LMFDB - Embedded newform 476.2.bl.a.129.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(5,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 40, 15]))

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

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

chi := DirichletCharacter("476.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bl (of order $48$, degree $16$, 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:	$3.80087913621$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$12$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			129.2
Character	$\chi$	$=$	476.129
Dual form			476.2.bl.a.369.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951503 - 1.92946i) q^{3} +(3.19070 - 2.79817i) q^{5} +(1.81126 - 1.92856i) q^{7} +(-0.991165 + 1.29171i) q^{9} +O(q^{10})$	\(q+(-0.951503 - 1.92946i) q^{3} +(3.19070 - 2.79817i) q^{5} +(1.81126 - 1.92856i) q^{7} +(-0.991165 + 1.29171i) q^{9} +(1.13208 - 0.0742006i) q^{11} +(3.38136 + 3.38136i) q^{13} +(-8.43491 - 3.49385i) q^{15} +(-1.61528 + 3.79353i) q^{17} +(0.342178 + 2.59910i) q^{19} +(-5.44450 - 1.65971i) q^{21} +(-1.44882 - 0.714478i) q^{23} +(1.69819 - 12.8990i) q^{25} +(-2.89454 - 0.575760i) q^{27} +(1.39736 + 7.02498i) q^{29} +(-2.18472 + 1.07739i) q^{31} +(-1.22035 - 2.11370i) q^{33} +(0.382731 - 11.2217i) q^{35} +(-0.312371 + 4.76586i) q^{37} +(3.30681 - 9.74155i) q^{39} +(-1.07292 + 5.39391i) q^{41} +(-2.41567 - 5.83195i) q^{43} +(0.451916 + 6.89491i) q^{45} +(-1.67072 + 6.23520i) q^{47} +(-0.438705 - 6.98624i) q^{49} +(8.85640 - 0.492931i) q^{51} +(-6.29792 - 8.20761i) q^{53} +(3.40451 - 3.40451i) q^{55} +(4.68927 - 3.13327i) q^{57} +(-6.62862 - 0.872675i) q^{59} +(3.08530 + 9.08901i) q^{61} +(0.695892 + 4.25114i) q^{63} +(20.2505 + 1.32729i) q^{65} +(-4.42247 - 2.55331i) q^{67} +3.47526i q^{69} +(2.82935 + 1.89051i) q^{71} +(1.40519 + 0.476998i) q^{73} +(-26.5039 + 8.99687i) q^{75} +(1.90739 - 2.31769i) q^{77} +(-5.29903 + 10.7454i) q^{79} +(2.90746 + 10.8508i) q^{81} +(-5.81987 + 14.0504i) q^{83} +(5.46104 + 16.6238i) q^{85} +(12.2248 - 9.38044i) q^{87} +(-1.50577 - 0.403470i) q^{89} +(12.6457 - 0.396655i) q^{91} +(4.15754 + 3.19019i) q^{93} +(8.36450 + 7.33547i) q^{95} +(15.8701 - 3.15675i) q^{97} +(-1.02623 + 1.53587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) $ 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.951503	−	1.92946i	−0.549351	−	1.11397i	−0.977631	−	0.210327i	$-0.932547\pi$
$3$	−0.951503	−	1.92946i	−0.549351	−	1.11397i	0.428280	−	0.903646i	$-0.359120\pi$
$4$		0			0
$5$	3.19070	−	2.79817i	1.42692	−	1.25138i	0.505497	−	0.862828i	$-0.331309\pi$
$5$	3.19070	−	2.79817i	1.42692	−	1.25138i	0.921427	−	0.388551i	$-0.127024\pi$
$6$		0			0
$7$	1.81126	−	1.92856i	0.684590	−	0.728928i
$7$	1.81126	−	1.92856i	0.684590	−	0.728928i
$8$		0			0
$9$	−0.991165	+	1.29171i	−0.330388	+	0.430570i
$10$		0			0
$11$	1.13208	−	0.0742006i	0.341336	−	0.0223723i	0.106228	−	0.994342i	$-0.466123\pi$
$11$	1.13208	−	0.0742006i	0.341336	−	0.0223723i	0.235107	+	0.971969i	$0.424456\pi$
$12$		0			0
$13$	3.38136	+	3.38136i	0.937819	+	0.937819i	0.998177	−	0.0603576i	$-0.0192241\pi$
$13$	3.38136	+	3.38136i	0.937819	+	0.937819i	−0.0603576	+	0.998177i	$0.519224\pi$
$14$		0			0
$15$	−8.43491	−	3.49385i	−2.17788	−	0.902109i
$16$		0			0
$17$	−1.61528	+	3.79353i	−0.391764	+	0.920066i
$17$	−1.61528	+	3.79353i	−0.391764	+	0.920066i
$18$		0			0
$19$	0.342178	+	2.59910i	0.0785010	+	0.596274i	0.984807	+	0.173652i	$0.0555568\pi$
$19$	0.342178	+	2.59910i	0.0785010	+	0.596274i	−0.906306	+	0.422622i	$0.861110\pi$
$20$		0			0
$21$	−5.44450	−	1.65971i	−1.18809	−	0.362178i
$22$		0			0
$23$	−1.44882	−	0.714478i	−0.302100	−	0.148979i	0.284921	−	0.958551i	$-0.408033\pi$
$23$	−1.44882	−	0.714478i	−0.302100	−	0.148979i	−0.587021	+	0.809572i	$0.699699\pi$
$24$		0			0
$25$	1.69819	−	12.8990i	0.339637	−	2.57980i
$26$		0			0
$27$	−2.89454	−	0.575760i	−0.557055	−	0.110805i
$28$		0			0
$29$	1.39736	+	7.02498i	0.259483	+	1.30451i	0.862206	+	0.506557i	$0.169082\pi$
$29$	1.39736	+	7.02498i	0.259483	+	1.30451i	−0.602724	+	0.797950i	$0.705918\pi$
$30$		0			0
$31$	−2.18472	+	1.07739i	−0.392388	+	0.193504i	−0.627770	−	0.778399i	$-0.716032\pi$
$31$	−2.18472	+	1.07739i	−0.392388	+	0.193504i	0.235383	+	0.971903i	$0.424366\pi$
$32$		0			0
$33$	−1.22035	−	2.11370i	−0.212435	−	0.367949i
$34$		0			0
$35$	0.382731	−	11.2217i	0.0646933	−	1.89681i
$36$		0			0
$37$	−0.312371	+	4.76586i	−0.0513535	+	0.783503i	0.892067	+	0.451904i	$0.149255\pi$
$37$	−0.312371	+	4.76586i	−0.0513535	+	0.783503i	−0.943420	+	0.331600i	$0.892412\pi$
$38$		0			0
$39$	3.30681	−	9.74155i	0.529514	−	1.55990i
$40$		0			0
$41$	−1.07292	+	5.39391i	−0.167561	+	0.842387i	0.801960	+	0.597378i	$0.203791\pi$
$41$	−1.07292	+	5.39391i	−0.167561	+	0.842387i	−0.969521	+	0.245009i	$0.921209\pi$
$42$		0			0
$43$	−2.41567	−	5.83195i	−0.368387	−	0.889364i	−0.994015	−	0.109243i	$-0.965157\pi$
$43$	−2.41567	−	5.83195i	−0.368387	−	0.889364i	0.625628	−	0.780121i	$-0.284843\pi$
$44$		0			0
$45$	0.451916	+	6.89491i	0.0673677	+	1.02783i
$46$		0			0
$47$	−1.67072	+	6.23520i	−0.243699	+	0.909498i	0.730334	+	0.683091i	$0.239365\pi$
$47$	−1.67072	+	6.23520i	−0.243699	+	0.909498i	−0.974033	+	0.226407i	$0.927302\pi$
$48$		0			0
$49$	−0.438705	−	6.98624i	−0.0626722	−	0.998034i
$50$		0			0
$51$	8.85640	−	0.492931i	1.24014	−	0.0690241i
$52$		0			0
$53$	−6.29792	−	8.20761i	−0.865086	−	1.12740i	−0.990800	−	0.135336i	$-0.956789\pi$
$53$	−6.29792	−	8.20761i	−0.865086	−	1.12740i	0.125714	−	0.992067i	$-0.459878\pi$
$54$		0			0
$55$	3.40451	−	3.40451i	0.459064	−	0.459064i
$56$		0			0
$57$	4.68927	−	3.13327i	0.621109	−	0.415011i
$58$		0			0
$59$	−6.62862	−	0.872675i	−0.862973	−	0.113613i	−0.313970	−	0.949433i	$-0.601659\pi$
$59$	−6.62862	−	0.872675i	−0.862973	−	0.113613i	−0.549003	+	0.835820i	$0.684993\pi$
$60$		0			0
$61$	3.08530	+	9.08901i	0.395033	+	1.16373i	0.944584	+	0.328269i	$0.106465\pi$
$61$	3.08530	+	9.08901i	0.395033	+	1.16373i	−0.549552	+	0.835460i	$0.685201\pi$
$62$		0			0
$63$	0.695892	+	4.25114i	0.0876742	+	0.535593i
$64$		0			0
$65$	20.2505	+	1.32729i	2.51176	+	0.164630i
$66$		0			0
$67$	−4.42247	−	2.55331i	−0.540290	−	0.311937i	0.204906	−	0.978782i	$-0.434311\pi$
$67$	−4.42247	−	2.55331i	−0.540290	−	0.311937i	−0.745197	+	0.666845i	$0.767644\pi$
$68$		0			0
$69$			3.47526i			0.418372i
$70$		0			0
$71$	2.82935	+	1.89051i	0.335782	+	0.224362i	0.712017	−	0.702162i	$-0.247782\pi$
$71$	2.82935	+	1.89051i	0.335782	+	0.224362i	−0.376236	+	0.926524i	$0.622782\pi$
$72$		0			0
$73$	1.40519	+	0.476998i	0.164465	+	0.0558284i	0.402458	−	0.915439i	$-0.368156\pi$
$73$	1.40519	+	0.476998i	0.164465	+	0.0558284i	−0.237993	+	0.971267i	$0.576489\pi$
$74$		0			0
$75$	−26.5039	+	8.99687i	−3.06041	+	1.03887i
$76$		0			0
$77$	1.90739	−	2.31769i	0.217367	−	0.264125i
