LMFDB - Embedded newform 380.2.r.a.349.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(49,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("380.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.r (of order $6$, degree $2$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + \cdots + 4096 $ x^20 - 20x^18 + 261x^16 - 1994x^14 + 11074x^12 - 39211x^10 + 99376x^8 - 134299x^6 + 124617x^4 - 24768*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.8
Root			$1.74361 + 1.00667i$ of defining polynomial
Character	$\chi$	$=$	380.349
Dual form			380.2.r.a.49.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.74361 - 1.00667i) q^{3} +(0.0408382 - 2.23570i) q^{5} +1.34403i q^{7} +(0.526784 - 0.912416i) q^{9} +5.25594 q^{11} +(-2.10918 - 1.21773i) q^{13} +(-2.17941 - 3.93929i) q^{15} +(1.17765 - 0.679914i) q^{17} +(2.89815 - 3.25587i) q^{19} +(1.35300 + 2.34346i) q^{21} +(-7.05514 - 4.07329i) q^{23} +(-4.99666 - 0.182603i) q^{25} +3.91884i q^{27} +(-1.03597 + 1.79435i) q^{29} -0.513207 q^{31} +(9.16431 - 5.29102i) q^{33} +(3.00483 + 0.0548876i) q^{35} +5.57175i q^{37} -4.90344 q^{39} +(2.70353 + 4.68265i) q^{41} +(-11.0197 + 6.36221i) q^{43} +(-2.01837 - 1.21499i) q^{45} +(2.82785 + 1.63266i) q^{47} +5.19359 q^{49} +(1.36890 - 2.37101i) q^{51} +(10.1892 + 5.88276i) q^{53} +(0.214643 - 11.7507i) q^{55} +(1.77564 - 8.59447i) q^{57} +(0.0175979 + 0.0304805i) q^{59} +(0.518372 - 0.897846i) q^{61} +(1.22631 + 0.708011i) q^{63} +(-2.80861 + 4.66574i) q^{65} +(0.664028 + 0.383377i) q^{67} -16.4019 q^{69} +(5.68450 + 9.84583i) q^{71} +(-1.86429 + 1.07635i) q^{73} +(-8.89606 + 4.71162i) q^{75} +7.06413i q^{77} +(-6.48576 - 11.2337i) q^{79} +(5.52535 + 9.57019i) q^{81} +4.20304i q^{83} +(-1.47199 - 2.66062i) q^{85} +4.17153i q^{87} +(-3.65426 + 6.32937i) q^{89} +(1.63667 - 2.83479i) q^{91} +(-0.894833 + 0.516632i) q^{93} +(-7.16079 - 6.61235i) q^{95} +(0.721716 - 0.416683i) q^{97} +(2.76875 - 4.79561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65}+ \cdots - 20 q^{99}+O(q^{100}) $ 20 * q + q^5 + 10 * q^9 - 5 * q^15 + 14 * q^19 - 8 * q^21 + 9 * q^25 - 16 * q^29 + 8 * q^31 - 2 * q^35 - 8 * q^39 + 26 * q^41 - 32 * q^45 - 44 * q^49 + 26 * q^51 - 12 * q^55 + 4 * q^59 + 2 * q^61 - 18 * q^65 + 48 * q^69 - 2 * q^71 + 46 * q^75 - 16 * q^79 + 26 * q^81 - 39 * q^85 - 40 * q^89 - 4 * q^91 - 43 * q^95 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.74361	−	1.00667i	1.00667	−	0.581203i	0.0964577	−	0.995337i	$-0.469249\pi$
$3$	1.74361	−	1.00667i	1.00667	−	0.581203i	0.910216	+	0.414134i	$0.135915\pi$
$4$		0			0
$5$	0.0408382	−	2.23570i	0.0182634	−	0.999833i
$5$	0.0408382	−	2.23570i	0.0182634	−	0.999833i
$6$		0			0
$7$			1.34403i			0.507994i	0.967205	+	0.253997i	$0.0817454\pi$
$7$			1.34403i			0.507994i	−0.967205	+	0.253997i	$0.918255\pi$
$8$		0			0
$9$	0.526784	−	0.912416i	0.175595	−	0.304139i
$10$		0			0
$11$	5.25594			1.58473			0.792363	−	0.610050i	$-0.208851\pi$
$11$	5.25594			1.58473			0.792363	+	0.610050i	$0.208851\pi$
$12$		0			0
$13$	−2.10918	−	1.21773i	−0.584980	−	0.337738i	0.178130	−	0.984007i	$-0.442995\pi$
$13$	−2.10918	−	1.21773i	−0.584980	−	0.337738i	−0.763110	+	0.646269i	$0.776329\pi$
$14$		0			0
$15$	−2.17941	−	3.93929i	−0.562721	−	1.01712i
$16$		0			0
$17$	1.17765	−	0.679914i	0.285621	−	0.164903i	−0.350344	−	0.936621i	$-0.613935\pi$
$17$	1.17765	−	0.679914i	0.285621	−	0.164903i	0.635965	+	0.771718i	$0.280602\pi$
$18$		0			0
$19$	2.89815	−	3.25587i	0.664882	−	0.746949i
$19$	2.89815	−	3.25587i	0.664882	−	0.746949i
$20$		0			0
$21$	1.35300	+	2.34346i	0.295248	+	0.511384i
$22$		0			0
$23$	−7.05514	−	4.07329i	−1.47110	−	0.849339i	−0.471625	−	0.881799i	$-0.656332\pi$
$23$	−7.05514	−	4.07329i	−1.47110	−	0.849339i	−0.999473	+	0.0324603i	$0.989666\pi$
$24$		0			0
$25$	−4.99666	−	0.182603i	−0.999333	−	0.0365207i
$26$		0			0
$27$			3.91884i			0.754182i
$28$		0			0
$29$	−1.03597	+	1.79435i	−0.192375	+	0.333203i	−0.946037	−	0.324059i	$-0.894952\pi$
$29$	−1.03597	+	1.79435i	−0.192375	+	0.333203i	0.753662	+	0.657262i	$0.228286\pi$
$30$		0			0
$31$	−0.513207			−0.0921747			−0.0460873	−	0.998937i	$-0.514675\pi$
$31$	−0.513207			−0.0921747			−0.0460873	+	0.998937i	$0.514675\pi$
$32$		0			0
$33$	9.16431	−	5.29102i	1.59530	−	0.921048i
$34$		0			0
$35$	3.00483	+	0.0548876i	0.507910	+	0.00927770i
$36$		0			0
$37$			5.57175i			0.915991i	0.888955	+	0.457995i	$0.151432\pi$
$37$			5.57175i			0.915991i	−0.888955	+	0.457995i	$0.848568\pi$
$38$		0			0
$39$	−4.90344			−0.785179
$40$		0			0
$41$	2.70353	+	4.68265i	0.422220	+	0.731307i	0.996156	−	0.0875933i	$-0.0279176\pi$
$41$	2.70353	+	4.68265i	0.422220	+	0.731307i	−0.573936	+	0.818900i	$0.694584\pi$
$42$		0			0
$43$	−11.0197	+	6.36221i	−1.68048	+	0.970228i	−0.719146	+	0.694859i	$0.755467\pi$
$43$	−11.0197	+	6.36221i	−1.68048	+	0.970228i	−0.961339	+	0.275369i	$0.911200\pi$
$44$		0			0
$45$	−2.01837	−	1.21499i	−0.300881	−	0.181120i
$46$		0			0
$47$	2.82785	+	1.63266i	0.412485	+	0.238148i	0.691857	−	0.722035i	$-0.256793\pi$
$47$	2.82785	+	1.63266i	0.412485	+	0.238148i	−0.279372	+	0.960183i	$0.590126\pi$
$48$		0			0
$49$	5.19359			0.741942
$50$		0			0
$51$	1.36890	−	2.37101i	0.191685	−	0.332008i
$52$		0			0
$53$	10.1892	+	5.88276i	1.39960	+	0.808060i	0.994351	−	0.106146i	$-0.0338512\pi$
$53$	10.1892	+	5.88276i	1.39960	+	0.808060i	0.405250	+	0.914206i	$0.367185\pi$
$54$		0			0
$55$	0.214643	−	11.7507i	0.0289425	−	1.58446i
$56$		0			0
$57$	1.77564	−	8.59447i	0.235190	−	1.13837i
$58$		0			0
$59$	0.0175979	+	0.0304805i	0.00229105	+	0.00396822i	0.867169	−	0.498015i	$-0.165937\pi$
$59$	0.0175979	+	0.0304805i	0.00229105	+	0.00396822i	−0.864878	+	0.501983i	$0.832604\pi$
$60$		0			0
$61$	0.518372	−	0.897846i	0.0663707	−	0.114957i	−0.830930	−	0.556376i	$-0.812191\pi$
$61$	0.518372	−	0.897846i	0.0663707	−	0.114957i	0.897301	+	0.441419i	$0.145525\pi$
$62$		0			0
$63$	1.22631	+	0.708011i	0.154501	+	0.0892010i
$64$		0			0
$65$	−2.80861	+	4.66574i	−0.348366	+	0.578714i
$66$		0			0
$67$	0.664028	+	0.383377i	0.0811239	+	0.0468369i	0.540013	−	0.841657i	$-0.318419\pi$
$67$	0.664028	+	0.383377i	0.0811239	+	0.0468369i	−0.458889	+	0.888493i	$0.651753\pi$
$68$		0			0
$69$	−16.4019			−1.97455
$70$		0			0
$71$	5.68450	+	9.84583i	0.674625	+	1.16849i	0.976578	+	0.215163i	$0.0690282\pi$
$71$	5.68450	+	9.84583i	0.674625	+	1.16849i	−0.301953	+	0.953323i	$0.597638\pi$
$72$		0			0
$73$	−1.86429	+	1.07635i	−0.218199	+	0.125977i	−0.605116	−	0.796137i	$-0.706873\pi$
$73$	−1.86429	+	1.07635i	−0.218199	+	0.125977i	0.386917	+	0.922115i	$0.373540\pi$
