LMFDB - Embedded newform 450.2.h.g.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (of order $5$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 6 x^{10} - 26 x^{9} + 61 x^{8} - 120 x^{7} + 465 x^{6} - 600 x^{5} + 1525 x^{4} + \cdots + 15625 $ x^12 - x^11 + 6x^10 - 26x^9 + 61x^8 - 120x^7 + 465x^6 - 600x^5 + 1525x^4 - 3250x^3 + 3750x^2 - 3125x + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$1.97131 + 1.05544i$ of defining polynomial
Character	$\chi$	$=$	450.91
Dual form			450.2.h.g.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.97131 - 1.05544i) q^{5} -5.04842 q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.97131 - 1.05544i) q^{5} -5.04842 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.974449 - 2.01257i) q^{10} +(-4.35193 - 3.16186i) q^{11} +(2.78032 - 2.02002i) q^{13} +(-4.08426 - 2.96739i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(1.15320 - 3.54919i) q^{17} +(-1.51156 + 4.65210i) q^{19} +(0.394615 - 2.20097i) q^{20} +(-1.66229 - 5.11600i) q^{22} +(-1.82772 - 1.32792i) q^{23} +(2.77210 + 4.16119i) q^{25} +3.43667 q^{26} +(-1.56005 - 4.80133i) q^{28} +(0.153872 + 0.473569i) q^{29} +(-2.05690 + 6.33050i) q^{31} -1.00000 q^{32} +(3.01912 - 2.19352i) q^{34} +(9.95198 + 5.32830i) q^{35} +(-0.558667 + 0.405896i) q^{37} +(-3.95731 + 2.87516i) q^{38} +(1.61295 - 1.54867i) q^{40} +(-9.12111 + 6.62688i) q^{41} +0.179186 q^{43} +(1.66229 - 5.11600i) q^{44} +(-0.698127 - 2.14861i) q^{46} +(-3.34708 - 10.3012i) q^{47} +18.4865 q^{49} +(-0.203212 + 4.99587i) q^{50} +(2.78032 + 2.02002i) q^{52} +(-0.526078 - 1.61910i) q^{53} +(5.24183 + 10.8262i) q^{55} +(1.56005 - 4.80133i) q^{56} +(-0.153872 + 0.473569i) q^{58} +(4.45949 - 3.24001i) q^{59} +(-8.55174 - 6.21320i) q^{61} +(-5.38505 + 3.91246i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-7.61288 + 1.04762i) q^{65} +(2.86319 - 8.81199i) q^{67} +3.73184 q^{68} +(4.91942 + 10.1603i) q^{70} +(1.15489 + 3.55439i) q^{71} +(-3.92773 - 2.85366i) q^{73} -0.690551 q^{74} -4.89151 q^{76} +(21.9704 + 15.9624i) q^{77} +(-2.52641 - 7.77549i) q^{79} +(2.21519 - 0.304836i) q^{80} -11.2743 q^{82} +(-3.72444 + 11.4626i) q^{83} +(-6.01927 + 5.77941i) q^{85} +(0.144965 + 0.105323i) q^{86} +(4.35193 - 3.16186i) q^{88} +(-1.89237 - 1.37488i) q^{89} +(-14.0362 + 10.1979i) q^{91} +(0.698127 - 2.14861i) q^{92} +(3.34708 - 10.3012i) q^{94} +(7.88976 - 7.57536i) q^{95} +(0.584325 + 1.79837i) q^{97} +(14.9559 + 10.8661i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8} + q^{10} - q^{11} + 4 q^{13} - 8 q^{14} - 3 q^{16} + 8 q^{17} - 8 q^{19} - q^{20} - 4 q^{22} - 11 q^{25} + 16 q^{26} - 7 q^{28} + 6 q^{29} - 3 q^{31} - 12 q^{32} + 2 q^{34} + 18 q^{35} - 8 q^{37} - 2 q^{38} + q^{40} - 20 q^{41} + 32 q^{43} + 4 q^{44} - 10 q^{46} + 34 q^{49} - 9 q^{50} + 4 q^{52} - 2 q^{53} + 44 q^{55} + 7 q^{56} - 6 q^{58} + 19 q^{59} - 26 q^{61} - 2 q^{62} - 3 q^{64} - 16 q^{65} - 16 q^{67} - 12 q^{68} - 23 q^{70} - 48 q^{71} - 30 q^{73} + 8 q^{74} + 12 q^{76} + 39 q^{77} - 18 q^{79} + 4 q^{80} - 40 q^{82} + 29 q^{83} - 4 q^{85} - 12 q^{86} + q^{88} - 62 q^{89} - 26 q^{91} + 10 q^{92} - 6 q^{95} + 23 q^{97} + 6 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8 + q^10 - q^11 + 4 * q^13 - 8 * q^14 - 3 * q^16 + 8 * q^17 - 8 * q^19 - q^20 - 4 * q^22 - 11 * q^25 + 16 * q^26 - 7 * q^28 + 6 * q^29 - 3 * q^31 - 12 * q^32 + 2 * q^34 + 18 * q^35 - 8 * q^37 - 2 * q^38 + q^40 - 20 * q^41 + 32 * q^43 + 4 * q^44 - 10 * q^46 + 34 * q^49 - 9 * q^50 + 4 * q^52 - 2 * q^53 + 44 * q^55 + 7 * q^56 - 6 * q^58 + 19 * q^59 - 26 * q^61 - 2 * q^62 - 3 * q^64 - 16 * q^65 - 16 * q^67 - 12 * q^68 - 23 * q^70 - 48 * q^71 - 30 * q^73 + 8 * q^74 + 12 * q^76 + 39 * q^77 - 18 * q^79 + 4 * q^80 - 40 * q^82 + 29 * q^83 - 4 * q^85 - 12 * q^86 + q^88 - 62 * q^89 - 26 * q^91 + 10 * q^92 - 6 * q^95 + 23 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.97131	−	1.05544i	−0.881595	−	0.472007i
$5$	−1.97131	−	1.05544i	−0.881595	−	0.472007i
$6$		0			0
$7$	−5.04842			−1.90812			−0.954061	−	0.299612i	$-0.903143\pi$
$7$	−5.04842			−1.90812			−0.954061	+	0.299612i	$0.903143\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$		0			0
$10$	−0.974449	−	2.01257i	−0.308148	−	0.636431i
$11$	−4.35193	−	3.16186i	−1.31216	−	0.953337i	−0.999995	−	0.00330824i	$-0.998947\pi$
$11$	−4.35193	−	3.16186i	−1.31216	−	0.953337i	−0.312162	−	0.950029i	$-0.601053\pi$
$12$		0			0
$13$	2.78032	−	2.02002i	0.771123	−	0.560254i	−0.131179	−	0.991359i	$-0.541876\pi$
$13$	2.78032	−	2.02002i	0.771123	−	0.560254i	0.902302	+	0.431105i	$0.141876\pi$
$14$	−4.08426	−	2.96739i	−1.09156	−	0.793067i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.15320	−	3.54919i	0.279693	−	0.860806i	−0.708247	−	0.705965i	$-0.750514\pi$
$17$	1.15320	−	3.54919i	0.279693	−	0.860806i	0.987939	−	0.154841i	$-0.0494865\pi$
$18$		0			0
$19$	−1.51156	+	4.65210i	−0.346776	+	1.06727i	0.613851	+	0.789422i	$0.289620\pi$
$19$	−1.51156	+	4.65210i	−0.346776	+	1.06727i	−0.960626	+	0.277843i	$0.910380\pi$
$20$	0.394615	−	2.20097i	0.0882386	−	0.492152i
$21$		0			0
$22$	−1.66229	−	5.11600i	−0.354401	−	1.09073i
$23$	−1.82772	−	1.32792i	−0.381106	−	0.276890i	0.380695	−	0.924701i	$-0.375685\pi$
$23$	−1.82772	−	1.32792i	−0.381106	−	0.276890i	−0.761801	+	0.647811i	$0.775685\pi$
$24$		0			0
$25$	2.77210	+	4.16119i	0.554419	+	0.832238i
$26$	3.43667			0.673986
$27$		0			0
$28$	−1.56005	−	4.80133i	−0.294821	−	0.907366i
$29$	0.153872	+	0.473569i	0.0285733	+	0.0879396i	0.964326	−	0.264717i	$-0.0852785\pi$
$29$	0.153872	+	0.473569i	0.0285733	+	0.0879396i	−0.935753	+	0.352656i	$0.885278\pi$
$30$		0			0
$31$	−2.05690	+	6.33050i	−0.369431	+	1.13699i	0.577729	+	0.816229i	$0.303939\pi$
$31$	−2.05690	+	6.33050i	−0.369431	+	1.13699i	−0.947160	+	0.320763i	$0.896061\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	3.01912	−	2.19352i	0.517776	−	0.376186i
$35$	9.95198	+	5.32830i	1.68219	+	0.900647i
$36$		0			0
$37$	−0.558667	+	0.405896i	−0.0918444	+	0.0667288i	−0.632760	−	0.774348i	$-0.718078\pi$
$37$	−0.558667	+	0.405896i	−0.0918444	+	0.0667288i	0.540915	+	0.841077i	$0.318078\pi$
$38$	−3.95731	+	2.87516i	−0.641961	+	0.466412i
$39$		0			0
$40$	1.61295	−	1.54867i	0.255030	−	0.244867i
$41$	−9.12111	+	6.62688i	−1.42448	+	1.03494i	−0.433467	+	0.901170i	$0.642710\pi$
$41$	−9.12111	+	6.62688i	−1.42448	+	1.03494i	−0.991012	+	0.133775i	$0.957290\pi$
$42$		0			0
$43$	0.179186			0.0273257			0.0136628	−	0.999907i	$-0.495651\pi$
$43$	0.179186			0.0273257			0.0136628	+	0.999907i	$0.495651\pi$
$44$	1.66229	−	5.11600i	0.250600	−	0.771266i
$45$		0			0
$46$	−0.698127	−	2.14861i	−0.102933	−	0.316796i
$47$	−3.34708	−	10.3012i	−0.488221	−	1.50259i	−0.827261	−	0.561818i	$-0.810102\pi$
$47$	−3.34708	−	10.3012i	−0.488221	−	1.50259i	0.339040	−	0.940772i	$-0.389898\pi$
$48$		0			0
$49$	18.4865			2.64093
$50$	−0.203212	+	4.99587i	−0.0287385	+	0.706523i
$51$		0			0
$52$	2.78032	+	2.02002i	0.385561	+	0.280127i
$53$	−0.526078	−	1.61910i	−0.0722624	−	0.222401i	0.908402	−	0.418098i	$-0.137303\pi$
$53$	−0.526078	−	1.61910i	−0.0722624	−	0.222401i	−0.980664	+	0.195697i	$0.937303\pi$
$54$		0			0
$55$	5.24183	+	10.8262i	0.706809	+	1.45980i
$56$	1.56005	−	4.80133i	0.208470	−	0.641605i
$57$		0			0
$58$	−0.153872	+	0.473569i	−0.0202044	+	0.0621827i
$59$	4.45949	−	3.24001i	0.580576	−	0.421813i	−0.258356	−	0.966050i	$-0.583181\pi$
$59$	4.45949	−	3.24001i	0.580576	−	0.421813i	0.838932	+	0.544237i	$0.183181\pi$
$60$		0			0
$61$	−8.55174	−	6.21320i	−1.09494	−	0.795519i	−0.114712	−	0.993399i	$-0.536594\pi$
$61$	−8.55174	−	6.21320i	−1.09494	−	0.795519i	−0.980226	+	0.197880i	$0.936594\pi$
