LMFDB - Embedded newform 637.2.h.m.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	16.0.468066644398978174550016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 $ x^16 + 8x^14 + 45x^12 + 124x^10 + 248x^8 + 250x^6 + 177x^4 + 14*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.1
Root			$0.558788 + 0.967849i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.m.471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.33152 q^{2} +(-1.15450 - 1.99966i) q^{3} +3.43596 q^{4} +(-1.68556 - 2.91947i) q^{5} +(2.69174 + 4.66224i) q^{6} -3.34797 q^{8} +(-1.16576 + 2.01915i) q^{9} +(3.92990 + 6.80679i) q^{10} +(-1.16576 - 2.01915i) q^{11} +(-3.96683 - 6.87075i) q^{12} +(0.408029 - 3.58239i) q^{13} +(-3.89197 + 6.74108i) q^{15} +0.933914 q^{16} -5.45734 q^{17} +(2.71798 - 4.70768i) q^{18} +(3.58410 - 6.20784i) q^{19} +(-5.79151 - 10.0312i) q^{20} +(2.71798 + 4.70768i) q^{22} -6.45242 q^{23} +(3.86524 + 6.69480i) q^{24} +(-3.18221 + 5.51175i) q^{25} +(-0.951325 + 8.35239i) q^{26} -1.54354 q^{27} +(4.22143 - 7.31174i) q^{29} +(9.07418 - 15.7169i) q^{30} +(1.52560 - 2.64242i) q^{31} +4.51850 q^{32} +(-2.69174 + 4.66224i) q^{33} +12.7239 q^{34} +(-4.00550 + 6.93773i) q^{36} +3.05653 q^{37} +(-8.35637 + 14.4737i) q^{38} +(-7.63463 + 3.31996i) q^{39} +(5.64320 + 9.77430i) q^{40} +(0.468833 - 0.812043i) q^{41} +(2.04605 + 3.54385i) q^{43} +(-4.00550 - 6.93773i) q^{44} +7.85981 q^{45} +15.0439 q^{46} +(1.73168 + 2.99936i) q^{47} +(-1.07821 - 1.86751i) q^{48} +(7.41937 - 12.8507i) q^{50} +(6.30052 + 10.9128i) q^{51} +(1.40197 - 12.3090i) q^{52} +(1.17194 - 2.02985i) q^{53} +3.59878 q^{54} +(-3.92990 + 6.80679i) q^{55} -16.5514 q^{57} +(-9.84233 + 17.0474i) q^{58} +7.24693 q^{59} +(-13.3726 + 23.1621i) q^{60} +(-3.19506 + 5.53401i) q^{61} +(-3.55697 + 6.16085i) q^{62} -12.4028 q^{64} +(-11.1464 + 4.84710i) q^{65} +(6.27584 - 10.8701i) q^{66} +(-2.30670 - 3.99532i) q^{67} -18.7512 q^{68} +(7.44934 + 12.9026i) q^{69} +(3.79370 + 6.57088i) q^{71} +(3.90292 - 6.76006i) q^{72} +(1.03498 - 1.79264i) q^{73} -7.12636 q^{74} +14.6955 q^{75} +(12.3148 - 21.3299i) q^{76} +(17.8002 - 7.74054i) q^{78} +(3.79434 + 6.57199i) q^{79} +(-1.57417 - 2.72654i) q^{80} +(5.27929 + 9.14400i) q^{81} +(-1.09309 + 1.89329i) q^{82} -2.89335 q^{83} +(9.19866 + 15.9326i) q^{85} +(-4.77039 - 8.26255i) q^{86} -19.4946 q^{87} +(3.90292 + 6.76006i) q^{88} +13.1597 q^{89} -18.3253 q^{90} -22.1703 q^{92} -7.04526 q^{93} +(-4.03744 - 6.99305i) q^{94} -24.1648 q^{95} +(-5.21663 - 9.03546i) q^{96} +(1.77856 + 3.08056i) q^{97} +5.43596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 24 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} + 8 q^{16} + 28 q^{18} + 28 q^{22} - 24 q^{23} + 12 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} + 16 q^{37} + 20 q^{39} + 32 q^{43} + 4 q^{44}+ \cdots + 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 + 24 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 + 8 * q^16 + 28 * q^18 + 28 * q^22 - 24 * q^23 + 12 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 + 16 * q^37 + 20 * q^39 + 32 * q^43 + 4 * q^44 + 8 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 - 48 * q^58 - 64 * q^60 - 64 * q^64 - 68 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 - 152 * q^74 + 28 * q^78 + 4 * q^79 + 56 * q^81 + 36 * q^85 - 4 * q^86 + 28 * q^88 - 160 * q^92 - 16 * q^93 - 104 * q^95 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.33152			−1.64863			−0.824315	−	0.566131i	$-0.808440\pi$
$2$	−2.33152			−1.64863			−0.824315	+	0.566131i	$0.808440\pi$
$3$	−1.15450	−	1.99966i	−0.666553	−	1.15450i	−0.978862	−	0.204523i	$-0.934436\pi$
$3$	−1.15450	−	1.99966i	−0.666553	−	1.15450i	0.312309	−	0.949981i	$-0.398898\pi$
$4$	3.43596			1.71798
$5$	−1.68556	−	2.91947i	−0.753804	−	1.30563i	−0.945966	−	0.324264i	$-0.894883\pi$
$5$	−1.68556	−	2.91947i	−0.753804	−	1.30563i	0.192162	−	0.981363i	$-0.438450\pi$
$6$	2.69174	+	4.66224i	1.09890	+	1.90335i
$7$		0			0
$7$		0			0
$8$	−3.34797			−1.18369
$9$	−1.16576	+	2.01915i	−0.388586	+	0.673050i
$10$	3.92990	+	6.80679i	1.24274	+	2.15250i
$11$	−1.16576	−	2.01915i	−0.351489	−	0.608797i	0.635021	−	0.772494i	$-0.280991\pi$
$11$	−1.16576	−	2.01915i	−0.351489	−	0.608797i	−0.986511	+	0.163697i	$0.947658\pi$
$12$	−3.96683	−	6.87075i	−1.14513	−	1.98342i
$13$	0.408029	−	3.58239i	0.113167	−	0.993576i
$13$	0.408029	−	3.58239i	0.113167	−	0.993576i
$14$		0			0
$15$	−3.89197	+	6.74108i	−1.00490	+	1.74054i
$16$	0.933914			0.233479
$17$	−5.45734			−1.32360			−0.661800	−	0.749681i	$-0.730207\pi$
$17$	−5.45734			−1.32360			−0.661800	+	0.749681i	$0.730207\pi$
$18$	2.71798	−	4.70768i	0.640634	−	1.10961i
$19$	3.58410	−	6.20784i	0.822248	−	1.42418i	−0.0817564	−	0.996652i	$-0.526053\pi$
$19$	3.58410	−	6.20784i	0.822248	−	1.42418i	0.904004	−	0.427523i	$-0.140614\pi$
$20$	−5.79151	−	10.0312i	−1.29502	−	2.24304i
$21$		0			0
$22$	2.71798	+	4.70768i	0.579476	+	1.00368i
$23$	−6.45242			−1.34542			−0.672711	−	0.739905i	$-0.734870\pi$
$23$	−6.45242			−1.34542			−0.672711	+	0.739905i	$0.734870\pi$
$24$	3.86524	+	6.69480i	0.788989	+	1.36657i
$25$	−3.18221	+	5.51175i	−0.636442	+	1.10235i
$26$	−0.951325	+	8.35239i	−0.186570	+	1.63804i
$27$	−1.54354			−0.297054
$28$		0			0
$29$	4.22143	−	7.31174i	0.783900	−	1.35776i	−0.145753	−	0.989321i	$-0.546561\pi$
$29$	4.22143	−	7.31174i	0.783900	−	1.35776i	0.929654	−	0.368434i	$-0.120106\pi$
$30$	9.07418	−	15.7169i	1.65671	−	2.86951i
$31$	1.52560	−	2.64242i	0.274007	−	0.474593i	−0.695877	−	0.718161i	$-0.744984\pi$
$31$	1.52560	−	2.64242i	0.274007	−	0.474593i	0.969884	+	0.243567i	$0.0783176\pi$
$32$	4.51850			0.798766
$33$	−2.69174	+	4.66224i	−0.468572	+	0.811591i
$34$	12.7239			2.18213
$35$		0			0
$36$	−4.00550	+	6.93773i	−0.667583	+	1.15629i
$37$	3.05653			0.502491			0.251246	−	0.967923i	$-0.419160\pi$
$37$	3.05653			0.502491			0.251246	+	0.967923i	$0.419160\pi$
$38$	−8.35637	+	14.4737i	−1.35558	+	2.34794i
$39$	−7.63463	+	3.31996i	−1.22252	+	0.531620i
$40$	5.64320	+	9.77430i	0.892268	+	1.54545i
$41$	0.468833	−	0.812043i	0.0732194	−	0.126820i	−0.827091	−	0.562068i	$-0.810006\pi$
$41$	0.468833	−	0.812043i	0.0732194	−	0.126820i	0.900311	+	0.435248i	$0.143339\pi$
$42$		0			0
$43$	2.04605	+	3.54385i	0.312019	+	0.540433i	0.978799	−	0.204822i	$-0.0656614\pi$
$43$	2.04605	+	3.54385i	0.312019	+	0.540433i	−0.666780	+	0.745254i	$0.732328\pi$
$44$	−4.00550	−	6.93773i	−0.603852	−	1.04590i
$45$	7.85981			1.17167
$46$	15.0439			2.21810
$47$	1.73168	+	2.99936i	0.252591	+	0.437501i	0.964239	−	0.265036i	$-0.0853838\pi$
$47$	1.73168	+	2.99936i	0.252591	+	0.437501i	−0.711647	+	0.702537i	$0.752050\pi$
$48$	−1.07821	−	1.86751i	−0.155626	−	0.269552i
$49$		0			0
$50$	7.41937	−	12.8507i	1.04926	−	1.81737i
$51$	6.30052	+	10.9128i	0.882249	+	1.52810i
$52$	1.40197	−	12.3090i	0.194418	−	1.70695i
$53$	1.17194	−	2.02985i	0.160978	−	0.278822i	−0.774242	−	0.632890i	$-0.781869\pi$
$53$	1.17194	−	2.02985i	0.160978	−	0.278822i	0.935220	+	0.354068i	$0.115202\pi$
$54$	3.59878			0.489732
$55$	−3.92990	+	6.80679i	−0.529908	+	0.917828i
$56$		0			0
$57$	−16.5514			−2.19229
$58$	−9.84233	+	17.0474i	−1.29236	+	2.23844i
$59$	7.24693			0.943470			0.471735	−	0.881740i	$-0.343628\pi$
$59$	7.24693			0.943470			0.471735	+	0.881740i	$0.343628\pi$
$60$	−13.3726	+	23.1621i	−1.72640	+	2.99022i
$61$	−3.19506	+	5.53401i	−0.409086	+	0.708558i	−0.994788	−	0.101969i	$-0.967486\pi$
$61$	−3.19506	+	5.53401i	−0.409086	+	0.708558i	0.585702	+	0.810527i	$0.300819\pi$
$62$	−3.55697	+	6.16085i	−0.451736	+	0.782429i
$63$		0			0
$64$	−12.4028			−1.55035
$65$	−11.1464	+	4.84710i	−1.38255	+	0.601208i
$66$	6.27584	−	10.8701i	0.772502	−	1.33801i
$67$	−2.30670	−	3.99532i	−0.281808	−	0.488106i	0.690022	−	0.723788i	$-0.257601\pi$
$67$	−2.30670	−	3.99532i	−0.281808	−	0.488106i	−0.971830	+	0.235682i	$0.924268\pi$
$68$	−18.7512			−2.27392
$69$	7.44934	+	12.9026i	0.896795	+	1.55329i
$70$		0			0
