LMFDB - Embedded newform 637.2.g.m.263.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (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:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
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			263.7
Root			$-0.558788 - 0.967849i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.m.373.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16576 - 2.01915i) q^{2} -2.30901 q^{3} +(-1.71798 - 2.97563i) q^{4} +(1.68556 + 2.91947i) q^{5} +(-2.69174 + 4.66224i) q^{6} -3.34797 q^{8} +2.33152 q^{9} +O(q^{10})$	\(q+(1.16576 - 2.01915i) q^{2} -2.30901 q^{3} +(-1.71798 - 2.97563i) q^{4} +(1.68556 + 2.91947i) q^{5} +(-2.69174 + 4.66224i) q^{6} -3.34797 q^{8} +2.33152 q^{9} +7.85981 q^{10} +2.33152 q^{11} +(3.96683 + 6.87075i) q^{12} +(-0.408029 - 3.58239i) q^{13} +(-3.89197 - 6.74108i) q^{15} +(-0.466957 + 0.808794i) q^{16} +(-2.72867 - 4.72620i) q^{17} +(2.71798 - 4.70768i) q^{18} +7.16819 q^{19} +(5.79151 - 10.0312i) q^{20} +(2.71798 - 4.70768i) q^{22} +(3.22621 - 5.58796i) q^{23} +7.73048 q^{24} +(-3.18221 + 5.51175i) q^{25} +(-7.70905 - 3.35233i) q^{26} +1.54354 q^{27} +(4.22143 + 7.31174i) q^{29} -18.1484 q^{30} +(-1.52560 + 2.64242i) q^{31} +(-2.25925 - 3.91314i) q^{32} -5.38349 q^{33} -12.7239 q^{34} +(-4.00550 - 6.93773i) q^{36} +(-1.52827 + 2.64704i) q^{37} +(8.35637 - 14.4737i) q^{38} +(0.942141 + 8.27176i) 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} +(3.92990 + 6.80679i) q^{45} +(-7.52195 - 13.0284i) 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} +(-9.95888 + 7.36862i) q^{52} +(1.17194 - 2.02985i) q^{53} +(1.79939 - 3.11663i) q^{54} +(3.92990 + 6.80679i) q^{55} -16.5514 q^{57} +19.6847 q^{58} +(3.62346 + 6.27602i) q^{59} +(-13.3726 + 23.1621i) q^{60} -6.39013 q^{61} +(3.55697 + 6.16085i) q^{62} -12.4028 q^{64} +(9.77093 - 7.22955i) q^{65} +(-6.27584 + 10.8701i) q^{66} +4.61340 q^{67} +(-9.37561 + 16.2390i) q^{68} +(-7.44934 + 12.9026i) q^{69} +(3.79370 - 6.57088i) q^{71} -7.80584 q^{72} +(-1.03498 + 1.79264i) q^{73} +(3.56318 + 6.17161i) q^{74} +(7.34775 - 12.7267i) q^{75} +(-12.3148 - 21.3299i) q^{76} +(17.8002 + 7.74054i) q^{78} +(3.79434 + 6.57199i) q^{79} -3.14833 q^{80} -10.5586 q^{81} -2.18618 q^{82} +2.89335 q^{83} +(9.19866 - 15.9326i) q^{85} +(-4.77039 - 8.26255i) q^{86} +(-9.74732 - 16.8829i) q^{87} -7.80584 q^{88} +(6.57984 - 11.3966i) q^{89} +18.3253 q^{90} -22.1703 q^{92} +(3.52263 - 6.10138i) q^{93} -8.07488 q^{94} +(12.0824 + 20.9273i) 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 + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9} + 8 q^{11} - 8 q^{15} - 4 q^{16} + 28 q^{18} + 28 q^{22} + 12 q^{23} + 12 q^{25} + 8 q^{29} - 56 q^{30} + 4 q^{36} - 8 q^{37} - 16 q^{39} + 32 q^{43} + 4 q^{44} - 4 q^{46} + 36 q^{50} + 44 q^{51} + 4 q^{53} - 96 q^{57} + 96 q^{58} - 64 q^{60} - 64 q^{64} + 52 q^{65} - 40 q^{67} + 8 q^{71} - 56 q^{72} + 76 q^{74} + 28 q^{78} + 4 q^{79} - 112 q^{81} + 36 q^{85} - 4 q^{86} - 56 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9 + 8 * q^11 - 8 * q^15 - 4 * q^16 + 28 * q^18 + 28 * q^22 + 12 * q^23 + 12 * q^25 + 8 * q^29 - 56 * q^30 + 4 * q^36 - 8 * q^37 - 16 * q^39 + 32 * q^43 + 4 * q^44 - 4 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 + 96 * q^58 - 64 * q^60 - 64 * q^64 + 52 * q^65 - 40 * q^67 + 8 * q^71 - 56 * q^72 + 76 * q^74 + 28 * q^78 + 4 * q^79 - 112 * q^81 + 36 * q^85 - 4 * q^86 - 56 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.16576	−	2.01915i	0.824315	−	1.42776i	−0.0781266	−	0.996943i	$-0.524894\pi$
$2$	1.16576	−	2.01915i	0.824315	−	1.42776i	0.902442	−	0.430812i	$-0.141773\pi$
$3$	−2.30901			−1.33311			−0.666553	−	0.745458i	$-0.732231\pi$
$3$	−2.30901			−1.33311			−0.666553	+	0.745458i	$0.732231\pi$
$4$	−1.71798	−	2.97563i	−0.858991	−	1.48782i
$5$	1.68556	+	2.91947i	0.753804	+	1.30563i	0.945966	+	0.324264i	$0.105117\pi$
$5$	1.68556	+	2.91947i	0.753804	+	1.30563i	−0.192162	+	0.981363i	$0.561550\pi$
$6$	−2.69174	+	4.66224i	−1.09890	+	1.90335i
$7$		0			0
$7$		0			0
$8$	−3.34797			−1.18369
$9$	2.33152			0.777172
$10$	7.85981			2.48549
$11$	2.33152			0.702978			0.351489	−	0.936192i	$-0.385675\pi$
$11$	2.33152			0.702978			0.351489	+	0.936192i	$0.385675\pi$
$12$	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
$16$	−0.466957	+	0.808794i	−0.116739	+	0.202198i
$17$	−2.72867	−	4.72620i	−0.661800	−	1.14627i	−0.980142	−	0.198295i	$-0.936460\pi$
$17$	−2.72867	−	4.72620i	−0.661800	−	1.14627i	0.318343	−	0.947976i	$-0.396874\pi$
$18$	2.71798	−	4.70768i	0.640634	−	1.10961i
$19$	7.16819			1.64450			0.822248	−	0.569129i	$-0.192720\pi$
$19$	7.16819			1.64450			0.822248	+	0.569129i	$0.192720\pi$
$20$	5.79151	−	10.0312i	1.29502	−	2.24304i
$21$		0			0
$22$	2.71798	−	4.70768i	0.579476	−	1.00368i
$23$	3.22621	−	5.58796i	0.672711	−	1.16517i	−0.304421	−	0.952537i	$-0.598463\pi$
$23$	3.22621	−	5.58796i	0.672711	−	1.16517i	0.977132	−	0.212632i	$-0.0682036\pi$
$24$	7.73048			1.57798
$25$	−3.18221	+	5.51175i	−0.636442	+	1.10235i
$26$	−7.70905	−	3.35233i	−1.51187	−	0.657445i
$27$	1.54354			0.297054
$28$		0			0
$29$	4.22143	+	7.31174i	0.783900	+	1.35776i	0.929654	+	0.368434i	$0.120106\pi$
$29$	4.22143	+	7.31174i	0.783900	+	1.35776i	−0.145753	+	0.989321i	$0.546561\pi$
$30$	−18.1484			−3.31342
$31$	−1.52560	+	2.64242i	−0.274007	+	0.474593i	−0.969884	−	0.243567i	$-0.921682\pi$
$31$	−1.52560	+	2.64242i	−0.274007	+	0.474593i	0.695877	+	0.718161i	$0.255016\pi$
$32$	−2.25925	−	3.91314i	−0.399383	−	0.691752i
$33$	−5.38349			−0.937145
$34$	−12.7239			−2.18213
$35$		0			0
$36$	−4.00550	−	6.93773i	−0.667583	−	1.15629i
$37$	−1.52827	+	2.64704i	−0.251246	+	0.435170i	−0.963869	−	0.266377i	$-0.914174\pi$
$37$	−1.52827	+	2.64704i	−0.251246	+	0.435170i	0.712623	+	0.701547i	$0.247507\pi$
$38$	8.35637	−	14.4737i	1.35558	−	2.34794i
$39$	0.942141	+	8.27176i	0.150863	+	1.32454i
$40$	−5.64320	−	9.77430i	−0.892268	−	1.54545i
$41$	−0.468833	−	0.812043i	−0.0732194	−	0.126820i	0.827091	−	0.562068i	$-0.189994\pi$
$41$	−0.468833	−	0.812043i	−0.0732194	−	0.126820i	−0.900311	+	0.435248i	$0.856661\pi$
$42$		0			0
$43$	2.04605	−	3.54385i	0.312019	−	0.540433i	−0.666780	−	0.745254i	$-0.732328\pi$
$43$	2.04605	−	3.54385i	0.312019	−	0.540433i	0.978799	+	0.204822i	$0.0656614\pi$
$44$	−4.00550	−	6.93773i	−0.603852	−	1.04590i
$45$	3.92990	+	6.80679i	0.585835	+	1.01470i
$46$	−7.52195	−	13.0284i	−1.10905	−	1.92093i
$47$	−1.73168	−	2.99936i	−0.252591	−	0.437501i	0.711647	−	0.702537i	$-0.247950\pi$
$47$	−1.73168	−	2.99936i	−0.252591	−	0.437501i	−0.964239	+	0.265036i	$0.914616\pi$
$48$	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
$52$	−9.95888	+	7.36862i	−1.38105	+	1.02184i
$53$	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	$0.115202\pi$
$54$	1.79939	−	3.11663i	0.244866	−	0.424120i
$55$	3.92990	+	6.80679i	0.529908	+	0.917828i
$56$		0			0
$57$	−16.5514			−2.19229
$58$	19.6847			2.58472
$59$	3.62346	+	6.27602i	0.471735	+	0.817069i	0.999477	−	0.0323358i	$-0.0102946\pi$
