LMFDB - Embedded newform 1008.2.cc.a.545.5

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			545.5
Root			$-1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	1008.545
Dual form			1008.2.cc.a.209.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.578751 + 1.63250i) q^{3} +(0.717144 - 1.24213i) q^{5} +(-2.16235 + 1.52455i) q^{7} +(-2.33009 + 1.88962i) q^{9} +O(q^{10})$	\(q+(0.578751 + 1.63250i) q^{3} +(0.717144 - 1.24213i) q^{5} +(-2.16235 + 1.52455i) q^{7} +(-2.33009 + 1.88962i) q^{9} +(-2.80150 + 1.61745i) q^{11} +(-4.43334 - 2.55959i) q^{13} +(2.44282 + 0.451852i) q^{15} -1.09132 q^{17} -4.48911i q^{19} +(-3.74028 - 2.64769i) q^{21} +(-3.47141 - 2.00422i) q^{23} +(1.47141 + 2.54856i) q^{25} +(-4.43334 - 2.71026i) q^{27} +(1.02859 - 0.593857i) q^{29} +(-3.24275 - 1.87220i) q^{31} +(-4.26186 - 3.63735i) q^{33} +(0.342971 + 3.77924i) q^{35} -0.239123 q^{37} +(1.61273 - 8.71878i) q^{39} +(-3.71620 + 6.43664i) q^{41} +(3.82326 + 6.62208i) q^{43} +(0.676137 + 4.24941i) q^{45} +(-2.11042 - 3.65536i) q^{47} +(2.35150 - 6.59321i) q^{49} +(-0.631600 - 1.78157i) q^{51} +7.01414i q^{53} +4.63977i q^{55} +(7.32846 - 2.59808i) q^{57} +(-4.73531 + 8.20179i) q^{59} +(2.82757 - 1.63250i) q^{61} +(2.15766 - 7.63836i) q^{63} +(-6.35868 + 3.67119i) q^{65} +(0.330095 - 0.571741i) q^{67} +(1.26280 - 6.82701i) q^{69} -3.82347i q^{71} +7.31073i q^{73} +(-3.30893 + 3.87705i) q^{75} +(3.59195 - 7.76852i) q^{77} +(1.83009 + 3.16982i) q^{79} +(1.85868 - 8.80598i) q^{81} +(-5.45245 - 9.44392i) q^{83} +(-0.782630 + 1.35556i) q^{85} +(1.56477 + 1.33548i) q^{87} -13.6915 q^{89} +(13.4887 - 1.22412i) q^{91} +(1.17962 - 6.37731i) q^{93} +(-5.57605 - 3.21934i) q^{95} +(-2.69709 + 1.55716i) q^{97} +(3.47141 - 9.06259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.578751	+	1.63250i	0.334142	+	0.942523i
$3$	0.578751	+	1.63250i	0.334142	+	0.942523i
$4$		0			0
$5$	0.717144	−	1.24213i	0.320716	−	0.555497i	−0.659920	−	0.751336i	$-0.729410\pi$
$5$	0.717144	−	1.24213i	0.320716	−	0.555497i	0.980636	+	0.195839i	$0.0627430\pi$
$6$		0			0
$7$	−2.16235	+	1.52455i	−0.817291	+	0.576225i
$7$	−2.16235	+	1.52455i	−0.817291	+	0.576225i
$8$		0			0
$9$	−2.33009	+	1.88962i	−0.776698	+	0.629873i
$10$		0			0
$11$	−2.80150	+	1.61745i	−0.844686	+	0.487679i	−0.858854	−	0.512220i	$-0.828823\pi$
$11$	−2.80150	+	1.61745i	−0.844686	+	0.487679i	0.0141686	+	0.999900i	$0.495490\pi$
$12$		0			0
$13$	−4.43334	−	2.55959i	−1.22959	−	0.709903i	−0.262644	−	0.964893i	$-0.584594\pi$
$13$	−4.43334	−	2.55959i	−1.22959	−	0.709903i	−0.966944	+	0.254990i	$0.917928\pi$
$14$		0			0
$15$	2.44282	+	0.451852i	0.630733	+	0.116668i
$16$		0			0
$17$	−1.09132			−0.264683			−0.132341	−	0.991204i	$-0.542250\pi$
$17$	−1.09132			−0.264683			−0.132341	+	0.991204i	$0.542250\pi$
$18$		0			0
$19$		−	4.48911i		−	1.02987i	−0.857228	−	0.514936i	$-0.827816\pi$
$19$		−	4.48911i		−	1.02987i	0.857228	−	0.514936i	$-0.172184\pi$
$20$		0			0
$21$	−3.74028	−	2.64769i	−0.816197	−	0.577774i
$22$		0			0
$23$	−3.47141	−	2.00422i	−0.723839	−	0.417909i	0.0923250	−	0.995729i	$-0.470570\pi$
$23$	−3.47141	−	2.00422i	−0.723839	−	0.417909i	−0.816164	+	0.577820i	$0.803903\pi$
$24$		0			0
$25$	1.47141	+	2.54856i	0.294282	+	0.509711i
$26$		0			0
$27$	−4.43334	−	2.71026i	−0.853197	−	0.521589i
$28$		0			0
$29$	1.02859	−	0.593857i	0.191004	−	0.110276i	−0.401448	−	0.915882i	$-0.631493\pi$
$29$	1.02859	−	0.593857i	0.191004	−	0.110276i	0.592453	+	0.805605i	$0.298160\pi$
$30$		0			0
$31$	−3.24275	−	1.87220i	−0.582414	−	0.336257i	0.179678	−	0.983726i	$-0.442494\pi$
$31$	−3.24275	−	1.87220i	−0.582414	−	0.336257i	−0.762092	+	0.647468i	$0.775828\pi$
$32$		0			0
$33$	−4.26186	−	3.63735i	−0.741894	−	0.633181i
$34$		0			0
$35$	0.342971	+	3.77924i	0.0579728	+	0.638808i
$36$		0			0
$37$	−0.239123			−0.0393116			−0.0196558	−	0.999807i	$-0.506257\pi$
$37$	−0.239123			−0.0393116			−0.0196558	+	0.999807i	$0.506257\pi$
$38$		0			0
$39$	1.61273	−	8.71878i	0.258243	−	1.39612i
$40$		0			0
$41$	−3.71620	+	6.43664i	−0.580373	+	1.00523i	0.415062	+	0.909793i	$0.363760\pi$
$41$	−3.71620	+	6.43664i	−0.580373	+	1.00523i	−0.995435	+	0.0954418i	$0.969574\pi$
$42$		0			0
$43$	3.82326	+	6.62208i	0.583041	+	1.00986i	0.995116	+	0.0987075i	$0.0314708\pi$
$43$	3.82326	+	6.62208i	0.583041	+	1.00986i	−0.412075	+	0.911150i	$0.635196\pi$
$44$		0			0
$45$	0.676137	+	4.24941i	0.100793	+	0.633464i
$46$		0			0
$47$	−2.11042	−	3.65536i	−0.307837	−	0.533189i	0.670052	−	0.742314i	$-0.266272\pi$
$47$	−2.11042	−	3.65536i	−0.307837	−	0.533189i	−0.977889	+	0.209125i	$0.932939\pi$
$48$		0			0
$49$	2.35150	−	6.59321i	0.335929	−	0.941887i
$50$		0			0
$51$	−0.631600	−	1.78157i	−0.0884417	−	0.249470i
$52$		0			0
$53$			7.01414i			0.963466i	0.876318	+	0.481733i	$0.159992\pi$
$53$			7.01414i			0.963466i	−0.876318	+	0.481733i	$0.840008\pi$
$54$		0			0
$55$			4.63977i			0.625627i
$56$		0			0
$57$	7.32846	−	2.59808i	0.970678	−	0.344124i
$58$		0			0
$59$	−4.73531	+	8.20179i	−0.616484	+	1.06778i	0.373638	+	0.927575i	$0.378110\pi$
$59$	−4.73531	+	8.20179i	−0.616484	+	1.06778i	−0.990122	+	0.140208i	$0.955223\pi$
$60$		0			0
$61$	2.82757	−	1.63250i	0.362033	−	0.209020i	−0.307939	−	0.951406i	$-0.599639\pi$
$61$	2.82757	−	1.63250i	0.362033	−	0.209020i	0.669972	+	0.742386i	$0.266306\pi$
$62$		0			0
$63$	2.15766	−	7.63836i	0.271840	−	0.962342i
$64$		0			0
$65$	−6.35868	+	3.67119i	−0.788698	+	0.455355i
$66$		0			0
$67$	0.330095	−	0.571741i	0.0403275	−	0.0698493i	−0.845157	−	0.534518i	$-0.820493\pi$
$67$	0.330095	−	0.571741i	0.0403275	−	0.0698493i	0.885485	+	0.464669i	$0.153827\pi$
$68$		0			0
$69$	1.26280	−	6.82701i	0.152023	−	0.821876i
$70$		0			0
$71$		−	3.82347i		−	0.453762i	−0.973922	−	0.226881i	$-0.927147\pi$
$71$		−	3.82347i		−	0.453762i	0.973922	−	0.226881i	$-0.0728529\pi$
$72$		0			0
$73$			7.31073i			0.855656i	0.903860	+	0.427828i	$0.140721\pi$
$73$			7.31073i			0.855656i	−0.903860	+	0.427828i	$0.859279\pi$
$74$		0			0
$75$	−3.30893	+	3.87705i	−0.382083	+	0.447683i
$76$		0			0
$77$	3.59195	−	7.76852i	0.409341	−	0.885305i
$78$		0			0
$79$	1.83009	+	3.16982i	0.205902	+	0.356632i	0.950420	−	0.310970i	$-0.100654\pi$
$79$	1.83009	+	3.16982i	0.205902	+	0.356632i	−0.744518	+	0.667602i	$0.767321\pi$
$80$		0			0
$81$	1.85868	−	8.80598i	0.206521	−	0.978442i
$82$		0			0
$83$	−5.45245	−	9.44392i	−0.598484	−	1.03660i	−0.993045	−	0.117735i	$-0.962437\pi$
$83$	−5.45245	−	9.44392i	−0.598484	−	1.03660i	0.394561	−	0.918870i	$-0.370897\pi$
$84$		0			0
$85$	−0.782630	+	1.35556i	−0.0848882	+	0.147031i
$86$		0			0
$87$	1.56477	+	1.33548i	0.167761	+	0.143178i
$88$		0			0
$89$	−13.6915			−1.45129			−0.725646	−	0.688068i	$-0.758459\pi$
$89$	−13.6915			−1.45129			−0.725646	+	0.688068i	$0.758459\pi$
