LMFDB - Embedded newform 450.2.h.f.181.1

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			181.1
Root			$-1.24741 - 1.85579i$ of defining polynomial
Character	$\chi$	$=$	450.181
Dual form			450.2.h.f.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-1.24741 - 1.85579i) q^{5} -2.68284 q^{7} +(-0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-1.24741 - 1.85579i) q^{5} -2.68284 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.37949 - 1.75983i) q^{10} +(-0.167451 - 0.515361i) q^{11} +(-1.55643 + 4.79019i) q^{13} +(-0.829042 - 2.55153i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-6.22521 - 4.52288i) q^{17} +(-5.05944 - 3.67590i) q^{19} +(2.09998 + 0.768160i) q^{20} +(0.438392 - 0.318511i) q^{22} +(-1.50887 - 4.64382i) q^{23} +(-1.88794 + 4.62987i) q^{25} -5.03670 q^{26} +(2.17046 - 1.57693i) q^{28} +(4.62991 - 3.36383i) q^{29} +(2.53838 + 1.84424i) q^{31} +1.00000 q^{32} +(2.37782 - 7.31818i) q^{34} +(3.34660 + 4.97879i) q^{35} +(-1.07737 + 3.31581i) q^{37} +(1.93253 - 5.94772i) q^{38} +(-0.0816329 + 2.23458i) q^{40} +(-1.70564 + 5.24942i) q^{41} +12.9002 q^{43} +(0.438392 + 0.318511i) q^{44} +(3.95027 - 2.87004i) q^{46} +(-1.41338 + 1.02688i) q^{47} +0.197613 q^{49} +(-4.98667 - 0.364830i) q^{50} +(-1.55643 - 4.79019i) q^{52} +(-8.24147 + 5.98778i) q^{53} +(-0.747524 + 0.953620i) q^{55} +(2.17046 + 1.57693i) q^{56} +(4.62991 + 3.36383i) q^{58} +(-0.245881 + 0.756745i) q^{59} +(-0.530688 - 1.63329i) q^{61} +(-0.969573 + 2.98404i) q^{62} +(0.309017 + 0.951057i) q^{64} +(10.8311 - 3.08692i) q^{65} +(-11.0177 - 8.00483i) q^{67} +7.69479 q^{68} +(-3.70096 + 4.72133i) q^{70} +(6.99463 - 5.08190i) q^{71} +(0.402106 + 1.23755i) q^{73} -3.48645 q^{74} +6.25381 q^{76} +(0.449244 + 1.38263i) q^{77} +(2.61562 - 1.90036i) q^{79} +(-2.15044 + 0.612885i) q^{80} -5.51957 q^{82} +(0.617229 + 0.448443i) q^{83} +(-0.628147 + 17.1946i) q^{85} +(3.98637 + 12.2688i) q^{86} +(-0.167451 + 0.515361i) q^{88} +(2.26290 + 6.96448i) q^{89} +(4.17564 - 12.8513i) q^{91} +(3.95027 + 2.87004i) q^{92} +(-1.41338 - 1.02688i) q^{94} +(-0.510516 + 13.9746i) q^{95} +(-9.24177 + 6.71454i) q^{97} +(0.0610656 + 0.187941i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.24741	−	1.85579i	−0.557858	−	0.829936i
$5$	−1.24741	−	1.85579i	−0.557858	−	0.829936i
$6$		0			0
$7$	−2.68284			−1.01402			−0.507008	−	0.861941i	$-0.669249\pi$
$7$	−2.68284			−1.01402			−0.507008	+	0.861941i	$0.669249\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$		0			0
$10$	1.37949	−	1.75983i	0.436234	−	0.556507i
$11$	−0.167451	−	0.515361i	−0.0504884	−	0.155387i	0.922634	−	0.385678i	$-0.126032\pi$
$11$	−0.167451	−	0.515361i	−0.0504884	−	0.155387i	−0.973122	+	0.230291i	$0.926032\pi$
$12$		0			0
$13$	−1.55643	+	4.79019i	−0.431675	+	1.32856i	0.464781	+	0.885426i	$0.346133\pi$
$13$	−1.55643	+	4.79019i	−0.431675	+	1.32856i	−0.896456	+	0.443133i	$0.853867\pi$
$14$	−0.829042	−	2.55153i	−0.221571	−	0.681925i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−6.22521	−	4.52288i	−1.50984	−	1.09696i	−0.966250	−	0.257606i	$-0.917066\pi$
$17$	−6.22521	−	4.52288i	−1.50984	−	1.09696i	−0.543586	−	0.839354i	$-0.682934\pi$
$18$		0			0
$19$	−5.05944	−	3.67590i	−1.16071	−	0.843308i	−0.170846	−	0.985298i	$-0.554650\pi$
$19$	−5.05944	−	3.67590i	−1.16071	−	0.843308i	−0.989868	+	0.141990i	$0.954650\pi$
$20$	2.09998	+	0.768160i	0.469571	+	0.171766i
$21$		0			0
$22$	0.438392	−	0.318511i	0.0934655	−	0.0679067i
$23$	−1.50887	−	4.64382i	−0.314621	−	0.968304i	−0.975910	−	0.218173i	$-0.929990\pi$
$23$	−1.50887	−	4.64382i	−0.314621	−	0.968304i	0.661289	−	0.750131i	$-0.270010\pi$
$24$		0			0
$25$	−1.88794	+	4.62987i	−0.377588	+	0.925974i
$26$	−5.03670			−0.987778
$27$		0			0
$28$	2.17046	−	1.57693i	0.410178	−	0.298012i
$29$	4.62991	−	3.36383i	0.859753	−	0.624647i	−0.0680646	−	0.997681i	$-0.521682\pi$
$29$	4.62991	−	3.36383i	0.859753	−	0.624647i	0.927818	+	0.373034i	$0.121682\pi$
$30$		0			0
$31$	2.53838	+	1.84424i	0.455906	+	0.331235i	0.791923	−	0.610621i	$-0.209080\pi$
$31$	2.53838	+	1.84424i	0.455906	+	0.331235i	−0.336017	+	0.941856i	$0.609080\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	2.37782	−	7.31818i	0.407793	−	1.25506i
$35$	3.34660	+	4.97879i	0.565678	+	0.841569i
$36$		0			0
$37$	−1.07737	+	3.31581i	−0.177119	+	0.545116i	−0.999724	−	0.0234975i	$-0.992520\pi$
$37$	−1.07737	+	3.31581i	−0.177119	+	0.545116i	0.822605	+	0.568613i	$0.192520\pi$
$38$	1.93253	−	5.94772i	0.313498	−	0.964848i
$39$		0			0
$40$	−0.0816329	+	2.23458i	−0.0129073	+	0.353318i
$41$	−1.70564	+	5.24942i	−0.266376	+	0.819822i	0.724997	+	0.688752i	$0.241841\pi$
$41$	−1.70564	+	5.24942i	−0.266376	+	0.819822i	−0.991373	+	0.131070i	$0.958159\pi$
$42$		0			0
$43$	12.9002			1.96726			0.983629	−	0.180206i	$-0.0576765\pi$
$43$	12.9002			1.96726			0.983629	+	0.180206i	$0.0576765\pi$
$44$	0.438392	+	0.318511i	0.0660901	+	0.0480173i
$45$		0			0
$46$	3.95027	−	2.87004i	0.582436	−	0.423164i
$47$	−1.41338	+	1.02688i	−0.206163	+	0.149786i	−0.686076	−	0.727530i	$-0.740668\pi$
$47$	−1.41338	+	1.02688i	−0.206163	+	0.149786i	0.479913	+	0.877316i	$0.340668\pi$
$48$		0			0
$49$	0.197613			0.0282304
$50$	−4.98667	−	0.364830i	−0.705222	−	0.0515947i
$51$		0			0
$52$	−1.55643	−	4.79019i	−0.215837	−	0.664279i
$53$	−8.24147	+	5.98778i	−1.13205	+	0.822485i	−0.985992	−	0.166790i	$-0.946660\pi$
$53$	−8.24147	+	5.98778i	−1.13205	+	0.822485i	−0.146061	+	0.989276i	$0.546660\pi$
$54$		0			0
$55$	−0.747524	+	0.953620i	−0.100796	+	0.128586i
$56$	2.17046	+	1.57693i	0.290040	+	0.210726i
$57$		0			0
$58$	4.62991	+	3.36383i	0.607937	+	0.441692i
$59$	−0.245881	+	0.756745i	−0.0320110	+	0.0985199i	−0.965785	−	0.259342i	$-0.916494\pi$
$59$	−0.245881	+	0.756745i	−0.0320110	+	0.0985199i	0.933774	+	0.357862i	$0.116494\pi$
$60$		0			0
$61$	−0.530688	−	1.63329i	−0.0679477	−	0.209121i	0.911317	−	0.411704i	$-0.135066\pi$
$61$	−0.530688	−	1.63329i	−0.0679477	−	0.209121i	−0.979265	+	0.202583i	$0.935066\pi$
$62$	−0.969573	+	2.98404i	−0.123136	+	0.378973i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	10.8311	−	3.08692i	1.34343	−	0.382885i
$66$		0			0
$67$	−11.0177	−	8.00483i	−1.34603	−	0.977946i	−0.999199	−	0.0400172i	$-0.987259\pi$
