LMFDB - Embedded newform 378.2.z.a.41.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.20
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 - 0.173648i) q^{2} +(0.419652 + 1.68044i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.95067 - 1.63681i) q^{5} +(0.705083 + 1.58204i) q^{6} +(1.19511 + 2.36045i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.64778 + 1.41040i) q^{9} +O(q^{10})$	\(q+(0.984808 - 0.173648i) q^{2} +(0.419652 + 1.68044i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.95067 - 1.63681i) q^{5} +(0.705083 + 1.58204i) q^{6} +(1.19511 + 2.36045i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.64778 + 1.41040i) q^{9} +(-2.20527 - 1.27321i) q^{10} +(3.38986 + 4.03988i) q^{11} +(0.969090 + 1.43557i) q^{12} +(4.61346 + 0.813477i) q^{13} +(1.58685 + 2.11706i) q^{14} +(1.93196 - 3.96488i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-2.45690 + 4.25548i) q^{17} +(-2.36264 + 1.84876i) q^{18} +(3.75220 - 2.16633i) q^{19} +(-2.39285 - 0.870927i) q^{20} +(-3.46506 + 2.99889i) q^{21} +(4.03988 + 3.38986i) q^{22} +(-2.80443 - 7.70512i) q^{23} +(1.20365 + 1.24548i) q^{24} +(0.257739 + 1.46171i) q^{25} +4.68463 q^{26} +(-3.48125 - 3.85757i) q^{27} +(1.93036 + 1.80934i) q^{28} +(-6.32009 + 1.11440i) q^{29} +(1.21411 - 4.24013i) q^{30} +(-2.00923 - 5.52031i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-5.36622 + 7.39181i) q^{33} +(-1.68062 + 4.61746i) q^{34} +(1.53232 - 6.56063i) q^{35} +(-2.00572 + 2.23094i) q^{36} +(0.448119 - 0.776165i) q^{37} +(3.31901 - 2.78498i) q^{38} +(0.569046 + 8.09404i) q^{39} +(-2.50773 - 0.442181i) q^{40} +(0.918246 - 5.20763i) q^{41} +(-2.89167 + 3.55503i) q^{42} +(-3.13499 + 2.63057i) q^{43} +(4.56714 + 2.63684i) q^{44} +(7.47352 + 1.58268i) q^{45} +(-4.09981 - 7.10107i) q^{46} +(2.09624 + 0.762970i) q^{47} +(1.40164 + 1.01755i) q^{48} +(-4.14340 + 5.64200i) q^{49} +(0.507646 + 1.39475i) q^{50} +(-8.18213 - 2.34286i) q^{51} +(4.61346 - 0.813477i) q^{52} -9.42246i q^{53} +(-4.09823 - 3.19445i) q^{54} -13.4290i q^{55} +(2.21522 + 1.44665i) q^{56} +(5.21502 + 5.39625i) q^{57} +(-6.03056 + 2.19494i) q^{58} +(0.881790 + 0.739910i) q^{59} +(0.459378 - 4.38654i) q^{60} +(2.05855 - 5.65582i) q^{61} +(-2.93730 - 5.08755i) q^{62} +(-6.49359 - 4.56435i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-7.66784 - 9.13817i) q^{65} +(-4.00112 + 8.21135i) q^{66} +(-1.26064 + 7.14945i) q^{67} +(-0.853272 + 4.83915i) q^{68} +(11.7711 - 7.94616i) q^{69} +(0.369799 - 6.72704i) q^{70} +(7.78966 + 4.49736i) q^{71} +(-1.58785 + 2.54534i) q^{72} +(7.53439 - 4.34998i) q^{73} +(0.306531 - 0.842188i) q^{74} +(-2.34816 + 1.04653i) q^{75} +(2.78498 - 3.31901i) q^{76} +(-5.48464 + 12.8297i) q^{77} +(1.96592 + 7.87226i) q^{78} +(1.83651 + 10.4153i) q^{79} -2.54642 q^{80} +(5.02152 - 7.46889i) q^{81} -5.28797i q^{82} +(-2.18909 - 12.4150i) q^{83} +(-2.23041 + 4.00316i) q^{84} +(11.7580 - 4.27956i) q^{85} +(-2.63057 + 3.13499i) q^{86} +(-4.52493 - 10.1529i) q^{87} +(4.95564 + 1.80371i) q^{88} +(4.96625 + 8.60180i) q^{89} +(7.63481 + 0.260870i) q^{90} +(3.59344 + 11.8620i) q^{91} +(-5.27061 - 6.28127i) q^{92} +(8.43339 - 5.69301i) q^{93} +(2.19688 + 0.387370i) q^{94} +(-10.8652 - 1.91582i) q^{95} +(1.55704 + 0.758696i) q^{96} +(4.09086 + 4.87530i) q^{97} +(-3.10073 + 6.27578i) q^{98} +(-14.6735 - 5.91565i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$3$	0.419652	+	1.68044i	0.242286	+	0.970205i
$3$	0.419652	+	1.68044i	0.242286	+	0.970205i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−1.95067	−	1.63681i	−0.872367	−	0.732003i	0.0922283	−	0.995738i	$-0.470601\pi$
$5$	−1.95067	−	1.63681i	−0.872367	−	0.732003i	−0.964595	+	0.263735i	$0.915045\pi$
$6$	0.705083	+	1.58204i	0.287849	+	0.645866i
$7$	1.19511	+	2.36045i	0.451711	+	0.892164i
$7$	1.19511	+	2.36045i	0.451711	+	0.892164i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−2.64778	+	1.41040i	−0.882595	+	0.470135i
$10$	−2.20527	−	1.27321i	−0.697366	−	0.402624i
$11$	3.38986	+	4.03988i	1.02208	+	1.21807i	0.975692	+	0.219145i	$0.0703269\pi$
$11$	3.38986	+	4.03988i	1.02208	+	1.21807i	0.0463888	+	0.998923i	$0.485229\pi$
$12$	0.969090	+	1.43557i	0.279752	+	0.414414i
$13$	4.61346	+	0.813477i	1.27954	+	0.225618i	0.771786	−	0.635882i	$-0.219364\pi$
$13$	4.61346	+	0.813477i	1.27954	+	0.225618i	0.507757	+	0.861500i	$0.330475\pi$
$14$	1.58685	+	2.11706i	0.424102	+	0.565807i
$15$	1.93196	−	3.96488i	0.498830	−	1.02373i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−2.45690	+	4.25548i	−0.595886	+	1.03210i	0.397535	+	0.917587i	$0.369866\pi$
$17$	−2.45690	+	4.25548i	−0.595886	+	1.03210i	−0.993421	+	0.114518i	$0.963468\pi$
$18$	−2.36264	+	1.84876i	−0.556880	+	0.435757i
$19$	3.75220	−	2.16633i	0.860813	−	0.496991i	−0.00347113	−	0.999994i	$-0.501105\pi$
$19$	3.75220	−	2.16633i	0.860813	−	0.496991i	0.864285	+	0.503003i	$0.167772\pi$
$20$	−2.39285	−	0.870927i	−0.535058	−	0.194745i
$21$	−3.46506	+	2.99889i	−0.756139	+	0.654411i
$22$	4.03988	+	3.38986i	0.861305	+	0.722720i
$23$	−2.80443	−	7.70512i	−0.584765	−	1.60663i	−0.779937	−	0.625859i	$-0.784749\pi$
$23$	−2.80443	−	7.70512i	−0.584765	−	1.60663i	0.195172	−	0.980769i	$-0.437474\pi$
$24$	1.20365	+	1.24548i	0.245694	+	0.254233i
$25$	0.257739	+	1.46171i	0.0515478	+	0.292342i
$26$	4.68463			0.918731
$27$	−3.48125	−	3.85757i	−0.669968	−	0.742390i
$28$	1.93036	+	1.80934i	0.364804	+	0.341933i
$29$	−6.32009	+	1.11440i	−1.17361	+	0.206939i	−0.726261	−	0.687419i	$-0.758743\pi$
$29$	−6.32009	+	1.11440i	−1.17361	+	0.206939i	−0.447351	+	0.894359i	$0.647632\pi$
$30$	1.21411	−	4.24013i	0.221666	−	0.774138i
$31$	−2.00923	−	5.52031i	−0.360868	−	0.991477i	−0.978723	−	0.205185i	$-0.934220\pi$
$31$	−2.00923	−	5.52031i	−0.360868	−	0.991477i	0.617855	−	0.786292i	$-0.288002\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	−5.36622	+	7.39181i	−0.934140	+	1.28675i
$34$	−1.68062	+	4.61746i	−0.288224	+	0.791888i
$35$	1.53232	−	6.56063i	0.259009	−	1.10895i
$36$	−2.00572	+	2.23094i	−0.334286	+	0.371824i
$37$	0.448119	−	0.776165i	0.0736703	−	0.127601i	−0.826837	−	0.562442i	$-0.809862\pi$
$37$	0.448119	−	0.776165i	0.0736703	−	0.127601i	0.900507	+	0.434841i	$0.143195\pi$
$38$	3.31901	−	2.78498i	0.538415	−	0.451784i
$39$	0.569046	+	8.09404i	0.0911203	+	1.29608i
$40$	−2.50773	−	0.442181i	−0.396508	−	0.0699150i
$41$	0.918246	−	5.20763i	0.143406	−	0.813296i	−0.825227	−	0.564801i	$-0.808953\pi$
$41$	0.918246	−	5.20763i	0.143406	−	0.813296i	0.968633	−	0.248495i	$-0.0799359\pi$
$42$	−2.89167	+	3.55503i	−0.446194	+	0.548553i
$43$	−3.13499	+	2.63057i	−0.478082	+	0.401158i	−0.849732	−	0.527214i	$-0.823236\pi$
$43$	−3.13499	+	2.63057i	−0.478082	+	0.401158i	0.371650	+	0.928373i	$0.378792\pi$
$44$	4.56714	+	2.63684i	0.688523	+	0.397519i
$45$	7.47352	+	1.58268i	1.11409	+	0.235932i
$46$	−4.09981	−	7.10107i	−0.604483	−	1.04700i
$47$	2.09624	+	0.762970i	0.305768	+	0.111291i	0.490347	−	0.871527i	$-0.336870\pi$
$47$	2.09624	+	0.762970i	0.305768	+	0.111291i	−0.184579	+	0.982818i	$0.559092\pi$
$48$	1.40164	+	1.01755i	0.202309	+	0.146870i
$49$	−4.14340	+	5.64200i	−0.591915	+	0.806001i
$50$	0.507646	+	1.39475i	0.0717920	+	0.197247i
$51$	−8.18213	−	2.34286i	−1.14573	−	0.328066i
$52$	4.61346	−	0.813477i	0.639772	−	0.112809i
$53$		−	9.42246i		−	1.29427i	−0.762373	−	0.647137i	$-0.775966\pi$
