LMFDB - Embedded newform 552.2.f.c.277.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$18$
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} - 4 x^{16} - 2 x^{15} + 5 x^{14} + 2 x^{13} + 6 x^{12} + 24 x^{11} - 12 x^{10} - 88 x^{9} + \cdots + 512 $ x^18 - 4x^16 - 2x^15 + 5x^14 + 2x^13 + 6x^12 + 24x^11 - 12x^10 - 88x^9 - 24x^8 + 96x^7 + 48x^6 + 32x^5 + 160x^4 - 128x^3 - 512*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.11
Root			$-1.38678 - 0.277192i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.c.277.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.277192 - 1.38678i) q^{2} +1.00000i q^{3} +(-1.84633 - 0.768809i) q^{4} -0.208104i q^{5} +(1.38678 + 0.277192i) q^{6} +4.69627 q^{7} +(-1.57796 + 2.34735i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.277192 - 1.38678i) q^{2} +1.00000i q^{3} +(-1.84633 - 0.768809i) q^{4} -0.208104i q^{5} +(1.38678 + 0.277192i) q^{6} +4.69627 q^{7} +(-1.57796 + 2.34735i) q^{8} -1.00000 q^{9} +(-0.288595 - 0.0576846i) q^{10} +1.69179i q^{11} +(0.768809 - 1.84633i) q^{12} +3.50493i q^{13} +(1.30177 - 6.51270i) q^{14} +0.208104 q^{15} +(2.81787 + 2.83895i) q^{16} +2.65659 q^{17} +(-0.277192 + 1.38678i) q^{18} -4.27489i q^{19} +(-0.159992 + 0.384228i) q^{20} +4.69627i q^{21} +(2.34615 + 0.468950i) q^{22} -1.00000 q^{23} +(-2.34735 - 1.57796i) q^{24} +4.95669 q^{25} +(4.86057 + 0.971536i) q^{26} -1.00000i q^{27} +(-8.67085 - 3.61053i) q^{28} +0.234233i q^{29} +(0.0576846 - 0.288595i) q^{30} +5.11755 q^{31} +(4.71809 - 3.12083i) q^{32} -1.69179 q^{33} +(0.736385 - 3.68412i) q^{34} -0.977311i q^{35} +(1.84633 + 0.768809i) q^{36} -5.07196i q^{37} +(-5.92834 - 1.18496i) q^{38} -3.50493 q^{39} +(0.488493 + 0.328379i) q^{40} +3.40685 q^{41} +(6.51270 + 1.30177i) q^{42} -4.62494i q^{43} +(1.30066 - 3.12360i) q^{44} +0.208104i q^{45} +(-0.277192 + 1.38678i) q^{46} -7.19329 q^{47} +(-2.83895 + 2.81787i) q^{48} +15.0549 q^{49} +(1.37395 - 6.87385i) q^{50} +2.65659i q^{51} +(2.69462 - 6.47125i) q^{52} -2.32408i q^{53} +(-1.38678 - 0.277192i) q^{54} +0.352068 q^{55} +(-7.41051 + 11.0238i) q^{56} +4.27489 q^{57} +(0.324830 + 0.0649273i) q^{58} +11.3367i q^{59} +(-0.384228 - 0.159992i) q^{60} +2.23067i q^{61} +(1.41854 - 7.09693i) q^{62} -4.69627 q^{63} +(-3.02010 - 7.40804i) q^{64} +0.729389 q^{65} +(-0.468950 + 2.34615i) q^{66} +9.97750i q^{67} +(-4.90495 - 2.04241i) q^{68} -1.00000i q^{69} +(-1.35532 - 0.270902i) q^{70} -16.6616 q^{71} +(1.57796 - 2.34735i) q^{72} +2.02340 q^{73} +(-7.03370 - 1.40590i) q^{74} +4.95669i q^{75} +(-3.28657 + 7.89286i) q^{76} +7.94510i q^{77} +(-0.971536 + 4.86057i) q^{78} -16.4842 q^{79} +(0.590796 - 0.586409i) q^{80} +1.00000 q^{81} +(0.944350 - 4.72456i) q^{82} -4.16368i q^{83} +(3.61053 - 8.67085i) q^{84} -0.552847i q^{85} +(-6.41378 - 1.28199i) q^{86} -0.234233 q^{87} +(-3.97122 - 2.66957i) q^{88} -8.85665 q^{89} +(0.288595 + 0.0576846i) q^{90} +16.4601i q^{91} +(1.84633 + 0.768809i) q^{92} +5.11755i q^{93} +(-1.99392 + 9.97552i) q^{94} -0.889621 q^{95} +(3.12083 + 4.71809i) q^{96} -2.22788 q^{97} +(4.17309 - 20.8779i) q^{98} -1.69179i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	$ 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.277192	−	1.38678i	0.196004	−	0.980603i
$2$	0.277192	−	1.38678i	0.196004	−	0.980603i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.84633	−	0.768809i	−0.923165	−	0.384404i
$5$		−	0.208104i		−	0.0930669i	−0.998917	−	0.0465334i	$-0.985183\pi$
$5$		−	0.208104i		−	0.0930669i	0.998917	−	0.0465334i	$-0.0148174\pi$
$6$	1.38678	+	0.277192i	0.566151	+	0.113163i
$7$	4.69627			1.77502			0.887511	−	0.460787i	$-0.152433\pi$
$7$	4.69627			1.77502			0.887511	+	0.460787i	$0.152433\pi$
$8$	−1.57796	+	2.34735i	−0.557892	+	0.829913i
$9$	−1.00000			−0.333333
$10$	−0.288595	−	0.0576846i	−0.0912617	−	0.0182415i
$11$			1.69179i			0.510094i	0.966929	+	0.255047i	$0.0820910\pi$
$11$			1.69179i			0.510094i	−0.966929	+	0.255047i	$0.917909\pi$
$12$	0.768809	−	1.84633i	0.221936	−	0.532989i
$13$			3.50493i			0.972092i	0.873933	+	0.486046i	$0.161561\pi$
$13$			3.50493i			0.972092i	−0.873933	+	0.486046i	$0.838439\pi$
$14$	1.30177	−	6.51270i	0.347911	−	1.74059i
$15$	0.208104			0.0537322
$16$	2.81787	+	2.83895i	0.704467	+	0.709737i
$17$	2.65659			0.644318			0.322159	−	0.946685i	$-0.395591\pi$
$17$	2.65659			0.644318			0.322159	+	0.946685i	$0.395591\pi$
$18$	−0.277192	+	1.38678i	−0.0653347	+	0.326868i
$19$		−	4.27489i		−	0.980727i	−0.871518	−	0.490364i	$-0.836864\pi$
$19$		−	4.27489i		−	0.980727i	0.871518	−	0.490364i	$-0.163136\pi$
$20$	−0.159992	+	0.384228i	−0.0357753	+	0.0859161i
$21$			4.69627i			1.02481i
$22$	2.34615	+	0.468950i	0.500200	+	0.0999805i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	−2.34735	−	1.57796i	−0.479151	−	0.322099i
$25$	4.95669			0.991339
$26$	4.86057	+	0.971536i	0.953236	+	0.190534i
$27$		−	1.00000i		−	0.192450i
$28$	−8.67085	−	3.61053i	−1.63864	−	0.682326i
$29$			0.234233i			0.0434959i	0.999763	+	0.0217480i	$0.00692313\pi$
$29$			0.234233i			0.0434959i	−0.999763	+	0.0217480i	$0.993077\pi$
$30$	0.0576846	−	0.288595i	0.0105317	−	0.0526899i
$31$	5.11755			0.919140			0.459570	−	0.888142i	$-0.348004\pi$
$31$	5.11755			0.919140			0.459570	+	0.888142i	$0.348004\pi$
$32$	4.71809	−	3.12083i	0.834049	−	0.551691i
$33$	−1.69179			−0.294503
$34$	0.736385	−	3.68412i	0.126289	−	0.631821i
$35$		−	0.977311i		−	0.165196i
$36$	1.84633	+	0.768809i	0.307722	+	0.128135i
$37$		−	5.07196i		−	0.833825i	−0.908947	−	0.416912i	$-0.863112\pi$
$37$		−	5.07196i		−	0.833825i	0.908947	−	0.416912i	$-0.136888\pi$
$38$	−5.92834	−	1.18496i	−0.961704	−	0.192227i
$39$	−3.50493			−0.561238
$40$	0.488493	+	0.328379i	0.0772375	+	0.0519213i
$41$	3.40685			0.532060			0.266030	−	0.963965i	$-0.414288\pi$
$41$	3.40685			0.532060			0.266030	+	0.963965i	$0.414288\pi$
$42$	6.51270	+	1.30177i	1.00493	+	0.200867i
$43$		−	4.62494i		−	0.705296i	−0.935756	−	0.352648i	$-0.885281\pi$
$43$		−	4.62494i		−	0.705296i	0.935756	−	0.352648i	$-0.114719\pi$
$44$	1.30066	−	3.12360i	0.196082	−	0.470901i
$45$			0.208104i			0.0310223i
$46$	−0.277192	+	1.38678i	−0.0408697	+	0.204470i
$47$	−7.19329			−1.04925			−0.524624	−	0.851334i	$-0.675794\pi$
$47$	−7.19329			−1.04925			−0.524624	+	0.851334i	$0.675794\pi$
$48$	−2.83895	+	2.81787i	−0.409767	+	0.406724i
$49$	15.0549			2.15070
$50$	1.37395	−	6.87385i	0.194306	−	0.972110i
$51$			2.65659i			0.371997i
$52$	2.69462	−	6.47125i	0.373676	−	0.897401i
$53$		−	2.32408i		−	0.319237i	−0.987179	−	0.159618i	$-0.948974\pi$
$53$		−	2.32408i		−	0.319237i	0.987179	−	0.159618i	$-0.0510263\pi$
$54$	−1.38678	−	0.277192i	−0.188717	−	0.0377210i
$55$	0.352068			0.0474729
$56$	−7.41051	+	11.0238i	−0.990271	+	1.47311i
$57$	4.27489			0.566223
$58$	0.324830	+	0.0649273i	0.0426522	+	0.00852537i
$59$			11.3367i			1.47591i	0.674848	+	0.737956i	$0.264209\pi$
$59$			11.3367i			1.47591i	−0.674848	+	0.737956i	$0.735791\pi$
$60$	−0.384228	−	0.159992i	−0.0496037	−	0.0206549i
$61$			2.23067i			0.285608i	0.989751	+	0.142804i	$0.0456118\pi$
$61$			2.23067i			0.285608i	−0.989751	+	0.142804i	$0.954388\pi$
$62$	1.41854	−	7.09693i	0.180155	−	0.901311i
$63$	−4.69627			−0.591674
$64$	−3.02010	−	7.40804i	−0.377513	−	0.926004i
$65$	0.729389			0.0904696
$66$	−0.468950	+	2.34615i	−0.0577238	+	0.288791i
$67$			9.97750i			1.21895i	0.792807	+	0.609473i	$0.208619\pi$
$67$			9.97750i			1.21895i	−0.792807	+	0.609473i	$0.791381\pi$
$68$	−4.90495	−	2.04241i	−0.594812	−	0.247679i
$69$		−	1.00000i		−	0.120386i
$70$	−1.35532	−	0.270902i	−0.161991	−	0.0323790i
$71$	−16.6616			−1.97736			−0.988681	−	0.150032i	$-0.952062\pi$
$71$	−16.6616			−1.97736			−0.988681	+	0.150032i	$0.952062\pi$
$72$	1.57796	−	2.34735i	0.185964	−	0.276638i
