LMFDB - Embedded newform 720.2.z.g.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(163,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("720.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.z (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.1
Root			$-1.08900 + 0.902261i$ of defining polynomial
Character	$\chi$	$=$	720.163
Dual form			720.2.z.g.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41267 - 0.0660953i) q^{2} +(1.99126 + 0.186742i) q^{4} +(2.00635 - 0.987189i) q^{5} +(1.55426 - 1.55426i) q^{7} +(-2.80065 - 0.395417i) q^{8} +O(q^{10})$	\(q+(-1.41267 - 0.0660953i) q^{2} +(1.99126 + 0.186742i) q^{4} +(2.00635 - 0.987189i) q^{5} +(1.55426 - 1.55426i) q^{7} +(-2.80065 - 0.395417i) q^{8} +(-2.89956 + 1.26196i) q^{10} +(4.19607 + 4.19607i) q^{11} +5.09530i q^{13} +(-2.29838 + 2.09292i) q^{14} +(3.93026 + 0.743703i) q^{16} +(-0.213542 + 0.213542i) q^{17} +(0.844754 + 0.844754i) q^{19} +(4.17953 - 1.59108i) q^{20} +(-5.65031 - 6.20499i) q^{22} +(-1.70744 - 1.70744i) q^{23} +(3.05092 - 3.96130i) q^{25} +(0.336775 - 7.19797i) q^{26} +(3.38518 - 2.80469i) q^{28} +(-2.24750 + 2.24750i) q^{29} -0.818209i q^{31} +(-5.50299 - 1.31038i) q^{32} +(0.315778 - 0.287550i) q^{34} +(1.58404 - 4.65273i) q^{35} +5.12639i q^{37} +(-1.13752 - 1.24919i) q^{38} +(-6.00945 + 1.97142i) q^{40} +3.34727i q^{41} -4.49131i q^{43} +(7.57189 + 9.13905i) q^{44} +(2.29920 + 2.52490i) q^{46} +(-4.29355 - 4.29355i) q^{47} +2.16858i q^{49} +(-4.57176 + 5.39435i) q^{50} +(-0.951504 + 10.1461i) q^{52} +1.00653 q^{53} +(12.5611 + 4.27649i) q^{55} +(-4.96751 + 3.73835i) q^{56} +(3.32352 - 3.02642i) q^{58} +(7.65005 - 7.65005i) q^{59} +(-1.90291 - 1.90291i) q^{61} +(-0.0540798 + 1.15586i) q^{62} +(7.68729 + 2.21485i) q^{64} +(5.03002 + 10.2230i) q^{65} -11.0221i q^{67} +(-0.465096 + 0.385341i) q^{68} +(-2.54525 + 6.46807i) q^{70} +10.5331 q^{71} +(2.70854 - 2.70854i) q^{73} +(0.338831 - 7.24189i) q^{74} +(1.52438 + 1.83988i) q^{76} +13.0435 q^{77} -8.32010 q^{79} +(8.61966 - 2.38777i) q^{80} +(0.221239 - 4.72858i) q^{82} +9.17237 q^{83} +(-0.217635 + 0.639248i) q^{85} +(-0.296855 + 6.34474i) q^{86} +(-10.0925 - 13.4109i) q^{88} +4.25101 q^{89} +(7.91940 + 7.91940i) q^{91} +(-3.08112 - 3.71882i) q^{92} +(5.78157 + 6.34914i) q^{94} +(2.52881 + 0.860944i) q^{95} +(-7.16000 + 7.16000i) q^{97} +(0.143333 - 3.06348i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−1.41267	−	0.0660953i	−0.998907	−	0.0467365i
$2$	−1.41267	−	0.0660953i	−0.998907	−	0.0467365i
$3$		0			0
$3$		0			0
$4$	1.99126	+	0.186742i	0.995631	+	0.0933708i
$5$	2.00635	−	0.987189i	0.897269	−	0.441484i
$5$	2.00635	−	0.987189i	0.897269	−	0.441484i
$6$		0			0
$7$	1.55426	−	1.55426i	0.587453	−	0.587453i	−0.349488	−	0.936941i	$-0.613644\pi$
$7$	1.55426	−	1.55426i	0.587453	−	0.587453i	0.936941	+	0.349488i	$0.113644\pi$
$8$	−2.80065	−	0.395417i	−0.990180	−	0.139801i
$9$		0			0
$10$	−2.89956	+	1.26196i	−0.916922	+	0.399067i
$11$	4.19607	+	4.19607i	1.26516	+	1.26516i	0.948558	+	0.316604i	$0.102543\pi$
$11$	4.19607	+	4.19607i	1.26516	+	1.26516i	0.316604	+	0.948558i	$0.397457\pi$
$12$		0			0
$13$			5.09530i			1.41318i	0.707622	+	0.706591i	$0.249768\pi$
$13$			5.09530i			1.41318i	−0.707622	+	0.706591i	$0.750232\pi$
$14$	−2.29838	+	2.09292i	−0.614267	+	0.559356i
$15$		0			0
$16$	3.93026	+	0.743703i	0.982564	+	0.185926i
$17$	−0.213542	+	0.213542i	−0.0517916	+	0.0517916i	−0.732528	−	0.680737i	$-0.761660\pi$
$17$	−0.213542	+	0.213542i	−0.0517916	+	0.0517916i	0.680737	+	0.732528i	$0.261660\pi$
$18$		0			0
$19$	0.844754	+	0.844754i	0.193800	+	0.193800i	0.797336	−	0.603536i	$-0.206242\pi$
$19$	0.844754	+	0.844754i	0.193800	+	0.193800i	−0.603536	+	0.797336i	$0.706242\pi$
$20$	4.17953	−	1.59108i	0.934571	−	0.355777i
$21$		0			0
$22$	−5.65031	−	6.20499i	−1.20465	−	1.32291i
$23$	−1.70744	−	1.70744i	−0.356027	−	0.356027i	0.506319	−	0.862346i	$-0.331006\pi$
$23$	−1.70744	−	1.70744i	−0.356027	−	0.356027i	−0.862346	+	0.506319i	$0.831006\pi$
$24$		0			0
$25$	3.05092	−	3.96130i	0.610183	−	0.792260i
$26$	0.336775	−	7.19797i	0.0660471	−	1.41164i
$27$		0			0
$28$	3.38518	−	2.80469i	0.639738	−	0.530036i
$29$	−2.24750	+	2.24750i	−0.417350	+	0.417350i	−0.884289	−	0.466939i	$-0.845357\pi$
$29$	−2.24750	+	2.24750i	−0.417350	+	0.417350i	0.466939	+	0.884289i	$0.345357\pi$
$30$		0			0
$31$		−	0.818209i		−	0.146955i	−0.997297	−	0.0734773i	$-0.976590\pi$
$31$		−	0.818209i		−	0.146955i	0.997297	−	0.0734773i	$-0.0234097\pi$
$32$	−5.50299	−	1.31038i	−0.972801	−	0.231644i
$33$		0			0
$34$	0.315778	−	0.287550i	0.0541556	−	0.0493144i
$35$	1.58404	−	4.65273i	0.267752	−	0.786455i
$36$		0			0
$37$			5.12639i			0.842774i	0.906881	+	0.421387i	$0.138457\pi$
$37$			5.12639i			0.842774i	−0.906881	+	0.421387i	$0.861543\pi$
$38$	−1.13752	−	1.24919i	−0.184531	−	0.202646i
$39$		0			0
$40$	−6.00945	+	1.97142i	−0.950177	+	0.311710i
$41$			3.34727i			0.522756i	0.965237	+	0.261378i	$0.0841769\pi$
$41$			3.34727i			0.522756i	−0.965237	+	0.261378i	$0.915823\pi$
$42$		0			0
$43$		−	4.49131i		−	0.684919i	−0.939533	−	0.342460i	$-0.888740\pi$
$43$		−	4.49131i		−	0.684919i	0.939533	−	0.342460i	$-0.111260\pi$
$44$	7.57189	+	9.13905i	1.14151	+	1.37776i
$45$		0			0
$46$	2.29920	+	2.52490i	0.338998	+	0.372277i
$47$	−4.29355	−	4.29355i	−0.626278	−	0.626278i	0.320851	−	0.947130i	$-0.396031\pi$
$47$	−4.29355	−	4.29355i	−0.626278	−	0.626278i	−0.947130	+	0.320851i	$0.896031\pi$
$48$		0			0
$49$			2.16858i			0.309797i
$50$	−4.57176	+	5.39435i	−0.646544	+	0.762877i
$51$		0			0
$52$	−0.951504	+	10.1461i	−0.131950	+	1.40701i
$53$	1.00653			0.138258			0.0691291	−	0.997608i	$-0.477978\pi$
$53$	1.00653			0.138258			0.0691291	+	0.997608i	$0.477978\pi$
$54$		0			0
$55$	12.5611	+	4.27649i	1.69374	+	0.576642i
$56$	−4.96751	+	3.73835i	−0.663811	+	0.499558i
$57$		0			0
$58$	3.32352	−	3.02642i	0.436399	−	0.397388i
$59$	7.65005	−	7.65005i	0.995952	−	0.995952i	−0.00404030	−	0.999992i	$-0.501286\pi$
$59$	7.65005	−	7.65005i	0.995952	−	0.995952i	0.999992	+	0.00404030i	$0.00128607\pi$
$60$		0			0
$61$	−1.90291	−	1.90291i	−0.243643	−	0.243643i	0.574712	−	0.818355i	$-0.305114\pi$
$61$	−1.90291	−	1.90291i	−0.243643	−	0.243643i	−0.818355	+	0.574712i	$0.805114\pi$
$62$	−0.0540798	+	1.15586i	−0.00686814	+	0.146794i
$63$		0			0
$64$	7.68729	+	2.21485i	0.960911	+	0.276856i
$65$	5.03002	+	10.2230i	0.623897	+	1.26800i
$66$		0			0
$67$		−	11.0221i		−	1.34656i	−0.739387	−	0.673280i	$-0.764885\pi$
$67$		−	11.0221i		−	1.34656i	0.739387	−	0.673280i	$-0.235115\pi$
$68$	−0.465096	+	0.385341i	−0.0564012	+	0.0467295i
$69$		0			0
$70$	−2.54525	+	6.46807i	−0.304216	+	0.773082i
$71$	10.5331			1.25005			0.625027	−	0.780604i	$-0.285088\pi$
$71$	10.5331			1.25005			0.625027	+	0.780604i	$0.285088\pi$
$72$		0			0
$73$	2.70854	−	2.70854i	0.317010	−	0.317010i	−0.530607	−	0.847618i	$-0.678036\pi$
$73$	2.70854	−	2.70854i	0.317010	−	0.317010i	0.847618	+	0.530607i	$0.178036\pi$
$74$	0.338831	−	7.24189i	0.0393883	−	0.841853i
$75$		0			0
$76$	1.52438	+	1.83988i	0.174858	+	0.211048i
$77$	13.0435			1.48645
$78$		0			0
$79$	−8.32010			−0.936085			−0.468042	−	0.883706i	$-0.655041\pi$
$79$	−8.32010			−0.936085			−0.468042	+	0.883706i	$0.655041\pi$
$80$	8.61966	−	2.38777i	0.963707	−	0.266961i
$81$		0			0
$82$	0.221239	−	4.72858i	0.0244317	−	0.522185i
$83$	9.17237			1.00680			0.503399	−	0.864054i	$-0.332083\pi$
