LMFDB - Embedded newform 968.2.c.h.485.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(485,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("968.485");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.c (of order $2$, degree $1$, 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} - 2 x^{16} - 2 x^{15} - 4 x^{14} - 4 x^{13} + 12 x^{12} + 16 x^{11} + 32 x^{9} + \cdots + 1024 $ x^20 - x^18 - 2x^16 - 2x^15 - 4x^14 - 4x^13 + 12x^12 + 16x^11 + 32x^9 + 48x^8 - 32x^7 - 64x^6 - 64x^5 - 128x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			485.12
Root			$0.324509 - 1.37648i$ of defining polynomial
Character	$\chi$	$=$	968.485
Dual form			968.2.c.h.485.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.324509 + 1.37648i) q^{2} -0.540427i q^{3} +(-1.78939 + 0.893360i) q^{4} +2.90090i q^{5} +(0.743887 - 0.175374i) q^{6} +2.60451 q^{7} +(-1.81036 - 2.17315i) q^{8} +2.70794 q^{9} +(-3.99302 + 0.941367i) q^{10} +(0.482796 + 0.967034i) q^{12} +2.61733i q^{13} +(0.845186 + 3.58505i) q^{14} +1.56772 q^{15} +(2.40382 - 3.19713i) q^{16} +6.89102 q^{17} +(0.878751 + 3.72742i) q^{18} +1.60066i q^{19} +(-2.59154 - 5.19083i) q^{20} -1.40755i q^{21} -4.01642 q^{23} +(-1.17443 + 0.978369i) q^{24} -3.41520 q^{25} +(-3.60270 + 0.849346i) q^{26} -3.08473i q^{27} +(-4.66047 + 2.32676i) q^{28} -1.99756i q^{29} +(0.508740 + 2.15794i) q^{30} -5.18052 q^{31} +(5.18085 + 2.27130i) q^{32} +(2.23620 + 9.48535i) q^{34} +7.55540i q^{35} +(-4.84555 + 2.41916i) q^{36} +8.58941i q^{37} +(-2.20327 + 0.519427i) q^{38} +1.41447 q^{39} +(6.30408 - 5.25167i) q^{40} +3.74881 q^{41} +(1.93746 - 0.456761i) q^{42} +2.47162i q^{43} +7.85545i q^{45} +(-1.30336 - 5.52851i) q^{46} -11.8468 q^{47} +(-1.72782 - 1.29909i) q^{48} -0.216545 q^{49} +(-1.10826 - 4.70095i) q^{50} -3.72410i q^{51} +(-2.33821 - 4.68341i) q^{52} -1.29380i q^{53} +(4.24606 - 1.00102i) q^{54} +(-4.71510 - 5.65999i) q^{56} +0.865038 q^{57} +(2.74960 - 0.648227i) q^{58} -0.351518i q^{59} +(-2.80526 + 1.40054i) q^{60} -3.08138i q^{61} +(-1.68113 - 7.13088i) q^{62} +7.05284 q^{63} +(-1.44517 + 7.86838i) q^{64} -7.59259 q^{65} -10.3946i q^{67} +(-12.3307 + 6.15616i) q^{68} +2.17058i q^{69} +(-10.3999 + 2.45180i) q^{70} +3.47027 q^{71} +(-4.90235 - 5.88476i) q^{72} +1.33440 q^{73} +(-11.8231 + 2.78734i) q^{74} +1.84566i q^{75} +(-1.42996 - 2.86419i) q^{76} +(0.459010 + 1.94699i) q^{78} +4.32281 q^{79} +(9.27455 + 6.97322i) q^{80} +6.45675 q^{81} +(1.21652 + 5.16015i) q^{82} +15.9824i q^{83} +(1.25744 + 2.51865i) q^{84} +19.9901i q^{85} +(-3.40214 + 0.802064i) q^{86} -1.07954 q^{87} -13.1240 q^{89} +(-10.8129 + 2.54916i) q^{90} +6.81685i q^{91} +(7.18692 - 3.58810i) q^{92} +2.79969i q^{93} +(-3.84438 - 16.3068i) q^{94} -4.64333 q^{95} +(1.22747 - 2.79987i) q^{96} +8.61256 q^{97} +(-0.0702709 - 0.298070i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{10} - 3 q^{12} - 4 q^{14} - 4 q^{15} + 10 q^{16} + 2 q^{17} - 5 q^{18} - 16 q^{20} - 4 q^{23} + 15 q^{24} - 2 q^{25} + 30 q^{26} - 14 q^{28} + 16 q^{30}+ \cdots - 72 q^{98}+O(q^{100}) $ 20 * q + 2 * q^4 - q^6 + 10 * q^7 - 10 * q^9 - 10 * q^10 - 3 * q^12 - 4 * q^14 - 4 * q^15 + 10 * q^16 + 2 * q^17 - 5 * q^18 - 16 * q^20 - 4 * q^23 + 15 * q^24 - 2 * q^25 + 30 * q^26 - 14 * q^28 + 16 * q^30 + 2 * q^31 + 10 * q^32 + 5 * q^34 + 9 * q^36 + 21 * q^38 + 28 * q^39 + 10 * q^40 - 2 * q^41 - 20 * q^42 + 24 * q^46 + 2 * q^47 - 41 * q^48 - 2 * q^49 - 22 * q^50 - 20 * q^52 + 54 * q^54 - 16 * q^56 + 22 * q^57 + 12 * q^58 - 48 * q^60 + 4 * q^62 - 30 * q^63 + 38 * q^64 - 18 * q^65 - 21 * q^68 - 44 * q^70 - 34 * q^71 + 57 * q^72 + 2 * q^73 - 28 * q^74 - 67 * q^76 - 6 * q^78 - 58 * q^79 + 28 * q^80 - 12 * q^81 - 23 * q^82 - 44 * q^84 + 25 * q^86 + 34 * q^87 - 8 * q^89 - 42 * q^90 + 68 * q^92 + 60 * q^94 - 92 * q^95 + 35 * q^96 + 10 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	0.324509	+	1.37648i	0.229463	+	0.973317i
$2$	0.324509	+	1.37648i	0.229463	+	0.973317i
$3$		−	0.540427i		−	0.312016i	−0.987756	−	0.156008i	$-0.950137\pi$
$3$		−	0.540427i		−	0.312016i	0.987756	−	0.156008i	$-0.0498625\pi$
$4$	−1.78939	+	0.893360i	−0.894694	+	0.446680i
$5$			2.90090i			1.29732i	0.761078	+	0.648660i	$0.224670\pi$
$5$			2.90090i			1.29732i	−0.761078	+	0.648660i	$0.775330\pi$
$6$	0.743887	−	0.175374i	0.303690	−	0.0715959i
$7$	2.60451			0.984411			0.492205	−	0.870479i	$-0.336191\pi$
$7$	2.60451			0.984411			0.492205	+	0.870479i	$0.336191\pi$
$8$	−1.81036	−	2.17315i	−0.640060	−	0.768325i
$9$	2.70794			0.902646
$10$	−3.99302	+	0.941367i	−1.26270	+	0.297686i
$11$		0			0
$11$		0			0
$12$	0.482796	+	0.967034i	0.139371	+	0.279159i
$13$			2.61733i			0.725916i	0.931806	+	0.362958i	$0.118233\pi$
$13$			2.61733i			0.725916i	−0.931806	+	0.362958i	$0.881767\pi$
$14$	0.845186	+	3.58505i	0.225885	+	0.958144i
$15$	1.56772			0.404784
$16$	2.40382	−	3.19713i	0.600954	−	0.799283i
$17$	6.89102			1.67132			0.835660	−	0.549248i	$-0.185086\pi$
$17$	6.89102			1.67132			0.835660	+	0.549248i	$0.185086\pi$
$18$	0.878751	+	3.72742i	0.207123	+	0.878561i
$19$			1.60066i			0.367215i	0.983000	+	0.183608i	$0.0587776\pi$
$19$			1.60066i			0.367215i	−0.983000	+	0.183608i	$0.941222\pi$
$20$	−2.59154	−	5.19083i	−0.579487	−	1.16070i
$21$		−	1.40755i		−	0.307152i
$22$		0			0
$23$	−4.01642			−0.837480			−0.418740	−	0.908106i	$-0.637528\pi$
$23$	−4.01642			−0.837480			−0.418740	+	0.908106i	$0.637528\pi$
$24$	−1.17443	+	0.978369i	−0.239730	+	0.199709i
$25$	−3.41520			−0.683039
$26$	−3.60270	+	0.849346i	−0.706547	+	0.166571i
$27$		−	3.08473i		−	0.593656i
$28$	−4.66047	+	2.32676i	−0.880746	+	0.439717i
$29$		−	1.99756i		−	0.370938i	−0.982650	−	0.185469i	$-0.940620\pi$
$29$		−	1.99756i		−	0.370938i	0.982650	−	0.185469i	$-0.0593805\pi$
$30$	0.508740	+	2.15794i	0.0928828	+	0.393984i
$31$	−5.18052			−0.930449			−0.465224	−	0.885193i	$-0.654026\pi$
$31$	−5.18052			−0.930449			−0.465224	+	0.885193i	$0.654026\pi$
$32$	5.18085	+	2.27130i	0.915853	+	0.401514i
$33$		0			0
$34$	2.23620	+	9.48535i	0.383505	+	1.62672i
$35$			7.55540i			1.27710i
$36$	−4.84555	+	2.41916i	−0.807592	+	0.403194i
$37$			8.58941i			1.41209i	0.708167	+	0.706045i	$0.249522\pi$
$37$			8.58941i			1.41209i	−0.708167	+	0.706045i	$0.750478\pi$
$38$	−2.20327	+	0.519427i	−0.357417	+	0.0842622i
$39$	1.41447			0.226497
$40$	6.30408	−	5.25167i	0.996763	−	0.830363i
$41$	3.74881			0.585465			0.292733	−	0.956194i	$-0.405435\pi$
$41$	3.74881			0.585465			0.292733	+	0.956194i	$0.405435\pi$
$42$	1.93746	−	0.456761i	0.298956	−	0.0704798i
$43$			2.47162i			0.376919i	0.982081	+	0.188460i	$0.0603494\pi$
$43$			2.47162i			0.376919i	−0.982081	+	0.188460i	$0.939651\pi$
$44$		0			0
$45$			7.85545i			1.17102i
$46$	−1.30336	−	5.52851i	−0.192170	−	0.815134i
$47$	−11.8468			−1.72803			−0.864014	−	0.503468i	$-0.832057\pi$
$47$	−11.8468			−1.72803			−0.864014	+	0.503468i	$0.832057\pi$
$48$	−1.72782	−	1.29909i	−0.249389	−	0.187507i
$49$	−0.216545			−0.0309350
$50$	−1.10826	−	4.70095i	−0.156732	−	0.664814i
$51$		−	3.72410i		−	0.521478i
$52$	−2.33821	−	4.68341i	−0.324252	−	0.649473i
$53$		−	1.29380i		−	0.177717i	−0.996044	−	0.0888587i	$-0.971678\pi$
$53$		−	1.29380i		−	0.177717i	0.996044	−	0.0888587i	$-0.0283220\pi$
$54$	4.24606	−	1.00102i	0.577815	−	0.136222i
$55$		0			0
$56$	−4.71510	−	5.65999i	−0.630082	−	0.756347i
$57$	0.865038			0.114577
$58$	2.74960	−	0.648227i	0.361041	−	0.0851164i
$59$		−	0.351518i		−	0.0457638i	−0.999738	−	0.0228819i	$-0.992716\pi$
$59$		−	0.351518i		−	0.0457638i	0.999738	−	0.0228819i	$-0.00728417\pi$
$60$	−2.80526	+	1.40054i	−0.362158	+	0.180809i
$61$		−	3.08138i		−	0.394530i	−0.980350	−	0.197265i	$-0.936794\pi$
$61$		−	3.08138i		−	0.394530i	0.980350	−	0.197265i	$-0.0632059\pi$
$62$	−1.68113	−	7.13088i	−0.213503	−	0.905622i
$63$	7.05284			0.888575
