LMFDB - Embedded newform 666.2.bs.b.449.7

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			449.7
Character	$\chi$	$=$	666.449
Dual form			666.2.bs.b.89.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.906308 + 0.422618i) q^{2} +(0.642788 + 0.766044i) q^{4} +(1.52173 + 1.06553i) q^{5} +(0.800320 + 4.53884i) q^{7} +(0.258819 + 0.965926i) q^{8} +O(q^{10})$	\(q+(0.906308 + 0.422618i) q^{2} +(0.642788 + 0.766044i) q^{4} +(1.52173 + 1.06553i) q^{5} +(0.800320 + 4.53884i) q^{7} +(0.258819 + 0.965926i) q^{8} +(0.928845 + 1.60881i) q^{10} +(-0.382482 + 0.662479i) q^{11} +(-5.11437 - 0.447449i) q^{13} +(-1.19286 + 4.45181i) q^{14} +(-0.173648 + 0.984808i) q^{16} +(-1.69790 + 0.148547i) q^{17} +(-2.29378 - 4.91902i) q^{19} +(0.161908 + 1.85062i) q^{20} +(-0.626623 + 0.438766i) q^{22} +(3.89704 + 1.04421i) q^{23} +(-0.529786 - 1.45557i) q^{25} +(-4.44609 - 2.56695i) q^{26} +(-2.96252 + 3.53059i) q^{28} +(9.12762 - 2.44574i) q^{29} +(1.11289 - 1.11289i) q^{31} +(-0.573576 + 0.819152i) q^{32} +(-1.60160 - 0.582935i) q^{34} +(-3.61838 + 7.75965i) q^{35} +(-1.35851 + 5.92912i) q^{37} -5.42754i q^{38} +(-0.635367 + 1.74566i) q^{40} +(1.15055 - 0.965428i) q^{41} +(5.40814 + 5.40814i) q^{43} +(-0.753343 + 0.132835i) q^{44} +(3.09061 + 2.59333i) q^{46} +(4.91397 - 2.83708i) q^{47} +(-13.3827 + 4.87090i) q^{49} +(0.135003 - 1.54310i) q^{50} +(-2.94469 - 4.20545i) q^{52} +(8.79657 + 1.55107i) q^{53} +(-1.28792 + 0.600569i) q^{55} +(-4.17704 + 1.94779i) q^{56} +(9.30605 + 1.64091i) q^{58} +(4.19571 + 5.99209i) q^{59} +(0.804553 - 9.19608i) q^{61} +(1.47895 - 0.538293i) q^{62} +(-0.866025 + 0.500000i) q^{64} +(-7.30592 - 6.13040i) q^{65} +(6.71231 - 1.18356i) q^{67} +(-1.20518 - 1.20518i) q^{68} +(-6.55874 + 5.50344i) q^{70} +(2.79944 - 7.69139i) q^{71} -2.36965i q^{73} +(-3.73698 + 4.79947i) q^{74} +(2.29378 - 4.91902i) q^{76} +(-3.31299 - 1.20583i) q^{77} +(-3.40635 + 4.86478i) q^{79} +(-1.31358 + 1.31358i) q^{80} +(1.45076 - 0.388731i) q^{82} +(6.85600 - 8.17067i) q^{83} +(-2.74203 - 1.58311i) q^{85} +(2.61586 + 7.18702i) q^{86} +(-0.738899 - 0.197987i) q^{88} +(-6.10056 + 4.27166i) q^{89} +(-2.06223 - 23.5714i) q^{91} +(1.70506 + 3.65651i) q^{92} +(5.65258 - 0.494536i) q^{94} +(1.75084 - 9.92951i) q^{95} +(-3.70181 + 13.8154i) q^{97} +(-14.1874 - 1.24123i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{23}{36}\right)$

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 $

$2$	0.906308	+	0.422618i	0.640856	+	0.298836i
$2$	0.906308	+	0.422618i	0.640856	+	0.298836i
$3$		0			0
$3$		0			0
$4$	0.642788	+	0.766044i	0.321394	+	0.383022i
$5$	1.52173	+	1.06553i	0.680538	+	0.476518i	0.862019	−	0.506876i	$-0.169200\pi$
$5$	1.52173	+	1.06553i	0.680538	+	0.476518i	−0.181480	+	0.983395i	$0.558089\pi$
$6$		0			0
$7$	0.800320	+	4.53884i	0.302492	+	1.71552i	0.635079	+	0.772447i	$0.280968\pi$
$7$	0.800320	+	4.53884i	0.302492	+	1.71552i	−0.332587	+	0.943073i	$0.607921\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$		0			0
$10$	0.928845	+	1.60881i	0.293727	+	0.508749i
$11$	−0.382482	+	0.662479i	−0.115323	+	0.199745i	−0.917909	−	0.396792i	$-0.870124\pi$
$11$	−0.382482	+	0.662479i	−0.115323	+	0.199745i	0.802586	+	0.596537i	$0.203457\pi$
$12$		0			0
$13$	−5.11437	−	0.447449i	−1.41847	−	0.124100i	−0.648032	−	0.761613i	$-0.724408\pi$
$13$	−5.11437	−	0.447449i	−1.41847	−	0.124100i	−0.770439	+	0.637513i	$0.779963\pi$
$14$	−1.19286	+	4.45181i	−0.318805	+	1.18980i
$15$		0			0
$16$	−0.173648	+	0.984808i	−0.0434120	+	0.246202i
$17$	−1.69790	+	0.148547i	−0.411802	+	0.0360280i	−0.291175	−	0.956670i	$-0.594046\pi$
$17$	−1.69790	+	0.148547i	−0.411802	+	0.0360280i	−0.120627	+	0.992698i	$0.538491\pi$
$18$		0			0
$19$	−2.29378	−	4.91902i	−0.526229	−	1.12850i	−0.972350	−	0.233529i	$-0.924973\pi$
$19$	−2.29378	−	4.91902i	−0.526229	−	1.12850i	0.446121	−	0.894973i	$-0.352805\pi$
$20$	0.161908	+	1.85062i	0.0362038	+	0.413811i
$21$		0			0
$22$	−0.626623	+	0.438766i	−0.133596	+	0.0935452i
$23$	3.89704	+	1.04421i	0.812589	+	0.217732i	0.641104	−	0.767454i	$-0.278477\pi$
$23$	3.89704	+	1.04421i	0.812589	+	0.217732i	0.171485	+	0.985187i	$0.445144\pi$
$24$		0			0
$25$	−0.529786	−	1.45557i	−0.105957	−	0.291115i
$26$	−4.44609	−	2.56695i	−0.871950	−	0.503421i
$27$		0			0
$28$	−2.96252	+	3.53059i	−0.559863	+	0.667219i
$29$	9.12762	−	2.44574i	1.69496	−	0.454162i	0.723295	−	0.690539i	$-0.242627\pi$
$29$	9.12762	−	2.44574i	1.69496	−	0.454162i	0.971661	+	0.236377i	$0.0759600\pi$
$30$		0			0
$31$	1.11289	−	1.11289i	0.199881	−	0.199881i	−0.600068	−	0.799949i	$-0.704860\pi$
$31$	1.11289	−	1.11289i	0.199881	−	0.199881i	0.799949	+	0.600068i	$0.204860\pi$
$32$	−0.573576	+	0.819152i	−0.101395	+	0.144807i
$33$		0			0
$34$	−1.60160	−	0.582935i	−0.274672	−	0.0999725i
$35$	−3.61838	+	7.75965i	−0.611619	+	1.31162i
$36$		0			0
$37$	−1.35851	+	5.92912i	−0.223338	+	0.974741i
$37$	−1.35851	+	5.92912i	−0.223338	+	0.974741i
$38$		−	5.42754i		−	0.880463i
$39$		0			0
$40$	−0.635367	+	1.74566i	−0.100460	+	0.276013i
$41$	1.15055	−	0.965428i	0.179686	−	0.150775i	−0.548508	−	0.836145i	$-0.684804\pi$
$41$	1.15055	−	0.965428i	0.179686	−	0.150775i	0.728195	+	0.685370i	$0.240360\pi$
$42$		0			0
$43$	5.40814	+	5.40814i	0.824733	+	0.824733i	0.986783	−	0.162049i	$-0.0518103\pi$
$43$	5.40814	+	5.40814i	0.824733	+	0.824733i	−0.162049	+	0.986783i	$0.551810\pi$
$44$	−0.753343	+	0.132835i	−0.113571	+	0.0200256i
$45$		0			0
$46$	3.09061	+	2.59333i	0.455686	+	0.382366i
$47$	4.91397	−	2.83708i	0.716777	−	0.413831i	−0.0967885	−	0.995305i	$-0.530857\pi$
$47$	4.91397	−	2.83708i	0.716777	−	0.413831i	0.813565	+	0.581474i	$0.197524\pi$
$48$		0			0
$49$	−13.3827	+	4.87090i	−1.91181	+	0.695843i
$50$	0.135003	−	1.54310i	0.0190924	−	0.218227i
$51$		0			0
$52$	−2.94469	−	4.20545i	−0.408355	−	0.583191i
$53$	8.79657	+	1.55107i	1.20830	+	0.213056i	0.741284	−	0.671192i	$-0.234217\pi$
$53$	8.79657	+	1.55107i	1.20830	+	0.213056i	0.467018	+	0.884248i	$0.345328\pi$
$54$		0			0
$55$	−1.28792	+	0.600569i	−0.173664	+	0.0809807i
$56$	−4.17704	+	1.94779i	−0.558181	+	0.260284i
$57$		0			0
$58$	9.30605	+	1.64091i	1.22194	+	0.215462i
$59$	4.19571	+	5.99209i	0.546234	+	0.780104i	0.993443	−	0.114326i	$-0.0364708\pi$
$59$	4.19571	+	5.99209i	0.546234	+	0.780104i	−0.447209	+	0.894430i	$0.647582\pi$
$60$		0			0
$61$	0.804553	−	9.19608i	0.103012	−	1.17744i	−0.752119	−	0.659027i	$-0.770968\pi$
$61$	0.804553	−	9.19608i	0.103012	−	1.17744i	0.855132	−	0.518411i	$-0.173476\pi$
$62$	1.47895	−	0.538293i	0.187826	−	0.0683632i
$63$		0			0
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$	−7.30592	−	6.13040i	−0.906188	−	0.760382i
$66$		0			0
$67$	6.71231	−	1.18356i	0.820040	−	0.144595i	0.252138	−	0.967691i	$-0.418866\pi$
$67$	6.71231	−	1.18356i	0.820040	−	0.144595i	0.567902	+	0.823096i	$0.307755\pi$
$68$	−1.20518	−	1.20518i	−0.146150	−	0.146150i
$69$		0			0
$70$	−6.55874	+	5.50344i	−0.783919	+	0.657786i
$71$	2.79944	−	7.69139i	0.332232	−	0.912800i	−0.655298	−	0.755370i	$-0.727457\pi$
$71$	2.79944	−	7.69139i	0.332232	−	0.912800i	0.987530	−	0.157430i	$-0.0503209\pi$
$72$		0			0
$73$		−	2.36965i		−	0.277347i	−0.990338	−	0.138673i	$-0.955716\pi$
$73$		−	2.36965i		−	0.277347i	0.990338	−	0.138673i	$-0.0442838\pi$
$74$	−3.73698	+	4.79947i	−0.434416	+	0.557928i
$75$		0			0
$76$	2.29378	−	4.91902i	0.263114	−	0.564251i
$77$	−3.31299	−	1.20583i	−0.377551	−	0.137417i
$78$		0			0
$79$	−3.40635	+	4.86478i	−0.383245	+	0.547330i	−0.963709	−	0.266956i	$-0.913982\pi$
$79$	−3.40635	+	4.86478i	−0.383245	+	0.547330i	0.580464	+	0.814286i	$0.302871\pi$
$80$	−1.31358	+	1.31358i	−0.146863	+	0.146863i
$81$		0			0
