LMFDB - Embedded newform 637.2.h.m.165.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(165,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [16,-8,0,24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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			165.5
Root			$1.04641 + 1.81243i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.m.471.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.579810 q^{2} +(-0.946019 - 1.63855i) q^{3} -1.66382 q^{4} +(0.736809 + 1.27619i) q^{5} +(0.548512 + 0.950050i) q^{6} +2.12432 q^{8} +(-0.289905 + 0.502131i) q^{9} +(-0.427209 - 0.739948i) q^{10} +(-0.289905 - 0.502131i) q^{11} +(1.57401 + 2.72626i) q^{12} +(0.128893 + 3.60325i) q^{13} +(1.39407 - 2.41460i) q^{15} +2.09594 q^{16} +1.19657 q^{17} +(0.168090 - 0.291141i) q^{18} +(-0.230479 + 0.399201i) q^{19} +(-1.22592 - 2.12335i) q^{20} +(0.168090 + 0.291141i) q^{22} +2.36795 q^{23} +(-2.00965 - 3.48081i) q^{24} +(1.41423 - 2.44951i) q^{25} +(-0.0747335 - 2.08920i) q^{26} -4.57909 q^{27} +(3.44550 - 5.96777i) q^{29} +(-0.808297 + 1.40001i) q^{30} +(2.22171 - 3.84811i) q^{31} -5.46389 q^{32} +(-0.548512 + 0.950050i) q^{33} -0.693783 q^{34} +(0.482350 - 0.835455i) q^{36} +9.16301 q^{37} +(0.133634 - 0.231461i) q^{38} +(5.78218 - 3.61994i) q^{39} +(1.56522 + 2.71104i) q^{40} +(-2.00845 + 3.47874i) q^{41} +(-4.02951 - 6.97931i) q^{43} +(0.482350 + 0.835455i) q^{44} -0.854419 q^{45} -1.37296 q^{46} +(-5.75964 - 9.97598i) q^{47} +(-1.98280 - 3.43430i) q^{48} +(-0.819983 + 1.42025i) q^{50} +(-1.13198 - 1.96064i) q^{51} +(-0.214455 - 5.99515i) q^{52} +(4.69760 - 8.13647i) q^{53} +2.65501 q^{54} +(0.427209 - 0.739948i) q^{55} +0.872150 q^{57} +(-1.99773 + 3.46018i) q^{58} -0.240919 q^{59} +(-2.31948 + 4.01746i) q^{60} +(3.86355 - 6.69187i) q^{61} +(-1.28817 + 2.23118i) q^{62} -1.02385 q^{64} +(-4.50346 + 2.81940i) q^{65} +(0.318033 - 0.550849i) q^{66} +(0.724287 + 1.25450i) q^{67} -1.99088 q^{68} +(-2.24013 - 3.88001i) q^{69} +(6.25725 + 10.8379i) q^{71} +(-0.615852 + 1.06669i) q^{72} +(-1.84701 + 3.19911i) q^{73} -5.31281 q^{74} -5.35154 q^{75} +(0.383476 - 0.664199i) q^{76} +(-3.35257 + 2.09888i) q^{78} +(-8.03967 - 13.9251i) q^{79} +(1.54430 + 2.67481i) q^{80} +(5.20163 + 9.00948i) q^{81} +(1.16452 - 2.01701i) q^{82} +15.4005 q^{83} +(0.881643 + 1.52705i) q^{85} +(2.33635 + 4.04668i) q^{86} -13.0380 q^{87} +(-0.615852 - 1.06669i) q^{88} -2.49107 q^{89} +0.495401 q^{90} -3.93984 q^{92} -8.40712 q^{93} +(3.33950 + 5.78418i) q^{94} -0.679276 q^{95} +(5.16894 + 8.95287i) q^{96} +(7.82275 + 13.5494i) q^{97} +0.336180 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 $

$2$	−0.579810			−0.409988			−0.204994	−	0.978763i	$-0.565717\pi$
$2$	−0.579810			−0.409988			−0.204994	+	0.978763i	$0.565717\pi$
$3$	−0.946019	−	1.63855i	−0.546185	−	0.946019i	−0.998531	−	0.0541772i	$-0.982746\pi$
$3$	−0.946019	−	1.63855i	−0.546185	−	0.946019i	0.452347	−	0.891842i	$-0.350587\pi$
$4$	−1.66382			−0.831910
$5$	0.736809	+	1.27619i	0.329511	+	0.570729i	0.982415	−	0.186711i	$-0.0597828\pi$
$5$	0.736809	+	1.27619i	0.329511	+	0.570729i	−0.652904	+	0.757441i	$0.726450\pi$
$6$	0.548512	+	0.950050i	0.223929	+	0.387856i
$7$		0			0
$7$		0			0
$8$	2.12432			0.751061
$9$	−0.289905	+	0.502131i	−0.0966351	+	0.167377i
$10$	−0.427209	−	0.739948i	−0.135095	−	0.233992i
$11$	−0.289905	−	0.502131i	−0.0874097	−	0.151398i	0.819006	−	0.573785i	$-0.194526\pi$
$11$	−0.289905	−	0.502131i	−0.0874097	−	0.151398i	−0.906415	+	0.422387i	$0.861192\pi$
$12$	1.57401	+	2.72626i	0.454376	+	0.787003i
$13$	0.128893	+	3.60325i	0.0357485	+	0.999361i
$13$	0.128893	+	3.60325i	0.0357485	+	0.999361i
$14$		0			0
$15$	1.39407	−	2.41460i	0.359947	−	0.623447i
$16$	2.09594			0.523984
$17$	1.19657			0.290211			0.145105	−	0.989416i	$-0.453648\pi$
$17$	1.19657			0.290211			0.145105	+	0.989416i	$0.453648\pi$
$18$	0.168090	−	0.291141i	0.0396192	−	0.0686225i
$19$	−0.230479	+	0.399201i	−0.0528755	+	0.0915831i	−0.891252	−	0.453509i	$-0.850172\pi$
$19$	−0.230479	+	0.399201i	−0.0528755	+	0.0915831i	0.838376	+	0.545092i	$0.183505\pi$
$20$	−1.22592	−	2.12335i	−0.274123	−	0.474796i
$21$		0			0
$22$	0.168090	+	0.291141i	0.0358369	+	0.0620714i
$23$	2.36795			0.493752			0.246876	−	0.969047i	$-0.420596\pi$
$23$	2.36795			0.493752			0.246876	+	0.969047i	$0.420596\pi$
$24$	−2.00965	−	3.48081i	−0.410218	−	0.710518i
$25$	1.41423	−	2.44951i	0.282845	−	0.489902i
$26$	−0.0747335	−	2.08920i	−0.0146565	−	0.409726i
$27$	−4.57909			−0.881247
$28$		0			0
$29$	3.44550	−	5.96777i	0.639813	−	1.10819i	−0.345661	−	0.938359i	$-0.612345\pi$
$29$	3.44550	−	5.96777i	0.639813	−	1.10819i	0.985474	−	0.169828i	$-0.0543214\pi$
$30$	−0.808297	+	1.40001i	−0.147574	+	0.255606i
$31$	2.22171	−	3.84811i	0.399031	−	0.691141i	−0.594576	−	0.804040i	$-0.702680\pi$
$31$	2.22171	−	3.84811i	0.399031	−	0.691141i	0.993607	+	0.112898i	$0.0360134\pi$
$32$	−5.46389			−0.965888
$33$	−0.548512	+	0.950050i	−0.0954837	+	0.165383i
$34$	−0.693783			−0.118983
$35$		0			0
$36$	0.482350	−	0.835455i	0.0803917	−	0.139242i
$37$	9.16301			1.50639			0.753195	−	0.657798i	$-0.228512\pi$
$37$	9.16301			1.50639			0.753195	+	0.657798i	$0.228512\pi$
$38$	0.133634	−	0.231461i	0.0216783	−	0.0375479i
$39$	5.78218	−	3.61994i	0.925889	−	0.579654i
$40$	1.56522	+	2.71104i	0.247483	+	0.428653i
$41$	−2.00845	+	3.47874i	−0.313667	+	0.543288i	−0.979153	−	0.203123i	$-0.934891\pi$
$41$	−2.00845	+	3.47874i	−0.313667	+	0.543288i	0.665486	+	0.746410i	$0.268224\pi$
$42$		0			0
$43$	−4.02951	−	6.97931i	−0.614494	−	1.06433i	−0.990473	−	0.137706i	$-0.956027\pi$
$43$	−4.02951	−	6.97931i	−0.614494	−	1.06433i	0.375979	−	0.926628i	$-0.377306\pi$
$44$	0.482350	+	0.835455i	0.0727170	+	0.125950i
$45$	−0.854419			−0.127369
$46$	−1.37296			−0.202432
$47$	−5.75964	−	9.97598i	−0.840129	−	1.45515i	−0.889785	−	0.456381i	$-0.849146\pi$
$47$	−5.75964	−	9.97598i	−0.840129	−	1.45515i	0.0496552	−	0.998766i	$-0.484188\pi$
$48$	−1.98280	−	3.43430i	−0.286192	−	0.495699i
$49$		0			0
$50$	−0.819983	+	1.42025i	−0.115963	+	0.200854i
$51$	−1.13198	−	1.96064i	−0.158509	−	0.274545i
$52$	−0.214455	−	5.99515i	−0.0297395	−	0.831378i
$53$	4.69760	−	8.13647i	0.645264	−	1.11763i	−0.338976	−	0.940795i	$-0.610081\pi$
$53$	4.69760	−	8.13647i	0.645264	−	1.11763i	0.984240	−	0.176836i	$-0.0565861\pi$
$54$	2.65501			0.361300
$55$	0.427209	−	0.739948i	0.0576049	−	0.0997746i
$56$		0			0
$57$	0.872150			0.115519
$58$	−1.99773	+	3.46018i	−0.262315	+	0.454344i
$59$	−0.240919			−0.0313650			−0.0156825	−	0.999877i	$-0.504992\pi$
$59$	−0.240919			−0.0313650			−0.0156825	+	0.999877i	$0.504992\pi$
$60$	−2.31948	+	4.01746i	−0.299444	+	0.518652i
$61$	3.86355	−	6.69187i	0.494677	−	0.856806i	−0.505304	−	0.862941i	$-0.668620\pi$
$61$	3.86355	−	6.69187i	0.494677	−	0.856806i	0.999981	+	0.00613544i	$0.00195298\pi$
$62$	−1.28817	+	2.23118i	−0.163598	+	0.283360i
$63$		0			0
$64$	−1.02385			−0.127982
$65$	−4.50346	+	2.81940i	−0.558585	+	0.349703i
$66$	0.318033	−	0.550849i	0.0391471	−	0.0678048i
$67$	0.724287	+	1.25450i	0.0884857	+	0.153262i	0.906871	−	0.421408i	$-0.138464\pi$
$67$	0.724287	+	1.25450i	0.0884857	+	0.153262i	−0.818385	+	0.574670i	$0.805131\pi$
$68$	−1.99088			−0.241429
$69$	−2.24013	−	3.88001i	−0.269680	−	0.467099i
$70$		0			0
$71$	6.25725	+	10.8379i	0.742599	+	1.28622i	0.951308	+	0.308241i	$0.0997405\pi$
$71$	6.25725	+	10.8379i	0.742599	+	1.28622i	−0.208709	+	0.977978i	$0.566926\pi$
$72$	−0.615852	+	1.06669i	−0.0725788	+	0.125710i
$73$	−1.84701	+	3.19911i	−0.216176	+	0.374427i	−0.953636	−	0.300963i	$-0.902692\pi$
$73$	−1.84701	+	3.19911i	−0.216176	+	0.374427i	0.737460	+	0.675391i	$0.236025\pi$
$74$	−5.31281			−0.617601
$75$	−5.35154			−0.617943
$76$	0.383476	−	0.664199i	0.0439877	−	0.0761889i
$77$		0			0
$78$	−3.35257	+	2.09888i	−0.379603	+	0.237651i
$79$	−8.03967	−	13.9251i	−0.904533	−	1.56670i	−0.821542	−	0.570147i	$-0.806886\pi$