$62$	−5.38505	+	3.91246i	−0.683901	+	0.496884i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−7.61288	+	1.04762i	−0.944262	+	0.129941i
$66$		0			0
$67$	2.86319	−	8.81199i	0.349794	−	1.07656i	−0.609173	−	0.793038i	$-0.708498\pi$
$67$	2.86319	−	8.81199i	0.349794	−	1.07656i	0.958967	−	0.283518i	$-0.0915016\pi$
$68$	3.73184			0.452552
$69$		0			0
$70$	4.91942	+	10.1603i	0.587984	+	1.21439i
$71$	1.15489	+	3.55439i	0.137060	+	0.421829i	0.995905	−	0.0904079i	$-0.0288171\pi$
$71$	1.15489	+	3.55439i	0.137060	+	0.421829i	−0.858844	+	0.512237i	$0.828817\pi$
$72$		0			0
$73$	−3.92773	−	2.85366i	−0.459706	−	0.333996i	0.333710	−	0.942676i	$-0.391699\pi$
$73$	−3.92773	−	2.85366i	−0.459706	−	0.333996i	−0.793416	+	0.608680i	$0.791699\pi$
$74$	−0.690551			−0.0802749
$75$		0			0
$76$	−4.89151			−0.561095
$77$	21.9704	+	15.9624i	2.50375	+	1.81908i
$78$		0			0
$79$	−2.52641	−	7.77549i	−0.284243	−	0.874811i	−0.986624	−	0.163010i	$-0.947880\pi$
$79$	−2.52641	−	7.77549i	−0.284243	−	0.874811i	0.702381	−	0.711801i	$-0.252120\pi$
$80$	2.21519	−	0.304836i	0.247666	−	0.0340818i
$81$		0			0
$82$	−11.2743			−1.24504
$83$	−3.72444	+	11.4626i	−0.408810	+	1.25819i	0.508861	+	0.860849i	$0.330067\pi$
$83$	−3.72444	+	11.4626i	−0.408810	+	1.25819i	−0.917671	+	0.397340i	$0.869933\pi$
$84$		0			0
$85$	−6.01927	+	5.77941i	−0.652882	+	0.626865i
$86$	0.144965	+	0.105323i	0.0156320	+	0.0113573i
$87$		0			0
$88$	4.35193	−	3.16186i	0.463917	−	0.337056i
$89$	−1.89237	−	1.37488i	−0.200590	−	0.145737i	0.482956	−	0.875645i	$-0.339563\pi$
$89$	−1.89237	−	1.37488i	−0.200590	−	0.145737i	−0.683546	+	0.729907i	$0.739563\pi$
$90$		0			0
$91$	−14.0362	+	10.1979i	−1.47140	+	1.06903i
$92$	0.698127	−	2.14861i	0.0727848	−	0.224009i
$93$		0			0
$94$	3.34708	−	10.3012i	0.345224	−	1.06249i
$95$	7.88976	−	7.57536i	0.809472	−	0.777215i
$96$		0			0
$97$	0.584325	+	1.79837i	0.0593292	+	0.182597i	0.976329	−	0.216292i	$-0.0693962\pi$
$97$	0.584325	+	1.79837i	0.0593292	+	0.182597i	−0.917000	+	0.398888i	$0.869396\pi$
$98$	14.9559	+	10.8661i	1.51077	+	1.09764i
$99$		0			0
$100$	−3.10090	+	3.92230i	−0.310090	+	0.392230i
$101$	4.35256			0.433096			0.216548	−	0.976272i	$-0.430520\pi$
$101$	4.35256			0.433096			0.216548	+	0.976272i	$0.430520\pi$
$102$		0			0
$103$	−1.11882	−	3.44339i	−0.110241	−	0.339287i	0.880684	−	0.473705i	$-0.157084\pi$
$103$	−1.11882	−	3.44339i	−0.110241	−	0.339287i	−0.990925	+	0.134418i	$0.957084\pi$
$104$	1.06199	+	3.26847i	0.104137	+	0.320499i
$105$		0			0
$106$	0.526078	−	1.61910i	0.0510972	−	0.157261i
$107$	5.39612			0.521662			0.260831	−	0.965384i	$-0.416003\pi$
$107$	5.39612			0.521662			0.260831	+	0.965384i	$0.416003\pi$
$108$		0			0
$109$	3.43929	−	2.49879i	0.329424	−	0.239341i	−0.410762	−	0.911743i	$-0.634737\pi$
$109$	3.43929	−	2.49879i	0.329424	−	0.239341i	0.740186	+	0.672402i	$0.234737\pi$
$110$	−2.12275	+	11.8396i	−0.202396	+	1.12887i
$111$		0			0
$112$	4.08426	−	2.96739i	0.385926	−	0.280392i
$113$	7.13157	−	5.18139i	0.670882	−	0.487424i	−0.199438	−	0.979910i	$-0.563912\pi$
$113$	7.13157	−	5.18139i	0.670882	−	0.487424i	0.870320	+	0.492486i	$0.163912\pi$
$114$		0			0
$115$	2.20146	+	4.54678i	0.205287	+	0.423989i
$116$	−0.402842	+	0.292682i	−0.0374030	+	0.0271748i
$117$		0			0
$118$	5.51223			0.507442
$119$	−5.82185	+	17.9178i	−0.533688	+	1.64252i
$120$		0			0
$121$	5.54273	+	17.0588i	0.503885	+	1.55080i
$122$	−3.26647	−	10.0532i	−0.295733	−	0.910171i
$123$		0			0
$124$	−6.65628			−0.597752
$125$	−1.07277	−	11.1288i	−0.0959515	−	0.995386i
$126$		0			0
$127$	−12.9407	−	9.40194i	−1.14830	−	0.834287i	−0.160044	−	0.987110i	$-0.551164\pi$
$127$	−12.9407	−	9.40194i	−1.14830	−	0.834287i	−0.988254	+	0.152823i	$0.951164\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$		0			0
$130$	−6.77473	−	3.62719i	−0.594183	−	0.318126i
$131$	0.617457	−	1.90034i	0.0539475	−	0.166033i	−0.920453	−	0.390854i	$-0.872180\pi$
$131$	0.617457	−	1.90034i	0.0539475	−	0.166033i	0.974400	+	0.224821i	$0.0721797\pi$
$132$		0			0
$133$	7.63098	−	23.4858i	0.661690	−	2.03647i
$134$	7.49592	−	5.44611i	0.647549	−	0.470472i
$135$		0			0
$136$	3.01912	+	2.19352i	0.258888	+	0.188093i
$137$	−1.19061	+	0.865029i	−0.101721	+	0.0739044i	−0.637483	−	0.770464i	$-0.720024\pi$
$137$	−1.19061	+	0.865029i	−0.101721	+	0.0739044i	0.535762	+	0.844369i	$0.320024\pi$
$138$		0			0
$139$	11.3373	+	8.23700i	0.961614	+	0.698654i	0.953525	−	0.301314i	$-0.0974251\pi$
$139$	11.3373	+	8.23700i	0.961614	+	0.698654i	0.00808914	+	0.999967i	$0.497425\pi$
$140$	−1.99218	+	11.1114i	−0.168370	+	0.939087i
$141$		0			0
$142$	−1.15489	+	3.55439i	−0.0969164	+	0.298278i
$143$	−18.4868			−1.54594
$144$		0			0
$145$	0.196495	−	1.09595i	0.0163180	−	0.0910139i
$146$	−1.50026	−	4.61732i	−0.124162	−	0.382133i
$147$		0			0
$148$	−0.558667	−	0.405896i	−0.0459222	−	0.0333644i
$149$	−1.86075			−0.152438			−0.0762191	−	0.997091i	$-0.524285\pi$
$149$	−1.86075			−0.152438			−0.0762191	+	0.997091i	$0.524285\pi$
$150$		0			0
$151$	−4.24990			−0.345852			−0.172926	−	0.984935i	$-0.555322\pi$
$151$	−4.24990			−0.345852			−0.172926	+	0.984935i	$0.555322\pi$
$152$	−3.95731	−	2.87516i	−0.320981	−	0.233206i
$153$		0			0
$154$	8.39193	+	25.8277i	0.676241	+	2.08126i
$155$	10.7362	−	10.3084i	0.862356	−	0.827992i
$156$		0			0
$157$	−9.94696			−0.793854			−0.396927	−	0.917850i	$-0.629923\pi$
$157$	−9.94696			−0.793854			−0.396927	+	0.917850i	$0.629923\pi$
$158$	2.52641	−	7.77549i	0.200990	−	0.618585i
$159$		0			0
$160$	1.97131	+	1.05544i	0.155845	+	0.0834398i
$161$	9.22710	+	6.70388i	0.727197	+	0.528340i
$162$		0			0
$163$	9.94101	−	7.22257i	0.778640	−	0.565715i	−0.125931	−	0.992039i	$-0.540192\pi$
$163$	9.94101	−	7.22257i	0.778640	−	0.565715i	0.904571	+	0.426324i	$0.140192\pi$
$164$	−9.12111	−	6.62688i	−0.712239	−	0.517472i
$165$		0			0
$166$	−9.75071	+	7.08430i	−0.756802	+	0.549849i
$167$	−3.06099	+	9.42075i	−0.236866	+	0.729000i	0.760002	+	0.649921i	$0.225198\pi$
$167$	−3.06099	+	9.42075i	−0.236866	+	0.729000i	−0.996868	+	0.0790789i	$0.974802\pi$
$168$		0			0
$169$	−0.367517	+	1.13110i	−0.0282705	+	0.0870078i
$170$	−8.26675	+	1.13760i	−0.634031	+	0.0872501i
$171$		0			0
$172$	0.0553716	+	0.170416i	0.00422205	+	0.0129941i
$173$	−14.5411	−	10.5647i	−1.10554	−	0.803221i	−0.123584	−	0.992334i	$-0.539439\pi$
$173$	−14.5411	−	10.5647i	−1.10554	−	0.803221i	−0.981955	+	0.189113i	$0.939439\pi$
$174$		0			0
$175$	−13.9947	−	21.0074i	−1.05790	−	1.58801i
$176$	5.37928			0.405479
$177$		0			0
$178$	−0.722819	−	2.22461i	−0.0541776	−	0.166741i
$179$	5.90754	+	18.1815i	0.441550	+	1.35895i	0.886223	+	0.463258i	$0.153320\pi$
$179$	5.90754	+	18.1815i	0.441550	+	1.35895i	−0.444673	+	0.895693i	$0.646680\pi$
$180$		0			0
$181$	4.58467	−	14.1102i	0.340776	−	1.04880i	−0.623031	−	0.782197i	$-0.714099\pi$
$181$	4.58467	−	14.1102i	0.340776	−	1.04880i	0.963807	−	0.266603i	$-0.0859011\pi$
$182$	−17.3497			−1.28605
$183$		0			0
$184$	1.82772	−	1.32792i	0.134741	−	0.0978953i
$185$	1.52970	−	0.210505i	0.112466	−	0.0154766i
$186$		0			0
$187$	−16.2407	+	11.7996i	−1.18764	+	0.862870i
$188$	8.76276	−	6.36652i	0.639090	−	0.464326i
$189$		0			0
$190$	10.8356	−	1.49111i	0.786099	−	0.108177i
$191$	−10.9557	+	7.95979i	−0.792727	+	0.575950i	−0.908772	−	0.417294i	$-0.862979\pi$
$191$	−10.9557	+	7.95979i	−0.792727	+	0.575950i	0.116044	+	0.993244i	$0.462979\pi$
$192$		0			0
$193$	6.41975			0.462104			0.231052	−	0.972941i	$-0.425783\pi$
$193$	6.41975			0.462104			0.231052	+	0.972941i	$0.425783\pi$
$194$	−0.584325	+	1.79837i	−0.0419521	+	0.129115i
$195$		0			0
$196$	5.71265	+	17.5817i	0.408046	+	1.25584i
