LMFDB - Embedded newform 666.2.bs.b.89.7

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			89.7
Character	$\chi$	$=$	666.89
Dual form			666.2.bs.b.449.7

$q$-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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{13}{36}\right)$

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	−0.181480	−	0.983395i	$-0.558089\pi$
$5$	1.52173	−	1.06553i	0.680538	−	0.476518i	0.862019	+	0.506876i	$0.169200\pi$
$6$		0			0
$7$	0.800320	−	4.53884i	0.302492	−	1.71552i	−0.332587	−	0.943073i	$-0.607921\pi$
$7$	0.800320	−	4.53884i	0.302492	−	1.71552i	0.635079	−	0.772447i	$-0.280968\pi$
$8$	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	0.802586	−	0.596537i	$-0.203457\pi$
$11$	−0.382482	−	0.662479i	−0.115323	−	0.199745i	−0.917909	+	0.396792i	$0.870124\pi$
$12$		0			0
$13$	−5.11437	+	0.447449i	−1.41847	+	0.124100i	−0.770439	−	0.637513i	$-0.779963\pi$
$13$	−5.11437	+	0.447449i	−1.41847	+	0.124100i	−0.648032	+	0.761613i	$0.724408\pi$
$14$	−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	−0.120627	−	0.992698i	$-0.538491\pi$
$17$	−1.69790	−	0.148547i	−0.411802	−	0.0360280i	−0.291175	+	0.956670i	$0.594046\pi$
$18$		0			0
$19$	−2.29378	+	4.91902i	−0.526229	+	1.12850i	0.446121	+	0.894973i	$0.352805\pi$
$19$	−2.29378	+	4.91902i	−0.526229	+	1.12850i	−0.972350	+	0.233529i	$0.924973\pi$
$20$	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	0.171485	−	0.985187i	$-0.445144\pi$
$23$	3.89704	−	1.04421i	0.812589	−	0.217732i	0.641104	+	0.767454i	$0.278477\pi$
$24$		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	0.971661	−	0.236377i	$-0.0759600\pi$
$29$	9.12762	+	2.44574i	1.69496	+	0.454162i	0.723295	+	0.690539i	$0.242627\pi$
$30$		0			0
$31$	1.11289	+	1.11289i	0.199881	+	0.199881i	0.799949	−	0.600068i	$-0.204860\pi$
$31$	1.11289	+	1.11289i	0.199881	+	0.199881i	−0.600068	+	0.799949i	$0.704860\pi$
$32$	−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	0.728195	−	0.685370i	$-0.240360\pi$
$41$	1.15055	+	0.965428i	0.179686	+	0.150775i	−0.548508	+	0.836145i	$0.684804\pi$
$42$		0			0
$43$	5.40814	−	5.40814i	0.824733	−	0.824733i	−0.162049	−	0.986783i	$-0.551810\pi$
$43$	5.40814	−	5.40814i	0.824733	−	0.824733i	0.986783	+	0.162049i	$0.0518103\pi$
$44$	−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	0.813565	−	0.581474i	$-0.197524\pi$
$47$	4.91397	+	2.83708i	0.716777	+	0.413831i	−0.0967885	+	0.995305i	$0.530857\pi$
$48$		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	0.467018	−	0.884248i	$-0.345328\pi$
$53$	8.79657	−	1.55107i	1.20830	−	0.213056i	0.741284	+	0.671192i	$0.234217\pi$
$54$		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	−0.447209	−	0.894430i	$-0.647582\pi$
$59$	4.19571	−	5.99209i	0.546234	−	0.780104i	0.993443	+	0.114326i	$0.0364708\pi$
$60$		0			0
$61$	0.804553	+	9.19608i	0.103012	+	1.17744i	0.855132	+	0.518411i	$0.173476\pi$
$61$	0.804553	+	9.19608i	0.103012	+	1.17744i	−0.752119	+	0.659027i	$0.770968\pi$
$62$	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	0.567902	−	0.823096i	$-0.307755\pi$
$67$	6.71231	+	1.18356i	0.820040	+	0.144595i	0.252138	+	0.967691i	$0.418866\pi$
$68$	−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	0.987530	+	0.157430i	$0.0503209\pi$
$71$	2.79944	+	7.69139i	0.332232	+	0.912800i	−0.655298	+	0.755370i	$0.727457\pi$
$72$		0			0
$73$			2.36965i			0.277347i	0.990338	+	0.138673i	$0.0442838\pi$
$73$			2.36965i			0.277347i	−0.990338	+	0.138673i	$0.955716\pi$
$74$	−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	0.580464	−	0.814286i	$-0.302871\pi$
$79$	−3.40635	−	4.86478i	−0.383245	−	0.547330i	−0.963709	+	0.266956i	$0.913982\pi$
$80$	−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	0.997352	−	0.0727245i	$-0.0231694\pi$