$78$		0			0
$79$	−5.29903	+	10.7454i	−0.596188	+	1.20895i	0.364470	+	0.931215i	$0.381250\pi$
$79$	−5.29903	+	10.7454i	−0.596188	+	1.20895i	−0.960658	+	0.277734i	$0.910417\pi$
$80$		0			0
$81$	2.90746	+	10.8508i	0.323051	+	1.20564i
$82$		0			0
$83$	−5.81987	+	14.0504i	−0.638814	+	1.54223i	0.189446	+	0.981891i	$0.439331\pi$
$83$	−5.81987	+	14.0504i	−0.638814	+	1.54223i	−0.828261	+	0.560343i	$0.810669\pi$
$84$		0			0
$85$	5.46104	+	16.6238i	0.592333	+	1.80311i
$86$		0			0
$87$	12.2248	−	9.38044i	1.31064	−	1.00569i
$88$		0			0
$89$	−1.50577	−	0.403470i	−0.159611	−	0.0427677i	0.178128	−	0.984007i	$-0.442996\pi$
$89$	−1.50577	−	0.403470i	−0.159611	−	0.0427677i	−0.337740	+	0.941240i	$0.609662\pi$
$90$		0			0
$91$	12.6457	−	0.396655i	1.32562	−	0.0415808i
$92$		0			0
$93$	4.15754	+	3.19019i	0.431117	+	0.330807i
$94$		0			0
$95$	8.36450	+	7.33547i	0.858180	+	0.752603i
$96$		0			0
$97$	15.8701	−	3.15675i	1.61136	−	0.320520i	0.694428	−	0.719562i	$-0.255657\pi$
$97$	15.8701	−	3.15675i	1.61136	−	0.320520i	0.916933	+	0.399042i	$0.130657\pi$
$98$		0			0
$99$	−1.02623	+	1.53587i	−0.103140	+	0.154361i
$100$		0			0
$101$	3.43285	−	5.94586i	0.341581	−	0.591635i	−0.643146	−	0.765744i	$-0.722371\pi$
$101$	3.43285	−	5.94586i	0.341581	−	0.591635i	0.984726	+	0.174108i	$0.0557043\pi$
$102$		0			0
$103$	3.48405	−	2.01152i	0.343294	−	0.198201i	−0.318434	−	0.947945i	$-0.603157\pi$
$103$	3.48405	−	2.01152i	0.343294	−	0.198201i	0.661728	+	0.749744i	$0.269824\pi$
$104$		0			0
$105$	−22.0159	+	9.93899i	−2.14853	+	0.969946i
$106$		0			0
$107$	4.11756	+	4.69517i	0.398059	+	0.453900i	0.915798	−	0.401639i	$-0.131559\pi$
$107$	4.11756	+	4.69517i	0.398059	+	0.453900i	−0.517739	+	0.855539i	$0.673226\pi$
$108$		0			0
$109$	−6.97202	+	7.95007i	−0.667799	+	0.761478i	−0.982205	−	0.187810i	$-0.939861\pi$
$109$	−6.97202	+	7.95007i	−0.667799	+	0.761478i	0.314407	+	0.949288i	$0.398194\pi$
$110$		0			0
$111$	9.49276	−	3.93203i	0.901012	−	0.373212i
$112$		0			0
$113$	−7.05269	−	10.5551i	−0.663462	−	0.992941i	−0.998708	−	0.0508102i	$-0.983820\pi$
$113$	−7.05269	−	10.5551i	−0.663462	−	0.992941i	0.335247	−	0.942130i	$-0.391180\pi$
$114$		0			0
$115$	−6.62198	+	1.77435i	−0.617502	+	0.165459i
$116$		0			0
$117$	−7.71921	+	1.01625i	−0.713641	+	0.0939527i
$118$		0			0
$119$	4.39036	+	9.98623i	0.402464	+	0.915436i
$120$		0			0
$121$	−9.62979	+	1.26779i	−0.875435	+	0.115253i
$122$		0			0
$123$	11.4282	−	3.06218i	1.03045	−	0.276107i
$124$		0			0
$125$	−18.8864	−	28.2655i	−1.68925	−	2.52814i
$126$		0			0
$127$	19.3278	−	8.00582i	1.71506	−	0.710402i	0.715127	−	0.698995i	$-0.246369\pi$
$127$	19.3278	−	8.00582i	1.71506	−	0.710402i	0.999935	−	0.0114074i	$-0.00363117\pi$
$128$		0			0
$129$	−8.95398	+	10.2101i	−0.788354	+	0.898946i
$130$		0			0
$131$	−14.6808	−	16.7402i	−1.28267	−	1.46260i	−0.815870	−	0.578236i	$-0.803741\pi$
$131$	−14.6808	−	16.7402i	−1.28267	−	1.46260i	−0.466796	−	0.884365i	$-0.654592\pi$
$132$		0			0
$133$	5.63229	+	4.04772i	0.488382	+	0.350982i
$134$		0			0
$135$	−10.8467	+	6.26234i	−0.933535	+	0.538977i
$136$		0			0
$137$	2.74743	−	4.75869i	0.234729	−	0.406562i	−0.724465	−	0.689311i	$-0.757913\pi$
$137$	2.74743	−	4.75869i	0.234729	−	0.406562i	0.959194	+	0.282749i	$0.0912465\pi$
$138$		0			0
$139$	1.01457	−	1.51841i	0.0860547	−	0.128790i	−0.785945	−	0.618297i	$-0.787823\pi$
$139$	1.01457	−	1.51841i	0.0860547	−	0.128790i	0.872000	+	0.489507i	$0.162823\pi$
$140$		0			0
$141$	13.6203	−	2.70924i	1.14703	−	0.228159i
$142$		0			0
$143$	4.07887	+	3.57708i	0.341092	+	0.299130i
$144$		0			0
$145$	24.1156	+	18.5046i	2.00269	+	1.53672i
$146$		0			0
$147$	−13.0622	+	7.49389i	−1.07735	+	0.618086i
$148$		0			0
$149$	−2.42773	−	0.650509i	−0.198888	−	0.0532918i	0.158000	−	0.987439i	$-0.449495\pi$
$149$	−2.42773	−	0.650509i	−0.198888	−	0.0532918i	−0.356888	+	0.934147i	$0.616162\pi$
$150$		0			0
$151$	9.42861	−	7.23483i	0.767290	−	0.588762i	−0.149206	−	0.988806i	$-0.547672\pi$
$151$	9.42861	−	7.23483i	0.767290	−	0.588762i	0.916496	+	0.400044i	$0.131005\pi$
$152$		0			0
$153$	−3.29913	−	5.84649i	−0.266719	−	0.472661i
$154$		0			0
$155$	−3.95608	+	9.55083i	−0.317760	+	0.767141i
$156$		0			0
$157$	−4.13941	−	15.4485i	−0.330361	−	1.23292i	−0.908812	−	0.417206i	$-0.863009\pi$
$157$	−4.13941	−	15.4485i	−0.330361	−	1.23292i	0.578451	−	0.815717i	$-0.303657\pi$
$158$		0			0
$159$	−9.84375	+	19.9611i	−0.780660	+	1.58302i
$160$		0			0
$161$	−4.00210	+	1.50003i	−0.315409	+	0.118219i
$162$		0			0
$163$	12.5849	−	4.27199i	0.985723	−	0.334608i	0.218394	−	0.975861i	$-0.429918\pi$
$163$	12.5849	−	4.27199i	0.985723	−	0.334608i	0.767330	+	0.641253i	$0.221585\pi$
$164$		0			0
$165$	−9.80826	−	3.32946i	−0.763572	−	0.259198i
$166$		0			0
$167$	6.17940	+	4.12894i	0.478176	+	0.319507i	0.771194	−	0.636600i	$-0.219660\pi$
$167$	6.17940	+	4.12894i	0.478176	+	0.319507i	−0.293018	+	0.956107i	$0.594660\pi$
$168$		0			0
$169$			9.86713i			0.759010i
$170$		0			0
$171$	−3.69644	−	2.13414i	−0.282674	−	0.163202i
$172$		0			0
$173$	−20.5030	−	1.34384i	−1.55881	−	0.102170i	−0.738566	−	0.674181i	$-0.764497\pi$
$173$	−20.5030	−	1.34384i	−1.55881	−	0.102170i	−0.820246	+	0.572012i	$0.806163\pi$
$174$		0			0
$175$	−21.8007	−	26.6385i	−1.64798	−	2.01368i
$176$		0			0
$177$	4.62337	+	13.6200i	0.347514	+	1.02374i
$178$		0			0
$179$	−12.4807	−	1.64311i	−0.932849	−	0.122812i	−0.351245	−	0.936284i	$-0.614241\pi$
$179$	−12.4807	−	1.64311i	−0.932849	−	0.122812i	−0.581604	+	0.813472i	$0.697575\pi$
$180$		0			0
$181$	−0.983831	+	0.657375i	−0.0731275	+	0.0488623i	−0.591597	−	0.806234i	$-0.701502\pi$
$181$	−0.983831	+	0.657375i	−0.0731275	+	0.0488623i	0.518469	+	0.855096i	$0.326502\pi$
$182$		0			0
$183$	14.6012	−	14.6012i	1.07935	−	1.07935i
$184$		0			0
$185$	12.3390	+	16.0805i	0.907182	+	1.18226i
$186$		0			0
$187$	−1.54715	+	4.41444i	−0.113139	+	0.322816i
$188$		0			0
$189$	−6.35315	+	4.53946i	−0.462123	+	0.330197i
$190$		0			0
$191$	3.53477	−	13.1919i	0.255767	−	0.954535i	−0.711895	−	0.702286i	$-0.752163\pi$
$191$	3.53477	−	13.1919i	0.255767	−	0.954535i	0.967662	−	0.252250i	$-0.0811704\pi$
$192$		0			0
$193$	−0.375314	−	5.72618i	−0.0270157	−	0.412179i	−0.989853	−	0.142097i	$-0.954616\pi$
$193$	−0.375314	−	5.72618i	−0.0270157	−	0.412179i	0.962837	−	0.270083i	$-0.0870511\pi$
$194$		0			0
$195$	−16.7075	−	40.3354i	−1.19645	−	2.88848i
$196$		0			0
$197$	4.21424	−	21.1864i	0.300252	−	1.50947i	−0.476225	−	0.879323i	$-0.657995\pi$
$197$	4.21424	−	21.1864i	0.300252	−	1.50947i	0.776477	−	0.630145i	$-0.217005\pi$
$198$		0			0
$199$	1.96823	−	5.79821i	0.139524	−	0.411024i	−0.854598	−	0.519290i	$-0.826196\pi$
$199$	1.96823	−	5.79821i	0.139524	−	0.411024i	0.994122	+	0.108266i	$0.0345298\pi$
$200$		0			0
$201$	−0.718517	+	10.9624i	−0.0506803	+	0.773232i
$202$		0			0
$203$	16.0791	+	10.0292i	1.12853	+	0.703909i