$83$	9.17237			1.00680			0.503399	+	0.864054i	$0.332083\pi$
$84$		0			0
$85$	−0.217635	+	0.639248i	−0.0236058	+	0.0693362i
$86$	−0.296855	+	6.34474i	−0.0320107	+	0.684171i
$87$		0			0
$88$	−10.0925	−	13.4109i	−1.07587	−	1.42961i
$89$	4.25101			0.450606			0.225303	−	0.974289i	$-0.427663\pi$
$89$	4.25101			0.450606			0.225303	+	0.974289i	$0.427663\pi$
$90$		0			0
$91$	7.91940	+	7.91940i	0.830178	+	0.830178i
$92$	−3.08112	−	3.71882i	−0.321229	−	0.387714i
$93$		0			0
$94$	5.78157	+	6.34914i	0.596324	+	0.654864i
$95$	2.52881	+	0.860944i	0.259450	+	0.0883310i
$96$		0			0
$97$	−7.16000	+	7.16000i	−0.726987	+	0.726987i	−0.970019	−	0.243031i	$-0.921858\pi$
$97$	−7.16000	+	7.16000i	−0.726987	+	0.726987i	0.243031	+	0.970019i	$0.421858\pi$
$98$	0.143333	−	3.06348i	0.0144788	−	0.309458i
$99$		0			0
$100$	6.81492	−	7.31826i	0.681492	−	0.731826i
$101$	−8.38846	+	8.38846i	−0.834683	+	0.834683i	−0.988153	−	0.153470i	$-0.950955\pi$
$101$	−8.38846	+	8.38846i	−0.834683	+	0.834683i	0.153470	+	0.988153i	$0.450955\pi$
$102$		0			0
$103$	−5.16478	−	5.16478i	−0.508901	−	0.508901i	0.405288	−	0.914189i	$-0.367171\pi$
$103$	−5.16478	−	5.16478i	−0.508901	−	0.508901i	−0.914189	+	0.405288i	$0.867171\pi$
$104$	2.01477	−	14.2702i	0.197564	−	1.39930i
$105$		0			0
$106$	−1.42190	−	0.0665272i	−0.138107	−	0.00646169i
$107$	−8.97973			−0.868103			−0.434052	−	0.900888i	$-0.642916\pi$
$107$	−8.97973			−0.868103			−0.434052	+	0.900888i	$0.642916\pi$
$108$		0			0
$109$	10.9081	−	10.9081i	1.04481	−	1.04481i	0.0458592	−	0.998948i	$-0.485397\pi$
$109$	10.9081	−	10.9081i	1.04481	−	1.04481i	0.998948	−	0.0458592i	$-0.0146025\pi$
$110$	−17.4620	−	6.87149i	−1.66494	−	0.655171i
$111$		0			0
$112$	7.26453	−	4.95272i	0.686433	−	0.467988i
$113$	4.29684	+	4.29684i	0.404212	+	0.404212i	0.879715	−	0.475502i	$-0.157734\pi$
$113$	4.29684	+	4.29684i	0.404212	+	0.404212i	−0.475502	+	0.879715i	$0.657734\pi$
$114$		0			0
$115$	−5.11131	−	1.74017i	−0.476632	−	0.162271i
$116$	−4.89506	+	4.05566i	−0.454495	+	0.376558i
$117$		0			0
$118$	−11.3126	+	10.3013i	−1.04141	+	0.948316i
$119$			0.663798i			0.0608503i
$120$		0			0
$121$			24.2140i			2.20127i
$122$	2.56241	+	2.81396i	0.231990	+	0.254764i
$123$		0			0
$124$	0.152794	−	1.62927i	0.0137213	−	0.146313i
$125$	2.21067	−	10.9596i	0.197728	−	0.980257i
$126$		0			0
$127$	0.759686	+	0.759686i	0.0674112	+	0.0674112i	0.740009	−	0.672597i	$-0.234821\pi$
$127$	0.759686	+	0.759686i	0.0674112	+	0.0674112i	−0.672597	+	0.740009i	$0.734821\pi$
$128$	−10.7132	−	3.63694i	−0.946922	−	0.321463i
$129$		0			0
$130$	−6.43006	−	14.7741i	−0.563954	−	1.29578i
$131$	−7.59995	+	7.59995i	−0.664010	+	0.664010i	−0.956323	−	0.292312i	$-0.905575\pi$
$131$	−7.59995	+	7.59995i	−0.664010	+	0.664010i	0.292312	+	0.956323i	$0.405575\pi$
$132$		0			0
$133$	2.62593			0.227697
$134$	−0.728507	+	15.5705i	−0.0629335	+	1.34509i
$135$		0			0
$136$	0.682495	−	0.513619i	0.0585235	−	0.0440425i
$137$	−12.7789	−	12.7789i	−1.09178	−	1.09178i	−0.995339	−	0.0964376i	$-0.969255\pi$
$137$	−12.7789	−	12.7789i	−1.09178	−	1.09178i	−0.0964376	−	0.995339i	$-0.530745\pi$
$138$		0			0
$139$	7.74227	−	7.74227i	0.656691	−	0.656691i	−0.297905	−	0.954596i	$-0.596288\pi$
$139$	7.74227	−	7.74227i	0.656691	−	0.656691i	0.954596	+	0.297905i	$0.0962877\pi$
$140$	4.02311	−	8.96900i	0.340015	−	0.758019i
$141$		0			0
$142$	−14.8798	−	0.696191i	−1.24869	−	0.0584230i
$143$	−21.3802	+	21.3802i	−1.78790	+	1.78790i
$144$		0			0
$145$	−2.29057	+	6.72798i	−0.190222	+	0.558728i
$146$	−4.00529	+	3.64724i	−0.331480	+	0.301848i
$147$		0			0
$148$	−0.957310	+	10.2080i	−0.0786904	+	0.839092i
$149$	−9.57165	−	9.57165i	−0.784140	−	0.784140i	0.196386	−	0.980527i	$-0.437079\pi$
$149$	−9.57165	−	9.57165i	−0.784140	−	0.784140i	−0.980527	+	0.196386i	$0.937079\pi$
$150$		0			0
$151$	−9.68791			−0.788391			−0.394195	−	0.919027i	$-0.628977\pi$
$151$	−9.68791			−0.788391			−0.394195	+	0.919027i	$0.628977\pi$
$152$	−2.03183	−	2.69989i	−0.164803	−	0.218990i
$153$		0			0
$154$	−18.4262	−	0.862116i	−1.48482	−	0.0694713i
$155$	−0.807726	−	1.64162i	−0.0648781	−	0.131858i
$156$		0			0
$157$	−9.97637			−0.796201			−0.398101	−	0.917342i	$-0.630331\pi$
$157$	−9.97637			−0.796201			−0.398101	+	0.917342i	$0.630331\pi$
$158$	11.7535	+	0.549920i	0.935062	+	0.0437493i
$159$		0			0
$160$	−12.3345	+	2.80341i	−0.975131	+	0.221629i
$161$	−5.30761			−0.418298
$162$		0			0
$163$	9.48267			0.742740			0.371370	−	0.928485i	$-0.378888\pi$
$163$	9.48267			0.742740			0.371370	+	0.928485i	$0.378888\pi$
$164$	−0.625074	+	6.66529i	−0.0488101	+	0.520472i
$165$		0			0
$166$	−12.9575	−	0.606250i	−1.00570	−	0.0470542i
$167$	9.43528	−	9.43528i	0.730124	−	0.730124i	−0.240520	−	0.970644i	$-0.577318\pi$
$167$	9.43528	−	9.43528i	0.730124	−	0.730124i	0.970644	+	0.240520i	$0.0773180\pi$
$168$		0			0
$169$	−12.9621			−0.997082
$170$	0.349697	−	0.888660i	0.0268206	−	0.0681571i
$171$		0			0
$172$	0.838715	−	8.94339i	0.0639514	−	0.681927i
$173$		−	8.94716i		−	0.680240i	−0.940382	−	0.340120i	$-0.889532\pi$
$173$		−	8.94716i		−	0.680240i	0.940382	−	0.340120i	$-0.110468\pi$
$174$		0			0
$175$	−1.41497	−	10.8988i	−0.106962	−	0.823870i
$176$	13.3710	+	19.6122i	1.00788	+	1.47833i
$177$		0			0
$178$	−6.00526	−	0.280972i	−0.450114	−	0.0210597i
$179$	3.02430	+	3.02430i	0.226047	+	0.226047i	0.811039	−	0.584992i	$-0.198902\pi$
$179$	3.02430	+	3.02430i	0.226047	+	0.226047i	−0.584992	+	0.811039i	$0.698902\pi$
$180$		0			0
$181$	−1.54845	+	1.54845i	−0.115095	+	0.115095i	−0.762309	−	0.647213i	$-0.775934\pi$
$181$	−1.54845	+	1.54845i	−0.115095	+	0.115095i	0.647213	+	0.762309i	$0.275934\pi$
$182$	−10.6640	−	11.7109i	−0.790472	−	0.868071i
$183$		0			0
$184$	4.10680	+	5.45710i	0.302757	+	0.402303i
$185$	5.06072	+	10.2854i	0.372071	+	0.756195i
$186$		0			0
$187$	−1.79208			−0.131050
$188$	−7.74779	−	9.35136i	−0.565066	−	0.682018i
$189$		0			0
$190$	−3.51546	−	1.38337i	−0.255038	−	0.100360i
$191$		−	20.1005i		−	1.45442i	−0.686415	−	0.727210i	$-0.740817\pi$
$191$		−	20.1005i		−	1.45442i	0.686415	−	0.727210i	$-0.259183\pi$
$192$		0			0
$193$	3.82483	+	3.82483i	0.275317	+	0.275317i	0.831236	−	0.555919i	$-0.187634\pi$
$193$	3.82483	+	3.82483i	0.275317	+	0.275317i	−0.555919	+	0.831236i	$0.687634\pi$
$194$	10.5879	−	9.64146i	0.760170	−	0.692216i
$195$		0			0
$196$	−0.404964	+	4.31821i	−0.0289260	+	0.308444i
$197$		−	1.11758i		−	0.0796246i	−0.999207	−	0.0398123i	$-0.987324\pi$
$197$		−	1.11758i		−	0.0796246i	0.999207	−	0.0398123i	$-0.0126760\pi$
$198$		0			0
$199$		−	25.5830i		−	1.81353i	−0.421635	−	0.906766i	$-0.638544\pi$
$199$		−	25.5830i		−	1.81353i	0.421635	−	0.906766i	$-0.361456\pi$
$200$	−10.1109	+	9.88784i	−0.714950	+	0.699176i
$201$		0			0
$202$	12.4046	−	11.2957i	0.872781	−	0.794761i
$203$			6.98637i			0.490347i
$204$		0			0
$205$	3.30439	+	6.71581i	0.230788	+	0.469053i
$206$	6.95475	+	7.63749i	0.484560	+	0.532129i
$207$		0			0
$208$	−3.78939	+	20.0258i	−0.262747	+	1.38854i
$209$			7.08929i			0.490376i
$210$		0			0
$211$	0.411613	−	0.411613i	0.0283366	−	0.0283366i	−0.692797	−	0.721133i	$-0.743622\pi$
$211$	0.411613	−	0.411613i	0.0283366	−	0.0283366i	0.721133	+	0.692797i	$0.243622\pi$
$212$	2.00427	+	0.187962i	0.137654	+	0.0129093i
$213$		0			0
$214$	12.6854	+	0.593518i	0.867155	+	0.0405721i
$215$	−4.43378	−	9.01117i	−0.302381	−	0.614557i
$216$		0			0
$217$	−1.27171	−	1.27171i	−0.0863290	−	0.0863290i