$71$	3.79370	+	6.57088i	0.450229	+	0.779819i	0.998400	−	0.0565468i	$-0.0180090\pi$
$71$	3.79370	+	6.57088i	0.450229	+	0.779819i	−0.548171	+	0.836366i	$0.684676\pi$
$72$	3.90292	−	6.76006i	0.459964	−	0.796680i
$73$	1.03498	−	1.79264i	0.121136	−	0.209813i	−0.799080	−	0.601224i	$-0.794680\pi$
$73$	1.03498	−	1.79264i	0.121136	−	0.209813i	0.920216	+	0.391412i	$0.128013\pi$
$74$	−7.12636			−0.828422
$75$	14.6955			1.69689
$76$	12.3148	−	21.3299i	1.41261	−	2.44671i
$77$		0			0
$78$	17.8002	−	7.74054i	2.01548	−	0.876444i
$79$	3.79434	+	6.57199i	0.426897	+	0.739407i	0.996595	−	0.0824467i	$-0.0262734\pi$
$79$	3.79434	+	6.57199i	0.426897	+	0.739407i	−0.569699	+	0.821854i	$0.692940\pi$
$80$	−1.57417	−	2.72654i	−0.175997	−	0.304836i
$81$	5.27929	+	9.14400i	0.586588	+	1.01600i
$82$	−1.09309	+	1.89329i	−0.120712	+	0.209079i
$83$	−2.89335			−0.317587			−0.158793	−	0.987312i	$-0.550760\pi$
$83$	−2.89335			−0.317587			−0.158793	+	0.987312i	$0.550760\pi$
$84$		0			0
$85$	9.19866	+	15.9326i	0.997735	+	1.72813i
$86$	−4.77039	−	8.26255i	−0.514404	−	0.890974i
$87$	−19.4946			−2.09004
$88$	3.90292	+	6.76006i	0.416053	+	0.720624i
$89$	13.1597			1.39492			0.697461	−	0.716622i	$-0.254313\pi$
$89$	13.1597			1.39492			0.697461	+	0.716622i	$0.254313\pi$
$90$	−18.3253			−1.93165
$91$		0			0
$92$	−22.1703			−2.31141
$93$	−7.04526			−0.730560
$94$	−4.03744	−	6.99305i	−0.416430	−	0.721278i
$95$	−24.1648			−2.47926
$96$	−5.21663	−	9.03546i	−0.532420	−	0.922178i
$97$	1.77856	+	3.08056i	0.180585	+	0.312783i	0.942080	−	0.335388i	$-0.108867\pi$
$97$	1.77856	+	3.08056i	0.180585	+	0.312783i	−0.761495	+	0.648171i	$0.775534\pi$
$98$		0			0
$99$	5.43596			0.546335
$100$	−10.9340	+	18.9382i	−1.09340	+	1.89382i
$101$	−2.36432	−	4.09513i	−0.235259	−	0.407481i	0.724089	−	0.689707i	$-0.242260\pi$
$101$	−2.36432	−	4.09513i	−0.235259	−	0.407481i	−0.959348	+	0.282226i	$0.908927\pi$
$102$	−14.6898	−	25.4434i	−1.45450	−	2.51927i
$103$	2.99143	+	5.18131i	0.294754	+	0.510529i	0.974928	−	0.222522i	$-0.0714289\pi$
$103$	2.99143	+	5.18131i	0.294754	+	0.510529i	−0.680173	+	0.733051i	$0.738096\pi$
$104$	−1.36607	+	11.9937i	−0.133954	+	1.17608i
$105$		0			0
$106$	−2.73239	+	4.73263i	−0.265393	+	0.459674i
$107$	13.1826			1.27441			0.637206	−	0.770694i	$-0.280090\pi$
$107$	13.1826			1.27441			0.637206	+	0.770694i	$0.280090\pi$
$108$	−5.30353			−0.510333
$109$	−2.05772	+	3.56408i	−0.197094	+	0.341377i	−0.947585	−	0.319504i	$-0.896484\pi$
$109$	−2.05772	+	3.56408i	−0.197094	+	0.341377i	0.750491	+	0.660881i	$0.229817\pi$
$110$	9.16263	−	15.8701i	0.873623	−	1.51316i
$111$	−3.52878	−	6.11203i	−0.334937	−	0.580128i
$112$		0			0
$113$	−7.14026	−	12.3673i	−0.671699	−	1.16342i	−0.977422	−	0.211297i	$-0.932231\pi$
$113$	−7.14026	−	12.3673i	−0.671699	−	1.16342i	0.305723	−	0.952121i	$-0.401102\pi$
$114$	38.5899			3.61427
$115$	10.8759	+	18.8376i	1.01418	+	1.75662i
$116$	14.5047	−	25.1229i	1.34673	−	2.33260i
$117$	6.75772	+	5.00007i	0.624752	+	0.462257i
$118$	−16.8963			−1.55543
$119$		0			0
$120$	13.0302	−	22.5689i	1.18949	−	2.06025i
$121$	2.78202	−	4.81860i	0.252911	−	0.438054i
$122$	7.44934	−	12.9026i	0.674431	−	1.16815i
$123$	−2.16508			−0.195219
$124$	5.24192	−	9.07927i	0.470738	−	0.815343i
$125$	4.59963			0.411403
$126$		0			0
$127$	5.53854	−	9.59304i	0.491466	−	0.851244i	−0.508486	−	0.861071i	$-0.669794\pi$
$127$	5.53854	−	9.59304i	0.491466	−	0.851244i	0.999952	+	0.00982616i	$0.00312781\pi$
$128$	19.8803			1.75718
$129$	4.72433	−	8.18279i	0.415954	−	0.720454i
$130$	25.9881	−	11.3011i	2.27931	−	0.991170i
$131$	0.336006	+	0.581979i	0.0293570	+	0.0508478i	0.880331	−	0.474361i	$-0.157321\pi$
$131$	0.336006	+	0.581979i	0.0293570	+	0.0508478i	−0.850974	+	0.525208i	$0.823987\pi$
$132$	−9.24873	+	16.0193i	−0.804998	+	1.39430i
$133$		0			0
$134$	5.37810	+	9.31515i	0.464597	+	0.804706i
$135$	2.60172	+	4.50631i	0.223920	+	0.387842i
$136$	18.2710			1.56673
$137$	7.83875			0.669709			0.334855	−	0.942270i	$-0.391313\pi$
$137$	7.83875			0.669709			0.334855	+	0.942270i	$0.391313\pi$
$138$	−17.3682	−	30.0827i	−1.47848	−	2.56081i
$139$	−1.63760	−	2.83641i	−0.138900	−	0.240581i	0.788181	−	0.615444i	$-0.211023\pi$
$139$	−1.63760	−	2.83641i	−0.138900	−	0.240581i	−0.927080	+	0.374863i	$0.877690\pi$
$140$		0			0
$141$	3.99846	−	6.92554i	0.336731	−	0.583236i
$142$	−8.84506	−	15.3201i	−0.742261	−	1.28563i
$143$	−7.70905	+	3.35233i	−0.644663	+	0.280336i
$144$	−1.08872	+	1.88571i	−0.0907265	+	0.157143i
$145$	−28.4619			−2.36363
$146$	−2.41308	+	4.17957i	−0.199708	+	0.345904i
$147$		0			0
$148$	10.5021			0.863270
$149$	7.08186	−	12.2661i	0.580169	−	1.00488i	−0.415290	−	0.909689i	$-0.636320\pi$
$149$	7.08186	−	12.2661i	0.580169	−	1.00488i	0.995459	−	0.0951925i	$-0.0303467\pi$
$150$	−34.2628			−2.79754
$151$	0.673125	−	1.16589i	0.0547781	−	0.0948785i	−0.837336	−	0.546689i	$-0.815888\pi$
$151$	0.673125	−	1.16589i	0.0547781	−	0.0948785i	0.892114	+	0.451810i	$0.149222\pi$
$152$	−11.9994	+	20.7836i	−0.973283	+	1.68578i
$153$	6.36194	−	11.0192i	0.514332	−	0.890849i
$154$		0			0
$155$	−10.2860			−0.826190
$156$	−26.2323	+	11.4073i	−2.10026	+	0.913313i
$157$	6.52006	−	11.2931i	0.520357	−	0.901285i	−0.479363	−	0.877617i	$-0.659132\pi$
$157$	6.52006	−	11.2931i	0.520357	−	0.901285i	0.999720	−	0.0236682i	$-0.00753454\pi$
$158$	−8.84657	−	15.3227i	−0.703795	−	1.21901i
$159$	−5.41202			−0.429201
$160$	−7.61620	−	13.1916i	−0.602113	−	1.04289i
$161$		0			0
$162$	−12.3087	−	21.3194i	−0.967067	−	1.67501i
$163$	−2.46628	+	4.27172i	−0.193174	+	0.334587i	−0.946300	−	0.323289i	$-0.895211\pi$
$163$	−2.46628	+	4.27172i	−0.193174	+	0.334587i	0.753127	+	0.657876i	$0.228545\pi$
$164$	1.61089	−	2.79015i	0.125790	−	0.217874i
$165$	18.1484			1.41285
$166$	6.74590			0.523583
$167$	−1.82128	+	3.15455i	−0.140935	+	0.244107i	−0.927849	−	0.372956i	$-0.878344\pi$
$167$	−1.82128	+	3.15455i	−0.140935	+	0.244107i	0.786914	+	0.617063i	$0.211678\pi$
$168$		0			0
$169$	−12.6670	−	2.92344i	−0.974387	−	0.224880i
$170$	−21.4468	−	37.1470i	−1.64490	−	2.84904i
$171$	8.35637	+	14.4737i	0.639028	+	1.10683i
$172$	7.03014	+	12.1766i	0.536043	+	0.928453i
$173$	−6.34584	+	10.9913i	−0.482465	+	0.835654i	−0.999797	−	0.0201306i	$-0.993592\pi$
$173$	−6.34584	+	10.9913i	−0.482465	+	0.835654i	0.517332	+	0.855785i	$0.326925\pi$
$174$	45.4520			3.44571
$175$		0			0
$176$	−1.08872	−	1.88571i	−0.0820652	−	0.142141i
$177$	−8.36661	−	14.4914i	−0.628873	−	1.08924i
$178$	−30.6820			−2.29971
$179$	4.39469	+	7.61183i	0.328475	+	0.568935i	0.982209	−	0.187789i	$-0.0601321\pi$
$179$	4.39469	+	7.61183i	0.328475	+	0.568935i	−0.653735	+	0.756724i	$0.726799\pi$
$180$	27.0060			2.01291
$181$	−17.1982			−1.27833			−0.639167	−	0.769068i	$-0.720721\pi$
$181$	−17.1982			−1.27833			−0.639167	+	0.769068i	$0.720721\pi$
$182$		0			0
$183$	14.7548			1.09071
$184$	21.6025			1.59256
$185$	−5.15197	−	8.92347i	−0.378780	−	0.656066i
$186$	16.4261			1.20442
$187$	6.36194	+	11.0192i	0.465231	+	0.805804i
$188$	5.94999	+	10.3057i	0.433947	+	0.751619i
$189$		0			0
$190$	56.3406			4.08738
$191$	−0.533902	+	0.924745i	−0.0386318	+	0.0669122i	−0.884695	−	0.466171i	$-0.845633\pi$
$191$	−0.533902	+	0.924745i	−0.0386318	+	0.0669122i	0.846063	+	0.533083i	$0.178967\pi$
$192$	14.3191	+	24.8013i	1.03339	+	1.78988i
$193$	−1.57790	−	2.73300i	−0.113580	−	0.196726i	0.803631	−	0.595127i	$-0.202898\pi$
$193$	−1.57790	−	2.73300i	−0.113580	−	0.196726i	−0.917211	+	0.398402i	$0.869565\pi$
$194$	−4.14674	−	7.18237i	−0.297719	−	0.515664i
$195$	22.5611	+	16.6931i	1.61564	+	1.19542i
$196$		0			0
$197$	8.84783	−	15.3249i	0.630382	−	1.09185i	−0.357092	−	0.934069i	$-0.616232\pi$
$197$	8.84783	−	15.3249i	0.630382	−	1.09185i	0.987474	−	0.157784i	$-0.0504351\pi$
$198$	−12.6740			−0.900704
$199$	12.9895			0.920803			0.460402	−	0.887711i	$-0.347705\pi$
$199$	12.9895			0.920803			0.460402	+	0.887711i	$0.347705\pi$
$200$	10.6539	−	18.4532i	0.753348	−	1.30484i
$201$	−5.32619	+	9.22522i	−0.375680	+	0.650697i
