LMFDB - Embedded newform 666.2.bs.b.35.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			35.5
Character	$\chi$	$=$	666.35
Dual form			666.2.bs.b.647.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-1.19510 + 2.56290i) q^{5} +(4.06568 - 1.47979i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-1.19510 + 2.56290i) q^{5} +(4.06568 - 1.47979i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-1.41393 + 2.44899i) q^{10} +(-2.59681 - 4.49780i) q^{11} +(3.18208 - 2.22812i) q^{13} +(4.17918 - 1.11981i) q^{14} +(0.939693 + 0.342020i) q^{16} +(3.57436 + 2.50279i) q^{17} +(0.628208 + 7.18045i) q^{19} +(-1.62199 + 2.31644i) q^{20} +(-2.19492 - 4.70701i) q^{22} +(1.42498 + 5.31811i) q^{23} +(-1.92627 - 2.29564i) q^{25} +(3.36417 - 1.94230i) q^{26} +(4.26087 - 0.751307i) q^{28} +(0.407716 - 1.52162i) q^{29} +(-5.60881 + 5.60881i) q^{31} +(0.906308 + 0.422618i) q^{32} +(3.34262 + 2.80479i) q^{34} +(-1.06635 + 12.1884i) q^{35} +(0.882519 - 6.01840i) q^{37} +7.20788i q^{38} +(-1.81771 + 2.16626i) q^{40} +(-0.393099 + 2.22937i) q^{41} +(-2.74808 - 2.74808i) q^{43} +(-1.77632 - 4.88040i) q^{44} +(0.956056 + 5.42207i) q^{46} +(-9.56567 - 5.52274i) q^{47} +(8.97765 - 7.53315i) q^{49} +(-1.71886 - 2.45479i) q^{50} +(3.52065 - 1.64170i) q^{52} +(4.10625 - 11.2818i) q^{53} +(14.6309 - 1.28004i) q^{55} +(4.31014 - 0.377088i) q^{56} +(0.538782 - 1.48029i) q^{58} +(1.38934 - 0.647858i) q^{59} +(1.95509 + 2.79216i) q^{61} +(-6.07631 + 5.09863i) q^{62} +(0.866025 + 0.500000i) q^{64} +(1.90754 + 10.8182i) q^{65} +(-4.58473 - 12.5964i) q^{67} +(3.08545 + 3.08545i) q^{68} +(-2.12458 + 12.0491i) q^{70} +(-5.99507 + 7.14465i) q^{71} -5.91546i q^{73} +(1.40370 - 5.91858i) q^{74} +(-0.628208 + 7.18045i) q^{76} +(-17.2136 - 14.4439i) q^{77} +(-2.76458 - 1.28915i) q^{79} +(-1.99959 + 1.99959i) q^{80} +(-0.585906 + 2.18663i) q^{82} +(4.06968 - 0.717595i) q^{83} +(-10.6861 + 6.16964i) q^{85} +(-2.49811 - 2.97713i) q^{86} +(-1.34421 - 5.01664i) q^{88} +(1.86644 + 4.00260i) q^{89} +(9.64018 - 13.7676i) q^{91} +(0.479854 + 5.48476i) q^{92} +(-9.04794 - 6.33543i) q^{94} +(-19.1536 - 6.97134i) q^{95} +(-11.6592 + 3.12407i) q^{97} +(9.60005 - 6.72203i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) $ 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{19}{36}\right)$

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 $

$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−1.19510	+	2.56290i	−0.534466	+	1.14617i	0.434885	+	0.900486i	$0.356789\pi$
$5$	−1.19510	+	2.56290i	−0.534466	+	1.14617i	−0.969351	+	0.245680i	$0.920989\pi$
$6$		0			0
$7$	4.06568	−	1.47979i	1.53668	−	0.559306i	0.571435	−	0.820647i	$-0.306387\pi$
$7$	4.06568	−	1.47979i	1.53668	−	0.559306i	0.965247	+	0.261341i	$0.0841647\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$		0			0
$10$	−1.41393	+	2.44899i	−0.447123	+	0.774439i
$11$	−2.59681	−	4.49780i	−0.782967	−	1.35614i	−0.930206	−	0.367037i	$-0.880372\pi$
$11$	−2.59681	−	4.49780i	−0.782967	−	1.35614i	0.147240	−	0.989101i	$-0.452961\pi$
$12$		0			0
$13$	3.18208	−	2.22812i	0.882551	−	0.617969i	−0.0419622	−	0.999119i	$-0.513361\pi$
$13$	3.18208	−	2.22812i	0.882551	−	0.617969i	0.924513	+	0.381151i	$0.124472\pi$
$14$	4.17918	−	1.11981i	1.11693	−	0.299281i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	3.57436	+	2.50279i	0.866909	+	0.607016i	0.920150	−	0.391566i	$-0.128066\pi$
$17$	3.57436	+	2.50279i	0.866909	+	0.607016i	−0.0532415	+	0.998582i	$0.516955\pi$
$18$		0			0
$19$	0.628208	+	7.18045i	0.144121	+	1.64731i	0.632415	+	0.774630i	$0.282064\pi$
$19$	0.628208	+	7.18045i	0.144121	+	1.64731i	−0.488294	+	0.872679i	$0.662381\pi$
$20$	−1.62199	+	2.31644i	−0.362688	+	0.517972i
$21$		0			0
$22$	−2.19492	−	4.70701i	−0.467958	−	1.00354i
$23$	1.42498	+	5.31811i	0.297129	+	1.10890i	0.939511	+	0.342517i	$0.111280\pi$
$23$	1.42498	+	5.31811i	0.297129	+	1.10890i	−0.642382	+	0.766385i	$0.722054\pi$
$24$		0			0
$25$	−1.92627	−	2.29564i	−0.385254	−	0.459128i
$26$	3.36417	−	1.94230i	0.659767	−	0.380917i
$27$		0			0
$28$	4.26087	−	0.751307i	0.805229	−	0.141984i
$29$	0.407716	−	1.52162i	0.0757110	−	0.282557i	−0.917683	−	0.397314i	$-0.869942\pi$
$29$	0.407716	−	1.52162i	0.0757110	−	0.282557i	0.993394	+	0.114757i	$0.0366090\pi$
$30$		0			0
$31$	−5.60881	+	5.60881i	−1.00737	+	1.00737i	−0.00739987	+	0.999973i	$0.502355\pi$
$31$	−5.60881	+	5.60881i	−1.00737	+	1.00737i	−0.999973	+	0.00739987i	$0.997645\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$		0			0
$34$	3.34262	+	2.80479i	0.573255	+	0.481018i
$35$	−1.06635	+	12.1884i	−0.180246	+	2.06022i
$36$		0			0
$37$	0.882519	−	6.01840i	0.145085	−	0.989419i
$37$	0.882519	−	6.01840i	0.145085	−	0.989419i
$38$			7.20788i			1.16927i
$39$		0			0
$40$	−1.81771	+	2.16626i	−0.287405	+	0.342516i
$41$	−0.393099	+	2.22937i	−0.0613917	+	0.348170i	0.938603	+	0.344998i	$0.112121\pi$
$41$	−0.393099	+	2.22937i	−0.0613917	+	0.348170i	−0.999995	+	0.00317131i	$0.998991\pi$
$42$		0			0
$43$	−2.74808	−	2.74808i	−0.419078	−	0.419078i	0.465808	−	0.884886i	$-0.345764\pi$
$43$	−2.74808	−	2.74808i	−0.419078	−	0.419078i	−0.884886	+	0.465808i	$0.845764\pi$
$44$	−1.77632	−	4.88040i	−0.267790	−	0.735748i
$45$		0			0
$46$	0.956056	+	5.42207i	0.140963	+	0.799440i
$47$	−9.56567	−	5.52274i	−1.39530	−	0.805575i	−0.401402	−	0.915902i	$-0.631477\pi$
$47$	−9.56567	−	5.52274i	−1.39530	−	0.805575i	−0.993895	+	0.110327i	$0.964810\pi$
$48$		0			0
$49$	8.97765	−	7.53315i	1.28252	−	1.07616i
$50$	−1.71886	−	2.45479i	−0.243084	−	0.347160i
$51$		0			0
$52$	3.52065	−	1.64170i	0.488226	−	0.227664i
$53$	4.10625	−	11.2818i	0.564037	−	1.54968i	−0.249625	−	0.968342i	$-0.580307\pi$
$53$	4.10625	−	11.2818i	0.564037	−	1.54968i	0.813663	−	0.581337i	$-0.197470\pi$
$54$		0			0
$55$	14.6309	−	1.28004i	1.97283	−	0.172600i
$56$	4.31014	−	0.377088i	0.575967	−	0.0503905i
$57$		0			0
$58$	0.538782	−	1.48029i	0.0707456	−	0.194372i
$59$	1.38934	−	0.647858i	0.180876	−	0.0843439i	−0.330071	−	0.943956i	$-0.607073\pi$
$59$	1.38934	−	0.647858i	0.180876	−	0.0843439i	0.510947	+	0.859612i	$0.329295\pi$
$60$		0			0
$61$	1.95509	+	2.79216i	0.250324	+	0.357499i	0.924573	−	0.381004i	$-0.124422\pi$
$61$	1.95509	+	2.79216i	0.250324	+	0.357499i	−0.674250	+	0.738504i	$0.735533\pi$
$62$	−6.07631	+	5.09863i	−0.771692	+	0.647527i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	1.90754	+	10.8182i	0.236601	+	1.34183i
$66$		0			0
$67$	−4.58473	−	12.5964i	−0.560114	−	1.53890i	−0.819472	−	0.573119i	$-0.805733\pi$
$67$	−4.58473	−	12.5964i	−0.560114	−	1.53890i	0.259358	−	0.965781i	$-0.416489\pi$
$68$	3.08545	+	3.08545i	0.374166	+	0.374166i
$69$		0			0
$70$	−2.12458	+	12.0491i	−0.253936	+	1.44014i
$71$	−5.99507	+	7.14465i	−0.711484	+	0.847914i	−0.993774	−	0.111416i	$-0.964462\pi$
$71$	−5.99507	+	7.14465i	−0.711484	+	0.847914i	0.282290	+	0.959329i	$0.408906\pi$
$72$		0			0
$73$		−	5.91546i		−	0.692352i	−0.938170	−	0.346176i	$-0.887480\pi$
$73$		−	5.91546i		−	0.692352i	0.938170	−	0.346176i	$-0.112520\pi$
$74$	1.40370	−	5.91858i	0.163177	−	0.688021i
$75$		0			0
$76$	−0.628208	+	7.18045i	−0.0720604	+	0.823654i
$77$	−17.2136	−	14.4439i	−1.96167	−	1.64603i
$78$		0			0
$79$	−2.76458	−	1.28915i	−0.311040	−	0.145040i	0.260830	−	0.965385i	$-0.416004\pi$
$79$	−2.76458	−	1.28915i	−0.311040	−	0.145040i	−0.571870	+	0.820345i	$0.693782\pi$
$80$	−1.99959	+	1.99959i	−0.223561	+	0.223561i
$81$		0			0
$82$	−0.585906	+	2.18663i	−0.0647025	+	0.241473i
$83$	4.06968	−	0.717595i	0.446706	−	0.0787663i	0.0542297	−	0.998528i	$-0.482730\pi$
