LMFDB - Embedded newform 756.2.n.b.19.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(19,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 5]))

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

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

chi := DirichletCharacter("756.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.n (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.17
Character	$\chi$	$=$	756.19
Dual form			756.2.n.b.199.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.581699 - 1.28904i) q^{2} +(-1.32325 + 1.49967i) q^{4} -0.299382i q^{5} +(-2.33495 + 1.24419i) q^{7} +(2.70287 + 0.833374i) q^{8} +O(q^{10})$	\(q+(-0.581699 - 1.28904i) q^{2} +(-1.32325 + 1.49967i) q^{4} -0.299382i q^{5} +(-2.33495 + 1.24419i) q^{7} +(2.70287 + 0.833374i) q^{8} +(-0.385916 + 0.174150i) q^{10} +0.0595863i q^{11} +(-1.63268 + 0.942631i) q^{13} +(2.96205 + 2.28611i) q^{14} +(-0.498000 - 3.96888i) q^{16} +(5.35164 - 3.08977i) q^{17} +(2.06839 - 3.58256i) q^{19} +(0.448974 + 0.396159i) q^{20} +(0.0768091 - 0.0346612i) q^{22} -5.76986i q^{23} +4.91037 q^{25} +(2.16482 + 1.55627i) q^{26} +(1.22387 - 5.14802i) q^{28} +(1.70505 - 2.95324i) q^{29} +(-3.14308 + 5.44397i) q^{31} +(-4.82636 + 2.95063i) q^{32} +(-7.09588 - 5.10116i) q^{34} +(0.372488 + 0.699044i) q^{35} +(1.19559 - 2.07083i) q^{37} +(-5.82124 - 0.582272i) q^{38} +(0.249498 - 0.809191i) q^{40} +(9.16797 - 5.29313i) q^{41} +(8.50766 + 4.91190i) q^{43} +(-0.0893595 - 0.0788477i) q^{44} +(-7.43759 + 3.35632i) q^{46} +(-1.95794 - 3.39125i) q^{47} +(3.90400 - 5.81023i) q^{49} +(-2.85636 - 6.32967i) q^{50} +(0.746824 - 3.69582i) q^{52} +(-3.44447 - 5.96600i) q^{53} +0.0178391 q^{55} +(-7.34794 + 1.41698i) q^{56} +(-4.79868 - 0.479989i) q^{58} +(-0.446612 + 0.773554i) q^{59} +(6.78818 - 3.91916i) q^{61} +(8.84582 + 0.884806i) q^{62} +(6.61097 + 4.50500i) q^{64} +(0.282207 + 0.488797i) q^{65} +(-9.83752 - 5.67969i) q^{67} +(-2.44795 + 12.1142i) q^{68} +(0.684420 - 0.886784i) q^{70} -1.25627i q^{71} +(-6.43167 + 3.71333i) q^{73} +(-3.36485 - 0.336571i) q^{74} +(2.63564 + 7.84253i) q^{76} +(-0.0741364 - 0.139131i) q^{77} +(1.34164 - 0.774598i) q^{79} +(-1.18821 + 0.149092i) q^{80} +(-12.1561 - 8.73889i) q^{82} +(-4.61172 + 7.98773i) q^{83} +(-0.925022 - 1.60219i) q^{85} +(1.38275 - 13.8240i) q^{86} +(-0.0496577 + 0.161054i) q^{88} +(-8.82012 - 5.09230i) q^{89} +(2.63943 - 4.23236i) q^{91} +(8.65287 + 7.63499i) q^{92} +(-3.23253 + 4.49655i) q^{94} +(-1.07255 - 0.619240i) q^{95} +(2.40408 + 1.38800i) q^{97} +(-9.76058 - 1.65261i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) $ 84 * q + q^2 + q^4 + 16 * q^8	$ 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) $ 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.581699	−	1.28904i	−0.411323	−	0.911490i
$2$	−0.581699	−	1.28904i	−0.411323	−	0.911490i
$3$		0			0
$3$		0			0
$4$	−1.32325	+	1.49967i	−0.661627	+	0.749833i
$5$		−	0.299382i		−	0.133888i	−0.997757	−	0.0669440i	$-0.978675\pi$
$5$		−	0.299382i		−	0.133888i	0.997757	−	0.0669440i	$-0.0213249\pi$
$6$		0			0
$7$	−2.33495	+	1.24419i	−0.882529	+	0.470258i
$7$	−2.33495	+	1.24419i	−0.882529	+	0.470258i
$8$	2.70287	+	0.833374i	0.955608	+	0.294642i
$9$		0			0
$10$	−0.385916	+	0.174150i	−0.122037	+	0.0550712i
$11$			0.0595863i			0.0179659i	0.999960	+	0.00898297i	$0.00285941\pi$
$11$			0.0595863i			0.0179659i	−0.999960	+	0.00898297i	$0.997141\pi$
$12$		0			0
$13$	−1.63268	+	0.942631i	−0.452825	+	0.261439i	−0.709023	−	0.705186i	$-0.750864\pi$
$13$	−1.63268	+	0.942631i	−0.452825	+	0.261439i	0.256197	+	0.966624i	$0.417530\pi$
$14$	2.96205	+	2.28611i	0.791640	+	0.610988i
$15$		0			0
$16$	−0.498000	−	3.96888i	−0.124500	−	0.992220i
$17$	5.35164	−	3.08977i	1.29796	−	0.749379i	0.317910	−	0.948121i	$-0.397019\pi$
$17$	5.35164	−	3.08977i	1.29796	−	0.749379i	0.980052	+	0.198742i	$0.0636855\pi$
$18$		0			0
$19$	2.06839	−	3.58256i	0.474521	−	0.821895i	−0.525053	−	0.851069i	$-0.675955\pi$
$19$	2.06839	−	3.58256i	0.474521	−	0.821895i	0.999574	+	0.0291746i	$0.00928788\pi$
$20$	0.448974	+	0.396159i	0.100394	+	0.0885838i
$21$		0			0
$22$	0.0768091	−	0.0346612i	0.0163758	−	0.00738980i
$23$		−	5.76986i		−	1.20310i	−0.798835	−	0.601550i	$-0.794550\pi$
$23$		−	5.76986i		−	1.20310i	0.798835	−	0.601550i	$-0.205450\pi$
$24$		0			0
$25$	4.91037			0.982074
$26$	2.16482	+	1.55627i	0.424556	+	0.305210i
$27$		0			0
$28$	1.22387	−	5.14802i	0.231289	−	0.972885i
$29$	1.70505	−	2.95324i	0.316621	−	0.548403i	−0.663160	−	0.748478i	$-0.730785\pi$
$29$	1.70505	−	2.95324i	0.316621	−	0.548403i	0.979781	+	0.200075i	$0.0641185\pi$
$30$		0			0
$31$	−3.14308	+	5.44397i	−0.564513	+	0.977765i	0.432582	+	0.901595i	$0.357603\pi$
$31$	−3.14308	+	5.44397i	−0.564513	+	0.977765i	−0.997095	+	0.0761706i	$0.975731\pi$
$32$	−4.82636	+	2.95063i	−0.853188	+	0.521603i
$33$		0			0
$34$	−7.09588	−	5.10116i	−1.21693	−	0.874842i
$35$	0.372488	+	0.699044i	0.0629619	+	0.118160i
$36$		0			0
$37$	1.19559	−	2.07083i	0.196554	−	0.340442i	−0.750855	−	0.660467i	$-0.770358\pi$
$37$	1.19559	−	2.07083i	0.196554	−	0.340442i	0.947409	+	0.320026i	$0.103692\pi$
$38$	−5.82124	−	0.582272i	−0.944330	−	0.0944570i
$39$		0			0
$40$	0.249498	−	0.809191i	0.0394490	−	0.127944i
$41$	9.16797	−	5.29313i	1.43180	−	0.826648i	0.434539	−	0.900653i	$-0.356911\pi$
$41$	9.16797	−	5.29313i	1.43180	−	0.826648i	0.997258	+	0.0740049i	$0.0235781\pi$
$42$		0			0
$43$	8.50766	+	4.91190i	1.29741	+	0.749058i	0.979955	−	0.199217i	$-0.0638399\pi$
$43$	8.50766	+	4.91190i	1.29741	+	0.749058i	0.317450	+	0.948275i	$0.397173\pi$
$44$	−0.0893595	−	0.0788477i	−0.0134715	−	0.0118867i
$45$		0			0
$46$	−7.43759	+	3.35632i	−1.09661	+	0.494862i
$47$	−1.95794	−	3.39125i	−0.285595	−	0.494664i	0.687159	−	0.726507i	$-0.258858\pi$
$47$	−1.95794	−	3.39125i	−0.285595	−	0.494664i	−0.972753	+	0.231843i	$0.925524\pi$
$48$		0			0
$49$	3.90400	−	5.81023i	0.557714	−	0.830033i
$50$	−2.85636	−	6.32967i	−0.403950	−	0.895150i
$51$		0			0
$52$	0.746824	−	3.69582i	0.103566	−	0.512518i
$53$	−3.44447	−	5.96600i	−0.473135	−	0.819494i	0.526392	−	0.850242i	$-0.323544\pi$
$53$	−3.44447	−	5.96600i	−0.473135	−	0.819494i	−0.999527	+	0.0307482i	$0.990211\pi$
$54$		0			0
$55$	0.0178391			0.00240542
$56$	−7.34794	+	1.41698i	−0.981909	+	0.189352i
$57$		0			0
$58$	−4.79868	−	0.479989i	−0.630097	−	0.0630257i
$59$	−0.446612	+	0.773554i	−0.0581439	+	0.100708i	−0.893632	−	0.448800i	$-0.851852\pi$
$59$	−0.446612	+	0.773554i	−0.0581439	+	0.100708i	0.835488	+	0.549508i	$0.185185\pi$
$60$		0			0
$61$	6.78818	−	3.91916i	0.869137	−	0.501797i	0.00207593	−	0.999998i	$-0.499339\pi$
$61$	6.78818	−	3.91916i	0.869137	−	0.501797i	0.867062	+	0.498201i	$0.166006\pi$
$62$	8.84582	+	0.884806i	1.12342	+	0.112370i
$63$		0			0
$64$	6.61097	+	4.50500i	0.826372	+	0.563125i
$65$	0.282207	+	0.488797i	0.0350035	+	0.0606278i
$66$		0			0
$67$	−9.83752	−	5.67969i	−1.20184	−	0.693885i	−0.240879	−	0.970555i	$-0.577436\pi$
$67$	−9.83752	−	5.67969i	−1.20184	−	0.693885i	−0.960965	+	0.276670i	$0.910769\pi$
$68$	−2.44795	+	12.1142i	−0.296857	+	1.46906i
$69$		0			0
$70$	0.684420	−	0.886784i	0.0818039	−	0.105991i
$71$		−	1.25627i		−	0.149092i	−0.997218	−	0.0745461i	$-0.976249\pi$
$71$		−	1.25627i		−	0.149092i	0.997218	−	0.0745461i	$-0.0237508\pi$
$72$		0			0
$73$	−6.43167	+	3.71333i	−0.752770	+	0.434612i	−0.826694	−	0.562652i	$-0.809781\pi$
$73$	−6.43167	+	3.71333i	−0.752770	+	0.434612i	0.0739240	+	0.997264i	$0.476448\pi$
$74$	−3.36485	−	0.336571i	−0.391156	−	0.0391255i
$75$		0			0