$74$		0			0
$75$	−8.89606	+	4.71162i	−1.02723	+	0.544051i
$76$		0			0
$77$			7.06413i			0.805032i
$78$		0			0
$79$	−6.48576	−	11.2337i	−0.729705	−	1.26389i	−0.957008	−	0.290062i	$-0.906324\pi$
$79$	−6.48576	−	11.2337i	−0.729705	−	1.26389i	0.227302	−	0.973824i	$-0.427009\pi$
$80$		0			0
$81$	5.52535	+	9.57019i	0.613928	+	1.06335i
$82$		0			0
$83$			4.20304i			0.461343i	0.973032	+	0.230672i	$0.0740923\pi$
$83$			4.20304i			0.461343i	−0.973032	+	0.230672i	$0.925908\pi$
$84$		0			0
$85$	−1.47199	−	2.66062i	−0.159660	−	0.288585i
$86$		0			0
$87$			4.17153i			0.447235i
$88$		0			0
$89$	−3.65426	+	6.32937i	−0.387351	+	0.670912i	−0.992092	−	0.125510i	$-0.959943\pi$
$89$	−3.65426	+	6.32937i	−0.387351	+	0.670912i	0.604741	+	0.796422i	$0.293277\pi$
$90$		0			0
$91$	1.63667	−	2.83479i	0.171569	−	0.297166i
$92$		0			0
$93$	−0.894833	+	0.516632i	−0.0927898	+	0.0535722i
$94$		0			0
$95$	−7.16079	−	6.61235i	−0.734681	−	0.678413i
$96$		0			0
$97$	0.721716	−	0.416683i	0.0732791	−	0.0423077i	−0.462913	−	0.886404i	$-0.653196\pi$
$97$	0.721716	−	0.416683i	0.0732791	−	0.0423077i	0.536192	+	0.844096i	$0.319862\pi$
$98$		0			0
$99$	2.76875	−	4.79561i	0.278269	−	0.481977i
$100$		0			0
$101$	−7.40992	+	12.8344i	−0.737315	+	1.27707i	0.216385	+	0.976308i	$0.430573\pi$
$101$	−7.40992	+	12.8344i	−0.737315	+	1.27707i	−0.953700	+	0.300759i	$0.902760\pi$
$102$		0			0
$103$		−	9.40773i		−	0.926971i	−0.886104	−	0.463486i	$-0.846599\pi$
$103$		−	9.40773i		−	0.926971i	0.886104	−	0.463486i	$-0.153401\pi$
$104$		0			0
$105$	5.29451	−	2.92918i	0.516691	−	0.285859i
$106$		0			0
$107$		−	12.8130i		−	1.23868i	−0.785124	−	0.619338i	$-0.787401\pi$
$107$		−	12.8130i		−	1.23868i	0.785124	−	0.619338i	$-0.212599\pi$
$108$		0			0
$109$	0.996875	+	1.72664i	0.0954833	+	0.165382i	0.909810	−	0.415025i	$-0.136227\pi$
$109$	0.996875	+	1.72664i	0.0954833	+	0.165382i	−0.814327	+	0.580406i	$0.802894\pi$
$110$		0			0
$111$	5.60894	+	9.71497i	0.532377	+	0.922104i
$112$		0			0
$113$			8.34647i			0.785170i	0.919716	+	0.392585i	$0.128419\pi$
$113$			8.34647i			0.785170i	−0.919716	+	0.392585i	$0.871581\pi$
$114$		0			0
$115$	−9.39474	+	15.6068i	−0.876064	+	1.45534i
$116$		0			0
$117$	−2.22216	+	1.28296i	−0.205439	+	0.118610i
$118$		0			0
$119$	0.913823	+	1.58279i	0.0837700	+	0.145094i
$120$		0			0
$121$	16.6249			1.51136
$122$		0			0
$123$	9.42780	+	5.44314i	0.850076	+	0.490791i
$124$		0			0
$125$	−0.612300	+	11.1636i	−0.0547658	+	0.998499i
$126$		0			0
$127$	−17.8240	−	10.2907i	−1.58163	−	0.913153i	−0.994622	−	0.103569i	$-0.966974\pi$
$127$	−17.8240	−	10.2907i	−1.58163	−	0.913153i	−0.587005	−	0.809583i	$-0.699693\pi$
$128$		0			0
$129$	−12.8093	+	22.1864i	−1.12780	+	1.95341i
$130$		0			0
$131$	−5.36554	−	9.29339i	−0.468790	−	0.811967i	0.530574	−	0.847639i	$-0.321976\pi$
$131$	−5.36554	−	9.29339i	−0.468790	−	0.811967i	−0.999364	+	0.0356712i	$0.988643\pi$
$132$		0			0
$133$	4.37598	+	3.89519i	0.379446	+	0.337756i
$134$		0			0
$135$	8.76134	+	0.160038i	0.754056	+	0.0137739i
$136$		0			0
$137$	−14.8771	−	8.58931i	−1.27104	−	0.733834i	−0.295855	−	0.955233i	$-0.595604\pi$
$137$	−14.8771	−	8.58931i	−1.27104	−	0.733834i	−0.975183	+	0.221399i	$0.928938\pi$
$138$		0			0
$139$	3.66394	−	6.34613i	0.310771	−	0.538272i	−0.667758	−	0.744378i	$-0.732746\pi$
$139$	3.66394	−	6.34613i	0.310771	−	0.538272i	0.978530	+	0.206106i	$0.0660793\pi$
$140$		0			0
$141$	6.57423			0.553650
$142$		0			0
$143$	−11.0857	−	6.40033i	−0.927033	−	0.535223i
$144$		0			0
$145$	3.96932	+	2.38939i	0.329634	+	0.198428i
$146$		0			0
$147$	9.05560	−	5.22825i	0.746893	−	0.431219i
$148$		0			0
$149$	−6.12292	−	10.6052i	−0.501609	−	0.868812i	−0.999998	−	0.00185904i	$-0.999408\pi$
$149$	−6.12292	−	10.6052i	−0.501609	−	0.868812i	0.498389	−	0.866953i	$-0.333925\pi$
$150$		0			0
$151$	−11.5577			−0.940549			−0.470274	−	0.882520i	$-0.655845\pi$
$151$	−11.5577			−0.940549			−0.470274	+	0.882520i	$0.655845\pi$
$152$		0			0
$153$		−	1.43267i		−	0.115825i
$154$		0			0
$155$	−0.0209584	+	1.14737i	−0.00168342	+	0.0921593i
$156$		0			0
$157$	3.58528	−	2.06996i	0.286137	−	0.165201i	−0.350062	−	0.936727i	$-0.613839\pi$
$157$	3.58528	−	2.06996i	0.286137	−	0.165201i	0.636198	+	0.771526i	$0.280506\pi$
$158$		0			0
$159$	23.6881			1.87859
$160$		0			0
$161$	5.47460	−	9.48229i	0.431459	−	0.747309i
$162$		0			0
$163$		−	9.41672i		−	0.737575i	−0.929514	−	0.368787i	$-0.879773\pi$
$163$		−	9.41672i		−	0.737575i	0.929514	−	0.368787i	$-0.120227\pi$
$164$		0			0
$165$	−11.4549	−	20.7047i	−0.891759	−	1.61186i
$166$		0			0
$167$	11.8395	+	6.83551i	0.916164	+	0.528948i	0.882409	−	0.470482i	$-0.155920\pi$
$167$	11.8395	+	6.83551i	0.916164	+	0.528948i	0.0337550	+	0.999430i	$0.489253\pi$
$168$		0			0
$169$	−3.53425	−	6.12151i	−0.271866	−	0.470885i
$170$		0			0
$171$	−1.44401	−	4.35946i	−0.110426	−	0.333376i
$172$		0			0
$173$	−10.1999	+	5.88891i	−0.775484	+	0.447726i	−0.834827	−	0.550512i	$-0.814433\pi$
$173$	−10.1999	+	5.88891i	−0.775484	+	0.447726i	0.0593437	+	0.998238i	$0.481099\pi$
$174$		0			0
$175$	0.245424	−	6.71565i	0.0185523	−	0.507655i
$176$		0			0
$177$	0.0613678	+	0.0354307i	0.00461269	+	0.00266314i
$178$		0			0
$179$	16.5727			1.23870			0.619350	−	0.785115i	$-0.287396\pi$
$179$	16.5727			1.23870			0.619350	+	0.785115i	$0.287396\pi$
$180$		0			0
$181$	7.19552	−	12.4630i	0.534839	−	0.926368i	−0.464332	−	0.885661i	$-0.653706\pi$
$181$	7.19552	−	12.4630i	0.534839	−	0.926368i	0.999171	−	0.0407069i	$-0.0129610\pi$
$182$		0			0
$183$		−	2.08733i		−	0.154300i
$184$		0			0
$185$	12.4567	+	0.227540i	0.915838	+	0.0167291i
$186$		0			0
$187$	6.18964	−	3.57359i	0.452631	−	0.261327i
$188$		0			0
$189$	−5.26703			−0.383120
$190$		0			0
$191$	−5.97170			−0.432097			−0.216049	−	0.976383i	$-0.569317\pi$
$191$	−5.97170			−0.432097			−0.216049	+	0.976383i	$0.569317\pi$
$192$		0			0
$193$	14.1046	−	8.14331i	1.01527	−	0.586168i	0.102542	−	0.994729i	$-0.467302\pi$
$193$	14.1046	−	8.14331i	1.01527	−	0.586168i	0.912731	+	0.408560i	$0.133969\pi$
$194$		0			0
$195$	−0.200247	+	10.9626i	−0.0143400	+	0.785048i
$196$		0			0
$197$		−	11.5233i		−	0.820998i	−0.911861	−	0.410499i	$-0.865355\pi$
$197$		−	11.5233i		−	0.820998i	0.911861	−	0.410499i	$-0.134645\pi$
$198$		0			0
$199$	4.79943	−	8.31285i	0.340222	−	0.589283i	−0.644251	−	0.764814i	$-0.722831\pi$
$199$	4.79943	−	8.31285i	0.340222	−	0.589283i	0.984474	+	0.175531i	$0.0561643\pi$
$200$		0			0
$201$	1.54374			0.108887
$202$		0			0
$203$	−2.41166	−	1.39237i	−0.169265	−	0.0977253i
$204$		0			0
