LMFDB - Embedded newform 189.2.s.b.89.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(17,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.s (of order $6$, degree $2$, not 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.3
Root			$-0.539982 - 0.935277i$ of defining polynomial
Character	$\chi$	$=$	189.89
Dual form			189.2.s.b.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.254498 - 0.146935i) q^{2} +(-0.956820 + 1.65726i) q^{4} -3.06027 q^{5} +(-1.22581 + 2.34465i) q^{7} +1.15010i q^{8} +O(q^{10})$	\(q+(0.254498 - 0.146935i) q^{2} +(-0.956820 + 1.65726i) q^{4} -3.06027 q^{5} +(-1.22581 + 2.34465i) q^{7} +1.15010i q^{8} +(-0.778834 + 0.449660i) q^{10} +3.89647i q^{11} +(2.02935 - 1.17164i) q^{13} +(0.0325450 + 0.776824i) q^{14} +(-1.74465 - 3.02182i) q^{16} +(-1.68263 - 2.91440i) q^{17} +(2.20696 + 1.27419i) q^{19} +(2.92813 - 5.07167i) q^{20} +(0.572527 + 0.991647i) q^{22} +2.98075i q^{23} +4.36525 q^{25} +(0.344311 - 0.596363i) q^{26} +(-2.71283 - 4.27489i) q^{28} +(3.67241 + 2.12027i) q^{29} +(-0.409400 - 0.236367i) q^{31} +(-2.88005 - 1.66280i) q^{32} +(-0.856452 - 0.494473i) q^{34} +(3.75130 - 7.17527i) q^{35} +(-3.89395 + 6.74451i) q^{37} +0.748891 q^{38} -3.51962i q^{40} +(3.12737 + 5.41676i) q^{41} +(2.06191 - 3.57133i) q^{43} +(-6.45748 - 3.72823i) q^{44} +(0.437976 + 0.758597i) q^{46} +(2.02694 + 3.51076i) q^{47} +(-3.99479 - 5.74818i) q^{49} +(1.11095 - 0.641408i) q^{50} +4.48421i q^{52} +(4.99439 - 2.88351i) q^{53} -11.9243i q^{55} +(-2.69658 - 1.40980i) q^{56} +1.24616 q^{58} +(2.34352 - 4.05910i) q^{59} +(-1.38580 + 0.800092i) q^{61} -0.138922 q^{62} +6.00131 q^{64} +(-6.21035 + 3.58555i) q^{65} +(-0.787831 + 1.36456i) q^{67} +6.43989 q^{68} +(-0.0995964 - 2.37729i) q^{70} +13.6132i q^{71} +(-0.856452 + 0.494473i) q^{73} +2.28862i q^{74} +(-4.22333 + 2.43834i) q^{76} +(-9.13588 - 4.77633i) q^{77} +(4.63908 + 8.03512i) q^{79} +(5.33910 + 9.24760i) q^{80} +(1.59182 + 0.919038i) q^{82} +(5.49361 - 9.51520i) q^{83} +(5.14930 + 8.91884i) q^{85} -1.21186i q^{86} -4.48133 q^{88} +(-2.15849 + 3.73861i) q^{89} +(0.259511 + 6.19433i) q^{91} +(-4.93989 - 2.85205i) q^{92} +(1.03171 + 0.595655i) q^{94} +(-6.75390 - 3.89937i) q^{95} +(-4.98797 - 2.87980i) q^{97} +(-1.86128 - 0.875930i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} + 3 q^{7}+O(q^{10}) $ 10 * q + 4 * q^4 + 3 * q^7	$ 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} + 6 q^{13} + 6 q^{14} - 6 q^{16} + 12 q^{17} + 3 q^{19} + 3 q^{20} + 5 q^{22} - 14 q^{25} - 3 q^{26} + 2 q^{28} + 15 q^{29} - 9 q^{31} - 48 q^{32} + 3 q^{34} + 15 q^{35} + 6 q^{37} - 36 q^{38} + 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} - 15 q^{47} - 23 q^{49} - 3 q^{50} + 9 q^{53} + 51 q^{56} - 16 q^{58} + 18 q^{59} + 12 q^{61} - 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} + 54 q^{68} + 9 q^{70} + 3 q^{73} + 9 q^{76} - 45 q^{77} + 20 q^{79} + 30 q^{80} + 9 q^{82} + 15 q^{83} + 18 q^{85} + 16 q^{88} - 24 q^{89} - 24 q^{91} - 39 q^{92} - 3 q^{94} + 6 q^{97} - 45 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 + 3 * q^7 - 15 * q^10 + 6 * q^13 + 6 * q^14 - 6 * q^16 + 12 * q^17 + 3 * q^19 + 3 * q^20 + 5 * q^22 - 14 * q^25 - 3 * q^26 + 2 * q^28 + 15 * q^29 - 9 * q^31 - 48 * q^32 + 3 * q^34 + 15 * q^35 + 6 * q^37 - 36 * q^38 + 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 - 15 * q^47 - 23 * q^49 - 3 * q^50 + 9 * q^53 + 51 * q^56 - 16 * q^58 + 18 * q^59 + 12 * q^61 - 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 + 54 * q^68 + 9 * q^70 + 3 * q^73 + 9 * q^76 - 45 * q^77 + 20 * q^79 + 30 * q^80 + 9 * q^82 + 15 * q^83 + 18 * q^85 + 16 * q^88 - 24 * q^89 - 24 * q^91 - 39 * q^92 - 3 * q^94 + 6 * q^97 - 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.254498	−	0.146935i	0.179958	−	0.103899i	−0.407315	−	0.913288i	$-0.633535\pi$
$2$	0.254498	−	0.146935i	0.179958	−	0.103899i	0.587273	+	0.809389i	$0.300202\pi$
$3$		0			0
$3$		0			0
$4$	−0.956820	+	1.65726i	−0.478410	+	0.828631i
$5$	−3.06027			−1.36859			−0.684297	−	0.729203i	$-0.739891\pi$
$5$	−3.06027			−1.36859			−0.684297	+	0.729203i	$0.739891\pi$
$6$		0			0
$7$	−1.22581	+	2.34465i	−0.463312	+	0.886195i
$7$	−1.22581	+	2.34465i	−0.463312	+	0.886195i
$8$			1.15010i			0.406622i
$9$		0			0
$10$	−0.778834	+	0.449660i	−0.246289	+	0.142195i
$11$			3.89647i			1.17483i	0.809285	+	0.587416i	$0.199855\pi$
$11$			3.89647i			1.17483i	−0.809285	+	0.587416i	$0.800145\pi$
$12$		0			0
$13$	2.02935	−	1.17164i	0.562840	−	0.324956i	−0.191445	−	0.981503i	$-0.561317\pi$
$13$	2.02935	−	1.17164i	0.562840	−	0.324956i	0.754285	+	0.656548i	$0.227984\pi$
$14$	0.0325450	+	0.776824i	0.00869801	+	0.207615i
$15$		0			0
$16$	−1.74465	−	3.02182i	−0.436163	−	0.755456i
$17$	−1.68263	−	2.91440i	−0.408097	−	0.706845i	0.586579	−	0.809892i	$-0.300474\pi$
$17$	−1.68263	−	2.91440i	−0.408097	−	0.706845i	−0.994677	+	0.103047i	$0.967141\pi$
$18$		0			0
$19$	2.20696	+	1.27419i	0.506312	+	0.292319i	0.731316	−	0.682038i	$-0.238906\pi$
$19$	2.20696	+	1.27419i	0.506312	+	0.292319i	−0.225004	+	0.974358i	$0.572240\pi$
$20$	2.92813	−	5.07167i	0.654750	−	1.13406i
$21$		0			0
$22$	0.572527	+	0.991647i	0.122063	+	0.211420i
$23$			2.98075i			0.621530i	0.950487	+	0.310765i	$0.100585\pi$
$23$			2.98075i			0.621530i	−0.950487	+	0.310765i	$0.899415\pi$
$24$		0			0
$25$	4.36525			0.873051
$26$	0.344311	−	0.596363i	0.0675249	−	0.116956i
$27$		0			0
$28$	−2.71283	−	4.27489i	−0.512676	−	0.807879i
$29$	3.67241	+	2.12027i	0.681949	+	0.393724i	0.800589	−	0.599214i	$-0.204520\pi$
$29$	3.67241	+	2.12027i	0.681949	+	0.393724i	−0.118640	+	0.992937i	$0.537853\pi$
$30$		0			0
$31$	−0.409400	−	0.236367i	−0.0735305	−	0.0424528i	0.462784	−	0.886471i	$-0.346851\pi$
$31$	−0.409400	−	0.236367i	−0.0735305	−	0.0424528i	−0.536314	+	0.844018i	$0.680184\pi$
$32$	−2.88005	−	1.66280i	−0.509126	−	0.293944i
$33$		0			0
$34$	−0.856452	−	0.494473i	−0.146880	−	0.0848014i
$35$	3.75130	−	7.17527i	0.634086	−	1.21284i
$36$		0			0
$37$	−3.89395	+	6.74451i	−0.640161	+	1.10879i	0.345236	+	0.938516i	$0.387799\pi$
$37$	−3.89395	+	6.74451i	−0.640161	+	1.10879i	−0.985397	+	0.170275i	$0.945534\pi$
$38$	0.748891			0.121486
$39$		0			0
$40$		−	3.51962i		−	0.556500i
$41$	3.12737	+	5.41676i	0.488413	+	0.845956i	0.999911	−	0.0133282i	$-0.00424262\pi$
$41$	3.12737	+	5.41676i	0.488413	+	0.845956i	−0.511498	+	0.859284i	$0.670909\pi$
$42$		0			0
$43$	2.06191	−	3.57133i	0.314438	−	0.544623i	−0.664880	−	0.746950i	$-0.731517\pi$
$43$	2.06191	−	3.57133i	0.314438	−	0.544623i	0.979318	+	0.202328i	$0.0648506\pi$
$44$	−6.45748	−	3.72823i	−0.973501	−	0.562051i
$45$		0			0
$46$	0.437976	+	0.758597i	0.0645761	+	0.111849i
$47$	2.02694	+	3.51076i	0.295659	+	0.512097i	0.975138	−	0.221598i	$-0.0711274\pi$
$47$	2.02694	+	3.51076i	0.295659	+	0.512097i	−0.679479	+	0.733695i	$0.737794\pi$
$48$		0			0
$49$	−3.99479	−	5.74818i	−0.570685	−	0.821169i
$50$	1.11095	−	0.641408i	0.157112	−	0.0907087i
$51$		0			0
$52$			4.48421i			0.621848i
$53$	4.99439	−	2.88351i	0.686033	−	0.396081i	−0.116091	−	0.993239i	$-0.537037\pi$
$53$	4.99439	−	2.88351i	0.686033	−	0.396081i	0.802124	+	0.597157i	$0.203703\pi$
$54$		0			0
$55$		−	11.9243i		−	1.60787i
$56$	−2.69658	−	1.40980i	−0.360346	−	0.188392i
$57$		0			0
$58$	1.24616			0.163629
$59$	2.34352	−	4.05910i	0.305101	−	0.528450i	−0.672183	−	0.740385i	$-0.734643\pi$
$59$	2.34352	−	4.05910i	0.305101	−	0.528450i	0.977284	+	0.211935i	$0.0679765\pi$
$60$		0			0
$61$	−1.38580	+	0.800092i	−0.177433	+	0.102441i	−0.586086	−	0.810249i	$-0.699332\pi$
$61$	−1.38580	+	0.800092i	−0.177433	+	0.102441i	0.408653	+	0.912690i	$0.365999\pi$
$62$	−0.138922			−0.0176432
$63$		0			0
$64$	6.00131			0.750164