$197$	1.57748	+	4.85499i	0.112391	+	0.345904i	0.991394	−	0.130913i	$-0.0417907\pi$
$197$	1.57748	+	4.85499i	0.112391	+	0.345904i	−0.879003	+	0.476816i	$0.841791\pi$
$198$		0			0
$199$	−10.3015			−0.730256			−0.365128	−	0.930957i	$-0.618975\pi$
$199$	−10.3015			−0.730256			−0.365128	+	0.930957i	$0.618975\pi$
$200$	−4.81415	+	1.35054i	−0.340412	+	0.0954978i
$201$		0			0
$202$	3.52130	+	2.55837i	0.247758	+	0.180006i
$203$	−0.776810	−	2.39078i	−0.0545214	−	0.167800i
$204$		0			0
$205$	24.9748	−	3.43682i	1.74431	−	0.240038i
$206$	1.11882	−	3.44339i	0.0779522	−	0.239912i
$207$		0			0
$208$	−1.06199	+	3.26847i	−0.0736357	+	0.226627i
$209$	21.2875	−	15.4663i	1.47249	−	1.06982i
$210$		0			0
$211$	2.11381	+	1.53577i	0.145521	+	0.105727i	0.658164	−	0.752875i	$-0.271334\pi$
$211$	2.11381	+	1.53577i	0.145521	+	0.105727i	−0.512643	+	0.858602i	$0.671334\pi$
$212$	1.37729	−	1.00066i	0.0945927	−	0.0687256i
$213$		0			0
$214$	4.36555	+	3.17176i	0.298423	+	0.216817i
$215$	−0.353231	−	0.189120i	−0.0240902	−	0.0128979i
$216$		0			0
$217$	10.3841	−	31.9590i	0.704919	−	2.16952i
$218$	4.25120			0.287927
$219$		0			0
$220$	−8.67651	+	8.33076i	−0.584970	+	0.561660i
$221$	−3.96318	−	12.1974i	−0.266592	−	0.820486i
$222$		0			0
$223$	−1.70751	−	1.24058i	−0.114344	−	0.0830755i	0.529144	−	0.848532i	$-0.322513\pi$
$223$	−1.70751	−	1.24058i	−0.114344	−	0.0830755i	−0.643488	+	0.765457i	$0.722513\pi$
$224$	5.04842			0.337312
$225$		0			0
$226$	8.81511			0.586372
$227$	−13.3453	−	9.69595i	−0.885760	−	0.643543i	0.0490087	−	0.998798i	$-0.484394\pi$
$227$	−13.3453	−	9.69595i	−0.885760	−	0.643543i	−0.934769	+	0.355256i	$0.884394\pi$
$228$		0			0
$229$	−4.31369	−	13.2762i	−0.285057	−	0.877315i	−0.986382	−	0.164473i	$-0.947408\pi$
$229$	−4.31369	−	13.2762i	−0.285057	−	0.877315i	0.701325	−	0.712842i	$-0.252592\pi$
$230$	−0.891510	+	4.97241i	−0.0587844	+	0.327871i
$231$		0			0
$232$	−0.497940			−0.0326914
$233$	8.63840	−	26.5863i	0.565920	−	1.74172i	−0.0992806	−	0.995059i	$-0.531654\pi$
$233$	8.63840	−	26.5863i	0.565920	−	1.74172i	0.665201	−	0.746664i	$-0.268346\pi$
$234$		0			0
$235$	−4.27422	+	23.8395i	−0.278819	+	1.55512i
$236$	4.45949	+	3.24001i	0.290288	+	0.210906i
$237$		0			0
$238$	−15.2418	+	11.0738i	−0.987979	+	0.717809i
$239$	−14.6357	−	10.6334i	−0.946704	−	0.687821i	0.00332110	−	0.999994i	$-0.498943\pi$
$239$	−14.6357	−	10.6334i	−0.946704	−	0.687821i	−0.950025	+	0.312174i	$0.898943\pi$
$240$		0			0
$241$	7.57117	−	5.50078i	0.487702	−	0.354336i	−0.316598	−	0.948560i	$-0.602541\pi$
$241$	7.57117	−	5.50078i	0.487702	−	0.354336i	0.804300	+	0.594224i	$0.202541\pi$
$242$	−5.54273	+	17.0588i	−0.356300	+	1.09658i
$243$		0			0
$244$	3.26647	−	10.0532i	0.209115	−	0.643588i
$245$	−36.4426	−	19.5114i	−2.32823	−	1.24654i
$246$		0			0
$247$	5.19473	+	15.9877i	0.330533	+	1.01728i
$248$	−5.38505	−	3.91246i	−0.341951	−	0.248442i
$249$		0			0
$250$	5.67343	−	9.63391i	0.358819	−	0.609302i
$251$	−7.00938			−0.442428			−0.221214	−	0.975225i	$-0.571002\pi$
$251$	−7.00938			−0.442428			−0.221214	+	0.975225i	$0.571002\pi$
$252$		0			0
$253$	3.75542	+	11.5580i	0.236101	+	0.726645i
$254$	−4.94289	−	15.2127i	−0.310145	−	0.954527i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−23.4992			−1.46584			−0.732920	−	0.680314i	$-0.761843\pi$
$257$	−23.4992			−1.46584			−0.732920	+	0.680314i	$0.761843\pi$
$258$		0			0
$259$	2.82039	−	2.04913i	0.175250	−	0.127327i
$260$	−3.34886	−	6.91655i	−0.207687	−	0.428946i
$261$		0			0
$262$	1.61652	−	1.17447i	0.0998692	−	0.0725592i
$263$	−0.591653	+	0.429861i	−0.0364829	+	0.0265064i	−0.605877	−	0.795558i	$-0.707178\pi$
$263$	−0.591653	+	0.429861i	−0.0364829	+	0.0265064i	0.569394	+	0.822064i	$0.307178\pi$
$264$		0			0
$265$	−0.671803	+	3.74699i	−0.0412685	+	0.230176i
$266$	19.9782	−	14.5150i	1.22494	−	0.889971i
$267$		0			0
$268$	9.26547			0.565979
$269$	−7.37942	+	22.7115i	−0.449931	+	1.38475i	0.427053	+	0.904227i	$0.359552\pi$
$269$	−7.37942	+	22.7115i	−0.449931	+	1.38475i	−0.876984	+	0.480519i	$0.840448\pi$
$270$		0			0
$271$	−7.45801	−	22.9534i	−0.453042	−	1.39432i	−0.873419	−	0.486970i	$-0.838102\pi$
$271$	−7.45801	−	22.9534i	−0.453042	−	1.39432i	0.420377	−	0.907350i	$-0.361898\pi$
$272$	1.15320	+	3.54919i	0.0699232	+	0.215201i
$273$		0			0
$274$	−1.47168			−0.0889072
$275$	1.09313	−	26.8742i	0.0659184	−	1.62057i
$276$		0			0
$277$	11.7921	+	8.56743i	0.708516	+	0.514767i	0.882694	−	0.469947i	$-0.155727\pi$
$277$	11.7921	+	8.56743i	0.708516	+	0.514767i	−0.174179	+	0.984714i	$0.555727\pi$
$278$	4.33045	+	13.3278i	0.259723	+	0.799346i
$279$		0			0
$280$	−8.14284	+	7.81836i	−0.486628	+	0.467236i
$281$	−5.96598	+	18.3614i	−0.355900	+	1.09535i	0.599585	+	0.800311i	$0.295332\pi$
$281$	−5.96598	+	18.3614i	−0.355900	+	1.09535i	−0.955486	+	0.295038i	$0.904668\pi$
$282$		0			0
$283$	−4.57079	+	14.0675i	−0.271706	+	0.836224i	0.718367	+	0.695665i	$0.244890\pi$
$283$	−4.57079	+	14.0675i	−0.271706	+	0.836224i	−0.990072	+	0.140559i	$0.955110\pi$
$284$	−3.02355	+	2.19674i	−0.179414	+	0.130352i
$285$		0			0
$286$	−14.9561	−	10.8663i	−0.884375	−	0.642536i
$287$	46.0472	−	33.4552i	2.71808	−	1.97480i
$288$		0			0
$289$	2.48639	+	1.80647i	0.146258	+	0.106263i
$290$	0.803153	−	0.771148i	0.0471627	−	0.0452834i
$291$		0			0
$292$	1.50026	−	4.61732i	0.0877961	−	0.270209i
$293$	2.44668			0.142936			0.0714682	−	0.997443i	$-0.477232\pi$
$293$	2.44668			0.142936			0.0714682	+	0.997443i	$0.477232\pi$
$294$		0			0
$295$	−12.2106	+	1.68033i	−0.710931	+	0.0978325i
$296$	−0.213392	−	0.656753i	−0.0124032	−	0.0381730i
$297$		0			0
$298$	−1.50537	−	1.09372i	−0.0872040	−	0.0633574i
$299$	−7.76408			−0.449008
$300$		0			0
$301$	−0.904607			−0.0521407
$302$	−3.43824	−	2.49803i	−0.197848	−	0.143745i
$303$		0			0
$304$	−1.51156	−	4.65210i	−0.0866939	−	0.266816i
$305$	10.3004	+	21.2740i	0.589801	+	1.21814i
$306$		0			0
$307$	7.54067			0.430369			0.215184	−	0.976573i	$-0.430965\pi$
$307$	7.54067			0.430369			0.215184	+	0.976573i	$0.430965\pi$
$308$	−8.39193	+	25.8277i	−0.478175	+	1.47167i
$309$		0			0
$310$	14.7449	−	2.02908i	0.837456	−	0.115244i
$311$	−8.41518	−	6.11399i	−0.477181	−	0.346692i	0.323052	−	0.946381i	$-0.395291\pi$
$311$	−8.41518	−	6.11399i	−0.477181	−	0.346692i	−0.800233	+	0.599689i	$0.795291\pi$
$312$		0			0
$313$	−16.3066	+	11.8474i	−0.921701	+	0.669655i	−0.943947	−	0.330097i	$-0.892918\pi$
$313$	−16.3066	+	11.8474i	−0.921701	+	0.669655i	0.0222457	+	0.999753i	$0.492918\pi$
$314$	−8.04726	−	5.84667i	−0.454133	−	0.329947i
$315$		0			0
$316$	6.61423	−	4.80552i	0.372079	−	0.270332i
$317$	−8.23461	+	25.3435i	−0.462502	+	1.42343i	0.399595	+	0.916692i	$0.369151\pi$
$317$	−8.23461	+	25.3435i	−0.462502	+	1.42343i	−0.862097	+	0.506743i	$0.830849\pi$
$318$		0			0
$319$	0.827721	−	2.54746i	0.0463435	−	0.142631i
$320$	0.974449	+	2.01257i	0.0544733	+	0.112506i
$321$		0			0
$322$	3.52444	+	10.8471i	0.196409	+	0.604485i
$323$	14.7681	+	10.7296i	0.821718	+	0.597013i
$324$		0			0
$325$	16.1130	+	5.96975i	0.893789	+	0.331142i
$326$	12.2878			0.680556
$327$		0			0
$328$	−3.48396	−	10.7225i	−0.192369	−	0.592052i
$329$	16.8974	+	52.0050i	0.931586	+	2.86713i
$330$		0			0
$331$	2.63714	−	8.11628i	0.144950	−	0.446111i	−0.852054	−	0.523453i	$-0.824643\pi$
$331$	2.63714	−	8.11628i	0.144950	−	0.446111i	0.997005	+	0.0773422i	$0.0246434\pi$
$332$	−12.0525			−0.661469
$333$		0			0
$334$	−8.01377	+	5.82234i	−0.438494	+	0.318584i
$335$	−14.9447	+	14.3492i	−0.816518	+	0.783981i
$336$		0			0
$337$	6.62011	−	4.80979i	0.360620	−	0.262006i	−0.392691	−	0.919671i	$-0.628456\pi$
$337$	6.62011	−	4.80979i	0.360620	−	0.262006i	0.753311	+	0.657665i	$0.228456\pi$
$338$	−0.962172	+	0.699059i	−0.0523353	+	0.0380238i