$205$	10.5794	−	5.85303i	0.738896	−	0.408794i
$206$		0			0
$207$	−7.43307	+	4.29148i	−0.516634	+	0.298279i
$208$		0			0
$209$	15.2325	−	17.1127i	1.05366	−	1.18371i
$210$		0			0
$211$	7.28207	+	12.6129i	0.501318	+	0.868308i	0.999999	+	0.00152265i	$0.000484675\pi$
$211$	7.28207	+	12.6129i	0.501318	+	0.868308i	−0.498681	+	0.866786i	$0.666182\pi$
$212$		0			0
$213$	19.8231	+	11.4449i	1.35826	+	0.784189i
$214$		0			0
$215$	13.7739	+	24.8964i	0.939375	+	1.69792i
$216$		0			0
$217$		−	0.689764i		−	0.0468242i
$218$		0			0
$219$	−2.16707	+	3.75347i	−0.146437	+	0.253636i
$220$		0			0
$221$	−3.31182			−0.222777
$222$		0			0
$223$	−6.55816	+	3.78635i	−0.439167	+	0.253553i	−0.703244	−	0.710949i	$-0.748266\pi$
$223$	−6.55816	+	3.78635i	−0.439167	+	0.253553i	0.264077	+	0.964501i	$0.414933\pi$
$224$		0			0
$225$	−2.79877	+	4.46285i	−0.186585	+	0.297523i
$226$		0			0
$227$		−	6.86640i		−	0.455739i	−0.973692	−	0.227869i	$-0.926824\pi$
$227$		−	6.86640i		−	0.455739i	0.973692	−	0.227869i	$-0.0731759\pi$
$228$		0			0
$229$	−22.1011			−1.46048			−0.730240	−	0.683191i	$-0.760592\pi$
$229$	−22.1011			−1.46048			−0.730240	+	0.683191i	$0.760592\pi$
$230$		0			0
$231$	7.11127	+	12.3171i	0.467887	+	0.810404i
$232$		0			0
$233$	2.57806	−	1.48844i	0.168894	−	0.0975111i	−0.413170	−	0.910654i	$-0.635579\pi$
$233$	2.57806	−	1.48844i	0.168894	−	0.0975111i	0.582064	+	0.813143i	$0.302245\pi$
$234$		0			0
$235$	3.76562	−	6.25555i	0.245642	−	0.408067i
$236$		0			0
$237$	−22.6173	−	13.0581i	−1.46915	−	0.848214i
$238$		0			0
$239$	9.71289			0.628275			0.314137	−	0.949378i	$-0.398285\pi$
$239$	9.71289			0.628275			0.314137	+	0.949378i	$0.398285\pi$
$240$		0			0
$241$	9.34287	−	16.1823i	0.601827	−	1.04239i	−0.390717	−	0.920511i	$-0.627773\pi$
$241$	9.34287	−	16.1823i	0.601827	−	1.04239i	0.992544	−	0.121884i	$-0.0388937\pi$
$242$		0			0
$243$	9.08665	+	5.24618i	0.582909	+	0.336543i
$244$		0			0
$245$	0.212097	−	11.6113i	0.0135504	−	0.741818i
$246$		0			0
$247$	−10.0775	+	3.33803i	−0.641216	+	0.212394i
$248$		0			0
$249$	4.23109	+	7.32846i	0.268134	+	0.464422i
$250$		0			0
$251$	2.10091	−	3.63888i	0.132608	−	0.229684i	−0.792073	−	0.610426i	$-0.790998\pi$
$251$	2.10091	−	3.63888i	0.132608	−	0.229684i	0.924681	+	0.380742i	$0.124332\pi$
$252$		0			0
$253$	−37.0814	−	21.4090i	−2.33129	−	1.34597i
$254$		0			0
$255$	−5.24495	−	3.15728i	−0.328452	−	0.197716i
$256$		0			0
$257$	24.3946	+	14.0842i	1.52169	+	0.878548i	0.999672	+	0.0256140i	$0.00815408\pi$
$257$	24.3946	+	14.0842i	1.52169	+	0.878548i	0.522018	+	0.852934i	$0.325179\pi$
$258$		0			0
$259$	−7.48859			−0.465318
$260$		0			0
$261$	1.09146	+	1.89047i	0.0675599	+	0.117017i
$262$		0			0
$263$	2.34563	−	1.35425i	0.144637	−	0.0835065i	−0.425935	−	0.904754i	$-0.640055\pi$
$263$	2.34563	−	1.35425i	0.144637	−	0.0835065i	0.570572	+	0.821247i	$0.306721\pi$
$264$		0			0
$265$	13.5682	−	22.5398i	0.833486	−	1.38461i
$266$		0			0
$267$			14.7146i			0.900519i
$268$		0			0
$269$	5.64101	+	9.77052i	0.343938	+	0.595719i	0.985160	−	0.171637i	$-0.0549055\pi$
$269$	5.64101	+	9.77052i	0.343938	+	0.595719i	−0.641222	+	0.767356i	$0.721572\pi$
$270$		0			0
$271$	−3.16690	−	5.48523i	−0.192375	−	0.333204i	0.753662	−	0.657263i	$-0.228286\pi$
$271$	−3.16690	−	5.48523i	−0.192375	−	0.333204i	−0.946037	+	0.324059i	$0.894952\pi$
$272$		0			0
$273$		−	6.59035i		−	0.398866i
$274$		0			0
$275$	−26.2622	−	0.959753i	−1.58367	−	0.0578753i
$276$		0			0
$277$			11.1435i			0.669549i	0.942298	+	0.334774i	$0.108660\pi$
$277$			11.1435i			0.669549i	−0.942298	+	0.334774i	$0.891340\pi$
$278$		0			0
$279$	−0.270349	+	0.468258i	−0.0161854	+	0.0280339i
$280$		0			0
$281$	−12.9061	+	22.3541i	−0.769916	+	1.33353i	0.167693	+	0.985839i	$0.446368\pi$
$281$	−12.9061	+	22.3541i	−0.769916	+	1.33353i	−0.937608	+	0.347694i	$0.886965\pi$
$282$		0			0
$283$	−24.9942	+	14.4304i	−1.48575	+	0.857799i	−0.999868	−	0.0162249i	$-0.994835\pi$
$283$	−24.9942	+	14.4304i	−1.48575	+	0.857799i	−0.485883	+	0.874024i	$0.661502\pi$
$284$		0			0
$285$	−19.1421	−	4.32078i	−1.13388	−	0.255941i
$286$		0			0
$287$	−6.29360	+	3.63361i	−0.371500	+	0.214485i
$288$		0			0
$289$	−7.57543	+	13.1210i	−0.445614	+	0.771826i
$290$		0			0
$291$	0.838927	−	1.45306i	0.0491788	−	0.0851801i
$292$		0			0
$293$		−	22.7742i		−	1.33048i	−0.746628	−	0.665242i	$-0.768328\pi$
$293$		−	22.7742i		−	1.33048i	0.746628	−	0.665242i	$-0.231672\pi$
$294$		0			0
$295$	0.0688637	−	0.0380988i	0.00400940	−	0.00221820i
$296$		0			0
$297$			20.5972i			1.19517i
$298$		0			0
$299$	9.92035	+	17.1825i	0.573709	+	0.993692i
$300$		0			0
$301$	−8.55098	−	14.8107i	−0.492870	−	0.853676i
$302$		0			0
$303$			29.8375i			1.71412i
$304$		0			0
$305$	−1.98614	−	1.19559i	−0.113726	−	0.0684592i
$306$		0			0
$307$	14.0275	−	8.09880i	0.800593	−	0.462223i	−0.0430854	−	0.999071i	$-0.513719\pi$
$307$	14.0275	−	8.09880i	0.800593	−	0.462223i	0.843679	+	0.536849i	$0.180385\pi$
$308$		0			0
$309$	−9.47052	−	16.4034i	−0.538759	−	0.933158i
$310$		0			0
$311$	−28.3483			−1.60749			−0.803743	−	0.594977i	$-0.797161\pi$
$311$	−28.3483			−1.60749			−0.803743	+	0.594977i	$0.797161\pi$
$312$		0			0
$313$	2.67539	+	1.54464i	0.151222	+	0.0873081i	0.573702	−	0.819064i	$-0.305507\pi$
$313$	2.67539	+	1.54464i	0.151222	+	0.0873081i	−0.422480	+	0.906372i	$0.638840\pi$
$314$		0			0
$315$	1.63298	−	2.71275i	0.0920079	−	0.152846i
$316$		0			0
$317$	20.8236	+	12.0225i	1.16957	+	0.675251i	0.953579	−	0.301144i	$-0.0973685\pi$
$317$	20.8236	+	12.0225i	1.16957	+	0.675251i	0.215991	+	0.976395i	$0.430702\pi$
$318$		0			0
$319$	−5.44500	+	9.43101i	−0.304861	+	0.528035i
$320$		0			0
$321$	−12.8985	−	22.3408i	−0.719923	−	1.24694i
$322$		0			0
$323$	1.19928	−	5.80476i	0.0667298	−	0.322986i
$324$		0			0
$325$	10.3165	+	6.46975i	0.572255	+	0.358877i
$326$		0			0
$327$	3.47632	+	2.00706i	0.192241	+	0.110990i
$328$		0			0
$329$	−2.19434	+	3.80071i	−0.120978	+	0.209540i
$330$		0			0
$331$	−20.7717			−1.14171			−0.570857	−	0.821049i	$-0.693389\pi$
$331$	−20.7717			−1.14171			−0.570857	+	0.821049i	$0.693389\pi$
$332$		0			0
$333$	5.08376	+	2.93511i	0.278588	+	0.160843i
$334$		0			0
$335$	0.884231	−	1.46891i	0.0483107	−	0.0802550i
$336$		0			0
$337$	−2.10139	+	1.21324i	−0.114470	+	0.0660892i	−0.556142	−	0.831087i	$-0.687719\pi$
$337$	−2.10139	+	1.21324i	−0.114470	+	0.0660892i	0.441672	+	0.897177i	$0.354386\pi$
$338$		0			0
$339$	8.40217	+	14.5530i	0.456343	+	0.790410i
$340$		0			0
$341$	−2.69739			−0.146072
$342$		0			0
$343$			16.3885i			0.884896i
$344$		0			0
$345$	−0.669823	+	36.6696i	−0.0360621	+	1.97423i