$65$	−6.21035	+	3.58555i	−0.770299	+	0.444733i
$66$		0			0
$67$	−0.787831	+	1.36456i	−0.0962489	+	0.166708i	−0.910129	−	0.414325i	$-0.864018\pi$
$67$	−0.787831	+	1.36456i	−0.0962489	+	0.166708i	0.813880	+	0.581033i	$0.197351\pi$
$68$	6.43989			0.780951
$69$		0			0
$70$	−0.0995964	−	2.37729i	−0.0119040	−	0.284141i
$71$			13.6132i			1.61559i	0.589462	+	0.807796i	$0.299340\pi$
$71$			13.6132i			1.61559i	−0.589462	+	0.807796i	$0.700660\pi$
$72$		0			0
$73$	−0.856452	+	0.494473i	−0.100240	+	0.0578737i	−0.549282	−	0.835637i	$-0.685099\pi$
$73$	−0.856452	+	0.494473i	−0.100240	+	0.0578737i	0.449042	+	0.893511i	$0.351765\pi$
$74$			2.28862i			0.266047i
$75$		0			0
$76$	−4.22333	+	2.43834i	−0.484450	+	0.279697i
$77$	−9.13588	−	4.77633i	−1.04113	−	0.544313i
$78$		0			0
$79$	4.63908	+	8.03512i	0.521937	+	0.904021i	0.999674	+	0.0255186i	$0.00812370\pi$
$79$	4.63908	+	8.03512i	0.521937	+	0.904021i	−0.477737	+	0.878503i	$0.658543\pi$
$80$	5.33910	+	9.24760i	0.596930	+	1.03391i
$81$		0			0
$82$	1.59182	+	0.919038i	0.175787	+	0.101491i
$83$	5.49361	−	9.51520i	0.603002	−	1.04443i	−0.389362	−	0.921085i	$-0.627305\pi$
$83$	5.49361	−	9.51520i	0.603002	−	1.04443i	0.992364	−	0.123345i	$-0.0393621\pi$
$84$		0			0
$85$	5.14930	+	8.91884i	0.558519	+	0.967384i
$86$		−	1.21186i		−	0.130679i
$87$		0			0
$88$	−4.48133			−0.477712
$89$	−2.15849	+	3.73861i	−0.228799	+	0.396292i	−0.957452	−	0.288591i	$-0.906813\pi$
$89$	−2.15849	+	3.73861i	−0.228799	+	0.396292i	0.728653	+	0.684883i	$0.240147\pi$
$90$		0			0
$91$	0.259511	+	6.19433i	0.0272041	+	0.649342i
$92$	−4.93989	−	2.85205i	−0.515019	−	0.297346i
$93$		0			0
$94$	1.03171	+	0.595655i	0.106412	+	0.0614371i
$95$	−6.75390	−	3.89937i	−0.692936	−	0.400067i
$96$		0			0
$97$	−4.98797	−	2.87980i	−0.506451	−	0.292400i	0.224923	−	0.974377i	$-0.427787\pi$
$97$	−4.98797	−	2.87980i	−0.506451	−	0.292400i	−0.731374	+	0.681977i	$0.761120\pi$
$98$	−1.86128	−	0.875930i	−0.188017	−	0.0884823i
$99$		0			0
$100$	−4.17676	+	7.23437i	−0.417676	+	0.723437i
$101$	−17.1580			−1.70728			−0.853642	−	0.520860i	$-0.825611\pi$
$101$	−17.1580			−1.70728			−0.853642	+	0.520860i	$0.825611\pi$
$102$		0			0
$103$			9.81983i			0.967577i	0.875185	+	0.483788i	$0.160740\pi$
$103$			9.81983i			0.967577i	−0.875185	+	0.483788i	$0.839260\pi$
$104$	1.34751	+	2.33395i	0.132134	+	0.228863i
$105$		0			0
$106$	0.847377	−	1.46770i	0.0823045	−	0.142556i
$107$	−3.00501	−	1.73494i	−0.290505	−	0.167723i	0.347664	−	0.937619i	$-0.386975\pi$
$107$	−3.00501	−	1.73494i	−0.290505	−	0.167723i	−0.638170	+	0.769896i	$0.720308\pi$
$108$		0			0
$109$	0.611066	+	1.05840i	0.0585295	+	0.101376i	0.893806	−	0.448455i	$-0.148025\pi$
$109$	0.611066	+	1.05840i	0.0585295	+	0.101376i	−0.835276	+	0.549831i	$0.814692\pi$
$110$	−1.75209	−	3.03471i	−0.167055	−	0.289348i
$111$		0			0
$112$	9.22374	−	0.386427i	0.871561	−	0.0365140i
$113$	1.87681	−	1.08358i	0.176555	−	0.101934i	−0.409118	−	0.912482i	$-0.634164\pi$
$113$	1.87681	−	1.08358i	0.176555	−	0.101934i	0.585673	+	0.810547i	$0.300830\pi$
$114$		0			0
$115$		−	9.12191i		−	0.850623i
$116$	−7.02767	+	4.05743i	−0.652503	+	0.376723i
$117$		0			0
$118$		−	1.37738i		−	0.126798i
$119$	8.89582	−	0.372690i	0.815479	−	0.0341644i
$120$		0			0
$121$	−4.18251			−0.380228
$122$	−0.235123	+	0.407244i	−0.0212870	+	0.0368702i
$123$		0			0
$124$	0.783445	−	0.452322i	0.0703555	−	0.0406198i
$125$	1.94249			0.173742
$126$		0			0
$127$	2.74889			0.243925			0.121962	−	0.992535i	$-0.461081\pi$
$127$	2.74889			0.243925			0.121962	+	0.992535i	$0.461081\pi$
$128$	7.28743	−	4.20740i	0.644124	−	0.371885i
$129$		0			0
$130$	−1.05368	+	1.82503i	−0.0924141	+	0.160066i
$131$	7.47821			0.653375			0.326687	−	0.945132i	$-0.394068\pi$
$131$	7.47821			0.653375			0.326687	+	0.945132i	$0.394068\pi$
$132$		0			0
$133$	−5.69285	+	3.61265i	−0.493632	+	0.313256i
$134$			0.463039i			0.0400005i
$135$		0			0
$136$	3.35185	−	1.93519i	0.287418	−	0.165941i
$137$			12.2088i			1.04307i	0.853231	+	0.521533i	$0.174640\pi$
$137$			12.2088i			1.04307i	−0.853231	+	0.521533i	$0.825360\pi$
$138$		0			0
$139$	11.5501	−	6.66842i	0.979663	−	0.565608i	0.0774943	−	0.996993i	$-0.475308\pi$
$139$	11.5501	−	6.66842i	0.979663	−	0.565608i	0.902168	+	0.431384i	$0.141975\pi$
$140$	8.30198	+	13.0823i	0.701645	+	1.10566i
$141$		0			0
$142$	2.00026	+	3.46454i	0.167858	+	0.290738i
$143$	4.56528	+	7.90730i	0.381768	+	0.661242i
$144$		0			0
$145$	−11.2386	−	6.48859i	−0.933312	−	0.538848i
$146$	−0.145310	+	0.251685i	−0.0120260	+	0.0208296i
$147$		0			0
$148$	−7.45161	−	12.9066i	−0.612519	−	1.06091i
$149$		−	8.47350i		−	0.694176i	−0.937832	−	0.347088i	$-0.887170\pi$
$149$		−	8.47350i		−	0.694176i	0.937832	−	0.347088i	$-0.112830\pi$
$150$		0			0
$151$	−3.35654			−0.273152			−0.136576	−	0.990630i	$-0.543610\pi$
$151$	−3.35654			−0.273152			−0.136576	+	0.990630i	$0.543610\pi$
$152$	−1.46545	+	2.53823i	−0.118863	+	0.205877i
$153$		0			0
$154$	−3.02688	+	0.126811i	−0.243913	+	0.0102187i
$155$	1.25288	+	0.723348i	0.100633	+	0.0581007i
$156$		0			0
$157$	−14.4700	−	8.35426i	−1.15483	−	0.666743i	−0.204772	−	0.978810i	$-0.565645\pi$
$157$	−14.4700	−	8.35426i	−1.15483	−	0.666743i	−0.950060	+	0.312067i	$0.898979\pi$
$158$	2.36128	+	1.36328i	0.187853	+	0.108457i
$159$		0			0
$160$	8.81374	+	5.08862i	0.696787	+	0.402290i
$161$	−6.98883	−	3.65383i	−0.550797	−	0.287962i
$162$		0			0
$163$	12.6662	−	21.9385i	0.992094	−	1.71836i	0.387363	−	0.921927i	$-0.373386\pi$
$163$	12.6662	−	21.9385i	0.992094	−	1.71836i	0.604731	−	0.796430i	$-0.293281\pi$
$164$	−11.9693			−0.934647
$165$		0			0
$166$		−	3.22881i		−	0.250604i
$167$	0.875828	+	1.51698i	0.0677736	+	0.117387i	0.897921	−	0.440157i	$-0.145077\pi$
$167$	0.875828	+	1.51698i	0.0677736	+	0.117387i	−0.830147	+	0.557544i	$0.811744\pi$
$168$		0			0
$169$	−3.75450	+	6.50298i	−0.288808	+	0.500229i
$170$	2.62097	+	1.51322i	0.201020	+	0.116059i
$171$		0			0
$172$	3.94575	+	6.83424i	0.300861	+	0.521106i
$173$	−11.9633	−	20.7210i	−0.909551	−	1.57539i	−0.814689	−	0.579898i	$-0.803092\pi$
$173$	−11.9633	−	20.7210i	−0.909551	−	1.57539i	−0.0948622	−	0.995490i	$-0.530241\pi$
$174$		0			0
$175$	−5.35096	+	10.2350i	−0.404495	+	0.773694i
$176$	11.7745	−	6.79799i	0.887533	−	0.512418i
$177$		0			0
$178$			1.26863i			0.0950875i
$179$	21.9857	−	12.6935i	1.64329	−	0.948755i	0.663639	−	0.748053i	$-0.269011\pi$
$179$	21.9857	−	12.6935i	1.64329	−	0.948755i	0.979652	−	0.200702i	$-0.0643223\pi$
$180$		0			0
$181$			22.4032i			1.66522i	0.553859	+	0.832610i	$0.313155\pi$
$181$			22.4032i			1.66522i	−0.553859	+	0.832610i	$0.686845\pi$
$182$	0.976207	+	1.53832i	0.0723613	+	0.114028i
$183$		0			0
$184$	−3.42816			−0.252728
$185$	11.9165	−	20.6400i	0.876121	−	1.51749i
$186$		0			0
$187$	11.3559	−	6.55631i	0.830423	−	0.479445i
$188$	−7.75766			−0.565786
$189$		0			0
$190$	−2.29181			−0.166265
$191$	3.71434	−	2.14447i	0.268760	−	0.155169i	−0.359564	−	0.933120i	$-0.617075\pi$
$191$	3.71434	−	2.14447i	0.268760	−	0.155169i	0.628324	+	0.777952i	$0.283741\pi$
$192$		0			0
$193$	11.6725	−	20.2173i	0.840203	−	1.45527i	−0.0495201	−	0.998773i	$-0.515769\pi$
$193$	11.6725	−	20.2173i	0.840203	−	1.45527i	0.889723	−	0.456501i	$-0.150897\pi$
$194$	−1.69257			−0.121520
$195$		0			0
$196$	13.3485	−	1.12044i	0.953467	−	0.0800313i
$197$		−	18.7811i		−	1.33809i	−0.743220	−	0.669047i	$-0.766702\pi$
$197$		−	18.7811i		−	1.33809i	0.743220	−	0.669047i	$-0.233298\pi$
$198$		0			0
$199$	−3.92927	+	2.26856i	−0.278539	+	0.160814i	−0.632762	−	0.774347i	$-0.718079\pi$
$199$	−3.92927	+	2.26856i	−0.278539	+	0.160814i	0.354223	+	0.935161i	$0.384745\pi$
$200$			5.02048i			0.355001i
$201$		0			0
$202$	−4.36668	+	2.52111i	−0.307239	+	0.177384i