$76$	2.63564	+	7.84253i	0.302328	+	0.899600i
$77$	−0.0741364	−	0.139131i	−0.00844863	−	0.0158555i
$78$		0			0
$79$	1.34164	−	0.774598i	0.150947	−	0.0871491i	−0.422624	−	0.906305i	$-0.638891\pi$
$79$	1.34164	−	0.774598i	0.150947	−	0.0871491i	0.573571	+	0.819156i	$0.305558\pi$
$80$	−1.18821	+	0.149092i	−0.132846	+	0.0166690i
$81$		0			0
$82$	−12.1561	−	8.73889i	−1.34241	−	0.965048i
$83$	−4.61172	+	7.98773i	−0.506202	+	0.876767i	0.493773	+	0.869591i	$0.335617\pi$
$83$	−4.61172	+	7.98773i	−0.506202	+	0.876767i	−0.999974	+	0.00717577i	$0.997716\pi$
$84$		0			0
$85$	−0.925022	−	1.60219i	−0.100333	−	0.173781i
$86$	1.38275	−	13.8240i	0.149105	−	1.49068i
$87$		0			0
$88$	−0.0496577	+	0.161054i	−0.00529352	+	0.0171684i
$89$	−8.82012	−	5.09230i	−0.934931	−	0.539783i	−0.0465634	−	0.998915i	$-0.514827\pi$
$89$	−8.82012	−	5.09230i	−0.934931	−	0.539783i	−0.888368	+	0.459133i	$0.848160\pi$
$90$		0			0
$91$	2.63943	−	4.23236i	0.276688	−	0.443672i
$92$	8.65287	+	7.63499i	0.902124	+	0.796003i
$93$		0			0
$94$	−3.23253	+	4.49655i	−0.333410	+	0.463783i
$95$	−1.07255	−	0.619240i	−0.110042	−	0.0635327i
$96$		0			0
$97$	2.40408	+	1.38800i	0.244098	+	0.140930i	0.617059	−	0.786917i	$-0.288324\pi$
$97$	2.40408	+	1.38800i	0.244098	+	0.140930i	−0.372961	+	0.927847i	$0.621657\pi$
$98$	−9.76058	−	1.65261i	−0.985967	−	0.166939i
$99$		0			0
$100$	−6.49767	+	7.36392i	−0.649767	+	0.736392i
$101$			9.14587i			0.910048i	0.890479	+	0.455024i	$0.150369\pi$
$101$			9.14587i			0.910048i	−0.890479	+	0.455024i	$0.849631\pi$
$102$		0			0
$103$	3.53149			0.347968			0.173984	−	0.984748i	$-0.444336\pi$
$103$	3.53149			0.347968			0.173984	+	0.984748i	$0.444336\pi$
$104$	−5.19849	+	1.18717i	−0.509754	+	0.116411i
$105$		0			0
$106$	−5.68678	+	7.91048i	−0.552349	+	0.768334i
$107$	13.6356	+	7.87251i	1.31820	+	0.761064i	0.983439	−	0.181238i	$-0.0580104\pi$
$107$	13.6356	+	7.87251i	1.31820	+	0.761064i	0.334763	+	0.942302i	$0.391344\pi$
$108$		0			0
$109$	2.10955	+	3.65384i	0.202058	+	0.349975i	0.949191	−	0.314699i	$-0.101904\pi$
$109$	2.10955	+	3.65384i	0.202058	+	0.349975i	−0.747133	+	0.664674i	$0.768570\pi$
$110$	−0.0103770	−	0.0229953i	−0.000989405	−	0.00219252i
$111$		0			0
$112$	6.10083	+	8.64754i	0.576474	+	0.817115i
$113$	−1.55133	−	2.68699i	−0.145937	−	0.252771i	0.783785	−	0.621032i	$-0.213286\pi$
$113$	−1.55133	−	2.68699i	−0.145937	−	0.252771i	−0.929722	+	0.368262i	$0.879953\pi$
$114$		0			0
$115$	−1.72740			−0.161080
$116$	2.17266	+	6.46490i	0.201726	+	0.600251i
$117$		0			0
$118$	1.25694	+	0.125725i	0.115710	+	0.0115740i
$119$	−8.65156	+	13.8729i	−0.793088	+	1.27173i
$120$		0			0
$121$	10.9964			0.999677
$122$	−9.00063	−	6.47047i	−0.814879	−	0.585809i
$123$		0			0
$124$	−4.00505	−	11.9173i	−0.359664	−	1.07021i
$125$		−	2.96699i		−	0.265376i
$126$		0			0
$127$		−	16.0235i		−	1.42186i	−0.703264	−	0.710928i	$-0.748275\pi$
$127$		−	16.0235i		−	1.42186i	0.703264	−	0.710928i	$-0.251725\pi$
$128$	1.96154	−	11.1424i	0.173377	−	0.984856i
$129$		0			0
$130$	0.465920	−	0.648109i	0.0408639	−	0.0568429i
$131$	−3.49672			−0.305509			−0.152755	−	0.988264i	$-0.548814\pi$
$131$	−3.49672			−0.305509			−0.152755	+	0.988264i	$0.548814\pi$
$132$		0			0
$133$	−0.372223	+	10.9386i	−0.0322758	+	0.948493i
$134$	−1.59889	+	15.9848i	−0.138123	+	1.38088i
$135$		0			0
$136$	17.0397	−	3.89131i	1.46114	−	0.333678i
$137$	9.47581			0.809573			0.404787	−	0.914411i	$-0.367346\pi$
$137$	9.47581			0.809573			0.404787	+	0.914411i	$0.367346\pi$
$138$		0			0
$139$	−10.2899	−	17.8226i	−0.872776	−	1.51169i	−0.859113	−	0.511785i	$-0.828984\pi$
$139$	−10.2899	−	17.8226i	−0.872776	−	1.51169i	−0.0136624	−	0.999907i	$-0.504349\pi$
$140$	−1.54123	−	0.366405i	−0.130258	−	0.0309669i
$141$		0			0
$142$	−1.61939	+	0.730772i	−0.135896	+	0.0613250i
$143$	−0.0561678	−	0.0972856i	−0.00469699	−	0.00813543i
$144$		0			0
$145$	−0.884148	−	0.510463i	−0.0734245	−	0.0423917i
$146$	8.52792	+	6.13065i	0.705776	+	0.507376i
$147$		0			0
$148$	1.52348	+	4.53322i	0.125229	+	0.372628i
$149$	−3.48322			−0.285357			−0.142678	−	0.989769i	$-0.545571\pi$
$149$	−3.48322			−0.285357			−0.142678	+	0.989769i	$0.545571\pi$
$150$		0			0
$151$			12.5277i			1.01949i	0.860326	+	0.509745i	$0.170260\pi$
$151$			12.5277i			1.01949i	−0.860326	+	0.509745i	$0.829740\pi$
$152$	8.57619	−	7.95943i	0.695621	−	0.645595i
$153$		0			0
$154$	−0.136221	+	0.176497i	−0.0109770	+	0.0142225i
$155$	1.62983	+	0.940982i	0.130911	+	0.0755815i
$156$		0			0
$157$	2.55710	+	1.47634i	0.204078	+	0.117825i	0.598556	−	0.801081i	$-0.295741\pi$
$157$	2.55710	+	1.47634i	0.204078	+	0.117825i	−0.394478	+	0.918905i	$0.629075\pi$
$158$	−1.77892	−	1.27885i	−0.141523	−	0.101740i
$159$		0			0
$160$	0.883368	+	1.44493i	0.0698363	+	0.114232i
$161$	7.17878	+	13.4723i	0.565767	+	1.06177i
$162$		0			0
$163$	12.0459	+	6.95471i	0.943509	+	0.544735i	0.891058	−	0.453888i	$-0.149964\pi$
$163$	12.0459	+	6.95471i	0.943509	+	0.544735i	0.0524503	+	0.998624i	$0.483297\pi$
$164$	−4.19362	+	20.7531i	−0.327467	+	1.62054i
$165$		0			0
$166$	12.9791	+	1.29824i	1.00738	+	0.100763i
$167$	−6.68416	−	11.5773i	−0.517236	−	0.895879i	−0.999800	−	0.0200183i	$-0.993628\pi$
$167$	−6.68416	−	11.5773i	−0.517236	−	0.895879i	0.482563	−	0.875861i	$-0.339706\pi$
$168$		0			0
$169$	−4.72289	+	8.18029i	−0.363300	+	0.629253i
$170$	−1.52720	+	2.12438i	−0.117131	+	0.162933i
$171$		0			0
$172$	−18.6240	+	6.25896i	−1.42007	+	0.477241i
$173$	−4.16668	+	2.40563i	−0.316787	+	0.182897i	−0.649960	−	0.759969i	$-0.725214\pi$
$173$	−4.16668	+	2.40563i	−0.316787	+	0.182897i	0.333173	+	0.942866i	$0.391881\pi$
$174$		0			0
$175$	−11.4655	+	6.10942i	−0.866709	+	0.461828i
$176$	0.236491	−	0.0296739i	0.0178262	−	0.00223676i
$177$		0			0
$178$	−1.43353	+	14.3317i	−0.107448	+	1.07421i
$179$	9.04033	−	5.21944i	0.675706	−	0.390119i	−0.122529	−	0.992465i	$-0.539100\pi$
$179$	9.04033	−	5.21944i	0.675706	−	0.390119i	0.798235	+	0.602346i	$0.205767\pi$
$180$		0			0
$181$			13.3604i			0.993072i	0.868016	+	0.496536i	$0.165395\pi$
$181$			13.3604i			0.993072i	−0.868016	+	0.496536i	$0.834605\pi$
$182$	−6.99104	−	0.940377i	−0.518210	−	0.0697054i
$183$		0			0
$184$	4.80845	−	15.5952i	0.354484	−	1.14969i
$185$	−0.619969	−	0.357939i	−0.0455810	−	0.0263162i
$186$		0			0
$187$	0.184108	+	0.318884i	0.0134633	+	0.0233191i
$188$	7.67659	+	1.55123i	0.559873	+	0.113135i
$189$		0			0
$190$	−0.174322	+	1.74278i	−0.0126466	+	0.126434i
$191$	16.7209	−	9.65383i	1.20988	−	0.698527i	0.247150	−	0.968977i	$-0.420506\pi$
$191$	16.7209	−	9.65383i	1.20988	−	0.698527i	0.962734	+	0.270450i	$0.0871726\pi$
$192$		0			0
$193$	−0.755905	+	1.30927i	−0.0544112	+	0.0942430i	−0.891948	−	0.452138i	$-0.850662\pi$
$193$	−0.755905	+	1.30927i	−0.0544112	+	0.0942430i	0.837537	+	0.546381i	$0.183995\pi$
$194$	0.390735	−	3.90636i	0.0280531	−	0.280460i
$195$		0			0
$196$	3.54743	+	13.5431i	0.253388	+	0.967365i
$197$	1.13305			0.0807266			0.0403633	−	0.999185i	$-0.487148\pi$
$197$	1.13305			0.0807266			0.0403633	+	0.999185i	$0.487148\pi$
$198$		0			0
$199$	9.90940	+	17.1636i	0.702458	+	1.21669i	0.967601	+	0.252484i	$0.0812477\pi$
$199$	9.90940	+	17.1636i	0.702458	+	1.21669i	−0.265143	+	0.964209i	$0.585419\pi$
$200$	13.2721	+	4.09218i	0.938477	+	0.289361i
$201$		0			0
$202$	11.7894	−	5.32014i	0.829500	−	0.374324i
$203$	−0.306838	+	9.01708i	−0.0215358	+	0.632875i
$204$		0			0
$205$	−1.58467	−	2.74473i	−0.110678	−	0.191700i
$206$	−2.05426	−	4.55224i	−0.143127	−	0.317169i
$207$		0			0
$208$	4.55426	+	6.01050i	0.315781	+	0.416753i
$209$	0.213471	+	0.123248i	0.0147661	+	0.00852522i