$67$	−11.0177	−	8.00483i	−1.34603	−	0.977946i	−0.346828	−	0.937929i	$-0.612741\pi$
$68$	7.69479			0.933130
$69$		0			0
$70$	−3.70096	+	4.72133i	−0.442349	+	0.564307i
$71$	6.99463	−	5.08190i	0.830110	−	0.603110i	−0.0894803	−	0.995989i	$-0.528521\pi$
$71$	6.99463	−	5.08190i	0.830110	−	0.603110i	0.919591	+	0.392878i	$0.128521\pi$
$72$		0			0
$73$	0.402106	+	1.23755i	0.0470629	+	0.144845i	0.971827	−	0.235697i	$-0.0757374\pi$
$73$	0.402106	+	1.23755i	0.0470629	+	0.144845i	−0.924764	+	0.380542i	$0.875737\pi$
$74$	−3.48645			−0.405291
$75$		0			0
$76$	6.25381			0.717361
$77$	0.449244	+	1.38263i	0.0511961	+	0.157565i
$78$		0			0
$79$	2.61562	−	1.90036i	0.294281	−	0.213807i	−0.430842	−	0.902428i	$-0.641783\pi$
$79$	2.61562	−	1.90036i	0.294281	−	0.213807i	0.725122	+	0.688620i	$0.241783\pi$
$80$	−2.15044	+	0.612885i	−0.240426	+	0.0685226i
$81$		0			0
$82$	−5.51957			−0.609535
$83$	0.617229	+	0.448443i	0.0677497	+	0.0492230i	0.621145	−	0.783696i	$-0.286668\pi$
$83$	0.617229	+	0.448443i	0.0677497	+	0.0492230i	−0.553395	+	0.832919i	$0.686668\pi$
$84$		0			0
$85$	−0.628147	+	17.1946i	−0.0681322	+	1.86502i
$86$	3.98637	+	12.2688i	0.429862	+	1.32298i
$87$		0			0
$88$	−0.167451	+	0.515361i	−0.0178503	+	0.0549377i
$89$	2.26290	+	6.96448i	0.239867	+	0.738234i	0.996438	+	0.0843230i	$0.0268727\pi$
$89$	2.26290	+	6.96448i	0.239867	+	0.738234i	−0.756572	+	0.653911i	$0.773127\pi$
$90$		0			0
$91$	4.17564	−	12.8513i	0.437726	−	1.34718i
$92$	3.95027	+	2.87004i	0.411844	+	0.299222i
$93$		0			0
$94$	−1.41338	−	1.02688i	−0.145779	−	0.105915i
$95$	−0.510516	+	13.9746i	−0.0523779	+	1.43377i
$96$		0			0
$97$	−9.24177	+	6.71454i	−0.938360	+	0.681759i	−0.948025	−	0.318195i	$-0.896923\pi$
$97$	−9.24177	+	6.71454i	−0.938360	+	0.681759i	0.00966528	+	0.999953i	$0.496923\pi$
$98$	0.0610656	+	0.187941i	0.00616856	+	0.0189849i
$99$		0			0
$100$	−1.19399	−	4.85535i	−0.119399	−	0.485535i
$101$	2.23667			0.222557			0.111278	−	0.993789i	$-0.464505\pi$
$101$	2.23667			0.222557			0.111278	+	0.993789i	$0.464505\pi$
$102$		0			0
$103$	−8.45660	+	6.14408i	−0.833253	+	0.605394i	−0.920478	−	0.390795i	$-0.872200\pi$
$103$	−8.45660	+	6.14408i	−0.833253	+	0.605394i	0.0872247	+	0.996189i	$0.472200\pi$
$104$	4.07478	−	2.96050i	0.399565	−	0.290301i
$105$		0			0
$106$	−8.24147	−	5.98778i	−0.800483	−	0.581585i
$107$	−5.92492			−0.572784			−0.286392	−	0.958113i	$-0.592456\pi$
$107$	−5.92492			−0.572784			−0.286392	+	0.958113i	$0.592456\pi$
$108$		0			0
$109$	2.65733	−	8.17842i	0.254526	−	0.783351i	−0.739397	−	0.673270i	$-0.764889\pi$
$109$	2.65733	−	8.17842i	0.254526	−	0.783351i	0.993923	−	0.110081i	$-0.0351109\pi$
$110$	−1.13794	−	0.416252i	−0.108499	−	0.0396881i
$111$		0			0
$112$	−0.829042	+	2.55153i	−0.0783371	+	0.241097i
$113$	0.748822	−	2.30464i	0.0704433	−	0.216802i	−0.909637	−	0.415404i	$-0.863640\pi$
$113$	0.748822	−	2.30464i	0.0704433	−	0.216802i	0.980080	+	0.198602i	$0.0636401\pi$
$114$		0			0
$115$	−6.73580	+	8.59290i	−0.628116	+	0.801292i
$116$	−1.76847	+	5.44279i	−0.164198	+	0.505350i
$117$		0			0
$118$	−0.795689			−0.0732491
$119$	16.7012	+	12.1342i	1.53100	+	1.11234i
$120$		0			0
$121$	8.66163	−	6.29304i	0.787421	−	0.572095i
$122$	1.38936	−	1.00943i	0.125787	−	0.0913894i
$123$		0			0
$124$	−3.13760			−0.281765
$125$	10.9471	−	2.27171i	0.979140	−	0.203188i
$126$		0			0
$127$	0.451862	+	1.39069i	0.0400963	+	0.123404i	0.969101	−	0.246664i	$-0.0793344\pi$
$127$	0.451862	+	1.39069i	0.0400963	+	0.123404i	−0.929005	+	0.370068i	$0.879334\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$		0			0
$130$	6.28283	+	9.34708i	0.551040	+	0.819793i
$131$	−15.9222	−	11.5682i	−1.39113	−	1.01072i	−0.995740	−	0.0922028i	$-0.970609\pi$
$131$	−15.9222	−	11.5682i	−1.39113	−	1.01072i	−0.395391	−	0.918513i	$-0.629391\pi$
$132$		0			0
$133$	13.5736	+	9.86183i	1.17698	+	0.855129i
$134$	4.20839	−	12.9521i	0.363549	−	1.11889i
$135$		0			0
$136$	2.37782	+	7.31818i	0.203896	+	0.627528i
$137$	1.82551	−	5.61833i	0.155964	−	0.480007i	−0.842294	−	0.539019i	$-0.818795\pi$
$137$	1.82551	−	5.61833i	0.155964	−	0.480007i	0.998257	+	0.0590123i	$0.0187951\pi$
$138$		0			0
$139$	−5.38071	−	16.5601i	−0.456386	−	1.40461i	−0.869500	−	0.493932i	$-0.835559\pi$
$139$	−5.38071	−	16.5601i	−0.456386	−	1.40461i	0.413115	−	0.910679i	$-0.364441\pi$
$140$	−5.63391	−	2.06085i	−0.476153	−	0.174173i
$141$		0			0
$142$	6.99463	+	5.08190i	0.586977	+	0.426463i
$143$	2.72930			0.228236
$144$		0			0
$145$	−12.0180	−	4.39609i	−0.998038	−	0.365076i
$146$	−1.05273	+	0.764851i	−0.0871243	+	0.0632995i
$147$		0			0
$148$	−1.07737	−	3.31581i	−0.0885594	−	0.272558i
$149$	−16.1584			−1.32375			−0.661874	−	0.749615i	$-0.730239\pi$
$149$	−16.1584			−1.32375			−0.661874	+	0.749615i	$0.730239\pi$
$150$		0			0
$151$	10.1900			0.829248			0.414624	−	0.909993i	$-0.363913\pi$
$151$	10.1900			0.829248			0.414624	+	0.909993i	$0.363913\pi$
$152$	1.93253	+	5.94772i	0.156749	+	0.482424i
$153$		0			0
$154$	−1.17613	+	0.854512i	−0.0947756	+	0.0688585i
$155$	0.256132	−	7.01122i	0.0205730	−	0.563155i
$156$		0			0
$157$	0.868121			0.0692836			0.0346418	−	0.999400i	$-0.488971\pi$
$157$	0.868121			0.0692836			0.0346418	+	0.999400i	$0.488971\pi$
$158$	2.61562	+	1.90036i	0.208088	+	0.151185i
$159$		0			0
$160$	−1.24741	−	1.85579i	−0.0986164	−	0.146713i
$161$	4.04805	+	12.4586i	0.319031	+	0.981877i
$162$		0			0
$163$	2.51983	−	7.75525i	0.197368	−	0.607438i	−0.802572	−	0.596555i	$-0.796536\pi$
$163$	2.51983	−	7.75525i	0.197368	−	0.607438i	0.999941	−	0.0108829i	$-0.00346420\pi$
$164$	−1.70564	−	5.24942i	−0.133188	−	0.409911i
$165$		0			0
$166$	−0.235761	+	0.725596i	−0.0182986	+	0.0563172i
$167$	4.15450	+	3.01842i	0.321485	+	0.233572i	0.736809	−	0.676101i	$-0.236332\pi$
$167$	4.15450	+	3.01842i	0.321485	+	0.233572i	−0.415324	+	0.909674i	$0.636332\pi$
$168$		0			0
$169$	−10.0062	−	7.26994i	−0.769709	−	0.559226i
$170$	−16.5471	+	4.71602i	−1.26911	+	0.361702i
$171$		0			0
$172$	−10.4365	+	7.58253i	−0.795772	+	0.578163i
$173$	5.45037	+	16.7745i	0.414384	+	1.27534i	0.912801	+	0.408405i	$0.133915\pi$
$173$	5.45037	+	16.7745i	0.414384	+	1.27534i	−0.498417	+	0.866937i	$0.666085\pi$
$174$		0			0
$175$	5.06504	−	12.4212i	0.382881	−	0.938953i
$176$	−0.541883			−0.0408459
$177$		0			0