$346$		0			0
$347$	2.48834	−	1.43664i	0.133581	−	0.0771230i	−0.431720	−	0.902008i	$-0.642093\pi$
$347$	2.48834	−	1.43664i	0.133581	−	0.0771230i	0.565301	+	0.824885i	$0.308760\pi$
$348$		0			0
$349$	5.89385			0.315490			0.157745	−	0.987480i	$-0.449578\pi$
$349$	5.89385			0.315490			0.157745	+	0.987480i	$0.449578\pi$
$350$		0			0
$351$	4.77211	−	8.26553i	0.254716	−	0.441181i
$352$		0			0
$353$		−	12.0238i		−	0.639962i	−0.947424	−	0.319981i	$-0.896324\pi$
$353$		−	12.0238i		−	0.639962i	0.947424	−	0.319981i	$-0.103676\pi$
$354$		0			0
$355$	22.2444	−	12.3067i	1.18061	−	0.653172i
$356$		0			0
$357$	3.18670	+	1.83984i	0.168658	+	0.0973748i
$358$		0			0
$359$	−2.26590	−	3.92466i	−0.119590	−	0.207136i	0.800015	−	0.599979i	$-0.204825\pi$
$359$	−2.26590	−	3.92466i	−0.119590	−	0.207136i	−0.919605	+	0.392844i	$0.871491\pi$
$360$		0			0
$361$	−2.20143	−	18.8720i	−0.115865	−	0.993265i
$362$		0			0
$363$	28.9874	−	16.7359i	1.52144	−	0.878406i
$364$		0			0
$365$	2.33026	+	4.21195i	0.121971	+	0.220463i
$366$		0			0
$367$	29.9143	+	17.2710i	1.56151	+	0.901539i	0.997105	+	0.0760429i	$0.0242286\pi$
$367$	29.9143	+	17.2710i	1.56151	+	0.901539i	0.564407	+	0.825496i	$0.309105\pi$
$368$		0			0
$369$	5.69670			0.296558
$370$		0			0
$371$	−7.90659	+	13.6946i	−0.410490	+	0.710989i
$372$		0			0
$373$			24.0801i			1.24682i	0.781894	+	0.623411i	$0.214254\pi$
$373$			24.0801i			1.24682i	−0.781894	+	0.623411i	$0.785746\pi$
$374$		0			0
$375$	10.1705	+	20.0813i	0.525200	+	1.03699i
$376$		0			0
$377$	4.37008	−	2.52307i	0.225071	−	0.129945i
$378$		0			0
$379$	−30.1565			−1.54904			−0.774518	−	0.632552i	$-0.782008\pi$
$379$	−30.1565			−1.54904			−0.774518	+	0.632552i	$0.782008\pi$
$380$		0			0
$381$	−41.4375			−2.12291
$382$		0			0
$383$	33.6192	−	19.4101i	1.71786	−	0.991809i	0.795066	−	0.606522i	$-0.207436\pi$
$383$	33.6192	−	19.4101i	1.71786	−	0.991809i	0.922797	−	0.385286i	$-0.125897\pi$
$384$		0			0
$385$	15.7932	+	0.288486i	0.804898	+	0.0147026i
$386$		0			0
$387$			13.4060i			0.681467i
$388$		0			0
$389$	18.6935	−	32.3781i	0.947799	−	1.64164i	0.197750	−	0.980252i	$-0.436636\pi$
$389$	18.6935	−	32.3781i	0.947799	−	1.64164i	0.750048	−	0.661383i	$-0.230030\pi$
$390$		0			0
$391$	−11.0779			−0.560236
$392$		0			0
$393$	−18.7108	−	10.8027i	−0.943836	−	0.544924i
$394$		0			0
$395$	−25.3799	+	14.0414i	−1.27700	+	0.706501i
$396$		0			0
$397$	−13.4790	+	7.78211i	−0.676492	+	0.390573i	−0.798532	−	0.601952i	$-0.794390\pi$
$397$	−13.4790	+	7.78211i	−0.676492	+	0.390573i	0.122040	+	0.992525i	$0.461056\pi$
$398$		0			0
$399$	11.5512	+	2.38651i	0.578283	+	0.119475i
$400$		0			0
$401$	−11.3113	−	19.5918i	−0.564860	−	0.978366i	−0.997063	−	0.0765898i	$-0.975597\pi$
$401$	−11.3113	−	19.5918i	−0.564860	−	0.978366i	0.432203	−	0.901777i	$-0.357737\pi$
$402$		0			0
$403$	1.08244	+	0.624949i	0.0539203	+	0.0311309i
$404$		0			0
$405$	21.6217	−	11.9622i	1.07439	−	0.594405i
$406$		0			0
$407$			29.2848i			1.45159i
$408$		0			0
$409$	−18.1239	+	31.3915i	−0.896169	+	1.55221i	−0.0638187	+	0.997962i	$0.520328\pi$
$409$	−18.1239	+	31.3915i	−0.896169	+	1.55221i	−0.832351	+	0.554249i	$0.813005\pi$
$410$		0			0
$411$	−34.5865			−1.70603
$412$		0			0
$413$	−0.0409666	+	0.0236521i	−0.00201583	+	0.00116384i
$414$		0			0
$415$	9.39671	+	0.171644i	0.461266	+	0.00842569i
$416$		0			0
$417$		−	14.7536i		−	0.722486i
$418$		0			0
$419$	14.5598			0.711293			0.355647	−	0.934621i	$-0.384261\pi$
$419$	14.5598			0.711293			0.355647	+	0.934621i	$0.384261\pi$
$420$		0			0
$421$	−0.784161	−	1.35821i	−0.0382177	−	0.0661950i	0.846284	−	0.532732i	$-0.178835\pi$
$421$	−0.784161	−	1.35821i	−0.0382177	−	0.0661950i	−0.884502	+	0.466537i	$0.845501\pi$
$422$		0			0
$423$	2.97934	−	1.72012i	0.144860	−	0.0836351i
$424$		0			0
$425$	−6.00846	+	3.18226i	−0.291453	+	0.154362i
$426$		0			0
$427$	1.20673	+	0.696705i	0.0583977	+	0.0337159i
$428$		0			0
$429$	−25.7722			−1.24429
$430$		0			0
$431$	12.7303	−	22.0495i	0.613197	−	1.06209i	−0.377500	−	0.926009i	$-0.623216\pi$
$431$	12.7303	−	22.0495i	0.613197	−	1.06209i	0.990698	−	0.136080i	$-0.0434503\pi$
$432$		0			0
$433$	14.6212	+	8.44155i	0.702650	+	0.405675i	0.808334	−	0.588725i	$-0.200370\pi$
$433$	14.6212	+	8.44155i	0.702650	+	0.405675i	−0.105684	+	0.994400i	$0.533703\pi$
$434$		0			0
$435$	9.32628	+	0.170358i	0.447161	+	0.00816803i
$436$		0			0
$437$	−33.7090	+	11.1656i	−1.61252	+	0.534125i
$438$		0			0
$439$	9.93240	+	17.2034i	0.474048	+	0.821075i	0.999558	−	0.0297121i	$-0.00945905\pi$
$439$	9.93240	+	17.2034i	0.474048	+	0.821075i	−0.525511	+	0.850787i	$0.676126\pi$
$440$		0			0
$441$	2.73590	−	4.73872i	0.130281	−	0.225653i
$442$		0			0
$443$	4.46422	+	2.57742i	0.212101	+	0.122457i	0.602288	−	0.798279i	$-0.294256\pi$
$443$	4.46422	+	2.57742i	0.212101	+	0.122457i	−0.390186	+	0.920736i	$0.627589\pi$
$444$		0			0
$445$	14.0013	+	8.42830i	0.663726	+	0.399540i
$446$		0			0
$447$	−21.3520	−	12.3276i	−1.00991	−	0.583074i
$448$		0			0
$449$	33.2207			1.56778			0.783892	−	0.620897i	$-0.213232\pi$
$449$	33.2207			1.56778			0.783892	+	0.620897i	$0.213232\pi$
$450$		0			0
$451$	14.2096	+	24.6117i	0.669103	+	1.15892i
$452$		0			0
$453$	−20.1520	+	11.6348i	−0.946826	+	0.546650i
$454$		0			0
$455$	−6.27088	−	3.77485i	−0.293983	−	0.176968i
$456$		0			0
$457$		−	11.7126i		−	0.547894i	−0.961745	−	0.273947i	$-0.911671\pi$
$457$		−	11.7126i		−	0.547894i	0.961745	−	0.273947i	$-0.0883293\pi$
$458$		0			0
$459$	2.66448	+	4.61501i	0.124367	+	0.215410i
$460$		0			0
$461$	3.68501	+	6.38263i	0.171628	+	0.297269i	0.938989	−	0.343947i	$-0.111764\pi$
$461$	3.68501	+	6.38263i	0.171628	+	0.297269i	−0.767361	+	0.641215i	$0.778431\pi$
$462$		0			0
$463$		−	28.8020i		−	1.33854i	−0.743019	−	0.669271i	$-0.766607\pi$
$463$		−	28.8020i		−	1.33854i	0.743019	−	0.669271i	$-0.233393\pi$
$464$		0			0
$465$	1.11849	+	2.02167i	0.0518686	+	0.0937528i
$466$		0			0
$467$		−	34.1251i		−	1.57912i	−0.613673	−	0.789561i	$-0.710309\pi$
$467$		−	34.1251i		−	1.57912i	0.613673	−	0.789561i	$-0.289691\pi$
$468$		0			0
$469$	−0.515268	+	0.892471i	−0.0237929	+	0.0412105i
$470$		0			0
$471$	4.16756	−	7.21842i	0.192031	−	0.332607i
$472$		0			0
$473$	−57.9188	+	33.4394i	−2.66311	+	1.53755i
$474$		0			0
$475$	−15.0756	+	15.7393i	−0.691717	+	0.722169i
$476$		0			0
$477$	10.7351	−	6.19789i	0.491525	−	0.283782i
$478$		0			0
$479$	14.4130	−	24.9640i	0.658546	−	1.14064i	−0.322446	−	0.946588i	$-0.604505\pi$
$479$	14.4130	−	24.9640i	0.658546	−	1.14064i	0.980992	−	0.194048i	$-0.0621617\pi$
$480$		0			0
$481$	6.78491	−	11.7518i	0.309365	−	0.535836i