$64$	−1.44517	+	7.86838i	−0.180646	+	0.983548i
$65$	−7.59259			−0.941745
$66$		0			0
$67$		−	10.3946i		−	1.26990i	−0.772553	−	0.634950i	$-0.781021\pi$
$67$		−	10.3946i		−	1.26990i	0.772553	−	0.634950i	$-0.218979\pi$
$68$	−12.3307	+	6.15616i	−1.49532	+	0.746544i
$69$			2.17058i			0.261307i
$70$	−10.3999	+	2.45180i	−1.24302	+	0.293046i
$71$	3.47027			0.411845			0.205922	−	0.978568i	$-0.433981\pi$
$71$	3.47027			0.411845			0.205922	+	0.978568i	$0.433981\pi$
$72$	−4.90235	−	5.88476i	−0.577748	−	0.693526i
$73$	1.33440			0.156180			0.0780901	−	0.996946i	$-0.475118\pi$
$73$	1.33440			0.156180			0.0780901	+	0.996946i	$0.475118\pi$
$74$	−11.8231	+	2.78734i	−1.37441	+	0.324022i
$75$			1.84566i			0.213119i
$76$	−1.42996	−	2.86419i	−0.164028	−	0.328545i
$77$		0			0
$78$	0.459010	+	1.94699i	0.0519726	+	0.220454i
$79$	4.32281			0.486355			0.243177	−	0.969982i	$-0.421810\pi$
$79$	4.32281			0.486355			0.243177	+	0.969982i	$0.421810\pi$
$80$	9.27455	+	6.97322i	1.03693	+	0.779630i
$81$	6.45675			0.717416
$82$	1.21652	+	5.16015i	0.134342	+	0.569844i
$83$			15.9824i			1.75429i	0.480223	+	0.877146i	$0.340556\pi$
$83$			15.9824i			1.75429i	−0.480223	+	0.877146i	$0.659444\pi$
$84$	1.25744	+	2.51865i	0.137198	+	0.274807i
$85$			19.9901i			2.16824i
$86$	−3.40214	+	0.802064i	−0.366862	+	0.0864888i
$87$	−1.07954			−0.115739
$88$		0			0
$89$	−13.1240			−1.39114			−0.695571	−	0.718457i	$-0.744849\pi$
$89$	−13.1240			−1.39114			−0.695571	+	0.718457i	$0.744849\pi$
$90$	−10.8129	+	2.54916i	−1.13978	+	0.268705i
$91$			6.81685i			0.714600i
$92$	7.18692	−	3.58810i	0.749289	−	0.374086i
$93$			2.79969i			0.290315i
$94$	−3.84438	−	16.3068i	−0.396518	−	1.68192i
$95$	−4.64333			−0.476396
$96$	1.22747	−	2.79987i	0.125279	−	0.285761i
$97$	8.61256			0.874473			0.437236	−	0.899347i	$-0.355957\pi$
$97$	8.61256			0.874473			0.437236	+	0.899347i	$0.355957\pi$
$98$	−0.0702709	−	0.298070i	−0.00709843	−	0.0301096i
$99$		0			0
$100$	6.11111	−	3.05100i	0.611111	−	0.305100i
$101$		−	8.70592i		−	0.866271i	−0.901329	−	0.433136i	$-0.857407\pi$
$101$		−	8.70592i		−	0.866271i	0.901329	−	0.433136i	$-0.142593\pi$
$102$	5.12614	−	1.20850i	0.507564	−	0.119660i
$103$	1.24758			0.122928			0.0614638	−	0.998109i	$-0.480423\pi$
$103$	1.24758			0.122928			0.0614638	+	0.998109i	$0.480423\pi$
$104$	5.68785	−	4.73831i	0.557739	−	0.464630i
$105$	4.08314			0.398474
$106$	1.78089	−	0.419851i	0.172975	−	0.0407795i
$107$		−	18.7777i		−	1.81531i	−0.419721	−	0.907653i	$-0.637872\pi$
$107$		−	18.7777i		−	1.81531i	0.419721	−	0.907653i	$-0.362128\pi$
$108$	2.75577	+	5.51977i	0.265174	+	0.531140i
$109$			12.1780i			1.16644i	0.812313	+	0.583221i	$0.198208\pi$
$109$			12.1780i			1.16644i	−0.812313	+	0.583221i	$0.801792\pi$
$110$		0			0
$111$	4.64195			0.440594
$112$	6.26076	−	8.32696i	0.591586	−	0.786823i
$113$	−5.30859			−0.499390			−0.249695	−	0.968325i	$-0.580330\pi$
$113$	−5.30859			−0.499390			−0.249695	+	0.968325i	$0.580330\pi$
$114$	0.280712	+	1.19071i	0.0262911	+	0.111520i
$115$		−	11.6512i		−	1.08648i
$116$	1.78454	+	3.57442i	0.165691	+	0.331876i
$117$			7.08756i			0.655245i
$118$	0.483858	−	0.114071i	0.0445427	−	0.0105011i
$119$	17.9477			1.64526
$120$	−2.83815	−	3.40690i	−0.259086	−	0.311006i
$121$		0			0
$122$	4.24145	−	0.999934i	0.384003	−	0.0905298i
$123$		−	2.02596i		−	0.182674i
$124$	9.26996	−	4.62807i	0.832467	−	0.415613i
$125$			4.59735i			0.411200i
$126$	2.28871	+	9.70809i	0.203895	+	0.864865i
$127$	9.91217			0.879562			0.439781	−	0.898105i	$-0.355056\pi$
$127$	9.91217			0.879562			0.439781	+	0.898105i	$0.355056\pi$
$128$	−11.2996	+	0.564115i	−0.998756	+	0.0498612i
$129$	1.33573			0.117605
$130$	−2.46387	−	10.4510i	−0.216095	−	0.916617i
$131$		−	11.4291i		−	0.998568i	−0.866438	−	0.499284i	$-0.833596\pi$
$131$		−	11.4291i		−	0.998568i	0.866438	−	0.499284i	$-0.166404\pi$
$132$		0			0
$133$			4.16892i			0.361491i
$134$	14.3079	−	3.37314i	1.23602	−	0.291395i
$135$	8.94847			0.770161
$136$	−12.4753	−	14.9752i	−1.06974	−	1.28412i
$137$	1.17343			0.100253			0.0501265	−	0.998743i	$-0.484038\pi$
$137$	1.17343			0.100253			0.0501265	+	0.998743i	$0.484038\pi$
$138$	−2.98776	+	0.704373i	−0.254335	+	0.0599602i
$139$		−	7.24148i		−	0.614214i	−0.951675	−	0.307107i	$-0.900639\pi$
$139$		−	7.24148i		−	0.614214i	0.951675	−	0.307107i	$-0.0993609\pi$
$140$	−6.74969	−	13.5195i	−0.570453	−	1.14261i
$141$			6.40231i			0.539172i
$142$	1.12613	+	4.77675i	0.0945029	+	0.400856i
$143$		0			0
$144$	6.50939	−	8.65764i	0.542449	−	0.721470i
$145$	5.79472			0.481226
$146$	0.433026	+	1.83678i	0.0358375	+	0.152013i
$147$			0.117027i			0.00965222i
$148$	−7.67343	−	15.3698i	−0.630752	−	1.26339i
$149$		−	12.2904i		−	1.00687i	−0.864034	−	0.503434i	$-0.832070\pi$
$149$		−	12.2904i		−	1.00687i	0.864034	−	0.503434i	$-0.167930\pi$
$150$	−2.54052	+	0.598935i	−0.207432	+	0.0489028i
$151$	14.4562			1.17643			0.588216	−	0.808704i	$-0.299831\pi$
$151$	14.4562			1.17643			0.588216	+	0.808704i	$0.299831\pi$
$152$	3.47847	−	2.89777i	0.282141	−	0.235040i
$153$	18.6605			1.50861
$154$		0			0
$155$		−	15.0281i		−	1.20709i
$156$	−2.53104	+	1.26363i	−0.202646	+	0.101172i
$157$		−	17.7462i		−	1.41630i	−0.706061	−	0.708151i	$-0.749529\pi$
$157$		−	17.7462i		−	1.41630i	0.706061	−	0.708151i	$-0.250471\pi$
$158$	1.40279	+	5.95026i	0.111600	+	0.473378i
$159$	−0.699206			−0.0554506
$160$	−6.58882	+	15.0291i	−0.520892	+	1.18815i
$161$	−10.4608			−0.824425
$162$	2.09527	+	8.88757i	0.164620	+	0.698274i
$163$			5.76348i			0.451431i	0.974193	+	0.225715i	$0.0724719\pi$
$163$			5.76348i			0.451431i	−0.974193	+	0.225715i	$0.927528\pi$
$164$	−6.70807	+	3.34903i	−0.523812	+	0.261516i
$165$		0			0
$166$	−21.9994	+	5.18642i	−1.70748	+	0.402545i
$167$	−2.36484			−0.182997			−0.0914983	−	0.995805i	$-0.529166\pi$
$167$	−2.36484			−0.182997			−0.0914983	+	0.995805i	$0.529166\pi$
$168$	−3.05881	+	2.54817i	−0.235992	+	0.196596i
$169$	6.14960			0.473046
$170$	−27.5160	+	6.48698i	−2.11038	+	0.497529i
$171$			4.33448i			0.331466i
$172$	−2.20805	−	4.42269i	−0.168362	−	0.337227i
$173$			2.47719i			0.188338i	0.995556	+	0.0941688i	$0.0300193\pi$
$173$			2.47719i			0.188338i	−0.995556	+	0.0941688i	$0.969981\pi$
$174$	−0.350320	−	1.48596i	−0.0265577	−	0.112650i
$175$	−8.89490			−0.672391
$176$		0			0
$177$	−0.189970			−0.0142790
$178$	−4.25886	−	18.0649i	−0.319215	−	1.35402i
$179$		−	20.4673i		−	1.52980i	−0.644148	−	0.764901i	$-0.722788\pi$
$179$		−	20.4673i		−	1.52980i	0.644148	−	0.764901i	$-0.277212\pi$
$180$	−7.01774	−	14.0564i	−0.523071	−	1.04771i
$181$			17.2443i			1.28176i	0.767641	+	0.640880i	$0.221430\pi$
$181$			17.2443i			1.28176i	−0.767641	+	0.640880i	$0.778570\pi$
$182$	−9.38324	+	2.21213i	−0.695532	+	0.163974i
$183$	−1.66526			−0.123100
$184$	7.27117	+	8.72828i	0.536038	+	0.643457i
$185$	−24.9170			−1.83193
$186$	−3.85372	+	0.908526i	−0.282568	+	0.0666164i
$187$		0			0
$188$	21.1985	−	10.5834i	1.54606	−	0.771875i
$189$		−	8.03419i		−	0.584401i
$190$	−1.50680	−	6.39145i	−0.109315	−	0.463685i
$191$	20.2776			1.46723			0.733617	−	0.679563i	$-0.237830\pi$
$191$	20.2776			1.46723			0.733617	+	0.679563i	$0.237830\pi$
$192$	4.25229	+	0.781010i	0.306883	+	0.0563645i
$193$	2.58140			0.185813			0.0929065	−	0.995675i	$-0.470384\pi$
$193$	2.58140			0.185813			0.0929065	+	0.995675i	$0.470384\pi$
$194$	2.79485	+	11.8550i	0.200659	+	0.851140i
$195$			4.10324i			0.293839i
$196$	0.387483	−	0.193453i	0.0276774	−	0.0138181i
$197$		−	21.0439i		−	1.49931i	−0.661826	−	0.749657i	$-0.730218\pi$
$197$		−	21.0439i		−	1.49931i	0.661826	−	0.749657i	$-0.269782\pi$
$198$		0			0
$199$	7.98438			0.565998			0.282999	−	0.959120i	$-0.408671\pi$
$199$	7.98438			0.565998			0.282999	+	0.959120i	$0.408671\pi$
$200$	6.18275	+	7.42174i	0.437186	+	0.524796i
$201$	−5.61752			−0.396229
$202$	11.9835	−	2.82515i	0.843157	−	0.198777i
