LMFDB - Embedded newform 1386.2.bu.a.701.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.12
Character	$\chi$	$=$	1386.701
Dual form			1386.2.bu.a.953.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.03332 - 2.79863i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.03332 - 2.79863i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +3.45929i q^{10} +(3.21924 - 0.797795i) q^{11} +(-2.39007 - 3.28964i) q^{13} +(-0.951057 + 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(5.58162 + 4.05529i) q^{17} +(3.73524 - 1.21365i) q^{19} +(-2.03332 - 2.79863i) q^{20} +(-2.13549 + 2.53765i) q^{22} +0.504619i q^{23} +(-2.15283 - 6.62572i) q^{25} +(3.86721 + 1.25653i) q^{26} +(0.587785 - 0.809017i) q^{28} +(-2.73069 + 8.40419i) q^{29} +(-0.241611 + 0.175540i) q^{31} +1.00000 q^{32} -6.89927 q^{34} +(2.79863 - 2.03332i) q^{35} +(1.61314 - 4.96475i) q^{37} +(-2.30851 + 3.17739i) q^{38} +(3.28998 + 1.06898i) q^{40} +(0.329578 + 1.01434i) q^{41} -6.11192i q^{43} +(0.236053 - 3.30821i) q^{44} +(-0.296608 - 0.408246i) q^{46} +(3.35357 - 1.08964i) q^{47} +(0.809017 + 0.587785i) q^{49} +(5.63618 + 4.09492i) q^{50} +(-3.86721 + 1.25653i) q^{52} +(1.04412 + 1.43710i) q^{53} +(4.31302 - 10.6316i) q^{55} +1.00000i q^{56} +(-2.73069 - 8.40419i) q^{58} +(-9.23398 - 3.00030i) q^{59} +(-5.18154 + 7.13178i) q^{61} +(0.0922870 - 0.284030i) q^{62} +(-0.809017 + 0.587785i) q^{64} -14.0662 q^{65} -7.92427 q^{67} +(5.58162 - 4.05529i) q^{68} +(-1.06898 + 3.28998i) q^{70} +(6.21939 - 8.56026i) q^{71} +(0.506041 + 0.164423i) q^{73} +(1.61314 + 4.96475i) q^{74} -3.92747i q^{76} +(3.30821 + 0.236053i) q^{77} +(-8.97815 - 12.3574i) q^{79} +(-3.28998 + 1.06898i) q^{80} +(-0.862845 - 0.626894i) q^{82} +(7.03976 + 5.11469i) q^{83} +(22.6985 - 7.37518i) q^{85} +(3.59250 + 4.94465i) q^{86} +(1.75355 + 2.81515i) q^{88} -13.3670i q^{89} +(-1.25653 - 3.86721i) q^{91} +(0.479922 + 0.155936i) q^{92} +(-2.07262 + 2.85271i) q^{94} +(4.19838 - 12.9213i) q^{95} +(-7.38698 + 5.36695i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.03332	−	2.79863i	0.909329	−	1.25158i	−0.0580668	−	0.998313i	$-0.518494\pi$
$5$	2.03332	−	2.79863i	0.909329	−	1.25158i	0.967395	−	0.253271i	$-0.0815064\pi$
$6$		0			0
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$		0			0
$10$			3.45929i			1.09392i
$11$	3.21924	−	0.797795i	0.970638	−	0.240544i
$11$	3.21924	−	0.797795i	0.970638	−	0.240544i
$12$		0			0
$13$	−2.39007	−	3.28964i	−0.662885	−	0.912383i	0.336688	−	0.941616i	$-0.390693\pi$
$13$	−2.39007	−	3.28964i	−0.662885	−	0.912383i	−0.999573	+	0.0292336i	$0.990693\pi$
$14$	−0.951057	+	0.309017i	−0.254181	+	0.0825883i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	5.58162	+	4.05529i	1.35374	+	0.983551i	0.998816	+	0.0486573i	$0.0154942\pi$
$17$	5.58162	+	4.05529i	1.35374	+	0.983551i	0.354927	+	0.934894i	$0.384506\pi$
$18$		0			0
$19$	3.73524	−	1.21365i	0.856923	−	0.278431i	0.152580	−	0.988291i	$-0.451242\pi$
$19$	3.73524	−	1.21365i	0.856923	−	0.278431i	0.704343	+	0.709860i	$0.251242\pi$
$20$	−2.03332	−	2.79863i	−0.454664	−	0.625792i
$21$		0			0
$22$	−2.13549	+	2.53765i	−0.455288	+	0.541029i
$23$			0.504619i			0.105220i	0.998615	+	0.0526102i	$0.0167541\pi$
$23$			0.504619i			0.105220i	−0.998615	+	0.0526102i	$0.983246\pi$
$24$		0			0
$25$	−2.15283	−	6.62572i	−0.430566	−	1.32514i
$26$	3.86721	+	1.25653i	0.758422	+	0.246426i
$27$		0			0
$28$	0.587785	−	0.809017i	0.111081	−	0.152890i
$29$	−2.73069	+	8.40419i	−0.507076	+	1.56062i	0.290177	+	0.956973i	$0.406286\pi$
$29$	−2.73069	+	8.40419i	−0.507076	+	1.56062i	−0.797253	+	0.603646i	$0.793714\pi$
$30$		0			0
$31$	−0.241611	+	0.175540i	−0.0433945	+	0.0315280i	−0.609271	−	0.792962i	$-0.708538\pi$
$31$	−0.241611	+	0.175540i	−0.0433945	+	0.0315280i	0.565877	+	0.824490i	$0.308538\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−6.89927			−1.18321
$35$	2.79863	−	2.03332i	0.473054	−	0.343694i
$36$		0			0
$37$	1.61314	−	4.96475i	0.265199	−	0.816200i	−0.726448	−	0.687221i	$-0.758830\pi$
$37$	1.61314	−	4.96475i	0.265199	−	0.816200i	0.991647	−	0.128978i	$-0.0411697\pi$
$38$	−2.30851	+	3.17739i	−0.374489	+	0.515440i
$39$		0			0
$40$	3.28998	+	1.06898i	0.520192	+	0.169021i
$41$	0.329578	+	1.01434i	0.0514714	+	0.158413i	0.973488	−	0.228737i	$-0.0734596\pi$
$41$	0.329578	+	1.01434i	0.0514714	+	0.158413i	−0.922017	+	0.387150i	$0.873460\pi$
$42$		0			0
$43$		−	6.11192i		−	0.932059i	−0.884769	−	0.466029i	$-0.845684\pi$
$43$		−	6.11192i		−	0.932059i	0.884769	−	0.466029i	$-0.154316\pi$
$44$	0.236053	−	3.30821i	0.0355863	−	0.498732i
$45$		0			0
$46$	−0.296608	−	0.408246i	−0.0437324	−	0.0601926i
$47$	3.35357	−	1.08964i	0.489168	−	0.158940i	−0.0540396	−	0.998539i	$-0.517210\pi$
$47$	3.35357	−	1.08964i	0.489168	−	0.158940i	0.543207	+	0.839599i	$0.317210\pi$
$48$		0			0
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	5.63618	+	4.09492i	0.797076	+	0.579110i
$51$		0			0
$52$	−3.86721	+	1.25653i	−0.536285	+	0.174250i
$53$	1.04412	+	1.43710i	0.143420	+	0.197401i	0.874684	−	0.484694i	$-0.161069\pi$
$53$	1.04412	+	1.43710i	0.143420	+	0.197401i	−0.731263	+	0.682095i	$0.761069\pi$
$54$		0			0
$55$	4.31302	−	10.6316i	0.581568	−	1.43357i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−2.73069	−	8.40419i	−0.358557	−	1.10352i
$59$	−9.23398	−	3.00030i	−1.20216	−	0.390606i	−0.361606	−	0.932331i	$-0.617771\pi$
$59$	−9.23398	−	3.00030i	−1.20216	−	0.390606i	−0.840556	+	0.541725i	$0.817771\pi$
$60$		0			0
$61$	−5.18154	+	7.13178i	−0.663428	+	0.913130i	−0.999589	−	0.0286742i	$-0.990871\pi$
$61$	−5.18154	+	7.13178i	−0.663428	+	0.913130i	0.336161	+	0.941805i	$0.390871\pi$
$62$	0.0922870	−	0.284030i	0.0117205	−	0.0360719i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−14.0662			−1.74470
$66$		0			0
$67$	−7.92427			−0.968104			−0.484052	−	0.875039i	$-0.660835\pi$
$67$	−7.92427			−0.968104			−0.484052	+	0.875039i	$0.660835\pi$
$68$	5.58162	−	4.05529i	0.676871	−	0.491776i
$69$		0			0
$70$	−1.06898	+	3.28998i	−0.127768	+	0.393228i
$71$	6.21939	−	8.56026i	0.738106	−	1.01592i	−0.260619	−	0.965442i	$-0.583927\pi$
$71$	6.21939	−	8.56026i	0.738106	−	1.01592i	0.998725	−	0.0504742i	$-0.0160733\pi$
$72$		0			0
$73$	0.506041	+	0.164423i	0.0592276	+	0.0192442i	0.338481	−	0.940973i	$-0.390087\pi$
$73$	0.506041	+	0.164423i	0.0592276	+	0.0192442i	−0.279253	+	0.960217i	$0.590087\pi$
$74$	1.61314	+	4.96475i	0.187524	+	0.577140i
$75$		0			0
$76$		−	3.92747i		−	0.450511i
$77$	3.30821	+	0.236053i	0.377006	+	0.0269007i
$78$		0			0
$79$	−8.97815	−	12.3574i	−1.01012	−	1.39031i	−0.918904	−	0.394482i	$-0.870924\pi$
$79$	−8.97815	−	12.3574i	−1.01012	−	1.39031i	−0.0912174	−	0.995831i	$-0.529076\pi$
$80$	−3.28998	+	1.06898i	−0.367831	+	0.119516i
$81$		0			0
$82$	−0.862845	−	0.626894i	−0.0952853	−	0.0692288i
$83$	7.03976	+	5.11469i	0.772714	+	0.561410i	0.902784	−	0.430095i	$-0.141520\pi$
$83$	7.03976	+	5.11469i	0.772714	+	0.561410i	−0.130069	+	0.991505i	$0.541520\pi$
$84$		0			0
$85$	22.6985	−	7.37518i	2.46199	−	0.799950i
$86$	3.59250	+	4.94465i	0.387389	+	0.533195i
$87$		0			0
$88$	1.75355	+	2.81515i	0.186929	+	0.300096i
$89$		−	13.3670i		−	1.41690i	−0.705763	−	0.708448i	$-0.749396\pi$
