LMFDB - Embedded newform 738.2.ba.d.233.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(17,738)] 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("738.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 33])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.ba (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0,0,0,0,-4,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$4$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			233.4
Character	$\chi$	$=$	738.233
Dual form			738.2.ba.d.719.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.587785 - 0.809017i) q^{4} +(0.499283 - 3.15235i) q^{5} +(0.671416 - 0.786128i) q^{7} +(0.987688 - 0.156434i) q^{8} +(2.58210 + 1.87600i) q^{10} +(0.100924 + 0.164693i) q^{11} +(-0.239053 + 3.03746i) q^{13} +(0.395628 + 0.955131i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.422714 - 1.76073i) q^{17} +(-0.00761038 - 0.0966990i) q^{19} +(-2.84378 + 1.44898i) q^{20} +(-0.192561 + 0.0151549i) q^{22} +(-2.70502 - 8.32519i) q^{23} +(-4.93275 - 1.60275i) q^{25} +(-2.59787 - 1.59198i) q^{26} +(-1.03064 - 0.0811131i) q^{28} +(-1.74742 - 7.27852i) q^{29} +(1.03824 - 1.42902i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.37691 + 1.17599i) q^{34} +(-2.14292 - 2.50904i) q^{35} +(3.06143 - 2.22426i) q^{37} +(0.0896145 + 0.0371195i) q^{38} -3.19165i q^{40} +(0.788009 - 6.35445i) q^{41} +(-3.32951 - 1.69647i) q^{43} +(0.0739177 - 0.178453i) q^{44} +(8.64585 + 1.36937i) q^{46} +(-7.60363 + 6.49411i) q^{47} +(0.927845 + 5.85818i) q^{49} +(3.66748 - 3.66748i) q^{50} +(2.59787 - 1.59198i) q^{52} +(6.19350 - 1.48693i) q^{53} +(0.569559 - 0.235919i) q^{55} +(0.540173 - 0.881482i) q^{56} +(7.27852 + 1.74742i) q^{58} +(2.72819 - 0.886444i) q^{59} +(-3.34936 - 6.57349i) q^{61} +(0.801911 + 1.57384i) q^{62} +(0.951057 - 0.309017i) q^{64} +(9.45579 + 2.27013i) q^{65} +(1.53604 - 2.50659i) q^{67} +(-1.67292 + 0.692948i) q^{68} +(3.20844 - 0.770278i) q^{70} +(-7.19946 + 4.41183i) q^{71} +(4.69223 - 4.69223i) q^{73} +(0.591970 + 3.73755i) q^{74} +(-0.0737579 + 0.0629952i) q^{76} +(0.197231 + 0.0312384i) q^{77} +(-1.03431 + 2.49705i) q^{79} +(2.84378 + 1.44898i) q^{80} +(5.30411 + 3.58698i) q^{82} +11.5641i q^{83} +(-5.33938 - 2.21164i) q^{85} +(3.02313 - 2.19643i) q^{86} +(0.125445 + 0.146877i) q^{88} +(11.9676 + 10.2213i) q^{89} +(2.22733 + 2.22733i) q^{91} +(-5.14525 + 7.08183i) q^{92} +(-2.33432 - 9.72315i) q^{94} +(-0.308629 - 0.0242896i) q^{95} +(0.141143 + 0.0864925i) q^{97} +(-5.64091 - 1.83284i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{7} + 8 q^{11} + 16 q^{13} - 4 q^{14} + 16 q^{16} + 16 q^{17} + 4 q^{19} - 4 q^{22} - 48 q^{23} + 40 q^{25} + 20 q^{26} + 4 q^{28} - 4 q^{29} + 40 q^{31} + 4 q^{34} + 52 q^{35} + 8 q^{37} - 16 q^{38}+ \cdots + 64 q^{97}+O(q^{100}) $ 64 * q - 4 * q^7 + 8 * q^11 + 16 * q^13 - 4 * q^14 + 16 * q^16 + 16 * q^17 + 4 * q^19 - 4 * q^22 - 48 * q^23 + 40 * q^25 + 20 * q^26 + 4 * q^28 - 4 * q^29 + 40 * q^31 + 4 * q^34 + 52 * q^35 + 8 * q^37 - 16 * q^38 - 12 * q^41 + 32 * q^43 + 4 * q^44 + 8 * q^47 + 48 * q^49 - 16 * q^50 - 20 * q^52 + 48 * q^53 - 36 * q^55 - 16 * q^56 - 20 * q^58 - 20 * q^59 + 24 * q^61 + 36 * q^62 - 60 * q^65 - 20 * q^67 - 12 * q^68 - 8 * q^70 + 8 * q^71 + 72 * q^73 + 12 * q^74 + 4 * q^76 + 76 * q^77 + 44 * q^79 - 68 * q^82 - 88 * q^85 + 32 * q^86 - 8 * q^88 - 84 * q^89 + 72 * q^91 + 12 * q^94 + 12 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$-1$	$e\left(\frac{11}{40}\right)$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$		0			0
$3$		0			0
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	0.499283	−	3.15235i	0.223286	−	1.40977i	−0.580211	−	0.814466i	$-0.697030\pi$
$5$	0.499283	−	3.15235i	0.223286	−	1.40977i	0.803497	−	0.595308i	$-0.202970\pi$
$6$		0			0
$7$	0.671416	−	0.786128i	0.253772	−	0.297128i	−0.618866	−	0.785496i	$-0.712408\pi$
$7$	0.671416	−	0.786128i	0.253772	−	0.297128i	0.872638	+	0.488368i	$0.162408\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$		0			0
$10$	2.58210	+	1.87600i	0.816530	+	0.593244i
$11$	0.100924	+	0.164693i	0.0304297	+	0.0496567i	0.867493	−	0.497449i	$-0.165730\pi$
$11$	0.100924	+	0.164693i	0.0304297	+	0.0496567i	−0.837064	+	0.547105i	$0.815730\pi$
$12$		0			0
$13$	−0.239053	+	3.03746i	−0.0663015	+	0.842440i	0.870408	+	0.492332i	$0.163855\pi$
$13$	−0.239053	+	3.03746i	−0.0663015	+	0.842440i	−0.936709	+	0.350108i	$0.886145\pi$
$14$	0.395628	+	0.955131i	0.105736	+	0.255269i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.422714	−	1.76073i	0.102523	−	0.427039i	−0.897376	−	0.441267i	$-0.854529\pi$
$17$	0.422714	−	1.76073i	0.102523	−	0.427039i	0.999899	+	0.0142280i	$0.00452905\pi$
$18$		0			0
$19$	−0.00761038	−	0.0966990i	−0.00174594	−	0.0221843i	0.995983	−	0.0895464i	$-0.0285417\pi$
$19$	−0.00761038	−	0.0966990i	−0.00174594	−	0.0221843i	−0.997729	+	0.0673621i	$0.978542\pi$
$20$	−2.84378	+	1.44898i	−0.635888	+	0.324001i
$21$		0			0
$22$	−0.192561	+	0.0151549i	−0.0410541	+	0.00323103i
$23$	−2.70502	−	8.32519i	−0.564035	−	1.73592i	−0.670800	−	0.741638i	$-0.734049\pi$
$23$	−2.70502	−	8.32519i	−0.564035	−	1.73592i	0.106764	−	0.994284i	$-0.465951\pi$
$24$		0			0
$25$	−4.93275	−	1.60275i	−0.986551	−	0.320550i
$26$	−2.59787	−	1.59198i	−0.509484	−	0.312212i
$27$		0			0
$28$	−1.03064	−	0.0811131i	−0.194773	−	0.0153289i
$29$	−1.74742	−	7.27852i	−0.324487	−	1.35159i	−0.861390	−	0.507943i	$-0.830406\pi$
$29$	−1.74742	−	7.27852i	−0.324487	−	1.35159i	0.536903	−	0.843644i	$-0.319594\pi$
$30$		0			0
$31$	1.03824	−	1.42902i	0.186473	−	0.256659i	−0.705537	−	0.708673i	$-0.749294\pi$
$31$	1.03824	−	1.42902i	0.186473	−	0.256659i	0.892011	+	0.452014i	$0.149294\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	1.37691	+	1.17599i	0.236139	+	0.201681i
$35$	−2.14292	−	2.50904i	−0.362220	−	0.424105i
$36$		0			0
$37$	3.06143	−	2.22426i	0.503296	−	0.365666i	−0.306978	−	0.951717i	$-0.599318\pi$
$37$	3.06143	−	2.22426i	0.503296	−	0.365666i	0.810275	+	0.586050i	$0.199318\pi$
$38$	0.0896145	+	0.0371195i	0.0145374	+	0.00602158i
$39$		0			0
$40$		−	3.19165i		−	0.504644i
$41$	0.788009	−	6.35445i	0.123066	−	0.992398i
$41$	0.788009	−	6.35445i	0.123066	−	0.992398i
$42$		0			0
$43$	−3.32951	−	1.69647i	−0.507745	−	0.258709i	0.181300	−	0.983428i	$-0.441970\pi$
$43$	−3.32951	−	1.69647i	−0.507745	−	0.258709i	−0.689045	+	0.724719i	$0.741970\pi$
$44$	0.0739177	−	0.178453i	0.0111435	−	0.0269028i
$45$		0			0
$46$	8.64585	+	1.36937i	1.27476	+	0.201902i
$47$	−7.60363	+	6.49411i	−1.10910	+	0.947263i	−0.998911	−	0.0466470i	$-0.985146\pi$
$47$	−7.60363	+	6.49411i	−1.10910	+	0.947263i	−0.110192	+	0.993910i	$0.535146\pi$
$48$		0			0
$49$	0.927845	+	5.85818i	0.132549	+	0.836883i
$50$	3.66748	−	3.66748i	0.518661	−	0.518661i
$51$		0			0
$52$	2.59787	−	1.59198i	0.360260	−	0.220767i
$53$	6.19350	−	1.48693i	0.850743	−	0.204245i	0.215448	−	0.976515i	$-0.430879\pi$
$53$	6.19350	−	1.48693i	0.850743	−	0.204245i	0.635294	+	0.772270i	$0.280879\pi$
$54$		0			0
$55$	0.569559	−	0.235919i	0.0767993	−	0.0318113i
$56$	0.540173	−	0.881482i	0.0721836	−	0.117793i
$57$		0			0
$58$	7.27852	+	1.74742i	0.955717	+	0.229447i
$59$	2.72819	−	0.886444i	0.355180	−	0.115405i	−0.125992	−	0.992031i	$-0.540211\pi$
$59$	2.72819	−	0.886444i	0.355180	−	0.115405i	0.481172	+	0.876626i	$0.340211\pi$
$60$		0			0
$61$	−3.34936	−	6.57349i	−0.428842	−	0.841649i	−0.999787	−	0.0206606i	$-0.993423\pi$
$61$	−3.34936	−	6.57349i	−0.428842	−	0.841649i	0.570945	−	0.820988i	$-0.306577\pi$
$62$	0.801911	+	1.57384i	0.101843	+	0.199878i
$63$		0			0
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	9.45579	+	2.27013i	1.17285	+	0.281575i
$66$		0			0
$67$	1.53604	−	2.50659i	0.187658	−	0.306229i	−0.744951	−	0.667119i	$-0.767527\pi$
$67$	1.53604	−	2.50659i	0.187658	−	0.306229i	0.932608	+	0.360890i	$0.117527\pi$
$68$	−1.67292	+	0.692948i	−0.202872	+	0.0840323i
$69$		0			0