$203$	−9.47295	+	6.01149i	−0.664871	+	0.421924i
$204$		0			0
$205$	−9.57060	−	16.5768i	−0.668439	−	1.15777i
$206$	1.44287	+	2.49913i	0.100530	+	0.174123i
$207$		0			0
$208$	−7.08101	−	4.08822i	−0.490980	−	0.283467i
$209$	−4.96485	+	8.59937i	−0.343426	+	0.594831i
$210$		0			0
$211$	−3.44148	−	5.96082i	−0.236921	−	0.410360i	0.722908	−	0.690944i	$-0.242805\pi$
$211$	−3.44148	−	5.96082i	−0.236921	−	0.410360i	−0.959829	+	0.280584i	$0.909472\pi$
$212$			11.0360i			0.757957i
$213$		0			0
$214$	−1.01969			−0.0697049
$215$	−6.31000	+	10.9292i	−0.430338	+	0.745368i
$216$		0			0
$217$	1.05605	−	0.670161i	0.0716890	−	0.0454935i
$218$	0.311031	+	0.179574i	0.0210657	+	0.0121623i
$219$		0			0
$220$	19.7616	+	11.4094i	1.33233	+	0.769220i
$221$	−6.82927	−	3.94288i	−0.459387	−	0.265227i
$222$		0			0
$223$	−5.57176	−	3.21686i	−0.373113	−	0.215417i	0.301705	−	0.953401i	$-0.402444\pi$
$223$	−5.57176	−	3.21686i	−0.373113	−	0.215417i	−0.674818	+	0.737985i	$0.735778\pi$
$224$	7.42908	−	4.71445i	0.496376	−	0.314998i
$225$		0			0
$226$	0.318430	−	0.551537i	0.0211816	−	0.0366877i
$227$	19.7397			1.31017			0.655084	−	0.755556i	$-0.272633\pi$
$227$	19.7397			1.31017			0.655084	+	0.755556i	$0.272633\pi$
$228$		0			0
$229$			10.9069i			0.720747i	0.932808	+	0.360373i	$0.117351\pi$
$229$			10.9069i			0.720747i	−0.932808	+	0.360373i	$0.882649\pi$
$230$	−1.34033	−	2.32151i	−0.0883785	−	0.153076i
$231$		0			0
$232$	−2.43852	+	4.22364i	−0.160097	+	0.277295i
$233$	17.9944	+	10.3891i	1.17885	+	0.680611i	0.955749	−	0.294184i	$-0.0950478\pi$
$233$	17.9944	+	10.3891i	1.17885	+	0.680611i	0.223104	+	0.974795i	$0.428381\pi$
$234$		0			0
$235$	−6.20298	−	10.7439i	−0.404638	−	0.700853i
$236$	4.48466	+	7.76766i	0.291927	+	0.505632i
$237$		0			0
$238$	2.20921	−	1.40195i	0.143202	−	0.0908752i
$239$	−23.6739	+	13.6681i	−1.53134	+	0.884119i	−0.532039	+	0.846720i	$0.678574\pi$
$239$	−23.6739	+	13.6681i	−1.53134	+	0.884119i	−0.999300	+	0.0373991i	$0.988093\pi$
$240$		0			0
$241$			21.3259i			1.37372i	0.726788	+	0.686861i	$0.241012\pi$
$241$			21.3259i			1.37372i	−0.726788	+	0.686861i	$0.758988\pi$
$242$	−1.06444	+	0.614556i	−0.0684250	+	0.0395052i
$243$		0			0
$244$		−	3.06218i		−	0.196036i
$245$	12.2251	+	17.5910i	0.781036	+	1.12385i
$246$		0			0
$247$	5.97159			0.379963
$248$	0.271846	−	0.470851i	0.0172622	−	0.0298991i
$249$		0			0
$250$	0.494361	−	0.285419i	0.0312661	−	0.0180515i
$251$	−26.7381			−1.68769			−0.843847	−	0.536584i	$-0.819714\pi$
$251$	−26.7381			−1.68769			−0.843847	+	0.536584i	$0.819714\pi$
$252$		0			0
$253$	−11.6144			−0.730193
$254$	0.699589	−	0.403908i	0.0438961	−	0.0253434i
$255$		0			0
$256$	−4.76489	+	8.25303i	−0.297805	+	0.515814i
$257$	3.05279			0.190428			0.0952140	−	0.995457i	$-0.469646\pi$
$257$	3.05279			0.190428			0.0952140	+	0.995457i	$0.469646\pi$
$258$		0			0
$259$	−11.0403	−	17.3974i	−0.686012	−	1.08102i
$260$		−	13.7229i		−	0.851058i
$261$		0			0
$262$	1.90319	−	1.09881i	0.117580	−	0.0678847i
$263$		−	16.2174i		−	1.00001i	−0.866024	−	0.500003i	$-0.833332\pi$
$263$		−	16.2174i		−	1.00001i	0.866024	−	0.500003i	$-0.166668\pi$
$264$		0			0
$265$	−15.2842	+	8.82433i	−0.938901	+	0.542074i
$266$	−0.917996	+	1.75589i	−0.0562860	+	0.107661i
$267$		0			0
$268$	−1.50763	−	2.61128i	−0.0920929	−	0.159510i
$269$	0.303255	+	0.525254i	0.0184898	+	0.0320253i	0.875122	−	0.483902i	$-0.160781\pi$
$269$	0.303255	+	0.525254i	0.0184898	+	0.0320253i	−0.856632	+	0.515927i	$0.827448\pi$
$270$		0			0
$271$	19.8948	+	11.4863i	1.20852	+	0.697742i	0.962437	−	0.271505i	$-0.0875215\pi$
$271$	19.8948	+	11.4863i	1.20852	+	0.697742i	0.246088	+	0.969248i	$0.420855\pi$
$272$	−5.87120	+	10.1692i	−0.355994	+	0.616599i
$273$		0			0
$274$	1.79389	+	3.10711i	0.108373	+	0.187708i
$275$			17.0091i			1.02569i
$276$		0			0
$277$	13.2835			0.798125			0.399063	−	0.916924i	$-0.369336\pi$
$277$	13.2835			0.798125			0.399063	+	0.916924i	$0.369336\pi$
$278$	1.95965	−	3.39421i	0.117532	−	0.203571i
$279$		0			0
$280$	8.25228	+	4.31437i	0.493168	+	0.257833i
$281$	−5.68377	−	3.28153i	−0.339065	−	0.195759i	0.320793	−	0.947149i	$-0.396050\pi$
$281$	−5.68377	−	3.28153i	−0.339065	−	0.195759i	−0.659859	+	0.751390i	$0.729384\pi$
$282$		0			0
$283$	2.57413	+	1.48617i	0.153016	+	0.0883437i	0.574553	−	0.818467i	$-0.305176\pi$
$283$	2.57413	+	1.48617i	0.153016	+	0.0883437i	−0.421537	+	0.906811i	$0.638509\pi$
$284$	−22.5607	−	13.0254i	−1.33873	−	0.772916i
$285$		0			0
$286$	2.32371	+	1.34160i	0.137404	+	0.0793303i
$287$	−16.5340	+	0.692689i	−0.975970	+	0.0408882i
$288$		0			0
$289$	2.83753	−	4.91475i	0.166914	−	0.289103i
$290$	−3.81360			−0.223942
$291$		0			0
$292$		−	1.89249i		−	0.110749i
$293$	3.03087	+	5.24962i	0.177065	+	0.306686i	0.940874	−	0.338756i	$-0.110006\pi$
$293$	3.03087	+	5.24962i	0.177065	+	0.306686i	−0.763809	+	0.645443i	$0.776673\pi$
$294$		0			0
$295$	−7.17181	+	12.4219i	−0.417559	+	0.723234i
$296$	−7.75686	−	4.47843i	−0.450858	−	0.260303i
$297$		0			0
$298$	−1.24505	−	2.15649i	−0.0721239	−	0.124922i
$299$	3.49238	+	6.04899i	0.201970	+	0.349822i
$300$		0			0
$301$	5.84603	+	9.21222i	0.336959	+	0.530984i
$302$	−0.854235	+	0.493193i	−0.0491557	+	0.0283801i
$303$		0			0
$304$		−	8.89207i		−	0.509995i
$305$	4.24092	−	2.44850i	0.242834	−	0.140201i
$306$		0			0
$307$			21.6030i			1.23295i	0.787375	+	0.616474i	$0.211439\pi$
$307$			21.6030i			1.23295i	−0.787375	+	0.616474i	$0.788561\pi$
$308$	16.6570	−	10.5705i	0.949122	−	0.602308i
$309$		0			0
$310$	0.425140			0.0241463
$311$	−5.51171	+	9.54656i	−0.312540	+	0.541336i	−0.978912	−	0.204284i	$-0.934513\pi$
$311$	−5.51171	+	9.54656i	−0.312540	+	0.541336i	0.666371	+	0.745620i	$0.267847\pi$
$312$		0			0
$313$	−11.7383	+	6.77710i	−0.663487	+	0.383064i	−0.793604	−	0.608434i	$-0.791798\pi$
$313$	−11.7383	+	6.77710i	−0.663487	+	0.383064i	0.130117	+	0.991499i	$0.458465\pi$
$314$	−4.91012			−0.277094
$315$		0			0
$316$	−17.7551			−0.998800
$317$	9.65977	−	5.57707i	0.542547	−	0.313240i	−0.203564	−	0.979062i	$-0.565252\pi$
$317$	9.65977	−	5.57707i	0.542547	−	0.313240i	0.746111	+	0.665822i	$0.231919\pi$
$318$		0			0
$319$	−8.26156	+	14.3094i	−0.462559	+	0.801175i
$320$	−18.3656			−1.02667
$321$		0			0
$322$	−2.31552	+	0.0970085i	−0.129039	+	0.00540607i
$323$		−	8.57595i		−	0.477179i
$324$		0			0
$325$	8.85862	−	5.11453i	0.491388	−	0.283703i
$326$		−	7.44442i		−	0.412308i
$327$		0			0
$328$	−6.22982	+	3.59679i	−0.343984	+	0.198599i
$329$	−10.7161	+	0.448952i	−0.590800	+	0.0247515i
$330$		0			0
$331$	9.51009	+	16.4720i	0.522722	+	0.905380i	0.999650	+	0.0264385i	$0.00841661\pi$
$331$	9.51009	+	16.4720i	0.522722	+	0.905380i	−0.476929	+	0.878942i	$0.658250\pi$
$332$	10.5128	+	18.2087i	0.576964	+	0.999331i
$333$		0			0
$334$	0.445794	+	0.257379i	0.0243927	+	0.0140832i
$335$	2.41098	−	4.17593i	0.131726	−	0.228156i
$336$		0			0
$337$	3.32635	+	5.76140i	0.181198	+	0.313843i	0.942289	−	0.334802i	$-0.108669\pi$
$337$	3.32635	+	5.76140i	0.181198	+	0.313843i	−0.761091	+	0.648645i	$0.775336\pi$
$338$			2.20666i			0.120027i
$339$		0			0
$340$	−19.7078			−1.06881
$341$	0.921000	−	1.59522i	0.0498749	−	0.0863859i
$342$		0			0
$343$	18.3743	−	2.32024i	0.992121	−	0.125281i
$344$	4.10738	+	2.37140i	0.221455	+	0.127857i
$345$		0			0
$346$	−6.08927	−	3.51564i	−0.327361	−	0.189002i
$347$	23.0796	+	13.3250i	1.23898	+	0.715325i	0.968886	−	0.247509i	$-0.0796118\pi$
$347$	23.0796	+	13.3250i	1.23898	+	0.715325i	0.270094	+	0.962834i	$0.412945\pi$
$348$		0			0
$349$	20.5135	+	11.8435i	1.09806	+	0.633966i	0.935711	−	0.352768i	$-0.114759\pi$
$349$	20.5135	+	11.8435i	1.09806	+	0.633966i	0.162350	+	0.986733i	$0.448093\pi$
$350$	0.142067	+	3.39104i	0.00759380	+	0.181258i
$351$		0			0
$352$	6.47905	−	11.2221i	0.345335	−	0.598137i