$53$		−	9.42246i		−	1.29427i	0.762373	−	0.647137i	$-0.224034\pi$
$54$	−4.09823	−	3.19445i	−0.557698	−	0.434710i
$55$		−	13.4290i		−	1.81077i
$56$	2.21522	+	1.44665i	0.296022	+	0.193316i
$57$	5.21502	+	5.39625i	0.690746	+	0.714751i
$58$	−6.03056	+	2.19494i	−0.791851	+	0.288210i
$59$	0.881790	+	0.739910i	0.114799	+	0.0963281i	0.698380	−	0.715727i	$-0.253904\pi$
$59$	0.881790	+	0.739910i	0.114799	+	0.0963281i	−0.583581	+	0.812055i	$0.698349\pi$
$60$	0.459378	−	4.38654i	0.0593054	−	0.566300i
$61$	2.05855	−	5.65582i	0.263570	−	0.724153i	−0.735350	−	0.677688i	$-0.762982\pi$
$61$	2.05855	−	5.65582i	0.263570	−	0.724153i	0.998920	−	0.0464655i	$-0.0147957\pi$
$62$	−2.93730	−	5.08755i	−0.373037	−	0.646119i
$63$	−6.49359	−	4.56435i	−0.818115	−	0.575054i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−7.66784	−	9.13817i	−0.951078	−	1.13345i
$66$	−4.00112	+	8.21135i	−0.492504	+	1.01075i
$67$	−1.26064	+	7.14945i	−0.154012	+	0.873444i	0.805672	+	0.592362i	$0.201804\pi$
$67$	−1.26064	+	7.14945i	−0.154012	+	0.873444i	−0.959684	+	0.281082i	$0.909307\pi$
$68$	−0.853272	+	4.83915i	−0.103474	+	0.586833i
$69$	11.7711	−	7.94616i	1.41708	−	0.956605i
$70$	0.369799	−	6.72704i	0.0441994	−	0.804035i
$71$	7.78966	+	4.49736i	0.924463	+	0.533739i	0.885056	−	0.465484i	$-0.154120\pi$
$71$	7.78966	+	4.49736i	0.924463	+	0.533739i	0.0394068	+	0.999223i	$0.487453\pi$
$72$	−1.58785	+	2.54534i	−0.187129	+	0.299971i
$73$	7.53439	−	4.34998i	0.881834	−	0.509127i	0.0105711	−	0.999944i	$-0.496635\pi$
$73$	7.53439	−	4.34998i	0.881834	−	0.509127i	0.871263	+	0.490817i	$0.163302\pi$
$74$	0.306531	−	0.842188i	0.0356335	−	0.0979024i
$75$	−2.34816	+	1.04653i	−0.271142	+	0.120842i
$76$	2.78498	−	3.31901i	0.319460	−	0.380717i
$77$	−5.48464	+	12.8297i	−0.625032	+	1.46208i
$78$	1.96592	+	7.87226i	0.222596	+	0.891357i
$79$	1.83651	+	10.4153i	0.206623	+	1.17182i	0.894865	+	0.446337i	$0.147272\pi$
$79$	1.83651	+	10.4153i	0.206623	+	1.17182i	−0.688242	+	0.725481i	$0.741617\pi$
$80$	−2.54642			−0.284698
$81$	5.02152	−	7.46889i	0.557946	−	0.829877i
$82$		−	5.28797i		−	0.583959i
$83$	−2.18909	−	12.4150i	−0.240284	−	1.36272i	−0.831194	−	0.555982i	$-0.812342\pi$
$83$	−2.18909	−	12.4150i	−0.240284	−	1.36272i	0.590910	−	0.806737i	$-0.298769\pi$
$84$	−2.23041	+	4.00316i	−0.243358	+	0.436780i
$85$	11.7580	−	4.27956i	1.27533	−	0.464184i
$86$	−2.63057	+	3.13499i	−0.283662	+	0.338055i
$87$	−4.52493	−	10.1529i	−0.485124	−	1.08850i
$88$	4.95564	+	1.80371i	0.528273	+	0.192276i
$89$	4.96625	+	8.60180i	0.526422	+	0.911789i	0.999526	+	0.0307827i	$0.00979998\pi$
$89$	4.96625	+	8.60180i	0.526422	+	0.911789i	−0.473104	+	0.881006i	$0.656867\pi$
$90$	7.63481	+	0.260870i	0.804779	+	0.0274981i
$91$	3.59344	+	11.8620i	0.376695	+	1.24348i
$92$	−5.27061	−	6.28127i	−0.549499	−	0.654867i
$93$	8.43339	−	5.69301i	0.874502	−	0.590337i
$94$	2.19688	+	0.387370i	0.226591	+	0.0399542i
$95$	−10.8652	−	1.91582i	−1.11474	−	0.196559i
$96$	1.55704	+	0.758696i	0.158915	+	0.0774341i
$97$	4.09086	+	4.87530i	0.415364	+	0.495012i	0.932641	−	0.360806i	$-0.117498\pi$
$97$	4.09086	+	4.87530i	0.415364	+	0.495012i	−0.517276	+	0.855818i	$0.673054\pi$
$98$	−3.10073	+	6.27578i	−0.313221	+	0.633950i
$99$	−14.6735	−	5.91565i	−1.47474	−	0.594545i
$100$	0.742129	+	1.28541i	0.0742129	+	0.128541i
$101$	−10.0462	−	3.65652i	−0.999636	−	0.363838i	−0.210192	−	0.977660i	$-0.567409\pi$
$101$	−10.0462	−	3.65652i	−0.999636	−	0.363838i	−0.789444	+	0.613823i	$0.789631\pi$
$102$	−8.46466	−	0.886457i	−0.838126	−	0.0877723i
$103$	−1.54935	+	1.84644i	−0.152662	+	0.181935i	−0.836955	−	0.547272i	$-0.815666\pi$
$103$	−1.54935	+	1.84644i	−0.152662	+	0.181935i	0.684293	+	0.729207i	$0.260111\pi$
$104$	4.40211	−	1.60224i	0.431662	−	0.157112i
$105$	11.6678	−	0.178206i	1.13866	−	0.0173912i
$106$	−1.63619	−	9.27931i	−0.158921	−	0.901287i
$107$		−	8.64382i		−	0.835630i	−0.908532	−	0.417815i	$-0.862796\pi$
$107$		−	8.64382i		−	0.835630i	0.908532	−	0.417815i	$-0.137204\pi$
$108$	−4.59068	−	2.43427i	−0.441738	−	0.234238i
$109$	−10.0711			−0.964636			−0.482318	−	0.875996i	$-0.660205\pi$
$109$	−10.0711			−0.964636			−0.482318	+	0.875996i	$0.660205\pi$
$110$	−2.33192	−	13.2250i	−0.222340	−	1.26095i
$111$	1.49236	+	0.427319i	0.141648	+	0.0405593i
$112$	2.43278	+	1.04000i	0.229876	+	0.0982709i
$113$	−0.126205	+	0.150405i	−0.0118724	+	0.0141489i	−0.771948	−	0.635686i	$-0.780717\pi$
$113$	−0.126205	+	0.150405i	−0.0118724	+	0.0141489i	0.760076	+	0.649835i	$0.225162\pi$
$114$	6.07284	+	4.40869i	0.568774	+	0.412912i
$115$	−7.14127	+	19.6205i	−0.665926	+	1.82962i
$116$	−5.55779	+	3.20879i	−0.516028	+	0.297929i
$117$	−13.3628	+	4.35293i	−1.23539	+	0.402429i
$118$	0.996878	+	0.575548i	0.0917701	+	0.0529835i
$119$	−12.9811	−	0.713596i	−1.18997	−	0.0654153i
$120$	−0.309316	−	4.39967i	−0.0282366	−	0.401633i
$121$	−2.91933	+	16.5563i	−0.265394	+	1.50512i
$122$	1.04515	−	5.92736i	0.0946237	−	0.536638i
$123$	9.13648	−	0.642334i	0.823809	−	0.0579173i
$124$	−3.77611	−	4.50020i	−0.339105	−	0.404130i
$125$	−4.47628	+	7.75314i	−0.400370	+	0.693462i
$126$	−7.18753	−	3.36741i	−0.640316	−	0.299993i
$127$	−9.42794	−	16.3297i	−0.836595	−	1.44902i	−0.892725	−	0.450601i	$-0.851210\pi$
$127$	−9.42794	−	16.3297i	−0.836595	−	1.44902i	0.0561306	−	0.998423i	$-0.482124\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	−5.73614	−	4.16425i	−0.505039	−	0.366642i
$130$	−9.13817	−	7.66784i	−0.801471	−	0.672514i
$131$	−8.02081	+	2.91934i	−0.700781	+	0.255064i	−0.667744	−	0.744391i	$-0.732740\pi$
$131$	−8.02081	+	2.91934i	−0.700781	+	0.255064i	−0.0330369	+	0.999454i	$0.510518\pi$
$132$	−2.51445	+	8.78139i	−0.218855	+	0.764322i
$133$	9.59782	+	6.26784i	0.832236	+	0.543491i
$134$			7.25974i			0.627146i
$135$	0.476679	+	13.2230i	0.0410260	+	1.13805i
$136$			4.91380i			0.421355i
$137$	−5.88182	+	1.03712i	−0.502518	+	0.0886075i	−0.419160	−	0.907912i	$-0.637676\pi$
$137$	−5.88182	+	1.03712i	−0.502518	+	0.0886075i	−0.0833577	+	0.996520i	$0.526564\pi$
$138$	10.2125	−	9.86948i	0.869342	−	0.840146i
$139$	−0.558807	−	1.53531i	−0.0473974	−	0.130223i	0.913735	−	0.406310i	$-0.133185\pi$
$139$	−0.558807	−	1.53531i	−0.0473974	−	0.130223i	−0.961133	+	0.276087i	$0.910962\pi$
$140$	−0.803958	−	6.68906i	−0.0679468	−	0.565328i
$141$	−0.402435	+	3.84280i	−0.0338911	+	0.323622i
$142$	8.45228	+	3.07638i	0.709299	+	0.258164i
$143$	12.3526	+	21.3954i	1.03298	+	1.78917i
$144$	−1.12173	+	2.78240i	−0.0934775	+	0.231866i
$145$	14.1525	+	8.17094i	1.17530	+	0.678560i
$146$	6.66456	−	5.59223i	0.551563	−	0.462816i
$147$	−11.2199	−	4.59507i	−0.925399	−	0.378995i
$148$	0.155630	−	0.882622i	0.0127927	−	0.0725511i
$149$	20.7850	+	3.66496i	1.70278	+	0.300246i	0.938663	−	0.344835i	$-0.112065\pi$
$149$	20.7850	+	3.66496i	1.70278	+	0.300246i	0.764114	+	0.645081i	$0.223176\pi$
$150$	−2.13076	+	1.43838i	−0.173976	+	0.117443i
$151$	16.8405	−	14.1309i	1.37046	−	1.14995i	0.397868	−	0.917443i	$-0.369750\pi$
$151$	16.8405	−	14.1309i	1.37046	−	1.14995i	0.972594	−	0.232511i	$-0.0746942\pi$
$152$	2.16633	−	3.75220i	0.175713	−	0.304344i
$153$	0.503398	−	14.7328i	0.0406973	−	1.19108i
$154$	−3.17346	+	13.5872i	−0.255725	+	1.09489i
$155$	−5.11634	+	14.0570i	−0.410954	+	1.12909i
$156$	3.30305	+	7.41128i	0.264456	+	0.593377i
$157$	−6.33840	+	7.55381i	−0.505859	+	0.602860i	−0.957177	−	0.289504i	$-0.906510\pi$