$204$		0			0
$205$	11.6697	+	20.2125i	0.815049	+	1.41171i
$206$		0			0
$207$	2.35892	−	1.16329i	0.163956	−	0.0808542i
$208$		0			0
$209$	0.580228	+	2.91700i	0.0401352	+	0.201773i
$210$		0			0
$211$	18.5100	+	3.68187i	1.27428	+	0.253470i	0.785459	−	0.618914i	$-0.212427\pi$
$211$	18.5100	+	3.68187i	1.27428	+	0.253470i	0.488822	+	0.872384i	$0.337427\pi$
$212$		0			0
$213$	0.955525	−	7.25793i	0.0654715	−	0.497305i
$214$		0			0
$215$	−24.0265	−	11.8485i	−1.63859	−	0.808064i
$216$		0			0
$217$	−1.87928	+	6.16479i	−0.127574	+	0.418493i
$218$		0			0
$219$	−0.416696	−	3.16512i	−0.0281577	−	0.213879i
$220$		0			0
$221$	−18.2891	+	7.36541i	−1.23026	+	0.495451i
$222$		0			0
$223$	−3.95252	−	1.63719i	−0.264680	−	0.109634i	0.246397	−	0.969169i	$-0.420753\pi$
$223$	−3.95252	−	1.63719i	−0.264680	−	0.109634i	−0.511077	+	0.859535i	$0.670753\pi$
$224$		0			0
$225$	14.9786	+	14.9786i	0.998574	+	0.998574i
$226$		0			0
$227$	7.52709	−	0.493352i	0.499591	−	0.0327449i	0.186475	−	0.982460i	$-0.440294\pi$
$227$	7.52709	−	0.493352i	0.499591	−	0.0327449i	0.313116	+	0.949715i	$0.398627\pi$
$228$		0			0
$229$	−0.592969	+	0.772772i	−0.0391845	+	0.0510662i	−0.812535	−	0.582913i	$-0.801913\pi$
$229$	−0.592969	+	0.772772i	−0.0391845	+	0.0510662i	0.773350	+	0.633979i	$0.218580\pi$
$230$		0			0
$231$	−6.28677	−	1.47494i	−0.413639	−	0.0970441i
$232$		0			0
$233$	6.41220	−	5.62335i	0.420077	−	0.368398i	−0.423055	−	0.906104i	$-0.639042\pi$
$233$	6.41220	−	5.62335i	0.420077	−	0.368398i	0.843132	+	0.537706i	$0.180709\pi$
$234$		0			0
$235$	12.1164	+	24.5696i	0.790386	+	1.60274i
$236$		0			0
$237$	25.7748			1.67425
$238$		0			0
$239$	−18.9287			−1.22440			−0.612199	−	0.790703i	$-0.709715\pi$
$239$	−18.9287			−1.22440			−0.612199	+	0.790703i	$0.709715\pi$
$240$		0			0
$241$	7.04070	+	14.2771i	0.453531	+	0.919670i	0.996787	+	0.0801027i	$0.0255248\pi$
$241$	7.04070	+	14.2771i	0.453531	+	0.919670i	−0.543255	+	0.839567i	$0.682809\pi$
$242$		0			0
$243$	11.5131	−	10.0967i	0.738565	−	0.647704i
$244$		0			0
$245$	−20.9485	−	21.0634i	−1.33835	−	1.34569i
$246$		0			0
$247$	−7.63145	+	9.94550i	−0.485577	+	0.632817i
$248$		0			0
$249$	32.6473	−	2.13982i	2.06894	−	0.135605i
$250$		0			0
$251$	7.77954	+	7.77954i	0.491040	+	0.491040i	0.908634	−	0.417593i	$-0.137126\pi$
$251$	7.77954	+	7.77954i	0.491040	+	0.491040i	−0.417593	+	0.908634i	$0.637126\pi$
$252$		0			0
$253$	−1.69320	−	0.701345i	−0.106450	−	0.0440932i
$254$		0			0
$255$	26.8788	−	26.3545i	1.68322	−	1.65038i
$256$		0			0
$257$	−2.02997	−	15.4192i	−0.126626	−	0.961821i	−0.930313	−	0.366768i	$-0.880464\pi$
$257$	−2.02997	−	15.4192i	−0.126626	−	0.961821i	0.803686	−	0.595053i	$-0.202869\pi$
$258$		0			0
$259$	8.62548	+	9.23463i	0.535961	+	0.573812i
$260$		0			0
$261$	−10.4593	−	5.15794i	−0.647412	−	0.319268i
$262$		0			0
$263$	2.61919	−	19.8947i	0.161506	−	1.22676i	−0.698174	−	0.715928i	$-0.746004\pi$
$263$	2.61919	−	19.8947i	0.161506	−	1.22676i	0.859680	−	0.510833i	$-0.170663\pi$
$264$		0			0
$265$	−43.0611	−	8.56538i	−2.64522	−	0.526167i
$266$		0			0
$267$	0.654267	+	3.28922i	0.0400405	+	0.201297i
$268$		0			0
$269$	−10.4343	+	5.14562i	−0.636190	+	0.313734i	−0.731631	−	0.681701i	$-0.761241\pi$
$269$	−10.4343	+	5.14562i	−0.636190	+	0.313734i	0.0954410	+	0.995435i	$0.469574\pi$
$270$		0			0
$271$	8.07533	+	13.9869i	0.490542	+	0.849643i	0.999941	−	0.0108875i	$-0.00346565\pi$
$271$	8.07533	+	13.9869i	0.490542	+	0.849643i	−0.509399	+	0.860530i	$0.670132\pi$
$272$		0			0
$273$	−12.7977	−	24.0218i	−0.774553	−	1.45387i
$274$		0			0
$275$	0.965374	−	14.7288i	0.0582142	−	0.888177i
$276$		0			0
$277$	4.96212	−	14.6179i	0.298145	−	0.878307i	−0.689868	−	0.723935i	$-0.742331\pi$
$277$	4.96212	−	14.6179i	0.298145	−	0.878307i	0.988013	−	0.154372i	$-0.0493353\pi$
$278$		0			0
$279$	0.773748	−	3.88989i	0.0463231	−	0.232882i
$280$		0			0
$281$	−7.32503	−	17.6842i	−0.436975	−	1.05495i	−0.976988	−	0.213294i	$-0.931581\pi$
$281$	−7.32503	−	17.6842i	−0.436975	−	1.05495i	0.540013	−	0.841656i	$-0.318419\pi$
$282$		0			0
$283$	1.69463	+	25.8550i	0.100735	+	1.53692i	0.686913	+	0.726739i	$0.258965\pi$
$283$	1.69463	+	25.8550i	0.100735	+	1.53692i	−0.586178	+	0.810182i	$0.699368\pi$
$284$		0			0
$285$	6.19463	−	23.1187i	0.366938	−	1.36943i
$286$		0			0
$287$	8.45917	+	11.8389i	0.499329	+	0.698830i
$288$		0			0
$289$	−11.7817	−	12.2553i	−0.693042	−	0.720897i
$290$		0			0
$291$	−21.1912	−	27.6170i	−1.24225	−	1.61893i
$292$		0			0
$293$	0.479712	−	0.479712i	0.0280251	−	0.0280251i	−0.692955	−	0.720980i	$-0.743692\pi$
$293$	0.479712	−	0.479712i	0.0280251	−	0.0280251i	0.720980	+	0.692955i	$0.243692\pi$
$294$		0			0
$295$	−23.5918	+	15.7636i	−1.37357	+	0.917790i
$296$		0			0
$297$	−3.31958	−	0.437032i	−0.192622	−	0.0253591i
$298$		0			0
$299$	−2.48307	−	7.31488i	−0.143599	−	0.423030i
$300$		0			0
$301$	−15.6227	−	5.90438i	−0.900477	−	0.340323i
$302$		0			0
$303$	−14.7387	−	0.966023i	−0.846714	−	0.0554965i
$304$		0			0
$305$	35.2769	+	20.3671i	2.01995	+	1.16622i
$306$		0			0
$307$			15.4903i			0.884080i	0.896995	+	0.442040i	$0.145745\pi$
$307$			15.4903i			0.884080i	−0.896995	+	0.442040i	$0.854255\pi$
$308$		0			0
$309$	−7.19622	−	4.80836i	−0.409379	−	0.273538i
$310$		0			0
$311$	13.3480	+	4.53103i	0.756895	+	0.256931i	0.673100	−	0.739552i	$-0.264963\pi$
$311$	13.3480	+	4.53103i	0.756895	+	0.256931i	0.0837951	+	0.996483i	$0.473296\pi$
$312$		0			0
$313$	20.7519	−	7.04434i	1.17297	−	0.398169i	0.334119	−	0.942531i	$-0.391561\pi$
$313$	20.7519	−	7.04434i	1.17297	−	0.398169i	0.838851	+	0.544362i	$0.183228\pi$
$314$		0			0
$315$	14.1158	+	11.6169i	0.795335	+	0.654538i
$316$		0			0
$317$	−0.873011	+	1.77029i	−0.0490332	+	0.0994295i	−0.920010	−	0.391894i	$-0.871820\pi$
$317$	−0.873011	+	1.77029i	−0.0490332	+	0.0994295i	0.870977	+	0.491323i	$0.163487\pi$
$318$		0			0
$319$	2.10318	+	7.84918i	0.117756	+	0.439470i
$320$		0			0
$321$	5.14127	−	12.4121i	0.286958	−	0.692777i
$322$		0			0
$323$	−10.4125	−	2.90022i	−0.579365	−	0.161373i
$324$		0			0
$325$	49.3583	−	37.8740i	2.73791	−	2.10087i
$326$		0			0
$327$	21.9732	+	5.88771i	1.21512	+	0.325591i
$328$		0			0
$329$	8.99888	+	14.5156i	0.496124	+	0.800273i
$330$		0			0
$331$	−6.00022	−	4.60413i	−0.329802	−	0.253066i	0.430565	−	0.902559i	$-0.358314\pi$
$331$	−6.00022	−	4.60413i	−0.329802	−	0.253066i	−0.760367	+	0.649494i	$0.774981\pi$
$332$		0			0
$333$	−5.84651	−	5.12725i	−0.320387	−	0.280971i
$334$		0			0
$335$	−21.2554	+	4.22796i	−1.16130	+	0.230998i
$336$		0			0
$337$	−6.35507	+	9.51103i	−0.346183	+	0.518099i	−0.963177	−	0.268869i	$-0.913350\pi$
$337$	−6.35507	+	9.51103i	−0.346183	+	0.518099i	0.616994	+	0.786968i	$0.288350\pi$
$338$		0			0
$339$	−13.6550	+	23.6511i	−0.741636	+	1.28455i
$340$		0			0
$341$	−2.39334	+	1.38180i	−0.129607	+	0.0748285i
$342$		0			0
$343$	−14.2680	−	11.8078i	−0.770400	−	0.637561i