$203$		−	5.20267i		−	0.365156i
$204$	3.32696	+	6.66385i	0.232934	+	0.466563i
$205$			10.8749i			0.759536i
$206$	0.404851	+	1.71727i	0.0282073	+	0.119648i
$207$	−10.8762			−0.755949
$208$	8.36794	+	6.29158i	0.580213	+	0.436242i
$209$		0			0
$210$	1.32502	+	5.62036i	0.0914349	+	0.387842i
$211$			9.42591i			0.648907i	0.945902	+	0.324453i	$0.105180\pi$
$211$			9.42591i			0.648907i	−0.945902	+	0.324453i	$0.894820\pi$
$212$	1.15583	+	2.31511i	0.0793828	+	0.159003i
$213$		−	1.87543i		−	0.128502i
$214$	25.8471	−	6.09352i	1.76687	−	0.416545i
$215$	−7.16992			−0.488985
$216$	−6.70357	+	5.58447i	−0.456120	+	0.379975i
$217$	−13.4927			−0.915944
$218$	−16.7628	+	3.95188i	−1.13532	+	0.267655i
$219$		−	0.721148i		−	0.0487307i
$220$		0			0
$221$			18.0361i			1.21324i
$222$	1.50635	+	6.38955i	0.101100	+	0.428838i
$223$	14.5073			0.971479			0.485739	−	0.874104i	$-0.338550\pi$
$223$	14.5073			0.971479			0.485739	+	0.874104i	$0.338550\pi$
$224$	13.4936	+	5.91563i	0.901576	+	0.395255i
$225$	−9.24814			−0.616543
$226$	−1.72269	−	7.30716i	−0.114591	−	0.486065i
$227$			2.72440i			0.180825i	0.995904	+	0.0904125i	$0.0288185\pi$
$227$			2.72440i			0.180825i	−0.995904	+	0.0904125i	$0.971181\pi$
$228$	−1.54789	+	0.772790i	−0.102511	+	0.0511792i
$229$		−	13.9615i		−	0.922599i	−0.887244	−	0.461300i	$-0.847383\pi$
$229$		−	13.9615i		−	0.922599i	0.887244	−	0.461300i	$-0.152617\pi$
$230$	16.0376	−	3.78092i	1.05749	−	0.249307i
$231$		0			0
$232$	−4.34101	+	3.61632i	−0.285001	+	0.237423i
$233$	12.4322			0.814463			0.407231	−	0.913325i	$-0.366494\pi$
$233$	12.4322			0.814463			0.407231	+	0.913325i	$0.366494\pi$
$234$	−9.75588	+	2.29998i	−0.637762	+	0.150354i
$235$		−	34.3662i		−	2.24181i
$236$	0.314032	+	0.629003i	0.0204418	+	0.0409446i
$237$		−	2.33617i		−	0.151750i
$238$	5.82420	+	24.7047i	0.377527	+	1.60136i
$239$	−17.8541			−1.15488			−0.577441	−	0.816432i	$-0.695949\pi$
$239$	−17.8541			−1.15488			−0.577441	+	0.816432i	$0.695949\pi$
$240$	3.76852	−	5.01222i	0.243257	−	0.323537i
$241$	0.714420			0.0460198			0.0230099	−	0.999735i	$-0.492675\pi$
$241$	0.714420			0.0460198			0.0230099	+	0.999735i	$0.492675\pi$
$242$		0			0
$243$		−	12.7436i		−	0.817501i
$244$	2.75278	+	5.51378i	0.176229	+	0.352983i
$245$		−	0.628175i		−	0.0401326i
$246$	2.78869	−	0.657442i	0.177800	−	0.0419169i
$247$	−4.18944			−0.266568
$248$	9.37862	+	11.2581i	0.595543	+	0.714887i
$249$	8.63731			0.547367
$250$	−6.32816	+	1.49188i	−0.400228	+	0.0943549i
$251$		−	1.51191i		−	0.0954307i	−0.998861	−	0.0477154i	$-0.984806\pi$
$251$		−	1.51191i		−	0.0954307i	0.998861	−	0.0477154i	$-0.0151940\pi$
$252$	−12.6203	+	6.30073i	−0.795002	+	0.396908i
$253$		0			0
$254$	3.21659	+	13.6439i	0.201827	+	0.856094i
$255$	10.8032			0.676524
$256$	−4.44333	−	15.3706i	−0.277708	−	0.960666i
$257$	−18.4287			−1.14955			−0.574776	−	0.818311i	$-0.694911\pi$
$257$	−18.4287			−1.14955			−0.574776	+	0.818311i	$0.694911\pi$
$258$	0.433457	+	1.83861i	0.0269859	+	0.114467i
$259$			22.3712i			1.39008i
$260$	13.5861	−	6.78292i	0.842574	−	0.420659i
$261$		−	5.40928i		−	0.334826i
$262$	15.7320	−	3.70886i	0.971924	−	0.229134i
$263$	11.2903			0.696191			0.348096	−	0.937459i	$-0.386828\pi$
$263$	11.2903			0.696191			0.348096	+	0.937459i	$0.386828\pi$
$264$		0			0
$265$	3.75319			0.230556
$266$	−5.73843	+	1.35285i	−0.351845	+	0.0829486i
$267$			7.09257i			0.434058i
$268$	9.28610	+	18.5999i	0.567239	+	1.13617i
$269$			17.5822i			1.07201i	0.844216	+	0.536003i	$0.180066\pi$
$269$			17.5822i			1.07201i	−0.844216	+	0.536003i	$0.819934\pi$
$270$	2.90386	+	12.3174i	0.176723	+	0.749612i
$271$	6.52674			0.396471			0.198235	−	0.980154i	$-0.436479\pi$
$271$	6.52674			0.396471			0.198235	+	0.980154i	$0.436479\pi$
$272$	16.5648	−	22.0315i	1.00439	−	1.33586i
$273$	3.68401			0.222966
$274$	0.380789	+	1.61520i	0.0230043	+	0.0975780i
$275$		0			0
$276$	−1.93911	−	3.88401i	−0.116721	−	0.233790i
$277$			0.256302i			0.0153997i	0.999970	+	0.00769986i	$0.00245096\pi$
$277$			0.256302i			0.0153997i	−0.999970	+	0.00769986i	$0.997549\pi$
$278$	9.96774	−	2.34992i	0.597825	−	0.140939i
$279$	−14.0285			−0.839866
$280$	16.4190	−	13.6780i	0.981225	−	0.817418i
$281$	−25.9584			−1.54855			−0.774275	−	0.632850i	$-0.781885\pi$
$281$	−25.9584			−1.54855			−0.774275	+	0.632850i	$0.781885\pi$
$282$	−8.81265	+	2.07761i	−0.524786	+	0.123720i
$283$		−	9.41124i		−	0.559440i	−0.960082	−	0.279720i	$-0.909758\pi$
$283$		−	9.41124i		−	0.559440i	0.960082	−	0.279720i	$-0.0902417\pi$
$284$	−6.20965	+	3.10020i	−0.368475	+	0.183963i
$285$			2.50938i			0.148643i
$286$		0			0
$287$	9.76379			0.576339
$288$	14.0294	+	6.15055i	0.826691	+	0.362425i
$289$	30.4862			1.79331
$290$	1.88044	+	7.97631i	0.110423	+	0.468385i
$291$		−	4.65446i		−	0.272849i
$292$	−2.38777	+	1.19210i	−0.139733	+	0.0697625i
$293$			1.91942i			0.112134i	0.998427	+	0.0560670i	$0.0178560\pi$
$293$			1.91942i			0.112134i	−0.998427	+	0.0560670i	$0.982144\pi$
$294$	−0.161085	+	0.0379763i	−0.00939467	+	0.00221482i
$295$	1.01972			0.0593703
$296$	18.6661	−	15.5499i	1.08494	−	0.903822i
$297$		0			0
$298$	16.9175	−	3.98834i	0.980002	−	0.231039i
$299$		−	10.5123i		−	0.607940i
$300$	−1.64884	−	3.30261i	−0.0951960	−	0.190676i
$301$			6.43736i			0.371043i
$302$	4.69118	+	19.8987i	0.269947	+	1.14504i
$303$	−4.70491			−0.270290
$304$	5.11751	+	3.84768i	0.293509	+	0.220680i
$305$	8.93875			0.511831
$306$	6.05549	+	25.6857i	0.346169	+	1.46836i
$307$			10.2272i			0.583696i	0.956465	+	0.291848i	$0.0942702\pi$
$307$			10.2272i			0.583696i	−0.956465	+	0.291848i	$0.905730\pi$
$308$		0			0
$309$		−	0.674226i		−	0.0383554i
$310$	20.6859	−	4.87677i	1.17488	−	0.276982i
$311$	−14.9593			−0.848265			−0.424132	−	0.905600i	$-0.639421\pi$
$311$	−14.9593			−0.848265			−0.424132	+	0.905600i	$0.639421\pi$
$312$	−2.56071	−	3.07387i	−0.144972	−	0.174023i
$313$	−4.86175			−0.274802			−0.137401	−	0.990515i	$-0.543875\pi$
$313$	−4.86175			−0.274802			−0.137401	+	0.990515i	$0.543875\pi$
$314$	24.4273	−	5.75881i	1.37851	−	0.324988i
$315$			20.4596i			1.15277i
$316$	−7.73519	+	3.86183i	−0.435139	+	0.217245i
$317$		−	10.6894i		−	0.600376i	−0.953880	−	0.300188i	$-0.902951\pi$
$317$		−	10.6894i		−	0.600376i	0.953880	−	0.300188i	$-0.0970495\pi$
$318$	−0.226899	−	0.962442i	−0.0127238	−	0.0539711i
$319$		0			0
$320$	−22.8254	−	4.19229i	−1.27598	−	0.234356i
$321$	−10.1480			−0.566404
$322$	−3.39462	−	14.3990i	−0.189175	−	0.802427i
$323$			11.0302i			0.613734i
$324$	−11.5536	+	5.76820i	−0.641868	+	0.320455i
$325$		−	8.93869i		−	0.495829i
$326$	−7.93331	+	1.87030i	−0.439385	+	0.103586i
$327$	6.58133			0.363948
$328$	−6.78670	−	8.14672i	−0.374733	−	0.449828i
$329$	−30.8550			−1.70109
$330$		0			0
$331$			21.3447i			1.17321i	0.809874	+	0.586604i	$0.199536\pi$
$331$			21.3447i			1.17321i	−0.809874	+	0.586604i	$0.800464\pi$
$332$	−14.2780	−	28.5987i	−0.783607	−	1.56956i
$333$			23.2596i			1.27462i
$334$	−0.767411	−	3.25515i	−0.0419909	−	0.178114i
$335$	30.1536			1.64747
$336$	−4.50011	−	3.38348i	−0.245501	−	0.184584i
$337$	7.83644			0.426878			0.213439	−	0.976956i	$-0.431534\pi$
$337$	7.83644			0.426878			0.213439	+	0.976956i	$0.431534\pi$
$338$	1.99560	+	8.46479i	0.108546	+	0.460424i
$339$			2.86891i			0.155818i
$340$	−17.8584	−	35.7701i	−0.968507	−	1.93991i
$341$		0			0
$342$	−5.96631	+	1.40658i	−0.322621	+	0.0760589i
$343$	−18.7955			−1.01486
$344$	5.37121	−	4.47454i	0.289596	−	0.241251i
$345$	−6.29663			−0.338999
$346$	−3.40981	+	0.803872i	−0.183312	+	0.0432164i
$347$		−	27.2739i		−	1.46414i	−0.681229	−	0.732071i	$-0.738554\pi$
$347$		−	27.2739i		−	1.46414i	0.681229	−	0.732071i	$-0.261446\pi$
$348$	1.93171	−	0.964415i	0.103551	−	0.0516981i
$349$			7.49428i			0.401160i	0.979677	+	0.200580i	$0.0642826\pi$
$349$			7.49428i			0.401160i	−0.979677	+	0.200580i	$0.935717\pi$