$157$	−6.33840	+	7.55381i	−0.505859	+	0.602860i	0.451318	+	0.892363i	$0.350954\pi$
$158$	3.61721	+	9.93821i	0.287770	+	0.790641i
$159$	15.8339	−	3.95416i	1.25571	−	0.313585i
$160$	−2.50773	+	0.442181i	−0.198254	+	0.0349575i
$161$	14.8359	−	15.8282i	1.16923	−	1.24744i
$162$	3.64827	−	8.22740i	0.286635	−	0.646406i
$163$	−6.19088			−0.484907			−0.242454	−	0.970163i	$-0.577952\pi$
$163$	−6.19088			−0.484907			−0.242454	+	0.970163i	$0.577952\pi$
$164$	−0.918246	−	5.20763i	−0.0717030	−	0.406648i
$165$	22.5667	−	5.63552i	1.75682	−	0.438725i
$166$	−4.31167	−	11.8462i	−0.334651	−	0.919445i
$167$	−3.15479	−	2.64718i	−0.244125	−	0.204845i	0.512513	−	0.858680i	$-0.328715\pi$
$167$	−3.15479	−	2.64718i	−0.244125	−	0.204845i	−0.756638	+	0.653835i	$0.773159\pi$
$168$	−1.50139	+	4.32965i	−0.115835	+	0.334039i
$169$	8.40625	+	3.05962i	0.646635	+	0.235356i
$170$	10.8362	−	6.25630i	0.831101	−	0.479836i
$171$	−6.87961	+	11.0281i	−0.526097	+	0.843340i
$172$	−2.04622	+	3.54416i	−0.156023	+	0.270240i
$173$	−5.13237	+	4.30657i	−0.390207	+	0.327423i	−0.816694	−	0.577071i	$-0.804195\pi$
$173$	−5.13237	+	4.30657i	−0.390207	+	0.327423i	0.426487	+	0.904494i	$0.359751\pi$
$174$	−6.21922	−	9.21290i	−0.471478	−	0.698428i
$175$	−3.14226	+	2.35529i	−0.237532	+	0.178043i
$176$	5.19357	+	0.915766i	0.391480	+	0.0690284i
$177$	−0.873332	+	1.79230i	−0.0656436	+	0.134718i
$178$	6.38449	+	7.60874i	0.478538	+	0.570299i
$179$	−0.794596	−	0.458760i	−0.0593909	−	0.0342893i	0.470011	−	0.882661i	$-0.344250\pi$
$179$	−0.794596	−	0.458760i	−0.0593909	−	0.0342893i	−0.529401	+	0.848371i	$0.677583\pi$
$180$	7.56412	−	1.06886i	0.563796	−	0.0796684i
$181$	6.84551	−	3.95226i	0.508823	−	0.293769i	−0.223527	−	0.974698i	$-0.571757\pi$
$181$	6.84551	−	3.95226i	0.508823	−	0.293769i	0.732350	+	0.680929i	$0.238424\pi$
$182$	5.59867	+	11.0578i	0.415001	+	0.819659i
$183$	10.3682	+	1.08580i	0.766437	+	0.0802646i
$184$	−6.28127	−	5.27061i	−0.463061	−	0.388554i
$185$	−2.14456	+	0.780558i	−0.157672	+	0.0573877i
$186$	7.31669	−	7.07096i	0.536486	−	0.518468i
$187$	−25.5201	+	4.49989i	−1.86622	+	0.329065i
$188$	2.23078			0.162696
$189$	4.94509	−	12.8276i	0.359702	−	0.933067i
$190$	−11.0328			−0.800403
$191$	13.9436	−	2.45864i	1.00893	−	0.177901i	0.355327	−	0.934742i	$-0.384370\pi$
$191$	13.9436	−	2.45864i	1.00893	−	0.177901i	0.653598	+	0.756841i	$0.273259\pi$
$192$	1.66513	+	0.476792i	0.120171	+	0.0344095i
$193$	−6.23166	+	2.26814i	−0.448565	+	0.163264i	−0.556418	−	0.830903i	$-0.687825\pi$
$193$	−6.23166	+	2.26814i	−0.448565	+	0.163264i	0.107853	+	0.994167i	$0.465602\pi$
$194$	4.87530	+	4.09086i	0.350026	+	0.293707i
$195$	12.1384	−	16.7202i	0.869246	−	1.19736i
$196$	−1.96384	+	6.71888i	−0.140275	+	0.479920i
$197$	0.128455	−	0.0741633i	0.00915201	−	0.00528392i	−0.495417	−	0.868655i	$-0.664985\pi$
$197$	0.128455	−	0.0741633i	0.00915201	−	0.00528392i	0.504569	+	0.863371i	$0.331651\pi$
$198$	−15.4778	−	3.27775i	−1.09996	−	0.232940i
$199$	1.74511	+	1.00754i	0.123708	+	0.0714226i	0.560577	−	0.828102i	$-0.310579\pi$
$199$	1.74511	+	1.00754i	0.123708	+	0.0714226i	−0.436869	+	0.899525i	$0.643913\pi$
$200$	0.954063	+	1.13701i	0.0674625	+	0.0803986i
$201$	−12.5433	+	0.881847i	−0.884735	+	0.0622007i
$202$	−10.5285	−	1.85647i	−0.740785	−	0.130620i
$203$	−10.1837	−	13.5864i	−0.714757	−	0.953577i
$204$	−8.48999	+	0.596884i	−0.594419	+	0.0417902i
$205$	−10.3151	+	8.65539i	−0.720437	+	0.604519i
$206$	−1.20518	+	2.08743i	−0.0839687	+	0.145438i
$207$	18.2929	+	16.4461i	1.27144	+	1.14308i
$208$	4.05701	−	2.34231i	0.281303	−	0.162410i
$209$	21.4711	+	7.81486i	1.48519	+	0.540565i
$210$	11.4596	−	2.20159i	0.790788	−	0.151924i
$211$	−7.67430	−	6.43950i	−0.528320	−	0.443314i	0.339201	−	0.940714i	$-0.389843\pi$
$211$	−7.67430	−	6.43950i	−0.528320	−	0.443314i	−0.867521	+	0.497401i	$0.834288\pi$
$212$	−3.22267	−	8.85422i	−0.221334	−	0.608110i
$213$	−4.28862	+	14.9774i	−0.293851	+	1.02624i
$214$	−1.50098	−	8.51250i	−0.102605	−	0.581903i
$215$	10.4211			0.710712
$216$	−4.94364	−	1.60013i	−0.336372	−	0.108875i
$217$	10.6291	−	11.3401i	0.721552	−	0.769815i
$218$	−9.91809	+	1.74883i	−0.671738	+	0.118445i
$219$	10.4717	+	10.8356i	0.707614	+	0.732205i
$220$	−4.59300	−	12.6192i	−0.309660	−	0.850783i
$221$	−14.7965	+	17.6338i	−0.995323	+	1.18618i
$222$	1.54389	+	0.161683i	0.103619	+	0.0108514i
$223$	6.12585	−	16.8306i	0.410217	−	1.12706i	−0.546859	−	0.837225i	$-0.684177\pi$
$223$	6.12585	−	16.8306i	0.410217	−	1.12706i	0.957076	−	0.289837i	$-0.0936012\pi$
$224$	2.57641	+	0.601754i	0.172144	+	0.0402064i
$225$	−2.74404	−	3.50677i	−0.182936	−	0.233785i
$226$	−0.0981700	+	0.170035i	−0.00653017	+	0.0113106i
$227$	−3.31314	+	2.78006i	−0.219901	+	0.184519i	−0.746083	−	0.665853i	$-0.768068\pi$
$227$	−3.31314	+	2.78006i	−0.219901	+	0.184519i	0.526182	+	0.850372i	$0.323623\pi$
$228$	6.74614	+	3.28718i	0.446774	+	0.217699i
$229$	11.5039	+	2.02846i	0.760202	+	0.134044i	0.540294	−	0.841476i	$-0.318313\pi$
$229$	11.5039	+	2.02846i	0.760202	+	0.134044i	0.219908	+	0.975521i	$0.429424\pi$
$230$	−3.62572	+	20.5625i	−0.239073	+	1.35585i
$231$	−23.8612	−	3.83261i	−1.56995	−	0.252168i
$232$	−4.91616	+	4.12515i	−0.322762	+	0.270829i
$233$	−5.83805	−	3.37060i	−0.382464	−	0.220816i	0.296426	−	0.955056i	$-0.404205\pi$
$233$	−5.83805	−	3.37060i	−0.382464	−	0.220816i	−0.678890	+	0.734240i	$0.737539\pi$
$234$	−12.4039	+	6.60722i	−0.810867	+	0.431928i
$235$	−2.84025	−	4.91945i	−0.185277	−	0.320910i
$236$	1.08168	+	0.393698i	0.0704111	+	0.0256275i
$237$	−16.7317	+	7.45697i	−1.08684	+	0.484382i
$238$	−12.9078	+	1.55139i	−0.836688	+	0.100562i
$239$	6.92882	+	19.0368i	0.448188	+	1.23139i	0.933984	+	0.357315i	$0.116308\pi$
$239$	6.92882	+	19.0368i	0.448188	+	1.23139i	−0.485796	+	0.874072i	$0.661470\pi$
$240$	−1.06861	−	4.27912i	−0.0689786	−	0.276216i
$241$	−1.77571	+	0.313105i	−0.114383	+	0.0201689i	−0.230547	−	0.973061i	$-0.574051\pi$
$241$	−1.77571	+	0.313105i	−0.114383	+	0.0201689i	0.116163	+	0.993230i	$0.462940\pi$
$242$			16.8118i			1.08070i
$243$	14.6583	+	5.30404i	0.940333	+	0.340254i
$244$		−	6.01880i		−	0.385314i
$245$	17.3173	−	4.22375i	1.10636	−	0.269845i
$246$	8.88614	−	2.21911i	0.566559	−	0.141485i
$247$	19.0729	−	6.94196i	1.21358	−	0.441706i
$248$	−4.50020	−	3.77611i	−0.285763	−	0.239784i
$249$	19.9440	−	8.88862i	1.26390	−	0.563293i
$250$	−3.06195	+	8.41265i	−0.193655	+	0.532063i
$251$	−2.51607	−	4.35797i	−0.158813	−	0.275073i	0.775628	−	0.631191i	$-0.217433\pi$
$251$	−2.51607	−	4.35797i	−0.158813	−	0.275073i	−0.934441	+	0.356118i	$0.884100\pi$
$252$	−7.66308	−	2.06815i	−0.482728	−	0.130281i
$253$	21.6211	−	37.4488i	1.35931	−	2.35439i
$254$	−12.1203	−	14.4444i	−0.760497	−	0.906325i
$255$	12.1258	+	17.9627i	0.759349	+	1.12487i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−3.84339	+	21.7969i	−0.239744	+	1.35966i	0.592645	+	0.805464i	$0.298084\pi$
$257$	−3.84339	+	21.7969i	−0.239744	+	1.35966i	−0.832389	+	0.554192i	$0.813027\pi$
$258$	−6.37211	−	3.10492i	−0.396710	−	0.193304i
$259$	2.36765	+	0.130154i	0.147118	+	0.00808739i
$260$	−10.3308	−	5.96452i	−0.640692	−	0.369904i
$261$	15.1625	−	11.8646i	0.938534	−	0.734399i
$262$	−7.39202	+	4.26778i	−0.456680	+	0.263665i
$263$	−4.76860	+	13.1016i	−0.294045	+	0.807881i	0.701420	+	0.712748i	$0.252550\pi$
$263$	−4.76860	+	13.1016i	−0.294045	+	0.807881i	−0.995465	+	0.0951329i	$0.969672\pi$