$178$	−5.92434	+	4.30429i	−0.444048	+	0.322620i
$179$	−13.3621	+	9.70812i	−0.998729	+	0.725619i	−0.961815	−	0.273699i	$-0.911753\pi$
$179$	−13.3621	+	9.70812i	−0.998729	+	0.725619i	−0.0369136	+	0.999318i	$0.511753\pi$
$180$		0			0
$181$	15.6169	+	11.3463i	1.16079	+	0.843366i	0.989878	−	0.141920i	$-0.0453274\pi$
$181$	15.6169	+	11.3463i	1.16079	+	0.843366i	0.170916	+	0.985286i	$0.445327\pi$
$182$	13.5126			1.00162
$183$		0			0
$184$	−1.50887	+	4.64382i	−0.111235	+	0.342347i
$185$	7.49738	−	2.13679i	0.551218	−	0.157100i
$186$		0			0
$187$	−1.28850	+	3.96559i	−0.0942244	+	0.289993i
$188$	0.539865	−	1.66153i	0.0393737	−	0.121180i
$189$		0			0
$190$	−13.4484	+	3.83286i	−0.975650	+	0.278065i
$191$	7.94718	−	24.4589i	0.575038	−	1.76978i	−0.0610119	−	0.998137i	$-0.519433\pi$
$191$	7.94718	−	24.4589i	0.575038	−	1.76978i	0.636050	−	0.771648i	$-0.280567\pi$
$192$		0			0
$193$	8.93834			0.643396			0.321698	−	0.946842i	$-0.395746\pi$
$193$	8.93834			0.643396			0.321698	+	0.946842i	$0.395746\pi$
$194$	−9.24177	−	6.71454i	−0.663521	−	0.482076i
$195$		0			0
$196$	−0.159872	+	0.116154i	−0.0114194	+	0.00829670i
$197$	−10.4272	+	7.57581i	−0.742908	+	0.539754i	−0.893620	−	0.448824i	$-0.851843\pi$
$197$	−10.4272	+	7.57581i	−0.742908	+	0.539754i	0.150713	+	0.988578i	$0.451843\pi$
$198$		0			0
$199$	16.5675			1.17444			0.587218	−	0.809428i	$-0.300223\pi$
$199$	16.5675			1.17444			0.587218	+	0.809428i	$0.300223\pi$
$200$	4.24874	−	2.63594i	0.300432	−	0.186389i
$201$		0			0
$202$	0.691168	+	2.12720i	0.0486304	+	0.149669i
$203$	−12.4213	+	9.02460i	−0.871804	+	0.633403i
$204$		0			0
$205$	11.8695	−	3.38286i	0.829000	−	0.236269i
$206$	−8.45660	−	6.14408i	−0.589199	−	0.428078i
$207$		0			0
$208$	4.07478	+	2.96050i	0.282535	+	0.205274i
$209$	−1.04721	+	3.22297i	−0.0724367	+	0.222937i
$210$		0			0
$211$	−7.07675	−	21.7800i	−0.487184	−	1.49940i	−0.828793	−	0.559555i	$-0.810972\pi$
$211$	−7.07675	−	21.7800i	−0.487184	−	1.49940i	0.341609	−	0.939842i	$-0.389028\pi$
$212$	3.14796	−	9.68843i	0.216203	−	0.665404i
$213$		0			0
$214$	−1.83090	−	5.63494i	−0.125158	−	0.385196i
$215$	−16.0918	−	23.9401i	−1.09745	−	1.63270i
$216$		0			0
$217$	−6.81005	−	4.94779i	−0.462296	−	0.335878i
$218$	8.59930			0.582418
$219$		0			0
$220$	0.0442354	−	1.21088i	0.00298235	−	0.0816374i
$221$	31.3545	−	22.7804i	2.10913	−	1.53238i
$222$		0			0
$223$	−2.79582	−	8.60464i	−0.187222	−	0.576209i	0.812758	−	0.582602i	$-0.197965\pi$
$223$	−2.79582	−	8.60464i	−0.187222	−	0.576209i	−0.999980	+	0.00639253i	$0.997965\pi$
$224$	−2.68284			−0.179255
$225$		0			0
$226$	2.42324			0.161192
$227$	−6.66088	−	20.5001i	−0.442098	−	1.36064i	−0.885635	−	0.464383i	$-0.846276\pi$
$227$	−6.66088	−	20.5001i	−0.442098	−	1.36064i	0.443536	−	0.896256i	$-0.353724\pi$
$228$		0			0
$229$	−9.95698	+	7.23417i	−0.657976	+	0.478047i	−0.865979	−	0.500081i	$-0.833304\pi$
$229$	−9.95698	+	7.23417i	−0.657976	+	0.478047i	0.208003	+	0.978128i	$0.433304\pi$
$230$	−10.2538	−	3.75077i	−0.676116	−	0.247319i
$231$		0			0
$232$	−5.72289			−0.375726
$233$	−23.4944	−	17.0697i	−1.53917	−	1.11827i	−0.950852	−	0.309645i	$-0.899790\pi$
$233$	−23.4944	−	17.0697i	−1.53917	−	1.11827i	−0.588319	−	0.808629i	$-0.700210\pi$
$234$		0			0
$235$	3.66875	+	1.34201i	0.239323	+	0.0875428i
$236$	−0.245881	−	0.756745i	−0.0160055	−	0.0492599i
$237$		0			0
$238$	−6.37930	+	19.6335i	−0.413509	+	1.27265i
$239$	3.16021	+	9.72613i	0.204417	+	0.629131i	0.999737	+	0.0229408i	$0.00730292\pi$
$239$	3.16021	+	9.72613i	0.204417	+	0.629131i	−0.795320	+	0.606190i	$0.792697\pi$
$240$		0			0
$241$	−2.55006	+	7.84827i	−0.164264	+	0.505551i	−0.998981	−	0.0451268i	$-0.985631\pi$
$241$	−2.55006	+	7.84827i	−0.164264	+	0.505551i	0.834718	+	0.550678i	$0.185631\pi$
$242$	8.66163	+	6.29304i	0.556791	+	0.404532i
$243$		0			0
$244$	1.38936	+	1.00943i	0.0889446	+	0.0646221i
$245$	−0.246504	−	0.366728i	−0.0157485	−	0.0234294i
$246$		0			0
$247$	25.4829	−	18.5144i	1.62144	−	1.17804i
$248$	−0.969573	−	2.98404i	−0.0615680	−	0.189487i
$249$		0			0
$250$	5.54337	+	9.70933i	0.350594	+	0.614072i
$251$	−20.2355			−1.27726			−0.638628	−	0.769515i	$-0.720498\pi$
$251$	−20.2355			−1.27726			−0.638628	+	0.769515i	$0.720498\pi$
$252$		0			0
$253$	−2.14058	+	1.55522i	−0.134577	+	0.0977761i
$254$	−1.18299	+	0.859493i	−0.0742274	+	0.0539294i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	3.26629			0.203745			0.101873	−	0.994797i	$-0.467517\pi$
$257$	3.26629			0.203745			0.101873	+	0.994797i	$0.467517\pi$
$258$		0			0
$259$	2.89041	−	8.89577i	0.179601	−	0.552757i
$260$	−6.94810	+	8.86373i	−0.430903	+	0.549705i
$261$		0			0
$262$	6.08175	−	18.7177i	0.375732	−	1.15638i
$263$	1.72720	−	5.31577i	0.106504	−	0.327784i	−0.883577	−	0.468286i	$-0.844872\pi$
$263$	1.72720	−	5.31577i	0.106504	−	0.327784i	0.990080	+	0.140502i	$0.0448716\pi$
$264$		0			0
$265$	21.3926	+	7.82526i	1.31414	+	0.480702i
$266$	−5.18467	+	15.9568i	−0.317892	+	0.978372i
$267$		0			0
$268$	13.6186			0.831890
$269$	−19.4406	−	14.1244i	−1.18531	−	0.861181i	−0.192553	−	0.981287i	$-0.561677\pi$
$269$	−19.4406	−	14.1244i	−1.18531	−	0.861181i	−0.992761	+	0.120105i	$0.961677\pi$
$270$		0			0
$271$	−7.32203	+	5.31977i	−0.444782	+	0.323153i	−0.787532	−	0.616274i	$-0.788642\pi$
$271$	−7.32203	+	5.31977i	−0.444782	+	0.323153i	0.342750	+	0.939427i	$0.388642\pi$
$272$	−6.22521	+	4.52288i	−0.377459	+	0.274240i
$273$		0			0
$274$	5.90747			0.356883
$275$	2.70219	+	0.197695i	0.162948	+	0.0119215i
$276$		0			0
$277$	0.765152	+	2.35490i	0.0459736	+	0.141492i	0.971408	−	0.237415i	$-0.0763001\pi$
$277$	0.765152	+	2.35490i	0.0459736	+	0.141492i	−0.925435	+	0.378907i	$0.876300\pi$
$278$	14.0869	−	10.2347i	0.844875	−	0.613838i
$279$		0			0
$280$	0.219008	−	5.99501i	0.0130882	−	0.358270i
$281$	−14.5421	−	10.5654i	−0.867506	−	0.630280i	0.0624105	−	0.998051i	$-0.480121\pi$
$281$	−14.5421	−	10.5654i	−0.867506	−	0.630280i	−0.929917	+	0.367770i	$0.880121\pi$
$282$		0			0
$283$	−12.9783	−	9.42925i	−0.771477	−	0.560511i	0.130932	−	0.991391i	$-0.458203\pi$
$283$	−12.9783	−	9.42925i	−0.771477	−	0.560511i	−0.902409	+	0.430880i	$0.858203\pi$
$284$	−2.67171	+	8.22268i	−0.158537	+	0.487927i
$285$		0			0
$286$	0.843400	+	2.59572i	0.0498713	+	0.153488i