$89$		−	13.3670i		−	1.41690i	0.705763	−	0.708448i	$-0.250604\pi$
$90$		0			0
$91$	−1.25653	−	3.86721i	−0.131720	−	0.405393i
$92$	0.479922	+	0.155936i	0.0500353	+	0.0162575i
$93$		0			0
$94$	−2.07262	+	2.85271i	−0.213774	+	0.294235i
$95$	4.19838	−	12.9213i	0.430745	−	1.32570i
$96$		0			0
$97$	−7.38698	+	5.36695i	−0.750034	+	0.544932i	−0.895837	−	0.444382i	$-0.853423\pi$
$97$	−7.38698	+	5.36695i	−0.750034	+	0.544932i	0.145803	+	0.989314i	$0.453423\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	−6.96670			−0.696670
$101$	12.3094	−	8.94328i	1.22483	−	0.889889i	0.228336	−	0.973582i	$-0.426671\pi$
$101$	12.3094	−	8.94328i	1.22483	−	0.889889i	0.996492	+	0.0836929i	$0.0266715\pi$
$102$		0			0
$103$	−2.82299	+	8.68826i	−0.278157	+	0.856079i	0.710210	+	0.703990i	$0.248600\pi$
$103$	−2.82299	+	8.68826i	−0.278157	+	0.856079i	−0.988367	+	0.152089i	$0.951400\pi$
$104$	2.39007	−	3.28964i	0.234365	−	0.322576i
$105$		0			0
$106$	−1.68942	−	0.548925i	−0.164091	−	0.0533163i
$107$	2.11755	+	6.51714i	0.204711	+	0.630035i	0.999725	+	0.0234446i	$0.00746334\pi$
$107$	2.11755	+	6.51714i	0.204711	+	0.630035i	−0.795014	+	0.606591i	$0.792537\pi$
$108$		0			0
$109$			6.51147i			0.623686i	0.950134	+	0.311843i	$0.100946\pi$
$109$			6.51147i			0.623686i	−0.950134	+	0.311843i	$0.899054\pi$
$110$	2.75981	+	11.1363i	0.263137	+	1.06180i
$111$		0			0
$112$	−0.587785	−	0.809017i	−0.0555405	−	0.0764449i
$113$	2.22247	−	0.722123i	0.209072	−	0.0679317i	−0.202609	−	0.979260i	$-0.564942\pi$
$113$	2.22247	−	0.722123i	0.209072	−	0.0679317i	0.411681	+	0.911328i	$0.364942\pi$
$114$		0			0
$115$	1.41224	+	1.02605i	0.131692	+	0.0956800i
$116$	7.14903	+	5.19407i	0.663771	+	0.482258i
$117$		0			0
$118$	9.23398	−	3.00030i	0.850057	−	0.276200i
$119$	4.05529	+	5.58162i	0.371747	+	0.511667i
$120$		0			0
$121$	9.72705	−	5.13659i	0.884277	−	0.466963i
$122$		−	8.81536i		−	0.798105i
$123$		0			0
$124$	0.0922870	+	0.284030i	0.00828762	+	0.0255067i
$125$	−6.47040	−	2.10236i	−0.578730	−	0.188041i
$126$		0			0
$127$	4.60102	−	6.33277i	0.408275	−	0.561942i	−0.554522	−	0.832169i	$-0.687099\pi$
$127$	4.60102	−	6.33277i	0.408275	−	0.561942i	0.962797	+	0.270227i	$0.0870988\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$		0			0
$130$	11.3798	−	8.26793i	0.998077	−	0.725146i
$131$	−1.44646			−0.126378			−0.0631890	−	0.998002i	$-0.520127\pi$
$131$	−1.44646			−0.126378			−0.0631890	+	0.998002i	$0.520127\pi$
$132$		0			0
$133$	3.92747			0.340554
$134$	6.41087	−	4.65777i	0.553815	−	0.402370i
$135$		0			0
$136$	−2.13199	+	6.56159i	−0.182817	+	0.562652i
$137$	−7.13789	+	9.82447i	−0.609831	+	0.839361i	−0.996564	−	0.0828313i	$-0.973604\pi$
$137$	−7.13789	+	9.82447i	−0.609831	+	0.839361i	0.386732	+	0.922192i	$0.373604\pi$
$138$		0			0
$139$	0.232310	+	0.0754820i	0.0197042	+	0.00640230i	0.318853	−	0.947804i	$-0.396703\pi$
$139$	0.232310	+	0.0754820i	0.0197042	+	0.00640230i	−0.299148	+	0.954207i	$0.596703\pi$
$140$	−1.06898	−	3.28998i	−0.0903453	−	0.278054i
$141$		0			0
$142$			10.5811i			0.887943i
$143$	−10.3187	−	8.68338i	−0.862890	−	0.726140i
$144$		0			0
$145$	17.9678	+	24.7306i	1.49215	+	2.05376i
$146$	−0.506041	+	0.164423i	−0.0418802	+	0.0136077i
$147$		0			0
$148$	−4.22327	−	3.06838i	−0.347150	−	0.252220i
$149$	−1.38345	−	1.00514i	−0.113337	−	0.0823440i	0.529673	−	0.848202i	$-0.322315\pi$
$149$	−1.38345	−	1.00514i	−0.113337	−	0.0823440i	−0.643010	+	0.765858i	$0.722315\pi$
$150$		0			0
$151$	13.6905	−	4.44831i	1.11412	−	0.361999i	0.306598	−	0.951839i	$-0.400809\pi$
$151$	13.6905	−	4.44831i	1.11412	−	0.361999i	0.807520	+	0.589840i	$0.200809\pi$
$152$	2.30851	+	3.17739i	0.187245	+	0.257720i
$153$		0			0
$154$	−2.81515	+	1.75355i	−0.226851	+	0.141305i
$155$			1.03311i			0.0829812i
$156$		0			0
$157$	6.19720	+	19.0730i	0.494591	+	1.52219i	0.817594	+	0.575796i	$0.195308\pi$
$157$	6.19720	+	19.0730i	0.494591	+	1.52219i	−0.323003	+	0.946398i	$0.604692\pi$
$158$	14.5270	+	4.72009i	1.15570	+	0.375511i
$159$		0			0
$160$	2.03332	−	2.79863i	0.160748	−	0.221251i
$161$	−0.155936	+	0.479922i	−0.0122895	+	0.0378231i
$162$		0			0
$163$	−2.20817	+	1.60433i	−0.172957	+	0.125661i	−0.670896	−	0.741551i	$-0.734090\pi$
$163$	−2.20817	+	1.60433i	−0.172957	+	0.125661i	0.497939	+	0.867212i	$0.334090\pi$
$164$	1.06654			0.0832824
$165$		0			0
$166$	−8.70163			−0.675377
$167$	15.8787	−	11.5365i	1.22873	−	0.892724i	0.231935	−	0.972731i	$-0.425494\pi$
$167$	15.8787	−	11.5365i	1.22873	−	0.892724i	0.996794	+	0.0800071i	$0.0254943\pi$
$168$		0			0
$169$	−1.09212	+	3.36119i	−0.0840089	+	0.258553i
$170$	−14.0284	+	19.3085i	−1.07593	+	1.48089i
$171$		0			0
$172$	−5.81278	−	1.88869i	−0.443220	−	0.144011i
$173$	5.56788	+	17.1362i	0.423318	+	1.30284i	0.904595	+	0.426271i	$0.140173\pi$
$173$	5.56788	+	17.1362i	0.423318	+	1.30284i	−0.481277	+	0.876569i	$0.659827\pi$
$174$		0			0
$175$		−	6.96670i		−	0.526633i
$176$	−3.07335	−	1.24679i	−0.231663	−	0.0939806i
$177$		0			0
$178$	7.85690	+	10.8141i	0.588900	+	0.810551i
$179$	−10.5258	+	3.42005i	−0.786737	+	0.255626i	−0.674714	−	0.738079i	$-0.735733\pi$
$179$	−10.5258	+	3.42005i	−0.786737	+	0.255626i	−0.112023	+	0.993706i	$0.535733\pi$
$180$		0			0
$181$	2.07397	+	1.50683i	0.154157	+	0.112002i	0.662190	−	0.749336i	$-0.269627\pi$
$181$	2.07397	+	1.50683i	0.154157	+	0.112002i	−0.508033	+	0.861338i	$0.669627\pi$
$182$	3.28964	+	2.39007i	0.243845	+	0.177163i
$183$		0			0
$184$	−0.479922	+	0.155936i	−0.0353803	+	0.0114958i
$185$	−10.6144	−	14.6095i	−0.780389	−	1.07411i
$186$		0			0
$187$	21.2039	+	8.60196i	1.55058	+	0.629038i
$188$		−	3.52615i		−	0.257171i
$189$		0			0
$190$	4.19838	+	12.9213i	0.304583	+	0.937409i
$191$	−15.9730	−	5.18993i	−1.15576	−	0.375530i	−0.332451	−	0.943120i	$-0.607876\pi$
$191$	−15.9730	−	5.18993i	−1.15576	−	0.375530i	−0.823311	+	0.567591i	$0.807876\pi$
$192$		0			0
$193$	−6.55214	+	9.01824i	−0.471633	+	0.649147i	−0.976870	−	0.213833i	$-0.931405\pi$
$193$	−6.55214	+	9.01824i	−0.471633	+	0.649147i	0.505237	+	0.862981i	$0.331405\pi$
$194$	2.82158	−	8.68392i	0.202577	−	0.623469i
$195$		0			0
$196$	0.809017	−	0.587785i	0.0577869	−	0.0419847i
$197$	19.6906			1.40290			0.701450	−	0.712719i	$-0.252536\pi$
$197$	19.6906			1.40290			0.701450	+	0.712719i	$0.252536\pi$
$198$		0			0
$199$	−8.67609			−0.615031			−0.307516	−	0.951543i	$-0.599498\pi$
$199$	−8.67609			−0.615031			−0.307516	+	0.951543i	$0.599498\pi$
$200$	5.63618	−	4.09492i	0.398538	−	0.289555i
$201$		0			0
$202$	−4.70176	+	14.4705i	−0.330815	+	1.01814i
$203$	−5.19407	+	7.14903i	−0.364553	+	0.501764i
$204$		0			0
$205$	3.50888	+	1.14011i	0.245071	+	0.0796284i
$206$	−2.82299	−	8.68826i	−0.196687	−	0.605340i
$207$		0			0
$208$			4.06622i			0.281942i
$209$	11.0564	−	6.88700i	0.764787	−	0.476384i
$210$		0			0
$211$	−10.0262	−	13.7999i	−0.690233	−	0.950024i	0.309767	−	0.950813i	$-0.399749\pi$
$211$	−10.0262	−	13.7999i	−0.690233	−	0.950024i	−1.00000		0.000788470i	$0.999749\pi$
$212$	1.68942	−	0.548925i	0.116030	−	0.0377003i
$213$		0			0
$214$	−5.54381	−	4.02781i	−0.378967	−	0.275336i
$215$	−17.1050	−	12.4275i	−1.16655	−	0.847548i
$216$		0			0
$217$	−0.284030	+	0.0922870i	−0.0192812	+	0.00626485i
$218$	−3.82735	−	5.26789i	−0.259221	−	0.356786i
$219$		0			0