$82$	1.45076	−	0.388731i	0.160210	−	0.0429281i
$83$	6.85600	−	8.17067i	0.752544	−	0.896847i	−0.244808	−	0.969572i	$-0.578725\pi$
$83$	6.85600	−	8.17067i	0.752544	−	0.896847i	0.997352	+	0.0727245i	$0.0231694\pi$
$84$		0			0
$85$	−2.74203	−	1.58311i	−0.297415	−	0.171713i
$86$	2.61586	+	7.18702i	0.282075	+	0.774996i
$87$		0			0
$88$	−0.738899	−	0.197987i	−0.0787669	−	0.0211055i
$89$	−6.10056	+	4.27166i	−0.646658	+	0.452795i	−0.850334	−	0.526243i	$-0.823600\pi$
$89$	−6.10056	+	4.27166i	−0.646658	+	0.452795i	0.203676	+	0.979038i	$0.434711\pi$
$90$		0			0
$91$	−2.06223	−	23.5714i	−0.216180	−	2.47095i
$92$	1.70506	+	3.65651i	0.177765	+	0.381217i
$93$		0			0
$94$	5.65258	−	0.494536i	0.583019	−	0.0510075i
$95$	1.75084	−	9.92951i	0.179632	−	1.01875i
$96$		0			0
$97$	−3.70181	+	13.8154i	−0.375862	+	1.40274i	0.476219	+	0.879327i	$0.342007\pi$
$97$	−3.70181	+	13.8154i	−0.375862	+	1.40274i	−0.852081	+	0.523410i	$0.824660\pi$
$98$	−14.1874	−	1.24123i	−1.43314	−	0.125384i
$99$		0			0
$100$	0.774495	−	1.34146i	0.0774495	−	0.134146i
$101$	−3.19546	−	5.53469i	−0.317960	−	0.550722i	0.662102	−	0.749413i	$-0.269664\pi$
$101$	−3.19546	−	5.53469i	−0.317960	−	0.550722i	−0.980062	+	0.198691i	$0.936331\pi$
$102$		0			0
$103$	−2.61420	−	9.75634i	−0.257585	−	0.961321i	−0.966634	−	0.256161i	$-0.917542\pi$
$103$	−2.61420	−	9.75634i	−0.257585	−	0.961321i	0.709049	−	0.705159i	$-0.249125\pi$
$104$	−0.891493	−	5.05591i	−0.0874181	−	0.495773i
$105$		0			0
$106$	7.31689	+	5.12334i	0.710679	+	0.497623i
$107$	13.2614	+	15.8043i	1.28203	+	1.52786i	0.697885	+	0.716210i	$0.254125\pi$
$107$	13.2614	+	15.8043i	1.28203	+	1.52786i	0.584143	+	0.811651i	$0.301431\pi$
$108$		0			0
$109$	−10.6648	−	4.97310i	−1.02151	−	0.476336i	−0.161637	−	0.986850i	$-0.551677\pi$
$109$	−10.6648	−	4.97310i	−1.02151	−	0.476336i	−0.859870	+	0.510514i	$0.829455\pi$
$110$	−1.42107			−0.135493
$111$		0			0
$112$	−4.60886			−0.435496
$113$	−16.8033	−	7.83553i	−1.58073	−	0.737104i	−0.583541	−	0.812084i	$-0.698333\pi$
$113$	−16.8033	−	7.83553i	−1.58073	−	0.737104i	−0.997185	+	0.0749795i	$0.976111\pi$
$114$		0			0
$115$	4.81761	+	5.74140i	0.449244	+	0.535389i
$116$	7.74067	+	5.42007i	0.718703	+	0.503241i
$117$		0			0
$118$	1.27023	+	7.20386i	0.116935	+	0.663169i
$119$	−2.03310	−	7.58762i	−0.186374	−	0.695556i
$120$		0			0
$121$	5.20741	+	9.01951i	0.473401	+	0.819955i
$122$	4.61560	−	7.99446i	0.417877	−	0.723784i
$123$		0			0
$124$	1.56787	+	0.137171i	0.140799	+	0.0123183i
$125$	3.14879	−	11.7514i	0.281636	−	1.05108i
$126$		0			0
$127$	0.597958	−	3.39119i	0.0530602	−	0.300919i	−0.946716	−	0.322069i	$-0.895622\pi$
$127$	0.597958	−	3.39119i	0.0530602	−	0.300919i	0.999776	+	0.0211499i	$0.00673272\pi$
$128$	−0.996195	+	0.0871557i	−0.0880520	+	0.00770355i
$129$		0			0
$130$	−4.03060	−	8.64364i	−0.353507	−	0.758097i
$131$	0.0480530	+	0.549249i	0.00419841	+	0.0479881i	0.998005	−	0.0631364i	$-0.0201103\pi$
$131$	0.0480530	+	0.549249i	0.00419841	+	0.0479881i	−0.993806	+	0.111124i	$0.964555\pi$
$132$		0			0
$133$	20.4909	−	14.3479i	1.77679	−	1.24412i
$134$	6.58362	+	1.76407i	0.568738	+	0.152393i
$135$		0			0
$136$	−0.582935	−	1.60160i	−0.0499863	−	0.137336i
$137$	−10.9115	−	6.29975i	−0.932231	−	0.538224i	−0.0447146	−	0.999000i	$-0.514238\pi$
$137$	−10.9115	−	6.29975i	−0.932231	−	0.538224i	−0.887517	+	0.460776i	$0.847571\pi$
$138$		0			0
$139$	5.32113	−	6.34148i	0.451332	−	0.537877i	−0.491618	−	0.870811i	$-0.663594\pi$
$139$	5.32113	−	6.34148i	0.451332	−	0.537877i	0.942950	+	0.332934i	$0.108039\pi$
$140$	−8.27009	+	2.21596i	−0.698950	+	0.187283i
$141$		0			0
$142$	5.78768	−	5.78768i	0.485691	−	0.485691i
$143$	2.25258	−	3.21702i	0.188370	−	0.269021i
$144$		0			0
$145$	16.4958	+	6.00397i	1.36990	+	0.498603i
$146$	1.00146	−	2.14763i	0.0828813	−	0.177739i
$147$		0			0
$148$	−5.41520	+	2.77048i	−0.445127	+	0.227732i
$149$			7.29821i			0.597892i	0.954270	+	0.298946i	$0.0966351\pi$
$149$			7.29821i			0.597892i	−0.954270	+	0.298946i	$0.903365\pi$
$150$		0			0
$151$	3.78811	−	10.4078i	0.308272	−	0.846971i	−0.684721	−	0.728805i	$-0.740076\pi$
$151$	3.78811	−	10.4078i	0.308272	−	0.846971i	0.992994	−	0.118166i	$-0.0377016\pi$
$152$	4.15774	−	3.48876i	0.337237	−	0.282975i
$153$		0			0
$154$	−2.49299	−	2.49299i	−0.200891	−	0.200891i
$155$	2.87933	−	0.507703i	0.231273	−	0.0407797i
$156$		0			0
$157$	8.86534	+	7.43891i	0.707531	+	0.593689i	0.923905	−	0.382621i	$-0.124979\pi$
$157$	8.86534	+	7.43891i	0.707531	+	0.593689i	−0.216374	+	0.976311i	$0.569423\pi$
$158$	−5.14315	+	2.96940i	−0.409167	+	0.236233i
$159$		0			0
$160$	−1.74566	+	0.635367i	−0.138006	+	0.0502302i
$161$	−1.62062	+	18.5237i	−0.127722	+	1.45987i
$162$		0			0
$163$	−11.4113	−	16.2971i	−0.893806	−	1.27649i	−0.960377	−	0.278705i	$-0.910095\pi$
$163$	−11.4113	−	16.2971i	−0.893806	−	1.27649i	0.0665709	−	0.997782i	$-0.478794\pi$
$164$	1.47912	+	0.260809i	0.115500	+	0.0203658i
$165$		0			0
$166$	9.66672	−	4.50767i	0.750283	−	0.349863i
$167$	−15.4398	+	7.19968i	−1.19477	+	0.557128i	−0.915201	−	0.402999i	$-0.867968\pi$
$167$	−15.4398	+	7.19968i	−1.19477	+	0.557128i	−0.279565	+	0.960127i	$0.590190\pi$
$168$		0			0
$169$	13.1541	+	2.31942i	1.01185	+	0.178417i
$170$	−1.81607	−	2.59362i	−0.139286	−	0.198921i
$171$		0			0
$172$	−0.666590	+	7.61916i	−0.0508270	+	0.580955i
$173$	−19.4091	+	7.06432i	−1.47564	+	0.537090i	−0.949627	−	0.313384i	$-0.898537\pi$
$173$	−19.4091	+	7.06432i	−1.47564	+	0.537090i	−0.526017	+	0.850474i	$0.676315\pi$
$174$		0			0
$175$	6.18262	−	3.56954i	0.467362	−	0.269832i
$176$	−0.585997	−	0.491710i	−0.0441712	−	0.0370640i
$177$		0			0
$178$	−7.33427	+	1.29323i	−0.549727	+	0.0969316i
$179$	−12.2715	−	12.2715i	−0.917214	−	0.917214i	0.0796123	−	0.996826i	$-0.474632\pi$
$179$	−12.2715	−	12.2715i	−0.917214	−	0.917214i	−0.996826	+	0.0796123i	$0.974632\pi$
$180$		0			0
$181$	−2.13211	+	1.78905i	−0.158478	+	0.132979i	−0.718579	−	0.695446i	$-0.755207\pi$
$181$	−2.13211	+	1.78905i	−0.158478	+	0.132979i	0.560100	+	0.828425i	$0.310763\pi$
$182$	8.09269	−	22.2345i	0.599870	−	1.64813i
$183$		0			0
$184$			4.03451i			0.297428i
$185$	−8.38492	+	7.57499i	−0.616472	+	0.556924i
$186$		0			0
$187$	0.551008	−	1.18164i	0.0402937	−	0.0864102i
$188$	5.33197	+	1.94068i	0.388874	+	0.141539i
$189$		0			0
$190$	5.78319	−	8.25925i	0.419557	−	0.599189i
$191$	6.90030	−	6.90030i	0.499288	−	0.499288i	−0.411928	−	0.911216i	$-0.635145\pi$
$191$	6.90030	−	6.90030i	0.499288	−	0.499288i	0.911216	+	0.411928i	$0.135145\pi$
$192$		0			0
$193$	−3.43915	+	0.921516i	−0.247555	+	0.0663322i	−0.380463	−	0.924796i	$-0.624235\pi$
$193$	−3.43915	+	0.921516i	−0.247555	+	0.0663322i	0.132908	+	0.991128i	$0.457569\pi$
$194$	−9.19361	+	10.9565i	−0.660062	+	0.786632i
$195$		0			0
$196$	−12.3336	−	7.12079i	−0.880969	−	0.508628i
$197$	0.132447	+	0.363896i	0.00943648	+	0.0259265i	0.944321	−	0.329024i	$-0.106720\pi$
$197$	0.132447	+	0.363896i	0.00943648	+	0.0259265i	−0.934885	+	0.354951i	$0.884498\pi$
$198$		0			0
$199$	−4.37182	−	1.17143i	−0.309910	−	0.0830402i	0.100512	−	0.994936i	$-0.467952\pi$
$199$	−4.37182	−	1.17143i	−0.309910	−	0.0830402i	−0.410422	+	0.911896i	$0.634619\pi$
$200$	1.26886	−	0.888464i	0.0897218	−	0.0628239i
$201$		0			0
$202$	−0.557005	−	6.36659i	−0.0391907	−	0.447952i
$203$	18.4058	+	39.4714i	1.29184	+	2.77035i
$204$		0			0
$205$	2.77952	−	0.243176i	0.194130	−	0.0169842i
$206$	1.75393	−	9.94706i	0.122202	−	0.693044i
$207$		0			0
$208$	1.32875	−	4.95897i	0.0921324	−	0.343843i
$209$	4.13608	+	0.361860i	0.286099	+	0.0250304i
$210$		0			0
$211$	−8.83213	+	15.2977i	−0.608029	+	1.05314i	0.383536	+	0.923526i	$0.374706\pi$