$83$	6.85600	+	8.17067i	0.752544	+	0.896847i	−0.244808	+	0.969572i	$0.578725\pi$
$84$		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	0.203676	−	0.979038i	$-0.434711\pi$
$89$	−6.10056	−	4.27166i	−0.646658	−	0.452795i	−0.850334	+	0.526243i	$0.823600\pi$
$90$		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	−0.852081	−	0.523410i	$-0.824660\pi$
$97$	−3.70181	−	13.8154i	−0.375862	−	1.40274i	0.476219	−	0.879327i	$-0.342007\pi$
$98$	−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	−0.980062	−	0.198691i	$-0.936331\pi$
$101$	−3.19546	+	5.53469i	−0.317960	+	0.550722i	0.662102	+	0.749413i	$0.269664\pi$
$102$		0			0
$103$	−2.61420	+	9.75634i	−0.257585	+	0.961321i	0.709049	+	0.705159i	$0.249125\pi$
$103$	−2.61420	+	9.75634i	−0.257585	+	0.961321i	−0.966634	+	0.256161i	$0.917542\pi$
$104$	−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	0.584143	−	0.811651i	$-0.301431\pi$
$107$	13.2614	−	15.8043i	1.28203	−	1.52786i	0.697885	−	0.716210i	$-0.254125\pi$
$108$		0			0
$109$	−10.6648	+	4.97310i	−1.02151	+	0.476336i	−0.859870	−	0.510514i	$-0.829455\pi$
$109$	−10.6648	+	4.97310i	−1.02151	+	0.476336i	−0.161637	+	0.986850i	$0.551677\pi$
$110$	−1.42107			−0.135493
$111$		0			0
$112$	−4.60886			−0.435496
$113$	−16.8033	+	7.83553i	−1.58073	+	0.737104i	−0.997185	−	0.0749795i	$-0.976111\pi$
$113$	−16.8033	+	7.83553i	−1.58073	+	0.737104i	−0.583541	+	0.812084i	$0.698333\pi$
$114$		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	0.999776	−	0.0211499i	$-0.00673272\pi$
$127$	0.597958	+	3.39119i	0.0530602	+	0.300919i	−0.946716	+	0.322069i	$0.895622\pi$
$128$	−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	−0.993806	−	0.111124i	$-0.964555\pi$
$131$	0.0480530	−	0.549249i	0.00419841	−	0.0479881i	0.998005	+	0.0631364i	$0.0201103\pi$
$132$		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	−0.887517	−	0.460776i	$-0.847571\pi$
$137$	−10.9115	+	6.29975i	−0.932231	+	0.538224i	−0.0447146	+	0.999000i	$0.514238\pi$
$138$		0			0
$139$	5.32113	+	6.34148i	0.451332	+	0.537877i	0.942950	−	0.332934i	$-0.108039\pi$
$139$	5.32113	+	6.34148i	0.451332	+	0.537877i	−0.491618	+	0.870811i	$0.663594\pi$
$140$	−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	$-0.903365\pi$
$149$		−	7.29821i		−	0.597892i	0.954270	−	0.298946i	$-0.0966351\pi$
$150$		0			0
$151$	3.78811	+	10.4078i	0.308272	+	0.846971i	0.992994	+	0.118166i	$0.0377016\pi$
$151$	3.78811	+	10.4078i	0.308272	+	0.846971i	−0.684721	+	0.728805i	$0.740076\pi$
$152$	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	−0.216374	−	0.976311i	$-0.569423\pi$
$157$	8.86534	−	7.43891i	0.707531	−	0.593689i	0.923905	+	0.382621i	$0.124979\pi$
$158$	−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	0.0665709	+	0.997782i	$0.478794\pi$
$163$	−11.4113	+	16.2971i	−0.893806	+	1.27649i	−0.960377	+	0.278705i	$0.910095\pi$
$164$	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	−0.279565	−	0.960127i	$-0.590190\pi$
$167$	−15.4398	−	7.19968i	−1.19477	−	0.557128i	−0.915201	+	0.402999i	$0.867968\pi$
$168$		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	−0.526017	−	0.850474i	$-0.676315\pi$
$173$	−19.4091	−	7.06432i	−1.47564	−	0.537090i	−0.949627	+	0.313384i	$0.898537\pi$
$174$		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	−0.996826	−	0.0796123i	$-0.974632\pi$
$179$	−12.2715	+	12.2715i	−0.917214	+	0.917214i	0.0796123	+	0.996826i	$0.474632\pi$
$180$		0			0
$181$	−2.13211	−	1.78905i	−0.158478	−	0.132979i	0.560100	−	0.828425i	$-0.310763\pi$
$181$	−2.13211	−	1.78905i	−0.158478	−	0.132979i	−0.718579	+	0.695446i	$0.755207\pi$
$182$	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	0.911216	−	0.411928i	$-0.135145\pi$
$191$	6.90030	+	6.90030i	0.499288	+	0.499288i	−0.411928	+	0.911216i	$0.635145\pi$
$192$		0			0
$193$	−3.43915	−	0.921516i	−0.247555	−	0.0663322i	0.132908	−	0.991128i	$-0.457569\pi$