$220$	−8.77848	−	7.38728i	−0.591845	−	0.498050i
$221$		−	28.0539i		−	1.88711i
$222$		0			0
$223$	−3.59820	−	11.0741i	−0.240953	−	0.741578i	−0.996276	−	0.0862246i	$-0.972520\pi$
$223$	−3.59820	−	11.0741i	−0.240953	−	0.741578i	0.755322	−	0.655353i	$-0.227480\pi$
$224$	0.951057	+	0.309017i	0.0635451	+	0.0206471i
$225$		0			0
$226$	−1.37356	+	1.89054i	−0.0913679	+	0.125757i
$227$	−7.44732	+	22.9205i	−0.494296	+	1.52129i	0.323756	+	0.946141i	$0.395054\pi$
$227$	−7.44732	+	22.9205i	−0.494296	+	1.52129i	−0.818051	+	0.575145i	$0.804946\pi$
$228$		0			0
$229$	4.64536	−	3.37505i	0.306974	−	0.223030i	−0.423623	−	0.905839i	$-0.639242\pi$
$229$	4.64536	−	3.37505i	0.306974	−	0.223030i	0.730597	+	0.682809i	$0.239242\pi$
$230$	−1.74563			−0.115103
$231$		0			0
$232$	−8.83669			−0.580157
$233$	−17.1420	+	12.4544i	−1.12301	+	0.815917i	−0.984663	−	0.174467i	$-0.944180\pi$
$233$	−17.1420	+	12.4544i	−1.12301	+	0.815917i	−0.138350	+	0.990383i	$0.544180\pi$
$234$		0			0
$235$	3.76938	−	11.6010i	0.245887	−	0.756763i
$236$	−5.70691	+	7.85489i	−0.371488	+	0.511310i
$237$		0			0
$238$	−6.56159	−	2.13199i	−0.425325	−	0.138196i
$239$	−4.22900	−	13.0155i	−0.273551	−	0.841904i	−0.989599	−	0.143853i	$-0.954051\pi$
$239$	−4.22900	−	13.0155i	−0.273551	−	0.841904i	0.716048	−	0.698051i	$-0.245949\pi$
$240$		0			0
$241$		−	20.0364i		−	1.29066i	−0.763905	−	0.645328i	$-0.776721\pi$
$241$		−	20.0364i		−	1.29066i	0.763905	−	0.645328i	$-0.223279\pi$
$242$	−4.85013	+	9.87300i	−0.311778	+	0.634661i
$243$		0			0
$244$	5.18154	+	7.13178i	0.331714	+	0.456565i
$245$	3.28998	−	1.06898i	0.210189	−	0.0682946i
$246$		0			0
$247$	−12.9200	−	9.38690i	−0.822077	−	0.597274i
$248$	−0.241611	−	0.175540i	−0.0153423	−	0.0111468i
$249$		0			0
$250$	6.47040	−	2.10236i	0.409224	−	0.132965i
$251$	11.8454	+	16.3039i	0.747678	+	1.02909i	0.998140	+	0.0609641i	$0.0194175\pi$
$251$	11.8454	+	16.3039i	0.747678	+	1.02909i	−0.250462	+	0.968126i	$0.580582\pi$
$252$		0			0
$253$	0.402583	+	1.62449i	0.0253102	+	0.102131i
$254$			7.82773i			0.491156i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−16.1238	−	5.23893i	−1.00577	−	0.326796i	−0.240603	−	0.970624i	$-0.577345\pi$
$257$	−16.1238	−	5.23893i	−1.00577	−	0.326796i	−0.765170	+	0.643828i	$0.777345\pi$
$258$		0			0
$259$	3.06838	−	4.22327i	0.190660	−	0.262421i
$260$	−4.34671	+	13.3778i	−0.269571	+	0.829656i
$261$		0			0
$262$	1.17021	−	0.850210i	0.0722960	−	0.0525261i
$263$	−24.4081			−1.50507			−0.752534	−	0.658554i	$-0.771169\pi$
$263$	−24.4081			−1.50507			−0.752534	+	0.658554i	$0.771169\pi$
$264$		0			0
$265$	6.14494			0.377481
$266$	−3.17739	+	2.30851i	−0.194818	+	0.141544i
$267$		0			0
$268$	−2.44873	+	7.53643i	−0.149580	+	0.460361i
$269$	−12.5662	+	17.2958i	−0.766173	+	1.05455i	0.230503	+	0.973072i	$0.425963\pi$
$269$	−12.5662	+	17.2958i	−0.766173	+	1.05455i	−0.996675	+	0.0814745i	$0.974037\pi$
$270$		0			0
$271$	6.23874	+	2.02709i	0.378976	+	0.123137i	0.492310	−	0.870420i	$-0.336153\pi$
$271$	6.23874	+	2.02709i	0.378976	+	0.123137i	−0.113333	+	0.993557i	$0.536153\pi$
$272$	−2.13199	−	6.56159i	−0.129271	−	0.397855i
$273$		0			0
$274$		−	12.1437i		−	0.733628i
$275$	−12.2164	−	19.6123i	−0.736679	−	1.18267i
$276$		0			0
$277$	−19.4495	−	26.7699i	−1.16861	−	1.60845i	−0.672234	−	0.740338i	$-0.734665\pi$
$277$	−19.4495	−	26.7699i	−1.16861	−	1.60845i	−0.496372	−	0.868110i	$-0.665335\pi$
$278$	−0.232310	+	0.0754820i	−0.0139330	+	0.00452711i
$279$		0			0
$280$	2.79863	+	2.03332i	0.167250	+	0.121514i
$281$	18.8045	+	13.6623i	1.12178	+	0.815023i	0.984478	−	0.175506i	$-0.0561562\pi$
$281$	18.8045	+	13.6623i	1.12178	+	0.815023i	0.137304	+	0.990529i	$0.456156\pi$
$282$		0			0
$283$	−13.1841	+	4.28377i	−0.783712	+	0.254644i	−0.673424	−	0.739256i	$-0.735177\pi$
$283$	−13.1841	+	4.28377i	−0.783712	+	0.254644i	−0.110288	+	0.993900i	$0.535177\pi$
$284$	−6.21939	−	8.56026i	−0.369053	−	0.507958i
$285$		0			0
$286$	13.4519	+	0.959842i	0.795429	+	0.0567567i
$287$			1.06654i			0.0629556i
$288$		0			0
$289$	9.45588	+	29.1022i	0.556228	+	1.71189i
$290$	−29.0725	−	9.44624i	−1.70720	−	0.554702i
$291$		0			0
$292$	0.312750	−	0.430464i	0.0183023	−	0.0251910i
$293$	−4.58227	+	14.1028i	−0.267699	+	0.823893i	0.723360	+	0.690471i	$0.242597\pi$
$293$	−4.58227	+	14.1028i	−0.267699	+	0.823893i	−0.991059	+	0.133422i	$0.957403\pi$
$294$		0			0
$295$	−27.1724	+	19.7419i	−1.58204	+	1.14942i
$296$	5.22024			0.303421
$297$		0			0
$298$	1.71004			0.0990600
$299$	1.66002	−	1.20607i	0.0960013	−	0.0697490i
$300$		0			0
$301$	1.88869	−	5.81278i	0.108862	−	0.335043i
$302$	−8.46120	+	11.6458i	−0.486887	+	0.670143i
$303$		0			0
$304$	−3.73524	−	1.21365i	−0.214231	−	0.0696078i
$305$	9.42344	+	29.0024i	0.539585	+	1.66067i
$306$		0			0
$307$			13.0044i			0.742200i	0.928593	+	0.371100i	$0.121019\pi$
$307$			13.0044i			0.742200i	−0.928593	+	0.371100i	$0.878981\pi$
$308$	1.24679	−	3.07335i	0.0710427	−	0.175121i
$309$		0			0
$310$	−0.607245	−	0.835802i	−0.0344892	−	0.0474703i
$311$	−31.1604	+	10.1246i	−1.76694	+	0.574114i	−0.997881	−	0.0650619i	$-0.979276\pi$
$311$	−31.1604	+	10.1246i	−1.76694	+	0.574114i	−0.769060	+	0.639176i	$0.779276\pi$
$312$		0			0
$313$	−17.6443	−	12.8193i	−0.997314	−	0.724591i	−0.0358033	−	0.999359i	$-0.511399\pi$
$313$	−17.6443	−	12.8193i	−0.997314	−	0.724591i	−0.961511	+	0.274768i	$0.911399\pi$
$314$	−16.2245	−	11.7878i	−0.915601	−	0.665223i
$315$		0			0
$316$	−14.5270	+	4.72009i	−0.817205	+	0.265526i
$317$	−14.4864	−	19.9388i	−0.813635	−	1.11987i	−0.990752	−	0.135683i	$-0.956677\pi$
$317$	−14.4864	−	19.9388i	−0.813635	−	1.11987i	0.177117	−	0.984190i	$-0.443323\pi$
$318$		0			0
$319$	−2.08592	+	29.2336i	−0.116789	+	1.63677i
$320$			3.45929i			0.193380i
$321$		0			0
$322$	−0.155936	−	0.479922i	−0.00868997	−	0.0267450i
$323$	25.7704	+	8.37332i	1.43390	+	0.465904i
$324$		0			0
$325$	−16.6509	+	22.9179i	−0.923624	+	1.27126i
$326$	0.843445	−	2.59586i	0.0467141	−	0.143771i
$327$		0			0
$328$	−0.862845	+	0.626894i	−0.0476427	+	0.0346144i
$329$	3.52615			0.194403
$330$		0			0
$331$	−1.44467			−0.0794060			−0.0397030	−	0.999212i	$-0.512641\pi$
$331$	−1.44467			−0.0794060			−0.0397030	+	0.999212i	$0.512641\pi$
$332$	7.03976	−	5.11469i	0.386357	−	0.280705i
$333$		0			0
$334$	−6.06512	+	18.6665i	−0.331868	+	1.02139i
$335$	−16.1126	+	22.1771i	−0.880325	+	1.21166i
$336$		0			0
$337$	31.3207	+	10.1767i	1.70615	+	0.554360i	0.989684	−	0.143266i	$-0.0457604\pi$
$337$	31.3207	+	10.1767i	1.70615	+	0.554360i	0.716462	+	0.697626i	$0.245760\pi$
$338$	−1.09212	−	3.36119i	−0.0594033	−	0.182824i
$339$		0			0
$340$		−	23.8666i		−	1.29435i
$341$	−0.637758	+	0.757863i	−0.0345365	+	0.0410406i
$342$		0			0
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	5.81278	−	1.88869i	0.313404	−	0.101831i
$345$		0			0
$346$	−14.5769	−	10.5907i	−0.783659	−	0.569362i
$347$	29.2945	+	21.2837i	1.57261	+	1.14257i	0.924603	+	0.380933i	$0.124397\pi$
$347$	29.2945	+	21.2837i	1.57261	+	1.14257i	0.648007	+	0.761634i	$0.275603\pi$
$348$		0			0
$349$	3.94603	−	1.28214i	0.211226	−	0.0686315i	−0.201493	−	0.979490i	$-0.564579\pi$
$349$	3.94603	−	1.28214i	0.211226	−	0.0686315i	0.412719	+	0.910859i	$0.364579\pi$
$350$	4.09492	+	5.63618i	0.218883	+	0.301266i