$73$	2.02340			0.236821			0.118410	−	0.992965i	$-0.462220\pi$
$73$	2.02340			0.236821			0.118410	+	0.992965i	$0.462220\pi$
$74$	−7.03370	−	1.40590i	−0.817651	−	0.163433i
$75$			4.95669i			0.572350i
$76$	−3.28657	+	7.89286i	−0.376996	+	0.905373i
$77$			7.94510i			0.905428i
$78$	−0.971536	+	4.86057i	−0.110005	+	0.550351i
$79$	−16.4842			−1.85462			−0.927308	−	0.374298i	$-0.877884\pi$
$79$	−16.4842			−1.85462			−0.927308	+	0.374298i	$0.877884\pi$
$80$	0.590796	−	0.586409i	0.0660530	−	0.0655625i
$81$	1.00000			0.111111
$82$	0.944350	−	4.72456i	0.104286	−	0.521740i
$83$		−	4.16368i		−	0.457024i	−0.973541	−	0.228512i	$-0.926614\pi$
$83$		−	4.16368i		−	0.457024i	0.973541	−	0.228512i	$-0.0733860\pi$
$84$	3.61053	−	8.67085i	0.393941	−	0.946068i
$85$		−	0.552847i		−	0.0599647i
$86$	−6.41378	−	1.28199i	−0.691616	−	0.138241i
$87$	−0.234233			−0.0251124
$88$	−3.97122	−	2.66957i	−0.423334	−	0.284578i
$89$	−8.85665			−0.938803			−0.469401	−	0.882985i	$-0.655530\pi$
$89$	−8.85665			−0.938803			−0.469401	+	0.882985i	$0.655530\pi$
$90$	0.288595	+	0.0576846i	0.0304206	+	0.00608050i
$91$			16.4601i			1.72548i
$92$	1.84633	+	0.768809i	0.192493	+	0.0801539i
$93$			5.11755i			0.530666i
$94$	−1.99392	+	9.97552i	−0.205657	+	1.02890i
$95$	−0.889621			−0.0912732
$96$	3.12083	+	4.71809i	0.318519	+	0.481538i
$97$	−2.22788			−0.226207			−0.113103	−	0.993583i	$-0.536079\pi$
$97$	−2.22788			−0.226207			−0.113103	+	0.993583i	$0.536079\pi$
$98$	4.17309	−	20.8779i	0.421546	−	2.10898i
$99$		−	1.69179i		−	0.170031i
$100$	−9.15169	−	3.81075i	−0.915169	−	0.381075i
$101$		−	3.28278i		−	0.326649i	−0.986572	−	0.163324i	$-0.947778\pi$
$101$		−	3.28278i		−	0.326649i	0.986572	−	0.163324i	$-0.0522217\pi$
$102$	3.68412	+	0.736385i	0.364782	+	0.0729130i
$103$	−1.05219			−0.103675			−0.0518374	−	0.998656i	$-0.516508\pi$
$103$	−1.05219			−0.103675			−0.0518374	+	0.998656i	$0.516508\pi$
$104$	−8.22729	−	5.53063i	−0.806752	−	0.542322i
$105$	0.977311			0.0953758
$106$	−3.22299	−	0.644215i	−0.313044	−	0.0625717i
$107$		−	12.5606i		−	1.21428i	−0.794595	−	0.607140i	$-0.792317\pi$
$107$		−	12.5606i		−	1.21428i	0.794595	−	0.607140i	$-0.207683\pi$
$108$	−0.768809	+	1.84633i	−0.0739787	+	0.177663i
$109$			16.7716i			1.60643i	0.595693	+	0.803213i	$0.296878\pi$
$109$			16.7716i			1.60643i	−0.595693	+	0.803213i	$0.703122\pi$
$110$	0.0975904	−	0.488242i	0.00930488	−	0.0465520i
$111$	5.07196			0.481409
$112$	13.2334	+	13.3325i	1.25044	+	1.25980i
$113$	−3.09186			−0.290857			−0.145429	−	0.989369i	$-0.546456\pi$
$113$	−3.09186			−0.290857			−0.145429	+	0.989369i	$0.546456\pi$
$114$	1.18496	−	5.92834i	0.110982	−	0.555240i
$115$			0.208104i			0.0194058i
$116$	0.180080	−	0.432471i	0.0167200	−	0.0401539i
$117$		−	3.50493i		−	0.324031i
$118$	15.7215	+	3.14244i	1.44728	+	0.289285i
$119$	12.4761			1.14368
$120$	−0.328379	+	0.488493i	−0.0299768	+	0.0445931i
$121$	8.13784			0.739804
$122$	3.09345	+	0.618322i	0.280068	+	0.0559802i
$123$			3.40685i			0.307185i
$124$	−9.44869	−	3.93442i	−0.848518	−	0.353321i
$125$		−	2.07203i		−	0.185328i
$126$	−1.30177	+	6.51270i	−0.115970	+	0.580197i
$127$	−4.66952			−0.414353			−0.207177	−	0.978304i	$-0.566427\pi$
$127$	−4.66952			−0.414353			−0.207177	+	0.978304i	$0.566427\pi$
$128$	−11.1105	+	2.13478i	−0.982037	+	0.188689i
$129$	4.62494			0.407203
$130$	0.202180	−	1.01150i	0.0177324	−	0.0887147i
$131$		−	20.4902i		−	1.79024i	−0.445828	−	0.895119i	$-0.647091\pi$
$131$		−	20.4902i		−	1.79024i	0.445828	−	0.895119i	$-0.352909\pi$
$132$	3.12360	+	1.30066i	0.271875	+	0.113208i
$133$		−	20.0760i		−	1.74081i
$134$	13.8366	+	2.76568i	1.19530	+	0.238918i
$135$	−0.208104			−0.0179107
$136$	−4.19199	+	6.23595i	−0.359460	+	0.534729i
$137$	7.23648			0.618254			0.309127	−	0.951021i	$-0.399963\pi$
$137$	7.23648			0.618254			0.309127	+	0.951021i	$0.399963\pi$
$138$	−1.38678	−	0.277192i	−0.118051	−	0.0235961i
$139$			15.1990i			1.28916i	0.764537	+	0.644580i	$0.222968\pi$
$139$			15.1990i			1.28916i	−0.764537	+	0.644580i	$0.777032\pi$
$140$	−0.751365	+	1.80444i	−0.0635020	+	0.152503i
$141$		−	7.19329i		−	0.605784i
$142$	−4.61844	+	23.1059i	−0.387571	+	1.93901i
$143$	−5.92960			−0.495858
$144$	−2.81787	−	2.83895i	−0.234822	−	0.236579i
$145$	0.0487447			0.00404803
$146$	0.560868	−	2.80601i	0.0464178	−	0.232227i
$147$			15.0549i			1.24171i
$148$	−3.89937	+	9.36451i	−0.320526	+	0.769758i
$149$		−	1.17050i		−	0.0958909i	−0.998850	−	0.0479454i	$-0.984733\pi$
$149$		−	1.17050i		−	0.0958909i	0.998850	−	0.0479454i	$-0.0152674\pi$
$150$	6.87385	+	1.37395i	0.561248	+	0.112183i
$151$	0.759045			0.0617702			0.0308851	−	0.999523i	$-0.490167\pi$
$151$	0.759045			0.0617702			0.0308851	+	0.999523i	$0.490167\pi$
$152$	10.0347	+	6.74560i	0.813919	+	0.547140i
$153$	−2.65659			−0.214773
$154$	11.0181	+	2.20232i	0.887866	+	0.177468i
$155$		−	1.06498i		−	0.0855415i
$156$	6.47125	+	2.69462i	0.518115	+	0.215742i
$157$		−	12.8062i		−	1.02204i	−0.859568	−	0.511021i	$-0.829267\pi$
$157$		−	12.8062i		−	1.02204i	0.859568	−	0.511021i	$-0.170733\pi$
$158$	−4.56928	+	22.8600i	−0.363512	+	1.81864i
$159$	2.32408			0.184311
$160$	−0.649458	−	0.981853i	−0.0513441	−	0.0776223i
$161$	−4.69627			−0.370118
$162$	0.277192	−	1.38678i	0.0217782	−	0.108956i
$163$		−	20.8843i		−	1.63579i	−0.575371	−	0.817893i	$-0.695142\pi$
$163$		−	20.8843i		−	1.63579i	0.575371	−	0.817893i	$-0.304858\pi$
$164$	−6.29017	−	2.61922i	−0.491179	−	0.204526i
$165$			0.352068i			0.0274085i
$166$	−5.77412	−	1.15414i	−0.448159	−	0.0895785i
$167$	−10.7586			−0.832523			−0.416261	−	0.909245i	$-0.636660\pi$
$167$	−10.7586			−0.832523			−0.416261	+	0.909245i	$0.636660\pi$
$168$	−11.0238	−	7.41051i	−0.850503	−	0.571733i
$169$	0.715485			0.0550373
$170$	−0.766679	−	0.153245i	−0.0588016	−	0.0117533i
$171$			4.27489i			0.326909i
$172$	−3.55569	+	8.53916i	−0.271119	+	0.651105i
$173$			21.3693i			1.62467i	0.583188	+	0.812337i	$0.301805\pi$
$173$			21.3693i			1.62467i	−0.583188	+	0.812337i	$0.698195\pi$
$174$	−0.0649273	+	0.324830i	−0.00492213	+	0.0246253i
$175$	23.2779			1.75965
$176$	−4.80291	+	4.76724i	−0.362033	+	0.359344i
$177$	−11.3367			−0.852119
$178$	−2.45499	+	12.2822i	−0.184009	+	0.920593i
$179$			1.77320i			0.132535i	0.997802	+	0.0662675i	$0.0211091\pi$
$179$			1.77320i			0.132535i	−0.997802	+	0.0662675i	$0.978891\pi$
$180$	0.159992	−	0.384228i	0.0119251	−	0.0286387i
$181$		−	13.3886i		−	0.995166i	−0.867416	−	0.497583i	$-0.834221\pi$
$181$		−	13.3886i		−	0.995166i	0.867416	−	0.497583i	$-0.165779\pi$
$182$	22.8265	+	4.56259i	1.69201	+	0.338202i
$183$	−2.23067			−0.164896
$184$	1.57796	−	2.34735i	0.116329	−	0.173049i
$185$	−1.05549			−0.0776015
$186$	7.09693	+	1.41854i	0.520372	+	0.104013i
$187$			4.49440i			0.328663i
$188$	13.2812	+	5.53026i	0.968630	+	0.403336i
$189$		−	4.69627i		−	0.341603i
$190$	−0.246596	+	1.23371i	−0.0178899	+	0.0895028i
$191$	−18.4481			−1.33486			−0.667428	−	0.744675i	$-0.732605\pi$
$191$	−18.4481			−1.33486			−0.667428	+	0.744675i	$0.732605\pi$
$192$	7.40804	−	3.02010i	0.534629	−	0.217957i
$193$	−25.1246			−1.80851			−0.904253	−	0.426997i	$-0.859571\pi$
$193$	−25.1246			−1.80851			−0.904253	+	0.426997i	$0.859571\pi$
$194$	−0.617549	+	3.08958i	−0.0443374	+	0.221819i
$195$			0.729389i			0.0522326i
$196$	−27.7963	−	11.5743i	−1.98545	−	0.826739i
$197$			19.2078i			1.36850i	0.729249	+	0.684248i	$0.239870\pi$
$197$			19.2078i			1.36850i	−0.729249	+	0.684248i	$0.760130\pi$
$198$	−2.34615	−	0.468950i	−0.166733	−	0.0333268i
$199$	17.0124			1.20597			0.602987	−	0.797751i	$-0.293977\pi$
$199$	17.0124			1.20597			0.602987	+	0.797751i	$0.293977\pi$
$200$	−7.82145	+	11.6351i	−0.553060	+	0.822725i
$201$	−9.97750			−0.703759
$202$	−4.55250	−	0.909959i	−0.320313	−	0.0640245i
$203$			1.10002i			0.0772062i