$79$	−8.03967	−	13.9251i	−0.904533	−	1.56670i	−0.0829909	−	0.996550i	$-0.526447\pi$
$80$	1.54430	+	2.67481i	0.172658	+	0.299053i
$81$	5.20163	+	9.00948i	0.577958	+	1.00105i
$82$	1.16452	−	2.01701i	0.128600	−	0.222741i
$83$	15.4005			1.69042			0.845212	−	0.534431i	$-0.179474\pi$
$83$	15.4005			1.69042			0.845212	+	0.534431i	$0.179474\pi$
$84$		0			0
$85$	0.881643	+	1.52705i	0.0956276	+	0.165632i
$86$	2.33635	+	4.04668i	0.251935	+	0.436364i
$87$	−13.0380			−1.39782
$88$	−0.615852	−	1.06669i	−0.0656500	−	0.113709i
$89$	−2.49107			−0.264052			−0.132026	−	0.991246i	$-0.542148\pi$
$89$	−2.49107			−0.264052			−0.132026	+	0.991246i	$0.542148\pi$
$90$	0.495401			0.0522198
$91$		0			0
$92$	−3.93984			−0.410757
$93$	−8.40712			−0.871778
$94$	3.33950	+	5.78418i	0.344443	+	0.596593i
$95$	−0.679276			−0.0696922
$96$	5.16894	+	8.95287i	0.527553	+	0.913749i
$97$	7.82275	+	13.5494i	0.794280	+	1.37573i	0.923295	+	0.384091i	$0.125485\pi$
$97$	7.82275	+	13.5494i	0.794280	+	1.37573i	−0.129015	+	0.991643i	$0.541182\pi$
$98$		0			0
$99$	0.336180			0.0337874
$100$	−2.35302	+	4.07555i	−0.235302	+	0.407555i
$101$	7.00682	+	12.1362i	0.697205	+	1.20759i	0.969432	+	0.245361i	$0.0789066\pi$
$101$	7.00682	+	12.1362i	0.697205	+	1.20759i	−0.272227	+	0.962233i	$0.587760\pi$
$102$	0.656332	+	1.13680i	0.0649866	+	0.112560i
$103$	5.37461	+	9.30910i	0.529576	+	0.917253i	0.999405	+	0.0344951i	$0.0109823\pi$
$103$	5.37461	+	9.30910i	0.529576	+	0.917253i	−0.469829	+	0.882758i	$0.655684\pi$
$104$	0.273810	+	7.65445i	0.0268493	+	0.750581i
$105$		0			0
$106$	−2.72371	+	4.71761i	−0.264551	+	0.458215i
$107$	3.75523			0.363031			0.181516	−	0.983388i	$-0.441900\pi$
$107$	3.75523			0.363031			0.181516	+	0.983388i	$0.441900\pi$
$108$	7.61878			0.733118
$109$	4.10417	−	7.10862i	0.393108	−	0.680883i	−0.599750	−	0.800187i	$-0.704733\pi$
$109$	4.10417	−	7.10862i	0.393108	−	0.680883i	0.992858	+	0.119305i	$0.0380666\pi$
$110$	−0.247700	+	0.429030i	−0.0236173	+	0.0409064i
$111$	−8.66838	−	15.0141i	−0.822766	−	1.42507i
$112$		0			0
$113$	3.90423	+	6.76233i	0.367279	+	0.636146i	0.989139	−	0.146982i	$-0.0469560\pi$
$113$	3.90423	+	6.76233i	0.367279	+	0.636146i	−0.621860	+	0.783129i	$0.713623\pi$
$114$	−0.505682			−0.0473614
$115$	1.74473	+	3.02196i	0.162697	+	0.281799i
$116$	−5.73269	+	9.92930i	−0.532266	+	0.921913i
$117$	−1.84667	−	0.979879i	−0.170724	−	0.0905898i
$118$	0.139687			0.0128593
$119$		0			0
$120$	2.96145	−	5.12939i	0.270342	−	0.468247i
$121$	5.33191	−	9.23514i	0.484719	−	0.839558i
$122$	−2.24013	+	3.88001i	−0.202812	+	0.351280i
$123$	7.60014			0.685281
$124$	−3.69652	+	6.40257i	−0.331958	+	0.574967i
$125$	11.5361			1.03182
$126$		0			0
$127$	0.469682	−	0.813513i	0.0416775	−	0.0721876i	−0.844434	−	0.535659i	$-0.820063\pi$
$127$	0.469682	−	0.813513i	0.0416775	−	0.0721876i	0.886112	+	0.463472i	$0.153396\pi$
$128$	11.5214			1.01836
$129$	−7.62398	+	13.2051i	−0.671254	+	1.16265i
$130$	2.61115	−	1.63471i	0.229013	−	0.143374i
$131$	−0.568583	−	0.984814i	−0.0496773	−	0.0860436i	0.840117	−	0.542404i	$-0.182486\pi$
$131$	−0.568583	−	0.984814i	−0.0496773	−	0.0860436i	−0.889795	+	0.456361i	$0.849153\pi$
$132$	0.912625	−	1.58071i	0.0794338	−	0.137583i
$133$		0			0
$134$	−0.419949	−	0.727373i	−0.0362781	−	0.0628355i
$135$	−3.37391	−	5.84379i	−0.290380	−	0.502954i
$136$	2.54190			0.217966
$137$	−8.63997			−0.738162			−0.369081	−	0.929397i	$-0.620328\pi$
$137$	−8.63997			−0.738162			−0.369081	+	0.929397i	$0.620328\pi$
$138$	1.29885	+	2.24967i	0.110565	+	0.191505i
$139$	−7.27709	−	12.6043i	−0.617235	−	1.06908i	−0.989988	−	0.141151i	$-0.954920\pi$
$139$	−7.27709	−	12.6043i	−0.617235	−	1.06908i	0.372753	−	0.927930i	$-0.378414\pi$
$140$		0			0
$141$	−10.8975	+	18.8749i	−0.917731	+	1.58956i
$142$	−3.62802	−	6.28391i	−0.304457	−	0.527334i
$143$	1.77193	−	1.10932i	0.148177	−	0.0927661i
$144$	−0.607623	+	1.05243i	−0.0506352	+	0.0877028i
$145$	10.1547			0.843301
$146$	1.07091	−	1.85488i	0.0886295	−	0.153511i
$147$		0			0
$148$	−15.2456			−1.25318
$149$	−6.69011	+	11.5876i	−0.548075	+	0.949294i	0.450331	+	0.892861i	$0.351306\pi$
$149$	−6.69011	+	11.5876i	−0.548075	+	0.949294i	−0.998406	+	0.0564323i	$0.982027\pi$
$150$	3.10288			0.253349
$151$	−8.06958	+	13.9769i	−0.656693	+	1.13743i	0.324774	+	0.945792i	$0.394712\pi$
$151$	−8.06958	+	13.9769i	−0.656693	+	1.13743i	−0.981467	+	0.191634i	$0.938621\pi$
$152$	−0.489611	+	0.848032i	−0.0397127	+	0.0687845i
$153$	−0.346892	+	0.600834i	−0.0280445	+	0.0485745i
$154$		0			0
$155$	6.54790			0.525940
$156$	−9.62050	+	6.02293i	−0.770257	+	0.482220i
$157$	−0.314340	+	0.544453i	−0.0250871	+	0.0434521i	−0.878296	−	0.478117i	$-0.841320\pi$
$157$	−0.314340	+	0.544453i	−0.0250871	+	0.0434521i	0.853209	+	0.521569i	$0.174653\pi$
$158$	4.66148	+	8.07393i	0.370848	+	0.642327i
$159$	−17.7761			−1.40973
$160$	−4.02584	−	6.97296i	−0.318271	−	0.551261i
$161$		0			0
$162$	−3.01596	−	5.22379i	−0.236956	−	0.410420i
$163$	5.84207	−	10.1188i	0.457586	−	0.792563i	−0.541246	−	0.840864i	$-0.682047\pi$
$163$	5.84207	−	10.1188i	0.457586	−	0.792563i	0.998833	+	0.0483011i	$0.0153807\pi$
$164$	3.34170	−	5.78800i	0.260943	−	0.451967i
$165$	−1.61659			−0.125852
$166$	−8.92937			−0.693054
$167$	11.0293	−	19.1033i	0.853474	−	1.47826i	−0.0245803	−	0.999698i	$-0.507825\pi$
$167$	11.0293	−	19.1033i	0.853474	−	1.47826i	0.878054	−	0.478562i	$-0.158842\pi$
$168$		0			0
$169$	−12.9668	+	0.928867i	−0.997444	+	0.0714513i
$170$	−0.511186	−	0.885399i	−0.0392061	−	0.0679070i
$171$	−0.133634	−	0.231461i	−0.0102193	−	0.0177003i
$172$	6.70437	+	11.6123i	0.511204	+	0.885431i
$173$	5.69534	−	9.86463i	0.433009	−	0.749994i	−0.564122	−	0.825692i	$-0.690785\pi$
$173$	5.69534	−	9.86463i	0.433009	−	0.749994i	0.997131	+	0.0756980i	$0.0241185\pi$
$174$	7.55958			0.573090
$175$		0			0
$176$	−0.607623	−	1.05243i	−0.0458013	−	0.0793302i
$177$	0.227914	+	0.394759i	0.0171311	+	0.0296719i
$178$	1.44435			0.108258
$179$	1.73621	+	3.00721i	0.129771	+	0.224769i	0.923588	−	0.383387i	$-0.125243\pi$
$179$	1.73621	+	3.00721i	0.129771	+	0.224769i	−0.793817	+	0.608157i	$0.791909\pi$
$180$	1.42160			0.105960
$181$	−21.0992			−1.56829			−0.784145	−	0.620578i	$-0.786898\pi$
$181$	−21.0992			−1.56829			−0.784145	+	0.620578i	$0.786898\pi$
$182$		0			0
$183$	−14.6200			−1.08074
$184$	5.03029			0.370838
$185$	6.75138	+	11.6937i	0.496372	+	0.859741i
$186$	4.87453			0.357418
$187$	−0.346892	−	0.600834i	−0.0253672	−	0.0439373i
$188$	9.58300	+	16.5982i	0.698912	+	1.21055i
$189$		0			0
$190$	0.393851			0.0285730
$191$	−5.95945	+	10.3221i	−0.431211	+	0.746879i	−0.996978	−	0.0776864i	$-0.975247\pi$
$191$	−5.95945	+	10.3221i	−0.431211	+	0.746879i	0.565767	+	0.824565i	$0.308580\pi$
$192$	0.968585	+	1.67764i	0.0699016	+	0.121073i
$193$	−7.18970	−	12.4529i	−0.517526	−	0.896381i	−0.999793	−	0.0203567i	$-0.993520\pi$
$193$	−7.18970	−	12.4529i	−0.517526	−	0.896381i	0.482267	−	0.876024i	$-0.339814\pi$
$194$	−4.53571	−	7.85608i	−0.325645	−	0.564034i
$195$	8.88009	+	4.71195i	0.635916	+	0.337430i
$196$		0			0
$197$	−3.48462	+	6.03553i	−0.248269	+	0.430014i	−0.963046	−	0.269339i	$-0.913195\pi$
$197$	−3.48462	+	6.03553i	−0.248269	+	0.430014i	0.714777	+	0.699353i	$0.246528\pi$
$198$	−0.194921			−0.0138524
$199$	−3.57352			−0.253320			−0.126660	−	0.991946i	$-0.540426\pi$
$199$	−3.57352			−0.253320			−0.126660	+	0.991946i	$0.540426\pi$
$200$	3.00427	−	5.20355i	0.212434	−	0.367946i
$201$	1.37038	−	2.37357i	0.0966591	−	0.167418i
$202$	−4.06263	−	7.03668i	−0.285846	−	0.495099i
$203$		0			0
$204$	1.88341	+	3.26216i	0.131865	+	0.228397i
$205$	−5.91938			−0.413427
$206$	−3.11626	−	5.39751i	−0.217120	−	0.376062i
$207$	−0.686481	+	1.18902i	−0.0477138	+	0.0826426i
$208$	0.270152	+	7.55218i	0.0187316	+	0.523649i
$209$	0.267268			0.0184873
$210$		0			0
$211$	7.05694	−	12.2230i	0.485820	−	0.841464i	−0.514048	−	0.857762i	$-0.671855\pi$