$344$		0			0
$345$	9.72437	+	11.0885i	0.523543	+	0.596986i
$346$		0			0
$347$	−6.12969	+	6.98957i	−0.329059	+	0.375220i	−0.892586	−	0.450878i	$-0.851111\pi$
$347$	−6.12969	+	6.98957i	−0.329059	+	0.375220i	0.563527	+	0.826098i	$0.309444\pi$
$348$		0			0
$349$	−24.3675	+	10.0933i	−1.30436	+	0.540284i	−0.923233	−	0.384239i	$-0.874464\pi$
$349$	−24.3675	+	10.0933i	−1.30436	+	0.540284i	−0.381126	+	0.924523i	$0.624464\pi$
$350$		0			0
$351$	−7.84063	−	11.7343i	−0.418502	−	0.626332i
$352$		0			0
$353$	−30.6742	+	8.21912i	−1.63262	+	0.437460i	−0.954675	−	0.297651i	$-0.903797\pi$
$353$	−30.6742	+	8.21912i	−1.63262	+	0.437460i	−0.677947	+	0.735110i	$0.737130\pi$
$354$		0			0
$355$	14.3176	−	1.88494i	0.759898	−	0.100042i
$356$		0			0
$357$	15.0906	−	17.9729i	0.798677	−	0.951229i
$358$		0			0
$359$	−17.7822	+	2.34107i	−0.938508	+	0.123557i	−0.584234	−	0.811585i	$-0.698605\pi$
$359$	−17.7822	+	2.34107i	−0.938508	+	0.123557i	−0.354273	+	0.935142i	$0.615272\pi$
$360$		0			0
$361$	11.7144	−	3.13885i	0.616546	−	0.165203i
$362$		0			0
$363$	11.6089	+	17.3740i	0.609310	+	0.911897i
$364$		0			0
$365$	5.81827	−	2.41000i	0.304542	−	0.126145i
$366$		0			0
$367$	10.6444	−	12.1376i	0.555634	−	0.633579i	−0.404024	−	0.914748i	$-0.632389\pi$
$367$	10.6444	−	12.1376i	0.555634	−	0.633579i	0.959658	+	0.281169i	$0.0907222\pi$
$368$		0			0
$369$	−5.90394	−	6.73215i	−0.307347	−	0.350462i
$370$		0			0
$371$	−27.2360	−	2.72015i	−1.41402	−	0.141223i
$372$		0			0
$373$	7.83816	−	4.52536i	0.405844	−	0.234314i	−0.283158	−	0.959073i	$-0.591382\pi$
$373$	7.83816	−	4.52536i	0.405844	−	0.234314i	0.689003	+	0.724759i	$0.258049\pi$
$374$		0			0
$375$	−36.5666	+	63.3352i	−1.88829	+	3.27062i
$376$		0			0
$377$	−19.0290	+	28.4789i	−0.980044	+	1.46674i
$378$		0			0
$379$	−33.1498	+	6.59390i	−1.70279	+	0.338706i	−0.948244	−	0.317541i	$-0.897143\pi$
$379$	−33.1498	+	6.59390i	−1.70279	+	0.338706i	−0.754546	+	0.656247i	$0.772143\pi$
$380$		0			0
$381$	−33.8373	−	29.6745i	−1.73354	−	1.52027i
$382$		0			0
$383$	4.35929	+	3.34500i	0.222750	+	0.170922i	0.714108	−	0.700036i	$-0.246833\pi$
$383$	4.35929	+	3.34500i	0.222750	+	0.170922i	−0.491358	+	0.870958i	$0.663499\pi$
$384$		0			0
$385$	−0.399372	−	12.7323i	−0.0203539	−	0.648896i
$386$		0			0
$387$	9.92753	+	2.66007i	0.504644	+	0.135219i
$388$		0			0
$389$	7.01508	−	5.38286i	0.355679	−	0.272922i	−0.415430	−	0.909625i	$-0.636369\pi$
$389$	7.01508	−	5.38286i	0.355679	−	0.272922i	0.771109	+	0.636703i	$0.219702\pi$
$390$		0			0
$391$	5.05065	−	4.34205i	0.255422	−	0.219587i
$392$		0			0
$393$	−18.3307	+	44.2543i	−0.924664	+	2.23234i
$394$		0			0
$395$	13.1597	+	49.1128i	0.662139	+	2.47114i
$396$		0			0
$397$	10.5593	−	21.4120i	0.529954	−	1.07464i	−0.453124	−	0.891448i	$-0.649690\pi$
$397$	10.5593	−	21.4120i	0.529954	−	1.07464i	0.983077	−	0.183192i	$-0.0586429\pi$
$398$		0			0
$399$	2.45076	−	14.7187i	0.122691	−	0.736856i
$400$		0			0
$401$	6.29483	−	2.13681i	0.314349	−	0.106707i	−0.159806	−	0.987148i	$-0.551087\pi$
$401$	6.29483	−	2.13681i	0.314349	−	0.106707i	0.474155	+	0.880441i	$0.342754\pi$
$402$		0			0
$403$	−11.0303	−	3.74430i	−0.549460	−	0.186517i
$404$		0			0
$405$	39.6392	+	26.4861i	1.96969	+	1.31610i
$406$		0			0
$407$			5.41853i			0.268587i
$408$		0			0
$409$	−23.8205	−	13.7528i	−1.17785	−	0.680031i	−0.222333	−	0.974971i	$-0.571367\pi$
$409$	−23.8205	−	13.7528i	−1.17785	−	0.680031i	−0.955516	+	0.294940i	$0.904700\pi$
$410$		0			0
$411$	−11.7959	−	0.773142i	−0.581847	−	0.0381363i
$412$		0			0
$413$	−13.6891	+	11.2031i	−0.673599	+	0.551267i
$414$		0			0
$415$	20.7460	+	61.1157i	1.01838	+	3.00005i
$416$		0			0
$417$	−3.89508	−	0.512797i	−0.190743	−	0.0251118i
$418$		0			0
$419$	21.2774	−	14.2171i	1.03947	−	0.694550i	0.0860773	−	0.996288i	$-0.472567\pi$
$419$	21.2774	−	14.2171i	1.03947	−	0.694550i	0.953391	+	0.301738i	$0.0975668\pi$
$420$		0			0
$421$	3.55894	−	3.55894i	0.173452	−	0.173452i	−0.615042	−	0.788494i	$-0.710861\pi$
$421$	3.55894	−	3.55894i	0.173452	−	0.173452i	0.788494	+	0.615042i	$0.210861\pi$
$422$		0			0
$423$	−6.39812	−	8.33820i	−0.311087	−	0.405417i
$424$		0			0
$425$	46.1897	+	27.2777i	2.24053	+	1.32316i
$426$		0			0
$427$	23.1170	+	10.5123i	1.11871	+	0.508727i
$428$		0			0
$429$	3.02076	−	11.2736i	0.145843	−	0.544295i
$430$		0			0
$431$	−0.297711	−	4.54220i	−0.0143403	−	0.218790i	−0.999014	−	0.0443861i	$-0.985867\pi$
$431$	−0.297711	−	4.54220i	−0.0143403	−	0.218790i	0.984674	−	0.174404i	$-0.0557999\pi$
$432$		0			0
$433$	14.3309	+	34.5978i	0.688698	+	1.66266i	0.747389	+	0.664387i	$0.231307\pi$
$433$	14.3309	+	34.5978i	0.688698	+	1.66266i	−0.0586912	+	0.998276i	$0.518693\pi$
$434$		0			0
$435$	12.7577	−	64.1373i	0.611685	−	3.07515i
$436$		0			0
$437$	1.36125	−	4.01010i	0.0651172	−	0.191829i
$438$		0			0
$439$	−0.685112	+	10.4528i	−0.0326986	+	0.498885i	0.949829	+	0.312769i	$0.101257\pi$
$439$	−0.685112	+	10.4528i	−0.0326986	+	0.498885i	−0.982528	+	0.186116i	$0.940410\pi$
$440$		0			0
$441$	9.45903	+	6.35783i	0.450430	+	0.302754i
$442$		0			0
$443$	14.9341	+	25.8666i	0.709540	+	1.22896i	0.965028	+	0.262147i	$0.0844304\pi$
$443$	14.9341	+	25.8666i	0.709540	+	1.22896i	−0.255488	+	0.966812i	$0.582236\pi$
$444$		0			0
$445$	−5.93344	+	2.92605i	−0.281272	+	0.138708i
$446$		0			0
$447$	1.05487	+	5.30317i	0.0498934	+	0.250831i
$448$		0			0
$449$	19.3626	+	3.85147i	0.913779	+	0.181762i	0.629519	−	0.776985i	$-0.283252\pi$
$449$	19.3626	+	3.85147i	0.913779	+	0.181762i	0.284260	+	0.958747i	$0.408252\pi$
$450$		0			0
$451$	−0.814398	+	6.18596i	−0.0383485	+	0.291286i
$452$		0			0
$453$	−22.9307	−	11.3081i	−1.07738	−	0.531303i
$454$		0			0
$455$	39.2386	−	36.6503i	1.83953	−	1.71819i
$456$		0			0
$457$	−2.90230	−	22.0451i	−0.135764	−	1.03123i	−0.914703	−	0.404128i	$-0.867575\pi$
$457$	−2.90230	−	22.0451i	−0.135764	−	1.03123i	0.778939	−	0.627100i	$-0.215758\pi$
$458$		0			0
$459$	6.85967	−	10.0505i	0.320182	−	0.469118i
$460$		0			0
$461$	−5.48378	−	2.27146i	−0.255405	−	0.105792i	0.251307	−	0.967907i	$-0.419140\pi$
$461$	−5.48378	−	2.27146i	−0.255405	−	0.105792i	−0.506713	+	0.862115i	$0.669140\pi$
$462$		0			0
$463$	4.97406	+	4.97406i	0.231164	+	0.231164i	0.813179	−	0.582014i	$-0.197735\pi$
$463$	4.97406	+	4.97406i	0.231164	+	0.231164i	−0.582014	+	0.813179i	$0.697735\pi$
$464$		0			0
$465$	22.1922	−	1.45455i	1.02914	−	0.0674532i
$466$		0			0
$467$	−18.1980	+	23.7161i	−0.842105	+	1.09745i	0.151930	+	0.988391i	$0.451451\pi$
$467$	−18.1980	+	23.7161i	−0.842105	+	1.09745i	−0.994035	+	0.109061i	$0.965216\pi$
$468$		0			0
$469$	−12.9344	+	3.90430i	−0.597257	+	0.180284i
$470$		0			0
$471$	−25.8685	+	22.6861i	−1.19196	+	1.04532i
$472$		0			0
$473$	−3.16748	−	6.42301i	−0.145641	−	0.295330i
$474$		0			0
$475$	34.1069			1.56493
$476$		0			0
$477$	16.8441			0.771240
$478$		0			0