$83$	4.06968	−	0.717595i	0.446706	−	0.0787663i	0.392476	+	0.919762i	$0.371619\pi$
$84$		0			0
$85$	−10.6861	+	6.16964i	−1.15907	+	0.669192i
$86$	−2.49811	−	2.97713i	−0.269378	−	0.321032i
$87$		0			0
$88$	−1.34421	−	5.01664i	−0.143293	−	0.534776i
$89$	1.86644	+	4.00260i	0.197843	+	0.424275i	0.980052	−	0.198741i	$-0.0636851\pi$
$89$	1.86644	+	4.00260i	0.197843	+	0.424275i	−0.782210	+	0.623015i	$0.785907\pi$
$90$		0			0
$91$	9.64018	−	13.7676i	1.01057	−	1.44324i
$92$	0.479854	+	5.48476i	0.0500283	+	0.571826i
$93$		0			0
$94$	−9.04794	−	6.33543i	−0.933223	−	0.653450i
$95$	−19.1536	−	6.97134i	−1.96512	−	0.715244i
$96$		0			0
$97$	−11.6592	+	3.12407i	−1.18381	+	0.317202i	−0.796438	−	0.604721i	$-0.793285\pi$
$97$	−11.6592	+	3.12407i	−1.18381	+	0.317202i	−0.387375	+	0.921922i	$0.626618\pi$
$98$	9.60005	−	6.72203i	0.969751	−	0.679027i
$99$		0			0
$100$	−1.49837	−	2.59526i	−0.149837	−	0.259526i
$101$	1.82665	−	3.16385i	0.181758	−	0.314814i	−0.760721	−	0.649079i	$-0.775155\pi$
$101$	1.82665	−	3.16385i	0.181758	−	0.314814i	0.942479	+	0.334264i	$0.108488\pi$
$102$		0			0
$103$	−9.68784	−	2.59585i	−0.954571	−	0.255777i	−0.252270	−	0.967657i	$-0.581177\pi$
$103$	−9.68784	−	2.59585i	−0.954571	−	0.255777i	−0.702301	+	0.711880i	$0.747844\pi$
$104$	3.65033	−	1.32861i	0.357945	−	0.130281i
$105$		0			0
$106$	5.07390	−	10.8810i	0.492821	−	1.05686i
$107$	−4.27087	−	0.753069i	−0.412880	−	0.0728019i	−0.0366500	−	0.999328i	$-0.511669\pi$
$107$	−4.27087	−	0.753069i	−0.412880	−	0.0728019i	−0.376230	+	0.926526i	$0.622780\pi$
$108$		0			0
$109$	−13.7347	−	1.20163i	−1.31555	−	0.115095i	−0.592318	−	0.805705i	$-0.701787\pi$
$109$	−13.7347	−	1.20163i	−1.31555	−	0.115095i	−0.723228	+	0.690609i	$0.757342\pi$
$110$	14.6868			1.40033
$111$		0			0
$112$	4.32660			0.408826
$113$	0.843016	+	0.0737543i	0.0793042	+	0.00693822i	0.126739	−	0.991936i	$-0.459549\pi$
$113$	0.843016	+	0.0737543i	0.0793042	+	0.00693822i	−0.0474346	+	0.998874i	$0.515105\pi$
$114$		0			0
$115$	−15.3328	−	2.70359i	−1.42979	−	0.252111i
$116$	0.665748	−	1.42770i	0.0618131	−	0.132559i
$117$		0			0
$118$	1.44051	−	0.524304i	0.132610	−	0.0482661i
$119$	18.2358	+	4.88626i	1.67167	+	0.447923i
$120$		0			0
$121$	−7.98681	+	13.8336i	−0.726073	+	1.25760i
$122$	1.70430	+	2.95193i	0.154300	+	0.267255i
$123$		0			0
$124$	−6.49756	+	4.54964i	−0.583498	+	0.408570i
$125$	−5.47187	+	1.46618i	−0.489419	+	0.131140i
$126$		0			0
$127$	20.2954	+	7.38693i	1.80093	+	0.655484i	0.998254	+	0.0590653i	$0.0188120\pi$
$127$	20.2954	+	7.38693i	1.80093	+	0.655484i	0.802673	+	0.596419i	$0.203410\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$		0			0
$130$	0.957414	+	10.9433i	0.0839707	+	0.959790i
$131$	−0.981647	+	1.40194i	−0.0857669	+	0.122488i	−0.859743	−	0.510727i	$-0.829376\pi$
$131$	−0.981647	+	1.40194i	−0.0857669	+	0.122488i	0.773976	+	0.633215i	$0.218265\pi$
$132$		0			0
$133$	13.1796	+	28.2638i	1.14282	+	2.45078i
$134$	−3.46943	−	12.9481i	−0.299713	−	1.11855i
$135$		0			0
$136$	2.80479	+	3.34262i	0.240509	+	0.286627i
$137$	17.7245	−	10.2333i	1.51431	−	0.874287i	0.514451	−	0.857520i	$-0.327996\pi$
$137$	17.7245	−	10.2333i	1.51431	−	0.874287i	0.999859	−	0.0167672i	$-0.00533741\pi$
$138$		0			0
$139$	5.54338	−	0.977447i	0.470183	−	0.0829060i	0.0664638	−	0.997789i	$-0.478828\pi$
$139$	5.54338	−	0.977447i	0.470183	−	0.0829060i	0.403719	+	0.914883i	$0.367717\pi$
$140$	−3.16665	+	11.8181i	−0.267631	+	0.998811i
$141$		0			0
$142$	−6.59495	+	6.59495i	−0.553436	+	0.553436i
$143$	−18.2849	−	8.52638i	−1.52906	−	0.713012i
$144$		0			0
$145$	3.41250	+	2.86342i	0.283392	+	0.237794i
$146$	0.515566	−	5.89294i	0.0426685	−	0.487704i
$147$		0			0
$148$	1.91420	−	5.77372i	0.157346	−	0.474597i
$149$			11.8204i			0.968365i	0.874967	+	0.484183i	$0.160883\pi$
$149$			11.8204i			0.968365i	−0.874967	+	0.484183i	$0.839117\pi$
$150$		0			0
$151$	−8.01971	+	9.55752i	−0.652635	+	0.777780i	−0.986309	−	0.164909i	$-0.947267\pi$
$151$	−8.01971	+	9.55752i	−0.652635	+	0.777780i	0.333674	+	0.942688i	$0.391711\pi$
$152$	−1.25164	+	7.09838i	−0.101521	+	0.575754i
$153$		0			0
$154$	−15.8892	−	15.8892i	−1.28039	−	1.28039i
$155$	−7.67175	−	21.0780i	−0.616210	−	1.69302i
$156$		0			0
$157$	−1.06729	−	6.05289i	−0.0851788	−	0.483073i	−0.997318	−	0.0731921i	$-0.976681\pi$
$157$	−1.06729	−	6.05289i	−0.0851788	−	0.483073i	0.912139	−	0.409881i	$-0.134430\pi$
$158$	−2.64170	−	1.52519i	−0.210163	−	0.121338i
$159$		0			0
$160$	−2.16626	+	1.81771i	−0.171258	+	0.143702i
$161$	13.6632	+	19.5130i	1.07681	+	1.53784i
$162$		0			0
$163$	−9.39952	+	4.38307i	−0.736227	+	0.343308i	−0.754301	−	0.656528i	$-0.772024\pi$
$163$	−9.39952	+	4.38307i	−0.736227	+	0.343308i	0.0180742	+	0.999837i	$0.494246\pi$
$164$	−0.774254	+	2.12724i	−0.0604591	+	0.166110i
$165$		0			0
$166$	4.11674	−	0.360168i	0.319521	−	0.0279545i
$167$	12.3387	−	1.07950i	0.954798	−	0.0835340i	0.400903	−	0.916120i	$-0.368696\pi$
$167$	12.3387	−	1.07950i	0.954798	−	0.0835340i	0.553895	+	0.832586i	$0.313141\pi$
$168$		0			0
$169$	0.714875	−	1.96410i	0.0549904	−	0.151085i
$170$	−11.1832	+	5.21481i	−0.857711	+	0.399957i
$171$		0			0
$172$	−2.22913	−	3.18352i	−0.169969	−	0.242741i
$173$	6.52994	−	5.47927i	0.496462	−	0.416581i	−0.359873	−	0.933001i	$-0.617180\pi$
$173$	6.52994	−	5.47927i	0.496462	−	0.416581i	0.856335	+	0.516420i	$0.172736\pi$
$174$		0			0
$175$	−11.2287	−	6.48287i	−0.848807	−	0.490059i
$176$	−0.901861	−	5.11471i	−0.0679804	−	0.385536i
$177$		0			0
$178$	1.51049	+	4.15004i	0.113216	+	0.311059i
$179$	−15.1490	−	15.1490i	−1.13229	−	1.13229i	−0.989796	−	0.142489i	$-0.954489\pi$
$179$	−15.1490	−	15.1490i	−1.13229	−	1.13229i	−0.142489	−	0.989796i	$-0.545511\pi$
$180$		0			0
$181$	−0.00166103	+	0.00942016i	−0.000123463	+	0.000700195i	−0.984869	−	0.173298i	$-0.944558\pi$
$181$	−0.00166103	+	0.00942016i	−0.000123463	+	0.000700195i	0.984746	+	0.173998i	$0.0556687\pi$
$182$	10.8034	−	12.8750i	0.800803	−	0.954360i
$183$		0			0
$184$			5.50571i			0.405886i
$185$	14.3699	+	9.45441i	1.05650	+	0.695102i
$186$		0			0
$187$	1.97514	−	22.5760i	0.144437	−	1.65092i
$188$	−8.46134	−	7.09990i	−0.617106	−	0.517814i
$189$		0			0
$190$	−18.4731	−	8.61415i	−1.34018	−	0.624936i
$191$	−2.07116	+	2.07116i	−0.149864	+	0.149864i	−0.778057	−	0.628193i	$-0.783795\pi$
$191$	−2.07116	+	2.07116i	−0.149864	+	0.149864i	0.628193	+	0.778057i	$0.283795\pi$
$192$		0			0
$193$	−4.84340	+	18.0758i	−0.348636	+	1.30113i	0.539671	+	0.841876i	$0.318549\pi$
$193$	−4.84340	+	18.0758i	−0.348636	+	1.30113i	−0.888307	+	0.459250i	$0.848118\pi$
$194$	−11.8871	+	2.09602i	−0.853445	+	0.150485i
$195$		0			0
$196$	10.1494	−	5.85975i	0.724956	−	0.418553i
$197$	−7.30054	−	8.70045i	−0.520142	−	0.619881i	0.440472	−	0.897766i	$-0.354811\pi$
$197$	−7.30054	−	8.70045i	−0.520142	−	0.619881i	−0.960614	+	0.277885i	$0.910367\pi$
$198$		0			0
$199$	−2.16939	−	8.09626i	−0.153784	−	0.573928i	−0.999206	−	0.0398307i	$-0.987318\pi$
$199$	−2.16939	−	8.09626i	−0.153784	−	0.573928i	0.845423	−	0.534098i	$-0.179349\pi$
$200$	−1.26648	−	2.71598i	−0.0895537	−	0.192048i
$201$		0			0
$202$	2.09544	−	2.99260i	0.147435	−	0.210559i
$203$	−0.594025	−	6.78974i	−0.0416924	−	0.476546i
$204$		0			0
$205$	−5.24388	−	3.67180i	−0.366248	−	0.256450i
$206$	−9.42473	−	3.43032i	−0.656652	−	0.239002i
$207$		0			0
$208$	3.75224	−	1.00541i	0.260171	−	0.0697126i
$209$	30.6649	−	21.4718i	2.12114	−	1.48524i
$210$		0			0
$211$	0.150366	+	0.260441i	0.0103516	+	0.0179295i	0.871155	−	0.491008i	$-0.163372\pi$
$211$	0.150366	+	0.260441i	0.0103516	+	0.0179295i	−0.860803	+	0.508938i	$0.830038\pi$