$339$		0			0
$340$	−7.35660	−	3.93873i	−0.398968	−	0.213608i
$341$	28.9677	−	21.0462i	1.56869	−	1.13972i
$342$		0			0
$343$	−57.9888			−3.13110
$344$	−0.0553716	+	0.170416i	−0.00298544	+	0.00918823i
$345$		0			0
$346$	−5.55421	−	17.0941i	−0.298596	−	0.918984i
$347$	0.524395	+	1.61392i	0.0281510	+	0.0866398i	0.964145	−	0.265376i	$-0.0854962\pi$
$347$	0.524395	+	1.61392i	0.0281510	+	0.0866398i	−0.935994	+	0.352016i	$0.885496\pi$
$348$		0			0
$349$	−19.6009			−1.04921			−0.524605	−	0.851346i	$-0.675787\pi$
$349$	−19.6009			−1.04921			−0.524605	+	0.851346i	$0.675787\pi$
$350$	1.02590	−	25.2212i	0.0548366	−	1.34813i
$351$		0			0
$352$	4.35193	+	3.16186i	0.231959	+	0.168528i
$353$	−9.55334	−	29.4021i	−0.508473	−	1.56492i	−0.794853	−	0.606802i	$-0.792452\pi$
$353$	−9.55334	−	29.4021i	−0.508473	−	1.56492i	0.286380	−	0.958116i	$-0.407548\pi$
$354$		0			0
$355$	1.47480	−	8.22571i	0.0782742	−	0.436576i
$356$	0.722819	−	2.22461i	0.0383093	−	0.117904i
$357$		0			0
$358$	−5.90754	+	18.1815i	−0.312223	+	0.960923i
$359$	16.5150	−	11.9988i	0.871627	−	0.633274i	−0.0593962	−	0.998234i	$-0.518918\pi$
$359$	16.5150	−	11.9988i	0.871627	−	0.633274i	0.931023	+	0.364961i	$0.118918\pi$
$360$		0			0
$361$	−3.98592	−	2.89594i	−0.209785	−	0.152418i
$362$	12.0028	−	8.72056i	0.630854	−	0.458342i
$363$		0			0
$364$	−14.0362	−	10.1979i	−0.735698	−	0.534516i
$365$	4.73089	+	9.77093i	0.247626	+	0.511434i
$366$		0			0
$367$	0.617756	−	1.90126i	0.0322466	−	0.0992448i	−0.933638	−	0.358218i	$-0.883384\pi$
$367$	0.617756	−	1.90126i	0.0322466	−	0.0992448i	0.965884	+	0.258974i	$0.0833843\pi$
$368$	2.25919			0.117768
$369$		0			0
$370$	1.36129	+	0.728834i	0.0707700	+	0.0378903i
$371$	2.65586	+	8.17391i	0.137886	+	0.424368i
$372$		0			0
$373$	17.9488	+	13.0405i	0.929352	+	0.675214i	0.945834	−	0.324650i	$-0.105247\pi$
$373$	17.9488	+	13.0405i	0.929352	+	0.675214i	−0.0164820	+	0.999864i	$0.505247\pi$
$374$	−20.0746			−1.03803
$375$		0			0
$376$	10.8314			0.558585
$377$	1.38444	+	1.00585i	0.0713020	+	0.0518040i
$378$		0			0
$379$	2.46397	+	7.58332i	0.126566	+	0.389529i	0.994183	−	0.107703i	$-0.0343497\pi$
$379$	2.46397	+	7.58332i	0.126566	+	0.389529i	−0.867617	+	0.497232i	$0.834350\pi$
$380$	9.64266	+	5.16269i	0.494658	+	0.264840i
$381$		0			0
$382$	−13.5420			−0.692869
$383$	1.48546	−	4.57179i	0.0759036	−	0.233607i	−0.905905	−	0.423481i	$-0.860808\pi$
$383$	1.48546	−	4.57179i	0.0759036	−	0.233607i	0.981808	+	0.189874i	$0.0608079\pi$
$384$		0			0
$385$	−26.4630	−	54.6552i	−1.34868	−	2.78548i
$386$	5.19369	+	3.77344i	0.264352	+	0.192063i
$387$		0			0
$388$	−1.52978	+	1.11145i	−0.0776630	+	0.0564255i
$389$	−5.32641	−	3.86987i	−0.270060	−	0.196210i	0.444510	−	0.895774i	$-0.353378\pi$
$389$	−5.32641	−	3.86987i	−0.270060	−	0.196210i	−0.714570	+	0.699564i	$0.753378\pi$
$390$		0			0
$391$	−6.82077	+	4.95558i	−0.344941	+	0.250614i
$392$	−5.71265	+	17.5817i	−0.288532	+	0.888011i
$393$		0			0
$394$	−1.57748	+	4.85499i	−0.0794724	+	0.244591i
$395$	−3.22623	+	17.9944i	−0.162329	+	0.905394i
$396$		0			0
$397$	2.42206	+	7.45433i	0.121560	+	0.374122i	0.993259	−	0.115920i	$-0.0369815\pi$
$397$	2.42206	+	7.45433i	0.121560	+	0.374122i	−0.871699	+	0.490042i	$0.836982\pi$
$398$	−8.33412	−	6.05509i	−0.417751	−	0.303514i
$399$		0			0
$400$	−4.68856	−	1.73707i	−0.234428	−	0.0868537i
$401$	−29.4295			−1.46964			−0.734820	−	0.678262i	$-0.762733\pi$
$401$	−29.4295			−1.46964			−0.734820	+	0.678262i	$0.762733\pi$
$402$		0			0
$403$	7.06890	+	21.7558i	0.352127	+	1.08374i
$404$	1.34502	+	4.13953i	0.0669170	+	0.205949i
$405$		0			0
$406$	0.776810	−	2.39078i	0.0385524	−	0.118652i
$407$	3.71467			0.184129
$408$		0			0
$409$	−8.24014	+	5.98681i	−0.407448	+	0.296029i	−0.772568	−	0.634932i	$-0.781028\pi$
$409$	−8.24014	+	5.98681i	−0.407448	+	0.296029i	0.365120	+	0.930961i	$0.381028\pi$
$410$	22.2251	+	11.8994i	1.09762	+	0.587667i
$411$		0			0
$412$	2.92912	−	2.12813i	0.144307	−	0.104846i
$413$	−22.5134	+	16.3569i	−1.10781	+	0.804871i
$414$		0			0
$415$	19.4401	−	18.6655i	0.954279	−	0.916251i
$416$	−2.78032	+	2.02002i	−0.136317	+	0.0990398i
$417$		0			0
$418$	26.3128			1.28700
$419$	1.79741	−	5.53185i	0.0878090	−	0.270248i	−0.897504	−	0.441006i	$-0.854622\pi$
$419$	1.79741	−	5.53185i	0.0878090	−	0.270248i	0.985313	+	0.170758i	$0.0546216\pi$
$420$		0			0
$421$	9.82013	+	30.2233i	0.478604	+	1.47299i	0.841035	+	0.540981i	$0.181947\pi$
$421$	9.82013	+	30.2233i	0.478604	+	1.47299i	−0.362431	+	0.932011i	$0.618053\pi$
$422$	0.807403	+	2.48493i	0.0393038	+	0.120965i
$423$		0			0
$424$	1.70243			0.0826771
$425$	17.9656	−	5.04001i	0.871462	−	0.244477i
$426$		0			0
$427$	43.1728	+	31.3668i	2.08928	+	1.51795i
$428$	1.66749	+	5.13201i	0.0806012	+	0.248065i
$429$		0			0
$430$	−0.174608	−	0.360626i	−0.00842034	−	0.0173909i
$431$	−9.77737	+	30.0916i	−0.470959	+	1.44946i	0.380371	+	0.924834i	$0.375796\pi$
$431$	−9.77737	+	30.0916i	−0.470959	+	1.44946i	−0.851331	+	0.524630i	$0.824204\pi$
$432$		0			0
$433$	−1.96383	+	6.04403i	−0.0943754	+	0.290458i	−0.987090	−	0.160164i	$-0.948798\pi$
$433$	−1.96383	+	6.04403i	−0.0943754	+	0.290458i	0.892715	+	0.450622i	$0.148798\pi$
$434$	27.1860	−	19.7518i	1.30497	−	0.948115i
$435$		0			0
$436$	3.43929	+	2.49879i	0.164712	+	0.119670i
$437$	8.94031	−	6.49552i	0.427673	−	0.310723i
$438$		0			0
$439$	−5.20060	−	3.77846i	−0.248211	−	0.180336i	0.456722	−	0.889609i	$-0.349023\pi$
$439$	−5.20060	−	3.77846i	−0.248211	−	0.180336i	−0.704934	+	0.709273i	$0.749023\pi$
$440$	−11.9161	+	1.63980i	−0.568080	+	0.0781744i
$441$		0			0
$442$	3.96318	−	12.1974i	0.188509	−	0.580171i
$443$	39.0619			1.85589			0.927943	−	0.372722i	$-0.121575\pi$
$443$	39.0619			1.85589			0.927943	+	0.372722i	$0.121575\pi$
$444$		0			0
$445$	2.27933	+	4.70759i	0.108050	+	0.223161i
$446$	−0.652212	−	2.00730i	−0.0308832	−	0.0950486i
$447$		0			0
$448$	4.08426	+	2.96739i	0.192963	+	0.140196i
$449$	38.7204			1.82733			0.913665	−	0.406468i	$-0.133240\pi$
$449$	38.7204			1.82733			0.913665	+	0.406468i	$0.133240\pi$
$450$		0			0
$451$	60.6477			2.85579
$452$	7.13157	+	5.18139i	0.335441	+	0.243712i
$453$		0			0
$454$	−5.09746	−	15.6884i	−0.239236	−	0.736292i
$455$	38.4330	−	5.28883i	1.80177	−	0.247944i
$456$		0			0
$457$	−14.0405			−0.656786			−0.328393	−	0.944541i	$-0.606507\pi$
$457$	−14.0405			−0.656786			−0.328393	+	0.944541i	$0.606507\pi$
$458$	4.31369	−	13.2762i	0.201566	−	0.620355i
$459$		0			0
$460$	−3.64395	+	3.49875i	−0.169900	+	0.163130i
$461$	25.3277	+	18.4017i	1.17963	+	0.857051i	0.992130	−	0.125214i	$-0.0399617\pi$
$461$	25.3277	+	18.4017i	1.17963	+	0.857051i	0.187500	+	0.982265i	$0.439962\pi$
$462$		0			0
$463$	31.6931	−	23.0264i	1.47290	−	1.07013i	0.493143	−	0.869948i	$-0.335848\pi$
$463$	31.6931	−	23.0264i	1.47290	−	1.07013i	0.979759	−	0.200179i	$-0.0641522\pi$
$464$	−0.402842	−	0.292682i	−0.0187015	−	0.0135874i
$465$		0			0
$466$	22.6156	−	16.4312i	1.04765	−	0.761161i
$467$	−5.72675	+	17.6251i	−0.265002	+	0.815593i	0.726691	+	0.686965i	$0.241057\pi$
$467$	−5.72675	+	17.6251i	−0.265002	+	0.815593i	−0.991693	+	0.128628i	$0.958943\pi$
$468$		0			0
$469$	−14.4546	+	44.4866i	−0.667450	+	2.05420i
$470$	−17.4704	+	16.7743i	−0.805851	+	0.773739i
$471$		0			0
$472$	1.70337	+	5.24244i	0.0784041	+	0.241303i
$473$	−0.779806	−	0.566562i	−0.0358555	−	0.0260506i
$474$		0			0
$475$	−23.5485	+	6.60619i	−1.08048	+	0.303113i
$476$	−18.8399			−0.863525
$477$		0			0
$478$	−5.59033	−	17.2053i	−0.255696	−	0.786951i
$479$	−1.36218	−	4.19235i	−0.0622395	−	0.191554i	0.915102	−	0.403223i	$-0.132110\pi$
$479$	−1.36218	−	4.19235i	−0.0622395	−	0.191554i	−0.977341	+	0.211669i	$0.932110\pi$