$193$	−3.43915	−	0.921516i	−0.247555	−	0.0663322i	−0.380463	+	0.924796i	$0.624235\pi$
$194$	−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	−0.934885	−	0.354951i	$-0.884498\pi$
$197$	0.132447	−	0.363896i	0.00943648	−	0.0259265i	0.944321	+	0.329024i	$0.106720\pi$
$198$		0			0
$199$	−4.37182	+	1.17143i	−0.309910	+	0.0830402i	−0.410422	−	0.911896i	$-0.634619\pi$
$199$	−4.37182	+	1.17143i	−0.309910	+	0.0830402i	0.100512	+	0.994936i	$0.467952\pi$
$200$	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	−0.991565	−	0.129611i	$-0.958627\pi$
$211$	−8.83213	−	15.2977i	−0.608029	−	1.05314i	0.383536	−	0.923526i	$-0.374706\pi$
$212$	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	−0.924496	−	0.381191i	$-0.875514\pi$
$227$	−13.2961	+	9.31000i	−0.882490	+	0.617926i	0.0420063	+	0.999117i	$0.486625\pi$
$228$		0			0
$229$	1.05335	−	5.97383i	0.0696072	−	0.394762i	−0.930021	−	0.367506i	$-0.880212\pi$
$229$	1.05335	−	5.97383i	0.0696072	−	0.394762i	0.999628	−	0.0272564i	$-0.00867705\pi$
$230$	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	0.792000	−	0.610520i	$-0.209040\pi$
$233$	−2.02597	−	3.50909i	−0.132726	−	0.229888i	−0.924726	+	0.380632i	$0.875706\pi$
$234$		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	0.191328	−	0.981526i	$-0.438721\pi$
$239$	3.23584	+	0.283099i	0.209309	+	0.0183122i	0.0179811	+	0.999838i	$0.494276\pi$
$240$		0			0
$241$	−11.9282	+	25.5802i	−0.768365	+	1.64776i	−0.00654205	+	0.999979i	$0.502082\pi$
$241$	−11.9282	+	25.5802i	−0.768365	+	1.64776i	−0.761823	+	0.647785i	$0.775695\pi$
$242$	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	0.791670	−	0.610948i	$-0.209212\pi$
$251$	18.5648	+	4.97444i	1.17180	+	0.313984i	0.380132	+	0.924932i	$0.375878\pi$
$252$		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	0.989741	+	0.142875i	$0.0456348\pi$
$257$	7.42240	+	15.9174i	0.462996	+	0.992899i	−0.526744	+	0.850024i	$0.676587\pi$
$258$		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	0.949681	−	0.313219i	$-0.101408\pi$
$263$	13.0732	+	10.9697i	0.806130	+	0.676424i	−0.143551	+	0.989643i	$0.545852\pi$
$264$		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	0.321014	−	0.947074i	$-0.395976\pi$
$269$	−5.55459	−	3.20694i	−0.338669	−	0.195531i	−0.659683	+	0.751544i	$0.729310\pi$
$270$		0			0
$271$	−9.08775	−	3.30767i	−0.552041	−	0.200927i	0.0509119	−	0.998703i	$-0.483787\pi$
$271$	−9.08775	−	3.30767i	−0.552041	−	0.200927i	−0.602953	+	0.797777i	$0.706009\pi$
$272$	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	−0.548248	−	0.836316i	$-0.684705\pi$
$277$	−25.6525	−	11.9620i	−1.54131	−	0.718725i	−0.993062	+	0.117591i	$0.962483\pi$
$278$	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	−0.999994	−	0.00335557i	$-0.998932\pi$
$281$	−10.9768	+	15.6765i	−0.654823	+	0.935184i	0.345171	+	0.938540i	$0.387821\pi$
$282$		0			0
$283$	−0.198981	−	2.27437i	−0.0118282	−	0.135197i	0.987984	−	0.154553i	$-0.0493939\pi$
$283$	−0.198981	−	2.27437i	−0.0118282	−	0.135197i	−0.999813	+	0.0193563i	$0.993838\pi$
$284$	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	0.929410	−	0.369049i	$-0.120317\pi$
$293$	−0.338573	−	0.930221i	−0.0197796	−	0.0543441i	−0.949190	+	0.314705i	$0.898094\pi$
$294$		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	0.366330	−	0.930485i	$-0.380614\pi$
$307$	23.7471	−	13.7104i	1.35532	−	0.782494i	0.988989	+	0.147991i	$0.0472807\pi$
$308$	−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	0.471250	−	0.882000i	$-0.343803\pi$
$311$	−3.46322	−	2.42497i	−0.196381	−	0.137508i	−0.667631	+	0.744492i	$0.732692\pi$
$312$		0			0
$313$	1.70566	−	19.4958i	0.0964095	−	1.10197i	−0.781748	−	0.623594i	$-0.785672\pi$
$313$	1.70566	−	19.4958i	0.0964095	−	1.10197i	0.878158	−	0.478371i	$-0.158773\pi$