$211$	7.05694	−	12.2230i	0.485820	−	0.841464i	0.999867	+	0.0162974i	$0.00518784\pi$
$212$	−7.81595	+	13.5376i	−0.536802	+	0.929768i
$213$	11.8390	−	20.5057i	0.811192	−	1.40503i
$214$	−2.17732			−0.148838
$215$	5.93795	−	10.2848i	0.404965	−	0.701420i
$216$	−9.72746			−0.661870
$217$		0			0
$218$	−2.37964	+	4.12165i	−0.161169	+	0.279154i
$219$	6.98922			0.472288
$220$	−0.710799	+	1.23114i	−0.0479221	+	0.0830035i
$221$	0.154229	+	4.31153i	0.0103746	+	0.290025i
$222$	5.02602	+	8.70532i	0.337324	+	0.584263i
$223$	−0.454565	+	0.787329i	−0.0304399	+	0.0527235i	−0.880844	−	0.473407i	$-0.843024\pi$
$223$	−0.454565	+	0.787329i	−0.0304399	+	0.0527235i	0.850404	+	0.526130i	$0.176357\pi$
$224$		0			0
$225$	0.819983	+	1.42025i	0.0546655	+	0.0946835i
$226$	−2.26371	−	3.92087i	−0.150580	−	0.260812i
$227$	2.33512			0.154988			0.0774938	−	0.996993i	$-0.475308\pi$
$227$	2.33512			0.154988			0.0774938	+	0.996993i	$0.475308\pi$
$228$	−1.45110			−0.0961015
$229$	−8.34036	−	14.4459i	−0.551147	−	0.954614i	−0.998192	−	0.0601030i	$-0.980857\pi$
$229$	−8.34036	−	14.4459i	−0.551147	−	0.954614i	0.447045	−	0.894511i	$-0.352476\pi$
$230$	−1.01161	−	1.75216i	−0.0667036	−	0.115534i
$231$		0			0
$232$	7.31934	−	12.6775i	0.480538	−	0.832317i
$233$	8.26321	+	14.3123i	0.541341	+	0.937630i	0.998827	+	0.0484137i	$0.0154166\pi$
$233$	8.26321	+	14.3123i	0.541341	+	0.937630i	−0.457486	+	0.889217i	$0.651250\pi$
$234$	1.07072	+	0.568144i	0.0699949	+	0.0371407i
$235$	8.48750	−	14.7008i	0.553664	−	0.958973i
$236$	0.400846			0.0260928
$237$	−15.2114	+	26.3469i	−0.988084	+	1.71141i
$238$		0			0
$239$	3.18043			0.205725			0.102862	−	0.994696i	$-0.467200\pi$
$239$	3.18043			0.205725			0.102862	+	0.994696i	$0.467200\pi$
$240$	2.92188	−	5.06085i	0.188607	−	0.326676i
$241$	−15.8598			−1.02162			−0.510811	−	0.859693i	$-0.670655\pi$
$241$	−15.8598			−1.02162			−0.510811	+	0.859693i	$0.670655\pi$
$242$	−3.09150	+	5.35463i	−0.198729	+	0.344209i
$243$	2.97304	−	5.14945i	0.190720	−	0.330338i
$244$	−6.42825	+	11.1341i	−0.411527	+	0.712785i
$245$		0			0
$246$	−4.40664			−0.280957
$247$	−1.46813	−	0.779018i	−0.0934147	−	0.0495677i
$248$	4.71962	−	8.17463i	0.299696	−	0.519089i
$249$	−14.5692	−	25.2345i	−0.923284	−	1.59917i
$250$	−6.68878			−0.423035
$251$	−1.24788	−	2.16139i	−0.0787654	−	0.136426i	0.823952	−	0.566659i	$-0.191764\pi$
$251$	−1.24788	−	2.16139i	−0.0787654	−	0.136426i	−0.902718	+	0.430234i	$0.858431\pi$
$252$		0			0
$253$	−0.686481	−	1.18902i	−0.0431587	−	0.0747531i
$254$	−0.272326	+	0.471683i	−0.0170873	+	0.0295960i
$255$	1.66810	−	2.88924i	0.104461	−	0.180931i
$256$	−4.63253			−0.289533
$257$	10.5204			0.656245			0.328123	−	0.944635i	$-0.393584\pi$
$257$	10.5204			0.656245			0.328123	+	0.944635i	$0.393584\pi$
$258$	4.42046	−	7.65647i	0.275206	−	0.476671i
$259$		0			0
$260$	7.49294	−	4.69097i	0.464693	−	0.290921i
$261$	1.99773	+	3.46018i	0.123657	+	0.214180i
$262$	0.329670	+	0.571006i	0.0203671	+	0.0352768i
$263$	15.6749	+	27.1498i	0.966558	+	1.67413i	0.705370	+	0.708839i	$0.250781\pi$
$263$	15.6749	+	27.1498i	0.966558	+	1.67413i	0.261188	+	0.965288i	$0.415886\pi$
$264$	−1.16522	+	2.01821i	−0.0717140	+	0.124212i
$265$	13.8449			0.850486
$266$		0			0
$267$	2.35660	+	4.08174i	0.144221	+	0.249799i
$268$	−1.20508	−	2.08727i	−0.0736122	−	0.127500i
$269$	−21.1265			−1.28811			−0.644054	−	0.764980i	$-0.722749\pi$
$269$	−21.1265			−1.28811			−0.644054	+	0.764980i	$0.722749\pi$
$270$	1.95623	+	3.38829i	0.119052	+	0.206205i
$271$	6.52007			0.396066			0.198033	−	0.980195i	$-0.436545\pi$
$271$	6.52007			0.396066			0.198033	+	0.980195i	$0.436545\pi$
$272$	2.50793			0.152066
$273$		0			0
$274$	5.00954			0.302638
$275$	−1.63997			−0.0988937
$276$	3.72717	+	6.45565i	0.224349	+	0.388584i
$277$	−14.5310			−0.873081			−0.436540	−	0.899685i	$-0.643796\pi$
$277$	−14.5310			−0.873081			−0.436540	+	0.899685i	$0.643796\pi$
$278$	4.21933	+	7.30810i	0.253059	+	0.438311i
$279$	1.28817	+	2.23118i	0.0771207	+	0.133577i
$280$		0			0
$281$	27.1832			1.62161			0.810807	−	0.585314i	$-0.199029\pi$
$281$	27.1832			1.62161			0.810807	+	0.585314i	$0.199029\pi$
$282$	6.31846	−	10.9439i	0.376259	−	0.651699i
$283$	−4.28791	−	7.42688i	−0.254890	−	0.441482i	0.709976	−	0.704226i	$-0.248706\pi$
$283$	−4.28791	−	7.42688i	−0.254890	−	0.441482i	−0.964866	+	0.262744i	$0.915373\pi$
$284$	−10.4109	−	18.0323i	−0.617775	−	1.07002i
$285$	0.642608	+	1.11303i	0.0380648	+	0.0659302i
$286$	−1.02739	+	0.643196i	−0.0607506	+	0.0380330i
$287$		0			0
$288$	1.58401	−	2.74358i	0.0933387	−	0.161667i
$289$	−15.5682			−0.915778
$290$	−5.88779			−0.345743
$291$	14.8009	−	25.6360i	0.867647	−	1.50281i
$292$	3.07309	−	5.32274i	0.179839	−	0.311490i
$293$	5.24356	+	9.08212i	0.306332	+	0.530583i	0.977557	−	0.210671i	$-0.0675648\pi$
$293$	5.24356	+	9.08212i	0.306332	+	0.530583i	−0.671225	+	0.741254i	$0.734232\pi$
$294$		0			0
$295$	−0.177511	−	0.307458i	−0.0103351	−	0.0179009i
$296$	19.4652			1.13139
$297$	1.32750	+	2.29930i	0.0770295	+	0.133419i
$298$	3.87899	−	6.71862i	0.224704	−	0.389199i
$299$	0.305213	+	8.53231i	0.0176509	+	0.493436i
$300$	8.90400			0.514073
$301$		0			0
$302$	4.67882	−	8.10396i	0.269236	−	0.466331i
$303$	13.2572	−	22.9621i	0.761605	−	1.31914i
$304$	−0.483069	+	0.836701i	−0.0277059	+	0.0479881i
$305$	11.3868			0.652006
$306$	0.201131	−	0.348370i	0.0114979	−	0.0199150i
$307$	−19.1751			−1.09438			−0.547190	−	0.837008i	$-0.684303\pi$
$307$	−19.1751			−1.09438			−0.547190	+	0.837008i	$0.684303\pi$
$308$		0			0
$309$	10.1690	−	17.6132i	0.578493	−	1.00198i
$310$	−3.79654			−0.215629
$311$	1.74427	−	3.02117i	0.0989086	−	0.171315i	−0.812325	−	0.583206i	$-0.801798\pi$
$311$	1.74427	−	3.02117i	0.0989086	−	0.171315i	0.911233	+	0.411891i	$0.135132\pi$
$312$	12.2832	−	7.68991i	0.695399	−	0.435356i
$313$	10.1607	+	17.5989i	0.574318	+	0.994748i	0.996115	+	0.0880579i	$0.0280661\pi$
$313$	10.1607	+	17.5989i	0.574318	+	0.994748i	−0.421797	+	0.906690i	$0.638601\pi$
$314$	0.182258	−	0.315680i	0.0102854	−	0.0178148i
$315$		0			0
$316$	13.3766	+	23.1689i	0.752490	+	1.30335i
$317$	13.9110	+	24.0946i	0.781320	+	1.35329i	0.931173	+	0.364578i	$0.118787\pi$
$317$	13.9110	+	24.0946i	0.781320	+	1.35329i	−0.149853	+	0.988708i	$0.547880\pi$
$318$	10.3067			0.577974
$319$	−3.99547			−0.223703
$320$	−0.754384	−	1.30663i	−0.0421714	−	0.0730429i
$321$	−3.55252	−	6.15314i	−0.198282	−	0.343435i
$322$		0			0
$323$	−0.275784	+	0.477672i	−0.0153450	+	0.0265784i
$324$	−8.65457	−	14.9902i	−0.480809	−	0.832786i
$325$	9.00848	+	4.78008i	0.499700	+	0.265151i
$326$	−3.38729	+	5.86697i	−0.187605	+	0.324941i
$327$	−15.5305			−0.858837
$328$	−4.26660	+	7.38996i	−0.235583	+	0.408042i
$329$		0			0
$330$	0.937318			0.0515976
$331$	4.67148	−	8.09123i	0.256768	−	0.444734i	−0.708607	−	0.705604i	$-0.750676\pi$
$331$	4.67148	−	8.09123i	0.256768	−	0.444734i	0.965374	+	0.260869i	$0.0840092\pi$
$332$	−25.6237			−1.40628
$333$	−2.65640	+	4.60103i	−0.145570	+	0.252135i
$334$	−6.39491	+	11.0763i	−0.349914	+	0.606069i
$335$	−1.06732	+	1.84866i	−0.0583140	+	0.101003i
$336$		0			0
$337$	22.9182			1.24844			0.624218	−	0.781250i	$-0.285418\pi$
$337$	22.9182			1.24844			0.624218	+	0.781250i	$0.285418\pi$
$338$	7.51827	−	0.538567i	0.408940	−	0.0292942i
$339$	7.38696	−	12.7946i	0.401205	−	0.694907i
$340$	−1.46689	−	2.54074i	−0.0795535	−	0.137791i
$341$	−2.57634			−0.139517
$342$	0.0774824	+	0.134204i	0.00418977	+	0.00725690i
$343$		0			0
$344$	−8.55996	−	14.8263i	−0.461522	−	0.799380i
$345$	3.30109	−	5.71766i	0.177725	−	0.307828i
$346$	−3.30222	+	5.71961i	−0.177528	+	0.307488i
$347$	−26.6711			−1.43178			−0.715889	−	0.698214i	$-0.753978\pi$
$347$	−26.6711			−1.43178			−0.715889	+	0.698214i	$0.753978\pi$
$348$	21.6929			1.16286
$349$	7.61723	−	13.1934i	0.407741	−	0.706228i	−0.586895	−	0.809663i	$-0.699650\pi$
$349$	7.61723	−	13.1934i	0.407741	−	0.706228i	0.994636	+	0.103435i	$0.0329832\pi$