$480$		0			0
$481$	−0.733357	+	2.25704i	−0.0334382	+	0.102912i
$482$	9.35848			0.426267
$483$		0			0
$484$	−14.5111	+	10.5429i	−0.659594	+	0.479223i
$485$	0.746184	−	4.16185i	0.0338825	−	0.188980i
$486$		0			0
$487$	5.98983	−	4.35187i	0.271425	−	0.197202i	−0.443743	−	0.896154i	$-0.646350\pi$
$487$	5.98983	−	4.35187i	0.271425	−	0.197202i	0.715169	+	0.698952i	$0.246350\pi$
$488$	8.55174	−	6.21320i	0.387119	−	0.281258i
$489$		0			0
$490$	−18.0142	−	37.2055i	−0.813797	−	1.68077i
$491$	−17.8506	+	12.9692i	−0.805585	+	0.585292i	−0.912547	−	0.408971i	$-0.865888\pi$
$491$	−17.8506	+	12.9692i	−0.805585	+	0.585292i	0.106962	+	0.994263i	$0.465888\pi$
$492$		0			0
$493$	1.85824			0.0836907
$494$	−5.19473	+	15.9877i	−0.233722	+	0.719322i
$495$		0			0
$496$	−2.05690	−	6.33050i	−0.0923577	−	0.284248i
$497$	−5.83038	−	17.9441i	−0.261528	−	0.804901i
$498$		0			0
$499$	−18.3376			−0.820906			−0.410453	−	0.911882i	$-0.634629\pi$
$499$	−18.3376			−0.820906			−0.410453	+	0.911882i	$0.634629\pi$
$500$	10.2526	−	4.45924i	0.458509	−	0.199423i
$501$		0			0
$502$	−5.67071	−	4.12001i	−0.253096	−	0.183885i
$503$	7.20450	+	22.1732i	0.321233	+	0.988653i	0.973113	+	0.230330i	$0.0739807\pi$
$503$	7.20450	+	22.1732i	0.321233	+	0.988653i	−0.651880	+	0.758322i	$0.726019\pi$
$504$		0			0
$505$	−8.58023	−	4.59386i	−0.381815	−	0.204424i
$506$	−3.75542	+	11.5580i	−0.166949	+	0.513816i
$507$		0			0
$508$	4.94289	−	15.2127i	0.219305	−	0.674952i
$509$	8.63861	−	6.27632i	0.382900	−	0.278193i	−0.379640	−	0.925134i	$-0.623952\pi$
$509$	8.63861	−	6.27632i	0.382900	−	0.278193i	0.762540	+	0.646941i	$0.223952\pi$
$510$		0			0
$511$	19.8288	+	14.4065i	0.877176	+	0.637305i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$		0			0
$514$	−19.0113	−	13.8125i	−0.838551	−	0.609243i
$515$	−1.42874	+	7.96883i	−0.0629579	+	0.351148i
$516$		0			0
$517$	−18.0049	+	55.4133i	−0.791853	+	2.43707i
$518$	3.48619			0.153174
$519$		0			0
$520$	1.35616	−	7.56401i	0.0594716	−	0.331704i
$521$	−6.93220	−	21.3351i	−0.303705	−	0.934708i	−0.980157	−	0.198222i	$-0.936483\pi$
$521$	−6.93220	−	21.3351i	−0.303705	−	0.934708i	0.676452	−	0.736487i	$-0.263517\pi$
$522$		0			0
$523$	17.0349	+	12.3766i	0.744885	+	0.541190i	0.894237	−	0.447594i	$-0.147719\pi$
$523$	17.0349	+	12.3766i	0.744885	+	0.541190i	−0.149353	+	0.988784i	$0.547719\pi$
$524$	1.99813			0.0872889
$525$		0			0
$526$	−0.731323			−0.0318872
$527$	20.0961	+	14.6007i	0.875402	+	0.636017i
$528$		0			0
$529$	−5.53019	−	17.0202i	−0.240443	−	0.740008i
$530$	−2.74593	+	2.63650i	−0.119275	+	0.114522i
$531$		0			0
$532$	24.6944			1.07064
$533$	−11.9732	+	36.8497i	−0.518617	+	1.59614i
$534$		0			0
$535$	−10.6374	−	5.69527i	−0.459895	−	0.246228i
$536$	7.49592	+	5.44611i	0.323775	+	0.235236i
$537$		0			0
$538$	−19.3196	+	14.0365i	−0.832926	+	0.605156i
$539$	−80.4520	−	58.4518i	−3.46531	−	2.51770i
$540$		0			0
$541$	22.5520	−	16.3850i	0.969585	−	0.704445i	0.0142281	−	0.999899i	$-0.495471\pi$
$541$	22.5520	−	16.3850i	0.969585	−	0.704445i	0.955357	+	0.295454i	$0.0954709\pi$
$542$	7.45801	−	22.9534i	0.320349	−	0.985933i
$543$		0			0
$544$	−1.15320	+	3.54919i	−0.0494432	+	0.152170i
$545$	−9.41722	+	1.29592i	−0.403389	+	0.0555111i
$546$		0			0
$547$	−2.96355	−	9.12088i	−0.126712	−	0.389981i	0.867497	−	0.497443i	$-0.165728\pi$
$547$	−2.96355	−	9.12088i	−0.126712	−	0.389981i	−0.994209	+	0.107462i	$0.965728\pi$
$548$	−1.19061	−	0.865029i	−0.0508604	−	0.0369522i
$549$		0			0
$550$	16.6806	−	21.0991i	0.711264	−	0.899670i
$551$	−2.43568			−0.103763
$552$		0			0
$553$	12.7544	+	39.2539i	0.542371	+	1.66925i
$554$	4.50416	+	13.8624i	0.191364	+	0.588956i
$555$		0			0
$556$	−4.33045	+	13.3278i	−0.183652	+	0.565223i
$557$	−14.0946			−0.597209			−0.298605	−	0.954377i	$-0.596521\pi$
$557$	−14.0946			−0.597209			−0.298605	+	0.954377i	$0.596521\pi$
$558$		0			0
$559$	0.498196	−	0.361961i	0.0210714	−	0.0153093i
$560$	−11.1832	+	1.53894i	−0.472577	+	0.0650322i
$561$		0			0
$562$	−15.6191	+	11.3480i	−0.658853	+	0.478685i
$563$	−13.9439	+	10.1308i	−0.587665	+	0.426964i	−0.841479	−	0.540289i	$-0.818315\pi$
$563$	−13.9439	+	10.1308i	−0.587665	+	0.426964i	0.253814	+	0.967253i	$0.418315\pi$
$564$		0			0
$565$	−19.5272	+	2.68717i	−0.821514	+	0.113050i
$566$	−11.9665	+	8.69417i	−0.502989	+	0.365443i
$567$		0			0
$568$	−3.73731			−0.156814
$569$	−3.08527	+	9.49547i	−0.129341	+	0.398071i	−0.994667	−	0.103139i	$-0.967111\pi$
$569$	−3.08527	+	9.49547i	−0.129341	+	0.398071i	0.865326	+	0.501210i	$0.167111\pi$
$570$		0			0
$571$	−7.81343	−	24.0473i	−0.326982	−	1.00635i	−0.970538	−	0.240948i	$-0.922542\pi$
$571$	−7.81343	−	24.0473i	−0.326982	−	1.00635i	0.643556	−	0.765399i	$-0.277458\pi$
$572$	−5.71274	−	17.5820i	−0.238862	−	0.735140i
$573$		0			0
$574$	56.9175			2.37569
$575$	0.459093	−	11.2866i	0.0191455	−	0.470684i
$576$		0			0
$577$	1.02493	+	0.744656i	0.0426684	+	0.0310004i	0.608915	−	0.793235i	$-0.291605\pi$
$577$	1.02493	+	0.744656i	0.0426684	+	0.0310004i	−0.566247	+	0.824236i	$0.691605\pi$
$578$	0.949717	+	2.92293i	0.0395030	+	0.121578i
$579$		0			0
$580$	1.10303	−	0.151790i	0.0458010	−	0.00630275i
$581$	18.8025	−	57.8682i	0.780060	−	2.40078i
$582$		0			0
$583$	−2.82992	+	8.70961i	−0.117203	+	0.360715i
$584$	3.92773	−	2.85366i	0.162531	−	0.118085i
$585$		0			0
$586$	1.97940	+	1.43812i	0.0817684	+	0.0594082i
$587$	14.9350	−	10.8509i	0.616434	−	0.447865i	−0.235240	−	0.971937i	$-0.575588\pi$
$587$	14.9350	−	10.8509i	0.616434	−	0.447865i	0.851674	+	0.524072i	$0.175588\pi$
$588$		0			0
$589$	−26.3410	−	19.1379i	−1.08536	−	0.788562i
$590$	−10.8663	−	5.81782i	−0.447358	−	0.239516i
$591$		0			0
$592$	0.213392	−	0.656753i	0.00877036	−	0.0269924i
$593$	−43.8465			−1.80056			−0.900280	−	0.435311i	$-0.856639\pi$
$593$	−43.8465			−1.80056			−0.900280	+	0.435311i	$0.856639\pi$
$594$		0			0
$595$	30.3878	−	29.1769i	1.24578	−	1.19614i
$596$	−0.575002	−	1.76967i	−0.0235530	−	0.0724887i
$597$		0			0
$598$	−6.28127	−	4.56361i	−0.256860	−	0.186620i
$599$	−26.3560			−1.07688			−0.538439	−	0.842664i	$-0.680986\pi$
$599$	−26.3560			−1.07688			−0.538439	+	0.842664i	$0.680986\pi$
$600$		0			0
$601$	−20.2074			−0.824275			−0.412138	−	0.911122i	$-0.635218\pi$
$601$	−20.2074			−0.824275			−0.412138	+	0.911122i	$0.635218\pi$
$602$	−0.731843	−	0.531715i	−0.0298277	−	0.0216711i
$603$		0			0
$604$	−1.31329	−	4.04189i	−0.0534370	−	0.164462i
$605$	7.07808	−	39.4781i	0.287765	−	1.60501i
$606$		0			0
$607$	6.08369			0.246929			0.123465	−	0.992349i	$-0.460599\pi$
$607$	6.08369			0.246929			0.123465	+	0.992349i	$0.460599\pi$
$608$	1.51156	−	4.65210i	0.0613018	−	0.188668i
$609$		0			0
$610$	−4.17129	+	23.2654i	−0.168891	+	0.941990i
$611$	−30.1147	−	21.8796i	−1.21831	−	0.885154i
$612$		0			0
$613$	−22.6689	+	16.4699i	−0.915589	+	0.665214i	−0.942422	−	0.334426i	$-0.891458\pi$
$613$	−22.6689	+	16.4699i	−0.915589	+	0.665214i	0.0268331	+	0.999640i	$0.491458\pi$
$614$	6.10053	+	4.43229i	0.246197	+	0.178873i
$615$		0			0
$616$	−21.9704	+	15.9624i	−0.885211	+	0.643143i
$617$	−0.732565	+	2.25460i	−0.0294920	+	0.0907669i	−0.964719	−	0.263282i	$-0.915195\pi$
$617$	−0.732565	+	2.25460i	−0.0294920	+	0.0907669i	0.935227	+	0.354048i	$0.115195\pi$
$618$		0			0
$619$	0.116715	−	0.359213i	0.00469119	−	0.0144380i	−0.948684	−	0.316227i	$-0.897584\pi$
$619$	0.116715	−	0.359213i	0.00469119	−	0.0144380i	0.953375	+	0.301789i	$0.0975838\pi$
$620$	13.1216	+	7.02530i	0.526975	+	0.282143i
$621$		0			0
$622$	−3.21431	−	9.89264i	−0.128882	−	0.396659i
$623$	9.55345	+	6.94099i	0.382751	+	0.278085i
$624$		0			0
$625$	−9.63097	+	23.0704i	−0.385239	+	0.922817i