$350$	−2.88648	−	12.2436i	−0.154289	−	0.654450i
$351$	8.07373			0.430944
$352$		0			0
$353$	18.1327			0.965105			0.482552	−	0.875867i	$-0.339710\pi$
$353$	18.1327			0.965105			0.482552	+	0.875867i	$0.339710\pi$
$354$	−0.0616470	−	0.261490i	−0.00327650	−	0.0138980i
$355$			10.0669i			0.534294i
$356$	23.4839	−	11.7245i	1.24465	−	0.621395i
$357$		−	9.69944i		−	0.513349i
$358$	28.1729	−	6.64184i	1.48898	−	0.351032i
$359$	−4.81766			−0.254266			−0.127133	−	0.991886i	$-0.540578\pi$
$359$	−4.81766			−0.254266			−0.127133	+	0.991886i	$0.540578\pi$
$360$	17.0711	−	14.2212i	0.899725	−	0.749524i
$361$	16.4379			0.865153
$362$	−23.7364	+	5.59594i	−1.24756	+	0.294116i
$363$		0			0
$364$	−6.08989	−	12.1980i	−0.319197	−	0.639348i
$365$			3.87097i			0.202616i
$366$	−0.540392	−	2.29219i	−0.0282467	−	0.119815i
$367$	−8.44724			−0.440943			−0.220471	−	0.975393i	$-0.570760\pi$
$367$	−8.44724			−0.440943			−0.220471	+	0.975393i	$0.570760\pi$
$368$	−9.65473	+	12.8410i	−0.503287	+	0.669384i
$369$	10.1515			0.528468
$370$	−8.08579	−	34.2977i	−0.420360	−	1.78305i
$371$		−	3.36972i		−	0.174947i
$372$	−2.50113	−	5.00974i	−0.129678	−	0.259743i
$373$			27.7651i			1.43762i	0.695207	+	0.718810i	$0.255313\pi$
$373$			27.7651i			1.43762i	−0.695207	+	0.718810i	$0.744687\pi$
$374$		0			0
$375$	2.48453			0.128301
$376$	21.4469	+	25.7448i	1.10604	+	1.32769i
$377$	5.22828			0.269270
$378$	11.0589	−	2.60717i	0.568808	−	0.134098i
$379$		−	15.3337i		−	0.787637i	−0.919188	−	0.393818i	$-0.871154\pi$
$379$		−	15.3337i		−	0.787637i	0.919188	−	0.393818i	$-0.128846\pi$
$380$	8.30872	−	4.14817i	0.426229	−	0.212796i
$381$		−	5.35680i		−	0.274437i
$382$	6.58026	+	27.9117i	0.336675	+	1.42809i
$383$	−11.8687			−0.606463			−0.303231	−	0.952917i	$-0.598066\pi$
$383$	−11.8687			−0.606463			−0.303231	+	0.952917i	$0.598066\pi$
$384$	0.304863	+	6.10663i	0.0155575	+	0.311628i
$385$		0			0
$386$	0.837687	+	3.55324i	0.0426371	+	0.180855i
$387$			6.69300i			0.340225i
$388$	−15.4112	+	7.69411i	−0.782385	+	0.390609i
$389$		−	4.54215i		−	0.230296i	−0.993348	−	0.115148i	$-0.963266\pi$
$389$		−	4.54215i		−	0.230296i	0.993348	−	0.115148i	$-0.0367343\pi$
$390$	−5.64803	+	1.33154i	−0.285999	+	0.0674251i
$391$	−27.6772			−1.39970
$392$	0.392025	+	0.470585i	0.0198003	+	0.0237682i
$393$	−6.17662			−0.311569
$394$	28.9665	−	6.82893i	1.45931	−	0.344036i
$395$			12.5400i			0.630958i
$396$		0			0
$397$		−	10.8631i		−	0.545204i	−0.962127	−	0.272602i	$-0.912116\pi$
$397$		−	10.8631i		−	0.545204i	0.962127	−	0.272602i	$-0.0878841\pi$
$398$	2.59100	+	10.9903i	0.129875	+	0.550895i
$399$	2.25300			0.112791
$400$	−8.20951	+	10.9188i	−0.410475	+	0.545942i
$401$	2.32150			0.115930			0.0579650	−	0.998319i	$-0.481539\pi$
$401$	2.32150			0.115930			0.0579650	+	0.998319i	$0.481539\pi$
$402$	−1.82293	−	7.73239i	−0.0909197	−	0.385657i
$403$		−	13.5591i		−	0.675428i
$404$	7.77751	+	15.5783i	0.386946	+	0.775047i
$405$			18.7303i			0.930718i
$406$	7.16136	−	1.68831i	0.355412	−	0.0837895i
$407$		0			0
$408$	−8.09303	+	6.74197i	−0.400664	+	0.333777i
$409$	−25.2296			−1.24752			−0.623762	−	0.781614i	$-0.714397\pi$
$409$	−25.2296			−1.24752			−0.623762	+	0.781614i	$0.714397\pi$
$410$	−14.9691	+	3.52900i	−0.739270	+	0.174285i
$411$		−	0.634154i		−	0.0312805i
$412$	−2.23240	+	1.11454i	−0.109983	+	0.0549093i
$413$		−	0.915532i		−	0.0450504i
$414$	−3.52943	−	14.9709i	−0.173462	−	0.735778i
$415$	−46.3632			−2.27588
$416$	−5.94475	+	13.5600i	−0.291465	+	0.664832i
$417$	−3.91349			−0.191644
$418$		0			0
$419$		−	16.7174i		−	0.816696i	−0.912826	−	0.408348i	$-0.866105\pi$
$419$		−	16.7174i		−	0.816696i	0.912826	−	0.408348i	$-0.133895\pi$
$420$	−7.30633	+	3.64772i	−0.356512	+	0.177990i
$421$		−	9.50223i		−	0.463110i	−0.972822	−	0.231555i	$-0.925619\pi$
$421$		−	9.50223i		−	0.463110i	0.972822	−	0.231555i	$-0.0743814\pi$
$422$	−12.9746	+	3.05879i	−0.631592	+	0.148900i
$423$	−32.0803			−1.55980
$424$	−2.81163	+	2.34225i	−0.136545	+	0.113750i
$425$	−23.5342			−1.14158
$426$	2.58148	−	0.608593i	0.125073	−	0.0294864i
$427$		−	8.02547i		−	0.388379i
$428$	16.7752	+	33.6005i	0.810860	+	1.62414i
$429$		0			0
$430$	−2.32670	−	9.86925i	−0.112204	−	0.475937i
$431$	−31.1582			−1.50084			−0.750419	−	0.660962i	$-0.770148\pi$
$431$	−31.1582			−1.50084			−0.750419	+	0.660962i	$0.770148\pi$
$432$	−9.86228	−	7.41512i	−0.474499	−	0.356760i
$433$	−4.99039			−0.239823			−0.119911	−	0.992785i	$-0.538261\pi$
$433$	−4.99039			−0.239823			−0.119911	+	0.992785i	$0.538261\pi$
$434$	−4.37850	−	18.5724i	−0.210175	−	0.891504i
$435$		−	3.13163i		−	0.150150i
$436$	−10.8793	−	21.7912i	−0.521026	−	1.04361i
$437$		−	6.42890i		−	0.307536i
$438$	0.992645	−	0.234019i	0.0474304	−	0.0111819i
$439$	22.9729			1.09644			0.548219	−	0.836335i	$-0.315306\pi$
$439$	22.9729			1.09644			0.548219	+	0.836335i	$0.315306\pi$
$440$		0			0
$441$	−0.586391			−0.0279234
$442$	−24.8263	+	5.85287i	−1.18086	+	0.278392i
$443$			28.4443i			1.35143i	0.737163	+	0.675714i	$0.236165\pi$
$443$			28.4443i			1.35143i	−0.737163	+	0.675714i	$0.763835\pi$
$444$	−8.30625	+	4.14693i	−0.394197	+	0.196805i
$445$		−	38.0714i		−	1.80476i
$446$	4.70774	+	19.9689i	0.222918	+	0.945557i
$447$	−6.64206			−0.314159
$448$	−3.76396	+	20.4933i	−0.177830	+	0.968216i
$449$	11.3900			0.537529			0.268764	−	0.963206i	$-0.413385\pi$
$449$	11.3900			0.537529			0.268764	+	0.963206i	$0.413385\pi$
$450$	−3.00111	−	12.7299i	−0.141473	−	0.600092i
$451$		0			0
$452$	9.49913	−	4.74248i	0.446801	−	0.223068i
$453$		−	7.81254i		−	0.367065i
$454$	−3.75008	+	0.884094i	−0.176000	+	0.0414926i
$455$	−19.7750			−0.927064
$456$	−1.56603	−	1.87986i	−0.0733362	−	0.0880324i
$457$	13.9263			0.651444			0.325722	−	0.945466i	$-0.394393\pi$
$457$	13.9263			0.651444			0.325722	+	0.945466i	$0.394393\pi$
$458$	19.2177	−	4.53062i	0.897982	−	0.211702i
$459$		−	21.2569i		−	0.992188i
$460$	10.4087	+	20.8485i	0.485309	+	0.972067i
$461$		−	12.8159i		−	0.596895i	−0.954426	−	0.298447i	$-0.903531\pi$
$461$		−	12.8159i		−	0.596895i	0.954426	−	0.298447i	$-0.0964687\pi$
$462$		0			0
$463$	−38.2137			−1.77594			−0.887970	−	0.459902i	$-0.847884\pi$
$463$	−38.2137			−1.77594			−0.887970	+	0.459902i	$0.847884\pi$
$464$	−6.38648	−	4.80178i	−0.296485	−	0.222917i
$465$	−8.12162			−0.376631
$466$	4.03437	+	17.1127i	0.186889	+	0.792731i
$467$			32.6478i			1.51076i	0.655286	+	0.755380i	$0.272548\pi$
$467$			32.6478i			1.51076i	−0.655286	+	0.755380i	$0.727452\pi$
$468$	−6.33174	−	12.6824i	−0.292685	−	0.586244i
$469$		−	27.0728i		−	1.25010i
$470$	47.3044	−	11.1521i	2.18199	−	0.514410i
$471$	−9.59054			−0.441909
$472$	−0.763903	+	0.636376i	−0.0351615	+	0.0292916i
$473$		0			0
$474$	3.21568	−	0.758107i	0.147701	−	0.0348210i
$475$		−	5.46655i		−	0.250823i
$476$	−32.1154	+	16.0338i	−1.47201	+	0.734907i
$477$		−	3.50354i		−	0.160416i
$478$	−5.79380	−	24.5757i	−0.265002	−	1.12407i
$479$	−26.0283			−1.18926			−0.594631	−	0.803999i	$-0.702702\pi$
$479$	−26.0283			−1.18926			−0.594631	+	0.803999i	$0.702702\pi$
$480$	8.12213	+	3.56078i	0.370723	+	0.162526i
$481$	−22.4813			−1.02506
$482$	0.231836	+	0.983384i	0.0105598	+	0.0447919i
$483$			5.65329i			0.257234i
$484$		0			0
$485$			24.9841i			1.13447i
$486$	17.5413	−	4.13541i	0.795688	−	0.187586i
$487$	5.58055			0.252879			0.126439	−	0.991974i	$-0.459645\pi$
$487$	5.58055			0.252879			0.126439	+	0.991974i	$0.459645\pi$
$488$	−6.69630	+	5.57841i	−0.303127	+	0.252523i
$489$	3.11474			0.140854
$490$	0.864670	−	0.203849i	0.0390618	−	0.00920894i
$491$		−	24.4765i		−	1.10461i	−0.833642	−	0.552306i	$-0.813748\pi$
$491$		−	24.4765i		−	1.10461i	0.833642	−	0.552306i	$-0.186252\pi$
$492$	1.80991	+	3.62522i	0.0815970	+	0.163438i
$493$		−	13.7653i		−	0.619956i
$494$	−1.35951	−	5.76667i	−0.0611673	−	0.259455i
$495$		0			0
$496$	−12.4530	+	16.5628i	−0.559157	+	0.743692i