$210$		0			0
$211$	19.2102	−	11.0910i	1.32248	−	0.763536i	0.338360	−	0.941017i	$-0.390128\pi$
$211$	19.2102	−	11.0910i	1.32248	−	0.763536i	0.984124	+	0.177480i	$0.0567946\pi$
$212$	13.5049	+	2.72897i	0.927522	+	0.187427i
$213$		0			0
$214$	2.21619	−	22.1563i	0.151495	−	1.51457i
$215$	1.47054	−	2.54704i	0.100290	−	0.173707i
$216$		0			0
$217$	0.565621	−	16.6220i	0.0383969	−	1.12837i
$218$	3.48283	−	4.84473i	0.235887	−	0.328126i
$219$		0			0
$220$	−0.0236056	+	0.0267527i	−0.00159149	+	0.00180366i
$221$	−5.82502	+	10.0892i	−0.391833	+	0.678675i
$222$		0			0
$223$	−5.48371	+	9.49807i	−0.367217	+	0.636038i	−0.989129	−	0.147049i	$-0.953023\pi$
$223$	−5.48371	+	9.49807i	−0.367217	+	0.636038i	0.621913	+	0.783087i	$0.286356\pi$
$224$	7.59819	−	12.8945i	0.507675	−	0.861549i
$225$		0			0
$226$	−2.56123	+	3.56275i	−0.170371	+	0.236991i
$227$	−13.5475			−0.899177			−0.449588	−	0.893236i	$-0.648429\pi$
$227$	−13.5475			−0.899177			−0.449588	+	0.893236i	$0.648429\pi$
$228$		0			0
$229$			22.5988i			1.49337i	0.665176	+	0.746687i	$0.268357\pi$
$229$			22.5988i			1.49337i	−0.665176	+	0.746687i	$0.731643\pi$
$230$	1.00482	+	2.22668i	0.0662561	+	0.146823i
$231$		0			0
$232$	7.06969	−	6.56127i	0.464148	−	0.430768i
$233$	−13.0592	+	22.6193i	−0.855539	+	1.48184i	0.0206048	+	0.999788i	$0.493441\pi$
$233$	−13.0592	+	22.6193i	−0.855539	+	1.48184i	−0.876144	+	0.482050i	$0.839892\pi$
$234$		0			0
$235$	−1.01528	+	0.586172i	−0.0662296	+	0.0382377i
$236$	−0.569093	−	1.69338i	−0.0370448	−	0.110229i
$237$		0			0
$238$	22.9153	+	3.08238i	1.48538	+	0.199801i
$239$	24.8327	−	14.3372i	1.60629	−	0.927393i	0.616102	−	0.787666i	$-0.288711\pi$
$239$	24.8327	−	14.3372i	1.60629	−	0.927393i	0.990190	−	0.139727i	$-0.0446226\pi$
$240$		0			0
$241$		−	10.6743i		−	0.687594i	−0.939044	−	0.343797i	$-0.888287\pi$
$241$		−	10.6743i		−	0.687594i	0.939044	−	0.343797i	$-0.111713\pi$
$242$	−6.39662	−	14.1749i	−0.411190	−	0.911195i
$243$		0			0
$244$	−3.10505	+	15.3660i	−0.198781	+	0.983710i
$245$	−1.73948	−	1.16879i	−0.111131	−	0.0746712i
$246$		0			0
$247$			7.79891i			0.496233i
$248$	−13.0322	+	12.0950i	−0.827544	+	0.768031i
$249$		0			0
$250$	−3.82457	+	1.72589i	−0.241887	+	0.109155i
$251$	−20.5004			−1.29397			−0.646987	−	0.762501i	$-0.723971\pi$
$251$	−20.5004			−1.29397			−0.646987	+	0.762501i	$0.723971\pi$
$252$		0			0
$253$	0.343804			0.0216148
$254$	−20.6550	+	9.32085i	−1.29601	+	0.584842i
$255$		0			0
$256$	−15.5040	+	3.95300i	−0.969000	+	0.247062i
$257$		−	4.62838i		−	0.288711i	−0.989526	−	0.144355i	$-0.953889\pi$
$257$		−	4.62838i		−	0.288711i	0.989526	−	0.144355i	$-0.0461108\pi$
$258$		0			0
$259$	−0.215156	+	6.32282i	−0.0133692	+	0.392881i
$260$	−1.10646	−	0.223586i	−0.0686200	−	0.0138662i
$261$		0			0
$262$	2.03403	+	4.50741i	0.125663	+	0.278469i
$263$		−	29.8367i		−	1.83981i	−0.392142	−	0.919905i	$-0.628266\pi$
$263$		−	29.8367i		−	1.83981i	0.392142	−	0.919905i	$-0.371734\pi$
$264$		0			0
$265$	−1.78612	+	1.03122i	−0.109720	+	0.0633470i
$266$	14.3168	−	5.88313i	0.877818	−	0.360718i
$267$		0			0
$268$	21.5352	−	7.23732i	1.31547	−	0.442090i
$269$	13.3935	−	7.73276i	0.816618	−	0.471475i	−0.0326305	−	0.999467i	$-0.510388\pi$
$269$	13.3935	−	7.73276i	0.816618	−	0.471475i	0.849249	+	0.527993i	$0.177055\pi$
$270$		0			0
$271$	11.4019	−	19.7487i	0.692616	−	1.19965i	−0.278362	−	0.960476i	$-0.589791\pi$
$271$	11.4019	−	19.7487i	0.692616	−	1.19965i	0.970978	−	0.239170i	$-0.0768752\pi$
$272$	−14.9280	−	19.7013i	−0.905145	−	1.19457i
$273$		0			0
$274$	−5.51206	−	12.2147i	−0.332996	−	0.737917i
$275$			0.292591i			0.0176439i
$276$		0			0
$277$	−19.5300			−1.17344			−0.586722	−	0.809788i	$-0.699582\pi$
$277$	−19.5300			−1.17344			−0.586722	+	0.809788i	$0.699582\pi$
$278$	−16.9884	+	23.6314i	−1.01890	+	1.41732i
$279$		0			0
$280$	0.424219	+	2.19984i	0.0253519	+	0.131466i
$281$	−3.65759	+	6.33513i	−0.218194	+	0.377922i	−0.954256	−	0.298992i	$-0.903350\pi$
$281$	−3.65759	+	6.33513i	−0.218194	+	0.377922i	0.736062	+	0.676914i	$0.236683\pi$
$282$		0			0
$283$	−9.39211	+	16.2676i	−0.558303	+	0.967009i	0.439335	+	0.898323i	$0.355214\pi$
$283$	−9.39211	+	16.2676i	−0.558303	+	0.967009i	−0.997638	+	0.0686860i	$0.978119\pi$
$284$	1.88399	+	1.66237i	0.111794	+	0.0986434i
$285$		0			0
$286$	−0.0927323	+	0.128994i	−0.00548338	+	0.00762755i
$287$	−14.8211	+	23.7659i	−0.874864	+	1.40286i
$288$		0			0
$289$	10.5933	−	18.3482i	0.623137	−	1.07931i
$290$	−0.143700	+	1.43664i	−0.00843837	+	0.0843624i
$291$		0			0
$292$	2.94198	−	14.5590i	0.172166	−	0.852003i
$293$	−27.7732	+	16.0349i	−1.62253	+	0.936766i	−0.636285	+	0.771454i	$0.719530\pi$
$293$	−27.7732	+	16.0349i	−1.62253	+	0.936766i	−0.986241	+	0.165312i	$0.947137\pi$
$294$		0			0
$295$	0.231588	+	0.133708i	0.0134836	+	0.00778476i
$296$	4.95730	−	4.60079i	0.288137	−	0.267416i
$297$		0			0
$298$	2.02619	+	4.49002i	0.117374	+	0.260100i
$299$	5.43885	+	9.42036i	0.314537	+	0.544794i
$300$		0			0
$301$	−25.9763	−	0.883935i	−1.49725	−	0.0509492i
$302$	16.1487	−	7.28734i	0.929254	−	0.419339i
$303$		0			0
$304$	−15.2488	−	6.42508i	−0.874578	−	0.368503i
$305$	−1.17333	−	2.03226i	−0.0671845	−	0.116367i
$306$		0			0
$307$	−11.7362			−0.669818			−0.334909	−	0.942251i	$-0.608706\pi$
$307$	−11.7362			−0.669818			−0.334909	+	0.942251i	$0.608706\pi$
$308$	0.306751	+	0.0729258i	0.0174788	+	0.00415533i
$309$		0			0
$310$	0.264895	−	2.64828i	0.0150450	−	0.150412i
$311$	−14.1670	+	24.5379i	−0.803336	+	1.39142i	0.114073	+	0.993472i	$0.463610\pi$
$311$	−14.1670	+	24.5379i	−0.803336	+	1.39142i	−0.917409	+	0.397947i	$0.869723\pi$
$312$		0			0
$313$	2.79032	−	1.61099i	0.157718	−	0.0910585i	−0.419064	−	0.907957i	$-0.637642\pi$
$313$	2.79032	−	1.61099i	0.157718	−	0.0910585i	0.576782	+	0.816898i	$0.304308\pi$
$314$	0.415604	−	4.15499i	0.0234539	−	0.234479i
$315$		0			0
$316$	−0.613696	+	3.03701i	−0.0345231	+	0.170845i
$317$	−15.3366	−	26.5637i	−0.861387	−	1.49197i	−0.870591	−	0.492008i	$-0.836263\pi$
$317$	−15.3366	−	26.5637i	−0.861387	−	1.49197i	0.00920371	−	0.999958i	$-0.497070\pi$
$318$		0			0
$319$	0.175973	+	0.101598i	0.00985257	+	0.00568838i
$320$	1.34872	−	1.97921i	0.0753956	−	0.110641i
$321$		0			0
$322$	13.1905	−	17.0906i	0.735079	−	0.952421i
$323$		−	25.5634i		−	1.42238i
$324$		0			0
$325$	−8.01709	+	4.62867i	−0.444708	+	0.256752i
$326$	1.95782	−	19.5732i	0.108434	−	1.08406i
$327$		0			0
$328$	29.1910	−	6.66627i	1.61180	−	0.368083i
$329$	8.79103	+	5.48236i	0.484665	+	0.302252i
$330$		0			0
$331$	−13.2595	+	7.65539i	−0.728810	+	0.420778i	−0.817987	−	0.575237i	$-0.804910\pi$
$331$	−13.2595	+	7.65539i	−0.728810	+	0.420778i	0.0891769	+	0.996016i	$0.471576\pi$
$332$	−5.87646	−	17.4858i	−0.322512	−	0.959659i
$333$		0			0
$334$	−11.0355	+	15.3507i	−0.603834	+	0.839951i
$335$	−1.70040	+	2.94518i	−0.0929028	+	0.160912i
$336$		0			0
$337$	−15.4560	−	26.7706i	−0.841943	−	1.45829i	−0.888250	−	0.459361i	$-0.848078\pi$
$337$	−15.4560	−	26.7706i	−0.841943	−	1.45829i	0.0463067	−	0.998927i	$-0.485255\pi$
$338$	13.2920	+	1.32954i	0.722991	+	0.0723175i
$339$		0			0
$340$	3.62678	+	0.732873i	0.196690	+	0.0397456i
$341$	−0.324386	−	0.187284i	−0.0175665	−	0.0101420i
$342$		0			0
$343$	−1.88664	+	18.4239i	−0.101869	+	0.994798i
$344$	18.9016	+	20.3663i	1.01911	+	1.09808i
$345$		0			0
$346$	5.52471	+	3.97167i	0.297010	+	0.213518i
$347$	−6.11697	−	3.53163i	−0.328376	−	0.189588i	0.326744	−	0.945113i	$-0.394049\pi$
$347$	−6.11697	−	3.53163i	−0.328376	−	0.189588i	−0.655120	+	0.755525i	$0.727382\pi$
$348$		0			0