$626$	−20.1560			−0.805596
$627$		0			0
$628$	−3.07378	−	9.46012i	−0.122657	−	0.377500i
$629$	0.796345	+	2.45090i	0.0317524	+	0.0977237i
$630$		0			0
$631$	10.1538	−	31.2501i	0.404216	−	1.24405i	−0.517332	−	0.855785i	$-0.673075\pi$
$631$	10.1538	−	31.2501i	0.404216	−	1.24405i	0.921548	−	0.388264i	$-0.126925\pi$
$632$	8.17564			0.325209
$633$		0			0
$634$	−21.5585	+	15.6632i	−0.856197	+	0.622064i
$635$	15.5868	+	32.1922i	0.618544	+	1.27751i
$636$		0			0
$637$	51.3985	−	37.3432i	2.03648	−	1.47959i
$638$	2.16700	−	1.57442i	0.0857924	−	0.0623318i
$639$		0			0
$640$	−0.394615	+	2.20097i	−0.0155985	+	0.0870011i
$641$	34.3726	−	24.9731i	1.35764	−	0.986380i	0.359044	−	0.933321i	$-0.383103\pi$
$641$	34.3726	−	24.9731i	1.35764	−	0.986380i	0.998591	−	0.0530594i	$-0.0168973\pi$
$642$		0			0
$643$	1.70055			0.0670633			0.0335316	−	0.999438i	$-0.489325\pi$
$643$	1.70055			0.0670633			0.0335316	+	0.999438i	$0.489325\pi$
$644$	−3.52444	+	10.8471i	−0.138882	+	0.427436i
$645$		0			0
$646$	5.64090	+	17.3609i	0.221938	+	0.683056i
$647$	−10.6378	−	32.7399i	−0.418217	−	1.28714i	−0.909342	−	0.416050i	$-0.863414\pi$
$647$	−10.6378	−	32.7399i	−0.418217	−	1.28714i	0.491125	−	0.871089i	$-0.336586\pi$
$648$		0			0
$649$	−29.6518			−1.16394
$650$	9.52678	+	14.3006i	0.373671	+	0.560917i
$651$		0			0
$652$	9.94101	+	7.22257i	0.389320	+	0.282858i
$653$	2.57723	+	7.93189i	0.100855	+	0.310399i	0.988735	−	0.149675i	$-0.0478228\pi$
$653$	2.57723	+	7.93189i	0.100855	+	0.310399i	−0.887880	+	0.460074i	$0.847823\pi$
$654$		0			0
$655$	−3.22289	+	3.09446i	−0.125929	+	0.120911i
$656$	3.48396	−	10.7225i	0.136026	−	0.418644i
$657$		0			0
$658$	−16.8974	+	52.0050i	−0.658731	+	2.02736i
$659$	19.4275	−	14.1149i	0.756789	−	0.549839i	−0.141135	−	0.989990i	$-0.545075\pi$
$659$	19.4275	−	14.1149i	0.756789	−	0.549839i	0.897924	+	0.440151i	$0.145075\pi$
$660$		0			0
$661$	−32.3548	−	23.5071i	−1.25845	−	0.914321i	−0.259774	−	0.965669i	$-0.583648\pi$
$661$	−32.3548	−	23.5071i	−1.25845	−	0.914321i	−0.998681	+	0.0513486i	$0.983648\pi$
$662$	6.90412	−	5.01614i	0.268336	−	0.194958i
$663$		0			0
$664$	−9.75071	−	7.08430i	−0.378401	−	0.274924i
$665$	−39.8308	+	38.2436i	−1.54457	+	1.48302i
$666$		0			0
$667$	0.347626	−	1.06988i	0.0134601	−	0.0414260i
$668$	−9.90556			−0.383258
$669$		0			0
$670$	−20.5248	+	2.82445i	−0.792942	+	0.109118i
$671$	17.5713	+	54.0788i	0.678332	+	2.08769i
$672$		0			0
$673$	−38.2296	−	27.7754i	−1.47364	−	1.07066i	−0.979538	−	0.201260i	$-0.935496\pi$
$673$	−38.2296	−	27.7754i	−1.47364	−	1.07066i	−0.494104	−	0.869403i	$-0.664504\pi$
$674$	8.18290			0.315194
$675$		0			0
$676$	−1.18931			−0.0457427
$677$	24.4111	+	17.7357i	0.938194	+	0.681638i	0.947985	−	0.318314i	$-0.103117\pi$
$677$	24.4111	+	17.7357i	0.938194	+	0.681638i	−0.00979088	+	0.999952i	$0.503117\pi$
$678$		0			0
$679$	−2.94992	−	9.07891i	−0.113207	−	0.348417i
$680$	−3.63649	−	7.51061i	−0.139453	−	0.288019i
$681$		0			0
$682$	35.8060			1.37108
$683$	1.18283	−	3.64038i	0.0452598	−	0.139295i	−0.925873	−	0.377835i	$-0.876669\pi$
$683$	1.18283	−	3.64038i	0.0452598	−	0.139295i	0.971133	+	0.238540i	$0.0766687\pi$
$684$		0			0
$685$	3.26004	−	0.448620i	0.124560	−	0.0171409i
$686$	−46.9139	−	34.0849i	−1.79118	−	1.30137i
$687$		0			0
$688$	−0.144965	+	0.105323i	−0.00552673	+	0.00401541i
$689$	−4.73329	−	3.43894i	−0.180324	−	0.131013i
$690$		0			0
$691$	−14.0464	+	10.2053i	−0.534351	+	0.388229i	−0.821983	−	0.569512i	$-0.807132\pi$
$691$	−14.0464	+	10.2053i	−0.534351	+	0.388229i	0.287632	+	0.957741i	$0.407132\pi$
$692$	5.55421	−	17.0941i	0.211139	−	0.649820i
$693$		0			0
$694$	−0.524395	+	1.61392i	−0.0199058	+	0.0612636i
$695$	−13.6556	−	28.2035i	−0.517985	−	1.06982i
$696$		0			0
$697$	13.0016	+	40.0147i	0.492470	+	1.51567i
$698$	−15.8574	−	11.5211i	−0.600213	−	0.436080i
$699$		0			0
$700$	15.6546	−	19.8014i	0.591690	−	0.748422i
$701$	30.6938			1.15929			0.579644	−	0.814870i	$-0.303192\pi$
$701$	30.6938			1.15929			0.579644	+	0.814870i	$0.303192\pi$
$702$		0			0
$703$	−1.04381	−	3.21251i	−0.0393680	−	0.121162i
$704$	1.66229	+	5.11600i	0.0626499	+	0.192817i
$705$		0			0
$706$	9.55334	−	29.4021i	0.359545	−	1.10656i
$707$	−21.9736			−0.826400
$708$		0			0
$709$	38.3044	−	27.8297i	1.43855	−	1.04517i	0.450207	−	0.892924i	$-0.351350\pi$
$709$	38.3044	−	27.8297i	1.43855	−	1.04517i	0.988343	−	0.152244i	$-0.0486498\pi$
$710$	6.02809	−	5.78788i	0.226230	−	0.217215i
$711$		0			0
$712$	1.89237	−	1.37488i	0.0709194	−	0.0515260i
$713$	12.1658	−	8.83899i	0.455614	−	0.331023i
$714$		0			0
$715$	36.4432	+	19.5117i	1.36290	+	0.729696i
$716$	−15.4661	+	11.2368i	−0.577996	+	0.419939i
$717$		0			0
$718$	20.4136			0.761830
$719$	8.85041	−	27.2387i	0.330064	−	1.01583i	−0.639038	−	0.769175i	$-0.720667\pi$
$719$	8.85041	−	27.2387i	0.330064	−	1.01583i	0.969102	−	0.246659i	$-0.0793327\pi$
$720$		0			0
$721$	5.64830	+	17.3837i	0.210354	+	0.647402i
$722$	−1.52249	−	4.68573i	−0.0566610	−	0.174385i
$723$		0			0
$724$	14.8363			0.551387
$725$	−1.54406	+	1.95307i	−0.0573451	+	0.0725352i
$726$		0			0
$727$	3.72535	+	2.70662i	0.138166	+	0.100383i	0.654721	−	0.755870i	$-0.272786\pi$
$727$	3.72535	+	2.70662i	0.138166	+	0.100383i	−0.516556	+	0.856254i	$0.672786\pi$
$728$	−5.36136	−	16.5006i	−0.198705	−	0.611552i
$729$		0			0
$730$	−1.91583	+	10.6856i	−0.0709082	+	0.395492i
$731$	0.206638	−	0.635967i	0.00764279	−	0.0235221i
$732$		0			0
$733$	5.33453	−	16.4180i	0.197036	−	0.606413i	−0.802911	−	0.596099i	$-0.796717\pi$
$733$	5.33453	−	16.4180i	0.197036	−	0.606413i	0.999947	−	0.0103145i	$-0.00328325\pi$
$734$	1.61731	−	1.17504i	0.0596958	−	0.0433716i
$735$		0			0
$736$	1.82772	+	1.32792i	0.0673707	+	0.0489477i
$737$	−40.3227	+	29.2961i	−1.48531	+	1.07914i
$738$		0			0
$739$	12.3468	+	8.97048i	0.454184	+	0.329984i	0.791246	−	0.611498i	$-0.209433\pi$
$739$	12.3468	+	8.97048i	0.454184	+	0.329984i	−0.337061	+	0.941483i	$0.609433\pi$
$740$	0.672906	+	1.38978i	0.0247365	+	0.0510895i
$741$		0			0
$742$	−2.65586	+	8.17391i	−0.0974998	+	0.300074i
$743$	5.21102			0.191174			0.0955869	−	0.995421i	$-0.469527\pi$
$743$	5.21102			0.191174			0.0955869	+	0.995421i	$0.469527\pi$
$744$		0			0
$745$	3.66810	+	1.96390i	0.134389	+	0.0719518i
$746$	6.85582	+	21.1000i	0.251009	+	0.772528i
$747$		0			0
$748$	−16.2407	−	11.7996i	−0.593819	−	0.431435i
$749$	−27.2418			−0.995395
$750$		0			0
$751$	−30.8064			−1.12414			−0.562070	−	0.827090i	$-0.689995\pi$
$751$	−30.8064			−1.12414			−0.562070	+	0.827090i	$0.689995\pi$
$752$	8.76276	+	6.36652i	0.319545	+	0.232163i
$753$		0			0
$754$	0.528807	+	1.62750i	0.0192580	+	0.0592701i
$755$	8.37785	+	4.48551i	0.304901	+	0.163244i
$756$		0			0
$757$	−23.4137			−0.850985			−0.425492	−	0.904962i	$-0.639899\pi$
$757$	−23.4137			−0.850985			−0.425492	+	0.904962i	$0.639899\pi$
$758$	−2.46397	+	7.58332i	−0.0894954	+	0.275439i
$759$		0			0
$760$	4.76652	+	9.84452i	0.172900	+	0.357098i
$761$	−26.9935	−	19.6119i	−0.978514	−	0.710932i	−0.0211379	−	0.999777i	$-0.506729\pi$
$761$	−26.9935	−	19.6119i	−0.978514	−	0.710932i	−0.957376	+	0.288845i	$0.906729\pi$
$762$		0			0
$763$	−17.3630	+	12.6149i	−0.628582	+	0.456692i
$764$	−10.9557	−	7.95979i	−0.396364	−	0.287975i
$765$		0			0
$766$	3.88899	−	2.82552i	0.140515	−	0.102090i
$767$	5.85393	−	18.0165i	0.211373	−	0.650539i
$768$		0			0
$769$	12.1223	−	37.3087i	0.437142	−	1.34538i	−0.453734	−	0.891137i	$-0.649908\pi$
$769$	12.1223	−	37.3087i	0.437142	−	1.34538i	0.890876	−	0.454247i	$-0.150092\pi$
$770$	10.7165	−	59.7715i	0.386196	−	2.15401i
$771$		0			0
$772$	1.98381	+	6.10555i	0.0713990	+	0.219744i
$773$	−7.58903	−	5.51376i	−0.272959	−	0.198316i	0.442882	−	0.896580i	$-0.353956\pi$