$314$	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	0.978751	+	0.205052i	$0.0657363\pi$
$317$	2.29959	+	13.0416i	0.129158	+	0.732490i	−0.849593	+	0.527438i	$0.823153\pi$
$318$		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	−0.302695	−	0.953088i	$-0.597886\pi$
$331$	4.23623	−	1.97539i	0.232844	−	0.108577i	0.535539	+	0.844511i	$0.320108\pi$
$332$	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	−0.986032	−	0.166556i	$-0.946735\pi$
$337$	−11.9468	+	14.2376i	−0.650784	+	0.775574i	0.335248	+	0.942130i	$0.391180\pi$
$338$	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	−0.915053	−	0.403334i	$-0.867851\pi$
$347$	−6.04031	−	22.5427i	−0.324261	−	1.21016i	0.590792	−	0.806824i	$-0.298815\pi$
$348$		0			0
$349$	3.04704	+	17.2806i	0.163104	+	0.925011i	0.950997	+	0.309199i	$0.100061\pi$
$349$	3.04704	+	17.2806i	0.163104	+	0.925011i	−0.787893	+	0.615812i	$0.788828\pi$
$350$	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	0.709969	+	0.704233i	$0.248709\pi$
$353$	−2.09495	+	23.9453i	−0.111503	+	1.27448i	−0.821472	+	0.570249i	$0.806847\pi$
$354$		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	−0.729875	−	0.683581i	$-0.760422\pi$
$359$	−9.52698	+	5.50040i	−0.502815	+	0.290300i	0.227061	+	0.973881i	$0.427088\pi$
$360$		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	−0.703917	−	0.710282i	$-0.748567\pi$
$367$	−15.0689	+	5.48462i	−0.786589	+	0.286295i	−0.0826716	+	0.996577i	$0.526345\pi$
$368$	−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	0.826694	−	0.562652i	$-0.190219\pi$
$373$	−3.24957	−	8.92813i	−0.168256	−	0.462281i	−0.994950	+	0.100372i	$0.967997\pi$
$374$	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	−0.938673	−	0.344808i	$-0.887944\pi$
$379$	−14.8365	+	12.4493i	−0.762102	+	0.639479i	0.176571	+	0.984288i	$0.443499\pi$
$380$	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	−0.805956	−	0.591976i	$-0.798348\pi$
$383$	−2.25137	−	25.7333i	−0.115040	−	1.31491i	0.690916	−	0.722935i	$-0.257208\pi$
$384$		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	0.825674	−	0.564148i	$-0.190795\pi$
$389$	18.2289	+	8.50030i	0.924244	+	0.430982i	0.0985704	+	0.995130i	$0.468573\pi$
$390$		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	0.998360	−	0.0572466i	$-0.0182321\pi$
$397$	28.8505	+	16.6568i	1.44796	+	0.835982i	0.449603	+	0.893228i	$0.351565\pi$
$398$	−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	−0.0961456	−	0.995367i	$-0.530651\pi$
$401$	18.0069	−	18.0069i	0.899222	−	0.899222i	0.995367	+	0.0961456i	$0.0306514\pi$
$402$		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	−0.999906	−	0.0137073i	$-0.995637\pi$
$409$	−7.43585	−	15.9462i	−0.367679	−	0.788491i	0.632227	−	0.774783i	$-0.282141\pi$
$410$	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	−0.951395	−	0.307973i	$-0.900349\pi$
$419$	−0.504021	+	1.38479i	−0.0246230	+	0.0676513i	0.926772	+	0.375624i	$0.122572\pi$
$420$		0			0
$421$	10.9886	−	2.94438i	0.535550	−	0.143500i	0.0191003	−	0.999818i	$-0.493920\pi$
$421$	10.9886	−	2.94438i	0.535550	−	0.143500i	0.516450	+	0.856317i	$0.327253\pi$
$422$	−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	0.861008	−	0.508591i	$-0.169833\pi$
$431$	37.3119	−	3.26437i	1.79725	−	0.157239i	0.936244	+	0.351352i	$0.114278\pi$
$432$		0			0
$433$	−13.9608	−	24.1808i	−0.670914	−	1.16206i	−0.977645	−	0.210260i	$-0.932569\pi$
$433$	−13.9608	−	24.1808i	−0.670914	−	1.16206i	0.306732	−	0.951796i	$-0.400765\pi$
$434$	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	−0.730936	−	0.682446i	$-0.760916\pi$
$439$	−7.11627	+	4.98287i	−0.339641	+	0.237819i	0.391295	+	0.920265i	$0.372027\pi$
$440$	−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	−0.854547	−	0.519374i	$-0.826165\pi$
$449$	−13.9590	+	9.77422i	−0.658768	+	0.461274i	0.195779	+	0.980648i	$0.437276\pi$