$204$	2.04241	−	4.90495i	0.142997	−	0.343415i
$205$		−	0.708978i		−	0.0495172i
$206$	−0.291657	+	1.45915i	−0.0203207	+	0.101664i
$207$	1.00000			0.0695048
$208$	−9.95031	+	9.87642i	−0.689930	+	0.684806i
$209$	7.23222			0.500263
$210$	0.270902	−	1.35532i	0.0186940	−	0.0935258i
$211$			7.41980i			0.510800i	0.966835	+	0.255400i	$0.0822071\pi$
$211$			7.41980i			0.510800i	−0.966835	+	0.255400i	$0.917793\pi$
$212$	−1.78677	+	4.29101i	−0.122716	+	0.294708i
$213$		−	16.6616i		−	1.14163i
$214$	−17.4188	−	3.48169i	−1.19073	−	0.238004i
$215$	−0.962467			−0.0656397
$216$	2.34735	+	1.57796i	0.159717	+	0.107366i
$217$	24.0334			1.63149
$218$	23.2585	+	4.64894i	1.57527	+	0.314866i
$219$			2.02340i			0.136728i
$220$	−0.650034	−	0.270673i	−0.0438253	−	0.0182488i
$221$			9.31117i			0.626337i
$222$	1.40590	−	7.03370i	0.0943581	−	0.472071i
$223$	−19.7808			−1.32462			−0.662310	−	0.749230i	$-0.730424\pi$
$223$	−19.7808			−1.32462			−0.662310	+	0.749230i	$0.730424\pi$
$224$	22.1574	−	14.6563i	1.48045	−	0.979263i
$225$	−4.95669			−0.330446
$226$	−0.857037	+	4.28773i	−0.0570093	+	0.285216i
$227$		−	17.8121i		−	1.18223i	−0.806586	−	0.591117i	$-0.798687\pi$
$227$		−	17.8121i		−	1.18223i	0.806586	−	0.591117i	$-0.201313\pi$
$228$	−7.89286	−	3.28657i	−0.522717	−	0.217659i
$229$		−	16.6554i		−	1.10062i	−0.834960	−	0.550311i	$-0.814509\pi$
$229$		−	16.6554i		−	1.10062i	0.834960	−	0.550311i	$-0.185491\pi$
$230$	0.288595	+	0.0576846i	0.0190294	+	0.00380361i
$231$	−7.94510			−0.522749
$232$	−0.549826	−	0.369609i	−0.0360978	−	0.0242660i
$233$	15.0697			0.987246			0.493623	−	0.869676i	$-0.335672\pi$
$233$	15.0697			0.987246			0.493623	+	0.869676i	$0.335672\pi$
$234$	−4.86057	−	0.971536i	−0.317745	−	0.0635113i
$235$			1.49695i			0.0976503i
$236$	8.71575	−	20.9313i	0.567347	−	1.36251i
$237$		−	16.4842i		−	1.07076i
$238$	3.45826	−	17.3016i	0.224166	−	1.12150i
$239$	20.1852			1.30567			0.652836	−	0.757499i	$-0.273579\pi$
$239$	20.1852			1.30567			0.652836	+	0.757499i	$0.273579\pi$
$240$	0.586409	+	0.590796i	0.0378525	+	0.0381357i
$241$	14.7363			0.949249			0.474624	−	0.880188i	$-0.342584\pi$
$241$	14.7363			0.949249			0.474624	+	0.880188i	$0.342584\pi$
$242$	2.25574	−	11.2854i	0.145005	−	0.725454i
$243$			1.00000i			0.0641500i
$244$	1.71496	−	4.11854i	0.109789	−	0.263663i
$245$		−	3.13298i		−	0.200159i
$246$	4.72456	+	0.944350i	0.301227	+	0.0602095i
$247$	14.9832			0.953357
$248$	−8.07528	+	12.0127i	−0.512781	+	0.762807i
$249$	4.16368			0.263863
$250$	−2.87345	−	0.574348i	−0.181733	−	0.0363250i
$251$		−	23.8216i		−	1.50360i	−0.659389	−	0.751802i	$-0.729185\pi$
$251$		−	23.8216i		−	1.50360i	0.659389	−	0.751802i	$-0.270815\pi$
$252$	8.67085	+	3.61053i	0.546212	+	0.227442i
$253$		−	1.69179i		−	0.106362i
$254$	−1.29435	+	6.47561i	−0.0812149	+	0.406316i
$255$	0.552847			0.0346206
$256$	−0.119262	+	15.9996i	−0.00745386	+	0.999972i
$257$	2.14202			0.133615			0.0668077	−	0.997766i	$-0.478719\pi$
$257$	2.14202			0.133615			0.0668077	+	0.997766i	$0.478719\pi$
$258$	1.28199	−	6.41378i	0.0798134	−	0.399304i
$259$		−	23.8193i		−	1.48006i
$260$	−1.34669	−	0.560761i	−0.0835183	−	0.0347769i
$261$		−	0.234233i		−	0.0144986i
$262$	−28.4154	−	5.67971i	−1.75551	−	0.350894i
$263$	−5.61106			−0.345993			−0.172996	−	0.984922i	$-0.555345\pi$
$263$	−5.61106			−0.345993			−0.172996	+	0.984922i	$0.555345\pi$
$264$	2.66957	−	3.97122i	0.164301	−	0.244412i
$265$	−0.483650			−0.0297104
$266$	−27.8411	−	5.56490i	−1.70705	−	0.341206i
$267$		−	8.85665i		−	0.542018i
$268$	7.67079	−	18.4218i	0.468568	−	1.12529i
$269$		−	15.2513i		−	0.929890i	−0.885340	−	0.464945i	$-0.846074\pi$
$269$		−	15.2513i		−	0.929890i	0.885340	−	0.464945i	$-0.153926\pi$
$270$	−0.0576846	+	0.288595i	−0.00351058	+	0.0175633i
$271$	−21.2552			−1.29116			−0.645580	−	0.763692i	$-0.723384\pi$
$271$	−21.2552			−1.29116			−0.645580	+	0.763692i	$0.723384\pi$
$272$	7.48592	+	7.54193i	0.453901	+	0.457297i
$273$	−16.4601			−0.996209
$274$	2.00589	−	10.0354i	0.121180	−	0.606262i
$275$			8.38569i			0.505676i
$276$	−0.768809	+	1.84633i	−0.0462769	+	0.111136i
$277$		−	0.667555i		−	0.0401095i	−0.999799	−	0.0200548i	$-0.993616\pi$
$277$		−	0.667555i		−	0.0401095i	0.999799	−	0.0200548i	$-0.00638405\pi$
$278$	21.0777	+	4.21303i	1.26415	+	0.252681i
$279$	−5.11755			−0.306380
$280$	2.29409	+	1.54216i	0.137098	+	0.0921614i
$281$	23.3203			1.39117			0.695587	−	0.718442i	$-0.255144\pi$
$281$	23.3203			1.39117			0.695587	+	0.718442i	$0.255144\pi$
$282$	−9.97552	−	1.99392i	−0.594034	−	0.118736i
$283$			12.1802i			0.724035i	0.932171	+	0.362018i	$0.117912\pi$
$283$			12.1802i			0.724035i	−0.932171	+	0.362018i	$0.882088\pi$
$284$	30.7627	+	12.8095i	1.82543	+	0.760107i
$285$		−	0.889621i		−	0.0526966i
$286$	−1.64364	+	8.22307i	−0.0971903	+	0.486240i
$287$	15.9995			0.944419
$288$	−4.71809	+	3.12083i	−0.278016	+	0.183897i
$289$	−9.94251			−0.584854
$290$	0.0135116	−	0.0675983i	0.000793430	−	0.00396951i
$291$		−	2.22788i		−	0.130600i
$292$	−3.73586	−	1.55560i	−0.218624	−	0.0910349i
$293$			13.5951i			0.794235i	0.917768	+	0.397118i	$0.129990\pi$
$293$			13.5951i			0.794235i	−0.917768	+	0.397118i	$0.870010\pi$
$294$	20.8779	+	4.17309i	1.21762	+	0.243380i
$295$	2.35921			0.137359
$296$	11.9057	+	8.00334i	0.692002	+	0.465184i
$297$	1.69179			0.0981677
$298$	−1.62323	−	0.324452i	−0.0940309	−	0.0187950i
$299$		−	3.50493i		−	0.202695i
$300$	3.81075	−	9.15169i	0.220014	−	0.528373i
$301$		−	21.7199i		−	1.25192i
$302$	0.210401	−	1.05263i	0.0121072	−	0.0605721i
$303$	3.28278			0.188591
$304$	12.1362	−	12.0461i	0.696059	−	0.690889i
$305$	0.464210			0.0265806
$306$	−0.736385	+	3.68412i	−0.0420963	+	0.210607i
$307$		−	3.01060i		−	0.171824i	−0.996303	−	0.0859121i	$-0.972620\pi$
$307$		−	3.01060i		−	0.171824i	0.996303	−	0.0859121i	$-0.0273804\pi$
$308$	6.10826	−	14.6693i	0.348051	−	0.835859i
$309$		−	1.05219i		−	0.0598567i
$310$	−1.47690	−	0.295204i	−0.0838822	−	0.0167665i
$311$	−31.8638			−1.80683			−0.903416	−	0.428766i	$-0.858948\pi$
$311$	−31.8638			−1.80683			−0.903416	+	0.428766i	$0.858948\pi$
$312$	5.53063	−	8.22729i	0.313110	−	0.465779i
$313$	−11.6841			−0.660426			−0.330213	−	0.943907i	$-0.607121\pi$
$313$	−11.6841			−0.660426			−0.330213	+	0.943907i	$0.607121\pi$
$314$	−17.7593	−	3.54976i	−1.00222	−	0.200324i
$315$			0.977311i			0.0550652i
$316$	30.4353	+	12.6732i	1.71212	+	0.712923i
$317$		−	1.57042i		−	0.0882033i	−0.999027	−	0.0441017i	$-0.985957\pi$
$317$		−	1.57042i		−	0.0882033i	0.999027	−	0.0441017i	$-0.0140426\pi$
$318$	0.644215	−	3.22299i	0.0361258	−	0.180736i
$319$	−0.396273			−0.0221870
$320$	−1.54164	+	0.628495i	−0.0861803	+	0.0351339i
$321$	12.5606			0.701065
$322$	−1.30177	+	6.51270i	−0.0725446	+	0.362938i
$323$		−	11.3566i		−	0.631901i
$324$	−1.84633	−	0.768809i	−0.102574	−	0.0427116i
$325$			17.3728i			0.963672i
$326$	−28.9620	−	5.78896i	−1.60406	−	0.320621i
$327$	−16.7716			−0.927470
$328$	−5.37586	+	7.99706i	−0.296832	+	0.441564i
$329$	−33.7816			−1.86244
$330$	0.488242	+	0.0975904i	0.0268768	+	0.00537217i
$331$		−	28.8962i		−	1.58828i	−0.607737	−	0.794138i	$-0.707923\pi$
$331$		−	28.8962i		−	1.58828i	0.607737	−	0.794138i	$-0.292077\pi$
$332$	−3.20108	+	7.68753i	−0.175682	+	0.421908i
$333$			5.07196i			0.277942i
$334$	−2.98218	+	14.9198i	−0.163178	+	0.816374i
$335$	2.07636			0.113444
$336$	−13.3325	+	13.2334i	−0.727345	+	0.721944i
$337$	1.00803			0.0549107			0.0274553	−	0.999623i	$-0.491260\pi$
$337$	1.00803			0.0549107			0.0274553	+	0.999623i	$0.491260\pi$
$338$	0.198327	−	0.992222i	0.0107875	−	0.0539698i
$339$		−	3.09186i		−	0.167927i
$340$	−0.425034	+	1.02074i	−0.0230507	+	0.0553573i
$341$			8.65783i			0.468848i
$342$	5.92834	+	1.18496i	0.320568	+	0.0640755i
$343$	37.8280			2.04252
$344$	10.8563	+	7.29795i	0.585335	+	0.393479i