$59$	3.62346	+	6.27602i	0.471735	+	0.817069i	−0.527742	+	0.849405i	$0.676961\pi$
$60$	−13.3726	+	23.1621i	−1.72640	+	2.99022i
$61$	−6.39013			−0.818172			−0.409086	−	0.912496i	$-0.634152\pi$
$61$	−6.39013			−0.818172			−0.409086	+	0.912496i	$0.634152\pi$
$62$	3.55697	+	6.16085i	0.451736	+	0.782429i
$63$		0			0
$64$	−12.4028			−1.55035
$65$	9.77093	−	7.22955i	1.21193	−	0.896716i
$66$	−6.27584	+	10.8701i	−0.772502	+	1.33801i
$67$	4.61340			0.563616			0.281808	−	0.959471i	$-0.409066\pi$
$67$	4.61340			0.563616			0.281808	+	0.959471i	$0.409066\pi$
$68$	−9.37561	+	16.2390i	−1.13696	+	1.96927i
$69$	−7.44934	+	12.9026i	−0.896795	+	1.55329i
$70$		0			0
$71$	3.79370	−	6.57088i	0.450229	−	0.779819i	−0.548171	−	0.836366i	$-0.684676\pi$
$71$	3.79370	−	6.57088i	0.450229	−	0.779819i	0.998400	+	0.0565468i	$0.0180090\pi$
$72$	−7.80584			−0.919927
$73$	−1.03498	+	1.79264i	−0.121136	+	0.209813i	−0.920216	−	0.391412i	$-0.871987\pi$
$73$	−1.03498	+	1.79264i	−0.121136	+	0.209813i	0.799080	+	0.601224i	$0.205320\pi$
$74$	3.56318	+	6.17161i	0.414211	+	0.717435i
$75$	7.34775	−	12.7267i	0.848445	−	1.46955i
$76$	−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	$0.692940\pi$
$80$	−3.14833			−0.351994
$81$	−10.5586			−1.17318
$82$	−2.18618			−0.241424
$83$	2.89335			0.317587			0.158793	−	0.987312i	$-0.449240\pi$
$83$	2.89335			0.317587			0.158793	+	0.987312i	$0.449240\pi$
$84$		0			0
$85$	9.19866	−	15.9326i	0.997735	−	1.72813i
$86$	−4.77039	−	8.26255i	−0.514404	−	0.890974i
$87$	−9.74732	−	16.8829i	−1.04502	−	1.81003i
$88$	−7.80584			−0.832105
$89$	6.57984	−	11.3966i	0.697461	−	1.20804i	−0.271882	−	0.962330i	$-0.587646\pi$
$89$	6.57984	−	11.3966i	0.697461	−	1.20804i	0.969344	−	0.245708i	$-0.0790205\pi$
$90$	18.3253			1.93165
$91$		0			0
$92$	−22.1703			−2.31141
$93$	3.52263	−	6.10138i	0.365280	−	0.632683i
$94$	−8.07488			−0.832860
$95$	12.0824	+	20.9273i	1.23963	+	2.14710i
$96$	5.21663	+	9.03546i	0.532420	+	0.922178i
$97$	−1.77856	+	3.08056i	−0.180585	+	0.312783i	−0.942080	−	0.335388i	$-0.891133\pi$
$97$	−1.77856	+	3.08056i	−0.180585	+	0.312783i	0.761495	+	0.648171i	$0.224466\pi$
$98$		0			0
$99$	5.43596			0.546335
$100$	21.8679			2.18679
$101$	−4.72865			−0.470518			−0.235259	−	0.971933i	$-0.575594\pi$
$101$	−4.72865			−0.470518			−0.235259	+	0.971933i	$0.575594\pi$
$102$	29.3795			2.90901
$103$	−2.99143	−	5.18131i	−0.294754	−	0.510529i	0.680173	−	0.733051i	$-0.261904\pi$
$103$	−2.99143	−	5.18131i	−0.294754	−	0.510529i	−0.974928	+	0.222522i	$0.928571\pi$
$104$	1.36607	+	11.9937i	0.133954	+	1.17608i
$105$		0			0
$106$	−2.73239	−	4.73263i	−0.265393	−	0.459674i
$107$	−6.59131	+	11.4165i	−0.637206	+	1.10367i	0.348837	+	0.937183i	$0.386577\pi$
$107$	−6.59131	+	11.4165i	−0.637206	+	1.10367i	−0.986043	+	0.166490i	$0.946757\pi$
$108$	−2.65177	−	4.59300i	−0.255166	−	0.441961i
$109$	−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	$0.229817\pi$
$110$	18.3253			1.74725
$111$	3.52878	−	6.11203i	0.334937	−	0.580128i
$112$		0			0
$113$	−7.14026	+	12.3673i	−0.671699	+	1.16342i	0.305723	+	0.952121i	$0.401102\pi$
$113$	−7.14026	+	12.3673i	−0.671699	+	1.16342i	−0.977422	+	0.211297i	$0.932231\pi$
$114$	−19.2949	+	33.4198i	−1.80714	+	3.13005i
$115$	21.7518			2.02837
$116$	14.5047	−	25.1229i	1.34673	−	2.33260i
$117$	−0.951325	−	8.35239i	−0.0879500	−	0.772179i
$118$	16.8963			1.55543
$119$		0			0
$120$	13.0302	+	22.5689i	1.18949	+	2.06025i
$121$	−5.56404			−0.505822
$122$	−7.44934	+	12.9026i	−0.674431	+	1.16815i
$123$	1.08254	+	1.87501i	0.0976093	+	0.169064i
$124$	10.4838			0.941477
$125$	−4.59963			−0.411403
$126$		0			0
$127$	5.53854	+	9.59304i	0.491466	+	0.851244i	0.999952	−	0.00982616i	$-0.00312781\pi$
$127$	5.53854	+	9.59304i	0.491466	+	0.851244i	−0.508486	+	0.861071i	$0.669794\pi$
$128$	−9.94014	+	17.2168i	−0.878592	+	1.52177i
$129$	−4.72433	+	8.18279i	−0.415954	+	0.720454i
$130$	−3.20703	−	28.1569i	−0.281275	−	2.46952i
$131$	−0.336006	−	0.581979i	−0.0293570	−	0.0508478i	0.850974	−	0.525208i	$-0.176013\pi$
$131$	−0.336006	−	0.581979i	−0.0293570	−	0.0508478i	−0.880331	+	0.474361i	$0.842679\pi$
$132$	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
$136$	9.13550	+	15.8232i	0.783363	+	1.35682i
$137$	−3.91937	−	6.78855i	−0.334855	−	0.579985i	0.648602	−	0.761128i	$-0.275354\pi$
$137$	−3.91937	−	6.78855i	−0.334855	−	0.579985i	−0.983457	+	0.181142i	$0.942021\pi$
$138$	17.3682	+	30.0827i	1.47848	+	2.56081i
$139$	1.63760	−	2.83641i	0.138900	−	0.240581i	−0.788181	−	0.615444i	$-0.788977\pi$
$139$	1.63760	−	2.83641i	0.138900	−	0.240581i	0.927080	+	0.374863i	$0.122310\pi$
$140$		0			0
$141$	3.99846	+	6.92554i	0.336731	+	0.583236i
$142$	−8.84506	−	15.3201i	−0.742261	−	1.28563i
$143$	−0.951325	−	8.35239i	−0.0795538	−	0.698462i
$144$	−1.08872	+	1.88571i	−0.0907265	+	0.157143i
$145$	−14.2309	+	24.6487i	−1.18182	+	2.04696i
$146$	2.41308	+	4.17957i	0.199708	+	0.345904i
$147$		0			0
$148$	10.5021			0.863270
$149$	−14.1637			−1.16034			−0.580169	−	0.814496i	$-0.697013\pi$
$149$	−14.1637			−1.16034			−0.580169	+	0.814496i	$0.697013\pi$
$150$	−17.1314	−	29.6724i	−1.39877	−	2.42274i
$151$	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	$0.149222\pi$
$152$	−23.9989			−1.94657
$153$	−6.36194	−	11.0192i	−0.514332	−	0.890849i
$154$		0			0
$155$	−10.2860			−0.826190
$156$	22.9951	−	17.0142i	1.84108	−	1.36223i
$157$	−6.52006	+	11.2931i	−0.520357	+	0.901285i	0.479363	+	0.877617i	$0.340868\pi$
$157$	−6.52006	+	11.2931i	−0.520357	+	0.901285i	−0.999720	+	0.0236682i	$0.992465\pi$
$158$	17.6931			1.40759
$159$	−2.70601	+	4.68695i	−0.214600	+	0.371699i
$160$	7.61620	−	13.1916i	0.602113	−	1.04289i
$161$		0			0
$162$	−12.3087	+	21.3194i	−0.967067	+	1.67501i
$163$	4.93256			0.386348			0.193174	−	0.981165i	$-0.438122\pi$
$163$	4.93256			0.386348			0.193174	+	0.981165i	$0.438122\pi$
$164$	−1.61089	+	2.79015i	−0.125790	+	0.217874i
$165$	−9.07418	−	15.7169i	−0.706424	−	1.22356i
$166$	3.37295	−	5.84212i	0.261792	−	0.453436i
$167$	1.82128	+	3.15455i	0.140935	+	0.244107i	0.927849	−	0.372956i	$-0.121656\pi$
$167$	1.82128	+	3.15455i	0.140935	+	0.244107i	−0.786914	+	0.617063i	$0.788322\pi$
$168$		0			0
$169$	−12.6670	+	2.92344i	−0.974387	+	0.224880i
$170$	−21.4468	−	37.1470i	−1.64490	−	2.84904i
$171$	16.7127			1.27806
$172$	−14.0603			−1.07209
$173$	−12.6917			−0.964930			−0.482465	−	0.875915i	$-0.660258\pi$
$173$	−12.6917			−0.964930			−0.482465	+	0.875915i	$0.660258\pi$
$174$	−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
$178$	−15.3410	−	26.5714i	−1.14986	−	1.99161i
$179$	−8.78939			−0.656950			−0.328475	−	0.944513i	$-0.606535\pi$
$179$	−8.78939			−0.656950			−0.328475	+	0.944513i	$0.606535\pi$
$180$	13.5030	−	23.3879i	1.00645	−	1.74323i
$181$	17.1982			1.27833			0.639167	−	0.769068i	$-0.279279\pi$
$181$	17.1982			1.27833			0.639167	+	0.769068i	$0.279279\pi$
$182$		0			0
$183$	14.7548			1.09071
$184$	−10.8012	+	18.7083i	−0.796278	+	1.37919i
$185$	−10.3039			−0.757560
$186$	−8.21307	−	14.2255i	−0.602212	−	1.04306i
$187$	−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