$350$		0			0
$351$	−0.590213	−	16.4996i	−0.0315033	−	0.880683i
$352$	1.58401	+	2.74358i	0.0844280	+	0.146234i
$353$	−11.2044	−	19.4066i	−0.596352	−	1.03291i	−0.993355	−	0.115094i	$-0.963283\pi$
$353$	−11.2044	−	19.4066i	−0.596352	−	1.03291i	0.397003	−	0.917817i	$-0.370050\pi$
$354$	−0.132147	−	0.228885i	−0.00702353	−	0.0121651i
$355$	−9.22079	+	15.9709i	−0.489389	+	0.847646i
$356$	4.14468			0.219668
$357$		0			0
$358$	−1.00667	−	1.74361i	−0.0532044	−	0.0921528i
$359$	−8.01927	−	13.8898i	−0.423241	−	0.733075i	0.573013	−	0.819546i	$-0.305774\pi$
$359$	−8.01927	−	13.8898i	−0.423241	−	0.733075i	−0.996254	+	0.0864711i	$0.972441\pi$
$360$	−1.81506			−0.0956620
$361$	9.39376	+	16.2705i	0.494408	+	0.856340i
$362$	12.2335			0.642980
$363$	−20.1764			−1.05898
$364$		0			0
$365$	−5.44356			−0.284929
$366$	8.47682			0.443090
$367$	−3.45002	−	5.97561i	−0.180090	−	0.311924i	0.761821	−	0.647787i	$-0.224305\pi$
$367$	−3.45002	−	5.97561i	−0.180090	−	0.311924i	−0.941911	+	0.335863i	$0.890972\pi$
$368$	4.96308			0.258718
$369$	−1.16452	−	2.01701i	−0.0606225	−	0.105001i
$370$	−3.91452	−	6.78015i	−0.203506	−	0.352483i
$371$		0			0
$372$	13.9879			0.725240
$373$	−3.84264	+	6.65566i	−0.198965	+	0.344617i	−0.948193	−	0.317695i	$-0.897091\pi$
$373$	−3.84264	+	6.65566i	−0.198965	+	0.344617i	0.749228	+	0.662312i	$0.230425\pi$
$374$	0.201131	+	0.348370i	0.0104003	+	0.0180138i
$375$	−10.9134	−	18.9026i	−0.563566	−	0.976125i
$376$	−12.2353	−	21.1922i	−0.630988	−	1.09290i
$377$	21.9475	+	11.6458i	1.13035	+	0.599788i
$378$		0			0
$379$	12.5817	−	21.7922i	0.646281	−	1.11939i	−0.337723	−	0.941245i	$-0.609657\pi$
$379$	12.5817	−	21.7922i	0.646281	−	1.11939i	0.984004	−	0.178146i	$-0.0570098\pi$
$380$	1.13019			0.0579776
$381$	−1.77731			−0.0910545
$382$	3.45535	−	5.98484i	0.176791	−	0.306211i
$383$	−11.0218	+	19.0904i	−0.563189	+	0.975473i	0.434026	+	0.900900i	$0.357093\pi$
$383$	−11.0218	+	19.0904i	−0.563189	+	0.975473i	−0.997216	+	0.0745724i	$0.976241\pi$
$384$	−10.8995	−	18.8785i	−0.556212	−	0.963387i
$385$		0			0
$386$	4.16866	+	7.22033i	0.212179	+	0.367505i
$387$	4.67270			0.237527
$388$	−13.0156	−	22.5438i	−0.660769	−	1.14449i
$389$	5.49058	−	9.50996i	0.278383	−	0.482174i	−0.692600	−	0.721322i	$-0.743535\pi$
$389$	5.49058	−	9.50996i	0.278383	−	0.482174i	0.970983	+	0.239148i	$0.0768681\pi$
$390$	−5.14877	−	2.73204i	−0.260718	−	0.138342i
$391$	2.83342			0.143292
$392$		0			0
$393$	−1.07578	+	1.86331i	−0.0542660	+	0.0939914i
$394$	2.02042	−	3.49946i	0.101787	−	0.176300i
$395$	11.8474	−	20.5203i	0.596107	−	1.03249i
$396$	−0.559343			−0.0281081
$397$	12.5382	−	21.7168i	0.629275	−	1.08994i	−0.358423	−	0.933559i	$-0.616685\pi$
$397$	12.5382	−	21.7168i	0.629275	−	1.08994i	0.987698	−	0.156377i	$-0.0499813\pi$
$398$	2.07196			0.103858
$399$		0			0
$400$	2.96413	−	5.13402i	0.148206	−	0.256701i
$401$	−22.6601			−1.13159			−0.565797	−	0.824545i	$-0.691431\pi$
$401$	−22.6601			−1.13159			−0.565797	+	0.824545i	$0.691431\pi$
$402$	−0.794560	+	1.37622i	−0.0396291	+	0.0686395i
$403$	14.1521	+	7.50937i	0.704964	+	0.374068i
$404$	−11.6581	−	20.1924i	−0.580012	−	1.00461i
$405$	−7.66521	+	13.2765i	−0.380887	+	0.659716i
$406$		0			0
$407$	−2.65640	−	4.60103i	−0.131673	−	0.228064i
$408$	−2.40468	−	4.16503i	−0.119050	−	0.206200i
$409$	17.1465			0.847839			0.423919	−	0.905700i	$-0.360654\pi$
$409$	17.1465			0.847839			0.423919	+	0.905700i	$0.360654\pi$
$410$	3.43212			0.169500
$411$	8.17358	+	14.1570i	0.403173	+	0.698316i
$412$	−8.94238	−	15.4887i	−0.440560	−	0.763072i
$413$		0			0
$414$	0.398029	−	0.689407i	0.0195621	−	0.0338825i
$415$	11.3472	+	19.6540i	0.557013	+	0.964775i
$416$	−0.704257	−	19.6877i	−0.0345291	−	0.965271i
$417$	−13.7685	+	23.8478i	−0.674248	+	1.16783i
$418$	−0.154965			−0.00757958
$419$	−16.9902	+	29.4279i	−0.830027	+	1.43765i	0.0679891	+	0.997686i	$0.478342\pi$
$419$	−16.9902	+	29.4279i	−0.830027	+	1.43765i	−0.898016	+	0.439963i	$0.854992\pi$
$420$		0			0
$421$	−32.3623			−1.57724			−0.788621	−	0.614879i	$-0.789205\pi$
$421$	−32.3623			−1.57724			−0.788621	+	0.614879i	$0.789205\pi$
$422$	−4.09169	+	7.08701i	−0.199180	+	0.344990i
$423$	6.67900			0.324744
$424$	9.97920	−	17.2845i	0.484633	−	0.839409i
$425$	1.69222	−	2.93101i	0.0820847	−	0.142175i
$426$	−6.86435	+	11.8894i	−0.332579	+	0.576044i
$427$		0			0
$428$	−6.24802			−0.302009
$429$	−3.49397	−	1.85397i	−0.168690	−	0.0895104i
$430$	−3.44288	+	5.96325i	−0.166031	+	0.287574i
$431$	9.45640	+	16.3790i	0.455499	+	0.788947i	0.998717	−	0.0506447i	$-0.0161276\pi$
$431$	9.45640	+	16.3790i	0.455499	+	0.788947i	−0.543218	+	0.839592i	$0.682794\pi$
$432$	−9.59749			−0.461759
$433$	9.57006	+	16.5758i	0.459908	+	0.796584i	0.998956	−	0.0456914i	$-0.0145491\pi$
$433$	9.57006	+	16.5758i	0.459908	+	0.796584i	−0.539048	+	0.842275i	$0.681216\pi$
$434$		0			0
$435$	−9.60653	−	16.6390i	−0.460598	−	0.797779i
$436$	−6.82859	+	11.8275i	−0.327030	+	0.566433i
$437$	−0.545763	+	0.945289i	−0.0261074	+	0.0452193i
$438$	−4.05242			−0.193632
$439$	−9.60289			−0.458321			−0.229160	−	0.973389i	$-0.573598\pi$
$439$	−9.60289			−0.458321			−0.229160	+	0.973389i	$0.573598\pi$
$440$	0.907530	−	1.57189i	0.0432648	−	0.0749368i
$441$		0			0
$442$	−0.0894239	−	2.49987i	−0.00425346	−	0.118907i
$443$	20.1998	+	34.9871i	0.959721	+	1.66229i	0.723175	+	0.690665i	$0.242682\pi$
$443$	20.1998	+	34.9871i	0.959721	+	1.66229i	0.236546	+	0.971620i	$0.423984\pi$
$444$	14.4226	+	24.9807i	0.684468	+	1.18553i
$445$	−1.83544	−	3.17907i	−0.0870081	−	0.150703i
$446$	0.263561	−	0.456502i	0.0124800	−	0.0216160i
$447$	25.3159			1.19740
$448$		0			0
$449$	13.3112	+	23.0556i	0.628194	+	1.08806i	0.987914	+	0.155003i	$0.0495387\pi$
$449$	13.3112	+	23.0556i	0.628194	+	1.08806i	−0.359720	+	0.933060i	$0.617128\pi$
$450$	−0.475435	−	0.823477i	−0.0224122	−	0.0388191i
$451$	2.32904			0.109670
$452$	−6.49594	−	11.2513i	−0.305543	−	0.529217i
$453$	30.5359			1.43470
$454$	−1.35393			−0.0635430
$455$		0			0
$456$	1.85273			0.0867619
$457$	−1.61287			−0.0754468			−0.0377234	−	0.999288i	$-0.512011\pi$
$457$	−1.61287			−0.0754468			−0.0377234	+	0.999288i	$0.512011\pi$
$458$	4.83583	+	8.37590i	0.225963	+	0.391380i
$459$	−5.47920			−0.255747
$460$	−2.90291	−	5.02799i	−0.135349	−	0.234431i
$461$	−7.96032	−	13.7877i	−0.370749	−	0.642156i	0.618932	−	0.785445i	$-0.287566\pi$
$461$	−7.96032	−	13.7877i	−0.370749	−	0.642156i	−0.989681	+	0.143289i	$0.954232\pi$
$462$		0			0
$463$	−28.8475			−1.34066			−0.670328	−	0.742065i	$-0.733847\pi$
$463$	−28.8475			−1.34066			−0.670328	+	0.742065i	$0.733847\pi$
$464$	7.22154	−	12.5081i	0.335252	−	0.580673i
$465$	−6.19444	−	10.7291i	−0.287260	−	0.497549i
$466$	−4.79110	−	8.29842i	−0.221943	−	0.384417i
$467$	−3.72268	−	6.44787i	−0.172265	−	0.298372i	0.766946	−	0.641711i	$-0.221775\pi$
$467$	−3.72268	−	6.44787i	−0.172265	−	0.298372i	−0.939211	+	0.343339i	$0.888442\pi$
$468$	3.07252	+	1.63034i	0.142027	+	0.0753626i
$469$		0			0
$470$	−4.92114	+	8.52367i	−0.226995	+	0.393167i
$471$	1.18949			0.0548087
$472$	−0.511789			−0.0235570
$473$	−2.33635	+	4.04668i	−0.107425	+	0.186066i
$474$	8.81971	−	15.2762i	0.405103	−	0.701658i
$475$	0.651899	+	1.12912i	0.0299112	+	0.0518077i
$476$		0			0
$477$	2.72371	+	4.71761i	0.124710	+	0.216005i
$478$	−1.84404			−0.0843446
$479$	18.6263	+	32.2617i	0.851058	+	1.47408i	0.880254	+	0.474503i	$0.157372\pi$
$479$	18.6263	+	32.2617i	0.851058	+	1.47408i	−0.0291956	+	0.999574i	$0.509295\pi$
$480$	−7.61704	+	13.1931i	−0.347669	+	0.602180i
$481$	1.18105	+	33.0166i	0.0538512	+	1.50543i
$482$	9.19570			0.418853
$483$		0			0
$484$	−8.87134	+	15.3656i	−0.403243	+	0.698437i
$485$	−11.5277	+	19.9666i	−0.523448	+	0.906638i
$486$	−1.72380	+	2.98571i	−0.0781931	+	0.135434i
$487$	24.1726			1.09537			0.547684	−	0.836686i	$-0.315510\pi$
$487$	24.1726			1.09537			0.547684	+	0.836686i	$0.315510\pi$
$488$	8.20742	−	14.2157i	0.371533	−	0.643513i