$202$	5.51246	+	9.54785i	0.387855	+	0.671785i
$203$		0			0
$204$	21.6484	+	37.4960i	1.51569	+	2.62525i
$205$	−3.16098			−0.220773
$206$	−6.97456	−	12.0803i	−0.485941	−	0.841674i
$207$	7.52195	−	13.0284i	0.522812	−	0.905537i
$208$	0.381064	−	3.34565i	0.0264220	−	0.231979i
$209$	−16.7127			−1.15605
$210$		0			0
$211$	−13.7701	+	23.8505i	−0.947974	+	1.64194i	−0.198289	+	0.980144i	$0.563538\pi$
$211$	−13.7701	+	23.8505i	−0.947974	+	1.64194i	−0.749685	+	0.661795i	$0.769795\pi$
$212$	4.02673	−	6.97450i	0.276557	−	0.479011i
$213$	8.75967	−	15.1722i	0.600203	−	1.03958i
$214$	−30.7355			−2.10103
$215$	6.89746	−	11.9467i	0.470403	−	0.814761i
$216$	5.16771			0.351618
$217$		0			0
$218$	4.79761	−	8.30971i	0.324935	−	0.562805i
$219$	−4.77956			−0.322973
$220$	−13.5030	+	23.3879i	−0.910372	+	1.57681i
$221$	−2.22675	+	19.5503i	−0.149788	+	1.31510i
$222$	8.22740	+	14.2503i	0.552187	+	0.956416i
$223$	4.35098	−	7.53612i	0.291363	−	0.504656i	−0.682769	−	0.730634i	$-0.739224\pi$
$223$	4.35098	−	7.53612i	0.291363	−	0.504656i	0.974132	+	0.225978i	$0.0725578\pi$
$224$		0			0
$225$	−7.41937	−	12.8507i	−0.494625	−	0.856715i
$226$	16.6476	+	28.8345i	1.10738	+	1.91805i
$227$	−21.9669			−1.45800			−0.728998	−	0.684516i	$-0.760013\pi$
$227$	−21.9669			−1.45800			−0.728998	+	0.684516i	$0.760013\pi$
$228$	−56.8700			−3.76631
$229$	−10.2594	−	17.7698i	−0.677959	−	1.17426i	−0.975595	−	0.219580i	$-0.929531\pi$
$229$	−10.2594	−	17.7698i	−0.677959	−	1.17426i	0.297636	−	0.954679i	$-0.403802\pi$
$230$	−25.3574	−	43.9203i	−1.67202	−	2.89602i
$231$		0			0
$232$	−14.1332	+	24.4795i	−0.927892	+	1.60716i
$233$	8.64439	+	14.9725i	0.566313	+	0.980883i	0.996926	+	0.0783463i	$0.0249640\pi$
$233$	8.64439	+	14.9725i	0.566313	+	0.980883i	−0.430613	+	0.902537i	$0.641703\pi$
$234$	−15.7557	−	11.6577i	−1.02998	−	0.762090i
$235$	5.83769	−	10.1112i	0.380809	−	0.659581i
$236$	24.9002			1.62086
$237$	8.76116	−	15.1748i	0.569099	−	0.985708i
$238$		0			0
$239$	3.25961			0.210847			0.105423	−	0.994427i	$-0.466380\pi$
$239$	3.25961			0.210847			0.105423	+	0.994427i	$0.466380\pi$
$240$	−3.63476	+	6.29559i	−0.234623	+	0.406379i
$241$	1.46571			0.0944149			0.0472074	−	0.998885i	$-0.484968\pi$
$241$	1.46571			0.0944149			0.0472074	+	0.998885i	$0.484968\pi$
$242$	−6.48632	+	11.2346i	−0.416956	+	0.722190i
$243$	9.87462	−	17.1033i	0.633457	−	1.09718i
$244$	−10.9781	+	19.0147i	−0.702802	+	1.21729i
$245$		0			0
$246$	5.04791			0.321843
$247$	−20.7765	−	15.3726i	−1.32198	−	0.978135i
$248$	−5.10768	+	8.84676i	−0.324338	+	0.561770i
$249$	3.34039	+	5.78572i	0.211688	+	0.366655i
$250$	−10.7241			−0.678252
$251$	8.55142	+	14.8115i	0.539761	+	0.934894i	0.998917	+	0.0465376i	$0.0148187\pi$
$251$	8.55142	+	14.8115i	0.539761	+	0.934894i	−0.459156	+	0.888356i	$0.651848\pi$
$252$		0			0
$253$	7.52195	+	13.0284i	0.472901	+	0.819089i
$254$	−12.9132	+	22.3663i	−0.810246	+	1.40339i
$255$	21.2398	−	36.7884i	1.33009	−	2.30378i
$256$	−21.5456			−1.34660
$257$	−3.85011			−0.240163			−0.120082	−	0.992764i	$-0.538316\pi$
$257$	−3.85011			−0.240163			−0.120082	+	0.992764i	$0.538316\pi$
$258$	−11.0149	+	19.0783i	−0.685755	+	1.18776i
$259$		0			0
$260$	−38.2988	+	16.6544i	−2.37519	+	1.03286i
$261$	9.84233	+	17.0474i	0.609225	+	1.05521i
$262$	−0.783403	−	1.35689i	−0.0483988	−	0.0838292i
$263$	15.2579	+	26.4275i	0.940844	+	1.62959i	0.763866	+	0.645375i	$0.223299\pi$
$263$	15.2579	+	26.4275i	0.940844	+	1.62959i	0.176978	+	0.984215i	$0.443368\pi$
$264$	9.01187	−	15.6090i	0.554642	−	0.960669i
$265$	−7.90147			−0.485383
$266$		0			0
$267$	−15.1929	−	26.3149i	−0.929790	−	1.61044i
$268$	−7.92573	−	13.7278i	−0.484141	−	0.838557i
$269$	−16.7771			−1.02292			−0.511460	−	0.859307i	$-0.670895\pi$
$269$	−16.7771			−1.02292			−0.511460	+	0.859307i	$0.670895\pi$
$270$	−6.06595	−	10.5065i	−0.369162	−	0.639407i
$271$	−31.1772			−1.89388			−0.946941	−	0.321407i	$-0.895844\pi$
$271$	−31.1772			−1.89388			−0.946941	+	0.321407i	$0.895844\pi$
$272$	−5.09669			−0.309032
$273$		0			0
$274$	−18.2762			−1.10410
$275$	14.8387			0.894810
$276$	25.5956	+	44.3330i	1.54068	+	2.66853i
$277$	0.395882			0.0237863			0.0118931	−	0.999929i	$-0.496214\pi$
$277$	0.395882			0.0237863			0.0118931	+	0.999929i	$0.496214\pi$
$278$	3.81810	+	6.61314i	0.228994	+	0.396630i
$279$	3.55697	+	6.16085i	0.212950	+	0.368841i
$280$		0			0
$281$	−22.9459			−1.36884			−0.684420	−	0.729088i	$-0.739944\pi$
$281$	−22.9459			−1.36884			−0.684420	+	0.729088i	$0.739944\pi$
$282$	−9.32247	+	16.1470i	−0.555145	+	0.961540i
$283$	9.67575	+	16.7589i	0.575164	+	0.996213i	0.996024	+	0.0890873i	$0.0283950\pi$
$283$	9.67575	+	16.7589i	0.575164	+	0.996213i	−0.420860	+	0.907126i	$0.638272\pi$
$284$	13.0350	+	22.5773i	0.773485	+	1.33972i
$285$	27.8984	+	48.3214i	1.65256	+	2.86231i
$286$	17.9738	−	7.81600i	1.06281	−	0.462170i
$287$		0			0
$288$	−5.26748	+	9.12354i	−0.310389	+	0.537610i
$289$	12.7826			0.751916
$290$	66.3593			3.89675
$291$	4.10671	−	7.11303i	0.240740	−	0.416973i
$292$	3.55616	−	6.15945i	0.208109	−	0.360455i
$293$	−7.88616	−	13.6592i	−0.460715	−	0.797981i	0.538282	−	0.842765i	$-0.319074\pi$
$293$	−7.88616	−	13.6592i	−0.460715	−	0.797981i	−0.998997	+	0.0447835i	$0.985740\pi$
$294$		0			0
$295$	−12.2151	−	21.1572i	−0.711192	−	1.23182i
$296$	−10.2332			−0.594792
$297$	1.79939	+	3.11663i	0.104411	+	0.180845i
$298$	−16.5115	+	28.5987i	−0.956483	+	1.65668i
$299$	−2.63277	+	23.1151i	−0.152257	+	1.33678i
$300$	50.4932			2.91523
$301$		0			0
$302$	−1.56940	+	2.71828i	−0.0903089	+	0.156420i
$303$	−5.45924	+	9.45568i	−0.313625	+	0.543215i
$304$	3.34724	−	5.79759i	0.191977	−	0.332515i
$305$	21.5419			1.23348
$306$	−14.8330	+	25.6914i	−0.847943	+	1.46868i
$307$	−19.2535			−1.09885			−0.549427	−	0.835542i	$-0.685154\pi$
$307$	−19.2535			−1.09885			−0.549427	+	0.835542i	$0.685154\pi$
$308$		0			0
$309$	6.90723	−	11.9637i	0.392939	−	0.680590i
$310$	23.9819			1.36208
$311$	1.53232	−	2.65405i	0.0868898	−	0.150498i	−0.819305	−	0.573358i	$-0.805641\pi$
$311$	1.53232	−	2.65405i	0.0868898	−	0.150498i	0.906195	+	0.422860i	$0.138974\pi$
$312$	25.5605	−	11.1151i	1.44708	−	0.629271i
$313$	−17.6376	−	30.5492i	−0.996934	−	1.72674i	−0.566229	−	0.824248i	$-0.691598\pi$
$313$	−17.6376	−	30.5492i	−0.996934	−	1.72674i	−0.430705	−	0.902493i	$-0.641735\pi$
$314$	−15.2016	+	26.3300i	−0.857877	+	1.48589i
$315$		0			0
$316$	13.0372	+	22.5811i	0.733401	+	1.27029i
$317$	−16.3533	−	28.3247i	−0.918490	−	1.59087i	−0.801709	−	0.597714i	$-0.796076\pi$
$317$	−16.3533	−	28.3247i	−0.918490	−	1.59087i	−0.116781	−	0.993158i	$-0.537258\pi$
$318$	12.6182			0.707594
$319$	−19.6847			−1.10213
$320$	20.9056	+	36.2096i	1.16866	+	2.02418i
$321$	−15.2194	−	26.3607i	−0.849463	−	1.47131i
$322$		0			0
$323$	−19.5596	+	33.8783i	−1.08833	+	1.88504i
$324$	18.1394	+	31.4184i	1.00775	+	1.74547i
$325$	18.4468	+	13.6489i	1.02324	+	0.757103i
$326$	5.75016	−	9.95958i	0.318472	−	0.551610i
$327$	9.50260			0.525495
$328$	−1.56964	+	2.71869i	−0.0866688	+	0.150115i
$329$		0			0
$330$	−42.3132			−2.32926
$331$	−2.38851	+	4.13703i	−0.131285	+	0.227392i	−0.924172	−	0.381977i	$-0.875244\pi$
$331$	−2.38851	+	4.13703i	−0.131285	+	0.227392i	0.792887	+	0.609368i	$0.208577\pi$
$332$	−9.94145			−0.545608
$333$	−3.56318	+	6.17161i	−0.195261	+	0.338202i
$334$	4.24635	−	7.35489i	0.232350	−	0.402442i
$335$	−7.77615	+	13.4687i	−0.424856	+	0.735873i
$336$		0			0
$337$	26.2392			1.42934			0.714669	−	0.699463i	$-0.246577\pi$
$337$	26.2392			1.42934			0.714669	+	0.699463i	$0.246577\pi$
$338$	29.5334	+	6.81603i	1.60640	+	0.370743i
$339$	−16.4869	+	28.5562i	−0.895447	+	1.55096i
$340$	31.6063	+	54.7437i	1.71409	+	2.96889i
$341$	−7.11394			−0.385241
$342$	−19.4830	−	33.7456i	−1.05352	−	1.82475i
$343$		0			0
$344$	−6.85010	−	11.8647i	−0.369332	−	0.639702i
$345$	25.1126	−	43.4963i	1.35202	−	2.34176i
$346$	14.7954	−	25.6264i	0.795407	−	1.37768i
$347$	−10.4442			−0.560675			−0.280338	−	0.959901i	$-0.590446\pi$