$212$	6.00294	−	10.3974i	0.412284	−	0.714096i
$213$		0			0
$214$	−4.18898	−	1.12243i	−0.286353	−	0.0767280i
$215$	10.3273	−	3.75882i	0.704315	−	0.256350i
$216$		0			0
$217$	−14.5038	+	31.1035i	−0.984581	+	2.11144i
$218$	−13.5777	−	2.39412i	−0.919598	−	0.162150i
$219$		0			0
$220$	14.6309	+	1.28004i	0.986414	+	0.0863000i
$221$	16.9504			1.14021
$222$		0			0
$223$	−20.4954			−1.37247			−0.686237	−	0.727378i	$-0.740739\pi$
$223$	−20.4954			−1.37247			−0.686237	+	0.727378i	$0.740739\pi$
$224$	4.31014	+	0.377088i	0.287983	+	0.0251953i
$225$		0			0
$226$	0.833380	+	0.146947i	0.0554356	+	0.00977479i
$227$	−4.89486	+	10.4971i	−0.324883	+	0.696714i	−0.999126	−	0.0417954i	$-0.986692\pi$
$227$	−4.89486	+	10.4971i	−0.324883	+	0.696714i	0.674243	+	0.738510i	$0.264470\pi$
$228$		0			0
$229$	0.300454	−	0.109356i	0.0198546	−	0.00722648i	−0.332074	−	0.943253i	$-0.607748\pi$
$229$	0.300454	−	0.109356i	0.0198546	−	0.00722648i	0.351928	+	0.936027i	$0.385526\pi$
$230$	−15.0388	−	4.02964i	−0.991630	−	0.265707i
$231$		0			0
$232$	0.787647	−	1.36424i	0.0517116	−	0.0895670i
$233$	2.20102	+	3.81228i	0.144194	+	0.249751i	0.929072	−	0.369899i	$-0.120608\pi$
$233$	2.20102	+	3.81228i	0.144194	+	0.249751i	−0.784878	+	0.619650i	$0.787274\pi$
$234$		0			0
$235$	25.5862	−	17.9157i	1.66906	−	1.16869i
$236$	1.48073	−	0.396760i	0.0963872	−	0.0258269i
$237$		0			0
$238$	17.7405	+	6.45702i	1.14995	+	0.418546i
$239$	−15.5103	−	10.8605i	−1.00328	−	0.702504i	−0.0481958	−	0.998838i	$-0.515347\pi$
$239$	−15.5103	−	10.8605i	−1.00328	−	0.702504i	−0.955085	+	0.296333i	$0.904236\pi$
$240$		0			0
$241$	0.358239	+	4.09469i	0.0230762	+	0.263762i	0.998965	+	0.0454925i	$0.0144857\pi$
$241$	0.358239	+	4.09469i	0.0230762	+	0.263762i	−0.975888	+	0.218270i	$0.929959\pi$
$242$	−9.16209	+	13.0848i	−0.588961	+	0.841124i
$243$		0			0
$244$	1.44053	+	3.08924i	0.0922208	+	0.197768i
$245$	8.57752	+	32.0117i	0.547998	+	2.04516i
$246$		0			0
$247$	17.9979	+	21.4491i	1.14518	+	1.36477i
$248$	−6.86936	+	3.96603i	−0.436205	+	0.251843i
$249$		0			0
$250$	−5.57884	+	0.983700i	−0.352837	+	0.0622146i
$251$	1.38631	−	5.17377i	0.0875030	−	0.326566i	−0.908273	−	0.418377i	$-0.862599\pi$
$251$	1.38631	−	5.17377i	0.0875030	−	0.326566i	0.995776	+	0.0918115i	$0.0292657\pi$
$252$		0			0
$253$	20.2194	−	20.2194i	1.27118	−	1.27118i
$254$	19.5744	+	9.12768i	1.22821	+	0.572722i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	0.898788	−	10.2732i	0.0560649	−	0.640824i	−0.915228	−	0.402937i	$-0.867989\pi$
$257$	0.898788	−	10.2732i	0.0560649	−	0.640824i	0.971293	−	0.237888i	$-0.0764550\pi$
$258$		0			0
$259$	−5.31791	−	25.7748i	−0.330439	−	1.60157i
$260$			10.9851i			0.681266i
$261$		0			0
$262$	−1.10010	+	1.31105i	−0.0679643	+	0.0809967i
$263$	−0.737733	+	4.18389i	−0.0454905	+	0.257990i	−0.999068	−	0.0431573i	$-0.986258\pi$
$263$	−0.737733	+	4.18389i	−0.0454905	+	0.257990i	0.953578	+	0.301147i	$0.0973695\pi$
$264$		0			0
$265$	24.0069	+	24.0069i	1.47473	+	1.47473i
$266$	10.6661	+	29.3049i	0.653982	+	1.79680i
$267$		0			0
$268$	−2.32773	−	13.2012i	−0.142189	−	0.806392i
$269$	−4.22324	−	2.43829i	−0.257495	−	0.148665i	0.365696	−	0.930734i	$-0.380831\pi$
$269$	−4.22324	−	2.43829i	−0.257495	−	0.148665i	−0.623191	+	0.782069i	$0.714164\pi$
$270$		0			0
$271$	−14.7816	+	12.4032i	−0.897919	+	0.753443i	−0.969782	−	0.243971i	$-0.921550\pi$
$271$	−14.7816	+	12.4032i	−0.897919	+	0.753443i	0.0718637	+	0.997414i	$0.477105\pi$
$272$	2.50279	+	3.57436i	0.151754	+	0.216727i
$273$		0			0
$274$	18.5490	−	8.64953i	1.12059	−	0.522537i
$275$	−5.32318	+	14.6253i	−0.321000	+	0.881940i
$276$		0			0
$277$	24.2384	−	2.12058i	1.45634	−	0.127413i	0.668694	−	0.743538i	$-0.266854\pi$
$277$	24.2384	−	2.12058i	1.45634	−	0.127413i	0.787649	+	0.616125i	$0.211298\pi$
$278$	5.60747	−	0.490590i	0.336314	−	0.0294237i
$279$		0			0
$280$	−4.18461	+	11.4971i	−0.250079	+	0.687085i
$281$	−16.0619	+	7.48980i	−0.958174	+	0.446804i	−0.837832	−	0.545928i	$-0.816177\pi$
$281$	−16.0619	+	7.48980i	−0.958174	+	0.446804i	−0.120343	+	0.992732i	$0.538399\pi$
$282$		0			0
$283$	−2.74172	−	3.91558i	−0.162978	−	0.232757i	0.729354	−	0.684137i	$-0.239821\pi$
$283$	−2.74172	−	3.91558i	−0.162978	−	0.232757i	−0.892332	+	0.451380i	$0.850932\pi$
$284$	−7.14465	+	5.99507i	−0.423957	+	0.355742i
$285$		0			0
$286$	−17.4722	−	10.0876i	−1.03315	−	0.596490i
$287$	1.70078	+	9.64562i	0.100394	+	0.569363i
$288$		0			0
$289$	0.697715	+	1.91695i	0.0410420	+	0.112762i
$290$	3.14995	+	3.14995i	0.184971	+	0.184971i
$291$		0			0
$292$	1.02721	−	5.82559i	0.0601128	−	0.340917i
$293$	−5.53176	+	6.59249i	−0.323169	+	0.385138i	−0.903030	−	0.429578i	$-0.858662\pi$
$293$	−5.53176	+	6.59249i	−0.323169	+	0.385138i	0.579861	+	0.814715i	$0.303107\pi$
$294$		0			0
$295$			4.33499i			0.252393i
$296$	2.41012	−	5.58492i	0.140086	−	0.324617i
$297$		0			0
$298$	−1.03022	+	11.7754i	−0.0596788	+	0.682132i
$299$	16.3838	+	13.7476i	0.947498	+	0.795046i
$300$		0			0
$301$	−15.2394	−	7.10623i	−0.878382	−	0.409596i
$302$	−8.82218	+	8.82218i	−0.507660	+	0.507660i
$303$		0			0
$304$	−1.86554	+	6.96228i	−0.106996	+	0.399314i
$305$	−9.49257	+	1.67380i	−0.543543	+	0.0958413i
$306$		0			0
$307$	12.2335	−	7.06302i	0.698203	−	0.403108i	−0.108474	−	0.994099i	$-0.534597\pi$
$307$	12.2335	−	7.06302i	0.698203	−	0.403108i	0.806678	+	0.590991i	$0.201263\pi$
$308$	−14.4439	−	17.2136i	−0.823017	−	0.980833i
$309$		0			0
$310$	−5.80549	−	21.6664i	−0.329730	−	1.23057i
$311$	0.0943992	+	0.202440i	0.00535289	+	0.0114793i	0.908966	−	0.416870i	$-0.136873\pi$
$311$	0.0943992	+	0.202440i	0.00535289	+	0.0114793i	−0.903613	+	0.428349i	$0.859095\pi$
$312$		0			0
$313$	8.99574	−	12.8472i	0.508469	−	0.726169i	−0.480054	−	0.877239i	$-0.659383\pi$
$313$	8.99574	−	12.8472i	0.508469	−	0.726169i	0.988523	+	0.151070i	$0.0482718\pi$
$314$	−0.535682	−	6.12287i	−0.0302303	−	0.345534i
$315$		0			0
$316$	−2.49872	−	1.74962i	−0.140564	−	0.0984241i
$317$	10.8309	+	3.94213i	0.608324	+	0.221412i	0.627770	−	0.778399i	$-0.283968\pi$
$317$	10.8309	+	3.94213i	0.608324	+	0.221412i	−0.0194458	+	0.999811i	$0.506190\pi$
$318$		0			0
$319$	−7.90269	+	2.11752i	−0.442466	+	0.118558i
$320$	−2.31644	+	1.62199i	−0.129493	+	0.0906720i
$321$		0			0
$322$	11.9105	+	20.6296i	0.663747	+	1.14964i
$323$	−15.7257	+	27.2378i	−0.875003	+	1.51555i
$324$		0			0
$325$	−11.2445	−	3.01296i	−0.623734	−	0.167129i
$326$	−9.74576	+	3.54717i	−0.539768	+	0.196459i
$327$		0			0
$328$	−0.956709	+	2.05167i	−0.0528254	+	0.113284i
$329$	−47.0634	−	8.29855i	−2.59469	−	0.457514i
$330$		0			0
$331$	15.5653	+	1.36179i	0.855548	+	0.0748507i	0.506485	−	0.862249i	$-0.330945\pi$
$331$	15.5653	+	1.36179i	0.855548	+	0.0748507i	0.349063	+	0.937099i	$0.386500\pi$
$332$	4.13246			0.226798
$333$		0			0
$334$	12.3858			0.677723
$335$	37.7627	+	3.30381i	2.06320	+	0.180506i
$336$		0			0
$337$	−7.14760	−	1.26031i	−0.389355	−	0.0686537i	−0.0244558	−	0.999701i	$-0.507785\pi$
$337$	−7.14760	−	1.26031i	−0.389355	−	0.0686537i	−0.364899	+	0.931047i	$0.618896\pi$
$338$	0.883338	−	1.89432i	0.0480472	−	0.103038i
$339$		0			0
$340$	−11.5951	+	4.22028i	−0.628834	+	0.228877i
$341$	39.7923	+	10.6623i	2.15488	+	0.577397i
$342$		0			0
$343$	10.2097	−	17.6837i	0.551272	−	0.954830i
$344$	−1.94318	−	3.36569i	−0.104769	−	0.181466i
$345$		0			0
$346$	6.98264	−	4.88930i	0.375389	−	0.262850i
$347$	−18.4941	+	4.95548i	−0.992815	+	0.266024i	−0.718433	−	0.695597i	$-0.755140\pi$
$347$	−18.4941	+	4.95548i	−0.992815	+	0.266024i	−0.274382	+	0.961621i	$0.588473\pi$
$348$		0			0
$349$	7.34403	+	2.67301i	0.393117	+	0.143083i	0.531013	−	0.847364i	$-0.321812\pi$