$90$		0			0
$91$	13.4887	−	1.22412i	1.41399	−	0.128322i
$92$		0			0
$93$	1.17962	−	6.37731i	0.122321	−	0.661297i
$94$		0			0
$95$	−5.57605	−	3.21934i	−0.572091	−	0.330297i
$96$		0			0
$97$	−2.69709	+	1.55716i	−0.273848	+	0.158106i	−0.630635	−	0.776080i	$-0.717205\pi$
$97$	−2.69709	+	1.55716i	−0.273848	+	0.158106i	0.356787	+	0.934186i	$0.383872\pi$
$98$		0			0
$99$	3.47141	−	9.06259i	0.348890	−	0.910824i
$100$		0			0
$101$	−3.54471	−	6.13962i	−0.352712	−	0.610915i	0.634012	−	0.773324i	$-0.281407\pi$
$101$	−3.54471	−	6.13962i	−0.352712	−	0.610915i	−0.986724	+	0.162408i	$0.948074\pi$
$102$		0			0
$103$	1.47529	+	0.851761i	0.145365	+	0.0839265i	0.570918	−	0.821007i	$-0.306587\pi$
$103$	1.47529	+	0.851761i	0.145365	+	0.0839265i	−0.425553	+	0.904933i	$0.639921\pi$
$104$		0			0
$105$	−5.97110	+	2.74714i	−0.582720	+	0.268093i
$106$		0			0
$107$			4.93582i			0.477164i	0.971122	+	0.238582i	$0.0766826\pi$
$107$			4.93582i			0.477164i	−0.971122	+	0.238582i	$0.923317\pi$
$108$		0			0
$109$	8.13844			0.779521			0.389760	−	0.920916i	$-0.372558\pi$
$109$	8.13844			0.779521			0.389760	+	0.920916i	$0.372558\pi$
$110$		0			0
$111$	−0.138393	−	0.390368i	−0.0131357	−	0.0370521i
$112$		0			0
$113$	−3.39699	−	1.96125i	−0.319562	−	0.184499i	0.331635	−	0.943408i	$-0.392400\pi$
$113$	−3.39699	−	1.96125i	−0.319562	−	0.184499i	−0.651197	+	0.758908i	$0.725733\pi$
$114$		0			0
$115$	−4.97900	+	2.87463i	−0.464294	+	0.268060i
$116$		0			0
$117$	15.1668	−	2.41323i	1.40217	−	0.223104i
$118$		0			0
$119$	2.35981	−	1.66376i	0.216323	−	0.152517i
$120$		0			0
$121$	−0.267713	+	0.463693i	−0.0243376	+	0.0421539i
$122$		0			0
$123$	−12.6586	−	2.34147i	−1.14138	−	0.211123i
$124$		0			0
$125$	11.3923			1.01896
$126$		0			0
$127$	−6.16827			−0.547345			−0.273673	−	0.961823i	$-0.588239\pi$
$127$	−6.16827			−0.547345			−0.273673	+	0.961823i	$0.588239\pi$
$128$		0			0
$129$	−8.59781	+	10.0740i	−0.756995	+	0.886966i
$130$		0			0
$131$	4.13138	−	7.15575i	0.360960	−	0.625201i	−0.627159	−	0.778891i	$-0.715782\pi$
$131$	4.13138	−	7.15575i	0.360960	−	0.625201i	0.988119	+	0.153690i	$0.0491158\pi$
$132$		0			0
$133$	6.84387	+	9.70702i	0.593438	+	0.841706i
$134$		0			0
$135$	−6.54583	+	3.56314i	−0.563375	+	0.306666i
$136$		0			0
$137$	−8.96169	+	5.17404i	−0.765649	+	0.442048i	−0.831320	−	0.555794i	$-0.812415\pi$
$137$	−8.96169	+	5.17404i	−0.765649	+	0.442048i	0.0656711	+	0.997841i	$0.479081\pi$
$138$		0			0
$139$	15.4589	+	8.92521i	1.31121	+	0.757026i	0.982296	−	0.187334i	$-0.0599848\pi$
$139$	15.4589	+	8.92521i	1.31121	+	0.757026i	0.328912	+	0.944361i	$0.393318\pi$
$140$		0			0
$141$	4.74596	−	5.56081i	0.399682	−	0.468304i
$142$		0			0
$143$	16.5600			1.38482
$144$		0			0
$145$		−	1.70352i		−	0.141470i
$146$		0			0
$147$	12.1243	+	0.0229982i	0.999998	+	0.00189686i
$148$		0			0
$149$	−15.1758	−	8.76175i	−1.24325	−	0.717790i	−0.273495	−	0.961873i	$-0.588180\pi$
$149$	−15.1758	−	8.76175i	−1.24325	−	0.717790i	−0.969754	+	0.244083i	$0.921513\pi$
$150$		0			0
$151$	0.550343	+	0.953223i	0.0447863	+	0.0775722i	0.887550	−	0.460712i	$-0.152406\pi$
$151$	0.550343	+	0.953223i	0.0447863	+	0.0775722i	−0.842763	+	0.538284i	$0.819073\pi$
$152$		0			0
$153$	2.54287	−	2.06217i	0.205579	−	0.166717i
$154$		0			0
$155$	−4.65103	+	2.68527i	−0.373580	+	0.215686i
$156$		0			0
$157$	8.45150	+	4.87948i	0.674503	+	0.389425i	0.797781	−	0.602947i	$-0.206007\pi$
$157$	8.45150	+	4.87948i	0.674503	+	0.389425i	−0.123277	+	0.992372i	$0.539340\pi$
$158$		0			0
$159$	−11.4506	+	4.05944i	−0.908088	+	0.321934i
$160$		0			0
$161$	10.5619	−	0.958511i	0.832397	−	0.0755413i
$162$		0			0
$163$	7.22545			0.565941			0.282970	−	0.959129i	$-0.408680\pi$
$163$	7.22545			0.565941			0.282970	+	0.959129i	$0.408680\pi$
$164$		0			0
$165$	−7.57442	+	2.68527i	−0.589668	+	0.209048i
$166$		0			0
$167$	−8.65419	+	14.9895i	−0.669681	+	1.15992i	0.308312	+	0.951285i	$0.400236\pi$
$167$	−8.65419	+	14.9895i	−0.669681	+	1.15992i	−0.977993	+	0.208637i	$0.933097\pi$
$168$		0			0
$169$	6.60301	+	11.4367i	0.507924	+	0.879750i
$170$		0			0
$171$	8.48270	+	10.4601i	0.648689	+	0.799900i
$172$		0			0
$173$	−0.978103	−	1.69412i	−0.0743638	−	0.128802i	0.826446	−	0.563017i	$-0.190359\pi$
$173$	−0.978103	−	1.69412i	−0.0743638	−	0.128802i	−0.900809	+	0.434215i	$0.857026\pi$
$174$		0			0
$175$	−7.06710	−	3.26763i	−0.534223	−	0.247010i
$176$		0			0
$177$	−16.1300	−	2.98358i	−1.21240	−	0.224260i
$178$		0			0
$179$			23.2017i			1.73418i	0.498152	+	0.867090i	$0.334012\pi$
$179$			23.2017i			1.73418i	−0.498152	+	0.867090i	$0.665988\pi$
$180$		0			0
$181$		−	10.2744i		−	0.763689i	−0.924226	−	0.381845i	$-0.875289\pi$
$181$		−	10.2744i		−	0.763689i	0.924226	−	0.381845i	$-0.124711\pi$
$182$		0			0
$183$	4.30150	+	3.67119i	0.317976	+	0.271382i
$184$		0			0
$185$	−0.171486	+	0.297022i	−0.0126079	+	0.0218375i
$186$		0			0
$187$	3.05733	−	1.76515i	0.223574	−	0.129080i
$188$		0			0
$189$	13.7183	−	0.898326i	0.997863	−	0.0653436i
$190$		0			0
$191$	−19.6758	+	11.3598i	−1.42369	+	0.821968i	−0.996612	−	0.0822464i	$-0.973791\pi$
$191$	−19.6758	+	11.3598i	−1.42369	+	0.821968i	−0.427079	+	0.904215i	$0.640457\pi$
$192$		0			0
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	0.384459	+	0.923142i	$0.374388\pi$
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	−0.991694	+	0.128620i	$0.958945\pi$
$194$		0			0
$195$	−9.67330	−	8.25583i	−0.692719	−	0.591212i
$196$		0			0
$197$			8.94426i			0.637252i	0.947880	+	0.318626i	$0.103221\pi$
$197$			8.94426i			0.637252i	−0.947880	+	0.318626i	$0.896779\pi$
$198$		0			0
$199$			5.78528i			0.410108i	0.978751	+	0.205054i	$0.0657369\pi$
$199$			5.78528i			0.410108i	−0.978751	+	0.205054i	$0.934263\pi$
$200$		0			0
$201$	1.12441	+	0.207983i	0.0793097	+	0.0146700i
$202$		0			0
$203$	−1.31881	+	2.85226i	−0.0925621	+	0.200189i
$204$		0			0
$205$	5.33009	+	9.23200i	0.372270	+	0.644791i
$206$		0			0
$207$	11.8759	−	1.88962i	0.825434	−	0.131338i
$208$		0			0
$209$	7.26091	+	12.5763i	0.502248	+	0.869918i
$210$		0			0
$211$	12.9451	−	22.4216i	0.891180	−	1.54357i	0.0527186	−	0.998609i	$-0.483211\pi$
$211$	12.9451	−	22.4216i	0.891180	−	1.54357i	0.838462	−	0.544960i	$-0.183455\pi$
$212$		0			0
$213$	6.24180	−	2.21284i	0.427681	−	0.151621i
$214$		0			0
$215$	10.9673			0.747964
$216$		0			0
$217$	9.86621	−	0.895374i	0.669762	−	0.0607819i
$218$		0			0
$219$	−11.9347	+	4.23109i	−0.806475	+	0.285910i
$220$		0			0
$221$	4.83818	+	2.79332i	0.325451	+	0.187899i
$222$		0			0
$223$	15.4827	−	8.93892i	1.03680	−	0.598594i	0.117871	−	0.993029i	$-0.462393\pi$
$223$	15.4827	−	8.93892i	1.03680	−	0.598594i	0.918924	+	0.394435i	$0.129060\pi$
$224$		0			0
$225$	−8.24433	−	3.15798i	−0.549622	−	0.210532i
$226$		0			0