$497$	9.03833			0.405425
$498$	2.80288	+	11.8891i	0.125600	+	0.532762i
$499$			20.9805i			0.939216i	0.882875	+	0.469608i	$0.155605\pi$
$499$			20.9805i			0.939216i	−0.882875	+	0.469608i	$0.844395\pi$
$500$	−4.10709	−	8.22644i	−0.183675	−	0.367898i
$501$			1.27802i			0.0570978i
$502$	2.08111	−	0.490627i	0.0928844	−	0.0218978i
$503$	24.3649			1.08638			0.543189	−	0.839611i	$-0.317217\pi$
$503$	24.3649			1.08638			0.543189	+	0.839611i	$0.317217\pi$
$504$	−12.7682	−	15.3269i	−0.568741	−	0.682714i
$505$	25.2550			1.12383
$506$		0			0
$507$		−	3.32341i		−	0.147598i
$508$	−17.7367	+	8.85513i	−0.786939	+	0.392883i
$509$			30.1621i			1.33691i	0.743751	+	0.668457i	$0.233045\pi$
$509$			30.1621i			1.33691i	−0.743751	+	0.668457i	$0.766955\pi$
$510$	3.50574	+	14.8704i	0.155237	+	0.658472i
$511$	3.47546			0.153745
$512$	19.7155	−	11.1041i	0.871309	−	0.490735i
$513$	4.93758			0.218000
$514$	−5.98029	−	25.3667i	−0.263779	−	1.11888i
$515$			3.61910i			0.159477i
$516$	−2.39014	+	1.19329i	−0.105220	+	0.0525316i
$517$		0			0
$518$	−30.7934	+	7.25965i	−1.35299	+	0.318971i
$519$	1.33874			0.0587643
$520$	13.7453	+	16.4999i	0.602773	+	0.723566i
$521$	−24.4683			−1.07198			−0.535988	−	0.844226i	$-0.680061\pi$
$521$	−24.4683			−1.07198			−0.535988	+	0.844226i	$0.680061\pi$
$522$	7.44576	−	1.75536i	0.325892	−	0.0768300i
$523$		−	16.4779i		−	0.720528i	−0.932850	−	0.360264i	$-0.882687\pi$
$523$		−	16.4779i		−	0.720528i	0.932850	−	0.360264i	$-0.117313\pi$
$524$	10.2103	+	20.4512i	0.446040	+	0.893413i
$525$			4.80705i			0.209797i
$526$	3.66381	+	15.5409i	0.159750	+	0.677615i
$527$	−35.6991			−1.55508
$528$		0			0
$529$	−6.86841			−0.298626
$530$	1.21794	+	5.16618i	0.0529041	+	0.224405i
$531$		−	0.951890i		−	0.0413085i
$532$	−3.72434	−	7.45981i	−0.161471	−	0.323424i
$533$			9.81186i			0.424999i
$534$	−9.76278	+	2.30160i	−0.422477	+	0.0996002i
$535$	54.4721			2.35503
$536$	−22.5890	+	18.8180i	−0.975696	+	0.812813i
$537$	−11.0611			−0.477322
$538$	−24.2015	+	5.70558i	−1.04340	+	0.245985i
$539$		0			0
$540$	−16.0123	+	7.99420i	−0.689059	+	0.344016i
$541$		−	14.6940i		−	0.631744i	−0.948802	−	0.315872i	$-0.897703\pi$
$541$		−	14.6940i		−	0.631744i	0.948802	−	0.315872i	$-0.102297\pi$
$542$	2.11798	+	8.98391i	0.0909752	+	0.385892i
$543$	9.31930			0.399929
$544$	35.7013	+	15.6516i	1.53068	+	0.671058i
$545$	−35.3272			−1.51325
$546$	1.19549	+	5.07096i	0.0511624	+	0.217017i
$547$			22.4034i			0.957902i	0.877842	+	0.478951i	$0.158983\pi$
$547$			22.4034i			0.957902i	−0.877842	+	0.478951i	$0.841017\pi$
$548$	−2.09972	+	1.04830i	−0.0896958	+	0.0447810i
$549$		−	8.34418i		−	0.356121i
$550$		0			0
$551$	3.19741			0.136214
$552$	4.71700	−	3.92954i	0.200769	−	0.167252i
$553$	11.2588			0.478773
$554$	−0.352795	+	0.0831724i	−0.0149888	+	0.00353366i
$555$			13.4658i			0.571592i
$556$	6.46924	+	12.9578i	0.274357	+	0.549533i
$557$			4.02807i			0.170675i	0.996352	+	0.0853375i	$0.0271968\pi$
$557$			4.02807i			0.170675i	−0.996352	+	0.0853375i	$0.972803\pi$
$558$	−4.55238	−	19.3100i	−0.192718	−	0.817456i
$559$	−6.46905			−0.273612
$560$	24.1556	+	18.1618i	1.02076	+	0.767476i
$561$		0			0
$562$	−8.42374	−	35.7312i	−0.355334	−	1.50723i
$563$		−	2.43561i		−	0.102649i	−0.998682	−	0.0513243i	$-0.983656\pi$
$563$		−	2.43561i		−	0.102649i	0.998682	−	0.0513243i	$-0.0163442\pi$
$564$	−5.71957	−	11.4562i	−0.240837	−	0.482394i
$565$		−	15.3997i		−	0.647869i
$566$	12.9544	−	3.05403i	0.544513	−	0.128371i
$567$	16.8166			0.706232
$568$	−6.28244	−	7.54141i	−0.263605	−	0.316431i
$569$	−3.82823			−0.160488			−0.0802439	−	0.996775i	$-0.525570\pi$
$569$	−3.82823			−0.160488			−0.0802439	+	0.996775i	$0.525570\pi$
$570$	−3.45411	+	0.814318i	−0.144677	+	0.0341080i
$571$		−	42.5296i		−	1.77981i	−0.456149	−	0.889903i	$-0.650772\pi$
$571$		−	42.5296i		−	1.77981i	0.456149	−	0.889903i	$-0.349228\pi$
$572$		0			0
$573$		−	10.9586i		−	0.457800i
$574$	3.16844	+	13.4397i	0.132248	+	0.560960i
$575$	13.7168			0.572032
$576$	−3.91343	+	21.3071i	−0.163060	+	0.887796i
$577$	17.8385			0.742626			0.371313	−	0.928508i	$-0.378908\pi$
$577$	17.8385			0.742626			0.371313	+	0.928508i	$0.378908\pi$
$578$	9.89305	+	41.9636i	0.411497	+	1.74546i
$579$		−	1.39506i		−	0.0579766i
$580$	−10.3690	+	5.17677i	−0.430550	+	0.214954i
$581$			41.6262i			1.72695i
$582$	6.40677	−	1.51041i	0.265569	−	0.0626087i
$583$		0			0
$584$	−2.41576	−	2.89986i	−0.0999647	−	0.119997i
$585$	−20.5603			−0.850063
$586$	−2.64205	+	0.622870i	−0.109142	+	0.0257305i
$587$			0.581502i			0.0240011i	0.999928	+	0.0120006i	$0.00381999\pi$
$587$			0.581502i			0.0240011i	−0.999928	+	0.0120006i	$0.996180\pi$
$588$	−0.104547	−	0.209407i	−0.00431145	−	0.00863578i
$589$		−	8.29223i		−	0.341675i
$590$	0.330908	+	1.40362i	0.0136233	+	0.0577861i
$591$	−11.3727			−0.467810
$592$	27.4615	+	20.6474i	1.12866	+	0.848602i
$593$	8.33594			0.342316			0.171158	−	0.985244i	$-0.445249\pi$
$593$	8.33594			0.342316			0.171158	+	0.985244i	$0.445249\pi$
$594$		0			0
$595$			52.0645i			2.13443i
$596$	10.9797	+	21.9923i	0.449748	+	0.900839i
$597$		−	4.31497i		−	0.176600i
$598$	14.4699	−	3.41133i	0.591719	−	0.139500i
$599$	−7.20030			−0.294196			−0.147098	−	0.989122i	$-0.546993\pi$
$599$	−7.20030			−0.294196			−0.147098	+	0.989122i	$0.546993\pi$
$600$	4.01091	−	3.34132i	0.163745	−	0.136409i
$601$	24.0666			0.981696			0.490848	−	0.871245i	$-0.336687\pi$
$601$	24.0666			0.981696			0.490848	+	0.871245i	$0.336687\pi$
$602$	−8.86089	+	2.08898i	−0.361143	+	0.0851405i
$603$		−	28.1479i		−	1.14627i
$604$	−25.8678	+	12.9146i	−1.05255	+	0.525488i
$605$		0			0
$606$	−1.52679	−	6.47621i	−0.0620215	−	0.263078i
$607$	23.5330			0.955176			0.477588	−	0.878584i	$-0.341511\pi$
$607$	23.5330			0.955176			0.477588	+	0.878584i	$0.341511\pi$
$608$	−3.63558	+	8.29275i	−0.147442	+	0.336315i
$609$	−2.81166			−0.113934
$610$	2.90071	+	12.3040i	0.117446	+	0.498174i
$611$		−	31.0069i		−	1.25440i
$612$	−33.3908	+	16.6705i	−1.34974	+	0.673865i
$613$		−	41.1938i		−	1.66380i	−0.554925	−	0.831900i	$-0.687253\pi$
$613$		−	41.1938i		−	1.66380i	0.554925	−	0.831900i	$-0.312747\pi$
$614$	−14.0775	+	3.31881i	−0.568122	+	0.133936i
$615$	5.87709			0.236987
$616$		0			0
$617$	14.6295			0.588961			0.294481	−	0.955657i	$-0.404853\pi$
$617$	14.6295			0.588961			0.294481	+	0.955657i	$0.404853\pi$
$618$	0.928058	−	0.218792i	0.0373320	−	0.00880112i
$619$		−	20.5011i		−	0.824009i	−0.911182	−	0.412005i	$-0.864829\pi$
$619$		−	20.5011i		−	0.824009i	0.911182	−	0.412005i	$-0.135171\pi$
$620$	13.4255	+	26.8912i	0.539183	+	1.07998i
$621$			12.3895i			0.497175i
$622$	−4.85443	−	20.5912i	−0.194645	−	0.825631i
$623$	−34.1816			−1.36946
$624$	3.40014	−	4.52226i	0.136114	−	0.181035i
$625$	−30.4124			−1.21650
$626$	−1.57768	−	6.69210i	−0.0630569	−	0.267470i
$627$		0			0
$628$	15.8538	+	31.7549i	0.632634	+	1.26716i
$629$			59.1898i			2.36005i
$630$	−28.1622	+	6.63931i	−1.12201	+	0.264517i
$631$	−34.0046			−1.35370			−0.676852	−	0.736119i	$-0.736656\pi$
$631$	−34.0046			−1.35370			−0.676852	+	0.736119i	$0.736656\pi$
$632$	−7.82586	−	9.39413i	−0.311296	−	0.373678i
$633$	5.09402			0.202469
$634$	14.7137	−	3.46881i	0.584357	−	0.137764i
$635$			28.7542i			1.14107i
$636$	1.25115	−	0.624642i	0.0496114	−	0.0247687i
$637$		−	0.566770i		−	0.0224562i
$638$		0			0
$639$	9.39727			0.371750
$640$	−1.63644	−	32.7791i	−0.0646859	−	1.29571i
$641$	−28.9334			−1.14280			−0.571400	−	0.820672i	$-0.693599\pi$
$641$	−28.9334			−1.14280			−0.571400	+	0.820672i	$0.693599\pi$
$642$	−3.29311	−	13.9685i	−0.129969	−	0.551291i
$643$		−	16.8449i		−	0.664297i	−0.943227	−	0.332149i	$-0.892226\pi$
$643$		−	16.8449i		−	0.664297i	0.943227	−	0.332149i	$-0.107774\pi$
$644$	18.7184	−	9.34524i	0.737608	−	0.368254i
$645$			3.87482i			0.152571i
$646$	−15.1828	+	3.57938i	−0.597358	+	0.140829i