$450$		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	0.0787915	−	0.996891i	$-0.474894\pi$
$457$	7.04378	−	0.616251i	0.329494	−	0.0288270i	0.250703	+	0.968064i	$0.419338\pi$
$458$	−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	0.521881	−	0.853018i	$-0.325230\pi$
$461$	19.0599	+	1.66753i	0.887709	+	0.0776645i	0.365828	+	0.930683i	$0.380786\pi$
$462$		0			0
$463$	5.94832	−	12.7562i	0.276442	−	0.592831i	−0.718244	−	0.695792i	$-0.755054\pi$
$463$	5.94832	−	12.7562i	0.276442	−	0.592831i	0.994685	+	0.102960i	$0.0328315\pi$
$464$	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	−0.340394	−	0.940283i	$-0.610560\pi$
$467$	−3.56658	+	0.955662i	−0.165042	+	0.0442227i	0.175352	+	0.984506i	$0.443894\pi$
$468$		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	−0.867711	−	0.497070i	$-0.834409\pi$
$479$	−15.1175	−	32.4195i	−0.690734	−	1.48128i	0.176976	−	0.984215i	$-0.443368\pi$
$480$		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	0.264469	−	0.964394i	$-0.414803\pi$
$487$	27.1187	−	27.1187i	1.22886	−	1.22886i	0.964394	−	0.264469i	$-0.0851968\pi$
$488$	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	−0.140668	−	0.990057i	$-0.544925\pi$
$491$	−23.6745	−	13.6685i	−1.06842	−	0.616851i	−0.927748	+	0.373206i	$0.878258\pi$
$492$		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	0.651727	−	0.758453i	$-0.274045\pi$
$499$	10.9377	+	5.10035i	0.489641	+	0.228323i	−0.162087	+	0.986777i	$0.551822\pi$
$500$	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	0.0578826	+	0.998323i	$0.481565\pi$
$503$	−20.1856	+	28.8280i	−0.900032	+	1.28538i	−0.957914	+	0.287055i	$0.907324\pi$
$504$		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	−0.852911	−	0.522056i	$-0.825165\pi$
$509$	−10.9848	+	9.21733i	−0.486892	+	0.408551i	0.366019	+	0.930607i	$0.380721\pi$
$510$		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	0.450577	−	0.892738i	$-0.351218\pi$
$521$	31.2612	−	11.3782i	1.36958	−	0.498486i	0.919003	+	0.394252i	$0.128996\pi$
$522$		0			0
$523$	13.4137	+	19.1567i	0.586538	+	0.837663i	0.997251	−	0.0741018i	$-0.0236090\pi$
$523$	13.4137	+	19.1567i	0.586538	+	0.837663i	−0.410713	+	0.911765i	$0.634720\pi$
$524$	−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	0.975992	−	0.217805i	$-0.0698896\pi$
$541$	0.508352	+	1.89720i	0.0218558	+	0.0815669i	−0.954137	+	0.299372i	$0.903223\pi$
$542$	−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	0.486961	+	0.873424i	$0.338105\pi$
$547$	−8.68799	+	32.4240i	−0.371471	+	1.38635i	−0.858432	+	0.512927i	$0.828561\pi$
$548$	−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	−0.837731	−	0.546084i	$-0.816118\pi$
$557$	−22.6070	+	10.5418i	−0.957889	+	0.446671i	−0.120158	+	0.992755i	$0.538340\pi$
$558$		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	−0.878560	−	0.477632i	$-0.841495\pi$
$563$	2.87368	−	10.7247i	0.121111	−	0.451993i	0.999671	+	0.0256388i	$0.00816198\pi$
$564$		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	−0.982258	−	0.187536i	$-0.939950\pi$
$569$	−5.37581	−	20.0628i	−0.225366	−	0.841076i	0.756892	−	0.653540i	$-0.226717\pi$
$570$		0			0
$571$	−4.08335	−	23.1578i	−0.170883	−	0.969126i	−0.942789	−	0.333389i	$-0.891808\pi$
$571$	−4.08335	−	23.1578i	−0.170883	−	0.969126i	0.771906	−	0.635736i	$-0.219303\pi$
$572$	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	0.813640	−	0.581369i	$-0.197483\pi$
$577$	13.1061	+	9.17696i	0.545612	+	0.382042i	−0.268027	+	0.963411i	$0.586372\pi$
$578$	−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	0.996361	−	0.0852329i	$-0.0271634\pi$
$587$	13.9431	+	19.9128i	0.575493	+	0.821889i	−0.420868	+	0.907122i	$0.638275\pi$
$588$		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	$0.173921\pi$