$287$	4.57596	−	14.0833i	0.270110	−	0.831314i
$288$		0			0
$289$	13.0435	+	40.1438i	0.767266	+	2.36140i
$290$	0.467176	−	12.7882i	0.0274335	−	0.750951i
$291$		0			0
$292$	−1.05273	−	0.764851i	−0.0616062	−	0.0447595i
$293$	4.97078			0.290396			0.145198	−	0.989403i	$-0.453618\pi$
$293$	4.97078			0.290396			0.145198	+	0.989403i	$0.453618\pi$
$294$		0			0
$295$	1.71108	−	0.487666i	0.0996228	−	0.0283930i
$296$	2.82060	−	2.04928i	0.163944	−	0.119112i
$297$		0			0
$298$	−4.99322	−	15.3676i	−0.289249	−	0.890218i
$299$	24.5932			1.42226
$300$		0			0
$301$	−34.6091			−1.99483
$302$	3.14888	+	9.69124i	0.181197	+	0.557668i
$303$		0			0
$304$	−5.05944	+	3.67590i	−0.290179	+	0.210827i
$305$	−2.36906	+	3.02223i	−0.135652	+	0.173052i
$306$		0			0
$307$	−12.0074			−0.685297			−0.342649	−	0.939464i	$-0.611324\pi$
$307$	−12.0074			−0.685297			−0.342649	+	0.939464i	$0.611324\pi$
$308$	−1.17613	−	0.854512i	−0.0670165	−	0.0486903i
$309$		0			0
$310$	6.74722	−	1.92299i	0.383216	−	0.109219i
$311$	5.84196	+	17.9797i	0.331267	+	1.01954i	0.968532	+	0.248890i	$0.0800659\pi$
$311$	5.84196	+	17.9797i	0.331267	+	1.01954i	−0.637265	+	0.770645i	$0.719934\pi$
$312$		0			0
$313$	−2.68893	+	8.27568i	−0.151987	+	0.467769i	−0.997843	−	0.0656426i	$-0.979090\pi$
$313$	−2.68893	+	8.27568i	−0.151987	+	0.467769i	0.845856	+	0.533412i	$0.179090\pi$
$314$	0.268264	+	0.825632i	0.0151390	+	0.0465931i
$315$		0			0
$316$	−0.999080	+	3.07485i	−0.0562026	+	0.172974i
$317$	−10.3238	−	7.50070i	−0.579844	−	0.421281i	0.258824	−	0.965925i	$-0.416665\pi$
$317$	−10.3238	−	7.50070i	−0.579844	−	0.421281i	−0.838668	+	0.544643i	$0.816665\pi$
$318$		0			0
$319$	−2.50887	−	1.82280i	−0.140470	−	0.102057i
$320$	1.37949	−	1.75983i	0.0771161	−	0.0983774i
$321$		0			0
$322$	−10.5979	+	7.69985i	−0.590600	+	0.429096i
$323$	14.8704	+	45.7665i	0.827412	+	2.54651i
$324$		0			0
$325$	−19.2395	−	16.2496i	−1.06722	−	0.901368i
$326$	8.15435			0.451628
$327$		0			0
$328$	4.46543	−	3.24432i	0.246562	−	0.179138i
$329$	3.79188	−	2.75496i	0.209053	−	0.151886i
$330$		0			0
$331$	−3.10477	−	2.25575i	−0.170654	−	0.123987i	0.499180	−	0.866498i	$-0.333635\pi$
$331$	−3.10477	−	2.25575i	−0.170654	−	0.123987i	−0.669834	+	0.742511i	$0.733635\pi$
$332$	−0.762937			−0.0418716
$333$		0			0
$334$	−1.58688	+	4.88390i	−0.0868300	+	0.267235i
$335$	−1.11173	+	30.4319i	−0.0607402	+	1.66267i
$336$		0			0
$337$	0.525700	−	1.61794i	0.0286367	−	0.0881348i	−0.935717	−	0.352752i	$-0.885246\pi$
$337$	0.525700	−	1.61794i	0.0286367	−	0.0881348i	0.964353	+	0.264618i	$0.0852458\pi$
$338$	3.82203	−	11.7630i	0.207891	−	0.639823i
$339$		0			0
$340$	−9.59855	−	14.2799i	−0.520554	−	0.774438i
$341$	0.525395	−	1.61700i	0.0284517	−	0.0875654i
$342$		0			0
$343$	18.2497			0.985391
$344$	−10.4365	−	7.58253i	−0.562696	−	0.408823i
$345$		0			0
$346$	−14.2692	+	10.3672i	−0.767119	+	0.557345i
$347$	21.5469	−	15.6547i	1.15670	−	0.840390i	0.167341	−	0.985899i	$-0.446482\pi$
$347$	21.5469	−	15.6547i	1.15670	−	0.840390i	0.989357	+	0.145509i	$0.0464818\pi$
$348$		0			0
$349$	−6.45413			−0.345482			−0.172741	−	0.984967i	$-0.555262\pi$
$349$	−6.45413			−0.345482			−0.172741	+	0.984967i	$0.555262\pi$
$350$	13.3784	+	0.978779i	0.715107	+	0.0523179i
$351$		0			0
$352$	−0.167451	−	0.515361i	−0.00892517	−	0.0274688i
$353$	−19.3743	+	14.0762i	−1.03119	+	0.749203i	−0.968546	−	0.248833i	$-0.919953\pi$
$353$	−19.3743	+	14.0762i	−1.03119	+	0.749203i	−0.0626429	+	0.998036i	$0.519953\pi$
$354$		0			0
$355$	−18.1561	−	6.64139i	−0.963627	−	0.352488i
$356$	−5.92434	−	4.30429i	−0.313989	−	0.228127i
$357$		0			0
$358$	−13.3621	−	9.70812i	−0.706208	−	0.513090i
$359$	−4.84566	+	14.9134i	−0.255744	+	0.787100i	0.737938	+	0.674868i	$0.235800\pi$
$359$	−4.84566	+	14.9134i	−0.255744	+	0.787100i	−0.993682	+	0.112231i	$0.964200\pi$
$360$		0			0
$361$	6.21436	+	19.1258i	0.327072	+	1.00662i
$362$	−5.96512	+	18.3587i	−0.313520	+	0.964914i
$363$		0			0
$364$	4.17564	+	12.8513i	0.218863	+	0.673591i
$365$	1.79505	−	2.28996i	0.0939575	−	0.119862i
$366$		0			0
$367$	11.5852	+	8.41711i	0.604740	+	0.439369i	0.847558	−	0.530702i	$-0.178072\pi$
$367$	11.5852	+	8.41711i	0.604740	+	0.439369i	−0.242818	+	0.970072i	$0.578072\pi$
$368$	−4.88280			−0.254534
$369$		0			0
$370$	4.34903	+	6.47013i	0.226095	+	0.336366i
$371$	22.1105	−	16.0642i	1.14792	−	0.834014i
$372$		0			0
$373$	−5.67003	−	17.4506i	−0.293583	−	0.903556i	−0.983694	−	0.179852i	$-0.942438\pi$
$373$	−5.67003	−	17.4506i	−0.293583	−	0.903556i	0.690110	−	0.723704i	$-0.257562\pi$
$374$	−4.16967			−0.215609
$375$		0			0
$376$	1.74704			0.0900967
$377$	8.90725	+	27.4137i	0.458747	+	1.41188i
$378$		0			0
$379$	−17.8579	+	12.9745i	−0.917298	+	0.666456i	−0.942850	−	0.333218i	$-0.891866\pi$
$379$	−17.8579	+	12.9745i	−0.917298	+	0.666456i	0.0255521	+	0.999673i	$0.491866\pi$
$380$	−7.80106	−	11.6058i	−0.400186	−	0.595364i
$381$		0			0
$382$	25.7176			1.31583
$383$	−10.9364	−	7.94573i	−0.558822	−	0.406008i	0.272206	−	0.962239i	$-0.412247\pi$
$383$	−10.9364	−	7.94573i	−0.558822	−	0.406008i	−0.831028	+	0.556231i	$0.812247\pi$
$384$		0			0
$385$	2.00548	−	2.55841i	0.102209	−	0.130389i
$386$	2.76210	+	8.50087i	0.140587	+	0.432683i
$387$		0			0
$388$	3.53004	−	10.8644i	0.179211	−	0.551554i
$389$	2.16552	+	6.66479i	0.109796	+	0.337918i	0.990826	−	0.135142i	$-0.0431492\pi$
$389$	2.16552	+	6.66479i	0.109796	+	0.337918i	−0.881030	+	0.473061i	$0.843149\pi$
$390$		0			0
$391$	−11.6104	+	35.7332i	−0.587164	+	1.80711i
$392$	−0.159872	−	0.116154i	−0.00807475	−	0.00586665i
$393$		0			0
$394$	−10.4272	−	7.57581i	−0.525315	−	0.381664i
$395$	−6.78943	−	2.48353i	−0.341614	−	0.124960i
$396$		0			0
$397$	7.29448	−	5.29975i	0.366099	−	0.265987i	−0.389492	−	0.921030i	$-0.627349\pi$
$397$	7.29448	−	5.29975i	0.366099	−	0.265987i	0.755592	+	0.655043i	$0.227349\pi$
$398$	5.11963	+	15.7566i	0.256624	+	0.789807i
$399$		0			0
$400$	3.81986	+	3.22625i	0.190993	+	0.161312i
$401$	−5.60409			−0.279855			−0.139927	−	0.990162i	$-0.544687\pi$
$401$	−5.60409			−0.279855			−0.139927	+	0.990162i	$0.544687\pi$
$402$		0			0
$403$	−12.7850	+	9.28888i	−0.636868	+	0.462712i
$404$	−1.80950	+	1.31468i	−0.0900261	+	0.0654078i
$405$		0			0
$406$	−12.4213	−	9.02460i	−0.616459	−	0.447884i