$351$		0			0
$352$	3.21924	−	0.797795i	0.171586	−	0.0425226i
$353$		−	13.9977i		−	0.745020i	−0.928028	−	0.372510i	$-0.878497\pi$
$353$		−	13.9977i		−	0.745020i	0.928028	−	0.372510i	$-0.121503\pi$
$354$		0			0
$355$	−11.3109	−	34.8115i	−0.600322	−	1.84760i
$356$	−12.7127	−	4.13062i	−0.673774	−	0.218922i
$357$		0			0
$358$	6.50532	−	8.95380i	0.343817	−	0.473223i
$359$	9.11755	−	28.0609i	0.481206	−	1.48100i	−0.356195	−	0.934412i	$-0.615926\pi$
$359$	9.11755	−	28.0609i	0.481206	−	1.48100i	0.837401	−	0.546588i	$-0.184074\pi$
$360$		0			0
$361$	−2.89225	+	2.10134i	−0.152224	+	0.110597i
$362$	−2.56357			−0.134738
$363$		0			0
$364$	−4.06622			−0.213128
$365$	1.48910	−	1.08189i	0.0779430	−	0.0566289i
$366$		0			0
$367$	0.385198	−	1.18552i	0.0201072	−	0.0618835i	−0.940499	−	0.339795i	$-0.889642\pi$
$367$	0.385198	−	1.18552i	0.0201072	−	0.0618835i	0.960607	+	0.277912i	$0.0896422\pi$
$368$	0.296608	−	0.408246i	0.0154618	−	0.0212813i
$369$		0			0
$370$	17.1745	+	5.58034i	0.892860	+	0.290108i
$371$	0.548925	+	1.68942i	0.0284988	+	0.0877101i
$372$		0			0
$373$			25.4617i			1.31836i	0.751986	+	0.659179i	$0.229096\pi$
$373$			25.4617i			1.31836i	−0.751986	+	0.659179i	$0.770904\pi$
$374$	−22.2104	+	5.50420i	−1.14847	+	0.284615i
$375$		0			0
$376$	2.07262	+	2.85271i	0.106887	+	0.147117i
$377$	34.1733	−	11.1036i	1.76001	−	0.571863i
$378$		0			0
$379$	−2.86948	−	2.08480i	−0.147395	−	0.107089i	0.511644	−	0.859198i	$-0.329037\pi$
$379$	−2.86948	−	2.08480i	−0.147395	−	0.107089i	−0.659039	+	0.752109i	$0.729037\pi$
$380$	−10.9915	−	7.98580i	−0.563852	−	0.409663i
$381$		0			0
$382$	15.9730	−	5.18993i	0.817247	−	0.265540i
$383$	−12.0364	−	16.5667i	−0.615030	−	0.846517i	0.381949	−	0.924183i	$-0.375253\pi$
$383$	−12.0364	−	16.5667i	−0.615030	−	0.846517i	−0.996979	+	0.0776668i	$0.975253\pi$
$384$		0			0
$385$	7.38728	−	8.77848i	0.376491	−	0.447393i
$386$		−	11.1472i		−	0.567375i
$387$		0			0
$388$	2.82158	+	8.68392i	0.143244	+	0.440859i
$389$	25.6768	+	8.34289i	1.30186	+	0.423001i	0.876229	−	0.481894i	$-0.160051\pi$
$389$	25.6768	+	8.34289i	1.30186	+	0.423001i	0.425634	+	0.904895i	$0.360051\pi$
$390$		0			0
$391$	−2.04638	+	2.81660i	−0.103490	+	0.142441i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$		0			0
$394$	−15.9301	+	11.5739i	−0.802545	+	0.583083i
$395$	−52.8391			−2.65862
$396$		0			0
$397$	11.7620			0.590320			0.295160	−	0.955448i	$-0.404627\pi$
$397$	11.7620			0.590320			0.295160	+	0.955448i	$0.404627\pi$
$398$	7.01910	−	5.09968i	0.351836	−	0.255624i
$399$		0			0
$400$	−2.15283	+	6.62572i	−0.107641	+	0.331286i
$401$	−0.0704704	+	0.0969942i	−0.00351912	+	0.00484366i	−0.810773	−	0.585361i	$-0.800953\pi$
$401$	−0.0704704	+	0.0969942i	−0.00351912	+	0.00484366i	0.807254	+	0.590204i	$0.200953\pi$
$402$		0			0
$403$	1.15493	+	0.375260i	0.0575312	+	0.0186930i
$404$	−4.70176	−	14.4705i	−0.233921	−	0.719936i
$405$		0			0
$406$		−	8.83669i		−	0.438557i
$407$	1.23225	−	17.2697i	0.0610805	−	0.856027i
$408$		0			0
$409$	4.22460	+	5.81466i	0.208893	+	0.287517i	0.900588	−	0.434673i	$-0.143136\pi$
$409$	4.22460	+	5.81466i	0.208893	+	0.287517i	−0.691695	+	0.722189i	$0.743136\pi$
$410$	−3.50888	+	1.14011i	−0.173291	+	0.0563058i
$411$		0			0
$412$	7.39067	+	5.36964i	0.364112	+	0.264543i
$413$	−7.85489	−	5.70691i	−0.386514	−	0.280819i
$414$		0			0
$415$	28.6282	−	9.30186i	1.40530	−	0.456610i
$416$	−2.39007	−	3.28964i	−0.117183	−	0.161288i
$417$		0			0
$418$	−4.89674	+	12.0705i	−0.239507	+	0.590387i
$419$			34.4025i			1.68067i	0.542067	+	0.840336i	$0.317642\pi$
$419$			34.4025i			1.68067i	−0.542067	+	0.840336i	$0.682358\pi$
$420$		0			0
$421$	4.79446	+	14.7558i	0.233668	+	0.719155i	0.997295	+	0.0734982i	$0.0234163\pi$
$421$	4.79446	+	14.7558i	0.233668	+	0.719155i	−0.763628	+	0.645657i	$0.776584\pi$
$422$	16.2228	+	5.27109i	0.789711	+	0.256593i
$423$		0			0
$424$	−1.04412	+	1.43710i	−0.0507068	+	0.0697919i
$425$	14.8529	−	45.7126i	0.720473	−	2.21739i
$426$		0			0
$427$	−7.13178	+	5.18154i	−0.345131	+	0.250752i
$428$	6.85252			0.331229
$429$		0			0
$430$	21.1429			1.01960
$431$	−26.0178	+	18.9030i	−1.25323	+	0.910527i	−0.998405	−	0.0564593i	$-0.982019\pi$
$431$	−26.0178	+	18.9030i	−1.25323	+	0.910527i	−0.254828	+	0.966986i	$0.582019\pi$
$432$		0			0
$433$	−9.27997	+	28.5608i	−0.445967	+	1.37255i	0.435453	+	0.900211i	$0.356588\pi$
$433$	−9.27997	+	28.5608i	−0.445967	+	1.37255i	−0.881420	+	0.472334i	$0.843412\pi$
$434$	0.175540	−	0.241611i	0.00842621	−	0.0115977i
$435$		0			0
$436$	6.19278	+	2.01215i	0.296580	+	0.0963647i
$437$	0.612433	+	1.88488i	0.0292967	+	0.0901658i
$438$		0			0
$439$			3.81805i			0.182225i	0.995841	+	0.0911127i	$0.0290424\pi$
$439$			3.81805i			0.182225i	−0.995841	+	0.0911127i	$0.970958\pi$
$440$	11.4441	+	0.816575i	0.545575	+	0.0389287i
$441$		0			0
$442$	16.4897	+	22.6961i	0.784335	+	1.07954i
$443$	38.5547	−	12.5272i	1.83179	−	0.595184i	0.832644	−	0.553808i	$-0.186826\pi$
$443$	38.5547	−	12.5272i	1.83179	−	0.595184i	0.999144	−	0.0413762i	$-0.0131742\pi$
$444$		0			0
$445$	−37.4091	−	27.1793i	−1.77336	−	1.28842i
$446$	9.42021	+	6.84418i	0.446060	+	0.324081i
$447$		0			0
$448$	−0.951057	+	0.309017i	−0.0449332	+	0.0145997i
$449$	−8.02605	−	11.0469i	−0.378773	−	0.521336i	0.576486	−	0.817107i	$-0.304423\pi$
$449$	−8.02605	−	11.0469i	−0.378773	−	0.521336i	−0.955259	+	0.295771i	$0.904423\pi$
$450$		0			0
$451$	1.87022	+	3.00246i	0.0880653	+	0.141380i
$452$		−	2.33684i		−	0.109916i
$453$		0			0
$454$	−7.44732	−	22.9205i	−0.349520	−	1.07571i
$455$	−13.3778	−	4.34671i	−0.627161	−	0.203777i
$456$		0			0
$457$	−23.8820	+	32.8708i	−1.11715	+	1.53763i	−0.306719	+	0.951800i	$0.599231\pi$
$457$	−23.8820	+	32.8708i	−1.11715	+	1.53763i	−0.810434	+	0.585830i	$0.800769\pi$
$458$	−1.77437	+	5.46095i	−0.0829108	+	0.255173i
$459$		0			0
$460$	1.41224	−	1.02605i	0.0658461	−	0.0478400i
$461$	−21.3938			−0.996409			−0.498205	−	0.867059i	$-0.666007\pi$
$461$	−21.3938			−0.996409			−0.498205	+	0.867059i	$0.666007\pi$
$462$		0			0
$463$	29.1597			1.35517			0.677583	−	0.735446i	$-0.263027\pi$
$463$	29.1597			1.35517			0.677583	+	0.735446i	$0.263027\pi$
$464$	7.14903	−	5.19407i	0.331885	−	0.241129i
$465$		0			0
$466$	6.54768	−	20.1517i	0.303315	−	0.933509i
$467$	−24.1375	+	33.2224i	−1.11695	+	1.53735i	−0.306189	+	0.951971i	$0.599054\pi$
$467$	−24.1375	+	33.2224i	−1.11695	+	1.53735i	−0.810761	+	0.585378i	$0.800946\pi$
$468$		0			0
$469$	−7.53643	−	2.44873i	−0.348000	−	0.113072i
$470$	3.76938	+	11.6010i	0.173869	+	0.535112i
$471$		0			0
$472$		−	9.70918i		−	0.446901i
$473$	−4.87606	−	19.6757i	−0.224201	−	0.904692i
$474$		0			0
$475$	−16.0827	−	22.1359i	−0.737923	−	1.01566i
$476$	6.56159	−	2.13199i	0.300750	−	0.0977196i
$477$		0			0
$478$	11.0717	+	8.04404i	0.506406	+	0.367926i
$479$	−16.5594	−	12.0311i	−0.756620	−	0.549717i	0.141251	−	0.989974i	$-0.454887\pi$
$479$	−16.5594	−	12.0311i	−0.756620	−	0.549717i	−0.897872	+	0.440257i	$0.854887\pi$
$480$		0			0
$481$	−20.1878	+	6.55940i	−0.920483	+	0.299083i
$482$	11.7771	+	16.2098i	0.536432	+	0.738335i
$483$		0			0
$484$	−1.87937	−	10.8383i	−0.0854257	−	0.492648i
$485$			31.5861i			1.43425i
$486$		0			0