$593$			25.3065i			1.03921i	−0.854406	+	0.519606i	$0.826079\pi$
$594$		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	−0.153436	−	0.988159i	$-0.549034\pi$
$599$	−15.5557	−	2.74289i	−0.635589	−	0.112072i	−0.482153	+	0.876087i	$0.660145\pi$
$600$		0			0
$601$	−7.59494	+	6.37291i	−0.309804	+	0.259956i	−0.784411	−	0.620241i	$-0.787035\pi$
$601$	−7.59494	+	6.37291i	−0.309804	+	0.259956i	0.474607	+	0.880198i	$0.342590\pi$
$602$	−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	−0.998597	−	0.0529575i	$-0.983135\pi$
$607$	−14.9621	+	21.3681i	−0.607293	+	0.867304i	0.391304	+	0.920261i	$0.372024\pi$
$608$	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	−0.472389	−	0.881390i	$-0.656608\pi$
$613$	−15.2226	+	2.68416i	−0.614837	+	0.108412i	−0.142447	+	0.989802i	$0.545497\pi$
$614$	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	0.759469	−	0.650543i	$-0.225459\pi$
$617$	22.9292	+	8.34555i	0.923096	+	0.335979i	0.163626	+	0.986522i	$0.447681\pi$
$618$		0			0
$619$	9.94091	+	5.73939i	0.399559	+	0.230685i	0.686294	−	0.727325i	$-0.259236\pi$
$619$	9.94091	+	5.73939i	0.399559	+	0.230685i	−0.286735	+	0.958010i	$0.592570\pi$
$620$	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	0.999546	+	0.0301361i	$0.00959408\pi$
$631$	9.54890	+	20.4777i	0.380136	+	0.815204i	−0.619410	+	0.785068i	$0.712628\pi$
$632$	−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	−0.800301	−	0.599598i	$-0.795327\pi$
$641$	5.01750	−	13.7855i	0.198179	−	0.544493i	0.998481	+	0.0551051i	$0.0175494\pi$
$642$		0			0
$643$	−8.32101	+	2.22961i	−0.328149	+	0.0879272i	−0.419132	−	0.907925i	$-0.637666\pi$
$643$	−8.32101	+	2.22961i	−0.328149	+	0.0879272i	0.0909834	+	0.995852i	$0.470999\pi$
$644$	−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	−0.928087	−	0.372364i	$-0.878547\pi$
$647$	−1.17711	+	2.52433i	−0.0462771	+	0.0992416i	0.881810	+	0.471605i	$0.156325\pi$
$648$		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	−0.517475	−	0.855699i	$-0.673128\pi$
$653$	−22.4490	+	1.96403i	−0.878497	+	0.0768585i	−0.361023	+	0.932557i	$0.617572\pi$
$654$		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	−0.882373	−	0.470551i	$-0.844055\pi$
$659$	2.76539	−	15.6833i	0.107724	−	0.610934i	0.990097	−	0.140384i	$-0.0448336\pi$
$660$		0			0
$661$	−5.25363	+	3.67863i	−0.204342	+	0.143082i	−0.671269	−	0.741214i	$-0.734250\pi$
$661$	−5.25363	+	3.67863i	−0.204342	+	0.143082i	0.466926	+	0.884296i	$0.345361\pi$
$662$	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	0.911865	+	0.410491i	$0.134643\pi$
$673$	−2.21557	+	12.5651i	−0.0854040	+	0.484350i	−0.997269	+	0.0738591i	$0.976468\pi$
$674$	−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	0.997647	+	0.0685661i	$0.0218424\pi$
$677$	14.5240	+	25.1563i	0.558203	+	0.966836i	−0.439443	+	0.898270i	$0.644824\pi$
$678$		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	0.882581	−	0.470161i	$-0.155804\pi$
$683$	43.6471	+	3.81863i	1.67011	+	0.146116i	0.787530	+	0.616277i	$0.211360\pi$
$684$		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	−0.720593	−	0.693359i	$-0.756130\pi$
$691$	7.28398	−	20.0126i	0.277096	−	0.761314i	0.997688	−	0.0679555i	$-0.0216476\pi$
$692$	−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	0.841204	+	0.540718i	$0.181847\pi$
$701$	18.9227	+	40.5800i	0.714702	+	1.53268i	−0.126502	+	0.991966i	$0.540375\pi$
$702$		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	−0.352727	−	0.935726i	$-0.614745\pi$
$709$	15.5236	−	15.5236i	0.583000	−	0.583000i	0.935726	+	0.352727i	$0.114745\pi$
$710$	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	−0.426067	−	0.904692i	$-0.640101\pi$
$719$	−13.8634	+	2.44448i	−0.517016	+	0.0911638i	−0.0909490	+	0.995856i	$0.528990\pi$
$720$		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	0.994616	−	0.103627i	$-0.0330448\pi$