$353$	−4.58845			−0.244218			−0.122109	−	0.992517i	$-0.538966\pi$
$353$	−4.58845			−0.244218			−0.122109	+	0.992517i	$0.538966\pi$
$354$		0			0
$355$		−	41.6602i		−	2.21109i
$356$	−4.13057	−	7.15435i	−0.218920	−	0.379180i
$357$		0			0
$358$	3.73022	−	6.46094i	0.197148	−	0.341471i
$359$	−5.30942	−	3.06540i	−0.280221	−	0.161785i	0.353303	−	0.935509i	$-0.385059\pi$
$359$	−5.30942	−	3.06540i	−0.280221	−	0.161785i	−0.633523	+	0.773724i	$0.718392\pi$
$360$		0			0
$361$	−6.25288	−	10.8303i	−0.329099	−	0.570016i
$362$	3.29182	+	5.70159i	0.173014	+	0.299669i
$363$		0			0
$364$	−10.5139	−	5.49678i	−0.551079	−	0.288110i
$365$	2.62097	−	1.51322i	0.137188	−	0.0792056i
$366$		0			0
$367$		−	26.4264i		−	1.37945i	−0.724072	−	0.689725i	$-0.757732\pi$
$367$		−	26.4264i		−	1.37945i	0.724072	−	0.689725i	$-0.242268\pi$
$368$	9.00732	−	5.20038i	0.469539	−	0.271088i
$369$		0			0
$370$		−	7.00381i		−	0.364111i
$371$	0.638677	+	15.2448i	0.0331585	+	0.791468i
$372$		0			0
$373$	20.1162			1.04158			0.520789	−	0.853686i	$-0.325638\pi$
$373$	20.1162			1.04158			0.520789	+	0.853686i	$0.325638\pi$
$374$	1.92670	−	3.33714i	0.0996273	−	0.172560i
$375$		0			0
$376$	−4.03772	+	2.33118i	−0.208230	+	0.120221i
$377$	9.93679			0.511771
$378$		0			0
$379$	−17.4561			−0.896660			−0.448330	−	0.893868i	$-0.647981\pi$
$379$	−17.4561			−0.896660			−0.448330	+	0.893868i	$0.647981\pi$
$380$	12.9245	−	7.46199i	0.663015	−	0.382792i
$381$		0			0
$382$	0.630195	−	1.09153i	0.0322436	−	0.0558476i
$383$	28.0633			1.43397			0.716985	−	0.697089i	$-0.245522\pi$
$383$	28.0633			1.43397			0.716985	+	0.697089i	$0.245522\pi$
$384$		0			0
$385$	27.9583	+	14.6168i	1.42488	+	0.744944i
$386$		−	6.86037i		−	0.349183i
$387$		0			0
$388$	9.54517	−	5.51091i	0.484583	−	0.279774i
$389$			34.2392i			1.73600i	0.496566	+	0.867999i	$0.334594\pi$
$389$			34.2392i			1.73600i	−0.496566	+	0.867999i	$0.665406\pi$
$390$		0			0
$391$	8.68710	−	5.01550i	0.439325	−	0.253645i
$392$	6.61098	−	4.59441i	0.333905	−	0.232053i
$393$		0			0
$394$	−2.75959	−	4.77975i	−0.139026	−	0.240800i
$395$	−14.1968	−	24.5896i	−0.714320	−	1.23724i
$396$		0			0
$397$	−11.2926	−	6.51981i	−0.566762	−	0.327220i	0.189093	−	0.981959i	$-0.439445\pi$
$397$	−11.2926	−	6.51981i	−0.566762	−	0.327220i	−0.755855	+	0.654739i	$0.772778\pi$
$398$	−0.666662	+	1.15469i	−0.0334167	+	0.0578795i
$399$		0			0
$400$	−7.61585	−	13.1910i	−0.380792	−	0.659552i
$401$		−	18.3532i		−	0.916514i	−0.888820	−	0.458257i	$-0.848474\pi$
$401$		−	18.3532i		−	0.916514i	0.888820	−	0.458257i	$-0.151526\pi$
$402$		0			0
$403$	−1.10775			−0.0551812
$404$	16.4171	−	28.4353i	0.816782	−	1.41471i
$405$		0			0
$406$	−1.52756	+	2.92182i	−0.0758113	+	0.145007i
$407$	−26.2798	−	15.1727i	−1.30264	−	0.752081i
$408$		0			0
$409$	−5.60133	−	3.23393i	−0.276968	−	0.159907i	0.355082	−	0.934835i	$-0.384453\pi$
$409$	−5.60133	−	3.23393i	−0.276968	−	0.159907i	−0.632050	+	0.774928i	$0.717786\pi$
$410$	−4.87140	−	2.81251i	−0.240581	−	0.138900i
$411$		0			0
$412$	−16.2740	−	9.39581i	−0.801764	−	0.462899i
$413$	6.64448	+	10.4704i	0.326953	+	0.515216i
$414$		0			0
$415$	−16.8119	+	29.1191i	−0.825265	+	1.42940i
$416$	−7.79284			−0.382075
$417$		0			0
$418$			2.91804i			0.142726i
$419$	7.11542	+	12.3243i	0.347611	+	0.602080i	0.985825	−	0.167779i	$-0.0536596\pi$
$419$	7.11542	+	12.3243i	0.347611	+	0.602080i	−0.638214	+	0.769859i	$0.720326\pi$
$420$		0			0
$421$	15.1718	−	26.2784i	0.739429	−	1.28073i	−0.213324	−	0.976982i	$-0.568429\pi$
$421$	15.1718	−	26.2784i	0.739429	−	1.28073i	0.952753	−	0.303747i	$-0.0982378\pi$
$422$	−1.75170	−	1.01135i	−0.0852716	−	0.0492316i
$423$		0			0
$424$	3.31633	+	5.74405i	0.161055	+	0.278956i
$425$	−7.34510	−	12.7221i	−0.356290	−	0.617112i
$426$		0			0
$427$	−0.177214	−	4.22998i	−0.00857601	−	0.204703i
$428$	5.75051	−	3.32006i	0.277962	−	0.160481i
$429$		0			0
$430$			3.70863i			0.178846i
$431$	−2.12663	+	1.22781i	−0.102436	+	0.0591415i	−0.550343	−	0.834939i	$-0.685503\pi$
$431$	−2.12663	+	1.22781i	−0.102436	+	0.0591415i	0.447907	+	0.894080i	$0.352170\pi$
$432$		0			0
$433$		−	12.4545i		−	0.598525i	−0.954171	−	0.299262i	$-0.903259\pi$
$433$		−	12.4545i		−	0.598525i	0.954171	−	0.299262i	$-0.0967406\pi$
$434$	0.170292	−	0.325725i	0.00817428	−	0.0156353i
$435$		0			0
$436$	−2.33872			−0.112004
$437$	−3.79805	+	6.57841i	−0.181685	+	0.314688i
$438$		0			0
$439$	−15.1815	+	8.76502i	−0.724571	+	0.418331i	−0.816433	−	0.577440i	$-0.804052\pi$
$439$	−15.1815	+	8.76502i	−0.724571	+	0.418331i	0.0918615	+	0.995772i	$0.470718\pi$
$440$	13.7141			0.653794
$441$		0			0
$442$	−2.31739			−0.110227
$443$	−7.79825	+	4.50232i	−0.370506	+	0.213912i	−0.673680	−	0.739024i	$-0.735287\pi$
$443$	−7.79825	+	4.50232i	−0.370506	+	0.213912i	0.303173	+	0.952935i	$0.401954\pi$
$444$		0			0
$445$	6.60555	−	11.4411i	0.313133	−	0.542362i
$446$	−1.89067			−0.0895260
$447$		0			0
$448$	−7.35645	+	14.0710i	−0.347560	+	0.664792i
$449$			30.8120i			1.45411i	0.686581	+	0.727054i	$0.259111\pi$
$449$			30.8120i			1.45411i	−0.686581	+	0.727054i	$0.740889\pi$
$450$		0			0
$451$	−21.1063	+	12.1857i	−0.993856	+	0.573803i
$452$			4.14715i			0.195065i
$453$		0			0
$454$	5.02371	−	2.90044i	0.235775	−	0.136125i
$455$	−0.794173	−	18.9563i	−0.0372314	−	0.888686i
$456$		0			0
$457$	−6.91430	−	11.9759i	−0.323437	−	0.560210i	0.657758	−	0.753230i	$-0.271505\pi$
$457$	−6.91430	−	11.9759i	−0.323437	−	0.560210i	−0.981195	+	0.193020i	$0.938172\pi$
$458$	1.60260	+	2.77578i	0.0748846	+	0.129704i
$459$		0			0
$460$	15.1174	+	8.72803i	0.704852	+	0.406947i
$461$	6.16989	−	10.6866i	0.287360	−	0.497723i	−0.685818	−	0.727773i	$-0.740556\pi$
$461$	6.16989	−	10.6866i	0.287360	−	0.497723i	0.973179	+	0.230050i	$0.0738889\pi$
$462$		0			0
$463$	6.37802	+	11.0471i	0.296412	+	0.513401i	0.975312	−	0.220830i	$-0.0708765\pi$
$463$	6.37802	+	11.0471i	0.296412	+	0.513401i	−0.678900	+	0.734230i	$0.737543\pi$
$464$		−	14.7965i		−	0.686910i
$465$		0			0
$466$	6.10606			0.282858
$467$	−5.48999	+	9.50894i	−0.254046	+	0.440021i	−0.964636	−	0.263585i	$-0.915095\pi$
$467$	−5.48999	+	9.50894i	−0.254046	+	0.440021i	0.710590	+	0.703607i	$0.248428\pi$
$468$		0			0
$469$	−2.23370	−	3.51988i	−0.103143	−	0.162533i
$470$	−3.15730	−	1.82287i	−0.145635	−	0.0840825i
$471$		0			0
$472$	4.66837	+	2.69528i	0.214879	+	0.124061i
$473$	13.9156	+	8.03417i	0.639840	+	0.369412i
$474$		0			0
$475$	9.63396	+	5.56217i	0.442036	+	0.255210i
$476$	−7.89406	+	15.0993i	−0.361824	+	0.692075i
$477$		0			0
$478$	−4.01665	+	6.95704i	−0.183717	+	0.318208i
$479$	11.1946			0.511493			0.255747	−	0.966744i	$-0.417679\pi$
$479$	11.1946			0.511493			0.255747	+	0.966744i	$0.417679\pi$
$480$		0			0
$481$			18.2493i			0.832096i
$482$	3.13352	+	5.42741i	0.142728	+	0.247212i
$483$		0			0
$484$	4.00191	−	6.93152i	0.181905	−	0.315069i
$485$	15.2645	+	8.81298i	0.693126	+	0.400177i
$486$		0			0
$487$	−1.48332	−	2.56919i	−0.0672158	−	0.116421i	0.830459	−	0.557080i	$-0.188078\pi$
$487$	−1.48332	−	2.56919i	−0.0672158	−	0.116421i	−0.897675	+	0.440659i	$0.854745\pi$
$488$	−0.920185	−	1.59381i	−0.0416548	−	0.0721483i
$489$		0			0
$490$	5.69601	+	2.68058i	0.257319	+	0.121096i
$491$	20.1795	−	11.6507i	0.910690	−	0.525787i	0.0300367	−	0.999549i	$-0.490438\pi$
$491$	20.1795	−	11.6507i	0.910690	−	0.525787i	0.880653	+	0.473762i	$0.157104\pi$
$492$		0			0
$493$		−	14.2705i		−	0.642710i
$494$	1.51976	−	0.877435i	0.0683773	−	0.0394776i
$495$		0			0
$496$			1.64952i			0.0740654i
$497$	−31.9183	−	16.6872i	−1.43173	−	0.748523i
$498$		0			0
$499$	−4.58592			−0.205294			−0.102647	−	0.994718i	$-0.532731\pi$
$499$	−4.58592			−0.205294			−0.102647	+	0.994718i	$0.532731\pi$
$500$	−1.85862	+	3.21922i	−0.0831198	+	0.143968i