$218$	−16.1305	+	14.6886i	−1.09250	+	0.994835i
$219$		0			0
$220$	24.2139	+	10.8613i	1.63250	+	0.732268i
$221$	−1.08806	−	1.08806i	−0.0731909	−	0.0731909i
$222$		0			0
$223$	−16.7466	+	16.7466i	−1.12143	+	1.12143i	−0.129908	+	0.991526i	$0.541468\pi$
$223$	−16.7466	+	16.7466i	−1.12143	+	1.12143i	−0.991526	+	0.129908i	$0.958532\pi$
$224$	−10.5897	+	6.51639i	−0.707555	+	0.435395i
$225$		0			0
$226$	−5.78600	−	6.35401i	−0.384879	−	0.422662i
$227$			13.7807i			0.914659i	0.889297	+	0.457330i	$0.151194\pi$
$227$			13.7807i			0.914659i	−0.889297	+	0.457330i	$0.848806\pi$
$228$		0			0
$229$	−7.90971	−	7.90971i	−0.522688	−	0.522688i	0.395694	−	0.918382i	$-0.370504\pi$
$229$	−7.90971	−	7.90971i	−0.522688	−	0.522688i	−0.918382	+	0.395694i	$0.870504\pi$
$230$	7.10556	+	2.79611i	0.468527	+	0.184370i
$231$		0			0
$232$	7.18315	−	5.40576i	0.471597	−	0.354905i
$233$	1.67997	−	1.67997i	0.110058	−	0.110058i	−0.649933	−	0.759991i	$-0.725203\pi$
$233$	1.67997	−	1.67997i	0.110058	−	0.110058i	0.759991	+	0.649933i	$0.225203\pi$
$234$		0			0
$235$	−12.8529	−	4.37583i	−0.838432	−	0.285448i
$236$	16.6618	−	13.8047i	1.08459	−	0.898608i
$237$		0			0
$238$	0.0438740	−	0.937727i	0.00284393	−	0.0607838i
$239$	−11.7685			−0.761241			−0.380620	−	0.924731i	$-0.624290\pi$
$239$	−11.7685			−0.761241			−0.380620	+	0.924731i	$0.624290\pi$
$240$		0			0
$241$	−13.2730			−0.854991			−0.427495	−	0.904018i	$-0.640604\pi$
$241$	−13.2730			−0.854991			−0.427495	+	0.904018i	$0.640604\pi$
$242$	1.60043	−	34.2063i	0.102880	−	2.19886i
$243$		0			0
$244$	−3.43385	−	4.14455i	−0.219830	−	0.265328i
$245$	2.14080	+	4.35094i	0.136770	+	0.277971i
$246$		0			0
$247$	−4.30427	+	4.30427i	−0.273874	+	0.273874i
$248$	−0.323534	+	2.29152i	−0.0205444	+	0.145511i
$249$		0			0
$250$	−3.84732	+	15.3362i	−0.243326	+	0.969945i
$251$	−10.3795	−	10.3795i	−0.655149	−	0.655149i	0.299079	−	0.954228i	$-0.403321\pi$
$251$	−10.3795	−	10.3795i	−0.655149	−	0.655149i	−0.954228	+	0.299079i	$0.903321\pi$
$252$		0			0
$253$		−	14.3291i		−	0.900863i
$254$	−1.02297	−	1.12340i	−0.0641870	−	0.0704881i
$255$		0			0
$256$	14.8938	+	5.84588i	0.930863	+	0.365368i
$257$	−20.4353	+	20.4353i	−1.27472	+	1.27472i	−0.331140	+	0.943582i	$0.607433\pi$
$257$	−20.4353	+	20.4353i	−1.27472	+	1.27472i	−0.943582	+	0.331140i	$0.892567\pi$
$258$		0			0
$259$	7.96772	+	7.96772i	0.495090	+	0.495090i
$260$	8.10704	+	21.2959i	0.502777	+	1.32072i
$261$		0			0
$262$	11.2385	−	10.2339i	0.694318	−	0.632251i
$263$	−14.0611	−	14.0611i	−0.867047	−	0.867047i	0.125098	−	0.992144i	$-0.460076\pi$
$263$	−14.0611	−	14.0611i	−0.867047	−	0.867047i	−0.992144	+	0.125098i	$0.960076\pi$
$264$		0			0
$265$	2.01946	−	0.993639i	0.124055	−	0.0610388i
$266$	−3.70956	−	0.173561i	−0.227448	−	0.0106417i
$267$		0			0
$268$	2.05828	−	21.9478i	0.125729	−	1.34068i
$269$	6.61443	−	6.61443i	0.403289	−	0.403289i	−0.476101	−	0.879390i	$-0.657950\pi$
$269$	6.61443	−	6.61443i	0.403289	−	0.403289i	0.879390	+	0.476101i	$0.157950\pi$
$270$		0			0
$271$		−	10.6219i		−	0.645237i	−0.946529	−	0.322619i	$-0.895437\pi$
$271$		−	10.6219i		−	0.645237i	0.946529	−	0.322619i	$-0.104563\pi$
$272$	−0.998087	+	0.680463i	−0.0605179	+	0.0412592i
$273$		0			0
$274$	17.2077	+	18.8970i	1.03956	+	1.14161i
$275$	29.4237	−	3.82004i	1.77432	−	0.230357i
$276$		0			0
$277$			8.28511i			0.497804i	0.968529	+	0.248902i	$0.0800697\pi$
$277$			8.28511i			0.497804i	−0.968529	+	0.248902i	$0.919930\pi$
$278$	−11.4490	+	10.4255i	−0.686665	+	0.625282i
$279$		0			0
$280$	−6.27612	+	12.4043i	−0.375070	+	0.741300i
$281$			21.0176i			1.25380i	0.779098	+	0.626902i	$0.215677\pi$
$281$			21.0176i			1.25380i	−0.779098	+	0.626902i	$0.784323\pi$
$282$		0			0
$283$			14.4748i			0.860436i	0.902725	+	0.430218i	$0.141563\pi$
$283$			14.4748i			0.860436i	−0.902725	+	0.430218i	$0.858437\pi$
$284$	20.9742	+	1.96697i	1.24459	+	0.116718i
$285$		0			0
$286$	31.6163	−	28.7900i	1.86951	−	1.70239i
$287$	5.20251	+	5.20251i	0.307095	+	0.307095i
$288$		0			0
$289$			16.9088i			0.994635i
$290$	3.68051	−	9.35301i	0.216127	−	0.549228i
$291$		0			0
$292$	5.89921	−	4.88761i	0.345225	−	0.286026i
$293$	11.9165			0.696171			0.348086	−	0.937463i	$-0.386832\pi$
$293$	11.9165			0.696171			0.348086	+	0.937463i	$0.386832\pi$
$294$		0			0
$295$	7.79667	−	22.9008i	0.453940	−	1.33333i
$296$	2.02706	−	14.3572i	0.117821	−	0.834497i
$297$		0			0
$298$	12.8889	+	14.1542i	0.746635	+	0.819931i
$299$	8.69993	−	8.69993i	0.503130	−	0.503130i
$300$		0			0
$301$	−6.98065	−	6.98065i	−0.402358	−	0.402358i
$302$	13.6858	+	0.640325i	0.787529	+	0.0368466i
$303$		0			0
$304$	2.69185	+	3.94834i	0.154388	+	0.226453i
$305$	−5.69645	−	1.93938i	−0.326178	−	0.111049i
$306$		0			0
$307$			25.4511i			1.45257i	0.687392	+	0.726287i	$0.258755\pi$
$307$			25.4511i			1.45257i	−0.687392	+	0.726287i	$0.741245\pi$
$308$	25.9731	+	2.43577i	1.47995	+	0.138791i
$309$		0			0
$310$	1.03255	+	2.37245i	0.0586447	+	0.134746i
$311$	−21.4775			−1.21788			−0.608939	−	0.793217i	$-0.708404\pi$
$311$	−21.4775			−1.21788			−0.608939	+	0.793217i	$0.708404\pi$
$312$		0			0
$313$	18.7965	−	18.7965i	1.06244	−	1.06244i	0.0645277	−	0.997916i	$-0.479446\pi$
$313$	18.7965	−	18.7965i	1.06244	−	1.06244i	0.997916	−	0.0645277i	$-0.0205541\pi$
$314$	14.0933	+	0.659392i	0.795331	+	0.0372116i
$315$		0			0
$316$	−16.5675	−	1.55371i	−0.931995	−	0.0874029i
$317$	−16.2531			−0.912864			−0.456432	−	0.889758i	$-0.650873\pi$
$317$	−16.2531			−0.912864			−0.456432	+	0.889758i	$0.650873\pi$
$318$		0			0
$319$	−18.8613			−1.05603
$320$	17.6099	−	3.14503i	0.984424	−	0.175813i
$321$		0			0
$322$	7.49789	+	0.350808i	0.417841	+	0.0195498i
$323$	−0.360781			−0.0200744
$324$		0			0
$325$	20.1840	+	15.5453i	1.11961	+	0.862300i
$326$	−13.3959	−	0.626760i	−0.741928	−	0.0347130i
$327$		0			0
$328$	1.32357	−	9.37453i	0.0730818	−	0.517622i
$329$	−13.3465			−0.735818
$330$		0			0
$331$	−8.71558	−	8.71558i	−0.479052	−	0.479052i	0.425777	−	0.904828i	$-0.360001\pi$
$331$	−8.71558	−	8.71558i	−0.479052	−	0.479052i	−0.904828	+	0.425777i	$0.860001\pi$
$332$	18.2646	+	1.71286i	1.00240	+	0.0940055i
$333$		0			0
$334$	−13.9526	+	12.7053i	−0.763450	+	0.695203i
$335$	−10.8809	−	22.1142i	−0.594485	−	1.20823i
$336$		0			0
$337$	0.0406874	−	0.0406874i	0.00221638	−	0.00221638i	−0.705998	−	0.708214i	$-0.749501\pi$
$337$	0.0406874	−	0.0406874i	0.00221638	−	0.00221638i	0.708214	+	0.705998i	$0.249501\pi$
$338$	18.3111	+	0.856732i	0.995993	+	0.0466001i
$339$		0			0
$340$	−0.552742	+	1.23227i	−0.0299767	+	0.0668292i
$341$	3.43326	−	3.43326i	0.185921	−	0.185921i
$342$		0			0
$343$	14.2503	+	14.2503i	0.769445	+	0.769445i
$344$	−1.77594	+	12.5786i	−0.0957524	+	0.678193i
$345$		0			0
$346$	−0.591366	+	12.6394i	−0.0317920	+	0.679497i
$347$	35.7094			1.91698			0.958491	−	0.285124i	$-0.0920348\pi$
$347$	35.7094			1.91698			0.958491	+	0.285124i	$0.0920348\pi$
$348$		0			0
$349$	−0.274452	+	0.274452i	−0.0146911	+	0.0146911i	−0.714414	−	0.699723i	$-0.753307\pi$
$349$	−0.274452	+	0.274452i	−0.0146911	+	0.0146911i	0.699723	+	0.714414i	$0.253307\pi$
$350$	1.27853	+	15.4899i	0.0683401	+	0.827969i
$351$		0			0
$352$	−17.5925	−	28.5894i	−0.937683	−	1.52382i
$353$	15.6215	+	15.6215i	0.831446	+	0.831446i	0.987715	−	0.156268i	$-0.0499464\pi$
$353$	15.6215	+	15.6215i	0.831446	+	0.831446i	−0.156268	+	0.987715i	$0.549946\pi$
$354$		0			0
$355$	21.1332	−	10.3982i	1.12163	−	0.551879i