$70$	3.20844	−	0.770278i	0.383482	−	0.0920658i
$71$	−7.19946	+	4.41183i	−0.854419	+	0.523588i	−0.879391	−	0.476100i	$-0.842050\pi$
$71$	−7.19946	+	4.41183i	−0.854419	+	0.523588i	0.0249727	+	0.999688i	$0.492050\pi$
$72$		0			0
$73$	4.69223	−	4.69223i	0.549184	−	0.549184i	−0.377021	−	0.926205i	$-0.623051\pi$
$73$	4.69223	−	4.69223i	0.549184	−	0.549184i	0.926205	+	0.377021i	$0.123051\pi$
$74$	0.591970	+	3.73755i	0.0688151	+	0.434481i
$75$		0			0
$76$	−0.0737579	+	0.0629952i	−0.00846061	+	0.00722604i
$77$	0.197231	+	0.0312384i	0.0224766	+	0.00355995i
$78$		0			0
$79$	−1.03431	+	2.49705i	−0.116369	+	0.280940i	−0.971323	−	0.237764i	$-0.923585\pi$
$79$	−1.03431	+	2.49705i	−0.116369	+	0.280940i	0.854954	+	0.518704i	$0.173585\pi$
$80$	2.84378	+	1.44898i	0.317944	+	0.162001i
$81$		0			0
$82$	5.30411	+	3.58698i	0.585741	+	0.396116i
$83$			11.5641i			1.26932i	0.772791	+	0.634661i	$0.218860\pi$
$83$			11.5641i			1.26932i	−0.772791	+	0.634661i	$0.781140\pi$
$84$		0			0
$85$	−5.33938	−	2.21164i	−0.579137	−	0.239887i
$86$	3.02313	−	2.19643i	0.325992	−	0.236847i
$87$		0			0
$88$	0.125445	+	0.146877i	0.0133725	+	0.0156572i
$89$	11.9676	+	10.2213i	1.26856	+	1.08346i	0.992491	+	0.122321i	$0.0390336\pi$
$89$	11.9676	+	10.2213i	1.26856	+	1.08346i	0.276074	+	0.961136i	$0.410966\pi$
$90$		0			0
$91$	2.22733	+	2.22733i	0.233487	+	0.233487i
$92$	−5.14525	+	7.08183i	−0.536430	+	0.738332i
$93$		0			0
$94$	−2.33432	−	9.72315i	−0.240767	−	1.00287i
$95$	−0.308629	−	0.0242896i	−0.0316647	−	0.00249206i
$96$		0			0
$97$	0.141143	+	0.0864925i	0.0143309	+	0.00878198i	0.529646	−	0.848219i	$-0.322325\pi$
$97$	0.141143	+	0.0864925i	0.0143309	+	0.00878198i	−0.515315	+	0.857001i	$0.672325\pi$
$98$	−5.64091	−	1.83284i	−0.569818	−	0.185145i
$99$		0			0
$100$	1.60275	+	4.93275i	0.160275	+	0.493275i
$101$	−0.458326	+	0.0360710i	−0.0456051	+	0.00358920i	−0.101241	−	0.994862i	$-0.532281\pi$
$101$	−0.458326	+	0.0360710i	−0.0456051	+	0.00358920i	0.0556360	+	0.998451i	$0.482281\pi$
$102$		0			0
$103$	7.49182	−	3.81727i	0.738191	−	0.376127i	−0.0441109	−	0.999027i	$-0.514045\pi$
$103$	7.49182	−	3.81727i	0.738191	−	0.376127i	0.782302	+	0.622900i	$0.214045\pi$
$104$	0.239053	+	3.03746i	0.0234411	+	0.297848i
$105$		0			0
$106$	−1.48693	+	6.19350i	−0.144423	+	0.601566i
$107$	3.30336	−	10.1667i	0.319348	−	0.982852i	−0.654580	−	0.755993i	$-0.727154\pi$
$107$	3.30336	−	10.1667i	0.319348	−	0.982852i	0.973928	−	0.226859i	$-0.0728457\pi$
$108$		0			0
$109$	−0.174439	−	0.421133i	−0.0167082	−	0.0403372i	0.915305	−	0.402761i	$-0.131949\pi$
$109$	−0.174439	−	0.421133i	−0.0167082	−	0.0403372i	−0.932013	+	0.362424i	$0.881949\pi$
$110$	−0.0483690	+	0.614586i	−0.00461180	+	0.0585985i
$111$		0			0
$112$	0.540173	+	0.881482i	0.0510415	+	0.0832922i
$113$	−5.44642	−	3.95706i	−0.512356	−	0.372249i	0.301360	−	0.953510i	$-0.402559\pi$
$113$	−5.44642	−	3.95706i	−0.512356	−	0.372249i	−0.813717	+	0.581262i	$0.802559\pi$
$114$		0			0
$115$	−27.5945	+	4.37054i	−2.57320	+	0.407555i
$116$	−4.86134	+	5.69190i	−0.451364	+	0.528480i
$117$		0			0
$118$	−0.448747	+	2.83327i	−0.0413105	+	0.260824i
$119$	−1.10034	−	1.51449i	−0.100868	−	0.138833i
$120$		0			0
$121$	4.97696	−	9.76783i	0.452451	−	0.887984i
$122$	7.37760			0.667936
$123$		0			0
$124$	−1.76636			−0.158624
$125$	−0.270387	+	0.530664i	−0.0241842	+	0.0474641i
$126$		0			0
$127$	−0.723642	−	0.996007i	−0.0642128	−	0.0883813i	0.775703	−	0.631098i	$-0.217396\pi$
$127$	−0.723642	−	0.996007i	−0.0642128	−	0.0883813i	−0.839916	+	0.542717i	$0.817396\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$		0			0
$130$	−6.31554	+	7.39455i	−0.553910	+	0.648545i
$131$	8.08858	−	1.28111i	0.706703	−	0.111931i	0.207271	−	0.978284i	$-0.433542\pi$
$131$	8.08858	−	1.28111i	0.706703	−	0.111931i	0.499432	+	0.866353i	$0.333542\pi$
$132$		0			0
$133$	−0.0811275	−	0.0589426i	−0.00703465	−	0.00511097i
$134$	1.53604	+	2.50659i	0.132694	+	0.216537i
$135$		0			0
$136$	0.142071	−	1.80518i	0.0121825	−	0.154793i
$137$	2.57178	+	6.20882i	0.219722	+	0.530456i	0.994851	−	0.101347i	$-0.0323153\pi$
$137$	2.57178	+	6.20882i	0.219722	+	0.530456i	−0.775129	+	0.631803i	$0.782315\pi$
$138$		0			0
$139$	−5.73405	+	17.6476i	−0.486356	+	1.49685i	0.343651	+	0.939097i	$0.388336\pi$
$139$	−5.73405	+	17.6476i	−0.486356	+	1.49685i	−0.830007	+	0.557753i	$0.811664\pi$
$140$	−0.770278	+	3.20844i	−0.0651004	+	0.271163i
$141$		0			0
$142$	−0.662487	−	8.41770i	−0.0555947	−	0.706397i
$143$	−0.524374	+	0.267182i	−0.0438503	+	0.0223429i
$144$		0			0
$145$	−23.8169	+	1.87443i	−1.97789	+	0.155663i
$146$	2.05058	+	6.31104i	0.169707	+	0.522305i
$147$		0			0
$148$	−3.59893	−	1.16936i	−0.295830	−	0.0961211i
$149$	2.07087	+	1.26903i	0.169652	+	0.103963i	0.604733	−	0.796429i	$-0.293280\pi$
$149$	2.07087	+	1.26903i	0.169652	+	0.103963i	−0.435080	+	0.900392i	$0.643280\pi$
$150$		0			0
$151$	12.2676	+	0.965483i	0.998325	+	0.0785699i	0.567078	−	0.823664i	$-0.308074\pi$
$151$	12.2676	+	0.965483i	0.998325	+	0.0785699i	0.431247	+	0.902234i	$0.358074\pi$
$152$	−0.0226437	−	0.0943179i	−0.00183665	−	0.00765020i
$153$		0			0
$154$	−0.117375	+	0.161553i	−0.00945833	+	0.0130183i
$155$	−3.98638	−	3.98638i	−0.320194	−	0.320194i
$156$		0			0
$157$	−14.4801	−	12.3672i	−1.15564	−	0.987008i	−0.155639	−	0.987814i	$-0.549743\pi$
$157$	−14.4801	−	12.3672i	−1.15564	−	0.987008i	−1.00000		0.000805828i	$0.999743\pi$
$158$	−1.75532	−	2.05522i	−0.139646	−	0.163504i
$159$		0			0
$160$	−2.58210	+	1.87600i	−0.204133	+	0.148311i
$161$	−8.36086	−	3.46318i	−0.658928	−	0.272937i
$162$		0			0
$163$			20.0952i			1.57398i	0.616969	+	0.786988i	$0.288360\pi$
$163$			20.0952i			1.57398i	−0.616969	+	0.786988i	$0.711640\pi$
$164$	−5.60404	+	3.09754i	−0.437602	+	0.241877i
$165$		0			0
$166$	−10.3037	−	5.24998i	−0.799719	−	0.407477i
$167$	−2.21195	+	5.34011i	−0.171165	+	0.413230i	−0.986062	−	0.166376i	$-0.946793\pi$
$167$	−2.21195	+	5.34011i	−0.171165	+	0.413230i	0.814897	+	0.579606i	$0.196793\pi$
$168$		0			0
$169$	3.67093	+	0.581418i	0.282379	+	0.0447245i
$170$	4.39462	−	3.75336i	0.337052	−	0.287869i
$171$		0			0
$172$	0.584563	+	3.69079i	0.0445725	+	0.281420i
$173$	1.54476	−	1.54476i	0.117446	−	0.117446i	−0.645941	−	0.763387i	$-0.723535\pi$
$173$	1.54476	−	1.54476i	0.117446	−	0.117446i	0.763387	+	0.645941i	$0.223535\pi$
$174$		0			0
$175$	−4.57190	+	2.80166i	−0.345603	+	0.211786i
$176$	−0.187819	+	0.0450914i	−0.0141574	+	0.00339889i
$177$		0			0
$178$	−14.5404	+	6.02285i	−1.08985	+	0.451431i
$179$	−10.3492	+	16.8883i	−0.773535	+	1.26229i	0.186512	+	0.982453i	$0.440282\pi$
$179$	−10.3492	+	16.8883i	−0.773535	+	1.26229i	−0.960046	+	0.279841i	$0.909718\pi$
$180$		0			0
$181$	17.5803	+	4.22065i	1.30673	+	0.313718i	0.826258	−	0.563291i	$-0.190465\pi$
$181$	17.5803	+	4.22065i	1.30673	+	0.313718i	0.480473	+	0.877010i	$0.340465\pi$
$182$	−2.99575	+	0.973378i	−0.222060	+	0.0721516i
$183$		0			0
$184$	−3.97406	−	7.79954i	−0.292972	−	0.574990i
$185$	−5.48313	−	10.7613i	−0.403128	−	0.791183i
$186$		0			0
$187$	0.332641	−	0.108082i	0.0243251	−	0.00790371i
$188$	9.72315	+	2.33432i	0.709133	+	0.170248i
$189$		0			0
$190$	0.161757	−	0.263963i	0.0117351	−	0.0191499i
$191$	13.0736	−	5.41528i	0.945976	−	0.391836i	0.144259	−	0.989540i	$-0.453920\pi$
$191$	13.0736	−	5.41528i	0.945976	−	0.391836i	0.801717	+	0.597704i	$0.203920\pi$
$192$		0			0
$193$	−1.07863	+	0.258957i	−0.0776416	+	0.0186401i	−0.272080	−	0.962275i	$-0.587712\pi$
$193$	−1.07863	+	0.258957i	−0.0776416	+	0.0186401i	0.194438	+	0.980915i	$0.437712\pi$
$194$	−0.141143	+	0.0864925i	−0.0101335	+	0.00620980i
$195$		0			0
$196$	4.19399	−	4.19399i	0.299571	−	0.299571i
$197$	2.47119	+	15.6025i	0.176065	+	1.11163i	0.904486	+	0.426503i	$0.140255\pi$
$197$	2.47119	+	15.6025i	0.176065	+	1.11163i	−0.728421	+	0.685130i	$0.759745\pi$
$198$		0			0
$199$	5.21104	−	4.45065i	0.369401	−	0.315498i	−0.445298	−	0.895382i	$-0.646902\pi$