$264$	−0.951380	+	9.08461i	−0.0585534	+	0.559119i
$265$	−15.4228	+	18.3801i	−0.947413	+	1.12908i
$266$	10.5404	+	4.50598i	0.646274	+	0.276279i
$267$	−12.3707	+	11.9553i	−0.757077	+	0.731651i
$268$	1.26064	+	7.14945i	0.0770059	+	0.436722i
$269$	5.96085			0.363440			0.181720	−	0.983350i	$-0.441834\pi$
$269$	5.96085			0.363440			0.181720	+	0.983350i	$0.441834\pi$
$270$	2.76559	+	12.9393i	0.168308	+	0.787463i
$271$			28.5645i			1.73517i	0.497287	+	0.867586i	$0.334330\pi$
$271$			28.5645i			1.73517i	−0.497287	+	0.867586i	$0.665670\pi$
$272$	0.853272	+	4.83915i	0.0517372	+	0.293416i
$273$	−18.4255	+	11.0165i	−1.11516	+	0.666749i
$274$	−5.61237	+	2.04274i	−0.339056	+	0.123406i
$275$	−5.03143	+	5.99622i	−0.303407	+	0.361586i
$276$	8.34349	−	11.4929i	0.502219	−	0.691792i
$277$	−19.9590	−	7.26448i	−1.19922	−	0.436480i	−0.336268	−	0.941766i	$-0.609165\pi$
$277$	−19.9590	−	7.26448i	−1.19922	−	0.436480i	−0.862952	+	0.505286i	$0.831387\pi$
$278$	−0.816921	−	1.41495i	−0.0489957	−	0.0848630i
$279$	13.1059	+	11.7828i	0.784628	+	0.705416i
$280$	−1.95329	−	6.44783i	−0.116731	−	0.385331i
$281$	0.144779	+	0.172541i	0.00863681	+	0.0102930i	0.770346	−	0.637627i	$-0.220084\pi$
$281$	0.144779	+	0.172541i	0.00863681	+	0.0102930i	−0.761709	+	0.647920i	$0.775639\pi$
$282$	0.270974	+	3.85430i	0.0161363	+	0.229520i
$283$	−20.6570	−	3.64238i	−1.22793	−	0.216517i	−0.478193	−	0.878255i	$-0.658708\pi$
$283$	−20.6570	−	3.64238i	−1.22793	−	0.216517i	−0.749735	+	0.661738i	$0.769819\pi$
$284$	8.85808	+	1.56192i	0.525630	+	0.0926828i
$285$	−1.34016	−	19.0623i	−0.0793844	−	1.12915i
$286$	15.8802	+	18.9253i	0.939018	+	1.11908i
$287$	13.3897	−	4.05625i	0.790372	−	0.239433i
$288$	−0.621530	+	2.93491i	−0.0366240	+	0.172941i
$289$	−3.57271	−	6.18812i	−0.210160	−	0.364007i
$290$	15.3563	+	5.58925i	0.901755	+	0.328212i
$291$	−6.47593	+	8.92040i	−0.379626	+	0.522923i
$292$	5.59223	−	6.66456i	0.327260	−	0.390014i
$293$	7.26899	−	2.64570i	0.424659	−	0.154563i	−0.120845	−	0.992671i	$-0.538560\pi$
$293$	7.26899	−	2.64570i	0.424659	−	0.154563i	0.545504	+	0.838108i	$0.316338\pi$
$294$	−11.8473	−	2.57696i	−0.690950	−	0.150291i
$295$	−0.508993	−	2.88664i	−0.0296347	−	0.168067i
$296$		−	0.896238i		−	0.0520928i
$297$	3.78316	−	27.1405i	0.219521	−	1.57485i
$298$	21.1057			1.22262
$299$	−6.67020	−	37.8286i	−0.385748	−	2.18768i
$300$	−1.84862	+	1.78653i	−0.106730	+	0.103145i
$301$	−9.95600	−	4.25614i	−0.573854	−	0.245320i
$302$	14.1309	−	16.8405i	0.813140	−	0.969063i
$303$	1.92866	−	18.4166i	0.110799	−	1.05800i
$304$	1.48186	−	4.07137i	0.0849904	−	0.233509i
$305$	−13.2730	+	7.66319i	−0.760012	+	0.438793i
$306$	−2.06257	−	14.5964i	−0.117910	−	0.834420i
$307$	−20.6696	−	11.9336i	−1.17968	−	0.681087i	−0.223737	−	0.974649i	$-0.571826\pi$
$307$	−20.6696	−	11.9336i	−1.17968	−	0.681087i	−0.955940	+	0.293562i	$0.905159\pi$
$308$	−0.765860	+	13.9318i	−0.0436389	+	0.793839i
$309$	−3.75303	−	1.82873i	−0.213502	−	0.104033i
$310$	−2.59763	+	14.7319i	−0.147536	+	0.836717i
$311$	−0.0614824	+	0.348684i	−0.00348634	+	0.0197720i	−0.986501	−	0.163753i	$-0.947640\pi$
$311$	−0.0614824	+	0.348684i	−0.00348634	+	0.0197720i	0.983015	+	0.183525i	$0.0587510\pi$
$312$	4.53983	+	6.72512i	0.257017	+	0.380735i
$313$	6.73049	+	8.02108i	0.380430	+	0.453378i	0.921950	−	0.387309i	$-0.126595\pi$
$313$	6.73049	+	8.02108i	0.380430	+	0.453378i	−0.541520	+	0.840688i	$0.682151\pi$
$314$	−4.93040	+	8.53970i	−0.278239	+	0.481923i
$315$	5.19589	+	19.5323i	0.292755	+	1.10052i
$316$	5.28801	+	9.15910i	0.297474	+	0.515240i
$317$	−3.47766	+	9.55480i	−0.195325	+	0.536651i	−0.998231	−	0.0594545i	$-0.981064\pi$
$317$	−3.47766	+	9.55480i	−0.195325	+	0.536651i	0.802906	+	0.596106i	$0.203286\pi$
$318$	14.9067	−	6.64362i	0.835928	−	0.372556i
$319$	−25.9263	−	21.7547i	−1.45159	−	1.21803i
$320$	−2.39285	+	0.870927i	−0.133765	+	0.0486863i
$321$	14.5255	−	3.62740i	0.810732	−	0.202462i
$322$	11.8620	−	18.1640i	0.661041	−	1.01224i
$323$			21.2899i			1.18460i
$324$	2.16417	−	8.73592i	0.120232	−	0.485329i
$325$			6.95320i			0.385694i
$326$	−6.09683	+	1.07503i	−0.337672	+	0.0595407i
$327$	−4.22636	−	16.9239i	−0.233718	−	0.935894i
$328$	−1.80859	−	4.96907i	−0.0998628	−	0.274371i
$329$	0.704302	+	5.85990i	0.0388294	+	0.323067i
$330$	21.2453	−	9.46857i	1.16951	−	0.521228i
$331$	−16.3609	−	5.95487i	−0.899276	−	0.327310i	−0.149313	−	0.988790i	$-0.547706\pi$
$331$	−16.3609	−	5.95487i	−0.899276	−	0.327310i	−0.749962	+	0.661480i	$0.769928\pi$
$332$	−6.30324	−	10.9175i	−0.345935	−	0.599178i
$333$	−0.0918157	+	2.68714i	−0.00503147	+	0.147255i
$334$	−3.56654	−	2.05914i	−0.195152	−	0.112671i
$335$	14.1614	−	11.8828i	0.773718	−	0.649227i
$336$	−0.726743	+	4.52458i	−0.0396471	+	0.246836i
$337$	−5.51923	+	31.3011i	−0.300652	+	1.70508i	0.342647	+	0.939464i	$0.388677\pi$
$337$	−5.51923	+	31.3011i	−0.300652	+	1.70508i	−0.643298	+	0.765616i	$0.722435\pi$
$338$	8.80984	+	1.55341i	0.479192	+	0.0844945i
$339$	−0.305710	−	0.148962i	−0.0166039	−	0.00809053i
$340$	9.58521	−	8.04295i	0.519831	−	0.436190i
$341$	15.4904	−	26.8301i	0.838851	−	1.45293i
$342$	−4.86008	+	12.0552i	−0.262803	+	0.651870i
$343$	−18.2695	−	3.03743i	−0.986459	−	0.164006i
$344$	−1.39970	+	3.84564i	−0.0754666	+	0.207343i
$345$	−35.9679	−	3.76672i	−1.93645	−	0.202793i
$346$	−4.30657	+	5.13237i	−0.231523	+	0.275918i
$347$	5.65025	+	15.5239i	0.303321	+	0.833369i	0.993917	+	0.110128i	$0.0351261\pi$
$347$	5.65025	+	15.5239i	0.303321	+	0.833369i	−0.690596	+	0.723241i	$0.742652\pi$
$348$	−7.72454	−	7.99298i	−0.414079	−	0.428469i
$349$	−22.1665	+	3.90856i	−1.18655	+	0.209220i	−0.731875	−	0.681439i	$-0.761355\pi$
$349$	−22.1665	+	3.90856i	−1.18655	+	0.209220i	−0.454672	+	0.890659i	$0.650244\pi$
$350$	−2.68553	+	2.86515i	−0.143548	+	0.153149i
$351$	−12.9226	−	20.6287i	−0.689756	−	1.10108i
$352$	5.27368			0.281088
$353$	6.42145	+	36.4179i	0.341779	+	1.93833i	0.345728	+	0.938335i	$0.387632\pi$
$353$	6.42145	+	36.4179i	0.341779	+	1.93833i	−0.00394896	+	0.999992i	$0.501257\pi$
$354$	−0.548834	+	1.91673i	−0.0291702	+	0.101873i
$355$	−7.83375	−	21.5231i	−0.415772	−	1.14233i
$356$	7.60874	+	6.38449i	0.403262	+	0.338377i
$357$	−4.24839	−	22.1135i	−0.224849	−	1.17037i
$358$	−0.862187	−	0.313810i	−0.0455680	−	0.0165854i
$359$	15.1046	−	8.72065i	0.797191	−	0.460258i	−0.0452971	−	0.998974i	$-0.514423\pi$
$359$	15.1046	−	8.72065i	0.797191	−	0.460258i	0.842488	+	0.538715i	$0.181090\pi$
$360$	7.26359	−	2.36612i	0.382825	−	0.124705i
$361$	−0.114002	+	0.197457i	−0.00600009	+	0.0103925i
$362$	6.05521	−	5.08092i	0.318255	−	0.267047i
$363$	−29.0471	+	2.04214i	−1.52458	+	0.107184i
$364$	7.43378	+	9.91762i	0.389636	+	0.519824i
$365$	−21.8172	−	3.84696i	−1.14196	−	0.201359i
$366$	10.3992	−	0.731109i	0.543575	−	0.0382157i
$367$	−10.2418	−	12.2057i	−0.534617	−	0.637131i	0.429355	−	0.903136i	$-0.358741\pi$
$367$	−10.2418	−	12.2057i	−0.534617	−	0.637131i	−0.963972	+	0.266005i	$0.914296\pi$
$368$	−7.10107	−	4.09981i	−0.370169	−	0.213717i
$369$	4.91355	+	15.0838i	0.255789	+	0.785231i
$370$	−1.97644	+	1.14110i	−0.102750	+	0.0593229i
$371$	22.2412	−	11.2609i	1.15471	−	0.584638i
$372$	5.97768	−	8.23407i	0.309928	−	0.426917i
$373$	17.5072	+	14.6903i	0.906490	+	0.760636i	0.971448	−	0.237252i	$-0.0762468\pi$
$373$	17.5072	+	14.6903i	0.906490	+	0.760636i	−0.0649577	+	0.997888i	$0.520691\pi$