$356$	8.46487	+	0.793840i	0.448637	+	0.0420734i
$357$		0			0
$358$	−4.07244	−	4.47222i	−0.215235	−	0.236364i
$359$		−	0.768787i		−	0.0405750i	−0.999794	−	0.0202875i	$-0.993542\pi$
$359$		−	0.768787i		−	0.0405750i	0.999794	−	0.0202875i	$-0.00645816\pi$
$360$		0			0
$361$		−	17.5728i		−	0.924883i
$362$	2.28979	−	2.08510i	0.120349	−	0.109591i
$363$		0			0
$364$	14.2907	+	17.2485i	0.749037	+	0.904066i
$365$	2.76045	−	8.10812i	0.144488	−	0.424399i
$366$		0			0
$367$	13.7849	+	13.7849i	0.719568	+	0.719568i	0.968517	−	0.248949i	$-0.0800852\pi$
$367$	13.7849	+	13.7849i	0.719568	+	0.719568i	−0.248949	+	0.968517i	$0.580085\pi$
$368$	−5.44086	−	7.98052i	−0.283624	−	0.416013i
$369$		0			0
$370$	−6.46930	−	14.8643i	−0.336323	−	0.772758i
$371$	1.56441	−	1.56441i	0.0812202	−	0.0812202i
$372$		0			0
$373$	−21.4003			−1.10806			−0.554031	−	0.832496i	$-0.686911\pi$
$373$	−21.4003			−1.10806			−0.554031	+	0.832496i	$0.686911\pi$
$374$	2.53161	+	0.118448i	0.130906	+	0.00612479i
$375$		0			0
$376$	10.3270	+	13.7225i	0.532573	+	0.707682i
$377$	−11.4517	−	11.4517i	−0.589791	−	0.589791i
$378$		0			0
$379$	11.3922	−	11.3922i	0.585180	−	0.585180i	−0.351142	−	0.936322i	$-0.614207\pi$
$379$	11.3922	−	11.3922i	0.585180	−	0.585180i	0.936322	+	0.351142i	$0.114207\pi$
$380$	4.87475	+	2.18660i	0.250069	+	0.112170i
$381$		0			0
$382$	−1.32855	+	28.3953i	−0.0679744	+	1.45283i
$383$	−4.42635	+	4.42635i	−0.226176	+	0.226176i	−0.811093	−	0.584917i	$-0.801127\pi$
$383$	−4.42635	+	4.42635i	−0.226176	+	0.226176i	0.584917	+	0.811093i	$0.301127\pi$
$384$		0			0
$385$	26.1699	−	12.8764i	1.33374	−	0.656243i
$386$	−5.15041	−	5.65602i	−0.262149	−	0.287884i
$387$		0			0
$388$	−15.5945	+	12.9204i	−0.791691	+	0.655932i
$389$	−12.3502	−	12.3502i	−0.626180	−	0.626180i	0.320924	−	0.947105i	$-0.396006\pi$
$389$	−12.3502	−	12.3502i	−0.626180	−	0.626180i	−0.947105	+	0.320924i	$0.896006\pi$
$390$		0			0
$391$	0.729222			0.0368784
$392$	0.857493	−	6.07343i	0.0433099	−	0.306755i
$393$		0			0
$394$	−0.0738671	+	1.57878i	−0.00372137	+	0.0795376i
$395$	−16.6931	+	8.21351i	−0.839920	+	0.413267i
$396$		0			0
$397$	17.9832			0.902551			0.451275	−	0.892385i	$-0.350969\pi$
$397$	17.9832			0.902551			0.451275	+	0.892385i	$0.350969\pi$
$398$	−1.69092	+	36.1403i	−0.0847580	+	1.81155i
$399$		0			0
$400$	14.9369	−	13.2999i	0.746846	−	0.664997i
$401$	−9.06570			−0.452720			−0.226360	−	0.974044i	$-0.572683\pi$
$401$	−9.06570			−0.452720			−0.226360	+	0.974044i	$0.572683\pi$
$402$		0			0
$403$	4.16902			0.207674
$404$	−18.2701	+	15.1372i	−0.908972	+	0.753102i
$405$		0			0
$406$	0.461766	−	9.86942i	0.0229171	−	0.489811i
$407$	−21.5107	+	21.5107i	−1.06625	+	1.06625i
$408$		0			0
$409$	−30.0616			−1.48645			−0.743226	−	0.669040i	$-0.766705\pi$
$409$	−30.0616			−1.48645			−0.743226	+	0.669040i	$0.766705\pi$
$410$	−4.22412	−	9.70562i	−0.208614	−	0.479326i
$411$		0			0
$412$	−9.31995	−	11.2489i	−0.459161	−	0.554194i
$413$		−	23.7803i		−	1.17015i
$414$		0			0
$415$	18.4030	−	9.05486i	0.903369	−	0.444485i
$416$	6.67676	−	28.0394i	0.327355	−	1.37474i
$417$		0			0
$418$	0.468569	−	10.0148i	0.0229184	−	0.489840i
$419$	15.3986	+	15.3986i	0.752271	+	0.752271i	0.974903	−	0.222631i	$-0.0714646\pi$
$419$	15.3986	+	15.3986i	0.752271	+	0.752271i	−0.222631	+	0.974903i	$0.571465\pi$
$420$		0			0
$421$	−3.86468	+	3.86468i	−0.188353	+	0.188353i	−0.794984	−	0.606631i	$-0.792521\pi$
$421$	−3.86468	+	3.86468i	−0.188353	+	0.188353i	0.606631	+	0.794984i	$0.292521\pi$
$422$	−0.608679	+	0.554267i	−0.0296300	+	0.0269813i
$423$		0			0
$424$	−2.81895	−	0.398001i	−0.136900	−	0.0193286i
$425$	0.194406	+	1.49740i	0.00943006	+	0.0726348i
$426$		0			0
$427$	−5.91523			−0.286258
$428$	−17.8810	−	1.67689i	−0.864311	−	0.0810555i
$429$		0			0
$430$	5.66786	+	13.0228i	0.273328	+	0.628017i
$431$			27.2692i			1.31351i	0.754103	+	0.656756i	$0.228072\pi$
$431$			27.2692i			1.31351i	−0.754103	+	0.656756i	$0.771928\pi$
$432$		0			0
$433$	19.1435	+	19.1435i	0.919978	+	0.919978i	0.997027	−	0.0770497i	$-0.0245500\pi$
$433$	19.1435	+	19.1435i	0.919978	+	0.919978i	−0.0770497	+	0.997027i	$0.524550\pi$
$434$	1.71244	+	1.88055i	0.0821999	+	0.0902694i
$435$		0			0
$436$	23.7579	−	19.6839i	1.13780	−	0.942688i
$437$		−	2.88474i		−	0.137996i
$438$		0			0
$439$			30.1995i			1.44134i	0.693276	+	0.720672i	$0.256167\pi$
$439$			30.1995i			1.44134i	−0.693276	+	0.720672i	$0.743833\pi$
$440$	−33.4883	−	16.9438i	−1.59649	−	0.807765i
$441$		0			0
$442$	1.46515	+	1.60899i	0.0696903	+	0.0765316i
$443$		−	27.7051i		−	1.31631i	−0.752884	−	0.658153i	$-0.771338\pi$
$443$		−	27.7051i		−	1.31631i	0.752884	−	0.658153i	$-0.228662\pi$
$444$		0			0
$445$	8.52903	−	4.19655i	0.404315	−	0.198935i
$446$	24.7642	−	22.5505i	1.17262	−	1.06780i
$447$		0			0
$448$	15.3905	−	8.50557i	0.727131	−	0.401851i
$449$			9.78315i			0.461695i	0.972990	+	0.230848i	$0.0741499\pi$
$449$			9.78315i			0.461695i	−0.972990	+	0.230848i	$0.925850\pi$
$450$		0			0
$451$	−14.0454	+	14.0454i	−0.661371	+	0.661371i
$452$	7.75373	+	9.35853i	0.364705	+	0.440188i
$453$		0			0
$454$	0.910842	−	19.4676i	0.0427479	−	0.913660i
$455$	23.7071	+	8.07118i	1.11140	+	0.378383i
$456$		0			0
$457$	−0.557108	−	0.557108i	−0.0260604	−	0.0260604i	0.693957	−	0.720017i	$-0.255866\pi$
$457$	−0.557108	−	0.557108i	−0.0260604	−	0.0260604i	−0.720017	+	0.693957i	$0.755866\pi$
$458$	10.6510	+	11.6966i	0.497689	+	0.546546i
$459$		0			0
$460$	−9.85299	−	4.41962i	−0.459398	−	0.206066i
$461$	12.5791	+	12.5791i	0.585865	+	0.585865i	0.936509	−	0.350644i	$-0.114037\pi$
$461$	12.5791	+	12.5791i	0.585865	+	0.585865i	−0.350644	+	0.936509i	$0.614037\pi$
$462$		0			0
$463$	−3.29549	+	3.29549i	−0.153154	+	0.153154i	−0.779525	−	0.626371i	$-0.784540\pi$
$463$	−3.29549	+	3.29549i	−0.153154	+	0.153154i	0.626371	+	0.779525i	$0.284540\pi$
$464$	−10.5047	+	7.16177i	−0.487669	+	0.332477i
$465$		0			0
$466$	−2.48427	+	2.26220i	−0.115082	+	0.104794i
$467$			10.1995i			0.471979i	0.971756	+	0.235989i	$0.0758331\pi$
$467$			10.1995i			0.471979i	−0.971756	+	0.235989i	$0.924167\pi$
$468$		0			0
$469$	−17.1311	−	17.1311i	−0.791042	−	0.791042i
$470$	17.8677	+	7.03112i	0.824175	+	0.324321i
$471$		0			0
$472$	−24.4501	+	18.4002i	−1.12541	+	0.846936i
$473$	18.8459	−	18.8459i	0.866534	−	0.866534i
$474$		0			0
$475$	5.92360	−	0.769051i	0.271793	−	0.0352865i
$476$	−0.123959	+	1.32180i	−0.00568164	+	0.0605845i
$477$		0			0
$478$	16.6250	+	0.777843i	0.760409	+	0.0355777i
$479$	−5.65795			−0.258518			−0.129259	−	0.991611i	$-0.541260\pi$
$479$	−5.65795			−0.258518			−0.129259	+	0.991611i	$0.541260\pi$
$480$		0			0
$481$	−26.1205			−1.19099
$482$	18.7504	+	0.877285i	0.854057	+	0.0399592i
$483$		0			0
$484$	−4.52175	+	48.2164i	−0.205534	+	2.19165i
$485$	−7.29722	+	21.4338i	−0.331350	+	0.973257i
$486$		0			0
$487$	−19.7470	+	19.7470i	−0.894823	+	0.894823i	−0.994972	−	0.100149i	$-0.968068\pi$
$487$	−19.7470	+	19.7470i	−0.894823	+	0.894823i	0.100149	+	0.994972i	$0.468068\pi$
$488$	4.57695	+	6.08184i	0.207189	+	0.275312i
$489$		0			0
$490$	−2.73666	−	6.28793i	−0.123630	−	0.284060i
$491$	4.21405	+	4.21405i	0.190177	+	0.190177i	0.795773	−	0.605595i	$-0.207065\pi$
$491$	4.21405	+	4.21405i	0.190177	+	0.190177i	−0.605595	+	0.795773i	$0.707065\pi$
$492$		0			0
$493$		−	0.959871i		−	0.0432304i
$494$	6.36500	−	5.79602i	0.286375	−	0.260775i
$495$		0			0