$191$	1.06780			0.0772636			0.0386318	−	0.999254i	$-0.487700\pi$
$191$	1.06780			0.0772636			0.0386318	+	0.999254i	$0.487700\pi$
$192$	28.6381			2.06678
$193$	3.15580			0.227159			0.113580	−	0.993529i	$-0.463768\pi$
$193$	3.15580			0.227159			0.113580	+	0.993529i	$0.463768\pi$
$194$	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	0.987474	+	0.157784i	$0.0504351\pi$
$197$	8.84783	+	15.3249i	0.630382	+	1.09185i	−0.357092	+	0.934069i	$0.616232\pi$
$198$	6.33701	−	10.9760i	0.450352	−	0.780033i
$199$	6.49476	+	11.2493i	0.460402	+	0.797439i	0.998981	−	0.0451359i	$-0.0143721\pi$
$199$	6.49476	+	11.2493i	0.460402	+	0.797439i	−0.538579	+	0.842575i	$0.681039\pi$
$200$	10.6539	−	18.4532i	0.753348	−	1.30484i
$201$	−10.6524			−0.751360
$202$	−5.51246	+	9.54785i	−0.387855	+	0.671785i
$203$		0			0
$204$	21.6484	−	37.4960i	1.51569	−	2.62525i
$205$	1.58049	−	2.73749i	0.110386	−	0.191195i
$206$	−13.9491			−0.971881
$207$	7.52195	−	13.0284i	0.522812	−	0.905537i
$208$	3.08795	+	1.34281i	0.214111	+	0.0931072i
$209$	16.7127			1.15605
$210$		0			0
$211$	−13.7701	−	23.8505i	−0.947974	−	1.64194i	−0.749685	−	0.661795i	$-0.769795\pi$
$211$	−13.7701	−	23.8505i	−0.947974	−	1.64194i	−0.198289	−	0.980144i	$-0.563538\pi$
$212$	−8.05346			−0.553114
$213$	−8.75967	+	15.1722i	−0.600203	+	1.03958i
$214$	15.3677	+	26.6177i	1.05052	+	1.81955i
$215$	13.7949			0.940805
$216$	−5.16771			−0.351618
$217$		0			0
$218$	4.79761	+	8.30971i	0.324935	+	0.562805i
$219$	2.38978	−	4.13922i	0.161487	−	0.279703i
$220$	13.5030	−	23.3879i	0.910372	−	1.57681i
$221$	−15.8177	+	11.7036i	−1.06401	+	0.787268i
$222$	−8.22740	−	14.2503i	−0.552187	−	0.956416i
$223$	−4.35098	−	7.53612i	−0.291363	−	0.504656i	0.682769	−	0.730634i	$-0.260776\pi$
$223$	−4.35098	−	7.53612i	−0.291363	−	0.504656i	−0.974132	+	0.225978i	$0.927442\pi$
$224$		0			0
$225$	−7.41937	+	12.8507i	−0.494625	+	0.856715i
$226$	16.6476	+	28.8345i	1.10738	+	1.91805i
$227$	−10.9835	−	19.0239i	−0.728998	−	1.26266i	−0.957307	−	0.289072i	$-0.906653\pi$
$227$	−10.9835	−	19.0239i	−0.728998	−	1.26266i	0.228310	−	0.973589i	$-0.426680\pi$
$228$	28.4350	+	49.2509i	1.88315	+	3.26172i
$229$	10.2594	+	17.7698i	0.677959	+	1.17426i	0.975595	+	0.219580i	$0.0704685\pi$
$229$	10.2594	+	17.7698i	0.677959	+	1.17426i	−0.297636	+	0.954679i	$0.596198\pi$
$230$	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	$0.641703\pi$
$234$	−17.9738	−	7.81600i	−1.17498	−	0.510948i
$235$	5.83769	−	10.1112i	0.380809	−	0.659581i
$236$	12.4501	−	21.5642i	0.810432	−	1.40371i
$237$	−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	$0.466380\pi$
$240$	7.26953			0.469246
$241$	0.732856	+	1.26934i	0.0472074	+	0.0817657i	0.888664	−	0.458560i	$-0.151634\pi$
$241$	0.732856	+	1.26934i	0.0472074	+	0.0817657i	−0.841456	+	0.540325i	$0.818301\pi$
$242$	−6.48632	+	11.2346i	−0.416956	+	0.722190i
$243$	19.7492			1.26691
$244$	10.9781	+	19.0147i	0.702802	+	1.21729i
$245$		0			0
$246$	5.04791			0.321843
$247$	−2.92483	−	25.6793i	−0.186102	−	1.63393i
$248$	5.10768	−	8.84676i	0.324338	−	0.561770i
$249$	−6.68077			−0.423377
$250$	−5.36205	+	9.28734i	−0.339126	+	0.587383i
$251$	−8.55142	+	14.8115i	−0.539761	+	0.934894i	0.459156	+	0.888356i	$0.348152\pi$
$251$	−8.55142	+	14.8115i	−0.539761	+	0.934894i	−0.998917	+	0.0465376i	$0.985181\pi$
$252$		0			0
$253$	7.52195	−	13.0284i	0.472901	−	0.819089i
$254$	25.8264			1.62049
$255$	−21.2398	+	36.7884i	−1.33009	+	2.30378i
$256$	10.7728	+	18.6590i	0.673300	+	1.16619i
$257$	−1.92506	+	3.33430i	−0.120082	+	0.207988i	−0.919800	−	0.392388i	$-0.871649\pi$
$257$	−1.92506	+	3.33430i	−0.120082	+	0.207988i	0.799718	+	0.600376i	$0.204982\pi$
$258$	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
$262$	−1.56681			−0.0967976
$263$	−30.5159			−1.88169			−0.940844	−	0.338840i	$-0.889966\pi$
$263$	−30.5159			−1.88169			−0.940844	+	0.338840i	$0.889966\pi$
$264$	18.0237			1.10928
$265$	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
$269$	−8.38857	−	14.5294i	−0.511460	−	0.885875i	−0.999912	−	0.0132842i	$-0.995771\pi$
$269$	−8.38857	−	14.5294i	−0.511460	−	0.885875i	0.488451	−	0.872591i	$-0.337562\pi$
$270$	12.1319			0.738324
$271$	−15.5886	+	27.0003i	−0.946941	+	1.64015i	−0.195124	+	0.980779i	$0.562511\pi$
$271$	−15.5886	+	27.0003i	−0.946941	+	1.64015i	−0.751817	+	0.659372i	$0.770822\pi$
$272$	5.09669			0.309032
$273$		0			0
$274$	−18.2762			−1.10410
$275$	−7.41937	+	12.8507i	−0.447405	+	0.774928i
$276$	51.1913			3.08135
$277$	−0.197941	−	0.342844i	−0.0118931	−	0.0205995i	0.860018	−	0.510264i	$-0.170452\pi$
$277$	−0.197941	−	0.342844i	−0.0118931	−	0.0205995i	−0.871911	+	0.489665i	$0.837119\pi$
$278$	−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	$0.739944\pi$
$282$	18.6449			1.11029
$283$	19.3515			1.15033			0.575164	−	0.818038i	$-0.304938\pi$
$283$	19.3515			1.15033			0.575164	+	0.818038i	$0.304938\pi$
$284$	−26.0700			−1.54697
$285$	−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
$289$	−6.39129	+	11.0700i	−0.375958	+	0.651178i
$290$	33.1796	+	57.4688i	1.94838	+	3.37469i
$291$	4.10671	−	7.11303i	0.240740	−	0.416973i
$292$	7.11232			0.416217
$293$	7.88616	−	13.6592i	0.460715	−	0.797981i	−0.538282	−	0.842765i	$-0.680926\pi$
$293$	7.88616	−	13.6592i	0.460715	−	0.797981i	0.998997	+	0.0447835i	$0.0142598\pi$
$294$		0			0
$295$	−12.2151	+	21.1572i	−0.711192	+	1.23182i
$296$	5.11659	−	8.86220i	0.297396	−	0.515105i
$297$	3.59878			0.208822
$298$	−16.5115	+	28.5987i	−0.956483	+	1.65668i
$299$	−21.3346	−	9.27749i	−1.23381	−	0.536531i
$300$	−50.4932			−2.91523
$301$		0			0
$302$	−1.56940	−	2.71828i	−0.0903089	−	0.156420i
$303$	10.9185			0.627250
$304$	−3.34724	+	5.79759i	−0.191977	+	0.332515i
$305$	−10.7709	−	18.6558i	−0.616742	−	1.06823i
$306$	−29.6659			−1.69589
$307$	19.2535			1.09885			0.549427	−	0.835542i	$-0.314846\pi$
$307$	19.2535			1.09885			0.549427	+	0.835542i	$0.314846\pi$
$308$		0			0
$309$	6.90723	+	11.9637i	0.392939	+	0.680590i
$310$	−11.9910	+	20.7689i	−0.681041	+	1.17960i
$311$	−1.53232	+	2.65405i	−0.0868898	+	0.150498i	−0.906195	−	0.422860i	$-0.861026\pi$
$311$	−1.53232	+	2.65405i	−0.0868898	+	0.150498i	0.819305	+	0.573358i	$0.194359\pi$
$312$	−3.15426	−	27.6936i	−0.178575	−	1.56784i
$313$	17.6376	+	30.5492i	0.996934	+	1.72674i	0.566229	+	0.824248i	$0.308402\pi$
$313$	17.6376	+	30.5492i	0.996934	+	1.72674i	0.430705	+	0.902493i	$0.358265\pi$
$314$	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	$-0.537258\pi$
$318$	6.30910	+	10.9277i	0.353797	+	0.612794i
$319$	9.84233	+	17.0474i	0.551065	+	0.954472i
$320$	−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
$325$	21.0437	+	9.15097i	1.16729	+	0.507604i
$326$	5.75016	−	9.95958i	0.318472	−	0.551610i
$327$	4.75130	−	8.22949i	0.262747	−	0.455092i
$328$	1.56964	+	2.71869i	0.0866688	+	0.150115i
$329$		0			0
$330$	−42.3132			−2.32926
$331$	4.77703			0.262569			0.131285	−	0.991345i	$-0.458090\pi$
$331$	4.77703			0.262569			0.131285	+	0.991345i	$0.458090\pi$
$332$	−4.97073	−	8.60955i	−0.272804	−	0.472511i
$333$	−3.56318	+	6.17161i	−0.195261	+	0.338202i
$334$	8.49269			0.464699