$211$	−8.83213	+	15.2977i	−0.608029	+	1.05314i	−0.991565	+	0.129611i	$0.958627\pi$
$212$	4.46614	+	7.73558i	0.306736	+	0.531281i
$213$		0			0
$214$	5.33971	+	19.9281i	0.365015	+	1.36226i
$215$	2.46721	+	13.9922i	0.168262	+	0.954263i
$216$		0			0
$217$	5.94189	+	4.16056i	0.403362	+	0.282437i
$218$	−7.56391	−	9.01432i	−0.512293	−	0.610527i
$219$		0			0
$220$	−1.28792	−	0.600569i	−0.0868318	−	0.0404904i
$221$	8.75016			0.588600
$222$		0			0
$223$	9.00255			0.602855			0.301428	−	0.953489i	$-0.402537\pi$
$223$	9.00255			0.602855			0.301428	+	0.953489i	$0.402537\pi$
$224$	−4.17704	−	1.94779i	−0.279090	−	0.130142i
$225$		0			0
$226$	−11.9176	−	14.2028i	−0.792745	−	0.944756i
$227$	−13.2961	−	9.31000i	−0.882490	−	0.617926i	0.0420063	−	0.999117i	$-0.486625\pi$
$227$	−13.2961	−	9.31000i	−0.882490	−	0.617926i	−0.924496	+	0.381191i	$0.875514\pi$
$228$		0			0
$229$	1.05335	+	5.97383i	0.0696072	+	0.394762i	0.999628	+	0.0272564i	$0.00867705\pi$
$229$	1.05335	+	5.97383i	0.0696072	+	0.394762i	−0.930021	+	0.367506i	$0.880212\pi$
$230$	1.93981	+	7.23949i	0.127908	+	0.477358i
$231$		0			0
$232$	4.72480	+	8.18360i	0.310199	+	0.537280i
$233$	−2.02597	+	3.50909i	−0.132726	+	0.229888i	−0.924726	−	0.380632i	$-0.875706\pi$
$233$	−2.02597	+	3.50909i	−0.132726	+	0.229888i	0.792000	+	0.610520i	$0.209040\pi$
$234$		0			0
$235$	10.5007	+	0.918695i	0.684992	+	0.0599290i
$236$	−1.89326	+	7.06574i	−0.123241	+	0.459940i
$237$		0			0
$238$	1.36406	−	7.73594i	0.0884186	−	0.501447i
$239$	3.23584	−	0.283099i	0.209309	−	0.0183122i	0.0179811	−	0.999838i	$-0.494276\pi$
$239$	3.23584	−	0.283099i	0.209309	−	0.0183122i	0.191328	+	0.981526i	$0.438721\pi$
$240$		0			0
$241$	−11.9282	−	25.5802i	−0.768365	−	1.64776i	−0.761823	−	0.647785i	$-0.775695\pi$
$241$	−11.9282	−	25.5802i	−0.768365	−	1.64776i	−0.00654205	−	0.999979i	$-0.502082\pi$
$242$	0.907712	+	10.3752i	0.0583499	+	0.666943i
$243$		0			0
$244$	7.56176	−	5.29480i	0.484092	−	0.338965i
$245$	−25.5549	−	6.84742i	−1.63265	−	0.437466i
$246$		0			0
$247$	9.53021	+	26.1840i	0.606393	+	1.66605i
$248$	1.36300	+	0.786931i	0.0865509	+	0.0499702i
$249$		0			0
$250$	7.82015	−	9.31969i	0.494590	−	0.589429i
$251$	18.5648	−	4.97444i	1.17180	−	0.313984i	0.380132	−	0.924932i	$-0.375878\pi$
$251$	18.5648	−	4.97444i	1.17180	−	0.313984i	0.791670	+	0.610948i	$0.209212\pi$
$252$		0			0
$253$	−2.18232	+	2.18232i	−0.137201	+	0.137201i
$254$	1.97511	−	2.82075i	0.123930	−	0.176990i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	7.42240	−	15.9174i	0.462996	−	0.992899i	−0.526744	−	0.850024i	$-0.676587\pi$
$257$	7.42240	−	15.9174i	0.462996	−	0.992899i	0.989741	−	0.142875i	$-0.0456348\pi$
$258$		0			0
$259$	−27.9986	−	1.42088i	−1.73975	−	0.0882889i
$260$		−	9.53720i		−	0.591472i
$261$		0			0
$262$	−0.188572	+	0.518096i	−0.0116500	+	0.0320081i
$263$	13.0732	−	10.9697i	0.806130	−	0.676424i	−0.143551	−	0.989643i	$-0.545852\pi$
$263$	13.0732	−	10.9697i	0.806130	−	0.676424i	0.949681	+	0.313219i	$0.101408\pi$
$264$		0			0
$265$	11.7333	+	11.7333i	0.720771	+	0.720771i
$266$	24.6347	−	4.34377i	1.51045	−	0.266333i
$267$		0			0
$268$	5.22125	+	4.38115i	0.318939	+	0.267621i
$269$	−5.55459	+	3.20694i	−0.338669	+	0.195531i	−0.659683	−	0.751544i	$-0.729310\pi$
$269$	−5.55459	+	3.20694i	−0.338669	+	0.195531i	0.321014	+	0.947074i	$0.395976\pi$
$270$		0			0
$271$	−9.08775	+	3.30767i	−0.552041	+	0.200927i	−0.602953	−	0.797777i	$-0.706009\pi$
$271$	−9.08775	+	3.30767i	−0.552041	+	0.200927i	0.0509119	+	0.998703i	$0.483787\pi$
$272$	0.148547	−	1.69790i	0.00900699	−	0.102950i
$273$		0			0
$274$	−7.22678	−	10.3209i	−0.436585	−	0.623509i
$275$	1.16692	+	0.205760i	0.0703680	+	0.0124078i
$276$		0			0
$277$	−25.6525	+	11.9620i	−1.54131	+	0.718725i	−0.993062	−	0.117591i	$-0.962483\pi$
$277$	−25.6525	+	11.9620i	−1.54131	+	0.718725i	−0.548248	+	0.836316i	$0.684705\pi$
$278$	7.50261	−	3.49852i	0.449976	−	0.209827i
$279$		0			0
$280$	−8.43175	−	1.48675i	−0.503894	−	0.0888500i
$281$	−10.9768	−	15.6765i	−0.654823	−	0.935184i	0.345171	−	0.938540i	$-0.387821\pi$
$281$	−10.9768	−	15.6765i	−0.654823	−	0.935184i	−0.999994	+	0.00335557i	$0.998932\pi$
$282$		0			0
$283$	−0.198981	+	2.27437i	−0.0118282	+	0.135197i	−0.999813	−	0.0193563i	$-0.993838\pi$
$283$	−0.198981	+	2.27437i	−0.0118282	+	0.135197i	0.987984	+	0.154553i	$0.0493939\pi$
$284$	7.69139	−	2.79944i	0.456400	−	0.166116i
$285$		0			0
$286$	3.40110	−	1.96363i	0.201112	−	0.116112i
$287$	5.30273	+	4.44952i	0.313010	+	0.262647i
$288$		0			0
$289$	−13.8809	+	2.44758i	−0.816525	+	0.143975i
$290$	12.4129	+	12.4129i	0.728908	+	0.728908i
$291$		0			0
$292$	1.81526	−	1.52318i	0.106230	−	0.0891375i
$293$	−0.338573	+	0.930221i	−0.0197796	+	0.0543441i	−0.949190	−	0.314705i	$-0.898094\pi$
$293$	−0.338573	+	0.930221i	−0.0197796	+	0.0543441i	0.929410	+	0.369049i	$0.120317\pi$
$294$		0			0
$295$			13.5890i			0.791181i
$296$	−6.07870	+	0.222347i	−0.353317	+	0.0129237i
$297$		0			0
$298$	−3.08436	+	6.61442i	−0.178672	+	0.383163i
$299$	−19.4637	−	7.08419i	−1.12561	−	0.409690i
$300$		0			0
$301$	−20.2184	+	28.8749i	−1.16537	+	1.66432i
$302$	7.83170	−	7.83170i	0.450664	−	0.450664i
$303$		0			0
$304$	5.24260	−	1.40475i	0.300684	−	0.0805680i
$305$	11.0230	−	13.1367i	0.631174	−	0.752204i
$306$		0			0
$307$	23.7471	+	13.7104i	1.35532	+	0.782494i	0.988989	−	0.147991i	$-0.0472807\pi$
$307$	23.7471	+	13.7104i	1.35532	+	0.782494i	0.366330	+	0.930485i	$0.380614\pi$
$308$	−1.20583	−	3.31299i	−0.0687086	−	0.188775i
$309$		0			0
$310$	2.82412	+	0.756722i	0.160399	+	0.0429789i
$311$	−3.46322	+	2.42497i	−0.196381	+	0.137508i	−0.667631	−	0.744492i	$-0.732692\pi$
$311$	−3.46322	+	2.42497i	−0.196381	+	0.137508i	0.471250	+	0.882000i	$0.343803\pi$
$312$		0			0
$313$	1.70566	+	19.4958i	0.0964095	+	1.10197i	0.878158	+	0.478371i	$0.158773\pi$
$313$	1.70566	+	19.4958i	0.0964095	+	1.10197i	−0.781748	+	0.623594i	$0.785672\pi$
$314$	4.89091	+	10.4886i	0.276010	+	0.591906i
$315$		0			0
$316$	−5.91620	+	0.517600i	−0.332812	+	0.0291173i
$317$	2.29959	−	13.0416i	0.129158	−	0.732490i	−0.849593	−	0.527438i	$-0.823153\pi$
$317$	2.29959	−	13.0416i	0.129158	−	0.732490i	0.978751	−	0.205052i	$-0.0657363\pi$
$318$		0			0
$319$	−1.87090	+	6.98231i	−0.104751	+	0.390934i
$320$	−1.85062	−	0.161908i	−0.103453	−	0.00905095i
$321$		0			0
$322$	−9.29724	+	16.1033i	−0.518115	+	0.897402i
$323$	4.62532	+	8.01128i	0.257359	+	0.445760i
$324$		0			0
$325$	2.05822	+	7.68140i	0.114170	+	0.426087i
$326$	−3.45474	−	19.5928i	−0.191341	−	1.08515i
$327$		0			0
$328$	1.23032	+	0.861477i	0.0679329	+	0.0475671i
$329$	16.8098	+	20.0332i	0.926755	+	1.10446i
$330$		0			0
$331$	4.23623	+	1.97539i	0.232844	+	0.108577i	0.535539	−	0.844511i	$-0.320108\pi$
$331$	4.23623	+	1.97539i	0.232844	+	0.108577i	−0.302695	+	0.953088i	$0.597886\pi$
$332$	10.6660			0.585375
$333$		0			0
$334$	−17.0359			−0.932163
$335$	11.4754	+	5.35109i	0.626971	+	0.292361i
$336$		0			0
$337$	−11.9468	−	14.2376i	−0.650784	−	0.775574i	0.335248	−	0.942130i	$-0.391180\pi$
$337$	−11.9468	−	14.2376i	−0.650784	−	0.775574i	−0.986032	+	0.166556i	$0.946735\pi$
$338$	10.9414	+	7.66125i	0.595134	+	0.416717i
$339$		0			0
$340$	−0.549809	−	3.11812i	−0.0298176	−	0.169104i
$341$	0.311605	+	1.16293i	0.0168744	+	0.0629760i
$342$		0			0
$343$	−16.6877	−	28.9039i	−0.901050	−	1.56066i
$344$	−3.82413	+	6.62359i	−0.206183	+	0.357120i
$345$		0			0
$346$	−20.5761	−	1.80017i	−1.10618	−	0.0967780i
$347$	−6.04031	+	22.5427i	−0.324261	+	1.21016i	0.590792	+	0.806824i	$0.298815\pi$
$347$	−6.04031	+	22.5427i	−0.324261	+	1.21016i	−0.915053	+	0.403334i	$0.867851\pi$
$348$		0			0