$349$	7.34403	+	2.67301i	0.393117	+	0.143083i	−0.137896	+	0.990447i	$0.544034\pi$
$350$	−10.6209	−	7.43684i	−0.567712	−	0.397516i
$351$		0			0
$352$	−0.452653	−	5.17385i	−0.0241265	−	0.275767i
$353$	12.3630	−	17.6562i	0.658015	−	0.939743i	−0.341985	−	0.939705i	$-0.611099\pi$
$353$	12.3630	−	17.6562i	0.658015	−	0.939743i	1.00000		3.73168e-5i	$-1.18783e-5\pi$
$354$		0			0
$355$	−11.1463	−	23.9034i	−0.591586	−	1.26866i
$356$	1.14304	+	4.26590i	0.0605812	+	0.226092i
$357$		0			0
$358$	−13.7710	−	16.4116i	−0.727819	−	0.867381i
$359$	2.97360	−	1.71681i	0.156941	−	0.0906098i	−0.419473	−	0.907768i	$-0.637785\pi$
$359$	2.97360	−	1.71681i	0.156941	−	0.0906098i	0.576414	+	0.817158i	$0.304452\pi$
$360$		0			0
$361$	−32.4529	+	5.72233i	−1.70805	+	0.301175i
$362$	−0.00247573	+	0.00923955i	−0.000130121	+	0.000485620i
$363$		0			0
$364$	11.8844	−	11.8844i	0.622914	−	0.622914i
$365$	15.1607	+	7.06957i	0.793550	+	0.370038i
$366$		0			0
$367$	22.1327	+	18.5715i	1.15532	+	0.969426i	0.999830	−	0.0184119i	$-0.00586102\pi$
$367$	22.1327	+	18.5715i	1.15532	+	0.969426i	0.155487	+	0.987838i	$0.450305\pi$
$368$	−0.479854	+	5.48476i	−0.0250141	+	0.285913i
$369$		0			0
$370$	13.4912	+	10.6709i	0.701374	+	0.554751i
$371$		−	51.9447i		−	2.69683i
$372$		0			0
$373$	−6.20942	+	7.40010i	−0.321512	+	0.383163i	−0.902457	−	0.430780i	$-0.858239\pi$
$373$	−6.20942	+	7.40010i	−0.321512	+	0.383163i	0.580945	+	0.813943i	$0.302683\pi$
$374$	3.93526	−	22.3179i	0.203487	−	1.15403i
$375$		0			0
$376$	−7.81034	−	7.81034i	−0.402788	−	0.402788i
$377$	−2.09296	−	5.75035i	−0.107793	−	0.296158i
$378$		0			0
$379$	0.528450	+	2.99699i	0.0271447	+	0.153945i	0.995367	−	0.0961444i	$-0.0306511\pi$
$379$	0.528450	+	2.99699i	0.0271447	+	0.153945i	−0.968223	+	0.250089i	$0.919540\pi$
$380$	−17.6520	−	10.1914i	−0.905531	−	0.522808i
$381$		0			0
$382$	−2.24379	+	1.88276i	−0.114802	+	0.0963305i
$383$	16.7291	+	23.8916i	0.854817	+	1.22081i	0.973686	+	0.227896i	$0.0731845\pi$
$383$	16.7291	+	23.8916i	0.854817	+	1.22081i	−0.118868	+	0.992910i	$0.537927\pi$
$384$		0			0
$385$	57.5903	−	26.8548i	2.93507	−	1.36865i
$386$	−6.40038	+	17.5849i	−0.325771	+	0.895048i
$387$		0			0
$388$	−12.0246	+	1.05201i	−0.610455	+	0.0534079i
$389$	−14.3109	+	1.25204i	−0.725590	+	0.0634809i	−0.443965	−	0.896044i	$-0.646429\pi$
$389$	−14.3109	+	1.25204i	−0.725590	+	0.0634809i	−0.281624	+	0.959525i	$0.590873\pi$
$390$		0			0
$391$	−8.21671	+	22.5752i	−0.415537	+	1.14168i
$392$	10.6215	−	4.95287i	0.536465	−	0.250158i
$393$		0			0
$394$	−6.51447	−	9.30362i	−0.328194	−	0.468710i
$395$	6.60791	−	5.54470i	0.332480	−	0.278984i
$396$		0			0
$397$	27.5058	+	15.8805i	1.38048	+	0.797018i	0.992216	−	0.124532i	$-0.0397428\pi$
$397$	27.5058	+	15.8805i	1.38048	+	0.797018i	0.388260	+	0.921550i	$0.373076\pi$
$398$	−1.45549	−	8.25452i	−0.0729574	−	0.413762i
$399$		0			0
$400$	−1.02495	−	2.81602i	−0.0512474	−	0.140801i
$401$	−11.8235	−	11.8235i	−0.590437	−	0.590437i	0.347312	−	0.937750i	$-0.387094\pi$
$401$	−11.8235	−	11.8235i	−0.590437	−	0.590437i	−0.937750	+	0.347312i	$0.887094\pi$
$402$		0			0
$403$	−5.35061	+	30.3448i	−0.266533	+	1.51158i
$404$	2.34829	−	2.79859i	0.116832	−	0.139235i
$405$		0			0
$406$		−	6.81567i		−	0.338256i
$407$	−29.3613	+	11.6592i	−1.45539	+	0.577927i
$408$		0			0
$409$	0.568035	−	6.49267i	0.0280875	−	0.321042i	−0.969133	−	0.246538i	$-0.920707\pi$
$409$	0.568035	−	6.49267i	0.0280875	−	0.321042i	0.997221	−	0.0745041i	$-0.0237374\pi$
$410$	−4.90391	−	4.11487i	−0.242187	−	0.203219i
$411$		0			0
$412$	−9.08990	−	4.23869i	−0.447827	−	0.208825i
$413$	4.68990	−	4.68990i	0.230775	−	0.230775i
$414$		0			0
$415$	−3.02456	+	11.2878i	−0.148470	+	0.554097i
$416$	3.82559	−	0.674555i	0.187565	−	0.0330728i
$417$		0			0
$418$	32.4196	−	18.7175i	1.58570	−	0.915502i
$419$	12.5139	+	14.9135i	0.611346	+	0.728574i	0.979557	−	0.201168i	$-0.0644738\pi$
$419$	12.5139	+	14.9135i	0.611346	+	0.728574i	−0.368210	+	0.929743i	$0.620029\pi$
$420$		0			0
$421$	8.36830	+	31.2309i	0.407846	+	1.52210i	0.798746	+	0.601669i	$0.205497\pi$
$421$	8.36830	+	31.2309i	0.407846	+	1.52210i	−0.390900	+	0.920433i	$0.627836\pi$
$422$	0.127095	+	0.272555i	0.00618687	+	0.0132678i
$423$		0			0
$424$	6.88629	−	9.83464i	0.334428	−	0.477612i
$425$	−1.13967	−	13.0265i	−0.0552822	−	0.631878i
$426$		0			0
$427$	12.0806	+	8.45890i	0.584619	+	0.409355i
$428$	−4.07521	−	1.48326i	−0.196983	−	0.0716959i
$429$		0			0
$430$	10.6156	−	2.84444i	0.511929	−	0.137171i
$431$	10.5552	−	7.39080i	0.508424	−	0.356002i	−0.291045	−	0.956709i	$-0.594003\pi$
$431$	10.5552	−	7.39080i	0.508424	−	0.356002i	0.799469	+	0.600707i	$0.205114\pi$
$432$		0			0
$433$	1.28526	+	2.22614i	0.0617659	+	0.106982i	0.895255	−	0.445555i	$-0.146993\pi$
$433$	1.28526	+	2.22614i	0.0617659	+	0.106982i	−0.833489	+	0.552536i	$0.813660\pi$
$434$	−17.1594	+	29.7210i	−0.823679	+	1.42665i
$435$		0			0
$436$	−13.3174	−	3.56838i	−0.637787	−	0.170894i
$437$	−37.2912	+	13.5729i	−1.78388	+	0.649280i
$438$		0			0
$439$	−0.274719	+	0.589138i	−0.0131116	+	0.0281180i	−0.912755	−	0.408508i	$-0.866049\pi$
$439$	−0.274719	+	0.589138i	−0.0131116	+	0.0281180i	0.899643	+	0.436626i	$0.143827\pi$
$440$	14.4636	+	2.55033i	0.689527	+	0.121582i
$441$		0			0
$442$	16.8859	+	1.47733i	0.803181	+	0.0702692i
$443$	3.36272			0.159767			0.0798837	−	0.996804i	$-0.474545\pi$
$443$	3.36272			0.159767			0.0798837	+	0.996804i	$0.474545\pi$
$444$		0			0
$445$	−12.4889			−0.592029
$446$	−20.4174	−	1.78629i	−0.966793	−	0.0845834i
$447$		0			0
$448$	4.26087	+	0.751307i	0.201307	+	0.0354959i
$449$	3.90033	−	8.36428i	0.184068	−	0.394735i	−0.792522	−	0.609843i	$-0.791233\pi$
$449$	3.90033	−	8.36428i	0.184068	−	0.394735i	0.976590	+	0.215108i	$0.0690104\pi$
$450$		0			0
$451$	11.0481	−	4.02117i	0.520234	−	0.189350i
$452$	0.817401	+	0.219022i	0.0384473	+	0.0103019i
$453$		0			0
$454$	−5.79111	+	10.0305i	−0.271790	+	0.470755i
$455$	23.7641	+	41.1606i	1.11408	+	1.92964i
$456$		0			0
$457$	−14.8861	+	10.4233i	−0.696340	+	0.487583i	−0.867358	−	0.497685i	$-0.834183\pi$
$457$	−14.8861	+	10.4233i	−0.696340	+	0.487583i	0.171017	+	0.985268i	$0.445295\pi$
$458$	0.308842	−	0.0827540i	0.0144312	−	0.00386684i
$459$		0			0
$460$	−14.6304	−	5.32503i	−0.682145	−	0.248281i
$461$	30.2023	+	21.1479i	1.40666	+	0.984954i	0.997365	+	0.0725517i	$0.0231142\pi$
$461$	30.2023	+	21.1479i	1.40666	+	0.984954i	0.409295	+	0.912402i	$0.365775\pi$
$462$		0			0
$463$	−0.313944	−	3.58840i	−0.0145902	−	0.166767i	0.985404	−	0.170233i	$-0.0544522\pi$
$463$	−0.313944	−	3.58840i	−0.0145902	−	0.166767i	−0.999994	+	0.00346638i	$0.998897\pi$
$464$	0.903551	−	1.29041i	0.0419463	−	0.0599056i
$465$		0			0
$466$	1.86038	+	3.98961i	0.0861806	+	0.184815i
$467$	0.649365	+	2.42346i	0.0300490	+	0.112145i	0.979321	−	0.202310i	$-0.0648450\pi$
$467$	0.649365	+	2.42346i	0.0300490	+	0.112145i	−0.949272	+	0.314455i	$0.898178\pi$
$468$		0			0
$469$	−37.2801	−	44.4287i	−1.72143	−	2.05152i
$470$	27.0503	−	15.6175i	1.24774	−	0.720382i
$471$		0			0
$472$	1.50967	−	0.266196i	0.0694884	−	0.0122527i
$473$	−5.22408	+	19.4965i	−0.240203	+	0.896451i
$474$		0			0
$475$	15.2736	−	15.2736i	0.700803	−	0.700803i
$476$	17.1102	+	7.97863i	0.784246	+	0.365700i
$477$		0			0
$478$	−14.5048	−	12.1709i	−0.663433	−	0.556686i
$479$	0.646260	−	7.38679i	0.0295284	−	0.337511i	−0.967033	−	0.254652i	$-0.918039\pi$
$479$	0.646260	−	7.38679i	0.0295284	−	0.337511i	0.996561	−	0.0828594i	$-0.0264053\pi$
$480$		0			0
$481$	−10.6015	−	21.1174i	−0.483385	−	0.962871i
$482$			4.11033i			0.187221i