$496$	0.608504	−	3.21577i	0.0273226	−	0.144392i
$497$	16.3712	−	16.3712i	0.734348	−	0.734348i
$498$		0			0
$499$	−16.8862	−	16.8862i	−0.755928	−	0.755928i	0.219650	−	0.975579i	$-0.429508\pi$
$499$	−16.8862	−	16.8862i	−0.755928	−	0.755928i	−0.975579	+	0.219650i	$0.929508\pi$
$500$	6.44863	−	21.4106i	0.288392	−	0.957513i
$501$		0			0
$502$	13.9768	+	15.3488i	0.623814	+	0.685053i
$503$	20.3714	+	20.3714i	0.908317	+	0.908317i	0.996136	−	0.0878190i	$-0.0279897\pi$
$503$	20.3714	+	20.3714i	0.908317	+	0.908317i	−0.0878190	+	0.996136i	$0.527990\pi$
$504$		0			0
$505$	−8.54923	+	25.1112i	−0.380436	+	1.11744i
$506$	−0.947086	+	20.2423i	−0.0421031	+	0.899878i
$507$		0			0
$508$	1.37087	+	1.65460i	0.0608225	+	0.0734110i
$509$	20.6309	−	20.6309i	0.914448	−	0.914448i	−0.0821701	−	0.996618i	$-0.526185\pi$
$509$	20.6309	−	20.6309i	0.914448	−	0.914448i	0.996618	+	0.0821701i	$0.0261851\pi$
$510$		0			0
$511$		−	8.41952i		−	0.372458i
$512$	−20.6536	−	9.24271i	−0.912770	−	0.408474i
$513$		0			0
$514$	30.2190	−	27.5177i	1.33290	−	1.21375i
$515$	−15.4610	−	5.26376i	−0.681293	−	0.231949i
$516$		0			0
$517$		−	36.0320i		−	1.58469i
$518$	−10.7291	−	11.7824i	−0.471411	−	0.517688i
$519$		0			0
$520$	−10.0450	−	30.6199i	−0.440502	−	1.34277i
$521$		−	19.0433i		−	0.834300i	−0.908838	−	0.417150i	$-0.863029\pi$
$521$		−	19.0433i		−	0.834300i	0.908838	−	0.417150i	$-0.136971\pi$
$522$		0			0
$523$		−	19.1782i		−	0.838603i	−0.907847	−	0.419301i	$-0.862275\pi$
$523$		−	19.1782i		−	0.838603i	0.907847	−	0.419301i	$-0.137725\pi$
$524$	−16.5527	+	13.7143i	−0.723109	+	0.599110i
$525$		0			0
$526$	18.9343	+	20.7931i	0.825577	+	0.906622i
$527$	0.174722	+	0.174722i	0.00761101	+	0.00761101i
$528$		0			0
$529$		−	17.1693i		−	0.746490i
$530$	−2.91851	+	1.27021i	−0.126772	+	0.0551742i
$531$		0			0
$532$	5.22891	+	0.490369i	0.226702	+	0.0212602i
$533$	−17.0553			−0.738749
$534$		0			0
$535$	−18.0165	+	8.86469i	−0.778922	+	0.383254i
$536$	−4.35831	+	30.8690i	−0.188251	+	1.33334i
$537$		0			0
$538$	−9.78118	+	8.90681i	−0.421697	+	0.384000i
$539$	−9.09950	+	9.09950i	−0.391943	+	0.391943i
$540$		0			0
$541$	14.5231	+	14.5231i	0.624398	+	0.624398i	0.946653	−	0.322255i	$-0.104441\pi$
$541$	14.5231	+	14.5231i	0.624398	+	0.624398i	−0.322255	+	0.946653i	$0.604441\pi$
$542$	−0.702061	+	15.0053i	−0.0301561	+	0.644532i
$543$		0			0
$544$	1.45494	−	0.895300i	0.0623801	−	0.0383857i
$545$	11.1172	−	32.6539i	0.476207	−	1.39874i
$546$		0			0
$547$			9.97058i			0.426311i	0.977018	+	0.213156i	$0.0683742\pi$
$547$			9.97058i			0.426311i	−0.977018	+	0.213156i	$0.931626\pi$
$548$	−23.0598	−	27.8325i	−0.985067	−	1.18895i
$549$		0			0
$550$	−41.8185	+	3.45167i	−1.78315	+	0.147180i
$551$	−3.79716			−0.161765
$552$		0			0
$553$	−12.9316	+	12.9316i	−0.549906	+	0.549906i
$554$	0.547607	−	11.7041i	0.0232656	−	0.497260i
$555$		0			0
$556$	16.8627	−	13.9711i	0.715138	−	0.592506i
$557$	−11.4424			−0.484831			−0.242416	−	0.970173i	$-0.577940\pi$
$557$	−11.4424			−0.484831			−0.242416	+	0.970173i	$0.577940\pi$
$558$		0			0
$559$	22.8846			0.967915
$560$	9.68595	−	17.1084i	0.409306	−	0.722960i
$561$		0			0
$562$	1.38916	−	29.6909i	0.0585984	−	1.25243i
$563$	−47.0585			−1.98328			−0.991640	−	0.129034i	$-0.958812\pi$
$563$	−47.0585			−1.98328			−0.991640	+	0.129034i	$0.958812\pi$
$564$		0			0
$565$	12.8628	+	4.37919i	0.541141	+	0.184234i
$566$	0.956715	−	20.4481i	0.0402137	−	0.859496i
$567$		0			0
$568$	−29.4996	−	4.16498i	−1.23778	−	0.174759i
$569$	−41.4684			−1.73845			−0.869224	−	0.494419i	$-0.835381\pi$
$569$	−41.4684			−1.73845			−0.869224	+	0.494419i	$0.835381\pi$
$570$		0			0
$571$	16.1745	+	16.1745i	0.676881	+	0.676881i	0.959293	−	0.282412i	$-0.0911347\pi$
$571$	16.1745	+	16.1745i	0.676881	+	0.676881i	−0.282412	+	0.959293i	$0.591135\pi$
$572$	−46.5662	+	38.5811i	−1.94703	+	1.61316i
$573$		0			0
$574$	−7.00556	−	7.69329i	−0.292407	−	0.321112i
$575$	−11.9730	+	1.55443i	−0.499307	+	0.0648242i
$576$		0			0
$577$	20.0316	−	20.0316i	0.833926	−	0.833926i	−0.154125	−	0.988051i	$-0.549256\pi$
$577$	20.0316	−	20.0316i	0.833926	−	0.833926i	0.988051	+	0.154125i	$0.0492560\pi$
$578$	1.11759	−	23.8865i	0.0464857	−	0.993548i
$579$		0			0
$580$	−5.81752	+	12.9694i	−0.241560	+	0.538526i
$581$	14.2562	−	14.2562i	0.591447	−	0.591447i
$582$		0			0
$583$	4.22349	+	4.22349i	0.174919	+	0.174919i
$584$	−8.65667	+	6.51467i	−0.358215	+	0.269579i
$585$		0			0
$586$	−16.8341	−	0.787627i	−0.695411	−	0.0325366i
$587$	−29.1190			−1.20187			−0.600935	−	0.799298i	$-0.705205\pi$
$587$	−29.1190			−1.20187			−0.600935	+	0.799298i	$0.705205\pi$
$588$		0			0
$589$	0.691185	−	0.691185i	0.0284798	−	0.0284798i
$590$	−12.5277	+	31.8358i	−0.515759	+	1.31066i
$591$		0			0
$592$	−3.81251	+	20.1480i	−0.156693	+	0.828079i
$593$	10.3431	+	10.3431i	0.424740	+	0.424740i	0.886832	−	0.462092i	$-0.152901\pi$
$593$	10.3431	+	10.3431i	0.424740	+	0.424740i	−0.462092	+	0.886832i	$0.652901\pi$
$594$		0			0
$595$	0.655294	+	1.33181i	0.0268644	+	0.0545991i
$596$	−17.2722	−	20.8471i	−0.707499	−	0.853930i
$597$		0			0
$598$	−12.8651	+	11.7151i	−0.526095	+	0.479066i
$599$		−	2.59479i		−	0.106020i	−0.998594	−	0.0530101i	$-0.983118\pi$
$599$		−	2.59479i		−	0.106020i	0.998594	−	0.0530101i	$-0.0168816\pi$
$600$		0			0
$601$		−	14.4092i		−	0.587765i	−0.955842	−	0.293882i	$-0.905053\pi$
$601$		−	14.4092i		−	0.587765i	0.955842	−	0.293882i	$-0.0949474\pi$
$602$	9.39996	+	10.3227i	0.383114	+	0.420723i
$603$		0			0
$604$	−19.2912	−	1.80913i	−0.784946	−	0.0736126i
$605$	23.9038	+	48.5818i	0.971826	+	1.97513i
$606$		0			0
$607$	−11.8502	−	11.8502i	−0.480985	−	0.480985i	0.424461	−	0.905446i	$-0.360464\pi$
$607$	−11.8502	−	11.8502i	−0.480985	−	0.480985i	−0.905446	+	0.424461i	$0.860464\pi$
$608$	−3.54173	−	5.75562i	−0.143636	−	0.233421i
$609$		0			0
$610$	7.91902	+	3.11622i	0.320632	+	0.126172i
$611$	21.8769	−	21.8769i	0.885045	−	0.885045i
$612$		0			0
$613$	16.8256			0.679579			0.339789	−	0.940502i	$-0.389644\pi$
$613$	16.8256			0.679579			0.339789	+	0.940502i	$0.389644\pi$
$614$	1.68220	−	35.9540i	0.0678881	−	1.45099i
$615$		0			0
$616$	−36.5304	−	5.15763i	−1.47185	−	0.207807i
$617$	22.4849	+	22.4849i	0.905209	+	0.905209i	0.995881	−	0.0906720i	$-0.0289015\pi$
$617$	22.4849	+	22.4849i	0.905209	+	0.905209i	−0.0906720	+	0.995881i	$0.528902\pi$
$618$		0			0
$619$	−14.1269	+	14.1269i	−0.567809	+	0.567809i	−0.931514	−	0.363705i	$-0.881512\pi$
$619$	−14.1269	+	14.1269i	−0.567809	+	0.567809i	0.363705	+	0.931514i	$0.381512\pi$
$620$	−1.30184	−	3.41973i	−0.0522831	−	0.137340i
$621$		0			0
$622$	30.3406	+	1.41956i	1.21655	+	0.0569193i
$623$	6.60715	−	6.60715i	0.264710	−	0.264710i
$624$		0			0
$625$	−6.38382	−	24.1712i	−0.255353	−	0.966848i
$626$	−27.7956	+	25.3109i	−1.11094	+	1.01163i
$627$		0			0
$628$	−19.8656	−	1.86300i	−0.792723	−	0.0743419i
$629$	−1.09470	−	1.09470i	−0.0436486	−	0.0436486i
$630$		0			0
$631$	−33.9235			−1.35047			−0.675236	−	0.737601i	$-0.735958\pi$
$631$	−33.9235			−1.35047			−0.675236	+	0.737601i	$0.735958\pi$
$632$	23.3017	+	3.28991i	0.926892	+	0.130866i
$633$		0			0
$634$	22.9602	+	1.07425i	0.911867	+	0.0426640i
$635$	2.27415	+	0.774246i	0.0902470	+	0.0307250i
$636$		0			0
$637$	−11.0496			−0.437799
$638$	26.6448	+	1.24664i	1.05488	+	0.0493551i
$639$		0			0
$640$	−25.0848	+	3.27896i	−0.991565	+	0.129612i
$641$	−18.8495			−0.744509			−0.372254	−	0.928131i	$-0.621415\pi$