$482$		0			0
$483$		−	22.0446i		−	1.00306i
$484$		0			0
$485$	−0.902102	−	1.63055i	−0.0409623	−	0.0740396i
$486$		0			0
$487$		−	16.5796i		−	0.751294i	−0.926763	−	0.375647i	$-0.877421\pi$
$487$		−	16.5796i		−	0.751294i	0.926763	−	0.375647i	$-0.122579\pi$
$488$		0			0
$489$	−9.47957	−	16.4191i	−0.428681	−	0.742497i
$490$		0			0
$491$	−4.94615	−	8.56698i	−0.223217	−	0.386623i	0.732566	−	0.680696i	$-0.238322\pi$
$491$	−4.94615	−	8.56698i	−0.223217	−	0.386623i	−0.955783	+	0.294073i	$0.904989\pi$
$492$		0			0
$493$			2.81748i			0.126893i
$494$		0			0
$495$	−10.6084	−	6.38591i	−0.476814	−	0.287026i
$496$		0			0
$497$	−13.2331	+	7.64011i	−0.593584	+	0.342706i
$498$		0			0
$499$	−15.4949	−	26.8380i	−0.693649	−	1.20144i	−0.970634	−	0.240561i	$-0.922669\pi$
$499$	−15.4949	−	26.8380i	−0.693649	−	1.20144i	0.276985	−	0.960874i	$-0.410665\pi$
$500$		0			0
$501$	27.5245			1.22970
$502$		0			0
$503$	11.1406	+	6.43203i	0.496735	+	0.286790i	0.727364	−	0.686252i	$-0.240745\pi$
$503$	11.1406	+	6.43203i	0.496735	+	0.286790i	−0.230629	+	0.973042i	$0.574078\pi$
$504$		0			0
$505$	28.3911	+	17.0905i	1.26339	+	0.760516i
$506$		0			0
$507$	−12.3247	−	7.11568i	−0.547360	−	0.316018i
$508$		0			0
$509$	−7.35312	+	12.7360i	−0.325921	+	0.564512i	−0.981698	−	0.190442i	$-0.939008\pi$
$509$	−7.35312	+	12.7360i	−0.325921	+	0.564512i	0.655777	+	0.754955i	$0.272341\pi$
$510$		0			0
$511$	−1.44664	−	2.50566i	−0.0639957	−	0.110844i
$512$		0			0
$513$	12.7593	+	11.3574i	0.563335	+	0.501442i
$514$		0			0
$515$	−21.0328	−	0.384195i	−0.926817	−	0.0169296i
$516$		0			0
$517$	14.8630	+	8.58118i	0.653676	+	0.377400i
$518$		0			0
$519$	−11.8564	+	20.5359i	−0.520439	+	0.901427i
$520$		0			0
$521$	5.35528			0.234619			0.117310	−	0.993095i	$-0.462573\pi$
$521$	5.35528			0.234619			0.117310	+	0.993095i	$0.462573\pi$
$522$		0			0
$523$	−13.8388	−	7.98981i	−0.605127	−	0.349370i	0.165929	−	0.986138i	$-0.446938\pi$
$523$	−13.8388	−	7.98981i	−0.605127	−	0.349370i	−0.771056	+	0.636768i	$0.780271\pi$
$524$		0			0
$525$	−6.33254	−	11.9565i	−0.276375	−	0.521826i
$526$		0			0
$527$	−0.604376	+	0.348937i	−0.0263270	+	0.0151999i
$528$		0			0
$529$	21.6833	+	37.5566i	0.942753	+	1.63290i
$530$		0			0
$531$	0.0370812			0.00160919
$532$		0			0
$533$		−	13.1687i		−	0.570400i
$534$		0			0
$535$	−28.6459	−	0.523258i	−1.23847	−	0.0226224i
$536$		0			0
$537$	28.8963	−	16.6833i	1.24697	−	0.719937i
$538$		0			0
$539$	27.2972			1.17577
$540$		0			0
$541$	−17.9500	+	31.0904i	−0.771732	+	1.33668i	0.164881	+	0.986313i	$0.447276\pi$
$541$	−17.9500	+	31.0904i	−0.771732	+	1.33668i	−0.936613	+	0.350366i	$0.886057\pi$
$542$		0			0
$543$		−	28.9742i		−	1.24340i
$544$		0			0
$545$	3.90095	−	2.15820i	0.167098	−	0.0924469i
$546$		0			0
$547$	−22.6473	−	13.0754i	−0.968327	−	0.559064i	−0.0696011	−	0.997575i	$-0.522173\pi$
$547$	−22.6473	−	13.0754i	−0.968327	−	0.559064i	−0.898726	+	0.438511i	$0.855506\pi$
$548$		0			0
$549$	−0.546140	−	0.945942i	−0.0233087	−	0.0403718i
$550$		0			0
$551$	2.83979	+	8.57329i	0.120979	+	0.365235i
$552$		0			0
$553$	15.0983	−	8.71704i	0.642047	−	0.370686i
$554$		0			0
$555$	21.9488	−	12.1431i	0.931673	−	0.515447i
$556$		0			0
$557$	−3.64444	−	2.10412i	−0.154420	−	0.0891543i	0.420799	−	0.907154i	$-0.361750\pi$
$557$	−3.64444	−	2.10412i	−0.154420	−	0.0891543i	−0.575219	+	0.818000i	$0.695083\pi$
$558$		0			0
$559$	30.9899			1.31073
$560$		0			0
$561$	7.19488	−	12.4619i	0.303768	−	0.526142i
$562$		0			0
$563$			40.5225i			1.70782i	0.520422	+	0.853909i	$0.325775\pi$
$563$			40.5225i			1.70782i	−0.520422	+	0.853909i	$0.674225\pi$
$564$		0			0
$565$	18.6602	+	0.340855i	0.785039	+	0.0143399i
$566$		0			0
$567$	−12.8626	+	7.42622i	−0.540178	+	0.311872i
$568$		0			0
$569$	−23.9522			−1.00413			−0.502064	−	0.864831i	$-0.667426\pi$
$569$	−23.9522			−1.00413			−0.502064	+	0.864831i	$0.667426\pi$
$570$		0			0
$571$	−7.78949			−0.325980			−0.162990	−	0.986628i	$-0.552114\pi$
$571$	−7.78949			−0.325980			−0.162990	+	0.986628i	$0.552114\pi$
$572$		0			0
$573$	−10.4123	+	6.01155i	−0.434981	+	0.251136i
$574$		0			0
$575$	34.5084	+	21.6411i	1.43910	+	0.902498i
$576$		0			0
$577$		−	34.1385i		−	1.42121i	−0.703593	−	0.710603i	$-0.748422\pi$
$577$		−	34.1385i		−	1.42121i	0.703593	−	0.710603i	$-0.251578\pi$
$578$		0			0
$579$	16.3953	−	28.3975i	0.681366	−	1.18016i
$580$		0			0
$581$	−5.64899			−0.234360
$582$		0			0
$583$	53.5541	+	30.9195i	2.21798	+	1.28055i
$584$		0			0
$585$	2.77757	+	5.02046i	0.114838	+	0.207571i
$586$		0			0
$587$	19.1737	−	11.0700i	0.791384	−	0.456906i	−0.0490654	−	0.998796i	$-0.515624\pi$
$587$	19.1737	−	11.0700i	0.791384	−	0.456906i	0.840450	+	0.541890i	$0.182291\pi$
$588$		0			0
$589$	−1.48735	+	1.67094i	−0.0612853	+	0.0688498i
$590$		0			0
$591$	−11.6002	−	20.0921i	−0.477167	−	0.826477i
$592$		0			0
$593$	−35.8131	−	20.6767i	−1.47067	−	0.849089i	−0.471208	−	0.882022i	$-0.656182\pi$
$593$	−35.8131	−	20.6767i	−1.47067	−	0.849089i	−0.999458	+	0.0329325i	$0.989515\pi$
$594$		0			0
$595$	3.57595	−	1.97839i	0.146600	−	0.0811061i
$596$		0			0
$597$		−	19.3258i		−	0.790954i
$598$		0			0
$599$	16.8243	−	29.1406i	0.687423	−	1.19065i	−0.285246	−	0.958454i	$-0.592075\pi$
$599$	16.8243	−	29.1406i	0.687423	−	1.19065i	0.972669	−	0.232197i	$-0.0745912\pi$
$600$		0			0
$601$	38.4939			1.57020			0.785100	−	0.619369i	$-0.212611\pi$
$601$	38.4939			1.57020			0.785100	+	0.619369i	$0.212611\pi$
$602$		0			0
$603$	0.699598	−	0.403913i	0.0284899	−	0.0164486i
$604$		0			0
$605$	0.678932	−	37.1683i	0.0276025	−	1.51111i
$606$		0			0
$607$			22.1827i			0.900367i	0.892936	+	0.450183i	$0.148641\pi$
$607$			22.1827i			0.900367i	−0.892936	+	0.450183i	$0.851359\pi$
$608$		0			0
$609$	−5.60665			−0.227193
$610$		0			0
$611$	−3.97629	−	6.88714i	−0.160864	−	0.278624i
$612$		0			0
$613$	4.13445	−	2.38703i	0.166989	−	0.0964111i	−0.414176	−	0.910197i	$-0.635930\pi$
$613$	4.13445	−	2.38703i	0.166989	−	0.0964111i	0.581165	+	0.813786i	$0.302597\pi$
$614$		0			0
$615$	12.5542	−	20.8554i	0.506235	−	0.840970i
$616$		0			0
$617$	−14.0178	−	8.09317i	−0.564335	−	0.325819i	0.190549	−	0.981678i	$-0.438973\pi$
$617$	−14.0178	−	8.09317i	−0.564335	−	0.325819i	−0.754883	+	0.655859i	$0.772307\pi$
$618$		0			0
$619$	−13.4892			−0.542176			−0.271088	−	0.962555i	$-0.587383\pi$
$619$	−13.4892			−0.542176			−0.271088	+	0.962555i	$0.587383\pi$
$620$		0			0
$621$	15.9626	−	27.6480i	0.640556	−	1.10948i
$622$		0			0
$623$	−8.50684	−	4.91143i	−0.340819	−	0.196772i
$624$		0			0
$625$	24.9333	+	1.82482i	0.997332	+	0.0729926i
$626$		0			0