$374$	−24.3510	+	8.86305i	−1.25916	+	0.458298i
$375$	−14.9072	−	4.26851i	−0.769805	−	0.220425i
$376$	2.19688	−	0.387370i	0.113296	−	0.0199771i
$377$	−30.0640			−1.54838
$378$	2.64248	−	13.4914i	0.135915	−	0.693922i
$379$	−4.48039			−0.230142			−0.115071	−	0.993357i	$-0.536710\pi$
$379$	−4.48039			−0.230142			−0.115071	+	0.993357i	$0.536710\pi$
$380$	−10.8652	+	1.91582i	−0.557372	+	0.0982797i
$381$	23.4847	−	22.6959i	1.20316	−	1.16275i
$382$	13.3048	−	4.84257i	0.680735	−	0.247767i
$383$	−5.35178	−	4.49067i	−0.273463	−	0.229463i	0.495734	−	0.868474i	$-0.334899\pi$
$383$	−5.35178	−	4.49067i	−0.273463	−	0.229463i	−0.769197	+	0.639012i	$0.779344\pi$
$384$	1.72263	+	0.180401i	0.0879076	+	0.00920607i
$385$	31.6985	−	16.0492i	1.61550	−	0.817944i
$386$	−5.74313	+	3.31580i	−0.292318	+	0.168770i
$387$	4.59061	−	11.3868i	0.233354	−	0.578823i
$388$	5.51161	+	3.18213i	0.279809	+	0.161548i
$389$	−8.41647	−	10.0304i	−0.426732	−	0.508559i	0.509244	−	0.860622i	$-0.329925\pi$
$389$	−8.41647	−	10.0304i	−0.426732	−	0.508559i	−0.935976	+	0.352062i	$0.885480\pi$
$390$	9.05051	−	18.5740i	0.458291	−	0.940532i
$391$	39.6791	+	6.99650i	2.00666	+	0.353828i
$392$	−0.767289	+	6.95782i	−0.0387539	+	0.351423i
$393$	−8.27173	−	12.2534i	−0.417254	−	0.618103i
$394$	0.113625	−	0.0953425i	0.00572434	−	0.00480329i
$395$	13.4655	−	23.3229i	0.677523	−	1.17350i
$396$	−15.8118	−	0.540266i	−0.794574	−	0.0271494i
$397$	−2.44969	+	1.41433i	−0.122946	+	0.0709830i	−0.560212	−	0.828349i	$-0.689280\pi$
$397$	−2.44969	+	1.41433i	−0.122946	+	0.0709830i	0.437266	+	0.899332i	$0.355947\pi$
$398$	1.89356	+	0.689198i	0.0949154	+	0.0345464i
$399$	−6.50501	+	18.7589i	−0.325658	+	0.939120i
$400$	1.13701	+	0.954063i	0.0568504	+	0.0477032i
$401$	−8.93683	−	24.5537i	−0.446284	−	1.22616i	−0.935292	−	0.353876i	$-0.884863\pi$
$401$	−8.93683	−	24.5537i	−0.446284	−	1.22616i	0.489008	−	0.872279i	$-0.337359\pi$
$402$	−12.1996	+	3.04657i	−0.608460	+	0.151949i
$403$	−4.77885	−	27.1022i	−0.238051	−	1.35006i
$404$	−10.6910			−0.531895
$405$	−22.0205	+	6.35010i	−1.09421	+	0.315539i
$406$	−12.3883	−	11.6116i	−0.614819	−	0.576274i
$407$	4.65467	−	0.820744i	0.230723	−	0.0406828i
$408$	−8.25736	+	2.06209i	−0.408800	+	0.102089i
$409$	−0.298506	−	0.820139i	−0.0147602	−	0.0405533i	0.932094	−	0.362217i	$-0.117980\pi$
$409$	−0.298506	−	0.820139i	−0.0147602	−	0.0405533i	−0.946854	+	0.321664i	$0.895758\pi$
$410$	−8.65539	+	10.3151i	−0.427459	+	0.509426i
$411$	−4.21115	−	9.44884i	−0.207721	−	0.466077i
$412$	−0.824390	+	2.26499i	−0.0406148	+	0.111588i
$413$	−0.692676	+	2.96569i	−0.0340844	+	0.145932i
$414$	20.8708	+	13.0197i	1.02574	+	0.639884i
$415$	−16.0507	+	27.8006i	−0.787898	+	1.36468i
$416$	3.58863	−	3.01122i	0.175947	−	0.147637i
$417$	2.34550	−	1.58334i	0.114859	−	0.0775365i
$418$	22.5020	+	3.96771i	1.10061	+	0.194067i
$419$	3.55710	−	20.1733i	0.173776	−	0.985532i	−0.765772	−	0.643113i	$-0.777643\pi$
$419$	3.55710	−	20.1733i	0.173776	−	0.985532i	0.939547	−	0.342419i	$-0.111246\pi$
$420$	10.9032	−	4.15808i	0.532022	−	0.202894i
$421$	3.29401	−	2.76400i	0.160540	−	0.134709i	−0.558979	−	0.829182i	$-0.688807\pi$
$421$	3.29401	−	2.76400i	0.160540	−	0.134709i	0.719519	+	0.694473i	$0.244362\pi$
$422$	−8.67592	−	5.00904i	−0.422337	−	0.243836i
$423$	−6.62649	+	0.936371i	−0.322191	+	0.0455279i
$424$	−4.71123	−	8.16009i	−0.228798	−	0.396289i
$425$	−6.85351	−	2.49447i	−0.332444	−	0.121000i
$426$	−1.62266	+	15.4946i	−0.0786182	+	0.750715i
$427$	15.8105	−	1.90026i	0.765121	−	0.0919599i
$428$	−2.95636	−	8.12254i	−0.142901	−	0.392618i
$429$	−30.7699	+	29.7365i	−1.48559	+	1.43569i
$430$	10.2628	−	1.80960i	0.494914	−	0.0872667i
$431$		−	5.00891i		−	0.241271i	−0.992697	−	0.120635i	$-0.961507\pi$
$431$		−	5.00891i		−	0.241271i	0.992697	−	0.120635i	$-0.0384932\pi$
$432$	−5.14640	−	0.717365i	−0.247606	−	0.0345142i
$433$		−	23.3737i		−	1.12327i	−0.827386	−	0.561633i	$-0.810173\pi$
$433$		−	23.3737i		−	1.12327i	0.827386	−	0.561633i	$-0.189827\pi$
$434$	8.49847	−	13.0135i	0.407939	−	0.624669i
$435$	−7.79168	+	27.2114i	−0.373583	+	1.30469i
$436$	−9.46373	+	3.44452i	−0.453231	+	0.164962i
$437$	−27.2146	−	22.8358i	−1.30185	−	1.09238i
$438$	12.1942	+	8.85263i	0.582663	+	0.422995i
$439$	−7.67296	+	21.0813i	−0.366210	+	1.00615i	0.610580	+	0.791955i	$0.290937\pi$
$439$	−7.67296	+	21.0813i	−0.366210	+	1.00615i	−0.976790	+	0.214200i	$0.931286\pi$
$440$	−6.71451	−	11.6299i	−0.320102	−	0.554432i
$441$	3.01332	−	20.7827i	0.143492	−	0.989652i
$442$	−11.5097	+	19.9353i	−0.547459	+	0.948227i
$443$	14.4266	+	17.1930i	0.685429	+	0.816863i	0.990795	−	0.135373i	$-0.0432232\pi$
$443$	14.4266	+	17.1930i	0.685429	+	0.816863i	−0.305366	+	0.952235i	$0.598779\pi$
$444$	1.54851	−	0.108867i	0.0734889	−	0.00516659i
$445$	4.39197	−	24.9081i	0.208199	−	1.18076i
$446$	3.11017	−	17.6387i	0.147271	−	0.835216i
$447$	2.56373	+	36.4661i	0.121260	+	1.72479i
$448$	2.64176	+	0.145223i	0.124812	+	0.00686114i
$449$	16.7414	+	9.66565i	0.790075	+	0.456150i	0.839989	−	0.542603i	$-0.182561\pi$
$449$	16.7414	+	9.66565i	0.790075	+	0.456150i	−0.0499138	+	0.998754i	$0.515895\pi$
$450$	−3.31130	−	2.97700i	−0.156096	−	0.140337i
$451$	24.1509	−	13.9435i	1.13722	−	0.656576i
$452$	−0.0671522	+	0.184499i	−0.00315858	+	0.00867811i
$453$	30.8133	+	22.3695i	1.44773	+	1.05101i
$454$	−2.78006	+	3.31314i	−0.130475	+	0.155494i
$455$	12.4062	−	29.0207i	0.581612	−	1.36051i
$456$	7.21447	+	2.06578i	0.337848	+	0.0967391i
$457$	−0.271050	−	1.53720i	−0.0126792	−	0.0719073i	0.977812	−	0.209486i	$-0.0671791\pi$
$457$	−0.271050	−	1.53720i	−0.0126792	−	0.0719073i	−0.990491	+	0.137579i	$0.956068\pi$
$458$	11.6814			0.545837
$459$	24.9689	−	5.33672i	1.16545	−	0.249097i
$460$			20.8797i			0.973519i
$461$	6.66828	+	37.8177i	0.310573	+	1.76135i	0.596037	+	0.802957i	$0.296741\pi$
$461$	6.66828	+	37.8177i	0.310573	+	1.76135i	−0.285465	+	0.958389i	$0.592148\pi$
$462$	−24.1642	+	0.369069i	−1.12422	+	0.0171706i
$463$	23.6904	−	8.62262i	1.10099	−	0.400727i	0.273308	−	0.961927i	$-0.411882\pi$
$463$	23.6904	−	8.62262i	1.10099	−	0.400727i	0.827681	+	0.561200i	$0.189660\pi$
$464$	−4.12515	+	4.91616i	−0.191505	+	0.228227i
$465$	−25.7691	−	2.69866i	−1.19502	−	0.125147i
$466$	−6.33466	−	2.30563i	−0.293447	−	0.106806i
$467$	15.5985	+	27.0174i	0.721813	+	1.25022i	0.960272	+	0.279064i	$0.0900243\pi$
$467$	15.5985	+	27.0174i	0.721813	+	1.25022i	−0.238459	+	0.971152i	$0.576642\pi$
$468$	−11.0681	+	8.66075i	−0.511624	+	0.400344i
$469$	−18.3825	+	5.56874i	−0.848825	+	0.257140i
$470$	−3.65135	−	4.35151i	−0.168424	−	0.200720i
$471$	−15.3537	−	7.48135i	−0.707460	−	0.344722i
$472$	1.13361	+	0.199886i	0.0521785	+	0.00920048i
$473$	−21.2544	−	3.74772i	−0.977277	−	0.172320i
$474$	−15.1826	+	10.2491i	−0.697361	+	0.470757i
$475$	4.13364	+	4.92628i	0.189664	+	0.226033i
$476$	−12.4423	+	3.76923i	−0.570292	+	0.172763i
$477$	13.2895	+	24.9486i	0.608484	+	1.14232i
$478$	10.1293	+	17.5444i	0.463302	+	0.802462i
$479$	−24.8417	−	9.04163i	−1.13504	−	0.413123i	−0.294923	−	0.955521i	$-0.595294\pi$
$479$	−24.8417	−	9.04163i	−1.13504	−	0.413123i	−0.840121	+	0.542398i	$0.817516\pi$
$480$	−1.79544	−	4.02855i	−0.0819502	−	0.183877i
$481$	2.69877	−	3.21627i	0.123053	−	0.146649i
$482$	−1.69436	+	0.616696i	−0.0771759	+	0.0280897i
$483$	32.8243	+	18.2885i	1.49356	+	0.832157i