$647$	27.2087			1.06968			0.534842	−	0.844952i	$-0.320371\pi$
$647$	27.2087			1.06968			0.534842	+	0.844952i	$0.320371\pi$
$648$	−11.6891	−	14.0315i	−0.459189	−	0.551209i
$649$		0			0
$650$	12.3039	−	2.90068i	0.482599	−	0.113774i
$651$			7.29182i			0.285789i
$652$	−5.14886	−	10.3131i	−0.201645	−	0.403892i
$653$		−	17.5375i		−	0.686294i	−0.939282	−	0.343147i	$-0.888507\pi$
$653$		−	17.5375i		−	0.686294i	0.939282	−	0.343147i	$-0.111493\pi$
$654$	2.13570	+	9.05906i	0.0835125	+	0.354237i
$655$	33.1547			1.29546
$656$	9.01145	−	11.9854i	0.351838	−	0.467953i
$657$	3.61348			0.140975
$658$	−10.0127	−	42.4712i	−0.390336	−	1.65570i
$659$			0.0398060i			0.00155062i	1.00000		0.000775311i	$0.000246789\pi$
$659$			0.0398060i			0.00155062i	−1.00000		0.000775311i	$0.999753\pi$
$660$		0			0
$661$		−	33.5882i		−	1.30643i	−0.757173	−	0.653214i	$-0.773420\pi$
$661$		−	33.5882i		−	1.30643i	0.757173	−	0.653214i	$-0.226580\pi$
$662$	−29.3805	+	6.92653i	−1.14190	+	0.269207i
$663$	9.74718			0.378549
$664$	34.7321	−	28.9339i	1.34787	−	1.12285i
$665$	−12.0936			−0.468969
$666$	−32.0163	+	7.54795i	−1.24061	+	0.292477i
$667$			8.02304i			0.310654i
$668$	4.23161	−	2.11265i	0.163726	−	0.0817409i
$669$		−	7.84012i		−	0.303117i
$670$	9.78512	+	41.5058i	0.378032	+	1.60351i
$671$		0			0
$672$	3.19697	−	7.29228i	0.123326	−	0.281306i
$673$	−5.01152			−0.193180			−0.0965899	−	0.995324i	$-0.530794\pi$
$673$	−5.01152			−0.193180			−0.0965899	+	0.995324i	$0.530794\pi$
$674$	2.54299	+	10.7867i	0.0979525	+	0.415488i
$675$			10.5349i			0.405490i
$676$	−11.0040	+	5.49380i	−0.423231	+	0.211300i
$677$			14.9041i			0.572812i	0.958108	+	0.286406i	$0.0924606\pi$
$677$			14.9041i			0.572812i	−0.958108	+	0.286406i	$0.907539\pi$
$678$	−3.94899	+	0.930986i	−0.151660	+	0.0357543i
$679$	22.4315			0.860840
$680$	43.4416	−	36.1894i	1.66591	−	1.38780i
$681$	1.47234			0.0564203
$682$		0			0
$683$			31.7556i			1.21510i	0.794283	+	0.607548i	$0.207847\pi$
$683$			31.7556i			1.21510i	−0.794283	+	0.607548i	$0.792153\pi$
$684$	−3.87225	−	7.75606i	−0.148059	−	0.296560i
$685$			3.40400i			0.130060i
$686$	−6.09932	−	25.8717i	−0.232873	−	0.987785i
$687$	−7.54515			−0.287866
$688$	7.90211	+	5.94133i	0.301265	+	0.226511i
$689$	3.38630			0.129008
$690$	−2.04331	−	8.66717i	−0.0777876	−	0.329954i
$691$			11.5627i			0.439867i	0.975515	+	0.219934i	$0.0705841\pi$
$691$			11.5627i			0.439867i	−0.975515	+	0.219934i	$0.929416\pi$
$692$	−2.21303	−	4.43266i	−0.0841266	−	0.168505i
$693$		0			0
$694$	37.5420	−	8.85064i	1.42507	−	0.335966i
$695$	21.0068			0.796832
$696$	1.95436	+	2.34600i	0.0740796	+	0.0889248i
$697$	25.8331			0.978499
$698$	−10.3157	+	2.43196i	−0.390456	+	0.0920511i
$699$		−	6.71872i		−	0.254125i
$700$	15.9164	−	7.94635i	0.601584	−	0.300344i
$701$		−	10.7576i		−	0.406308i	−0.979147	−	0.203154i	$-0.934881\pi$
$701$		−	10.7576i		−	0.406308i	0.979147	−	0.203154i	$-0.0651192\pi$
$702$	2.62000	+	11.1133i	0.0988855	+	0.419445i
$703$	−13.7487			−0.518541
$704$		0			0
$705$	−18.5724			−0.699479
$706$	5.88421	+	24.9592i	0.221455	+	0.939353i
$707$		−	22.6746i		−	0.852767i
$708$	0.339930	−	0.169712i	0.0127754	−	0.00637815i
$709$		−	28.6318i		−	1.07529i	−0.843171	−	0.537646i	$-0.819314\pi$
$709$		−	28.6318i		−	1.07529i	0.843171	−	0.537646i	$-0.180686\pi$
$710$	−13.8568	+	3.26679i	−0.520038	+	0.122601i
$711$	11.7059			0.439006
$712$	23.7592	+	28.5205i	0.890415	+	1.06885i
$713$	20.8071			0.779233
$714$	13.3511	−	3.14755i	0.499651	−	0.117794i
$715$		0			0
$716$	18.2847	+	36.6240i	0.683331	+	1.36870i
$717$			9.64882i			0.360342i
$718$	−1.56337	−	6.63140i	−0.0583446	−	0.247482i
$719$	3.13553			0.116935			0.0584677	−	0.998289i	$-0.481379\pi$
$719$	3.13553			0.116935			0.0584677	+	0.998289i	$0.481379\pi$
$720$	25.1149	+	18.8831i	0.935978	+	0.703730i
$721$	3.24933			0.121011
$722$	5.33425	+	22.6264i	0.198520	+	0.842068i
$723$		−	0.386092i		−	0.0143589i
$724$	−15.4054	−	30.8568i	−0.572536	−	1.14678i
$725$			6.82207i			0.253365i
$726$		0			0
$727$	43.0374			1.59617			0.798084	−	0.602546i	$-0.205847\pi$
$727$	43.0374			1.59617			0.798084	+	0.602546i	$0.205847\pi$
$728$	14.8140	−	12.3410i	0.549045	−	0.457387i
$729$	12.4833			0.462343
$730$	−5.32830	+	1.25616i	−0.197209	+	0.0464927i
$731$			17.0320i			0.629952i
$732$	2.97980	−	1.48768i	0.110136	−	0.0549861i
$733$			27.4472i			1.01379i	0.862009	+	0.506893i	$0.169206\pi$
$733$			27.4472i			1.01379i	−0.862009	+	0.506893i	$0.830794\pi$
$734$	−2.74121	−	11.6275i	−0.101180	−	0.429177i
$735$	−0.339483			−0.0125220
$736$	−20.8084	−	9.12250i	−0.767009	−	0.336260i
$737$		0			0
$738$	3.29427	+	13.9734i	0.121264	+	0.514367i
$739$		−	40.2106i		−	1.47917i	−0.673063	−	0.739585i	$-0.735022\pi$
$739$		−	40.2106i		−	1.47917i	0.673063	−	0.739585i	$-0.264978\pi$
$740$	44.5861	−	22.2598i	1.63902	−	0.818287i
$741$			2.26409i			0.0831733i
$742$	4.63834	−	1.09350i	0.170279	−	0.0401438i
$743$	33.4306			1.22645			0.613225	−	0.789908i	$-0.289872\pi$
$743$	33.4306			1.22645			0.613225	+	0.789908i	$0.289872\pi$
$744$	6.08416	−	5.06846i	0.223056	−	0.185819i
$745$	35.6531			1.30623
$746$	−38.2180	+	9.01001i	−1.39926	+	0.329880i
$747$			43.2793i			1.58351i
$748$		0			0
$749$		−	48.9066i		−	1.78701i
$750$	0.806253	+	3.41991i	0.0294402	+	0.124877i
$751$	−24.4414			−0.891878			−0.445939	−	0.895063i	$-0.647130\pi$
$751$	−24.4414			−0.891878			−0.445939	+	0.895063i	$0.647130\pi$
$752$	−28.4775	+	37.8757i	−1.03847	+	1.38118i
$753$	−0.817076			−0.0297759
$754$	1.69662	+	7.19661i	0.0617874	+	0.262085i
$755$			41.9360i			1.52621i
$756$	7.17742	+	14.3763i	0.261040	+	0.522860i
$757$		−	50.5921i		−	1.83880i	−0.393323	−	0.919400i	$-0.628675\pi$
$757$		−	50.5921i		−	1.83880i	0.393323	−	0.919400i	$-0.371325\pi$
$758$	21.1064	−	4.97591i	0.766621	−	0.180733i
$759$		0			0
$760$	8.40612	+	10.0907i	0.304922	+	0.366027i
$761$	22.8562			0.828538			0.414269	−	0.910154i	$-0.364037\pi$
$761$	22.8562			0.828538			0.414269	+	0.910154i	$0.364037\pi$
$762$	7.37353	−	1.73833i	0.267115	−	0.0629731i
$763$			31.7177i			1.14826i
$764$	−36.2845	+	18.1152i	−1.31273	+	0.655384i
$765$			54.1321i			1.95715i
$766$	−3.85150	−	16.3370i	−0.139161	−	0.590281i
$767$	0.920039			0.0332207
$768$	−8.30672	+	2.40129i	−0.299743	+	0.0866492i
$769$	10.5112			0.379044			0.189522	−	0.981877i	$-0.439306\pi$
$769$	10.5112			0.379044			0.189522	+	0.981877i	$0.439306\pi$
$770$		0			0
$771$			9.95938i			0.358678i
$772$	−4.61912	+	2.30612i	−0.166246	+	0.0829990i
$773$		−	33.7821i		−	1.21506i	−0.794297	−	0.607529i	$-0.792161\pi$
$773$		−	33.7821i		−	1.21506i	0.794297	−	0.607529i	$-0.207839\pi$
$774$	−9.21278	+	2.17194i	−0.331147	+	0.0780688i
$775$	17.6925			0.635533
$776$	−15.5919	−	18.7164i	−0.559715	−	0.671879i
$777$	12.0900			0.433726
$778$	6.25217	−	1.47397i	0.224151	−	0.0528444i
$779$			6.00055i			0.214992i
$780$	−3.66567	−	7.34229i	−0.131252	−	0.262896i
$781$		0			0
$782$	−8.98151	−	38.0971i	−0.321178	−	1.36235i
$783$	−6.16193			−0.220210
$784$	−0.520535	+	0.692324i	−0.0185905	+	0.0247259i
$785$	51.4799			1.83740
$786$	−2.00437	−	8.50198i	−0.0714934	−	0.303256i
$787$			28.3659i			1.01114i	0.862787	+	0.505568i	$0.168717\pi$
$787$			28.3659i			1.01114i	−0.862787	+	0.505568i	$0.831283\pi$
$788$	18.7998	+	37.6557i	0.669713	+	1.34143i
$789$		−	6.10160i		−	0.217223i
$790$	−17.2611	+	4.06935i	−0.614122	+	0.144781i
$791$	−13.8263			−0.491605
$792$		0			0
$793$	8.06497			0.286395
$794$	14.9528	−	3.52518i	0.530656	−	0.125104i
$795$		−	2.02832i		−	0.0719372i
$796$	−14.2871	+	7.13292i	−0.506395	+	0.252820i
$797$		−	24.1090i		−	0.853983i	−0.904256	−	0.426992i	$-0.859573\pi$
$797$		−	24.1090i		−	0.853983i	0.904256	−	0.426992i	$-0.140427\pi$
$798$	0.731118	+	3.10120i	0.0258813	+	0.109781i
$799$	−81.6363			−2.88809
$800$	−17.6936	−	7.75695i	−0.625564	−	0.274250i
$801$	−35.5390			−1.25571