$641$	−18.8495			−0.744509			−0.372254	+	0.928131i	$0.621415\pi$
$642$		0			0
$643$	−16.4916			−0.650364			−0.325182	−	0.945652i	$-0.605426\pi$
$643$	−16.4916			−0.650364			−0.325182	+	0.945652i	$0.605426\pi$
$644$	−10.5688	−	0.991150i	−0.416471	−	0.0390568i
$645$		0			0
$646$	0.509664	+	0.0238459i	0.0200525	+	0.000938206i
$647$	0.316870	−	0.316870i	0.0124574	−	0.0124574i	−0.700851	−	0.713308i	$-0.747196\pi$
$647$	0.316870	−	0.316870i	0.0124574	−	0.0124574i	0.713308	+	0.700851i	$0.247196\pi$
$648$		0			0
$649$	64.2002			2.52008
$650$	−27.4858	−	23.2945i	−1.07808	−	0.913684i
$651$		0			0
$652$	18.8825	+	1.77081i	0.739495	+	0.0693502i
$653$			17.0751i			0.668200i	0.942538	+	0.334100i	$0.108432\pi$
$653$			17.0751i			0.668200i	−0.942538	+	0.334100i	$0.891568\pi$
$654$		0			0
$655$	−7.74560	+	22.7508i	−0.302646	+	0.888946i
$656$	−2.48937	+	13.1556i	−0.0971937	+	0.513641i
$657$		0			0
$658$	18.8542	+	0.882144i	0.735014	+	0.0343895i
$659$	7.42245	+	7.42245i	0.289138	+	0.289138i	0.836739	−	0.547601i	$-0.184459\pi$
$659$	7.42245	+	7.42245i	0.289138	+	0.289138i	−0.547601	+	0.836739i	$0.684459\pi$
$660$		0			0
$661$	31.7614	−	31.7614i	1.23538	−	1.23538i	0.273507	−	0.961870i	$-0.411816\pi$
$661$	31.7614	−	31.7614i	1.23538	−	1.23538i	0.961870	−	0.273507i	$-0.0881837\pi$
$662$	11.7362	+	12.8883i	0.456139	+	0.500917i
$663$		0			0
$664$	−25.6886	−	3.62691i	−0.996911	−	0.140751i
$665$	5.26854	−	2.59229i	0.204305	−	0.100525i
$666$		0			0
$667$	7.67495			0.297175
$668$	20.5501	−	17.0262i	0.795107	−	0.658762i
$669$		0			0
$670$	13.9094	+	31.9592i	0.537367	+	1.23469i
$671$		−	15.9695i		−	0.616496i
$672$		0			0
$673$	4.14672	+	4.14672i	0.159844	+	0.159844i	0.782498	−	0.622653i	$-0.213945\pi$
$673$	4.14672	+	4.14672i	0.159844	+	0.159844i	−0.622653	+	0.782498i	$0.713945\pi$
$674$	−0.0601670	+	0.0547885i	−0.00231755	+	0.00211037i
$675$		0			0
$676$	−25.8109	−	2.42056i	−0.992727	−	0.0930983i
$677$		−	25.2618i		−	0.970890i	−0.874267	−	0.485445i	$-0.838658\pi$
$677$		−	25.2618i		−	0.970890i	0.874267	−	0.485445i	$-0.161342\pi$
$678$		0			0
$679$			22.2569i			0.854143i
$680$	0.862289	−	1.70425i	0.0330673	−	0.0653551i
$681$		0			0
$682$	−5.07698	+	4.62313i	−0.194408	+	0.177029i
$683$			8.20306i			0.313881i	0.987608	+	0.156941i	$0.0501631\pi$
$683$			8.20306i			0.313881i	−0.987608	+	0.156941i	$0.949837\pi$
$684$		0			0
$685$	−38.2542	−	13.0238i	−1.46162	−	0.497615i
$686$	−19.1891	−	21.0728i	−0.732643	−	0.804565i
$687$		0			0
$688$	3.34020	−	17.6520i	0.127344	−	0.672977i
$689$			5.12859i			0.195384i
$690$		0			0
$691$	−7.89158	+	7.89158i	−0.300210	+	0.300210i	−0.841096	−	0.540886i	$-0.818089\pi$
$691$	−7.89158	+	7.89158i	−0.300210	+	0.300210i	0.540886	+	0.841096i	$0.318089\pi$
$692$	1.67081	−	17.8162i	0.0635145	−	0.677268i
$693$		0			0
$694$	−50.4455	−	2.36022i	−1.91489	−	0.0895929i
$695$	7.89066	−	23.1768i	0.299310	−	0.879147i
$696$		0			0
$697$	−0.714783	−	0.714783i	−0.0270744	−	0.0270744i
$698$	0.405850	−	0.369570i	0.0153616	−	0.0139884i
$699$		0			0
$700$	−0.782324	−	21.9666i	−0.0295691	−	0.830258i
$701$	−1.50228	−	1.50228i	−0.0567405	−	0.0567405i	0.678167	−	0.734908i	$-0.262775\pi$
$701$	−1.50228	−	1.50228i	−0.0567405	−	0.0567405i	−0.734908	+	0.678167i	$0.762775\pi$
$702$		0			0
$703$	−4.33054	+	4.33054i	−0.163329	+	0.163329i
$704$	22.9627	+	41.5501i	0.865441	+	1.56598i
$705$		0			0
$706$	−21.0354	−	23.1004i	−0.791679	−	0.869397i
$707$			26.0756i			0.980675i
$708$		0			0
$709$	−36.0738	−	36.0738i	−1.35478	−	1.35478i	−0.880228	−	0.474551i	$-0.842610\pi$
$709$	−36.0738	−	36.0738i	−1.35478	−	1.35478i	−0.474551	−	0.880228i	$-0.657390\pi$
$710$	−30.5415	+	13.2924i	−1.14620	+	0.498854i
$711$		0			0
$712$	−11.9056	−	1.68092i	−0.446181	−	0.0629952i
$713$	−1.39704	+	1.39704i	−0.0523197	+	0.0523197i
$714$		0			0
$715$	−21.7900	+	64.0026i	−0.814899	+	2.39356i
$716$	5.45741	+	6.58694i	0.203953	+	0.246165i
$717$		0			0
$718$	−0.0508132	+	1.08604i	−0.00189633	+	0.0405307i
$719$	35.0340			1.30655			0.653274	−	0.757121i	$-0.273395\pi$
$719$	35.0340			1.30655			0.653274	+	0.757121i	$0.273395\pi$
$720$		0			0
$721$	−16.0548			−0.597911
$722$	−1.16148	+	24.8245i	−0.0432258	+	0.923873i
$723$		0			0
$724$	−3.37253	+	2.79421i	−0.125339	+	0.103846i
$725$	2.04609	+	15.7599i	0.0759898	+	0.585310i
$726$		0			0
$727$	25.4241	−	25.4241i	0.942928	−	0.942928i	−0.0555295	−	0.998457i	$-0.517685\pi$
$727$	25.4241	−	25.4241i	0.942928	−	0.942928i	0.998457	+	0.0555295i	$0.0176847\pi$
$728$	−19.0480	−	25.3109i	−0.705966	−	0.938085i
$729$		0			0
$730$	−4.43551	+	11.2716i	−0.164165	+	0.417182i
$731$	0.959085	+	0.959085i	0.0354731	+	0.0354731i
$732$		0			0
$733$		−	7.37554i		−	0.272422i	−0.990680	−	0.136211i	$-0.956508\pi$
$733$		−	7.37554i		−	0.272422i	0.990680	−	0.136211i	$-0.0434925\pi$
$734$	−18.5624	−	20.3847i	−0.685151	−	0.752411i
$735$		0			0
$736$	7.15865	+	11.6334i	0.263871	+	0.428814i
$737$	46.2494	−	46.2494i	1.70362	−	1.70362i
$738$		0			0
$739$	5.55025	+	5.55025i	0.204169	+	0.204169i	0.801784	−	0.597614i	$-0.203885\pi$
$739$	5.55025	+	5.55025i	0.204169	+	0.204169i	−0.597614	+	0.801784i	$0.703885\pi$
$740$	8.15651	+	21.4259i	0.299839	+	0.787632i
$741$		0			0
$742$	−2.31339	+	2.10659i	−0.0849274	+	0.0773355i
$743$	6.78835	+	6.78835i	0.249040	+	0.249040i	0.820577	−	0.571536i	$-0.193652\pi$
$743$	6.78835	+	6.78835i	0.249040	+	0.249040i	−0.571536	+	0.820577i	$0.693652\pi$
$744$		0			0
$745$	−28.6532	−	9.75510i	−1.04977	−	0.357399i
$746$	30.2315	+	1.41446i	1.10685	+	0.0517869i
$747$		0			0
$748$	−3.56849	−	0.334655i	−0.130477	−	0.0122362i
$749$	−13.9568	+	13.9568i	−0.509970	+	0.509970i
$750$		0			0
$751$		−	3.93385i		−	0.143548i	−0.997421	−	0.0717742i	$-0.977134\pi$
$751$		−	3.93385i		−	0.143548i	0.997421	−	0.0717742i	$-0.0228661\pi$
$752$	−13.6816	−	20.0679i	−0.498917	−	0.731799i
$753$		0			0
$754$	15.4205	+	16.9343i	0.561582	+	0.616711i
$755$	−19.4374	+	9.56379i	−0.707398	+	0.348062i
$756$		0			0
$757$			21.8327i			0.793525i	0.917921	+	0.396762i	$0.129866\pi$
$757$			21.8327i			0.793525i	−0.917921	+	0.396762i	$0.870134\pi$
$758$	−16.8464	+	15.3405i	−0.611890	+	0.557191i
$759$		0			0
$760$	−6.74187	−	3.41114i	−0.244553	−	0.123735i
$761$		−	4.27291i		−	0.154893i	−0.996997	−	0.0774464i	$-0.975323\pi$
$761$		−	4.27291i		−	0.154893i	0.996997	−	0.0774464i	$-0.0246767\pi$
$762$		0			0
$763$		−	33.9080i		−	1.22755i
$764$	3.75359	−	40.0253i	0.135800	−	1.44807i
$765$		0			0
$766$	6.54552	−	5.96040i	0.236499	−	0.215358i
$767$	38.9793	+	38.9793i	1.40746	+	1.40746i
$768$		0			0
$769$		−	26.1800i		−	0.944074i	−0.881579	−	0.472037i	$-0.843519\pi$
$769$		−	26.1800i		−	0.944074i	0.881579	−	0.472037i	$-0.156481\pi$
$770$	−37.8205	+	16.4604i	−1.36296	+	0.593192i
$771$		0			0
$772$	6.90198	+	8.33049i	0.248408	+	0.299821i
$773$	15.0077			0.539791			0.269895	−	0.962890i	$-0.413011\pi$
$773$	15.0077			0.539791			0.269895	+	0.962890i	$0.413011\pi$
$774$		0			0
$775$	−3.24117	−	2.49629i	−0.116426	−	0.0896693i
$776$	22.8838	−	17.2215i	0.821482	−	0.618215i
$777$		0			0
$778$	16.6305	+	18.2630i	0.596231	+	0.654762i
$779$	−2.82762	+	2.82762i	−0.101310	+	0.101310i
$780$		0			0
$781$	44.1977	+	44.1977i	1.58152	+	1.58152i
$782$	−1.03015	−	0.0481982i	−0.0368381	−	0.00172356i
$783$		0			0
$784$	−1.61278	+	8.52307i	−0.0575992	+	0.304395i
$785$	−20.0161	+	9.84856i	−0.714407	+	0.351510i
$786$		0			0