$347$	−10.4442			−0.560675			−0.280338	+	0.959901i	$0.590446\pi$
$348$	−66.9829			−3.59066
$349$	11.7344	−	20.3246i	0.628128	−	1.08795i	−0.359799	−	0.933030i	$-0.617155\pi$
$349$	11.7344	−	20.3246i	0.628128	−	1.08795i	0.987927	−	0.154920i	$-0.0495118\pi$
$350$		0			0
$351$	−0.629807	+	5.52955i	−0.0336166	+	0.295145i
$352$	−5.26748	−	9.12354i	−0.280758	−	0.486286i
$353$	1.46567	+	2.53862i	0.0780099	+	0.135117i	0.902391	−	0.430918i	$-0.141810\pi$
$353$	1.46567	+	2.53862i	0.0780099	+	0.135117i	−0.824381	+	0.566035i	$0.808477\pi$
$354$	19.5069	+	33.7869i	1.03678	+	1.79575i
$355$	12.7890	−	22.1512i	0.678769	−	1.17566i
$356$	45.2162			2.39645
$357$		0			0
$358$	−10.2463	−	17.7471i	−0.541533	−	0.937963i
$359$	8.55069	+	14.8102i	0.451288	+	0.781654i	0.998466	−	0.0553624i	$-0.0176314\pi$
$359$	8.55069	+	14.8102i	0.451288	+	0.781654i	−0.547178	+	0.837016i	$0.684298\pi$
$360$	−26.3144			−1.38689
$361$	−16.1915	−	28.0445i	−0.852184	−	1.47603i
$362$	40.0979			2.10750
$363$	−12.8474			−0.674314
$364$		0			0
$365$	−6.97809			−0.365250
$366$	−34.4012			−1.79818
$367$	−0.524301	−	0.908115i	−0.0273683	−	0.0474032i	0.852017	−	0.523514i	$-0.175379\pi$
$367$	−0.524301	−	0.908115i	−0.0273683	−	0.0474032i	−0.879385	+	0.476111i	$0.842046\pi$
$368$	−6.02600			−0.314127
$369$	1.09309	+	1.89329i	0.0569041	+	0.0985608i
$370$	12.0119	+	20.8052i	0.624468	+	1.08161i
$371$		0			0
$372$	−24.2073			−1.25509
$373$	7.50536	−	12.9997i	0.388613	−	0.673098i	−0.603650	−	0.797249i	$-0.706288\pi$
$373$	7.50536	−	12.9997i	0.388613	−	0.673098i	0.992263	+	0.124152i	$0.0396210\pi$
$374$	−14.8330	−	25.6914i	−0.766994	−	1.32847i
$375$	−5.31029	−	9.19768i	−0.274222	−	0.474966i
$376$	−5.79761	−	10.0418i	−0.298989	−	0.517864i
$377$	−24.4710	−	18.1062i	−1.26032	−	0.932517i
$378$		0			0
$379$	13.5749	−	23.5123i	0.697294	−	1.20775i	−0.272108	−	0.962267i	$-0.587721\pi$
$379$	13.5749	−	23.5123i	0.697294	−	1.20775i	0.969401	−	0.245481i	$-0.0789459\pi$
$380$	−83.0294			−4.25932
$381$	−25.5771			−1.31035
$382$	1.24480	−	2.15606i	0.0636895	−	0.110314i
$383$	−8.01320	+	13.8793i	−0.409455	+	0.709197i	−0.994829	−	0.101566i	$-0.967615\pi$
$383$	−8.01320	+	13.8793i	−0.409455	+	0.709197i	0.585373	+	0.810764i	$0.300948\pi$
$384$	−22.9519	−	39.7538i	−1.17126	−	2.02868i
$385$		0			0
$386$	3.67890	+	6.37203i	0.187251	+	0.324328i
$387$	−9.54077			−0.484985
$388$	6.11107	+	10.5847i	0.310242	+	0.537356i
$389$	−3.99714	+	6.92324i	−0.202663	+	0.351022i	−0.949386	−	0.314113i	$-0.898293\pi$
$389$	−3.99714	+	6.92324i	−0.202663	+	0.351022i	0.746723	+	0.665136i	$0.231626\pi$
$390$	−52.6017	−	38.9202i	−2.66359	−	1.97080i
$391$	35.2130			1.78080
$392$		0			0
$393$	0.775840	−	1.34379i	0.0391360	−	0.0677855i
$394$	−20.6289	+	35.7302i	−1.03927	+	1.80006i
$395$	12.7912	−	22.1550i	0.643593	−	1.11474i
$396$	18.6778			0.938593
$397$	−6.10435	+	10.5731i	−0.306369	+	0.530646i	−0.977565	−	0.210633i	$-0.932447\pi$
$397$	−6.10435	+	10.5731i	−0.306369	+	0.530646i	0.671196	+	0.741280i	$0.265781\pi$
$398$	−30.2853			−1.51806
$399$		0			0
$400$	−2.97191	+	5.14750i	−0.148596	+	0.257375i
$401$	37.8412			1.88970			0.944850	−	0.327503i	$-0.106207\pi$
$401$	37.8412			1.88970			0.944850	+	0.327503i	$0.106207\pi$
$402$	12.4181	−	21.5087i	0.619358	−	1.07276i
$403$	−8.84370	−	6.54349i	−0.440536	−	0.325955i
$404$	−8.12373	−	14.0707i	−0.404171	−	0.700044i
$405$	17.7971	−	30.8255i	0.884345	−	1.53173i
$406$		0			0
$407$	−3.56318	−	6.17161i	−0.176620	−	0.305915i
$408$	−21.0939	−	36.5358i	−1.04431	−	1.80879i
$409$	−0.235074			−0.0116237			−0.00581184	−	0.999983i	$-0.501850\pi$
$409$	−0.235074			−0.0116237			−0.00581184	+	0.999983i	$0.501850\pi$
$410$	7.36988			0.363972
$411$	−9.04986	−	15.6748i	−0.446397	−	0.773182i
$412$	10.2784	+	17.8028i	0.506382	+	0.877080i
$413$		0			0
$414$	−17.5375	+	30.3759i	−0.861923	+	1.49290i
$415$	4.87692	+	8.44706i	0.239398	+	0.414650i
$416$	1.84368	−	16.1870i	0.0903938	−	0.793635i
$417$	−3.78124	+	6.54930i	−0.185168	+	0.320720i
$418$	38.9660			1.90589
$419$	0.222023	−	0.384555i	0.0108465	−	0.0187868i	−0.860551	−	0.509364i	$-0.829881\pi$
$419$	0.222023	−	0.384555i	0.0108465	−	0.0187868i	0.871398	+	0.490577i	$0.163214\pi$
$420$		0			0
$421$	9.45998			0.461051			0.230526	−	0.973066i	$-0.425955\pi$
$421$	9.45998			0.461051			0.230526	+	0.973066i	$0.425955\pi$
$422$	32.1052	−	55.6079i	1.56286	−	2.70695i
$423$	−8.07488			−0.392614
$424$	−3.92361	+	6.79588i	−0.190547	+	0.330037i
$425$	17.3664	−	30.0795i	0.842395	−	1.45907i
$426$	−20.4233	+	35.3742i	−0.989513	+	1.71389i
$427$		0			0
$428$	45.2950			2.18942
$429$	15.6036	+	11.5452i	0.753351	+	0.557407i
$430$	−16.0815	+	27.8540i	−0.775520	+	1.34324i
$431$	−10.7723	−	18.6582i	−0.518883	−	0.898732i	−0.999759	−	0.0219436i	$-0.993015\pi$
$431$	−10.7723	−	18.6582i	−0.518883	−	0.898732i	0.480876	−	0.876789i	$-0.340319\pi$
$432$	−1.44153			−0.0693557
$433$	−6.57949	−	11.3960i	−0.316190	−	0.547657i	0.663500	−	0.748176i	$-0.269070\pi$
$433$	−6.57949	−	11.3960i	−0.316190	−	0.547657i	−0.979690	+	0.200519i	$0.935737\pi$
$434$		0			0
$435$	32.8593	+	56.9141i	1.57548	+	2.72882i
$436$	−7.07026	+	12.2461i	−0.338604	+	0.586479i
$437$	−23.1261	+	40.0555i	−1.10627	+	1.91612i
$438$	11.1436			0.532463
$439$	29.7847			1.42155			0.710773	−	0.703422i	$-0.248345\pi$
$439$	29.7847			1.42155			0.710773	+	0.703422i	$0.248345\pi$
$440$	13.1572	−	22.7889i	0.627245	−	1.08642i
$441$		0			0
$442$	5.19171	−	45.5819i	0.246944	−	2.16811i
$443$	−7.42333	−	12.8576i	−0.352693	−	0.610883i	0.634027	−	0.773311i	$-0.281401\pi$
$443$	−7.42333	−	12.8576i	−0.352693	−	0.610883i	−0.986720	+	0.162428i	$0.948067\pi$
$444$	−12.1248	−	21.0007i	−0.575416	−	0.996649i
$445$	−22.1814	−	38.4193i	−1.05150	−	1.82125i
$446$	−10.1444	+	17.5706i	−0.480351	+	0.831992i
$447$	−32.7041			−1.54685
$448$		0			0
$449$	13.1114	+	22.7095i	0.618763	+	1.07173i	0.989712	+	0.143075i	$0.0456992\pi$
$449$	13.1114	+	22.7095i	0.618763	+	1.07173i	−0.370949	+	0.928653i	$0.620968\pi$
$450$	17.2984	+	29.9617i	0.815454	+	1.41241i
$451$	−2.18618			−0.102943
$452$	−24.5337	−	42.4936i	−1.15397	−	1.99873i
$453$	−3.10850			−0.146050
$454$	51.2162			2.40369
$455$		0			0
$456$	55.4136			2.59498
$457$	−15.8708			−0.742406			−0.371203	−	0.928552i	$-0.621055\pi$
$457$	−15.8708			−0.742406			−0.371203	+	0.928552i	$0.621055\pi$
$458$	23.9199	+	41.4305i	1.11770	+	1.93592i
$459$	8.42361			0.393180
$460$	37.3693	+	64.7255i	1.74235	+	3.01784i
$461$	11.0443	+	19.1293i	0.514384	+	0.890940i	0.999861	+	0.0166900i	$0.00531285\pi$
$461$	11.0443	+	19.1293i	0.514384	+	0.890940i	−0.485476	+	0.874250i	$0.661354\pi$
$462$		0			0
$463$	18.2887			0.849949			0.424974	−	0.905205i	$-0.360283\pi$
$463$	18.2887			0.849949			0.424974	+	0.905205i	$0.360283\pi$
$464$	3.94246	−	6.82854i	0.183024	−	0.317007i
$465$	11.8752	+	20.5685i	0.550699	+	0.953839i
$466$	−20.1545	−	34.9087i	−0.933641	−	1.61711i
$467$	2.26659	+	3.92585i	0.104885	+	0.181667i	0.913691	−	0.406409i	$-0.133219\pi$
$467$	2.26659	+	3.92585i	0.104885	+	0.181667i	−0.808806	+	0.588076i	$0.799886\pi$
$468$	23.2193	+	17.1801i	1.07331	+	0.794148i
$469$		0			0
$470$	−13.6107	+	23.5744i	−0.627813	+	1.08740i
$471$	−30.1097			−1.38738
$472$	−24.2625			−1.11677
$473$	4.77039	−	8.26255i	0.219343	−	0.379912i
$474$	−20.4268	+	35.3802i	−0.938233	+	1.62507i
$475$	22.8107	+	39.5093i	1.04663	+	1.81281i
$476$		0			0
$477$	2.73239	+	4.73263i	0.125107	+	0.216692i
$478$	−7.59984			−0.347609
$479$	−5.22303	−	9.04655i	−0.238646	−	0.413347i	0.721680	−	0.692227i	$-0.243370\pi$
$479$	−5.22303	−	9.04655i	−0.238646	−	0.413347i	−0.960326	+	0.278880i	$0.910037\pi$
$480$	−17.5859	+	30.4596i	−0.802681	+	1.39028i
$481$	1.24715	−	10.9497i	0.0568653	−	0.499263i
$482$	−3.41733			−0.155655
$483$		0			0
$484$	9.55891	−	16.5565i	0.434496	−	0.752569i
$485$	5.99573	−	10.3849i	0.272252	−	0.471555i
$486$	−23.0228	+	39.8767i	−1.04434	+	1.80884i
$487$	35.9143			1.62743			0.813715	−	0.581263i	$-0.197441\pi$
$487$	35.9143			1.62743			0.813715	+	0.581263i	$0.197441\pi$