$227$	−5.48365	−	9.49796i	−0.363963	−	0.630402i	0.624646	−	0.780908i	$-0.285243\pi$
$227$	−5.48365	−	9.49796i	−0.363963	−	0.630402i	−0.988609	+	0.150506i	$0.951910\pi$
$228$		0			0
$229$	16.8349	+	9.71965i	1.11248	+	0.642293i	0.939471	−	0.342627i	$-0.111317\pi$
$229$	16.8349	+	9.71965i	1.11248	+	0.642293i	0.173012	+	0.984920i	$0.444650\pi$
$230$		0			0
$231$	14.7609	+	1.36781i	0.971198	+	0.0899954i
$232$		0			0
$233$		−	2.94031i		−	0.192626i	−0.995351	−	0.0963131i	$-0.969295\pi$
$233$		−	2.94031i		−	0.192626i	0.995351	−	0.0963131i	$-0.0307050\pi$
$234$		0			0
$235$	−6.05391			−0.394914
$236$		0			0
$237$	−4.11555	+	4.82216i	−0.267334	+	0.313233i
$238$		0			0
$239$	10.7255	+	6.19234i	0.693772	+	0.400549i	0.805023	−	0.593243i	$-0.202153\pi$
$239$	10.7255	+	6.19234i	0.693772	+	0.400549i	−0.111252	+	0.993792i	$0.535486\pi$
$240$		0			0
$241$	−11.6943	+	6.75168i	−0.753293	+	0.434914i	−0.826882	−	0.562375i	$-0.809888\pi$
$241$	−11.6943	+	6.75168i	−0.753293	+	0.434914i	0.0735896	+	0.997289i	$0.476555\pi$
$242$		0			0
$243$	15.4515	−	2.06217i	0.991211	−	0.132288i
$244$		0			0
$245$	−6.50325	−	7.64915i	−0.415478	−	0.488686i
$246$		0			0
$247$	−11.4903	+	19.9018i	−0.731109	+	1.26632i
$248$		0			0
$249$	12.2616	−	14.3668i	0.777045	−	0.910458i
$250$		0			0
$251$	7.51441			0.474305			0.237153	−	0.971472i	$-0.423786\pi$
$251$	7.51441			0.474305			0.237153	+	0.971472i	$0.423786\pi$
$252$		0			0
$253$	12.9669			0.815222
$254$		0			0
$255$	−2.66589	−	0.493113i	−0.166944	−	0.0308799i
$256$		0			0
$257$	−3.87788	+	6.71668i	−0.241895	+	0.418975i	−0.961254	−	0.275664i	$-0.911102\pi$
$257$	−3.87788	+	6.71668i	−0.241895	+	0.418975i	0.719359	+	0.694639i	$0.244436\pi$
$258$		0			0
$259$	0.517068	−	0.364555i	0.0321290	−	0.0226523i
$260$		0			0
$261$	−1.27455	+	3.32738i	−0.0788927	+	0.205960i
$262$		0			0
$263$	12.1127	−	6.99329i	0.746903	−	0.431224i	−0.0776710	−	0.996979i	$-0.524748\pi$
$263$	12.1127	−	6.99329i	0.746903	−	0.431224i	0.824574	+	0.565755i	$0.191415\pi$
$264$		0			0
$265$	8.71246	+	5.03014i	0.535202	+	0.308999i
$266$		0			0
$267$	−7.92395	−	22.3513i	−0.484938	−	1.36788i
$268$		0			0
$269$	25.8321			1.57501			0.787505	−	0.616308i	$-0.211372\pi$
$269$	25.8321			1.57501			0.787505	+	0.616308i	$0.211372\pi$
$270$		0			0
$271$		−	16.6537i		−	1.01164i	−0.862639	−	0.505821i	$-0.831190\pi$
$271$		−	16.6537i		−	1.01164i	0.862639	−	0.505821i	$-0.168810\pi$
$272$		0			0
$273$	9.80493	+	21.3117i	0.593422	+	1.28984i
$274$		0			0
$275$	−8.24433	−	4.75986i	−0.497152	−	0.287031i
$276$		0			0
$277$	−15.7044	−	27.2008i	−0.943585	−	1.63434i	−0.758560	−	0.651603i	$-0.774097\pi$
$277$	−15.7044	−	27.2008i	−0.943585	−	1.63434i	−0.185025	−	0.982734i	$-0.559237\pi$
$278$		0			0
$279$	11.0937	−	1.76515i	0.664160	−	0.105677i
$280$		0			0
$281$	8.10464	−	4.67922i	0.483483	−	0.279139i	−0.238384	−	0.971171i	$-0.576618\pi$
$281$	8.10464	−	4.67922i	0.483483	−	0.279139i	0.721867	+	0.692032i	$0.243284\pi$
$282$		0			0
$283$	−13.6603	−	7.88676i	−0.812018	−	0.468819i	0.0356380	−	0.999365i	$-0.488654\pi$
$283$	−13.6603	−	7.88676i	−0.812018	−	0.468819i	−0.847656	+	0.530546i	$0.821987\pi$
$284$		0			0
$285$	2.02841	−	10.9661i	0.120153	−	0.649575i
$286$		0			0
$287$	−1.77726	−	19.5838i	−0.104908	−	1.15599i
$288$		0			0
$289$	−15.8090			−0.929943
$290$		0			0
$291$	−4.10301	−	3.50178i	−0.240523	−	0.205278i
$292$		0			0
$293$	−12.4287	+	21.5271i	−0.726090	+	1.25762i	0.232434	+	0.972612i	$0.425331\pi$
$293$	−12.4287	+	21.5271i	−0.726090	+	1.25762i	−0.958524	+	0.285013i	$0.908002\pi$
$294$		0			0
$295$	6.79179	+	11.7637i	0.395433	+	0.684911i
$296$		0			0
$297$	16.8037	+	0.422088i	0.975051	+	0.0244920i
$298$		0			0
$299$	10.2600	+	17.7708i	0.593349	+	1.02771i
$300$		0			0
$301$	−18.3629	−	8.49050i	−1.05842	−	0.489384i
$302$		0			0
$303$	7.97141	−	9.34004i	0.457946	−	0.536571i
$304$		0			0
$305$		−	4.68294i		−	0.268144i
$306$		0			0
$307$			18.8878i			1.07799i	0.842310	+	0.538993i	$0.181195\pi$
$307$			18.8878i			1.07799i	−0.842310	+	0.538993i	$0.818805\pi$
$308$		0			0
$309$	−0.536670	+	2.90137i	−0.0305301	+	0.165053i
$310$		0			0
$311$	3.97716	−	6.88864i	0.225524	−	0.390619i	−0.730953	−	0.682428i	$-0.760924\pi$
$311$	3.97716	−	6.88864i	0.225524	−	0.390619i	0.956476	+	0.291809i	$0.0942573\pi$
$312$		0			0
$313$	−9.64210	+	5.56687i	−0.545004	+	0.314658i	−0.747104	−	0.664707i	$-0.768556\pi$
$313$	−9.64210	+	5.56687i	−0.545004	+	0.314658i	0.202101	+	0.979365i	$0.435223\pi$
$314$		0			0
$315$	−7.94047	−	8.15790i	−0.447395	−	0.459645i
$316$		0			0
$317$	−20.1380	+	11.6267i	−1.13107	+	0.653021i	−0.944203	−	0.329365i	$-0.893165\pi$
$317$	−20.1380	+	11.6267i	−1.13107	+	0.653021i	−0.186863	+	0.982386i	$0.559832\pi$
$318$		0			0
$319$	−1.92107	+	3.32738i	−0.107559	+	0.186298i
$320$		0			0
$321$	−8.05772	+	2.85661i	−0.449738	+	0.159441i
$322$		0			0
$323$			4.89904i			0.272590i
$324$		0			0
$325$		−	15.0648i		−	0.835646i
$326$		0			0
$327$	4.71013	+	13.2860i	0.260471	+	0.734716i
$328$		0			0
$329$	10.1363	+	4.68672i	0.558830	+	0.258387i
$330$		0			0
$331$	−9.57962	−	16.5924i	−0.526544	−	0.912000i	−0.999522	−	0.0309261i	$-0.990154\pi$
$331$	−9.57962	−	16.5924i	−0.526544	−	0.912000i	0.472978	−	0.881074i	$-0.343179\pi$
$332$		0			0
$333$	0.557180	−	0.451852i	0.0305333	−	0.0247613i
$334$		0			0
$335$	−0.473451	−	0.820041i	−0.0258674	−	0.0448036i
$336$		0			0
$337$	14.2781	−	24.7304i	0.777779	−	1.34715i	−0.155441	−	0.987845i	$-0.549680\pi$
$337$	14.2781	−	24.7304i	0.777779	−	1.34715i	0.933219	−	0.359307i	$-0.116987\pi$
$338$		0			0
$339$	1.23573	−	6.68065i	0.0671156	−	0.362843i
$340$		0			0
$341$	12.1128			0.655943
$342$		0			0
$343$	4.96690	+	17.8418i	0.268187	+	0.963367i
$344$		0			0
$345$	−7.57442	−	6.46451i	−0.407793	−	0.348038i
$346$		0			0
$347$	−2.56690	−	1.48200i	−0.137798	−	0.0795578i	0.429516	−	0.903059i	$-0.358684\pi$
$347$	−2.56690	−	1.48200i	−0.137798	−	0.0795578i	−0.567314	+	0.823501i	$0.692017\pi$
$348$		0			0
$349$	23.3885	−	13.5034i	1.25196	−	0.722818i	0.280460	−	0.959866i	$-0.409513\pi$
$349$	23.3885	−	13.5034i	1.25196	−	0.722818i	0.971498	+	0.237048i	$0.0761797\pi$
$350$		0			0
$351$	12.7174	+	23.3630i	0.678803	+	1.24703i
$352$		0			0
$353$	−14.8238	−	25.6755i	−0.788990	−	1.36657i	−0.926586	−	0.376083i	$-0.877271\pi$
$353$	−14.8238	−	25.6755i	−0.788990	−	1.36657i	0.137596	−	0.990488i	$-0.456063\pi$
$354$		0			0
$355$	−4.74924	−	2.74198i	−0.252064	−	0.145529i
$356$		0			0
$357$	4.08183	+	2.88947i	0.216033	+	0.152927i
$358$		0			0
$359$		−	24.6261i		−	1.29972i	−0.760056	−	0.649858i	$-0.774828\pi$
$359$		−	24.6261i		−	1.29972i	0.760056	−	0.649858i	$-0.225172\pi$
$360$		0			0
$361$	−1.15211			−0.0606373
$362$		0			0
$363$	−0.911917	−	0.168678i	−0.0478632	−	0.00885332i