$483$		0			0
$484$	−10.2676	+	12.2365i	−0.466711	+	0.556204i
$485$	5.92723	−	33.6150i	0.269142	−	1.52638i
$486$		0			0
$487$	20.4001	+	20.4001i	0.924418	+	0.924418i	0.997338	−	0.0729198i	$-0.0232317\pi$
$487$	20.4001	+	20.4001i	0.924418	+	0.924418i	−0.0729198	+	0.997338i	$0.523232\pi$
$488$	1.16581	+	3.20303i	0.0527737	+	0.144994i
$489$		0			0
$490$	5.75487	+	32.6375i	0.259979	+	1.47441i
$491$	−8.11990	−	4.68803i	−0.366446	−	0.211568i	0.305459	−	0.952205i	$-0.401190\pi$
$491$	−8.11990	−	4.68803i	−0.366446	−	0.211568i	−0.671905	+	0.740638i	$0.734524\pi$
$492$		0			0
$493$	5.26561	−	4.41837i	0.237151	−	0.198993i
$494$	16.0600	+	22.9361i	0.722574	+	1.03194i
$495$		0			0
$496$	−7.18889	+	3.35223i	−0.322791	+	0.150520i
$497$	−13.8015	+	37.9192i	−0.619081	+	1.70091i
$498$		0			0
$499$	−11.3299	+	0.991238i	−0.507196	+	0.0443739i	−0.337883	−	0.941188i	$-0.609711\pi$
$499$	−11.3299	+	0.991238i	−0.507196	+	0.0443739i	−0.169314	+	0.985562i	$0.554155\pi$
$500$	−5.64334	+	0.493729i	−0.252378	+	0.0220802i
$501$		0			0
$502$	1.83196	−	5.03326i	0.0817643	−	0.224645i
$503$	20.0132	−	9.33229i	0.892343	−	0.416106i	0.0783126	−	0.996929i	$-0.475047\pi$
$503$	20.0132	−	9.33229i	0.892343	−	0.416106i	0.814030	+	0.580823i	$0.197269\pi$
$504$		0			0
$505$	5.92561	+	8.46264i	0.263686	+	0.376583i
$506$	21.9047	−	18.3802i	0.973782	−	0.817100i
$507$		0			0
$508$	18.7044	+	10.7990i	0.829872	+	0.479127i
$509$	−4.23969	−	24.0445i	−0.187921	−	1.06575i	−0.922145	−	0.386845i	$-0.873565\pi$
$509$	−4.23969	−	24.0445i	−0.187921	−	1.06575i	0.734224	−	0.678908i	$-0.237546\pi$
$510$		0			0
$511$	−8.75360	−	24.0503i	−0.387237	−	1.06392i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	1.79074	−	10.1558i	0.0789860	−	0.447952i
$515$	18.2309	−	21.7267i	0.803348	−	0.957393i
$516$		0			0
$517$			57.3660i			2.52295i
$518$	−3.05125	−	26.1402i	−0.134064	−	1.14854i
$519$		0			0
$520$	−0.957414	+	10.9433i	−0.0419854	+	0.479895i
$521$	27.1536	+	22.7846i	1.18962	+	0.998211i	0.999866	+	0.0163802i	$0.00521421\pi$
$521$	27.1536	+	22.7846i	1.18962	+	0.998211i	0.189756	+	0.981831i	$0.439230\pi$
$522$		0			0
$523$	−6.56159	−	3.05972i	−0.286918	−	0.133792i	0.273831	−	0.961778i	$-0.411709\pi$
$523$	−6.56159	−	3.05972i	−0.286918	−	0.133792i	−0.560749	+	0.827986i	$0.689487\pi$
$524$	−1.21018	+	1.21018i	−0.0528669	+	0.0528669i
$525$		0			0
$526$	−1.09958	+	4.10367i	−0.0479438	+	0.178929i
$527$	−34.0856	+	6.01021i	−1.48479	+	0.261809i
$528$		0			0
$529$	−6.33310	+	3.65642i	−0.275352	+	0.158975i
$530$	21.8232	+	26.0079i	0.947939	+	1.12971i
$531$		0			0
$532$	8.07144	+	30.1230i	0.349941	+	1.30600i
$533$	3.71644	+	7.96992i	0.160977	+	0.345216i
$534$		0			0
$535$	7.03416	−	10.0458i	0.304113	−	0.434319i
$536$	−1.16831	−	13.3538i	−0.0504633	−	0.576798i
$537$		0			0
$538$	−3.99466	−	2.79709i	−0.172222	−	0.120591i
$539$	−57.1958	−	20.8176i	−2.46360	−	0.896677i
$540$		0			0
$541$	25.7843	−	6.90890i	1.10856	−	0.297037i	0.342312	−	0.939586i	$-0.388790\pi$
$541$	25.7843	−	6.90890i	1.10856	−	0.297037i	0.766244	+	0.642550i	$0.222123\pi$
$542$	−15.8064	+	11.0677i	−0.678942	+	0.475400i
$543$		0			0
$544$	2.18174	+	3.77889i	0.0935414	+	0.162018i
$545$	19.4940	−	33.7647i	0.835032	−	1.44632i
$546$		0			0
$547$	17.4340	+	4.67144i	0.745426	+	0.199736i	0.611488	−	0.791254i	$-0.290571\pi$
$547$	17.4340	+	4.67144i	0.745426	+	0.199736i	0.133937	+	0.990990i	$0.457238\pi$
$548$	19.2323	−	6.99997i	0.821561	−	0.299024i
$549$		0			0
$550$	−6.57761	+	14.1057i	−0.280470	+	0.601470i
$551$	11.1820	+	1.97169i	0.476371	+	0.0839970i
$552$		0			0
$553$	−13.1476	−	1.15026i	−0.559091	−	0.0489141i
$554$	24.3310			1.03372
$555$		0			0
$556$	5.62889			0.238718
$557$	−7.77789	−	0.680477i	−0.329560	−	0.0288327i	−0.0788247	−	0.996888i	$-0.525117\pi$
$557$	−7.77789	−	0.680477i	−0.329560	−	0.0288327i	−0.250735	+	0.968056i	$0.580672\pi$
$558$		0			0
$559$	−14.8676	−	2.62157i	−0.628834	−	0.110880i
$560$	−5.17073	+	11.0887i	−0.218503	+	0.468582i
$561$		0			0
$562$	−16.6536	+	6.06141i	−0.702489	+	0.255685i
$563$	−3.93634	−	1.05474i	−0.165897	−	0.0444519i	0.174915	−	0.984584i	$-0.444035\pi$
$563$	−3.93634	−	1.05474i	−0.165897	−	0.0444519i	−0.340811	+	0.940132i	$0.610702\pi$
$564$		0			0
$565$	−1.19651	+	2.07242i	−0.0503378	+	0.0871875i
$566$	−2.39002	−	4.13964i	−0.100460	−	0.174002i
$567$		0			0
$568$	−7.63996	+	5.34956i	−0.320566	+	0.224463i
$569$	9.06019	−	2.42767i	0.379823	−	0.101773i	−0.0638558	−	0.997959i	$-0.520340\pi$
$569$	9.06019	−	2.42767i	0.379823	−	0.101773i	0.443679	+	0.896186i	$0.353673\pi$
$570$		0			0
$571$	−36.4747	−	13.2757i	−1.52642	−	0.555571i	−0.563677	−	0.825995i	$-0.690614\pi$
$571$	−36.4747	−	13.2757i	−1.52642	−	0.555571i	−0.962741	+	0.270424i	$0.912836\pi$
$572$	−16.5265	−	11.5720i	−0.691008	−	0.483849i
$573$		0			0
$574$	0.853640	+	9.75715i	0.0356302	+	0.407255i
$575$	9.46356	−	13.5154i	0.394658	−	0.563630i
$576$		0			0
$577$	−12.0134	−	25.7629i	−0.500125	−	1.07252i	−0.980691	−	0.195563i	$-0.937347\pi$
$577$	−12.0134	−	25.7629i	−0.500125	−	1.07252i	0.480566	−	0.876959i	$-0.340431\pi$
$578$	0.527986	+	1.97047i	0.0219613	+	0.0819608i
$579$		0			0
$580$	2.86342	+	3.41250i	0.118897	+	0.141696i
$581$	15.4841	−	8.93977i	0.642390	−	0.370884i
$582$		0			0
$583$	−61.4066	+	10.8276i	−2.54320	+	0.448435i
$584$	1.53103	−	5.71389i	0.0633546	−	0.236442i
$585$		0			0
$586$	−6.08528	+	6.08528i	−0.251381	+	0.251381i
$587$	−39.9518	−	18.6298i	−1.64899	−	0.768935i	−0.999967	−	0.00816373i	$-0.997401\pi$
$587$	−39.9518	−	18.6298i	−1.64899	−	0.768935i	−0.649020	−	0.760771i	$-0.724821\pi$
$588$		0			0
$589$	−43.7973	−	36.7503i	−1.80464	−	1.51427i
$590$	−0.377819	+	4.31850i	−0.0155546	+	0.177790i
$591$		0			0
$592$	2.88771	−	5.35361i	0.118684	−	0.220032i
$593$			16.9034i			0.694138i	0.937840	+	0.347069i	$0.112823\pi$
$593$			16.9034i			0.694138i	−0.937840	+	0.347069i	$0.887177\pi$
$594$		0			0
$595$	−34.3166	+	40.8970i	−1.40684	+	1.67661i
$596$	−2.05259	+	11.6408i	−0.0840774	+	0.476827i
$597$		0			0
$598$	15.1232	+	15.1232i	0.618436	+	0.618436i
$599$	−4.23377	−	11.6322i	−0.172987	−	0.475279i	0.822654	−	0.568542i	$-0.192492\pi$
$599$	−4.23377	−	11.6322i	−0.172987	−	0.475279i	−0.995641	+	0.0932634i	$0.970270\pi$
$600$		0			0
$601$	−4.63780	−	26.3023i	−0.189180	−	1.07289i	−0.920466	−	0.390822i	$-0.872191\pi$
$601$	−4.63780	−	26.3023i	−0.189180	−	1.07289i	0.731287	−	0.682070i	$-0.238920\pi$
$602$	−14.5620	−	8.40738i	−0.593503	−	0.342659i
$603$		0			0
$604$	−9.55752	+	8.01971i	−0.388890	+	0.326317i
$605$	−25.9090	−	37.0019i	−1.05335	−	1.50434i
$606$		0			0
$607$	19.2246	−	8.96458i	0.780303	−	0.363861i	0.00869704	−	0.999962i	$-0.497232\pi$
$607$	19.2246	−	8.96458i	0.780303	−	0.363861i	0.771606	+	0.636101i	$0.219454\pi$
$608$	−2.46524	+	6.77319i	−0.0999787	+	0.274689i
$609$		0			0
$610$	−9.60233	+	0.840095i	−0.388787	+	0.0340144i
$611$	−42.7441	+	3.73962i	−1.72924	+	0.151289i
$612$		0			0
$613$	−2.21722	+	6.09175i	−0.0895525	+	0.246043i	−0.976381	−	0.216055i	$-0.930681\pi$
$613$	−2.21722	+	6.09175i	−0.0895525	+	0.246043i	0.886829	+	0.462098i	$0.152903\pi$
$614$	12.8025	−	5.96992i	0.516669	−	0.240927i
$615$		0			0
$616$	−12.8887	−	18.4069i	−0.519299	−	0.741636i
$617$	34.9859	−	29.3567i	1.40848	−	1.18186i	0.451296	−	0.892374i	$-0.350962\pi$
$617$	34.9859	−	29.3567i	1.40848	−	1.18186i	0.957184	−	0.289481i	$-0.0934827\pi$
$618$		0			0
$619$	35.0392	+	20.2299i	1.40834	+	0.813107i	0.995228	−	0.0975724i	$-0.0311077\pi$
$619$	35.0392	+	20.2299i	1.40834	+	0.813107i	0.413114	+	0.910679i	$0.364441\pi$