$488$	10.6970	−	18.5277i	0.484229	−	0.838710i
$489$	11.3893			0.515042
$490$		0			0
$491$	−3.85124	+	6.67054i	−0.173804	+	0.301037i	−0.939747	−	0.341871i	$-0.888939\pi$
$491$	−3.85124	+	6.67054i	−0.173804	+	0.301037i	0.765943	+	0.642909i	$0.222273\pi$
$492$	−7.43913			−0.335382
$493$	−23.0378	+	39.9026i	−1.03757	+	1.79712i
$494$	48.4407	+	35.8415i	2.17945	+	1.61258i
$495$	−9.16263	−	15.8701i	−0.411830	−	0.713310i
$496$	1.42478	−	2.46780i	0.0639747	−	0.110807i
$497$		0			0
$498$	−7.78816	−	13.4895i	−0.348996	−	0.604479i
$499$	−4.24539	−	7.35323i	−0.190050	−	0.329176i	0.755217	−	0.655475i	$-0.227532\pi$
$499$	−4.24539	−	7.35323i	−0.190050	−	0.329176i	−0.945266	+	0.326299i	$0.894198\pi$
$500$	15.8041			0.706783
$501$	8.41071			0.375763
$502$	−19.9378	−	34.5332i	−0.889866	−	1.54129i
$503$	15.2000	+	26.3272i	0.677736	+	1.17387i	0.975661	+	0.219285i	$0.0703723\pi$
$503$	15.2000	+	26.3272i	0.677736	+	1.17387i	−0.297924	+	0.954589i	$0.596294\pi$
$504$		0			0
$505$	−7.97041	+	13.8052i	−0.354679	+	0.614321i
$506$	−17.5375	−	30.3759i	−0.779639	−	1.35037i
$507$	8.77825	+	28.7048i	0.389856	+	1.27483i
$508$	19.0302	−	32.9613i	0.844330	−	1.46242i
$509$	15.5801			0.690578			0.345289	−	0.938496i	$-0.387781\pi$
$509$	15.5801			0.690578			0.345289	+	0.938496i	$0.387781\pi$
$510$	−49.5209	+	85.7727i	−2.19282	+	3.79808i
$511$		0			0
$512$	10.4733			0.462860
$513$	−5.53218	+	9.58202i	−0.244252	+	0.423057i
$514$	8.97660			0.395941
$515$	10.0845	−	17.4668i	0.444374	−	0.769678i
$516$	16.2326	−	28.1157i	0.714602	−	1.23773i
$517$	4.03744	−	6.99305i	0.177566	−	0.307554i
$518$		0			0
$519$	29.3052			1.28635
$520$	37.3179	−	16.2279i	1.63650	−	0.711642i
$521$	13.5787	−	23.5190i	0.594893	−	1.03039i	−0.398669	−	0.917095i	$-0.630528\pi$
$521$	13.5787	−	23.5190i	0.594893	−	1.03039i	0.993562	−	0.113290i	$-0.0361390\pi$
$522$	−22.9476	−	39.7463i	−1.00439	−	1.73965i
$523$	18.0575			0.789598			0.394799	−	0.918767i	$-0.370814\pi$
$523$	18.0575			0.789598			0.394799	+	0.918767i	$0.370814\pi$
$524$	1.15450	+	1.99966i	0.0504347	+	0.0873555i
$525$		0			0
$526$	−35.5741	−	61.6161i	−1.55110	−	2.68659i
$527$	−8.32574	+	14.4206i	−0.362675	+	0.628172i
$528$	−2.51386	+	4.35413i	−0.109402	+	0.189489i
$529$	18.6337			0.810160
$530$	18.4224			0.800217
$531$	−8.44816	+	14.6326i	−0.366619	+	0.635003i
$532$		0			0
$533$	−2.71776	−	2.01088i	−0.117719	−	0.0871009i
$534$	35.4225	+	61.3535i	1.53288	+	2.65503i
$535$	−22.2201	−	38.4863i	−0.960657	−	1.66391i
$536$	7.72276	+	13.3762i	0.333572	+	0.577764i
$537$	10.1474	−	17.5758i	0.437892	−	0.758451i
$538$	39.1162			1.68642
$539$		0			0
$540$	8.93941	+	15.4835i	0.384691	+	0.666305i
$541$	−19.9941	−	34.6308i	−0.859613	−	1.48889i	−0.872298	−	0.488974i	$-0.837371\pi$
$541$	−19.9941	−	34.6308i	−0.859613	−	1.48889i	0.0126849	−	0.999920i	$-0.495962\pi$
$542$	72.6902			3.12231
$543$	19.8554	+	34.3906i	0.852077	+	1.47584i
$544$	−24.6590			−1.05725
$545$	13.8736			0.594282
$546$		0			0
$547$	−22.6124			−0.966836			−0.483418	−	0.875390i	$-0.660605\pi$
$547$	−22.6124			−0.966836			−0.483418	+	0.875390i	$0.660605\pi$
$548$	26.9336			1.15055
$549$	−7.44934	−	12.9026i	−0.317930	−	0.550671i
$550$	−34.5968			−1.47521
$551$	−30.2600	−	52.4119i	−1.28912	−	2.23282i
$552$	−24.9402	−	43.1976i	−1.06152	−	1.83861i
$553$		0			0
$554$	−0.923005			−0.0392147
$555$	−11.8959	+	20.6043i	−0.504954	+	0.874606i
$556$	−5.62674	−	9.74581i	−0.238627	−	0.413314i
$557$	4.98686	+	8.63750i	0.211300	+	0.365983i	0.952122	−	0.305719i	$-0.0988969\pi$
$557$	4.98686	+	8.63750i	0.211300	+	0.365983i	−0.740822	+	0.671702i	$0.765564\pi$
$558$	−8.29313	−	14.3641i	−0.351076	−	0.608082i
$559$	13.5303	−	5.88374i	0.572271	−	0.248856i
$560$		0			0
$561$	14.6898	−	25.4434i	0.620202	−	1.07422i
$562$	53.4988			2.25671
$563$	21.5279			0.907294			0.453647	−	0.891181i	$-0.350123\pi$
$563$	21.5279			0.907294			0.453647	+	0.891181i	$0.350123\pi$
$564$	13.7386	−	23.7959i	0.578498	−	1.00199i
$565$	−24.0707	+	41.6916i	−1.01266	+	1.75398i
$566$	−22.5592	−	39.0736i	−0.948232	−	1.64239i
$567$		0			0
$568$	−12.7012	−	21.9991i	−0.532930	−	0.923061i
$569$	−33.1004			−1.38764			−0.693819	−	0.720149i	$-0.744073\pi$
$569$	−33.1004			−1.38764			−0.693819	+	0.720149i	$0.744073\pi$
$570$	−65.0454	−	112.662i	−2.72445	−	4.71889i
$571$	−9.96786	+	17.2648i	−0.417142	+	0.722511i	−0.995651	−	0.0931651i	$-0.970302\pi$
$571$	−9.96786	+	17.2648i	−0.417142	+	0.722511i	0.578509	+	0.815676i	$0.303635\pi$
$572$	−26.4880	+	11.5185i	−1.10752	+	0.481611i
$573$	2.46557			0.103001
$574$		0			0
$575$	20.5330	−	35.5641i	0.856283	−	1.48313i
$576$	14.4586	−	25.0431i	0.602443	−	1.04346i
$577$	14.7348	−	25.5214i	0.613416	−	1.06247i	−0.377244	−	0.926114i	$-0.623128\pi$
$577$	14.7348	−	25.5214i	0.613416	−	1.06247i	0.990660	−	0.136354i	$-0.0435385\pi$
$578$	−29.8028			−1.23963
$579$	−3.64338	+	6.31052i	−0.151414	+	0.262256i
$580$	−97.7939			−4.06067
$581$		0			0
$582$	−9.57486	+	16.5841i	−0.396891	+	0.687435i
$583$	−5.46477			−0.226328
$584$	−3.46509	+	6.00171i	−0.143386	+	0.248353i
$585$	3.20703	−	28.1569i	0.132594	−	1.16414i
$586$	18.3867	+	31.8467i	0.759548	+	1.31558i
$587$	3.49429	−	6.05229i	0.144225	−	0.249805i	−0.784859	−	0.619675i	$-0.787264\pi$
$587$	3.49429	−	6.05229i	0.144225	−	0.249805i	0.929084	+	0.369870i	$0.120598\pi$
$588$		0			0
$589$	−10.9358	−	18.9414i	−0.450603	−	0.780467i
$590$	28.4797	+	49.3283i	1.17249	+	2.03082i
$591$	−40.8594			−1.68073
$592$	2.85454			0.117321
$593$	0.485124	+	0.840259i	0.0199216	+	0.0345053i	0.875814	−	0.482648i	$-0.160325\pi$
$593$	0.485124	+	0.840259i	0.0199216	+	0.0345053i	−0.855893	+	0.517153i	$0.826992\pi$
$594$	−4.19530	−	7.26648i	−0.172135	−	0.298147i
$595$		0			0
$596$	24.3330	−	42.1460i	0.996719	−	1.72637i
$597$	−14.9965	−	25.9746i	−0.613764	−	1.06307i
$598$	6.13835	−	53.8931i	0.251016	−	2.20385i
$599$	11.2999	−	19.5720i	0.461702	−	0.799692i	−0.537344	−	0.843363i	$-0.680572\pi$
$599$	11.2999	−	19.5720i	0.461702	−	0.799692i	0.999046	+	0.0436716i	$0.0139055\pi$
$600$	−49.2001			−2.00858
$601$	−15.2146	+	26.3525i	−0.620617	+	1.07494i	0.368754	+	0.929527i	$0.379785\pi$
$601$	−15.2146	+	26.3525i	−0.620617	+	1.07494i	−0.989371	+	0.145414i	$0.953549\pi$
$602$		0			0
$603$	10.7562			0.438027
$604$	2.31283	−	4.00594i	0.0941078	−	0.163000i
$605$	−18.7570			−0.762581
$606$	12.7283	−	22.0461i	0.517052	−	0.895560i
$607$	−16.0788	+	27.8493i	−0.652618	+	1.13037i	0.329868	+	0.944027i	$0.392996\pi$
$607$	−16.0788	+	27.8493i	−0.652618	+	1.13037i	−0.982485	+	0.186340i	$0.940337\pi$
$608$	16.1947	−	28.0501i	0.656784	−	1.13758i
$609$		0			0
$610$	−50.2252			−2.03356
$611$	11.4514	−	4.97973i	0.463276	−	0.201458i
$612$	21.8594	−	37.8616i	0.883613	−	1.53046i
$613$	−6.96043	−	12.0558i	−0.281129	−	0.486930i	0.690534	−	0.723300i	$-0.257376\pi$
$613$	−6.96043	−	12.0558i	−0.281129	−	0.486930i	−0.971663	+	0.236370i	$0.924042\pi$
$614$	44.8898			1.81160
$615$	3.64937	+	6.32089i	0.147157	+	0.254883i
$616$		0			0
$617$	5.08394	+	8.80565i	0.204672	+	0.354502i	0.950028	−	0.312164i	$-0.101054\pi$
$617$	5.08394	+	8.80565i	0.204672	+	0.354502i	−0.745356	+	0.666666i	$0.767721\pi$
$618$	−16.1043	+	27.8935i	−0.647810	+	1.12204i
$619$	−21.8952	+	37.9237i	−0.880044	+	1.52428i	−0.0287526	+	0.999587i	$0.509154\pi$
$619$	−21.8952	+	37.9237i	−0.880044	+	1.52428i	−0.851291	+	0.524694i	$0.824180\pi$
$620$	−35.3422			−1.41938
$621$	9.95954			0.399663
$622$	−3.57262	+	6.18796i	−0.143249	+	0.248115i
$623$		0			0
$624$	−7.13009	+	3.10056i	−0.285432	+	0.124122i
$625$	8.15812	+	14.1303i	0.326325	+	0.565211i
$626$	41.1223	+	71.2258i	1.64358	+	2.84676i
$627$	19.2949	+	33.4198i	0.770565	+	1.33466i
$628$	22.4027	−	38.8026i	0.893964	−	1.54839i
$629$	−16.6806			−0.665097
$630$		0			0
$631$	−8.04464	−	13.9337i	−0.320252	−	0.554693i	0.660288	−	0.751013i	$-0.270434\pi$
$631$	−8.04464	−	13.9337i	−0.320252	−	0.554693i	−0.980540	+	0.196320i	$0.937101\pi$
$632$	−12.7033	−	22.0028i	−0.505312	−	0.875226i