$484$	2.91933	+	16.5563i	0.132697	+	0.752561i
$485$		−	16.2061i		−	0.735880i
$486$	15.3567	+	2.67807i	0.696594	+	0.121479i
$487$	−6.11954			−0.277303			−0.138651	−	0.990341i	$-0.544277\pi$
$487$	−6.11954			−0.277303			−0.138651	+	0.990341i	$0.544277\pi$
$488$	−1.04515	−	5.92736i	−0.0473119	−	0.268319i
$489$	−2.59802	−	10.4034i	−0.117486	−	0.470459i
$490$	16.3208	−	7.16669i	0.737297	−	0.323758i
$491$	12.1413	−	14.4695i	0.547930	−	0.652998i	−0.419016	−	0.907979i	$-0.637625\pi$
$491$	12.1413	−	14.4695i	0.547930	−	0.652998i	0.966946	+	0.254981i	$0.0820693\pi$
$492$	8.36579	−	3.72846i	0.377159	−	0.168092i
$493$	10.7855	−	29.6330i	0.485755	−	1.33460i
$494$	17.5777	−	10.1485i	0.790856	−	0.456601i
$495$	18.9404	+	35.5571i	0.851306	+	1.59817i
$496$	−5.08755	−	2.93730i	−0.228438	−	0.131888i
$497$	−1.30624	+	23.7619i	−0.0585929	+	1.06587i
$498$	18.0975	−	12.2168i	0.810969	−	0.547449i
$499$	−0.224409	+	1.27269i	−0.0100459	+	0.0569733i	−0.989419	−	0.145089i	$-0.953653\pi$
$499$	−0.224409	+	1.27269i	−0.0100459	+	0.0569733i	0.979373	+	0.202062i	$0.0647643\pi$
$500$	−1.55460	+	8.81655i	−0.0695236	+	0.394288i
$501$	3.12453	−	6.41235i	0.139594	−	0.286482i
$502$	−3.23460	−	3.85485i	−0.144367	−	0.172050i
$503$	−1.03602	+	1.79445i	−0.0461941	+	0.0800105i	−0.888198	−	0.459461i	$-0.848043\pi$
$503$	−1.03602	+	1.79445i	−0.0461941	+	0.0800105i	0.842004	+	0.539471i	$0.181376\pi$
$504$	−7.90579	−	0.706052i	−0.352152	−	0.0314500i
$505$	13.6118	+	23.5764i	0.605719	+	1.04914i
$506$	14.7897	−	40.6343i	0.657482	−	1.80642i
$507$	−1.61383	+	15.4102i	−0.0716725	+	0.684391i
$508$	−14.4444	−	12.1203i	−0.640869	−	0.537753i
$509$	−26.3345	+	9.58496i	−1.16725	+	0.424846i	−0.851684	−	0.524056i	$-0.824418\pi$
$509$	−26.3345	+	9.58496i	−1.16725	+	0.424846i	−0.315571	+	0.948902i	$0.602196\pi$
$510$	15.0608	+	15.5842i	0.666904	+	0.690080i
$511$	19.2724	+	12.5858i	0.852559	+	0.556762i
$512$		−	1.00000i		−	0.0441942i
$513$	−21.4191	−	6.93282i	−0.945678	−	0.306092i
$514$			22.1332i			0.976254i
$515$	6.04453	−	1.06581i	0.266354	−	0.0469654i
$516$	−6.81446	−	1.95125i	−0.299990	−	0.0858988i
$517$	4.02366	+	11.0549i	0.176961	+	0.486195i
$518$	2.35428	−	0.282961i	0.103441	−	0.0124326i
$519$	−9.39076	−	6.81740i	−0.412209	−	0.299251i
$520$	−11.2096	−	4.07997i	−0.491575	−	0.178919i
$521$	−8.50594	−	14.7327i	−0.372652	−	0.645452i	0.617321	−	0.786712i	$-0.288218\pi$
$521$	−8.50594	−	14.7327i	−0.372652	−	0.645452i	−0.989973	+	0.141260i	$0.954885\pi$
$522$	12.8719	−	14.3173i	0.563386	−	0.626650i
$523$	−22.5596	−	13.0248i	−0.986461	−	0.569533i	−0.0822461	−	0.996612i	$-0.526209\pi$
$523$	−22.5596	−	13.0248i	−0.986461	−	0.569533i	−0.904214	+	0.427079i	$0.859543\pi$
$524$	−6.53862	+	5.48656i	−0.285641	+	0.239681i
$525$	−5.27659	−	4.29199i	−0.230289	−	0.187318i
$526$	−2.42108	+	13.7306i	−0.105564	+	0.598685i
$527$	28.4280	+	5.01263i	1.23834	+	0.218353i
$528$	0.640599	+	9.11180i	0.0278785	+	0.396540i
$529$	−33.8849	+	28.4328i	−1.47326	+	1.23621i
$530$	−11.9968	+	20.7790i	−0.521107	+	0.902583i
$531$	−3.37836	−	0.715440i	−0.146608	−	0.0310475i
$532$	11.1627	+	2.60720i	0.483966	+	0.113036i
$533$	8.47258	−	23.2782i	0.366988	−	1.00829i
$534$	−10.1068	+	13.9218i	−0.437364	+	0.602455i
$535$	−14.1483	+	16.8613i	−0.611683	+	0.728976i
$536$	2.48298	+	6.82193i	0.107248	+	0.294662i
$537$	0.437467	−	1.52779i	0.0188781	−	0.0659291i
$538$	5.87030	−	1.03509i	0.253086	−	0.0446260i
$539$	−36.8386	+	2.38677i	−1.58675	+	0.102805i
$540$	4.97046	+	12.2625i	0.213895	+	0.527695i
$541$	4.76276			0.204767			0.102384	−	0.994745i	$-0.467353\pi$
$541$	4.76276			0.204767			0.102384	+	0.994745i	$0.467353\pi$
$542$	4.96018	+	28.1306i	0.213058	+	1.20831i
$543$	9.51428	+	9.84492i	0.408297	+	0.422486i
$544$	1.68062	+	4.61746i	0.0720559	+	0.197972i
$545$	19.6454	+	16.4844i	0.841516	+	0.706116i
$546$	−16.2325	+	14.0487i	−0.694688	+	0.601228i
$547$	−9.23709	−	3.36202i	−0.394949	−	0.143750i	0.136908	−	0.990584i	$-0.456284\pi$
$547$	−9.23709	−	3.36202i	−0.394949	−	0.143750i	−0.531857	+	0.846834i	$0.678506\pi$
$548$	−5.17239	+	2.98628i	−0.220953	+	0.127568i
$549$	2.52640	+	17.8788i	0.107824	+	0.763047i
$550$	−3.91376	+	6.77882i	−0.166883	+	0.289050i
$551$	−21.3001	+	17.8729i	−0.907413	+	0.761410i
$552$	6.22101	−	12.7671i	0.264784	−	0.543406i
$553$	−22.3900	+	16.7825i	−0.952120	+	0.713665i
$554$	−20.9172	−	3.68827i	−0.888688	−	0.156700i
$555$	−2.21166	−	3.27626i	−0.0938795	−	0.139069i
$556$	−1.05021	−	1.25160i	−0.0445390	−	0.0530795i
$557$	−18.1232	−	10.4635i	−0.767906	−	0.443351i	0.0642211	−	0.997936i	$-0.479544\pi$
$557$	−18.1232	−	10.4635i	−0.767906	−	0.443351i	−0.832127	+	0.554585i	$0.812877\pi$
$558$	14.9528	+	9.32794i	0.633003	+	0.394883i
$559$	−16.6031	+	9.58579i	−0.702235	+	0.405436i
$560$	−3.04326	−	6.01069i	−0.128601	−	0.253998i
$561$	−18.2714	−	40.9968i	−0.771419	−	1.73089i
$562$	0.172541	+	0.144779i	0.00727822	+	0.00610715i
$563$	17.7561	−	6.46269i	0.748330	−	0.272370i	0.0604272	−	0.998173i	$-0.480754\pi$
$563$	17.7561	−	6.46269i	0.748330	−	0.272370i	0.687903	+	0.725803i	$0.258531\pi$
$564$	0.936150	+	3.74869i	0.0394190	+	0.157848i
$565$	0.492369	−	0.0868179i	0.0207141	−	0.00365246i
$566$	−20.9756			−0.881671
$567$	23.6312	+	2.92683i	0.992417	+	0.122915i
$568$	8.99473			0.377410
$569$	9.63394	−	1.69872i	0.403876	−	0.0712142i	0.0319797	−	0.999489i	$-0.489819\pi$
$569$	9.63394	−	1.69872i	0.403876	−	0.0712142i	0.371896	+	0.928274i	$0.378708\pi$
$570$	−4.62994	−	18.5400i	−0.193927	−	0.776555i
$571$	20.3261	−	7.39809i	0.850620	−	0.309601i	0.120327	−	0.992734i	$-0.461606\pi$
$571$	20.3261	−	7.39809i	0.850620	−	0.309601i	0.730293	+	0.683134i	$0.239383\pi$
$572$	18.9253	+	15.8802i	0.791307	+	0.663986i
$573$	9.98308	+	22.3997i	0.417049	+	0.935761i
$574$	12.4820	−	6.31973i	0.520987	−	0.263780i
$575$	10.5398	−	6.08517i	0.439541	−	0.253769i
$576$	−0.102446	+	2.99825i	−0.00426857	+	0.124927i
$577$	32.7558	+	18.9115i	1.36364	+	0.787298i	0.990106	−	0.140319i	$-0.0448127\pi$
$577$	32.7558	+	18.9115i	1.36364	+	0.787298i	0.373534	+	0.927617i	$0.378146\pi$
$578$	−4.59299	−	5.47371i	−0.191043	−	0.227677i
$579$	−6.42661	−	9.52013i	−0.267081	−	0.395643i
$580$	16.0936	+	2.83774i	0.668251	+	0.117831i
$581$	26.6886	−	20.0045i	1.10723	−	0.829928i
$582$	−4.82854	+	9.90941i	−0.200149	+	0.410758i
$583$	38.0656	−	31.9408i	1.57652	−	1.32285i
$584$	4.34998	−	7.53439i	0.180004	−	0.311775i
$585$	33.1913	+	13.3812i	1.37229	+	0.553242i
$586$	6.69914	−	3.86775i	0.276739	−	0.159775i
$587$	−23.0197	−	8.37850i	−0.950127	−	0.345818i	−0.179970	−	0.983672i	$-0.557600\pi$
$587$	−23.0197	−	8.37850i	−0.950127	−	0.345818i	−0.770157	+	0.637854i	$0.779822\pi$
$588$	−12.1148	−	0.480539i	−0.499607	−	0.0198171i
$589$	−19.4979	−	16.3606i	−0.803395	−	0.674129i
$590$	−1.00252	−	2.75440i	−0.0412731	−	0.113397i
$591$	0.178534	+	0.184738i	0.00734389	+	0.00759911i
$592$	−0.155630	−	0.882622i	−0.00639635	−	0.0362755i
$593$	−0.129923			−0.00533529			−0.00266765	−	0.999996i	$-0.500849\pi$
$593$	−0.129923			−0.00533529			−0.00266765	+	0.999996i	$0.500849\pi$
$594$	−0.987212	−	27.3851i	−0.0405058	−	1.12362i
$595$	24.1538	+	22.6395i	0.990210	+	0.928131i
$596$	20.7850	−	3.66496i	0.851389	−	0.150123i
$597$	−0.960775	+	3.35538i	−0.0393219	+	0.137326i
$598$	−13.1377	−	36.0956i	−0.537242	−	1.47606i