$345$	−0.208104			−0.0112039
$346$	29.6345	+	5.92338i	1.59316	+	0.318443i
$347$			2.83122i			0.151988i	0.997108	+	0.0759939i	$0.0242130\pi$
$347$			2.83122i			0.151988i	−0.997108	+	0.0759939i	$0.975787\pi$
$348$	0.432471	+	0.180080i	0.0231829	+	0.00965331i
$349$		−	26.3270i		−	1.40925i	−0.709579	−	0.704626i	$-0.751115\pi$
$349$		−	26.3270i		−	1.40925i	0.709579	−	0.704626i	$-0.248885\pi$
$350$	6.45245	−	32.2814i	0.344898	−	1.72552i
$351$	3.50493			0.187079
$352$	5.27980	+	7.98203i	0.281414	+	0.425443i
$353$	−27.3734			−1.45694			−0.728469	−	0.685079i	$-0.759768\pi$
$353$	−27.3734			−1.45694			−0.728469	+	0.685079i	$0.759768\pi$
$354$	−3.14244	+	15.7215i	−0.167019	+	0.835590i
$355$			3.46733i			0.184027i
$356$	16.3523	+	6.80907i	0.866670	+	0.360880i
$357$			12.4761i			0.660303i
$358$	2.45904	+	0.491515i	0.129964	+	0.0259774i
$359$	−11.3303			−0.597991			−0.298996	−	0.954254i	$-0.596652\pi$
$359$	−11.3303			−0.597991			−0.298996	+	0.954254i	$0.596652\pi$
$360$	−0.488493	−	0.328379i	−0.0257458	−	0.0173071i
$361$	0.725312			0.0381743
$362$	−18.5671	−	3.71121i	−0.975863	−	0.195057i
$363$			8.13784i			0.427126i
$364$	12.6546	−	30.3907i	0.663284	−	1.59291i
$365$		−	0.421076i		−	0.0220402i
$366$	−0.618322	+	3.09345i	−0.0323202	+	0.161697i
$367$	−1.47268			−0.0768733			−0.0384367	−	0.999261i	$-0.512238\pi$
$367$	−1.47268			−0.0768733			−0.0384367	+	0.999261i	$0.512238\pi$
$368$	−2.81787	−	2.83895i	−0.146891	−	0.147990i
$369$	−3.40685			−0.177353
$370$	−0.292574	+	1.46374i	−0.0152102	+	0.0760962i
$371$		−	10.9145i		−	0.566652i
$372$	3.93442	−	9.44869i	0.203990	−	0.489892i
$373$		−	22.8159i		−	1.18136i	−0.806905	−	0.590682i	$-0.798859\pi$
$373$		−	22.8159i		−	1.18136i	0.806905	−	0.590682i	$-0.201141\pi$
$374$	6.23275	+	1.24581i	0.322288	+	0.0644193i
$375$	2.07203			0.106999
$376$	11.3507	−	16.8852i	0.585368	−	0.870786i
$377$	−0.820968			−0.0422820
$378$	−6.51270	−	1.30177i	−0.334977	−	0.0669556i
$379$		−	1.11943i		−	0.0575012i	−0.999587	−	0.0287506i	$-0.990847\pi$
$379$		−	1.11943i		−	0.0575012i	0.999587	−	0.0287506i	$-0.00915286\pi$
$380$	1.64253	+	0.683949i	0.0842602	+	0.0350858i
$381$		−	4.66952i		−	0.239227i
$382$	−5.11365	+	25.5834i	−0.261637	+	1.30896i
$383$	37.0400			1.89266			0.946329	−	0.323205i	$-0.104760\pi$
$383$	37.0400			1.89266			0.946329	+	0.323205i	$0.104760\pi$
$384$	−2.13478	−	11.1105i	−0.108940	−	0.566979i
$385$	1.65341			0.0842654
$386$	−6.96432	+	34.8423i	−0.354475	+	1.77343i
$387$			4.62494i			0.235099i
$388$	4.11340	+	1.71281i	0.208826	+	0.0869549i
$389$			20.6653i			1.04777i	0.851788	+	0.523887i	$0.175519\pi$
$389$			20.6653i			1.04777i	−0.851788	+	0.523887i	$0.824481\pi$
$390$	1.01150	+	0.202180i	0.0512195	+	0.0102378i
$391$	−2.65659			−0.134350
$392$	−23.7560	+	35.3391i	−1.19986	+	1.78490i
$393$	20.4902			1.03359
$394$	26.6370	+	5.32423i	1.34195	+	0.268231i
$395$			3.43042i			0.172603i
$396$	−1.30066	+	3.12360i	−0.0653608	+	0.156967i
$397$			13.8473i			0.694977i	0.937684	+	0.347488i	$0.112965\pi$
$397$			13.8473i			0.694977i	−0.937684	+	0.347488i	$0.887035\pi$
$398$	4.71569	−	23.5924i	0.236376	−	1.18258i
$399$	20.0760			1.00506
$400$	13.9673	+	14.0718i	0.698365	+	0.703590i
$401$	15.9746			0.797734			0.398867	−	0.917009i	$-0.369403\pi$
$401$	15.9746			0.797734			0.398867	+	0.917009i	$0.369403\pi$
$402$	−2.76568	+	13.8366i	−0.137940	+	0.690108i
$403$			17.9367i			0.893488i
$404$	−2.52383	+	6.06109i	−0.125565	+	0.301551i
$405$		−	0.208104i		−	0.0103408i
$406$	1.52549	+	0.304916i	0.0757086	+	0.0151327i
$407$	8.58069			0.425329
$408$	−6.23595	−	4.19199i	−0.308726	−	0.207534i
$409$	−19.4312			−0.960812			−0.480406	−	0.877046i	$-0.659511\pi$
$409$	−19.4312			−0.960812			−0.480406	+	0.877046i	$0.659511\pi$
$410$	−0.983199	−	0.196523i	−0.0485567	−	0.00970557i
$411$			7.23648i			0.356949i
$412$	1.94268	+	0.808929i	0.0957090	+	0.0398531i
$413$			53.2402i			2.61978i
$414$	0.277192	−	1.38678i	0.0136232	−	0.0681566i
$415$	−0.866479			−0.0425338
$416$	10.9383	+	16.5366i	0.536294	+	0.810772i
$417$	−15.1990			−0.744297
$418$	2.00471	−	10.0295i	0.0980536	−	0.490560i
$419$		−	34.9811i		−	1.70894i	−0.519502	−	0.854470i	$-0.673882\pi$
$419$		−	34.9811i		−	1.70894i	0.519502	−	0.854470i	$-0.326118\pi$
$420$	−1.80444	−	0.751365i	−0.0880476	−	0.0366629i
$421$			38.2874i			1.86602i	0.359856	+	0.933008i	$0.382826\pi$
$421$			38.2874i			1.86602i	−0.359856	+	0.933008i	$0.617174\pi$
$422$	10.2896	+	2.05671i	0.500892	+	0.100119i
$423$	7.19329			0.349750
$424$	5.45542	+	3.66730i	0.264939	+	0.178100i
$425$	13.1679			0.638738
$426$	−23.1059	−	4.61844i	−1.11949	−	0.223764i
$427$			10.4758i			0.506960i
$428$	−9.65670	+	23.1910i	−0.466774	+	1.12098i
$429$		−	5.92960i		−	0.286284i
$430$	−0.266788	+	1.33473i	−0.0128657	+	0.0643665i
$431$	7.66017			0.368977			0.184489	−	0.982835i	$-0.440937\pi$
$431$	7.66017			0.368977			0.184489	+	0.982835i	$0.440937\pi$
$432$	2.83895	−	2.81787i	0.136589	−	0.135575i
$433$	−12.9635			−0.622986			−0.311493	−	0.950248i	$-0.600829\pi$
$433$	−12.9635			−0.622986			−0.311493	+	0.950248i	$0.600829\pi$
$434$	6.66186	−	33.3291i	0.319779	−	1.59985i
$435$			0.0487447i			0.00233713i
$436$	12.8941	−	30.9658i	0.617517	−	1.48300i
$437$			4.27489i			0.204496i
$438$	2.80601	+	0.560868i	0.134076	+	0.0267993i
$439$	−5.44408			−0.259832			−0.129916	−	0.991525i	$-0.541471\pi$
$439$	−5.44408			−0.259832			−0.129916	+	0.991525i	$0.541471\pi$
$440$	−0.555549	+	0.826427i	−0.0264847	+	0.0393984i
$441$	−15.0549			−0.716900
$442$	12.9126	+	2.58098i	0.614188	+	0.122765i
$443$			31.9442i			1.51772i	0.651255	+	0.758859i	$0.274243\pi$
$443$			31.9442i			1.51772i	−0.651255	+	0.758859i	$0.725757\pi$
$444$	−9.36451	−	3.89937i	−0.444420	−	0.185056i
$445$			1.84310i			0.0873714i
$446$	−5.48307	+	27.4316i	−0.259631	+	1.29893i
$447$	1.17050			0.0553626
$448$	−14.1832	−	34.7901i	−0.670093	−	1.64368i
$449$	9.30804			0.439273			0.219637	−	0.975582i	$-0.429513\pi$
$449$	9.30804			0.439273			0.219637	+	0.975582i	$0.429513\pi$
$450$	−1.37395	+	6.87385i	−0.0647688	+	0.324037i
$451$			5.76368i			0.271401i
$452$	5.70859	+	2.37705i	0.268509	+	0.111807i
$453$			0.759045i			0.0356631i
$454$	−24.7016	−	4.93738i	−1.15930	−	0.231723i
$455$	3.42540			0.160585
$456$	−6.74560	+	10.0347i	−0.315891	+	0.469916i
$457$	−37.5841			−1.75811			−0.879055	−	0.476721i	$-0.841825\pi$
$457$	−37.5841			−1.75811			−0.879055	+	0.476721i	$0.841825\pi$
$458$	−23.0975	−	4.61675i	−1.07927	−	0.215726i
$459$		−	2.65659i		−	0.123999i
$460$	0.159992	−	0.384228i	0.00745967	−	0.0179147i
$461$		−	13.2460i		−	0.616929i	−0.951236	−	0.308464i	$-0.900185\pi$
$461$		−	13.2460i		−	0.616929i	0.951236	−	0.308464i	$-0.0998150\pi$
$462$	−2.20232	+	11.0181i	−0.102461	+	0.512609i
$463$	−8.50801			−0.395401			−0.197700	−	0.980263i	$-0.563347\pi$
$463$	−8.50801			−0.395401			−0.197700	+	0.980263i	$0.563347\pi$
$464$	−0.664974	+	0.660036i	−0.0308707	+	0.0306414i
$465$	1.06498			0.0493874
$466$	4.17718	−	20.8983i	0.193504	−	0.968097i
$467$			26.5929i			1.23057i	0.788305	+	0.615285i	$0.210959\pi$
$467$			26.5929i			1.23057i	−0.788305	+	0.615285i	$0.789041\pi$
$468$	−2.69462	+	6.47125i	−0.124559	+	0.299134i
$469$			46.8570i			2.16366i
$470$	2.07594	+	0.414942i	0.0957562	+	0.0191399i
$471$	12.8062			0.590076
$472$	−26.6112	−	17.8888i	−1.22488	−	0.823400i
$473$	7.82443			0.359767
$474$	−22.8600	−	4.56928i	−1.04999	−	0.209874i
$475$		−	21.1893i		−	0.972233i
$476$	−23.0349	−	9.59171i	−1.05580	−	0.439635i
$477$			2.32408i			0.106412i
$478$	5.59517	−	27.9925i	0.255917	−	1.28035i
$479$	24.1047			1.10137			0.550686	−	0.834713i	$-0.314366\pi$
$479$	24.1047			1.10137			0.550686	+	0.834713i	$0.314366\pi$
$480$	0.981853	−	0.649458i	0.0448153	−	0.0296435i