$199$	5.21104	−	4.45065i	0.369401	−	0.315498i	0.814699	+	0.579884i	$0.196902\pi$
$200$	−5.12275	−	0.811364i	−0.362233	−	0.0573721i
$201$		0			0
$202$	0.175936	−	0.424747i	0.0123788	−	0.0298851i
$203$	−6.89509	−	3.51322i	−0.483941	−	0.246580i
$204$		0			0
$205$	−19.6380	−	5.65675i	−1.37158	−	0.395085i
$206$			8.40827i			0.585832i
$207$		0			0
$208$	−2.81492	−	1.16598i	−0.195180	−	0.0808462i
$209$	0.0151576	−	0.0110126i	0.00104847	−	0.000761758i
$210$		0			0
$211$	13.8241	+	16.1859i	0.951688	+	1.11428i	0.993348	+	0.115152i	$0.0367354\pi$
$211$	13.8241	+	16.1859i	0.951688	+	1.11428i	−0.0416600	+	0.999132i	$0.513265\pi$
$212$	−4.84340	−	4.13665i	−0.332646	−	0.284106i
$213$		0			0
$214$	7.55890	+	7.55890i	0.516716	+	0.516716i
$215$	−7.01023	+	9.64875i	−0.478094	+	0.658040i
$216$		0			0
$217$	−0.426297	−	1.77565i	−0.0289389	−	0.120539i
$218$	0.454426	+	0.0357641i	0.0307776	+	0.00242225i
$219$		0			0
$220$	−0.525641	−	0.322113i	−0.0354387	−	0.0217169i
$221$	5.24709	+	1.70488i	0.352958	+	0.114683i
$222$		0			0
$223$	−3.13806	−	9.65797i	−0.210140	−	0.646745i	−0.999463	−	0.0327668i	$-0.989568\pi$
$223$	−3.13806	−	9.65797i	−0.210140	−	0.646745i	0.789323	−	0.613979i	$-0.210432\pi$
$224$	−1.03064	+	0.0811131i	−0.0688625	+	0.00541960i
$225$		0			0
$226$	5.99839	−	3.05633i	0.399007	−	0.203304i
$227$	0.684714	+	8.70012i	0.0454461	+	0.577447i	0.976915	+	0.213627i	$0.0685277\pi$
$227$	0.684714	+	8.70012i	0.0454461	+	0.577447i	−0.931469	+	0.363820i	$0.881472\pi$
$228$		0			0
$229$	0.697256	−	2.90428i	0.0460760	−	0.191920i	−0.944585	−	0.328266i	$-0.893536\pi$
$229$	0.697256	−	2.90428i	0.0460760	−	0.191920i	0.990661	+	0.136346i	$0.0435358\pi$
$230$	8.63346	−	26.5711i	0.569274	−	1.75204i
$231$		0			0
$232$	−2.86452	−	6.91555i	−0.188065	−	0.454028i
$233$	−0.306839	+	3.89876i	−0.0201017	+	0.255417i	0.978653	+	0.205521i	$0.0658889\pi$
$233$	−0.306839	+	3.89876i	−0.0201017	+	0.255417i	−0.998754	+	0.0498956i	$0.984111\pi$
$234$		0			0
$235$	16.6754	+	27.2117i	1.08778	+	1.77510i
$236$	−2.32074	−	1.68612i	−0.151067	−	0.109757i
$237$		0			0
$238$	1.84896	−	0.292847i	0.119851	−	0.0189825i
$239$	−18.8816	+	22.1075i	−1.22135	+	1.43002i	−0.351867	+	0.936050i	$0.614453\pi$
$239$	−18.8816	+	22.1075i	−1.22135	+	1.43002i	−0.869482	+	0.493965i	$0.835547\pi$
$240$		0			0
$241$	4.37057	−	27.5947i	0.281533	−	1.77753i	−0.290075	−	0.957004i	$-0.593680\pi$
$241$	4.37057	−	27.5947i	0.281533	−	1.77753i	0.571608	−	0.820527i	$-0.306320\pi$
$242$	6.44371	+	8.86900i	0.414217	+	0.570121i
$243$		0			0
$244$	−3.34936	+	6.57349i	−0.214421	+	0.420824i
$245$	18.9303			1.20941
$246$		0			0
$247$	0.295539			0.0188047
$248$	0.801911	−	1.57384i	0.0509214	−	0.0999388i
$249$		0			0
$250$	−0.350072	−	0.481833i	−0.0221405	−	0.0304738i
$251$	−0.0404107	+	0.255143i	−0.00255070	+	0.0161045i	−0.988931	−	0.148377i	$-0.952595\pi$
$251$	−0.0404107	+	0.255143i	−0.00255070	+	0.0161045i	0.986380	+	0.164482i	$0.0525951\pi$
$252$		0			0
$253$	1.09810	−	1.28571i	0.0690368	−	0.0808317i
$254$	1.21598	−	0.192592i	0.0762971	−	0.0120843i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	12.6396	+	20.6259i	0.788434	+	1.28661i	0.953820	+	0.300379i	$0.0971132\pi$
$257$	12.6396	+	20.6259i	0.788434	+	1.28661i	−0.165386	+	0.986229i	$0.552887\pi$
$258$		0			0
$259$	0.306943	−	3.90008i	0.0190725	−	0.242339i
$260$	−3.72140	−	8.98424i	−0.230791	−	0.557179i
$261$		0			0
$262$	−2.53067	+	7.78859i	−0.156345	+	0.481181i
$263$	4.47956	−	18.6587i	0.276222	−	1.15055i	−0.645831	−	0.763481i	$-0.723489\pi$
$263$	4.47956	−	18.6587i	0.276222	−	1.15055i	0.922052	−	0.387065i	$-0.126511\pi$
$264$		0			0
$265$	−1.59501	−	20.2665i	−0.0979805	−	1.24496i
$266$	0.0893493	−	0.0455258i	0.00547836	−	0.00279136i
$267$		0			0
$268$	−2.93074	+	0.230654i	−0.179023	+	0.0140895i
$269$	−0.197841	−	0.608893i	−0.0120626	−	0.0371249i	0.944844	−	0.327521i	$-0.106213\pi$
$269$	−0.197841	−	0.608893i	−0.0120626	−	0.0371249i	−0.956907	+	0.290396i	$0.906213\pi$
$270$		0			0
$271$	17.8412	+	5.79696i	1.08378	+	0.352140i	0.795838	−	0.605509i	$-0.207031\pi$
$271$	17.8412	+	5.79696i	1.08378	+	0.352140i	0.287937	+	0.957649i	$0.407031\pi$
$272$	1.54393	+	0.946119i	0.0936143	+	0.0573669i
$273$		0			0
$274$	−6.69966	−	0.527275i	−0.404742	−	0.0318539i
$275$	−0.233871	−	0.974145i	−0.0141030	−	0.0587431i
$276$		0			0
$277$	−18.4023	+	25.3286i	−1.10569	+	1.52185i	−0.278070	+	0.960561i	$0.589695\pi$
$277$	−18.4023	+	25.3286i	−1.10569	+	1.52185i	−0.827620	+	0.561289i	$0.810305\pi$
$278$	−13.1209	−	13.1209i	−0.786941	−	0.786941i
$279$		0			0
$280$	−2.50904	−	2.14292i	−0.149944	−	0.128064i
$281$	−11.8516	−	13.8764i	−0.707008	−	0.827800i	0.284387	−	0.958710i	$-0.408210\pi$
$281$	−11.8516	−	13.8764i	−0.707008	−	0.827800i	−0.991394	+	0.130910i	$0.958210\pi$
$282$		0			0
$283$	−9.58565	+	6.96438i	−0.569808	+	0.413990i	−0.835035	−	0.550196i	$-0.814553\pi$
$283$	−9.58565	+	6.96438i	−0.569808	+	0.413990i	0.265228	+	0.964186i	$0.414553\pi$
$284$	7.80099	+	3.23127i	0.462903	+	0.191741i
$285$		0			0
$286$		−	0.588519i		−	0.0347998i
$287$	−4.46633	−	4.88596i	−0.263639	−	0.288409i
$288$		0			0
$289$	12.2256	+	6.22927i	0.719155	+	0.366428i
$290$	9.14252	−	22.0720i	0.536867	−	1.29611i
$291$		0			0
$292$	−6.55412	−	1.03807i	−0.383551	−	0.0607485i
$293$	−17.8872	+	15.2771i	−1.04498	+	0.892500i	−0.994343	−	0.106217i	$-0.966126\pi$
$293$	−17.8872	+	15.2771i	−1.04498	+	0.892500i	−0.0506399	+	0.998717i	$0.516126\pi$
$294$		0			0
$295$	−1.43224	−	9.04281i	−0.0833883	−	0.526493i
$296$	2.67579	−	2.67579i	0.155527	−	0.155527i
$297$		0			0
$298$	−2.07087	+	1.26903i	−0.119962	+	0.0735131i
$299$	25.9341	−	6.22622i	1.49981	−	0.360072i
$300$		0			0
$301$	−3.56913	+	1.47838i	−0.205721	+	0.0852124i
$302$	−6.42964	+	10.4922i	−0.369984	+	0.603759i
$303$		0			0
$304$	0.0943179	+	0.0226437i	0.00540951	+	0.00129871i
$305$	−22.3942	+	7.27633i	−1.28229	+	0.416641i
$306$		0			0
$307$	−0.934393	−	1.83385i	−0.0533286	−	0.104663i	0.862804	−	0.505538i	$-0.168706\pi$
$307$	−0.934393	−	1.83385i	−0.0533286	−	0.104663i	−0.916133	+	0.400875i	$0.868706\pi$
$308$	−0.0906574	−	0.177925i	−0.00516568	−	0.0101382i
$309$		0			0
$310$	5.36167	−	1.74211i	0.304523	−	0.0989454i
$311$	25.9835	+	6.23808i	1.47339	+	0.353729i	0.889061	−	0.457789i	$-0.151358\pi$
$311$	25.9835	+	6.23808i	1.47339	+	0.353729i	0.584327	+	0.811518i	$0.301358\pi$
$312$		0			0
$313$	0.978527	−	1.59681i	0.0553096	−	0.0902571i	−0.823790	−	0.566895i	$-0.808145\pi$
$313$	0.978527	−	1.59681i	0.0553096	−	0.0902571i	0.879100	+	0.476638i	$0.158145\pi$
$314$	17.5931	−	7.28729i	0.992834	−	0.411245i
$315$		0			0
$316$	2.62811	−	0.630953i	0.147843	−	0.0354939i
$317$	18.6531	−	11.4307i	1.04766	−	0.642009i	0.111569	−	0.993757i	$-0.464412\pi$
$317$	18.6531	−	11.4307i	1.04766	−	0.642009i	0.936095	+	0.351747i	$0.114412\pi$
$318$		0			0
$319$	1.02236	−	1.02236i	0.0572414	−	0.0572414i
$320$	−0.499283	−	3.15235i	−0.0279108	−	0.176222i
$321$		0			0
$322$	6.88147	−	5.87733i	0.383489	−	0.327531i
$323$	−0.173478	−	0.0274762i	−0.00965256	−	0.00152881i
$324$		0			0
$325$	6.04748	−	14.5999i	0.335454	−	0.809857i
$326$	−17.9049	−	9.12302i	−0.991662	−	0.505277i
$327$		0			0
$328$	−0.215748	−	6.39949i	−0.0119127	−	0.353353i
$329$			10.3377i			0.569934i
$330$		0			0
$331$	21.1875	+	8.77616i	1.16457	+	0.482381i	0.879395	−	0.476094i	$-0.157948\pi$
$331$	21.1875	+	8.77616i	1.16457	+	0.482381i	0.285177	+	0.958475i	$0.407948\pi$
$332$	9.35553	−	6.79719i	0.513451	−	0.373044i
$333$		0			0
$334$	−3.75387	−	4.39522i	−0.205403	−	0.240496i
$335$	−7.13475	−	6.09365i	−0.389813	−	0.332932i
$336$		0			0
$337$	6.65207	+	6.65207i	0.362362	+	0.362362i	0.864682	−	0.502320i	$-0.167520\pi$
$337$	6.65207	+	6.65207i	0.362362	+	0.362362i	−0.502320	+	0.864682i	$0.667520\pi$
$338$	−2.18461	+	3.00686i	−0.118827	+	0.163552i
$339$		0			0
$340$	1.34915	+	5.61962i	0.0731680	+	0.304767i