$407$	1.88925			0.0936464
$408$		0			0
$409$	7.25729	−	22.3357i	0.358850	−	1.10443i	−0.594893	−	0.803805i	$-0.702806\pi$
$409$	7.25729	−	22.3357i	0.358850	−	1.10443i	0.953743	−	0.300622i	$-0.0971943\pi$
$410$	6.88516	+	10.2432i	0.340034	+	0.505875i
$411$		0			0
$412$	3.23013	−	9.94132i	0.159137	−	0.489774i
$413$	0.659660	−	2.03022i	0.0324597	−	0.0999008i
$414$		0			0
$415$	0.0622808	−	1.70484i	0.00305724	−	0.0836874i
$416$	−1.55643	+	4.79019i	−0.0763101	+	0.234858i
$417$		0			0
$418$	−3.38883			−0.165753
$419$	8.60618	+	6.25276i	0.420439	+	0.305467i	0.777815	−	0.628494i	$-0.216328\pi$
$419$	8.60618	+	6.25276i	0.420439	+	0.305467i	−0.357375	+	0.933961i	$0.616328\pi$
$420$		0			0
$421$	5.58833	−	4.06016i	0.272359	−	0.197880i	−0.443219	−	0.896413i	$-0.646164\pi$
$421$	5.58833	−	4.06016i	0.272359	−	0.197880i	0.715578	+	0.698533i	$0.246164\pi$
$422$	18.5272	−	13.4608i	0.901889	−	0.655261i
$423$		0			0
$424$	10.1870			0.494726
$425$	32.6932	−	20.2830i	1.58585	−	0.983869i
$426$		0			0
$427$	1.42375	+	4.38185i	0.0689001	+	0.212053i
$428$	4.79336	−	3.48258i	0.231696	−	0.168337i
$429$		0			0
$430$	17.7957	−	22.7021i	0.858185	−	1.09479i
$431$	−2.79764	−	2.03261i	−0.134758	−	0.0979073i	0.518364	−	0.855160i	$-0.326541\pi$
$431$	−2.79764	−	2.03261i	−0.134758	−	0.0979073i	−0.653122	+	0.757253i	$0.726541\pi$
$432$		0			0
$433$	−17.9929	−	13.0726i	−0.864681	−	0.628228i	0.0644731	−	0.997919i	$-0.479463\pi$
$433$	−17.9929	−	13.0726i	−0.864681	−	0.628228i	−0.929155	+	0.369692i	$0.879463\pi$
$434$	2.60121	−	8.00569i	0.124862	−	0.384285i
$435$		0			0
$436$	2.65733	+	8.17842i	0.127263	+	0.391675i
$437$	−9.43618	+	29.0416i	−0.451394	+	1.38925i
$438$		0			0
$439$	7.73905	+	23.8184i	0.369365	+	1.13679i	0.947202	+	0.320636i	$0.103897\pi$
$439$	7.73905	+	23.8184i	0.369365	+	1.13679i	−0.577838	+	0.816152i	$0.696103\pi$
$440$	1.16528	−	0.332112i	0.0555527	−	0.0158328i
$441$		0			0
$442$	31.3545	+	22.7804i	1.49138	+	1.08355i
$443$	32.7481			1.55591			0.777955	−	0.628320i	$-0.216257\pi$
$443$	32.7481			1.55591			0.777955	+	0.628320i	$0.216257\pi$
$444$		0			0
$445$	10.1019	−	12.8870i	0.478875	−	0.610904i
$446$	7.31954	−	5.31796i	0.346590	−	0.251813i
$447$		0			0
$448$	−0.829042	−	2.55153i	−0.0391686	−	0.120548i
$449$	20.5341			0.969064			0.484532	−	0.874774i	$-0.338990\pi$
$449$	20.5341			0.969064			0.484532	+	0.874774i	$0.338990\pi$
$450$		0			0
$451$	2.99096			0.140839
$452$	0.748822	+	2.30464i	0.0352216	+	0.108401i
$453$		0			0
$454$	17.4384	−	12.6698i	0.818426	−	0.594621i
$455$	−29.0581	+	8.28170i	−1.36226	+	0.388252i
$456$		0			0
$457$	37.1312			1.73693			0.868463	−	0.495755i	$-0.165108\pi$
$457$	37.1312			1.73693			0.868463	+	0.495755i	$0.165108\pi$
$458$	−9.95698	−	7.23417i	−0.465259	−	0.338031i
$459$		0			0
$460$	0.398597	−	10.9110i	0.0185847	−	0.508728i
$461$	11.3976	+	35.0781i	0.530838	+	1.63375i	0.752475	+	0.658621i	$0.228860\pi$
$461$	11.3976	+	35.0781i	0.530838	+	1.63375i	−0.221637	+	0.975129i	$0.571140\pi$
$462$		0			0
$463$	−7.57829	+	23.3236i	−0.352193	+	1.08394i	0.605426	+	0.795901i	$0.293003\pi$
$463$	−7.57829	+	23.3236i	−0.352193	+	1.08394i	−0.957619	+	0.288037i	$0.906997\pi$
$464$	−1.76847	−	5.44279i	−0.0820991	−	0.252675i
$465$		0			0
$466$	8.97408	−	27.6194i	0.415716	−	1.27944i
$467$	−14.0385	−	10.1995i	−0.649622	−	0.471978i	0.213520	−	0.976939i	$-0.431507\pi$
$467$	−14.0385	−	10.1995i	−0.649622	−	0.471978i	−0.863142	+	0.504960i	$0.831507\pi$
$468$		0			0
$469$	29.5587	+	21.4757i	1.36489	+	0.991654i
$470$	−0.142616	+	3.90389i	−0.00657838	+	0.180073i
$471$		0			0
$472$	0.643726	−	0.467694i	0.0296299	−	0.0215274i
$473$	−2.16015	−	6.64825i	−0.0993236	−	0.305687i
$474$		0			0
$475$	26.5708	−	16.4847i	1.21915	−	0.756368i
$476$	−20.6439			−0.946209
$477$		0			0
$478$	−8.27354	+	6.01108i	−0.378423	+	0.274940i
$479$	−12.4299	+	9.03087i	−0.567938	+	0.412631i	−0.834356	−	0.551227i	$-0.814160\pi$
$479$	−12.4299	+	9.03087i	−0.567938	+	0.412631i	0.266418	+	0.963858i	$0.414160\pi$
$480$		0			0
$481$	−14.2065	−	10.3216i	−0.647761	−	0.470626i
$482$	−8.25216			−0.375875
$483$		0			0
$484$	−3.30845	+	10.1824i	−0.150384	+	0.462834i
$485$	23.9891	+	8.77505i	1.08929	+	0.398454i
$486$		0			0
$487$	−11.9390	+	36.7445i	−0.541009	+	1.66505i	0.189287	+	0.981922i	$0.439382\pi$
$487$	−11.9390	+	36.7445i	−0.541009	+	1.66505i	−0.730295	+	0.683132i	$0.760618\pi$
$488$	−0.530688	+	1.63329i	−0.0240231	+	0.0739356i
$489$		0			0
$490$	0.272605	−	0.347764i	0.0123151	−	0.0157104i
$491$	−12.9351	+	39.8103i	−0.583755	+	1.79661i	0.0204596	+	0.999791i	$0.493487\pi$
$491$	−12.9351	+	39.8103i	−0.583755	+	1.79661i	−0.604214	+	0.796822i	$0.706513\pi$
$492$		0			0
$493$	−44.0364			−1.98330
$494$	25.4829	+	18.5144i	1.14653	+	0.833002i
$495$		0			0
$496$	2.53838	−	1.84424i	0.113976	−	0.0828087i
$497$	−18.7655	+	13.6339i	−0.841746	+	0.611564i
$498$		0			0
$499$	−5.05384			−0.226241			−0.113120	−	0.993581i	$-0.536085\pi$
$499$	−5.05384			−0.226241			−0.113120	+	0.993581i	$0.536085\pi$
$500$	−7.52112	+	8.27241i	−0.336355	+	0.369953i
$501$		0			0
$502$	−6.25313	−	19.2451i	−0.279091	−	0.858953i
$503$	18.2724	−	13.2757i	0.814725	−	0.591932i	−0.100472	−	0.994940i	$-0.532035\pi$
$503$	18.2724	−	13.2757i	0.814725	−	0.591932i	0.915197	+	0.403008i	$0.132035\pi$
$504$		0			0
$505$	−2.79004	−	4.15079i	−0.124155	−	0.184708i
$506$	−2.14058	−	1.55522i	−0.0951605	−	0.0691382i
$507$		0			0
$508$	−1.18299	−	0.859493i	−0.0524867	−	0.0381338i
$509$	10.9142	−	33.5905i	0.483765	−	1.48887i	−0.349997	−	0.936751i	$-0.613818\pi$
$509$	10.9142	−	33.5905i	0.483765	−	1.48887i	0.833762	−	0.552124i	$-0.186182\pi$
$510$		0			0
$511$	−1.07878	−	3.32016i	−0.0477226	−	0.146875i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$		0			0
$514$	1.00934	+	3.10642i	0.0445200	+	0.137018i
$515$	21.9510	+	8.02952i	0.967276	+	0.353823i
$516$		0			0
$517$	0.765889	+	0.556451i	0.0336837	+	0.0244727i
$518$	9.35357			0.410972
$519$		0			0
$520$	−10.5770	−	3.86899i	−0.463832	−	0.169667i
$521$	22.7441	−	16.5245i	0.996437	−	0.723954i	0.0351154	−	0.999383i	$-0.488820\pi$
$521$	22.7441	−	16.5245i	0.996437	−	0.723954i	0.961321	+	0.275430i	$0.0888201\pi$
$522$		0			0
$523$	−10.2019	−	31.3982i	−0.446098	−	1.37295i	−0.881275	−	0.472603i	$-0.843314\pi$