$364$		0			0
$365$	9.08087	+	5.24284i	0.475314	+	0.274423i
$366$		0			0
$367$	−4.85598	+	2.80360i	−0.253480	+	0.146347i	−0.621357	−	0.783528i	$-0.713418\pi$
$367$	−4.85598	+	2.80360i	−0.253480	+	0.146347i	0.367877	+	0.929875i	$0.380085\pi$
$368$		0			0
$369$	−3.50371	−	22.0202i	−0.182396	−	1.14633i
$370$		0			0
$371$	−10.6934	−	15.1670i	−0.555173	−	0.787432i
$372$		0			0
$373$	1.86677	−	3.23333i	0.0966574	−	0.167416i	−0.813642	−	0.581367i	$-0.802518\pi$
$373$	1.86677	−	3.23333i	0.0966574	−	0.167416i	0.910299	+	0.413951i	$0.135852\pi$
$374$		0			0
$375$	6.59329	+	18.5979i	0.340476	+	0.960390i
$376$		0			0
$377$	−6.08012			−0.313142
$378$		0			0
$379$	30.4419			1.56369			0.781847	−	0.623470i	$-0.214278\pi$
$379$	30.4419			1.56369			0.781847	+	0.623470i	$0.214278\pi$
$380$		0			0
$381$	−3.56989	−	10.0697i	−0.182891	−	0.515886i
$382$		0			0
$383$	−8.49251	+	14.7095i	−0.433947	+	0.751618i	−0.997209	−	0.0746601i	$-0.976213\pi$
$383$	−8.49251	+	14.7095i	−0.433947	+	0.751618i	0.563262	+	0.826278i	$0.309546\pi$
$384$		0			0
$385$	−7.07356	−	10.0328i	−0.360502	−	0.511319i
$386$		0			0
$387$	−21.4218	−	8.20557i	−1.08893	−	0.417113i
$388$		0			0
$389$	9.43310	−	5.44621i	0.478277	−	0.276134i	−0.241421	−	0.970420i	$-0.577613\pi$
$389$	9.43310	−	5.44621i	0.478277	−	0.276134i	0.719698	+	0.694287i	$0.244280\pi$
$390$		0			0
$391$	3.78840	+	2.18724i	0.191588	+	0.110613i
$392$		0			0
$393$	14.0728	+	2.60306i	0.709878	+	0.131307i
$394$		0			0
$395$	5.24976			0.264144
$396$		0			0
$397$			22.3035i			1.11938i	0.828702	+	0.559690i	$0.189080\pi$
$397$			22.3035i			1.11938i	−0.828702	+	0.559690i	$0.810920\pi$
$398$		0			0
$399$	−11.8858	+	16.7905i	−0.595034	+	0.840578i
$400$		0			0
$401$	20.8554	+	12.0409i	1.04147	+	0.601293i	0.920249	−	0.391333i	$-0.127986\pi$
$401$	20.8554	+	12.0409i	1.04147	+	0.601293i	0.121221	+	0.992626i	$0.461319\pi$
$402$		0			0
$403$	9.58414	+	16.6002i	0.477420	+	0.826915i
$404$		0			0
$405$	−9.60522	−	8.62388i	−0.477287	−	0.428524i
$406$		0			0
$407$	0.669905	−	0.386770i	0.0332060	−	0.0191715i
$408$		0			0
$409$	−22.8191	−	13.1746i	−1.12833	−	0.651443i	−0.184817	−	0.982773i	$-0.559169\pi$
$409$	−22.8191	−	13.1746i	−1.12833	−	0.651443i	−0.943515	+	0.331330i	$0.892503\pi$
$410$		0			0
$411$	−13.6332	−	11.6355i	−0.672476	−	0.573935i
$412$		0			0
$413$	−2.26464	−	24.9543i	−0.111436	−	1.22792i
$414$		0			0
$415$	−15.6408			−0.767775
$416$		0			0
$417$	−5.62352	+	30.4021i	−0.275385	+	1.48880i
$418$		0			0
$419$	−16.1761	+	28.0178i	−0.790252	+	1.36876i	0.135558	+	0.990769i	$0.456717\pi$
$419$	−16.1761	+	28.0178i	−0.790252	+	1.36876i	−0.925811	+	0.377988i	$0.876616\pi$
$420$		0			0
$421$	−5.54746	−	9.60849i	−0.270367	−	0.468289i	0.698589	−	0.715523i	$-0.253812\pi$
$421$	−5.54746	−	9.60849i	−0.270367	−	0.468289i	−0.968956	+	0.247234i	$0.920478\pi$
$422$		0			0
$423$	11.8247	+	4.52945i	0.574938	+	0.220229i
$424$		0			0
$425$	−1.60577	−	2.78128i	−0.0778914	−	0.134912i
$426$		0			0
$427$	−3.62537	+	7.84079i	−0.175444	+	0.379443i
$428$		0			0
$429$	9.58414	+	27.0342i	0.462726	+	1.30522i
$430$		0			0
$431$		−	16.3047i		−	0.785368i	−0.919673	−	0.392684i	$-0.871547\pi$
$431$		−	16.3047i		−	0.785368i	0.919673	−	0.392684i	$-0.128453\pi$
$432$		0			0
$433$			12.5359i			0.602438i	0.953555	+	0.301219i	$0.0973936\pi$
$433$			12.5359i			0.602438i	−0.953555	+	0.301219i	$0.902606\pi$
$434$		0			0
$435$	2.78100	−	0.985915i	0.133339	−	0.0472710i
$436$		0			0
$437$	−8.99716	+	15.5835i	−0.430393	+	0.745462i
$438$		0			0
$439$	−16.1276	+	9.31127i	−0.769728	+	0.444403i	−0.832778	−	0.553608i	$-0.813251\pi$
$439$	−16.1276	+	9.31127i	−0.769728	+	0.444403i	0.0630496	+	0.998010i	$0.479917\pi$
$440$		0			0
$441$	6.97942	+	19.8063i	0.332354	+	0.943155i
$442$		0			0
$443$	−4.11436	+	2.37543i	−0.195479	+	0.112860i	−0.594545	−	0.804062i	$-0.702668\pi$
$443$	−4.11436	+	2.37543i	−0.195479	+	0.112860i	0.399066	+	0.916922i	$0.369334\pi$
$444$		0			0
$445$	−9.81875	+	17.0066i	−0.465453	+	0.806189i
$446$		0			0
$447$	5.52053	−	29.8453i	0.261112	−	1.41163i
$448$		0			0
$449$			16.2393i			0.766379i	0.923670	+	0.383189i	$0.125174\pi$
$449$			16.2393i			0.766379i	−0.923670	+	0.383189i	$0.874826\pi$
$450$		0			0
$451$		−	24.0431i		−	1.13214i
$452$		0			0
$453$	−1.23762	+	1.45011i	−0.0581485	+	0.0681322i
$454$		0			0
$455$	8.15279	−	17.6325i	0.382209	−	0.826625i
$456$		0			0
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	0.925376	−	0.379050i	$-0.123749\pi$
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	−0.790955	+	0.611874i	$0.790416\pi$
$458$		0			0
$459$	4.83818	+	2.95774i	0.225827	+	0.138056i
$460$		0			0
$461$	−18.1346	−	31.4101i	−0.844613	−	1.46291i	−0.885957	−	0.463768i	$-0.846497\pi$
$461$	−18.1346	−	31.4101i	−0.844613	−	1.46291i	0.0413440	−	0.999145i	$-0.486836\pi$
$462$		0			0
$463$	−14.6202	+	25.3230i	−0.679461	+	1.17686i	0.295683	+	0.955286i	$0.404453\pi$
$463$	−14.6202	+	25.3230i	−0.679461	+	1.17686i	−0.975144	+	0.221574i	$0.928881\pi$
$464$		0			0
$465$	−7.07549	−	6.03869i	−0.328118	−	0.280038i
$466$		0			0
$467$	2.64215			0.122264			0.0611320	−	0.998130i	$-0.480529\pi$
$467$	2.64215			0.122264			0.0611320	+	0.998130i	$0.480529\pi$
$468$		0			0
$469$	0.157867	+	1.73955i	0.00728961	+	0.0803249i
$470$		0			0
$471$	−3.07442	+	16.6211i	−0.141662	+	0.765858i
$472$		0			0
$473$	−21.4218	−	12.3679i	−0.984973	−	0.568675i
$474$		0			0
$475$	11.4408	−	6.60532i	0.524938	−	0.303073i
$476$		0			0
$477$	−13.2540	−	16.3436i	−0.606861	−	0.748322i
$478$		0			0
$479$	−15.5409	−	26.9177i	−0.710083	−	1.22990i	−0.964826	−	0.262891i	$-0.915324\pi$
$479$	−15.5409	−	26.9177i	−0.710083	−	1.22990i	0.254742	−	0.967009i	$-0.418009\pi$
$480$		0			0
$481$	1.06012	+	0.612058i	0.0483371	+	0.0279074i
$482$		0			0
$483$	7.67749	+	16.6876i	0.349338	+	0.759311i
$484$		0			0
$485$			4.46684i			0.202829i
$486$		0			0
$487$	−34.8720			−1.58020			−0.790100	−	0.612978i	$-0.789971\pi$
$487$	−34.8720			−1.58020			−0.790100	+	0.612978i	$0.789971\pi$
$488$		0			0
$489$	4.18174	+	11.7955i	0.189105	+	0.533412i
$490$		0			0
$491$	22.6758	+	13.0919i	1.02334	+	0.590828i	0.915071	−	0.403293i	$-0.132134\pi$
$491$	22.6758	+	13.0919i	1.02334	+	0.590828i	0.108273	+	0.994121i	$0.465468\pi$
$492$		0			0
$493$	−1.12252	+	0.648085i	−0.0505556	+	0.0291883i
$494$		0			0
$495$	−8.76740	−	10.8111i	−0.394065	−	0.485924i
$496$		0			0
$497$	5.82906	+	8.26767i	0.261469	+	0.370856i
$498$		0			0
$499$	6.23912	−	10.8065i	0.279302	−	0.483764i	−0.691910	−	0.721984i	$-0.743230\pi$
$499$	6.23912	−	10.8065i	0.279302	−	0.483764i	0.971211	+	0.238220i	$0.0765638\pi$
$500$		0			0
$501$	−29.4789	−	5.45276i	−1.31702	−	0.243611i
$502$		0			0
$503$	−37.8479			−1.68756			−0.843778	−	0.536693i	$-0.819673\pi$