$341$	0.340132	+	0.0267689i	0.0184192	+	0.00144962i
$342$		0			0
$343$	11.3986	+	6.98508i	0.615468	+	0.377159i
$344$	−3.55390	−	1.15473i	−0.191613	−	0.0622590i
$345$		0			0
$346$	0.675086	+	2.07770i	0.0362929	+	0.111698i
$347$	−28.1721	+	2.21719i	−1.51236	+	0.119025i	−0.807307	−	0.590131i	$-0.799076\pi$
$347$	−28.1721	+	2.21719i	−1.51236	+	0.119025i	−0.705051	+	0.709157i	$0.749076\pi$
$348$		0			0
$349$	11.4651	−	5.84174i	0.613711	−	0.312701i	−0.119363	−	0.992851i	$-0.538085\pi$
$349$	11.4651	−	5.84174i	0.613711	−	0.312701i	0.733073	+	0.680150i	$0.238085\pi$
$350$	−0.420702	−	5.34552i	−0.0224874	−	0.285730i
$351$		0			0
$352$	0.0450914	−	0.187819i	0.00240338	−	0.0100108i
$353$	10.7225	−	33.0003i	0.570699	−	1.75643i	−0.0796791	−	0.996821i	$-0.525390\pi$
$353$	10.7225	−	33.0003i	0.570699	−	1.75643i	0.650378	−	0.759611i	$-0.274610\pi$
$354$		0			0
$355$	10.3131	+	24.8980i	0.547362	+	1.32145i
$356$	1.23483	−	15.6899i	0.0654456	−	0.831565i
$357$		0			0
$358$	−10.3492	−	16.8883i	−0.546972	−	0.892577i
$359$	−17.1311	−	12.4465i	−0.904144	−	0.656899i	0.0353827	−	0.999374i	$-0.488735\pi$
$359$	−17.1311	−	12.4465i	−0.904144	−	0.656899i	−0.939527	+	0.342474i	$0.888735\pi$
$360$		0			0
$361$	18.7568	−	2.97078i	0.987199	−	0.156357i
$362$	−11.7419	+	13.7480i	−0.617141	+	0.722579i
$363$		0			0
$364$	0.492756	−	3.11114i	0.0258274	−	0.163068i
$365$	−12.4488	−	17.1343i	−0.651600	−	0.896851i
$366$		0			0
$367$	12.9653	−	25.4459i	0.676785	−	1.32826i	−0.255595	−	0.966784i	$-0.582271\pi$
$367$	12.9653	−	25.4459i	0.676785	−	1.32826i	0.932380	−	0.361481i	$-0.117729\pi$
$368$	8.75363			0.456314
$369$		0			0
$370$	12.0776			0.627886
$371$	2.98950	−	5.86723i	0.155207	−	0.304611i
$372$		0			0
$373$	−15.2908	−	21.0459i	−0.791726	−	1.08972i	−0.993891	−	0.110366i	$-0.964798\pi$
$373$	−15.2908	−	21.0459i	−0.791726	−	1.08972i	0.202165	−	0.979351i	$-0.435202\pi$
$374$	−0.0547144	+	0.345453i	−0.00282922	+	0.0178630i
$375$		0			0
$376$	−6.49411	+	7.60363i	−0.334908	+	0.392127i
$377$	22.5259	−	3.56776i	1.16015	−	0.183749i
$378$		0			0
$379$	−4.42268	−	3.21326i	−0.227178	−	0.165054i	0.468374	−	0.883530i	$-0.344840\pi$
$379$	−4.42268	−	3.21326i	−0.227178	−	0.165054i	−0.695552	+	0.718476i	$0.744840\pi$
$380$	0.161757	+	0.263963i	0.00829795	+	0.0135410i
$381$		0			0
$382$	−1.11026	+	14.1072i	−0.0568058	+	0.721787i
$383$	−2.46936	−	5.96155i	−0.126178	−	0.304621i	0.848149	−	0.529758i	$-0.177717\pi$
$383$	−2.46936	−	5.96155i	−0.126178	−	0.304621i	−0.974327	+	0.225137i	$0.927717\pi$
$384$		0			0
$385$	0.196949	−	0.606146i	0.0100374	−	0.0308921i
$386$	0.258957	−	1.07863i	0.0131805	−	0.0549009i
$387$		0			0
$388$	−0.0129878	−	0.165026i	−0.000659357	−	0.00837793i
$389$	−33.4642	+	17.0509i	−1.69670	+	0.864513i	−0.709565	+	0.704640i	$0.751108\pi$
$389$	−33.4642	+	17.0509i	−1.69670	+	0.864513i	−0.987138	+	0.159873i	$0.948892\pi$
$390$		0			0
$391$	−15.8019	+	1.24363i	−0.799134	+	0.0628932i
$392$	1.83284	+	5.64091i	0.0925725	+	0.284909i
$393$		0			0
$394$	−15.0238	−	4.88154i	−0.756890	−	0.245928i
$395$	7.35516	+	4.50725i	0.370078	+	0.226784i
$396$		0			0
$397$	34.1208	+	2.68537i	1.71247	+	0.134775i	0.896422	−	0.443203i	$-0.146158\pi$
$397$	34.1208	+	2.68537i	1.71247	+	0.134775i	0.816053	+	0.577977i	$0.196158\pi$
$398$	1.59979	+	6.66362i	0.0801904	+	0.334017i
$399$		0			0
$400$	3.04861	−	4.19605i	0.152431	−	0.209803i
$401$	−9.27216	−	9.27216i	−0.463030	−	0.463030i	0.436618	−	0.899647i	$-0.356176\pi$
$401$	−9.27216	−	9.27216i	−0.463030	−	0.463030i	−0.899647	+	0.436618i	$0.856176\pi$
$402$		0			0
$403$	4.09238	+	3.49523i	0.203856	+	0.174110i
$404$	0.298579	+	0.349591i	0.0148549	+	0.0173928i
$405$		0			0
$406$	6.26061	−	4.54860i	0.310709	−	0.225743i
$407$	0.675291	+	0.279715i	0.0334729	+	0.0138649i
$408$		0			0
$409$		−	15.8476i		−	0.783615i	−0.920047	−	0.391808i	$-0.871850\pi$
$409$		−	15.8476i		−	0.783615i	0.920047	−	0.391808i	$-0.128150\pi$
$410$	13.9557	−	14.9295i	0.689222	−	0.737315i
$411$		0			0
$412$	−7.49182	−	3.81727i	−0.369095	−	0.188064i
$413$	1.13490	−	2.73988i	0.0558446	−	0.134821i
$414$		0			0
$415$	36.4540	+	5.77375i	1.78946	+	0.283422i
$416$	2.31685	−	1.97877i	0.113593	−	0.0970173i
$417$		0			0
$418$	0.00293092	+	0.0185051i	0.000143356	+	0.000905114i
$419$	3.58472	−	3.58472i	0.175125	−	0.175125i	−0.614102	−	0.789227i	$-0.710482\pi$
$419$	3.58472	−	3.58472i	0.175125	−	0.175125i	0.789227	+	0.614102i	$0.210482\pi$
$420$		0			0
$421$	0.625389	−	0.383239i	0.0304796	−	0.0186779i	−0.507175	−	0.861843i	$-0.669310\pi$
$421$	0.625389	−	0.383239i	0.0304796	−	0.0186779i	0.537655	+	0.843165i	$0.319310\pi$
$422$	−20.6977	+	4.96909i	−1.00755	+	0.241891i
$423$		0			0
$424$	5.88464	−	2.43750i	0.285783	−	0.118375i
$425$	−4.90715	+	8.00774i	−0.238032	+	0.388432i
$426$		0			0
$427$	−7.41642	−	1.78052i	−0.358906	−	0.0861656i
$428$	−10.1667	+	3.30336i	−0.491426	+	0.159674i
$429$		0			0
$430$	−5.41452	−	10.6266i	−0.261112	−	0.512460i
$431$	−2.44393	−	4.79648i	−0.117720	−	0.231038i	0.824626	−	0.565678i	$-0.191385\pi$
$431$	−2.44393	−	4.79648i	−0.117720	−	0.231038i	−0.942346	+	0.334640i	$0.891385\pi$
$432$		0			0
$433$	−10.4805	+	3.40531i	−0.503660	+	0.163649i	−0.549817	−	0.835285i	$-0.685302\pi$
$433$	−10.4805	+	3.40531i	−0.503660	+	0.163649i	0.0461572	+	0.998934i	$0.485302\pi$
$434$	1.77565	+	0.426297i	0.0852341	+	0.0204629i
$435$		0			0
$436$	−0.238171	+	0.388660i	−0.0114063	+	0.0186134i
$437$	−0.784452	+	0.324930i	−0.0375254	+	0.0155435i
$438$		0			0
$439$	24.4741	−	5.87572i	1.16809	−	0.280433i	0.397399	−	0.917646i	$-0.369913\pi$
$439$	24.4741	−	5.87572i	1.16809	−	0.280433i	0.770688	+	0.637213i	$0.219913\pi$
$440$	0.525641	−	0.322113i	0.0250590	−	0.0153561i
$441$		0			0
$442$	−3.90119	+	3.90119i	−0.185561	+	0.185561i
$443$	3.92228	+	24.7643i	0.186353	+	1.17659i	0.886548	+	0.462637i	$0.153097\pi$
$443$	3.92228	+	24.7643i	0.186353	+	1.17659i	−0.700195	+	0.713952i	$0.746903\pi$
$444$		0			0
$445$	38.1964	−	32.6228i	1.81068	−	1.54647i
$446$	10.0300	+	1.58859i	0.474933	+	0.0752219i
$447$		0			0
$448$	0.395628	−	0.955131i	0.0186917	−	0.0451257i
$449$	25.4948	+	12.9902i	1.20317	+	0.613047i	0.936475	−	0.350734i	$-0.114068\pi$
$449$	25.4948	+	12.9902i	1.20317	+	0.613047i	0.266697	+	0.963780i	$0.414068\pi$
$450$		0			0
$451$	1.12606	−	0.511536i	0.0530241	−	0.0240873i
$452$			6.73215i			0.316654i
$453$		0			0
$454$	−8.06271	−	3.33969i	−0.378402	−	0.156739i
$455$	8.13339	−	5.90925i	0.381299	−	0.277030i
$456$		0			0
$457$	13.2037	+	15.4596i	0.617645	+	0.723169i	0.977757	−	0.209740i	$-0.0672617\pi$
$457$	13.2037	+	15.4596i	0.617645	+	0.723169i	−0.360112	+	0.932909i	$0.617262\pi$
$458$	2.27118	+	1.93977i	0.106125	+	0.0906397i
$459$		0			0
$460$	19.7555	+	19.7555i	0.921104	+	0.921104i
$461$	15.3676	−	21.1517i	0.715739	−	0.985131i	−0.283915	−	0.958849i	$-0.591633\pi$
$461$	15.3676	−	21.1517i	0.715739	−	0.985131i	0.999655	−	0.0262814i	$-0.00836658\pi$
$462$		0			0
$463$	1.54080	+	6.41787i	0.0716068	+	0.298264i	0.996669	−	0.0815515i	$-0.0259875\pi$
$463$	1.54080	+	6.41787i	0.0716068	+	0.298264i	−0.925062	+	0.379815i	$0.875988\pi$
$464$	7.46227	+	0.587293i	0.346427	+	0.0272644i
$465$		0			0
$466$	−3.33452	−	2.04340i	−0.154469	−	0.0946586i
$467$	−9.67732	−	3.14435i	−0.447813	−	0.145503i	0.0764246	−	0.997075i	$-0.475650\pi$
$467$	−9.67732	−	3.14435i	−0.447813	−	0.145503i	−0.524237	+	0.851572i	$0.675650\pi$
$468$		0			0
$469$	−0.939179	−	2.89049i	−0.0433672	−	0.133471i
$470$	−31.8163	+	2.50399i	−1.46757	+	0.115501i
$471$		0			0
$472$	2.55593	−	1.30231i	0.117646	−	0.0599438i
$473$	−0.0566306	−	0.719559i	−0.00260388	−	0.0330854i
$474$		0			0
$475$	−0.117444	+	0.489190i	−0.00538871	+	0.0224456i
$476$	−0.578483	+	1.78039i	−0.0265147	+	0.0816040i
$477$		0			0
$478$	−11.1259	−	26.8602i	−0.508885	−	1.22856i
$479$	−0.762773	+	9.69194i	−0.0348520	+	0.442836i	0.954592	+	0.297918i	$0.0962921\pi$