$523$	−10.2019	−	31.3982i	−0.446098	−	1.37295i	0.435177	−	0.900345i	$-0.356686\pi$
$524$	19.6809			0.859766
$525$		0			0
$526$	5.58933			0.243706
$527$	−7.46066	−	22.9615i	−0.324991	−	1.00022i
$528$		0			0
$529$	−0.681006	+	0.494780i	−0.0296090	+	0.0215122i
$530$	−0.831596	+	22.7637i	−0.0361222	+	0.988792i
$531$		0			0
$532$	−16.7779			−0.727416
$533$	−22.4910	−	16.3407i	−0.974194	−	0.707794i
$534$		0			0
$535$	7.39080	+	10.9954i	0.319532	+	0.475374i
$536$	4.20839	+	12.9521i	0.181775	+	0.559445i
$537$		0			0
$538$	7.42565	−	22.8538i	0.320142	−	0.985297i
$539$	−0.0330904	−	0.101842i	−0.00142530	−	0.00438664i
$540$		0			0
$541$	−0.101192	+	0.311437i	−0.00435058	+	0.0133897i	−0.953208	−	0.302314i	$-0.902241\pi$
$541$	−0.101192	+	0.311437i	−0.00435058	+	0.0133897i	0.948858	+	0.315704i	$0.102241\pi$
$542$	−7.32203	−	5.31977i	−0.314508	−	0.228504i
$543$		0			0
$544$	−6.22521	−	4.52288i	−0.266904	−	0.193917i
$545$	−18.4922	+	5.27038i	−0.792121	+	0.225758i
$546$		0			0
$547$	22.5274	−	16.3671i	0.963201	−	0.699806i	0.00930869	−	0.999957i	$-0.497037\pi$
$547$	22.5274	−	16.3671i	0.963201	−	0.699806i	0.953892	+	0.300151i	$0.0970369\pi$
$548$	1.82551	+	5.61833i	0.0779818	+	0.240003i
$549$		0			0
$550$	0.647004	+	2.63103i	0.0275883	+	0.112187i
$551$	−35.7898			−1.52470
$552$		0			0
$553$	−7.01729	+	5.09836i	−0.298406	+	0.216804i
$554$	−2.00319	+	1.45541i	−0.0851076	+	0.0618343i
$555$		0			0
$556$	14.0869	+	10.2347i	0.597417	+	0.434049i
$557$	−20.5761			−0.871836			−0.435918	−	0.899986i	$-0.643576\pi$
$557$	−20.5761			−0.871836			−0.435918	+	0.899986i	$0.643576\pi$
$558$		0			0
$559$	−20.0782	+	61.7942i	−0.849216	+	2.61362i
$560$	5.76927	−	1.64427i	0.243796	−	0.0694831i
$561$		0			0
$562$	5.55457	−	17.0952i	0.234305	−	0.721118i
$563$	13.6583	−	42.0358i	0.575627	−	1.77160i	−0.0584058	−	0.998293i	$-0.518602\pi$
$563$	13.6583	−	42.0358i	0.575627	−	1.77160i	0.634033	−	0.773306i	$-0.281398\pi$
$564$		0			0
$565$	−5.21102	+	1.48517i	−0.219229	+	0.0624815i
$566$	4.95725	−	15.2569i	0.208369	−	0.641293i
$567$		0			0
$568$	−8.64584			−0.362771
$569$	−1.91682	−	1.39265i	−0.0803571	−	0.0583829i	0.546881	−	0.837210i	$-0.315815\pi$
$569$	−1.91682	−	1.39265i	−0.0803571	−	0.0583829i	−0.627239	+	0.778827i	$0.715815\pi$
$570$		0			0
$571$	−16.0097	+	11.6317i	−0.669985	+	0.486773i	−0.870020	−	0.493016i	$-0.835894\pi$
$571$	−16.0097	+	11.6317i	−0.669985	+	0.486773i	0.200035	+	0.979789i	$0.435894\pi$
$572$	−2.20805	+	1.60424i	−0.0923232	+	0.0670768i
$573$		0			0
$574$	14.8081			0.618078
$575$	24.3489	+	1.78139i	1.01542	+	0.0742892i
$576$		0			0
$577$	9.16650	+	28.2116i	0.381607	+	1.17446i	0.938912	+	0.344157i	$0.111835\pi$
$577$	9.16650	+	28.2116i	0.381607	+	1.17446i	−0.557306	+	0.830307i	$0.688165\pi$
$578$	−34.1484	+	24.8103i	−1.42039	+	1.03197i
$579$		0			0
$580$	12.3067	−	3.50747i	0.511008	−	0.145640i
$581$	−1.65592	−	1.20310i	−0.0686993	−	0.0499130i
$582$		0			0
$583$	4.46591	+	3.24468i	0.184959	+	0.134381i
$584$	0.402106	−	1.23755i	0.0166393	−	0.0512104i
$585$		0			0
$586$	1.53605	+	4.72749i	0.0634538	+	0.195291i
$587$	−0.933553	+	2.87318i	−0.0385318	+	0.118589i	−0.968472	−	0.249121i	$-0.919858\pi$
$587$	−0.933553	+	2.87318i	−0.0385318	+	0.118589i	0.929940	+	0.367710i	$0.119858\pi$
$588$		0			0
$589$	−6.06352	−	18.6616i	−0.249843	−	0.768938i
$590$	0.992550	+	1.47663i	0.0408626	+	0.0607921i
$591$		0			0
$592$	2.82060	+	2.04928i	0.115926	+	0.0842250i
$593$	−23.6709			−0.972046			−0.486023	−	0.873946i	$-0.661553\pi$
$593$	−23.6709			−0.972046			−0.486023	+	0.873946i	$0.661553\pi$
$594$		0			0
$595$	1.68522	−	46.1303i	0.0690872	−	1.89116i
$596$	13.0724	−	9.49767i	0.535467	−	0.389040i
$597$		0			0
$598$	7.59972	+	23.3895i	0.310776	+	0.956470i
$599$	−33.2245			−1.35752			−0.678759	−	0.734361i	$-0.737482\pi$
$599$	−33.2245			−1.35752			−0.678759	+	0.734361i	$0.737482\pi$
$600$		0			0
$601$	−34.9169			−1.42429			−0.712146	−	0.702032i	$-0.752277\pi$
$601$	−34.9169			−1.42429			−0.712146	+	0.702032i	$0.752277\pi$
$602$	−10.6948	−	32.9152i	−0.435887	−	1.34152i
$603$		0			0
$604$	−8.24386	+	5.98952i	−0.335438	+	0.243710i
$605$	−22.4832	−	8.22420i	−0.914071	−	0.334361i
$606$		0			0
$607$	14.1488			0.574282			0.287141	−	0.957888i	$-0.407295\pi$
$607$	14.1488			0.574282			0.287141	+	0.957888i	$0.407295\pi$
$608$	−5.05944	−	3.67590i	−0.205187	−	0.149077i
$609$		0			0
$610$	−3.60639	−	1.31919i	−0.146019	−	0.0534126i
$611$	−2.71914	−	8.36865i	−0.110005	−	0.338559i
$612$		0			0
$613$	12.9536	−	39.8671i	0.523191	−	1.61022i	−0.244675	−	0.969605i	$-0.578681\pi$
$613$	12.9536	−	39.8671i	0.523191	−	1.61022i	0.767866	−	0.640611i	$-0.221319\pi$
$614$	−3.71048	−	11.4197i	−0.149743	−	0.460861i
$615$		0			0
$616$	0.449244	−	1.38263i	0.0181005	−	0.0557077i
$617$	32.5377	+	23.6400i	1.30992	+	0.951712i	1.00000		0.000948881i	$0.000302038\pi$
$617$	32.5377	+	23.6400i	1.30992	+	0.951712i	0.309919	+	0.950763i	$0.399698\pi$
$618$		0			0
$619$	19.0988	+	13.8761i	0.767644	+	0.557726i	0.901245	−	0.433309i	$-0.142654\pi$
$619$	19.0988	+	13.8761i	0.767644	+	0.557726i	−0.133601	+	0.991035i	$0.542654\pi$
$620$	3.91388	+	5.82275i	0.157185	+	0.233847i
$621$		0			0
$622$	−15.2944	+	11.1121i	−0.613252	+	0.445553i
$623$	−6.07098	−	18.6846i	−0.243229	−	0.748581i
$624$		0			0
$625$	−17.8714	−	17.4818i	−0.714854	−	0.699273i
$626$	−8.70156			−0.347784
$627$		0			0
$628$	−0.702324	+	0.510268i	−0.0280258	+	0.0203619i
$629$	21.7039	−	15.7688i	0.865390	−	0.628743i
$630$		0			0
$631$	14.0785	+	10.2286i	0.560455	+	0.407195i	0.831626	−	0.555337i	$-0.187411\pi$
$631$	14.0785	+	10.2286i	0.560455	+	0.407195i	−0.271170	+	0.962531i	$0.587411\pi$
$632$	−3.23309			−0.128605
$633$		0			0
$634$	3.94335	−	12.1364i	0.156610	−	0.481998i
$635$	2.01717	−	2.57332i	0.0800491	−	0.102119i
$636$		0			0
$637$	−0.307569	+	0.946601i	−0.0121863	+	0.0375057i
$638$	0.958303	−	2.94935i	0.0379396	−	0.116766i
$639$		0			0
$640$	2.09998	+	0.768160i	0.0830091	+	0.0303642i
$641$	−6.36332	+	19.5843i	−0.251336	+	0.773533i	0.743194	+	0.669077i	$0.233310\pi$
$641$	−6.36332	+	19.5843i	−0.251336	+	0.773533i	−0.994529	+	0.104456i	$0.966690\pi$
$642$		0			0
$643$	−13.1725			−0.519473			−0.259736	−	0.965680i	$-0.583636\pi$