$487$	−4.31736	−	13.2875i	−0.195638	−	0.602113i	−0.999969	−	0.00793029i	$-0.997476\pi$
$487$	−4.31736	−	13.2875i	−0.195638	−	0.602113i	0.804330	−	0.594183i	$-0.202524\pi$
$488$	−8.38391	−	2.72410i	−0.379522	−	0.123314i
$489$		0			0
$490$	−2.03332	+	2.79863i	−0.0918561	+	0.126429i
$491$	−8.51515	+	26.2069i	−0.384283	+	1.18270i	0.552716	+	0.833370i	$0.313592\pi$
$491$	−8.51515	+	26.2069i	−0.384283	+	1.18270i	−0.936999	+	0.349332i	$0.886408\pi$
$492$		0			0
$493$	−49.3231	+	35.8353i	−2.22140	+	1.61394i
$494$	15.9699			0.718522
$495$		0			0
$496$	0.298647			0.0134097
$497$	8.56026	−	6.21939i	0.383980	−	0.278978i
$498$		0			0
$499$	−5.19242	+	15.9806i	−0.232445	+	0.715391i	0.765005	+	0.644024i	$0.222736\pi$
$499$	−5.19242	+	15.9806i	−0.232445	+	0.715391i	−0.997450	+	0.0713674i	$0.977264\pi$
$500$	−3.99893	+	5.50405i	−0.178838	+	0.246149i
$501$		0			0
$502$	−19.1663	−	6.22752i	−0.855436	−	0.277948i
$503$	−0.470777	−	1.44890i	−0.0209909	−	0.0646034i	0.940012	−	0.341140i	$-0.110813\pi$
$503$	−0.470777	−	1.44890i	−0.0209909	−	0.0646034i	−0.961003	+	0.276537i	$0.910813\pi$
$504$		0			0
$505$		−	52.6339i		−	2.34218i
$506$	−1.28055	−	1.07761i	−0.0569274	−	0.0479056i
$507$		0			0
$508$	−4.60102	−	6.33277i	−0.204137	−	0.280971i
$509$	35.1141	−	11.4093i	1.55641	−	0.505707i	0.600561	−	0.799579i	$-0.294944\pi$
$509$	35.1141	−	11.4093i	1.55641	−	0.505707i	0.955845	+	0.293872i	$0.0949441\pi$
$510$		0			0
$511$	0.430464	+	0.312750i	0.0190426	+	0.0138353i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	16.1238	−	5.23893i	0.711189	−	0.231079i
$515$	18.5751	+	25.5665i	0.818519	+	1.12659i
$516$		0			0
$517$	9.92663	−	6.18327i	0.436573	−	0.271940i
$518$			5.22024i			0.229364i
$519$		0			0
$520$	−4.34671	−	13.3778i	−0.190616	−	0.586655i
$521$	12.3160	+	4.00170i	0.539573	+	0.175318i	0.566110	−	0.824330i	$-0.308448\pi$
$521$	12.3160	+	4.00170i	0.539573	+	0.175318i	−0.0265368	+	0.999648i	$0.508448\pi$
$522$		0			0
$523$	−14.7549	+	20.3084i	−0.645187	+	0.888023i	−0.998879	−	0.0473387i	$-0.984926\pi$
$523$	−14.7549	+	20.3084i	−0.645187	+	0.888023i	0.353692	+	0.935362i	$0.384926\pi$
$524$	−0.446982	+	1.37567i	−0.0195265	+	0.0600964i
$525$		0			0
$526$	19.7466	−	14.3467i	0.860991	−	0.625547i
$527$	−2.06045			−0.0897544
$528$		0			0
$529$	22.7454			0.988929
$530$	−4.97136	+	3.61190i	−0.215942	+	0.156891i
$531$		0			0
$532$	1.21365	−	3.73524i	0.0526186	−	0.161943i
$533$	2.54909	−	3.50852i	0.110413	−	0.151971i
$534$		0			0
$535$	22.5447	+	7.32521i	0.974691	+	0.316696i
$536$	−2.44873	−	7.53643i	−0.105769	−	0.325524i
$537$		0			0
$538$		−	21.3788i		−	0.921707i
$539$	3.07335	+	1.24679i	0.132379	+	0.0537032i
$540$		0			0
$541$	16.4681	+	22.6664i	0.708019	+	0.974504i	0.999837	+	0.0180308i	$0.00573968\pi$
$541$	16.4681	+	22.6664i	0.708019	+	0.974504i	−0.291818	+	0.956474i	$0.594260\pi$
$542$	−6.23874	+	2.02709i	−0.267977	+	0.0870710i
$543$		0			0
$544$	5.58162	+	4.05529i	0.239310	+	0.173869i
$545$	18.2232	+	13.2399i	0.780595	+	0.567135i
$546$		0			0
$547$	39.6134	−	12.8712i	1.69375	−	0.550332i	0.706249	−	0.707964i	$-0.250386\pi$
$547$	39.6134	−	12.8712i	1.69375	−	0.550332i	0.987498	+	0.157632i	$0.0503859\pi$
$548$	7.13789	+	9.82447i	0.304916	+	0.419680i
$549$		0			0
$550$	21.4111	+	8.68604i	0.912974	+	0.370374i
$551$			34.7058i			1.47852i
$552$		0			0
$553$	−4.72009	−	14.5270i	−0.200719	−	0.617749i
$554$	31.4699	+	10.2252i	1.33703	+	0.434427i
$555$		0			0
$556$	0.143575	−	0.197614i	0.00608895	−	0.00838072i
$557$	−2.34133	+	7.20587i	−0.0992054	+	0.305323i	−0.988327	−	0.152349i	$-0.951316\pi$
$557$	−2.34133	+	7.20587i	−0.0992054	+	0.305323i	0.889121	+	0.457671i	$0.151316\pi$
$558$		0			0
$559$	−20.1060	+	14.6079i	−0.850394	+	0.617848i
$560$	−3.45929			−0.146182
$561$		0			0
$562$	−23.2436			−0.980474
$563$	−21.4494	+	15.5839i	−0.903985	+	0.656784i	−0.939486	−	0.342586i	$-0.888697\pi$
$563$	−21.4494	+	15.5839i	−0.903985	+	0.656784i	0.0355014	+	0.999370i	$0.488697\pi$
$564$		0			0
$565$	2.49804	−	7.68816i	0.105093	−	0.323443i
$566$	8.14821	−	11.2150i	0.342495	−	0.471404i
$567$		0			0
$568$	10.0632	+	3.26973i	0.422242	+	0.137195i
$569$	0.199823	+	0.614993i	0.00837702	+	0.0257818i	0.955158	−	0.296098i	$-0.0956854\pi$
$569$	0.199823	+	0.614993i	0.00837702	+	0.0257818i	−0.946781	+	0.321880i	$0.895685\pi$
$570$		0			0
$571$		−	19.7626i		−	0.827039i	−0.910495	−	0.413520i	$-0.864299\pi$
$571$		−	19.7626i		−	0.827039i	0.910495	−	0.413520i	$-0.135701\pi$
$572$	−11.4470	+	7.13032i	−0.478624	+	0.298134i
$573$		0			0
$574$	−0.626894	−	0.862845i	−0.0261660	−	0.0360145i
$575$	3.34347	−	1.08636i	0.139432	−	0.0453043i
$576$		0			0
$577$	32.8251	+	23.8488i	1.36653	+	0.992840i	0.997999	+	0.0632226i	$0.0201378\pi$
$577$	32.8251	+	23.8488i	1.36653	+	0.992840i	0.368527	+	0.929617i	$0.379862\pi$
$578$	−24.7558	−	17.9861i	−1.02971	−	0.748125i
$579$		0			0
$580$	29.0725	−	9.44624i	1.20717	−	0.392234i
$581$	5.11469	+	7.03976i	0.212193	+	0.292059i
$582$		0			0
$583$	4.50778	+	3.79339i	0.186693	+	0.157106i
$584$			0.532082i			0.0220177i
$585$		0			0
$586$	−4.58227	−	14.1028i	−0.189292	−	0.582580i
$587$	25.5666	+	8.30709i	1.05525	+	0.342870i	0.784725	−	0.619844i	$-0.212804\pi$
$587$	25.5666	+	8.30709i	1.05525	+	0.342870i	0.270521	+	0.962714i	$0.412804\pi$
$588$		0			0
$589$	−0.689429	+	0.948917i	−0.0284074	+	0.0390995i
$590$	10.3789	−	31.9430i	0.427293	−	1.31507i
$591$		0			0
$592$	−4.22327	+	3.06838i	−0.173575	+	0.126110i
$593$	−26.4875			−1.08771			−0.543856	−	0.839179i	$-0.683036\pi$
$593$	−26.4875			−1.08771			−0.543856	+	0.839179i	$0.683036\pi$
$594$		0			0
$595$	23.8666			0.978434
$596$	−1.38345	+	1.00514i	−0.0566684	+	0.0411720i
$597$		0			0
$598$	−0.634070	+	1.95147i	−0.0259291	+	0.0798015i
$599$	8.74977	−	12.0430i	0.357506	−	0.492065i	−0.591946	−	0.805978i	$-0.701640\pi$
$599$	8.74977	−	12.0430i	0.357506	−	0.492065i	0.949452	+	0.313913i	$0.101640\pi$
$600$		0			0
$601$	−40.3320	−	13.1047i	−1.64518	−	0.534550i	−0.667490	−	0.744618i	$-0.732632\pi$
$601$	−40.3320	−	13.1047i	−1.64518	−	0.534550i	−0.977687	+	0.210068i	$0.932632\pi$
$602$	1.88869	+	5.81278i	0.0769771	+	0.236911i
$603$		0			0
$604$		−	14.3950i		−	0.585726i
$605$	5.40281	−	37.6667i	0.219655	−	1.53137i
$606$		0			0
$607$	2.63984	+	3.63343i	0.107148	+	0.147476i	0.859223	−	0.511600i	$-0.170947\pi$
$607$	2.63984	+	3.63343i	0.107148	+	0.147476i	−0.752076	+	0.659077i	$0.770947\pi$
$608$	3.73524	−	1.21365i	0.151484	−	0.0492201i
$609$		0			0
$610$	−24.6709	−	17.9245i	−0.998895	−	0.725740i
$611$	−11.5998	−	8.42772i	−0.469276	−	0.340949i
$612$		0			0
$613$	2.26626	−	0.736351i	0.0915332	−	0.0297409i	−0.262892	−	0.964825i	$-0.584676\pi$
$613$	2.26626	−	0.736351i	0.0915332	−	0.0297409i	0.354426	+	0.935084i	$0.384676\pi$
$614$	−7.64379	−	10.5208i	−0.308478	−	0.424584i
$615$		0			0
$616$	0.797795	+	3.21924i	0.0321441	+	0.129707i
$617$			13.3188i			0.536194i	0.963392	+	0.268097i	$0.0863947\pi$
$617$			13.3188i			0.536194i	−0.963392	+	0.268097i	$0.913605\pi$
$618$		0			0
$619$	−13.7272	−	42.2480i	−0.551743	−	1.69809i	−0.704393	−	0.709810i	$-0.748781\pi$
$619$	−13.7272	−	42.2480i	−0.551743	−	1.69809i	0.152650	−	0.988280i	$-0.451219\pi$
$620$	0.982544	+	0.319248i	0.0394599	+	0.0128213i
$621$		0			0