$501$		0			0
$502$	−6.80480	+	3.92875i	−0.303713	+	0.175349i
$503$	−23.1383			−1.03169			−0.515844	−	0.856683i	$-0.672521\pi$
$503$	−23.1383			−1.03169			−0.515844	+	0.856683i	$0.672521\pi$
$504$		0			0
$505$	52.5081			2.33658
$506$	−2.95585	+	1.70656i	−0.131404	+	0.0758660i
$507$		0			0
$508$	−2.63020	+	4.55563i	−0.116696	+	0.202123i
$509$	−9.65706			−0.428042			−0.214021	−	0.976829i	$-0.568656\pi$
$509$	−9.65706			−0.428042			−0.214021	+	0.976829i	$0.568656\pi$
$510$		0			0
$511$	−0.109522	−	2.61421i	−0.00484497	−	0.115646i
$512$			19.6301i			0.867536i
$513$		0			0
$514$	0.776931	−	0.448561i	0.0342690	−	0.0197852i
$515$		−	30.0513i		−	1.32422i
$516$		0			0
$517$	−13.6796	+	7.89791i	−0.601627	+	0.347350i
$518$	−5.36603	−	2.80541i	−0.235770	−	0.123263i
$519$		0			0
$520$	−4.12374	−	7.14252i	−0.180838	−	0.313220i
$521$	5.00035	+	8.66086i	0.219069	+	0.379439i	0.954524	−	0.298135i	$-0.0963646\pi$
$521$	5.00035	+	8.66086i	0.219069	+	0.379439i	−0.735454	+	0.677574i	$0.763031\pi$
$522$		0			0
$523$	−10.7796	−	6.22361i	−0.471359	−	0.272139i	0.245449	−	0.969409i	$-0.421065\pi$
$523$	−10.7796	−	6.22361i	−0.471359	−	0.272139i	−0.716809	+	0.697270i	$0.754398\pi$
$524$	−7.15531	+	12.3934i	−0.312581	+	0.541406i
$525$		0			0
$526$	−2.38289	−	4.12729i	−0.103899	−	0.179959i
$527$			1.59087i			0.0692995i
$528$		0			0
$529$	14.1151			0.613700
$530$	−2.59320	+	4.49156i	−0.112641	+	0.195101i
$531$		0			0
$532$	−0.540075	−	12.8912i	−0.0234152	−	0.558904i
$533$	12.6930	+	7.32833i	0.549797	+	0.317425i
$534$		0			0
$535$	9.19615	+	5.30940i	0.397584	+	0.229545i
$536$	−1.56938	−	0.906084i	−0.0677870	−	0.0391369i
$537$		0			0
$538$	0.154356	+	0.0891175i	0.00665476	+	0.00384213i
$539$	22.3977	−	15.5656i	0.964735	−	0.670458i
$540$		0			0
$541$	6.96514	−	12.0640i	0.299455	−	0.518671i	−0.676557	−	0.736391i	$-0.736529\pi$
$541$	6.96514	−	12.0640i	0.299455	−	0.518671i	0.976011	+	0.217720i	$0.0698619\pi$
$542$	6.75094			0.289978
$543$		0			0
$544$			11.1915i			0.479831i
$545$	−1.87003	−	3.23898i	−0.0801032	−	0.138743i
$546$		0			0
$547$	−21.6768	+	37.5454i	−0.926834	+	1.60532i	−0.138250	+	0.990397i	$0.544148\pi$
$547$	−21.6768	+	37.5454i	−0.926834	+	1.60532i	−0.788584	+	0.614926i	$0.789186\pi$
$548$	−20.2331	−	11.6816i	−0.864316	−	0.499013i
$549$		0			0
$550$	2.49923	+	4.32879i	0.106567	+	0.184580i
$551$	5.40325	+	9.35870i	0.230186	+	0.398694i
$552$		0			0
$553$	−24.5262	+	1.02752i	−1.04296	+	0.0436947i
$554$	3.38062	−	1.95180i	0.143629	−	0.0829241i
$555$		0			0
$556$			25.5219i			1.08237i
$557$	−31.1339	+	17.9752i	−1.31919	+	0.761632i	−0.983598	−	0.180377i	$-0.942268\pi$
$557$	−31.1339	+	17.9752i	−1.31919	+	0.761632i	−0.335588	+	0.942009i	$0.608935\pi$
$558$		0			0
$559$		−	9.66329i		−	0.408714i
$560$	−28.2271	+	1.18257i	−1.19281	+	0.0499728i
$561$		0			0
$562$	−1.92868			−0.0813565
$563$	−3.05554	+	5.29235i	−0.128776	+	0.223046i	−0.923202	−	0.384314i	$-0.874438\pi$
$563$	−3.05554	+	5.29235i	−0.128776	+	0.223046i	0.794427	+	0.607360i	$0.207771\pi$
$564$		0			0
$565$	−5.74354	+	3.31603i	−0.241633	+	0.139507i
$566$	0.873481			0.0367151
$567$		0			0
$568$	−15.6566			−0.656935
$569$	−16.7182	+	9.65223i	−0.700861	+	0.404642i	−0.807668	−	0.589637i	$-0.799271\pi$
$569$	−16.7182	+	9.65223i	−0.700861	+	0.404642i	0.106807	+	0.994280i	$0.465937\pi$
$570$		0			0
$571$	−6.36118	+	11.0179i	−0.266207	+	0.461085i	−0.967879	−	0.251416i	$-0.919104\pi$
$571$	−6.36118	+	11.0179i	−0.266207	+	0.461085i	0.701672	+	0.712500i	$0.252437\pi$
$572$	−17.4726			−0.730567
$573$		0			0
$574$	−4.10609	+	2.60570i	−0.171385	+	0.108760i
$575$			13.0118i			0.542628i
$576$		0			0
$577$	7.05520	−	4.07332i	0.293712	−	0.169575i	−0.345903	−	0.938270i	$-0.612427\pi$
$577$	7.05520	−	4.07332i	0.293712	−	0.169575i	0.639615	+	0.768696i	$0.279094\pi$
$578$		−	1.66773i		−	0.0693683i
$579$		0			0
$580$	21.5066	−	12.4168i	0.893012	−	0.515581i
$581$	15.5757	+	24.5444i	0.646191	+	1.01827i
$582$		0			0
$583$	11.2355	+	19.4605i	0.465328	+	0.805973i
$584$	−0.568693	−	0.985005i	−0.0235327	−	0.0407598i
$585$		0			0
$586$	1.54270	+	0.890680i	0.0637285	+	0.0367937i
$587$	12.3041	−	21.3113i	0.507843	−	0.879610i	−0.492116	−	0.870530i	$-0.663776\pi$
$587$	12.3041	−	21.3113i	0.507843	−	0.879610i	0.999959	−	0.00908019i	$-0.00289036\pi$
$588$		0			0
$589$	−0.602354	−	1.04331i	−0.0248196	−	0.0429888i
$590$			4.21515i			0.173535i
$591$		0			0
$592$	27.1743			1.11686
$593$	−18.9321	+	32.7913i	−0.777447	+	1.34658i	0.155962	+	0.987763i	$0.450152\pi$
$593$	−18.9321	+	32.7913i	−0.777447	+	1.34658i	−0.933409	+	0.358814i	$0.883181\pi$
$594$		0			0
$595$	−27.2236	+	1.14053i	−1.11606	+	0.0467572i
$596$	14.0428	+	8.10762i	0.575216	+	0.332101i
$597$		0			0
$598$	1.77761	+	1.02631i	0.0726920	+	0.0419687i
$599$	−9.22572	−	5.32647i	−0.376953	−	0.217634i	0.299539	−	0.954084i	$-0.403167\pi$
$599$	−9.22572	−	5.32647i	−0.376953	−	0.217634i	−0.676492	+	0.736450i	$0.736501\pi$
$600$		0			0
$601$	−39.8636	−	23.0153i	−1.62607	−	0.938812i	−0.985250	−	0.171122i	$-0.945261\pi$
$601$	−39.8636	−	23.0153i	−1.62607	−	0.938812i	−0.640821	−	0.767691i	$-0.721406\pi$
$602$	2.84140	+	1.48551i	0.115807	+	0.0605449i
$603$		0			0
$604$	3.21161	−	5.56267i	0.130679	−	0.226342i
$605$	12.7996			0.520378
$606$		0			0
$607$			4.31931i			0.175315i	0.996151	+	0.0876576i	$0.0279381\pi$
$607$			4.31931i			0.175315i	−0.996151	+	0.0876576i	$0.972062\pi$
$608$	−4.23745	−	7.33947i	−0.171851	−	0.297655i
$609$		0			0
$610$	0.719539	−	1.24628i	0.0291333	−	0.0504603i
$611$	8.22672	+	4.74970i	0.332818	+	0.192152i
$612$		0			0
$613$	14.3838	+	24.9135i	0.580956	+	1.00624i	0.995366	+	0.0961549i	$0.0306544\pi$
$613$	14.3838	+	24.9135i	0.580956	+	1.00624i	−0.414411	+	0.910090i	$0.636012\pi$
$614$	3.17423	+	5.49793i	0.128102	+	0.221878i
$615$		0			0
$616$	5.49325	−	10.5072i	0.221329	−	0.423346i
$617$	−0.935498	+	0.540110i	−0.0376617	+	0.0217440i	−0.518713	−	0.854949i	$-0.673589\pi$
$617$	−0.935498	+	0.540110i	−0.0376617	+	0.0217440i	0.481051	+	0.876693i	$0.340255\pi$
$618$		0			0
$619$			7.58787i			0.304982i	0.988305	+	0.152491i	$0.0487295\pi$
$619$			7.58787i			0.304982i	−0.988305	+	0.152491i	$0.951270\pi$
$620$	−2.39755	+	1.38423i	−0.0962881	+	0.0555920i
$621$		0			0
$622$			3.23944i			0.129890i
$623$	−6.11985	−	9.64371i	−0.245187	−	0.386367i
$624$		0			0
$625$	−27.7708			−1.11083
$626$	−1.99158	+	3.44952i	−0.0795996	+	0.137871i
$627$		0			0
$628$	27.6904	−	15.9871i	1.10497	−	0.637953i
$629$	26.2082			1.04499
$630$		0			0
$631$	35.0387			1.39487			0.697435	−	0.716648i	$-0.254325\pi$
$631$	35.0387			1.39487			0.697435	+	0.716648i	$0.254325\pi$
$632$	−9.24118	+	5.33540i	−0.367595	+	0.212231i
$633$		0			0
$634$	1.63893	−	2.83871i	0.0650903	−	0.112740i
$635$	−8.41235			−0.333834
$636$		0			0
$637$	−14.8417	−	6.98459i	−0.588048	−	0.276739i
$638$			4.85564i			0.192237i
$639$		0			0
$640$	−22.3015	+	12.8758i	−0.881544	+	0.508960i
$641$		−	31.0879i		−	1.22790i	−0.789346	−	0.613949i	$-0.789580\pi$
$641$		−	31.0879i		−	1.22790i	0.789346	−	0.613949i	$-0.210420\pi$
$642$		0			0
$643$	−0.977928	+	0.564607i	−0.0385657	+	0.0222659i	−0.519159	−	0.854678i	$-0.673755\pi$
$643$	−0.977928	+	0.564607i	−0.0385657	+	0.0222659i	0.480593	+	0.876944i	$0.340421\pi$
$644$	12.7424	−	8.08627i	0.502121	−	0.318644i
$645$		0			0
$646$	−1.26011	−	2.18257i	−0.0495782	−	0.0858719i
$647$	−13.5992	−	23.5545i	−0.534640	−	0.926023i	−0.999181	−	0.0404713i	$-0.987114\pi$
$647$	−13.5992	−	23.5545i	−0.534640	−	0.926023i	0.464541	−	0.885552i	$-0.346219\pi$
$648$		0			0
$649$	15.8162	+	9.13148i	0.620839	+	0.358442i
$650$	1.50300	−	2.60328i	0.0589526	−	0.102109i
$651$		0			0
$652$	24.2386	+	41.9824i	0.949256	+	1.64416i