$620$	−3.89505	−	22.0899i	−0.156429	−	0.887152i
$621$		0			0
$622$	0.0763962	+	0.209897i	0.00306321	+	0.00841610i
$623$	13.5113	+	13.5113i	0.541321	+	0.541321i
$624$		0			0
$625$	5.38366	−	30.5322i	0.215346	−	1.22129i
$626$	10.0812	−	12.0143i	0.402927	−	0.480189i
$627$		0			0
$628$		−	6.14626i		−	0.245263i
$629$	18.2172	−	19.3031i	0.726369	−	0.769667i
$630$		0			0
$631$	0.997174	−	11.3978i	0.0396969	−	0.453737i	−0.950169	−	0.311734i	$-0.899090\pi$
$631$	0.997174	−	11.3978i	0.0396969	−	0.453737i	0.989866	−	0.142003i	$-0.0453543\pi$
$632$	−2.33673	−	1.96075i	−0.0929499	−	0.0779943i
$633$		0			0
$634$	10.4461	+	4.87110i	0.414868	+	0.193456i
$635$	−43.1871	+	43.1871i	−1.71383	+	1.71383i
$636$		0			0
$637$	11.7829	−	43.9744i	0.466855	−	1.74233i
$638$	−8.05717	+	1.42070i	−0.318986	+	0.0562459i
$639$		0			0
$640$	−2.44899	+	1.41393i	−0.0968049	+	0.0558903i
$641$	5.88695	+	7.01580i	0.232521	+	0.277107i	0.869671	−	0.493633i	$-0.164331\pi$
$641$	5.88695	+	7.01580i	0.232521	+	0.277107i	−0.637150	+	0.770740i	$0.719887\pi$
$642$		0			0
$643$	−12.8252	−	47.8645i	−0.505778	−	1.88759i	−0.458470	−	0.888710i	$-0.651602\pi$
$643$	−12.8252	−	47.8645i	−0.505778	−	1.88759i	−0.0473084	−	0.998880i	$-0.515064\pi$
$644$	10.0672	+	21.5892i	0.396703	+	0.850733i
$645$		0			0
$646$	−18.0398	+	25.7635i	−0.709767	+	1.01365i
$647$	−2.11511	−	24.1759i	−0.0831537	−	0.950452i	−0.917113	−	0.398626i	$-0.869487\pi$
$647$	−2.11511	−	24.1759i	−0.0831537	−	0.950452i	0.833960	−	0.551825i	$-0.186068\pi$
$648$		0			0
$649$	−6.52177	−	4.56659i	−0.256002	−	0.179255i
$650$	−10.9391	−	3.98152i	−0.429068	−	0.156168i
$651$		0			0
$652$	−10.0178	+	2.68427i	−0.392329	+	0.105124i
$653$	23.5653	−	16.5006i	0.922180	−	0.645718i	−0.0129902	−	0.999916i	$-0.504135\pi$
$653$	23.5653	−	16.5006i	0.922180	−	0.645718i	0.935170	+	0.354198i	$0.115246\pi$
$654$		0			0
$655$	−2.41986	−	4.19133i	−0.0945519	−	0.163769i
$656$	−1.13188	+	1.96048i	−0.0441926	+	0.0765438i
$657$		0			0
$658$	−46.1611	−	12.3688i	−1.79955	−	0.482187i
$659$	14.9946	−	5.45759i	0.584107	−	0.212598i	−0.0330285	−	0.999454i	$-0.510515\pi$
$659$	14.9946	−	5.45759i	0.584107	−	0.212598i	0.617136	+	0.786857i	$0.288293\pi$
$660$		0			0
$661$	−4.24158	+	9.09610i	−0.164978	+	0.353797i	−0.971365	−	0.237591i	$-0.923642\pi$
$661$	−4.24158	+	9.09610i	−0.164978	+	0.353797i	0.806387	+	0.591388i	$0.201420\pi$
$662$	15.3874	+	2.71321i	0.598049	+	0.105452i
$663$		0			0
$664$	4.11674	+	0.360168i	0.159760	+	0.0139772i
$665$	−88.1884			−3.41980
$666$		0			0
$667$	8.67311			0.335824
$668$	12.3387	+	1.07950i	0.477399	+	0.0417670i
$669$		0			0
$670$	37.3311	+	6.58247i	1.44222	+	0.254303i
$671$	7.48158	−	16.0443i	0.288823	−	0.619383i
$672$		0			0
$673$	−24.2140	+	8.81319i	−0.933382	+	0.339723i	−0.763549	−	0.645750i	$-0.776545\pi$
$673$	−24.2140	+	8.81319i	−0.933382	+	0.339723i	−0.169833	+	0.985473i	$0.554323\pi$
$674$	−7.01056	−	1.87847i	−0.270037	−	0.0723561i
$675$		0			0
$676$	1.04508	−	1.81013i	0.0401953	−	0.0696203i
$677$	19.1769	+	33.2154i	0.737029	+	1.27657i	0.953827	+	0.300355i	$0.0971053\pi$
$677$	19.1769	+	33.2154i	0.737029	+	1.27657i	−0.216798	+	0.976216i	$0.569561\pi$
$678$		0			0
$679$	−42.7796	+	29.9546i	−1.64173	+	1.14955i
$680$	−11.9188	+	3.19364i	−0.457066	+	0.122471i
$681$		0			0
$682$	38.7116	+	14.0899i	1.48234	+	0.539529i
$683$	−0.833042	−	0.583303i	−0.0318755	−	0.0223195i	0.557530	−	0.830157i	$-0.311749\pi$
$683$	−0.833042	−	0.583303i	−0.0318755	−	0.0223195i	−0.589406	+	0.807837i	$0.700638\pi$
$684$		0			0
$685$	5.04426	+	57.6561i	0.192731	+	2.20293i
$686$	11.7121	−	16.7266i	0.447169	−	0.638624i
$687$		0			0
$688$	−1.64245	−	3.52224i	−0.0626178	−	0.134284i
$689$	−12.0708	−	45.0490i	−0.459862	−	1.71623i
$690$		0			0
$691$	14.5428	+	17.3315i	0.553235	+	0.659320i	0.968100	−	0.250563i	$-0.0806158\pi$
$691$	14.5428	+	17.3315i	0.553235	+	0.659320i	−0.414865	+	0.909883i	$0.636171\pi$
$692$	7.38220	−	4.26212i	0.280629	−	0.162021i
$693$		0			0
$694$	−18.8556	+	3.32475i	−0.715749	+	0.126206i
$695$	−4.11980	+	15.3753i	−0.156273	+	0.583218i
$696$		0			0
$697$	−6.98473	+	6.98473i	−0.264566	+	0.264566i
$698$	7.08311	+	3.30291i	0.268100	+	0.125017i
$699$		0			0
$700$	−9.93233	−	8.33422i	−0.375407	−	0.315004i
$701$	−3.45083	+	39.4431i	−0.130336	+	1.48975i	0.596321	+	0.802746i	$0.296628\pi$
$701$	−3.45083	+	39.4431i	−0.130336	+	1.48975i	−0.726657	+	0.687000i	$0.758927\pi$
$702$		0			0
$703$	43.7693	+	2.55607i	1.65079	+	0.0964042i
$704$		−	5.19361i		−	0.195742i
$705$		0			0
$706$	13.8548	−	16.5115i	0.521431	−	0.621417i
$707$	2.74475	−	15.5662i	0.103227	−	0.585428i
$708$		0			0
$709$	25.3658	+	25.3658i	0.952631	+	0.952631i	0.998928	−	0.0462964i	$-0.0147419\pi$
$709$	25.3658	+	25.3658i	0.952631	+	0.952631i	−0.0462964	+	0.998928i	$0.514742\pi$
$710$	−9.02059	−	24.7839i	−0.338537	−	0.930122i
$711$		0			0
$712$	0.766896	+	4.34929i	0.0287407	+	0.162996i
$713$	−37.8207	−	21.8358i	−1.41640	−	0.817757i
$714$		0			0
$715$	43.7046	−	36.6725i	1.63446	−	1.37147i
$716$	−12.2882	−	17.5494i	−0.459232	−	0.655852i
$717$		0			0
$718$	3.11192	−	1.45111i	0.116136	−	0.0541550i
$719$	−2.53416	+	6.96254i	−0.0945081	+	0.259659i	−0.977935	−	0.208911i	$-0.933008\pi$
$719$	−2.53416	+	6.96254i	−0.0945081	+	0.259659i	0.883427	+	0.468569i	$0.155230\pi$
$720$		0			0
$721$	−43.2289	+	3.78204i	−1.60993	+	0.140851i
$722$	−32.8282	+	2.87209i	−1.22174	+	0.106888i
$723$		0			0
$724$	−0.00327159	+	0.00898862i	−0.000121588	+	0.000334059i
$725$	−4.27846	+	1.99508i	−0.158898	+	0.0740954i
$726$		0			0
$727$	−2.62627	−	3.75071i	−0.0974031	−	0.139106i	0.767492	−	0.641058i	$-0.221504\pi$
$727$	−2.62627	−	3.75071i	−0.0974031	−	0.139106i	−0.864895	+	0.501952i	$0.832615\pi$
$728$	12.8750	−	10.8034i	0.477180	−	0.400402i
$729$		0			0
$730$	14.4869	+	8.36402i	0.536184	+	0.309566i
$731$	−2.94474	−	16.7005i	−0.108915	−	0.617689i
$732$		0			0
$733$	−9.03687	−	24.8286i	−0.333784	−	0.917065i	−0.987118	−	0.159995i	$-0.948852\pi$
$733$	−9.03687	−	24.8286i	−0.333784	−	0.917065i	0.653334	−	0.757070i	$-0.273370\pi$
$734$	20.4299	+	20.4299i	0.754080	+	0.754080i
$735$		0			0
$736$	−0.956056	+	5.42207i	−0.0352407	+	0.199860i
$737$	−44.7506	+	53.3317i	−1.64841	+	1.96450i
$738$		0			0
$739$		−	13.3784i		−	0.492131i	−0.969253	−	0.246065i	$-0.920862\pi$
$739$		−	13.3784i		−	0.492131i	0.969253	−	0.246065i	$-0.0791378\pi$
$740$	12.5098	+	11.8061i	0.459871	+	0.434000i
$741$		0			0
$742$	4.52728	−	51.7470i	0.166202	−	1.89969i
$743$	39.5503	+	33.1866i	1.45096	+	1.21750i	0.931877	+	0.362773i	$0.118170\pi$
$743$	39.5503	+	33.1866i	1.45096	+	1.21750i	0.519081	+	0.854725i	$0.326274\pi$
$744$		0			0
$745$	−30.2946	−	14.1266i	−1.10991	−	0.517558i
$746$	−6.83076	+	6.83076i	−0.250092	+	0.250092i
$747$		0			0
$748$	5.86542	−	21.8900i	0.214461	−	0.800379i
$749$	−18.4783	+	3.25823i	−0.675184	+	0.119053i
$750$		0			0
$751$	35.1370	−	20.2864i	1.28217	−	0.740260i	0.304923	−	0.952377i	$-0.401369\pi$
$751$	35.1370	−	20.2864i	1.28217	−	0.740260i	0.977244	+	0.212117i	$0.0680359\pi$
$752$	−7.09990	−	8.46134i	−0.258907	−	0.308553i
$753$		0			0
$754$	−1.58382	−	5.91088i	−0.0576792	−	0.215262i
$755$	−14.9106	−	31.9760i	−0.542653	−	1.16372i
$756$		0			0
$757$	6.59263	−	9.41525i	0.239613	−	0.342203i	−0.681277	−	0.732026i	$-0.738575\pi$
$757$	6.59263	−	9.41525i	0.239613	−	0.342203i	0.920890	+	0.389823i	$0.127464\pi$
$758$	0.265234	+	3.03164i	0.00963375	+	0.110114i
$759$		0			0
$760$	−16.6966	−	11.6911i	−0.605650	−	0.424081i
$761$	6.27877	+	2.28528i	0.227605	+	0.0828415i	0.453305	−	0.891355i	$-0.350245\pi$