$627$	9.33268	−	45.1720i	0.372711	−	1.80400i
$628$		0			0
$629$	3.78832	+	6.56156i	0.151050	+	0.261626i
$630$		0			0
$631$	13.2207	−	22.8989i	0.526308	−	0.911592i	−0.473222	−	0.880943i	$-0.656909\pi$
$631$	13.2207	−	22.8989i	0.526308	−	0.911592i	0.999530	−	0.0306488i	$-0.00975735\pi$
$632$		0			0
$633$	25.3942	+	14.6613i	1.00933	+	0.582735i
$634$		0			0
$635$	−23.7348	+	39.4288i	−0.941886	+	1.56469i
$636$		0			0
$637$	−10.9542	−	6.32441i	−0.434021	−	0.250582i
$638$		0			0
$639$	11.9780			0.473842
$640$		0			0
$641$	−4.27817	−	7.41000i	−0.168977	−	0.292677i	0.769083	−	0.639149i	$-0.220713\pi$
$641$	−4.27817	−	7.41000i	−0.168977	−	0.292677i	−0.938061	+	0.346471i	$0.887380\pi$
$642$		0			0
$643$	−24.2681	+	14.0112i	−0.957042	+	0.552548i	−0.895261	−	0.445541i	$-0.853011\pi$
$643$	−24.2681	+	14.0112i	−0.957042	+	0.552548i	−0.0617804	+	0.998090i	$0.519678\pi$
$644$		0			0
$645$	49.0790	+	29.5438i	1.93248	+	1.16329i
$646$		0			0
$647$			9.57376i			0.376383i	0.982132	+	0.188192i	$0.0602626\pi$
$647$			9.57376i			0.376383i	−0.982132	+	0.188192i	$0.939737\pi$
$648$		0			0
$649$	0.0924936	+	0.160204i	0.00363069	+	0.00628854i
$650$		0			0
$651$	−0.694367	−	1.20268i	−0.0272144	−	0.0471367i
$652$		0			0
$653$			16.4168i			0.642439i	0.947005	+	0.321219i	$0.104093\pi$
$653$			16.4168i			0.642439i	−0.947005	+	0.321219i	$0.895907\pi$
$654$		0			0
$655$	−20.9963	+	11.6162i	−0.820394	+	0.453882i
$656$		0			0
$657$			2.26801i			0.0884837i
$658$		0			0
$659$	7.08162	−	12.2657i	0.275861	−	0.477805i	−0.694491	−	0.719501i	$-0.744371\pi$
$659$	7.08162	−	12.2657i	0.275861	−	0.477805i	0.970352	+	0.241697i	$0.0777039\pi$
$660$		0			0
$661$	−18.5170	+	32.0724i	−0.720229	+	1.24747i	0.240679	+	0.970605i	$0.422630\pi$
$661$	−18.5170	+	32.0724i	−0.720229	+	1.24747i	−0.960908	+	0.276868i	$0.910704\pi$
$662$		0			0
$663$	−5.77452	+	3.33392i	−0.224264	+	0.129479i
$664$		0			0
$665$	8.88717	−	9.62429i	0.344630	−	0.373214i
$666$		0			0
$667$	14.6178	−	8.43960i	0.566004	−	0.326783i
$668$		0			0
$669$	−7.62324	+	13.2038i	−0.294732	+	0.510490i
$670$		0			0
$671$	2.72453	−	4.71903i	0.105179	−	0.182176i
$672$		0			0
$673$		−	42.3293i		−	1.63167i	−0.578282	−	0.815837i	$-0.696277\pi$
$673$		−	42.3293i		−	1.63167i	0.578282	−	0.815837i	$-0.303723\pi$
$674$		0			0
$675$	0.715594	−	19.5812i	0.0275432	−	0.753679i
$676$		0			0
$677$			13.9856i			0.537510i	0.963209	+	0.268755i	$0.0866121\pi$
$677$			13.9856i			0.537510i	−0.963209	+	0.268755i	$0.913388\pi$
$678$		0			0
$679$	0.560033	+	0.970005i	0.0214921	+	0.0372254i
$680$		0			0
$681$	−6.91222	−	11.9723i	−0.264877	−	0.458780i
$682$		0			0
$683$			11.6668i			0.446416i	0.974771	+	0.223208i	$0.0716529\pi$
$683$			11.6668i			0.446416i	−0.974771	+	0.223208i	$0.928347\pi$
$684$		0			0
$685$	−19.8106	+	32.9099i	−0.756925	+	1.25742i
$686$		0			0
$687$	−38.5356	+	22.2486i	−1.47023	+	0.848835i
$688$		0			0
$689$	−14.3273	−	24.8156i	−0.545825	−	0.945397i
$690$		0			0
$691$	−15.7886			−0.600627			−0.300313	−	0.953841i	$-0.597091\pi$
$691$	−15.7886			−0.600627			−0.300313	+	0.953841i	$0.597091\pi$
$692$		0			0
$693$	6.44542	+	3.72127i	0.244841	+	0.141359i
$694$		0			0
$695$	−14.0384	−	8.45062i	−0.532506	−	0.320550i
$696$		0			0
$697$	6.36760	+	3.67633i	0.241190	+	0.139251i
$698$		0			0
$699$	2.99675	−	5.19053i	0.113348	−	0.196324i
$700$		0			0
$701$	2.64450	+	4.58042i	0.0998816	+	0.173000i	0.911635	−	0.411000i	$-0.134820\pi$
$701$	2.64450	+	4.58042i	0.0998816	+	0.173000i	−0.811754	+	0.584000i	$0.801487\pi$
$702$		0			0
$703$	18.1409	+	16.1478i	0.684198	+	0.609025i
$704$		0			0
$705$	0.268480	−	14.6980i	0.0101115	−	0.553558i
$706$		0			0
$707$	−17.2497	−	9.95913i	−0.648743	−	0.374552i
$708$		0			0
$709$	−12.2529	+	21.2226i	−0.460166	+	0.797031i	−0.998969	−	0.0454011i	$-0.985543\pi$
$709$	−12.2529	+	21.2226i	−0.460166	+	0.797031i	0.538803	+	0.842432i	$0.318877\pi$
$710$		0			0
$711$	−13.6664			−0.512529
$712$		0			0
$713$	3.62075	+	2.09044i	0.135598	+	0.0782875i
$714$		0			0
$715$	−14.7619	+	24.5229i	−0.552064	+	0.917104i
$716$		0			0
$717$	16.9355	−	9.77771i	0.632467	−	0.365155i
$718$		0			0
$719$	22.4239	+	38.8393i	0.836269	+	1.44846i	0.892993	+	0.450071i	$0.148601\pi$
$719$	22.4239	+	38.8393i	0.836269	+	1.44846i	−0.0567236	+	0.998390i	$0.518065\pi$
$720$		0			0
$721$	12.6442			0.470896
$722$		0			0
$723$		−	37.6209i		−	1.39914i
$724$		0			0
$725$	5.50405	−	8.77660i	0.204415	−	0.325955i
$726$		0			0
$727$	−28.1376	+	16.2453i	−1.04357	+	0.602504i	−0.920842	−	0.389937i	$-0.872497\pi$
$727$	−28.1376	+	16.2453i	−1.04357	+	0.602504i	−0.122726	+	0.992441i	$0.539164\pi$
$728$		0			0
$729$	−12.0273			−0.445457
$730$		0			0
$731$	−8.65152	+	14.9849i	−0.319988	+	0.554235i
$732$		0			0
$733$		−	11.1969i		−	0.413568i	−0.978387	−	0.206784i	$-0.933700\pi$
$733$		−	11.1969i		−	0.413568i	0.978387	−	0.206784i	$-0.0662998\pi$
$734$		0			0
$735$	−11.3190	−	20.4591i	−0.417506	−	0.754644i
$736$		0			0
$737$	3.49009	+	2.01501i	0.128559	+	0.0742237i
$738$		0			0
$739$	0.466361	+	0.807761i	0.0171554	+	0.0297140i	0.874476	−	0.485069i	$-0.161206\pi$
$739$	0.466361	+	0.807761i	0.0171554	+	0.0297140i	−0.857320	+	0.514783i	$0.827872\pi$
$740$		0			0
$741$	−14.2109	+	15.9650i	−0.522051	+	0.586488i
$742$		0			0
$743$	−23.3370	+	13.4736i	−0.856153	+	0.494300i	−0.862722	−	0.505678i	$-0.831242\pi$
$743$	−23.3370	+	13.4736i	−0.856153	+	0.494300i	0.00656939	+	0.999978i	$0.497909\pi$
$744$		0			0
$745$	−23.9601	+	13.2559i	−0.877829	+	0.485658i
$746$		0			0
$747$	3.83492	+	2.21409i	0.140312	+	0.0810094i
$748$		0			0
$749$	17.2210			0.629240
$750$		0			0
$751$	2.33645	−	4.04686i	0.0852584	−	0.147672i	−0.820243	−	0.572015i	$-0.806162\pi$
$751$	2.33645	−	4.04686i	0.0852584	−	0.147672i	0.905501	+	0.424343i	$0.139495\pi$
$752$		0			0
$753$		−	8.45971i		−	0.308289i
$754$		0			0
$755$	−0.471994	+	25.8394i	−0.0171776	+	0.940392i
$756$		0			0
$757$	37.0902	−	21.4140i	1.34807	−	0.778306i	0.360090	−	0.932918i	$-0.382746\pi$
$757$	37.0902	−	21.4140i	1.34807	−	0.778306i	0.987975	+	0.154612i	$0.0494126\pi$
$758$		0			0
$759$	−86.2073			−3.12913
$760$		0			0
$761$	−16.7169			−0.605987			−0.302994	−	0.952993i	$-0.597986\pi$
$761$	−16.7169			−0.605987			−0.302994	+	0.952993i	$0.597986\pi$
$762$		0			0
$763$	−2.32065	+	1.33983i	−0.0840131	+	0.0485050i
$764$		0			0
$765$	−3.20302	−	0.0585077i	−0.115805	−	0.00211535i
$766$		0			0
$767$		−	0.0857182i		−	0.00309511i
$768$		0			0
$769$	−7.70852	+	13.3516i	−0.277976	+	0.481469i	−0.970882	−	0.239559i	$-0.922997\pi$