$335$	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	$0.246577\pi$
$338$	−8.86382	+	28.9847i	−0.482128	+	1.57656i
$339$	16.4869	−	28.5562i	0.895447	−	1.55096i
$340$	−63.2125			−3.42818
$341$	−3.55697	+	6.16085i	−0.192621	+	0.333629i
$342$	19.4830	−	33.7456i	1.05352	−	1.82475i
$343$		0			0
$344$	−6.85010	+	11.8647i	−0.369332	+	0.639702i
$345$	−50.2252			−2.70403
$346$	−14.7954	+	25.6264i	−0.795407	+	1.37768i
$347$	5.22211	+	9.04496i	0.280338	+	0.485559i	0.971468	−	0.237171i	$-0.0762202\pi$
$347$	5.22211	+	9.04496i	0.280338	+	0.485559i	−0.691130	+	0.722730i	$0.742887\pi$
$348$	−33.4914	+	58.0088i	−1.79533	+	3.10960i
$349$	−11.7344	−	20.3246i	−0.628128	−	1.08795i	−0.987927	−	0.154920i	$-0.950488\pi$
$349$	−11.7344	−	20.3246i	−0.628128	−	1.08795i	0.359799	−	0.933030i	$-0.382845\pi$
$350$		0			0
$351$	−0.629807	−	5.52955i	−0.0336166	−	0.295145i
$352$	−5.26748	−	9.12354i	−0.280758	−	0.486286i
$353$	2.93135			0.156020			0.0780099	−	0.996953i	$-0.475143\pi$
$353$	2.93135			0.156020			0.0780099	+	0.996953i	$0.475143\pi$
$354$	−39.0137			−2.07356
$355$	25.5780			1.35754
$356$	−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	$0.684298\pi$
$360$	−13.1572	−	22.7889i	−0.693445	−	1.20108i
$361$	32.3830			1.70437
$362$	20.0490	−	34.7258i	1.05375	−	1.82515i
$363$	12.8474			0.674314
$364$		0			0
$365$	−6.97809			−0.365250
$366$	17.2006	−	29.7923i	0.899089	−	1.55727i
$367$	−1.04860			−0.0547365			−0.0273683	−	0.999625i	$-0.508713\pi$
$367$	−1.04860			−0.0547365			−0.0273683	+	0.999625i	$0.508713\pi$
$368$	3.01300	+	5.21867i	0.157064	+	0.272042i
$369$	−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
$373$	−15.0107			−0.777226			−0.388613	−	0.921401i	$-0.627046\pi$
$373$	−15.0107			−0.777226			−0.388613	+	0.921401i	$0.627046\pi$
$374$	−29.6659			−1.53399
$375$	10.6206			0.548444
$376$	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	0.969401	+	0.245481i	$0.0789459\pi$
$379$	13.5749	+	23.5123i	0.697294	+	1.20775i	−0.272108	+	0.962267i	$0.587721\pi$
$380$	41.5147	−	71.9056i	2.12966	−	3.68868i
$381$	−12.7885	−	22.1504i	−0.655177	−	1.13480i
$382$	1.24480	−	2.15606i	0.0636895	−	0.110314i
$383$	−16.0264			−0.818911			−0.409455	−	0.912330i	$-0.634281\pi$
$383$	−16.0264			−0.818911			−0.409455	+	0.912330i	$0.634281\pi$
$384$	22.9519	−	39.7538i	1.17126	−	2.02868i
$385$		0			0
$386$	3.67890	−	6.37203i	0.187251	−	0.324328i
$387$	4.77039	−	8.26255i	0.242492	−	0.420009i
$388$	12.2221			0.620485
$389$	−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	$0.231626\pi$
$390$	7.40505	+	65.0145i	0.374969	+	3.29214i
$391$	−35.2130			−1.78080
$392$		0			0
$393$	0.775840	+	1.34379i	0.0391360	+	0.0677855i
$394$	41.2577			2.07853
$395$	−12.7912	+	22.1550i	−0.643593	+	1.11474i
$396$	−9.33888	−	16.1754i	−0.469297	−	0.812845i
$397$	−12.2087			−0.612738			−0.306369	−	0.951913i	$-0.599114\pi$
$397$	−12.2087			−0.612738			−0.306369	+	0.951913i	$0.599114\pi$
$398$	30.2853			1.51806
$399$		0			0
$400$	−2.97191	−	5.14750i	−0.148596	−	0.257375i
$401$	−18.9206	+	32.7715i	−0.944850	+	1.63653i	−0.188799	+	0.982016i	$0.560459\pi$
$401$	−18.9206	+	32.7715i	−0.944850	+	1.63653i	−0.756051	+	0.654513i	$0.772874\pi$
$402$	−12.4181	+	21.5087i	−0.619358	+	1.07276i
$403$	10.0887	+	4.38712i	0.502553	+	0.218538i
$404$	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
$409$	−0.117537	−	0.203580i	−0.00581184	−	0.0100664i	0.863105	−	0.505025i	$-0.168517\pi$
$409$	−0.117537	−	0.203580i	−0.00581184	−	0.0100664i	−0.868917	+	0.494958i	$0.835183\pi$
$410$	−3.68494	−	6.38250i	−0.181986	−	0.315209i
$411$	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
$416$	−13.0965	+	9.69019i	−0.642111	+	0.475101i
$417$	−3.78124	+	6.54930i	−0.185168	+	0.320720i
$418$	19.4830	−	33.7456i	0.952945	−	1.65055i
$419$	−0.222023	−	0.384555i	−0.0108465	−	0.0187868i	0.860551	−	0.509364i	$-0.170119\pi$
$419$	−0.222023	−	0.384555i	−0.0108465	−	0.0187868i	−0.871398	+	0.490577i	$0.836786\pi$
$420$		0			0
$421$	9.45998			0.461051			0.230526	−	0.973066i	$-0.425955\pi$
$421$	9.45998			0.461051			0.230526	+	0.973066i	$0.425955\pi$
$422$	−64.2105			−3.12572
$423$	−4.03744	−	6.99305i	−0.196307	−	0.340014i
$424$	−3.92361	+	6.79588i	−0.190547	+	0.330037i
$425$	34.7328			1.68479
$426$	20.4233	+	35.3742i	0.989513	+	1.71389i
$427$		0			0
$428$	45.2950			2.18942
$429$	2.19662	+	19.2857i	0.106054	+	0.931124i
$430$	16.0815	−	27.8540i	0.775520	−	1.34324i
$431$	21.5446			1.03777			0.518883	−	0.854845i	$-0.326348\pi$
$431$	21.5446			1.03777			0.518883	+	0.854845i	$0.326348\pi$
$432$	−0.720766	+	1.24840i	−0.0346778	+	0.0600638i
$433$	6.57949	−	11.3960i	0.316190	−	0.547657i	−0.663500	−	0.748176i	$-0.730930\pi$
$433$	6.57949	−	11.3960i	0.316190	−	0.547657i	0.979690	+	0.200519i	$0.0642630\pi$
$434$		0			0
$435$	32.8593	−	56.9141i	1.57548	−	2.72882i
$436$	14.1405			0.677208
$437$	23.1261	−	40.0555i	1.10627	−	1.91612i
$438$	−5.57181	−	9.65066i	−0.266232	−	0.461127i
$439$	14.8923	−	25.7943i	0.710773	−	1.23109i	−0.253795	−	0.967258i	$-0.581679\pi$
$439$	14.8923	−	25.7943i	0.710773	−	1.23109i	0.964568	−	0.263836i	$-0.0849878\pi$
$440$	−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	$0.948067\pi$
$444$	−24.2495			−1.15083
$445$	44.3628			2.10300
$446$	−20.2888			−0.960701
$447$	32.7041			1.54685
$448$		0			0
$449$	13.1114	−	22.7095i	0.618763	−	1.07173i	−0.370949	−	0.928653i	$-0.620968\pi$
$449$	13.1114	−	22.7095i	0.618763	−	1.07173i	0.989712	−	0.143075i	$-0.0456992\pi$
$450$	17.2984	+	29.9617i	0.815454	+	1.41241i
$451$	−1.09309	−	1.89329i	−0.0514717	−	0.0891516i
$452$	49.0674			2.30793
$453$	−1.55425	+	2.69204i	−0.0730251	+	0.126483i
$454$	−51.2162			−2.40369
$455$		0			0
$456$	55.4136			2.59498
$457$	7.93542	−	13.7445i	0.371203	−	0.642943i	−0.618548	−	0.785747i	$-0.712279\pi$
$457$	7.93542	−	13.7445i	0.371203	−	0.642943i	0.989751	+	0.142804i	$0.0456120\pi$
$458$	47.8398			2.23541
$459$	−4.21180	−	7.29506i	−0.196590	−	0.340504i
$460$	−37.3693	−	64.7255i	−1.74235	−	3.01784i
$461$	−11.0443	+	19.1293i	−0.514384	+	0.890940i	0.485476	+	0.874250i	$0.338646\pi$
$461$	−11.0443	+	19.1293i	−0.514384	+	0.890940i	−0.999861	+	0.0166900i	$0.994687\pi$
$462$		0			0
$463$	18.2887			0.849949			0.424974	−	0.905205i	$-0.360283\pi$
$463$	18.2887			0.849949			0.424974	+	0.905205i	$0.360283\pi$
$464$	−7.88491			−0.366048
$465$	23.7504			1.10140
$466$	40.3091			1.86728
$467$	−2.26659	−	3.92585i	−0.104885	−	0.181667i	0.808806	−	0.588076i	$-0.200114\pi$
$467$	−2.26659	−	3.92585i	−0.104885	−	0.181667i	−0.913691	+	0.406409i	$0.866781\pi$
$468$	−23.2193	+	17.1801i	−1.07331	+	0.794148i
$469$		0			0
$470$	−13.6107	−	23.5744i	−0.627813	−	1.08740i
$471$	15.0549	−	26.0758i	0.693691	−	1.20151i
$472$	−12.1312	−	21.0119i	−0.558386	−	0.967153i
$473$	4.77039	−	8.26255i	0.219343	−	0.379912i
$474$	−40.8536			−1.87647
$475$	−22.8107	+	39.5093i	−1.04663	+	1.81281i
$476$		0			0
$477$	2.73239	−	4.73263i	0.125107	−	0.216692i
$478$	3.79992	−	6.58165i	0.173804	−	0.301038i
$479$	−10.4461			−0.477293			−0.238646	−	0.971107i	$-0.576704\pi$