$761$	6.27877	+	2.28528i	0.227605	+	0.0828415i	−0.225700	+	0.974197i	$0.572467\pi$
$762$		0			0
$763$	−57.6190	+	15.4390i	−2.08595	+	0.558928i
$764$	−2.39934	+	1.68004i	−0.0868052	+	0.0607817i
$765$		0			0
$766$	14.5832	+	25.2588i	0.526911	+	0.912636i
$767$	2.97748	−	5.15714i	0.107510	−	0.186214i
$768$		0			0
$769$	43.7077	+	11.7114i	1.57614	+	0.422325i	0.937728	−	0.347370i	$-0.112925\pi$
$769$	43.7077	+	11.7114i	1.57614	+	0.422325i	0.638412	+	0.769695i	$0.279592\pi$
$770$	59.7117	−	21.7333i	2.15186	−	0.783213i
$771$		0			0
$772$	−7.90866	+	16.9602i	−0.284639	+	0.610410i
$773$	13.4563	+	2.37271i	0.483990	+	0.0853405i	0.410319	−	0.911942i	$-0.365417\pi$
$773$	13.4563	+	2.37271i	0.483990	+	0.0853405i	0.0736711	+	0.997283i	$0.476529\pi$
$774$		0			0
$775$	23.6799	+	2.07173i	0.850608	+	0.0744186i
$776$	−12.0705			−0.433305
$777$		0			0
$778$	−14.3655			−0.515029
$779$	−16.2549	−	1.42212i	−0.582391	−	0.0509526i
$780$		0			0
$781$	47.7032	+	8.41137i	1.70696	+	0.300982i
$782$	−10.1530	+	21.7732i	−0.363071	+	0.778608i
$783$		0			0
$784$	11.0127	−	4.00830i	0.393312	−	0.143154i
$785$	16.7885	+	4.49846i	0.599207	+	0.160557i
$786$		0			0
$787$	−13.7014	+	23.7316i	−0.488403	+	0.845939i	−0.999911	−	0.0133393i	$-0.995754\pi$
$787$	−13.7014	+	23.7316i	−0.488403	+	0.845939i	0.511508	+	0.859279i	$0.329087\pi$
$788$	−5.67881	−	9.83600i	−0.202299	−	0.350393i
$789$		0			0
$790$	7.06602	−	4.94768i	0.251398	−	0.176031i
$791$	3.53657	−	0.947621i	0.125746	−	0.0336935i
$792$		0			0
$793$	12.4425	+	4.52871i	0.441847	+	0.160819i
$794$	26.0170	+	18.2173i	0.923310	+	0.646509i
$795$		0			0
$796$	−0.730527	−	8.34997i	−0.0258929	−	0.295957i
$797$	−29.7599	+	42.5015i	−1.05415	+	1.50548i	−0.203977	+	0.978976i	$0.565387\pi$
$797$	−29.7599	+	42.5015i	−1.05415	+	1.50548i	−0.850172	+	0.526505i	$0.823502\pi$
$798$		0			0
$799$	−20.3688	−	43.6811i	−0.720598	−	1.54533i
$800$	−0.775615	−	2.89464i	−0.0274221	−	0.102341i
$801$		0			0
$802$	−10.7480	−	12.8090i	−0.379526	−	0.452301i
$803$	−26.6065	+	15.3613i	−0.938924	+	0.542088i
$804$		0			0
$805$	−66.3389	+	11.6973i	−2.33814	+	0.412277i
$806$	−7.97497	+	29.7630i	−0.280906	+	1.04836i
$807$		0			0
$808$	2.58327	−	2.58327i	0.0908791	−	0.0908791i
$809$	−2.39390	−	1.11629i	−0.0841650	−	0.0392468i	0.380080	−	0.924954i	$-0.375896\pi$
$809$	−2.39390	−	1.11629i	−0.0841650	−	0.0392468i	−0.464245	+	0.885707i	$0.653674\pi$
$810$		0			0
$811$	−35.7569	−	30.0036i	−1.25559	−	1.05357i	−0.996137	−	0.0878131i	$-0.972012\pi$
$811$	−35.7569	−	30.0036i	−1.25559	−	1.05357i	−0.259456	−	0.965755i	$-0.583543\pi$
$812$	0.594025	−	6.78974i	0.0208462	−	0.238273i
$813$		0			0
$814$	−30.2657	+	9.05586i	−1.06081	+	0.317408i
$815$		−	29.3283i		−	1.02732i
$816$		0			0
$817$	18.0061	−	21.4588i	0.629952	−	0.750748i
$818$	1.13175	−	6.41846i	0.0395706	−	0.224416i
$819$		0			0
$820$	−4.52661	−	4.52661i	−0.158076	−	0.158076i
$821$	7.93974	+	21.8143i	0.277099	+	0.761323i	0.997688	+	0.0679605i	$0.0216492\pi$
$821$	7.93974	+	21.8143i	0.277099	+	0.761323i	−0.720589	+	0.693362i	$0.756129\pi$
$822$		0			0
$823$	8.72522	+	49.4832i	0.304142	+	1.72487i	0.627516	+	0.778604i	$0.284072\pi$
$823$	8.72522	+	49.4832i	0.304142	+	1.72487i	−0.323374	+	0.946271i	$0.604817\pi$
$824$	−8.68588	−	5.01480i	−0.302587	−	0.174699i
$825$		0			0
$826$	5.08081	−	4.26330i	0.176784	−	0.148339i
$827$	6.40780	+	9.15128i	0.222821	+	0.318221i	0.914961	−	0.403542i	$-0.132221\pi$
$827$	6.40780	+	9.15128i	0.222821	+	0.318221i	−0.692140	+	0.721763i	$0.743332\pi$
$828$		0			0
$829$	−36.2345	+	16.8964i	−1.25848	+	0.586837i	−0.933395	−	0.358850i	$-0.883169\pi$
$829$	−36.2345	+	16.8964i	−1.25848	+	0.586837i	−0.325080	+	0.945687i	$0.605391\pi$
$830$	−3.99685	+	10.9812i	−0.138733	+	0.381165i
$831$		0			0
$832$	3.86982	−	0.338566i	0.134162	−	0.0117377i
$833$	50.9432	−	4.45695i	1.76508	−	0.154424i
$834$		0			0
$835$	−11.9794	+	32.9130i	−0.414563	+	1.13900i
$836$	33.9276	−	15.8207i	1.17341	−	0.547170i
$837$		0			0
$838$	11.1665	+	15.9475i	0.385741	+	0.550896i
$839$	−6.01490	+	5.04710i	−0.207658	+	0.174245i	−0.740685	−	0.671853i	$-0.765499\pi$
$839$	−6.01490	+	5.04710i	−0.207658	+	0.174245i	0.533027	+	0.846098i	$0.321054\pi$
$840$		0			0
$841$	22.9657	+	13.2592i	0.791919	+	0.457215i
$842$	5.61450	+	31.8414i	0.193488	+	1.09733i
$843$		0			0
$844$	0.102856	+	0.282595i	0.00354046	+	0.00972733i
$845$	4.17946	+	4.17946i	0.143778	+	0.143778i
$846$		0			0
$847$	−12.0011	+	68.0615i	−0.412362	+	2.33862i
$848$	7.71723	−	9.19704i	0.265011	−	0.315828i
$849$		0			0
$850$		−	13.0763i		−	0.448512i
$851$	33.2641	−	3.88279i	1.14028	−	0.133100i
$852$		0			0
$853$	2.54401	−	29.0781i	0.0871052	−	0.995617i	−0.819344	−	0.573302i	$-0.805662\pi$
$853$	2.54401	−	29.0781i	0.0871052	−	0.995617i	0.906449	−	0.422315i	$-0.138782\pi$
$854$	11.2973	+	9.47960i	0.386587	+	0.324385i
$855$		0			0
$856$	−3.93043	−	1.83279i	−0.134339	−	0.0626435i
$857$	−22.7578	+	22.7578i	−0.777393	+	0.777393i	−0.979387	−	0.201994i	$-0.935258\pi$
$857$	−22.7578	+	22.7578i	−0.777393	+	0.777393i	0.201994	+	0.979387i	$0.435258\pi$
$858$		0			0
$859$	0.407625	−	1.52128i	0.0139080	−	0.0519054i	−0.958623	−	0.284678i	$-0.908113\pi$
$859$	0.407625	−	1.52128i	0.0139080	−	0.0519054i	0.972531	+	0.232773i	$0.0747799\pi$
$860$	10.8231	−	1.90841i	0.369065	−	0.0650761i
$861$		0			0
$862$	11.1591	−	6.44273i	0.380082	−	0.219440i
$863$	−26.4541	−	31.5268i	−0.900509	−	1.07318i	−0.996965	−	0.0778473i	$-0.975195\pi$
$863$	−26.4541	−	31.5268i	−0.900509	−	1.07318i	0.0964566	−	0.995337i	$-0.469249\pi$
$864$		0			0
$865$	6.23890	+	23.2839i	0.212129	+	0.791676i
$866$	1.08635	+	2.32969i	0.0369158	+	0.0791661i
$867$		0			0
$868$	−19.6845	+	28.1124i	−0.668135	+	0.954196i
$869$	1.38076	+	15.7822i	0.0468392	+	0.535374i
$870$		0			0
$871$	−42.6553	−	29.8676i	−1.44532	−	1.01202i
$872$	−12.9557	−	4.71549i	−0.438735	−	0.159687i
$873$		0			0
$874$	−38.3323	+	10.2711i	−1.29661	+	0.347425i
$875$	−20.0772	+	14.0582i	−0.678734	+	0.475255i
$876$		0			0
$877$	−17.1659	−	29.7321i	−0.579650	−	1.00398i	−0.995519	−	0.0945584i	$-0.969856\pi$
$877$	−17.1659	−	29.7321i	−0.579650	−	1.00398i	0.415870	−	0.909424i	$-0.363477\pi$
$878$	−0.325021	+	0.562952i	−0.0109689	+	0.0189987i
$879$		0			0
$880$	14.1863	+	3.80122i	0.478221	+	0.128139i
$881$	−9.34031	+	3.39959i	−0.314683	+	0.114535i	−0.494533	−	0.869159i	$-0.664661\pi$
$881$	−9.34031	+	3.39959i	−0.314683	+	0.114535i	0.179850	+	0.983694i	$0.442439\pi$
$882$		0			0
$883$	6.25411	−	13.4120i	0.210468	−	0.451349i	−0.772528	−	0.634981i	$-0.781008\pi$
$883$	6.25411	−	13.4120i	0.210468	−	0.451349i	0.982995	+	0.183632i	$0.0587856\pi$
$884$	16.6929	+	2.94341i	0.561443	+	0.0989975i
$885$		0			0
$886$	3.34992	+	0.293080i	0.112543	+	0.00984621i
$887$	34.1292			1.14595			0.572973	−	0.819574i	$-0.305790\pi$
$887$	34.1292			1.14595			0.572973	+	0.819574i	$0.305790\pi$
$888$		0			0
$889$	93.4457			3.13407
$890$	−12.4413	−	1.08848i	−0.417035	−	0.0364858i
$891$		0			0
$892$	−20.1840	−	3.55899i	−0.675812	−	0.119164i
$893$	33.6466	−	72.1553i	1.12594	−	2.41459i
$894$		0			0
$895$	56.9299	−	20.7208i	1.90296	−	0.692619i
$896$	4.17918	+	1.11981i	0.139617	+	0.0374101i
$897$		0			0
$898$	4.61448	−	7.99251i	0.153987	−	0.266714i
$899$	6.24766	+	10.8213i	0.208371	+	0.360909i
$900$		0			0
$901$	42.9133	−	30.0482i	1.42965	−	1.00105i
$902$	11.3565	−	3.04297i	0.378130	−	0.101320i
$903$		0			0
$904$	0.795201	+	0.289430i	0.0264480	+	0.00962629i
$905$	−0.0221579	−	0.0155151i	−0.000736553	−	0.000515740i
$906$		0			0
$907$	0.503882	+	5.75940i	0.0167311	+	0.191238i	0.999961	+	0.00886551i	$0.00282202\pi$