$349$	3.04704	−	17.2806i	0.163104	−	0.925011i	−0.787893	−	0.615812i	$-0.788828\pi$
$349$	3.04704	−	17.2806i	0.163104	−	0.925011i	0.950997	−	0.309199i	$-0.100061\pi$
$350$	7.11191	−	0.622211i	0.380147	−	0.0332586i
$351$		0			0
$352$	−0.323288	−	0.693294i	−0.0172313	−	0.0369527i
$353$	−2.09495	−	23.9453i	−0.111503	−	1.27448i	−0.821472	−	0.570249i	$-0.806847\pi$
$353$	−2.09495	−	23.9453i	−0.111503	−	1.27448i	0.709969	−	0.704233i	$-0.248709\pi$
$354$		0			0
$355$	12.4554	−	8.72135i	0.661063	−	0.462881i
$356$	−7.19365	−	1.92753i	−0.381263	−	0.102159i
$357$		0			0
$358$	−5.93559	−	16.3079i	−0.313706	−	0.861899i
$359$	−9.52698	−	5.50040i	−0.502815	−	0.290300i	0.227061	−	0.973881i	$-0.427088\pi$
$359$	−9.52698	−	5.50040i	−0.502815	−	0.290300i	−0.729875	+	0.683581i	$0.760422\pi$
$360$		0			0
$361$	−6.72240	+	8.01144i	−0.353810	+	0.421655i
$362$	−2.68843	+	0.720362i	−0.141301	+	0.0378614i
$363$		0			0
$364$	16.7312	−	16.7312i	0.876951	−	0.876951i
$365$	2.52493	−	3.60597i	0.132161	−	0.188745i
$366$		0			0
$367$	−15.0689	−	5.48462i	−0.786589	−	0.286295i	−0.0826716	−	0.996577i	$-0.526345\pi$
$367$	−15.0689	−	5.48462i	−0.786589	−	0.286295i	−0.703917	+	0.710282i	$0.748567\pi$
$368$	−1.70506	+	3.65651i	−0.0888823	+	0.190609i
$369$		0			0
$370$	−10.8007	+	3.32165i	−0.561499	+	0.172684i
$371$			41.1676i			2.13731i
$372$		0			0
$373$	−3.24957	+	8.92813i	−0.168256	+	0.462281i	−0.994950	−	0.100372i	$-0.967997\pi$
$373$	−3.24957	+	8.92813i	−0.168256	+	0.462281i	0.826694	+	0.562652i	$0.190219\pi$
$374$	0.998766	−	0.838064i	0.0516450	−	0.0433353i
$375$		0			0
$376$	4.01224	+	4.01224i	0.206916	+	0.206916i
$377$	−47.7764	+	8.42426i	−2.46061	+	0.433872i
$378$		0			0
$379$	−14.8365	−	12.4493i	−0.762102	−	0.639479i	0.176571	−	0.984288i	$-0.443499\pi$
$379$	−14.8365	−	12.4493i	−0.762102	−	0.639479i	−0.938673	+	0.344808i	$0.887944\pi$
$380$	8.73186	−	5.04134i	0.447935	−	0.258615i
$381$		0			0
$382$	9.16999	−	3.33760i	0.469177	−	0.170767i
$383$	−2.25137	+	25.7333i	−0.115040	+	1.31491i	0.690916	+	0.722935i	$0.257208\pi$
$383$	−2.25137	+	25.7333i	−0.115040	+	1.31491i	−0.805956	+	0.591976i	$0.798348\pi$
$384$		0			0
$385$	−3.75664	−	5.36503i	−0.191456	−	0.273427i
$386$	−3.50637	−	0.618268i	−0.178470	−	0.0314690i
$387$		0			0
$388$	−12.9627	+	6.04459i	−0.658079	+	0.306867i
$389$	18.2289	−	8.50030i	0.924244	−	0.430982i	0.0985704	−	0.995130i	$-0.468573\pi$
$389$	18.2289	−	8.50030i	0.924244	−	0.430982i	0.825674	+	0.564148i	$0.190795\pi$
$390$		0			0
$391$	−6.77190	−	1.19407i	−0.342470	−	0.0603867i
$392$	−8.16863	−	11.6660i	−0.412578	−	0.589223i
$393$		0			0
$394$	−0.0337510	+	0.385776i	−0.00170035	+	0.0194351i
$395$	−10.3671	+	3.77332i	−0.521626	+	0.189856i
$396$		0			0
$397$	28.8505	−	16.6568i	1.44796	−	0.835982i	0.449603	−	0.893228i	$-0.351565\pi$
$397$	28.8505	−	16.6568i	1.44796	−	0.835982i	0.998360	+	0.0572466i	$0.0182321\pi$
$398$	−3.46715	−	2.90929i	−0.173793	−	0.145829i
$399$		0			0
$400$	1.52546	−	0.268979i	0.0762728	−	0.0134490i
$401$	18.0069	+	18.0069i	0.899222	+	0.899222i	0.995367	−	0.0961456i	$-0.0306514\pi$
$401$	18.0069	+	18.0069i	0.899222	+	0.899222i	−0.0961456	+	0.995367i	$0.530651\pi$
$402$		0			0
$403$	−6.18969	+	5.19376i	−0.308330	+	0.258720i
$404$	2.18582	−	6.00549i	0.108749	−	0.298784i
$405$		0			0
$406$			43.5519i			2.16144i
$407$	−3.40831	−	3.16777i	−0.168944	−	0.157021i
$408$		0			0
$409$	−7.43585	+	15.9462i	−0.367679	+	0.788491i	0.632227	+	0.774783i	$0.282141\pi$
$409$	−7.43585	+	15.9462i	−0.367679	+	0.788491i	−0.999906	+	0.0137073i	$0.995637\pi$
$410$	2.62187	+	0.954283i	0.129485	+	0.0471287i
$411$		0			0
$412$	5.79341	−	8.27385i	0.285421	−	0.407623i
$413$	−23.8392	+	23.8392i	−1.17305	+	1.17305i
$414$		0			0
$415$	19.1391	−	5.12829i	0.939499	−	0.251738i
$416$	3.30001	−	3.93280i	0.161796	−	0.192821i
$417$		0			0
$418$	3.59563	+	2.07594i	0.175868	+	0.101537i
$419$	−0.504021	−	1.38479i	−0.0246230	−	0.0676513i	0.926772	−	0.375624i	$-0.122572\pi$
$419$	−0.504021	−	1.38479i	−0.0246230	−	0.0676513i	−0.951395	+	0.307973i	$0.900349\pi$
$420$		0			0
$421$	10.9886	+	2.94438i	0.535550	+	0.143500i	0.516450	−	0.856317i	$-0.327253\pi$
$421$	10.9886	+	2.94438i	0.535550	+	0.143500i	0.0191003	+	0.999818i	$0.493920\pi$
$422$	−14.4697	+	10.1318i	−0.704375	+	0.493209i
$423$		0			0
$424$	0.778499	+	8.89828i	0.0378072	+	0.432139i
$425$	1.11575	+	2.39272i	0.0541216	+	0.116064i
$426$		0			0
$427$	42.3834	−	3.70807i	2.05108	−	0.179446i
$428$	−3.58255	+	20.3176i	−0.173169	+	0.982090i
$429$		0			0
$430$	−3.67733	+	13.7240i	−0.177336	+	0.661829i
$431$	37.3119	+	3.26437i	1.79725	+	0.157239i	0.936244	−	0.351352i	$-0.114278\pi$
$431$	37.3119	+	3.26437i	1.79725	+	0.157239i	0.861008	+	0.508591i	$0.169833\pi$
$432$		0			0
$433$	−13.9608	+	24.1808i	−0.670914	+	1.16206i	0.306732	+	0.951796i	$0.400765\pi$
$433$	−13.9608	+	24.1808i	−0.670914	+	1.16206i	−0.977645	+	0.210260i	$0.932569\pi$
$434$	3.62685	+	6.28190i	0.174095	+	0.301541i
$435$		0			0
$436$	−3.04562	−	11.3664i	−0.145859	−	0.544351i
$437$	−3.80246	−	21.5648i	−0.181896	−	1.03158i
$438$		0			0
$439$	−7.11627	−	4.98287i	−0.339641	−	0.237819i	0.391295	−	0.920265i	$-0.372027\pi$
$439$	−7.11627	−	4.98287i	−0.339641	−	0.237819i	−0.730936	+	0.682446i	$0.760916\pi$
$440$	−0.913445	−	1.08860i	−0.0435468	−	0.0518970i
$441$		0			0
$442$	7.93034	+	3.69798i	0.377208	+	0.175895i
$443$	37.9608			1.80357			0.901785	−	0.432185i	$-0.142257\pi$
$443$	37.9608			1.80357			0.901785	+	0.432185i	$0.142257\pi$
$444$		0			0
$445$	−13.8350			−0.655841
$446$	8.15908	+	3.80464i	0.386344	+	0.180155i
$447$		0			0
$448$	−2.96252	−	3.53059i	−0.139966	−	0.166805i
$449$	−13.9590	−	9.77422i	−0.658768	−	0.461274i	0.195779	−	0.980648i	$-0.437276\pi$
$449$	−13.9590	−	9.77422i	−0.658768	−	0.461274i	−0.854547	+	0.519374i	$0.826165\pi$
$450$		0			0
$451$	0.199510	+	1.13148i	0.00939455	+	0.0532791i
$452$	−4.79862	−	17.9087i	−0.225708	−	0.842354i
$453$		0			0
$454$	−8.11574	−	14.0569i	−0.380891	−	0.659722i
$455$	21.9778	−	38.0667i	1.03034	−	1.78459i
$456$		0			0
$457$	7.04378	+	0.616251i	0.329494	+	0.0288270i	0.250703	−	0.968064i	$-0.419338\pi$
$457$	7.04378	+	0.616251i	0.329494	+	0.0288270i	0.0787915	+	0.996891i	$0.474894\pi$
$458$	−1.56999	+	5.85930i	−0.0733610	+	0.273787i
$459$		0			0
$460$	−1.30147	+	7.38101i	−0.0606814	+	0.344141i
$461$	19.0599	−	1.66753i	0.887709	−	0.0776645i	0.365828	−	0.930683i	$-0.380786\pi$
$461$	19.0599	−	1.66753i	0.887709	−	0.0776645i	0.521881	+	0.853018i	$0.325230\pi$
$462$		0			0
$463$	5.94832	+	12.7562i	0.276442	+	0.592831i	0.994685	−	0.102960i	$-0.0328315\pi$
$463$	5.94832	+	12.7562i	0.276442	+	0.592831i	−0.718244	+	0.695792i	$0.755054\pi$
$464$	0.823588	+	9.41365i	0.0382341	+	0.437018i
$465$		0			0
$466$	−3.31916	+	2.32410i	−0.153757	+	0.107662i
$467$	−3.56658	−	0.955662i	−0.165042	−	0.0442227i	0.175352	−	0.984506i	$-0.443894\pi$
$467$	−3.56658	−	0.955662i	−0.165042	−	0.0442227i	−0.340394	+	0.940283i	$0.610560\pi$
$468$		0			0
$469$	10.7440	+	29.5189i	0.496112	+	1.36306i
$470$	9.12864	+	5.27042i	0.421073	+	0.243106i
$471$		0			0
$472$	−4.70199	+	5.60361i	−0.216426	+	0.257927i
$473$	−5.65130	+	1.51426i	−0.259847	+	0.0696258i
$474$		0			0
$475$	−5.94479	+	5.94479i	−0.272766	+	0.272766i
$476$	4.50560	−	6.43467i	0.206514	−	0.294933i
$477$		0			0
$478$	3.05231	+	1.11095i	0.139609	+	0.0508137i
$479$	−15.1175	+	32.4195i	−0.690734	+	1.48128i	0.176976	+	0.984215i	$0.443368\pi$
$479$	−15.1175	+	32.4195i	−0.690734	+	1.48128i	−0.867711	+	0.497070i	$0.834409\pi$
$480$		0			0
$481$	9.60091	−	29.7158i	0.437764	−	1.35493i
$482$		−	28.2246i		−	1.28560i
$483$		0			0
$484$	−3.56208	+	9.78674i	−0.161913	+	0.444852i