$622$	19.2582	−	26.5066i	0.772182	−	1.06282i
$623$	4.13062	−	12.7127i	0.165490	−	0.509325i
$624$		0			0
$625$	9.14076	−	6.64115i	0.365631	−	0.265646i
$626$	21.8095			0.871684
$627$		0			0
$628$	20.0546			0.800264
$629$	29.1374	−	21.1696i	1.16179	−	0.844087i
$630$		0			0
$631$	2.83329	−	8.71996i	0.112791	−	0.347136i	−0.878689	−	0.477395i	$-0.841581\pi$
$631$	2.83329	−	8.71996i	0.112791	−	0.347136i	0.991480	+	0.130259i	$0.0415810\pi$
$632$	8.97815	−	12.3574i	0.357132	−	0.491550i
$633$		0			0
$634$	23.4394	+	7.61593i	0.930898	+	0.302467i
$635$	−8.36769	−	25.7531i	−0.332062	−	1.02198i
$636$		0			0
$637$		−	4.06622i		−	0.161110i
$638$	−15.4956	−	24.8766i	−0.613475	−	0.984874i
$639$		0			0
$640$	−2.03332	−	2.79863i	−0.0803741	−	0.110625i
$641$	8.88830	−	2.88798i	0.351067	−	0.114068i	−0.128175	−	0.991752i	$-0.540912\pi$
$641$	8.88830	−	2.88798i	0.351067	−	0.114068i	0.479241	+	0.877683i	$0.340912\pi$
$642$		0			0
$643$	−15.4968	−	11.2591i	−0.611134	−	0.444015i	0.238680	−	0.971098i	$-0.423285\pi$
$643$	−15.4968	−	11.2591i	−0.611134	−	0.444015i	−0.849813	+	0.527084i	$0.823285\pi$
$644$	0.408246	+	0.296608i	0.0160871	+	0.0116880i
$645$		0			0
$646$	−25.7704	+	8.37332i	−1.01392	+	0.329444i
$647$	13.2560	+	18.2453i	0.521145	+	0.717295i	0.985749	−	0.168224i	$-0.0538031\pi$
$647$	13.2560	+	18.2453i	0.521145	+	0.717295i	−0.464603	+	0.885519i	$0.653803\pi$
$648$		0			0
$649$	−32.1201	−	2.29188i	−1.26082	−	0.0899641i
$650$		−	28.3281i		−	1.11112i
$651$		0			0
$652$	0.843445	+	2.59586i	0.0330319	+	0.101662i
$653$	0.844245	+	0.274312i	0.0330378	+	0.0107346i	0.325489	−	0.945546i	$-0.394471\pi$
$653$	0.844245	+	0.274312i	0.0330378	+	0.0107346i	−0.292451	+	0.956280i	$0.594471\pi$
$654$		0			0
$655$	−2.94112	+	4.04811i	−0.114919	+	0.158173i
$656$	0.329578	−	1.01434i	0.0128678	−	0.0396032i
$657$		0			0
$658$	−2.85271	+	2.07262i	−0.111210	+	0.0807990i
$659$	20.5604			0.800921			0.400461	−	0.916314i	$-0.368850\pi$
$659$	20.5604			0.800921			0.400461	+	0.916314i	$0.368850\pi$
$660$		0			0
$661$	−32.3861			−1.25968			−0.629838	−	0.776727i	$-0.716879\pi$
$661$	−32.3861			−1.25968			−0.629838	+	0.776727i	$0.716879\pi$
$662$	1.16876	−	0.849153i	0.0454251	−	0.0330033i
$663$		0			0
$664$	−2.68895	+	8.27574i	−0.104352	+	0.321161i
$665$	7.98580	−	10.9915i	0.309676	−	0.426232i
$666$		0			0
$667$	−4.24092	−	1.37796i	−0.164209	−	0.0533547i
$668$	−6.06512	−	18.6665i	−0.234666	−	0.722229i
$669$		0			0
$670$		−	27.4124i		−	1.05903i
$671$	−10.9909	+	27.0927i	−0.424300	+	1.04590i
$672$		0			0
$673$	7.95742	+	10.9524i	0.306736	+	0.422186i	0.934360	−	0.356331i	$-0.115972\pi$
$673$	7.95742	+	10.9524i	0.306736	+	0.422186i	−0.627624	+	0.778517i	$0.715972\pi$
$674$	−31.3207	+	10.1767i	−1.20643	+	0.391992i
$675$		0			0
$676$	2.85920	+	2.07733i	0.109969	+	0.0798972i
$677$	24.3891	+	17.7197i	0.937349	+	0.681024i	0.947781	−	0.318922i	$-0.103321\pi$
$677$	24.3891	+	17.7197i	0.937349	+	0.681024i	−0.0104322	+	0.999946i	$0.503321\pi$
$678$		0			0
$679$	−8.68392	+	2.82158i	−0.333258	+	0.108282i
$680$	14.0284	+	19.3085i	0.537965	+	0.740446i
$681$		0			0
$682$	0.0704964	−	0.987989i	0.00269945	−	0.0378320i
$683$			10.6073i			0.405876i	0.979192	+	0.202938i	$0.0650491\pi$
$683$			10.6073i			0.405876i	−0.979192	+	0.202938i	$0.934951\pi$
$684$		0			0
$685$	12.9814	+	39.9526i	0.495993	+	1.52651i
$686$	−0.951057	−	0.309017i	−0.0363115	−	0.0117983i
$687$		0			0
$688$	−3.59250	+	4.94465i	−0.136963	+	0.188513i
$689$	2.23205	−	6.86954i	0.0850343	−	0.261709i
$690$		0			0
$691$	28.1851	−	20.4777i	1.07221	−	0.779009i	0.0959047	−	0.995391i	$-0.469426\pi$
$691$	28.1851	−	20.4777i	1.07221	−	0.779009i	0.976309	+	0.216382i	$0.0694256\pi$
$692$	18.0181			0.684943
$693$		0			0
$694$	−36.2100			−1.37451
$695$	0.683606	−	0.496669i	0.0259306	−	0.0188397i
$696$		0			0
$697$	−2.27384	+	6.99817i	−0.0861280	+	0.265075i
$698$	−2.43878	+	3.35669i	−0.0923091	+	0.127053i
$699$		0			0
$700$	−6.62572	−	2.15283i	−0.250429	−	0.0813693i
$701$	−15.6713	−	48.2312i	−0.591895	−	1.82167i	−0.569611	−	0.821914i	$-0.692906\pi$
$701$	−15.6713	−	48.2312i	−0.591895	−	1.82167i	−0.0222841	−	0.999752i	$-0.507094\pi$
$702$		0			0
$703$		−	20.5023i		−	0.773260i
$704$	−2.13549	+	2.53765i	−0.0804843	+	0.0956414i
$705$		0			0
$706$	8.22761	+	11.3243i	0.309650	+	0.426197i
$707$	14.4705	−	4.70176i	0.544220	−	0.176828i
$708$		0			0
$709$	5.86911	+	4.26416i	0.220419	+	0.160144i	0.692515	−	0.721403i	$-0.256503\pi$
$709$	5.86911	+	4.26416i	0.220419	+	0.160144i	−0.472096	+	0.881547i	$0.656503\pi$
$710$	29.6124	+	21.5147i	1.11133	+	0.807432i
$711$		0			0
$712$	12.7127	−	4.13062i	0.476430	−	0.154802i
$713$	−0.0885811	−	0.121921i	−0.00331739	−	0.00456599i
$714$		0			0
$715$	−45.2827	+	11.2220i	−1.69348	+	0.419678i
$716$			11.0675i			0.413612i
$717$		0			0
$718$	9.11755	+	28.0609i	0.340264	+	1.04723i
$719$	20.8525	+	6.77540i	0.777669	+	0.252680i	0.670845	−	0.741598i	$-0.265932\pi$
$719$	20.8525	+	6.77540i	0.777669	+	0.252680i	0.106824	+	0.994278i	$0.465932\pi$
$720$		0			0
$721$	−5.36964	+	7.39067i	−0.199976	+	0.275243i
$722$	1.10474	−	3.40004i	0.0411142	−	0.126537i
$723$		0			0
$724$	2.07397	−	1.50683i	0.0770786	−	0.0560009i
$725$	61.5625			2.28638
$726$		0			0
$727$	−12.6373			−0.468691			−0.234345	−	0.972153i	$-0.575295\pi$
$727$	−12.6373			−0.468691			−0.234345	+	0.972153i	$0.575295\pi$
$728$	3.28964	−	2.39007i	0.121922	−	0.0885817i
$729$		0			0
$730$	−0.568785	+	1.75054i	−0.0210517	+	0.0647905i
$731$	24.7856	−	34.1144i	0.916728	−	1.26177i
$732$		0			0
$733$	27.1165	+	8.81069i	1.00157	+	0.325430i	0.763493	−	0.645816i	$-0.223483\pi$
$733$	27.1165	+	8.81069i	1.00157	+	0.325430i	0.238078	+	0.971246i	$0.423483\pi$
$734$	0.385198	+	1.18552i	0.0142179	+	0.0437583i
$735$		0			0
$736$			0.504619i			0.0186005i
$737$	−25.5102	+	6.32194i	−0.939679	+	0.232872i
$738$		0			0
$739$	11.7502	+	16.1728i	0.432239	+	0.594926i	0.968465	−	0.249148i	$-0.0801507\pi$
$739$	11.7502	+	16.1728i	0.432239	+	0.594926i	−0.536226	+	0.844074i	$0.680151\pi$
$740$	−17.1745	+	5.58034i	−0.631348	+	0.205137i
$741$		0			0
$742$	−1.43710	−	1.04412i	−0.0527577	−	0.0383307i
$743$	6.58621	+	4.78516i	0.241625	+	0.175551i	0.702007	−	0.712170i	$-0.252288\pi$
$743$	6.58621	+	4.78516i	0.241625	+	0.175551i	−0.460382	+	0.887721i	$0.652288\pi$
$744$		0			0
$745$	−5.62600	+	1.82800i	−0.206121	+	0.0669727i
$746$	−14.9660	−	20.5990i	−0.547945	−	0.754181i
$747$		0			0
$748$	14.7333	−	17.5079i	0.538703	−	0.640154i
$749$			6.85252i			0.250386i
$750$		0			0
$751$	−12.4364	−	38.2752i	−0.453810	−	1.39668i	−0.872527	−	0.488566i	$-0.837520\pi$
$751$	−12.4364	−	38.2752i	−0.453810	−	1.39668i	0.418717	−	0.908117i	$-0.362480\pi$
$752$	−3.35357	−	1.08964i	−0.122292	−	0.0397351i
$753$		0			0
$754$	−21.1203	+	29.0695i	−0.769154	+	1.05865i
$755$	15.3880	−	47.3594i	0.560027	−	1.72359i
$756$		0			0
$757$	−1.10602	+	0.803567i	−0.0401988	+	0.0292062i	−0.607703	−	0.794164i	$-0.707909\pi$
$757$	−1.10602	+	0.803567i	−0.0401988	+	0.0292062i	0.567504	+	0.823370i	$0.307909\pi$
$758$	3.54687			0.128828
$759$		0			0
$760$	13.5862			0.492825
$761$	8.12517	−	5.90328i	0.294537	−	0.213994i	−0.430696	−	0.902497i	$-0.641732\pi$