$653$		−	22.2892i		−	0.872243i	−0.899888	−	0.436121i	$-0.856352\pi$
$653$		−	22.2892i		−	0.872243i	0.899888	−	0.436121i	$-0.143648\pi$
$654$		0			0
$655$	−22.8854			−0.894205
$656$	10.9123	−	18.9007i	0.426055	−	0.737949i
$657$		0			0
$658$	−2.66128	+	1.68883i	−0.103747	+	0.0658375i
$659$	7.69208	+	4.44103i	0.299641	+	0.172998i	0.642282	−	0.766469i	$-0.277988\pi$
$659$	7.69208	+	4.44103i	0.299641	+	0.172998i	−0.342641	+	0.939467i	$0.611321\pi$
$660$		0			0
$661$	16.7724	+	9.68352i	0.652369	+	0.376645i	0.789363	−	0.613926i	$-0.210411\pi$
$661$	16.7724	+	9.68352i	0.652369	+	0.376645i	−0.136994	+	0.990572i	$0.543744\pi$
$662$	4.84060	+	2.79472i	0.188135	+	0.108620i
$663$		0			0
$664$	10.9434	+	6.31819i	0.424687	+	0.245193i
$665$	17.4216	−	11.0557i	0.675583	−	0.428721i
$666$		0			0
$667$	−6.31999	+	10.9465i	−0.244711	+	0.423852i
$668$	−3.35204			−0.129694
$669$		0			0
$670$		−	1.41702i		−	0.0547444i
$671$	−3.11754	−	5.39973i	−0.120351	−	0.208454i
$672$		0			0
$673$	11.5828	−	20.0620i	0.446484	−	0.773333i	−0.551670	−	0.834062i	$-0.686009\pi$
$673$	11.5828	−	20.0620i	0.446484	−	0.773333i	0.998154	+	0.0607292i	$0.0193426\pi$
$674$	1.69310	+	0.977511i	0.0652157	+	0.0376523i
$675$		0			0
$676$	−7.18476	−	12.4444i	−0.276337	−	0.478630i
$677$	−1.56346	−	2.70800i	−0.0600887	−	0.104077i	0.834416	−	0.551135i	$-0.185805\pi$
$677$	−1.56346	−	2.70800i	−0.0600887	−	0.104077i	−0.894505	+	0.447058i	$0.852472\pi$
$678$		0			0
$679$	12.8664	−	8.16496i	0.493768	−	0.313343i
$680$	−10.2576	+	5.92220i	−0.393359	+	0.227106i
$681$		0			0
$682$		−	0.541307i		−	0.0207277i
$683$	−27.1966	+	15.7020i	−1.04065	+	0.600819i	−0.920017	−	0.391878i	$-0.871825\pi$
$683$	−27.1966	+	15.7020i	−1.04065	+	0.600819i	−0.120632	+	0.992697i	$0.538492\pi$
$684$		0			0
$685$		−	37.3621i		−	1.42753i
$686$	4.33532	−	3.29033i	0.165523	−	0.125625i
$687$		0			0
$688$	−14.3892			−0.548585
$689$	6.75691	−	11.7033i	0.257418	−	0.445860i
$690$		0			0
$691$	38.2557	−	22.0869i	1.45532	−	0.840227i	0.456540	−	0.889703i	$-0.349088\pi$
$691$	38.2557	−	22.0869i	1.45532	−	0.840227i	0.998775	+	0.0494760i	$0.0157551\pi$
$692$	45.7868			1.74055
$693$		0			0
$694$	7.83164			0.297285
$695$	−35.3463	+	20.4072i	−1.34076	+	0.774089i
$696$		0			0
$697$	10.5244	−	18.2288i	0.398640	−	0.690465i
$698$	6.96086			0.263472
$699$		0			0
$700$	−11.8422	−	18.6610i	−0.447592	−	0.705320i
$701$		−	9.69906i		−	0.366328i	−0.983082	−	0.183164i	$-0.941366\pi$
$701$		−	9.69906i		−	0.366328i	0.983082	−	0.183164i	$-0.0586340\pi$
$702$		0			0
$703$	−17.1876	+	9.92326i	−0.648242	+	0.374263i
$704$			23.3840i			0.881316i
$705$		0			0
$706$	−1.16775	+	0.674202i	−0.0439490	+	0.0253739i
$707$	21.0324	−	40.2295i	0.791005	−	1.51299i
$708$		0			0
$709$	0.548932	+	0.950778i	0.0206156	+	0.0357072i	0.876149	−	0.482040i	$-0.160104\pi$
$709$	0.548932	+	0.950778i	0.0206156	+	0.0357072i	−0.855534	+	0.517747i	$0.826771\pi$
$710$	−6.12132	−	10.6024i	−0.229729	−	0.397903i
$711$		0			0
$712$	−4.29977	−	2.48247i	−0.161141	−	0.0930346i
$713$	0.704553	−	1.22032i	0.0263857	−	0.0457014i
$714$		0			0
$715$	−13.9710	−	24.1985i	−0.522486	−	0.904972i
$716$			48.5815i			1.81558i
$717$		0			0
$718$	−1.80165			−0.0672371
$719$	11.3648	−	19.6844i	0.423835	−	0.734103i	−0.572476	−	0.819921i	$-0.694017\pi$
$719$	11.3648	−	19.6844i	0.423835	−	0.734103i	0.996311	+	0.0858183i	$0.0273505\pi$
$720$		0			0
$721$	−23.0241	−	12.0372i	−0.857462	−	0.448289i
$722$	−3.18269	−	1.83753i	−0.118448	−	0.0683858i
$723$		0			0
$724$	−37.1280	−	21.4359i	−1.37985	−	0.796658i
$725$	16.0310	+	9.25550i	0.595376	+	0.343741i
$726$		0			0
$727$	3.47919	+	2.00871i	0.129036	+	0.0744990i	0.563129	−	0.826369i	$-0.309598\pi$
$727$	3.47919	+	2.00871i	0.129036	+	0.0744990i	−0.434093	+	0.900868i	$0.642931\pi$
$728$	−7.12409	+	0.298463i	−0.264036	+	0.0110618i
$729$		0			0
$730$	0.444689	−	0.770224i	0.0164587	−	0.0285073i
$731$	−13.8777			−0.513285
$732$		0			0
$733$		−	8.31602i		−	0.307159i	−0.988136	−	0.153580i	$-0.950920\pi$
$733$		−	8.31602i		−	0.307159i	0.988136	−	0.153580i	$-0.0490801\pi$
$734$	−3.88296	−	6.72549i	−0.143323	−	0.248242i
$735$		0			0
$736$	4.95640	−	8.58473i	0.182695	−	0.316437i
$737$	−5.31698	−	3.06976i	−0.195854	−	0.113076i
$738$		0			0
$739$	−2.28507	−	3.95785i	−0.0840576	−	0.145592i	0.820932	−	0.571026i	$-0.193455\pi$
$739$	−2.28507	−	3.95785i	−0.0840576	−	0.145592i	−0.904989	+	0.425434i	$0.860121\pi$
$740$	22.8040	+	39.4976i	0.838290	+	1.45196i
$741$		0			0
$742$	2.40253	+	3.78592i	0.0881995	+	0.138986i
$743$	−1.51258	+	0.873286i	−0.0554910	+	0.0320378i	−0.527489	−	0.849562i	$-0.676866\pi$
$743$	−1.51258	+	0.873286i	−0.0554910	+	0.0320378i	0.471998	+	0.881600i	$0.343533\pi$
$744$		0			0
$745$			25.9312i			0.950046i
$746$	5.11954	−	2.95577i	0.187440	−	0.108218i
$747$		0			0
$748$			25.0929i			0.917486i
$749$	7.75141	−	4.91900i	0.283230	−	0.179736i
$750$		0			0
$751$	5.83293			0.212847			0.106423	−	0.994321i	$-0.466060\pi$
$751$	5.83293			0.212847			0.106423	+	0.994321i	$0.466060\pi$
$752$	7.07260	−	12.2501i	0.257911	−	0.446715i
$753$		0			0
$754$	2.52890	−	1.46006i	0.0920970	−	0.0531723i
$755$	10.2719			0.373834
$756$		0			0
$757$	−42.0967			−1.53003			−0.765015	−	0.644013i	$-0.777268\pi$
$757$	−42.0967			−1.53003			−0.765015	+	0.644013i	$0.777268\pi$
$758$	−4.44255	+	2.56491i	−0.161361	+	0.0931617i
$759$		0			0
$760$	4.48466	−	7.76766i	0.162676	−	0.281763i
$761$	−0.586863			−0.0212738			−0.0106369	−	0.999943i	$-0.503386\pi$
$761$	−0.586863			−0.0212738			−0.0106369	+	0.999943i	$0.503386\pi$
$762$		0			0
$763$	−3.23062	+	0.135347i	−0.116956	+	0.00489988i
$764$			8.20750i			0.296937i
$765$		0			0
$766$	7.14208	−	4.12348i	0.258054	−	0.148987i
$767$		−	10.9831i		−	0.396577i
$768$		0			0
$769$	45.1905	−	26.0907i	1.62961	−	0.940856i	0.645403	−	0.763843i	$-0.276690\pi$
$769$	45.1905	−	26.0907i	1.62961	−	0.940856i	0.984208	−	0.177014i	$-0.0566437\pi$
$770$	9.26306	−	0.388075i	0.333817	−	0.0139852i
$771$		0			0
$772$	22.3369	+	38.6887i	0.803923	+	1.39244i
$773$	−16.3906	−	28.3894i	−0.589530	−	1.02110i	−0.994294	−	0.106674i	$-0.965980\pi$
$773$	−16.3906	−	28.3894i	−0.589530	−	1.02110i	0.404764	−	0.914421i	$-0.367354\pi$
$774$		0			0
$775$	−1.78714	−	1.03180i	−0.0641959	−	0.0370635i
$776$	3.31206	−	5.73666i	0.118896	−	0.205934i
$777$		0			0
$778$	5.03093	+	8.71383i	0.180368	+	0.312406i
$779$			15.9395i			0.571090i
$780$		0			0
$781$	−53.0436			−1.89805
$782$	1.47390	−	2.55287i	0.0527066	−	0.0912906i
$783$		0			0
$784$	−10.4005	+	22.1001i	−0.371446	+	0.789291i
$785$	44.2821	+	25.5663i	1.58050	+	0.912500i
$786$		0			0
$787$	−35.5013	−	20.4967i	−1.26549	−	0.730628i	−0.291355	−	0.956615i	$-0.594106\pi$
$787$	−35.5013	−	20.4967i	−1.26549	−	0.730628i	−0.974130	+	0.225987i	$0.927439\pi$
$788$	31.1251	+	17.9701i	1.10879	+	0.640158i
$789$		0			0
$790$	−7.22614	−	4.17201i	−0.257095	−	0.148434i
$791$	0.240004	+	5.72872i	0.00853356	+	0.203690i
$792$		0			0
$793$	−1.87485	+	3.24733i	−0.0665778	+	0.115316i
$794$	−3.83195			−0.135991
$795$		0			0
$796$		−	8.68244i		−	0.307741i
$797$	−17.0441	−	29.5213i	−0.603734	−	1.04570i	−0.992250	−	0.124256i	$-0.960346\pi$
$797$	−17.0441	−	29.5213i	−0.603734	−	1.04570i	0.388516	−	0.921442i	$-0.372988\pi$
$798$		0			0
$799$	6.82116	−	11.8146i	0.241315	−	0.417971i
$800$	−12.5722	−	7.25854i	−0.444493	−	0.256628i
$801$		0			0
$802$	−2.69672	−	4.67086i	−0.0952245	−	0.164934i
$803$	−1.92670	−	3.33714i	−0.0679918	−	0.117765i
$804$		0			0
$805$	21.3877	+	11.1817i	0.753818	+	0.394103i
$806$	−0.281922	+	0.162768i	−0.00993027	+	0.00573324i
$807$		0			0
$808$		−	19.7334i		−	0.694219i
$809$	−6.01547	+	3.47304i	−0.211493	+	0.122105i	−0.602005	−	0.798492i	$-0.705631\pi$