$485$	−20.3538	+	17.0789i	−0.924218	+	0.775511i
$486$		0			0
$487$	27.1187	+	27.1187i	1.22886	+	1.22886i	0.964394	+	0.264469i	$0.0851968\pi$
$487$	27.1187	+	27.1187i	1.22886	+	1.22886i	0.264469	+	0.964394i	$0.414803\pi$
$488$	9.09097	−	1.60298i	0.411529	−	0.0725636i
$489$		0			0
$490$	−20.2668	−	17.0059i	−0.915560	−	0.768246i
$491$	−23.6745	+	13.6685i	−1.06842	+	0.616851i	−0.927748	−	0.373206i	$-0.878258\pi$
$491$	−23.6745	+	13.6685i	−1.06842	+	0.616851i	−0.140668	+	0.990057i	$0.544925\pi$
$492$		0			0
$493$	−15.1345	+	5.50851i	−0.681623	+	0.248091i
$494$	−2.42855	+	27.7584i	−0.109266	+	1.24891i
$495$		0			0
$496$	0.902730	+	1.28923i	0.0405338	+	0.0578883i
$497$	37.1504	+	6.55063i	1.66643	+	0.293836i
$498$		0			0
$499$	10.9377	−	5.10035i	0.489641	−	0.228323i	−0.162087	−	0.986777i	$-0.551822\pi$
$499$	10.9377	−	5.10035i	0.489641	−	0.228323i	0.651727	+	0.758453i	$0.274045\pi$
$500$	11.0261	−	5.14157i	0.493104	−	0.229938i
$501$		0			0
$502$	18.9278	+	3.33747i	0.844787	+	0.148959i
$503$	−20.1856	−	28.8280i	−0.900032	−	1.28538i	−0.957914	−	0.287055i	$-0.907324\pi$
$503$	−20.1856	−	28.8280i	−0.900032	−	1.28538i	0.0578826	−	0.998323i	$-0.481565\pi$
$504$		0			0
$505$	1.03474	−	11.8272i	0.0460454	−	0.526301i
$506$	−2.90014	+	1.05556i	−0.128927	+	0.0469255i
$507$		0			0
$508$	2.98216	−	1.72175i	0.132312	−	0.0763904i
$509$	−10.9848	−	9.21733i	−0.486892	−	0.408551i	0.366019	−	0.930607i	$-0.380721\pi$
$509$	−10.9848	−	9.21733i	−0.486892	−	0.408551i	−0.852911	+	0.522056i	$0.825165\pi$
$510$		0			0
$511$	10.7555	−	1.89648i	0.475794	−	0.0838953i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	13.4540	−	11.2892i	0.593428	−	0.497946i
$515$	6.41753	−	17.6320i	0.282790	−	0.776960i
$516$		0			0
$517$			4.34054i			0.190897i
$518$	−24.7748	−	13.1205i	−1.08854	−	0.576480i
$519$		0			0
$520$	4.03060	−	8.64364i	0.176753	−	0.379049i
$521$	31.2612	+	11.3782i	1.36958	+	0.498486i	0.919003	−	0.394252i	$-0.128996\pi$
$521$	31.2612	+	11.3782i	1.36958	+	0.498486i	0.450577	+	0.892738i	$0.351218\pi$
$522$		0			0
$523$	13.4137	−	19.1567i	0.586538	−	0.837663i	−0.410713	−	0.911765i	$-0.634720\pi$
$523$	13.4137	−	19.1567i	0.586538	−	0.837663i	0.997251	+	0.0741018i	$0.0236090\pi$
$524$	−0.389861	+	0.389861i	−0.0170312	+	0.0170312i
$525$		0			0
$526$	16.4844	−	4.41698i	0.718754	−	0.192589i
$527$	−1.72426	+	2.05489i	−0.0751099	+	0.0895125i
$528$		0			0
$529$	−5.82205	−	3.36136i	−0.253132	−	0.146146i
$530$	5.67527	+	15.5927i	0.246518	+	0.677303i
$531$		0			0
$532$	24.1624	+	6.47430i	1.04757	+	0.280696i
$533$	−6.31633	+	4.42274i	−0.273591	+	0.191570i
$534$		0			0
$535$	3.34034	+	38.1803i	0.144416	+	1.65068i
$536$	2.88051	+	6.17727i	0.124419	+	0.266817i
$537$		0			0
$538$	−6.38948	+	0.559007i	−0.275470	+	0.0241005i
$539$	1.89178	−	10.7288i	0.0814846	−	0.462122i
$540$		0			0
$541$	0.508352	−	1.89720i	0.0218558	−	0.0815669i	−0.954137	−	0.299372i	$-0.903223\pi$
$541$	0.508352	−	1.89720i	0.0218558	−	0.0815669i	0.975992	+	0.217805i	$0.0698896\pi$
$542$	−9.63418	−	0.842881i	−0.413823	−	0.0362049i
$543$		0			0
$544$	0.852194	−	1.47604i	0.0365375	−	0.0632848i
$545$	−10.9300	−	18.9314i	−0.468192	−	0.810932i
$546$		0			0
$547$	−8.68799	−	32.4240i	−0.371471	−	1.38635i	−0.858432	−	0.512927i	$-0.828561\pi$
$547$	−8.68799	−	32.4240i	−0.371471	−	1.38635i	0.486961	−	0.873424i	$-0.338105\pi$
$548$	−2.18788	−	12.4081i	−0.0934616	−	0.530047i
$549$		0			0
$550$	0.970632	+	0.679644i	0.0413879	+	0.0289801i
$551$	−32.9674	−	39.2890i	−1.40446	−	1.67377i
$552$		0			0
$553$	−24.8066	−	11.5675i	−1.05488	−	0.491901i
$554$	−28.3044			−1.20254
$555$		0			0
$556$	8.27821			0.351074
$557$	−22.6070	−	10.5418i	−0.957889	−	0.446671i	−0.120158	−	0.992755i	$-0.538340\pi$
$557$	−22.6070	−	10.5418i	−0.957889	−	0.446671i	−0.837731	+	0.546084i	$0.816118\pi$
$558$		0			0
$559$	−25.2394	−	30.0791i	−1.06751	−	1.27221i
$560$	−7.01344	−	4.91086i	−0.296372	−	0.207522i
$561$		0			0
$562$	−3.32320	−	18.8468i	−0.140181	−	0.795004i
$563$	2.87368	+	10.7247i	0.121111	+	0.451993i	0.999671	−	0.0256388i	$-0.00816198\pi$
$563$	2.87368	+	10.7247i	0.121111	+	0.451993i	−0.878560	+	0.477632i	$0.841495\pi$
$564$		0			0
$565$	−17.2212	−	29.8280i	−0.724501	−	1.25487i
$566$	−1.14153	+	1.97718i	−0.0479819	+	0.0831072i
$567$		0			0
$568$	8.15386	+	0.713371i	0.342129	+	0.0299324i
$569$	−5.37581	+	20.0628i	−0.225366	+	0.841076i	0.756892	+	0.653540i	$0.226717\pi$
$569$	−5.37581	+	20.0628i	−0.225366	+	0.841076i	−0.982258	+	0.187536i	$0.939950\pi$
$570$		0			0
$571$	−4.08335	+	23.1578i	−0.170883	+	0.969126i	0.771906	+	0.635736i	$0.219303\pi$
$571$	−4.08335	+	23.1578i	−0.170883	+	0.969126i	−0.942789	+	0.333389i	$0.891808\pi$
$572$	3.91231	−	0.342283i	0.163582	−	0.0143116i
$573$		0			0
$574$	2.92546	+	6.27367i	0.122106	+	0.261858i
$575$	−0.544672	−	6.22563i	−0.0227144	−	0.259627i
$576$		0			0
$577$	13.1061	−	9.17696i	0.545612	−	0.382042i	−0.268027	−	0.963411i	$-0.586372\pi$
$577$	13.1061	−	9.17696i	0.545612	−	0.382042i	0.813640	+	0.581369i	$0.197483\pi$
$578$	−13.6148	−	3.64807i	−0.566300	−	0.151740i
$579$		0			0
$580$	6.00397	+	16.4958i	0.249301	+	0.684950i
$581$	42.5723	+	24.5791i	1.76620	+	1.01971i
$582$		0			0
$583$	−4.39209	+	5.23429i	−0.181902	+	0.216782i
$584$	2.28891	−	0.613311i	0.0947157	−	0.0253790i
$585$		0			0
$586$	−0.699979	+	0.699979i	−0.0289159	+	0.0289159i
$587$	13.9431	−	19.9128i	0.575493	−	0.821889i	−0.420868	−	0.907122i	$-0.638275\pi$
$587$	13.9431	−	19.9128i	0.575493	−	0.821889i	0.996361	+	0.0852329i	$0.0271634\pi$
$588$		0			0
$589$	−8.02704	−	2.92160i	−0.330749	−	0.120383i
$590$	−5.74295	+	12.3158i	−0.236434	+	0.507033i
$591$		0			0
$592$	−5.60314	−	2.36745i	−0.230288	−	0.0973017i
$593$		−	25.3065i		−	1.03921i	−0.854406	−	0.519606i	$-0.826079\pi$
$593$		−	25.3065i		−	1.03921i	0.854406	−	0.519606i	$-0.173921\pi$
$594$		0			0
$595$	4.99099	−	13.7126i	0.204611	−	0.562163i
$596$	−5.59075	+	4.69120i	−0.229006	+	0.192159i
$597$		0			0
$598$	−14.6462	−	14.6462i	−0.598926	−	0.598926i
$599$	−15.5557	+	2.74289i	−0.635589	+	0.112072i	−0.482153	−	0.876087i	$-0.660145\pi$
$599$	−15.5557	+	2.74289i	−0.635589	+	0.112072i	−0.153436	+	0.988159i	$0.549034\pi$
$600$		0			0
$601$	−7.59494	−	6.37291i	−0.309804	−	0.259956i	0.474607	−	0.880198i	$-0.342590\pi$
$601$	−7.59494	−	6.37291i	−0.309804	−	0.259956i	−0.784411	+	0.620241i	$0.787035\pi$
$602$	−30.5272	+	17.6249i	−1.24420	+	0.718337i
$603$		0			0
$604$	10.4078	−	3.78811i	0.423486	−	0.154136i
$605$	−1.68625	+	19.2739i	−0.0685557	+	0.783595i
$606$		0			0
$607$	−14.9621	−	21.3681i	−0.607293	−	0.867304i	0.391304	−	0.920261i	$-0.372024\pi$
$607$	−14.9621	−	21.3681i	−0.607293	−	0.867304i	−0.998597	+	0.0529575i	$0.983135\pi$
$608$	5.34508	+	0.942482i	0.216772	+	0.0382227i
$609$		0			0
$610$	15.5420	−	7.24736i	0.629278	−	0.293437i
$611$	−26.4013	+	12.3111i	−1.06808	+	0.498055i
$612$		0			0
$613$	−15.2226	−	2.68416i	−0.614837	−	0.108412i	−0.142447	−	0.989802i	$-0.545497\pi$
$613$	−15.2226	−	2.68416i	−0.614837	−	0.108412i	−0.472389	+	0.881390i	$0.656608\pi$
$614$	15.7279	+	22.4618i	0.634727	+	0.906485i
$615$		0			0
$616$	0.307278	−	3.51220i	0.0123806	−	0.141511i
$617$	22.9292	−	8.34555i	0.923096	−	0.335979i	0.163626	−	0.986522i	$-0.447681\pi$
$617$	22.9292	−	8.34555i	0.923096	−	0.335979i	0.759469	+	0.650543i	$0.225459\pi$
$618$		0			0
$619$	9.94091	−	5.73939i	0.399559	−	0.230685i	−0.286735	−	0.958010i	$-0.592570\pi$
$619$	9.94091	−	5.73939i	0.399559	−	0.230685i	0.686294	+	0.727325i	$0.259236\pi$
$620$	2.23972	+	1.87935i	0.0899493	+	0.0754765i
$621$		0			0
$622$	−4.16358	+	0.734152i	−0.166944	+	0.0294368i