$643$	−13.1725			−0.519473			−0.259736	+	0.965680i	$0.583636\pi$
$644$	−10.5979	−	7.69985i	−0.417617	−	0.303417i
$645$		0			0
$646$	−38.9313	+	28.2852i	−1.53173	+	1.11287i
$647$	17.8760	−	12.9877i	0.702780	−	0.510599i	−0.178057	−	0.984020i	$-0.556981\pi$
$647$	17.8760	−	12.9877i	0.702780	−	0.510599i	0.880836	+	0.473421i	$0.156981\pi$
$648$		0			0
$649$	0.431170			0.0169249
$650$	9.50899	−	23.3193i	0.372973	−	0.914657i
$651$		0			0
$652$	2.51983	+	7.75525i	0.0986842	+	0.303719i
$653$	−16.1998	+	11.7698i	−0.633947	+	0.460589i	−0.857765	−	0.514042i	$-0.828148\pi$
$653$	−16.1998	+	11.7698i	−0.633947	+	0.460589i	0.223818	+	0.974631i	$0.428148\pi$
$654$		0			0
$655$	−1.60661	+	43.9786i	−0.0627755	+	1.71839i
$656$	4.46543	+	3.24432i	0.174346	+	0.126670i
$657$		0			0
$658$	3.79188	+	2.75496i	0.147823	+	0.107400i
$659$	−7.56699	+	23.2888i	−0.294768	+	0.907203i	0.688531	+	0.725207i	$0.258256\pi$
$659$	−7.56699	+	23.2888i	−0.294768	+	0.907203i	−0.983299	+	0.181996i	$0.941744\pi$
$660$		0			0
$661$	−5.65040	−	17.3901i	−0.219775	−	0.676398i	−0.998780	−	0.0493804i	$-0.984275\pi$
$661$	−5.65040	−	17.3901i	−0.219775	−	0.676398i	0.779005	−	0.627018i	$-0.215725\pi$
$662$	1.18592	−	3.64987i	0.0460919	−	0.141856i
$663$		0			0
$664$	−0.235761	−	0.725596i	−0.00914928	−	0.0281586i
$665$	1.36963	−	37.4916i	0.0531120	−	1.45386i
$666$		0			0
$667$	−22.6070	−	16.4249i	−0.875345	−	0.635975i
$668$	−5.13524			−0.198688
$669$		0			0
$670$	−29.2860	+	8.34666i	−1.13142	+	0.322459i
$671$	−0.752870	+	0.546992i	−0.0290642	+	0.0211164i
$672$		0			0
$673$	−2.28629	−	7.03648i	−0.0881301	−	0.271236i	0.897272	−	0.441477i	$-0.145545\pi$
$673$	−2.28629	−	7.03648i	−0.0881301	−	0.271236i	−0.985402	+	0.170241i	$0.945545\pi$
$674$	1.70120			0.0655279
$675$		0			0
$676$	12.3684			0.475706
$677$	−4.06460	−	12.5096i	−0.156215	−	0.480782i	0.842067	−	0.539374i	$-0.181339\pi$
$677$	−4.06460	−	12.5096i	−0.156215	−	0.480782i	−0.998282	+	0.0585919i	$0.981339\pi$
$678$		0			0
$679$	24.7942	−	18.0140i	0.951513	−	0.691315i
$680$	10.6149	−	13.5415i	0.407063	−	0.519293i
$681$		0			0
$682$	1.70021			0.0651045
$683$	17.3035	+	12.5717i	0.662099	+	0.481043i	0.867371	−	0.497662i	$-0.165808\pi$
$683$	17.3035	+	12.5717i	0.662099	+	0.481043i	−0.205272	+	0.978705i	$0.565808\pi$
$684$		0			0
$685$	−12.7036	+	3.62060i	−0.485381	+	0.138336i
$686$	5.63947	+	17.3565i	0.215316	+	0.662674i
$687$		0			0
$688$	3.98637	−	12.2688i	0.151979	−	0.467743i
$689$	−15.8554	−	48.7978i	−0.604041	−	1.85905i
$690$		0			0
$691$	−12.5117	+	38.5071i	−0.475968	+	1.46488i	0.368681	+	0.929556i	$0.379810\pi$
$691$	−12.5117	+	38.5071i	−0.475968	+	1.46488i	−0.844648	+	0.535321i	$0.820190\pi$
$692$	−14.2692	−	10.3672i	−0.542435	−	0.394102i
$693$		0			0
$694$	21.5469	+	15.6547i	0.817909	+	0.594246i
$695$	−24.0202	+	30.6427i	−0.911139	+	1.16235i
$696$		0			0
$697$	34.3605	−	24.9644i	1.30150	−	0.945593i
$698$	−1.99444	−	6.13824i	−0.0754905	−	0.232336i
$699$		0			0
$700$	3.20329	+	13.0261i	0.121073	+	0.492340i
$701$	21.5704			0.814704			0.407352	−	0.913271i	$-0.366452\pi$
$701$	21.5704			0.814704			0.407352	+	0.913271i	$0.366452\pi$
$702$		0			0
$703$	17.6395	−	12.8158i	0.665285	−	0.483358i
$704$	0.438392	−	0.318511i	0.0165225	−	0.0120043i
$705$		0			0
$706$	−19.3743	−	14.0762i	−0.729161	−	0.529766i
$707$	−6.00061			−0.225676
$708$		0			0
$709$	−1.59709	+	4.91534i	−0.0599800	+	0.184600i	−0.976557	−	0.215259i	$-0.930941\pi$
$709$	−1.59709	+	4.91534i	−0.0599800	+	0.184600i	0.916577	+	0.399858i	$0.130941\pi$
$710$	0.705785	−	19.3198i	0.0264876	−	0.725059i
$711$		0			0
$712$	2.26290	−	6.96448i	0.0848057	−	0.261005i
$713$	4.73424	−	14.5705i	0.177299	−	0.545669i
$714$		0			0
$715$	−3.40456	−	5.06502i	−0.127323	−	0.189421i
$716$	5.10386	−	15.7081i	0.190740	−	0.587038i
$717$		0			0
$718$	−15.6809			−0.585205
$719$	−14.8280	−	10.7732i	−0.552991	−	0.401771i	0.275896	−	0.961187i	$-0.411025\pi$
$719$	−14.8280	−	10.7732i	−0.552991	−	0.401771i	−0.828887	+	0.559416i	$0.811025\pi$
$720$		0			0
$721$	22.6877	−	16.4836i	0.844933	−	0.613880i
$722$	−16.2694	+	11.8204i	−0.605485	+	0.439910i
$723$		0			0
$724$	−19.3035			−0.717410
$725$	6.83308	+	27.7866i	0.253774	+	1.03197i
$726$		0			0
$727$	−1.14016	−	3.50905i	−0.0422862	−	0.130144i	0.927685	−	0.373365i	$-0.121796\pi$
$727$	−1.14016	−	3.50905i	−0.0422862	−	0.130144i	−0.969971	+	0.243221i	$0.921796\pi$
$728$	−10.9320	+	7.94253i	−0.405165	+	0.294370i
$729$		0			0
$730$	2.73259	+	0.999561i	0.101138	+	0.0369954i
$731$	−80.3063	−	58.3459i	−2.97024	−	2.15800i
$732$		0			0
$733$	25.4477	+	18.4888i	0.939932	+	0.682901i	0.948404	−	0.317064i	$-0.102697\pi$
$733$	25.4477	+	18.4888i	0.939932	+	0.682901i	−0.00847226	+	0.999964i	$0.502697\pi$
$734$	−4.42514	+	13.6192i	−0.163335	+	0.502693i
$735$		0			0
$736$	−1.50887	−	4.64382i	−0.0556177	−	0.171174i
$737$	−2.28045	+	7.01851i	−0.0840016	+	0.258530i
$738$		0			0
$739$	−6.57476	−	20.2350i	−0.241856	−	0.744357i	−0.996138	−	0.0878059i	$-0.972014\pi$
$739$	−6.57476	−	20.2350i	−0.241856	−	0.744357i	0.754281	−	0.656551i	$-0.227986\pi$
$740$	−4.80953	+	6.13555i	−0.176802	+	0.225547i
$741$		0			0
$742$	22.1105	+	16.0642i	0.811703	+	0.589737i
$743$	41.2006			1.51150			0.755751	−	0.654859i	$-0.227272\pi$
$743$	41.2006			1.51150			0.755751	+	0.654859i	$0.227272\pi$
$744$		0			0
$745$	20.1561	+	29.9867i	0.738464	+	1.09863i
$746$	14.8443	−	10.7850i	0.543490	−	0.394868i
$747$		0			0
$748$	−1.28850	−	3.96559i	−0.0471122	−	0.144996i
$749$	15.8956			0.580813
$750$		0			0
$751$	−21.6837			−0.791251			−0.395625	−	0.918412i	$-0.629472\pi$
$751$	−21.6837			−0.791251			−0.395625	+	0.918412i	$0.629472\pi$
$752$	0.539865	+	1.66153i	0.0196868	+	0.0605899i
$753$		0			0
$754$	−23.3195	+	16.9426i	−0.849246	+	0.617013i
$755$	−12.7111	−	18.9105i	−0.462603	−	0.688223i
$756$		0			0
$757$	−9.12978			−0.331828			−0.165914	−	0.986140i	$-0.553057\pi$
$757$	−9.12978			−0.331828			−0.165914	+	0.986140i	$0.553057\pi$
$758$	−17.8579	−	12.9745i	−0.648628	−	0.471255i
$759$		0			0
$760$	8.62709	−	11.0056i	0.312937	−	0.399216i
$761$	15.0615	+	46.3546i	0.545979	+	1.68035i	0.718650	+	0.695372i	$0.244760\pi$
$761$	15.0615	+	46.3546i	0.545979	+	1.68035i	−0.172670	+	0.984980i	$0.555240\pi$