$599$	17.6534	−	21.0385i	0.721297	−	0.859608i	−0.273459	−	0.961884i	$-0.588168\pi$
$599$	17.6534	−	21.0385i	0.721297	−	0.859608i	0.994756	+	0.102276i	$0.0326124\pi$
$600$	−1.51030	+	2.08040i	−0.0616579	+	0.0849319i
$601$	−4.87437	+	13.3922i	−0.198830	+	0.546280i	−0.998535	−	0.0541131i	$-0.982767\pi$
$601$	−4.87437	+	13.3922i	−0.198830	+	0.546280i	0.799705	+	0.600393i	$0.204989\pi$
$602$	−10.5438	−	2.46264i	−0.429734	−	0.100370i
$603$	−6.74571	−	20.7082i	−0.274707	−	0.843304i
$604$	10.9919	−	19.0385i	0.447253	−	0.774664i
$605$	32.7942	−	27.5176i	1.33327	−	1.11875i
$606$	−1.29864	−	18.4717i	−0.0527536	−	0.750361i
$607$	21.3829	+	3.77039i	0.867907	+	0.153035i	0.589834	−	0.807525i	$-0.299193\pi$
$607$	21.3829	+	3.77039i	0.867907	+	0.153035i	0.278073	+	0.960560i	$0.410304\pi$
$608$	0.752360	−	4.26684i	0.0305122	−	0.173043i
$609$	18.5575	−	22.8147i	0.751989	−	0.924499i
$610$	−11.7407	+	9.85161i	−0.475367	+	0.398880i
$611$	9.05027	+	5.22518i	0.366135	+	0.211388i
$612$	−4.56588	−	14.0165i	−0.184565	−	0.566582i
$613$	4.50406	+	7.80126i	0.181917	+	0.315090i	0.942533	−	0.334112i	$-0.108436\pi$
$613$	4.50406	+	7.80126i	0.181917	+	0.315090i	−0.760616	+	0.649202i	$0.775103\pi$
$614$	−22.4278	−	8.16307i	−0.905114	−	0.329435i
$615$	−18.8737	−	13.7017i	−0.761059	−	0.552505i
$616$	1.66501	+	13.8532i	0.0670852	+	0.558160i
$617$	8.72811	+	23.9803i	0.351380	+	0.965410i	0.981927	+	0.189259i	$0.0606084\pi$
$617$	8.72811	+	23.9803i	0.351380	+	0.965410i	−0.630547	+	0.776151i	$0.717169\pi$
$618$	−4.01356	−	1.14924i	−0.161449	−	0.0462292i
$619$	27.0379	−	4.76752i	1.08675	−	0.191623i	0.398549	−	0.917147i	$-0.369514\pi$
$619$	27.0379	−	4.76752i	1.08675	−	0.191623i	0.688197	+	0.725524i	$0.258403\pi$
$620$			14.9592i			0.600775i
$621$	−19.9601	+	37.6418i	−0.800971	+	1.51051i
$622$			0.354063i			0.0141966i
$623$	−14.3688	+	22.0027i	−0.575675	+	0.881520i
$624$	5.63866	+	5.83462i	0.225727	+	0.233572i
$625$	28.3959	−	10.3353i	1.13584	−	0.413410i
$626$	8.02108	+	6.73049i	0.320587	+	0.269004i
$627$	−4.12201	+	39.3606i	−0.164617	+	1.57191i
$628$	−3.37259	+	9.26612i	−0.134581	+	0.369758i
$629$	2.20197	+	3.81392i	0.0877981	+	0.152071i
$630$	8.50870	+	18.3333i	0.338995	+	0.730417i
$631$	12.0161	−	20.8125i	0.478354	−	0.828533i	−0.521338	−	0.853350i	$-0.674567\pi$
$631$	12.0161	−	20.8125i	0.478354	−	0.828533i	0.999692	+	0.0248169i	$0.00790027\pi$
$632$	6.79813	+	8.10170i	0.270415	+	0.322268i
$633$	7.60068	−	15.5986i	0.302100	−	0.619988i
$634$	−1.76566	+	10.0135i	−0.0701232	+	0.397688i
$635$	−8.33772	+	47.2856i	−0.330872	+	1.87647i
$636$	13.5266	−	9.13121i	0.536365	−	0.362076i
$637$	−23.7051	+	22.6586i	−0.939229	+	0.897766i
$638$	−29.3101	−	16.9222i	−1.16040	−	0.669955i
$639$	−26.9684	−	0.921471i	−1.06686	−	0.0364528i
$640$	−2.20527	+	1.27321i	−0.0871708	+	0.0503281i
$641$	−6.87187	+	18.8803i	−0.271423	+	0.745728i	0.726840	+	0.686807i	$0.240988\pi$
$641$	−6.87187	+	18.8803i	−0.271423	+	0.745728i	−0.998263	+	0.0589209i	$0.981234\pi$
$642$	13.6749	−	6.09461i	0.539705	−	0.240535i
$643$	−25.3998	+	30.2703i	−1.00167	+	1.19374i	−0.0206609	+	0.999787i	$0.506577\pi$
$643$	−25.3998	+	30.2703i	−1.00167	+	1.19374i	−0.981010	+	0.193958i	$0.937867\pi$
$644$	8.52761	−	19.9478i	0.336035	−	0.786054i
$645$	4.37323	+	17.5120i	0.172196	+	0.689536i
$646$	3.69694	+	20.9664i	0.145454	+	0.824912i
$647$	10.2344			0.402357			0.201178	−	0.979555i	$-0.435523\pi$
$647$	10.2344			0.402357			0.201178	+	0.979555i	$0.435523\pi$
$648$	0.614316	−	8.97901i	0.0241326	−	0.352729i
$649$			6.07051i			0.238289i
$650$	1.20741	+	6.84757i	0.0473585	+	0.268584i
$651$	23.5169	+	13.1028i	0.921700	+	0.513538i
$652$	−5.81752	+	2.11741i	−0.227832	+	0.0829240i
$653$	1.38321	−	1.64844i	0.0541290	−	0.0645085i	−0.738301	−	0.674472i	$-0.764371\pi$
$653$	1.38321	−	1.64844i	0.0541290	−	0.0645085i	0.792430	+	0.609963i	$0.208816\pi$
$654$	−7.10096	−	15.9329i	−0.277669	−	0.623025i
$655$	20.4244	+	7.43386i	0.798046	+	0.290465i
$656$	−2.64399	−	4.57952i	−0.103230	−	0.178800i
$657$	−13.8142	+	22.1444i	−0.538943	+	0.863933i
$658$	1.71116	+	5.64858i	0.0667081	+	0.220204i
$659$	8.04128	+	9.58322i	0.313244	+	0.373309i	0.899578	−	0.436760i	$-0.143874\pi$
$659$	8.04128	+	9.58322i	0.313244	+	0.373309i	−0.586334	+	0.810069i	$0.699430\pi$
$660$	19.2783	−	13.0139i	0.750407	−	0.506566i
$661$	30.0972	+	5.30694i	1.17064	+	0.206416i	0.724971	−	0.688779i	$-0.241853\pi$
$661$	30.0972	+	5.30694i	1.17064	+	0.206416i	0.445673	+	0.895196i	$0.352964\pi$
$662$	−17.1464	−	3.02337i	−0.666413	−	0.117507i
$663$	−35.8421	−	17.4647i	−1.39199	−	0.678272i
$664$	−8.10329	−	9.65713i	−0.314469	−	0.374769i
$665$	−8.46294	−	27.9363i	−0.328179	−	1.08332i
$666$	0.376197	+	2.66226i	0.0145773	+	0.103161i
$667$	26.3109	+	45.5718i	1.01876	+	1.76455i
$668$	−3.86992	−	1.40854i	−0.149732	−	0.0544979i
$669$	30.8537	+	3.23113i	1.19287	+	0.124923i
$670$	11.8828	−	14.1614i	0.459073	−	0.547101i
$671$	29.8270	−	10.8561i	1.15146	−	0.419097i
$672$	0.0699831	+	4.58204i	0.00269966	+	0.176756i
$673$	−2.38731	−	13.5391i	−0.0920239	−	0.521893i	−0.995619	−	0.0935053i	$-0.970193\pi$
$673$	−2.38731	−	13.5391i	−0.0920239	−	0.521893i	0.903595	−	0.428388i	$-0.140918\pi$
$674$			31.7840i			1.22427i
$675$	4.74140	−	6.08283i	0.182496	−	0.234128i
$676$	8.94574			0.344067
$677$	−4.78160	−	27.1178i	−0.183772	−	1.04222i	−0.927523	−	0.373766i	$-0.878066\pi$
$677$	−4.78160	−	27.1178i	−0.183772	−	1.04222i	0.743751	−	0.668457i	$-0.233045\pi$
$678$	−0.326932	−	0.0936134i	−0.0125558	−	0.00359520i
$679$	−6.61883	+	15.4828i	−0.254007	+	0.594176i
$680$	8.04295	−	9.58521i	0.308433	−	0.367576i
$681$	−6.06210	−	4.40089i	−0.232300	−	0.168643i
$682$	10.5960	−	29.1124i	0.405743	−	1.11477i
$683$	−23.1093	+	13.3421i	−0.884251	+	0.510523i	−0.872058	−	0.489403i	$-0.837215\pi$
$683$	−23.1093	+	13.3421i	−0.884251	+	0.510523i	−0.0121934	+	0.999926i	$0.503881\pi$
$684$	−2.69288	+	12.7160i	−0.102965	+	0.486208i
$685$	13.1711	+	7.60432i	0.503241	+	0.290546i
$686$	−18.5194	+	0.181177i	−0.707073	+	0.00691739i
$687$	1.41895	+	20.1830i	0.0541364	+	0.770029i
$688$	−0.710645	+	4.03027i	−0.0270931	+	0.153653i
$689$	7.66496	−	43.4701i	0.292012	−	1.65608i
$690$	−36.0756	+	2.53627i	−1.37337	+	0.0965542i
$691$	−25.9753	−	30.9562i	−0.988148	−	1.17763i	−0.984096	−	0.177637i	$-0.943155\pi$
$691$	−25.9753	−	30.9562i	−0.988148	−	1.17763i	−0.00405194	−	0.999992i	$-0.501290\pi$
$692$	−3.34992	+	5.80223i	−0.127345	+	0.220568i
$693$	−3.57292	−	41.7058i	−0.135724	−	1.58427i
$694$	8.26012	+	14.3069i	0.313550	+	0.543084i
$695$	−1.42296	+	3.90954i	−0.0539758	+	0.148297i
$696$	−8.99515	−	6.53020i	−0.340960	−	0.247527i
$697$	19.9049	+	16.7022i	0.753953	+	0.632641i
$698$	−21.1511	+	7.69836i	−0.800579	+	0.291387i
$699$	3.21416	−	11.2250i	0.121571	−	0.424569i
$700$	−2.14720	+	3.28796i	−0.0811565	+	0.124273i
$701$			2.80042i			0.105770i	0.998601	+	0.0528851i	$0.0168417\pi$
$701$			2.80042i			0.105770i	−0.998601	+	0.0528851i	$0.983158\pi$
$702$	−16.3084	−	18.0713i	−0.615520	−	0.682057i
$703$		−	3.88310i		−	0.146454i
$704$	5.19357	−	0.915766i	0.195740	−	0.0345142i
$705$	7.07494	−	6.83733i	0.266458	−	0.257509i
$706$	12.6478	+	34.7495i	0.476006	+	1.30782i
$707$	−3.37536	−	28.0835i	−0.126943	−	1.05619i
$708$	−0.207659	+	1.98291i	−0.00780431	+	0.0745224i
$709$	−1.69734	−	0.617781i	−0.0637450	−	0.0232013i	0.309951	−	0.950753i	$-0.399687\pi$