$623$	−24.2708	−	24.2708i	−0.972388	−	0.972388i
$624$		0			0
$625$	11.3801	−	9.54905i	0.455205	−	0.381962i
$626$	−6.69341	+	18.3900i	−0.267522	+	0.735012i
$627$		0			0
$628$			11.5729i			0.461808i
$629$	1.42587	−	10.2689i	0.0568530	−	0.409446i
$630$		0			0
$631$	9.54890	−	20.4777i	0.380136	−	0.815204i	−0.619410	−	0.785068i	$-0.712628\pi$
$631$	9.54890	−	20.4777i	0.380136	−	0.815204i	0.999546	−	0.0301361i	$-0.00959408\pi$
$632$	−5.58064	−	2.03119i	−0.221986	−	0.0807963i
$633$		0			0
$634$	7.59576	−	10.8479i	0.301666	−	0.430824i
$635$	4.52333	−	4.52333i	0.179503	−	0.179503i
$636$		0			0
$637$	70.6235	−	18.9235i	2.79821	−	0.749777i
$638$	−4.64647	+	5.53744i	−0.183955	+	0.219229i
$639$		0			0
$640$	−1.60881	−	0.928845i	−0.0635937	−	0.0367158i
$641$	5.01750	+	13.7855i	0.198179	+	0.544493i	0.998481	−	0.0551051i	$-0.0175494\pi$
$641$	5.01750	+	13.7855i	0.198179	+	0.544493i	−0.800301	+	0.599598i	$0.795327\pi$
$642$		0			0
$643$	−8.32101	−	2.22961i	−0.328149	−	0.0879272i	0.0909834	−	0.995852i	$-0.470999\pi$
$643$	−8.32101	−	2.22961i	−0.328149	−	0.0879272i	−0.419132	+	0.907925i	$0.637666\pi$
$644$	−15.2317	+	10.6654i	−0.600214	+	0.420274i
$645$		0			0
$646$	0.806246	+	9.21543i	0.0317213	+	0.362576i
$647$	−1.17711	−	2.52433i	−0.0462771	−	0.0992416i	0.881810	−	0.471605i	$-0.156325\pi$
$647$	−1.17711	−	2.52433i	−0.0462771	−	0.0992416i	−0.928087	+	0.372364i	$0.878547\pi$
$648$		0			0
$649$	−5.57442	+	0.487698i	−0.218815	+	0.0191438i
$650$	−1.38091	+	7.83155i	−0.0541639	+	0.307179i
$651$		0			0
$652$	5.14923	−	19.2172i	0.201659	−	0.752603i
$653$	−22.4490	−	1.96403i	−0.878497	−	0.0768585i	−0.361023	−	0.932557i	$-0.617572\pi$
$653$	−22.4490	−	1.96403i	−0.878497	−	0.0768585i	−0.517475	+	0.855699i	$0.673128\pi$
$654$		0			0
$655$	−0.512115	+	0.887010i	−0.0200100	+	0.0346584i
$656$	0.750970	+	1.30072i	0.0293204	+	0.0507845i
$657$		0			0
$658$	6.76849	+	25.2603i	0.263863	+	0.984751i
$659$	2.76539	+	15.6833i	0.107724	+	0.610934i	0.990097	+	0.140384i	$0.0448336\pi$
$659$	2.76539	+	15.6833i	0.107724	+	0.610934i	−0.882373	+	0.470551i	$0.844055\pi$
$660$		0			0
$661$	−5.25363	−	3.67863i	−0.204342	−	0.143082i	0.466926	−	0.884296i	$-0.345361\pi$
$661$	−5.25363	−	3.67863i	−0.204342	−	0.143082i	−0.671269	+	0.741214i	$0.734250\pi$
$662$	3.00449	+	3.58062i	0.116773	+	0.139165i
$663$		0			0
$664$	9.66672	+	4.50767i	0.375142	+	0.174931i
$665$	46.4697			1.80202
$666$		0			0
$667$	38.1245			1.47619
$668$	−15.4398	−	7.19968i	−0.597383	−	0.278564i
$669$		0			0
$670$	8.13882	+	9.69947i	0.314430	+	0.374723i
$671$	5.78448	+	4.05034i	0.223308	+	0.156362i
$672$		0			0
$673$	−2.21557	−	12.5651i	−0.0854040	−	0.484350i	−0.997269	−	0.0738591i	$-0.976468\pi$
$673$	−2.21557	−	12.5651i	−0.0854040	−	0.484350i	0.911865	−	0.410491i	$-0.134643\pi$
$674$	−4.81039	−	17.9526i	−0.185289	−	0.691509i
$675$		0			0
$676$	6.67849	+	11.5675i	0.256865	+	0.444903i
$677$	14.5240	−	25.1563i	0.558203	−	0.966836i	−0.439443	−	0.898270i	$-0.644824\pi$
$677$	14.5240	−	25.1563i	0.558203	−	0.966836i	0.997647	−	0.0685661i	$-0.0218424\pi$
$678$		0			0
$679$	−65.6683	−	5.74523i	−2.52012	−	0.220482i
$680$	0.819479	−	3.05834i	0.0314256	−	0.117282i
$681$		0			0
$682$	−0.209064	+	1.18566i	−0.00800546	+	0.0454012i
$683$	43.6471	−	3.81863i	1.67011	−	0.146116i	0.787530	−	0.616277i	$-0.211360\pi$
$683$	43.6471	−	3.81863i	1.67011	−	0.146116i	0.882581	+	0.470161i	$0.155804\pi$
$684$		0			0
$685$	−9.89178	−	21.2130i	−0.377946	−	0.810507i
$686$	−2.90886	−	33.2484i	−0.111061	−	1.26943i
$687$		0			0
$688$	−6.26509	+	4.38686i	−0.238854	+	0.167248i
$689$	−44.2949	−	11.8688i	−1.68750	−	0.452165i
$690$		0			0
$691$	7.28398	+	20.0126i	0.277096	+	0.761314i	0.997688	+	0.0679555i	$0.0216476\pi$
$691$	7.28398	+	20.0126i	0.277096	+	0.761314i	−0.720593	+	0.693359i	$0.756130\pi$
$692$	−17.8875	−	10.3273i	−0.679980	−	0.392587i
$693$		0			0
$694$	−15.0014	+	17.8779i	−0.569444	+	0.678636i
$695$	14.8543	−	3.98021i	0.563457	−	0.150978i
$696$		0			0
$697$	−1.81011	+	1.81011i	−0.0685629	+	0.0685629i
$698$	10.0647	−	14.3738i	0.380953	−	0.544058i
$699$		0			0
$700$	6.70853	+	2.44171i	0.253559	+	0.0922878i
$701$	18.9227	−	40.5800i	0.714702	−	1.53268i	−0.126502	−	0.991966i	$-0.540375\pi$
$701$	18.9227	−	40.5800i	0.714702	−	1.53268i	0.841204	−	0.540718i	$-0.181847\pi$
$702$		0			0
$703$	32.2816	−	6.91753i	1.21752	−	0.260900i
$704$		−	0.764965i		−	0.0288307i
$705$		0			0
$706$	8.22107	−	22.5872i	0.309404	−	0.850081i
$707$	22.5637	−	18.9332i	0.848595	−	0.712056i
$708$		0			0
$709$	15.5236	+	15.5236i	0.583000	+	0.583000i	0.935726	−	0.352727i	$-0.114745\pi$
$709$	15.5236	+	15.5236i	0.583000	+	0.583000i	−0.352727	+	0.935726i	$0.614745\pi$
$710$	14.9742	−	2.64036i	0.561972	−	0.0990908i
$711$		0			0
$712$	−5.70505	−	4.78710i	−0.213806	−	0.179404i
$713$	5.49906	−	3.17488i	0.205941	−	0.118900i
$714$		0			0
$715$	6.85565	−	2.49525i	0.256387	−	0.0933171i
$716$	1.51254	−	17.2885i	0.0565264	−	0.646100i
$717$		0			0
$718$	−6.30980	−	9.01133i	−0.235480	−	0.336300i
$719$	−13.8634	−	2.44448i	−0.517016	−	0.0911638i	−0.0909490	−	0.995856i	$-0.528990\pi$
$719$	−13.8634	−	2.44448i	−0.517016	−	0.0911638i	−0.426067	+	0.904692i	$0.640101\pi$
$720$		0			0
$721$	42.1903	−	19.6736i	1.57125	−	0.732685i
$722$	−9.47834	+	4.41982i	−0.352747	+	0.164489i
$723$		0			0
$724$	−2.74098	−	0.483309i	−0.101868	−	0.0179620i
$725$	−8.39564	−	11.9902i	−0.311806	−	0.445305i
$726$		0			0
$727$	−0.0777661	+	0.888870i	−0.00288418	+	0.0329664i	−0.997500	−	0.0706606i	$-0.977489\pi$
$727$	−0.0777661	+	0.888870i	−0.00288418	+	0.0329664i	0.994616	+	0.103627i	$0.0330448\pi$
$728$	22.2345	−	8.09269i	0.824065	−	0.299935i
$729$		0			0
$730$	3.81231	−	2.20104i	0.141100	−	0.0814641i
$731$	−9.98585	−	8.37913i	−0.369340	−	0.309913i
$732$		0			0
$733$	26.1844	−	4.61701i	0.967142	−	0.170533i	0.332299	−	0.943174i	$-0.392176\pi$
$733$	26.1844	−	4.61701i	0.967142	−	0.170533i	0.634843	+	0.772641i	$0.281065\pi$
$734$	−11.3391	−	11.3391i	−0.418535	−	0.418535i
$735$		0			0
$736$	−3.09061	+	2.59333i	−0.113922	+	0.0955915i
$737$	−1.78326	+	4.89946i	−0.0656871	+	0.180474i
$738$		0			0
$739$			46.7086i			1.71820i	0.511805	+	0.859102i	$0.328977\pi$
$739$			46.7086i			1.71820i	−0.511805	+	0.859102i	$0.671023\pi$
$740$	−11.1925	−	1.55412i	−0.411445	−	0.0571305i
$741$		0			0
$742$	−17.3982	+	37.3105i	−0.638707	+	1.36971i
$743$	6.10600	+	2.22240i	0.224007	+	0.0815321i	0.451586	−	0.892228i	$-0.350859\pi$
$743$	6.10600	+	2.22240i	0.224007	+	0.0815321i	−0.227578	+	0.973760i	$0.573081\pi$
$744$		0			0
$745$	−7.77644	+	11.1059i	−0.284907	+	0.406889i
$746$	−6.71830	+	6.71830i	−0.245975	+	0.245975i
$747$		0			0
$748$	1.25937	−	0.337447i	0.0460472	−	0.0123383i
$749$	−61.1199	+	72.8398i	−2.23327	+	2.66151i
$750$		0			0
$751$	−41.9214	−	24.2034i	−1.52974	−	0.883193i	−0.999372	−	0.0354225i	$-0.988722\pi$
$751$	−41.9214	−	24.2034i	−1.52974	−	0.883193i	−0.530363	−	0.847771i	$-0.677944\pi$
$752$	1.94068	+	5.33197i	0.0707693	+	0.194437i
$753$		0			0
$754$	−46.8603	−	12.5562i	−1.70655	−	0.457269i
$755$	16.8542	−	11.8015i	0.613388	−	0.429499i
$756$		0			0
$757$	2.70655	+	30.9360i	0.0983711	+	1.12439i	0.871586	+	0.490243i	$0.163092\pi$
$757$	2.70655	+	30.9360i	0.0983711	+	1.12439i	−0.773215	+	0.634144i	$0.781352\pi$
$758$	−8.18516	−	17.5531i	−0.297298	−	0.637558i
$759$		0			0
$760$	10.0443	−	0.878764i	0.364346	−	0.0318761i
$761$	−8.10617	+	45.9724i	−0.293848	+	1.66650i	0.377998	+	0.925807i	$0.376613\pi$
$761$	−8.10617	+	45.9724i	−0.293848	+	1.66650i	−0.671846	+	0.740691i	$0.734498\pi$
$762$		0			0
$763$	14.0368	−	52.3861i	0.508167	−	1.89650i
$764$	9.72136	+	0.850509i	0.351707	+	0.0307703i