$809$	−6.01547	+	3.47304i	−0.211493	+	0.122105i	0.390512	+	0.920598i	$0.372298\pi$
$810$		0			0
$811$		−	39.8573i		−	1.39958i	−0.714350	−	0.699789i	$-0.753277\pi$
$811$		−	39.8573i		−	1.39958i	0.714350	−	0.699789i	$-0.246723\pi$
$812$	−0.898690	−	21.4511i	−0.0315379	−	0.752785i
$813$		0			0
$814$	−8.91756			−0.312560
$815$	−38.7620	+	67.1378i	−1.35777	+	2.35173i
$816$		0			0
$817$	9.10111	−	5.25453i	0.318408	−	0.183833i
$818$	−1.90071			−0.0664566
$819$		0			0
$820$	36.6294			1.27915
$821$	36.4612	−	21.0509i	1.27250	−	0.734680i	0.297045	−	0.954863i	$-0.403999\pi$
$821$	36.4612	−	21.0509i	1.27250	−	0.734680i	0.975459	+	0.220183i	$0.0706655\pi$
$822$		0			0
$823$	−16.3411	+	28.3035i	−0.569614	+	0.986600i	0.426990	+	0.904256i	$0.359574\pi$
$823$	−16.3411	+	28.3035i	−0.569614	+	0.986600i	−0.996604	+	0.0823435i	$0.973760\pi$
$824$	−11.2938			−0.393438
$825$		0			0
$826$	3.22948	+	1.68840i	0.112368	+	0.0587470i
$827$		−	31.4399i		−	1.09327i	−0.837370	−	0.546637i	$-0.815908\pi$
$827$		−	31.4399i		−	1.09327i	0.837370	−	0.546637i	$-0.184092\pi$
$828$		0			0
$829$	35.7122	−	20.6185i	1.24034	−	0.716109i	0.271174	−	0.962530i	$-0.412588\pi$
$829$	35.7122	−	20.6185i	1.24034	−	0.716109i	0.969163	+	0.246421i	$0.0792547\pi$
$830$			9.88102i			0.342975i
$831$		0			0
$832$	12.1788	−	7.03141i	0.422222	−	0.243770i
$833$	−10.0307	+	21.3145i	−0.347544	+	0.738502i
$834$		0			0
$835$	−2.68027	−	4.64236i	−0.0927546	−	0.160656i
$836$	−9.50094	−	16.4561i	−0.328597	−	0.569147i
$837$		0			0
$838$	3.62173	+	2.09100i	0.125110	+	0.0722326i
$839$	−4.04385	+	7.00416i	−0.139609	+	0.241810i	−0.927349	−	0.374198i	$-0.877918\pi$
$839$	−4.04385	+	7.00416i	−0.139609	+	0.241810i	0.787740	+	0.616009i	$0.211251\pi$
$840$		0			0
$841$	−5.50894	−	9.54177i	−0.189963	−	0.329026i
$842$		−	8.91707i		−	0.307302i
$843$		0			0
$844$	13.1715			0.453382
$845$	11.4898	−	19.9009i	0.395260	−	0.684611i
$846$		0			0
$847$	5.12695	−	9.80654i	0.176164	−	0.336957i
$848$	−17.4269	−	10.0615i	−0.598444	−	0.345512i
$849$		0			0
$850$	−3.73863	−	2.15850i	−0.128234	−	0.0740359i
$851$	−20.1037	−	11.6069i	−0.689147	−	0.397879i
$852$		0			0
$853$	24.5887	+	14.1963i	0.841900	+	0.486071i	0.857910	−	0.513801i	$-0.171763\pi$
$853$	24.5887	+	14.1963i	0.841900	+	0.486071i	−0.0160098	+	0.999872i	$0.505096\pi$
$854$	−0.666631	−	1.05048i	−0.0228117	−	0.0359468i
$855$		0			0
$856$	1.99536	−	3.45606i	0.0682000	−	0.118126i
$857$	51.3174			1.75297			0.876485	−	0.481429i	$-0.159882\pi$
$857$	51.3174			1.75297			0.876485	+	0.481429i	$0.159882\pi$
$858$		0			0
$859$			16.7702i			0.572191i	0.958201	+	0.286096i	$0.0923575\pi$
$859$			16.7702i			0.572191i	−0.958201	+	0.286096i	$0.907642\pi$
$860$	−12.0751	−	20.9146i	−0.411756	−	0.713183i
$861$		0			0
$862$	−0.360816	+	0.624951i	−0.0122894	+	0.0212859i
$863$	−14.2380	−	8.22033i	−0.484668	−	0.279823i	0.237692	−	0.971341i	$-0.423609\pi$
$863$	−14.2380	−	8.22033i	−0.484668	−	0.279823i	−0.722360	+	0.691517i	$0.756943\pi$
$864$		0			0
$865$	36.6109	+	63.4119i	1.24481	+	2.15607i
$866$	−1.83000	−	3.16965i	−0.0621859	−	0.107709i
$867$		0			0
$868$	0.100186	+	2.39137i	0.00340054	+	0.0811683i
$869$	−31.3086	+	18.0760i	−1.06207	+	0.613188i
$870$		0			0
$871$			3.69223i			0.125106i
$872$	−1.21726	+	0.702787i	−0.0412217	+	0.0237994i
$873$		0			0
$874$			2.23226i			0.0755074i
$875$	−2.38112	+	4.55447i	−0.0804965	+	0.153969i
$876$		0			0
$877$	6.12350			0.206776			0.103388	−	0.994641i	$-0.467032\pi$
$877$	6.12350			0.206776			0.103388	+	0.994641i	$0.467032\pi$
$878$	−2.57577	+	4.46137i	−0.0869281	+	0.150564i
$879$		0			0
$880$	−36.0330	+	20.8037i	−1.21467	+	0.701292i
$881$	41.3283			1.39238			0.696192	−	0.717855i	$-0.254876\pi$
$881$	41.3283			1.39238			0.696192	+	0.717855i	$0.254876\pi$
$882$		0			0
$883$	24.2918			0.817483			0.408741	−	0.912650i	$-0.365968\pi$
$883$	24.2918			0.817483			0.408741	+	0.912650i	$0.365968\pi$
$884$	13.0688	−	7.54526i	0.439550	−	0.253775i
$885$		0			0
$886$	−1.32310	+	2.29167i	−0.0444502	+	0.0769901i
$887$	−6.70071			−0.224988			−0.112494	−	0.993652i	$-0.535884\pi$
$887$	−6.70071			−0.224988			−0.112494	+	0.993652i	$0.535884\pi$
$888$		0			0
$889$	−3.36961	+	6.44520i	−0.113013	+	0.216165i
$890$		−	3.88234i		−	0.130136i
$891$		0			0
$892$	10.6624	−	6.15591i	0.357002	−	0.206115i
$893$			10.3308i			0.345708i
$894$		0			0
$895$	−67.2823	+	38.8455i	−2.24900	+	1.29846i
$896$	0.931908	+	22.2440i	0.0311329	+	0.743118i
$897$		0			0
$898$	4.52735	+	7.84160i	0.151080	+	0.261678i
$899$	−1.00232	−	1.73608i	−0.0334294	−	0.0579014i
$900$		0			0
$901$	−16.8074	−	9.70376i	−0.559936	−	0.323279i
$902$	−3.58101	+	6.20249i	−0.119235	+	0.206520i
$903$		0			0
$904$	1.24622	+	2.15852i	0.0414487	+	0.0717912i
$905$		−	68.5600i		−	2.27901i
$906$		0			0
$907$	20.2988			0.674010			0.337005	−	0.941503i	$-0.390586\pi$
$907$	20.2988			0.674010			0.337005	+	0.941503i	$0.390586\pi$
$908$	−18.8873	+	32.7138i	−0.626798	+	1.08565i
$909$		0			0
$910$	−2.98746	−	4.70766i	−0.0990332	−	0.156057i
$911$	30.3982	+	17.5504i	1.00714	+	0.581472i	0.910353	−	0.413833i	$-0.135810\pi$
$911$	30.3982	+	17.5504i	1.00714	+	0.581472i	0.0967861	+	0.995305i	$0.469144\pi$
$912$		0			0
$913$	37.0757	+	21.4057i	1.22703	+	0.708425i
$914$	−3.51936	−	2.03190i	−0.116410	−	0.0672093i
$915$		0			0
$916$	−18.0756	−	10.4359i	−0.597233	−	0.344813i
$917$	−9.16685	+	17.5338i	−0.302716	+	0.579018i
$918$		0			0
$919$	−16.9132	+	29.2946i	−0.557916	+	0.966339i	0.439754	+	0.898118i	$0.355066\pi$
$919$	−16.9132	+	29.2946i	−0.557916	+	0.966339i	−0.997670	+	0.0682206i	$0.978268\pi$
$920$	10.4911			0.345882
$921$		0			0
$922$		−	3.62629i		−	0.119425i
$923$	15.9499	+	27.6260i	0.524996	+	0.909320i
$924$		0			0
$925$	−16.9981	+	29.4415i	−0.558893	+	0.968031i
$926$	3.24639	+	1.87431i	0.106683	+	0.0615935i
$927$		0			0
$928$	−7.05115	−	12.2130i	−0.231465	−	0.400910i
$929$	−16.0586	−	27.8142i	−0.526864	−	0.912555i	−0.999510	−	0.0313029i	$-0.990034\pi$
$929$	−16.0586	−	27.8142i	−0.526864	−	0.912555i	0.472646	−	0.881252i	$-0.343299\pi$
$930$		0			0
$931$	−1.49208	−	17.7762i	−0.0489009	−	0.582590i
$932$	−34.4348	+	19.8810i	−1.12795	+	0.651222i
$933$		0			0
$934$			3.22668i			0.105580i
$935$	−34.7520	+	20.0641i	−1.13651	+	0.656166i
$936$		0			0
$937$			13.9224i			0.454824i	0.973799	+	0.227412i	$0.0730263\pi$
$937$			13.9224i			0.454824i	−0.973799	+	0.227412i	$0.926974\pi$
$938$	−1.08567	−	0.567596i	−0.0354482	−	0.0185327i
$939$		0			0
$940$	23.7405			0.774331
$941$	−28.6047	+	49.5448i	−0.932487	+	1.61512i	−0.153433	+	0.988159i	$0.549033\pi$
$941$	−28.6047	+	49.5448i	−0.932487	+	1.61512i	−0.779054	+	0.626956i	$0.784300\pi$
$942$		0			0
$943$	−16.1460	+	9.32192i	−0.525787	+	0.303563i
$944$	−16.3545			−0.532294
$945$		0			0
$946$	4.72200			0.153525
$947$	−29.8658	+	17.2430i	−0.970509	+	0.560324i	−0.899391	−	0.437144i	$-0.855990\pi$
$947$	−29.8658	+	17.2430i	−0.970509	+	0.560324i	−0.0711175	+	0.997468i	$0.522657\pi$
$948$		0			0
$949$	−1.15869	+	2.00691i	−0.0376128	+	0.0651472i
$950$	3.26910			0.106064
$951$		0			0
$952$	0.428630	+	10.2311i	0.0138920	+	0.331591i
$953$			2.58761i			0.0838209i	0.999121	+	0.0419104i	$0.0133444\pi$
$953$			2.58761i			0.0838209i	−0.999121	+	0.0419104i	$0.986656\pi$
$954$		0			0
$955$	−11.3669	+	6.56267i	−0.367824	+	0.212363i
$956$		−	52.3119i		−	1.69189i
$957$		0			0
$958$	2.84900	−	1.64487i	0.0920470	−	0.0531434i
$959$	−28.6253	−	14.9656i	−0.924360	−	0.483264i
$960$		0			0
$961$	−15.3883	−	26.6532i	−0.496396	−	0.859782i
$962$	2.68145	+	4.64441i	0.0864535	+	0.149742i
$963$		0			0
$964$	−35.3426	−	20.4051i	−1.13831	−	0.657203i
$965$	−35.7209	+	61.8704i	−1.14990	+	1.99168i
$966$		0			0