$773$	−7.58903	−	5.51376i	−0.272959	−	0.198316i	−0.715840	+	0.698264i	$0.753956\pi$
$774$		0			0
$775$	−32.0443	+	8.98959i	−1.15107	+	0.322916i
$776$	−1.89092			−0.0678799
$777$		0			0
$778$	−2.03451	−	6.26157i	−0.0729407	−	0.224488i
$779$	−17.0418	−	52.4493i	−0.610586	−	1.87919i
$780$		0			0
$781$	6.21249	−	19.1201i	0.222300	−	0.684170i
$782$	−8.43093			−0.301489
$783$		0			0
$784$	−14.9559	+	10.8661i	−0.534140	+	0.388075i
$785$	19.6085	+	10.4984i	0.699857	+	0.374704i
$786$		0			0
$787$	−5.32633	+	3.86981i	−0.189863	+	0.137944i	−0.678656	−	0.734456i	$-0.737437\pi$
$787$	−5.32633	+	3.86981i	−0.189863	+	0.137944i	0.488793	+	0.872400i	$0.337437\pi$
$788$	−4.12990	+	3.00055i	−0.147122	+	0.106890i
$789$		0			0
$790$	−13.1869	+	12.6614i	−0.469168	+	0.450473i
$791$	−36.0032	+	26.1578i	−1.28012	+	0.930065i
$792$		0			0
$793$	−36.3274			−1.29002
$794$	−2.42206	+	7.45433i	−0.0859557	+	0.264544i
$795$		0			0
$796$	−3.18335	−	9.79734i	−0.112831	−	0.347258i
$797$	−3.44128	−	10.5912i	−0.121896	−	0.375158i	0.871427	−	0.490526i	$-0.163195\pi$
$797$	−3.44128	−	10.5912i	−0.121896	−	0.375158i	−0.993323	+	0.115368i	$0.963195\pi$
$798$		0			0
$799$	−40.4209			−1.42999
$800$	−2.77210	−	4.16119i	−0.0980084	−	0.147120i
$801$		0			0
$802$	−23.8090	−	17.2982i	−0.840724	−	0.610822i
$803$	8.07032	+	24.8379i	0.284795	+	0.876510i
$804$		0			0
$805$	−11.1139	−	22.9540i	−0.391713	−	0.809024i
$806$	−7.06890	+	21.7558i	−0.248991	+	0.766317i
$807$		0			0
$808$	−1.34502	+	4.13953i	−0.0473175	+	0.145628i
$809$	27.7387	−	20.1533i	0.975241	−	0.708554i	0.0186007	−	0.999827i	$-0.494079\pi$
$809$	27.7387	−	20.1533i	0.975241	−	0.708554i	0.956640	+	0.291273i	$0.0940789\pi$
$810$		0			0
$811$	37.0793	+	26.9397i	1.30203	+	0.945980i	0.999973	−	0.00731019i	$-0.00232693\pi$
$811$	37.0793	+	26.9397i	1.30203	+	0.945980i	0.302056	+	0.953290i	$0.402327\pi$
$812$	2.03372	−	1.47758i	0.0713694	−	0.0518529i
$813$		0			0
$814$	3.00523	+	2.18343i	0.105333	+	0.0765291i
$815$	−27.2198	+	3.74576i	−0.953466	+	0.131208i
$816$		0			0
$817$	−0.270851	+	0.833593i	−0.00947587	+	0.0291637i
$818$	−10.1854			−0.356123
$819$		0			0
$820$	10.9862	+	22.6904i	0.383656	+	0.792383i
$821$	2.49186	+	7.66917i	0.0869667	+	0.267656i	0.985077	−	0.172114i	$-0.0550599\pi$
$821$	2.49186	+	7.66917i	0.0869667	+	0.267656i	−0.898110	+	0.439770i	$0.855060\pi$
$822$		0			0
$823$	19.7737	+	14.3664i	0.689267	+	0.500782i	0.876419	−	0.481549i	$-0.159926\pi$
$823$	19.7737	+	14.3664i	0.689267	+	0.500782i	−0.187152	+	0.982331i	$0.559926\pi$
$824$	3.62059			0.126129
$825$		0			0
$826$	−27.8280			−0.968261
$827$	14.2534	+	10.3557i	0.495641	+	0.360104i	0.807349	−	0.590074i	$-0.200901\pi$
$827$	14.2534	+	10.3557i	0.495641	+	0.360104i	−0.311709	+	0.950178i	$0.600901\pi$
$828$		0			0
$829$	15.9374	+	49.0502i	0.553528	+	1.70358i	0.699800	+	0.714338i	$0.253272\pi$
$829$	15.9374	+	49.0502i	0.553528	+	1.70358i	−0.146273	+	0.989244i	$0.546728\pi$
$830$	26.6987	−	3.67405i	0.926725	−	0.127528i
$831$		0			0
$832$	−3.43667			−0.119145
$833$	21.3187	−	65.6122i	0.738649	−	2.27333i
$834$		0			0
$835$	15.9772	−	15.3405i	0.552913	−	0.530880i
$836$	21.2875	+	15.4663i	0.736244	+	0.534912i
$837$		0			0
$838$	4.70567	−	3.41887i	0.162555	−	0.118103i
$839$	36.0522	+	26.1935i	1.24466	+	0.904298i	0.997900	−	0.0647781i	$-0.0206340\pi$
$839$	36.0522	+	26.1935i	1.24466	+	0.904298i	0.246760	+	0.969077i	$0.420634\pi$
$840$		0			0
$841$	23.2609	−	16.9000i	0.802100	−	0.582760i
$842$	−9.82013	+	30.2233i	−0.338424	+	1.04156i
$843$		0			0
$844$	−0.807403	+	2.48493i	−0.0277920	+	0.0855349i
$845$	1.91830	−	1.84185i	0.0659914	−	0.0633617i
$846$		0			0
$847$	−27.9820	−	86.1198i	−0.961474	−	2.95911i
$848$	1.37729	+	1.00066i	0.0472964	+	0.0343628i
$849$		0			0
$850$	17.4970	+	6.48249i	0.600141	+	0.222348i
$851$	1.56008			0.0534790
$852$		0			0
$853$	9.80437	+	30.1747i	0.335695	+	1.03316i	0.966379	+	0.257123i	$0.0827746\pi$
$853$	9.80437	+	30.1747i	0.335695	+	1.03316i	−0.630683	+	0.776040i	$0.717225\pi$
$854$	16.4905	+	50.7526i	0.564294	+	1.73672i
$855$		0			0
$856$	−1.66749	+	5.13201i	−0.0569937	+	0.175409i
$857$	−42.8506			−1.46375			−0.731874	−	0.681440i	$-0.761354\pi$
$857$	−42.8506			−1.46375			−0.731874	+	0.681440i	$0.761354\pi$
$858$		0			0
$859$	26.0964	−	18.9602i	0.890399	−	0.646912i	−0.0455834	−	0.998961i	$-0.514515\pi$
$859$	26.0964	−	18.9602i	0.890399	−	0.646912i	0.935982	+	0.352048i	$0.114515\pi$
$860$	0.0707097	−	0.394384i	0.00241118	−	0.0134484i
$861$		0			0
$862$	−25.5975	+	18.5977i	−0.871854	+	0.633439i
$863$	4.38976	−	3.18935i	0.149429	−	0.108567i	−0.510559	−	0.859843i	$-0.670561\pi$
$863$	4.38976	−	3.18935i	0.149429	−	0.108567i	0.659988	+	0.751276i	$0.270561\pi$
$864$		0			0
$865$	17.5145	+	36.1736i	0.595512	+	1.22994i
$866$	−5.14136	+	3.73542i	−0.174711	+	0.126935i
$867$		0			0
$868$	33.6037			1.14058
$869$	−13.5903	+	41.8266i	−0.461018	+	1.41887i
$870$		0			0
$871$	−9.83983	−	30.2839i	−0.333410	−	1.02613i
$872$	1.31369	+	4.04313i	0.0444872	+	0.136918i
$873$		0			0
$874$	11.0508			0.373800
$875$	5.41579	+	56.1826i	0.183087	+	1.89932i
$876$		0			0
$877$	−42.5102	−	30.8855i	−1.43547	−	1.04293i	−0.988965	−	0.148147i	$-0.952669\pi$
$877$	−42.5102	−	30.8855i	−1.43547	−	1.04293i	−0.446503	−	0.894782i	$-0.647331\pi$
$878$	−1.98645	−	6.11368i	−0.0670396	−	0.206327i
$879$		0			0
$880$	−10.6042	−	5.67750i	−0.357468	−	0.191389i
$881$	3.81610	−	11.7448i	0.128568	−	0.395691i	−0.865966	−	0.500102i	$-0.833296\pi$
$881$	3.81610	−	11.7448i	0.128568	−	0.395691i	0.994534	+	0.104411i	$0.0332958\pi$
$882$		0			0
$883$	15.2451	−	46.9197i	0.513040	−	1.57897i	−0.273781	−	0.961792i	$-0.588274\pi$
$883$	15.2451	−	46.9197i	0.513040	−	1.57897i	0.786821	−	0.617182i	$-0.211726\pi$
$884$	10.3757	−	7.53841i	0.348974	−	0.253544i
$885$		0			0
$886$	31.6017	+	22.9600i	1.06168	+	0.771356i
$887$	−10.3174	+	7.49602i	−0.346424	+	0.251692i	−0.747367	−	0.664411i	$-0.768682\pi$
$887$	−10.3174	+	7.49602i	−0.346424	+	0.251692i	0.400943	+	0.916103i	$0.368682\pi$
$888$		0			0
$889$	65.3298	+	47.4649i	2.19109	+	1.59192i
$890$	−0.923041	+	5.14828i	−0.0309404	+	0.172571i
$891$		0			0
$892$	0.652212	−	2.00730i	0.0218377	−	0.0672095i
$893$	52.9817			1.77297
$894$		0			0
$895$	7.54393	−	42.0764i	0.252166	−	1.40646i
$896$	1.56005	+	4.80133i	0.0521175	+	0.160401i
$897$		0			0
$898$	31.3255	+	22.7593i	1.04534	+	0.759487i
$899$	−3.31443			−0.110542
$900$		0			0
$901$	−6.35318			−0.211655
$902$	49.0650	+	35.6478i	1.63369	+	1.18694i
$903$		0			0
$904$	2.72402	+	8.38367i	0.0905995	+	0.278837i
$905$	−23.9302	+	22.9766i	−0.795467	+	0.763768i
$906$		0			0
$907$	34.0967			1.13216			0.566082	−	0.824349i	$-0.308459\pi$
$907$	34.0967			1.13216			0.566082	+	0.824349i	$0.308459\pi$
$908$	5.09746	−	15.6884i	0.169165	−	0.520637i
$909$		0			0
$910$	34.2016	+	18.3116i	1.13377	+	0.607023i
$911$	16.4225	+	11.9316i	0.544100	+	0.395312i	0.825606	−	0.564248i	$-0.190834\pi$
$911$	16.4225	+	11.9316i	0.544100	+	0.395312i	−0.281505	+	0.959560i	$0.590834\pi$
$912$		0			0
$913$	52.4518	−	38.1085i	1.73590	−	1.26121i
$914$	−11.3590	−	8.25279i	−0.375722	−	0.272978i
$915$		0			0
$916$	11.2934	−	8.20513i	0.373144	−	0.271105i
$917$	−3.11718	+	9.59370i	−0.102938	+	0.316812i
$918$		0			0
$919$	3.96344	−	12.1982i	0.130742	−	0.402382i	−0.864162	−	0.503214i	$-0.832151\pi$
$919$	3.96344	−	12.1982i	0.130742	−	0.402382i	0.994903	+	0.100833i	$0.0321507\pi$
$920$	−5.00453	+	0.688683i	−0.164995	+	0.0227052i
$921$		0			0
$922$	9.67433	+	29.7745i	0.318607	+	0.980571i
$923$	10.3909	+	7.54945i	0.342022	+	0.248493i
$924$		0			0
$925$	−3.23769	−	1.19954i	−0.106455	−	0.0394406i