$633$	63.5906			2.52750
$634$	38.1279	+	66.0394i	1.51425	+	2.62276i
$635$	−37.3421			−1.48188
$636$	−18.5955			−0.737359
$637$		0			0
$638$	45.8951			1.81700
$639$	−17.6901			−0.699810
$640$	−33.5094	−	58.0399i	−1.32457	−	2.29423i
$641$	−49.2508			−1.94529			−0.972645	−	0.232296i	$-0.925376\pi$
$641$	−49.2508			−1.94529			−0.972645	+	0.232296i	$0.925376\pi$
$642$	35.4842	+	61.4605i	1.40045	+	2.42565i
$643$	−1.33579	−	2.31366i	−0.0526784	−	0.0912417i	0.838484	−	0.544927i	$-0.183442\pi$
$643$	−1.33579	−	2.31366i	−0.0526784	−	0.0912417i	−0.891162	+	0.453685i	$0.850109\pi$
$644$		0			0
$645$	−31.8526			−1.25419
$646$	45.6036	−	78.9877i	1.79425	−	3.10773i
$647$	−16.6814	−	28.8930i	−0.655814	−	1.13590i	−0.981689	−	0.190490i	$-0.938992\pi$
$647$	−16.6814	−	28.8930i	−0.655814	−	1.13590i	0.325876	−	0.945413i	$-0.394341\pi$
$648$	−17.6749	−	30.6138i	−0.694336	−	1.20262i
$649$	−8.44816	−	14.6326i	−0.331619	−	0.574382i
$650$	−43.0090	−	31.8226i	−1.68695	−	1.24818i
$651$		0			0
$652$	−8.47404	+	14.6775i	−0.331869	+	0.574814i
$653$	23.8487			0.933274			0.466637	−	0.884449i	$-0.345466\pi$
$653$	23.8487			0.933274			0.466637	+	0.884449i	$0.345466\pi$
$654$	−22.1554			−0.866347
$655$	1.13271	−	1.96192i	0.0442588	−	0.0766585i
$656$	0.437850	−	0.758379i	0.0170952	−	0.0296097i
$657$	2.41308	+	4.17957i	0.0941431	+	0.163061i
$658$		0			0
$659$	8.58114	+	14.8630i	0.334274	+	0.578979i	0.983345	−	0.181749i	$-0.0581757\pi$
$659$	8.58114	+	14.8630i	0.334274	+	0.578979i	−0.649071	+	0.760727i	$0.724842\pi$
$660$	62.3571			2.42725
$661$	0.233201	+	0.403917i	0.00907048	+	0.0157105i	0.870525	−	0.492124i	$-0.163779\pi$
$661$	0.233201	+	0.403917i	0.00907048	+	0.0157105i	−0.861455	+	0.507835i	$0.830446\pi$
$662$	5.56886	−	9.64554i	0.216440	−	0.374885i
$663$	41.6648	−	18.1182i	1.61813	−	0.703652i
$664$	9.68686			0.375923
$665$		0			0
$666$	8.30760	−	14.3892i	0.321913	−	0.557570i
$667$	−27.2384	+	47.1784i	−1.05468	+	1.82675i
$668$	−6.25786	+	10.8389i	−0.242124	+	0.419371i
$669$	−20.0929			−0.776837
$670$	18.1302	−	31.4024i	0.700431	−	1.21318i
$671$	14.8987			0.575157
$672$		0			0
$673$	−8.77061	+	15.1911i	−0.338082	+	0.585576i	−0.984072	−	0.177770i	$-0.943112\pi$
$673$	−8.77061	+	15.1911i	−0.338082	+	0.585576i	0.645990	+	0.763346i	$0.276445\pi$
$674$	−61.1770			−2.35645
$675$	4.91186	−	8.50759i	0.189058	−	0.327457i
$676$	−43.5234	−	10.0448i	−1.67398	−	0.386339i
$677$	4.85980	+	8.41743i	0.186777	+	0.323508i	0.944174	−	0.329447i	$-0.106862\pi$
$677$	4.85980	+	8.41743i	0.186777	+	0.323508i	−0.757397	+	0.652955i	$0.773529\pi$
$678$	38.4395	−	66.5792i	1.47626	−	2.55696i
$679$		0			0
$680$	−30.7968	−	53.3417i	−1.18101	−	2.04556i
$681$	25.3609	+	43.9263i	0.971831	+	1.68326i
$682$	16.5863			0.635121
$683$	−36.1154			−1.38192			−0.690960	−	0.722893i	$-0.742812\pi$
$683$	−36.1154			−1.38192			−0.690960	+	0.722893i	$0.742812\pi$
$684$	28.7122	+	49.7310i	1.09784	+	1.90151i
$685$	−13.2127	−	22.8850i	−0.504830	−	0.874391i
$686$		0			0
$687$	−23.6890	+	41.0305i	−0.903791	+	1.56541i
$688$	1.91083	+	3.30966i	0.0728498	+	0.126179i
$689$	−6.79354	−	5.02657i	−0.258813	−	0.191497i
$690$	−58.5504	+	101.412i	−2.22897	+	3.86070i
$691$	−8.77269			−0.333729			−0.166864	−	0.985980i	$-0.553364\pi$
$691$	−8.77269			−0.333729			−0.166864	+	0.985980i	$0.553364\pi$
$692$	−21.8041	+	37.7657i	−0.828866	+	1.43564i
$693$		0			0
$694$	24.3509			0.924346
$695$	−5.52055	+	9.56187i	−0.209406	+	0.362703i
$696$	65.2674			2.47396
$697$	−2.55858	+	4.43160i	−0.0969132	+	0.167859i
$698$	−27.3589	+	47.3870i	−1.03555	+	1.79363i
$699$	19.9600	−	34.5717i	0.754955	−	1.30762i
$700$		0			0
$701$	1.51585			0.0572530			0.0286265	−	0.999590i	$-0.490887\pi$
$701$	1.51585			0.0572530			0.0286265	+	0.999590i	$0.490887\pi$
$702$	1.46841	−	12.8922i	0.0554214	−	0.486586i
$703$	10.9549	−	18.9745i	0.413172	−	0.715636i
$704$	14.4586	+	25.0431i	0.544930	+	0.943847i
$705$	−26.9586			−1.01532
$706$	−3.41724	−	5.91883i	−0.128609	−	0.222758i
$707$		0			0
$708$	−28.7473	−	49.7919i	−1.08039	−	1.87129i
$709$	7.55100	−	13.0787i	0.283584	−	0.491182i	−0.688681	−	0.725065i	$-0.741810\pi$
$709$	7.55100	−	13.0787i	0.283584	−	0.491182i	0.972265	+	0.233883i	$0.0751433\pi$
$710$	−29.8177	+	51.6458i	−1.11904	+	1.93823i
$711$	−17.6931			−0.663544
$712$	−44.0582			−1.65115
$713$	−9.84384	+	17.0500i	−0.368655	+	0.638528i
$714$		0			0
$715$	22.7811	+	16.8558i	0.851964	+	0.630372i
$716$	15.1000	+	26.1540i	0.564314	+	0.977420i
$717$	−3.76324	−	6.51812i	−0.140541	−	0.243424i
$718$	−19.9361	−	34.5303i	−0.744007	−	1.28866i
$719$	9.59946	−	16.6267i	0.357999	−	0.620073i	−0.629627	−	0.776897i	$-0.716792\pi$
$719$	9.59946	−	16.6267i	0.357999	−	0.620073i	0.987626	+	0.156824i	$0.0501257\pi$
$720$	7.34039			0.273560
$721$		0			0
$722$	37.7507	+	65.3861i	1.40494	+	2.43342i
$723$	−1.69217	−	2.93093i	−0.0629325	−	0.109002i
$724$	−59.0925			−2.19615
$725$	26.8670	+	46.5350i	0.997815	+	1.72827i
$726$	29.9539			1.11169
$727$	2.41101			0.0894195			0.0447098	−	0.999000i	$-0.485764\pi$
$727$	2.41101			0.0894195			0.0447098	+	0.999000i	$0.485764\pi$
$728$		0			0
$729$	−13.9254			−0.515755
$730$	16.2695			0.602162
$731$	−11.1660	−	19.3400i	−0.412988	−	0.715317i
$732$	50.6971			1.87382
$733$	−6.74959	−	11.6906i	−0.249302	−	0.431804i	0.714030	−	0.700115i	$-0.246868\pi$
$733$	−6.74959	−	11.6906i	−0.249302	−	0.431804i	−0.963332	+	0.268311i	$0.913534\pi$
$734$	1.22241	+	2.11728i	0.0451201	+	0.0781504i
$735$		0			0
$736$	−29.1553			−1.07468
$737$	−5.37810	+	9.31515i	−0.198105	+	0.343128i
$738$	−2.54856	−	4.41423i	−0.0938138	−	0.162490i
$739$	0.0214096	+	0.0370824i	0.000787563	+	0.00136410i	0.866419	−	0.499318i	$-0.166416\pi$
$739$	0.0214096	+	0.0370824i	0.000787563	+	0.00136410i	−0.865631	+	0.500682i	$0.833083\pi$
$740$	−17.7020	−	30.6607i	−0.650737	−	1.12711i
$741$	−6.75345	+	59.2936i	−0.248094	+	2.17820i
$742$		0			0
$743$	10.8254	−	18.7501i	0.397145	−	0.687875i	−0.596228	−	0.802815i	$-0.703334\pi$
$743$	10.8254	−	18.7501i	0.397145	−	0.687875i	0.993372	+	0.114941i	$0.0366678\pi$
$744$	23.5873			0.864753
$745$	−47.7475			−1.74933
$746$	−17.4989	+	30.3089i	−0.640679	+	1.10969i
$747$	3.37295	−	5.84212i	0.123410	−	0.213752i
$748$	21.8594	+	37.8616i	0.799258	+	1.38436i
$749$		0			0
$750$	12.3810	+	21.4445i	0.452091	+	0.783044i
$751$	−44.8858			−1.63791			−0.818953	−	0.573860i	$-0.805445\pi$
$751$	−44.8858			−1.63791			−0.818953	+	0.573860i	$0.805445\pi$
$752$	1.61724	+	2.80114i	0.0589747	+	0.102147i
$753$	19.7453	−	34.1999i	0.719559	−	1.24631i
$754$	57.0545	+	42.2149i	2.07780	+	1.53738i
$755$	−4.53837			−0.165168
$756$		0			0
$757$	3.77726	−	6.54240i	0.137287	−	0.237788i	−0.789182	−	0.614159i	$-0.789495\pi$
$757$	3.77726	−	6.54240i	0.137287	−	0.237788i	0.926469	+	0.376372i	$0.122828\pi$
$758$	−31.6500	+	54.8194i	−1.14958	+	1.99113i
$759$	17.3682	−	30.0827i	0.630427	−	1.09193i
$760$	80.9030			2.93466
$761$	11.6946	−	20.2556i	0.423928	−	0.734265i	−0.572392	−	0.819980i	$-0.693984\pi$
$761$	11.6946	−	20.2556i	0.423928	−	0.734265i	0.996320	+	0.0857157i	$0.0273177\pi$
$762$	59.6333			2.16029
$763$		0			0
$764$	−1.83447	+	3.17739i	−0.0663687	+	0.114954i
$765$	−42.8937			−1.55082
$766$	18.6829	−	32.3597i	0.675040	−	1.16920i
$767$	2.95696	−	25.9613i	0.106769	−	0.937409i
$768$	24.8745	+	43.0838i	0.897580	+	1.55465i
$769$	−21.9255	+	37.9760i	−0.790652	+	1.36945i	0.134911	+	0.990858i	$0.456925\pi$
$769$	−21.9255	+	37.9760i	−0.790652	+	1.36945i	−0.925564	+	0.378592i	$0.876408\pi$
$770$		0			0
$771$	4.44497	+	7.69891i	0.160082	+	0.277270i
$772$	−5.42160	−	9.39049i	−0.195128	−	0.337971i
$773$	43.1225			1.55101			0.775505	−	0.631341i	$-0.217495\pi$
$773$	43.1225			1.55101			0.775505	+	0.631341i	$0.217495\pi$
$774$	22.2445			0.799560
$775$	9.70959	+	16.8175i	0.348779	+	0.604103i
$776$	−5.95457	−	10.3136i	−0.213756	−	0.370237i
$777$		0			0
$778$	9.31939	−	16.1417i	0.334116	−	0.578706i
$779$	−3.36069	−	5.82088i	−0.120409	−	0.208555i