$481$	17.7768			0.810554
$482$	4.08478	−	20.4360i	0.186057	−	0.930836i
$483$		−	4.69627i		−	0.213687i
$484$	−15.0251	−	6.25645i	−0.682961	−	0.284384i
$485$			0.463630i			0.0210524i
$486$	1.38678	+	0.277192i	0.0629057	+	0.0125737i
$487$	8.17867			0.370611			0.185305	−	0.982681i	$-0.440673\pi$
$487$	8.17867			0.370611			0.185305	+	0.982681i	$0.440673\pi$
$488$	−5.23615	−	3.51990i	−0.237030	−	0.159338i
$489$	20.8843			0.944421
$490$	−4.34477	−	0.868437i	−0.196277	−	0.0392320i
$491$			38.8836i			1.75479i	0.479765	+	0.877397i	$0.340722\pi$
$491$			38.8836i			1.75479i	−0.479765	+	0.877397i	$0.659278\pi$
$492$	2.61922	−	6.29017i	0.118083	−	0.283583i
$493$			0.622261i			0.0280252i
$494$	4.15321	−	20.7784i	0.186862	−	0.934865i
$495$	−0.352068			−0.0158243
$496$	14.4206	+	14.5285i	0.647503	+	0.652348i
$497$	−78.2471			−3.50986
$498$	1.15414	−	5.77412i	0.0517182	−	0.258745i
$499$			3.35080i			0.150003i	0.997183	+	0.0750013i	$0.0238961\pi$
$499$			3.35080i			0.150003i	−0.997183	+	0.0750013i	$0.976104\pi$
$500$	−1.59299	+	3.82564i	−0.0712408	+	0.171088i
$501$		−	10.7586i		−	0.480657i
$502$	−33.0353	−	6.60314i	−1.47444	−	0.294713i
$503$	41.2228			1.83803			0.919016	−	0.394220i	$-0.128985\pi$
$503$	41.2228			1.83803			0.919016	+	0.394220i	$0.128985\pi$
$504$	7.41051	−	11.0238i	0.330090	−	0.491038i
$505$	−0.683159			−0.0304002
$506$	−2.34615	−	0.468950i	−0.104299	−	0.0208474i
$507$			0.715485i			0.0317758i
$508$	8.62148	+	3.58997i	0.382516	+	0.159279i
$509$		−	13.8997i		−	0.616095i	−0.951371	−	0.308047i	$-0.900324\pi$
$509$		−	13.8997i		−	0.616095i	0.951371	−	0.308047i	$-0.0996755\pi$
$510$	0.153245	−	0.766679i	0.00678579	−	0.0339491i
$511$	9.50240			0.420362
$512$	22.1548	+	4.60033i	0.979115	+	0.203308i
$513$	−4.27489			−0.188741
$514$	0.593749	−	2.97051i	0.0261891	−	0.131024i
$515$			0.218964i			0.00964870i
$516$	−8.53916	−	3.55569i	−0.375915	−	0.156531i
$517$		−	12.1695i		−	0.535216i
$518$	−33.0321	−	6.60250i	−1.45135	−	0.290097i
$519$	−21.3693			−0.938007
$520$	−1.15094	+	1.71213i	−0.0504723	+	0.0750819i
$521$	−10.0027			−0.438227			−0.219114	−	0.975699i	$-0.570317\pi$
$521$	−10.0027			−0.438227			−0.219114	+	0.975699i	$0.570317\pi$
$522$	−0.324830	−	0.0649273i	−0.0142174	−	0.00284179i
$523$			31.5415i			1.37921i	0.724184	+	0.689606i	$0.242216\pi$
$523$			31.5415i			1.37921i	−0.724184	+	0.689606i	$0.757784\pi$
$524$	−15.7530	+	37.8317i	−0.688175	+	1.65268i
$525$			23.2779i			1.01593i
$526$	−1.55534	+	7.78132i	−0.0678160	+	0.339282i
$527$	13.5953			0.592219
$528$	−4.76724	−	4.80291i	−0.207468	−	0.209020i
$529$	1.00000			0.0434783
$530$	−0.134064	+	0.670717i	−0.00582335	+	0.0291341i
$531$		−	11.3367i		−	0.491971i
$532$	−15.4346	+	37.0669i	−0.669176	+	1.60706i
$533$			11.9408i			0.517212i
$534$	−12.2822	−	2.45499i	−0.531505	−	0.106238i
$535$	−2.61391			−0.113009
$536$	−23.4207	−	15.7441i	−1.01162	−	0.680041i
$537$	−1.77320			−0.0765191
$538$	−21.1503	−	4.22754i	−0.911853	−	0.182262i
$539$			25.4698i			1.09706i
$540$	0.384228	+	0.159992i	0.0165346	+	0.00688496i
$541$		−	1.69955i		−	0.0730693i	−0.999332	−	0.0365347i	$-0.988368\pi$
$541$		−	1.69955i		−	0.0730693i	0.999332	−	0.0365347i	$-0.0116319\pi$
$542$	−5.89176	+	29.4763i	−0.253073	+	1.26612i
$543$	13.3886			0.574560
$544$	12.5341	−	8.29078i	0.537393	−	0.355464i
$545$	3.49023			0.149505
$546$	−4.56259	+	22.8265i	−0.195261	+	0.976885i
$547$		−	38.5636i		−	1.64886i	−0.565963	−	0.824431i	$-0.691495\pi$
$547$		−	38.5636i		−	1.64886i	0.565963	−	0.824431i	$-0.308505\pi$
$548$	−13.3609	−	5.56347i	−0.570750	−	0.237660i
$549$		−	2.23067i		−	0.0952025i
$550$	11.6291	+	2.32444i	0.495867	+	0.0991146i
$551$	1.00132			0.0426576
$552$	2.34735	+	1.57796i	0.0999098	+	0.0671623i
$553$	−77.4141			−3.29198
$554$	−0.925754	−	0.185041i	−0.0393315	−	0.00786163i
$555$		−	1.05549i		−	0.0448032i
$556$	11.6851	−	28.0623i	0.495559	−	1.19011i
$557$		−	24.7684i		−	1.04947i	−0.851265	−	0.524736i	$-0.824164\pi$
$557$		−	24.7684i		−	1.04947i	0.851265	−	0.524736i	$-0.175836\pi$
$558$	−1.41854	+	7.09693i	−0.0600517	+	0.300437i
$559$	16.2101			0.685613
$560$	2.77454	−	2.75393i	0.117246	−	0.116375i
$561$	−4.49440			−0.189754
$562$	6.46420	−	32.3402i	0.272676	−	1.36419i
$563$		−	35.1907i		−	1.48311i	−0.670892	−	0.741555i	$-0.734089\pi$
$563$		−	35.1907i		−	1.48311i	0.670892	−	0.741555i	$-0.265911\pi$
$564$	−5.53026	+	13.2812i	−0.232866	+	0.559239i
$565$			0.643427i			0.0270692i
$566$	16.8912	+	3.37624i	0.709991	+	0.141914i
$567$	4.69627			0.197225
$568$	26.2912	−	39.1105i	1.10316	−	1.64104i
$569$	17.9377			0.751988			0.375994	−	0.926622i	$-0.377301\pi$
$569$	17.9377			0.751988			0.375994	+	0.926622i	$0.377301\pi$
$570$	−1.23371	−	0.246596i	−0.0516745	−	0.0103288i
$571$			42.5544i			1.78084i	0.455136	+	0.890422i	$0.349591\pi$
$571$			42.5544i			1.78084i	−0.455136	+	0.890422i	$0.650409\pi$
$572$	10.9480	+	4.55873i	0.457759	+	0.190610i
$573$		−	18.4481i		−	0.770679i
$574$	4.43492	−	22.1878i	0.185110	−	0.926100i
$575$	−4.95669			−0.206708
$576$	3.02010	+	7.40804i	0.125838	+	0.308668i
$577$	27.9156			1.16214			0.581072	−	0.813852i	$-0.302634\pi$
$577$	27.9156			1.16214			0.581072	+	0.813852i	$0.302634\pi$
$578$	−2.75598	+	13.7881i	−0.114634	+	0.573509i
$579$		−	25.1246i		−	1.04414i
$580$	−0.0899988	−	0.0374754i	−0.00373700	−	0.00155608i
$581$		−	19.5538i		−	0.811227i
$582$	−3.08958	−	0.617549i	−0.128067	−	0.0255982i
$583$	3.93185			0.162841
$584$	−3.19283	+	4.74962i	−0.132120	+	0.196541i
$585$	−0.729389			−0.0301565
$586$	18.8535	+	3.76845i	0.778830	+	0.155673i
$587$			8.34346i			0.344372i	0.985064	+	0.172186i	$0.0550829\pi$
$587$			8.34346i			0.344372i	−0.985064	+	0.172186i	$0.944917\pi$
$588$	11.5743	−	27.7963i	0.477318	−	1.14630i
$589$		−	21.8770i		−	0.901425i
$590$	0.653954	−	3.27171i	0.0269228	−	0.134694i
$591$	−19.2078			−0.790102
$592$	14.3990	−	14.2921i	0.591797	−	0.587402i
$593$	5.75819			0.236461			0.118230	−	0.992986i	$-0.462278\pi$
$593$	5.75819			0.236461			0.118230	+	0.992986i	$0.462278\pi$
$594$	0.468950	−	2.34615i	0.0192413	−	0.0962635i
$595$		−	2.59632i		−	0.106439i
$596$	−0.899889	+	2.16112i	−0.0368609	+	0.0885231i
$597$			17.0124i			0.696270i
$598$	−4.86057	−	0.971536i	−0.198764	−	0.0397291i
$599$	12.5983			0.514753			0.257377	−	0.966311i	$-0.417142\pi$
$599$	12.5983			0.514753			0.257377	+	0.966311i	$0.417142\pi$
$600$	−11.6351	−	7.82145i	−0.475001	−	0.319309i
$601$	5.64388			0.230219			0.115109	−	0.993353i	$-0.463278\pi$
$601$	5.64388			0.230219			0.115109	+	0.993353i	$0.463278\pi$
$602$	−30.1208	−	6.02058i	−1.22763	−	0.245381i
$603$		−	9.97750i		−	0.406315i
$604$	−1.40145	−	0.583561i	−0.0570241	−	0.0237447i
$605$		−	1.69352i		−	0.0688512i
$606$	0.909959	−	4.55250i	0.0369645	−	0.184933i
$607$	−30.8708			−1.25301			−0.626504	−	0.779418i	$-0.715515\pi$
$607$	−30.8708			−1.25301			−0.626504	+	0.779418i	$0.715515\pi$
$608$	−13.3412	−	20.1693i	−0.541058	−	0.817974i
$609$	−1.10002			−0.0445750
$610$	0.128675	−	0.643759i	0.00520991	−	0.0260650i
$611$		−	25.2119i		−	1.01997i
$612$	4.90495	+	2.04241i	0.198271	+	0.0825596i
$613$			20.5714i			0.830870i	0.909623	+	0.415435i	$0.136371\pi$
$613$			20.5714i			0.830870i	−0.909623	+	0.415435i	$0.863629\pi$
$614$	−4.17505	−	0.834514i	−0.168491	−	0.0336783i
$615$	0.708978			0.0285888
$616$	−18.6499	−	12.5370i	−0.751427	−	0.505131i
$617$	42.2581			1.70125			0.850624	−	0.525775i	$-0.176225\pi$
$617$	42.2581			1.70125			0.850624	+	0.525775i	$0.176225\pi$
$618$	−1.45915	−	0.291657i	−0.0586957	−	0.0117322i
$619$		−	21.7502i		−	0.874216i	−0.899409	−	0.437108i	$-0.856003\pi$
$619$		−	21.7502i		−	0.874216i	0.899409	−	0.437108i	$-0.143997\pi$
$620$	−0.818768	+	1.96631i	−0.0328825	+	0.0789689i
$621$			1.00000i			0.0401286i
$622$	−8.83238	+	44.1882i	−0.354146	+	1.77178i