$349$	−17.0097	−	9.82058i	−0.910510	−	0.525683i	−0.0299150	−	0.999552i	$-0.509524\pi$
$349$	−17.0097	−	9.82058i	−0.910510	−	0.525683i	−0.880595	+	0.473869i	$0.842857\pi$
$350$	14.5447	+	11.2256i	0.777449	+	0.600035i
$351$		0			0
$352$	−0.175817	−	0.287585i	−0.00937109	−	0.0153283i
$353$			4.34597i			0.231313i	0.993289	+	0.115656i	$0.0368971\pi$
$353$			4.34597i			0.231313i	−0.993289	+	0.115656i	$0.963103\pi$
$354$		0			0
$355$	−0.376106			−0.0199616
$356$	19.3080	−	6.48884i	1.02332	−	0.343908i
$357$		0			0
$358$	−11.9868	−	8.61722i	−0.633523	−	0.455434i
$359$	8.64868	+	4.99331i	0.456460	+	0.263537i	0.710554	−	0.703642i	$-0.248444\pi$
$359$	8.64868	+	4.99331i	0.456460	+	0.263537i	−0.254095	+	0.967179i	$0.581778\pi$
$360$		0			0
$361$	0.943525	+	1.63423i	0.0496592	+	0.0860122i
$362$	17.2221	−	7.77173i	0.905175	−	0.408473i
$363$		0			0
$364$	2.85449	+	9.55876i	0.149616	+	0.501015i
$365$	1.11170	+	1.92553i	0.0581893	+	0.100787i
$366$		0			0
$367$	−6.60005			−0.344520			−0.172260	−	0.985052i	$-0.555107\pi$
$367$	−6.60005			−0.344520			−0.172260	+	0.985052i	$0.555107\pi$
$368$	−22.8999	+	2.87339i	−1.19374	+	0.149786i
$369$		0			0
$370$	−0.100763	+	1.00738i	−0.00523844	+	0.0523711i
$371$	15.4655	+	9.64476i	0.802929	+	0.500731i
$372$		0			0
$373$	−26.5380			−1.37409			−0.687043	−	0.726617i	$-0.741092\pi$
$373$	−26.5380			−1.37409			−0.687043	+	0.726617i	$0.741092\pi$
$374$	0.303959	−	0.422817i	0.0157174	−	0.0218633i
$375$		0			0
$376$	−2.46587	−	10.7978i	−0.127167	−	0.556853i
$377$			6.42895i			0.331108i
$378$		0			0
$379$		−	25.5334i		−	1.31156i	−0.754951	−	0.655781i	$-0.772339\pi$
$379$		−	25.5334i		−	1.31156i	0.754951	−	0.655781i	$-0.227661\pi$
$380$	2.34792	−	0.789063i	0.120445	−	0.0404781i
$381$		0			0
$382$	−22.1707	−	15.9383i	−1.13435	−	0.815477i
$383$	16.9100			0.864059			0.432029	−	0.901860i	$-0.357798\pi$
$383$	16.9100			0.864059			0.432029	+	0.901860i	$0.357798\pi$
$384$		0			0
$385$	−0.0416534	+	0.0221951i	−0.00212285	+	0.00113117i
$386$	2.12740	+	0.212794i	0.108282	+	0.0108310i
$387$		0			0
$388$	−5.26275	+	1.76865i	−0.267176	+	0.0897896i
$389$	−20.6965			−1.04935			−0.524677	−	0.851301i	$-0.675814\pi$
$389$	−20.6965			−1.04935			−0.524677	+	0.851301i	$0.675814\pi$
$390$		0			0
$391$	−17.8275	−	30.8782i	−0.901577	−	1.56158i
$392$	15.3941	−	12.4508i	0.777519	−	0.628860i
$393$		0			0
$394$	−0.659095	−	1.46055i	−0.0332047	−	0.0735815i
$395$	−0.231901	−	0.401665i	−0.0116682	−	0.0202099i
$396$		0			0
$397$	−14.8979	−	8.60130i	−0.747703	−	0.431687i	0.0771601	−	0.997019i	$-0.475415\pi$
$397$	−14.8979	−	8.60130i	−0.747703	−	0.431687i	−0.824863	+	0.565332i	$0.808748\pi$
$398$	16.3603	−	22.7576i	0.820066	−	1.14074i
$399$		0			0
$400$	−2.44536	−	19.4887i	−0.122268	−	0.974433i
$401$	22.0882			1.10303			0.551517	−	0.834164i	$-0.314049\pi$
$401$	22.0882			1.10303			0.551517	+	0.834164i	$0.314049\pi$
$402$		0			0
$403$		−	11.8510i		−	0.590342i
$404$	−13.7158	−	12.1023i	−0.682385	−	0.602112i
$405$		0			0
$406$	11.8019	−	4.84969i	0.585717	−	0.240686i
$407$	0.123393	+	0.0712409i	0.00611635	+	0.00353128i
$408$		0			0
$409$	22.5386	+	13.0126i	1.11446	+	0.643434i	0.939981	−	0.341227i	$-0.110842\pi$
$409$	22.5386	+	13.0126i	1.11446	+	0.643434i	0.174480	+	0.984661i	$0.444176\pi$
$410$	−2.61627	+	3.63931i	−0.129208	+	0.179733i
$411$		0			0
$412$	−4.67306	+	5.29606i	−0.230225	+	0.260918i
$413$	0.0803713	−	2.36188i	0.00395481	−	0.116220i
$414$		0			0
$415$	2.39138	+	1.38067i	0.117388	+	0.0677743i
$416$	5.09857	−	9.36693i	0.249978	−	0.459252i
$417$		0			0
$418$	0.0346954	−	0.346866i	0.00169701	−	0.0169658i
$419$	4.48691	+	7.77155i	0.219200	+	0.379665i	0.954564	−	0.298007i	$-0.0963220\pi$
$419$	4.48691	+	7.77155i	0.219200	+	0.379665i	−0.735364	+	0.677673i	$0.762989\pi$
$420$		0			0
$421$	5.23952	−	9.07511i	0.255358	−	0.442294i	−0.709634	−	0.704570i	$-0.751140\pi$
$421$	5.23952	−	9.07511i	0.255358	−	0.442294i	0.964993	+	0.262276i	$0.0844732\pi$
$422$	−25.4713	−	18.3111i	−1.23992	−	0.891370i
$423$		0			0
$424$	−4.33804	−	18.9958i	−0.210674	−	0.922520i
$425$	26.2785	−	15.1719i	1.27470	−	0.735946i
$426$		0			0
$427$	−10.9739	+	17.5968i	−0.531065	+	0.851569i
$428$	−29.8495	+	10.0315i	−1.44283	+	0.484891i
$429$		0			0
$430$	−4.13865	−	0.413970i	−0.199584	−	0.0199634i
$431$	3.87571	−	2.23764i	0.186687	−	0.107784i	−0.403744	−	0.914872i	$-0.632291\pi$
$431$	3.87571	−	2.23764i	0.186687	−	0.107784i	0.590430	+	0.807088i	$0.298958\pi$
$432$		0			0
$433$		−	19.2972i		−	0.927365i	−0.886001	−	0.463683i	$-0.846528\pi$
$433$		−	19.2972i		−	0.927365i	0.886001	−	0.463683i	$-0.153472\pi$
$434$	−21.7554	+	8.93987i	−1.04429	+	0.429127i
$435$		0			0
$436$	−8.27101	−	1.67134i	−0.396110	−	0.0800428i
$437$	−20.6709	−	11.9343i	−0.988821	−	0.570896i
$438$		0			0
$439$	11.9973	+	20.7798i	0.572598	+	0.991768i	0.996298	+	0.0859657i	$0.0273975\pi$
$439$	11.9973	+	20.7798i	0.572598	+	0.991768i	−0.423701	+	0.905802i	$0.639269\pi$
$440$	0.0482167	+	0.0148666i	0.00229864	+	0.000708739i
$441$		0			0
$442$	16.3938	+	1.63980i	0.779776	+	0.0779973i
$443$	0.541223	−	0.312475i	0.0257143	−	0.0148461i	−0.487088	−	0.873353i	$-0.661941\pi$
$443$	0.541223	−	0.312475i	0.0257143	−	0.0148461i	0.512802	+	0.858507i	$0.328607\pi$
$444$		0			0
$445$	−1.52455	+	2.64059i	−0.0722704	+	0.125176i
$446$	15.4333	+	1.54372i	0.730787	+	0.0730972i
$447$		0			0
$448$	−21.0414	−	2.29367i	−0.994111	−	0.108366i
$449$	22.2301			1.04910			0.524551	−	0.851379i	$-0.324233\pi$
$449$	22.2301			1.04910			0.524551	+	0.851379i	$0.324233\pi$
$450$		0			0
$451$	0.315398	+	0.546285i	0.0148515	+	0.0257236i
$452$	6.08240	+	1.22908i	0.286092	+	0.0578113i
$453$		0			0
$454$	7.88054	+	17.4632i	0.369852	+	0.819590i
$455$	−1.26709	−	0.790199i	−0.0594023	−	0.0370451i
$456$		0			0
$457$	−1.91116	−	3.31023i	−0.0894004	−	0.154846i	0.817857	−	0.575421i	$-0.195162\pi$
$457$	−1.91116	−	3.31023i	−0.0894004	−	0.154846i	−0.907258	+	0.420575i	$0.861828\pi$
$458$	29.1308	−	13.1457i	1.36119	−	0.614259i
$459$		0			0
$460$	2.28578	−	2.59052i	0.106575	−	0.120783i
$461$	−0.767044	−	0.442853i	−0.0357248	−	0.0206257i	0.482031	−	0.876154i	$-0.339899\pi$
$461$	−0.767044	−	0.442853i	−0.0357248	−	0.0206257i	−0.517756	+	0.855528i	$0.673233\pi$
$462$		0			0
$463$	15.7549	−	9.09610i	0.732193	−	0.422732i	−0.0870311	−	0.996206i	$-0.527738\pi$
$463$	15.7549	−	9.09610i	0.732193	−	0.422732i	0.819224	+	0.573474i	$0.194405\pi$
$464$	−12.5702	−	5.29644i	−0.583555	−	0.245881i
$465$		0			0
$466$	36.7537	+	3.67630i	1.70258	+	0.170301i
$467$	3.88452	−	6.72818i	0.179754	−	0.311343i	−0.762042	−	0.647527i	$-0.775803\pi$
$467$	3.88452	−	6.72818i	0.179754	−	0.311343i	0.941796	+	0.336184i	$0.109136\pi$
$468$		0			0
$469$	30.0367	+	1.02211i	1.38697	+	0.0471964i
$470$	1.34619	+	0.967762i	0.0620950	+	0.0446395i
$471$		0			0
$472$	−1.85179	+	1.71862i	−0.0852356	+	0.0791058i
$473$	−0.292682	+	0.506940i	−0.0134575	+	0.0233091i
$474$		0			0
$475$	10.1566	−	17.5917i	0.466015	−	0.807162i
$476$	−9.35650	−	31.3318i	−0.428854	−	1.43609i
$477$		0			0
$478$	−32.9263	−	23.6704i	−1.50601	−	1.08266i
$479$	3.38462			0.154647			0.0773237	−	0.997006i	$-0.475363\pi$
$479$	3.38462			0.154647			0.0773237	+	0.997006i	$0.475363\pi$
$480$		0			0
$481$			4.50801i			0.205547i
$482$	−13.7596	+	6.20924i	−0.626735	+	0.282823i
$483$		0			0
$484$	−14.5511	+	16.4910i	−0.661413	+	0.749591i
$485$	0.415542	−	0.719741i	0.0188688	−	0.0326817i
$486$		0			0
$487$	17.1308	−	9.89047i	0.776271	−	0.448180i	−0.0588362	−	0.998268i	$-0.518739\pi$