$780$	77.5193	+	57.3568i	2.77563	+	2.05370i
$781$	8.84506	−	15.3201i	0.316501	−	0.548196i
$782$	−82.0997			−2.93588
$783$	−6.51594	+	11.2859i	−0.232861	+	0.403326i
$784$		0			0
$785$	−43.9597			−1.56899
$786$	−1.80888	+	3.13308i	−0.0645207	+	0.111753i
$787$	24.8960			0.887446			0.443723	−	0.896164i	$-0.353657\pi$
$787$	24.8960			0.887446			0.443723	+	0.896164i	$0.353657\pi$
$788$	30.4008	−	52.6558i	1.08298	−	1.87578i
$789$	35.2307	−	61.0213i	1.25424	−	2.17242i
$790$	−29.8228	+	51.6546i	−1.06105	+	1.83779i
$791$		0			0
$792$	−18.1994			−0.646689
$793$	18.5213	+	13.7040i	0.657711	+	0.486643i
$794$	14.2324	−	24.6512i	0.505089	−	0.874839i
$795$	9.12227	+	15.8002i	0.323534	+	0.560377i
$796$	44.6315			1.58192
$797$	15.6211	+	27.0565i	0.553327	+	0.958391i	0.998032	+	0.0627134i	$0.0199754\pi$
$797$	15.6211	+	27.0565i	0.553327	+	0.958391i	−0.444704	+	0.895677i	$0.646691\pi$
$798$		0			0
$799$	−9.45037	−	16.3685i	−0.334330	−	0.579077i
$800$	−14.3788	+	24.9049i	−0.508368	+	0.880520i
$801$	−15.3410	+	26.5714i	−0.542047	+	0.938853i
$802$	−88.2274			−3.11542
$803$	−4.82615			−0.170311
$804$	−18.3006	+	31.6975i	−0.645412	+	1.11789i
$805$		0			0
$806$	20.6192	+	15.2563i	0.726281	+	0.537379i
$807$	19.3693	+	33.5486i	0.681831	+	1.18097i
$808$	7.91568	+	13.7104i	0.278473	+	0.482329i
$809$	−19.7729	−	34.2477i	−0.695179	−	1.20409i	−0.970120	−	0.242624i	$-0.921992\pi$
$809$	−19.7729	−	34.2477i	−0.695179	−	1.20409i	0.274941	−	0.961461i	$-0.411342\pi$
$810$	−41.4942	+	71.8701i	−1.45796	+	2.52526i
$811$	43.8260			1.53894			0.769470	−	0.638683i	$-0.220520\pi$
$811$	43.8260			1.53894			0.769470	+	0.638683i	$0.220520\pi$
$812$		0			0
$813$	35.9942	+	62.3439i	1.26237	+	2.18649i
$814$	8.30760	+	14.3892i	0.291181	+	0.504341i
$815$	16.6282			0.582461
$816$	5.88415	+	10.1916i	0.205986	+	0.356779i
$817$	29.3329			1.02623
$818$	0.548079			0.0191631
$819$		0			0
$820$	−10.8610			−0.379283
$821$	45.0324			1.57164			0.785820	−	0.618455i	$-0.212241\pi$
$821$	45.0324			1.57164			0.785820	+	0.618455i	$0.212241\pi$
$822$	21.0999	+	36.5461i	0.735943	+	1.27469i
$823$	25.1987			0.878373			0.439186	−	0.898396i	$-0.355267\pi$
$823$	25.1987			0.878373			0.439186	+	0.898396i	$0.355267\pi$
$824$	−10.0152	−	17.3469i	−0.348896	−	0.604306i
$825$	−17.1314	−	29.6724i	−0.596438	−	1.03306i
$826$		0			0
$827$	−22.3091			−0.775762			−0.387881	−	0.921709i	$-0.626793\pi$
$827$	−22.3091			−0.775762			−0.387881	+	0.921709i	$0.626793\pi$
$828$	25.8452	−	44.7651i	0.898181	−	1.55570i
$829$	13.0981	+	22.6866i	0.454917	+	0.787939i	0.998683	−	0.0512972i	$-0.0163356\pi$
$829$	13.0981	+	22.6866i	0.454917	+	0.787939i	−0.543766	+	0.839237i	$0.683002\pi$
$830$	−11.3706	−	19.6945i	−0.394679	−	0.683605i
$831$	−0.457047	−	0.791629i	−0.0158548	−	0.0274613i
$832$	−5.06069	+	44.4316i	−0.175448	+	1.54039i
$833$		0			0
$834$	8.81601	−	15.2698i	0.305274	−	0.528749i
$835$	12.2795			0.424950
$836$	−57.4244			−1.98606
$837$	−2.35483	+	4.07868i	−0.0813947	+	0.140980i
$838$	−0.517650	+	0.896597i	−0.0178819	+	0.0309724i
$839$	21.7207	+	37.6214i	0.749882	+	1.29883i	0.947879	+	0.318631i	$0.103223\pi$
$839$	21.7207	+	37.6214i	0.749882	+	1.29883i	−0.197997	+	0.980203i	$0.563443\pi$
$840$		0			0
$841$	−21.1410	−	36.6173i	−0.729000	−	1.26266i
$842$	−22.0561			−0.760103
$843$	26.4912	+	45.8840i	0.912404	+	1.58033i
$844$	−47.3136	+	81.9496i	−1.62860	+	2.82082i
$845$	12.8161	+	41.9086i	0.440888	+	1.44170i
$846$	18.8267			0.647275
$847$		0			0
$848$	1.09449	−	1.89571i	0.0375849	−	0.0650989i
$849$	22.3414	−	38.6964i	0.766754	−	1.32806i
$850$	−40.4901	+	70.1308i	−1.38880	+	2.40547i
$851$	−19.7220			−0.676063
$852$	30.0979	−	52.1311i	1.03114	−	1.78598i
$853$	−1.15312			−0.0394820			−0.0197410	−	0.999805i	$-0.506284\pi$
$853$	−1.15312			−0.0394820			−0.0197410	+	0.999805i	$0.506284\pi$
$854$		0			0
$855$	28.1703	−	48.7924i	0.963404	−	1.66866i
$856$	−44.1350			−1.50850
$857$	−12.5043	+	21.6582i	−0.427140	+	0.739828i	−0.996618	−	0.0821785i	$-0.973812\pi$
$857$	−12.5043	+	21.6582i	−0.427140	+	0.739828i	0.569477	+	0.822007i	$0.307146\pi$
$858$	−36.3801	−	26.9178i	−1.24200	−	0.918959i
$859$	−2.04457	−	3.54130i	−0.0697598	−	0.120827i	0.829036	−	0.559196i	$-0.188890\pi$
$859$	−2.04457	−	3.54130i	−0.0697598	−	0.120827i	−0.898795	+	0.438368i	$0.855557\pi$
$860$	23.6994	−	41.0486i	0.808143	−	1.39974i
$861$		0			0
$862$	25.1158	+	43.5018i	0.855447	+	1.48168i
$863$	−8.69644	−	15.0627i	−0.296030	−	0.512739i	0.679194	−	0.733959i	$-0.262330\pi$
$863$	−8.69644	−	15.0627i	−0.296030	−	0.512739i	−0.975224	+	0.221220i	$0.928996\pi$
$864$	−6.97447			−0.237276
$865$	42.7851			1.45474
$866$	15.3402	+	26.5700i	0.521280	+	0.902884i
$867$	−14.7575	−	25.5608i	−0.501192	−	0.868090i
$868$		0			0
$869$	8.84657	−	15.3227i	0.300099	−	0.519787i
$870$	−76.6121	−	132.696i	−2.59739	−	4.49881i
$871$	−15.2540	+	6.63329i	−0.516862	+	0.224760i
$872$	6.88919	−	11.9324i	0.233298	−	0.404083i
$873$	−8.29348			−0.280692
$874$	53.9188	−	93.3901i	1.82383	−	3.15897i
$875$		0			0
$876$	−16.4224			−0.554862
$877$	7.49082	−	12.9745i	0.252947	−	0.438117i	−0.711389	−	0.702799i	$-0.751933\pi$
$877$	7.49082	−	12.9745i	0.252947	−	0.438117i	0.964336	+	0.264681i	$0.0852668\pi$
$878$	−69.4434			−2.34360
$879$	−18.2092	+	31.5393i	−0.614182	+	1.06379i
$880$	−3.67019	+	6.35696i	−0.123722	+	0.214293i
$881$	21.3382	−	36.9588i	0.718901	−	1.24517i	−0.242534	−	0.970143i	$-0.577979\pi$
$881$	21.3382	−	36.9588i	0.718901	−	1.24517i	0.961436	−	0.275030i	$-0.0886879\pi$
$882$		0			0
$883$	35.8874			1.20771			0.603854	−	0.797095i	$-0.293631\pi$
$883$	35.8874			1.20771			0.603854	+	0.797095i	$0.293631\pi$
$884$	−7.65104	+	67.1742i	−0.257332	+	2.25931i
$885$	−28.2048	+	48.8521i	−0.948094	+	1.64215i
$886$	17.3076	+	29.9777i	0.581461	+	1.00712i
$887$	−27.6672			−0.928975			−0.464488	−	0.885580i	$-0.653761\pi$
$887$	−27.6672			−0.928975			−0.464488	+	0.885580i	$0.653761\pi$
$888$	11.8142	+	20.4629i	0.396460	+	0.686689i
$889$		0			0
$890$	51.7163	+	89.5752i	1.73353	+	3.00257i
$891$	12.3087	−	21.3194i	0.412359	−	0.714226i
$892$	14.9498	−	25.8938i	0.500557	−	0.866990i
$893$	24.8260			0.830771
$894$	76.2502			2.55019
$895$	14.8150	−	25.6604i	0.495211	−	0.857731i
$896$		0			0
$897$	49.2618	−	21.4218i	1.64480	−	0.715253i
$898$	−30.5693	−	52.9476i	−1.02011	−	1.76688i
$899$	−12.8805	−	22.3096i	−0.429588	−	0.744068i
$900$	−25.4927	−	44.1546i	−0.849756	−	1.47182i
$901$	−6.39566	+	11.0776i	−0.213070	+	0.369048i
$902$	5.09712			0.169716
$903$		0			0
$904$	23.9054	+	41.4053i	0.795081	+	1.37712i
$905$	28.9886	+	50.2097i	0.963614	+	1.66903i
$906$	7.24752			0.240783
$907$	−9.09663	−	15.7558i	−0.302049	−	0.523164i	0.674551	−	0.738228i	$-0.264337\pi$
$907$	−9.09663	−	15.7558i	−0.302049	−	0.523164i	−0.976600	+	0.215064i	$0.931004\pi$
$908$	−75.4775			−2.50481
$909$	11.0249			0.365673
$910$		0			0
$911$	−33.1527			−1.09840			−0.549199	−	0.835691i	$-0.685067\pi$
$911$	−33.1527			−1.09840			−0.549199	+	0.835691i	$0.685067\pi$
$912$	−15.4576			−0.511852
$913$	3.37295	+	5.84212i	0.111628	+	0.193346i
$914$	37.0031			1.22395
$915$	−24.8702	−	43.0764i	−0.822182	−	1.42406i
$916$	−35.2508	−	61.0562i	−1.16472	−	2.01736i
$917$		0			0
$918$	−19.6398			−0.648209
$919$	−1.49164	+	2.58359i	−0.0492046	+	0.0852249i	−0.889579	−	0.456782i	$-0.849002\pi$
$919$	−1.49164	+	2.58359i	−0.0492046	+	0.0852249i	0.840374	+	0.542007i	$0.182335\pi$
$920$	−36.4122	−	63.0679i	−1.20048	−	2.07929i
$921$	22.2282	+	38.5004i	0.732444	+	1.26863i
$922$	−25.7500	−	44.6002i	−0.848030	−	1.46883i
$923$	25.0874	−	10.9094i	0.825761	−	0.359087i
$924$		0			0
$925$	−9.72654	+	16.8469i	−0.319807	+	0.553921i
$926$	−42.6404			−1.40125
$927$	−13.9491			−0.458149
$928$	19.0746	−	33.0381i	0.626153	−	1.08453i
$929$	−16.6990	+	28.9235i	−0.547876	+	0.948948i	0.450544	+	0.892754i	$0.351230\pi$
$929$	−16.6990	+	28.9235i	−0.547876	+	0.948948i	−0.998420	+	0.0561943i	$0.982103\pi$
$930$	−27.6872	−	47.9557i	−0.907899	−	1.57253i