$727$	−0.0777661	−	0.888870i	−0.00288418	−	0.0329664i	−0.997500	+	0.0706606i	$0.977489\pi$
$728$	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	0.634843	−	0.772641i	$-0.281065\pi$
$733$	26.1844	+	4.61701i	0.967142	+	0.170533i	0.332299	+	0.943174i	$0.392176\pi$
$734$	−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	$-0.671023\pi$
$739$		−	46.7086i		−	1.71820i	0.511805	−	0.859102i	$-0.328977\pi$
$740$	−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	−0.227578	−	0.973760i	$-0.573081\pi$
$743$	6.10600	−	2.22240i	0.224007	−	0.0815321i	0.451586	+	0.892228i	$0.350859\pi$
$744$		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	−0.530363	+	0.847771i	$0.677944\pi$
$751$	−41.9214	+	24.2034i	−1.52974	+	0.883193i	−0.999372	+	0.0354225i	$0.988722\pi$
$752$	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	−0.773215	−	0.634144i	$-0.781352\pi$
$757$	2.70655	−	30.9360i	0.0983711	−	1.12439i	0.871586	−	0.490243i	$-0.163092\pi$
$758$	−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	−0.671846	−	0.740691i	$-0.734498\pi$
$761$	−8.10617	−	45.9724i	−0.293848	−	1.66650i	0.377998	−	0.925807i	$-0.376613\pi$
$762$		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	0.708546	+	0.705665i	$0.249351\pi$
$769$	−7.15193	+	26.6914i	−0.257905	+	0.962515i	−0.966451	+	0.256850i	$0.917315\pi$
$770$	−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	−0.00573006	−	0.999984i	$-0.501824\pi$
$773$	27.2484	−	32.4734i	0.980057	−	1.16799i	0.985787	−	0.168002i	$-0.0537316\pi$
$774$		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	−0.693674	−	0.720289i	$-0.744009\pi$
$787$	7.76945	−	13.4571i	0.276951	−	0.479693i	0.970626	+	0.240595i	$0.0773427\pi$
$788$	−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	0.759213	+	0.650843i	$0.225584\pi$
$797$	−2.86500	+	32.7471i	−0.101484	+	1.15996i	−0.860696	+	0.509119i	$0.829971\pi$
$798$		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	0.913983	−	0.405752i	$-0.132990\pi$
$809$	6.26031	+	8.94065i	0.220101	+	0.314337i	−0.693883	+	0.720088i	$0.744101\pi$
$810$		0			0
$811$	−20.0302	+	7.29041i	−0.703356	+	0.256001i	−0.668843	−	0.743403i	$-0.733210\pi$
$811$	−20.0302	+	7.29041i	−0.703356	+	0.256001i	−0.0345131	+	0.999404i	$0.510988\pi$
$812$	−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	0.0306963	−	0.999529i	$-0.490228\pi$
$821$	−8.08927	−	1.42636i	−0.282318	−	0.0497802i	−0.313014	+	0.949749i	$0.601339\pi$
$822$		0			0
$823$	−35.0370	+	29.3995i	−1.22131	+	1.02480i	−0.222558	+	0.974919i	$0.571441\pi$
$823$	−35.0370	+	29.3995i	−1.22131	+	1.02480i	−0.998755	+	0.0498838i	$0.984115\pi$
$824$	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	−0.517475	−	0.855698i	$-0.673128\pi$
$827$	−4.49919	−	51.4260i	−0.156452	−	1.78826i	0.361023	−	0.932557i	$-0.382428\pi$
$828$		0			0
$829$	−20.3619	+	29.0798i	−0.707197	+	1.00998i	0.291377	+	0.956608i	$0.405886\pi$
$829$	−20.3619	+	29.0798i	−0.707197	+	1.00998i	−0.998575	+	0.0533740i	$0.983002\pi$
$830$	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	0.146835	−	0.989161i	$-0.453091\pi$
$839$	−10.9056	−	3.96931i	−0.376503	−	0.137036i	−0.523338	+	0.852125i	$0.675314\pi$
$840$		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	0.969879	−	0.243586i	$-0.0783238\pi$
$853$	4.66876	+	10.0122i	0.159855	+	0.342811i	−0.810024	+	0.586397i	$0.800546\pi$
$854$	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	0.882635	+	0.470059i	$0.155768\pi$
$857$	39.5995	+	39.5995i	1.35269	+	1.35269i	0.470059	+	0.882635i	$0.344232\pi$
$858$		0			0
$859$	17.8671	+	4.78747i	0.609617	+	0.163346i	0.550403	−	0.834899i	$-0.314474\pi$
$859$	17.8671	+	4.78747i	0.609617	+	0.163346i	0.0592139	+	0.998245i	$0.481141\pi$
$860$	−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	−0.351747	−	0.936095i	$-0.614412\pi$