$623$	−41.5932			−1.66640
$624$	−9.87642	−	9.95031i	−0.395373	−	0.398331i
$625$	24.3523			0.974091
$626$	−3.23874	+	16.2033i	−0.129446	+	0.647615i
$627$			7.23222i			0.288827i
$628$	−9.84548	+	23.6444i	−0.392877	+	0.943513i
$629$		−	13.4741i		−	0.537249i
$630$	1.35532	+	0.270902i	0.0539971	+	0.0107930i
$631$	−29.4814			−1.17364			−0.586818	−	0.809719i	$-0.699620\pi$
$631$	−29.4814			−1.17364			−0.586818	+	0.809719i	$0.699620\pi$
$632$	26.0114	−	38.6942i	1.03468	−	1.53917i
$633$	−7.41980			−0.294910
$634$	−2.17782	−	0.435306i	−0.0864925	−	0.0172882i
$635$			0.971746i			0.0385626i
$636$	−4.29101	−	1.78677i	−0.170150	−	0.0708501i
$637$			52.7664i			2.09068i
$638$	−0.109843	+	0.549544i	−0.00434874	+	0.0217566i
$639$	16.6616			0.659121
$640$	0.444255	+	2.31213i	0.0175607	+	0.0913951i
$641$	−5.32059			−0.210151			−0.105075	−	0.994464i	$-0.533508\pi$
$641$	−5.32059			−0.210151			−0.105075	+	0.994464i	$0.533508\pi$
$642$	3.48169	−	17.4188i	0.137412	−	0.687466i
$643$			31.0638i			1.22504i	0.790456	+	0.612519i	$0.209844\pi$
$643$			31.0638i			1.22504i	−0.790456	+	0.612519i	$0.790156\pi$
$644$	8.67085	+	3.61053i	0.341680	+	0.142275i
$645$		−	0.962467i		−	0.0378971i
$646$	−15.7492	−	3.14797i	−0.619644	−	0.123855i
$647$	0.0560646			0.00220413			0.00110206	−	0.999999i	$-0.499649\pi$
$647$	0.0560646			0.00220413			0.00110206	+	0.999999i	$0.499649\pi$
$648$	−1.57796	+	2.34735i	−0.0619880	+	0.0922126i
$649$	−19.1793			−0.752854
$650$	24.0924	+	4.81561i	0.944980	+	0.188884i
$651$			24.0334i			0.941943i
$652$	−16.0560	+	38.5593i	−0.628803	+	1.51010i
$653$			24.5445i			0.960501i	0.877131	+	0.480250i	$0.159454\pi$
$653$			24.5445i			0.960501i	−0.877131	+	0.480250i	$0.840546\pi$
$654$	−4.64894	+	23.2585i	−0.181788	+	0.909480i
$655$	−4.26409			−0.166612
$656$	9.60004	+	9.67187i	0.374819	+	0.377623i
$657$	−2.02340			−0.0789402
$658$	−9.36397	+	46.8477i	−0.365046	+	1.82631i
$659$			16.9566i			0.660534i	0.943888	+	0.330267i	$0.107139\pi$
$659$			16.9566i			0.660534i	−0.943888	+	0.330267i	$0.892861\pi$
$660$	0.270673	−	0.650034i	0.0105359	−	0.0253025i
$661$		−	33.0139i		−	1.28409i	−0.766667	−	0.642045i	$-0.778086\pi$
$661$		−	33.0139i		−	1.28409i	0.766667	−	0.642045i	$-0.221914\pi$
$662$	−40.0727	−	8.00977i	−1.55747	−	0.311309i
$663$	−9.31117			−0.361616
$664$	9.77362	+	6.57012i	0.379290	+	0.254970i
$665$	−4.17790			−0.162012
$666$	7.03370	+	1.40590i	0.272550	+	0.0544777i
$667$		−	0.234233i		−	0.00906952i
$668$	19.8639	+	8.27128i	0.768556	+	0.320025i
$669$		−	19.7808i		−	0.764770i
$670$	0.575549	−	2.87946i	0.0222354	−	0.111243i
$671$	−3.77382			−0.145687
$672$	14.6563	+	22.1574i	0.565378	+	0.854741i
$673$	13.7987			0.531902			0.265951	−	0.963987i	$-0.414314\pi$
$673$	13.7987			0.531902			0.265951	+	0.963987i	$0.414314\pi$
$674$	0.279416	−	1.39791i	0.0107627	−	0.0538456i
$675$		−	4.95669i		−	0.190783i
$676$	−1.32102	−	0.550071i	−0.0508085	−	0.0211566i
$677$			39.3976i			1.51417i	0.653314	+	0.757087i	$0.273378\pi$
$677$			39.3976i			1.51417i	−0.653314	+	0.757087i	$0.726622\pi$
$678$	−4.28773	−	0.857037i	−0.164669	−	0.0329143i
$679$	−10.4627			−0.401522
$680$	1.29773	+	0.872369i	0.0497655	+	0.0334538i
$681$	17.8121			0.682563
$682$	12.0065	+	2.39988i	0.459754	+	0.0918961i
$683$			11.1278i			0.425795i	0.977075	+	0.212897i	$0.0682900\pi$
$683$			11.1278i			0.425795i	−0.977075	+	0.212897i	$0.931710\pi$
$684$	3.28657	−	7.89286i	0.125665	−	0.301791i
$685$		−	1.50594i		−	0.0575390i
$686$	10.4856	−	52.4592i	0.400342	−	2.00290i
$687$	16.6554			0.635444
$688$	13.1300	−	13.0325i	0.500575	−	0.496858i
$689$	8.14572			0.310327
$690$	−0.0576846	+	0.288595i	−0.00219602	+	0.0109866i
$691$		−	36.8370i		−	1.40135i	−0.713482	−	0.700674i	$-0.752883\pi$
$691$		−	36.8370i		−	1.40135i	0.713482	−	0.700674i	$-0.247117\pi$
$692$	16.4289	−	39.4547i	0.624532	−	1.49984i
$693$		−	7.94510i		−	0.301809i
$694$	3.92629	+	0.784791i	0.149040	+	0.0297902i
$695$	3.16297			0.119978
$696$	0.369609	−	0.549826i	0.0140100	−	0.0208411i
$697$	9.05061			0.342816
$698$	−36.5098	−	7.29762i	−1.38192	−	0.276219i
$699$			15.0697i			0.569987i
$700$	−42.9788	−	17.8963i	−1.62444	−	0.676416i
$701$		−	17.7525i		−	0.670501i	−0.942129	−	0.335251i	$-0.891179\pi$
$701$		−	17.7525i		−	0.670501i	0.942129	−	0.335251i	$-0.108821\pi$
$702$	0.971536	−	4.86057i	0.0366683	−	0.183450i
$703$	−21.6821			−0.817755
$704$	12.5328	−	5.10938i	0.472349	−	0.192567i
$705$	−1.49695			−0.0563784
$706$	−7.58767	+	37.9609i	−0.285566	+	1.42868i
$707$		−	15.4168i		−	0.579808i
$708$	20.9313	+	8.71575i	0.786646	+	0.327558i
$709$			16.3885i			0.615481i	0.951470	+	0.307741i	$0.0995729\pi$
$709$			16.3885i			0.615481i	−0.951470	+	0.307741i	$0.900427\pi$
$710$	4.80844	+	0.961116i	0.180457	+	0.0360700i
$711$	16.4842			0.618206
$712$	13.9754	−	20.7897i	0.523751	−	0.779125i
$713$	−5.11755			−0.191654
$714$	17.3016	+	3.45826i	0.647496	+	0.129422i
$715$			1.23397i			0.0461480i
$716$	1.36325	−	3.27390i	0.0509470	−	0.122352i
$717$			20.1852i			0.753830i
$718$	−3.14067	+	15.7127i	−0.117209	+	0.586392i
$719$	−20.1942			−0.753116			−0.376558	−	0.926393i	$-0.622893\pi$
$719$	−20.1942			−0.753116			−0.376558	+	0.926393i	$0.622893\pi$
$720$	−0.590796	+	0.586409i	−0.0220177	+	0.0218542i
$721$	−4.94134			−0.184025
$722$	0.201051	−	1.00585i	0.00748233	−	0.0374339i
$723$			14.7363i			0.548049i
$724$	−10.2933	+	24.7198i	−0.382546	+	0.918703i
$725$			1.16102i			0.0431192i
$726$	11.2854	+	2.25574i	0.418841	+	0.0837184i
$727$	24.3339			0.902494			0.451247	−	0.892399i	$-0.350979\pi$
$727$	24.3339			0.902494			0.451247	+	0.892399i	$0.350979\pi$
$728$	−38.6375	−	25.9733i	−1.43200	−	0.962634i
$729$	−1.00000			−0.0370370
$730$	−0.583941	−	0.116719i	−0.0216126	−	0.00431996i
$731$		−	12.2866i		−	0.454435i
$732$	4.11854	+	1.71496i	0.152226	+	0.0633866i
$733$			1.13588i			0.0419547i	0.999780	+	0.0209773i	$0.00667779\pi$
$733$			1.13588i			0.0419547i	−0.999780	+	0.0209773i	$0.993322\pi$
$734$	−0.408215	+	2.04229i	−0.0150675	+	0.0753822i
$735$	3.13298			0.115562
$736$	−4.71809	+	3.12083i	−0.173911	+	0.115035i
$737$	−16.8799			−0.621777
$738$	−0.944350	+	4.72456i	−0.0347620	+	0.173913i
$739$			17.0620i			0.627636i	0.949483	+	0.313818i	$0.101608\pi$
$739$			17.0620i			0.627636i	−0.949483	+	0.313818i	$0.898392\pi$
$740$	1.94879	+	0.811473i	0.0716390	+	0.0298304i
$741$			14.9832i			0.550421i
$742$	−15.1360	−	3.02540i	−0.555661	−	0.111066i
$743$	45.5322			1.67041			0.835207	−	0.549935i	$-0.185348\pi$
$743$	45.5322			1.67041			0.835207	+	0.549935i	$0.185348\pi$
$744$	−12.0127	−	8.07528i	−0.440407	−	0.296054i
$745$	−0.243585			−0.00892427
$746$	−31.6407	−	6.32438i	−1.15845	−	0.231552i
$747$			4.16368i			0.152341i
$748$	3.45533	−	8.29814i	0.126340	−	0.303410i
$749$		−	58.9879i		−	2.15537i
$750$	0.574348	−	2.87345i	0.0209722	−	0.104924i
$751$	27.7231			1.01163			0.505816	−	0.862642i	$-0.331192\pi$
$751$	27.7231			1.01163			0.505816	+	0.862642i	$0.331192\pi$
$752$	−20.2697	−	20.4214i	−0.739161	−	0.744691i
$753$	23.8216			0.868107
$754$	−0.227566	+	1.13850i	−0.00828745	+	0.0414619i
$755$		−	0.157960i		−	0.00574876i
$756$	−3.61053	+	8.67085i	−0.131314	+	0.315356i
$757$			29.2337i			1.06252i	0.847210	+	0.531258i	$0.178280\pi$
$757$			29.2337i			1.06252i	−0.847210	+	0.531258i	$0.821720\pi$
$758$	−1.55240	−	0.310296i	−0.0563859	−	0.0112705i
$759$	1.69179			0.0614081
$760$	1.40378	−	2.08825i	0.0509206	−	0.0757489i
$761$	−5.97580			−0.216623			−0.108311	−	0.994117i	$-0.534544\pi$
$761$	−5.97580			−0.216623			−0.108311	+	0.994117i	$0.534544\pi$
$762$	−6.47561	−	1.29435i	−0.234587	−	0.0468895i
$763$			78.7637i			2.85144i
$764$	34.0612	+	14.1830i	1.23229	+	0.513124i
$765$			0.552847i			0.0199882i
$766$	10.2672	−	51.3665i	0.370969	−	1.85595i