$479$	−10.4461			−0.477293			−0.238646	+	0.971107i	$0.576704\pi$
$480$	−17.5859	+	30.4596i	−0.802681	+	1.39028i
$481$	10.1063	+	4.39478i	0.460807	+	0.200385i
$482$	3.41733			0.155655
$483$		0			0
$484$	9.55891	+	16.5565i	0.434496	+	0.752569i
$485$	−11.9915			−0.544505
$486$	23.0228	−	39.8767i	1.04434	−	1.80884i
$487$	−17.9571	−	31.1027i	−0.813715	−	1.40940i	−0.910247	−	0.414067i	$-0.864108\pi$
$487$	−17.9571	−	31.1027i	−0.813715	−	1.40940i	0.0965311	−	0.995330i	$-0.469225\pi$
$488$	21.3939			0.968458
$489$	−11.3893			−0.515042
$490$		0			0
$491$	−3.85124	−	6.67054i	−0.173804	−	0.301037i	0.765943	−	0.642909i	$-0.222273\pi$
$491$	−3.85124	−	6.67054i	−0.173804	−	0.301037i	−0.939747	+	0.341871i	$0.888939\pi$
$492$	3.71956	−	6.44247i	0.167691	−	0.290449i
$493$	23.0378	−	39.9026i	1.03757	−	1.79712i
$494$	−55.2599	−	24.0301i	−2.48626	−	1.08117i
$495$	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	$0.894198\pi$
$500$	7.90207	+	13.6868i	0.353391	+	0.612092i
$501$	−4.20535	−	7.28389i	−0.187881	−	0.325420i
$502$	19.9378	+	34.5332i	0.889866	+	1.54129i
$503$	−15.2000	+	26.3272i	−0.677736	+	1.17387i	0.297924	+	0.954589i	$0.403706\pi$
$503$	−15.2000	+	26.3272i	−0.677736	+	1.17387i	−0.975661	+	0.219285i	$0.929628\pi$
$504$		0			0
$505$	−7.97041	−	13.8052i	−0.354679	−	0.614321i
$506$	−17.5375	−	30.3759i	−0.779639	−	1.35037i
$507$	29.2483	−	6.75023i	1.29896	−	0.299788i
$508$	19.0302	−	32.9613i	0.844330	−	1.46242i
$509$	7.79007	−	13.4928i	0.345289	−	0.598058i	−0.640117	−	0.768277i	$-0.721114\pi$
$509$	7.79007	−	13.4928i	0.345289	−	0.598058i	0.985406	+	0.170219i	$0.0544476\pi$
$510$	49.5209	+	85.7727i	2.19282	+	3.79808i
$511$		0			0
$512$	10.4733			0.462860
$513$	11.0644			0.488504
$514$	4.48830	+	7.77396i	0.197970	+	0.342895i
$515$	10.0845	−	17.4668i	0.444374	−	0.769678i
$516$	32.4653			1.42920
$517$	−4.03744	−	6.99305i	−0.177566	−	0.307554i
$518$		0			0
$519$	29.3052			1.28635
$520$	−32.7128	+	24.2043i	−1.43455	+	1.06143i
$521$	−13.5787	+	23.5190i	−0.594893	+	1.03039i	0.398669	+	0.917095i	$0.369472\pi$
$521$	−13.5787	+	23.5190i	−0.594893	+	1.03039i	−0.993562	+	0.113290i	$0.963861\pi$
$522$	45.8951			2.00877
$523$	9.02874	−	15.6382i	0.394799	−	0.683812i	−0.598276	−	0.801290i	$-0.704147\pi$
$523$	9.02874	−	15.6382i	0.394799	−	0.683812i	0.993076	+	0.117478i	$0.0374808\pi$
$524$	−1.15450	+	1.99966i	−0.0504347	+	0.0873555i
$525$		0			0
$526$	−35.5741	+	61.6161i	−1.55110	+	2.68659i
$527$	16.6515			0.725350
$528$	2.51386	−	4.35413i	0.109402	−	0.189489i
$529$	−9.31684	−	16.1372i	−0.405080	−	0.701619i
$530$	9.21119	−	15.9543i	0.400109	−	0.693008i
$531$	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
$535$	−44.4401			−1.92131
$536$	−15.4455			−0.667145
$537$	20.2948			0.875783
$538$	−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	$-0.495962\pi$
$542$	36.3451	+	62.9516i	1.56116	+	2.70400i
$543$	−39.7108			−1.70415
$544$	−12.3295	+	21.3553i	−0.528623	+	0.915602i
$545$	−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	$0.660605\pi$
$548$	−13.4668	+	23.3252i	−0.575274	+	0.996404i
$549$	−14.8987			−0.635860
$550$	17.2984	+	29.9617i	0.737605	+	1.27757i
$551$	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
$555$	23.7919			1.00991
$556$	−11.2535			−0.477254
$557$	−9.97372			−0.422600			−0.211300	−	0.977421i	$-0.567770\pi$
$557$	−9.97372			−0.422600			−0.211300	+	0.977421i	$0.567770\pi$
$558$	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
$562$	−26.7494	+	46.3313i	−1.12836	+	1.95437i
$563$	10.7640	+	18.6437i	0.453647	+	0.785740i	0.998609	−	0.0527209i	$-0.0167894\pi$
$563$	10.7640	+	18.6437i	0.453647	+	0.785740i	−0.544962	+	0.838461i	$0.683456\pi$
$564$	13.7386	−	23.7959i	0.578498	−	1.00199i
$565$	−48.1413			−2.02532
$566$	22.5592	−	39.0736i	0.948232	−	1.64239i
$567$		0			0
$568$	−12.7012	+	21.9991i	−0.532930	+	0.923061i
$569$	16.5502	−	28.6657i	0.693819	−	1.20173i	−0.276758	−	0.960940i	$-0.589260\pi$
$569$	16.5502	−	28.6657i	0.693819	−	1.20173i	0.970577	−	0.240791i	$-0.0774068\pi$
$570$	−130.091			−5.44891
$571$	−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	$0.303635\pi$
$572$	−23.2193	+	17.1801i	−0.970847	+	0.718334i
$573$	−2.46557			−0.103001
$574$		0			0
$575$	20.5330	+	35.5641i	0.856283	+	1.48313i
$576$	−28.9173			−1.20489
$577$	−14.7348	+	25.5214i	−0.613416	+	1.06247i	0.377244	+	0.926114i	$0.376872\pi$
$577$	−14.7348	+	25.5214i	−0.613416	+	1.06247i	−0.990660	+	0.136354i	$0.956462\pi$
$578$	14.9014	+	25.8100i	0.619816	+	1.07355i
$579$	−7.28676			−0.302827
$580$	97.7939			4.06067
$581$		0			0
$582$	−9.57486	−	16.5841i	−0.396891	−	0.687435i
$583$	2.73239	−	4.73263i	0.113164	−	0.196006i
$584$	3.46509	−	6.00171i	0.143386	−	0.248353i
$585$	22.7811	−	16.8558i	0.941881	−	0.696902i
$586$	−18.3867	−	31.8467i	−0.759548	−	1.31558i
$587$	−3.49429	−	6.05229i	−0.144225	−	0.249805i	0.784859	−	0.619675i	$-0.212736\pi$
$587$	−3.49429	−	6.05229i	−0.144225	−	0.249805i	−0.929084	+	0.369870i	$0.879402\pi$
$588$		0			0
$589$	−10.9358	+	18.9414i	−0.450603	+	0.780467i
$590$	28.4797	+	49.3283i	1.17249	+	2.03082i
$591$	−20.4297	−	35.3853i	−0.840366	−	1.45556i
$592$	−1.42727	−	2.47211i	−0.0586605	−	0.101603i
$593$	−0.485124	−	0.840259i	−0.0199216	−	0.0345053i	0.855893	−	0.517153i	$-0.173008\pi$
$593$	−0.485124	−	0.840259i	−0.0199216	−	0.0345053i	−0.875814	+	0.482648i	$0.839675\pi$
$594$	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
$598$	−43.6036	+	32.2625i	−1.78309	+	1.31931i
$599$	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	$0.0139055\pi$
$600$	−24.6000	+	42.6085i	−1.00429	+	1.73949i
$601$	15.2146	+	26.3525i	0.620617	+	1.07494i	0.989371	+	0.145414i	$0.0464513\pi$
$601$	15.2146	+	26.3525i	0.620617	+	1.07494i	−0.368754	+	0.929527i	$0.620215\pi$
$602$		0			0
$603$	10.7562			0.438027
$604$	−4.62567			−0.188216
$605$	−9.37851	−	16.2441i	−0.381291	−	0.660415i
$606$	12.7283	−	22.0461i	0.517052	−	0.895560i
$607$	−32.1576			−1.30524			−0.652618	−	0.757687i	$-0.726329\pi$
$607$	−32.1576			−1.30524			−0.652618	+	0.757687i	$0.726329\pi$
$608$	−16.1947	−	28.0501i	−0.656784	−	1.13758i
$609$		0			0
$610$	−50.2252			−2.03356
$611$	−10.0383	+	7.42738i	−0.406106	+	0.300479i
$612$	−21.8594	+	37.8616i	−0.883613	+	1.53046i
$613$	13.9209			0.562258			0.281129	−	0.959670i	$-0.409291\pi$
$613$	13.9209			0.562258			0.281129	+	0.959670i	$0.409291\pi$
$614$	22.4449	−	38.8757i	0.905801	−	1.56889i
$615$	−3.64937	+	6.32089i	−0.147157	+	0.254883i
$616$		0			0
$617$	5.08394	−	8.80565i	0.204672	−	0.354502i	−0.745356	−	0.666666i	$-0.767721\pi$
$617$	5.08394	−	8.80565i	0.204672	−	0.354502i	0.950028	+	0.312164i	$0.101054\pi$
$618$	32.2086			1.29562
$619$	21.8952	−	37.9237i	0.880044	−	1.52428i	0.0287526	−	0.999587i	$-0.490846\pi$
$619$	21.8952	−	37.9237i	0.880044	−	1.52428i	0.851291	−	0.524694i	$-0.175820\pi$
$620$	17.6711	+	30.6073i	0.709689	+	1.22922i
$621$	4.97977	−	8.62522i	0.199831	−	0.346118i
$622$	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
$626$	82.2445			3.28715
$627$	−38.5899			−1.54113
$628$	44.8053			1.78793