$479$	12.7761	+	25.9073i	0.583753	+	1.18373i	0.965727	+	0.259560i	$0.0835776\pi$
$479$	12.7761	+	25.9073i	0.583753	+	1.18373i	−0.381974	+	0.924173i	$0.624756\pi$
$480$		0			0
$481$	−17.1713	+	15.0588i	−0.782945	+	0.686624i
$482$		0			0
$483$	6.70226	+	6.29459i	0.304963	+	0.286414i
$484$		0			0
$485$	41.8035	−	54.4794i	1.89820	−	2.47378i
$486$		0			0
$487$	5.79051	−	0.379530i	0.262393	−	0.0171982i	0.0663612	−	0.997796i	$-0.478861\pi$
$487$	5.79051	−	0.379530i	0.262393	−	0.0171982i	0.196032	+	0.980598i	$0.437194\pi$
$488$		0			0
$489$	−20.2172	−	20.2172i	−0.914252	−	0.914252i
$490$		0			0
$491$	−1.36143	−	0.563923i	−0.0614405	−	0.0254495i	0.351752	−	0.936093i	$-0.385586\pi$
$491$	−1.36143	−	0.563923i	−0.0614405	−	0.0254495i	−0.413192	+	0.910644i	$0.635586\pi$
$492$		0			0
$493$	−28.9066	−	6.04644i	−1.30189	−	0.272318i
$494$		0			0
$495$	1.02321	+	7.77207i	0.0459900	+	0.349329i
$496$		0			0
$497$	8.77064	−	2.03238i	0.393417	−	0.0911646i
$498$		0			0
$499$	−1.72112	−	0.848760i	−0.0770477	−	0.0379957i	0.403357	−	0.915043i	$-0.367843\pi$
$499$	−1.72112	−	0.848760i	−0.0770477	−	0.0379957i	−0.480404	+	0.877047i	$0.659510\pi$
$500$		0			0
$501$	2.08690	−	15.8516i	0.0932359	−	0.708197i
$502$		0			0
$503$	−2.25910	−	0.449363i	−0.100728	−	0.0200361i	0.144469	−	0.989509i	$-0.453853\pi$
$503$	−2.25910	−	0.449363i	−0.100728	−	0.0200361i	−0.245197	+	0.969473i	$0.578853\pi$
$504$		0			0
$505$	−5.68435	−	28.5771i	−0.252950	−	1.27167i
$506$		0			0
$507$	19.0382	−	9.38860i	0.845516	−	0.416962i
$508$		0			0
$509$	1.92187	+	3.32878i	0.0851854	+	0.147545i	0.905470	−	0.424410i	$-0.139518\pi$
$509$	1.92187	+	3.32878i	0.0851854	+	0.147545i	−0.820285	+	0.571955i	$0.806185\pi$
$510$		0			0
$511$	3.46508	−	1.84603i	0.153286	−	0.0816637i
$512$		0			0
$513$	0.506010	−	7.72021i	0.0223409	−	0.340856i
$514$		0			0
$515$	5.48799	−	16.1671i	0.241830	−	0.712408i
$516$		0			0
$517$	−1.42873	+	7.18273i	−0.0628357	+	0.315896i
$518$		0			0
$519$	16.9158	+	40.8383i	0.742520	+	1.79260i
$520$		0			0
$521$	0.546324	+	8.33530i	0.0239349	+	0.365176i	0.992979	+	0.118289i	$0.0377410\pi$
$521$	0.546324	+	8.33530i	0.0239349	+	0.365176i	−0.969044	+	0.246887i	$0.920592\pi$
$522$		0			0
$523$	10.9426	−	40.8383i	0.478486	−	1.78573i	−0.129269	−	0.991610i	$-0.541263\pi$
$523$	10.9426	−	40.8383i	0.478486	−	1.78573i	0.607755	−	0.794124i	$-0.292070\pi$
$524$		0			0
$525$	−30.6544	+	67.4101i	−1.33787	+	2.94202i
$526$		0			0
$527$	−0.558145	−	10.0281i	−0.0243132	−	0.436830i
$528$		0			0
$529$	−12.4129	−	16.1768i	−0.539692	−	0.703340i
$530$		0			0
$531$	7.69730	−	7.69730i	0.334034	−	0.334034i
$532$		0			0
$533$	−21.8666	+	14.6108i	−0.947149	+	0.632865i
$534$		0			0
$535$	26.2758	+	3.45927i	1.13600	+	0.149557i
$536$		0			0
$537$	8.70509	+	25.6444i	0.375652	+	1.10664i
$538$		0			0
$539$	−1.01503	−	7.87645i	−0.0437206	−	0.339263i
$540$		0			0
$541$	−15.2866	−	1.00194i	−0.657224	−	0.0430767i	−0.266857	−	0.963736i	$-0.585985\pi$
$541$	−15.2866	−	1.00194i	−0.657224	−	0.0430767i	−0.390367	+	0.920659i	$0.627652\pi$
$542$		0			0
$543$	2.20449	+	1.27277i	0.0946039	+	0.0546196i
$544$		0			0
$545$			44.8752i			1.92224i
$546$		0			0
$547$	−19.3574	−	12.9342i	−0.827661	−	0.553025i	0.0680398	−	0.997683i	$-0.478326\pi$
$547$	−19.3574	−	12.9342i	−0.827661	−	0.553025i	−0.895701	+	0.444657i	$0.853326\pi$
$548$		0			0
$549$	−14.7984	−	5.02338i	−0.631581	−	0.214393i
$550$		0			0
$551$	−17.7805	+	6.03566i	−0.757474	+	0.257128i
$552$		0			0
$553$	11.1252	+	29.6821i	0.473092	+	1.26221i
$554$		0			0
$555$	19.2861	−	39.1083i	0.818647	−	1.66005i
$556$		0			0
$557$	1.96236	+	7.32365i	0.0831481	+	0.310313i	0.994957	−	0.100302i	$-0.0319808\pi$
$557$	1.96236	+	7.32365i	0.0831481	+	0.310313i	−0.911809	+	0.410615i	$0.865314\pi$
$558$		0			0
$559$	11.5517	−	27.8882i	0.488583	−	1.17954i
$560$		0			0
$561$	9.98960	−	1.21519i	0.421761	−	0.0513053i
$562$		0			0
$563$	−35.0010	+	26.8572i	−1.47512	+	1.13190i	−0.513300	+	0.858210i	$0.671577\pi$
$563$	−35.0010	+	26.8572i	−1.47512	+	1.13190i	−0.961818	+	0.273688i	$0.911756\pi$
$564$		0			0
$565$	−52.0380	−	13.9435i	−2.18925	−	0.586609i
$566$		0			0
$567$	26.1926	+	14.0463i	1.09999	+	0.589891i
$568$		0			0
$569$	3.49608	+	2.68264i	0.146563	+	0.112462i	0.679441	−	0.733731i	$-0.262223\pi$
$569$	3.49608	+	2.68264i	0.146563	+	0.112462i	−0.532877	+	0.846193i	$0.678889\pi$
$570$		0			0
$571$	17.3814	+	15.2431i	0.727388	+	0.637903i	0.940762	−	0.339068i	$-0.110112\pi$
$571$	17.3814	+	15.2431i	0.727388	+	0.637903i	−0.213373	+	0.976971i	$0.568445\pi$
$572$		0			0
$573$	−28.8166	+	5.73199i	−1.20383	+	0.239457i
$574$		0			0
$575$	−11.6764	+	17.4750i	−0.486941	+	0.728758i
$576$		0			0
$577$	15.4226	−	26.7127i	0.642052	−	1.11207i	−0.342922	−	0.939364i	$-0.611417\pi$
$577$	15.4226	−	26.7127i	0.642052	−	1.11207i	0.984974	−	0.172702i	$-0.0552499\pi$
$578$		0			0
$579$	−10.6913	+	6.17263i	−0.444316	+	0.256526i
$580$		0			0
$581$	16.5558	+	36.6729i	0.686852	+	1.52145i
$582$		0			0
$583$	−7.73878	−	8.82439i	−0.320508	−	0.365469i
$584$		0			0
$585$	−21.7860	+	24.8422i	−0.900742	+	1.02710i
$586$		0			0
$587$	9.04166	−	3.74518i	0.373189	−	0.154580i	−0.188202	−	0.982130i	$-0.560266\pi$
$587$	9.04166	−	3.74518i	0.373189	−	0.154580i	0.561392	+	0.827550i	$0.310266\pi$
$588$		0			0
$589$	−3.54779	−	5.30965i	−0.146184	−	0.218780i
$590$		0			0
$591$	−44.8881	+	12.0277i	−1.84645	+	0.494755i
$592$		0			0
$593$	−5.76694	+	0.759232i	−0.236820	+	0.0311779i	−0.248002	−	0.968760i	$-0.579774\pi$
$593$	−5.76694	+	0.759232i	−0.236820	+	0.0311779i	0.0111821	+	0.999937i	$0.496441\pi$
$594$		0			0
$595$	41.9515	+	19.5781i	1.71984	+	0.802623i
$596$		0			0
$597$	−13.0602	+	1.71940i	−0.534517	+	0.0703706i
$598$		0			0
$599$	−33.8694	+	9.07528i	−1.38387	+	0.370806i	−0.872524	−	0.488571i	$-0.837518\pi$
$599$	−33.8694	+	9.07528i	−1.38387	+	0.370806i	−0.511343	+	0.859377i	$0.670852\pi$
$600$		0			0
$601$	15.4651	+	23.1452i	0.630836	+	0.944113i	0.999892	+	0.0147059i	$0.00468120\pi$
$601$	15.4651	+	23.1452i	0.630836	+	0.944113i	−0.369056	+	0.929407i	$0.620319\pi$
$602$		0			0
$603$	7.68153	−	3.18180i	0.312816	−	0.129573i
$604$		0			0
$605$	−27.1783	+	30.9909i	−1.10495	+	1.25996i
$606$		0			0
$607$	6.98015	+	7.95933i	0.283315	+	0.323059i	0.875941	−	0.482419i	$-0.160242\pi$
$607$	6.98015	+	7.95933i	0.283315	+	0.323059i	−0.592625	+	0.805478i	$0.701908\pi$
$608$		0			0
$609$	4.05152	−	40.5667i	0.164176	−	1.64385i
$610$		0			0
$611$	−26.7327	+	15.4341i	−1.08149	+	0.624399i
$612$		0			0
$613$	−7.08927	+	12.2790i	−0.286333	+	0.495943i	−0.972932	−	0.231093i	$-0.925770\pi$
$613$	−7.08927	+	12.2790i	−0.286333	+	0.495943i	0.686599	+	0.727037i	$0.259103\pi$
$614$		0			0
$615$	27.8955	−	41.7485i	1.12485	−	1.68346i
$616$		0			0
$617$	36.8009	−	7.32016i	1.48155	−	0.294699i	0.612914	−	0.790150i	$-0.289997\pi$
$617$	36.8009	−	7.32016i	1.48155	−	0.294699i	0.868636	+	0.495451i	$0.164997\pi$