$487$	17.1308	−	9.89047i	0.776271	−	0.448180i	0.835107	+	0.550087i	$0.185406\pi$
$488$	21.6137	−	4.93586i	0.978405	−	0.223436i
$489$		0			0
$490$	−0.494764	+	2.92215i	−0.0223511	+	0.132009i
$491$	−21.6474	+	12.4982i	−0.976935	+	0.564034i	−0.901343	−	0.433105i	$-0.857418\pi$
$491$	−21.6474	+	12.4982i	−0.976935	+	0.564034i	−0.0755917	+	0.997139i	$0.524085\pi$
$492$		0			0
$493$		−	21.0729i		−	0.949075i
$494$	10.0531	−	4.53662i	0.452311	−	0.204112i
$495$		0			0
$496$	23.1717	+	9.76339i	1.04044	+	0.438389i
$497$	1.56304	+	2.93334i	0.0701118	+	0.131578i
$498$		0			0
$499$			1.32045i			0.0591114i	0.999563	+	0.0295557i	$0.00940925\pi$
$499$			1.32045i			0.0591114i	−0.999563	+	0.0295557i	$0.990591\pi$
$500$	4.44950	+	3.92608i	0.198988	+	0.175580i
$501$		0			0
$502$	11.9251	+	26.4259i	0.532242	+	1.17944i
$503$	−30.0706			−1.34078			−0.670391	−	0.742008i	$-0.733874\pi$
$503$	−30.0706			−1.34078			−0.670391	+	0.742008i	$0.733874\pi$
$504$		0			0
$505$	2.73811			0.121844
$506$	−0.199991	−	0.443178i	−0.00889066	−	0.0197017i
$507$		0			0
$508$	24.0299	+	21.2032i	1.06616	+	0.940739i
$509$			30.5614i			1.35461i	0.735701	+	0.677306i	$0.236853\pi$
$509$			30.5614i			1.35461i	−0.735701	+	0.677306i	$0.763147\pi$
$510$		0			0
$511$	10.3976	−	16.6726i	0.459961	−	0.737554i
$512$	14.1142	+	17.6858i	0.623767	+	0.781611i
$513$		0			0
$514$	−5.96617	+	2.69232i	−0.263157	+	0.118753i
$515$		−	1.05727i		−	0.0465887i
$516$		0			0
$517$	0.202072	−	0.116666i	0.00888711	−	0.00513097i
$518$	8.27553	−	3.40063i	0.363606	−	0.149415i
$519$		0			0
$520$	0.355417	+	1.55634i	0.0155861	+	0.0682499i
$521$	−4.05425	+	2.34072i	−0.177620	+	0.102549i	−0.586174	−	0.810185i	$-0.699367\pi$
$521$	−4.05425	+	2.34072i	−0.177620	+	0.102549i	0.408554	+	0.912734i	$0.366033\pi$
$522$		0			0
$523$	−13.1758	+	22.8212i	−0.576139	+	0.997902i	0.419778	+	0.907627i	$0.362108\pi$
$523$	−13.1758	+	22.8212i	−0.576139	+	0.997902i	−0.995917	+	0.0902752i	$0.971225\pi$
$524$	4.62704	−	5.24391i	0.202133	−	0.229081i
$525$		0			0
$526$	−38.4607	+	17.3560i	−1.67697	+	0.756756i
$527$			38.8455i			1.69214i
$528$		0			0
$529$	−10.2913			−0.447447
$530$	2.36826	+	1.70252i	0.102871	+	0.0739528i
$531$		0			0
$532$	−15.9116	−	15.0327i	−0.689857	−	0.651750i
$533$	−9.97894	+	17.2840i	−0.432236	+	0.748654i
$534$		0			0
$535$	2.35689	−	4.08226i	0.101897	−	0.176491i
$536$	−21.8562	−	23.5498i	−0.944043	−	1.01720i
$537$		0			0
$538$	−17.7589	−	12.7667i	−0.765638	−	0.550411i
$539$	0.346210	+	0.232625i	0.0149123	+	0.0100199i
$540$		0			0
$541$	−14.8912	+	25.7923i	−0.640223	+	1.10890i	0.345160	+	0.938544i	$0.387825\pi$
$541$	−14.8912	+	25.7923i	−0.640223	+	1.10890i	−0.985383	+	0.170354i	$0.945509\pi$
$542$	−32.0893	−	3.20974i	−1.37835	−	0.137870i
$543$		0			0
$544$	−16.7122	+	30.7031i	−0.716528	+	1.31638i
$545$	1.09390	−	0.631561i	0.0468574	−	0.0270531i
$546$		0			0
$547$	23.9968	+	13.8546i	1.02603	+	0.592379i	0.915845	−	0.401532i	$-0.131522\pi$
$547$	23.9968	+	13.8546i	1.02603	+	0.592379i	0.110186	+	0.993911i	$0.464855\pi$
$548$	−12.5389	+	14.2106i	−0.535635	+	0.607045i
$549$		0			0
$550$	0.377161	−	0.170200i	0.0160822	−	0.00725733i
$551$	−7.05343	−	12.2169i	−0.300486	−	0.520458i
$552$		0			0
$553$	−2.16893	+	3.47790i	−0.0922322	+	0.147896i
$554$	11.3606	+	25.1750i	0.482665	+	1.06958i
$555$		0			0
$556$	40.3440	+	8.15242i	1.71097	+	0.345740i
$557$	4.72713	+	8.18763i	0.200295	+	0.346921i	0.948623	−	0.316407i	$-0.102477\pi$
$557$	4.72713	+	8.18763i	0.200295	+	0.346921i	−0.748329	+	0.663328i	$0.769143\pi$
$558$		0			0
$559$	−18.5204			−0.783331
$560$	2.58892	−	1.82648i	0.109402	−	0.0771829i
$561$		0			0
$562$	10.2939	+	1.02965i	0.434220	+	0.0434330i
$563$	7.93913	−	13.7510i	0.334594	−	0.579534i	−0.648812	−	0.760948i	$-0.724734\pi$
$563$	7.93913	−	13.7510i	0.334594	−	0.579534i	0.983407	+	0.181414i	$0.0580674\pi$
$564$		0			0
$565$	−0.804438	+	0.464442i	−0.0338429	+	0.0195392i
$566$	26.4330	+	2.64397i	1.11106	+	0.111134i
$567$		0			0
$568$	1.04695	−	3.39554i	0.0439289	−	0.142474i
$569$	−1.38828	−	2.40458i	−0.0581999	−	0.100805i	0.835457	−	0.549555i	$-0.185203\pi$
$569$	−1.38828	−	2.40458i	−0.0581999	−	0.100805i	−0.893657	+	0.448750i	$0.851869\pi$
$570$		0			0
$571$	11.0493	+	6.37929i	0.462397	+	0.266965i	0.713052	−	0.701112i	$-0.247313\pi$
$571$	11.0493	+	6.37929i	0.462397	+	0.266965i	−0.250655	+	0.968077i	$0.580646\pi$
$572$	0.220220	+	0.0445004i	0.00920787	+	0.00186066i
$573$		0			0
$574$	39.2566	+	5.28047i	1.63854	+	0.220403i
$575$		−	28.3322i		−	1.18153i
$576$		0			0
$577$	−20.4229	+	11.7912i	−0.850217	+	0.490873i	−0.860724	−	0.509072i	$-0.829989\pi$
$577$	−20.4229	+	11.7912i	−0.850217	+	0.490873i	0.0105071	+	0.999945i	$0.496655\pi$
$578$	−29.8137	−	2.98213i	−1.24009	−	0.124040i
$579$		0			0
$580$	1.93548	−	0.650455i	0.0803663	−	0.0270087i
$581$	0.829915	−	24.3888i	0.0344307	−	1.01182i
$582$		0			0
$583$	0.355492	−	0.205243i	0.0147230	−	0.00850031i
$584$	−20.4785	+	4.67663i	−0.847408	+	0.193521i
$585$		0			0
$586$	36.8252	+	26.4733i	1.52124	+	1.09360i
$587$	−2.57608	+	4.46190i	−0.106326	+	0.184162i	−0.914279	−	0.405084i	$-0.867242\pi$
$587$	−2.57608	+	4.46190i	−0.106326	+	0.184162i	0.807953	+	0.589247i	$0.200575\pi$
$588$		0			0
$589$	13.0022	+	22.5205i	0.535747	+	0.927941i
$590$	0.0376400	−	0.376305i	0.00154961	−	0.0154922i
$591$		0			0
$592$	−8.81426	−	3.71389i	−0.362264	−	0.152640i
$593$	−11.5704	−	6.68019i	−0.475141	−	0.274323i	0.243248	−	0.969964i	$-0.421787\pi$
$593$	−11.5704	−	6.68019i	−0.475141	−	0.274323i	−0.718389	+	0.695641i	$0.755120\pi$
$594$		0			0
$595$	4.15330	+	2.59013i	0.170269	+	0.106185i
$596$	4.60919	−	5.22368i	0.188800	−	0.213970i
$597$		0			0
$598$	8.97946	−	12.4907i	0.367198	−	0.510783i
$599$	13.4121	+	7.74350i	0.548005	+	0.316391i	0.748317	−	0.663341i	$-0.230862\pi$
$599$	13.4121	+	7.74350i	0.548005	+	0.316391i	−0.200312	+	0.979732i	$0.564196\pi$
$600$		0			0
$601$	26.0865	+	15.0610i	1.06409	+	0.614353i	0.926561	−	0.376145i	$-0.122751\pi$
$601$	26.0865	+	15.0610i	1.06409	+	0.614353i	0.137529	+	0.990498i	$0.456084\pi$
$602$	13.9709	+	33.9987i	0.569413	+	1.38568i
$603$		0			0
$604$	−18.7874	−	16.5773i	−0.764447	−	0.674522i
$605$		−	3.29214i		−	0.133845i
$606$		0			0
$607$	−4.34028			−0.176167			−0.0880833	−	0.996113i	$-0.528074\pi$
$607$	−4.34028			−0.176167			−0.0880833	+	0.996113i	$0.528074\pi$
$608$	0.588011	+	23.3938i	0.0238470	+	0.948743i
$609$		0			0
$610$	−1.93715	+	2.69463i	−0.0784328	+	0.109102i
$611$	6.39339	+	3.69123i	0.258649	+	0.149331i
$612$		0			0
$613$	13.1740	+	22.8180i	0.532091	+	0.921609i	0.999298	+	0.0374608i	$0.0119269\pi$
$613$	13.1740	+	22.8180i	0.532091	+	0.921609i	−0.467207	+	0.884148i	$0.654740\pi$
$614$	6.82690	+	15.1284i	0.275511	+	0.610532i
$615$		0			0
$616$	−0.0844326	−	0.437836i	−0.00340188	−	0.0176409i
$617$	−8.15464	−	14.1243i	−0.328294	−	0.568621i	0.653880	−	0.756598i	$-0.273140\pi$
$617$	−8.15464	−	14.1243i	−0.328294	−	0.568621i	−0.982173	+	0.187977i	$0.939807\pi$
$618$		0			0
$619$	−20.8242			−0.836995			−0.418497	−	0.908218i	$-0.637443\pi$
$619$	−20.8242			−0.836995			−0.418497	+	0.908218i	$0.637443\pi$
$620$	−3.56784	+	1.19904i	−0.143288	+	0.0481547i
$621$		0			0
$622$	39.8713	+	3.98814i	1.59869	+	0.159910i
$623$	26.9303	+	0.916400i	1.07894	+	0.0367148i
$624$		0			0
$625$	23.6636			0.946543
$626$	−3.69975	−	2.65972i	−0.147872	−	0.106304i
$627$		0			0
$628$	−5.59770	+	1.88122i	−0.223373	+	0.0750688i
$629$		−	14.7764i		−	0.589174i
$630$		0			0
$631$		−	17.7969i		−	0.708484i	−0.935154	−	0.354242i	$-0.884739\pi$