$767$	−39.7343			−1.43472
$768$	−15.9996	−	0.119262i	−0.577334	−	0.00430349i
$769$	−13.6742			−0.493103			−0.246552	−	0.969130i	$-0.579297\pi$
$769$	−13.6742			−0.493103			−0.246552	+	0.969130i	$0.579297\pi$
$770$	0.458310	−	2.29291i	0.0165164	−	0.0826309i
$771$			2.14202i			0.0771428i
$772$	46.3882	+	19.3160i	1.66955	+	0.695198i
$773$			17.5387i			0.630822i	0.948955	+	0.315411i	$0.102142\pi$
$773$			17.5387i			0.630822i	−0.948955	+	0.315411i	$0.897858\pi$
$774$	6.41378	+	1.28199i	0.230539	+	0.0460803i
$775$	25.3661			0.911179
$776$	3.51550	−	5.22961i	0.126199	−	0.187732i
$777$	23.8193			0.854511
$778$	28.6583	+	5.72825i	1.02745	+	0.205368i
$779$		−	14.5639i		−	0.521806i
$780$	0.560761	−	1.34669i	0.0200785	−	0.0482193i
$781$		−	28.1879i		−	1.00864i
$782$	−0.736385	+	3.68412i	−0.0263331	+	0.131744i
$783$	0.234233			0.00837079
$784$	42.4227	+	42.7401i	1.51510	+	1.52643i
$785$	−2.66501			−0.0951183
$786$	5.67971	−	28.4154i	0.202589	−	1.01355i
$787$			43.9092i			1.56520i	0.622528	+	0.782598i	$0.286106\pi$
$787$			43.9092i			1.56520i	−0.622528	+	0.782598i	$0.713894\pi$
$788$	14.7671	−	35.4639i	0.526056	−	1.26335i
$789$		−	5.61106i		−	0.199759i
$790$	4.75725	+	0.950885i	0.169255	+	0.0338310i
$791$	−14.5202			−0.516278
$792$	3.97122	+	2.66957i	0.141111	+	0.0948592i
$793$	−7.81832			−0.277637
$794$	19.2032	+	3.83836i	0.681497	+	0.136218i
$795$		−	0.483650i		−	0.0171533i
$796$	−31.4104	−	13.0793i	−1.11331	−	0.463582i
$797$		−	0.252400i		−	0.00894046i	−0.999990	−	0.00447023i	$-0.998577\pi$
$797$		−	0.252400i		−	0.00894046i	0.999990	−	0.00447023i	$-0.00142292\pi$
$798$	5.56490	−	27.8411i	0.196995	−	0.985563i
$799$	−19.1096			−0.676050
$800$	23.3861	−	15.4690i	0.826825	−	0.546912i
$801$	8.85665			0.312934
$802$	4.42803	−	22.1533i	0.156359	−	0.782261i
$803$			3.42316i			0.120801i
$804$	18.4218	+	7.67079i	0.649685	+	0.270528i
$805$			0.977311i			0.0344457i
$806$	24.8742	+	4.97189i	0.876158	+	0.175127i
$807$	15.2513			0.536872
$808$	7.70583	+	5.18009i	0.271090	+	0.182235i
$809$	44.1065			1.55070			0.775351	−	0.631530i	$-0.217573\pi$
$809$	44.1065			1.55070			0.775351	+	0.631530i	$0.217573\pi$
$810$	−0.288595	−	0.0576846i	−0.0101402	−	0.00202683i
$811$		−	34.9846i		−	1.22848i	−0.789121	−	0.614238i	$-0.789464\pi$
$811$		−	34.9846i		−	1.22848i	0.789121	−	0.614238i	$-0.210536\pi$
$812$	0.845704	−	2.03100i	0.0296784	−	0.0712740i
$813$		−	21.2552i		−	0.745452i
$814$	2.37850	−	11.8996i	0.0833663	−	0.417079i
$815$	−4.34611			−0.152237
$816$	−7.54193	+	7.48592i	−0.264020	+	0.262060i
$817$	−19.7711			−0.691703
$818$	−5.38617	+	26.9469i	−0.188323	+	0.942176i
$819$		−	16.4601i		−	0.575161i
$820$	−0.545069	+	1.30901i	−0.0190346	+	0.0457125i
$821$			13.3041i			0.464318i	0.972678	+	0.232159i	$0.0745790\pi$
$821$			13.3041i			0.464318i	−0.972678	+	0.232159i	$0.925421\pi$
$822$	10.0354	+	2.00589i	0.350025	+	0.0699635i
$823$	0.106793			0.00372257			0.00186128	−	0.999998i	$-0.499408\pi$
$823$	0.106793			0.00372257			0.00186128	+	0.999998i	$0.499408\pi$
$824$	1.66030	−	2.46985i	0.0578394	−	0.0860412i
$825$	−8.38569			−0.291952
$826$	73.8325	+	14.7577i	2.56896	+	0.513487i
$827$		−	18.5942i		−	0.646585i	−0.946299	−	0.323293i	$-0.895210\pi$
$827$		−	18.5942i		−	0.646585i	0.946299	−	0.323293i	$-0.104790\pi$
$828$	−1.84633	−	0.768809i	−0.0641644	−	0.0267180i
$829$		−	29.2344i		−	1.01535i	−0.861548	−	0.507677i	$-0.830504\pi$
$829$		−	29.2344i		−	1.01535i	0.861548	−	0.507677i	$-0.169496\pi$
$830$	−0.240181	+	1.20162i	−0.00833679	+	0.0417087i
$831$	0.667555			0.0231572
$832$	25.9646	−	10.5852i	0.900161	−	0.366977i
$833$	39.9948			1.38574
$834$	−4.21303	+	21.0777i	−0.145885	+	0.729860i
$835$			2.23890i			0.0774803i
$836$	−13.3531	−	5.56020i	−0.461825	−	0.192303i
$837$		−	5.11755i		−	0.176889i
$838$	−48.5112	−	9.69647i	−1.67579	−	0.334959i
$839$	25.6644			0.886035			0.443017	−	0.896513i	$-0.353908\pi$
$839$	25.6644			0.886035			0.443017	+	0.896513i	$0.353908\pi$
$840$	−1.54216	+	2.29409i	−0.0532094	+	0.0791536i
$841$	28.9451			0.998108
$842$	53.0963	+	10.6130i	1.82982	+	0.365747i
$843$			23.3203i			0.803194i
$844$	5.70441	−	13.6994i	0.196354	−	0.471553i
$845$		−	0.148895i		−	0.00512215i
$846$	1.99392	−	9.97552i	0.0685523	−	0.342966i
$847$	38.2175			1.31317
$848$	6.59794	−	6.54894i	0.226574	−	0.224892i
$849$	−12.1802			−0.418022
$850$	3.65004	−	18.2610i	0.125195	−	0.626348i
$851$			5.07196i			0.173865i
$852$	−12.8095	+	30.7627i	−0.438848	+	1.05391i
$853$			7.55678i			0.258739i	0.991596	+	0.129370i	$0.0412954\pi$
$853$			7.55678i			0.258739i	−0.991596	+	0.129370i	$0.958705\pi$
$854$	14.5277	+	2.90380i	0.497126	+	0.0993661i
$855$	0.889621			0.0304244
$856$	29.4841	+	19.8201i	1.00775	+	0.677437i
$857$	−23.3681			−0.798240			−0.399120	−	0.916899i	$-0.630684\pi$
$857$	−23.3681			−0.798240			−0.399120	+	0.916899i	$0.630684\pi$
$858$	−8.22307	−	1.64364i	−0.280731	−	0.0561128i
$859$			13.0778i			0.446207i	0.974795	+	0.223104i	$0.0716188\pi$
$859$			13.0778i			0.446207i	−0.974795	+	0.223104i	$0.928381\pi$
$860$	1.77703	+	0.739953i	0.0605963	+	0.0252322i
$861$			15.9995i			0.545260i
$862$	2.12334	−	10.6230i	0.0723211	−	0.361820i
$863$	44.1463			1.50276			0.751379	−	0.659871i	$-0.229389\pi$
$863$	44.1463			1.50276			0.751379	+	0.659871i	$0.229389\pi$
$864$	−3.12083	−	4.71809i	−0.106173	−	0.160513i
$865$	4.44703			0.151203
$866$	−3.59337	+	17.9775i	−0.122108	+	0.610902i
$867$		−	9.94251i		−	0.337665i
$868$	−44.3736	−	18.4771i	−1.50614	−	0.627153i
$869$		−	27.8878i		−	0.946029i
$870$	0.0675983	+	0.0135116i	0.00229180	+	0.000458087i
$871$	−34.9704			−1.18493
$872$	−39.3687	−	26.4648i	−1.33319	−	0.896212i
$873$	2.22788			0.0754022
$874$	5.92834	+	1.18496i	0.200529	+	0.0400820i
$875$		−	9.73079i		−	0.328961i
$876$	1.55560	−	3.73586i	0.0525590	−	0.126223i
$877$		−	24.7148i		−	0.834561i	−0.908778	−	0.417280i	$-0.862983\pi$
$877$		−	24.7148i		−	0.834561i	0.908778	−	0.417280i	$-0.137017\pi$
$878$	−1.50905	+	7.54975i	−0.0509281	+	0.254792i
$879$	−13.5951			−0.458552
$880$	0.992081	+	0.999504i	0.0334430	+	0.0336933i
$881$	23.6227			0.795870			0.397935	−	0.917414i	$-0.369727\pi$
$881$	23.6227			0.795870			0.397935	+	0.917414i	$0.369727\pi$
$882$	−4.17309	+	20.8779i	−0.140515	+	0.702995i
$883$		−	17.2321i		−	0.579908i	−0.957041	−	0.289954i	$-0.906360\pi$
$883$		−	17.2321i		−	0.579908i	0.957041	−	0.289954i	$-0.0936400\pi$
$884$	7.15851	−	17.1915i	0.240767	−	0.578212i
$885$			2.35921i			0.0793040i
$886$	44.2997	+	8.85468i	1.48828	+	0.297479i
$887$	−22.0492			−0.740341			−0.370170	−	0.928964i	$-0.620701\pi$
$887$	−22.0492			−0.740341			−0.370170	+	0.928964i	$0.620701\pi$
$888$	−8.00334	+	11.9057i	−0.268574	+	0.399528i
$889$	−21.9293			−0.735486
$890$	2.55598	+	0.510893i	0.0856767	+	0.0171252i
$891$			1.69179i			0.0566771i
$892$	36.5219	+	15.2076i	1.22284	+	0.509190i
$893$			30.7505i			1.02903i
$894$	0.324452	−	1.62323i	0.0108513	−	0.0542888i
$895$	0.369009			0.0123346
$896$	−52.1778	+	10.0255i	−1.74314	+	0.334928i
$897$	3.50493			0.117026
$898$	2.58011	−	12.9082i	0.0860994	−	0.430753i
$899$			1.19870i			0.0399788i
$900$	9.15169	+	3.81075i	0.305056	+	0.127025i
$901$		−	6.17413i		−	0.205690i
$902$	7.99296	+	1.59764i	0.266137	+	0.0531957i
$903$	21.7199			0.722794
$904$	4.87882	−	7.25767i	0.162267	−	0.241387i
$905$	−2.78622			−0.0926170
$906$	1.05263	+	0.210401i	0.0349713	+	0.00699010i
$907$			33.5067i			1.11257i	0.830991	+	0.556285i	$0.187774\pi$
$907$			33.5067i			1.11257i	−0.830991	+	0.556285i	$0.812226\pi$
$908$	−13.6941	+	32.8871i	−0.454456	+	1.09140i
$909$			3.28278i			0.108883i
$910$	0.949493	−	4.75029i	0.0314754	−	0.157471i
$911$	−37.6574			−1.24765			−0.623823	−	0.781566i	$-0.714421\pi$
$911$	−37.6574			−1.24765			−0.623823	+	0.781566i	$0.714421\pi$