$765$		0			0
$766$	−12.9158	+	22.3708i	−0.466667	+	0.808291i
$767$	−18.7772	−	32.5231i	−0.678007	−	1.17434i
$768$		0			0
$769$	−7.15193	−	26.6914i	−0.257905	−	0.962515i	−0.966451	−	0.256850i	$-0.917315\pi$
$769$	−7.15193	−	26.6914i	−0.257905	−	0.962515i	0.708546	−	0.705665i	$-0.249351\pi$
$770$	−1.13731	−	6.45000i	−0.0409857	−	0.232442i
$771$		0			0
$772$	−2.91656	−	2.04220i	−0.104969	−	0.0735003i
$773$	27.2484	+	32.4734i	0.980057	+	1.16799i	0.985787	+	0.168002i	$0.0537316\pi$
$773$	27.2484	+	32.4734i	0.980057	+	1.16799i	−0.00573006	+	0.999984i	$0.501824\pi$
$774$		0			0
$775$	−2.20948	−	1.03030i	−0.0793670	−	0.0370094i
$776$	−14.3027			−0.513437
$777$		0			0
$778$	20.1134			0.721101
$779$	−7.38807	−	3.44511i	−0.264705	−	0.123434i
$780$		0			0
$781$	4.02465	+	4.79639i	0.144013	+	0.171628i
$782$	−5.63279	−	3.94412i	−0.201428	−	0.141042i
$783$		0			0
$784$	−2.47302	−	14.0252i	−0.0883222	−	0.500900i
$785$	5.56431	+	20.7663i	0.198599	+	0.741180i
$786$		0			0
$787$	7.76945	+	13.4571i	0.276951	+	0.479693i	0.970626	−	0.240595i	$-0.0773427\pi$
$787$	7.76945	+	13.4571i	0.276951	+	0.479693i	−0.693674	+	0.720289i	$0.744009\pi$
$788$	−0.193625	+	0.335368i	−0.00689760	+	0.0119470i
$789$		0			0
$790$	−10.9905	−	0.961541i	−0.391023	−	0.0342101i
$791$	22.1162	−	82.5386i	0.786360	−	2.93473i
$792$		0			0
$793$	−8.22956	+	46.6722i	−0.292240	+	1.65738i
$794$	33.1869	−	2.90348i	1.17776	−	0.103040i
$795$		0			0
$796$	−1.91279	−	4.10199i	−0.0677970	−	0.145391i
$797$	−2.86500	−	32.7471i	−0.101484	−	1.15996i	−0.860696	−	0.509119i	$-0.829971\pi$
$797$	−2.86500	−	32.7471i	−0.101484	−	1.15996i	0.759213	−	0.650843i	$-0.225584\pi$
$798$		0			0
$799$	−7.92200	+	5.54705i	−0.280260	+	0.196240i
$800$	1.49621	+	0.400908i	0.0528990	+	0.0141742i
$801$		0			0
$802$	8.70975	+	23.9298i	0.307552	+	0.844992i
$803$	1.56984	+	0.906350i	0.0553986	+	0.0319844i
$804$		0			0
$805$	−22.2037	+	26.4613i	−0.782577	+	0.932639i
$806$	−7.80474	+	2.09127i	−0.274910	+	0.0736620i
$807$		0			0
$808$	4.51906	−	4.51906i	0.158980	−	0.158980i
$809$	6.26031	−	8.94065i	0.220101	−	0.314337i	−0.693883	−	0.720088i	$-0.744101\pi$
$809$	6.26031	−	8.94065i	0.220101	−	0.314337i	0.913983	+	0.405752i	$0.132990\pi$
$810$		0			0
$811$	−20.0302	−	7.29041i	−0.703356	−	0.256001i	−0.0345131	−	0.999404i	$-0.510988\pi$
$811$	−20.0302	−	7.29041i	−0.703356	−	0.256001i	−0.668843	+	0.743403i	$0.733210\pi$
$812$	−18.4058	+	39.4714i	−0.645918	+	1.38518i
$813$		0			0
$814$	−1.75022	−	4.31139i	−0.0613452	−	0.151114i
$815$		−	36.9589i		−	1.29461i
$816$		0			0
$817$	14.1977	−	39.0078i	0.496714	−	1.36471i
$818$	−13.4783	+	11.3097i	−0.471259	+	0.395433i
$819$		0			0
$820$	1.97292	+	1.97292i	0.0688975	+	0.0688975i
$821$	−8.08927	+	1.42636i	−0.282318	+	0.0497802i	−0.313014	−	0.949749i	$-0.601339\pi$
$821$	−8.08927	+	1.42636i	−0.282318	+	0.0497802i	0.0306963	+	0.999529i	$0.490228\pi$
$822$		0			0
$823$	−35.0370	−	29.3995i	−1.22131	−	1.02480i	−0.998755	−	0.0498838i	$-0.984115\pi$
$823$	−35.0370	−	29.3995i	−1.22131	−	1.02480i	−0.222558	−	0.974919i	$-0.571441\pi$
$824$	8.74730	−	5.05025i	0.304726	−	0.175934i
$825$		0			0
$826$	−31.6806	+	11.5308i	−1.10231	+	0.401207i
$827$	−4.49919	+	51.4260i	−0.156452	+	1.78826i	0.361023	+	0.932557i	$0.382428\pi$
$827$	−4.49919	+	51.4260i	−0.156452	+	1.78826i	−0.517475	+	0.855698i	$0.673128\pi$
$828$		0			0
$829$	−20.3619	−	29.0798i	−0.707197	−	1.00998i	−0.998575	−	0.0533740i	$-0.983002\pi$
$829$	−20.3619	−	29.0798i	−0.707197	−	1.00998i	0.291377	−	0.956608i	$-0.405886\pi$
$830$	19.5132	+	3.44070i	0.677312	+	0.119428i
$831$		0			0
$832$	4.65290	−	2.16968i	0.161310	−	0.0752202i
$833$	21.9989	−	10.2583i	0.762218	−	0.355428i
$834$		0			0
$835$	−31.1666	−	5.49552i	−1.07857	−	0.190180i
$836$	2.38142	+	3.40102i	0.0823631	+	0.117627i
$837$		0			0
$838$	0.128438	−	1.46805i	0.00443681	−	0.0507130i
$839$	−10.9056	+	3.96931i	−0.376503	+	0.137036i	−0.523338	−	0.852125i	$-0.675314\pi$
$839$	−10.9056	+	3.96931i	−0.376503	+	0.137036i	0.146835	+	0.989161i	$0.453091\pi$
$840$		0			0
$841$	52.2171	−	30.1475i	1.80059	−	1.03957i
$842$	8.71468	+	7.31249i	0.300328	+	0.252005i
$843$		0			0
$844$	−17.3959	+	3.06737i	−0.598792	+	0.105583i
$845$	17.5455	+	17.5455i	0.603585	+	0.603585i
$846$		0			0
$847$	−36.7705	+	30.8541i	−1.26345	+	1.06016i
$848$	−3.05502	+	8.39359i	−0.104910	+	0.288237i
$849$		0			0
$850$			2.64008i			0.0905539i
$851$	−11.4854	+	21.6874i	−0.393715	+	0.743436i
$852$		0			0
$853$	4.66876	−	10.0122i	0.159855	−	0.342811i	−0.810024	−	0.586397i	$-0.800546\pi$
$853$	4.66876	−	10.0122i	0.159855	−	0.342811i	0.969879	+	0.243586i	$0.0783238\pi$
$854$	39.9795	+	14.5514i	1.36807	+	0.497937i
$855$		0			0
$856$	−11.8335	+	16.9000i	−0.404461	+	0.577630i
$857$	39.5995	−	39.5995i	1.35269	−	1.35269i	0.470059	−	0.882635i	$-0.344232\pi$
$857$	39.5995	−	39.5995i	1.35269	−	1.35269i	0.882635	−	0.470059i	$-0.155768\pi$
$858$		0			0
$859$	17.8671	−	4.78747i	0.609617	−	0.163346i	0.0592139	−	0.998245i	$-0.481141\pi$
$859$	17.8671	−	4.78747i	0.609617	−	0.163346i	0.550403	+	0.834899i	$0.314474\pi$
$860$	−9.13279	+	10.8840i	−0.311426	+	0.371143i
$861$		0			0
$862$	32.4365	+	18.7272i	1.10479	+	0.637852i
$863$	15.2588	+	41.9233i	0.519417	+	1.42709i	0.871164	+	0.490992i	$0.163366\pi$
$863$	15.2588	+	41.9233i	0.519417	+	1.42709i	−0.351747	+	0.936095i	$0.614412\pi$
$864$		0			0
$865$	−37.0626	−	9.93089i	−1.26017	−	0.337660i
$866$	−22.8720	+	16.0152i	−0.777224	+	0.544218i
$867$		0			0
$868$	0.632202	+	7.22611i	0.0214583	+	0.245270i
$869$	−1.91994	−	4.11733i	−0.0651296	−	0.139671i
$870$		0			0
$871$	−34.8588	+	3.04975i	−1.18115	+	0.103337i
$872$	2.04338	−	11.5886i	0.0691976	−	0.392439i
$873$		0			0
$874$	5.66748	−	21.1513i	0.191705	−	0.715455i
$875$	55.8579	+	4.88694i	1.88834	+	0.165209i
$876$		0			0
$877$	−20.9170	+	36.2294i	−0.706319	+	1.22338i	0.259895	+	0.965637i	$0.416312\pi$
$877$	−20.9170	+	36.2294i	−0.706319	+	1.22338i	−0.966214	+	0.257743i	$0.917021\pi$
$878$	−4.34368	−	7.52347i	−0.146592	−	0.253905i
$879$		0			0
$880$	−0.367799	−	1.37265i	−0.0123985	−	0.0462719i
$881$	2.32008	+	13.1578i	0.0781656	+	0.443299i	0.998623	+	0.0524567i	$0.0167051\pi$
$881$	2.32008	+	13.1578i	0.0781656	+	0.443299i	−0.920458	+	0.390842i	$0.872184\pi$
$882$		0			0
$883$	19.1640	+	13.4188i	0.644920	+	0.451578i	0.849726	−	0.527225i	$-0.176767\pi$
$883$	19.1640	+	13.4188i	0.644920	+	0.451578i	−0.204806	+	0.978803i	$0.565656\pi$
$884$	5.62450	+	6.70301i	0.189172	+	0.225447i
$885$		0			0
$886$	34.4041	+	16.0429i	1.15583	+	0.538972i
$887$	−45.4923			−1.52748			−0.763742	−	0.645522i	$-0.776640\pi$
$887$	−45.4923			−1.52748			−0.763742	+	0.645522i	$0.776640\pi$
$888$		0			0
$889$	15.8706			0.532283
$890$	−12.5387	−	5.84691i	−0.420300	−	0.195989i
$891$		0			0
$892$	5.78673	+	6.89635i	0.193754	+	0.230907i
$893$	−25.2272	−	17.6643i	−0.844197	−	0.591113i
$894$		0			0
$895$	−5.59829	−	31.7495i	−0.187130	−	1.06127i
$896$	−1.19286	−	4.45181i	−0.0398507	−	0.148725i
$897$		0			0
$898$	−8.52042	−	14.7578i	−0.284330	−	0.492474i
$899$	7.43619	−	12.8799i	0.248011	−	0.429567i
$900$		0			0
$901$	−15.1661	−	1.32686i	−0.505257	−	0.0442042i
$902$	−0.297365	+	1.10978i	−0.00990118	+	0.0369517i
$903$		0			0
$904$	3.21951	−	18.2588i	0.107079	−	0.607278i
$905$	−5.15077	+	0.450634i	−0.171217	+	0.0149796i
$906$		0			0
$907$	18.2216	+	39.0764i	0.605039	+	1.29751i	0.935379	+	0.353648i	$0.115059\pi$
$907$	18.2216	+	39.0764i	0.605039	+	1.29751i	−0.330340	+	0.943862i	$0.607163\pi$
$908$	−1.41467	−	16.1697i	−0.0469474	−	0.536611i
$909$		0			0
$910$	36.0063	−	25.2119i	1.19360	−	0.835766i