$503$	−37.8479			−1.68756			−0.843778	+	0.536693i	$0.819673\pi$
$504$		0			0
$505$	−10.1683			−0.452482
$506$		0			0
$507$	−14.8490	+	17.3984i	−0.659466	+	0.772691i
$508$		0			0
$509$	−17.6924	+	30.6441i	−0.784200	+	1.35827i	0.145276	+	0.989391i	$0.453593\pi$
$509$	−17.6924	+	30.6441i	−0.784200	+	1.35827i	−0.929476	+	0.368883i	$0.879740\pi$
$510$		0			0
$511$	−11.1456	−	15.8083i	−0.493050	−	0.699320i
$512$		0			0
$513$	−12.1666	+	19.9018i	−0.537170	+	0.878684i
$514$		0			0
$515$	2.11599	−	1.22167i	0.0932419	−	0.0538332i
$516$		0			0
$517$	11.8247	+	6.82701i	0.520051	+	0.300252i
$518$		0			0
$519$	2.19957	−	2.57723i	0.0965506	−	0.113128i
$520$		0			0
$521$	2.31879			0.101588			0.0507940	−	0.998709i	$-0.483825\pi$
$521$	2.31879			0.101588			0.0507940	+	0.998709i	$0.483825\pi$
$522$		0			0
$523$			20.1840i			0.882585i	0.897363	+	0.441293i	$0.145480\pi$
$523$			20.1840i			0.882585i	−0.897363	+	0.441293i	$0.854520\pi$
$524$		0			0
$525$	1.24431	−	13.4282i	0.0543062	−	0.586053i
$526$		0			0
$527$	3.53886	+	2.04316i	0.154155	+	0.0890015i
$528$		0			0
$529$	−3.46621	−	6.00365i	−0.150705	−	0.261028i
$530$		0			0
$531$	−4.46454	−	28.0589i	−0.193745	−	1.21765i
$532$		0			0
$533$	32.9503	−	19.0239i	1.42724	−	0.824016i
$534$		0			0
$535$	6.13093	+	3.53970i	0.265063	+	0.153034i
$536$		0			0
$537$	−37.8768	+	13.4280i	−1.63450	+	0.579462i
$538$		0			0
$539$	4.07644	+	22.2744i	0.175585	+	0.959424i
$540$		0			0
$541$	−22.7713			−0.979014			−0.489507	−	0.871999i	$-0.662823\pi$
$541$	−22.7713			−0.979014			−0.489507	+	0.871999i	$0.662823\pi$
$542$		0			0
$543$	16.7729	−	5.94631i	0.719795	−	0.255181i
$544$		0			0
$545$	5.83643	−	10.1090i	0.250005	−	0.433022i
$546$		0			0
$547$	−14.7918	−	25.6201i	−0.632451	−	1.09544i	−0.987049	−	0.160419i	$-0.948716\pi$
$547$	−14.7918	−	25.6201i	−0.632451	−	1.09544i	0.354598	−	0.935019i	$-0.384618\pi$
$548$		0			0
$549$	−3.50371	+	9.14690i	−0.149535	+	0.390380i
$550$		0			0
$551$	−2.66589	−	4.61745i	−0.113571	−	0.196710i
$552$		0			0
$553$	−8.78984	−	4.06418i	−0.373782	−	0.172827i
$554$		0			0
$555$	−0.584135	−	0.108048i	−0.0247952	−	0.00458639i
$556$		0			0
$557$		−	4.71407i		−	0.199741i	−0.995000	−	0.0998707i	$-0.968157\pi$
$557$		−	4.71407i		−	0.199741i	0.995000	−	0.0998707i	$-0.0318429\pi$
$558$		0			0
$559$		−	39.1439i		−	1.65561i
$560$		0			0
$561$	4.65103	+	3.96950i	0.196367	+	0.167592i
$562$		0			0
$563$	13.6742	−	23.6844i	0.576299	−	0.998179i	−0.419601	−	0.907709i	$-0.637830\pi$
$563$	13.6742	−	23.6844i	0.576299	−	0.998179i	0.995899	−	0.0904697i	$-0.0288368\pi$
$564$		0			0
$565$	−4.87226	+	2.81300i	−0.204977	+	0.118344i
$566$		0			0
$567$	9.40602	+	21.8753i	0.395016	+	0.918674i
$568$		0			0
$569$	20.4018	−	11.7790i	0.855288	−	0.493801i	−0.00714355	−	0.999974i	$-0.502274\pi$
$569$	20.4018	−	11.7790i	0.855288	−	0.493801i	0.862432	+	0.506174i	$0.168941\pi$
$570$		0			0
$571$	9.59385	−	16.6170i	0.401490	−	0.695401i	−0.592416	−	0.805632i	$-0.701826\pi$
$571$	9.59385	−	16.6170i	0.401490	−	0.695401i	0.993906	+	0.110231i	$0.0351591\pi$
$572$		0			0
$573$	−29.9323	−	25.5462i	−1.25044	−	1.06721i
$574$		0			0
$575$		−	11.7961i		−	0.491932i
$576$		0			0
$577$		−	2.23413i		−	0.0930079i	−0.998918	−	0.0465039i	$-0.985192\pi$
$577$		−	2.23413i		−	0.0930079i	0.998918	−	0.0465039i	$-0.0148080\pi$
$578$		0			0
$579$	−28.7357	−	5.31527i	−1.19421	−	0.220895i
$580$		0			0
$581$	26.1878	+	12.1085i	1.08645	+	0.502346i
$582$		0			0
$583$	−11.3450	−	19.6501i	−0.469862	−	0.813826i
$584$		0			0
$585$	7.87919	−	20.5697i	0.325765	−	0.850453i
$586$		0			0
$587$	12.9883	+	22.4963i	0.536083	+	0.928522i	0.999110	+	0.0421784i	$0.0134298\pi$
$587$	12.9883	+	22.4963i	0.536083	+	0.928522i	−0.463028	+	0.886344i	$0.653237\pi$
$588$		0			0
$589$	−8.40451	+	14.5570i	−0.346302	+	0.599813i
$590$		0			0
$591$	−14.6015	+	5.17650i	−0.600625	+	0.212933i
$592$		0			0
$593$	5.71754			0.234791			0.117396	−	0.993085i	$-0.462545\pi$
$593$	5.71754			0.234791			0.117396	+	0.993085i	$0.462545\pi$
$594$		0			0
$595$	−0.374290	−	4.12434i	−0.0153444	−	0.169081i
$596$		0			0
$597$	−9.44445	+	3.34824i	−0.386536	+	0.137034i
$598$		0			0
$599$	−21.8662	−	12.6245i	−0.893429	−	0.515822i	−0.0183665	−	0.999831i	$-0.505847\pi$
$599$	−21.8662	−	12.6245i	−0.893429	−	0.515822i	−0.875063	+	0.484010i	$0.839180\pi$
$600$		0			0
$601$	40.2546	−	23.2410i	1.64202	−	0.948021i	0.661907	−	0.749586i	$-0.269748\pi$
$601$	40.2546	−	23.2410i	1.64202	−	0.948021i	0.980114	−	0.198435i	$-0.0635858\pi$
$602$		0			0
$603$	0.311220	+	1.95596i	0.0126739	+	0.0796530i
$604$		0			0
$605$	0.383978	+	0.665069i	0.0156109	+	0.0270389i
$606$		0			0
$607$	6.09405	+	3.51840i	0.247350	+	0.142808i	0.618550	−	0.785745i	$-0.287720\pi$
$607$	6.09405	+	3.51840i	0.247350	+	0.142808i	−0.371200	+	0.928553i	$0.621054\pi$
$608$		0			0
$609$	−5.41957	−	0.502201i	−0.219612	−	0.0203502i
$610$		0			0
$611$			21.6073i			0.874138i
$612$		0			0
$613$	6.54256			0.264252			0.132126	−	0.991233i	$-0.457820\pi$
$613$	6.54256			0.264252			0.132126	+	0.991233i	$0.457820\pi$
$614$		0			0
$615$	−11.9864	+	14.0444i	−0.483339	+	0.566324i
$616$		0			0
$617$	−30.0043	−	17.3230i	−1.20793	−	0.697396i	−0.245620	−	0.969366i	$-0.578992\pi$
$617$	−30.0043	−	17.3230i	−1.20793	−	0.697396i	−0.962306	+	0.271970i	$0.912325\pi$
$618$		0			0
$619$	−14.7072	+	8.49123i	−0.591134	+	0.341291i	−0.765546	−	0.643381i	$-0.777531\pi$
$619$	−14.7072	+	8.49123i	−0.591134	+	0.341291i	0.174412	+	0.984673i	$0.444198\pi$
$620$		0			0
$621$	9.95800	+	18.2938i	0.399601	+	0.734105i
$622$		0			0
$623$	29.6057	−	20.8733i	1.18613	−	0.836271i
$624$		0			0
$625$	0.812855	−	1.40791i	0.0325142	−	0.0563162i
$626$		0			0
$627$	−16.3285	+	19.1319i	−0.652096	+	0.764056i
$628$		0			0
$629$	0.260959			0.0104051
$630$		0			0
$631$	−26.2438			−1.04475			−0.522374	−	0.852716i	$-0.674953\pi$
$631$	−26.2438			−1.04475			−0.522374	+	0.852716i	$0.674953\pi$
$632$		0			0
$633$	44.0953	+	8.15637i	1.75263	+	0.324186i
$634$		0			0
$635$	−4.42354	+	7.66179i	−0.175543	+	0.304049i
$636$		0			0
$637$	−27.3009	+	23.2111i	−1.08170	+	0.919656i
$638$		0			0
$639$	7.22489	+	8.90904i	0.285812	+	0.352436i
$640$		0			0
$641$	16.5092	−	9.53157i	0.652073	−	0.376474i	−0.137177	−	0.990547i	$-0.543803\pi$
$641$	16.5092	−	9.53157i	0.652073	−	0.376474i	0.789250	+	0.614072i	$0.210470\pi$
$642$		0			0
$643$	−15.3447	−	8.85928i	−0.605136	−	0.349376i	0.165923	−	0.986139i	$-0.446940\pi$
$643$	−15.3447	−	8.85928i	−0.605136	−	0.349376i	−0.771060	+	0.636763i	$0.780273\pi$
$644$		0			0
$645$	6.34733	+	17.9041i	0.249926	+	0.704973i
$646$		0			0
$647$	21.7902			0.856661			0.428330	−	0.903622i	$-0.359102\pi$
$647$	21.7902			0.856661			0.428330	+	0.903622i	$0.359102\pi$
$648$		0			0