$618$		0			0
$619$	−27.3749	−	24.0072i	−1.10029	−	0.964929i	−0.100741	−	0.994913i	$-0.532121\pi$
$619$	−27.3749	−	24.0072i	−1.10029	−	0.964929i	−0.999550	+	0.0299835i	$0.990455\pi$
$620$		0			0
$621$	3.78230	+	2.90226i	0.151778	+	0.116464i
$622$		0			0
$623$	−3.50545	+	2.17319i	−0.140443	+	0.0870668i
$624$		0			0
$625$	−76.5175	−	20.5028i	−3.06070	−	0.820112i
$626$		0			0
$627$	5.07615	−	3.89507i	0.202722	−	0.155554i
$628$		0			0
$629$	−17.5749	−	8.88322i	−0.700756	−	0.354197i
$630$		0			0
$631$	12.9984	−	31.3808i	0.517457	−	1.24925i	−0.422004	−	0.906594i	$-0.638673\pi$
$631$	12.9984	−	31.3808i	0.517457	−	1.24925i	0.939461	−	0.342657i	$-0.111327\pi$
$632$		0			0
$633$	−10.5083	−	39.2176i	−0.417668	−	1.55876i
$634$		0			0
$635$	39.2675	−	79.6265i	1.55828	−	3.15988i
$636$		0			0
$637$	22.1395	−	25.1064i	0.877200	−	0.994751i
$638$		0			0
$639$	−5.24634	+	1.78089i	−0.207542	+	0.0704510i
$640$		0			0
$641$	33.6980	+	11.4389i	1.33099	+	0.451811i	0.894166	−	0.447735i	$-0.147769\pi$
$641$	33.6980	+	11.4389i	1.33099	+	0.451811i	0.436826	+	0.899546i	$0.356103\pi$
$642$		0			0
$643$	−24.0404	−	16.0633i	−0.948063	−	0.633475i	−0.0175934	−	0.999845i	$-0.505600\pi$
$643$	−24.0404	−	16.0633i	−0.948063	−	0.633475i	−0.930469	+	0.366370i	$0.880600\pi$
$644$		0			0
$645$			57.6320i			2.26926i
$646$		0			0
$647$	−39.9056	−	23.0395i	−1.56885	−	0.905776i	−0.996303	−	0.0859044i	$-0.972622\pi$
$647$	−39.9056	−	23.0395i	−1.56885	−	0.905776i	−0.572547	−	0.819872i	$-0.694045\pi$
$648$		0			0
$649$	−7.56890	−	0.496092i	−0.297105	−	0.0194733i
$650$		0			0
$651$	13.6829	−	2.23982i	0.536273	−	0.0877855i
$652$		0			0
$653$	−11.8356	−	34.8666i	−0.463163	−	1.36444i	−0.888282	−	0.459298i	$-0.848101\pi$
$653$	−11.8356	−	34.8666i	−0.463163	−	1.36444i	0.425119	−	0.905138i	$-0.360232\pi$
$654$		0			0
$655$	−93.6840	−	12.3337i	−3.66054	−	0.481919i
$656$		0			0
$657$	−2.00892	+	1.34232i	−0.0783754	+	0.0523688i
$658$		0			0
$659$	−4.50409	+	4.50409i	−0.175455	+	0.175455i	−0.789371	−	0.613916i	$-0.789593\pi$
$659$	−4.50409	+	4.50409i	−0.175455	+	0.175455i	0.613916	+	0.789371i	$0.289593\pi$
$660$		0			0
$661$	−7.74715	−	10.0963i	−0.301329	−	0.392700i	0.618007	−	0.786172i	$-0.287940\pi$
$661$	−7.74715	−	10.0963i	−0.301329	−	0.392700i	−0.919336	+	0.393473i	$0.871274\pi$
$662$		0			0
$663$	31.6134	+	28.2799i	1.22776	+	1.09830i
$664$		0			0
$665$	29.2972	−	2.84505i	1.13610	−	0.110326i
$666$		0			0
$667$	2.99468	−	11.1763i	0.115955	−	0.432748i
$668$		0			0
$669$	0.601952	+	9.18402i	0.0232728	+	0.355075i
$670$		0			0
$671$	4.16723	+	10.0606i	0.160874	+	0.388384i
$672$		0			0
$673$	−1.40773	+	7.07715i	−0.0542641	+	0.272804i	−0.998386	−	0.0567925i	$-0.981913\pi$
$673$	−1.40773	+	7.07715i	−0.0542641	+	0.272804i	0.944122	+	0.329596i	$0.106913\pi$
$674$		0			0
$675$	−12.3422	+	36.3590i	−0.475052	+	1.39946i
$676$		0			0
$677$	0.570396	−	8.70256i	0.0219221	−	0.334467i	−0.972785	−	0.231711i	$-0.925567\pi$
$677$	0.570396	−	8.70256i	0.0219221	−	0.334467i	0.994707	−	0.102755i	$-0.0327658\pi$
$678$		0			0
$679$	22.6568	−	36.3241i	0.869486	−	1.39399i
$680$		0			0
$681$	−8.11396	−	14.0538i	−0.310927	−	0.538542i
$682$		0			0
$683$	0.375105	−	0.184981i	0.0143530	−	0.00707811i	−0.435098	−	0.900383i	$-0.643286\pi$
$683$	0.375105	−	0.184981i	0.0143530	−	0.00707811i	0.449451	+	0.893305i	$0.351620\pi$
$684$		0			0
$685$	−4.54939	−	22.8713i	−0.173823	−	0.873868i
$686$		0			0
$687$	2.05524	+	0.408813i	0.0784124	+	0.0155972i
$688$		0			0
$689$	6.45734	−	49.0484i	0.246005	−	1.86859i
$690$		0			0
$691$	46.9059	+	23.1314i	1.78438	+	0.879961i	0.937320	+	0.348470i	$0.113299\pi$
$691$	46.9059	+	23.1314i	1.78438	+	0.879961i	0.847064	+	0.531491i	$0.178368\pi$
$692$		0			0
$693$	1.10325	+	4.76101i	0.0419088	+	0.180856i
$694$		0			0
$695$	−1.01158	−	7.68373i	−0.0383715	−	0.291461i
$696$		0			0
$697$	−18.7289	−	12.7828i	−0.709407	−	0.484184i
$698$		0			0
$699$	−16.9512	−	7.02144i	−0.641155	−	0.265575i
$700$		0			0
$701$	4.99551	+	4.99551i	0.188678	+	0.188678i	0.795124	−	0.606447i	$-0.207406\pi$
$701$	4.99551	+	4.99551i	0.188678	+	0.188678i	−0.606447	+	0.795124i	$0.707406\pi$
$702$		0			0
$703$	−12.4938	+	0.818889i	−0.471214	+	0.0308850i
$704$		0			0
$705$	35.8772	−	46.7561i	1.35122	−	1.76094i
$706$		0			0
$707$	−5.24921	−	17.3899i	−0.197417	−	0.654016i
$708$		0			0
$709$	−12.4604	+	10.9275i	−0.467960	+	0.410389i	−0.860583	−	0.509310i	$-0.829901\pi$
$709$	−12.4604	+	10.9275i	−0.467960	+	0.410389i	0.392624	+	0.919699i	$0.371567\pi$
$710$		0			0
$711$	−8.62770	−	17.4952i	−0.323564	−	0.656123i
$712$		0			0
$713$	3.93503			0.147368
$714$		0			0
$715$	23.0237			0.861038
$716$		0			0
$717$	18.0108	+	36.5222i	0.672624	+	1.36395i
$718$		0			0
$719$	25.0191	−	21.9412i	0.933057	−	0.818269i	−0.0505268	−	0.998723i	$-0.516090\pi$
$719$	25.0191	−	21.9412i	0.933057	−	0.818269i	0.983583	+	0.180454i	$0.0577567\pi$
$720$		0			0
$721$	2.43117	−	10.3626i	0.0905414	−	0.385923i
$722$		0			0
$723$	20.8479	−	27.1695i	0.775340	−	1.01044i
$724$		0			0
$725$	92.9883	−	6.09478i	3.45350	−	0.226354i
$726$		0			0
$727$	13.9910	+	13.9910i	0.518898	+	0.518898i	0.917238	−	0.398340i	$-0.130414\pi$
$727$	13.9910	+	13.9910i	0.518898	+	0.518898i	−0.398340	+	0.917238i	$0.630414\pi$
$728$		0			0
$729$	0.699477	+	0.289733i	0.0259066	+	0.0107308i
$730$		0			0
$731$	26.0257	+	0.256337i	0.962594	+	0.00948097i
$732$		0			0
$733$	−2.26708	−	17.2201i	−0.0837363	−	0.636041i	−0.980924	−	0.194391i	$-0.937727\pi$
$733$	−2.26708	−	17.2201i	−0.0837363	−	0.636041i	0.897188	−	0.441649i	$-0.145606\pi$
$734$		0			0
$735$	−20.7085	+	60.4611i	−0.763843	+	2.23014i
$736$		0			0
$737$	−5.19606	−	2.56241i	−0.191399	−	0.0943876i
$738$		0			0
$739$	−2.03187	+	15.4336i	−0.0747436	+	0.567734i	0.912566	+	0.408929i	$0.134098\pi$
$739$	−2.03187	+	15.4336i	−0.0747436	+	0.567734i	−0.987310	+	0.158805i	$0.949236\pi$
$740$		0			0
$741$	26.4508	+	5.26138i	0.971693	+	0.193282i
$742$		0			0
$743$	−4.59177	−	23.0844i	−0.168456	−	0.846884i	−0.968895	−	0.247471i	$-0.920401\pi$
$743$	−4.59177	−	23.0844i	−0.168456	−	0.846884i	0.800440	−	0.599413i	$-0.204599\pi$
$744$		0			0
$745$	−9.56640	+	4.71762i	−0.350486	+	0.172840i
$746$		0			0
$747$	−12.3806	−	21.4439i	−0.452983	−	0.784590i
$748$		0			0
$749$	16.5129	+	0.563195i	0.603368	+	0.0205787i
$750$		0			0
$751$	0.492789	−	7.51851i	0.0179821	−	0.274354i	−0.979394	−	0.201959i	$-0.935269\pi$
$751$	0.492789	−	7.51851i	0.0179821	−	0.274354i	0.997376	−	0.0723949i	$-0.0230642\pi$
$752$		0			0
$753$	7.60804	−	22.4126i	0.277252	−	0.816759i
$754$		0			0
$755$	9.83960	−	49.4670i	0.358100	−	1.80029i
$756$		0			0
$757$	9.26055	+	22.3570i	0.336581	+	0.812577i	0.998039	+	0.0625956i	$0.0199378\pi$
$757$	9.26055	+	22.3570i	0.336581	+	0.812577i	−0.661458	+	0.749982i	$0.730062\pi$
$758$		0			0