$489$	−22.1069			−0.999707
$490$		0			0
$491$	−3.03571	+	5.25800i	−0.137000	+	0.237290i	−0.926360	−	0.376640i	$-0.877079\pi$
$491$	−3.03571	+	5.25800i	−0.137000	+	0.237290i	0.789360	+	0.613931i	$0.210413\pi$
$492$	−12.6453			−0.570092
$493$	4.12277	−	7.14086i	0.185680	−	0.321608i
$494$	0.851236	+	0.451683i	0.0382989	+	0.0203222i
$495$	0.247700	+	0.429030i	0.0111333	+	0.0192835i
$496$	4.65656	−	8.06540i	0.209086	−	0.362147i
$497$		0			0
$498$	8.44736	+	14.6313i	0.378535	+	0.655642i
$499$	1.25782	+	2.17861i	0.0563079	+	0.0975281i	0.892805	−	0.450443i	$-0.148734\pi$
$499$	1.25782	+	2.17861i	0.0563079	+	0.0975281i	−0.836497	+	0.547971i	$0.815400\pi$
$500$	−19.1941			−0.858385
$501$	−41.7358			−1.86462
$502$	0.723533	+	1.25320i	0.0322929	+	0.0559329i
$503$	−17.0026	−	29.4493i	−0.758107	−	1.31308i	−0.943815	−	0.330474i	$-0.892791\pi$
$503$	−17.0026	−	29.4493i	−0.758107	−	1.31308i	0.185708	−	0.982605i	$-0.440542\pi$
$504$		0			0
$505$	−10.3254	+	17.8841i	−0.459473	+	0.795831i
$506$	0.398029	+	0.689407i	0.0176946	+	0.0306479i
$507$	13.7888	+	20.3680i	0.612383	+	0.904576i
$508$	−0.781466	+	1.35354i	−0.0346719	+	0.0600536i
$509$	−29.3048			−1.29891			−0.649457	−	0.760399i	$-0.725004\pi$
$509$	−29.3048			−1.29891			−0.649457	+	0.760399i	$0.725004\pi$
$510$	−0.967183	+	1.67521i	−0.0428276	+	0.0741795i
$511$		0			0
$512$	−20.3568			−0.899654
$513$	1.05538	−	1.82798i	0.0465964	−	0.0807073i
$514$	−6.09984			−0.269053
$515$	−7.92012	+	13.7180i	−0.349002	+	0.604489i
$516$	12.6849	−	21.9709i	0.558423	−	0.967217i
$517$	−3.33950	+	5.78418i	−0.146871	+	0.254388i
$518$		0			0
$519$	−21.5516			−0.946011
$520$	−9.56679	+	5.98930i	−0.419531	+	0.262648i
$521$	−4.57386	+	7.92216i	−0.200385	+	0.347076i	−0.948652	−	0.316321i	$-0.897552\pi$
$521$	−4.57386	+	7.92216i	−0.200385	+	0.347076i	0.748268	+	0.663397i	$0.230886\pi$
$522$	−1.15831	−	2.00625i	−0.0506977	−	0.0878111i
$523$	14.1075			0.616876			0.308438	−	0.951244i	$-0.400194\pi$
$523$	14.1075			0.616876			0.308438	+	0.951244i	$0.400194\pi$
$524$	0.946019	+	1.63855i	0.0413270	+	0.0715805i
$525$		0			0
$526$	−9.08849	−	15.7417i	−0.396277	−	0.686372i
$527$	2.65843	−	4.60453i	0.115803	−	0.200577i
$528$	−1.14965	+	1.99125i	−0.0500319	+	0.0866578i
$529$	−17.3928			−0.756209
$530$	−8.02743			−0.348689
$531$	0.0698437	−	0.120973i	0.00303096	−	0.00524977i
$532$		0			0
$533$	−12.7936	−	6.78856i	−0.554154	−	0.294045i
$534$	−1.36638	−	2.36664i	−0.0591290	−	0.102414i
$535$	2.76688	+	4.79238i	0.119623	+	0.207193i
$536$	1.53862	+	2.66496i	0.0664582	+	0.115109i
$537$	3.28498	−	5.68976i	0.141758	−	0.245531i
$538$	12.2494			0.528109
$539$		0			0
$540$	5.61359	+	9.72302i	0.241570	+	0.418412i
$541$	−3.90147	−	6.75754i	−0.167737	−	0.290529i	0.769887	−	0.638181i	$-0.220313\pi$
$541$	−3.90147	−	6.75754i	−0.167737	−	0.290529i	−0.937624	+	0.347651i	$0.886979\pi$
$542$	−3.78041			−0.162382
$543$	19.9602	+	34.5721i	0.856576	+	1.48363i
$544$	−6.53792			−0.280311
$545$	12.0959			0.518133
$546$		0			0
$547$	6.99390			0.299038			0.149519	−	0.988759i	$-0.452228\pi$
$547$	6.99390			0.299038			0.149519	+	0.988759i	$0.452228\pi$
$548$	14.3753			0.614084
$549$	2.24013	+	3.88001i	0.0956063	+	0.165595i
$550$	0.950869			0.0405452
$551$	1.58823	+	2.75089i	0.0676608	+	0.117192i
$552$	−4.75875	−	8.24240i	−0.202546	−	0.350820i
$553$		0			0
$554$	8.42520			0.357952
$555$	12.7739	−	22.1250i	0.542221	−	0.939154i
$556$	12.1078	+	20.9713i	0.513484	+	0.889380i
$557$	3.62124	+	6.27218i	0.153437	+	0.265761i	0.932489	−	0.361199i	$-0.117632\pi$
$557$	3.62124	+	6.27218i	0.153437	+	0.265761i	−0.779052	+	0.626960i	$0.784299\pi$
$558$	−0.746894	−	1.29366i	−0.0316186	−	0.0547650i
$559$	24.6288	−	15.4189i	1.04169	−	0.652149i
$560$		0			0
$561$	−0.656332	+	1.13680i	−0.0277104	+	0.0479958i
$562$	−15.7611			−0.664842
$563$	−15.9321			−0.671459			−0.335730	−	0.941958i	$-0.608983\pi$
$563$	−15.9321			−0.671459			−0.335730	+	0.941958i	$0.608983\pi$
$564$	18.1314	−	31.4045i	0.763470	−	1.32237i
$565$	−5.75334	+	9.96509i	−0.242045	+	0.419234i
$566$	2.48618	+	4.30618i	0.104502	+	0.181002i
$567$		0			0
$568$	13.2924	+	23.0231i	0.557737	+	0.966029i
$569$	−42.2759			−1.77230			−0.886149	−	0.463401i	$-0.846629\pi$
$569$	−42.2759			−1.77230			−0.886149	+	0.463401i	$0.846629\pi$
$570$	−0.372591	−	0.645346i	−0.0156061	−	0.0270306i
$571$	−6.81247	+	11.7995i	−0.285093	+	0.493795i	−0.972632	−	0.232352i	$-0.925358\pi$
$571$	−6.81247	+	11.7995i	−0.285093	+	0.493795i	0.687539	+	0.726148i	$0.258691\pi$
$572$	−2.94818	+	1.84571i	−0.123270	+	0.0771730i
$573$	22.5510			0.942082
$574$		0			0
$575$	3.34882	−	5.80032i	0.139655	−	0.241890i
$576$	0.296821	−	0.514108i	0.0123675	−	0.0214212i
$577$	13.1925	−	22.8500i	0.549209	−	0.951258i	−0.449120	−	0.893472i	$-0.648262\pi$
$577$	13.1925	−	22.8500i	0.549209	−	0.951258i	0.998329	−	0.0577867i	$-0.0184043\pi$
$578$	9.02662			0.375458
$579$	−13.6032	+	23.5614i	−0.565329	+	0.979179i
$580$	−16.8956			−0.701550
$581$		0			0
$582$	−8.58174	+	14.8640i	−0.355725	+	0.616133i
$583$	−5.44743			−0.225609
$584$	−3.92364	+	6.79594i	−0.162361	+	0.281218i
$585$	−0.110129	−	3.07868i	−0.00455326	−	0.127288i
$586$	−3.04027	−	5.26591i	−0.125592	−	0.217533i
$587$	11.0720	−	19.1773i	0.456990	−	0.791530i	−0.541810	−	0.840501i	$-0.682261\pi$
$587$	11.0720	−	19.1773i	0.456990	−	0.791530i	0.998800	+	0.0489708i	$0.0155941\pi$
$588$		0			0
$589$	1.02411	+	1.77382i	0.0421979	+	0.0730889i
$590$	0.102923	+	0.178268i	0.00423727	+	0.00733916i
$591$	13.1861			0.542402
$592$	19.2051			0.789324
$593$	13.0419	+	22.5893i	0.535568	+	0.927630i	0.999136	+	0.0415689i	$0.0132356\pi$
$593$	13.0419	+	22.5893i	0.535568	+	0.927630i	−0.463568	+	0.886061i	$0.653431\pi$
$594$	−0.769700	−	1.33316i	−0.0315812	−	0.0547002i
$595$		0			0
$596$	11.1311	−	19.2797i	0.455949	−	0.789727i
$597$	3.38062	+	5.85540i	0.138360	+	0.239646i
$598$	−0.176965	−	4.94712i	−0.00723665	−	0.202303i
$599$	8.42202	−	14.5874i	0.344114	−	0.596024i	−0.641078	−	0.767476i	$-0.721512\pi$
$599$	8.42202	−	14.5874i	0.344114	−	0.596024i	0.985192	+	0.171452i	$0.0548458\pi$
$600$	−11.3684			−0.464113
$601$	−4.31691	+	7.47710i	−0.176090	+	0.304997i	−0.940538	−	0.339688i	$-0.889678\pi$
$601$	−4.31691	+	7.47710i	−0.176090	+	0.304997i	0.764448	+	0.644686i	$0.223012\pi$
$602$		0			0
$603$	−0.839898			−0.0342033
$604$	13.4263	−	23.2551i	0.546309	−	0.946235i
$605$	15.7144			0.638881
$606$	−7.68665	+	13.3137i	−0.312249	+	0.540831i
$607$	−10.9181	+	18.9107i	−0.443153	+	0.767564i	−0.997922	−	0.0644411i	$-0.979474\pi$
$607$	−10.9181	+	18.9107i	−0.443153	+	0.767564i	0.554768	+	0.832005i	$0.312807\pi$
$608$	1.25931	−	2.18119i	0.0510718	−	0.0884590i
$609$		0			0
$610$	−6.60218			−0.267315
$611$	35.2036	−	22.0392i	1.42418	−	0.891612i
$612$	0.577165	−	0.999680i	0.0233305	−	0.0404096i
$613$	24.0244	+	41.6114i	0.970334	+	1.68067i	0.694543	+	0.719451i	$0.255607\pi$
$613$	24.0244	+	41.6114i	0.970334	+	1.68067i	0.275791	+	0.961218i	$0.411060\pi$
$614$	11.1179			0.448683
$615$	5.59985	+	9.69922i	0.225808	+	0.391110i
$616$		0			0
$617$	8.23709	+	14.2671i	0.331613	+	0.574370i	0.982828	−	0.184523i	$-0.0590739\pi$
$617$	8.23709	+	14.2671i	0.331613	+	0.574370i	−0.651215	+	0.758893i	$0.725741\pi$
$618$	−5.89608	+	10.2123i	−0.237175	+	0.410799i
$619$	−21.0267	+	36.4192i	−0.845133	+	1.46381i	0.0403733	+	0.999185i	$0.487145\pi$
$619$	−21.0267	+	36.4192i	−0.845133	+	1.46381i	−0.885506	+	0.464628i	$0.846188\pi$
$620$	−10.8945			−0.437535
$621$	−10.8431			−0.435117
$622$	−1.01135	+	1.75170i	−0.0405513	+	0.0702370i
$623$		0			0
$624$	12.1191	−	7.58716i	0.485151	−	0.303730i
$625$	1.42880	+	2.47475i	0.0571519	+	0.0989900i
$626$	−5.89129	−	10.2040i	−0.235463	−	0.407835i
$627$	−0.252841	−	0.437933i	−0.0100975	−	0.0174894i
$628$	0.523006	−	0.905872i	0.0208702	−	0.0361482i
$629$	10.9642			0.437170
$630$		0			0
$631$	6.06667	+	10.5078i	0.241510	+	0.418308i	0.961145	−	0.276045i	$-0.0890239\pi$