$649$		−	30.6365i		−	1.20259i
$650$		0			0
$651$	7.17177	+	15.5884i	0.281084	+	0.610956i
$652$		0			0
$653$	−13.0852	−	7.55475i	−0.512064	−	0.295640i	0.221618	−	0.975134i	$-0.428866\pi$
$653$	−13.0852	−	7.55475i	−0.512064	−	0.295640i	−0.733682	+	0.679493i	$0.762200\pi$
$654$		0			0
$655$	−5.92558	−	10.2634i	−0.231532	−	0.401024i
$656$		0			0
$657$	−13.8145	−	17.0347i	−0.538954	−	0.664586i
$658$		0			0
$659$	27.1850	−	15.6952i	1.05898	−	0.611400i	0.133827	−	0.991005i	$-0.457273\pi$
$659$	27.1850	−	15.6952i	1.05898	−	0.611400i	0.925149	+	0.379605i	$0.123940\pi$
$660$		0			0
$661$	−37.8554	−	21.8558i	−1.47240	−	0.850093i	−0.472885	−	0.881124i	$-0.656787\pi$
$661$	−37.8554	−	21.8558i	−1.47240	−	0.850093i	−0.999518	+	0.0310314i	$0.990121\pi$
$662$		0			0
$663$	−1.75999	+	9.51495i	−0.0683524	+	0.369530i
$664$		0			0
$665$	16.9654	−	1.53964i	0.657890	−	0.0597046i
$666$		0			0
$667$	−4.76088			−0.184342
$668$		0			0
$669$	23.5534	+	20.1020i	0.910625	+	0.777188i
$670$		0			0
$671$	−5.28096	+	9.14690i	−0.203869	+	0.353112i
$672$		0			0
$673$	−4.60589	−	7.97763i	−0.177544	−	0.307515i	0.763495	−	0.645814i	$-0.223482\pi$
$673$	−4.60589	−	7.97763i	−0.177544	−	0.307515i	−0.941039	+	0.338299i	$0.890149\pi$
$674$		0			0
$675$	0.383978	−	15.2865i	0.0147793	−	0.588378i
$676$		0			0
$677$	−11.4194	−	19.7789i	−0.438882	−	0.760165i	0.558722	−	0.829355i	$-0.311292\pi$
$677$	−11.4194	−	19.7789i	−0.438882	−	0.760165i	−0.997604	+	0.0691899i	$0.977959\pi$
$678$		0			0
$679$	3.45807	−	7.47898i	0.132709	−	0.287017i
$680$		0			0
$681$	12.3317	−	14.4490i	0.472553	−	0.553687i
$682$		0			0
$683$			34.1826i			1.30796i	0.756511	+	0.653981i	$0.226902\pi$
$683$			34.1826i			1.30796i	−0.756511	+	0.653981i	$0.773098\pi$
$684$		0			0
$685$			14.8421i			0.567088i
$686$		0			0
$687$	−6.12408	+	33.1082i	−0.233648	+	1.26316i
$688$		0			0
$689$	17.9533	−	31.0961i	0.683967	−	1.18467i
$690$		0			0
$691$	0.224082	−	0.129374i	0.00852446	−	0.00492160i	−0.495732	−	0.868476i	$-0.665100\pi$
$691$	0.224082	−	0.129374i	0.00852446	−	0.00492160i	0.504256	+	0.863554i	$0.331767\pi$
$692$		0			0
$693$	6.30995	+	24.8888i	0.239695	+	0.945448i
$694$		0			0
$695$	22.1725	−	12.8013i	0.841052	−	0.485582i
$696$		0			0
$697$	4.05555	−	7.02441i	0.153615	−	0.266069i
$698$		0			0
$699$	4.80005	−	1.70171i	0.181555	−	0.0643645i
$700$		0			0
$701$		−	5.16189i		−	0.194962i	−0.995237	−	0.0974810i	$-0.968921\pi$
$701$		−	5.16189i		−	0.194962i	0.995237	−	0.0974810i	$-0.0310785\pi$
$702$		0			0
$703$			1.07345i			0.0404860i
$704$		0			0
$705$	−3.50371	−	9.88299i	−0.131957	−	0.372215i
$706$		0			0
$707$	17.0251	+	7.87192i	0.640293	+	0.296054i
$708$		0			0
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	0.556602	−	0.830780i	$-0.312105\pi$
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	−0.997777	+	0.0666412i	$0.978772\pi$
$710$		0			0
$711$	−10.2540	−	3.92779i	−0.384557	−	0.147304i
$712$		0			0
$713$	7.50460	+	12.9984i	0.281050	+	0.486792i
$714$		0			0
$715$	11.8759	−	20.5697i	0.444134	−	0.769263i
$716$		0			0
$717$	−3.90162	+	21.0931i	−0.145709	+	0.787736i
$718$		0			0
$719$	10.1566			0.378776			0.189388	−	0.981902i	$-0.439350\pi$
$719$	10.1566			0.378776			0.189388	+	0.981902i	$0.439350\pi$
$720$		0			0
$721$	−4.48865	+	0.407352i	−0.167166	+	0.0151706i
$722$		0			0
$723$	−17.7902	−	15.1833i	−0.661623	−	0.564673i
$724$		0			0
$725$	3.02696	+	1.74761i	0.112418	+	0.0649047i
$726$		0			0
$727$	5.74874	−	3.31904i	0.213209	−	0.123096i	−0.389593	−	0.920987i	$-0.627384\pi$
$727$	5.74874	−	3.31904i	0.213209	−	0.123096i	0.602802	+	0.797891i	$0.294051\pi$
$728$		0			0
$729$	12.3090	+	24.0310i	0.455890	+	0.890036i
$730$		0			0
$731$	−4.17238	−	7.22678i	−0.154321	−	0.267292i
$732$		0			0
$733$	5.20130	+	3.00297i	0.192114	+	0.110917i	0.592972	−	0.805223i	$-0.297954\pi$
$733$	5.20130	+	3.00297i	0.192114	+	0.110917i	−0.400858	+	0.916140i	$0.631288\pi$
$734$		0			0
$735$	8.72346	−	15.0435i	0.321770	−	0.554888i
$736$		0			0
$737$			2.13565i			0.0786676i
$738$		0			0
$739$	15.6386			0.575275			0.287638	−	0.957739i	$-0.407130\pi$
$739$	15.6386			0.575275			0.287638	+	0.957739i	$0.407130\pi$
$740$		0			0
$741$	−39.1396	−	7.23970i	−1.43783	−	0.265957i
$742$		0			0
$743$	−27.3807	−	15.8083i	−1.00450	−	0.579949i	−0.0949246	−	0.995484i	$-0.530261\pi$
$743$	−27.3807	−	15.8083i	−1.00450	−	0.579949i	−0.909577	+	0.415535i	$0.863594\pi$
$744$		0			0
$745$	−21.7664	+	12.5669i	−0.797461	+	0.460414i
$746$		0			0
$747$	30.5501	+	11.7022i	1.11777	+	0.428160i
$748$		0			0
$749$	−7.52490	−	10.6730i	−0.274954	−	0.389982i
$750$		0			0
$751$	−7.13680	+	12.3613i	−0.260426	+	0.451070i	−0.966355	−	0.257212i	$-0.917196\pi$
$751$	−7.13680	+	12.3613i	−0.260426	+	0.451070i	0.705929	+	0.708282i	$0.250530\pi$
$752$		0			0
$753$	4.34897	+	12.2673i	0.158485	+	0.447043i
$754$		0			0
$755$	1.57870			0.0574548
$756$		0			0
$757$	−10.8227			−0.393358			−0.196679	−	0.980468i	$-0.563016\pi$
$757$	−10.8227			−0.393358			−0.196679	+	0.980468i	$0.563016\pi$
$758$		0			0
$759$	7.50460	+	21.1684i	0.272400	+	0.768365i
$760$		0			0
$761$	2.93098	−	5.07660i	0.106248	−	0.184027i	−0.808000	−	0.589183i	$-0.799450\pi$
$761$	2.93098	−	5.07660i	0.106248	−	0.184027i	0.914247	+	0.405157i	$0.132783\pi$
$762$		0			0
$763$	−17.5981	+	12.4074i	−0.637095	+	0.449180i
$764$		0			0
$765$	−0.737879	−	4.63744i	−0.0266781	−	0.167667i
$766$		0			0
$767$	41.9865	−	24.2409i	1.51604	−	0.875288i
$768$		0			0
$769$	27.5683	+	15.9166i	0.994140	+	0.573967i	0.906509	−	0.422186i	$-0.138737\pi$
$769$	27.5683	+	15.9166i	0.994140	+	0.573967i	0.0876307	+	0.996153i	$0.472070\pi$
$770$		0			0
$771$	−13.2093	−	2.44334i	−0.475721	−	0.0879947i
$772$		0			0
$773$	19.0382			0.684755			0.342378	−	0.939562i	$-0.388768\pi$
$773$	19.0382			0.684755			0.342378	+	0.939562i	$0.388768\pi$
$774$		0			0
$775$		−	11.0191i		−	0.395818i
$776$		0			0
$777$	0.894389	+	0.633125i	0.0320860	+	0.0227132i
$778$		0			0
$779$	28.8948	+	16.6824i	1.03526	+	0.597710i
$780$		0			0
$781$	6.18427	+	10.7115i	0.221290	+	0.383286i
$782$		0			0
$783$	−6.16959	−	0.154972i	−0.220483	−	0.00553826i
$784$		0			0
$785$	12.1219	−	6.99857i	0.432649	−	0.249790i
$786$		0			0
$787$	16.4123	+	9.47564i	0.585035	+	0.337770i	0.763132	−	0.646243i	$-0.223661\pi$
$787$	16.4123	+	9.47564i	0.585035	+	0.337770i	−0.178097	+	0.984013i	$0.556994\pi$
$788$		0			0
$789$	18.4268	+	15.7266i	0.656010	+	0.559883i
$790$		0			0
$791$	10.3355	−	0.937963i	0.367488	−	0.0333501i
$792$		0			0
$793$	−16.7141			−0.593535
$794$		0			0
$795$	−3.16935	+	17.1343i	−0.112405	+	0.607690i
$796$		0			0
$797$	−26.7207	+	46.2816i	−0.946497	+	1.63938i	−0.193770	+	0.981047i	$0.562071\pi$
$797$	−26.7207	+	46.2816i	−0.946497	+	1.63938i	−0.752727	+	0.658333i	$0.771262\pi$
