$	14.1959	−	24.5881i	0.456983	−	0.791518i
$966$		0			0
$967$	−25.0275	−	43.3489i	−0.804831	−	1.39401i	−0.916405	−	0.400252i	$-0.868923\pi$
$967$	−25.0275	−	43.3489i	−0.804831	−	1.39401i	0.111574	−	0.993756i	$-0.464411\pi$
$968$		0			0
$969$	44.1937	−	10.7687i	1.41971	−	0.345940i
$970$		0			0
$971$	−1.04188			−0.0334354			−0.0167177	−	0.999860i	$-0.505322\pi$
$971$	−1.04188			−0.0334354			−0.0167177	+	0.999860i	$0.505322\pi$
$972$		0			0
$973$	−18.3844	−	46.5102i	−0.589378	−	1.49105i
$974$		0			0
$975$	20.2645	−	4.93786i	0.648983	−	0.158138i
$976$		0			0
$977$	21.1765	−	12.2262i	0.677495	−	0.391152i	−0.121416	−	0.992602i	$-0.538743\pi$
$977$	21.1765	−	12.2262i	0.677495	−	0.391152i	0.798910	+	0.601450i	$0.205410\pi$
$978$		0			0
$979$	0.690703	+	0.398777i	0.0220750	+	0.0127450i
$980$		0			0
$981$	−35.2901	+	18.2839i	−1.12673	+	0.583760i
$982$		0			0
$983$	−28.0788	+	48.6339i	−0.895575	+	1.55118i	−0.0624829	+	0.998046i	$0.519902\pi$
$983$	−28.0788	+	48.6339i	−0.895575	+	1.55118i	−0.833092	+	0.553135i	$0.813431\pi$
$984$		0			0
$985$	−49.4050	+	28.5240i	−1.57417	+	0.908850i
$986$		0			0
$987$	16.6211	−	36.0741i	0.529055	−	1.14825i
$988$		0			0
$989$		−	3.58731i		−	0.114070i
$990$		0			0
$991$	−18.2278			−0.579025			−0.289513	−	0.957174i	$-0.593493\pi$
$991$	−18.2278			−0.579025			−0.289513	+	0.957174i	$0.593493\pi$
$992$		0			0
$993$	−32.0229	−	9.36753i	−1.01622	−	0.297270i
$994$		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	$0.483102\pi$
$998$		0			0
$999$	−8.40183	−	9.63688i	−0.265822	−	0.304898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cc.a.209.3		12
3.2	odd	2		3024.2.cc.a.2897.6		12
4.3	odd	2		63.2.o.a.20.6	yes	12
7.6	odd	2	inner	1008.2.cc.a.209.4		12
9.4	even	3		3024.2.cc.a.881.1		12
9.5	odd	6	inner	1008.2.cc.a.545.4		12
12.11	even	2		189.2.o.a.62.2		12
21.20	even	2		3024.2.cc.a.2897.1		12
28.3	even	6		441.2.s.c.362.1		12
28.11	odd	6		441.2.s.c.362.2		12
28.19	even	6		441.2.i.c.227.2		12
28.23	odd	6		441.2.i.c.227.1		12
28.27	even	2		63.2.o.a.20.5	✓	12
36.7	odd	6		567.2.c.c.566.4		12
36.11	even	6		567.2.c.c.566.9		12
36.23	even	6		63.2.o.a.41.5	yes	12
36.31	odd	6		189.2.o.a.125.1		12
63.13	odd	6		3024.2.cc.a.881.6		12
63.41	even	6	inner	1008.2.cc.a.545.3		12
84.11	even	6		1323.2.s.c.656.5		12
84.23	even	6		1323.2.i.c.521.6		12
84.47	odd	6		1323.2.i.c.521.5		12
84.59	odd	6		1323.2.s.c.656.6		12
84.83	odd	2		189.2.o.a.62.1		12
252.23	even	6		441.2.s.c.374.1		12
252.31	even	6		1323.2.i.c.1097.2		12
252.59	odd	6		441.2.i.c.68.5		12
252.67	odd	6		1323.2.i.c.1097.1		12
252.83	odd	6		567.2.c.c.566.10		12
252.95	even	6		441.2.i.c.68.6		12
252.103	even	6		1323.2.s.c.962.5		12
252.131	odd	6		441.2.s.c.374.2		12
252.139	even	6		189.2.o.a.125.2		12
252.167	odd	6		63.2.o.a.41.6	yes	12
252.223	even	6		567.2.c.c.566.3		12
252.247	odd	6		1323.2.s.c.962.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.5	✓	12	28.27	even	2
63.2.o.a.20.6	yes	12	4.3	odd	2
63.2.o.a.41.5	yes	12	36.23	even	6
63.2.o.a.41.6	yes	12	252.167	odd	6
189.2.o.a.62.1		12	84.83	odd	2
189.2.o.a.62.2		12	12.11	even	2
189.2.o.a.125.1		12	36.31	odd	6
189.2.o.a.125.2		12	252.139	even	6
441.2.i.c.68.5		12	252.59	odd	6
441.2.i.c.68.6		12	252.95	even	6
441.2.i.c.227.1		12	28.23	odd	6