$761$	8.12517	−	5.90328i	0.294537	−	0.213994i	0.725233	+	0.688503i	$0.241732\pi$
$762$		0			0
$763$	−2.01215	+	6.19278i	−0.0728449	+	0.224194i
$764$	−9.87183	+	13.5874i	−0.357150	+	0.491575i
$765$		0			0
$766$	19.4753	+	6.32790i	0.703670	+	0.228636i
$767$	12.1999	+	37.5474i	0.440513	+	1.35576i
$768$		0			0
$769$			8.29828i			0.299243i	0.988743	+	0.149622i	$0.0478056\pi$
$769$			8.29828i			0.299243i	−0.988743	+	0.149622i	$0.952194\pi$
$770$	−0.816575	+	11.4441i	−0.0294273	+	0.412416i
$771$		0			0
$772$	6.55214	+	9.01824i	0.235817	+	0.324574i
$773$	−15.0974	+	4.90545i	−0.543017	+	0.176437i	−0.567666	−	0.823259i	$-0.692153\pi$
$773$	−15.0974	+	4.90545i	−0.543017	+	0.176437i	0.0246486	+	0.999696i	$0.492153\pi$
$774$		0			0
$775$	1.68323	+	1.22294i	0.0604633	+	0.0439292i
$776$	−7.38698	−	5.36695i	−0.265177	−	0.192662i
$777$		0			0
$778$	−25.6768	+	8.34289i	−0.920557	+	0.299107i
$779$	2.46210	+	3.38880i	0.0882140	+	0.121416i
$780$		0			0
$781$	13.1924	−	32.5193i	0.472061	−	1.16363i
$782$		−	3.48150i		−	0.124498i
$783$		0			0
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	65.9792	+	21.4379i	2.35490	+	0.765153i
$786$		0			0
$787$	−27.2838	+	37.5530i	−0.972563	+	1.33862i	−0.0318221	+	0.999494i	$0.510131\pi$
$787$	−27.2838	+	37.5530i	−0.972563	+	1.33862i	−0.940741	+	0.339125i	$0.889869\pi$
$788$	6.08474	−	18.7269i	0.216760	−	0.667118i
$789$		0			0
$790$	42.7477	−	31.0581i	1.52090	−	1.10500i
$791$	2.33684			0.0830885
$792$		0			0
$793$	35.8452			1.27290
$794$	−9.51569	+	6.91355i	−0.337699	+	0.245353i
$795$		0			0
$796$	−2.68106	+	8.25145i	−0.0950276	+	0.292465i
$797$	−30.8421	+	42.4506i	−1.09248	+	1.50368i	−0.247498	+	0.968888i	$0.579608\pi$
$797$	−30.8421	+	42.4506i	−1.09248	+	1.50368i	−0.844986	+	0.534788i	$0.820392\pi$
$798$		0			0
$799$	23.1371	+	7.51771i	0.818533	+	0.265958i
$800$	−2.15283	−	6.62572i	−0.0761140	−	0.234255i
$801$		0			0
$802$		−	0.119891i		−	0.00423351i
$803$	1.76024	+	0.125599i	0.0621176	+	0.00443231i
$804$		0			0
$805$	1.02605	+	1.41224i	0.0361636	+	0.0497750i
$806$	−1.15493	+	0.375260i	−0.0406807	+	0.0132180i
$807$		0			0
$808$	12.3094	+	8.94328i	0.433042	+	0.314623i
$809$	17.3773	+	12.6254i	0.610954	+	0.443884i	0.849750	−	0.527186i	$-0.176753\pi$
$809$	17.3773	+	12.6254i	0.610954	+	0.443884i	−0.238796	+	0.971070i	$0.576753\pi$
$810$		0			0
$811$	8.72885	−	2.83618i	0.306511	−	0.0995916i	−0.151723	−	0.988423i	$-0.548482\pi$
$811$	8.72885	−	2.83618i	0.306511	−	0.0995916i	0.458234	+	0.888831i	$0.348482\pi$
$812$	5.19407	+	7.14903i	0.182276	+	0.250882i
$813$		0			0
$814$	9.15395	+	14.6958i	0.320846	+	0.515086i
$815$			9.44195i			0.330737i
$816$		0			0
$817$	−7.41775	−	22.8295i	−0.259514	−	0.798703i
$818$	−6.83555	−	2.22100i	−0.238999	−	0.0776556i
$819$		0			0
$820$	2.16861	−	2.98483i	0.0757311	−	0.104235i
$821$	5.25230	−	16.1649i	0.183307	−	0.564160i	−0.816609	−	0.577192i	$-0.804148\pi$
$821$	5.25230	−	16.1649i	0.183307	−	0.564160i	0.999915	+	0.0130324i	$0.00414845\pi$
$822$		0			0
$823$	0.133208	−	0.0967814i	0.00464335	−	0.00337359i	−0.585461	−	0.810700i	$-0.699087\pi$
$823$	0.133208	−	0.0967814i	0.00464335	−	0.00337359i	0.590105	+	0.807327i	$0.299087\pi$
$824$	−9.13537			−0.318246
$825$		0			0
$826$	9.70918			0.337826
$827$	10.9034	−	7.92181i	0.379150	−	0.275468i	−0.381845	−	0.924226i	$-0.624711\pi$
$827$	10.9034	−	7.92181i	0.379150	−	0.275468i	0.760995	+	0.648758i	$0.224711\pi$
$828$		0			0
$829$	−1.44988	+	4.46228i	−0.0503565	+	0.154981i	−0.973073	−	0.230499i	$-0.925964\pi$
$829$	−1.44988	+	4.46228i	−0.0503565	+	0.154981i	0.922716	+	0.385480i	$0.125964\pi$
$830$	−17.6932	+	24.3526i	−0.614140	+	0.845291i
$831$		0			0
$832$	3.86721	+	1.25653i	0.134071	+	0.0435624i
$833$	2.13199	+	6.56159i	0.0738691	+	0.227346i
$834$		0			0
$835$		−	67.8960i		−	2.34964i
$836$	−3.13331	−	12.6435i	−0.108368	−	0.437283i
$837$		0			0
$838$	−20.2213	−	27.8322i	−0.698532	−	0.961447i
$839$	17.6985	−	5.75060i	0.611021	−	0.198533i	0.0128714	−	0.999917i	$-0.495903\pi$
$839$	17.6985	−	5.75060i	0.611021	−	0.198533i	0.598150	+	0.801384i	$0.295903\pi$
$840$		0			0
$841$	−39.7122	−	28.8526i	−1.36939	−	0.994918i
$842$	−12.5521	−	9.11960i	−0.432572	−	0.314282i
$843$		0			0
$844$	−16.2228	+	5.27109i	−0.558410	+	0.181438i
$845$	7.18608	+	9.89079i	0.247209	+	0.340254i
$846$		0			0
$847$	10.8383	−	1.87937i	0.372407	−	0.0645758i
$848$		−	1.77636i		−	0.0610004i
$849$		0			0
$850$	14.8529	+	45.7126i	0.509451	+	1.56793i
$851$	2.50531	+	0.814024i	0.0858809	+	0.0279044i
$852$		0			0
$853$	13.2135	−	18.1868i	0.452421	−	0.622703i	−0.520495	−	0.853865i	$-0.674253\pi$
$853$	13.2135	−	18.1868i	0.452421	−	0.622703i	0.972915	+	0.231161i	$0.0742525\pi$
$854$	2.72410	−	8.38391i	0.0932167	−	0.286891i
$855$		0			0
$856$	−5.54381	+	4.02781i	−0.189483	+	0.137668i
$857$	17.3406			0.592343			0.296171	−	0.955135i	$-0.404290\pi$
$857$	17.3406			0.592343			0.296171	+	0.955135i	$0.404290\pi$
$858$		0			0
$859$	−11.9833			−0.408865			−0.204432	−	0.978881i	$-0.565535\pi$
$859$	−11.9833			−0.408865			−0.204432	+	0.978881i	$0.565535\pi$
$860$	−17.1050	+	12.4275i	−0.583275	+	0.423774i
$861$		0			0
$862$	9.93791	−	30.5858i	0.338487	−	1.04175i
$863$	8.36827	−	11.5179i	0.284859	−	0.392075i	−0.642477	−	0.766305i	$-0.722093\pi$
$863$	8.36827	−	11.5179i	0.284859	−	0.392075i	0.927336	+	0.374230i	$0.122093\pi$
$864$		0			0
$865$	59.2791	+	19.2609i	2.01555	+	0.654891i
$866$	−9.27997	−	28.5608i	−0.315346	−	0.970536i
$867$		0			0
$868$			0.298647i			0.0101367i
$869$	−38.7615	−	32.6186i	−1.31489	−	1.10651i
$870$		0			0
$871$	18.9395	+	26.0680i	0.641741	+	0.883281i
$872$	−6.19278	+	2.01215i	−0.209714	+	0.0681402i
$873$		0			0
$874$	−1.60337	−	1.16492i	−0.0542348	−	0.0394039i
$875$	−5.50405	−	3.99893i	−0.186071	−	0.135188i
$876$		0			0
$877$	23.1235	−	7.51328i	0.780825	−	0.253705i	0.108632	−	0.994082i	$-0.465353\pi$
$877$	23.1235	−	7.51328i	0.780825	−	0.253705i	0.672192	+	0.740377i	$0.265353\pi$
$878$	−2.24419	−	3.08887i	−0.0757378	−	0.104244i
$879$		0			0
$880$	−9.73842	+	6.06604i	−0.328282	+	0.204486i
$881$			9.32819i			0.314275i	0.987577	+	0.157137i	$0.0502266\pi$
$881$			9.32819i			0.314275i	−0.987577	+	0.157137i	$0.949773\pi$
$882$		0			0
$883$	−12.4187	−	38.2208i	−0.417922	−	1.28623i	−0.909611	−	0.415461i	$-0.863620\pi$
$883$	−12.4187	−	38.2208i	−0.417922	−	1.28623i	0.491689	−	0.870771i	$-0.336380\pi$
$884$	−26.6809	−	8.66915i	−0.897375	−	0.291575i
$885$		0			0
$886$	−23.8281	+	32.7966i	−0.800521	+	1.10182i
$887$	1.44348	−	4.44258i	0.0484674	−	0.149167i	−0.923894	−	0.382649i	$-0.875012\pi$
$887$	1.44348	−	4.44258i	0.0484674	−	0.149167i	0.972361	+	0.233482i	$0.0750119\pi$
$888$		0			0
$889$	6.33277	−	4.60102i	0.212394	−	0.154313i
$890$	46.2402			1.54998
$891$		0			0
$892$	−11.6440			−0.389871
$893$	11.2039	−	8.14013i	0.374925	−	0.272399i
$894$		0			0
$895$	−11.8309	+	36.4119i	−0.395465	+	1.21712i
$896$	0.587785	−	0.809017i	0.0196365	−	0.0270274i
$897$		0			0
$898$	12.9864	+	4.21954i	0.433362	+	0.140808i
$899$	−0.815512	−	2.50989i	−0.0271988	−	0.0837094i
$900$		0			0
$901$			12.2556i			0.408292i
$902$	−3.27784	−	1.32975i	−0.109140	−	0.0442758i
$903$		0			0
$904$	1.37356	+	1.89054i	0.0456839	+	0.0628785i
$905$	8.43411	−	2.74041i	0.280359	−	0.0910942i