$798$		0			0
$799$	2.30314	+	3.98916i	0.0814792	+	0.141126i
$800$		0			0
$801$	31.9024	−	25.8716i	1.12722	−	0.914129i
$802$		0			0
$803$	−11.8247	−	20.4810i	−0.417286	−	0.722760i
$804$		0			0
$805$	6.38383	−	13.8067i	0.225000	−	0.486621i
$806$		0			0
$807$	14.9503	+	42.1708i	0.526277	+	1.48448i
$808$		0			0
$809$			2.58095i			0.0907413i	0.998970	+	0.0453706i	$0.0144469\pi$
$809$			2.58095i			0.0907413i	−0.998970	+	0.0453706i	$0.985553\pi$
$810$		0			0
$811$			6.06938i			0.213125i	0.994306	+	0.106562i	$0.0339844\pi$
$811$			6.06938i			0.213125i	−0.994306	+	0.106562i	$0.966016\pi$
$812$		0			0
$813$	27.1871	−	9.63835i	0.953495	−	0.338032i
$814$		0			0
$815$	5.18169	−	8.97494i	0.181507	−	0.314379i
$816$		0			0
$817$	29.7272	−	17.1630i	1.04002	−	0.600458i
$818$		0			0
$819$	−29.1167	+	28.3407i	−1.01742	+	0.990304i
$820$		0			0
$821$	8.03938	−	4.64154i	0.280576	−	0.161991i	−0.353108	−	0.935583i	$-0.614875\pi$
$821$	8.03938	−	4.64154i	0.280576	−	0.161991i	0.633684	+	0.773592i	$0.281542\pi$
$822$		0			0
$823$	9.03448	−	15.6482i	0.314922	−	0.545461i	−0.664499	−	0.747289i	$-0.731355\pi$
$823$	9.03448	−	15.6482i	0.314922	−	0.545461i	0.979421	+	0.201828i	$0.0646882\pi$
$824$		0			0
$825$	2.99905	−	16.2136i	0.104414	−	0.564486i
$826$		0			0
$827$		−	48.5440i		−	1.68804i	−0.536310	−	0.844021i	$-0.680182\pi$
$827$		−	48.5440i		−	1.68804i	0.536310	−	0.844021i	$-0.319818\pi$
$828$		0			0
$829$			5.44792i			0.189214i	0.995515	+	0.0946071i	$0.0301595\pi$
$829$			5.44792i			0.189214i	−0.995515	+	0.0946071i	$0.969841\pi$
$830$		0			0
$831$	35.3163	−	41.3798i	1.22511	−	1.43545i
$832$		0			0
$833$	−2.56623	+	7.19527i	−0.0889147	+	0.249302i
$834$		0			0
$835$	12.4126	+	21.4992i	0.429556	+	0.744012i
$836$		0			0
$837$	9.30206	+	17.0888i	0.321526	+	0.590675i
$838$		0			0
$839$	24.2673	+	42.0322i	0.837801	+	1.45111i	0.891729	+	0.452569i	$0.149492\pi$
$839$	24.2673	+	42.0322i	0.837801	+	1.45111i	−0.0539281	+	0.998545i	$0.517174\pi$
$840$		0			0
$841$	−13.7947	+	23.8931i	−0.475678	+	0.823899i
$842$		0			0
$843$	12.3294	+	10.5227i	0.424646	+	0.362421i
$844$		0			0
$845$	18.9412			0.651598
$846$		0			0
$847$	−0.128033	−	1.41081i	−0.00439926	−	0.0484759i
$848$		0			0
$849$	4.96922	−	26.8648i	0.170543	−	0.921998i
$850$		0			0
$851$	0.830095	+	0.479256i	0.0284553	+	0.0164287i
$852$		0			0
$853$	−10.7703	+	6.21823i	−0.368768	+	0.212908i	−0.672920	−	0.739715i	$-0.734960\pi$
$853$	−10.7703	+	6.21823i	−0.368768	+	0.212908i	0.304152	+	0.952623i	$0.401627\pi$
$854$		0			0
$855$	19.0761	−	3.03526i	0.652387	−	0.103804i
$856$		0			0
$857$	5.29077	+	9.16388i	0.180729	+	0.313032i	0.942129	−	0.335250i	$-0.108821\pi$
$857$	5.29077	+	9.16388i	0.180729	+	0.313032i	−0.761400	+	0.648283i	$0.775488\pi$
$858$		0			0
$859$	28.1452	+	16.2496i	0.960302	+	0.554431i	0.896266	−	0.443517i	$-0.146269\pi$
$859$	28.1452	+	16.2496i	0.960302	+	0.554431i	0.0640360	+	0.997948i	$0.479603\pi$
$860$		0			0
$861$	30.9419	−	14.2355i	1.05450	−	0.485145i
$862$		0			0
$863$		−	25.2203i		−	0.858510i	−0.903183	−	0.429255i	$-0.858776\pi$
$863$		−	25.2203i		−	0.858510i	0.903183	−	0.429255i	$-0.141224\pi$
$864$		0			0
$865$	−2.80576			−0.0953987
$866$		0			0
$867$	−9.14949	−	25.8082i	−0.310733	−	0.876492i
$868$		0			0
$869$	−10.2540	−	5.92017i	−0.347844	−	0.200828i
$870$		0			0
$871$	−2.92685	+	1.68982i	−0.0991724	+	0.0572572i
$872$		0			0
$873$	3.34203	−	8.72481i	0.113110	−	0.295290i
$874$		0			0
$875$	−24.6341	+	17.3681i	−0.832784	+	0.587149i
$876$		0			0
$877$	7.47893	−	12.9539i	0.252546	−	0.437422i	−0.711680	−	0.702503i	$-0.752066\pi$
$877$	7.47893	−	12.9539i	0.252546	−	0.437422i	0.964226	+	0.265082i	$0.0853989\pi$
$878$		0			0
$879$	−42.3360	−	7.83094i	−1.42796	−	0.264131i
$880$		0			0
$881$	−36.4482			−1.22797			−0.613985	−	0.789318i	$-0.710434\pi$
$881$	−36.4482			−1.22797			−0.613985	+	0.789318i	$0.710434\pi$
$882$		0			0
$883$	−15.9831			−0.537873			−0.268936	−	0.963158i	$-0.586672\pi$
$883$	−15.9831			−0.537873			−0.268936	+	0.963158i	$0.586672\pi$
$884$		0			0
$885$	−15.2735	+	17.8958i	−0.513413	+	0.601562i
$886$		0			0
$887$	−24.5208	+	42.4713i	−0.823329	+	1.42605i	0.0798613	+	0.996806i	$0.474552\pi$
$887$	−24.5208	+	42.4713i	−0.823329	+	1.42605i	−0.903190	+	0.429241i	$0.858781\pi$
$888$		0			0
$889$	13.3380	−	9.40383i	0.447341	−	0.315394i
$890$		0			0
$891$	9.03611	+	27.6763i	0.302721	+	0.927192i
$892$		0			0
$893$	−16.4093	+	9.47393i	−0.549117	+	0.317033i
$894$		0			0
$895$	28.8196	+	16.6390i	0.963332	+	0.556180i
$896$		0			0
$897$	−23.0728	+	27.0342i	−0.770378	+	0.902646i
$898$		0			0
$899$	−4.44728			−0.148325
$900$		0			0
$901$		−	7.65464i		−	0.255013i
$902$		0			0
$903$	3.23318	−	34.8913i	0.107593	−	1.16111i
$904$		0			0
$905$	−12.7621	−	7.36821i	−0.424227	−	0.244928i
$906$		0			0
$907$	−2.42915	−	4.20741i	−0.0806585	−	0.139705i	0.822874	−	0.568223i	$-0.192369\pi$
$907$	−2.42915	−	4.20741i	−0.0806585	−	0.139705i	−0.903533	+	0.428519i	$0.859036\pi$
$908$		0			0
$909$	19.8611	+	7.60775i	0.658750	+	0.252333i
$910$		0			0
$911$	−14.4945	+	8.36843i	−0.480226	+	0.277258i	−0.720510	−	0.693444i	$-0.756092\pi$
$911$	−14.4945	+	8.36843i	−0.480226	+	0.277258i	0.240285	+	0.970702i	$0.422759\pi$
$912$		0			0
$913$	30.5501	+	17.6381i	1.01106	+	0.583737i
$914$		0			0
$915$	7.64489	−	2.71026i	0.252732	−	0.0895983i
$916$		0			0
$917$	1.97582	+	21.7717i	0.0652472	+	0.718965i
$918$		0			0
$919$	−30.6400			−1.01072			−0.505360	−	0.862909i	$-0.668640\pi$
$919$	−30.6400			−1.01072			−0.505360	+	0.862909i	$0.668640\pi$
$920$		0			0
$921$	−30.8344	+	10.9314i	−1.01603	+	0.360200i
$922$		0			0
$923$	−9.78651	+	16.9507i	−0.322127	+	0.557940i
$924$		0			0
$925$	−0.351848	−	0.609419i	−0.0115687	−	0.0200376i
$926$		0			0
$927$	−5.04708	+	0.803057i	−0.165768	+	0.0263759i
$928$		0			0
$929$	14.8723	+	25.7595i	0.487943	+	0.845142i	0.999904	−	0.0138670i	$-0.00441415\pi$
$929$	14.8723	+	25.7595i	0.487943	+	0.845142i	−0.511961	+	0.859009i	$0.671081\pi$
$930$		0			0
$931$	−29.5976	−	10.5562i	−0.970024	−	0.345964i
$932$		0			0
$933$	13.5475	+	2.50589i	0.443524	+	0.0820393i
$934$		0			0
$935$		−	5.06346i		−	0.165593i
$936$		0			0
$937$		−	4.03712i		−	0.131887i	−0.997823	−	0.0659434i	$-0.978994\pi$
$937$		−	4.03712i		−	0.131887i	0.997823	−	0.0659434i	$-0.0210057\pi$
$938$		0			0
$939$	−14.6683	−	12.5189i	−0.478681	−	0.408538i
$940$		0			0
$941$	7.20264	−	12.4753i	0.234799	−	0.406684i	−0.724415	−	0.689364i	$-0.757890\pi$
$941$	7.20264	−	12.4753i	0.234799	−	0.406684i	0.959214	+	0.282680i	$0.0912234\pi$
$942$		0			0
$943$	25.8009	−	14.8962i	0.840193	−	0.485085i
$944$		0			0
$945$	8.72219	−	17.6842i	0.283733	−	0.575267i
$946$		0			0
$947$	−27.0334	+	15.6077i	−0.878467	+	0.507183i	−0.870153	−	0.492782i	$-0.835980\pi$