$629$	16.6806			0.665097
$630$		0			0
$631$	−8.04464	+	13.9337i	−0.320252	+	0.554693i	−0.980540	−	0.196320i	$-0.937101\pi$
$631$	−8.04464	+	13.9337i	−0.320252	+	0.554693i	0.660288	+	0.751013i	$0.270434\pi$
$632$	−12.7033	−	22.0028i	−0.505312	−	0.875226i
$633$	31.7953	+	55.0711i	1.26375	+	2.18888i
$634$	−76.2557			−3.02850
$635$	−18.6711	+	32.3392i	−0.740939	+	1.28334i
$636$	18.5955			0.737359
$637$		0			0
$638$	45.8951			1.81700
$639$	8.84506	−	15.3201i	0.349905	−	0.606054i
$640$	−67.0187			−2.64915
$641$	24.6254	+	42.6525i	0.972645	+	1.68467i	0.687497	+	0.726187i	$0.258709\pi$
$641$	24.6254	+	42.6525i	0.972645	+	1.68467i	0.285148	+	0.958483i	$0.407957\pi$
$642$	−35.4842	−	61.4605i	−1.40045	−	2.42565i
$643$	1.33579	−	2.31366i	0.0526784	−	0.0912417i	−0.838484	−	0.544927i	$-0.816558\pi$
$643$	1.33579	−	2.31366i	0.0526784	−	0.0912417i	0.891162	+	0.453685i	$0.149891\pi$
$644$		0			0
$645$	−31.8526			−1.25419
$646$	−91.2072			−3.58850
$647$	−33.3628			−1.31163			−0.655814	−	0.754923i	$-0.727674\pi$
$647$	−33.3628			−1.31163			−0.655814	+	0.754923i	$0.727674\pi$
$648$	35.3498			1.38867
$649$	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
$653$	−11.9244	+	20.6536i	−0.466637	+	0.808239i	−0.999274	−	0.0381052i	$-0.987868\pi$
$653$	−11.9244	+	20.6536i	−0.466637	+	0.808239i	0.532637	+	0.846344i	$0.321201\pi$
$654$	−11.0777	−	19.1872i	−0.433173	−	0.750278i
$655$	1.13271	−	1.96192i	0.0442588	−	0.0766585i
$656$	0.875700			0.0341903
$657$	−2.41308	+	4.17957i	−0.0941431	+	0.163061i
$658$		0			0
$659$	8.58114	−	14.8630i	0.334274	−	0.578979i	−0.649071	−	0.760727i	$-0.724842\pi$
$659$	8.58114	−	14.8630i	0.334274	−	0.578979i	0.983345	+	0.181749i	$0.0581757\pi$
$660$	−31.1785	+	54.0028i	−1.21362	+	2.10206i
$661$	0.466403			0.0181410			0.00907048	−	0.999959i	$-0.497113\pi$
$661$	0.466403			0.0181410			0.00907048	+	0.999959i	$0.497113\pi$
$662$	5.56886	−	9.64554i	0.216440	−	0.374885i
$663$	36.5232	−	27.0237i	1.41844	−	1.04951i
$664$	−9.68686			−0.375923
$665$		0			0
$666$	8.30760	+	14.3892i	0.321913	+	0.557570i
$667$	54.4769			2.10935
$668$	6.25786	−	10.8389i	0.242124	−	0.419371i
$669$	10.0465	+	17.4010i	0.388418	+	0.672760i
$670$	36.2604			1.40086
$671$	−14.8987			−0.575157
$672$		0			0
$673$	−8.77061	−	15.1911i	−0.338082	−	0.585576i	0.645990	−	0.763346i	$-0.276445\pi$
$673$	−8.77061	−	15.1911i	−0.338082	−	0.585576i	−0.984072	+	0.177770i	$0.943112\pi$
$674$	30.5885	−	52.9808i	1.17822	−	2.04075i
$675$	−4.91186	+	8.50759i	−0.189058	+	0.327457i
$676$	30.4608	+	32.6700i	1.17157	+	1.25654i
$677$	−4.85980	−	8.41743i	−0.186777	−	0.323508i	0.757397	−	0.652955i	$-0.226471\pi$
$677$	−4.85980	−	8.41743i	−0.186777	−	0.323508i	−0.944174	+	0.329447i	$0.893138\pi$
$678$	−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
$682$	8.29313	+	14.3641i	0.317560	+	0.550031i
$683$	18.0577	+	31.2769i	0.690960	+	1.19678i	0.971524	+	0.236942i	$0.0761451\pi$
$683$	18.0577	+	31.2769i	0.690960	+	1.19678i	−0.280564	+	0.959835i	$0.590522\pi$
$684$	−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
$689$	−7.74991	−	3.37009i	−0.295248	−	0.128390i
$690$	−58.5504	+	101.412i	−2.22897	+	3.86070i
$691$	−4.38634	+	7.59737i	−0.166864	+	0.289018i	−0.937316	−	0.348481i	$-0.886698\pi$
$691$	−4.38634	+	7.59737i	−0.166864	+	0.289018i	0.770451	+	0.637499i	$0.220031\pi$
$692$	21.8041	+	37.7657i	0.828866	+	1.43564i
$693$		0			0
$694$	24.3509			0.924346
$695$	11.0411			0.418813
$696$	32.6337	+	56.5233i	1.23698	+	2.14251i
$697$	−2.55858	+	4.43160i	−0.0969132	+	0.167859i
$698$	−54.7178			−2.07110
$699$	−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	$0.490887\pi$
$702$	−11.8992	−	5.17444i	−0.449106	−	0.195297i
$703$	−10.9549	+	18.9745i	−0.413172	+	0.715636i
$704$	−28.9173			−1.08986
$705$	−13.4793	+	23.3468i	−0.507659	+	0.879291i
$706$	3.41724	−	5.91883i	0.128609	−	0.222758i
$707$		0			0
$708$	−28.7473	+	49.7919i	−1.08039	+	1.87129i
$709$	−15.1020			−0.567168			−0.283584	−	0.958947i	$-0.591523\pi$
$709$	−15.1020			−0.567168			−0.283584	+	0.958947i	$0.591523\pi$
$710$	29.8177	−	51.6458i	1.11904	−	1.93823i
$711$	8.84657	+	15.3227i	0.331772	+	0.574646i
$712$	−22.0291	+	38.1555i	−0.825575	+	1.42994i
$713$	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
$717$	−7.52647			−0.281081
$718$	39.8721			1.48801
$719$	19.1989			0.715999			0.357999	−	0.933722i	$-0.383459\pi$
$719$	19.1989			0.715999			0.357999	+	0.933722i	$0.383459\pi$
$720$	−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
$724$	−29.5462	−	51.1756i	−1.09808	−	1.90193i
$725$	−53.7340			−1.99563
$726$	14.9770	−	25.9409i	0.555847	−	0.962755i
$727$	−2.41101			−0.0894195			−0.0447098	−	0.999000i	$-0.514236\pi$
$727$	−2.41101			−0.0894195			−0.0447098	+	0.999000i	$0.514236\pi$
$728$		0			0
$729$	−13.9254			−0.515755
$730$	−8.13476	+	14.0898i	−0.301081	+	0.521488i
$731$	−22.3319			−0.825976
$732$	−25.3486	−	43.9050i	−0.936910	−	1.62278i
$733$	6.74959	+	11.6906i	0.249302	+	0.431804i	0.963332	−	0.268311i	$-0.0864655\pi$
$733$	6.74959	+	11.6906i	0.249302	+	0.431804i	−0.714030	+	0.700115i	$0.753132\pi$
$734$	−1.22241	+	2.11728i	−0.0451201	+	0.0781504i
$735$		0			0
$736$	−29.1553			−1.07468
$737$	10.7562			0.396210
$738$	−5.09712			−0.187628
$739$	−0.0428191			−0.00157513			−0.000787563	−	1.00000i	$-0.500251\pi$
$739$	−0.0428191			−0.00157513			−0.000787563		1.00000i	$0.500251\pi$
$740$	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	0.993372	−	0.114941i	$-0.0366678\pi$
$743$	10.8254	+	18.7501i	0.397145	+	0.687875i	−0.596228	+	0.802815i	$0.703334\pi$
$744$	−11.7937	+	20.4272i	−0.432377	+	0.748898i
$745$	−23.8738	−	41.3506i	−0.874667	−	1.51497i
$746$	−17.4989	+	30.3089i	−0.640679	+	1.10969i
$747$	6.74590			0.246819
$748$	−21.8594	+	37.8616i	−0.799258	+	1.38436i
$749$		0			0
$750$	12.3810	−	21.4445i	0.452091	−	0.783044i
$751$	22.4429	−	38.8723i	0.818953	−	1.41847i	−0.0875006	−	0.996164i	$-0.527888\pi$
$751$	22.4429	−	38.8723i	0.818953	−	1.41847i	0.906454	−	0.422304i	$-0.138779\pi$
$752$	3.23448			0.117949
$753$	19.7453	−	34.1999i	0.719559	−	1.24631i
$754$	−8.03191	−	70.5181i	−0.292505	−	2.56812i
$755$	4.53837			0.165168
$756$		0			0
$757$	3.77726	+	6.54240i	0.137287	+	0.237788i	0.926469	−	0.376372i	$-0.122828\pi$
$757$	3.77726	+	6.54240i	0.137287	+	0.237788i	−0.789182	+	0.614159i	$0.789495\pi$
$758$	63.3000			2.29916
$759$	−17.3682	+	30.0827i	−0.630427	+	1.09193i
$760$	−40.4515	−	70.0641i	−1.46733	−	2.54149i
$761$	23.3891			0.847856			0.423928	−	0.905696i	$-0.360651\pi$
$761$	23.3891			0.847856			0.423928	+	0.905696i	$0.360651\pi$
$762$	−59.6333			−2.16029
$763$		0			0
$764$	−1.83447	−	3.17739i	−0.0663687	−	0.114954i
$765$	21.4468	−	37.1470i	0.775412	−	1.34305i
$766$	−18.6829	+	32.3597i	−0.675040	+	1.16920i
$767$	21.0047	−	15.5415i	0.758435	−	0.561170i
$768$	−24.8745	−	43.0838i	−0.897580	−	1.55465i
$769$	21.9255	+	37.9760i	0.790652	+	1.36945i	0.925564	+	0.378592i	$0.123592\pi$
$769$	21.9255	+	37.9760i	0.790652	+	1.36945i	−0.134911	+	0.990858i	$0.543075\pi$
$770$		0			0
$771$	4.44497	−	7.69891i	0.160082	−	0.277270i