$906$		0			0
$907$	−7.73694	−	5.62122i	−0.256901	−	0.186649i	0.451879	−	0.892079i	$-0.350754\pi$
$907$	−7.73694	−	5.62122i	−0.256901	−	0.186649i	−0.708780	+	0.705430i	$0.750754\pi$
$908$	19.4973	+	14.1656i	0.647041	+	0.470103i
$909$		0			0
$910$	13.3778	−	4.34671i	0.443470	−	0.144092i
$911$	−22.3498	−	30.7619i	−0.740482	−	1.01919i	−0.998591	−	0.0530699i	$-0.983099\pi$
$911$	−22.3498	−	30.7619i	−0.740482	−	1.01919i	0.258109	−	0.966116i	$-0.416901\pi$
$912$		0			0
$913$	26.7432	+	10.8491i	0.885070	+	0.359054i
$914$		−	40.6305i		−	1.34394i
$915$		0			0
$916$	−1.77437	−	5.46095i	−0.0586268	−	0.180435i
$917$	−1.37567	−	0.446982i	−0.0454286	−	0.0147606i
$918$		0			0
$919$	−22.1257	+	30.4535i	−0.729861	+	1.00457i	0.269277	+	0.963063i	$0.413215\pi$
$919$	−22.1257	+	30.4535i	−0.729861	+	1.00457i	−0.999138	+	0.0415047i	$0.986785\pi$
$920$	−0.539428	+	1.66019i	−0.0177844	+	0.0547348i
$921$		0			0
$922$	17.3080	−	12.5750i	0.570007	−	0.414135i
$923$	−43.0249			−1.41618
$924$		0			0
$925$	−36.3679			−1.19577
$926$	−23.5907	+	17.1396i	−0.775238	+	0.563244i
$927$		0			0
$928$	−2.73069	+	8.40419i	−0.0896392	+	0.275881i
$929$	−10.1884	+	14.0231i	−0.334271	+	0.460084i	−0.942757	−	0.333480i	$-0.891777\pi$
$929$	−10.1884	+	14.0231i	−0.334271	+	0.460084i	0.608486	+	0.793564i	$0.291777\pi$
$930$		0			0
$931$	3.73524	+	1.21365i	0.122418	+	0.0397759i
$932$	6.54768	+	20.1517i	0.214476	+	0.660090i
$933$		0			0
$934$		−	41.0651i		−	1.34369i
$935$	67.1880	−	41.8512i	2.19728	−	1.36868i
$936$		0			0
$937$	13.7238	+	18.8891i	0.448336	+	0.617081i	0.972039	−	0.234819i	$-0.0754499\pi$
$937$	13.7238	+	18.8891i	0.448336	+	0.617081i	−0.523703	+	0.851901i	$0.675450\pi$
$938$	7.53643	−	2.44873i	0.246073	−	0.0799540i
$939$		0			0
$940$	−9.86837	−	7.16979i	−0.321871	−	0.233853i
$941$	6.79416	+	4.93625i	0.221483	+	0.160917i	0.692994	−	0.720943i	$-0.256291\pi$
$941$	6.79416	+	4.93625i	0.221483	+	0.160917i	−0.471511	+	0.881860i	$0.656291\pi$
$942$		0			0
$943$	−0.511854	+	0.166311i	−0.0166682	+	0.00541584i
$944$	5.70691	+	7.85489i	0.185744	+	0.255655i
$945$		0			0
$946$	15.5099	+	13.0519i	0.504271	+	0.424355i
$947$			20.6485i			0.670986i	0.942043	+	0.335493i	$0.108903\pi$
$947$			20.6485i			0.670986i	−0.942043	+	0.335493i	$0.891097\pi$
$948$		0			0
$949$	−0.668578	−	2.05767i	−0.0217030	−	0.0667949i
$950$	26.0223	+	8.45516i	0.844275	+	0.274322i
$951$		0			0
$952$	−4.05529	+	5.58162i	−0.131433	+	0.180901i
$953$	−16.4088	+	50.5012i	−0.531534	+	1.63589i	0.219488	+	0.975615i	$0.429561\pi$
$953$	−16.4088	+	50.5012i	−0.531534	+	1.63589i	−0.751022	+	0.660278i	$0.770439\pi$
$954$		0			0
$955$	−47.0028	+	34.1495i	−1.52097	+	1.10505i
$956$	−13.6853			−0.442615
$957$		0			0
$958$	20.4686			0.661311
$959$	−9.82447	+	7.13789i	−0.317249	+	0.230495i
$960$		0			0
$961$	−9.55197	+	29.3979i	−0.308128	+	0.948320i
$962$	12.4767	−	17.1727i	0.402266	−	0.553671i
$963$		0			0
$964$	−19.0557	−	6.19158i	−0.613744	−	0.199417i
$965$	11.9161	+	36.6740i	0.383592	+	1.18058i
$966$		0			0
$967$		−	41.8042i		−	1.34433i	−0.740400	−	0.672166i	$-0.765364\pi$
$967$		−	41.8042i		−	1.34433i	0.740400	−	0.672166i	$-0.234636\pi$
$968$	7.89101	+	7.66368i	0.253627	+	0.246320i
$969$		0			0
$970$	−18.5659	−	25.5537i	−0.596114	−	0.820480i
$971$	−2.03007	+	0.659608i	−0.0651479	+	0.0211678i	−0.341410	−	0.939915i	$-0.610904\pi$
$971$	−2.03007	+	0.659608i	−0.0651479	+	0.0211678i	0.276262	+	0.961082i	$0.410904\pi$
$972$		0			0
$973$	0.197614	+	0.143575i	0.00633523	+	0.00460281i
$974$	11.3030	+	8.21211i	0.362171	+	0.263133i
$975$		0			0
$976$	8.38391	−	2.72410i	0.268362	−	0.0871962i
$977$	0.317090	+	0.436438i	0.0101446	+	0.0139629i	0.814059	−	0.580782i	$-0.197253\pi$
$977$	0.317090	+	0.436438i	0.0101446	+	0.0139629i	−0.803915	+	0.594745i	$0.797253\pi$
$978$		0			0
$979$	−10.6641	−	43.0315i	−0.340826	−	1.37529i
$980$		−	3.45929i		−	0.110503i
$981$		0			0
$982$	−8.51515	−	26.2069i	−0.271729	−	0.836297i
$983$	18.2350	+	5.92491i	0.581606	+	0.188975i	0.585020	−	0.811019i	$-0.301087\pi$
$983$	18.2350	+	5.92491i	0.581606	+	0.188975i	−0.00341398	+	0.999994i	$0.501087\pi$
$984$		0			0
$985$	40.0374	−	55.1067i	1.27570	−	1.75585i
$986$	18.8397	−	57.9827i	0.599979	−	1.84655i
$987$		0			0
$988$	−12.9200	+	9.38690i	−0.411039	+	0.298637i
$989$	3.08419			0.0980716
$990$		0			0
$991$	−7.86347			−0.249791			−0.124896	−	0.992170i	$-0.539860\pi$
$991$	−7.86347			−0.249791			−0.124896	+	0.992170i	$0.539860\pi$
$992$	−0.241611	+	0.175540i	−0.00767114	+	0.00557341i
$993$		0			0
$994$	−3.26973	+	10.0632i	−0.103709	+	0.319185i
$995$	−17.6413	+	24.2811i	−0.559266	+	0.769763i
$996$		0			0
$997$	13.9532	+	4.53367i	0.441902	+	0.143583i	0.521513	−	0.853243i	$-0.325368\pi$
$997$	13.9532	+	4.53367i	0.441902	+	0.143583i	−0.0796108	+	0.996826i	$0.525368\pi$
$998$	−5.19242	−	15.9806i	−0.164363	−	0.505858i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.a.701.12	✓	48
3.2	odd	2		1386.2.bu.b.701.1	yes	48
11.7	odd	10		1386.2.bu.b.953.1	yes	48
33.29	even	10	inner	1386.2.bu.a.953.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.701.12	✓	48	1.1	even	1	trivial
1386.2.bu.a.953.12	yes	48	33.29	even	10	inner
1386.2.bu.b.701.1	yes	48	3.2	odd	2
1386.2.bu.b.953.1	yes	48	11.7	odd	10

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.03332 - 2.79863i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.03332 - 2.79863i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +3.45929i q^{10} +(3.21924 - 0.797795i) q^{11} +(-2.39007 - 3.28964i) q^{13} +(-0.951057 + 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(5.58162 + 4.05529i) q^{17} +(3.73524 - 1.21365i) q^{19} +(-2.03332 - 2.79863i) q^{20} +(-2.13549 + 2.53765i) q^{22} +0.504619i q^{23} +(-2.15283 - 6.62572i) q^{25} +(3.86721 + 1.25653i) q^{26} +(0.587785 - 0.809017i) q^{28} +(-2.73069 + 8.40419i) q^{29} +(-0.241611 + 0.175540i) q^{31} +1.00000 q^{32} -6.89927 q^{34} +(2.79863 - 2.03332i) q^{35} +(1.61314 - 4.96475i) q^{37} +(-2.30851 + 3.17739i) q^{38} +(3.28998 + 1.06898i) q^{40} +(0.329578 + 1.01434i) q^{41} -6.11192i q^{43} +(0.236053 - 3.30821i) q^{44} +(-0.296608 - 0.408246i) q^{46} +(3.35357 - 1.08964i) q^{47} +(0.809017 + 0.587785i) q^{49} +(5.63618 + 4.09492i) q^{50} +(-3.86721 + 1.25653i) q^{52} +(1.04412 + 1.43710i) q^{53} +(4.31302 - 10.6316i) q^{55} +1.00000i q^{56} +(-2.73069 - 8.40419i) q^{58} +(-9.23398 - 3.00030i) q^{59} +(-5.18154 + 7.13178i) q^{61} +(0.0922870 - 0.284030i) q^{62} +(-0.809017 + 0.587785i) q^{64} -14.0662 q^{65} -7.92427 q^{67} +(5.58162 - 4.05529i) q^{68} +(-1.06898 + 3.28998i) q^{70} +(6.21939 - 8.56026i) q^{71} +(0.506041 + 0.164423i) q^{73} +(1.61314 + 4.96475i) q^{74} -3.92747i q^{76} +(3.30821 + 0.236053i) q^{77} +(-8.97815 - 12.3574i) q^{79} +(-3.28998 + 1.06898i) q^{80} +(-0.862845 - 0.626894i) q^{82} +(7.03976 + 5.11469i) q^{83} +(22.6985 - 7.37518i) q^{85} +(3.59250 + 4.94465i) q^{86} +(1.75355 + 2.81515i) q^{88} -13.3670i q^{89} +(-1.25653 - 3.86721i) q^{91} +(0.479922 + 0.155936i) q^{92} +(-2.07262 + 2.85271i) q^{94} +(4.19838 - 12.9213i) q^{95} +(-7.38698 + 5.36695i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

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