$479$	−0.762773	+	9.69194i	−0.0348520	+	0.442836i	−0.989444	+	0.144919i	$0.953708\pi$
$480$		0			0
$481$	6.02426	+	9.83070i	0.274683	+	0.448241i
$482$	22.6029	+	16.4219i	1.02953	+	0.747999i
$483$		0			0
$484$	−10.8277	+	1.71494i	−0.492169	+	0.0779519i
$485$	0.343125	−	0.401748i	0.0155805	−	0.0182424i
$486$		0			0
$487$	0.129469	−	0.817433i	0.00586679	−	0.0370414i	−0.984581	−	0.174928i	$-0.944031\pi$
$487$	0.129469	−	0.817433i	0.00586679	−	0.0370414i	0.990448	+	0.137886i	$0.0440308\pi$
$488$	−4.33644	−	5.96860i	−0.196302	−	0.270186i
$489$		0			0
$490$	−8.59418	+	16.8670i	−0.388245	+	0.761974i
$491$	2.11859			0.0956107			0.0478053	−	0.998857i	$-0.484777\pi$
$491$	2.11859			0.0956107			0.0478053	+	0.998857i	$0.484777\pi$
$492$		0			0
$493$	−13.5542			−0.610449
$494$	−0.134172	+	0.263327i	−0.00603667	+	0.0118476i
$495$		0			0
$496$	1.03824	+	1.42902i	0.0466184	+	0.0641647i
$497$	−1.36557	+	8.62187i	−0.0612542	+	0.386744i
$498$		0			0
$499$	−17.7288	+	20.7577i	−0.793649	+	0.929244i	−0.998775	−	0.0494916i	$-0.984240\pi$
$499$	−17.7288	+	20.7577i	−0.793649	+	0.929244i	0.205125	+	0.978736i	$0.434240\pi$
$500$	0.588246	−	0.0931690i	0.0263072	−	0.00416665i
$501$		0			0
$502$	−0.208988	−	0.151839i	−0.00932761	−	0.00677690i
$503$	−19.2139	−	31.3543i	−0.856706	−	1.39802i	−0.916597	−	0.399812i	$-0.869075\pi$
$503$	−19.2139	−	31.3543i	−0.856706	−	1.39802i	0.0598908	−	0.998205i	$-0.480925\pi$
$504$		0			0
$505$	−0.115126	+	1.46281i	−0.00512304	+	0.0650944i
$506$	0.647048	+	1.56211i	0.0287648	+	0.0694443i
$507$		0			0
$508$	−0.380441	+	1.17088i	−0.0168793	+	0.0519493i
$509$	6.30348	−	26.2559i	0.279397	−	1.16377i	−0.639347	−	0.768918i	$-0.720795\pi$
$509$	6.30348	−	26.2559i	0.279397	−	1.16377i	0.918744	−	0.394853i	$-0.129205\pi$
$510$		0			0
$511$	−0.538251	−	6.83913i	−0.0238108	−	0.302545i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$		0			0
$514$	−24.1160	+	1.89797i	−1.06371	+	0.0837161i
$515$	−8.29285	−	25.5228i	−0.365426	−	1.12467i
$516$		0			0
$517$	−1.83692	−	0.596852i	−0.0807877	−	0.0262495i
$518$	3.33565	+	2.04409i	0.146560	+	0.0898121i
$519$		0			0
$520$	9.69450	+	0.762974i	0.425132	+	0.0334586i
$521$	−5.43119	−	22.6225i	−0.237945	−	0.991111i	−0.955589	−	0.294702i	$-0.904780\pi$
$521$	−5.43119	−	22.6225i	−0.237945	−	0.991111i	0.717645	−	0.696410i	$-0.245220\pi$
$522$		0			0
$523$	−17.3700	+	23.9078i	−0.759539	+	1.04542i	0.237714	+	0.971335i	$0.423602\pi$
$523$	−17.3700	+	23.9078i	−0.759539	+	1.04542i	−0.997252	+	0.0740801i	$0.976398\pi$
$524$	−5.79079	−	5.79079i	−0.252972	−	0.252972i
$525$		0			0
$526$	14.5914	+	12.4622i	0.636214	+	0.543378i
$527$	−2.07723	−	2.43212i	−0.0904856	−	0.105945i
$528$		0			0
$529$	−43.3843	+	31.5205i	−1.88627	+	1.37046i
$530$	18.7817	+	7.77963i	0.815825	+	0.337926i
$531$		0			0
$532$			0.100279i			0.00434765i
$533$	19.1130	+	3.91260i	0.827877	+	0.169473i
$534$		0			0
$535$	−30.3997	−	15.4894i	−1.31429	−	0.669666i
$536$	1.12501	−	2.71602i	0.0485932	−	0.117314i
$537$		0			0
$538$	0.632346	+	0.100154i	0.0272624	+	0.00431793i
$539$	−0.871158	+	0.744039i	−0.0375234	+	0.0320480i
$540$		0			0
$541$	3.64465	+	23.0114i	0.156696	+	0.989337i	0.933234	+	0.359268i	$0.116974\pi$
$541$	3.64465	+	23.0114i	0.156696	+	0.989337i	−0.776539	+	0.630069i	$0.783026\pi$
$542$	−13.2649	+	13.2649i	−0.569775	+	0.569775i
$543$		0			0
$544$	−1.54393	+	0.946119i	−0.0661953	+	0.0405645i
$545$	−1.41465	+	0.339628i	−0.0605971	+	0.0145481i
$546$		0			0
$547$	−18.1894	+	7.53430i	−0.777723	+	0.322143i	−0.735996	−	0.676986i	$-0.763286\pi$
$547$	−18.1894	+	7.53430i	−0.777723	+	0.322143i	−0.0417266	+	0.999129i	$0.513286\pi$
$548$	3.51139	−	5.73007i	0.149999	−	0.244776i
$549$		0			0
$550$	0.974145	+	0.233871i	0.0415377	+	0.00997231i
$551$	−0.690527	+	0.224366i	−0.0294174	+	0.00955831i
$552$		0			0
$553$	1.26855	+	2.48966i	0.0539441	+	0.105871i
$554$	−14.2135	−	27.8956i	−0.603874	−	1.18517i
$555$		0			0
$556$	17.6476	−	5.73405i	0.748425	−	0.243178i
$557$	2.71149	+	0.650970i	0.114889	+	0.0275825i	0.290482	−	0.956880i	$-0.406184\pi$
$557$	2.71149	+	0.650970i	0.114889	+	0.0275825i	−0.175593	+	0.984463i	$0.556184\pi$
$558$		0			0
$559$	5.94888	−	9.70769i	0.251611	−	0.410592i
$560$	3.04844	−	1.26271i	0.128820	−	0.0533590i
$561$		0			0
$562$	17.7445	−	4.26008i	0.748508	−	0.179701i
$563$	−39.6018	+	24.2680i	−1.66902	+	1.02277i	−0.727325	+	0.686293i	$0.759237\pi$
$563$	−39.6018	+	24.2680i	−1.66902	+	1.02277i	−0.941690	+	0.336481i	$0.890763\pi$
$564$		0			0
$565$	−15.1933	+	15.1933i	−0.639189	+	0.639189i
$566$	−1.85352	−	11.7026i	−0.0779091	−	0.491899i
$567$		0			0
$568$	−6.42066	+	5.48376i	−0.269405	+	0.230094i
$569$	31.3769	+	4.96961i	1.31539	+	0.208337i	0.774401	−	0.632695i	$-0.218051\pi$
$569$	31.3769	+	4.96961i	1.31539	+	0.208337i	0.540986	+	0.841032i	$0.318051\pi$
$570$		0			0
$571$	14.2005	−	34.2831i	0.594274	−	1.43470i	−0.285066	−	0.958508i	$-0.592015\pi$
$571$	14.2005	−	34.2831i	0.594274	−	1.43470i	0.879339	−	0.476196i	$-0.157985\pi$
$572$	0.524374	+	0.267182i	0.0219252	+	0.0111714i
$573$		0			0
$574$	6.38109	−	1.76135i	0.266342	−	0.0735173i
$575$			45.4016i			1.89338i
$576$		0			0
$577$	−37.8707	−	15.6866i	−1.57658	−	0.653040i	−0.588711	−	0.808343i	$-0.700364\pi$
$577$	−37.8707	−	15.6866i	−1.57658	−	0.653040i	−0.987867	+	0.155303i	$0.950364\pi$
$578$	−11.1006	+	8.06509i	−0.461726	+	0.335463i
$579$		0			0
$580$	15.5157	+	18.1665i	0.644254	+	0.754324i
$581$	9.09083	+	7.76430i	0.377151	+	0.322118i
$582$		0			0
$583$	0.869958	+	0.869958i	0.0360300	+	0.0360300i
$584$	3.90044	−	5.36849i	0.161401	−	0.222150i
$585$		0			0
$586$	−5.49140	−	22.8733i	−0.226847	−	0.944888i
$587$	−15.3447	−	1.20765i	−0.633342	−	0.0498451i	−0.242276	−	0.970207i	$-0.577894\pi$
$587$	−15.3447	−	1.20765i	−0.633342	−	0.0498451i	−0.391067	+	0.920362i	$0.627894\pi$
$588$		0			0
$589$	−0.146086	−	0.0895215i	−0.00601936	−	0.00368867i
$590$	8.70743	+	2.82921i	0.358479	+	0.116477i
$591$		0			0
$592$	1.16936	+	3.59893i	0.0480605	+	0.147915i
$593$	4.43759	−	0.349246i	0.182230	−	0.0143418i	0.0129843	−	0.999916i	$-0.495867\pi$
$593$	4.43759	−	0.349246i	0.182230	−	0.0143418i	0.169246	+	0.985574i	$0.445867\pi$
$594$		0			0
$595$	−5.32358	+	2.71250i	−0.218246	+	0.111202i
$596$	−0.190560	−	2.42129i	−0.00780563	−	0.0991799i
$597$		0			0
$598$	−6.22622	+	25.9341i	−0.254609	+	1.06052i
$599$	−12.7242	+	39.1611i	−0.519898	+	1.60008i	0.254292	+	0.967127i	$0.418158\pi$
$599$	−12.7242	+	39.1611i	−0.519898	+	1.60008i	−0.774190	+	0.632954i	$0.781842\pi$
$600$		0			0
$601$	11.3018	+	27.2849i	0.461008	+	1.11297i	0.967984	+	0.251012i	$0.0807633\pi$
$601$	11.3018	+	27.2849i	0.461008	+	1.11297i	−0.506976	+	0.861960i	$0.669237\pi$
$602$	0.303103	−	3.85128i	0.0123535	−	0.156967i
$603$		0			0
$604$	−6.42964	−	10.4922i	−0.261618	−	0.426922i
$605$	−28.3067	−	20.5660i	−1.15083	−	0.836128i
$606$		0			0
$607$	−37.4339	+	5.92895i	−1.51940	+	0.240649i	−0.859667	−	0.510855i	$-0.829329\pi$
$607$	−37.4339	+	5.92895i	−1.51940	+	0.240649i	−0.659729	+	0.751504i	$0.729329\pi$
$608$	−0.0629952	+	0.0737579i	−0.00255479	+	0.00299128i
$609$		0			0
$610$	3.68351	−	23.2568i	0.149141	−	0.941640i
$611$	−17.9079	−	24.6482i	−0.724477	−	0.997158i
$612$		0			0
$613$	−14.4487	+	28.3572i	−0.583579	+	1.14534i	0.390811	+	0.920471i	$0.372195\pi$
$613$	−14.4487	+	28.3572i	−0.583579	+	1.14534i	−0.974390	+	0.224866i	$0.927805\pi$
$614$	2.05818			0.0830613
$615$		0			0
$616$	0.199690			0.00804574
$617$	2.10922	−	4.13959i	0.0849142	−	0.166653i	−0.844645	−	0.535328i	$-0.820188\pi$
$617$	2.10922	−	4.13959i	0.0849142	−	0.166653i	0.929559	+	0.368674i	$0.120188\pi$
$618$		0			0
$619$	−21.4091	−	29.4671i	−0.860504	−	1.18438i	−0.981449	−	0.191723i	$-0.938593\pi$
$619$	−21.4091	−	29.4671i	−0.860504	−	1.18438i	0.120946	−	0.992659i	$-0.461407\pi$
$620$	−0.881914	+	5.56819i	−0.0354185	+	0.223624i
$621$		0			0
$622$	−17.3544	+	20.3194i	−0.695849	+	0.814735i