$863$	15.2588	−	41.9233i	0.519417	−	1.42709i	0.871164	−	0.490992i	$-0.163366\pi$
$864$		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	−0.966214	−	0.257743i	$-0.917021\pi$
$877$	−20.9170	−	36.2294i	−0.706319	−	1.22338i	0.259895	−	0.965637i	$-0.416312\pi$
$878$	−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	−0.920458	−	0.390842i	$-0.872184\pi$
$881$	2.32008	−	13.1578i	0.0781656	−	0.443299i	0.998623	−	0.0524567i	$-0.0167051\pi$
$882$		0			0
$883$	19.1640	−	13.4188i	0.644920	−	0.451578i	−0.204806	−	0.978803i	$-0.565656\pi$
$883$	19.1640	−	13.4188i	0.644920	−	0.451578i	0.849726	+	0.527225i	$0.176767\pi$
$884$	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	−0.330340	−	0.943862i	$-0.607163\pi$
$907$	18.2216	−	39.0764i	0.605039	−	1.29751i	0.935379	−	0.353648i	$-0.115059\pi$
$908$	−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	−0.202339	−	0.979316i	$-0.564854\pi$
$911$	3.38314	−	0.906510i	0.112088	−	0.0300340i	0.314427	+	0.949282i	$0.398188\pi$
$912$		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	0.439878	−	0.898058i	$-0.355022\pi$
$919$	−13.8897	−	13.8897i	−0.458180	−	0.458180i	−0.898058	+	0.439878i	$0.855022\pi$
$920$	−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	0.617369	−	0.786674i	$-0.288198\pi$
$929$	−1.52848	−	1.28255i	−0.0501479	−	0.0420791i	−0.667517	+	0.744594i	$0.732643\pi$
$930$		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	−0.221684	−	0.975119i	$-0.571155\pi$
$937$	−31.1706	−	11.3452i	−1.01830	−	0.370630i	−0.796614	+	0.604488i	$0.793378\pi$
$938$	−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	−0.212518	−	0.977157i	$-0.568166\pi$
$941$	−2.39309	+	0.421966i	−0.0780125	+	0.0137557i	0.134506	+	0.990913i	$0.457055\pi$
$942$		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	−0.413998	−	0.910278i	$-0.635868\pi$
$947$	17.9402	−	25.6213i	0.582979	−	0.832581i	0.996977	+	0.0776973i	$0.0247568\pi$
$948$		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	−0.457805	−	0.889052i	$-0.651364\pi$
$953$	10.4418	−	8.76171i	0.338243	−	0.283820i	0.796049	+	0.605233i	$0.206920\pi$
$954$		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	0.623562	−	0.781774i	$-0.285685\pi$
$967$	−10.0857	−	14.4039i	−0.324336	−	0.463199i	−0.947898	+	0.318574i	$0.896796\pi$
$968$	−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	−0.898380	−	0.439219i	$-0.855255\pi$
$971$	−36.6117	−	43.6321i	−1.17492	−	1.40022i	−0.276544	−	0.961001i	$-0.589189\pi$
$972$		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	0.980792	−	0.195057i	$-0.0624893\pi$
$977$	35.4126	+	24.7961i	1.13295	+	0.793299i	0.152157	+	0.988356i	$0.451378\pi$
$978$		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	−0.763328	−	0.646011i	$-0.776436\pi$
$983$	−8.37067	−	47.4725i	−0.266983	−	1.51414i	0.496345	−	0.868125i	$-0.334675\pi$
$984$		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	−0.901328	−	0.433137i	$-0.857407\pi$
$991$	3.01622	−	11.2567i	0.0958135	−	0.357581i	0.997142	+	0.0755563i	$0.0240732\pi$
$992$	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	−0.802830	−	0.596208i	$-0.796673\pi$
$997$	−27.2229	+	12.6942i	−0.862157	+	0.402031i	−0.0593274	+	0.998239i	$0.518896\pi$
$998$	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.89.7	yes	96
3.2	odd	2	inner	666.2.bs.b.89.2	✓	96
37.5	odd	36	inner	666.2.bs.b.449.2	yes	96
111.5	even	36	inner	666.2.bs.b.449.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.89.2	✓	96	3.2	odd	2	inner
666.2.bs.b.89.7	yes	96	1.1	even	1	trivial
666.2.bs.b.449.2	yes	96	37.5	odd	36	inner
666.2.bs.b.449.7	yes	96	111.5	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)

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

Groups

Database

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