$709$	−1.69734	−	0.617781i	−0.0637450	−	0.0232013i	−0.373696	+	0.927551i	$0.621910\pi$
$710$	−11.4522	−	19.8358i	−0.429793	−	0.744423i
$711$	−19.5525	−	24.9874i	−0.733277	−	0.937100i
$712$	8.60180	+	4.96625i	0.322366	+	0.186118i
$713$	−36.8999	+	30.9627i	−1.38191	+	1.15956i
$714$	−8.02381	−	21.0398i	−0.300283	−	0.787394i
$715$	10.9242	−	61.9542i	0.408542	−	2.31696i
$716$	−0.903581	−	0.159326i	−0.0337684	−	0.00595428i
$717$	−29.0826	+	19.6323i	−1.08611	+	0.733183i
$718$	13.3608	−	11.2111i	0.498621	−	0.418393i
$719$	−1.87236	+	3.24302i	−0.0698272	+	0.120944i	−0.898825	−	0.438307i	$-0.855578\pi$
$719$	−1.87236	+	3.24302i	−0.0698272	+	0.120944i	0.828998	+	0.559252i	$0.188911\pi$
$720$	6.74237	−	3.59148i	0.251273	−	0.133847i
$721$	−6.21007	−	1.45044i	−0.231275	−	0.0540173i
$722$	−0.0779817	+	0.214253i	−0.00290218	+	0.00797367i
$723$	−1.27133	−	2.85258i	−0.0472814	−	0.106089i
$724$	5.08092	−	6.05521i	0.188831	−	0.225040i
$725$	−3.25787	−	8.95091i	−0.120994	−	0.332428i
$726$	−28.2512	+	7.05509i	−1.04850	+	0.261839i
$727$	23.0697	−	4.06780i	0.855607	−	0.150867i	0.271395	−	0.962468i	$-0.412515\pi$
$727$	23.0697	−	4.06780i	0.855607	−	0.150867i	0.584211	+	0.811602i	$0.301404\pi$
$728$	9.04302	+	8.47608i	0.335157	+	0.314145i
$729$	−2.76173	+	26.8584i	−0.102286	+	0.994755i
$730$	−22.1538			−0.819948
$731$	−3.49197	−	19.8039i	−0.129155	−	0.732475i
$732$	10.1143	−	2.52580i	0.373833	−	0.0933563i
$733$	−14.2849	−	39.2474i	−0.527624	−	1.44964i	−0.861860	−	0.507146i	$-0.830700\pi$
$733$	−14.2849	−	39.2474i	−0.527624	−	1.44964i	0.334236	−	0.942490i	$-0.391522\pi$
$734$	−12.2057	−	10.2418i	−0.450520	−	0.378031i
$735$	14.3650	+	27.3282i	0.529861	+	1.00802i
$736$	−7.70512	−	2.80443i	−0.284014	−	0.103373i
$737$	−33.1563	+	19.1428i	−1.22133	+	0.705134i
$738$	7.45818	+	14.0014i	0.274539	+	0.515399i
$739$	12.1995	−	21.1302i	0.448766	−	0.777286i	−0.549540	−	0.835467i	$-0.685197\pi$
$739$	12.1995	−	21.1302i	0.448766	−	0.777286i	0.998306	+	0.0581818i	$0.0185303\pi$
$740$	−1.74827	+	1.46697i	−0.0642675	+	0.0539268i
$741$	19.6696	+	29.1377i	0.722579	+	1.07040i
$742$	19.9479	−	14.9520i	0.732309	−	0.548905i
$743$	5.60455	+	0.988234i	0.205611	+	0.0362548i	0.275505	−	0.961300i	$-0.411155\pi$
$743$	5.60455	+	0.988234i	0.205611	+	0.0362548i	−0.0698939	+	0.997554i	$0.522266\pi$
$744$	4.45703	−	9.14699i	0.163403	−	0.335345i
$745$	−34.5460	−	41.1703i	−1.26567	−	1.50836i
$746$	19.7922	+	11.4270i	0.724644	+	0.418374i
$747$	23.3064	+	29.7846i	0.852735	+	1.08976i
$748$	−22.4420	+	12.9569i	−0.820562	+	0.473752i
$749$	20.4033	−	10.3304i	0.745519	−	0.377463i
$750$	−15.4219	−	1.61505i	−0.563130	−	0.0589734i
$751$	−31.5031	−	26.4342i	−1.14956	−	0.964599i	−0.149854	−	0.988708i	$-0.547881\pi$
$751$	−31.5031	−	26.4342i	−1.14956	−	0.964599i	−0.999709	+	0.0241096i	$0.992325\pi$
$752$	2.09624	−	0.762970i	0.0764421	−	0.0278227i
$753$	6.26745	−	6.05695i	0.228398	−	0.220728i
$754$	−29.6073	+	5.22056i	−1.07823	+	0.190122i
$755$	−55.9798			−2.03731
$756$	0.259584	−	13.7453i	0.00944096	−	0.499911i
$757$	−49.1050			−1.78475			−0.892376	−	0.451292i	$-0.850963\pi$
$757$	−49.1050			−1.78475			−0.892376	+	0.451292i	$0.850963\pi$
$758$	−4.41232	+	0.778011i	−0.160263	+	0.0282586i
$759$	72.0040	+	20.6175i	2.61358	+	0.748369i
$760$	−10.3674	+	3.77344i	−0.376066	+	0.136877i
$761$	7.94534	+	6.66693i	0.288018	+	0.241676i	0.775336	−	0.631548i	$-0.217580\pi$
$761$	7.94534	+	6.66693i	0.288018	+	0.241676i	−0.487318	+	0.873225i	$0.662025\pi$
$762$	19.1868	−	26.4292i	0.695063	−	0.957428i
$763$	−12.0361	−	23.7723i	−0.435736	−	0.860614i
$764$	12.2618	−	7.07936i	0.443617	−	0.256122i
$765$	−25.0967	+	27.9149i	−0.907374	+	1.00926i
$766$	−6.05027	−	3.49313i	−0.218605	−	0.126212i
$767$	3.46620	+	4.13086i	0.125157	+	0.149157i
$768$	1.72779	−	0.121471i	0.0623461	−	0.00438320i
$769$	18.7911	+	3.31338i	0.677626	+	0.119484i	0.501861	−	0.864948i	$-0.332649\pi$
$769$	18.7911	+	3.31338i	0.677626	+	0.119484i	0.175765	+	0.984432i	$0.443760\pi$

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(0.419652 + 1.68044i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.95067 - 1.63681i) q^{5} +(0.705083 + 1.58204i) q^{6} +(1.19511 + 2.36045i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.64778 + 1.41040i) q^{9} +O(q^{10})\)	\(q+(0.984808 - 0.173648i) q^{2} +(0.419652 + 1.68044i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.95067 - 1.63681i) q^{5} +(0.705083 + 1.58204i) q^{6} +(1.19511 + 2.36045i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.64778 + 1.41040i) q^{9} +(-2.20527 - 1.27321i) q^{10} +(3.38986 + 4.03988i) q^{11} +(0.969090 + 1.43557i) q^{12} +(4.61346 + 0.813477i) q^{13} +(1.58685 + 2.11706i) q^{14} +(1.93196 - 3.96488i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-2.45690 + 4.25548i) q^{17} +(-2.36264 + 1.84876i) q^{18} +(3.75220 - 2.16633i) q^{19} +(-2.39285 - 0.870927i) q^{20} +(-3.46506 + 2.99889i) q^{21} +(4.03988 + 3.38986i) q^{22} +(-2.80443 - 7.70512i) q^{23} +(1.20365 + 1.24548i) q^{24} +(0.257739 + 1.46171i) q^{25} +4.68463 q^{26} +(-3.48125 - 3.85757i) q^{27} +(1.93036 + 1.80934i) q^{28} +(-6.32009 + 1.11440i) q^{29} +(1.21411 - 4.24013i) q^{30} +(-2.00923 - 5.52031i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-5.36622 + 7.39181i) q^{33} +(-1.68062 + 4.61746i) q^{34} +(1.53232 - 6.56063i) q^{35} +(-2.00572 + 2.23094i) q^{36} +(0.448119 - 0.776165i) q^{37} +(3.31901 - 2.78498i) q^{38} +(0.569046 + 8.09404i) q^{39} +(-2.50773 - 0.442181i) q^{40} +(0.918246 - 5.20763i) q^{41} +(-2.89167 + 3.55503i) q^{42} +(-3.13499 + 2.63057i) q^{43} +(4.56714 + 2.63684i) q^{44} +(7.47352 + 1.58268i) q^{45} +(-4.09981 - 7.10107i) q^{46} +(2.09624 + 0.762970i) q^{47} +(1.40164 + 1.01755i) q^{48} +(-4.14340 + 5.64200i) q^{49} +(0.507646 + 1.39475i) q^{50} +(-8.18213 - 2.34286i) q^{51} +(4.61346 - 0.813477i) q^{52} -9.42246i q^{53} +(-4.09823 - 3.19445i) q^{54} -13.4290i q^{55} +(2.21522 + 1.44665i) q^{56} +(5.21502 + 5.39625i) q^{57} +(-6.03056 + 2.19494i) q^{58} +(0.881790 + 0.739910i) q^{59} +(0.459378 - 4.38654i) q^{60} +(2.05855 - 5.65582i) q^{61} +(-2.93730 - 5.08755i) q^{62} +(-6.49359 - 4.56435i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-7.66784 - 9.13817i) q^{65} +(-4.00112 + 8.21135i) q^{66} +(-1.26064 + 7.14945i) q^{67} +(-0.853272 + 4.83915i) q^{68} +(11.7711 - 7.94616i) q^{69} +(0.369799 - 6.72704i) q^{70} +(7.78966 + 4.49736i) q^{71} +(-1.58785 + 2.54534i) q^{72} +(7.53439 - 4.34998i) q^{73} +(0.306531 - 0.842188i) q^{74} +(-2.34816 + 1.04653i) q^{75} +(2.78498 - 3.31901i) q^{76} +(-5.48464 + 12.8297i) q^{77} +(1.96592 + 7.87226i) q^{78} +(1.83651 + 10.4153i) q^{79} -2.54642 q^{80} +(5.02152 - 7.46889i) q^{81} -5.28797i q^{82} +(-2.18909 - 12.4150i) q^{83} +(-2.23041 + 4.00316i) q^{84} +(11.7580 - 4.27956i) q^{85} +(-2.63057 + 3.13499i) q^{86} +(-4.52493 - 10.1529i) q^{87} +(4.95564 + 1.80371i) q^{88} +(4.96625 + 8.60180i) q^{89} +(7.63481 + 0.260870i) q^{90} +(3.59344 + 11.8620i) q^{91} +(-5.27061 - 6.28127i) q^{92} +(8.43339 - 5.69301i) q^{93} +(2.19688 + 0.387370i) q^{94} +(-10.8652 - 1.91582i) q^{95} +(1.55704 + 0.758696i) q^{96} +(4.09086 + 4.87530i) q^{97} +(-3.10073 + 6.27578i) q^{98} +(-14.6735 - 5.91565i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

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