$631$		−	17.7969i		−	0.708484i	0.935154	−	0.354242i	$-0.115261\pi$
$632$	4.27181	−	0.975544i	0.169924	−	0.0388051i
$633$		0			0
$634$	−25.3204	+	35.2215i	−1.00560	+	1.39883i
$635$	−4.79716			−0.190369
$636$		0			0
$637$	−0.897099	+	13.1663i	−0.0355443	+	0.521668i
$638$	0.0286008	−	0.285935i	0.00113231	−	0.0113203i
$639$		0			0
$640$	−3.33583	−	0.587249i	−0.131860	−	0.0232131i
$641$	22.5339			0.890034			0.445017	−	0.895522i	$-0.353198\pi$
$641$	22.5339			0.890034			0.445017	+	0.895522i	$0.353198\pi$
$642$		0			0
$643$	8.66706	+	15.0118i	0.341795	+	0.592007i	0.984766	−	0.173884i	$-0.0556317\pi$
$643$	8.66706	+	15.0118i	0.341795	+	0.592007i	−0.642971	+	0.765891i	$0.722298\pi$
$644$	−29.7034	−	7.06155i	−1.17048	−	0.278264i
$645$		0			0
$646$	−32.9523	+	14.8702i	−1.29649	+	0.585060i
$647$	−3.63507	−	6.29613i	−0.142909	−	0.247526i	0.785682	−	0.618631i	$-0.212312\pi$
$647$	−3.63507	−	6.29613i	−0.142909	−	0.247526i	−0.928591	+	0.371105i	$0.878979\pi$
$648$		0			0
$649$	−0.0460932	−	0.0266119i	−0.00180932	−	0.00104461i
$650$	10.6301	+	7.64186i	0.416946	+	0.299739i
$651$		0			0
$652$	−26.3695	+	8.86201i	−1.03271	+	0.347063i
$653$	33.4221			1.30791			0.653955	−	0.756534i	$-0.273109\pi$
$653$	33.4221			1.30791			0.653955	+	0.756534i	$0.273109\pi$
$654$		0			0
$655$			1.04686i			0.0409040i
$656$	−25.5734	−	33.7506i	−0.998475	−	1.31774i
$657$		0			0
$658$	1.95326	−	14.5211i	0.0761459	−	0.566091i
$659$	−30.9707	−	17.8810i	−1.20645	−	0.696543i	−0.244467	−	0.969658i	$-0.578613\pi$
$659$	−30.9707	−	17.8810i	−1.20645	−	0.696543i	−0.961982	+	0.273115i	$0.911946\pi$
$660$		0			0
$661$	22.3667	+	12.9134i	0.869962	+	0.502273i	0.867336	−	0.497724i	$-0.165831\pi$
$661$	22.3667	+	12.9134i	0.869962	+	0.502273i	0.00262630	+	0.999997i	$0.499164\pi$
$662$	17.5812	+	12.6389i	0.683311	+	0.491227i
$663$		0			0
$664$	−19.1216	+	17.7465i	−0.742063	+	0.688697i
$665$	3.27481	+	0.111437i	0.126992	+	0.00432134i
$666$		0			0
$667$	−17.0398	−	9.83792i	−0.659783	−	0.380926i
$668$	26.2070	+	5.29570i	1.01398	+	0.204897i
$669$		0			0
$670$	4.78558	+	0.478679i	0.184883	+	0.0184930i
$671$	0.233528	+	0.404482i	0.00901525	+	0.0156149i
$672$		0			0
$673$	−4.61265	+	7.98935i	−0.177805	+	0.307967i	−0.941128	−	0.338050i	$-0.890233\pi$
$673$	−4.61265	+	7.98935i	−0.177805	+	0.307967i	0.763324	+	0.646016i	$0.223566\pi$
$674$	−25.5177	+	35.4959i	−0.982904	+	1.36725i
$675$		0			0
$676$	−6.01812	−	17.9074i	−0.231466	−	0.688745i
$677$	11.3545	−	6.55552i	0.436389	−	0.251949i	−0.265676	−	0.964062i	$-0.585595\pi$
$677$	11.3545	−	6.55552i	0.436389	−	0.251949i	0.702065	+	0.712113i	$0.252262\pi$
$678$		0			0
$679$	−7.34035	−	0.249781i	−0.281697	−	0.00958573i
$680$	−1.16499	−	5.10138i	−0.0446754	−	0.195629i
$681$		0			0
$682$	−0.0527223	+	0.527089i	−0.00201884	+	0.0201833i
$683$	3.02310	−	1.74539i	0.115676	−	0.0667853i	−0.441046	−	0.897485i	$-0.645392\pi$
$683$	3.02310	−	1.74539i	0.115676	−	0.0667853i	0.556721	+	0.830699i	$0.312059\pi$
$684$		0			0
$685$		−	2.83689i		−	0.108392i
$686$	24.8466	−	8.28520i	0.948649	−	0.316330i
$687$		0			0
$688$	15.2579	−	36.2120i	0.581703	−	1.38057i
$689$	11.2475	+	6.49374i	0.428495	+	0.247392i
$690$		0			0
$691$	−3.22262	−	5.58174i	−0.122594	−	0.212339i	0.798196	−	0.602398i	$-0.205788\pi$
$691$	−3.22262	−	5.58174i	−0.122594	−	0.212339i	−0.920790	+	0.390059i	$0.872455\pi$
$692$	1.90593	−	9.43190i	0.0724525	−	0.358547i
$693$		0			0
$694$	−0.994188	+	9.93937i	−0.0377389	+	0.377293i
$695$	−5.33577	+	3.08061i	−0.202397	+	0.116854i
$696$		0			0
$697$	32.7091	−	56.6538i	1.23895	−	2.14592i
$698$	−2.76459	+	27.6389i	−0.104641	+	1.04615i
$699$		0			0
$700$	6.00965	−	25.2787i	0.227143	−	0.955445i
$701$	−33.8067			−1.27686			−0.638431	−	0.769679i	$-0.720416\pi$
$701$	−33.8067			−1.27686			−0.638431	+	0.769679i	$0.720416\pi$
$702$		0			0
$703$	−4.94590	−	8.56655i	−0.186538	−	0.323094i
$704$	−0.268436	+	0.393923i	−0.0101171	+	0.0148465i
$705$		0			0
$706$	5.60213	−	2.52804i	0.210839	−	0.0951442i
$707$	−11.3792	−	21.3552i	−0.427958	−	0.803144i
$708$		0			0
$709$	23.8280	+	41.2713i	0.894880	+	1.54998i	0.833953	+	0.551835i	$0.186072\pi$
$709$	23.8280	+	41.2713i	0.894880	+	1.54998i	0.0609262	+	0.998142i	$0.480595\pi$
$710$	0.218780	+	0.484816i	0.00821068	+	0.0181948i
$711$		0			0
$712$	−19.5958	−	21.1143i	−0.734384	−	0.791291i
$713$	31.4109	+	18.1351i	1.17635	+	0.679165i
$714$		0			0
$715$	−0.0291256	+	0.0168157i	−0.00108924	+	0.000628870i
$716$	−4.13524	+	20.4641i	−0.154541	+	0.764780i
$717$		0			0
$718$	1.40567	−	14.0531i	0.0524590	−	0.524457i
$719$	−20.7997	+	36.0262i	−0.775699	+	1.34355i	0.158702	+	0.987327i	$0.449269\pi$
$719$	−20.7997	+	36.0262i	−0.775699	+	1.34355i	−0.934401	+	0.356224i	$0.884064\pi$
$720$		0			0
$721$	−8.24586	+	4.39383i	−0.307092	+	0.163635i
$722$	1.55775	−	2.16687i	0.0579733	−	0.0806426i
$723$		0			0
$724$	−20.0362	−	17.6792i	−0.744638	−	0.657043i
$725$	8.37245	−	14.5015i	0.310945	−	0.538572i
$726$		0			0
$727$	12.4339	−	21.5361i	0.461147	−	0.798730i	−0.537871	−	0.843027i	$-0.680771\pi$
$727$	12.4339	−	21.5361i	0.461147	−	0.798730i	0.999018	+	0.0442969i	$0.0141048\pi$
$728$	10.6612	−	9.23987i	0.395129	−	0.342453i
$729$		0			0
$730$	1.83541	−	2.55311i	0.0679315	−	0.0944948i
$731$	60.7065			2.24531
$732$		0			0
$733$		−	25.6869i		−	0.948766i	−0.880319	−	0.474383i	$-0.842671\pi$
$733$		−	25.6869i		−	0.948766i	0.880319	−	0.474383i	$-0.157329\pi$
$734$	3.83924	+	8.50774i	0.141709	+	0.314026i
$735$		0			0
$736$	17.0247	+	27.8474i	0.627540	+	1.02647i
$737$	0.338432	−	0.586181i	0.0124663	−	0.0215922i
$738$		0			0
$739$	7.36004	−	4.24932i	0.270743	−	0.156314i	−0.358482	−	0.933537i	$-0.616706\pi$
$739$	7.36004	−	4.24932i	0.270743	−	0.156314i	0.629225	+	0.777223i	$0.283372\pi$
$740$	1.35717	−	0.456102i	0.0498904	−	0.0167667i
$741$		0			0
$742$	3.43624	−	25.5460i	0.126148	−	0.937824i
$743$	−7.11078	+	4.10541i	−0.260869	+	0.150613i	−0.624731	−	0.780840i	$-0.714791\pi$
$743$	−7.11078	+	4.10541i	−0.260869	+	0.150613i	0.363862	+	0.931453i	$0.381458\pi$
$744$		0			0
$745$			1.04282i			0.0382058i
$746$	15.4371	+	34.2086i	0.565193	+	1.25246i
$747$		0			0
$748$	−0.721841	−	0.145864i	−0.0263931	−	0.00533332i
$749$	−41.6333	−	1.41672i	−1.52125	−	0.0517658i
$750$		0			0
$751$			40.8218i			1.48961i	0.667283	+	0.744804i	$0.267457\pi$
$751$			40.8218i			1.48961i	−0.667283	+	0.744804i	$0.732543\pi$
$752$	−12.4844	+	9.45966i	−0.455259	+	0.344958i
$753$		0			0
$754$	8.28718	−	3.73971i	0.301801	−	0.136192i
$755$	3.75057			0.136497
$756$		0			0
$757$	−7.66392			−0.278550			−0.139275	−	0.990254i	$-0.544477\pi$
$757$	−7.66392			−0.278550			−0.139275	+	0.990254i	$0.544477\pi$
$758$	−32.9136	+	14.8527i	−1.19548	+	0.539476i
$759$		0			0
$760$	−2.38291	−	2.56756i	−0.0864374	−	0.0931353i
$761$			0.807681i			0.0292784i	0.999893	+	0.0146392i	$0.00465997\pi$
$761$			0.807681i			0.0292784i	−0.999893	+	0.0146392i	$0.995340\pi$
$762$		0			0
$763$	−9.47175	−	5.90688i	−0.342900	−	0.213843i
$764$	−7.64850	+	37.8503i	−0.276713	+	1.36938i
$765$		0			0
$766$	−9.83650	−	21.7976i	−0.355407	−	0.787581i
$767$		−	1.68396i		−	0.0608042i
$768$		0			0
$769$	4.81745	−	2.78135i	0.173722	−	0.100298i	−0.410618	−	0.911808i	$-0.634687\pi$
$769$	4.81745	−	2.78135i	0.173722	−	0.100298i	0.584339	+	0.811509i	$0.301354\pi$
$770$	0.0528402	+	0.0407821i	0.00190423	+	0.00146968i
$771$		0			0
$772$	−0.963208	−	2.86609i	−0.0346666	−	0.103153i
$773$	−28.2130	+	16.2888i	−1.01475	+	0.585867i	−0.912579	−	0.408900i	$-0.865913\pi$
$773$	−28.2130	+	16.2888i	−1.01475	+	0.585867i	−0.102172	+	0.994767i	$0.532579\pi$