$912$	12.0461	+	12.1362i	0.398885	+	0.401870i
$913$	7.04408			0.233125
$914$	−10.4180	+	52.1209i	−0.344597	+	1.72401i
$915$			0.464210i			0.0153463i
$916$	−12.8048	+	30.7514i	−0.423084	+	1.01606i
$917$		−	96.2274i		−	3.17771i
$918$	−3.68412	−	0.736385i	−0.121594	−	0.0243043i
$919$	−2.15691			−0.0711498			−0.0355749	−	0.999367i	$-0.511326\pi$
$919$	−2.15691			−0.0711498			−0.0355749	+	0.999367i	$0.511326\pi$
$920$	−0.488493	−	0.328379i	−0.0161051	−	0.0108263i
$921$	3.01060			0.0992028
$922$	−18.3693	−	3.67169i	−0.604962	−	0.120921i
$923$		−	58.3975i		−	1.92218i
$924$	14.6693	+	6.10826i	0.482584	+	0.200947i
$925$		−	25.1401i		−	0.826603i
$926$	−2.35835	+	11.7988i	−0.0775001	+	0.387731i
$927$	1.05219			0.0345583
$928$	0.731001	+	1.10513i	0.0239963	+	0.0362777i
$929$	−22.5541			−0.739975			−0.369987	−	0.929037i	$-0.620638\pi$
$929$	−22.5541			−0.739975			−0.369987	+	0.929037i	$0.620638\pi$
$930$	0.295204	−	1.47690i	0.00968013	−	0.0484294i
$931$		−	64.3581i		−	2.10925i
$932$	−27.8236	−	11.5857i	−0.911391	−	0.379502i
$933$		−	31.8638i		−	1.04317i
$934$	36.8785	+	7.37132i	1.20670	+	0.241197i
$935$	0.935302			0.0305876
$936$	8.22729	+	5.53063i	0.268917	+	0.180774i
$937$	−31.9167			−1.04267			−0.521337	−	0.853351i	$-0.674566\pi$
$937$	−31.9167			−1.04267			−0.521337	+	0.853351i	$0.674566\pi$
$938$	64.9805	+	12.9884i	2.12169	+	0.424085i
$939$		−	11.6841i		−	0.381297i
$940$	1.15087	−	2.76386i	0.0375372	−	0.0901473i
$941$			2.18372i			0.0711872i	0.999366	+	0.0355936i	$0.0113322\pi$
$941$			2.18372i			0.0711872i	−0.999366	+	0.0355936i	$0.988668\pi$
$942$	3.54976	−	17.7593i	0.115657	−	0.578631i
$943$	−3.40685			−0.110942
$944$	−32.1843	+	31.9453i	−1.04751	+	1.03973i
$945$	−0.977311			−0.0317919
$946$	2.16887	−	10.8508i	0.0705159	−	0.352789i
$947$		−	56.8500i		−	1.84738i	−0.383146	−	0.923688i	$-0.625160\pi$
$947$		−	56.8500i		−	1.84738i	0.383146	−	0.923688i	$-0.374840\pi$
$948$	−12.6732	+	30.4353i	−0.411606	+	0.988491i
$949$			7.09186i			0.230211i
$950$	−29.3850	−	5.87350i	−0.953374	−	0.190562i
$951$	1.57042			0.0509242
$952$	−19.6867	+	29.2857i	−0.638050	+	0.949155i
$953$	−18.5216			−0.599972			−0.299986	−	0.953944i	$-0.596982\pi$
$953$	−18.5216			−0.599972			−0.299986	+	0.953944i	$0.596982\pi$
$954$	3.22299	+	0.644215i	0.104348	+	0.0208572i
$955$			3.83911i			0.124231i
$956$	−37.2685	−	15.5186i	−1.20535	−	0.501906i
$957$		−	0.396273i		−	0.0128097i
$958$	6.68162	−	33.4280i	0.215873	−	1.08001i
$959$	33.9844			1.09741
$960$	−0.628495	−	1.54164i	−0.0202846	−	0.0497562i
$961$	−4.81064			−0.155182
$962$	4.92759	−	24.6526i	0.158872	−	0.794832i
$963$			12.5606i			0.404760i
$964$	−27.2081	−	11.3294i	−0.876313	−	0.364895i
$965$			5.22852i			0.168312i
$966$	−6.51270	−	1.30177i	−0.209543	−	0.0418836i
$967$	−36.4615			−1.17252			−0.586261	−	0.810122i	$-0.699401\pi$
$967$	−36.4615			−1.17252			−0.586261	+	0.810122i	$0.699401\pi$
$968$	−12.8412	+	19.1024i	−0.412731	+	0.613973i
$969$	11.3566			0.364828
$970$	0.642954	+	0.128514i	0.0206440	+	0.00412635i
$971$		−	12.4864i		−	0.400707i	−0.979724	−	0.200354i	$-0.935791\pi$
$971$		−	12.4864i		−	0.400707i	0.979724	−	0.200354i	$-0.0642091\pi$
$972$	0.768809	−	1.84633i	0.0246596	−	0.0592210i
$973$			71.3784i			2.28829i
$974$	2.26706	−	11.3420i	0.0726412	−	0.363422i
$975$	−17.3728			−0.556376
$976$	−6.33275	+	6.28572i	−0.202706	+	0.201201i
$977$	−2.28485			−0.0730987			−0.0365493	−	0.999332i	$-0.511637\pi$
$977$	−2.28485			−0.0730987			−0.0365493	+	0.999332i	$0.511637\pi$
$978$	5.78896	−	28.9620i	0.185110	−	0.926102i
$979$		−	14.9836i		−	0.478878i
$980$	−2.40867	+	5.78452i	−0.0769420	+	0.184780i
$981$		−	16.7716i		−	0.535475i
$982$	53.9231	+	10.7782i	1.72076	+	0.343947i
$983$	−56.7812			−1.81104			−0.905520	−	0.424305i	$-0.860519\pi$
$983$	−56.7812			−1.81104			−0.905520	+	0.424305i	$0.860519\pi$
$984$	−7.99706	−	5.37586i	−0.254937	−	0.171376i
$985$	3.99721			0.127362
$986$	0.862940	+	0.172485i	0.0274816	+	0.00549306i
$987$		−	33.7816i		−	1.07528i
$988$	−27.6639	−	11.5192i	−0.880106	−	0.366475i
$989$			4.62494i			0.147064i
$990$	−0.0975904	+	0.488242i	−0.00310163	+	0.0155173i
$991$	−25.6573			−0.815032			−0.407516	−	0.913198i	$-0.633605\pi$
$991$	−25.6573			−0.815032			−0.407516	+	0.913198i	$0.633605\pi$
$992$	24.1451	−	15.9710i	0.766608	−	0.507081i
$993$	28.8962			0.916992
$994$	−21.6894	+	108.512i	−0.687947	+	3.44178i
$995$		−	3.54034i		−	0.112236i
$996$	−7.68753	−	3.20108i	−0.243589	−	0.101430i
$997$		−	3.85222i		−	0.122001i	−0.998138	−	0.0610006i	$-0.980571\pi$
$997$		−	3.85222i		−	0.122001i	0.998138	−	0.0610006i	$-0.0194291\pi$
$998$	4.64683	+	0.928814i	0.147093	+	0.0294011i
$999$	−5.07196			−0.160470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.c.277.11	✓	18
4.3	odd	2		2208.2.f.c.1105.6		18
8.3	odd	2		2208.2.f.c.1105.13		18
8.5	even	2	inner	552.2.f.c.277.12	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.c.277.11	✓	18	1.1	even	1	trivial
552.2.f.c.277.12	yes	18	8.5	even	2	inner
2208.2.f.c.1105.6		18	4.3	odd	2
2208.2.f.c.1105.13		18	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.277192 - 1.38678i) q^{2} +1.00000i q^{3} +(-1.84633 - 0.768809i) q^{4} -0.208104i q^{5} +(1.38678 + 0.277192i) q^{6} +4.69627 q^{7} +(-1.57796 + 2.34735i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.277192 - 1.38678i) q^{2} +1.00000i q^{3} +(-1.84633 - 0.768809i) q^{4} -0.208104i q^{5} +(1.38678 + 0.277192i) q^{6} +4.69627 q^{7} +(-1.57796 + 2.34735i) q^{8} -1.00000 q^{9} +(-0.288595 - 0.0576846i) q^{10} +1.69179i q^{11} +(0.768809 - 1.84633i) q^{12} +3.50493i q^{13} +(1.30177 - 6.51270i) q^{14} +0.208104 q^{15} +(2.81787 + 2.83895i) q^{16} +2.65659 q^{17} +(-0.277192 + 1.38678i) q^{18} -4.27489i q^{19} +(-0.159992 + 0.384228i) q^{20} +4.69627i q^{21} +(2.34615 + 0.468950i) q^{22} -1.00000 q^{23} +(-2.34735 - 1.57796i) q^{24} +4.95669 q^{25} +(4.86057 + 0.971536i) q^{26} -1.00000i q^{27} +(-8.67085 - 3.61053i) q^{28} +0.234233i q^{29} +(0.0576846 - 0.288595i) q^{30} +5.11755 q^{31} +(4.71809 - 3.12083i) q^{32} -1.69179 q^{33} +(0.736385 - 3.68412i) q^{34} -0.977311i q^{35} +(1.84633 + 0.768809i) q^{36} -5.07196i q^{37} +(-5.92834 - 1.18496i) q^{38} -3.50493 q^{39} +(0.488493 + 0.328379i) q^{40} +3.40685 q^{41} +(6.51270 + 1.30177i) q^{42} -4.62494i q^{43} +(1.30066 - 3.12360i) q^{44} +0.208104i q^{45} +(-0.277192 + 1.38678i) q^{46} -7.19329 q^{47} +(-2.83895 + 2.81787i) q^{48} +15.0549 q^{49} +(1.37395 - 6.87385i) q^{50} +2.65659i q^{51} +(2.69462 - 6.47125i) q^{52} -2.32408i q^{53} +(-1.38678 - 0.277192i) q^{54} +0.352068 q^{55} +(-7.41051 + 11.0238i) q^{56} +4.27489 q^{57} +(0.324830 + 0.0649273i) q^{58} +11.3367i q^{59} +(-0.384228 - 0.159992i) q^{60} +2.23067i q^{61} +(1.41854 - 7.09693i) q^{62} -4.69627 q^{63} +(-3.02010 - 7.40804i) q^{64} +0.729389 q^{65} +(-0.468950 + 2.34615i) q^{66} +9.97750i q^{67} +(-4.90495 - 2.04241i) q^{68} -1.00000i q^{69} +(-1.35532 - 0.270902i) q^{70} -16.6616 q^{71} +(1.57796 - 2.34735i) q^{72} +2.02340 q^{73} +(-7.03370 - 1.40590i) q^{74} +4.95669i q^{75} +(-3.28657 + 7.89286i) q^{76} +7.94510i q^{77} +(-0.971536 + 4.86057i) q^{78} -16.4842 q^{79} +(0.590796 - 0.586409i) q^{80} +1.00000 q^{81} +(0.944350 - 4.72456i) q^{82} -4.16368i q^{83} +(3.61053 - 8.67085i) q^{84} -0.552847i q^{85} +(-6.41378 - 1.28199i) q^{86} -0.234233 q^{87} +(-3.97122 - 2.66957i) q^{88} -8.85665 q^{89} +(0.288595 + 0.0576846i) q^{90} +16.4601i q^{91} +(1.84633 + 0.768809i) q^{92} +5.11755i q^{93} +(-1.99392 + 9.97552i) q^{94} -0.889621 q^{95} +(3.12083 + 4.71809i) q^{96} -2.22788 q^{97} +(4.17309 - 20.8779i) q^{98} -1.69179i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

Introduction

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