$772$	−5.42160	−	9.39049i	−0.195128	−	0.337971i
$773$	21.5613	+	37.3452i	0.775505	+	1.34321i	0.934510	+	0.355936i	$0.115838\pi$
$773$	21.5613	+	37.3452i	0.775505	+	1.34321i	−0.159005	+	0.987278i	$0.550829\pi$
$774$	−11.1222	−	19.2643i	−0.399780	−	0.692440i
$775$	−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
$780$	88.4321	+	38.4552i	3.16638	+	1.37692i
$781$	8.84506	−	15.3201i	0.316501	−	0.548196i
$782$	−41.0499	+	71.1005i	−1.46794	+	2.54255i
$783$	6.51594	+	11.2859i	0.232861	+	0.403326i
$784$		0			0
$785$	−43.9597			−1.56899
$786$	3.61777			0.129041
$787$	12.4480	+	21.5606i	0.443723	+	0.768551i	0.997962	−	0.0638066i	$-0.0203241\pi$
$787$	12.4480	+	21.5606i	0.443723	+	0.768551i	−0.554239	+	0.832357i	$0.686991\pi$
$788$	30.4008	−	52.6558i	1.08298	−	1.87578i
$789$	70.4613			2.50849
$790$	29.8228	+	51.6546i	1.06105	+	1.83779i
$791$		0			0
$792$	−18.1994			−0.646689
$793$	2.60736	+	22.8919i	0.0925899	+	0.812916i
$794$	−14.2324	+	24.6512i	−0.505089	+	0.874839i
$795$	−18.2445			−0.647067
$796$	22.3158	−	38.6520i	0.790961	−	1.36999i
$797$	−15.6211	+	27.0565i	−0.553327	+	0.958391i	0.444704	+	0.895677i	$0.353309\pi$
$797$	−15.6211	+	27.0565i	−0.553327	+	0.958391i	−0.998032	+	0.0627134i	$0.980025\pi$
$798$		0			0
$799$	−9.45037	+	16.3685i	−0.334330	+	0.579077i
$800$	28.7577			1.01674
$801$	15.3410	−	26.5714i	0.542047	−	0.938853i
$802$	44.1137	+	76.4071i	1.55771	+	2.69803i
$803$	−2.41308	+	4.17957i	−0.0851556	+	0.147494i
$804$	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
$808$	15.8314			0.556945
$809$	39.5458			1.39036			0.695179	−	0.718837i	$-0.255325\pi$
$809$	39.5458			1.39036			0.695179	+	0.718837i	$0.255325\pi$
$810$	−82.9884			−2.91592
$811$	−43.8260			−1.53894			−0.769470	−	0.638683i	$-0.779480\pi$
$811$	−43.8260			−1.53894			−0.769470	+	0.638683i	$0.779480\pi$
$812$		0			0
$813$	35.9942	−	62.3439i	1.26237	−	2.18649i
$814$	8.30760	+	14.3892i	0.291181	+	0.504341i
$815$	8.31411	+	14.4005i	0.291231	+	0.504426i
$816$	−11.7683			−0.411973
$817$	14.6664	−	25.4030i	0.513114	−	0.888740i
$818$	−0.548079			−0.0191631
$819$		0			0
$820$	−10.8610			−0.379283
$821$	−22.5162	+	38.9992i	−0.785820	+	1.36108i	0.142688	+	0.989768i	$0.454426\pi$
$821$	−22.5162	+	38.9992i	−0.785820	+	1.36108i	−0.928508	+	0.371313i	$0.878908\pi$
$822$	42.1998			1.47189
$823$	−12.5994	−	21.8227i	−0.439186	−	0.760693i	0.558441	−	0.829545i	$-0.311400\pi$
$823$	−12.5994	−	21.8227i	−0.439186	−	0.760693i	−0.997627	+	0.0688515i	$0.978067\pi$
$824$	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	$0.626793\pi$
$828$	−51.6903			−1.79636
$829$	26.1963			0.909834			0.454917	−	0.890534i	$-0.349669\pi$
$829$	26.1963			0.909834			0.454917	+	0.890534i	$0.349669\pi$
$830$	22.7412			0.789359
$831$	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
$835$	−6.13975	+	10.6344i	−0.212475	+	0.368017i
$836$	−28.7122	−	49.7310i	−0.993032	−	1.71998i
$837$	−2.35483	+	4.07868i	−0.0813947	+	0.140980i
$838$	−1.03530			−0.0357639
$839$	−21.7207	+	37.6214i	−0.749882	+	1.29883i	0.197997	+	0.980203i	$0.436557\pi$
$839$	−21.7207	+	37.6214i	−0.749882	+	1.29883i	−0.947879	+	0.318631i	$0.896777\pi$
$840$		0			0
$841$	−21.1410	+	36.6173i	−0.729000	+	1.26266i
$842$	11.0280	−	19.1011i	0.380051	−	0.658268i
$843$	52.9823			1.82481
$844$	−47.3136	+	81.9496i	−1.62860	+	2.82082i
$845$	−29.8859	−	32.0534i	−1.02811	−	1.10267i
$846$	−18.8267			−0.647275
$847$		0			0
$848$	1.09449	+	1.89571i	0.0375849	+	0.0650989i
$849$	−44.6828			−1.53351
$850$	40.4901	−	70.1308i	1.38880	−	2.40547i
$851$	9.86102	+	17.0798i	0.338031	+	0.585487i
$852$	60.1958			2.06227
$853$	1.15312			0.0394820			0.0197410	−	0.999805i	$-0.493716\pi$
$853$	1.15312			0.0394820			0.0197410	+	0.999805i	$0.493716\pi$
$854$		0			0
$855$	28.1703	+	48.7924i	0.963404	+	1.66866i
$856$	22.0675	−	38.2220i	0.754252	−	1.30640i
$857$	12.5043	−	21.6582i	0.427140	−	0.739828i	−0.569477	−	0.822007i	$-0.692854\pi$
$857$	12.5043	−	21.6582i	0.427140	−	0.739828i	0.996618	+	0.0821785i	$0.0261878\pi$
$858$	41.5016	+	18.0472i	1.41684	+	0.616121i
$859$	2.04457	+	3.54130i	0.0697598	+	0.120827i	0.898795	−	0.438368i	$-0.144443\pi$
$859$	2.04457	+	3.54130i	0.0697598	+	0.120827i	−0.829036	+	0.559196i	$0.811110\pi$
$860$	−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	$0.928996\pi$
$864$	−3.48724	−	6.04007i	−0.118638	−	0.205487i
$865$	−21.3926	−	37.0530i	−0.727369	−	1.25984i
$866$	−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
$871$	−1.88240	−	16.5270i	−0.0637827	−	0.559996i
$872$	6.88919	−	11.9324i	0.233298	−	0.404083i
$873$	−4.14674	+	7.18237i	−0.140346	+	0.243086i
$874$	−53.9188	−	93.3901i	−1.82383	−	3.15897i
$875$		0			0
$876$	−16.4224			−0.554862
$877$	−14.9816			−0.505894			−0.252947	−	0.967480i	$-0.581400\pi$
$877$	−14.9816			−0.505894			−0.252947	+	0.967480i	$0.581400\pi$
$878$	−34.7217	−	60.1398i	−1.17180	−	2.02962i
$879$	−18.2092	+	31.5393i	−0.614182	+	1.06379i
$880$	−7.34039			−0.247444
$881$	−21.3382	−	36.9588i	−0.718901	−	1.24517i	−0.961436	−	0.275030i	$-0.911312\pi$
$881$	−21.3382	−	36.9588i	−0.718901	−	1.24517i	0.242534	−	0.970143i	$-0.422021\pi$
$882$		0			0
$883$	35.8874			1.20771			0.603854	−	0.797095i	$-0.293631\pi$
$883$	35.8874			1.20771			0.603854	+	0.797095i	$0.293631\pi$
$884$	62.0001	+	26.9611i	2.08529	+	0.906800i
$885$	28.2048	−	48.8521i	0.948094	−	1.64215i
$886$	−34.6152			−1.16292
$887$	−13.8336	+	23.9605i	−0.464488	+	0.804516i	−0.999178	−	0.0405317i	$-0.987095\pi$
$887$	−13.8336	+	23.9605i	−0.464488	+	0.804516i	0.534691	+	0.845048i	$0.320428\pi$
$888$	−11.8142	+	20.4629i	−0.396460	+	0.686689i
$889$		0			0
$890$	51.7163	−	89.5752i	1.73353	−	3.00257i
$891$	−24.6175			−0.824717
$892$	−14.9498	+	25.8938i	−0.500557	+	0.866990i
$893$	−12.4130	−	21.5000i	−0.415386	−	0.719469i
$894$	38.1251	−	66.0346i	1.27509	−	2.20853i
$895$	−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
$899$	−25.7609			−0.859176
$900$	50.9854			1.69951
$901$	−12.7913			−0.426140
$902$	−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
$906$	3.62376	+	6.27654i	0.120391	+	0.208524i
$907$	18.1933			0.604097			0.302049	−	0.953293i	$-0.402330\pi$
$907$	18.1933			0.604097			0.302049	+	0.953293i	$0.402330\pi$
$908$	−37.7387	+	65.3654i	−1.25240	+	2.16923i
$909$	−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	$0.685067\pi$
$912$	7.72880	−	13.3867i	0.255926	−	0.443277i
$913$	6.74590			0.223257
$914$	−18.5015	−	32.0456i	−0.611977	−	1.05998i
$915$	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
$919$	2.98328			0.0984092			0.0492046	−	0.998789i	$-0.484331\pi$
$919$	2.98328			0.0984092			0.0492046	+	0.998789i	$0.484331\pi$
$920$	−72.8245			−2.40095
$921$	−44.4564			−1.46489
$922$	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
$926$	21.3202	−	36.9277i	0.700626	−	1.21352i
$927$	−6.97456	−	12.0803i	−0.229075	−	0.396769i
$928$	19.0746	−	33.0381i	0.626153	−	1.08453i
$929$	−33.3980			−1.09575			−0.547876	−	0.836560i	$-0.684563\pi$
$929$	−33.3980			−1.09575			−0.547876	+	0.836560i	$0.684563\pi$