$759$	0.257867	+	3.93429i	0.00935997	+	0.142806i
$760$		0			0
$761$	−3.21161	+	11.9859i	−0.116421	+	0.434488i	−0.999389	−	0.0349440i	$-0.988875\pi$
$761$	−3.21161	+	11.9859i	−0.116421	+	0.434488i	0.882969	+	0.469432i	$0.155541\pi$
$762$		0			0
$763$	2.70409	+	27.8456i	0.0978945	+	1.00808i
$764$		0			0
$765$	−26.8860	−	9.42288i	−0.972065	−	0.340685i
$766$		0			0
$767$	−19.4629	−	25.3646i	−0.702765	−	0.915861i
$768$		0			0
$769$	−0.0227138	+	0.0227138i	−0.000819079	+	0.000819079i	−0.707516	−	0.706697i	$-0.750184\pi$
$769$	−0.0227138	+	0.0227138i	−0.000819079	+	0.000819079i	0.706697	+	0.707516i	$0.250184\pi$
$770$		0			0
$771$	−27.8191	+	18.5881i	−1.00188	+	0.669435i
$772$		0			0
$773$	−3.65511	−	0.481204i	−0.131465	−	0.0173077i	0.0645064	−	0.997917i	$-0.479453\pi$
$773$	−3.65511	−	0.481204i	−0.131465	−	0.0173077i	−0.195972	+	0.980610i	$0.562786\pi$
$774$		0			0
$775$	10.1871	+	30.0103i	0.365933	+	1.07800i
$776$		0			0
$777$	9.61065	−	25.4293i	0.344780	−	0.912270i
$778$		0			0
$779$	−14.3864	−	0.942936i	−0.515447	−	0.0337842i
$780$		0			0
$781$	3.34333	+	1.93027i	0.119634	+	0.0690707i
$782$		0			0
$783$		−	21.1387i		−	0.755434i
$784$		0			0
$785$	−56.4351	−	37.7087i	−2.01425	−	1.34588i
$786$		0			0
$787$	9.19954	+	3.12282i	0.327928	+	0.111317i	0.480548	−	0.876968i	$-0.340438\pi$
$787$	9.19954	+	3.12282i	0.327928	+	0.111317i	−0.152620	+	0.988285i	$0.548771\pi$
$788$		0			0
$789$	−40.8782	+	13.8763i	−1.45530	+	0.494009i
$790$		0			0
$791$	−33.1304	−	5.51643i	−1.17798	−	0.196142i
$792$		0			0
$793$	−20.3007	+	41.1657i	−0.720898	+	1.46184i
$794$		0			0
$795$	24.4462	+	91.2345i	0.867018	+	3.23575i
$796$		0			0
$797$	7.16310	−	17.2932i	0.253730	−	0.612558i	−0.744769	−	0.667322i	$-0.767441\pi$
$797$	7.16310	−	17.2932i	0.253730	−	0.612558i	0.998499	+	0.0547637i	$0.0174405\pi$
$798$		0			0
$799$	−20.9547	−	16.4095i	−0.741325	−	0.580528i
$800$		0			0
$801$	2.01363	−	1.54511i	0.0711482	−	0.0545940i
$802$		0			0
$803$	1.62619	+	0.435735i	0.0573869	+	0.0153768i
$804$		0			0
$805$	−8.57214	+	15.9847i	−0.302128	+	0.563387i
$806$		0			0
$807$	19.8565	+	15.2364i	0.698983	+	0.536348i
$808$		0			0
$809$	−14.5988	−	12.8028i	−0.513268	−	0.450124i	0.363111	−	0.931746i	$-0.381715\pi$
$809$	−14.5988	−	12.8028i	−0.513268	−	0.450124i	−0.876379	+	0.481622i	$0.840048\pi$
$810$		0			0
$811$	−10.7083	+	2.13001i	−0.376018	+	0.0747947i	−0.379482	−	0.925199i	$-0.623898\pi$
$811$	−10.7083	+	2.13001i	−0.376018	+	0.0747947i	0.00346319	+	0.999994i	$0.498898\pi$
$812$		0			0
$813$	19.3034	−	28.8896i	0.677000	−	1.01320i
$814$		0			0
$815$	28.2008	−	48.8452i	0.987831	−	1.71097i
$816$		0			0
$817$	14.3312	−	8.27414i	0.501386	−	0.289475i
$818$		0			0
$819$	−12.0216	+	16.7277i	−0.420067	+	0.584512i
$820$		0			0
$821$	3.05013	+	3.47800i	0.106450	+	0.121383i	0.802611	−	0.596502i	$-0.203443\pi$
$821$	3.05013	+	3.47800i	0.106450	+	0.121383i	−0.696161	+	0.717886i	$0.745110\pi$
$822$		0			0
$823$	20.1120	−	22.9333i	0.701060	−	0.799405i	−0.286260	−	0.958152i	$-0.592412\pi$
$823$	20.1120	−	22.9333i	0.701060	−	0.799405i	0.987319	+	0.158747i	$0.0507453\pi$
$824$		0			0
$825$	−29.3371	+	12.1518i	−1.02139	+	0.423072i
$826$		0			0
$827$	−4.96269	−	7.42720i	−0.172570	−	0.258269i	0.735096	−	0.677963i	$-0.237137\pi$
$827$	−4.96269	−	7.42720i	−0.172570	−	0.258269i	−0.907665	+	0.419694i	$0.862137\pi$
$828$		0			0
$829$	20.9245	−	5.60671i	0.726739	−	0.194729i	0.123562	−	0.992337i	$-0.460568\pi$
$829$	20.9245	−	5.60671i	0.726739	−	0.194729i	0.603177	+	0.797608i	$0.293901\pi$
$830$		0			0
$831$	−32.9262	+	4.33481i	−1.14220	+	0.150373i
$832$		0			0
$833$	27.2111	+	9.62052i	0.942810	+	0.333331i
$834$		0			0
$835$	31.2701	−	4.11679i	1.08215	−	0.142467i
$836$		0			0
$837$	6.94409	−	1.86066i	0.240023	−	0.0643139i
$838$		0			0
$839$	26.6297	+	39.8542i	0.919360	+	1.37592i	0.926642	+	0.375946i	$0.122682\pi$
$839$	26.6297	+	39.8542i	0.919360	+	1.37592i	−0.00728165	+	0.999973i	$0.502318\pi$
$840$		0			0
$841$	−20.6053	+	8.53500i	−0.710528	+	0.294310i
$842$		0			0
$843$	−27.1511	+	30.9599i	−0.935134	+	1.06632i
$844$		0			0
$845$	27.6099	+	31.4830i	0.949809	+	1.08305i
$846$		0			0
$847$	−14.9970	+	20.8679i	−0.515303	+	0.717031i
$848$		0			0
$849$	48.2737	−	27.8709i	1.65675	−	0.956525i
$850$		0			0
$851$	3.85768	−	6.68169i	0.132239	−	0.229045i
$852$		0			0
$853$	−4.65272	+	6.96329i	−0.159306	+	0.238418i	−0.902533	−	0.430621i	$-0.858294\pi$
$853$	−4.65272	+	6.96329i	−0.159306	+	0.238418i	0.743227	+	0.669040i	$0.233294\pi$
$854$		0			0
$855$	−17.7659	+	3.53386i	−0.607581	+	0.120855i
$856$		0			0
$857$	17.9760	+	15.7645i	0.614047	+	0.538505i	0.908887	−	0.417042i	$-0.136933\pi$
$857$	17.9760	+	15.7645i	0.614047	+	0.538505i	−0.294840	+	0.955547i	$0.595266\pi$
$858$		0			0
$859$	19.8303	+	15.2163i	0.676601	+	0.519175i	0.888941	−	0.458021i	$-0.151442\pi$
$859$	19.8303	+	15.2163i	0.676601	+	0.519175i	−0.212340	+	0.977196i	$0.568108\pi$
$860$		0			0
$861$	14.7938	−	27.5864i	0.504171	−	0.940142i
$862$		0			0
$863$	19.1344	+	5.12705i	0.651343	+	0.174527i	0.569336	−	0.822105i	$-0.307200\pi$
$863$	19.1344	+	5.12705i	0.651343	+	0.174527i	0.0820070	+	0.996632i	$0.473867\pi$
$864$		0			0
$865$	−69.1791	+	53.0830i	−2.35216	+	1.80488i
$866$		0			0
$867$	−12.4357	+	34.3932i	−0.422337	+	1.16806i
$868$		0			0
$869$	−5.20163	+	12.5578i	−0.176453	+	0.425996i
$870$		0			0
$871$	−6.32028	−	23.5876i	−0.214154	−	0.799235i
$872$		0			0
$873$	−11.6522	+	23.6284i	−0.394368	+	0.799700i
$874$		0			0
$875$	−88.7199	−	14.7724i	−2.99928	−	0.499400i
$876$		0			0
$877$	36.7532	−	12.4760i	1.24107	−	0.421285i	0.377731	−	0.925916i	$-0.376705\pi$
$877$	36.7532	−	12.4760i	1.24107	−	0.421285i	0.863335	+	0.504630i	$0.168371\pi$
$878$		0			0
$879$	−1.38203	−	0.469137i	−0.0466148	−	0.0158236i
$880$		0			0
$881$	18.7076	+	12.5000i	0.630274	+	0.421136i	0.829257	−	0.558867i	$-0.188764\pi$
$881$	18.7076	+	12.5000i	0.630274	+	0.421136i	−0.198983	+	0.980003i	$0.563764\pi$
$882$		0			0
$883$			47.1867i			1.58796i	0.607945	+	0.793979i	$0.291994\pi$
$883$			47.1867i			1.58796i	−0.607945	+	0.793979i	$0.708006\pi$
$884$		0			0
$885$	52.8628	+	30.5204i	1.77696	+	1.02593i
$886$		0			0
$887$	7.65469	+	0.501715i	0.257019	+	0.0168459i	0.193368	−	0.981126i	$-0.438059\pi$
$887$	7.65469	+	0.501715i	0.257019	+	0.0168459i	0.0636512	+	0.997972i	$0.479725\pi$
$888$		0			0
$889$	19.5678	−	51.7754i	0.656283	−	1.73649i
$890$		0			0
$891$	4.09662	+	12.0683i	0.137242	+	0.404302i
$892$		0			0
$893$	−16.7776	−	2.20881i	−0.561440	−	0.0739150i
$894$		0			0
$895$	−44.4198	+	29.6803i	−1.48479	+	0.992105i
$896$		0			0
$897$	−11.7511	+	11.7511i	−0.392358	+	0.392358i
$898$		0			0
$899$	−10.6215	−	13.8421i	−0.354245	−	0.461661i
$900$		0			0
$901$	41.3087	−	10.6337i	1.37619	−	0.354260i
$902$		0			0
$903$	3.47279	+	35.7613i	0.115567	+	1.19006i
$904$		0			0