$623$	16.0705	−	2.54532i	0.643851	−	0.101976i
$624$		0			0
$625$	−19.4424	−	14.1257i	−0.777697	−	0.565030i
$626$	0.978527	+	1.59681i	0.0391098	+	0.0638214i
$627$		0			0
$628$	−1.49406	+	18.9839i	−0.0596197	+	0.757540i
$629$	−2.62221	−	6.33058i	−0.104554	−	0.252417i
$630$		0			0
$631$	1.90239	−	5.85496i	0.0757330	−	0.233082i	−0.906023	−	0.423229i	$-0.860896\pi$
$631$	1.90239	−	5.85496i	0.0757330	−	0.233082i	0.981756	+	0.190147i	$0.0608965\pi$
$632$	−0.630953	+	2.62811i	−0.0250980	+	0.104541i
$633$		0			0
$634$	1.71644	+	21.8095i	0.0681686	+	0.866165i
$635$	−3.50107	+	1.78388i	−0.138936	+	0.0707912i
$636$		0			0
$637$	−18.0158	+	1.41787i	−0.713812	+	0.0561782i
$638$	0.446789	+	1.37508i	0.0176886	+	0.0544398i
$639$		0			0
$640$	3.03544	+	0.986273i	0.119986	+	0.0389859i
$641$	19.0098	+	11.6492i	0.750842	+	0.460117i	0.844546	−	0.535484i	$-0.179871\pi$
$641$	19.0098	+	11.6492i	0.750842	+	0.460117i	−0.0937037	+	0.995600i	$0.529871\pi$
$642$		0			0
$643$	0.00489964		0.000385610i	0.000193223		1.52070e-5i	0.0785557	−	0.996910i	$-0.474969\pi$
$643$	0.00489964		0.000385610i	0.000193223		1.52070e-5i	−0.0783625	+	0.996925i	$0.524969\pi$
$644$	2.11262	+	8.79968i	0.0832488	+	0.346756i
$645$		0			0
$646$	0.103239	−	0.142096i	0.00406187	−	0.00559069i
$647$	31.9459	+	31.9459i	1.25592	+	1.25592i	0.953023	+	0.302898i	$0.0979542\pi$
$647$	31.9459	+	31.9459i	1.25592	+	1.25592i	0.302898	+	0.953023i	$0.402046\pi$
$648$		0			0
$649$	0.421331	+	0.359850i	0.0165387	+	0.0141254i
$650$	10.2631	+	12.0166i	0.402552	+	0.471328i
$651$		0			0
$652$	16.2573	−	11.8116i	0.636686	−	0.462580i
$653$	12.4805	+	5.16959i	0.488400	+	0.202302i	0.613273	−	0.789871i	$-0.289853\pi$
$653$	12.4805	+	5.16959i	0.488400	+	0.202302i	−0.124874	+	0.992173i	$0.539853\pi$
$654$		0			0
$655$		−	26.1377i		−	1.02128i
$656$	5.79993	+	2.71307i	0.226449	+	0.105928i
$657$		0			0
$658$	−9.21094	−	4.69321i	−0.359080	−	0.182960i
$659$	−0.987660	+	2.38442i	−0.0384738	+	0.0928839i	−0.941948	−	0.335758i	$-0.891008\pi$
$659$	−0.987660	+	2.38442i	−0.0384738	+	0.0928839i	0.903475	+	0.428642i	$0.141008\pi$
$660$		0			0
$661$	1.68479	+	0.266844i	0.0655307	+	0.0103790i	0.189114	−	0.981955i	$-0.439439\pi$
$661$	1.68479	+	0.266844i	0.0655307	+	0.0103790i	−0.123583	+	0.992334i	$0.539439\pi$
$662$	−17.4385	+	14.8939i	−0.677768	+	0.578869i
$663$		0			0
$664$	1.80902	+	11.4217i	0.0702035	+	0.443248i
$665$	−0.226313	+	0.226313i	−0.00877605	+	0.00877605i
$666$		0			0
$667$	−55.8683	+	34.2361i	−2.16323	+	1.32563i
$668$	5.62039	−	1.34934i	0.217459	−	0.0522074i
$669$		0			0
$670$	8.66859	−	3.59065i	0.334897	−	0.138719i
$671$	0.744576	−	1.21504i	0.0287440	−	0.0469060i
$672$		0			0
$673$	4.09277	+	0.982588i	0.157765	+	0.0378760i	0.311558	−	0.950227i	$-0.399149\pi$
$673$	4.09277	+	0.982588i	0.157765	+	0.0378760i	−0.153794	+	0.988103i	$0.549149\pi$
$674$	−8.94702	+	2.90706i	−0.344626	+	0.111976i
$675$		0			0
$676$	−1.68734	−	3.31159i	−0.0648977	−	0.127369i
$677$	10.2797	+	20.1751i	0.395082	+	0.775392i	0.999778	−	0.0210644i	$-0.00670549\pi$
$677$	10.2797	+	20.1751i	0.395082	+	0.775392i	−0.604696	+	0.796456i	$0.706705\pi$
$678$		0			0
$679$	0.162760	−	0.0528839i	0.00624615	−	0.00202950i
$680$	−5.61962	−	1.34915i	−0.215503	−	0.0517376i
$681$		0			0
$682$	−0.178268	+	0.290907i	−0.00682623	+	0.0111394i
$683$	−12.7371	+	5.27587i	−0.487371	+	0.201876i	−0.612817	−	0.790225i	$-0.709964\pi$
$683$	−12.7371	+	5.27587i	−0.487371	+	0.201876i	0.125446	+	0.992100i	$0.459964\pi$
$684$		0			0
$685$	20.8564	−	5.00719i	0.796884	−	0.191315i
$686$	−11.3986	+	6.98508i	−0.435201	+	0.266692i
$687$		0			0
$688$	2.64231	−	2.64231i	0.100737	−	0.100737i
$689$	3.03591	+	19.1680i	0.115659	+	0.730241i
$690$		0			0
$691$	26.9222	−	22.9938i	1.02417	−	0.874724i	0.0319841	−	0.999488i	$-0.489817\pi$
$691$	26.9222	−	22.9938i	1.02417	−	0.874724i	0.992186	+	0.124764i	$0.0398174\pi$
$692$	−2.15773	−	0.341751i	−0.0820245	−	0.0129914i
$693$		0			0
$694$	10.8143	−	26.1081i	0.410507	−	0.991051i
$695$	52.7685	+	26.8869i	2.00162	+	1.01988i
$696$		0			0
$697$	−10.8554	−	4.07358i	−0.411176	−	0.154298i
$698$			12.8675i			0.487044i
$699$		0			0
$700$	4.95389	+	2.05197i	0.187239	+	0.0775571i
$701$	8.87847	−	6.45059i	0.335335	−	0.243635i	−0.407356	−	0.913270i	$-0.633549\pi$
$701$	8.87847	−	6.45059i	0.335335	−	0.243635i	0.742691	+	0.669634i	$0.233549\pi$
$702$		0			0
$703$	−0.238382	−	0.279110i	−0.00899077	−	0.0105268i
$704$	0.146877	+	0.125445i	0.00553564	+	0.00472788i
$705$		0			0
$706$	24.5356	+	24.5356i	0.923410	+	0.923410i
$707$	−0.279371	+	0.384521i	−0.0105068	+	0.0144614i
$708$		0			0
$709$	3.76643	+	15.6883i	0.141451	+	0.589187i	0.997396	+	0.0721194i	$0.0229763\pi$
$709$	3.76643	+	15.6883i	0.141451	+	0.589187i	−0.855945	+	0.517067i	$0.827024\pi$
$710$	−26.8663	−	2.11442i	−1.00827	−	0.0793529i
$711$		0			0
$712$	13.4192	+	8.22332i	0.502907	+	0.308182i
$713$	−14.7053	−	4.77804i	−0.550717	−	0.178939i
$714$		0			0
$715$	0.580440	+	1.78641i	0.0217072	+	0.0668080i
$716$	19.7461	−	1.55405i	0.737945	−	0.0580775i
$717$		0			0
$718$	18.8672	−	9.61334i	0.704119	−	0.358767i
$719$	−1.42125	−	18.0587i	−0.0530038	−	0.673477i	−0.964826	−	0.262891i	$-0.915324\pi$
$719$	−1.42125	−	18.0587i	−0.0530038	−	0.673477i	0.911822	−	0.410586i	$-0.134676\pi$
$720$		0			0
$721$	2.02927	−	8.45251i	0.0755739	−	0.314788i
$722$	−5.86842	+	18.0611i	−0.218400	+	0.672165i
$723$		0			0
$724$	−6.91885	−	16.7036i	−0.257137	−	0.620783i
$725$	−3.04606	+	38.7038i	−0.113128	+	1.43742i
$726$		0			0
$727$	−19.7300	−	32.1964i	−0.731745	−	1.19410i	−0.974582	−	0.224032i	$-0.928078\pi$
$727$	−19.7300	−	32.1964i	−0.731745	−	1.19410i	0.242836	−	0.970067i	$-0.421922\pi$
$728$	2.54834	+	1.85147i	0.0944476	+	0.0686202i
$729$		0			0
$730$	20.9184	−	3.31315i	0.774226	−	0.122625i
$731$	−4.39445	+	5.14524i	−0.162534	+	0.190303i
$732$		0			0
$733$	2.15648	−	13.6155i	0.0796513	−	0.502899i	−0.915319	−	0.402729i	$-0.868062\pi$
$733$	2.15648	−	13.6155i	0.0796513	−	0.502899i	0.994970	−	0.100169i	$-0.0319385\pi$
$734$	16.7863	+	23.1044i	0.619594	+	0.852798i
$735$		0			0
$736$	−3.97406	+	7.79954i	−0.146486	+	0.287495i
$737$	0.567841			0.0209167
$738$		0			0
$739$	32.9738			1.21296			0.606481	−	0.795098i	$-0.292581\pi$
$739$	32.9738			1.21296			0.606481	+	0.795098i	$0.292581\pi$
$740$	−5.48313	+	10.7613i	−0.201564	+	0.395591i
$741$		0			0
$742$	3.87053	+	5.32733i	0.142092	+	0.195573i
$743$	−0.962172	+	6.07491i	−0.0352987	+	0.222867i	−0.999031	−	0.0440022i	$-0.985989\pi$
$743$	−0.962172	+	6.07491i	−0.0352987	+	0.222867i	0.963733	+	0.266869i	$0.0859891\pi$
$744$		0			0
$745$	5.03439	−	5.89451i	0.184446	−	0.215958i
$746$	25.6939	−	4.06952i	0.940722	−	0.148996i
$747$		0			0
$748$	−0.282961	−	0.205583i	−0.0103461	−	0.00751688i
$749$	−5.77440	−	9.42296i	−0.210992	−	0.344307i
$750$		0			0
$751$	0.0299838	−	0.380981i	0.00109413	−	0.0139022i	−0.996346	−	0.0854083i	$-0.972781\pi$
$751$	0.0299838	−	0.380981i	0.00109413	−	0.0139022i	0.997440	+	0.0715061i	$0.0227805\pi$
$752$	−3.82662	−	9.23827i	−0.139542	−	0.336885i
$753$		0			0
$754$	−7.04767	+	21.6905i	−0.256661	+	0.789921i
$755$	9.16857	−	38.1898i	0.333678	−	1.38987i
$756$		0			0
$757$	−3.79660	−	48.2403i	−0.137990	−	1.75332i	−0.543660	−	0.839305i	$-0.682962\pi$
$757$	−3.79660	−	48.2403i	−0.137990	−	1.75332i	0.405671	−	0.914019i	$-0.367038\pi$
$758$	4.87089	−	2.48184i	0.176919	−	0.0901446i
$759$		0			0
$760$	−0.308629	+	0.0242896i	−0.0111952	+	0.000881077i
$761$	−5.72042	−	17.6057i	−0.207365	−	0.638205i	−0.999608	−	0.0279985i	$-0.991087\pi$
$761$	−5.72042	−	17.6057i	−0.207365	−	0.638205i	0.792243	−	0.610206i	$-0.208913\pi$
$762$		0			0
$763$	−0.448185	−	0.145624i	−0.0162254	−	0.00527195i
$764$	−12.0656	−	7.39378i	−0.436516	−	0.267498i
$765$		0			0
$766$	6.43285	+	0.506276i	0.232428	+	0.0182925i
$767$	2.04035	+	8.49869i	0.0736729	+	0.306870i
$768$		0			0