$787$			42.9223i			1.53001i	0.644022	+	0.765007i	$0.277264\pi$
$787$			42.9223i			1.53001i	−0.644022	+	0.765007i	$0.722736\pi$
$788$	0.208699	−	2.22540i	0.00743461	−	0.0792767i
$789$		0			0
$790$	24.1247	−	10.4996i	0.858317	−	0.373560i
$791$	13.3568			0.474912
$792$		0			0
$793$	9.69591	−	9.69591i	0.344312	−	0.344312i
$794$	−25.4043	−	1.18861i	−0.901565	−	0.0421820i
$795$		0			0
$796$	4.77741	−	50.9425i	0.169331	−	1.80561i
$797$	−0.280831			−0.00994753			−0.00497377	−	0.999988i	$-0.501583\pi$
$797$	−0.280831			−0.00994753			−0.00497377	+	0.999988i	$0.501583\pi$
$798$		0			0
$799$	1.83371			0.0648719
$800$	−21.9800	+	17.8012i	−0.777109	+	0.629366i
$801$		0			0
$802$	12.8068	+	0.599200i	0.452225	+	0.0211585i
$803$	22.7304			0.802139
$804$		0			0
$805$	−10.6489	+	5.23961i	−0.375326	+	0.184672i
$806$	−5.88944	−	0.275553i	−0.207447	−	0.00970593i
$807$		0			0
$808$	26.8101	−	20.1762i	0.943176	−	0.709797i
$809$	16.5787			0.582876			0.291438	−	0.956590i	$-0.405866\pi$
$809$	16.5787			0.582876			0.291438	+	0.956590i	$0.405866\pi$
$810$		0			0
$811$	7.25384	+	7.25384i	0.254717	+	0.254717i	0.822901	−	0.568184i	$-0.192354\pi$
$811$	7.25384	+	7.25384i	0.254717	+	0.254717i	−0.568184	+	0.822901i	$0.692354\pi$
$812$	−1.30465	+	13.9117i	−0.0457841	+	0.488205i
$813$		0			0
$814$	31.8092	−	28.9657i	1.11491	−	1.01525i
$815$	19.0256	−	9.36118i	0.666437	−	0.327908i
$816$		0			0
$817$	3.79405	−	3.79405i	0.132737	−	0.132737i
$818$	42.4671	+	1.98693i	1.48483	+	0.0694715i
$819$		0			0
$820$	5.32578	+	13.9900i	0.185984	+	0.488552i
$821$	15.3525	−	15.3525i	0.535806	−	0.535806i	−0.386489	−	0.922294i	$-0.626312\pi$
$821$	15.3525	−	15.3525i	0.535806	−	0.535806i	0.922294	+	0.386489i	$0.126312\pi$
$822$		0			0
$823$	−26.7794	−	26.7794i	−0.933472	−	0.933472i	0.0644492	−	0.997921i	$-0.479471\pi$
$823$	−26.7794	−	26.7794i	−0.933472	−	0.933472i	−0.997921	+	0.0644492i	$0.979471\pi$
$824$	12.4225	+	16.5070i	0.432758	+	0.575048i
$825$		0			0
$826$	−1.57176	+	33.5936i	−0.0546887	+	1.16887i
$827$	39.4186			1.37072			0.685359	−	0.728205i	$-0.259645\pi$
$827$	39.4186			1.37072			0.685359	+	0.728205i	$0.259645\pi$
$828$		0			0
$829$	−20.7102	+	20.7102i	−0.719296	+	0.719296i	−0.968461	−	0.249165i	$-0.919844\pi$
$829$	−20.7102	+	20.7102i	−0.719296	+	0.719296i	0.249165	+	0.968461i	$0.419844\pi$
$830$	−26.5958	+	11.5752i	−0.923155	+	0.401779i
$831$		0			0
$832$	−11.2853	+	39.1690i	−0.391248	+	1.35794i
$833$	−0.463083	−	0.463083i	−0.0160449	−	0.0160449i
$834$		0			0
$835$	9.61612	−	28.2449i	0.332779	−	0.977456i
$836$	−1.32386	+	14.1166i	−0.0457868	+	0.488234i
$837$		0			0
$838$	−20.7354	−	22.7709i	−0.716291	−	0.786608i
$839$		−	31.8706i		−	1.10029i	−0.835068	−	0.550147i	$-0.814572\pi$
$839$		−	31.8706i		−	1.10029i	0.835068	−	0.550147i	$-0.185428\pi$
$840$		0			0
$841$			18.8975i			0.651638i
$842$	5.71495	−	5.20408i	0.196950	−	0.179344i
$843$		0			0
$844$	0.896495	−	0.742765i	0.0308586	−	0.0255670i
$845$	−26.0065	+	12.7960i	−0.894651	+	0.440196i
$846$		0			0
$847$	37.6347	+	37.6347i	1.29314	+	1.29314i
$848$	3.95594	+	0.748562i	0.135847	+	0.0257057i
$849$		0			0
$850$	−0.175659	−	2.12819i	−0.00602506	−	0.0729961i
$851$	8.75302	−	8.75302i	0.300050	−	0.300050i
$852$		0			0
$853$	−26.5538			−0.909185			−0.454592	−	0.890700i	$-0.650215\pi$
$853$	−26.5538			−0.909185			−0.454592	+	0.890700i	$0.650215\pi$
$854$	8.35626	+	0.390969i	0.285945	+	0.0133787i
$855$		0			0
$856$	25.1491	+	3.55074i	0.859578	+	0.121362i
$857$	20.7249	+	20.7249i	0.707951	+	0.707951i	0.966104	−	0.258153i	$-0.0831140\pi$
$857$	20.7249	+	20.7249i	0.707951	+	0.707951i	−0.258153	+	0.966104i	$0.583114\pi$
$858$		0			0
$859$	35.9248	−	35.9248i	1.22574	−	1.22574i	0.260176	−	0.965561i	$-0.416219\pi$
$859$	35.9248	−	35.9248i	1.22574	−	1.22574i	0.965561	−	0.260176i	$-0.0837807\pi$
$860$	−7.14605	−	18.7716i	−0.243678	−	0.640105i
$861$		0			0
$862$	1.80237	−	38.5224i	0.0613889	−	1.31208i
$863$	−9.19232	+	9.19232i	−0.312910	+	0.312910i	−0.846036	−	0.533126i	$-0.821017\pi$
$863$	−9.19232	+	9.19232i	−0.312910	+	0.312910i	0.533126	+	0.846036i	$0.321017\pi$
$864$		0			0
$865$	−8.83254	−	17.9512i	−0.300315	−	0.610358i
$866$	−25.7781	−	28.3087i	−0.875976	−	0.961969i
$867$		0			0
$868$	−2.29482	−	2.76978i	−0.0778913	−	0.0940125i
$869$	−34.9117	−	34.9117i	−1.18430	−	1.18430i
$870$		0			0
$871$	56.1608			1.90293
$872$	−34.8630	+	26.2365i	−1.18061	+	0.888482i
$873$		0			0
$874$	−0.190668	+	4.07518i	−0.00644943	+	0.137845i
$875$	−13.5981	−	20.4700i	−0.459699	−	0.692011i
$876$		0			0
$877$	−17.9106			−0.604799			−0.302399	−	0.953181i	$-0.597788\pi$
$877$	−17.9106			−0.604799			−0.302399	+	0.953181i	$0.597788\pi$
$878$	1.99605	−	42.6619i	0.0673633	−	1.43977i
$879$		0			0
$880$	46.1879	+	26.1494i	1.55699	+	0.881497i
$881$	−6.01537			−0.202663			−0.101332	−	0.994853i	$-0.532310\pi$
$881$	−6.01537			−0.202663			−0.101332	+	0.994853i	$0.532310\pi$
$882$		0			0
$883$	19.8374			0.667580			0.333790	−	0.942647i	$-0.391672\pi$
$883$	19.8374			0.667580			0.333790	+	0.942647i	$0.391672\pi$
$884$	−1.96343	−	2.36980i	−0.0660373	−	0.0797051i
$885$		0			0
$886$	−1.83117	+	39.1381i	−0.0615195	+	1.31487i
$887$	−14.3740	+	14.3740i	−0.482632	+	0.482632i	−0.905971	−	0.423339i	$-0.860858\pi$
$887$	−14.3740	+	14.3740i	−0.482632	+	0.482632i	0.423339	+	0.905971i	$0.360858\pi$
$888$		0			0
$889$	2.36149			0.0792019
$890$	−12.3261	+	5.36460i	−0.413171	+	0.179822i
$891$		0			0
$892$	−36.4741	+	30.2196i	−1.22124	+	1.01183i
$893$		−	7.25398i		−	0.242745i
$894$		0			0
$895$	9.05337	+	3.08226i	0.302621	+	0.103029i
$896$	−22.3038	+	10.9983i	−0.745117	+	0.367428i
$897$		0			0
$898$	0.646620	−	13.8203i	0.0215780	−	0.461191i
$899$	1.83892	+	1.83892i	0.0613315	+	0.0613315i
$900$		0			0
$901$	−0.214938	+	0.214938i	−0.00716061	+	0.00716061i
$902$	20.7698	−	18.9131i	0.691558	−	0.629738i
$903$		0			0
$904$	−10.3349	−	13.7330i	−0.343734	−	0.456752i
$905$	−1.57813	+	4.63536i	−0.0524588	+	0.154084i
$906$		0			0
$907$	−39.0417			−1.29636			−0.648180	−	0.761487i	$-0.724469\pi$
$907$	−39.0417			−1.29636			−0.648180	+	0.761487i	$0.724469\pi$
$908$	−2.57343	+	27.4411i	−0.0854024	+	0.910663i
$909$		0			0
$910$	−32.9567	−	12.9688i	−1.09251	−	0.429912i
$911$		−	14.0166i		−	0.464392i	−0.972669	−	0.232196i	$-0.925409\pi$
$911$		−	14.0166i		−	0.464392i	0.972669	−	0.232196i	$-0.0745911\pi$
$912$		0			0
$913$	38.4879	+	38.4879i	1.27376	+	1.27376i
$914$	0.750187	+	0.823831i	0.0248140	+	0.0272499i
$915$		0			0
$916$	−14.2732	−	17.2274i	−0.471601	−	0.569209i
$917$			23.6245i			0.780150i
$918$		0			0
$919$			8.15149i			0.268893i	0.990921	+	0.134446i	$0.0429256\pi$
$919$			8.15149i			0.268893i	−0.990921	+	0.134446i	$0.957074\pi$
$920$	13.6269	+	6.89470i	0.449265	+	0.227311i
$921$		0			0
$922$	−16.9386	−	18.6015i	−0.557844	−	0.612606i
$923$			53.6695i			1.76655i
$924$		0			0
$925$	20.3072	+	15.6402i	0.667696	+	0.514247i
$926$	4.87325	−	4.43762i	0.160145	−	0.145829i
$927$		0			0
$928$	15.3130	−	9.42289i	0.502675	−	0.309322i
$929$		−	13.4779i		−	0.442196i	−0.975252	−	0.221098i	$-0.929036\pi$
$929$		−	13.4779i		−	0.442196i	0.975252	−	0.221098i	$-0.0709641\pi$
$930$		0			0
$931$	−1.83192	+	1.83192i	−0.0600386	+	0.0600386i
$932$	3.65898	−	3.03154i	0.119854	−	0.0993013i
$933$		0			0
$934$	0.674142	−	14.4086i	0.0220586	−	0.471463i
$935$	−3.59554	+	1.76912i	−0.117587	+	0.0578563i
$936$		0			0