$931$		0			0
$932$	29.7018	+	51.4450i	0.972915	+	1.68514i
$933$	−7.07627			−0.231667
$934$	−5.28459	−	9.15318i	−0.172917	−	0.299501i
$935$	21.4468	−	37.1470i	0.701386	−	1.21484i
$936$	−22.6246	−	16.7401i	−0.739510	−	0.547166i
$937$	−51.3187			−1.67651			−0.838254	−	0.545279i	$-0.816424\pi$
$937$	−51.3187			−1.67651			−0.838254	+	0.545279i	$0.816424\pi$
$938$		0			0
$939$	−40.7253	+	70.5382i	−1.32902	+	2.30193i
$940$	20.0581	−	34.7416i	0.654223	−	1.13315i
$941$	−9.50195	+	16.4579i	−0.309755	+	0.536511i	−0.978309	−	0.207153i	$-0.933580\pi$
$941$	−9.50195	+	16.4579i	−0.309755	+	0.536511i	0.668554	+	0.743664i	$0.266914\pi$
$942$	70.2013			2.28728
$943$	−3.02511	+	5.23964i	−0.0985110	+	0.170626i
$944$	6.76801			0.220280
$945$		0			0
$946$	−11.1222	+	19.2643i	−0.361615	+	0.626335i
$947$	−46.7080			−1.51780			−0.758902	−	0.651204i	$-0.774264\pi$
$947$	−46.7080			−1.51780			−0.758902	+	0.651204i	$0.774264\pi$
$948$	30.1030	−	52.1400i	0.977701	−	1.69343i
$949$	−5.99964	−	4.43916i	−0.194757	−	0.144101i
$950$	−53.1835	−	92.1165i	−1.72550	−	2.98865i
$951$	−37.7598	+	65.4019i	−1.22444	+	2.12080i
$952$		0			0
$953$	0.865567	+	1.49921i	0.0280385	+	0.0485640i	0.879704	−	0.475521i	$-0.157741\pi$
$953$	0.865567	+	1.49921i	0.0280385	+	0.0485640i	−0.851666	+	0.524085i	$0.824407\pi$
$954$	−6.37060	−	11.0342i	−0.206256	−	0.357246i
$955$	3.59969			0.116483
$956$	11.1999			0.362231
$957$	22.7260	+	39.3626i	0.734628	+	1.27241i
$958$	12.1776	+	21.0922i	0.393439	+	0.681457i
$959$		0			0
$960$	48.2712	−	83.6082i	1.55795	−	2.69844i
$961$	10.8451	+	18.7842i	0.349841	+	0.605942i
$962$	−2.90776	+	25.5294i	−0.0937499	+	0.823100i
$963$	−15.3677	+	26.6177i	−0.495218	+	0.857744i
$964$	5.03613			0.162203
$965$	−5.31928	+	9.21326i	−0.171234	+	0.296585i
$966$		0			0
$967$	−4.88811			−0.157191			−0.0785955	−	0.996907i	$-0.525044\pi$
$967$	−4.88811			−0.157191			−0.0785955	+	0.996907i	$0.525044\pi$
$968$	−9.31411	+	16.1325i	−0.299367	+	0.518519i
$969$	90.3267			2.90171
$970$	−13.9791	+	24.2126i	−0.448843	+	0.777419i
$971$	−4.28576	+	7.42316i	−0.137537	+	0.238220i	−0.926564	−	0.376138i	$-0.877252\pi$
$971$	−4.28576	+	7.42316i	−0.137537	+	0.238220i	0.789027	+	0.614359i	$0.210585\pi$
$972$	33.9288	−	58.7664i	1.08827	−	1.88493i
$973$		0			0
$974$	−83.7347			−2.68303
$975$	5.99619	−	52.6450i	0.192032	−	1.68599i
$976$	−2.98392	+	5.16829i	−0.0955128	+	0.165433i
$977$	20.0191	+	34.6741i	0.640467	+	1.10932i	0.985329	+	0.170668i	$0.0545927\pi$
$977$	20.0191	+	34.6741i	0.640467	+	1.10932i	−0.344861	+	0.938654i	$0.612074\pi$
$978$	−26.5543			−0.849114
$979$	−15.3410	−	26.5714i	−0.490300	−	0.849225i
$980$		0			0
$981$	−4.79761	−	8.30971i	−0.153176	−	0.265309i
$982$	8.97922	−	15.5525i	0.286539	−	0.496299i
$983$	−11.9560	+	20.7084i	−0.381337	+	0.660496i	−0.991254	−	0.131970i	$-0.957870\pi$
$983$	−11.9560	+	20.7084i	−0.381337	+	0.660496i	0.609916	+	0.792466i	$0.291203\pi$
$984$	7.24862			0.231077
$985$	−59.6541			−1.90074
$986$	53.7130	−	93.0336i	1.71057	−	2.96279i
$987$		0			0
$988$	−71.3872	−	52.8197i	−2.27113	−	1.68042i
$989$	−13.2019	−	22.8664i	−0.419797	−	0.727110i
$990$	21.3628	+	37.0015i	0.678955	+	1.17598i
$991$	−20.5069	−	35.5190i	−0.651424	−	1.12830i	−0.982778	−	0.184792i	$-0.940839\pi$
$991$	−20.5069	−	35.5190i	−0.651424	−	1.12830i	0.331354	−	0.943506i	$-0.392495\pi$
$992$	6.89345	−	11.9398i	0.218867	−	0.379089i
$993$	11.0302			0.350033
$994$		0			0
$995$	−21.8946	−	37.9226i	−0.694106	−	1.20223i
$996$	11.4774	+	19.8795i	0.363677	+	0.629907i
$997$	25.4245			0.805201			0.402600	−	0.915376i	$-0.368106\pi$
$997$	25.4245			0.805201			0.402600	+	0.915376i	$0.368106\pi$
$998$	9.89819	+	17.1442i	0.313322	+	0.542689i
$999$	−4.71787			−0.149267

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.m.165.1		16
7.2	even	3		637.2.g.m.373.8		16
7.3	odd	6		637.2.f.l.295.8	yes	16
7.4	even	3		637.2.f.l.295.7	✓	16
7.5	odd	6		637.2.g.m.373.7		16
7.6	odd	2	inner	637.2.h.m.165.2		16
13.3	even	3		637.2.g.m.263.8		16
91.3	odd	6		637.2.f.l.393.8	yes	16
91.4	even	6		8281.2.a.cl.1.8		8
91.16	even	3	inner	637.2.h.m.471.1		16
91.17	odd	6		8281.2.a.cl.1.7		8
91.55	odd	6		637.2.g.m.263.7		16
91.68	odd	6	inner	637.2.h.m.471.2		16
91.74	even	3		8281.2.a.ci.1.2		8
91.81	even	3		637.2.f.l.393.7	yes	16
91.87	odd	6		8281.2.a.ci.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.7	✓	16	7.4	even	3
637.2.f.l.295.8	yes	16	7.3	odd	6
637.2.f.l.393.7	yes	16	91.81	even	3
637.2.f.l.393.8	yes	16	91.3	odd	6
637.2.g.m.263.7		16	91.55	odd	6
637.2.g.m.263.8		16	13.3	even	3
637.2.g.m.373.7		16	7.5	odd	6
637.2.g.m.373.8		16	7.2	even	3
637.2.h.m.165.1		16	1.1	even	1	trivial
637.2.h.m.165.2		16	7.6	odd	2	inner
637.2.h.m.471.1		16	91.16	even	3	inner
637.2.h.m.471.2		16	91.68	odd	6	inner
8281.2.a.ci.1.1		8	91.87	odd	6
8281.2.a.ci.1.2		8	91.74	even	3
8281.2.a.cl.1.7		8	91.17	odd	6
8281.2.a.cl.1.8		8	91.4	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.33152 q^{2} +(-1.15450 - 1.99966i) q^{3} +3.43596 q^{4} +(-1.68556 - 2.91947i) q^{5} +(2.69174 + 4.66224i) q^{6} -3.34797 q^{8} +(-1.16576 + 2.01915i) q^{9} +(3.92990 + 6.80679i) q^{10} +(-1.16576 - 2.01915i) q^{11} +(-3.96683 - 6.87075i) q^{12} +(0.408029 - 3.58239i) q^{13} +(-3.89197 + 6.74108i) q^{15} +0.933914 q^{16} -5.45734 q^{17} +(2.71798 - 4.70768i) q^{18} +(3.58410 - 6.20784i) q^{19} +(-5.79151 - 10.0312i) q^{20} +(2.71798 + 4.70768i) q^{22} -6.45242 q^{23} +(3.86524 + 6.69480i) q^{24} +(-3.18221 + 5.51175i) q^{25} +(-0.951325 + 8.35239i) q^{26} -1.54354 q^{27} +(4.22143 - 7.31174i) q^{29} +(9.07418 - 15.7169i) q^{30} +(1.52560 - 2.64242i) q^{31} +4.51850 q^{32} +(-2.69174 + 4.66224i) q^{33} +12.7239 q^{34} +(-4.00550 + 6.93773i) q^{36} +3.05653 q^{37} +(-8.35637 + 14.4737i) q^{38} +(-7.63463 + 3.31996i) q^{39} +(5.64320 + 9.77430i) q^{40} +(0.468833 - 0.812043i) q^{41} +(2.04605 + 3.54385i) q^{43} +(-4.00550 - 6.93773i) q^{44} +7.85981 q^{45} +15.0439 q^{46} +(1.73168 + 2.99936i) q^{47} +(-1.07821 - 1.86751i) q^{48} +(7.41937 - 12.8507i) q^{50} +(6.30052 + 10.9128i) q^{51} +(1.40197 - 12.3090i) q^{52} +(1.17194 - 2.02985i) q^{53} +3.59878 q^{54} +(-3.92990 + 6.80679i) q^{55} -16.5514 q^{57} +(-9.84233 + 17.0474i) q^{58} +7.24693 q^{59} +(-13.3726 + 23.1621i) q^{60} +(-3.19506 + 5.53401i) q^{61} +(-3.55697 + 6.16085i) q^{62} -12.4028 q^{64} +(-11.1464 + 4.84710i) q^{65} +(6.27584 - 10.8701i) q^{66} +(-2.30670 - 3.99532i) q^{67} -18.7512 q^{68} +(7.44934 + 12.9026i) q^{69} +(3.79370 + 6.57088i) q^{71} +(3.90292 - 6.76006i) q^{72} +(1.03498 - 1.79264i) q^{73} -7.12636 q^{74} +14.6955 q^{75} +(12.3148 - 21.3299i) q^{76} +(17.8002 - 7.74054i) q^{78} +(3.79434 + 6.57199i) q^{79} +(-1.57417 - 2.72654i) q^{80} +(5.27929 + 9.14400i) q^{81} +(-1.09309 + 1.89329i) q^{82} -2.89335 q^{83} +(9.19866 + 15.9326i) q^{85} +(-4.77039 - 8.26255i) q^{86} -19.4946 q^{87} +(3.90292 + 6.76006i) q^{88} +13.1597 q^{89} -18.3253 q^{90} -22.1703 q^{92} -7.04526 q^{93} +(-4.03744 - 6.99305i) q^{94} -24.1648 q^{95} +(-5.21663 - 9.03546i) q^{96} +(1.77856 + 3.08056i) q^{97} +5.43596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 24 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} + 8 q^{16} + 28 q^{18} + 28 q^{22} - 24 q^{23} + 12 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} + 16 q^{37} + 20 q^{39} + 32 q^{43} + 4 q^{44}+ \cdots + 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 + 24 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 + 8 * q^16 + 28 * q^18 + 28 * q^22 - 24 * q^23 + 12 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 + 16 * q^37 + 20 * q^39 + 32 * q^43 + 4 * q^44 + 8 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 - 48 * q^58 - 64 * q^60 - 64 * q^64 - 68 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 - 152 * q^74 + 28 * q^78 + 4 * q^79 + 56 * q^81 + 36 * q^85 - 4 * q^86 + 28 * q^88 - 160 * q^92 - 16 * q^93 - 104 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more