$911$	3.38314	+	0.906510i	0.112088	+	0.0300340i	0.314427	−	0.949282i	$-0.398188\pi$
$911$	3.38314	+	0.906510i	0.112088	+	0.0300340i	−0.202339	+	0.979316i	$0.564854\pi$
$912$		0			0
$913$	2.79059	+	7.66709i	0.0923552	+	0.253744i
$914$	6.12340	+	3.53534i	0.202544	+	0.116939i
$915$		0			0
$916$	−3.89914	+	4.64682i	−0.128831	+	0.153535i
$917$	−2.45449	+	0.657680i	−0.0810545	+	0.0217185i
$918$		0			0
$919$	−13.8897	+	13.8897i	−0.458180	+	0.458180i	−0.898058	−	0.439878i	$-0.855022\pi$
$919$	−13.8897	+	13.8897i	−0.458180	+	0.458180i	0.439878	+	0.898058i	$0.355022\pi$
$920$	−4.29888	+	6.13944i	−0.141730	+	0.202411i
$921$		0			0
$922$	17.9789	+	6.54378i	0.592103	+	0.215508i
$923$	−17.7589	+	38.0840i	−0.584540	+	1.25355i
$924$		0			0
$925$	9.34999	−	1.16375i	0.307426	−	0.0382638i
$926$			14.0749i			0.462531i
$927$		0			0
$928$	−3.23196	+	8.87973i	−0.106094	+	0.291491i
$929$	−1.52848	+	1.28255i	−0.0501479	+	0.0420791i	−0.667517	−	0.744594i	$-0.732643\pi$
$929$	−1.52848	+	1.28255i	−0.0501479	+	0.0420791i	0.617369	+	0.786674i	$0.288198\pi$
$930$		0			0
$931$	54.6570	+	54.6570i	1.79131	+	1.79131i
$932$	−3.99039	+	0.703613i	−0.130710	+	0.0230476i
$933$		0			0
$934$	−2.82854	−	2.37342i	−0.0925526	−	0.0776608i
$935$	2.09756	−	1.21102i	0.0685974	−	0.0396047i
$936$		0			0
$937$	−31.1706	+	11.3452i	−1.01830	+	0.370630i	−0.796614	−	0.604488i	$-0.793378\pi$
$937$	−31.1706	+	11.3452i	−1.01830	+	0.370630i	−0.221684	+	0.975119i	$0.571155\pi$
$938$	−2.73785	+	31.2938i	−0.0893941	+	1.02178i
$939$		0			0
$940$	6.04598	+	8.63455i	0.197198	+	0.281628i
$941$	−2.39309	−	0.421966i	−0.0780125	−	0.0137557i	0.134506	−	0.990913i	$-0.457055\pi$
$941$	−2.39309	−	0.421966i	−0.0780125	−	0.0137557i	−0.212518	+	0.977157i	$0.568166\pi$
$942$		0			0
$943$	5.49185	−	2.56089i	0.178839	−	0.0833942i
$944$	−6.62963	+	3.09145i	−0.215776	+	0.100618i
$945$		0			0
$946$	−5.76177	−	1.01596i	−0.187331	−	0.0330316i
$947$	17.9402	+	25.6213i	0.582979	+	0.832581i	0.996977	−	0.0776973i	$-0.0247568\pi$
$947$	17.9402	+	25.6213i	0.582979	+	0.832581i	−0.413998	+	0.910278i	$0.635868\pi$
$948$		0			0
$949$	−1.06030	+	12.1193i	−0.0344188	+	0.393408i
$950$	−7.90019	+	2.87543i	−0.256316	+	0.0932914i
$951$		0			0
$952$	6.80287	−	3.92764i	0.220482	−	0.127296i
$953$	10.4418	+	8.76171i	0.338243	+	0.283820i	0.796049	−	0.605233i	$-0.206920\pi$
$953$	10.4418	+	8.76171i	0.338243	+	0.283820i	−0.457805	+	0.889052i	$0.651364\pi$
$954$		0			0
$955$	17.8529	−	3.14794i	0.577705	−	0.101865i
$956$	2.29682	+	2.29682i	0.0742846	+	0.0742846i
$957$		0			0
$958$	−27.4021	+	22.9931i	−0.885323	+	0.742874i
$959$	19.8609	−	54.5673i	0.641341	−	1.76207i
$960$		0			0
$961$			28.5230i			0.920095i
$962$	21.2598	−	22.8742i	0.685445	−	0.737493i
$963$		0			0
$964$	11.9282	−	25.5802i	0.384182	−	0.823882i
$965$	−6.21535	−	2.26220i	−0.200079	−	0.0728229i
$966$		0			0
$967$	−10.0857	+	14.4039i	−0.324336	+	0.463199i	−0.947898	−	0.318574i	$-0.896796\pi$
$967$	−10.0857	+	14.4039i	−0.324336	+	0.463199i	0.623562	+	0.781774i	$0.285685\pi$
$968$	−7.36440	+	7.36440i	−0.236701	+	0.236701i
$969$		0			0
$970$	−25.6646	+	6.87682i	−0.824042	+	0.220801i
$971$	−36.6117	+	43.6321i	−1.17492	+	1.40022i	−0.276544	+	0.961001i	$0.589189\pi$
$971$	−36.6117	+	43.6321i	−1.17492	+	1.40022i	−0.898380	+	0.439219i	$0.855255\pi$
$972$		0			0
$973$	33.0416	+	19.0765i	1.05926	+	0.611566i
$974$	13.1170	+	36.0387i	0.420296	+	1.15475i
$975$		0			0
$976$	8.91666	+	2.38921i	0.285415	+	0.0764768i
$977$	35.4126	−	24.7961i	1.13295	−	0.793299i	0.152157	−	0.988356i	$-0.451378\pi$
$977$	35.4126	−	24.7961i	1.13295	−	0.793299i	0.980792	+	0.195057i	$0.0624893\pi$
$978$		0			0
$979$	−0.496527	−	5.67533i	−0.0158691	−	0.181384i
$980$	−11.1810	−	23.9777i	−0.357163	−	0.765938i
$981$		0			0
$982$	−27.2330	+	2.38258i	−0.869039	+	0.0760310i
$983$	−8.37067	+	47.4725i	−0.266983	+	1.51414i	0.496345	+	0.868125i	$0.334675\pi$
$983$	−8.37067	+	47.4725i	−0.266983	+	1.51414i	−0.763328	+	0.646011i	$0.776436\pi$
$984$		0			0
$985$	−0.186192	+	0.694877i	−0.00593256	+	0.0221406i
$986$	−16.0445	−	1.40371i	−0.510961	−	0.0447033i
$987$		0			0
$988$	−13.9322	+	24.1313i	−0.443244	+	0.767720i
$989$	15.4285	+	26.7230i	0.490598	+	0.849740i
$990$		0			0
$991$	3.01622	+	11.2567i	0.0958135	+	0.357581i	0.997142	−	0.0755563i	$-0.0240732\pi$
$991$	3.01622	+	11.2567i	0.0958135	+	0.357581i	−0.901328	+	0.433137i	$0.857407\pi$
$992$	0.273298	+	1.54995i	0.00867723	+	0.0492110i
$993$		0			0
$994$	30.9013	+	21.6373i	0.980130	+	0.686295i
$995$	−5.40455	−	6.44089i	−0.171336	−	0.204190i
$996$		0			0
$997$	−27.2229	−	12.6942i	−0.862157	−	0.402031i	−0.0593274	−	0.998239i	$-0.518896\pi$
$997$	−27.2229	−	12.6942i	−0.862157	−	0.402031i	−0.802830	+	0.596208i	$0.796673\pi$
$998$	12.0685			0.382020
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.449.7	yes	96
3.2	odd	2	inner	666.2.bs.b.449.2	yes	96
37.15	odd	36	inner	666.2.bs.b.89.2	✓	96
111.89	even	36	inner	666.2.bs.b.89.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.89.2	✓	96	37.15	odd	36	inner
666.2.bs.b.89.7	yes	96	111.89	even	36	inner
666.2.bs.b.449.2	yes	96	3.2	odd	2	inner
666.2.bs.b.449.7	yes	96	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.906308 + 0.422618i) q^{2} +(0.642788 + 0.766044i) q^{4} +(1.52173 + 1.06553i) q^{5} +(0.800320 + 4.53884i) q^{7} +(0.258819 + 0.965926i) q^{8} +O(q^{10})\)	\(q+(0.906308 + 0.422618i) q^{2} +(0.642788 + 0.766044i) q^{4} +(1.52173 + 1.06553i) q^{5} +(0.800320 + 4.53884i) q^{7} +(0.258819 + 0.965926i) q^{8} +(0.928845 + 1.60881i) q^{10} +(-0.382482 + 0.662479i) q^{11} +(-5.11437 - 0.447449i) q^{13} +(-1.19286 + 4.45181i) q^{14} +(-0.173648 + 0.984808i) q^{16} +(-1.69790 + 0.148547i) q^{17} +(-2.29378 - 4.91902i) q^{19} +(0.161908 + 1.85062i) q^{20} +(-0.626623 + 0.438766i) q^{22} +(3.89704 + 1.04421i) q^{23} +(-0.529786 - 1.45557i) q^{25} +(-4.44609 - 2.56695i) q^{26} +(-2.96252 + 3.53059i) q^{28} +(9.12762 - 2.44574i) q^{29} +(1.11289 - 1.11289i) q^{31} +(-0.573576 + 0.819152i) q^{32} +(-1.60160 - 0.582935i) q^{34} +(-3.61838 + 7.75965i) q^{35} +(-1.35851 + 5.92912i) q^{37} -5.42754i q^{38} +(-0.635367 + 1.74566i) q^{40} +(1.15055 - 0.965428i) q^{41} +(5.40814 + 5.40814i) q^{43} +(-0.753343 + 0.132835i) q^{44} +(3.09061 + 2.59333i) q^{46} +(4.91397 - 2.83708i) q^{47} +(-13.3827 + 4.87090i) q^{49} +(0.135003 - 1.54310i) q^{50} +(-2.94469 - 4.20545i) q^{52} +(8.79657 + 1.55107i) q^{53} +(-1.28792 + 0.600569i) q^{55} +(-4.17704 + 1.94779i) q^{56} +(9.30605 + 1.64091i) q^{58} +(4.19571 + 5.99209i) q^{59} +(0.804553 - 9.19608i) q^{61} +(1.47895 - 0.538293i) q^{62} +(-0.866025 + 0.500000i) q^{64} +(-7.30592 - 6.13040i) q^{65} +(6.71231 - 1.18356i) q^{67} +(-1.20518 - 1.20518i) q^{68} +(-6.55874 + 5.50344i) q^{70} +(2.79944 - 7.69139i) q^{71} -2.36965i q^{73} +(-3.73698 + 4.79947i) q^{74} +(2.29378 - 4.91902i) q^{76} +(-3.31299 - 1.20583i) q^{77} +(-3.40635 + 4.86478i) q^{79} +(-1.31358 + 1.31358i) q^{80} +(1.45076 - 0.388731i) q^{82} +(6.85600 - 8.17067i) q^{83} +(-2.74203 - 1.58311i) q^{85} +(2.61586 + 7.18702i) q^{86} +(-0.738899 - 0.197987i) q^{88} +(-6.10056 + 4.27166i) q^{89} +(-2.06223 - 23.5714i) q^{91} +(1.70506 + 3.65651i) q^{92} +(5.65258 - 0.494536i) q^{94} +(1.75084 - 9.92951i) q^{95} +(-3.70181 + 13.8154i) q^{97} +(-14.1874 - 1.24123i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 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

Modular forms

Varieties

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Representations

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Database

Properties

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