$769$	−7.70852	+	13.3516i	−0.277976	+	0.481469i	0.692905	+	0.721029i	$0.256330\pi$
$770$		0			0
$771$	56.7128			2.04246
$772$		0			0
$773$	28.7343	+	16.5897i	1.03350	+	0.596691i	0.917985	−	0.396615i	$-0.129815\pi$
$773$	28.7343	+	16.5897i	1.03350	+	0.596691i	0.115514	+	0.993306i	$0.463148\pi$
$774$		0			0
$775$	2.56432	+	0.0937133i	0.0921132	+	0.00336628i
$776$		0			0
$777$	−13.0572	+	7.53856i	−0.468423	+	0.270444i
$778$		0			0
$779$	23.0813	+	4.76868i	0.826975	+	0.170856i
$780$		0			0
$781$	29.8774	+	51.7491i	1.06910	+	1.85173i
$782$		0			0
$783$	−7.03179	−	4.05980i	−0.251296	−	0.145086i
$784$		0			0
$785$	−4.48139	−	8.10014i	−0.159948	−	0.289106i
$786$		0			0
$787$			12.8318i			0.457405i	0.973496	+	0.228702i	$0.0734483\pi$
$787$			12.8318i			0.457405i	−0.973496	+	0.228702i	$0.926552\pi$
$788$		0			0
$789$	2.72657	−	4.72256i	0.0970685	−	0.168128i
$790$		0			0
$791$	−11.2179			−0.398862
$792$		0			0
$793$	−2.18667	+	1.26248i	−0.0776511	+	0.0448319i
$794$		0			0
$795$	0.967378	−	52.9593i	0.0343094	−	1.87827i
$796$		0			0
$797$			2.28485i			0.0809336i	0.999181	+	0.0404668i	$0.0128845\pi$
$797$			2.28485i			0.0809336i	−0.999181	+	0.0404668i	$0.987115\pi$
$798$		0			0
$799$	4.44028			0.157086
$800$		0			0
$801$	3.85001	+	6.66842i	0.136034	+	0.235617i
$802$		0			0
$803$	−9.79861	+	5.65723i	−0.345786	+	0.199639i
$804$		0			0
$805$	−20.9759	−	12.6268i	−0.739305	−	0.445036i
$806$		0			0
$807$	19.6714	+	11.3573i	0.692468	+	0.399796i
$808$		0			0
$809$	−17.3304			−0.609305			−0.304652	−	0.952464i	$-0.598540\pi$
$809$	−17.3304			−0.609305			−0.304652	+	0.952464i	$0.598540\pi$
$810$		0			0
$811$	−24.7926	+	42.9420i	−0.870586	+	1.50790i	−0.00919378	+	0.999958i	$0.502927\pi$
$811$	−24.7926	+	42.9420i	−0.870586	+	1.50790i	−0.861392	+	0.507941i	$0.830407\pi$
$812$		0			0
$813$	−11.0437	−	6.37606i	−0.387318	−	0.223618i
$814$		0			0
$815$	−21.0529	−	0.384562i	−0.737452	−	0.0134706i
$816$		0			0
$817$	−11.2221	+	54.3173i	−0.392612	+	1.90032i
$818$		0			0
$819$	−1.72434	−	2.98664i	−0.0602532	−	0.104362i
$820$		0			0
$821$	−11.1029	+	19.2308i	−0.387495	+	0.671160i	−0.992112	−	0.125356i	$-0.959993\pi$
$821$	−11.1029	+	19.2308i	−0.387495	+	0.671160i	0.604617	+	0.796516i	$0.293326\pi$
$822$		0			0
$823$	−16.5674	−	9.56519i	−0.577503	−	0.333422i	0.182637	−	0.983180i	$-0.441537\pi$
$823$	−16.5674	−	9.56519i	−0.577503	−	0.333422i	−0.760141	+	0.649759i	$0.774870\pi$
$824$		0			0
$825$	−46.7572	+	24.7640i	−1.62788	+	0.862172i
$826$		0			0
$827$	13.0330	+	7.52461i	0.453202	+	0.261656i	0.709182	−	0.705026i	$-0.249065\pi$
$827$	13.0330	+	7.52461i	0.453202	+	0.261656i	−0.255980	+	0.966682i	$0.582398\pi$
$828$		0			0
$829$	−3.62995			−0.126074			−0.0630368	−	0.998011i	$-0.520079\pi$
$829$	−3.62995			−0.126074			−0.0630368	+	0.998011i	$0.520079\pi$
$830$		0			0
$831$	11.2179	+	19.4299i	0.389144	+	0.674017i
$832$		0			0
$833$	6.11621	−	3.53120i	0.211914	−	0.122349i
$834$		0			0
$835$	15.7656	−	26.1903i	0.545592	−	0.906351i
$836$		0			0
$837$		−	2.01118i		−	0.0695165i
$838$		0			0
$839$	−9.47453	−	16.4104i	−0.327097	−	0.566549i	0.654838	−	0.755770i	$-0.272737\pi$
$839$	−9.47453	−	16.4104i	−0.327097	−	0.566549i	−0.981935	+	0.189221i	$0.939404\pi$
$840$		0			0
$841$	12.3535	+	21.3969i	0.425984	+	0.737826i
$842$		0			0
$843$			51.9691i			1.78991i
$844$		0			0
$845$	−13.8302	+	7.65152i	−0.475772	+	0.263220i
$846$		0			0
$847$			22.3443i			0.767761i
$848$		0			0
$849$	−29.0534	+	50.3220i	−0.997111	+	1.72705i
$850$		0			0
$851$	22.6954	−	39.3095i	0.777987	−	1.34751i
$852$		0			0
$853$	37.0287	−	21.3785i	1.26784	−	0.731987i	0.293260	−	0.956033i	$-0.405260\pi$
$853$	37.0287	−	21.3785i	1.26784	−	0.731987i	0.974579	+	0.224045i	$0.0719264\pi$
$854$		0			0
$855$	−9.80540	+	3.05034i	−0.335338	+	0.104319i
$856$		0			0
$857$	−2.71973	+	1.57024i	−0.0929043	+	0.0536383i	−0.545732	−	0.837960i	$-0.683748\pi$
$857$	−2.71973	+	1.57024i	−0.0929043	+	0.0536383i	0.452828	+	0.891598i	$0.350415\pi$
$858$		0			0
$859$	3.53437	−	6.12170i	0.120591	−	0.208870i	−0.799410	−	0.600786i	$-0.794854\pi$
$859$	3.53437	−	6.12170i	0.120591	−	0.208870i	0.920001	+	0.391916i	$0.128188\pi$
$860$		0			0
$861$	−7.31572	+	12.6712i	−0.249319	+	0.431834i
$862$		0			0
$863$		−	0.464328i		−	0.0158059i	−0.999969	−	0.00790296i	$-0.997484\pi$
$863$		−	0.464328i		−	0.0158059i	0.999969	−	0.00790296i	$-0.00251562\pi$
$864$		0			0
$865$	12.7493	+	23.0443i	0.433488	+	0.783531i
$866$		0			0
$867$			30.5040i			1.03597i
$868$		0			0
$869$	−34.0888	−	59.0435i	−1.15638	−	2.00291i
$870$		0			0
$871$	−0.933701	−	1.61722i	−0.0316373	−	0.0547973i
$872$		0			0
$873$		−	0.878007i		−	0.0297160i
$874$		0			0
$875$	−15.0041	−	0.822948i	−0.507232	−	0.0278207i
$876$		0			0
$877$	0.802896	−	0.463552i	0.0271119	−	0.0156530i	−0.486383	−	0.873746i	$-0.661684\pi$
$877$	0.802896	−	0.463552i	0.0271119	−	0.0156530i	0.513495	+	0.858093i	$0.328351\pi$
$878$		0			0
$879$	−22.9262	−	39.7094i	−0.773282	−	1.33936i
$880$		0			0
$881$	4.50850			0.151895			0.0759477	−	0.997112i	$-0.475802\pi$
$881$	4.50850			0.151895			0.0759477	+	0.997112i	$0.475802\pi$
$882$		0			0
$883$	29.6605	+	17.1245i	0.998156	+	0.576286i	0.907702	−	0.419615i	$-0.137835\pi$
$883$	29.6605	+	17.1245i	0.998156	+	0.576286i	0.0904542	+	0.995901i	$0.471168\pi$
$884$		0			0
$885$	0.0817184	−	0.135753i	0.00274694	−	0.00456328i
$886$		0			0
$887$	−24.7321	−	14.2791i	−0.830423	−	0.479445i	0.0235747	−	0.999722i	$-0.492495\pi$
$887$	−24.7321	−	14.2791i	−0.830423	−	0.479445i	−0.853997	+	0.520277i	$0.825829\pi$
$888$		0			0
$889$	13.8310	−	23.9560i	0.463876	−	0.803457i
$890$		0			0
$891$	29.0409	+	50.3003i	0.972907	+	1.68512i
$892$		0			0
$893$	13.5113	−	4.47544i	0.452138	−	0.149765i
$894$		0			0
$895$	0.676798	−	37.0515i	0.0226229	−	1.23849i
$896$		0			0
$897$	34.5944	+	19.9731i	1.15507	+	0.666883i
$898$		0			0
$899$	0.531667	−	0.920874i	0.0177321	−	0.0307129i
$900$		0			0
$901$	15.9991			0.533007
$902$		0			0
$903$	−29.8191	−	17.2161i	−0.992319	−	0.572916i
$904$		0			0
$905$	−27.5696	−	16.5960i	−0.916445	−	0.551668i
$906$		0			0
$907$	13.6098	−	7.85765i	0.451907	−	0.260909i	−0.256728	−	0.966484i	$-0.582644\pi$
$907$	13.6098	−	7.85765i	0.451907	−	0.260909i	0.708635	+	0.705575i	$0.249311\pi$
$908$		0			0
$909$	7.80686	+	13.5219i	0.258937	+	0.448492i
$910$		0			0
$911$	20.7125			0.686237			0.343119	−	0.939292i	$-0.388517\pi$
$911$	20.7125			0.686237			0.343119	+	0.939292i	$0.388517\pi$
$912$		0			0
$913$			22.0909i			0.731103i
$914$		0			0
$915$	−4.66662	−	0.0852426i	−0.154274	−	0.00281803i
$916$		0			0