$774$		0			0
$775$	−15.4337	+	26.7319i	−0.554394	+	0.960238i
$776$	5.34120	+	5.75508i	0.191738	+	0.206595i
$777$		0			0
$778$	12.0391	+	26.6786i	0.431624	+	0.956476i
$779$		−	43.7930i		−	1.56905i
$780$		0			0
$781$	0.0748566			0.00267858
$782$	−29.4330	+	40.9422i	−1.05252	+	1.46409i
$783$		0			0
$784$	−25.0043	−	12.6010i	−0.893010	−	0.450036i
$785$	0.441990	−	0.765550i	0.0157753	−	0.0273236i
$786$		0			0
$787$	0.708366	−	1.22693i	0.0252505	−	0.0437352i	−0.853124	−	0.521708i	$-0.825295\pi$
$787$	0.708366	−	1.22693i	0.0252505	−	0.0437352i	0.878375	+	0.477973i	$0.158628\pi$
$788$	−1.49932	+	1.69920i	−0.0534109	+	0.0605315i
$789$		0			0
$790$	−0.382866	+	0.532578i	−0.0136217	+	0.0189483i
$791$	6.96541	+	4.34384i	0.247661	+	0.154449i
$792$		0			0
$793$	−7.38864	+	12.7975i	−0.262378	+	0.454452i
$794$	−2.42135	+	24.2073i	−0.0859304	+	0.859087i
$795$		0			0
$796$	−38.8523	−	7.85098i	−1.37708	−	0.278270i
$797$	12.1430	−	7.01075i	0.430126	−	0.248333i	−0.269274	−	0.963064i	$-0.586784\pi$
$797$	12.1430	−	7.01075i	0.430126	−	0.248333i	0.699400	+	0.714730i	$0.253450\pi$
$798$		0			0
$799$	−20.9563	−	12.0991i	−0.741382	−	0.428037i
$800$	−23.6992	+	14.4887i	−0.837894	+	0.512253i
$801$		0			0
$802$	−12.8487	−	28.4726i	−0.453703	−	1.00540i
$803$	−0.221263	−	0.383239i	−0.00780821	−	0.0135242i
$804$		0			0
$805$	4.03338	−	2.14920i	0.142158	−	0.0757494i
$806$	−15.2765	+	6.89373i	−0.538091	+	0.242821i
$807$		0			0
$808$	−7.62194	+	24.7201i	−0.268139	+	0.869649i
$809$	−9.64172	−	16.7000i	−0.338985	−	0.587139i	0.645257	−	0.763965i	$-0.276750\pi$
$809$	−9.64172	−	16.7000i	−0.338985	−	0.587139i	−0.984242	+	0.176826i	$0.943417\pi$
$810$		0			0
$811$	18.8626			0.662355			0.331178	−	0.943568i	$-0.392554\pi$
$811$	18.8626			0.662355			0.331178	+	0.943568i	$0.392554\pi$
$812$	−13.1166	−	12.3920i	−0.460302	−	0.434875i
$813$		0			0
$814$	0.0200550	−	0.200499i	0.000702927	−	0.00702749i
$815$	2.08212	−	3.60634i	0.0729334	−	0.126324i
$816$		0			0
$817$	35.1943	−	20.3194i	1.23129	−	0.710887i
$818$	3.66319	−	36.6226i	0.128080	−	1.28048i
$819$		0			0
$820$	6.21310	+	1.25550i	0.216971	+	0.0438438i
$821$	3.93309	+	6.81232i	0.137266	+	0.237751i	0.926461	−	0.376391i	$-0.122835\pi$
$821$	3.93309	+	6.81232i	0.137266	+	0.237751i	−0.789195	+	0.614143i	$0.789502\pi$
$822$		0			0
$823$	18.4164	+	10.6327i	0.641955	+	0.370633i	0.785367	−	0.619030i	$-0.212474\pi$
$823$	18.4164	+	10.6327i	0.641955	+	0.370633i	−0.143412	+	0.989663i	$0.545808\pi$
$824$	9.54515	+	2.94305i	0.332521	+	0.102526i
$825$		0			0
$826$	−3.09131	+	1.27030i	−0.107560	+	0.0441994i
$827$			18.3753i			0.638973i	0.947591	+	0.319486i	$0.103510\pi$
$827$			18.3753i			0.638973i	−0.947591	+	0.319486i	$0.896490\pi$
$828$		0			0
$829$	24.2558	−	14.0041i	0.842438	−	0.486382i	−0.0156543	−	0.999877i	$-0.504983\pi$
$829$	24.2558	−	14.0041i	0.842438	−	0.486382i	0.858092	+	0.513496i	$0.171650\pi$
$830$	0.388671	−	3.88573i	0.0134910	−	0.134875i
$831$		0			0
$832$	−15.0402	−	1.12353i	−0.521425	−	0.0389516i
$833$	2.94052	−	43.1567i	0.101883	−	1.49529i
$834$		0			0
$835$	−3.46604	+	2.00112i	−0.119947	+	0.0692517i
$836$	−0.467307	+	0.157048i	−0.0161621	+	0.00543161i
$837$		0			0
$838$	7.40782	−	10.3045i	0.255899	−	0.355963i
$839$	2.88329	−	4.99401i	0.0995422	−	0.172412i	−0.811953	−	0.583723i	$-0.801595\pi$
$839$	2.88329	−	4.99401i	0.0995422	−	0.172412i	0.911495	+	0.411311i	$0.134929\pi$
$840$		0			0
$841$	8.68558	+	15.0439i	0.299503	+	0.518754i
$842$	−14.7460	−	1.47497i	−0.508181	−	0.0508310i
$843$		0			0
$844$	−8.78714	+	43.4851i	−0.302466	+	1.49682i
$845$	2.44904	+	1.41395i	0.0842494	+	0.0486414i
$846$		0			0
$847$	−25.6762	+	13.6816i	−0.882244	+	0.470106i
$848$	−21.9630	+	16.6418i	−0.754212	+	0.571481i
$849$		0			0
$850$	−34.8434	−	25.0486i	−1.19512	−	0.859160i
$851$	−11.9484	−	6.89840i	−0.409585	−	0.236474i
$852$		0			0
$853$	17.4956	+	10.1011i	0.599039	+	0.345855i	0.768663	−	0.639653i	$-0.220922\pi$
$853$	17.4956	+	10.1011i	0.599039	+	0.345855i	−0.169624	+	0.985509i	$0.554255\pi$
$854$	29.0665	+	3.90979i	0.994636	+	0.133790i
$855$		0			0
$856$	30.2944	+	32.6419i	1.03544	+	1.11568i
$857$			35.0153i			1.19610i	0.801459	+	0.598050i	$0.204058\pi$
$857$			35.0153i			1.19610i	−0.801459	+	0.598050i	$0.795942\pi$
$858$		0			0
$859$	37.1598			1.26788			0.633938	−	0.773384i	$-0.281437\pi$
$859$	37.1598			1.26788			0.633938	+	0.773384i	$0.281437\pi$
$860$	1.87382	+	5.57570i	0.0638969	+	0.190130i
$861$		0			0
$862$	−5.13891	−	3.69432i	−0.175032	−	0.125829i
$863$	−1.14573	−	0.661488i	−0.0390012	−	0.0225173i	0.480373	−	0.877064i	$-0.340501\pi$
$863$	−1.14573	−	0.661488i	−0.0390012	−	0.0225173i	−0.519374	+	0.854547i	$0.673835\pi$
$864$		0			0
$865$	0.720205	+	1.24743i	0.0244877	+	0.0424139i
$866$	−24.8749	+	11.2252i	−0.845284	+	0.381447i
$867$		0			0
$868$	24.1790	+	22.8433i	0.820687	+	0.775353i
$869$	0.0461554	+	0.0799435i	0.00156571	+	0.00271190i
$870$		0			0
$871$	21.4154			0.725634
$872$	2.65681	+	11.6339i	0.0899708	+	0.393973i
$873$		0			0
$874$	−3.35963	+	33.5878i	−0.113641	+	1.13612i
$875$	3.69149	+	6.92778i	0.124795	+	0.234202i
$876$		0			0
$877$	−39.7761			−1.34314			−0.671572	−	0.740940i	$-0.734381\pi$
$877$	−39.7761			−1.34314			−0.671572	+	0.740940i	$0.734381\pi$
$878$	19.8073	−	27.5526i	0.668464	−	0.929854i
$879$		0			0
$880$	−0.00888386	−	0.0708011i	−0.000299475	−	0.00238671i
$881$		−	9.29402i		−	0.313123i	−0.987668	−	0.156562i	$-0.949959\pi$
$881$		−	9.29402i		−	0.313123i	0.987668	−	0.156562i	$-0.0500410\pi$
$882$		0			0
$883$			52.5549i			1.76861i	0.466905	+	0.884307i	$0.345369\pi$
$883$			52.5549i			1.76861i	−0.466905	+	0.884307i	$0.654631\pi$
$884$	−7.42251	−	22.0862i	−0.249646	−	0.742840i
$885$		0			0
$886$	−0.717622	−	0.515892i	−0.0241090	−	0.0173317i
$887$	48.5811			1.63119			0.815596	−	0.578622i	$-0.196409\pi$
$887$	48.5811			1.63119			0.815596	+	0.578622i	$0.196409\pi$
$888$		0			0
$889$	19.9362	+	37.4141i	0.668640	+	1.25483i
$890$	4.29065	+	0.429174i	0.143823	+	0.0143860i
$891$		0			0
$892$	−6.98760	−	20.7921i	−0.233962	−	0.696171i
$893$	−16.1991			−0.542083
$894$		0			0
$895$	−1.56261	−	2.70652i	−0.0522322	−	0.0904689i
$896$	9.28309	+	28.4574i	0.310126	+	0.950695i
$897$		0			0
$898$	−12.9312	−	28.6555i	−0.431520	−	0.956245i
$899$	10.7182	+	18.5645i	0.357473	+	0.619161i
$900$		0			0
$901$	−36.8671	−	21.2853i	−1.22822	−	0.709115i
$902$	0.520717	−	0.724334i	0.0173380	−	0.0241177i
$903$		0			0
$904$	−1.95378	−	8.55542i	−0.0649818	−	0.284549i
$905$	3.99987			0.132960
$906$		0			0
$907$			3.30830i			0.109850i	0.998490	+	0.0549251i	$0.0174920\pi$
$907$			3.30830i			0.109850i	−0.998490	+	0.0549251i	$0.982508\pi$
$908$	17.9267	−	20.3167i	0.594919	−	0.674233i
$909$		0			0
$910$	−0.281532	+	2.09300i	−0.00933271	+	0.0693821i
$911$	−30.5080	−	17.6138i	−1.01078	−	0.583571i	−0.0993568	−	0.995052i	$-0.531679\pi$
$911$	−30.5080	−	17.6138i	−1.01078	−	0.583571i	−0.911419	+	0.411480i	$0.865012\pi$
$912$		0			0
$913$	−0.475959	−	0.274795i	−0.0157519	−	0.00909438i
$914$	−3.15530	+	4.38912i	−0.104368	+	0.145179i
$915$		0			0
$916$	−33.8907	−	29.9040i	−1.11978	−	0.988056i
$917$	8.16466	−	4.35057i	0.269621	−	0.143668i
$918$		0			0
$919$	17.1249	+	9.88707i	0.564899	+	0.326144i	0.755109	−	0.655599i	$-0.227584\pi$
$919$	17.1249	+	9.88707i	0.564899	+	0.326144i	−0.190211	+	0.981743i	$0.560917\pi$
$920$	−4.66892	−	1.43957i	−0.153930	−	0.0474611i
$921$		0			0
$922$	−0.124667	+	1.24636i	−0.00410570	+	0.0410466i
$923$	1.18420	+	2.05110i	0.0389785	+	0.0675127i
$924$		0			0