$947$	−27.0334	+	15.6077i	−0.878467	+	0.507183i	−0.00831468	+	0.999965i	$0.502647\pi$
$948$		0			0
$949$	18.7125	−	32.4109i	0.607432	−	1.05210i
$950$		0			0
$951$	−30.6355	−	26.1463i	−0.993423	−	0.847853i
$952$		0			0
$953$		−	8.55869i		−	0.277243i	−0.990345	−	0.138622i	$-0.955733\pi$
$953$		−	8.55869i		−	0.277243i	0.990345	−	0.138622i	$-0.0442672\pi$
$954$		0			0
$955$			32.5865i			1.05447i
$956$		0			0
$957$	−6.54377	−	1.21041i	−0.211530	−	0.0391270i
$958$		0			0
$959$	11.4902	−	24.8506i	0.371039	−	0.802468i
$960$		0			0
$961$	−8.48973	−	14.7046i	−0.273862	−	0.474343i
$962$		0			0
$963$	−9.32683	−	11.5009i	−0.300553	−	0.370613i
$964$		0			0
$965$	12.0996	+	20.9572i	0.389501	+	0.674635i
$966$		0			0
$967$	−16.0280	+	27.7614i	−0.515427	+	0.892745i	0.484413	+	0.874840i	$0.339033\pi$
$967$	−16.0280	+	27.7614i	−0.515427	+	0.892745i	−0.999840	+	0.0179059i	$0.994300\pi$
$968$		0			0
$969$	−7.99766	+	2.83532i	−0.256922	+	0.0910837i
$970$		0			0
$971$	−33.2366			−1.06661			−0.533307	−	0.845922i	$-0.679051\pi$
$971$	−33.2366			−1.06661			−0.533307	+	0.845922i	$0.679051\pi$
$972$		0			0
$973$	−47.0345	+	4.26845i	−1.50786	+	0.136840i
$974$		0			0
$975$	24.5933	−	8.71878i	0.787616	−	0.279225i
$976$		0			0
$977$	45.1558	+	26.0707i	1.44466	+	0.834076i	0.998156	−	0.0607042i	$-0.0193346\pi$
$977$	45.1558	+	26.0707i	1.44466	+	0.834076i	0.446507	+	0.894780i	$0.352668\pi$
$978$		0			0
$979$	38.3567	−	22.1453i	1.22589	−	0.707765i
$980$		0			0
$981$	−18.9633	+	15.3785i	−0.605453	+	0.490999i
$982$		0			0
$983$	12.1192	+	20.9911i	0.386544	+	0.669513i	0.991982	−	0.126379i	$-0.0403356\pi$
$983$	12.1192	+	20.9911i	0.386544	+	0.669513i	−0.605438	+	0.795892i	$0.707002\pi$
$984$		0			0
$985$	11.1099	+	6.41432i	0.353992	+	0.204377i
$986$		0			0
$987$	−1.78470	+	19.2598i	−0.0568077	+	0.613048i
$988$		0			0
$989$		−	30.6506i		−	0.974632i
$990$		0			0
$991$	24.1981			0.768678			0.384339	−	0.923192i	$-0.374429\pi$
$991$	24.1981			0.768678			0.384339	+	0.923192i	$0.374429\pi$
$992$		0			0
$993$	21.5428	−	25.2416i	0.683641	−	0.801017i
$994$		0			0
$995$	7.18607	+	4.14888i	0.227814	+	0.131528i
$996$		0			0
$997$	8.81920	−	5.09177i	0.279307	−	0.161258i	−0.353803	−	0.935320i	$-0.615112\pi$
$997$	8.81920	−	5.09177i	0.279307	−	0.161258i	0.633110	+	0.774062i	$0.281778\pi$
$998$		0			0
$999$	1.06012	+	0.648085i	0.0335406	+	0.0205045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cc.a.545.5		12
3.2	odd	2		3024.2.cc.a.881.3		12
4.3	odd	2		63.2.o.a.41.1	yes	12
7.6	odd	2	inner	1008.2.cc.a.545.2		12
9.2	odd	6	inner	1008.2.cc.a.209.2		12
9.7	even	3		3024.2.cc.a.2897.4		12
12.11	even	2		189.2.o.a.125.5		12
21.20	even	2		3024.2.cc.a.881.4		12
28.3	even	6		441.2.i.c.68.2		12
28.11	odd	6		441.2.i.c.68.1		12
28.19	even	6		441.2.s.c.374.5		12
28.23	odd	6		441.2.s.c.374.6		12
28.27	even	2		63.2.o.a.41.2	yes	12
36.7	odd	6		189.2.o.a.62.6		12
36.11	even	6		63.2.o.a.20.2	yes	12
36.23	even	6		567.2.c.c.566.12		12
36.31	odd	6		567.2.c.c.566.1		12
63.20	even	6	inner	1008.2.cc.a.209.5		12
63.34	odd	6		3024.2.cc.a.2897.3		12
84.11	even	6		1323.2.i.c.1097.5		12
84.23	even	6		1323.2.s.c.962.2		12
84.47	odd	6		1323.2.s.c.962.1		12
84.59	odd	6		1323.2.i.c.1097.6		12
84.83	odd	2		189.2.o.a.125.6		12
252.11	even	6		441.2.s.c.362.5		12
252.47	odd	6		441.2.i.c.227.5		12
252.79	odd	6		1323.2.i.c.521.2		12
252.83	odd	6		63.2.o.a.20.1	✓	12
252.115	even	6		1323.2.s.c.656.2		12
252.139	even	6		567.2.c.c.566.2		12
252.151	odd	6		1323.2.s.c.656.1		12
252.167	odd	6		567.2.c.c.566.11		12
252.187	even	6		1323.2.i.c.521.1		12
252.191	even	6		441.2.i.c.227.6		12
252.223	even	6		189.2.o.a.62.5		12
252.227	odd	6		441.2.s.c.362.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.1	✓	12	252.83	odd	6
63.2.o.a.20.2	yes	12	36.11	even	6
63.2.o.a.41.1	yes	12	4.3	odd	2
63.2.o.a.41.2	yes	12	28.27	even	2
189.2.o.a.62.5		12	252.223	even	6
189.2.o.a.62.6		12	36.7	odd	6
189.2.o.a.125.5		12	12.11	even	2
189.2.o.a.125.6		12	84.83	odd	2
441.2.i.c.68.1		12	28.11	odd	6
441.2.i.c.68.2		12	28.3	even	6
441.2.i.c.227.5		12	252.47	odd	6
441.2.i.c.227.6		12	252.191	even	6
441.2.s.c.362.5		12	252.11	even	6
441.2.s.c.362.6		12	252.227	odd	6
441.2.s.c.374.5		12	28.19	even	6
441.2.s.c.374.6		12	28.23	odd	6
567.2.c.c.566.1		12	36.31	odd	6
567.2.c.c.566.2		12	252.139	even	6
567.2.c.c.566.11		12	252.167	odd	6
567.2.c.c.566.12		12	36.23	even	6
1008.2.cc.a.209.2		12	9.2	odd	6	inner
1008.2.cc.a.209.5		12	63.20	even	6	inner
1008.2.cc.a.545.2		12	7.6	odd	2	inner
1008.2.cc.a.545.5		12	1.1	even	1	trivial
1323.2.i.c.521.1		12	252.187	even	6
1323.2.i.c.521.2		12	252.79	odd	6
1323.2.i.c.1097.5		12	84.11	even	6
1323.2.i.c.1097.6		12	84.59	odd	6
1323.2.s.c.656.1		12	252.151	odd	6
1323.2.s.c.656.2		12	252.115	even	6
1323.2.s.c.962.1		12	84.47	odd	6
1323.2.s.c.962.2		12	84.23	even	6
3024.2.cc.a.881.3		12	3.2	odd	2
3024.2.cc.a.881.4		12	21.20	even	2
3024.2.cc.a.2897.3		12	63.34	odd	6
3024.2.cc.a.2897.4		12	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(0.578751 + 1.63250i) q^{3} +(0.717144 - 1.24213i) q^{5} +(-2.16235 + 1.52455i) q^{7} +(-2.33009 + 1.88962i) q^{9} +O(q^{10})\)	\(q+(0.578751 + 1.63250i) q^{3} +(0.717144 - 1.24213i) q^{5} +(-2.16235 + 1.52455i) q^{7} +(-2.33009 + 1.88962i) q^{9} +(-2.80150 + 1.61745i) q^{11} +(-4.43334 - 2.55959i) q^{13} +(2.44282 + 0.451852i) q^{15} -1.09132 q^{17} -4.48911i q^{19} +(-3.74028 - 2.64769i) q^{21} +(-3.47141 - 2.00422i) q^{23} +(1.47141 + 2.54856i) q^{25} +(-4.43334 - 2.71026i) q^{27} +(1.02859 - 0.593857i) q^{29} +(-3.24275 - 1.87220i) q^{31} +(-4.26186 - 3.63735i) q^{33} +(0.342971 + 3.77924i) q^{35} -0.239123 q^{37} +(1.61273 - 8.71878i) q^{39} +(-3.71620 + 6.43664i) q^{41} +(3.82326 + 6.62208i) q^{43} +(0.676137 + 4.24941i) q^{45} +(-2.11042 - 3.65536i) q^{47} +(2.35150 - 6.59321i) q^{49} +(-0.631600 - 1.78157i) q^{51} +7.01414i q^{53} +4.63977i q^{55} +(7.32846 - 2.59808i) q^{57} +(-4.73531 + 8.20179i) q^{59} +(2.82757 - 1.63250i) q^{61} +(2.15766 - 7.63836i) q^{63} +(-6.35868 + 3.67119i) q^{65} +(0.330095 - 0.571741i) q^{67} +(1.26280 - 6.82701i) q^{69} -3.82347i q^{71} +7.31073i q^{73} +(-3.30893 + 3.87705i) q^{75} +(3.59195 - 7.76852i) q^{77} +(1.83009 + 3.16982i) q^{79} +(1.85868 - 8.80598i) q^{81} +(-5.45245 - 9.44392i) q^{83} +(-0.782630 + 1.35556i) q^{85} +(1.56477 + 1.33548i) q^{87} -13.6915 q^{89} +(13.4887 - 1.22412i) q^{91} +(1.17962 - 6.37731i) q^{93} +(-5.57605 - 3.21934i) q^{95} +(-2.69709 + 1.55716i) q^{97} +(3.47141 - 9.06259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7} - 12 q^{9}+O(q^{10}) \) 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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