$802$	0.753347	+	3.19549i	0.0266016	+	0.112837i
$803$		0			0
$804$	10.0519	−	5.01846i	0.354504	−	0.176987i
$805$		−	30.3456i		−	1.06954i
$806$	18.6638	−	4.40006i	0.657406	−	0.154985i
$807$	9.50190			0.334483
$808$	−18.9193	+	15.7609i	−0.665578	+	0.554465i
$809$	−22.6657			−0.796884			−0.398442	−	0.917194i	$-0.630449\pi$
$809$	−22.6657			−0.796884			−0.398442	+	0.917194i	$0.630449\pi$
$810$	−25.7819	+	6.07817i	−0.905885	+	0.213565i
$811$			50.2243i			1.76361i	0.471610	+	0.881807i	$0.343673\pi$
$811$			50.2243i			1.76361i	−0.471610	+	0.881807i	$0.656327\pi$
$812$	4.64785	+	9.30959i	0.163108	+	0.326703i
$813$		−	3.52723i		−	0.123705i
$814$		0			0
$815$	−16.7193			−0.585650
$816$	−11.9064	−	8.95205i	−0.416809	−	0.313384i
$817$	−3.95622			−0.138411
$818$	−8.18724	−	34.7280i	−0.286260	−	1.21424i
$819$			18.4596i			0.645031i
$820$	−9.71520	−	19.4594i	−0.339269	−	0.679552i
$821$		−	22.8916i		−	0.798924i	−0.916750	−	0.399462i	$-0.869197\pi$
$821$		−	22.8916i		−	0.798924i	0.916750	−	0.399462i	$-0.130803\pi$
$822$	0.872900	−	0.205789i	0.0304459	−	0.00717771i
$823$	25.0958			0.874783			0.437392	−	0.899271i	$-0.355902\pi$
$823$	25.0958			0.874783			0.437392	+	0.899271i	$0.355902\pi$
$824$	−2.25857	−	2.71118i	−0.0786811	−	0.0944484i
$825$		0			0
$826$	1.26021	−	0.297098i	0.0438483	−	0.0103374i
$827$			13.2175i			0.459617i	0.973236	+	0.229808i	$0.0738099\pi$
$827$			13.2175i			0.459617i	−0.973236	+	0.229808i	$0.926190\pi$
$828$	19.4617	−	9.71636i	0.676343	−	0.337667i
$829$			30.0150i			1.04246i	0.853415	+	0.521231i	$0.174527\pi$
$829$			30.0150i			1.04246i	−0.853415	+	0.521231i	$0.825473\pi$
$830$	−15.0453	−	63.8179i	−0.522229	−	2.21515i
$831$	0.138513			0.00480495
$832$	−20.5941	−	3.78249i	−0.713973	−	0.131134i
$833$	−1.49222			−0.0517023
$834$	−1.26996	−	5.38684i	−0.0439752	−	0.186531i
$835$		−	6.86015i		−	0.237405i
$836$		0			0
$837$			15.9805i			0.552366i
$838$	23.0111	−	5.42493i	0.794905	−	0.187401i
$839$	−2.71509			−0.0937355			−0.0468677	−	0.998901i	$-0.514924\pi$
$839$	−2.71509			−0.0937355			−0.0468677	+	0.998901i	$0.514924\pi$
$840$	−7.39197	−	8.87329i	−0.255047	−	0.306158i
$841$	25.0097			0.862405
$842$	13.0796	−	3.08356i	0.450753	−	0.106266i
$843$			14.0286i			0.483172i
$844$	−8.42073	−	16.8666i	−0.289853	−	0.580573i
$845$			17.8393i			0.613692i
$846$	−10.4103	−	44.1579i	−0.357915	−	1.51818i
$847$		0			0
$848$	−4.13646	−	3.11006i	−0.142047	−	0.106800i
$849$	−5.08609			−0.174554
$850$	−7.63706	−	32.3943i	−0.261949	−	1.11112i
$851$		−	34.4986i		−	1.18260i
$852$	1.67543	+	3.35586i	0.0573993	+	0.114970i
$853$			14.9555i			0.512066i	0.966668	+	0.256033i	$0.0824156\pi$
$853$			14.9555i			0.512066i	−0.966668	+	0.256033i	$0.917584\pi$
$854$	11.0469	−	2.60434i	0.378017	−	0.0891185i
$855$	−12.5739			−0.430017
$856$	−40.8067	+	33.9944i	−1.39474	+	1.16190i
$857$	−13.6354			−0.465776			−0.232888	−	0.972504i	$-0.574818\pi$
$857$	−13.6354			−0.465776			−0.232888	+	0.972504i	$0.574818\pi$
$858$		0			0
$859$			5.59465i			0.190887i	0.995435	+	0.0954434i	$0.0304269\pi$
$859$			5.59465i			0.190887i	−0.995435	+	0.0954434i	$0.969573\pi$
$860$	12.8298	−	6.40532i	0.437492	−	0.218420i
$861$		−	5.27662i		−	0.179827i
$862$	−10.1111	−	42.8886i	−0.344386	−	1.46079i
$863$	−4.45988			−0.151816			−0.0759081	−	0.997115i	$-0.524186\pi$
$863$	−4.45988			−0.151816			−0.0759081	+	0.997115i	$0.524186\pi$
$864$	7.00635	−	15.9815i	0.238361	−	0.543701i
$865$	−7.18608			−0.244334
$866$	−1.61943	−	6.86917i	−0.0550304	−	0.233424i
$867$		−	16.4756i		−	0.559540i
$868$	24.1437	−	12.0538i	0.819490	−	0.409134i
$869$		0			0
$870$	4.31062	−	1.01624i	0.146144	−	0.0344538i
$871$	27.2060			0.921841
$872$	26.4647	−	22.0466i	0.896207	−	0.746593i
$873$	23.3223			0.789339
$874$	8.84924	−	2.08623i	0.299330	−	0.0705679i
$875$			11.9738i			0.404789i
$876$	0.644245	+	1.29041i	0.0217670	+	0.0435990i
$877$		−	37.1599i		−	1.25480i	−0.778697	−	0.627400i	$-0.784119\pi$
$877$		−	37.1599i		−	1.25480i	0.778697	−	0.627400i	$-0.215881\pi$
$878$	7.45492	+	31.6217i	0.251591	+	1.06718i
$879$	1.03731			0.0349876
$880$		0			0
$881$	−30.4894			−1.02721			−0.513607	−	0.858025i	$-0.671691\pi$
$881$	−30.4894			−1.02721			−0.513607	+	0.858025i	$0.671691\pi$
$882$	−0.190289	−	0.807155i	−0.00640737	−	0.0271783i
$883$			31.0427i			1.04467i	0.852740	+	0.522335i	$0.174939\pi$
$883$			31.0427i			1.04467i	−0.852740	+	0.522335i	$0.825061\pi$
$884$	−16.1127	−	32.2735i	−0.541928	−	1.08548i
$885$		−	0.551083i		−	0.0185245i
$886$	−39.1530	+	9.23043i	−1.31537	+	0.310102i
$887$	33.4530			1.12324			0.561620	−	0.827395i	$-0.310178\pi$
$887$	33.4530			1.12324			0.561620	+	0.827395i	$0.310178\pi$
$888$	−8.40362	−	10.0877i	−0.282007	−	0.338520i
$889$	25.8163			0.865851
$890$	52.4045	−	12.3545i	1.75660	−	0.414124i
$891$		0			0
$892$	−25.9591	+	12.9602i	−0.869176	+	0.433940i
$893$		−	18.9626i		−	0.634559i
$894$	−2.15541	−	9.14266i	−0.0720877	−	0.305776i
$895$	59.3736			1.98464
$896$	−29.4300	+	1.46924i	−0.983187	+	0.0490839i
$897$	−5.68112			−0.189687
$898$	3.69617	+	15.6781i	0.123343	+	0.523186i
$899$			10.3484i			0.345139i
$900$	16.5485	−	8.26192i	0.551617	−	0.275397i
$901$		−	8.91562i		−	0.297023i
$902$		0			0
$903$	3.47892			0.115771
$904$	9.61048	+	11.5364i	0.319640	+	0.383694i
$905$	−50.0240			−1.66285
$906$	10.7538	−	2.53524i	0.357271	−	0.0842277i
$907$			35.1153i			1.16598i	0.812478	+	0.582992i	$0.198118\pi$
$907$			35.1153i			1.16598i	−0.812478	+	0.582992i	$0.801882\pi$
$908$	−2.43387	−	4.87501i	−0.0807709	−	0.161783i
$909$		−	23.5751i		−	0.781936i
$910$	−6.41715	−	27.2198i	−0.212727	−	0.902328i
$911$	−21.2878			−0.705295			−0.352647	−	0.935756i	$-0.614718\pi$
$911$	−21.2878			−0.705295			−0.352647	+	0.935756i	$0.614718\pi$
$912$	2.07939	−	2.76564i	0.0688556	−	0.0915795i
$913$		0			0
$914$	4.51921	+	19.1692i	0.149482	+	0.634062i
$915$		−	4.83074i		−	0.159699i
$916$	12.4726	+	24.9825i	0.412107	+	0.825444i
$917$		−	29.7673i		−	0.983001i
$918$	29.2597	−	6.89806i	0.965714	−	0.227670i
$919$	−4.39758			−0.145063			−0.0725314	−	0.997366i	$-0.523108\pi$
$919$	−4.39758			−0.145063			−0.0725314	+	0.997366i	$0.523108\pi$
$920$	−25.3198	+	21.0929i	−0.834770	+	0.695413i
$921$	5.52705			0.182122
$922$	17.6408	−	4.15887i	0.580968	−	0.136965i
$923$			9.08282i			0.298965i
$924$		0			0
$925$		−	29.3345i		−	0.964513i
$926$	−12.4007	−	52.6003i	−0.407512	−	1.72855i
$927$	3.37837			0.110960
$928$	4.53708	−	10.3491i	0.148937	−	0.339725i
$929$	19.7905			0.649305			0.324652	−	0.945833i	$-0.394753\pi$
$929$	19.7905			0.649305			0.324652	+	0.945833i	$0.394753\pi$
$930$	−2.63554	−	11.1792i	−0.0864227	−	0.366582i
$931$		−	0.346614i		−	0.0113598i
$932$	−22.2461	+	11.1065i	−0.728695	+	0.363804i
$933$			8.08442i			0.264672i
$934$	−44.9390	+	10.5945i	−1.47045	+	0.346663i
$935$		0			0
$936$	15.4023	−	12.8311i	0.503441	−	0.419396i
$937$	46.4538			1.51758			0.758789	−	0.651336i	$-0.225791\pi$
$937$	46.4538			1.51758			0.758789	+	0.651336i	$0.225791\pi$
$938$	37.2651	−	8.78536i	1.21675	−	0.286852i
$939$			2.62742i			0.0857427i
$940$	30.7014	+	61.4945i	1.00137	+	2.00573i
$941$			47.1462i			1.53692i	0.639897	+	0.768460i	$0.278977\pi$
$941$			47.1462i			1.53692i	−0.639897	+	0.768460i	$0.721023\pi$
$942$	−3.11222	−	13.2012i	−0.101402	−	0.430118i
$943$	−15.0568			−0.490316
$944$	−1.12385	−	0.844986i	−0.0365782	−	0.0275019i
$945$	23.3063			0.758155
$946$		0			0
$947$		−	5.18884i		−	0.168615i	−0.996440	−	0.0843074i	$-0.973132\pi$
$947$		−	5.18884i		−	0.168615i	0.996440	−	0.0843074i	$-0.0268678\pi$
$948$	2.08704	+	4.18031i	0.0677838	+	0.135770i
$949$			3.49257i			0.113374i
$950$	7.52459	−	1.77395i	0.244130	−	0.0575544i
$951$	−5.77684			−0.187327
$952$	−32.4919	−	39.0031i	−1.05307	−	1.26410i
$953$	−17.4648			−0.565739			−0.282869	−	0.959158i	$-0.591286\pi$