$631$	6.06667	+	10.5078i	0.241510	+	0.418308i	−0.719634	+	0.694353i	$0.755691\pi$
$632$	−17.0788	−	29.5814i	−0.679360	−	1.17669i
$633$	−26.7040			−1.06139
$634$	−8.06575	−	13.9703i	−0.320332	−	0.554831i
$635$	1.38426			0.0549328
$636$	29.5762			1.17277
$637$		0			0
$638$	2.31661			0.0917157
$639$	−7.25604			−0.287044
$640$	8.48908	+	14.7035i	0.335560	+	0.581207i
$641$	−0.404355			−0.0159711			−0.00798553	−	0.999968i	$-0.502542\pi$
$641$	−0.404355			−0.0159711			−0.00798553	+	0.999968i	$0.502542\pi$
$642$	2.05979	+	3.56765i	0.0812933	+	0.140804i
$643$	−14.1741	−	24.5503i	−0.558973	−	0.968169i	−0.997583	−	0.0694914i	$-0.977862\pi$
$643$	−14.1741	−	24.5503i	−0.558973	−	0.968169i	0.438610	−	0.898678i	$-0.355471\pi$
$644$		0			0
$645$	−22.4697			−0.884742
$646$	0.159902	−	0.276959i	0.00629128	−	0.0108968i
$647$	17.4045	+	30.1455i	0.684242	+	1.18514i	0.973675	+	0.227943i	$0.0731999\pi$
$647$	17.4045	+	30.1455i	0.684242	+	1.18514i	−0.289433	+	0.957198i	$0.593467\pi$
$648$	11.0499	+	19.1390i	0.434082	+	0.751852i
$649$	0.0698437	+	0.120973i	0.00274160	+	0.00474860i
$650$	−5.22321	−	2.77154i	−0.204871	−	0.108709i
$651$		0			0
$652$	−9.72016	+	16.8358i	−0.380671	+	0.659341i
$653$	−25.1500			−0.984195			−0.492098	−	0.870540i	$-0.663770\pi$
$653$	−25.1500			−0.984195			−0.492098	+	0.870540i	$0.663770\pi$
$654$	9.00473			0.352113
$655$	0.837873	−	1.45124i	0.0327384	−	0.0567046i
$656$	−4.20959	+	7.29122i	−0.164357	+	0.284674i
$657$	−1.07091	−	1.85488i	−0.0417803	−	0.0723657i
$658$		0			0
$659$	−4.33723	−	7.51230i	−0.168954	−	0.292638i	0.769098	−	0.639131i	$-0.220706\pi$
$659$	−4.33723	−	7.51230i	−0.168954	−	0.292638i	−0.938053	+	0.346493i	$0.887372\pi$
$660$	2.68972			0.104697
$661$	−9.50000	−	16.4545i	−0.369507	−	0.640005i	0.619982	−	0.784616i	$-0.287140\pi$
$661$	−9.50000	−	16.4545i	−0.369507	−	0.640005i	−0.989489	+	0.144612i	$0.953807\pi$
$662$	−2.70857	+	4.69138i	−0.105272	+	0.182336i
$663$	6.91878	−	4.33151i	0.268703	−	0.168222i
$664$	32.7156			1.26961
$665$		0			0
$666$	1.54021	−	2.66772i	0.0596819	−	0.103372i
$667$	8.15877	−	14.1314i	0.315909	−	0.547170i
$668$	−18.3508	+	31.7845i	−0.710013	+	1.22978i
$669$	1.72011			0.0665032
$670$	0.618844	−	1.07187i	0.0239080	−	0.0414099i
$671$	−4.48026			−0.172958
$672$		0			0
$673$	0.284273	−	0.492376i	0.0109579	−	0.0189797i	−0.860494	−	0.509460i	$-0.829845\pi$
$673$	0.284273	−	0.492376i	0.0109579	−	0.0189797i	0.871452	+	0.490480i	$0.163179\pi$
$674$	−13.2882			−0.511843
$675$	−6.47587	+	11.2165i	−0.249256	+	0.431725i
$676$	21.5744	−	1.54547i	0.829784	−	0.0594411i
$677$	−13.8398	−	23.9713i	−0.531908	−	0.921292i	−0.999306	−	0.0372449i	$-0.988142\pi$
$677$	−13.8398	−	23.9713i	−0.531908	−	0.921292i	0.467398	−	0.884047i	$-0.345191\pi$
$678$	−4.28304	+	7.41844i	−0.164489	+	0.284903i
$679$		0			0
$680$	1.87289	+	3.24394i	0.0718221	+	0.124400i
$681$	−2.20907	−	3.82622i	−0.0846518	−	0.146621i
$682$	1.49379			0.0572001
$683$	−23.7917			−0.910363			−0.455181	−	0.890399i	$-0.650426\pi$
$683$	−23.7917			−0.910363			−0.455181	+	0.890399i	$0.650426\pi$
$684$	0.222343	+	0.385110i	0.00850150	+	0.0147250i
$685$	−6.36600	−	11.0262i	−0.243232	−	0.421291i
$686$		0			0
$687$	−15.7803	+	27.3323i	−0.602056	+	1.04279i
$688$	−8.44559	−	14.6282i	−0.321985	−	0.557694i
$689$	29.9232	+	15.8779i	1.13998	+	0.604898i
$690$	−1.91401	+	3.31516i	−0.0728650	+	0.126206i
$691$	36.8433			1.40159			0.700793	−	0.713365i	$-0.252830\pi$
$691$	36.8433			1.40159			0.700793	+	0.713365i	$0.252830\pi$
$692$	−9.47603	+	16.4130i	−0.360224	+	0.623927i
$693$		0			0
$694$	15.4642			0.587012
$695$	10.7236	−	18.5739i	0.406771	−	0.704548i
$696$	−27.6969			−1.04985
$697$	−2.40325	+	4.16255i	−0.0910296	+	0.157668i
$698$	−4.41655	+	7.64969i	−0.167169	+	0.289545i
$699$	15.6343	−	27.0794i	0.591344	−	1.02424i
$700$		0			0
$701$	2.34987			0.0887533			0.0443767	−	0.999015i	$-0.485870\pi$
$701$	2.34987			0.0887533			0.0443767	+	0.999015i	$0.485870\pi$
$702$	0.342212	+	9.56664i	0.0129160	+	0.361070i
$703$	−2.11188	+	3.65788i	−0.0796511	+	0.137960i
$704$	0.296821	+	0.514108i	0.0111868	+	0.0193762i
$705$	−32.1174			−1.20961
$706$	6.49645	+	11.2522i	0.244497	+	0.423481i
$707$		0			0
$708$	−0.379208	−	0.656807i	−0.0142515	−	0.0246843i
$709$	−5.04160	+	8.73231i	−0.189341	+	0.327949i	−0.945031	−	0.326981i	$-0.893969\pi$
$709$	−5.04160	+	8.73231i	−0.189341	+	0.327949i	0.755689	+	0.654930i	$0.227302\pi$
$710$	5.34631	−	9.26008i	0.200643	−	0.347525i
$711$	9.32297			0.349639
$712$	−5.29182			−0.198319
$713$	5.26090	−	9.11214i	0.197022	−	0.341252i
$714$		0			0
$715$	2.72128	+	1.44397i	0.101770	+	0.0540013i
$716$	−2.88875	−	5.00346i	−0.107958	−	0.186988i
$717$	−3.00875	−	5.21130i	−0.112364	−	0.194620i
$718$	4.64966	+	8.05344i	0.173524	+	0.300552i
$719$	−3.25113	+	5.63113i	−0.121247	+	0.210006i	−0.920260	−	0.391308i	$-0.872023\pi$
$719$	−3.25113	+	5.63113i	−0.121247	+	0.210006i	0.799013	+	0.601314i	$0.205356\pi$
$720$	−1.79081			−0.0667394
$721$		0			0
$722$	−5.44660	−	9.43379i	−0.202701	−	0.351089i
$723$	15.0037	+	25.9872i	0.557994	+	0.966474i
$724$	35.1052			1.30468
$725$	−9.74542	−	16.8796i	−0.361936	−	0.626891i
$726$	11.6985			0.434171
$727$	−3.12636			−0.115950			−0.0579750	−	0.998318i	$-0.518464\pi$
$727$	−3.12636			−0.115950			−0.0579750	+	0.998318i	$0.518464\pi$
$728$		0			0
$729$	19.9595			0.739242
$730$	3.15623			0.116817
$731$	−4.82158	−	8.35123i	−0.178333	−	0.308881i
$732$	24.3250			0.899078
$733$	3.83220	+	6.63756i	0.141545	+	0.245164i	0.928079	−	0.372384i	$-0.121460\pi$
$733$	3.83220	+	6.63756i	0.141545	+	0.245164i	−0.786533	+	0.617548i	$0.788126\pi$
$734$	2.00036	+	3.46472i	0.0738346	+	0.127885i
$735$		0			0
$736$	−12.9382			−0.476909
$737$	0.419949	−	0.727373i	0.0154690	−	0.0267931i
$738$	0.675201	+	1.16948i	0.0248545	+	0.0430493i
$739$	−10.2162	−	17.6950i	−0.375810	−	0.650922i	0.614638	−	0.788809i	$-0.289302\pi$
$739$	−10.2162	−	17.6950i	−0.375810	−	0.650922i	−0.990448	+	0.137887i	$0.955969\pi$
$740$	−11.2331	−	19.4563i	−0.412936	−	0.715227i
$741$	0.112414	+	3.14257i	0.00412964	+	0.115445i
$742$		0			0
$743$	−5.07080	+	8.78288i	−0.186030	+	0.322213i	−0.943923	−	0.330166i	$-0.892895\pi$
$743$	−5.07080	+	8.78288i	−0.186030	+	0.322213i	0.757893	+	0.652378i	$0.226229\pi$
$744$	−17.8594			−0.654758
$745$	−19.7173			−0.722387
$746$	2.22801	−	3.85902i	0.0815731	−	0.141289i
$747$	−4.46469	+	7.73306i	−0.163354	+	0.282938i
$748$	0.577165	+	0.999680i	0.0211033	+	0.0365519i
$749$		0			0
$750$	6.32771	+	10.9599i	0.231055	+	0.400200i
$751$	−22.2961			−0.813598			−0.406799	−	0.913518i	$-0.633355\pi$
$751$	−22.2961			−0.813598			−0.406799	+	0.913518i	$0.633355\pi$
$752$	−12.0718	−	20.9090i	−0.440214	−	0.762474i
$753$	−2.36104	+	4.08943i	−0.0860409	+	0.149027i
$754$	−12.7254	−	6.75234i	−0.463431	−	0.245906i
$755$	−23.7829			−0.865550
$756$		0			0
$757$	−12.2909	+	21.2884i	−0.446720	+	0.773741i	−0.998170	−	0.0604666i	$-0.980741\pi$
$757$	−12.2909	+	21.2884i	−0.446720	+	0.773741i	0.551451	+	0.834207i	$0.314074\pi$
$758$	−7.29503	+	12.6354i	−0.264967	+	0.458937i
$759$	−1.29885	+	2.24967i	−0.0471452	+	0.0816580i
$760$	−1.44300			−0.0523431
$761$	17.6167	−	30.5130i	0.638603	−	1.10609i	−0.347136	−	0.937815i	$-0.612846\pi$
$761$	17.6167	−	30.5130i	0.638603	−	1.10609i	0.985739	−	0.168279i	$-0.0538209\pi$
$762$	1.03050			0.0373312
$763$		0			0
$764$	9.91545	−	17.1741i	0.358728	−	0.621336i
$765$	−1.02237			−0.0369639
$766$	6.39057	−	11.0688i	0.230901	−	0.399932i
$767$	−0.0310528	−	0.868091i	−0.00112125	−	0.0313449i
$768$	4.38246	+	7.59065i	0.158138	+	0.273904i
$769$	−4.62257	+	8.00653i	−0.166694	+	0.288723i	−0.937256	−	0.348643i	$-0.886643\pi$
$769$	−4.62257	+	8.00653i	−0.166694	+	0.288723i	0.770561	+	0.637366i	$0.219976\pi$
$770$		0			0
$771$	−9.95251	−	17.2383i	−0.358431	−	0.620821i
$772$	11.9624	+	20.7194i	0.430535	+	0.745708i