$930$	27.6872	−	47.9557i	0.907899	−	1.57253i
$931$		0			0
$932$	29.7018	−	51.4450i	0.972915	−	1.68514i
$933$	3.53813	−	6.12823i	0.115833	−	0.200629i
$934$	−10.5692			−0.345834
$935$	21.4468	−	37.1470i	0.701386	−	1.21484i
$936$	3.18501	+	27.9636i	0.104105	+	0.914017i
$937$	51.3187			1.67651			0.838254	−	0.545279i	$-0.183576\pi$
$937$	51.3187			1.67651			0.838254	+	0.545279i	$0.183576\pi$
$938$		0			0
$939$	−40.7253	−	70.5382i	−1.32902	−	2.30193i
$940$	−40.1162			−1.30845
$941$	9.50195	−	16.4579i	0.309755	−	0.536511i	−0.668554	−	0.743664i	$-0.733086\pi$
$941$	9.50195	−	16.4579i	0.309755	−	0.536511i	0.978309	+	0.207153i	$0.0664197\pi$
$942$	−35.1006	−	60.7961i	−1.14364	−	1.98084i
$943$	−6.05021			−0.197022
$944$	−6.76801			−0.220280
$945$		0			0
$946$	−11.1222	−	19.2643i	−0.361615	−	0.626335i
$947$	23.3540	−	40.4503i	0.758902	−	1.31446i	−0.184508	−	0.982831i	$-0.559069\pi$
$947$	23.3540	−	40.4503i	0.758902	−	1.31446i	0.943411	−	0.331626i	$-0.107597\pi$
$948$	−30.1030	+	52.1400i	−0.977701	+	1.69343i
$949$	6.84424	+	2.97626i	0.222174	+	0.0966135i
$950$	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	−0.851666	−	0.524085i	$-0.824407\pi$
$953$	0.865567	−	1.49921i	0.0280385	−	0.0485640i	0.879704	+	0.475521i	$0.157741\pi$
$954$	−6.37060	−	11.0342i	−0.206256	−	0.357246i
$955$	1.79985	+	3.11742i	0.0582416	+	0.100877i
$956$	−5.59996	−	9.69941i	−0.181116	−	0.313701i
$957$	−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
$962$	20.6552	−	15.2829i	0.665951	−	0.492740i
$963$	−15.3677	+	26.6177i	−0.495218	+	0.857744i
$964$	2.51807	−	4.36142i	0.0811015	−	0.140472i
$965$	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	$0.525044\pi$
$968$	18.6282			0.598734
$969$	45.1633	+	78.2252i	1.45086	+	2.51296i
$970$	−13.9791	+	24.2126i	−0.448843	+	0.777419i
$971$	−8.57152			−0.275073			−0.137537	−	0.990497i	$-0.543918\pi$
$971$	−8.57152			−0.275073			−0.137537	+	0.990497i	$0.543918\pi$
$972$	−33.9288	−	58.7664i	−1.08827	−	1.88493i
$973$		0			0
$974$	−83.7347			−2.68303
$975$	−48.5900	−	21.1296i	−1.55613	−	0.676690i
$976$	2.98392	−	5.16829i	0.0955128	−	0.165433i
$977$	−40.0382			−1.28093			−0.640467	−	0.767985i	$-0.721259\pi$
$977$	−40.0382			−1.28093			−0.640467	+	0.767985i	$0.721259\pi$
$978$	−13.2772	+	22.9967i	−0.424557	+	0.735355i
$979$	15.3410	−	26.5714i	0.490300	−	0.849225i
$980$		0			0
$981$	−4.79761	+	8.30971i	−0.153176	+	0.265309i
$982$	−17.9584			−0.573077
$983$	11.9560	−	20.7084i	0.381337	−	0.660496i	−0.609916	−	0.792466i	$-0.708797\pi$
$983$	11.9560	−	20.7084i	0.381337	−	0.660496i	0.991254	+	0.131970i	$0.0421303\pi$
$984$	−3.62431	−	6.27749i	−0.115539	−	0.200119i
$985$	−29.8271	+	51.6620i	−0.950370	+	1.64609i
$986$	−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
$990$	42.7256			1.35791
$991$	41.0138			1.30285			0.651424	−	0.758714i	$-0.274172\pi$
$991$	41.0138			1.30285			0.651424	+	0.758714i	$0.274172\pi$
$992$	13.7869			0.437734
$993$	−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
$997$	12.7122	+	22.0182i	0.402600	+	0.697324i	0.994039	−	0.109026i	$-0.0347731\pi$
$997$	12.7122	+	22.0182i	0.402600	+	0.697324i	−0.591439	+	0.806350i	$0.701440\pi$
$998$	−19.7964			−0.626643
$999$	−2.35894	+	4.08580i	−0.0746334	+	0.129269i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.7	✓	16	91.87	odd	6
637.2.f.l.295.8	yes	16	91.74	even	3
637.2.f.l.393.7	yes	16	7.3	odd	6
637.2.f.l.393.8	yes	16	7.4	even	3
637.2.g.m.263.7		16	1.1	even	1	trivial
637.2.g.m.263.8		16	7.6	odd	2	inner
637.2.g.m.373.7		16	91.9	even	3	inner
637.2.g.m.373.8		16	91.61	odd	6	inner
637.2.h.m.165.1		16	91.48	odd	6
637.2.h.m.165.2		16	13.9	even	3
637.2.h.m.471.1		16	7.5	odd	6
637.2.h.m.471.2		16	7.2	even	3
8281.2.a.ci.1.1		8	91.81	even	3
8281.2.a.ci.1.2		8	91.3	odd	6
8281.2.a.cl.1.7		8	91.88	even	6
8281.2.a.cl.1.8		8	91.10	odd	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.16576 - 2.01915i) q^{2} -2.30901 q^{3} +(-1.71798 - 2.97563i) q^{4} +(1.68556 + 2.91947i) q^{5} +(-2.69174 + 4.66224i) q^{6} -3.34797 q^{8} +2.33152 q^{9} +O(q^{10})\)	\(q+(1.16576 - 2.01915i) q^{2} -2.30901 q^{3} +(-1.71798 - 2.97563i) q^{4} +(1.68556 + 2.91947i) q^{5} +(-2.69174 + 4.66224i) q^{6} -3.34797 q^{8} +2.33152 q^{9} +7.85981 q^{10} +2.33152 q^{11} +(3.96683 + 6.87075i) q^{12} +(-0.408029 - 3.58239i) q^{13} +(-3.89197 - 6.74108i) q^{15} +(-0.466957 + 0.808794i) q^{16} +(-2.72867 - 4.72620i) q^{17} +(2.71798 - 4.70768i) q^{18} +7.16819 q^{19} +(5.79151 - 10.0312i) q^{20} +(2.71798 - 4.70768i) q^{22} +(3.22621 - 5.58796i) q^{23} +7.73048 q^{24} +(-3.18221 + 5.51175i) q^{25} +(-7.70905 - 3.35233i) q^{26} +1.54354 q^{27} +(4.22143 + 7.31174i) q^{29} -18.1484 q^{30} +(-1.52560 + 2.64242i) q^{31} +(-2.25925 - 3.91314i) q^{32} -5.38349 q^{33} -12.7239 q^{34} +(-4.00550 - 6.93773i) q^{36} +(-1.52827 + 2.64704i) q^{37} +(8.35637 - 14.4737i) q^{38} +(0.942141 + 8.27176i) 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} +(3.92990 + 6.80679i) q^{45} +(-7.52195 - 13.0284i) 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} +(-9.95888 + 7.36862i) q^{52} +(1.17194 - 2.02985i) q^{53} +(1.79939 - 3.11663i) q^{54} +(3.92990 + 6.80679i) q^{55} -16.5514 q^{57} +19.6847 q^{58} +(3.62346 + 6.27602i) q^{59} +(-13.3726 + 23.1621i) q^{60} -6.39013 q^{61} +(3.55697 + 6.16085i) q^{62} -12.4028 q^{64} +(9.77093 - 7.22955i) q^{65} +(-6.27584 + 10.8701i) q^{66} +4.61340 q^{67} +(-9.37561 + 16.2390i) q^{68} +(-7.44934 + 12.9026i) q^{69} +(3.79370 - 6.57088i) q^{71} -7.80584 q^{72} +(-1.03498 + 1.79264i) q^{73} +(3.56318 + 6.17161i) q^{74} +(7.34775 - 12.7267i) q^{75} +(-12.3148 - 21.3299i) q^{76} +(17.8002 + 7.74054i) q^{78} +(3.79434 + 6.57199i) q^{79} -3.14833 q^{80} -10.5586 q^{81} -2.18618 q^{82} +2.89335 q^{83} +(9.19866 - 15.9326i) q^{85} +(-4.77039 - 8.26255i) q^{86} +(-9.74732 - 16.8829i) q^{87} -7.80584 q^{88} +(6.57984 - 11.3966i) q^{89} +18.3253 q^{90} -22.1703 q^{92} +(3.52263 - 6.10138i) q^{93} -8.07488 q^{94} +(12.0824 + 20.9273i) q^{95} +(5.21663 + 9.03546i) q^{96} +(-1.77856 + 3.08056i) q^{97} +5.43596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9} + 8 q^{11} - 8 q^{15} - 4 q^{16} + 28 q^{18} + 28 q^{22} + 12 q^{23} + 12 q^{25} + 8 q^{29} - 56 q^{30} + 4 q^{36} - 8 q^{37} - 16 q^{39} + 32 q^{43} + 4 q^{44} - 4 q^{46} + 36 q^{50} + 44 q^{51} + 4 q^{53} - 96 q^{57} + 96 q^{58} - 64 q^{60} - 64 q^{64} + 52 q^{65} - 40 q^{67} + 8 q^{71} - 56 q^{72} + 76 q^{74} + 28 q^{78} + 4 q^{79} - 112 q^{81} + 36 q^{85} - 4 q^{86} - 56 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9 + 8 * q^11 - 8 * q^15 - 4 * q^16 + 28 * q^18 + 28 * q^22 + 12 * q^23 + 12 * q^25 + 8 * q^29 - 56 * q^30 + 4 * q^36 - 8 * q^37 - 16 * q^39 + 32 * q^43 + 4 * q^44 - 4 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 + 96 * q^58 - 64 * q^60 - 64 * q^64 + 52 * q^65 - 40 * q^67 + 8 * q^71 - 56 * q^72 + 76 * q^74 + 28 * q^78 + 4 * q^79 - 112 * q^81 + 36 * q^85 - 4 * q^86 - 56 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Introduction

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