$967$	2.79472	+	4.84059i	0.0898721	+	0.155663i	0.907457	−	0.420145i	$-0.138021\pi$
$967$	2.79472	+	4.84059i	0.0898721	+	0.155663i	−0.817585	+	0.575808i	$0.804688\pi$
$968$		−	4.81030i		−	0.154609i
$969$		0			0
$970$	5.17973			0.166311
$971$	8.01661	−	13.8852i	0.257265	−	0.445597i	−0.708243	−	0.705969i	$-0.750512\pi$
$971$	8.01661	−	13.8852i	0.257265	−	0.445597i	0.965508	+	0.260372i	$0.0838452\pi$
$972$		0			0
$973$	1.47701	+	35.2551i	0.0473507	+	1.13023i
$974$	−0.755007	−	0.435904i	−0.0241920	−	0.0139673i
$975$		0			0
$976$	4.83547	+	2.79176i	0.154780	+	0.0893621i
$977$	38.0208	+	21.9513i	1.21639	+	0.702285i	0.964144	−	0.265378i	$-0.0854967\pi$
$977$	38.0208	+	21.9513i	1.21639	+	0.702285i	0.252248	+	0.967663i	$0.418830\pi$
$978$		0			0
$979$	−14.5674	−	8.41048i	−0.465576	−	0.268800i
$980$	−40.8502	+	3.42884i	−1.30491	+	0.109530i
$981$		0			0
$982$	3.42377	−	5.93015i	0.109257	−	0.189239i
$983$	18.1762			0.579730			0.289865	−	0.957068i	$-0.406390\pi$
$983$	18.1762			0.579730			0.289865	+	0.957068i	$0.406390\pi$
$984$		0			0
$985$			57.4751i			1.83131i
$986$	−2.09683	−	3.63181i	−0.0667766	−	0.115660i
$987$		0			0
$988$	−5.71374	+	9.89649i	−0.181778	+	0.314849i
$989$	10.6453	+	6.14604i	0.338499	+	0.195433i
$990$		0			0
$991$	−23.8146	−	41.2481i	−0.756496	−	1.31029i	−0.944627	−	0.328145i	$-0.893576\pi$
$991$	−23.8146	−	41.2481i	−0.756496	−	1.31029i	0.188131	−	0.982144i	$-0.439757\pi$
$992$	0.786063	+	1.36150i	0.0249575	+	0.0432277i
$993$		0			0
$994$	−10.5751	+	0.443042i	−0.335421	+	0.0140524i
$995$	12.0246	−	6.94242i	0.381206	−	0.220090i
$996$		0			0
$997$		−	32.8902i		−	1.04164i	−0.853666	−	0.520822i	$-0.825626\pi$
$997$		−	32.8902i		−	1.04164i	0.853666	−	0.520822i	$-0.174374\pi$
$998$	−1.16711	+	0.673830i	−0.0369442	+	0.0213297i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.s.b.89.3		10
3.2	odd	2		63.2.s.b.47.3	yes	10
4.3	odd	2		3024.2.df.b.1601.1		10
7.2	even	3		1323.2.o.d.440.3		10
7.3	odd	6		189.2.i.b.143.3		10
7.4	even	3		1323.2.i.b.521.3		10
7.5	odd	6		1323.2.o.c.440.3		10
7.6	odd	2		1323.2.s.b.656.3		10
9.2	odd	6		567.2.p.c.404.3		10
9.4	even	3		63.2.i.b.5.3	✓	10
9.5	odd	6		189.2.i.b.152.3		10
9.7	even	3		567.2.p.d.404.3		10
12.11	even	2		1008.2.df.b.929.5		10
21.2	odd	6		441.2.o.c.146.3		10
21.5	even	6		441.2.o.d.146.3		10
21.11	odd	6		441.2.i.b.227.3		10
21.17	even	6		63.2.i.b.38.3	yes	10
21.20	even	2		441.2.s.b.362.3		10
28.3	even	6		3024.2.ca.b.2033.1		10
36.23	even	6		3024.2.ca.b.2609.1		10
36.31	odd	6		1008.2.ca.b.257.4		10
63.4	even	3		441.2.s.b.374.3		10
63.5	even	6		1323.2.o.d.881.3		10
63.13	odd	6		441.2.i.b.68.3		10
63.23	odd	6		1323.2.o.c.881.3		10
63.31	odd	6		63.2.s.b.59.3	yes	10
63.32	odd	6		1323.2.s.b.962.3		10
63.38	even	6		567.2.p.d.80.3		10
63.40	odd	6		441.2.o.c.293.3		10
63.41	even	6		1323.2.i.b.1097.3		10
63.52	odd	6		567.2.p.c.80.3		10
63.58	even	3		441.2.o.d.293.3		10
63.59	even	6	inner	189.2.s.b.17.3		10
84.59	odd	6		1008.2.ca.b.353.4		10
252.31	even	6		1008.2.df.b.689.5		10
252.59	odd	6		3024.2.df.b.17.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.3	✓	10	9.4	even	3
63.2.i.b.38.3	yes	10	21.17	even	6
63.2.s.b.47.3	yes	10	3.2	odd	2
63.2.s.b.59.3	yes	10	63.31	odd	6
189.2.i.b.143.3		10	7.3	odd	6
189.2.i.b.152.3		10	9.5	odd	6
189.2.s.b.17.3		10	63.59	even	6	inner
189.2.s.b.89.3		10	1.1	even	1	trivial
441.2.i.b.68.3		10	63.13	odd	6
441.2.i.b.227.3		10	21.11	odd	6
441.2.o.c.146.3		10	21.2	odd	6
441.2.o.c.293.3		10	63.40	odd	6
441.2.o.d.146.3		10	21.5	even	6
441.2.o.d.293.3		10	63.58	even	3
441.2.s.b.362.3		10	21.20	even	2
441.2.s.b.374.3		10	63.4	even	3
567.2.p.c.80.3		10	63.52	odd	6
567.2.p.c.404.3		10	9.2	odd	6
567.2.p.d.80.3		10	63.38	even	6
567.2.p.d.404.3		10	9.7	even	3
1008.2.ca.b.257.4		10	36.31	odd	6
1008.2.ca.b.353.4		10	84.59	odd	6
1008.2.df.b.689.5		10	252.31	even	6
1008.2.df.b.929.5		10	12.11	even	2
1323.2.i.b.521.3		10	7.4	even	3
1323.2.i.b.1097.3		10	63.41	even	6
1323.2.o.c.440.3		10	7.5	odd	6
1323.2.o.c.881.3		10	63.23	odd	6
1323.2.o.d.440.3		10	7.2	even	3
1323.2.o.d.881.3		10	63.5	even	6
1323.2.s.b.656.3		10	7.6	odd	2
1323.2.s.b.962.3		10	63.32	odd	6
3024.2.ca.b.2033.1		10	28.3	even	6
3024.2.ca.b.2609.1		10	36.23	even	6
3024.2.df.b.17.1		10	252.59	odd	6
3024.2.df.b.1601.1		10	4.3	odd	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.254498 - 0.146935i) q^{2} +(-0.956820 + 1.65726i) q^{4} -3.06027 q^{5} +(-1.22581 + 2.34465i) q^{7} +1.15010i q^{8} +O(q^{10})\)	\(q+(0.254498 - 0.146935i) q^{2} +(-0.956820 + 1.65726i) q^{4} -3.06027 q^{5} +(-1.22581 + 2.34465i) q^{7} +1.15010i q^{8} +(-0.778834 + 0.449660i) q^{10} +3.89647i q^{11} +(2.02935 - 1.17164i) q^{13} +(0.0325450 + 0.776824i) q^{14} +(-1.74465 - 3.02182i) q^{16} +(-1.68263 - 2.91440i) q^{17} +(2.20696 + 1.27419i) q^{19} +(2.92813 - 5.07167i) q^{20} +(0.572527 + 0.991647i) q^{22} +2.98075i q^{23} +4.36525 q^{25} +(0.344311 - 0.596363i) q^{26} +(-2.71283 - 4.27489i) q^{28} +(3.67241 + 2.12027i) q^{29} +(-0.409400 - 0.236367i) q^{31} +(-2.88005 - 1.66280i) q^{32} +(-0.856452 - 0.494473i) q^{34} +(3.75130 - 7.17527i) q^{35} +(-3.89395 + 6.74451i) q^{37} +0.748891 q^{38} -3.51962i q^{40} +(3.12737 + 5.41676i) q^{41} +(2.06191 - 3.57133i) q^{43} +(-6.45748 - 3.72823i) q^{44} +(0.437976 + 0.758597i) q^{46} +(2.02694 + 3.51076i) q^{47} +(-3.99479 - 5.74818i) q^{49} +(1.11095 - 0.641408i) q^{50} +4.48421i q^{52} +(4.99439 - 2.88351i) q^{53} -11.9243i q^{55} +(-2.69658 - 1.40980i) q^{56} +1.24616 q^{58} +(2.34352 - 4.05910i) q^{59} +(-1.38580 + 0.800092i) q^{61} -0.138922 q^{62} +6.00131 q^{64} +(-6.21035 + 3.58555i) q^{65} +(-0.787831 + 1.36456i) q^{67} +6.43989 q^{68} +(-0.0995964 - 2.37729i) q^{70} +13.6132i q^{71} +(-0.856452 + 0.494473i) q^{73} +2.28862i q^{74} +(-4.22333 + 2.43834i) q^{76} +(-9.13588 - 4.77633i) q^{77} +(4.63908 + 8.03512i) q^{79} +(5.33910 + 9.24760i) q^{80} +(1.59182 + 0.919038i) q^{82} +(5.49361 - 9.51520i) q^{83} +(5.14930 + 8.91884i) q^{85} -1.21186i q^{86} -4.48133 q^{88} +(-2.15849 + 3.73861i) q^{89} +(0.259511 + 6.19433i) q^{91} +(-4.93989 - 2.85205i) q^{92} +(1.03171 + 0.595655i) q^{94} +(-6.75390 - 3.89937i) q^{95} +(-4.98797 - 2.87980i) q^{97} +(-1.86128 - 0.875930i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} + 3 q^{7}+O(q^{10}) \) 10 * q + 4 * q^4 + 3 * q^7	\( 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} + 6 q^{13} + 6 q^{14} - 6 q^{16} + 12 q^{17} + 3 q^{19} + 3 q^{20} + 5 q^{22} - 14 q^{25} - 3 q^{26} + 2 q^{28} + 15 q^{29} - 9 q^{31} - 48 q^{32} + 3 q^{34} + 15 q^{35} + 6 q^{37} - 36 q^{38} + 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} - 15 q^{47} - 23 q^{49} - 3 q^{50} + 9 q^{53} + 51 q^{56} - 16 q^{58} + 18 q^{59} + 12 q^{61} - 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} + 54 q^{68} + 9 q^{70} + 3 q^{73} + 9 q^{76} - 45 q^{77} + 20 q^{79} + 30 q^{80} + 9 q^{82} + 15 q^{83} + 18 q^{85} + 16 q^{88} - 24 q^{89} - 24 q^{91} - 39 q^{92} - 3 q^{94} + 6 q^{97} - 45 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 + 3 * q^7 - 15 * q^10 + 6 * q^13 + 6 * q^14 - 6 * q^16 + 12 * q^17 + 3 * q^19 + 3 * q^20 + 5 * q^22 - 14 * q^25 - 3 * q^26 + 2 * q^28 + 15 * q^29 - 9 * q^31 - 48 * q^32 + 3 * q^34 + 15 * q^35 + 6 * q^37 - 36 * q^38 + 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 - 15 * q^47 - 23 * q^49 - 3 * q^50 + 9 * q^53 + 51 * q^56 - 16 * q^58 + 18 * q^59 + 12 * q^61 - 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 + 54 * q^68 + 9 * q^70 + 3 * q^73 + 9 * q^76 - 45 * q^77 + 20 * q^79 + 30 * q^80 + 9 * q^82 + 15 * q^83 + 18 * q^85 + 16 * q^88 - 24 * q^89 - 24 * q^91 - 39 * q^92 - 3 * q^94 + 6 * q^97 - 45 * q^98

Introduction

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