$937$	−15.8564	−	15.8564i	−0.518005	−	0.518005i	0.398963	−	0.916967i	$-0.369370\pi$
$937$	−15.8564	−	15.8564i	−0.518005	−	0.518005i	−0.916967	+	0.398963i	$0.869370\pi$
$938$	23.0683	+	25.3329i	0.753207	+	0.827148i
$939$		0			0
$940$	−24.7764	−	11.1136i	−0.808116	−	0.362486i
$941$	−15.7073	−	15.7073i	−0.512044	−	0.512044i	0.403108	−	0.915152i	$-0.367930\pi$
$941$	−15.7073	−	15.7073i	−0.512044	−	0.512044i	−0.915152	+	0.403108i	$0.867930\pi$
$942$		0			0
$943$	5.71527	−	5.71527i	0.186115	−	0.186115i
$944$	35.7560	−	24.3773i	1.16376	−	0.793413i
$945$		0			0
$946$	−27.8686	+	25.3773i	−0.906085	+	0.825088i
$947$		−	33.6925i		−	1.09486i	−0.836852	−	0.547430i	$-0.815606\pi$
$947$		−	33.6925i		−	1.09486i	0.836852	−	0.547430i	$-0.184394\pi$
$948$		0			0
$949$	13.8008	+	13.8008i	0.447993	+	0.447993i
$950$	−8.41891	+	0.694892i	−0.273145	+	0.0225453i
$951$		0			0
$952$	0.262477	−	1.85907i	0.00850693	−	0.0602527i
$953$	33.5702	−	33.5702i	1.08745	−	1.08745i	0.0916550	−	0.995791i	$-0.470784\pi$
$953$	33.5702	−	33.5702i	1.08745	−	1.08745i	0.995791	−	0.0916550i	$-0.0292157\pi$
$954$		0			0
$955$	−19.8430	−	40.3287i	−0.642103	−	1.30501i
$956$	−23.4342	−	2.19767i	−0.757915	−	0.0710776i
$957$		0			0
$958$	7.99281	+	0.373964i	0.258236	+	0.0120822i
$959$	−39.7234			−1.28274
$960$		0			0
$961$	30.3305			0.978404
$962$	36.8996	+	1.72644i	1.18969	+	0.0556628i
$963$		0			0
$964$	−26.4301	−	2.47863i	−0.851256	−	0.0798311i
$965$	11.4498	+	3.89813i	0.368582	+	0.125485i
$966$		0			0
$967$	28.6436	−	28.6436i	0.921115	−	0.921115i	−0.0759933	−	0.997108i	$-0.524213\pi$
$967$	28.6436	−	28.6436i	0.921115	−	0.921115i	0.997108	+	0.0759933i	$0.0242128\pi$
$968$	9.57461	−	67.8149i	0.307740	−	2.17965i
$969$		0			0
$970$	11.7252	−	29.7965i	0.376474	−	0.956707i
$971$	35.7115	+	35.7115i	1.14604	+	1.14604i	0.987325	+	0.158713i	$0.0507345\pi$
$971$	35.7115	+	35.7115i	1.14604	+	1.14604i	0.158713	+	0.987325i	$0.449266\pi$
$972$		0			0
$973$		−	24.0669i		−	0.771551i
$974$	29.2012	−	26.5908i	0.935666	−	0.852024i
$975$		0			0
$976$	−6.06373	−	8.89414i	−0.194095	−	0.284694i
$977$	−7.12822	+	7.12822i	−0.228052	+	0.228052i	−0.811879	−	0.583826i	$-0.801555\pi$
$977$	−7.12822	+	7.12822i	−0.228052	+	0.228052i	0.583826	+	0.811879i	$0.301555\pi$
$978$		0			0
$979$	17.8375	+	17.8375i	0.570090	+	0.570090i
$980$	3.45039	+	9.06364i	0.110219	+	0.289527i
$981$		0			0
$982$	−5.67452	−	6.23158i	−0.181081	−	0.198858i
$983$	23.9941	+	23.9941i	0.765292	+	0.765292i	0.977274	−	0.211982i	$-0.0679918\pi$
$983$	23.9941	+	23.9941i	0.765292	+	0.765292i	−0.211982	+	0.977274i	$0.567992\pi$
$984$		0			0
$985$	−1.10327	−	2.24227i	−0.0351530	−	0.0714447i
$986$	−0.0634430	+	1.35598i	−0.00202044	+	0.0431832i
$987$		0			0
$988$	−9.37472	+	7.76715i	−0.298250	+	0.247106i
$989$	−7.66866	+	7.66866i	−0.243849	+	0.243849i
$990$		0			0
$991$		−	40.6040i		−	1.28983i	−0.764255	−	0.644914i	$-0.776893\pi$
$991$		−	40.6040i		−	1.28983i	0.764255	−	0.644914i	$-0.223107\pi$
$992$	−1.07216	+	4.50260i	−0.0340412	+	0.142958i
$993$		0			0
$994$	−24.2091	+	22.0450i	−0.767866	+	0.699225i
$995$	−25.2553	−	51.3286i	−0.800645	−	1.62723i
$996$		0			0
$997$			54.9087i			1.73898i	0.493953	+	0.869488i	$0.335551\pi$
$997$			54.9087i			1.73898i	−0.493953	+	0.869488i	$0.664449\pi$
$998$	22.7384	+	24.9706i	0.719773	+	0.790431i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.z.g.163.1		18
3.2	odd	2		80.2.s.b.3.9	yes	18
5.2	odd	4		720.2.bd.g.307.4		18
12.11	even	2		320.2.s.b.303.6		18
15.2	even	4		80.2.j.b.67.6	yes	18
15.8	even	4		400.2.j.d.307.4		18
15.14	odd	2		400.2.s.d.243.1		18
16.11	odd	4		720.2.bd.g.523.4		18
24.5	odd	2		640.2.s.d.223.6		18
24.11	even	2		640.2.s.c.223.4		18
48.5	odd	4		320.2.j.b.143.6		18
48.11	even	4		80.2.j.b.43.6	✓	18
48.29	odd	4		640.2.j.c.543.4		18
48.35	even	4		640.2.j.d.543.6		18
60.23	odd	4		1600.2.j.d.1007.6		18
60.47	odd	4		320.2.j.b.47.4		18
60.59	even	2		1600.2.s.d.943.4		18
80.27	even	4	inner	720.2.z.g.667.1		18
120.77	even	4		640.2.j.d.607.4		18
120.107	odd	4		640.2.j.c.607.6		18
240.53	even	4		1600.2.s.d.207.4		18
240.59	even	4		400.2.j.d.43.4		18
240.77	even	4		640.2.s.c.287.4		18
240.107	odd	4		80.2.s.b.27.9	yes	18
240.149	odd	4		1600.2.j.d.143.4		18
240.197	even	4		320.2.s.b.207.6		18
240.203	odd	4		400.2.s.d.107.1		18
240.227	odd	4		640.2.s.d.287.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.6	✓	18	48.11	even	4
80.2.j.b.67.6	yes	18	15.2	even	4
80.2.s.b.3.9	yes	18	3.2	odd	2
80.2.s.b.27.9	yes	18	240.107	odd	4
320.2.j.b.47.4		18	60.47	odd	4
320.2.j.b.143.6		18	48.5	odd	4
320.2.s.b.207.6		18	240.197	even	4
320.2.s.b.303.6		18	12.11	even	2
400.2.j.d.43.4		18	240.59	even	4
400.2.j.d.307.4		18	15.8	even	4
400.2.s.d.107.1		18	240.203	odd	4
400.2.s.d.243.1		18	15.14	odd	2
640.2.j.c.543.4		18	48.29	odd	4
640.2.j.c.607.6		18	120.107	odd	4
640.2.j.d.543.6		18	48.35	even	4
640.2.j.d.607.4		18	120.77	even	4
640.2.s.c.223.4		18	24.11	even	2
640.2.s.c.287.4		18	240.77	even	4
640.2.s.d.223.6		18	24.5	odd	2
640.2.s.d.287.6		18	240.227	odd	4
720.2.z.g.163.1		18	1.1	even	1	trivial
720.2.z.g.667.1		18	80.27	even	4	inner
720.2.bd.g.307.4		18	5.2	odd	4
720.2.bd.g.523.4		18	16.11	odd	4
1600.2.j.d.143.4		18	240.149	odd	4
1600.2.j.d.1007.6		18	60.23	odd	4
1600.2.s.d.207.4		18	240.53	even	4
1600.2.s.d.943.4		18	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41267 - 0.0660953i) q^{2} +(1.99126 + 0.186742i) q^{4} +(2.00635 - 0.987189i) q^{5} +(1.55426 - 1.55426i) q^{7} +(-2.80065 - 0.395417i) q^{8} +O(q^{10})\)	\(q+(-1.41267 - 0.0660953i) q^{2} +(1.99126 + 0.186742i) q^{4} +(2.00635 - 0.987189i) q^{5} +(1.55426 - 1.55426i) q^{7} +(-2.80065 - 0.395417i) q^{8} +(-2.89956 + 1.26196i) q^{10} +(4.19607 + 4.19607i) q^{11} +5.09530i q^{13} +(-2.29838 + 2.09292i) q^{14} +(3.93026 + 0.743703i) q^{16} +(-0.213542 + 0.213542i) q^{17} +(0.844754 + 0.844754i) q^{19} +(4.17953 - 1.59108i) q^{20} +(-5.65031 - 6.20499i) q^{22} +(-1.70744 - 1.70744i) q^{23} +(3.05092 - 3.96130i) q^{25} +(0.336775 - 7.19797i) q^{26} +(3.38518 - 2.80469i) q^{28} +(-2.24750 + 2.24750i) q^{29} -0.818209i q^{31} +(-5.50299 - 1.31038i) q^{32} +(0.315778 - 0.287550i) q^{34} +(1.58404 - 4.65273i) q^{35} +5.12639i q^{37} +(-1.13752 - 1.24919i) q^{38} +(-6.00945 + 1.97142i) q^{40} +3.34727i q^{41} -4.49131i q^{43} +(7.57189 + 9.13905i) q^{44} +(2.29920 + 2.52490i) q^{46} +(-4.29355 - 4.29355i) q^{47} +2.16858i q^{49} +(-4.57176 + 5.39435i) q^{50} +(-0.951504 + 10.1461i) q^{52} +1.00653 q^{53} +(12.5611 + 4.27649i) q^{55} +(-4.96751 + 3.73835i) q^{56} +(3.32352 - 3.02642i) q^{58} +(7.65005 - 7.65005i) q^{59} +(-1.90291 - 1.90291i) q^{61} +(-0.0540798 + 1.15586i) q^{62} +(7.68729 + 2.21485i) q^{64} +(5.03002 + 10.2230i) q^{65} -11.0221i q^{67} +(-0.465096 + 0.385341i) q^{68} +(-2.54525 + 6.46807i) q^{70} +10.5331 q^{71} +(2.70854 - 2.70854i) q^{73} +(0.338831 - 7.24189i) q^{74} +(1.52438 + 1.83988i) q^{76} +13.0435 q^{77} -8.32010 q^{79} +(8.61966 - 2.38777i) q^{80} +(0.221239 - 4.72858i) q^{82} +9.17237 q^{83} +(-0.217635 + 0.639248i) q^{85} +(-0.296855 + 6.34474i) q^{86} +(-10.0925 - 13.4109i) q^{88} +4.25101 q^{89} +(7.91940 + 7.91940i) q^{91} +(-3.08112 - 3.71882i) q^{92} +(5.78157 + 6.34914i) q^{94} +(2.52881 + 0.860944i) q^{95} +(-7.16000 + 7.16000i) q^{97} +(0.143333 - 3.06348i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

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