$953$	−17.4648			−0.565739			−0.282869	+	0.959158i	$0.591286\pi$
$954$	4.82255	−	1.13693i	0.156136	−	0.0368095i
$955$			58.8232i			1.90347i
$956$	31.9478	−	15.9501i	1.03327	−	0.515863i
$957$		0			0
$958$	−8.44641	−	35.8274i	−0.272891	−	1.15753i
$959$	3.05621			0.0986902
$960$	−2.26563	+	12.3354i	−0.0731228	+	0.398125i
$961$	−4.16221			−0.134265
$962$	−7.29538	−	30.9450i	−0.235213	−	0.997708i
$963$		−	50.8488i		−	1.63858i
$964$	−1.27837	+	0.638234i	−0.0411737	+	0.0205561i
$965$			7.48837i			0.241059i
$966$	−7.78163	+	1.83454i	−0.250370	+	0.0590255i
$967$	22.0455			0.708936			0.354468	−	0.935068i	$-0.384662\pi$
$967$	22.0455			0.708936			0.354468	+	0.935068i	$0.384662\pi$
$968$		0			0
$969$	5.96100			0.191495
$970$	−34.3901	+	8.10758i	−1.10420	+	0.260319i
$971$		−	25.7769i		−	0.827221i	−0.910454	−	0.413610i	$-0.864268\pi$
$971$		−	25.7769i		−	0.827221i	0.910454	−	0.413610i	$-0.135732\pi$
$972$	11.3846	+	22.8032i	0.365161	+	0.731413i
$973$		−	18.8605i		−	0.604639i
$974$	1.81094	+	7.68151i	0.0580262	+	0.246131i
$975$	−4.83071			−0.154706
$976$	−9.85157	−	7.40707i	−0.315341	−	0.237094i
$977$	29.3226			0.938115			0.469057	−	0.883168i	$-0.344594\pi$
$977$	29.3226			0.938115			0.469057	+	0.883168i	$0.344594\pi$
$978$	1.01076	+	4.28738i	0.0323206	+	0.137095i
$979$		0			0
$980$	0.561186	+	1.12405i	0.0179264	+	0.0359064i
$981$			32.9773i			1.05288i
$982$	33.6915	−	7.94286i	1.07514	−	0.253467i
$983$	−28.7938			−0.918379			−0.459190	−	0.888338i	$-0.651860\pi$
$983$	−28.7938			−0.918379			−0.459190	+	0.888338i	$0.651860\pi$
$984$	−4.40271	+	3.66772i	−0.140353	+	0.116923i
$985$	61.0461			1.94509
$986$	18.9476	−	4.46695i	0.603414	−	0.142257i
$987$			16.6749i			0.530767i
$988$	7.49653	−	3.74267i	0.238496	−	0.119070i
$989$		−	9.92707i		−	0.315662i
$990$		0			0
$991$	−50.7188			−1.61113			−0.805567	−	0.592504i	$-0.798139\pi$
$991$	−50.7188			−1.61113			−0.805567	+	0.592504i	$0.798139\pi$
$992$	−26.8395	−	11.7665i	−0.852154	−	0.373588i
$993$	11.5352			0.366060
$994$	2.93302	+	12.4411i	0.0930297	+	0.394607i
$995$			23.1618i			0.734280i
$996$	−15.4555	+	7.71622i	−0.489726	+	0.244498i
$997$			13.2861i			0.420775i	0.977618	+	0.210387i	$0.0674726\pi$
$997$			13.2861i			0.420775i	−0.977618	+	0.210387i	$0.932527\pi$
$998$	−28.8792	+	6.80836i	−0.914155	+	0.215515i
$999$	26.4960			0.838295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.c.h.485.12		20
4.3	odd	2		3872.2.c.h.1937.12		20
8.3	odd	2		3872.2.c.h.1937.9		20
8.5	even	2	inner	968.2.c.h.485.11		20
11.2	odd	10		968.2.o.d.565.5		40
11.3	even	5		88.2.o.a.53.10	yes	40
11.4	even	5		88.2.o.a.5.3	✓	40
11.5	even	5		968.2.o.j.245.2		40
11.6	odd	10		968.2.o.d.245.9		40
11.7	odd	10		968.2.o.i.269.8		40
11.8	odd	10		968.2.o.i.493.1		40
11.9	even	5		968.2.o.j.565.6		40
11.10	odd	2		968.2.c.i.485.9		20
33.14	odd	10		792.2.br.b.757.1		40
33.26	odd	10		792.2.br.b.181.8		40
44.3	odd	10		352.2.w.a.273.4		40
44.15	odd	10		352.2.w.a.49.7		40
44.43	even	2		3872.2.c.i.1937.12		20
88.3	odd	10		352.2.w.a.273.7		40
88.5	even	10		968.2.o.j.245.6		40
88.13	odd	10		968.2.o.d.565.9		40
88.21	odd	2		968.2.c.i.485.10		20
88.29	odd	10		968.2.o.i.269.1		40
88.37	even	10		88.2.o.a.5.10	yes	40
88.43	even	2		3872.2.c.i.1937.9		20
88.53	even	10		968.2.o.j.565.2		40
88.59	odd	10		352.2.w.a.49.4		40
88.61	odd	10		968.2.o.d.245.5		40
88.69	even	10		88.2.o.a.53.3	yes	40
88.85	odd	10		968.2.o.i.493.8		40
264.125	odd	10		792.2.br.b.181.1		40
264.245	odd	10		792.2.br.b.757.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.5.3	✓	40	11.4	even	5
88.2.o.a.5.10	yes	40	88.37	even	10
88.2.o.a.53.3	yes	40	88.69	even	10
88.2.o.a.53.10	yes	40	11.3	even	5
352.2.w.a.49.4		40	88.59	odd	10
352.2.w.a.49.7		40	44.15	odd	10
352.2.w.a.273.4		40	44.3	odd	10
352.2.w.a.273.7		40	88.3	odd	10
792.2.br.b.181.1		40	264.125	odd	10
792.2.br.b.181.8		40	33.26	odd	10
792.2.br.b.757.1		40	33.14	odd	10
792.2.br.b.757.8		40	264.245	odd	10
968.2.c.h.485.11		20	8.5	even	2	inner
968.2.c.h.485.12		20	1.1	even	1	trivial
968.2.c.i.485.9		20	11.10	odd	2
968.2.c.i.485.10		20	88.21	odd	2
968.2.o.d.245.5		40	88.61	odd	10
968.2.o.d.245.9		40	11.6	odd	10
968.2.o.d.565.5		40	11.2	odd	10
968.2.o.d.565.9		40	88.13	odd	10
968.2.o.i.269.1		40	88.29	odd	10
968.2.o.i.269.8		40	11.7	odd	10
968.2.o.i.493.1		40	11.8	odd	10
968.2.o.i.493.8		40	88.85	odd	10
968.2.o.j.245.2		40	11.5	even	5
968.2.o.j.245.6		40	88.5	even	10
968.2.o.j.565.2		40	88.53	even	10
968.2.o.j.565.6		40	11.9	even	5
3872.2.c.h.1937.9		20	8.3	odd	2
3872.2.c.h.1937.12		20	4.3	odd	2
3872.2.c.i.1937.9		20	88.43	even	2
3872.2.c.i.1937.12		20	44.43	even	2

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.324509 + 1.37648i) q^{2} -0.540427i q^{3} +(-1.78939 + 0.893360i) q^{4} +2.90090i q^{5} +(0.743887 - 0.175374i) q^{6} +2.60451 q^{7} +(-1.81036 - 2.17315i) q^{8} +2.70794 q^{9} +(-3.99302 + 0.941367i) q^{10} +(0.482796 + 0.967034i) q^{12} +2.61733i q^{13} +(0.845186 + 3.58505i) q^{14} +1.56772 q^{15} +(2.40382 - 3.19713i) q^{16} +6.89102 q^{17} +(0.878751 + 3.72742i) q^{18} +1.60066i q^{19} +(-2.59154 - 5.19083i) q^{20} -1.40755i q^{21} -4.01642 q^{23} +(-1.17443 + 0.978369i) q^{24} -3.41520 q^{25} +(-3.60270 + 0.849346i) q^{26} -3.08473i q^{27} +(-4.66047 + 2.32676i) q^{28} -1.99756i q^{29} +(0.508740 + 2.15794i) q^{30} -5.18052 q^{31} +(5.18085 + 2.27130i) q^{32} +(2.23620 + 9.48535i) q^{34} +7.55540i q^{35} +(-4.84555 + 2.41916i) q^{36} +8.58941i q^{37} +(-2.20327 + 0.519427i) q^{38} +1.41447 q^{39} +(6.30408 - 5.25167i) q^{40} +3.74881 q^{41} +(1.93746 - 0.456761i) q^{42} +2.47162i q^{43} +7.85545i q^{45} +(-1.30336 - 5.52851i) q^{46} -11.8468 q^{47} +(-1.72782 - 1.29909i) q^{48} -0.216545 q^{49} +(-1.10826 - 4.70095i) q^{50} -3.72410i q^{51} +(-2.33821 - 4.68341i) q^{52} -1.29380i q^{53} +(4.24606 - 1.00102i) q^{54} +(-4.71510 - 5.65999i) q^{56} +0.865038 q^{57} +(2.74960 - 0.648227i) q^{58} -0.351518i q^{59} +(-2.80526 + 1.40054i) q^{60} -3.08138i q^{61} +(-1.68113 - 7.13088i) q^{62} +7.05284 q^{63} +(-1.44517 + 7.86838i) q^{64} -7.59259 q^{65} -10.3946i q^{67} +(-12.3307 + 6.15616i) q^{68} +2.17058i q^{69} +(-10.3999 + 2.45180i) q^{70} +3.47027 q^{71} +(-4.90235 - 5.88476i) q^{72} +1.33440 q^{73} +(-11.8231 + 2.78734i) q^{74} +1.84566i q^{75} +(-1.42996 - 2.86419i) q^{76} +(0.459010 + 1.94699i) q^{78} +4.32281 q^{79} +(9.27455 + 6.97322i) q^{80} +6.45675 q^{81} +(1.21652 + 5.16015i) q^{82} +15.9824i q^{83} +(1.25744 + 2.51865i) q^{84} +19.9901i q^{85} +(-3.40214 + 0.802064i) q^{86} -1.07954 q^{87} -13.1240 q^{89} +(-10.8129 + 2.54916i) q^{90} +6.81685i q^{91} +(7.18692 - 3.58810i) q^{92} +2.79969i q^{93} +(-3.84438 - 16.3068i) q^{94} -4.64333 q^{95} +(1.22747 - 2.79987i) q^{96} +8.61256 q^{97} +(-0.0702709 - 0.298070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{10} - 3 q^{12} - 4 q^{14} - 4 q^{15} + 10 q^{16} + 2 q^{17} - 5 q^{18} - 16 q^{20} - 4 q^{23} + 15 q^{24} - 2 q^{25} + 30 q^{26} - 14 q^{28} + 16 q^{30}+ \cdots - 72 q^{98}+O(q^{100}) \) 20 * q + 2 * q^4 - q^6 + 10 * q^7 - 10 * q^9 - 10 * q^10 - 3 * q^12 - 4 * q^14 - 4 * q^15 + 10 * q^16 + 2 * q^17 - 5 * q^18 - 16 * q^20 - 4 * q^23 + 15 * q^24 - 2 * q^25 + 30 * q^26 - 14 * q^28 + 16 * q^30 + 2 * q^31 + 10 * q^32 + 5 * q^34 + 9 * q^36 + 21 * q^38 + 28 * q^39 + 10 * q^40 - 2 * q^41 - 20 * q^42 + 24 * q^46 + 2 * q^47 - 41 * q^48 - 2 * q^49 - 22 * q^50 - 20 * q^52 + 54 * q^54 - 16 * q^56 + 22 * q^57 + 12 * q^58 - 48 * q^60 + 4 * q^62 - 30 * q^63 + 38 * q^64 - 18 * q^65 - 21 * q^68 - 44 * q^70 - 34 * q^71 + 57 * q^72 + 2 * q^73 - 28 * q^74 - 67 * q^76 - 6 * q^78 - 58 * q^79 + 28 * q^80 - 12 * q^81 - 23 * q^82 - 44 * q^84 + 25 * q^86 + 34 * q^87 - 8 * q^89 - 42 * q^90 + 68 * q^92 + 60 * q^94 - 92 * q^95 + 35 * q^96 + 10 * q^97 - 72 * q^98

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