$773$	−6.32671			−0.227556			−0.113778	−	0.993506i	$-0.536295\pi$
$773$	−6.32671			−0.227556			−0.113778	+	0.993506i	$0.536295\pi$
$774$	−2.70928			−0.0973830
$775$	−6.28400	−	10.8842i	−0.225728	−	0.390972i
$776$	16.6180	+	28.7833i	0.596553	+	1.03326i
$777$		0			0
$778$	−3.18349	+	5.51397i	−0.114134	+	0.197686i
$779$	−0.925812	−	1.60355i	−0.0331706	−	0.0574532i
$780$	−14.7749	−	7.83984i	−0.529025	−	0.280711i
$781$	3.62802	−	6.28391i	0.129821	−	0.224856i
$782$	−1.64285			−0.0587480
$783$	−15.7772	+	27.3270i	−0.563833	+	0.976587i
$784$		0			0
$785$	−0.926435			−0.0330659
$786$	0.623749	−	1.08036i	0.0222484	−	0.0385353i
$787$	46.0057			1.63993			0.819963	−	0.572416i	$-0.193994\pi$
$787$	46.0057			1.63993			0.819963	+	0.572416i	$0.193994\pi$
$788$	5.79777	−	10.0420i	0.206537	−	0.357733i
$789$	29.6576	−	51.3684i	1.05584	−	1.82876i
$790$	−6.86924	+	11.8979i	−0.244397	+	0.423307i
$791$		0			0
$792$	0.714154			0.0253764
$793$	24.6104	+	13.0588i	0.873942	+	0.463731i
$794$	−7.26979	+	12.5916i	−0.257995	+	0.446861i
$795$	−13.0976	−	22.6856i	−0.464523	−	0.804577i
$796$	5.94569			0.210740
$797$	−12.3745	−	21.4333i	−0.438327	−	0.759205i	0.559233	−	0.829010i	$-0.311096\pi$
$797$	−12.3745	−	21.4333i	−0.438327	−	0.759205i	−0.997561	+	0.0698051i	$0.977762\pi$
$798$		0			0
$799$	−6.89181	−	11.9370i	−0.243815	−	0.422299i
$800$	−7.72717	+	13.3839i	−0.273197	+	0.473191i
$801$	0.722173	−	1.25084i	0.0255167	−	0.0441963i
$802$	13.1386			0.463940
$803$	2.14183			0.0755835
$804$	−2.28006	+	3.94919i	−0.0804117	+	0.139277i
$805$		0			0
$806$	−8.20551	−	4.35401i	−0.289027	−	0.153363i
$807$	19.9861	+	34.6170i	0.703545	+	1.21858i
$808$	14.8847	+	25.7811i	0.523643	+	0.906977i
$809$	−15.0174	−	26.0109i	−0.527983	−	0.914494i	−0.999468	−	0.0326194i	$-0.989615\pi$
$809$	−15.0174	−	26.0109i	−0.527983	−	0.914494i	0.471485	−	0.881874i	$-0.343718\pi$
$810$	4.44437	−	7.69787i	0.156159	−	0.270475i
$811$	−13.4160			−0.471101			−0.235550	−	0.971862i	$-0.575689\pi$
$811$	−13.4160			−0.471101			−0.235550	+	0.971862i	$0.575689\pi$
$812$		0			0
$813$	−6.16812	−	10.6835i	−0.216325	−	0.374686i
$814$	1.54021	+	2.66772i	0.0539843	+	0.0935036i
$815$	17.2180			0.603119
$816$	−2.37255	−	4.10938i	−0.0830560	−	0.143857i
$817$	3.71487			0.129967
$818$	−9.94171			−0.347604
$819$		0			0
$820$	9.84878			0.343934
$821$	10.1506			0.354257			0.177128	−	0.984188i	$-0.443319\pi$
$821$	10.1506			0.354257			0.177128	+	0.984188i	$0.443319\pi$
$822$	−4.73912	−	8.20840i	−0.165296	−	0.286301i
$823$	−48.0434			−1.67469			−0.837344	−	0.546676i	$-0.815893\pi$
$823$	−48.0434			−1.67469			−0.837344	+	0.546676i	$0.815893\pi$
$824$	11.4174	+	19.7755i	0.397744	+	0.688913i
$825$	1.55144	+	2.68717i	0.0540142	+	0.0935553i
$826$		0			0
$827$	8.41781			0.292716			0.146358	−	0.989232i	$-0.453245\pi$
$827$	8.41781			0.292716			0.146358	+	0.989232i	$0.453245\pi$
$828$	1.14218	−	1.97832i	0.0396935	−	0.0687512i
$829$	−28.0821	−	48.6396i	−0.975331	−	1.68932i	−0.678837	−	0.734289i	$-0.737516\pi$
$829$	−28.0821	−	48.6396i	−0.975331	−	1.68932i	−0.296495	−	0.955034i	$-0.595818\pi$
$830$	−6.57924	−	11.3956i	−0.228369	−	0.395546i
$831$	13.7466	+	23.8098i	0.476863	+	0.825951i
$832$	−0.131968	−	3.68920i	−0.00457516	−	0.127900i
$833$		0			0
$834$	7.98314	−	13.8272i	0.276434	−	0.478797i
$835$	32.5060			1.12492
$836$	−0.444686			−0.0153798
$837$	−10.1734	+	17.6209i	−0.351645	+	0.609066i
$838$	9.85111	−	17.0626i	0.340301	−	0.589419i
$839$	−13.0690	−	22.6362i	−0.451192	−	0.781488i	0.547268	−	0.836957i	$-0.315668\pi$
$839$	−13.0690	−	22.6362i	−0.451192	−	0.781488i	−0.998460	+	0.0554692i	$0.982335\pi$
$840$		0			0
$841$	−9.24289	−	16.0092i	−0.318720	−	0.552040i
$842$	18.7640			0.646650
$843$	−25.7158	−	44.5411i	−0.885700	−	1.53408i
$844$	−11.7415	+	20.3368i	−0.404158	+	0.700023i
$845$	−10.7394	−	15.8637i	−0.369448	−	0.545727i
$846$	−3.87255			−0.133141
$847$		0			0
$848$	9.84586	−	17.0535i	0.338108	−	0.585621i
$849$	−8.11290	+	14.0519i	−0.278434	+	0.482262i
$850$	−0.981166	+	1.69943i	−0.0336537	+	0.0582900i
$851$	21.6976			0.743783
$852$	−19.6979	+	34.1178i	−0.674839	+	1.16886i
$853$	−9.56236			−0.327409			−0.163705	−	0.986509i	$-0.552344\pi$
$853$	−9.56236			−0.327409			−0.163705	+	0.986509i	$0.552344\pi$
$854$		0			0
$855$	0.196926	−	0.341085i	0.00673471	−	0.0116649i
$856$	7.97730			0.272659
$857$	2.83687	−	4.91361i	0.0969058	−	0.167846i	−0.813497	−	0.581570i	$-0.802439\pi$
$857$	2.83687	−	4.91361i	0.0969058	−	0.167846i	0.910402	+	0.413724i	$0.135772\pi$
$858$	2.02584	+	1.07495i	0.0691610	+	0.0366982i
$859$	−13.2675	−	22.9801i	−0.452683	−	0.784070i	0.545869	−	0.837871i	$-0.316200\pi$
$859$	−13.2675	−	22.9801i	−0.452683	−	0.784070i	−0.998552	+	0.0538010i	$0.982866\pi$
$860$	−9.87968	+	17.1121i	−0.336894	+	0.583518i
$861$		0			0
$862$	−5.48292	−	9.49669i	−0.186749	−	0.323459i
$863$	−9.52402	−	16.4961i	−0.324202	−	0.561533i	0.657149	−	0.753761i	$-0.271762\pi$
$863$	−9.52402	−	16.4961i	−0.324202	−	0.561533i	−0.981350	+	0.192227i	$0.938429\pi$
$864$	25.0196			0.851186
$865$	16.7855			0.570725
$866$	−5.54882	−	9.61084i	−0.188557	−	0.326590i
$867$	14.7278	+	25.5094i	0.500184	+	0.866343i
$868$		0			0
$869$	−4.66148	+	8.07393i	−0.158130	+	0.273889i
$870$	5.56997	+	9.64746i	0.188840	+	0.327080i
$871$	−4.42692	+	2.77148i	−0.150001	+	0.0939081i
$872$	8.71856	−	15.1010i	0.295248	−	0.511384i
$873$	−9.07143			−0.307021
$874$	0.316439	−	0.548089i	0.0107037	−	0.0185394i
$875$		0			0
$876$	−11.6288			−0.392901
$877$	−13.2586	+	22.9645i	−0.447710	+	0.775456i	−0.998237	−	0.0593613i	$-0.981094\pi$
$877$	−13.2586	+	22.9645i	−0.447710	+	0.775456i	0.550527	+	0.834818i	$0.314427\pi$
$878$	5.56785			0.187906
$879$	9.92102	−	17.1837i	0.334628	−	0.579592i
$880$	0.895404	−	1.55088i	0.0301840	−	0.0522803i
$881$	−2.02357	+	3.50492i	−0.0681757	+	0.118084i	−0.898098	−	0.439795i	$-0.855051\pi$
$881$	−2.02357	+	3.50492i	−0.0681757	+	0.118084i	0.829923	+	0.557879i	$0.188385\pi$
$882$		0			0
$883$	44.7968			1.50753			0.753766	−	0.657142i	$-0.228235\pi$
$883$	44.7968			1.50753			0.753766	+	0.657142i	$0.228235\pi$
$884$	−0.256610	−	7.17362i	−0.00863073	−	0.241275i
$885$	−0.335858	+	0.581723i	−0.0112897	+	0.0195544i
$886$	−11.7120	−	20.2859i	−0.393474	−	0.681517i
$887$	50.1066			1.68241			0.841207	−	0.540714i	$-0.181846\pi$
$887$	50.1066			1.68241			0.841207	+	0.540714i	$0.181846\pi$
$888$	−18.4144	−	31.8947i	−0.617948	−	1.07032i
$889$		0			0
$890$	1.06421	+	1.84326i	0.0356723	+	0.0617862i
$891$	3.01596	−	5.22379i	0.101038	−	0.175004i
$892$	0.756314	−	1.30997i	0.0253233	−	0.0438612i
$893$	5.30990			0.177689
$894$	−14.6784			−0.490920
$895$	−2.55851	+	4.43148i	−0.0855217	+	0.148128i
$896$		0			0
$897$	13.6919	−	8.57184i	0.457160	−	0.286205i
$898$	−7.71796	−	13.3679i	−0.257552	−	0.446093i
$899$	−15.3098	−	26.5173i	−0.510610	−	0.884402i
$900$	−1.36430	−	2.36304i	−0.0454768	−	0.0787681i
$901$	5.62100	−	9.73586i	0.187263	−	0.324348i
$902$	−1.35040			−0.0449635
$903$		0			0
$904$	8.29384	+	14.3654i	0.275849	+	0.477785i
$905$	−15.5461	−	26.9266i	−0.516769	−	0.895069i
$906$	−17.7050			−0.588210
$907$	−2.77789	−	4.81144i	−0.0922382	−	0.159761i	0.816214	−	0.577749i	$-0.196069\pi$
$907$	−2.77789	−	4.81144i	−0.0922382	−	0.159761i	−0.908453	+	0.417988i	$0.862735\pi$
$908$	−3.88522			−0.128936
$909$	−8.12526			−0.269498
$910$		0			0
$911$	−14.5845			−0.483205			−0.241603	−	0.970375i	$-0.577673\pi$
$911$	−14.5845			−0.483205			−0.241603	+	0.970375i	$0.577673\pi$
$912$	1.82797			0.0605302
$913$	−4.46469	−	7.73306i	−0.147760	−	0.255927i
$914$	0.935158			0.0309323
$915$	−10.7721	−	18.6579i	−0.356116	−	0.616810i
$916$	13.8769	+	24.0354i	0.458504	+	0.794153i
$917$		0			0
$918$	3.17690			0.104853
$919$	3.50823	−	6.07643i	0.115726	−	0.200443i	−0.802344	−	0.596862i	$-0.796414\pi$
$919$	3.50823	−	6.07643i	0.115726	−	0.200443i	0.918070	+	0.396419i	$0.129747\pi$