$905$	−1.29966	+	4.85041i	−0.0432023	+	0.161233i
$906$		0			0
$907$	−0.274398	−	4.18650i	−0.00911122	−	0.139010i	−0.999991	−	0.00426090i	$-0.998644\pi$
$907$	−0.274398	−	4.18650i	−0.00911122	−	0.139010i	0.990880	−	0.134749i	$-0.0430230\pi$
$908$		0			0
$909$	4.27782	+	10.3276i	0.141886	+	0.342544i
$910$		0			0
$911$	0.803527	−	4.03960i	0.0266220	−	0.133838i	−0.965189	−	0.261555i	$-0.915765\pi$
$911$	0.803527	−	4.03960i	0.0266220	−	0.133838i	0.991811	+	0.127717i	$0.0407648\pi$
$912$		0			0
$913$	−5.54603	+	16.3381i	−0.183547	+	0.540711i
$914$		0			0
$915$	5.73142	−	87.4446i	0.189475	−	2.89083i
$916$		0			0
$917$	−58.8752	−	2.00802i	−1.94423	−	0.0663108i
$918$		0			0
$919$	−3.84927	−	6.66713i	−0.126976	−	0.219928i	0.795528	−	0.605917i	$-0.207194\pi$
$919$	−3.84927	−	6.66713i	−0.126976	−	0.219928i	−0.922503	+	0.385989i	$0.873860\pi$
$920$		0			0
$921$	29.8880	−	14.7391i	0.984842	−	0.485670i
$922$		0			0
$923$	3.17455	+	15.9595i	0.104491	+	0.525314i
$924$		0			0
$925$	60.9445	+	12.1226i	2.00384	+	0.398589i
$926$		0			0
$927$	−0.854968	+	6.49413i	−0.0280808	+	0.213295i
$928$		0			0
$929$	11.8201	+	5.82901i	0.387804	+	0.191244i	0.625730	−	0.780040i	$-0.284801\pi$
$929$	11.8201	+	5.82901i	0.387804	+	0.191244i	−0.237927	+	0.971283i	$0.576468\pi$
$930$		0			0
$931$	18.0078	−	3.53077i	0.590182	−	0.115716i
$932$		0			0
$933$	−3.95822	−	30.0657i	−0.129586	−	0.984305i
$934$		0			0
$935$	7.41585	+	18.4144i	0.242524	+	0.602214i
$936$		0			0
$937$	−52.1431	−	21.5984i	−1.70344	−	0.705588i	−0.703455	−	0.710740i	$-0.748360\pi$
$937$	−52.1431	−	21.5984i	−1.70344	−	0.705588i	−0.999987	+	0.00515180i	$0.998360\pi$
$938$		0			0
$939$	−33.3373	−	33.3373i	−1.08792	−	1.08792i
$940$		0			0
$941$	26.1278	−	1.71251i	0.851742	−	0.0558261i	0.366723	−	0.930330i	$-0.380480\pi$
$941$	26.1278	−	1.71251i	0.851742	−	0.0558261i	0.485018	+	0.874504i	$0.338813\pi$
$942$		0			0
$943$	5.40829	−	7.04822i	0.176118	−	0.229522i
$944$		0			0
$945$	−7.56882	+	32.2612i	−0.246214	+	1.04946i
$946$		0			0
$947$	−26.6581	+	23.3785i	−0.866272	+	0.759700i	−0.972071	−	0.234688i	$-0.924593\pi$
$947$	−26.6581	+	23.3785i	−0.866272	+	0.759700i	0.105799	+	0.994388i	$0.466260\pi$
$948$		0			0
$949$	3.13855	+	6.36435i	0.101882	+	0.206596i
$950$		0			0
$951$	4.24638			0.137698
$952$		0			0
$953$	41.0835			1.33083			0.665413	−	0.746475i	$-0.268255\pi$
$953$	41.0835			1.33083			0.665413	+	0.746475i	$0.268255\pi$
$954$		0			0
$955$	−25.6349	−	51.9824i	−0.829525	−	1.68211i
$956$		0			0
$957$	13.1435	−	11.5265i	0.424868	−	0.372600i
$958$		0			0
$959$	−4.20113	−	13.9178i	−0.135661	−	0.449429i
$960$		0			0
$961$	−15.2594	+	19.8864i	−0.492237	+	0.641496i
$962$		0			0
$963$	−10.1460	+	0.665003i	−0.326950	+	0.0214294i
$964$		0			0
$965$	−17.2203	−	17.2203i	−0.554342	−	0.554342i
$966$		0			0
$967$	−8.61658	−	3.56911i	−0.277091	−	0.114775i	0.239811	−	0.970820i	$-0.422915\pi$
$967$	−8.61658	−	3.56911i	−0.277091	−	0.114775i	−0.516901	+	0.856045i	$0.672915\pi$
$968$		0			0
$969$	4.31164	+	22.8500i	0.138510	+	0.734047i
$970$		0			0
$971$	1.87055	+	14.2082i	0.0600287	+	0.455963i	0.994891	+	0.100953i	$0.0321892\pi$
$971$	1.87055	+	14.2082i	0.0600287	+	0.455963i	−0.934863	+	0.355010i	$0.884477\pi$
$972$		0			0
$973$	−1.09071	−	4.70689i	−0.0349664	−	0.150896i
$974$		0			0
$975$	−120.041	−	59.1976i	−3.84438	−	1.89584i
$976$		0			0
$977$	−1.81913	+	13.8177i	−0.0581993	+	0.442067i	0.937393	+	0.348275i	$0.113232\pi$
$977$	−1.81913	+	13.8177i	−0.0581993	+	0.442067i	−0.995592	+	0.0937925i	$0.970101\pi$
$978$		0			0
$979$	−1.73459	−	0.345032i	−0.0554379	−	0.0110273i
$980$		0			0
$981$	−3.35877	−	16.8857i	−0.107237	−	0.539118i
$982$		0			0
$983$	−14.1592	+	6.98252i	−0.451607	+	0.222708i	−0.653845	−	0.756628i	$-0.726845\pi$
$983$	−14.1592	+	6.98252i	−0.451607	+	0.222708i	0.202238	+	0.979336i	$0.435179\pi$
$984$		0			0
$985$	−45.8368	−	79.3916i	−1.46048	−	2.52963i
$986$		0			0
$987$	19.4448	−	31.1746i	0.618936	−	0.992299i
$988$		0			0
$989$	−0.666930	+	10.1754i	−0.0212071	+	0.323558i
$990$		0			0
$991$	−2.29970	+	6.77469i	−0.0730523	+	0.215205i	−0.977323	−	0.211755i	$-0.932082\pi$
$991$	−2.29970	+	6.77469i	−0.0730523	+	0.215205i	0.904270	+	0.426960i	$0.140415\pi$
$992$		0			0
$993$	−3.17424	+	15.9580i	−0.100732	+	0.506412i
$994$		0			0
$995$	−9.94435	−	24.0078i	−0.315257	−	0.761098i
$996$		0			0
$997$	0.910305	+	13.8886i	0.0288296	+	0.439855i	0.987736	+	0.156133i	$0.0499028\pi$
$997$	0.910305	+	13.8886i	0.0288296	+	0.439855i	−0.958906	+	0.283723i	$0.908431\pi$
$998$		0			0
$999$	3.64817	−	13.6151i	0.115423	−	0.430764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.129.2	yes	192
7.5	odd	6	inner	476.2.bl.a.61.2	✓	192
17.12	odd	16	inner	476.2.bl.a.437.2	yes	192
119.12	even	48	inner	476.2.bl.a.369.2	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.61.2	✓	192	7.5	odd	6	inner
476.2.bl.a.129.2	yes	192	1.1	even	1	trivial
476.2.bl.a.369.2	yes	192	119.12	even	48	inner
476.2.bl.a.437.2	yes	192	17.12	odd	16	inner

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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951503 - 1.92946i) q^{3} +(3.19070 - 2.79817i) q^{5} +(1.81126 - 1.92856i) q^{7} +(-0.991165 + 1.29171i) q^{9} +O(q^{10})\)	\(q+(-0.951503 - 1.92946i) q^{3} +(3.19070 - 2.79817i) q^{5} +(1.81126 - 1.92856i) q^{7} +(-0.991165 + 1.29171i) q^{9} +(1.13208 - 0.0742006i) q^{11} +(3.38136 + 3.38136i) q^{13} +(-8.43491 - 3.49385i) q^{15} +(-1.61528 + 3.79353i) q^{17} +(0.342178 + 2.59910i) q^{19} +(-5.44450 - 1.65971i) q^{21} +(-1.44882 - 0.714478i) q^{23} +(1.69819 - 12.8990i) q^{25} +(-2.89454 - 0.575760i) q^{27} +(1.39736 + 7.02498i) q^{29} +(-2.18472 + 1.07739i) q^{31} +(-1.22035 - 2.11370i) q^{33} +(0.382731 - 11.2217i) q^{35} +(-0.312371 + 4.76586i) q^{37} +(3.30681 - 9.74155i) q^{39} +(-1.07292 + 5.39391i) q^{41} +(-2.41567 - 5.83195i) q^{43} +(0.451916 + 6.89491i) q^{45} +(-1.67072 + 6.23520i) q^{47} +(-0.438705 - 6.98624i) q^{49} +(8.85640 - 0.492931i) q^{51} +(-6.29792 - 8.20761i) q^{53} +(3.40451 - 3.40451i) q^{55} +(4.68927 - 3.13327i) q^{57} +(-6.62862 - 0.872675i) q^{59} +(3.08530 + 9.08901i) q^{61} +(0.695892 + 4.25114i) q^{63} +(20.2505 + 1.32729i) q^{65} +(-4.42247 - 2.55331i) q^{67} +3.47526i q^{69} +(2.82935 + 1.89051i) q^{71} +(1.40519 + 0.476998i) q^{73} +(-26.5039 + 8.99687i) q^{75} +(1.90739 - 2.31769i) q^{77} +(-5.29903 + 10.7454i) q^{79} +(2.90746 + 10.8508i) q^{81} +(-5.81987 + 14.0504i) q^{83} +(5.46104 + 16.6238i) q^{85} +(12.2248 - 9.38044i) q^{87} +(-1.50577 - 0.403470i) q^{89} +(12.6457 - 0.396655i) q^{91} +(4.15754 + 3.19019i) q^{93} +(8.36450 + 7.33547i) q^{95} +(15.8701 - 3.15675i) q^{97} +(-1.02623 + 1.53587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) \) 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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