$769$	0.809111	−	1.11365i	0.0291773	−	0.0401591i	−0.794179	−	0.607684i	$-0.792099\pi$
$769$	0.809111	−	1.11365i	0.0291773	−	0.0401591i	0.823356	+	0.567525i	$0.192099\pi$
$770$	0.450667	+	0.450667i	0.0162409	+	0.0162409i
$771$		0			0
$772$	0.843504	+	0.720421i	0.0303584	+	0.0259285i
$773$	19.8106	+	23.1953i	0.712539	+	0.834276i	0.992047	−	0.125868i	$-0.0401715\pi$
$773$	19.8106	+	23.1953i	0.712539	+	0.834276i	−0.279508	+	0.960143i	$0.590171\pi$
$774$		0			0
$775$	−7.41174	+	5.38494i	−0.266238	+	0.193433i
$776$	0.152936	+	0.0633480i	0.00549007	+	0.00227406i
$777$		0			0
$778$		−	37.5578i		−	1.34651i
$779$	−0.620466	−	0.0278399i	−0.0222305	−	0.000997468i
$780$		0			0
$781$	−1.45319	−	0.740439i	−0.0519994	−	0.0264950i
$782$	6.06581	−	14.6442i	0.216913	−	0.523674i
$783$		0			0
$784$	−5.85818	−	0.927845i	−0.209221	−	0.0331373i
$785$	−46.2154	+	39.4717i	−1.64950	+	1.40880i
$786$		0			0
$787$	−2.76527	−	17.4592i	−0.0985712	−	0.622354i	−0.986674	−	0.162709i	$-0.947977\pi$
$787$	−2.76527	−	17.4592i	−0.0985712	−	0.622354i	0.888103	−	0.459645i	$-0.152023\pi$
$788$	11.1702	−	11.1702i	0.397921	−	0.397921i
$789$		0			0
$790$	−7.35516	+	4.50725i	−0.261685	+	0.160361i
$791$	−6.76757	+	1.62475i	−0.240627	+	0.0577695i
$792$		0			0
$793$	20.7674	−	8.60213i	0.737472	−	0.305471i
$794$	−17.8832	+	29.1827i	−0.634651	+	1.03566i
$795$		0			0
$796$	−6.66362	−	1.59979i	−0.236186	−	0.0567032i
$797$	−17.7740	+	5.77513i	−0.629588	+	0.204566i	−0.606393	−	0.795165i	$-0.707384\pi$
$797$	−17.7740	+	5.77513i	−0.629588	+	0.204566i	−0.0231956	+	0.999731i	$0.507384\pi$
$798$		0			0
$799$	8.22021	+	16.1331i	0.290810	+	0.570747i
$800$	2.35467	+	4.62130i	0.0832501	+	0.163388i
$801$		0			0
$802$	12.4710	−	4.05208i	0.440367	−	0.143084i
$803$	1.24633	+	0.299218i	0.0439822	+	0.0105592i
$804$		0			0
$805$	−15.0916	+	24.6273i	−0.531909	+	0.867997i
$806$	−4.97217	+	2.05954i	−0.175137	+	0.0725442i
$807$		0			0
$808$	−0.447040	+	0.107325i	−0.0157268	+	0.00377568i
$809$	−14.3790	+	8.81145i	−0.505538	+	0.309794i	−0.751780	−	0.659414i	$-0.770804\pi$
$809$	−14.3790	+	8.81145i	−0.505538	+	0.309794i	0.246242	+	0.969208i	$0.420804\pi$
$810$		0			0
$811$	−26.8765	+	26.8765i	−0.943762	+	0.943762i	−0.998501	−	0.0547386i	$-0.982567\pi$
$811$	−26.8765	+	26.8765i	−0.943762	+	0.943762i	0.0547386	+	0.998501i	$0.482567\pi$
$812$	1.21057	+	7.64327i	0.0424828	+	0.268226i
$813$		0			0
$814$	−0.555804	+	0.474701i	−0.0194809	+	0.0166383i
$815$	63.3470	+	10.0332i	2.21895	+	0.351447i
$816$		0			0
$817$	−0.138708	+	0.334871i	−0.00485278	+	0.0117156i
$818$	14.1203	+	7.19468i	0.493706	+	0.251556i
$819$		0			0
$820$	6.96653	+	19.2125i	0.243282	+	0.670928i
$821$		−	5.77958i		−	0.201709i	−0.994901	−	0.100854i	$-0.967842\pi$
$821$		−	5.77958i		−	0.201709i	0.994901	−	0.100854i	$-0.0321576\pi$
$822$		0			0
$823$	1.75197	+	0.725689i	0.0610697	+	0.0252959i	0.413009	−	0.910727i	$-0.364478\pi$
$823$	1.75197	+	0.725689i	0.0610697	+	0.0252959i	−0.351939	+	0.936023i	$0.614478\pi$
$824$	6.80243	−	4.94225i	0.236974	−	0.172172i
$825$		0			0
$826$	1.92602	+	2.25508i	0.0670148	+	0.0784643i
$827$	−32.5026	−	27.7598i	−1.13023	−	0.965304i	−0.130568	−	0.991439i	$-0.541680\pi$
$827$	−32.5026	−	27.7598i	−1.13023	−	0.965304i	−0.999658	+	0.0261352i	$0.991680\pi$
$828$		0			0
$829$	9.00340	+	9.00340i	0.312701	+	0.312701i	0.845955	−	0.533254i	$-0.179031\pi$
$829$	9.00340	+	9.00340i	0.312701	+	0.312701i	−0.533254	+	0.845955i	$0.679031\pi$
$830$	−21.6942	+	29.8595i	−0.753017	+	1.03644i
$831$		0			0
$832$	0.711274	+	2.96267i	0.0246590	+	0.102712i
$833$	10.7069	+	0.842650i	0.370971	+	0.0291961i
$834$		0			0
$835$	15.7295	+	9.63906i	0.544342	+	0.333573i
$836$	−0.0178188	−	0.00578967i	−0.000616275	−	0.000200240i
$837$		0			0
$838$	1.56658	+	4.82144i	0.0541166	+	0.166554i
$839$	38.9567	−	3.06596i	1.34494	−	0.105849i	0.614547	−	0.788880i	$-0.289339\pi$
$839$	38.9567	−	3.06596i	1.34494	−	0.105849i	0.730389	+	0.683031i	$0.239339\pi$
$840$		0			0
$841$	−24.0842	+	12.2715i	−0.830490	+	0.423156i
$842$	0.0575477	+	0.731212i	0.00198322	+	0.0251992i
$843$		0			0
$844$	4.96909	−	20.6977i	0.171043	−	0.712446i
$845$	3.66567	−	11.2818i	0.126103	−	0.388105i
$846$		0			0
$847$	−4.33715	−	10.4708i	−0.149026	−	0.359781i
$848$	−0.499744	+	6.34985i	−0.0171613	+	0.218055i
$849$		0			0
$850$	−4.90715	−	8.00774i	−0.168314	−	0.274663i
$851$	−26.7986	−	19.4704i	−0.918645	−	0.667435i
$852$		0			0
$853$	16.7011	−	2.64520i	0.571836	−	0.0905699i	0.136181	−	0.990684i	$-0.456517\pi$
$853$	16.7011	−	2.64520i	0.571836	−	0.0905699i	0.435654	+	0.900114i	$0.356517\pi$
$854$	4.95344	−	5.79973i	0.169503	−	0.198463i
$855$		0			0
$856$	1.67227	−	10.5583i	0.0571570	−	0.360875i
$857$	−23.7616	−	32.7050i	−0.811681	−	1.11718i	−0.991062	−	0.133403i	$-0.957410\pi$
$857$	−23.7616	−	32.7050i	−0.811681	−	1.11718i	0.179381	−	0.983780i	$-0.442590\pi$
$858$		0			0
$859$	5.27974	−	10.3621i	0.180142	−	0.353549i	−0.783223	−	0.621740i	$-0.786426\pi$
$859$	5.27974	−	10.3621i	0.180142	−	0.353549i	0.963366	+	0.268191i	$0.0864259\pi$
$860$	11.9265			0.406691
$861$		0			0
$862$	5.38321			0.183353
$863$	−0.895650	+	1.75781i	−0.0304883	+	0.0598366i	−0.905748	−	0.423816i	$-0.860690\pi$
$863$	−0.895650	+	1.75781i	−0.0304883	+	0.0598366i	0.875260	+	0.483653i	$0.160690\pi$
$864$		0			0
$865$	−4.09836	−	5.64091i	−0.139349	−	0.191797i
$866$	1.72388	−	10.8842i	0.0585799	−	0.369859i
$867$		0			0
$868$	−1.18596	+	1.38858i	−0.0402542	+	0.0471316i
$869$	−0.515633	+	0.0816682i	−0.0174916	+	0.00277040i
$870$		0			0
$871$	7.24648	+	5.26488i	0.245538	+	0.178394i
$872$	−0.238171	−	0.388660i	−0.00806549	−	0.0131617i
$873$		0			0
$874$	0.0666184	−	0.846467i	0.00225340	−	0.0286322i
$875$	0.235628	+	0.568856i	0.00796567	+	0.0192308i
$876$		0			0
$877$	−2.63522	+	8.11039i	−0.0889852	+	0.273868i	−0.985640	−	0.168863i	$-0.945990\pi$
$877$	−2.63522	+	8.11039i	−0.0889852	+	0.273868i	0.896654	+	0.442731i	$0.145990\pi$
$878$	−5.87572	+	24.4741i	−0.198296	+	0.825963i
$879$		0			0
$880$	0.0483690	+	0.614586i	0.00163052	+	0.0207177i
$881$	15.0967	−	7.69216i	0.508622	−	0.259156i	−0.180795	−	0.983521i	$-0.557867\pi$
$881$	15.0967	−	7.69216i	0.508622	−	0.259156i	0.689416	+	0.724365i	$0.257867\pi$
$882$		0			0
$883$	−51.1111	+	4.02253i	−1.72003	+	0.135369i	−0.899695	−	0.436519i	$-0.856211\pi$
$883$	−51.1111	+	4.02253i	−1.72003	+	0.135369i	−0.820332	+	0.571888i	$0.806211\pi$
$884$	−1.70488	−	5.24709i	−0.0573414	−	0.176479i
$885$		0			0
$886$	−23.8459	−	7.74799i	−0.801117	−	0.260299i
$887$	47.8878	+	29.3457i	1.60791	+	0.985331i	0.977984	+	0.208680i	$0.0669167\pi$
$887$	47.8878	+	29.3457i	1.60791	+	0.985331i	0.629931	+	0.776651i	$0.283083\pi$
$888$		0			0
$889$	−1.26885	−	0.0998609i	−0.0425560	−	0.00334923i
$890$	11.7263	+	48.8437i	0.393068	+	1.63724i
$891$		0			0
$892$	−5.96895	+	8.21556i	−0.199855	+	0.275077i
$893$	0.685840	+	0.685840i	0.0229508	+	0.0229508i
$894$		0			0
$895$	48.0708	+	41.0564i	1.60683	+	1.37236i
$896$	0.671416	+	0.786128i	0.0224304	+	0.0262627i
$897$		0			0
$898$	−23.1488	+	16.8186i	−0.772484	+	0.561243i
$899$	−12.2154	−	5.05977i	−0.407405	−	0.168753i
$900$		0			0
$901$		−	11.5336i		−	0.384240i
$902$	−0.0554387	+	1.23556i	−0.00184591	+	0.0411397i
$903$		0			0
$904$	−5.99839	−	3.05633i	−0.199503	−	0.101652i
$905$	22.0825	−	53.3119i	0.734047	−	1.77215i
$906$		0			0
$907$	−22.3480	−	3.53958i	−0.742053	−	0.117530i	−0.226049	−	0.974116i	$-0.572581\pi$
$907$	−22.3480	−	3.53958i	−0.742053	−	0.117530i	−0.516004	+	0.856586i	$0.672581\pi$
$908$	6.63608	−	5.66774i	0.220226	−	0.188091i
$909$		0			0
$910$	1.57270	+	9.92965i	0.0521345	+	0.329165i
$911$	22.1906	−	22.1906i	0.735209	−	0.735209i	−0.236438	−	0.971647i	$-0.575980\pi$
$911$	22.1906	−	22.1906i	0.735209	−	0.735209i	0.971647	+	0.236438i	$0.0759800\pi$
$912$		0			0
$913$	−1.90452	+	1.16709i	−0.0630303	+	0.0386250i
$914$	−19.7690	+	4.74611i	−0.653899	+	0.156987i
$915$		0			0