$920$	3.70636	+	6.41960i	0.122195	+	0.211648i
$921$	18.1400	+	31.4194i	0.597734	+	1.03531i
$922$	4.61548	+	7.99424i	0.152003	+	0.263276i
$923$	−38.2450	+	23.9433i	−1.25885	+	0.788105i
$924$		0			0
$925$	12.9586	−	22.4449i	0.426075	−	0.737984i
$926$	16.7261			0.549653
$927$	−6.23251			−0.204702
$928$	−18.8258	+	32.6072i	−0.617987	+	1.07039i
$929$	−29.8098	+	51.6321i	−0.978028	+	1.69399i	−0.308469	+	0.951234i	$0.599817\pi$
$929$	−29.8098	+	51.6321i	−0.978028	+	1.69399i	−0.669558	+	0.742760i	$0.733517\pi$
$930$	3.59160	+	6.22083i	0.117773	+	0.203989i
$931$		0			0
$932$	−13.7485	−	23.8131i	−0.450347	−	0.780024i
$933$	−6.60046			−0.216089
$934$	2.15845	+	3.73854i	0.0706266	+	0.122329i
$935$	0.511186	−	0.885399i	0.0167176	−	0.0289557i
$936$	−3.92291	−	2.08158i	−0.128224	−	0.0680385i
$937$	14.5256			0.474531			0.237266	−	0.971445i	$-0.423749\pi$
$937$	14.5256			0.474531			0.237266	+	0.971445i	$0.423749\pi$
$938$		0			0
$939$	19.2245	−	33.2978i	0.627367	−	1.08663i
$940$	−14.1217	+	24.4595i	−0.460598	+	0.797779i
$941$	15.1230	−	26.1937i	0.492994	−	0.853891i	−0.506973	−	0.861962i	$-0.669236\pi$
$941$	15.1230	−	26.1937i	0.492994	−	0.853891i	0.999967	+	0.00807086i	$0.00256906\pi$
$942$	−0.689678			−0.0224709
$943$	−4.75591	+	8.23749i	−0.154874	+	0.268249i
$944$	−0.504951			−0.0164348
$945$		0			0
$946$	1.35464	−	2.34630i	0.0440431	−	0.0762849i
$947$	15.5278			0.504585			0.252292	−	0.967651i	$-0.418816\pi$
$947$	15.5278			0.504585			0.252292	+	0.967651i	$0.418816\pi$
$948$	25.3090	−	43.8364i	0.821997	−	1.42374i
$949$	−11.7652	−	6.24288i	−0.381916	−	0.202652i
$950$	−0.377978	−	0.654677i	−0.0122632	−	0.0212405i
$951$	26.3202	−	45.5879i	0.853490	−	1.47829i
$952$		0			0
$953$	−10.8527	−	18.7974i	−0.351554	−	0.608909i	0.634968	−	0.772538i	$-0.281013\pi$
$953$	−10.8527	−	18.7974i	−0.351554	−	0.608909i	−0.986522	+	0.163629i	$0.947680\pi$
$954$	−1.57924	−	2.73532i	−0.0511297	−	0.0885593i
$955$	−17.5639			−0.568354
$956$	−5.29166			−0.171144
$957$	3.77979	+	6.54679i	0.122183	+	0.211628i
$958$	−10.7997	−	18.7057i	−0.348924	−	0.604353i
$959$		0			0
$960$	−1.42732	+	2.47220i	−0.0460667	+	0.0797899i
$961$	5.62802	+	9.74801i	0.181549	+	0.314452i
$962$	−0.684784	−	19.1434i	−0.0220783	−	0.617207i
$963$	−1.08866	+	1.88561i	−0.0350816	+	0.0607630i
$964$	26.3879			0.849898
$965$	10.5949	−	18.3508i	0.341061	−	0.590735i
$966$		0			0
$967$	22.7524			0.731667			0.365833	−	0.930680i	$-0.380784\pi$
$967$	22.7524			0.731667			0.365833	+	0.930680i	$0.380784\pi$
$968$	11.3267	−	19.6184i	0.364054	−	0.630559i
$969$	1.04359			0.0335249
$970$	6.68390	−	11.5769i	0.214607	−	0.371711i
$971$	−26.5064	+	45.9105i	−0.850632	+	1.47334i	0.0300076	+	0.999550i	$0.490447\pi$
$971$	−26.5064	+	45.9105i	−0.850632	+	1.47334i	−0.880639	+	0.473787i	$0.842886\pi$
$972$	−4.94660	+	8.56776i	−0.158662	+	0.274811i
$973$		0			0
$974$	−14.0156			−0.449087
$975$	−0.689777	−	19.2829i	−0.0220905	−	0.617548i
$976$	8.09776	−	14.0257i	0.259203	−	0.448953i
$977$	2.32294	+	4.02345i	0.0743174	+	0.128722i	0.900789	−	0.434257i	$-0.142989\pi$
$977$	2.32294	+	4.02345i	0.0743174	+	0.128722i	−0.826472	+	0.562978i	$0.809656\pi$
$978$	12.8178			0.409868
$979$	0.722173	+	1.25084i	0.0230807	+	0.0399770i
$980$		0			0
$981$	2.37964	+	4.12165i	0.0759760	+	0.131594i
$982$	1.76014	−	3.04865i	0.0561682	−	0.0972862i
$983$	3.91896	−	6.78783i	0.124995	−	0.216498i	−0.796736	−	0.604328i	$-0.793442\pi$
$983$	3.91896	−	6.78783i	0.124995	−	0.216498i	0.921731	+	0.387830i	$0.126775\pi$
$984$	16.1451			0.514688
$985$	−10.2700			−0.327229
$986$	−2.39043	+	4.14034i	−0.0761267	+	0.131855i
$987$		0			0
$988$	2.44270	+	1.29615i	0.0777127	+	0.0412359i
$989$	−9.54167	−	16.5267i	−0.303408	−	0.525517i
$990$	−0.143619	−	0.248756i	−0.00456452	−	0.00790598i
$991$	8.87507	+	15.3721i	0.281926	+	0.488310i	0.971859	−	0.235563i	$-0.0756935\pi$
$991$	8.87507	+	15.3721i	0.281926	+	0.488310i	−0.689933	+	0.723873i	$0.742360\pi$
$992$	−12.1392	+	21.0257i	−0.385419	+	0.667565i
$993$	−17.6772			−0.560970
$994$		0			0
$995$	−2.63300	−	4.56049i	−0.0834717	−	0.144577i
$996$	24.2405	+	41.9857i	0.768089	+	1.33037i
$997$	35.3203			1.11861			0.559303	−	0.828963i	$-0.311069\pi$
$997$	35.3203			1.11861			0.559303	+	0.828963i	$0.311069\pi$
$998$	−0.729299	−	1.26318i	−0.0230855	−	0.0399853i
$999$	−41.9583			−1.32750

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.m.165.5		16
7.2	even	3		637.2.g.m.373.4		16
7.3	odd	6		637.2.f.l.295.4	yes	16
7.4	even	3		637.2.f.l.295.3	✓	16
7.5	odd	6		637.2.g.m.373.3		16
7.6	odd	2	inner	637.2.h.m.165.6		16
13.3	even	3		637.2.g.m.263.4		16
91.3	odd	6		637.2.f.l.393.4	yes	16
91.4	even	6		8281.2.a.cl.1.4		8
91.16	even	3	inner	637.2.h.m.471.5		16
91.17	odd	6		8281.2.a.cl.1.3		8
91.55	odd	6		637.2.g.m.263.3		16
91.68	odd	6	inner	637.2.h.m.471.6		16
91.74	even	3		8281.2.a.ci.1.6		8
91.81	even	3		637.2.f.l.393.3	yes	16
91.87	odd	6		8281.2.a.ci.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.3	✓	16	7.4	even	3
637.2.f.l.295.4	yes	16	7.3	odd	6
637.2.f.l.393.3	yes	16	91.81	even	3
637.2.f.l.393.4	yes	16	91.3	odd	6
637.2.g.m.263.3		16	91.55	odd	6
637.2.g.m.263.4		16	13.3	even	3
637.2.g.m.373.3		16	7.5	odd	6
637.2.g.m.373.4		16	7.2	even	3
637.2.h.m.165.5		16	1.1	even	1	trivial
637.2.h.m.165.6		16	7.6	odd	2	inner
637.2.h.m.471.5		16	91.16	even	3	inner
637.2.h.m.471.6		16	91.68	odd	6	inner
8281.2.a.ci.1.5		8	91.87	odd	6
8281.2.a.ci.1.6		8	91.74	even	3
8281.2.a.cl.1.3		8	91.17	odd	6
8281.2.a.cl.1.4		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 $\F_{q}$
Belyi maps

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-0.579810 q^{2} +(-0.946019 - 1.63855i) q^{3} -1.66382 q^{4} +(0.736809 + 1.27619i) q^{5} +(0.548512 + 0.950050i) q^{6} +2.12432 q^{8} +(-0.289905 + 0.502131i) q^{9} +(-0.427209 - 0.739948i) q^{10} +(-0.289905 - 0.502131i) q^{11} +(1.57401 + 2.72626i) q^{12} +(0.128893 + 3.60325i) q^{13} +(1.39407 - 2.41460i) q^{15} +2.09594 q^{16} +1.19657 q^{17} +(0.168090 - 0.291141i) q^{18} +(-0.230479 + 0.399201i) q^{19} +(-1.22592 - 2.12335i) q^{20} +(0.168090 + 0.291141i) q^{22} +2.36795 q^{23} +(-2.00965 - 3.48081i) q^{24} +(1.41423 - 2.44951i) q^{25} +(-0.0747335 - 2.08920i) q^{26} -4.57909 q^{27} +(3.44550 - 5.96777i) q^{29} +(-0.808297 + 1.40001i) q^{30} +(2.22171 - 3.84811i) q^{31} -5.46389 q^{32} +(-0.548512 + 0.950050i) q^{33} -0.693783 q^{34} +(0.482350 - 0.835455i) q^{36} +9.16301 q^{37} +(0.133634 - 0.231461i) q^{38} +(5.78218 - 3.61994i) q^{39} +(1.56522 + 2.71104i) q^{40} +(-2.00845 + 3.47874i) q^{41} +(-4.02951 - 6.97931i) q^{43} +(0.482350 + 0.835455i) q^{44} -0.854419 q^{45} -1.37296 q^{46} +(-5.75964 - 9.97598i) q^{47} +(-1.98280 - 3.43430i) q^{48} +(-0.819983 + 1.42025i) q^{50} +(-1.13198 - 1.96064i) q^{51} +(-0.214455 - 5.99515i) q^{52} +(4.69760 - 8.13647i) q^{53} +2.65501 q^{54} +(0.427209 - 0.739948i) q^{55} +0.872150 q^{57} +(-1.99773 + 3.46018i) q^{58} -0.240919 q^{59} +(-2.31948 + 4.01746i) q^{60} +(3.86355 - 6.69187i) q^{61} +(-1.28817 + 2.23118i) q^{62} -1.02385 q^{64} +(-4.50346 + 2.81940i) q^{65} +(0.318033 - 0.550849i) q^{66} +(0.724287 + 1.25450i) q^{67} -1.99088 q^{68} +(-2.24013 - 3.88001i) q^{69} +(6.25725 + 10.8379i) q^{71} +(-0.615852 + 1.06669i) q^{72} +(-1.84701 + 3.19911i) q^{73} -5.31281 q^{74} -5.35154 q^{75} +(0.383476 - 0.664199i) q^{76} +(-3.35257 + 2.09888i) q^{78} +(-8.03967 - 13.9251i) q^{79} +(1.54430 + 2.67481i) q^{80} +(5.20163 + 9.00948i) q^{81} +(1.16452 - 2.01701i) q^{82} +15.4005 q^{83} +(0.881643 + 1.52705i) q^{85} +(2.33635 + 4.04668i) q^{86} -13.0380 q^{87} +(-0.615852 - 1.06669i) q^{88} -2.49107 q^{89} +0.495401 q^{90} -3.93984 q^{92} -8.40712 q^{93} +(3.33950 + 5.78418i) q^{94} -0.679276 q^{95} +(5.16894 + 8.95287i) q^{96} +(7.82275 + 13.5494i) q^{97} +0.336180 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

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