$926$	39.1748			1.28736
$927$		0			0
$928$	−0.153872	−	0.473569i	−0.00505110	−	0.0155457i
$929$	8.92328	+	27.4630i	0.292763	+	0.901033i	0.983964	+	0.178370i	$0.0570823\pi$
$929$	8.92328	+	27.4630i	0.292763	+	0.901033i	−0.691200	+	0.722663i	$0.742918\pi$
$930$		0			0
$931$	−27.9435	+	86.0012i	−0.915810	+	2.81857i
$932$	27.9544			0.915678
$933$		0			0
$934$	−14.9928	+	10.8929i	−0.490580	+	0.356427i
$935$	44.4692	−	6.11948i	1.45430	−	0.200128i
$936$		0			0
$937$	−44.2904	+	32.1789i	−1.44690	+	1.05124i	−0.460363	+	0.887731i	$0.652281\pi$
$937$	−44.2904	+	32.1789i	−1.44690	+	1.05124i	−0.986542	+	0.163507i	$0.947719\pi$
$938$	−37.8426	+	27.4942i	−1.23560	+	0.897718i
$939$		0			0
$940$	−23.9935	+	3.30179i	−0.782583	+	0.107693i
$941$	10.6128	−	7.71063i	0.345967	−	0.251359i	−0.401208	−	0.915987i	$-0.631410\pi$
$941$	10.6128	−	7.71063i	0.345967	−	0.251359i	0.747175	+	0.664627i	$0.231410\pi$
$942$		0			0
$943$	25.4708			0.829443
$944$	−1.70337	+	5.24244i	−0.0554400	+	0.170627i
$945$		0			0
$946$	−0.297860	−	0.916717i	−0.00968425	−	0.0298051i
$947$	−17.7342	−	54.5802i	−0.576283	−	1.77362i	−0.631767	−	0.775158i	$-0.717670\pi$
$947$	−17.7342	−	54.5802i	−0.576283	−	1.77362i	0.0554842	−	0.998460i	$-0.482330\pi$
$948$		0			0
$949$	−16.6848			−0.541612
$950$	−22.9341	−	8.49692i	−0.744081	−	0.275676i
$951$		0			0
$952$	−15.2418	−	11.0738i	−0.493990	−	0.358904i
$953$	9.86978	+	30.3761i	0.319713	+	0.983977i	0.973771	+	0.227532i	$0.0730655\pi$
$953$	9.86978	+	30.3761i	0.319713	+	0.983977i	−0.654057	+	0.756445i	$0.726934\pi$
$954$		0			0
$955$	29.9981	−	4.12810i	0.970717	−	0.133582i
$956$	5.59033	−	17.2053i	0.180804	−	0.556459i
$957$		0			0
$958$	1.36218	−	4.19235i	0.0440100	−	0.135449i
$959$	6.01070	−	4.36703i	0.194096	−	0.141019i
$960$		0			0
$961$	−10.7649	−	7.82113i	−0.347253	−	0.252294i
$962$	−1.91995	+	1.39493i	−0.0619018	+	0.0449743i
$963$		0			0
$964$	7.57117	+	5.50078i	0.243851	+	0.177168i
$965$	−12.6553	−	6.77566i	−0.407389	−	0.218116i
$966$		0			0
$967$	3.12337	−	9.61274i	0.100441	−	0.309125i	−0.888193	−	0.459471i	$-0.848039\pi$
$967$	3.12337	−	9.61274i	0.100441	−	0.309125i	0.988633	+	0.150346i	$0.0480389\pi$
$968$	−17.9367			−0.576506
$969$		0			0
$970$	3.04995	−	2.92841i	0.0979281	−	0.0940257i
$971$	−8.57960	−	26.4053i	−0.275333	−	0.847386i	−0.989131	−	0.147036i	$-0.953027\pi$
$971$	−8.57960	−	26.4053i	−0.275333	−	0.847386i	0.713799	−	0.700351i	$-0.246973\pi$
$972$		0			0
$973$	−57.2352	−	41.5838i	−1.83488	−	1.33312i
$974$	7.40384			0.237234
$975$		0			0
$976$	10.5705			0.338354
$977$	17.9779	+	13.0617i	0.575165	+	0.417882i	0.836978	−	0.547237i	$-0.184320\pi$
$977$	17.9779	+	13.0617i	0.575165	+	0.417882i	−0.261813	+	0.965119i	$0.584320\pi$
$978$		0			0
$979$	3.88825	+	11.9668i	0.124269	+	0.382460i
$980$	7.29506	−	40.6883i	0.233032	−	1.29974i
$981$		0			0
$982$	−22.0645			−0.704107
$983$	−14.0395	+	43.2090i	−0.447789	+	1.37815i	0.431606	+	0.902062i	$0.357947\pi$
$983$	−14.0395	+	43.2090i	−0.447789	+	1.37815i	−0.879396	+	0.476092i	$0.842053\pi$
$984$		0			0
$985$	2.01445	−	11.2356i	0.0641856	−	0.357996i
$986$	1.50334	+	1.09224i	0.0478762	+	0.0347841i
$987$		0			0
$988$	−13.6000	+	9.88096i	−0.432673	+	0.314355i
$989$	−0.327503	−	0.237945i	−0.0104140	−	0.00756620i
$990$		0			0
$991$	12.5332	−	9.10592i	0.398131	−	0.289259i	−0.370648	−	0.928773i	$-0.620864\pi$
$991$	12.5332	−	9.10592i	0.398131	−	0.289259i	0.768779	+	0.639514i	$0.220864\pi$
$992$	2.05690	−	6.33050i	0.0653068	−	0.200994i
$993$		0			0
$994$	5.83038	−	17.9441i	0.184928	−	0.569151i
$995$	20.3075	+	10.8726i	0.643790	+	0.344686i
$996$		0			0
$997$	−6.66765	−	20.5209i	−0.211167	−	0.649904i	−0.999404	−	0.0345322i	$-0.989006\pi$
$997$	−6.66765	−	20.5209i	−0.211167	−	0.649904i	0.788237	−	0.615372i	$-0.210994\pi$
$998$	−14.8355	−	10.7786i	−0.469608	−	0.341191i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.g.91.1	yes	12
3.2	odd	2		450.2.h.f.91.3	✓	12
25.11	even	5	inner	450.2.h.g.361.1	yes	12
75.11	odd	10		450.2.h.f.361.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.h.f.91.3	✓	12	3.2	odd	2
450.2.h.f.361.3	yes	12	75.11	odd	10
450.2.h.g.91.1	yes	12	1.1	even	1	trivial
450.2.h.g.361.1	yes	12	25.11	even	5	inner

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.97131 - 1.05544i) q^{5} -5.04842 q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.97131 - 1.05544i) q^{5} -5.04842 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.974449 - 2.01257i) q^{10} +(-4.35193 - 3.16186i) q^{11} +(2.78032 - 2.02002i) q^{13} +(-4.08426 - 2.96739i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(1.15320 - 3.54919i) q^{17} +(-1.51156 + 4.65210i) q^{19} +(0.394615 - 2.20097i) q^{20} +(-1.66229 - 5.11600i) q^{22} +(-1.82772 - 1.32792i) q^{23} +(2.77210 + 4.16119i) q^{25} +3.43667 q^{26} +(-1.56005 - 4.80133i) q^{28} +(0.153872 + 0.473569i) q^{29} +(-2.05690 + 6.33050i) q^{31} -1.00000 q^{32} +(3.01912 - 2.19352i) q^{34} +(9.95198 + 5.32830i) q^{35} +(-0.558667 + 0.405896i) q^{37} +(-3.95731 + 2.87516i) q^{38} +(1.61295 - 1.54867i) q^{40} +(-9.12111 + 6.62688i) q^{41} +0.179186 q^{43} +(1.66229 - 5.11600i) q^{44} +(-0.698127 - 2.14861i) q^{46} +(-3.34708 - 10.3012i) q^{47} +18.4865 q^{49} +(-0.203212 + 4.99587i) q^{50} +(2.78032 + 2.02002i) q^{52} +(-0.526078 - 1.61910i) q^{53} +(5.24183 + 10.8262i) q^{55} +(1.56005 - 4.80133i) q^{56} +(-0.153872 + 0.473569i) q^{58} +(4.45949 - 3.24001i) q^{59} +(-8.55174 - 6.21320i) q^{61} +(-5.38505 + 3.91246i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-7.61288 + 1.04762i) q^{65} +(2.86319 - 8.81199i) q^{67} +3.73184 q^{68} +(4.91942 + 10.1603i) q^{70} +(1.15489 + 3.55439i) q^{71} +(-3.92773 - 2.85366i) q^{73} -0.690551 q^{74} -4.89151 q^{76} +(21.9704 + 15.9624i) q^{77} +(-2.52641 - 7.77549i) q^{79} +(2.21519 - 0.304836i) q^{80} -11.2743 q^{82} +(-3.72444 + 11.4626i) q^{83} +(-6.01927 + 5.77941i) q^{85} +(0.144965 + 0.105323i) q^{86} +(4.35193 - 3.16186i) q^{88} +(-1.89237 - 1.37488i) q^{89} +(-14.0362 + 10.1979i) q^{91} +(0.698127 - 2.14861i) q^{92} +(3.34708 - 10.3012i) q^{94} +(7.88976 - 7.57536i) q^{95} +(0.584325 + 1.79837i) q^{97} +(14.9559 + 10.8661i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8} + q^{10} - q^{11} + 4 q^{13} - 8 q^{14} - 3 q^{16} + 8 q^{17} - 8 q^{19} - q^{20} - 4 q^{22} - 11 q^{25} + 16 q^{26} - 7 q^{28} + 6 q^{29} - 3 q^{31} - 12 q^{32} + 2 q^{34} + 18 q^{35} - 8 q^{37} - 2 q^{38} + q^{40} - 20 q^{41} + 32 q^{43} + 4 q^{44} - 10 q^{46} + 34 q^{49} - 9 q^{50} + 4 q^{52} - 2 q^{53} + 44 q^{55} + 7 q^{56} - 6 q^{58} + 19 q^{59} - 26 q^{61} - 2 q^{62} - 3 q^{64} - 16 q^{65} - 16 q^{67} - 12 q^{68} - 23 q^{70} - 48 q^{71} - 30 q^{73} + 8 q^{74} + 12 q^{76} + 39 q^{77} - 18 q^{79} + 4 q^{80} - 40 q^{82} + 29 q^{83} - 4 q^{85} - 12 q^{86} + q^{88} - 62 q^{89} - 26 q^{91} + 10 q^{92} - 6 q^{95} + 23 q^{97} + 6 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8 + q^10 - q^11 + 4 * q^13 - 8 * q^14 - 3 * q^16 + 8 * q^17 - 8 * q^19 - q^20 - 4 * q^22 - 11 * q^25 + 16 * q^26 - 7 * q^28 + 6 * q^29 - 3 * q^31 - 12 * q^32 + 2 * q^34 + 18 * q^35 - 8 * q^37 - 2 * q^38 + q^40 - 20 * q^41 + 32 * q^43 + 4 * q^44 - 10 * q^46 + 34 * q^49 - 9 * q^50 + 4 * q^52 - 2 * q^53 + 44 * q^55 + 7 * q^56 - 6 * q^58 + 19 * q^59 - 26 * q^61 - 2 * q^62 - 3 * q^64 - 16 * q^65 - 16 * q^67 - 12 * q^68 - 23 * q^70 - 48 * q^71 - 30 * q^73 + 8 * q^74 + 12 * q^76 + 39 * q^77 - 18 * q^79 + 4 * q^80 - 40 * q^82 + 29 * q^83 - 4 * q^85 - 12 * q^86 + q^88 - 62 * q^89 - 26 * q^91 + 10 * q^92 - 6 * q^95 + 23 * q^97 + 6 * q^98

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