441.2.i.c.227.2		12	28.19	even	6
441.2.s.c.362.1		12	28.3	even	6
441.2.s.c.362.2		12	28.11	odd	6
441.2.s.c.374.1		12	252.23	even	6
441.2.s.c.374.2		12	252.131	odd	6
567.2.c.c.566.3		12	252.223	even	6
567.2.c.c.566.4		12	36.7	odd	6
567.2.c.c.566.9		12	36.11	even	6
567.2.c.c.566.10		12	252.83	odd	6
1008.2.cc.a.209.3		12	1.1	even	1	trivial
1008.2.cc.a.209.4		12	7.6	odd	2	inner
1008.2.cc.a.545.3		12	63.41	even	6	inner
1008.2.cc.a.545.4		12	9.5	odd	6	inner
1323.2.i.c.521.5		12	84.47	odd	6
1323.2.i.c.521.6		12	84.23	even	6
1323.2.i.c.1097.1		12	252.67	odd	6
1323.2.i.c.1097.2		12	252.31	even	6
1323.2.s.c.656.5		12	84.11	even	6
1323.2.s.c.656.6		12	84.59	odd	6
1323.2.s.c.962.5		12	252.103	even	6
1323.2.s.c.962.6		12	252.247	odd	6
3024.2.cc.a.881.1		12	9.4	even	3
3024.2.cc.a.881.6		12	63.13	odd	6
3024.2.cc.a.2897.1		12	21.20	even	2
3024.2.cc.a.2897.6		12	3.2	odd	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.410052 - 1.68281i) q^{3} +(-1.41899 - 2.45776i) q^{5} +(0.387972 - 2.61715i) q^{7} +(-2.66372 + 1.38008i) q^{9} +O(q^{10})\)	\(q+(-0.410052 - 1.68281i) q^{3} +(-1.41899 - 2.45776i) q^{5} +(0.387972 - 2.61715i) q^{7} +(-2.66372 + 1.38008i) q^{9} +(-0.136673 - 0.0789082i) q^{11} +(3.41468 - 1.97146i) q^{13} +(-3.55408 + 3.39569i) q^{15} -4.14487 q^{17} -6.33597i q^{19} +(-4.56326 + 0.420284i) q^{21} +(-0.472958 + 0.273062i) q^{23} +(-1.52704 + 2.64491i) q^{25} +(3.41468 + 3.91663i) q^{27} +(4.02704 + 2.32501i) q^{29} +(0.112086 - 0.0647129i) q^{31} +(-0.0767447 + 0.262352i) q^{33} +(-6.98284 + 2.76016i) q^{35} -2.46050 q^{37} +(-4.71780 - 4.93786i) q^{39} +(1.99569 + 3.45664i) q^{41} +(-3.28434 + 5.68864i) q^{43} +(7.17167 + 4.58845i) q^{45} +(-4.33370 + 7.50619i) q^{47} +(-6.69896 - 2.03076i) q^{49} +(1.69961 + 6.97504i) q^{51} +2.60234i q^{53} +0.447879i q^{55} +(-10.6623 + 2.59808i) q^{57} +(1.80686 + 3.12957i) q^{59} +(2.91472 + 1.68281i) q^{61} +(2.57843 + 7.50678i) q^{63} +(-9.69076 - 5.59496i) q^{65} +(0.663715 + 1.14959i) q^{67} +(0.653450 + 0.683930i) q^{69} -0.409310i q^{71} -15.0124i q^{73} +(5.07706 + 1.48517i) q^{75} +(-0.259540 + 0.327080i) q^{77} +(2.16372 - 3.74766i) q^{79} +(5.19076 - 7.35228i) q^{81} +(3.22585 - 5.58733i) q^{83} +(5.88151 + 10.1871i) q^{85} +(2.26127 - 7.73013i) q^{87} -5.05368 q^{89} +(-3.83482 - 9.70160i) q^{91} +(-0.154861 - 0.162084i) q^{93} +(-15.5723 + 8.99066i) q^{95} +(2.18452 + 1.26123i) q^{97} +(0.472958 + 0.0215693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q + 2 * q^7 - 12 * q^9	\( 12 q + 2 q^{7} - 12 q^{9} - 6 q^{15} - 24 q^{21} - 24 q^{23} + 30 q^{29} - 4 q^{37} + 10 q^{43} + 6 q^{49} + 42 q^{51} - 18 q^{57} - 24 q^{63} - 78 q^{65} - 12 q^{67} - 24 q^{77} + 6 q^{79} + 24 q^{81} - 6 q^{85} + 24 q^{91} + 78 q^{93} - 72 q^{95} + 24 q^{99}+O(q^{100}) \) 12 * q + 2 * q^7 - 12 * q^9 - 6 * q^15 - 24 * q^21 - 24 * q^23 + 30 * q^29 - 4 * q^37 + 10 * q^43 + 6 * q^49 + 42 * q^51 - 18 * q^57 - 24 * q^63 - 78 * q^65 - 12 * q^67 - 24 * q^77 + 6 * q^79 + 24 * q^81 - 6 * q^85 + 24 * q^91 + 78 * q^93 - 72 * q^95 + 24 * q^99

Introduction

L-functions

Modular forms

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Database

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