$907$	0.503882	+	5.75940i	0.0167311	+	0.191238i	−0.983230	+	0.182372i	$0.941622\pi$
$908$	−6.64329	+	9.48760i	−0.220465	+	0.314857i
$909$		0			0
$910$	20.0863	+	43.0751i	0.665853	+	1.42793i
$911$	6.98572	+	26.0710i	0.231447	+	0.863772i	0.979718	+	0.200379i	$0.0642175\pi$
$911$	6.98572	+	26.0710i	0.231447	+	0.863772i	−0.748271	+	0.663393i	$0.769116\pi$
$912$		0			0
$913$	−13.7958	−	16.4412i	−0.456574	−	0.544123i
$914$	−15.7379	+	9.08626i	−0.520562	+	0.300547i
$915$		0			0
$916$	0.314879	−	0.0555217i	0.0104039	−	0.00183449i
$917$	−1.91649	+	7.15245i	−0.0632882	+	0.236195i
$918$		0			0
$919$	36.6151	−	36.6151i	1.20782	−	1.20782i	0.236089	−	0.971731i	$-0.424134\pi$
$919$	36.6151	−	36.6151i	1.20782	−	1.20782i	0.971731	−	0.236089i	$-0.0758658\pi$
$920$	−14.1106	−	6.57988i	−0.465213	−	0.216932i
$921$		0			0
$922$	28.2442	+	23.6997i	0.930173	+	0.780507i
$923$	−3.15769	+	36.0926i	−0.103937	+	1.18800i
$924$		0			0
$925$	−15.5161	+	9.56713i	−0.510165	+	0.314565i
$926$		−	3.60211i		−	0.118373i
$927$		0			0
$928$	1.01258	−	1.20675i	0.0332395	−	0.0396133i
$929$	−2.97185	+	16.8542i	−0.0975033	+	0.552969i	0.896448	+	0.443149i	$0.146139\pi$
$929$	−2.97185	+	16.8542i	−0.0975033	+	0.552969i	−0.993951	+	0.109820i	$0.964973\pi$
$930$		0			0
$931$	59.7312	+	59.7312i	1.95761	+	1.95761i
$932$	1.50559	+	4.13657i	0.0493172	+	0.135498i
$933$		0			0
$934$	0.435675	+	2.47084i	0.0142557	+	0.0808483i
$935$	55.4996	+	32.0427i	1.81503	+	1.04791i
$936$		0			0
$937$	31.6703	−	26.5746i	1.03462	−	0.868153i	0.0432302	−	0.999065i	$-0.486235\pi$
$937$	31.6703	−	26.5746i	1.03462	−	0.868153i	0.991394	+	0.130912i	$0.0417907\pi$
$938$	−33.2660	−	47.5088i	−1.08617	−	1.55122i
$939$		0			0
$940$	28.3085	−	13.2005i	0.923323	−	0.430552i
$941$	−19.1481	+	52.6091i	−0.624211	+	1.71501i	0.0722254	+	0.997388i	$0.476990\pi$
$941$	−19.1481	+	52.6091i	−0.624211	+	1.71501i	−0.696437	+	0.717618i	$0.745232\pi$
$942$		0			0
$943$	−12.4162	+	1.08628i	−0.404327	+	0.0353741i
$944$	1.52713	−	0.133607i	0.0497038	−	0.00434852i
$945$		0			0
$946$	−6.90343	+	18.9670i	−0.224450	+	0.616671i
$947$	−26.5573	+	12.3839i	−0.862996	+	0.402422i	−0.803144	−	0.595786i	$-0.796841\pi$
$947$	−26.5573	+	12.3839i	−0.862996	+	0.402422i	−0.0598525	+	0.998207i	$0.519063\pi$
$948$		0			0
$949$	−13.1803	−	18.8235i	−0.427852	−	0.611035i
$950$	16.5467	−	13.8843i	0.536846	−	0.450468i
$951$		0			0
$952$	16.3497	+	9.43953i	0.529898	+	0.305937i
$953$	−8.22506	−	46.6466i	−0.266436	−	1.51103i	−0.764915	−	0.644131i	$-0.777219\pi$
$953$	−8.22506	−	46.6466i	−0.266436	−	1.51103i	0.498480	−	0.866901i	$-0.333892\pi$
$954$		0			0
$955$	−2.83293	−	7.78342i	−0.0916716	−	0.251866i
$956$	−13.3888	−	13.3888i	−0.433025	−	0.433025i
$957$		0			0
$958$	1.28760	−	7.30236i	0.0416005	−	0.235928i
$959$	56.9192	−	67.8337i	1.83802	−	2.19046i
$960$		0			0
$961$		−	31.9176i		−	1.02960i
$962$	−8.72062	−	21.9610i	−0.281164	−	0.708052i
$963$		0			0
$964$	−0.358239	+	4.09469i	−0.0115381	+	0.131881i
$965$	−40.5383	−	34.0156i	−1.30497	−	1.09500i
$966$		0			0
$967$	−11.8923	−	5.54549i	−0.382432	−	0.178331i	0.221889	−	0.975072i	$-0.428778\pi$
$967$	−11.8923	−	5.54549i	−0.382432	−	0.178331i	−0.604321	+	0.796741i	$0.706556\pi$
$968$	−11.2951	+	11.2951i	−0.363037	+	0.363037i
$969$		0			0
$970$	8.83442	−	32.9705i	0.283656	−	1.05862i
$971$	16.4495	−	2.90049i	0.527889	−	0.0930811i	0.0966495	−	0.995318i	$-0.469187\pi$
$971$	16.4495	−	2.90049i	0.527889	−	0.0930811i	0.431240	+	0.902237i	$0.358076\pi$
$972$		0			0
$973$	21.0912	−	12.1770i	0.676152	−	0.390376i
$974$	18.5445	+	22.1005i	0.594204	+	0.708145i
$975$		0			0
$976$	0.882210	+	3.29245i	0.0282388	+	0.105389i
$977$	2.20318	+	4.72474i	0.0704860	+	0.151158i	0.938394	−	0.345567i	$-0.112314\pi$
$977$	2.20318	+	4.72474i	0.0704860	+	0.151158i	−0.867908	+	0.496725i	$0.834536\pi$
$978$		0			0
$979$	13.1561	−	18.7889i	0.420471	−	0.600495i
$980$	2.88843	+	33.0149i	0.0922675	+	1.05462i
$981$		0			0
$982$	−7.68041	−	5.37788i	−0.245092	−	0.171615i
$983$	13.8825	+	5.05280i	0.442781	+	0.161159i	0.553783	−	0.832661i	$-0.313184\pi$
$983$	13.8825	+	5.05280i	0.442781	+	0.161159i	−0.111002	+	0.993820i	$0.535406\pi$
$984$		0			0
$985$	31.0233	−	8.31267i	0.988485	−	0.264864i
$986$	5.63066	−	3.94263i	0.179317	−	0.125559i
$987$		0			0
$988$	13.9999	+	24.2485i	0.445396	+	0.771448i
$989$	10.6986	−	18.5305i	0.340196	−	0.589236i
$990$		0			0
$991$	2.03001	+	0.543939i	0.0644854	+	0.0172788i	0.290917	−	0.956748i	$-0.406039\pi$
$991$	2.03001	+	0.543939i	0.0644854	+	0.0172788i	−0.226432	+	0.974027i	$0.572706\pi$
$992$	−7.45370	+	2.71292i	−0.236655	+	0.0861354i
$993$		0			0
$994$	−17.0538	+	36.5721i	−0.540915	+	1.16000i
$995$	23.3426	+	4.11592i	0.740009	+	0.130484i
$996$		0			0
$997$	−49.9396	−	4.36915i	−1.58160	−	0.138372i	−0.737798	−	0.675022i	$-0.764134\pi$
$997$	−49.9396	−	4.36915i	−1.58160	−	0.138372i	−0.843805	+	0.536649i	$0.819690\pi$
$998$	−11.3732			−0.360012
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.35.5	yes	96
3.2	odd	2	inner	666.2.bs.b.35.4	✓	96
37.18	odd	36	inner	666.2.bs.b.647.4	yes	96
111.92	even	36	inner	666.2.bs.b.647.5	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.35.4	✓	96	3.2	odd	2	inner
666.2.bs.b.35.5	yes	96	1.1	even	1	trivial
666.2.bs.b.647.4	yes	96	37.18	odd	36	inner
666.2.bs.b.647.5	yes	96	111.92	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-1.19510 + 2.56290i) q^{5} +(4.06568 - 1.47979i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-1.19510 + 2.56290i) q^{5} +(4.06568 - 1.47979i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-1.41393 + 2.44899i) q^{10} +(-2.59681 - 4.49780i) q^{11} +(3.18208 - 2.22812i) q^{13} +(4.17918 - 1.11981i) q^{14} +(0.939693 + 0.342020i) q^{16} +(3.57436 + 2.50279i) q^{17} +(0.628208 + 7.18045i) q^{19} +(-1.62199 + 2.31644i) q^{20} +(-2.19492 - 4.70701i) q^{22} +(1.42498 + 5.31811i) q^{23} +(-1.92627 - 2.29564i) q^{25} +(3.36417 - 1.94230i) q^{26} +(4.26087 - 0.751307i) q^{28} +(0.407716 - 1.52162i) q^{29} +(-5.60881 + 5.60881i) q^{31} +(0.906308 + 0.422618i) q^{32} +(3.34262 + 2.80479i) q^{34} +(-1.06635 + 12.1884i) q^{35} +(0.882519 - 6.01840i) q^{37} +7.20788i q^{38} +(-1.81771 + 2.16626i) q^{40} +(-0.393099 + 2.22937i) q^{41} +(-2.74808 - 2.74808i) q^{43} +(-1.77632 - 4.88040i) q^{44} +(0.956056 + 5.42207i) q^{46} +(-9.56567 - 5.52274i) q^{47} +(8.97765 - 7.53315i) q^{49} +(-1.71886 - 2.45479i) q^{50} +(3.52065 - 1.64170i) q^{52} +(4.10625 - 11.2818i) q^{53} +(14.6309 - 1.28004i) q^{55} +(4.31014 - 0.377088i) q^{56} +(0.538782 - 1.48029i) q^{58} +(1.38934 - 0.647858i) q^{59} +(1.95509 + 2.79216i) q^{61} +(-6.07631 + 5.09863i) q^{62} +(0.866025 + 0.500000i) q^{64} +(1.90754 + 10.8182i) q^{65} +(-4.58473 - 12.5964i) q^{67} +(3.08545 + 3.08545i) q^{68} +(-2.12458 + 12.0491i) q^{70} +(-5.99507 + 7.14465i) q^{71} -5.91546i q^{73} +(1.40370 - 5.91858i) q^{74} +(-0.628208 + 7.18045i) q^{76} +(-17.2136 - 14.4439i) q^{77} +(-2.76458 - 1.28915i) q^{79} +(-1.99959 + 1.99959i) q^{80} +(-0.585906 + 2.18663i) q^{82} +(4.06968 - 0.717595i) q^{83} +(-10.6861 + 6.16964i) q^{85} +(-2.49811 - 2.97713i) q^{86} +(-1.34421 - 5.01664i) q^{88} +(1.86644 + 4.00260i) q^{89} +(9.64018 - 13.7676i) q^{91} +(0.479854 + 5.48476i) q^{92} +(-9.04794 - 6.33543i) q^{94} +(-19.1536 - 6.97134i) q^{95} +(-11.6592 + 3.12407i) q^{97} +(9.60005 - 6.72203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Introduction

L-functions

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Database

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