$917$	12.4906	−	7.21143i	0.412475	−	0.238142i
$918$		0			0
$919$	−30.6628			−1.01147			−0.505737	−	0.862688i	$-0.668779\pi$
$919$	−30.6628			−1.01147			−0.505737	+	0.862688i	$0.668779\pi$
$920$		0			0
$921$	16.3057	−	28.2423i	0.537291	−	0.930615i
$922$		0			0
$923$		−	27.6888i		−	0.911388i
$924$		0			0
$925$	1.01742	−	27.8402i	0.0334526	−	0.915380i
$926$		0			0
$927$	−8.58377	−	4.95584i	−0.281928	−	0.162771i
$928$		0			0
$929$	−7.65011	−	13.2504i	−0.250992	−	0.434731i	0.712807	−	0.701360i	$-0.247423\pi$
$929$	−7.65011	−	13.2504i	−0.250992	−	0.434731i	−0.963799	+	0.266629i	$0.914090\pi$
$930$		0			0
$931$	15.0518	−	16.9097i	0.493303	−	0.554193i
$932$		0			0
$933$	−49.4284	+	28.5375i	−1.61821	+	0.934276i
$934$		0			0
$935$	−7.73669	−	13.9841i	−0.253017	−	0.457329i
$936$		0			0
$937$	3.83862	+	2.21623i	0.125402	+	0.0724011i	0.561389	−	0.827552i	$-0.310267\pi$
$937$	3.83862	+	2.21623i	0.125402	+	0.0724011i	−0.435987	+	0.899953i	$0.643601\pi$
$938$		0			0
$939$	6.21978			0.202975
$940$		0			0
$941$	−17.3400	+	30.0338i	−0.565268	+	0.979073i	0.431757	+	0.901990i	$0.357894\pi$
$941$	−17.3400	+	30.0338i	−0.565268	+	0.979073i	−0.997025	+	0.0770825i	$0.975440\pi$
$942$		0			0
$943$		−	44.0490i		−	1.43443i
$944$		0			0
$945$	−0.215096	+	11.7755i	−0.00699707	+	0.383056i
$946$		0			0
$947$	−1.04606	+	0.603945i	−0.0339925	+	0.0196256i	−0.516900	−	0.856046i	$-0.672914\pi$
$947$	−1.04606	+	0.603945i	−0.0339925	+	0.0196256i	0.482907	+	0.875671i	$0.339581\pi$
$948$		0			0
$949$	5.24283			0.170189
$950$		0			0
$951$	48.4110			1.56983
$952$		0			0
$953$	51.3773	−	29.6627i	1.66427	−	0.960868i	0.693633	−	0.720329i	$-0.256009\pi$
$953$	51.3773	−	29.6627i	1.66427	−	0.960868i	0.970639	−	0.240540i	$-0.0773244\pi$
$954$		0			0
$955$	−0.243873	+	13.3509i	−0.00789156	+	0.432025i
$956$		0			0
$957$			21.9253i			0.708746i
$958$		0			0
$959$	11.5443	−	19.9952i	0.372784	−	0.645680i
$960$		0			0
$961$	−30.7366			−0.991504
$962$		0			0
$963$	−11.6908	−	6.74966i	−0.376729	−	0.217505i
$964$		0			0
$965$	−17.6300	−	31.8662i	−0.567528	−	1.02581i
$966$		0			0
$967$	39.4450	−	22.7736i	1.26847	−	0.732350i	0.293769	−	0.955876i	$-0.405090\pi$
$967$	39.4450	−	22.7736i	1.26847	−	0.732350i	0.974698	+	0.223527i	$0.0717570\pi$
$968$		0			0
$969$	−3.75242	−	11.3285i	−0.120545	−	0.363925i
$970$		0			0
$971$	−0.738715	−	1.27949i	−0.0237065	−	0.0410608i	0.853929	−	0.520390i	$-0.174213\pi$
$971$	−0.738715	−	1.27949i	−0.0237065	−	0.0410608i	−0.877635	+	0.479329i	$0.840880\pi$
$972$		0			0
$973$	8.52937	+	4.92443i	0.273439	+	0.157870i
$974$		0			0
$975$	24.5008	+	0.895385i	0.784655	+	0.0286753i
$976$		0			0
$977$			46.8443i			1.49868i	0.662184	+	0.749341i	$0.269630\pi$
$977$			46.8443i			1.49868i	−0.662184	+	0.749341i	$0.730370\pi$
$978$		0			0
$979$	−19.2066	+	33.2668i	−0.613846	+	1.06321i
$980$		0			0
$981$	2.10055			0.0670654
$982$		0			0
$983$	17.4012	−	10.0466i	0.555011	−	0.320436i	−0.196130	−	0.980578i	$-0.562837\pi$
$983$	17.4012	−	10.0466i	0.555011	−	0.320436i	0.751141	+	0.660142i	$0.229504\pi$
$984$		0			0
$985$	−25.7625	−	0.470589i	−0.820861	−	0.0149942i
$986$		0			0
$987$			8.83595i			0.281251i
$988$		0			0
$989$	103.660			3.29621
$990$		0			0
$991$	−8.95274	−	15.5066i	−0.284393	−	0.492583i	0.688069	−	0.725646i	$-0.258459\pi$
$991$	−8.95274	−	15.5066i	−0.284393	−	0.492583i	−0.972462	+	0.233062i	$0.925125\pi$
$992$		0			0
$993$	−36.2177	+	20.9103i	−1.14933	+	0.663568i
$994$		0			0
$995$	−18.3890	−	11.0695i	−0.582971	−	0.350928i
$996$		0			0
$997$	1.71445	+	0.989838i	0.0542972	+	0.0313485i	0.526903	−	0.849926i	$-0.323353\pi$
$997$	1.71445	+	0.989838i	0.0542972	+	0.0313485i	−0.472606	+	0.881274i	$0.656686\pi$
$998$		0			0
$999$	−21.8348			−0.690824

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.r.a.349.8	yes	20
3.2	odd	2		3420.2.bj.c.2629.6		20
5.2	odd	4		1900.2.i.g.501.3		20
5.3	odd	4		1900.2.i.g.501.8		20
5.4	even	2	inner	380.2.r.a.349.3	yes	20
15.14	odd	2		3420.2.bj.c.2629.8		20
19.11	even	3	inner	380.2.r.a.49.3	✓	20
57.11	odd	6		3420.2.bj.c.1189.8		20
95.49	even	6	inner	380.2.r.a.49.8	yes	20
95.68	odd	12		1900.2.i.g.201.8		20
95.87	odd	12		1900.2.i.g.201.3		20
285.239	odd	6		3420.2.bj.c.1189.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.3	✓	20	19.11	even	3	inner
380.2.r.a.49.8	yes	20	95.49	even	6	inner
380.2.r.a.349.3	yes	20	5.4	even	2	inner
380.2.r.a.349.8	yes	20	1.1	even	1	trivial
1900.2.i.g.201.3		20	95.87	odd	12
1900.2.i.g.201.8		20	95.68	odd	12
1900.2.i.g.501.3		20	5.2	odd	4
1900.2.i.g.501.8		20	5.3	odd	4
3420.2.bj.c.1189.6		20	285.239	odd	6
3420.2.bj.c.1189.8		20	57.11	odd	6
3420.2.bj.c.2629.6		20	3.2	odd	2
3420.2.bj.c.2629.8		20	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74361 - 1.00667i) q^{3} +(0.0408382 - 2.23570i) q^{5} +1.34403i q^{7} +(0.526784 - 0.912416i) q^{9} +5.25594 q^{11} +(-2.10918 - 1.21773i) q^{13} +(-2.17941 - 3.93929i) q^{15} +(1.17765 - 0.679914i) q^{17} +(2.89815 - 3.25587i) q^{19} +(1.35300 + 2.34346i) q^{21} +(-7.05514 - 4.07329i) q^{23} +(-4.99666 - 0.182603i) q^{25} +3.91884i q^{27} +(-1.03597 + 1.79435i) q^{29} -0.513207 q^{31} +(9.16431 - 5.29102i) q^{33} +(3.00483 + 0.0548876i) q^{35} +5.57175i q^{37} -4.90344 q^{39} +(2.70353 + 4.68265i) q^{41} +(-11.0197 + 6.36221i) q^{43} +(-2.01837 - 1.21499i) q^{45} +(2.82785 + 1.63266i) q^{47} +5.19359 q^{49} +(1.36890 - 2.37101i) q^{51} +(10.1892 + 5.88276i) q^{53} +(0.214643 - 11.7507i) q^{55} +(1.77564 - 8.59447i) q^{57} +(0.0175979 + 0.0304805i) q^{59} +(0.518372 - 0.897846i) q^{61} +(1.22631 + 0.708011i) q^{63} +(-2.80861 + 4.66574i) q^{65} +(0.664028 + 0.383377i) q^{67} -16.4019 q^{69} +(5.68450 + 9.84583i) q^{71} +(-1.86429 + 1.07635i) q^{73} +(-8.89606 + 4.71162i) q^{75} +7.06413i q^{77} +(-6.48576 - 11.2337i) q^{79} +(5.52535 + 9.57019i) q^{81} +4.20304i q^{83} +(-1.47199 - 2.66062i) q^{85} +4.17153i q^{87} +(-3.65426 + 6.32937i) q^{89} +(1.63667 - 2.83479i) q^{91} +(-0.894833 + 0.516632i) q^{93} +(-7.16079 - 6.61235i) q^{95} +(0.721716 - 0.416683i) q^{97} +(2.76875 - 4.79561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65}+ \cdots - 20 q^{99}+O(q^{100}) \) 20 * q + q^5 + 10 * q^9 - 5 * q^15 + 14 * q^19 - 8 * q^21 + 9 * q^25 - 16 * q^29 + 8 * q^31 - 2 * q^35 - 8 * q^39 + 26 * q^41 - 32 * q^45 - 44 * q^49 + 26 * q^51 - 12 * q^55 + 4 * q^59 + 2 * q^61 - 18 * q^65 + 48 * q^69 - 2 * q^71 + 46 * q^75 - 16 * q^79 + 26 * q^81 - 39 * q^85 - 40 * q^89 - 4 * q^91 - 43 * q^95 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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