$925$	5.87080	−	10.1685i	0.193031	−	0.334339i
$926$	−20.8899	−	15.0175i	−0.686483	−	0.493507i
$927$		0			0
$928$	0.484720	+	19.2844i	0.0159117	+	0.633041i
$929$	−1.72842	+	0.997906i	−0.0567077	+	0.0327402i	−0.528086	−	0.849191i	$-0.677090\pi$
$929$	−1.72842	+	0.997906i	−0.0567077	+	0.0327402i	0.471378	+	0.881931i	$0.343757\pi$
$930$		0			0
$931$	−12.7405	−	26.0041i	−0.417553	−	0.852251i
$932$	−16.6407	−	49.5155i	−0.545083	−	1.62194i
$933$		0			0
$934$	−10.9325	−	1.09353i	−0.357723	−	0.0357814i
$935$	0.0954683	−	0.0551186i	0.00312215	−	0.00180257i
$936$		0			0
$937$		−	21.3537i		−	0.697596i	−0.937198	−	0.348798i	$-0.886590\pi$
$937$		−	21.3537i		−	0.697596i	0.937198	−	0.348798i	$-0.113410\pi$
$938$	−16.1548	−	39.3131i	−0.527472	−	1.28362i
$939$		0			0
$940$	0.464410	−	2.29824i	0.0151474	−	0.0749602i
$941$	−22.2954	−	12.8723i	−0.726809	−	0.419624i	0.0904445	−	0.995901i	$-0.471171\pi$
$941$	−22.2954	−	12.8723i	−0.726809	−	0.419624i	−0.817254	+	0.576278i	$0.804505\pi$
$942$		0			0
$943$	−30.5406	−	52.8979i	−0.994540	−	1.72259i
$944$	3.29255	+	1.38732i	0.107163	+	0.0451533i
$945$		0			0
$946$	0.823718	+	0.0823927i	0.0267814	+	0.00267882i
$947$	−10.7886	+	6.22880i	−0.350582	+	0.202409i	−0.664942	−	0.746895i	$-0.731544\pi$
$947$	−10.7886	+	6.22880i	−0.350582	+	0.202409i	0.314360	+	0.949304i	$0.398210\pi$
$948$		0			0
$949$	7.00059	−	12.1254i	0.227249	−	0.393606i
$950$	−28.5845	−	2.85917i	−0.927402	−	0.0927637i
$951$		0			0
$952$	−34.9453	+	30.2866i	−1.13258	+	0.981594i
$953$	−4.74584			−0.153733			−0.0768665	−	0.997041i	$-0.524492\pi$
$953$	−4.74584			−0.153733			−0.0768665	+	0.997041i	$0.524492\pi$
$954$		0			0
$955$	−2.89019	−	5.00595i	−0.0935243	−	0.161989i
$956$	−11.3590	+	56.2124i	−0.367376	+	1.81804i
$957$		0			0
$958$	−1.96883	−	4.36292i	−0.0636100	−	0.140960i
$959$	−22.1256	+	11.7897i	−0.714472	+	0.380708i
$960$		0			0
$961$	−4.25785	−	7.37481i	−0.137350	−	0.237897i
$962$	5.81101	−	2.62230i	0.187354	−	0.0845464i
$963$		0			0
$964$	16.0079	+	14.1248i	0.515581	+	0.454931i
$965$	0.391971	+	0.226305i	0.0126180	+	0.00728500i
$966$		0			0
$967$	24.7846	−	14.3094i	0.797020	−	0.460160i	−0.0454079	−	0.998969i	$-0.514459\pi$
$967$	24.7846	−	14.3094i	0.797020	−	0.460160i	0.842428	+	0.538809i	$0.181125\pi$
$968$	29.7219	+	9.16416i	0.955299	+	0.294547i
$969$		0			0
$970$	−1.16950	−	0.116979i	−0.0375502	−	0.00375598i
$971$	23.7362	−	41.1122i	0.761729	−	1.31935i	−0.180229	−	0.983625i	$-0.557684\pi$
$971$	23.7362	−	41.1122i	0.761729	−	1.31935i	0.941958	−	0.335729i	$-0.108983\pi$
$972$		0			0
$973$	46.2010	+	28.8124i	1.48114	+	0.923682i
$974$	−22.7142	−	16.3290i	−0.727810	−	0.523216i
$975$		0			0
$976$	−18.9352	−	24.9897i	−0.606100	−	0.799902i
$977$	4.69969	−	8.14011i	0.150357	−	0.260425i	−0.781002	−	0.624529i	$-0.785291\pi$
$977$	4.69969	−	8.14011i	0.150357	−	0.260425i	0.931359	+	0.364103i	$0.118624\pi$
$978$		0			0
$979$	0.303431	−	0.525558i	0.00969770	−	0.0167969i
$980$	4.05457	−	1.06204i	0.129518	−	0.0339255i
$981$		0			0
$982$	28.7029	+	20.6343i	0.915947	+	0.658466i
$983$	−41.1538			−1.31260			−0.656301	−	0.754499i	$-0.727880\pi$
$983$	−41.1538			−1.31260			−0.656301	+	0.754499i	$0.727880\pi$
$984$		0			0
$985$		−	0.339216i		−	0.0108083i
$986$	−27.1638	+	12.2581i	−0.865072	+	0.390376i
$987$		0			0
$988$	−11.6958	−	10.3199i	−0.372092	−	0.328321i
$989$	28.3410	−	49.0880i	0.901191	−	1.56091i
$990$		0			0
$991$	−16.7767	+	9.68604i	−0.532930	+	0.307687i	−0.742209	−	0.670169i	$-0.766222\pi$
$991$	−16.7767	+	9.68604i	−0.532930	+	0.307687i	0.209279	+	0.977856i	$0.432888\pi$
$992$	−0.893527	−	35.5486i	−0.0283695	−	1.12867i
$993$		0			0
$994$	2.87197	−	3.72114i	0.0910935	−	0.118027i
$995$	5.13847	−	2.96670i	0.162901	−	0.0940507i
$996$		0			0
$997$		−	22.2704i		−	0.705310i	−0.935753	−	0.352655i	$-0.885279\pi$
$997$		−	22.2704i		−	0.705310i	0.935753	−	0.352655i	$-0.114721\pi$
$998$	1.70211	−	0.768104i	0.0538795	−	0.0243139i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.b.19.17		84
3.2	odd	2		252.2.n.b.187.26	yes	84
4.3	odd	2	inner	756.2.n.b.19.12		84
7.3	odd	6		756.2.bj.b.451.40		84
9.4	even	3		756.2.bj.b.523.40		84
9.5	odd	6		252.2.bj.b.103.3	yes	84
12.11	even	2		252.2.n.b.187.31	yes	84
21.17	even	6		252.2.bj.b.115.3	yes	84
28.3	even	6		756.2.bj.b.451.39		84
36.23	even	6		252.2.bj.b.103.4	yes	84
36.31	odd	6		756.2.bj.b.523.39		84
63.31	odd	6	inner	756.2.n.b.199.12		84
63.59	even	6		252.2.n.b.31.31	yes	84
84.59	odd	6		252.2.bj.b.115.4	yes	84
252.31	even	6	inner	756.2.n.b.199.17		84
252.59	odd	6		252.2.n.b.31.26	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.26	✓	84	252.59	odd	6
252.2.n.b.31.31	yes	84	63.59	even	6
252.2.n.b.187.26	yes	84	3.2	odd	2
252.2.n.b.187.31	yes	84	12.11	even	2
252.2.bj.b.103.3	yes	84	9.5	odd	6
252.2.bj.b.103.4	yes	84	36.23	even	6
252.2.bj.b.115.3	yes	84	21.17	even	6
252.2.bj.b.115.4	yes	84	84.59	odd	6
756.2.n.b.19.12		84	4.3	odd	2	inner
756.2.n.b.19.17		84	1.1	even	1	trivial
756.2.n.b.199.12		84	63.31	odd	6	inner
756.2.n.b.199.17		84	252.31	even	6	inner
756.2.bj.b.451.39		84	28.3	even	6
756.2.bj.b.451.40		84	7.3	odd	6
756.2.bj.b.523.39		84	36.31	odd	6
756.2.bj.b.523.40		84	9.4	even	3

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.581699 - 1.28904i) q^{2} +(-1.32325 + 1.49967i) q^{4} -0.299382i q^{5} +(-2.33495 + 1.24419i) q^{7} +(2.70287 + 0.833374i) q^{8} +O(q^{10})\)	\(q+(-0.581699 - 1.28904i) q^{2} +(-1.32325 + 1.49967i) q^{4} -0.299382i q^{5} +(-2.33495 + 1.24419i) q^{7} +(2.70287 + 0.833374i) q^{8} +(-0.385916 + 0.174150i) q^{10} +0.0595863i q^{11} +(-1.63268 + 0.942631i) q^{13} +(2.96205 + 2.28611i) q^{14} +(-0.498000 - 3.96888i) q^{16} +(5.35164 - 3.08977i) q^{17} +(2.06839 - 3.58256i) q^{19} +(0.448974 + 0.396159i) q^{20} +(0.0768091 - 0.0346612i) q^{22} -5.76986i q^{23} +4.91037 q^{25} +(2.16482 + 1.55627i) q^{26} +(1.22387 - 5.14802i) q^{28} +(1.70505 - 2.95324i) q^{29} +(-3.14308 + 5.44397i) q^{31} +(-4.82636 + 2.95063i) q^{32} +(-7.09588 - 5.10116i) q^{34} +(0.372488 + 0.699044i) q^{35} +(1.19559 - 2.07083i) q^{37} +(-5.82124 - 0.582272i) q^{38} +(0.249498 - 0.809191i) q^{40} +(9.16797 - 5.29313i) q^{41} +(8.50766 + 4.91190i) q^{43} +(-0.0893595 - 0.0788477i) q^{44} +(-7.43759 + 3.35632i) q^{46} +(-1.95794 - 3.39125i) q^{47} +(3.90400 - 5.81023i) q^{49} +(-2.85636 - 6.32967i) q^{50} +(0.746824 - 3.69582i) q^{52} +(-3.44447 - 5.96600i) q^{53} +0.0178391 q^{55} +(-7.34794 + 1.41698i) q^{56} +(-4.79868 - 0.479989i) q^{58} +(-0.446612 + 0.773554i) q^{59} +(6.78818 - 3.91916i) q^{61} +(8.84582 + 0.884806i) q^{62} +(6.61097 + 4.50500i) q^{64} +(0.282207 + 0.488797i) q^{65} +(-9.83752 - 5.67969i) q^{67} +(-2.44795 + 12.1142i) q^{68} +(0.684420 - 0.886784i) q^{70} -1.25627i q^{71} +(-6.43167 + 3.71333i) q^{73} +(-3.36485 - 0.336571i) q^{74} +(2.63564 + 7.84253i) q^{76} +(-0.0741364 - 0.139131i) q^{77} +(1.34164 - 0.774598i) q^{79} +(-1.18821 + 0.149092i) q^{80} +(-12.1561 - 8.73889i) q^{82} +(-4.61172 + 7.98773i) q^{83} +(-0.925022 - 1.60219i) q^{85} +(1.38275 - 13.8240i) q^{86} +(-0.0496577 + 0.161054i) q^{88} +(-8.82012 - 5.09230i) q^{89} +(2.63943 - 4.23236i) q^{91} +(8.65287 + 7.63499i) q^{92} +(-3.23253 + 4.49655i) q^{94} +(-1.07255 - 0.619240i) q^{95} +(2.40408 + 1.38800i) q^{97} +(-9.76058 - 1.65261i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) 84 * q + q^2 + q^4 + 16 * q^8	\( 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) \) 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

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