$916$	−2.75945	+	1.14300i	−0.0911747	+	0.0377658i
$917$	4.42370	−	7.21881i	0.146083	−	0.238386i
$918$		0			0
$919$	10.5216	+	2.52601i	0.347076	+	0.0833255i	0.403235	−	0.915096i	$-0.367886\pi$
$919$	10.5216	+	2.52601i	0.347076	+	0.0833255i	−0.0561596	+	0.998422i	$0.517886\pi$
$920$	−26.5711	+	8.63346i	−0.876022	+	0.284637i
$921$		0			0
$922$	11.8695	+	23.2953i	0.390902	+	0.767189i
$923$	−11.6797	−	22.9227i	−0.384443	−	0.754511i
$924$		0			0
$925$	−18.6662	+	6.06503i	−0.613742	+	0.199417i
$926$	−6.41787	−	1.54080i	−0.210904	−	0.0506337i
$927$		0			0
$928$	−3.91108	+	6.38230i	−0.128387	+	0.209509i
$929$	18.9417	−	7.84593i	0.621459	−	0.257417i	−0.0496605	−	0.998766i	$-0.515814\pi$
$929$	18.9417	−	7.84593i	0.621459	−	0.257417i	0.671119	+	0.741350i	$0.265814\pi$
$930$		0			0
$931$	0.559419	−	0.134305i	0.0183342	−	0.00440166i
$932$	3.33452	−	2.04340i	0.109226	−	0.0669337i
$933$		0			0
$934$	7.19505	−	7.19505i	0.235429	−	0.235429i
$935$	−0.174629	−	1.10257i	−0.00571098	−	0.0360577i
$936$		0			0
$937$	4.10837	−	3.50888i	0.134215	−	0.114630i	−0.579807	−	0.814754i	$-0.696872\pi$
$937$	4.10837	−	3.50888i	0.134215	−	0.114630i	0.714021	+	0.700124i	$0.246872\pi$
$938$	3.00183	+	0.475443i	0.0980132	+	0.0155238i
$939$		0			0
$940$	12.2132	−	29.4853i	0.398351	−	0.961704i
$941$	−34.3641	−	17.5094i	−1.12024	−	0.570789i	−0.207050	−	0.978330i	$-0.566386\pi$
$941$	−34.3641	−	17.5094i	−1.12024	−	0.570789i	−0.913187	+	0.407541i	$0.866386\pi$
$942$		0			0
$943$	−55.0336	+	10.6286i	−1.79214	+	0.346114i
$944$			2.86859i			0.0933647i
$945$		0			0
$946$	0.666842	+	0.276215i	0.0216809	+	0.00898052i
$947$	7.30635	−	5.30837i	0.237424	−	0.172499i	−0.462711	−	0.886509i	$-0.653123\pi$
$947$	7.30635	−	5.30837i	0.237424	−	0.172499i	0.700135	+	0.714010i	$0.253123\pi$
$948$		0			0
$949$	13.1308	+	15.3742i	0.426243	+	0.499066i
$950$	−0.382553	−	0.326731i	−0.0124117	−	0.0106006i
$951$		0			0
$952$	−1.32371	−	1.32371i	−0.0429017	−	0.0429017i
$953$	15.6246	−	21.5054i	0.506130	−	0.696628i	−0.477131	−	0.878832i	$-0.658323\pi$
$953$	15.6246	−	21.5054i	0.506130	−	0.696628i	0.983261	+	0.182204i	$0.0583231\pi$
$954$		0			0
$955$	−10.5434	−	43.9165i	−0.341177	−	1.42110i
$956$	28.9837	+	2.28106i	0.937399	+	0.0737749i
$957$		0			0
$958$	−8.28929	−	5.07969i	−0.267815	−	0.164117i
$959$	6.60766	+	2.14696i	0.213373	+	0.0693289i
$960$		0			0
$961$	8.61539	+	26.5154i	0.277916	+	0.855336i
$962$	−11.4942	+	0.904611i	−0.370587	+	0.0291658i
$963$		0			0
$964$	−24.8935	+	12.6839i	−0.801767	+	0.408521i
$965$	0.277779	+	3.52952i	0.00894203	+	0.113619i
$966$		0			0
$967$	8.47280	−	35.2917i	0.272467	−	1.13491i	−0.653387	−	0.757024i	$-0.726653\pi$
$967$	8.47280	−	35.2917i	0.272467	−	1.13491i	0.925854	−	0.377882i	$-0.123347\pi$
$968$	3.38766	−	10.4261i	0.108883	−	0.335109i
$969$		0			0
$970$	0.202184	+	0.488116i	0.00649175	+	0.0156725i
$971$	2.88749	−	36.6890i	0.0926638	−	1.17741i	−0.758201	−	0.652021i	$-0.773921\pi$
$971$	2.88749	−	36.6890i	0.0926638	−	1.17741i	0.850865	−	0.525385i	$-0.176079\pi$
$972$		0			0
$973$	10.0233	+	16.3566i	0.321333	+	0.524368i
$974$	0.669561	+	0.486464i	0.0214541	+	0.0155873i
$975$		0			0
$976$	7.28677	−	1.15411i	0.233244	−	0.0369422i
$977$	−17.5781	+	20.5813i	−0.562374	+	0.658456i	−0.966626	−	0.256192i	$-0.917532\pi$
$977$	−17.5781	+	20.5813i	−0.562374	+	0.658456i	0.404252	+	0.914648i	$0.367532\pi$
$978$		0			0
$979$	−0.475558	+	3.00255i	−0.0151989	+	0.0959620i
$980$	−11.1270	−	15.3149i	−0.355437	−	0.489218i
$981$		0			0
$982$	−0.961820	+	1.88768i	−0.0306929	+	0.0602382i
$983$	−37.2360			−1.18764			−0.593822	−	0.804597i	$-0.702381\pi$
$983$	−37.2360			−1.18764			−0.593822	+	0.804597i	$0.702381\pi$
$984$		0			0
$985$	50.4184			1.60646
$986$	6.15346	−	12.0768i	0.195966	−	0.384605i
$987$		0			0
$988$	−0.173713	−	0.239096i	−0.00552656	−	0.00760665i
$989$	−5.11705	+	32.3078i	−0.162713	+	1.02733i
$990$		0			0
$991$	33.1123	−	38.7696i	1.05185	−	1.23156i	0.0797906	−	0.996812i	$-0.474575\pi$
$991$	33.1123	−	38.7696i	1.05185	−	1.23156i	0.972057	−	0.234744i	$-0.0754252\pi$
$992$	−1.74461	+	0.276320i	−0.0553915	+	0.00877316i
$993$		0			0
$994$	−7.06219	−	5.13098i	−0.223999	−	0.162745i
$995$	−11.4282	−	18.6492i	−0.362299	−	0.591218i
$996$		0			0
$997$	0.479867	−	6.09729i	0.0151975	−	0.193103i	−0.984632	−	0.174642i	$-0.944123\pi$
$997$	0.479867	−	6.09729i	0.0151975	−	0.193103i	0.999830	−	0.0184613i	$-0.00587674\pi$
$998$	−10.4466	−	25.2203i	−0.330681	−	0.798334i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.ba.d.233.4	yes	64
3.2	odd	2		738.2.ba.c.233.1	✓	64
41.22	odd	40		738.2.ba.c.719.1	yes	64
123.104	even	40	inner	738.2.ba.d.719.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.ba.c.233.1	✓	64	3.2	odd	2
738.2.ba.c.719.1	yes	64	41.22	odd	40
738.2.ba.d.233.4	yes	64	1.1	even	1	trivial
738.2.ba.d.719.4	yes	64	123.104	even	40	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.587785 - 0.809017i) q^{4} +(0.499283 - 3.15235i) q^{5} +(0.671416 - 0.786128i) q^{7} +(0.987688 - 0.156434i) q^{8} +(2.58210 + 1.87600i) q^{10} +(0.100924 + 0.164693i) q^{11} +(-0.239053 + 3.03746i) q^{13} +(0.395628 + 0.955131i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.422714 - 1.76073i) q^{17} +(-0.00761038 - 0.0966990i) q^{19} +(-2.84378 + 1.44898i) q^{20} +(-0.192561 + 0.0151549i) q^{22} +(-2.70502 - 8.32519i) q^{23} +(-4.93275 - 1.60275i) q^{25} +(-2.59787 - 1.59198i) q^{26} +(-1.03064 - 0.0811131i) q^{28} +(-1.74742 - 7.27852i) q^{29} +(1.03824 - 1.42902i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.37691 + 1.17599i) q^{34} +(-2.14292 - 2.50904i) q^{35} +(3.06143 - 2.22426i) q^{37} +(0.0896145 + 0.0371195i) q^{38} -3.19165i q^{40} +(0.788009 - 6.35445i) q^{41} +(-3.32951 - 1.69647i) q^{43} +(0.0739177 - 0.178453i) q^{44} +(8.64585 + 1.36937i) q^{46} +(-7.60363 + 6.49411i) q^{47} +(0.927845 + 5.85818i) q^{49} +(3.66748 - 3.66748i) q^{50} +(2.59787 - 1.59198i) q^{52} +(6.19350 - 1.48693i) q^{53} +(0.569559 - 0.235919i) q^{55} +(0.540173 - 0.881482i) q^{56} +(7.27852 + 1.74742i) q^{58} +(2.72819 - 0.886444i) q^{59} +(-3.34936 - 6.57349i) q^{61} +(0.801911 + 1.57384i) q^{62} +(0.951057 - 0.309017i) q^{64} +(9.45579 + 2.27013i) q^{65} +(1.53604 - 2.50659i) q^{67} +(-1.67292 + 0.692948i) q^{68} +(3.20844 - 0.770278i) q^{70} +(-7.19946 + 4.41183i) q^{71} +(4.69223 - 4.69223i) q^{73} +(0.591970 + 3.73755i) q^{74} +(-0.0737579 + 0.0629952i) q^{76} +(0.197231 + 0.0312384i) q^{77} +(-1.03431 + 2.49705i) q^{79} +(2.84378 + 1.44898i) q^{80} +(5.30411 + 3.58698i) q^{82} +11.5641i q^{83} +(-5.33938 - 2.21164i) q^{85} +(3.02313 - 2.19643i) q^{86} +(0.125445 + 0.146877i) q^{88} +(11.9676 + 10.2213i) q^{89} +(2.22733 + 2.22733i) q^{91} +(-5.14525 + 7.08183i) q^{92} +(-2.33432 - 9.72315i) q^{94} +(-0.308629 - 0.0242896i) q^{95} +(0.141143 + 0.0864925i) q^{97} +(-5.64091 - 1.83284i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{7} + 8 q^{11} + 16 q^{13} - 4 q^{14} + 16 q^{16} + 16 q^{17} + 4 q^{19} - 4 q^{22} - 48 q^{23} + 40 q^{25} + 20 q^{26} + 4 q^{28} - 4 q^{29} + 40 q^{31} + 4 q^{34} + 52 q^{35} + 8 q^{37} - 16 q^{38}+ \cdots + 64 q^{97}+O(q^{100}) \) 64 * q - 4 * q^7 + 8 * q^11 + 16 * q^13 - 4 * q^14 + 16 * q^16 + 16 * q^17 + 4 * q^19 - 4 * q^22 - 48 * q^23 + 40 * q^25 + 20 * q^26 + 4 * q^28 - 4 * q^29 + 40 * q^31 + 4 * q^34 + 52 * q^35 + 8 * q^37 - 16 * q^38 - 12 * q^41 + 32 * q^43 + 4 * q^44 + 8 * q^47 + 48 * q^49 - 16 * q^50 - 20 * q^52 + 48 * q^53 - 36 * q^55 - 16 * q^56 - 20 * q^58 - 20 * q^59 + 24 * q^61 + 36 * q^62 - 60 * q^65 - 20 * q^67 - 12 * q^68 - 8 * q^70 + 8 * q^71 + 72 * q^73 + 12 * q^74 + 4 * q^76 + 76 * q^77 + 44 * q^79 - 68 * q^82 - 88 * q^85 + 32 * q^86 - 8 * q^88 - 84 * q^89 + 72 * q^91 + 12 * q^94 + 12 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

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Database

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