$762$		0			0
$763$	−7.12918	+	21.9414i	−0.258094	+	0.794331i
$764$	7.94718	+	24.4589i	0.287519	+	0.884892i
$765$		0			0
$766$	4.17732	−	12.8565i	0.150933	−	0.464523i
$767$	−3.24226	−	2.35564i	−0.117071	−	0.0850571i
$768$		0			0
$769$	−22.9587	−	16.6805i	−0.827911	−	0.601513i	0.0910564	−	0.995846i	$-0.470976\pi$
$769$	−22.9587	−	16.6805i	−0.827911	−	0.601513i	−0.918968	+	0.394333i	$0.870976\pi$
$770$	3.05292	+	1.11674i	0.110020	+	0.0402444i
$771$		0			0
$772$	−7.23127	+	5.25383i	−0.260259	+	0.189089i
$773$	−7.90525	−	24.3299i	−0.284332	−	0.875084i	−0.986598	−	0.163170i	$-0.947828\pi$
$773$	−7.90525	−	24.3299i	−0.284332	−	0.875084i	0.702266	−	0.711915i	$-0.252172\pi$
$774$		0			0
$775$	−13.3309	+	8.27053i	−0.478859	+	0.297086i
$776$	11.4235			0.410078
$777$		0			0
$778$	−5.66941	+	4.11906i	−0.203258	+	0.147676i
$779$	27.9259	−	20.2894i	1.00055	−	0.726942i
$780$		0			0
$781$	−3.79027	−	2.75379i	−0.135627	−	0.0985384i
$782$	−37.5721			−1.34358
$783$		0			0
$784$	0.0610656	−	0.187941i	0.00218092	−	0.00671217i
$785$	−1.08290	−	1.61105i	−0.0386504	−	0.0575009i
$786$		0			0
$787$	2.64111	−	8.12849i	0.0941453	−	0.289749i	−0.892885	−	0.450285i	$-0.851322\pi$
$787$	2.64111	−	8.12849i	0.0941453	−	0.289749i	0.987030	+	0.160536i	$0.0513222\pi$
$788$	3.98284	−	12.2579i	0.141883	−	0.436670i
$789$		0			0
$790$	0.263926	−	7.22459i	0.00939008	−	0.257039i
$791$	−2.00897	+	6.18297i	−0.0714307	+	0.219841i
$792$		0			0
$793$	8.64974			0.307161
$794$	7.29448	+	5.29975i	0.258871	+	0.188081i
$795$		0			0
$796$	−13.4034	+	9.73812i	−0.475070	+	0.345158i
$797$	−4.31303	+	3.13360i	−0.152775	+	0.110998i	−0.661547	−	0.749904i	$-0.730100\pi$
$797$	−4.31303	+	3.13360i	−0.152775	+	0.110998i	0.508772	+	0.860902i	$0.330100\pi$
$798$		0			0
$799$	13.4431			0.475582
$800$	−1.88794	+	4.62987i	−0.0667488	+	0.163691i
$801$		0			0
$802$	−1.73176	−	5.32981i	−0.0611505	−	0.188202i
$803$	0.570454	−	0.414459i	0.0201309	−	0.0146259i
$804$		0			0
$805$	18.0710	−	23.0533i	0.636921	−	0.812523i
$806$	−12.7850	−	9.28888i	−0.450334	−	0.327187i
$807$		0			0
$808$	−1.80950	−	1.31468i	−0.0636581	−	0.0462503i
$809$	−2.71203	+	8.34677i	−0.0953499	+	0.293457i	−0.987345	−	0.158589i	$-0.949306\pi$
$809$	−2.71203	+	8.34677i	−0.0953499	+	0.293457i	0.891995	+	0.452046i	$0.149306\pi$
$810$		0			0
$811$	2.35490	+	7.24763i	0.0826916	+	0.254499i	0.983851	−	0.178989i	$-0.0572827\pi$
$811$	2.35490	+	7.24763i	0.0826916	+	0.254499i	−0.901159	+	0.433488i	$0.857283\pi$
$812$	4.74451	−	14.6021i	0.166500	−	0.512434i
$813$		0			0
$814$	0.583809	+	1.79678i	0.0204625	+	0.0629771i
$815$	−17.5354	+	4.99768i	−0.614238	+	0.175061i
$816$		0			0
$817$	−65.2676	−	47.4197i	−2.28342	−	1.65900i
$818$	23.4851			0.821137
$819$		0			0
$820$	−7.61422	+	9.71350i	−0.265900	+	0.339210i
$821$	−19.5644	+	14.2143i	−0.682801	+	0.496084i	−0.874286	−	0.485412i	$-0.838670\pi$
$821$	−19.5644	+	14.2143i	−0.682801	+	0.496084i	0.191485	+	0.981496i	$0.438670\pi$
$822$		0			0
$823$	11.4452	+	35.2248i	0.398955	+	1.22786i	0.925838	+	0.377920i	$0.123361\pi$
$823$	11.4452	+	35.2248i	0.398955	+	1.22786i	−0.526883	+	0.849938i	$0.676639\pi$
$824$	10.4529			0.364145
$825$		0			0
$826$	2.13470			0.0742759
$827$	10.3423	+	31.8302i	0.359635	+	1.10684i	0.953273	+	0.302111i	$0.0976913\pi$
$827$	10.3423	+	31.8302i	0.359635	+	1.10684i	−0.593637	+	0.804733i	$0.702309\pi$
$828$		0			0
$829$	7.26918	−	5.28137i	0.252469	−	0.183430i	−0.454351	−	0.890823i	$-0.650129\pi$
$829$	7.26918	−	5.28137i	0.252469	−	0.183430i	0.706820	+	0.707393i	$0.250129\pi$
$830$	1.64065	−	0.467593i	0.0569477	−	0.0162304i
$831$		0			0
$832$	−5.03670			−0.174616
$833$	−1.23018	−	0.893778i	−0.0426232	−	0.0309676i
$834$		0			0
$835$	0.419205	−	11.4751i	0.0145072	−	0.397112i
$836$	−1.04721	−	3.22297i	−0.0362184	−	0.111469i
$837$		0			0
$838$	−3.28727	+	10.1172i	−0.113557	+	0.349492i
$839$	−3.32934	−	10.2467i	−0.114942	−	0.353754i	0.876993	−	0.480503i	$-0.159546\pi$
$839$	−3.32934	−	10.2467i	−0.114942	−	0.353754i	−0.991935	+	0.126749i	$0.959546\pi$
$840$		0			0
$841$	1.15926	−	3.56783i	0.0399744	−	0.123028i
$842$	5.58833	+	4.06016i	0.192587	+	0.139922i
$843$		0			0
$844$	18.5272	+	13.4608i	0.637732	+	0.463339i
$845$	−1.00966	+	27.6381i	−0.0347335	+	0.950778i
$846$		0			0
$847$	−23.2377	+	16.8832i	−0.798458	+	0.580114i
$848$	3.14796	+	9.68843i	0.108102	+	0.332702i
$849$		0			0
$850$	29.3930	+	24.8253i	1.00817	+	0.851500i
$851$	17.0236			0.583563
$852$		0			0
$853$	25.6142	−	18.6098i	0.877012	−	0.637187i	−0.0554472	−	0.998462i	$-0.517658\pi$
$853$	25.6142	−	18.6098i	0.877012	−	0.637187i	0.932459	+	0.361275i	$0.117658\pi$
$854$	−3.72742	+	2.70813i	−0.127550	+	0.0926704i
$855$		0			0
$856$	4.79336	+	3.48258i	0.163834	+	0.119032i
$857$	19.3605			0.661343			0.330671	−	0.943746i	$-0.392725\pi$
$857$	19.3605			0.661343			0.330671	+	0.943746i	$0.392725\pi$
$858$		0			0
$859$	−0.0770598	+	0.237166i	−0.00262925	+	0.00809199i	−0.952363	−	0.304968i	$-0.901354\pi$
$859$	−0.0770598	+	0.237166i	−0.00262925	+	0.00809199i	0.949733	+	0.313060i	$0.101354\pi$
$860$	27.0901	+	9.90939i	0.923766	+	0.337908i
$861$		0			0
$862$	1.06861	−	3.28883i	0.0363968	−	0.112018i
$863$	−1.65408	+	5.09074i	−0.0563056	+	0.173291i	−0.975254	−	0.221086i	$-0.929040\pi$
$863$	−1.65408	+	5.09074i	−0.0563056	+	0.173291i	0.918949	+	0.394377i	$0.129040\pi$
$864$		0			0
$865$	24.3312	−	31.0394i	0.827285	−	1.05537i
$866$	6.87266	−	21.1519i	0.233542	−	0.718770i
$867$		0			0
$868$	8.41768			0.285715
$869$	−1.41736	−	1.02977i	−0.0480807	−	0.0349327i
$870$		0			0
$871$	55.4929	−	40.3179i	1.88030	−	1.36612i
$872$	−6.95698	+	5.05454i	−0.235593	+	0.171168i
$873$		0			0
$874$	−30.5361			−1.03290
$875$	−29.3693	+	6.09463i	−0.992864	+	0.206036i
$876$		0			0
$877$	0.678510	+	2.08824i	0.0229116	+	0.0705148i	0.961859	−	0.273547i	$-0.0881970\pi$
$877$	0.678510	+	2.08824i	0.0229116	+	0.0705148i	−0.938947	+	0.344062i	$0.888197\pi$
$878$	−20.2611	+	14.7206i	−0.683779	+	0.496795i
$879$		0			0
$880$	0.675949	+	1.00562i	0.0227862	+	0.0338995i
$881$	37.9834	+	27.5966i	1.27969	+	0.929751i	0.999544	−	0.0302050i	$-0.00961603\pi$
$881$	37.9834	+	27.5966i	1.27969	+	0.929751i	0.280149	+	0.959956i	$0.409616\pi$
$882$		0			0
$883$	−19.6566	−	14.2814i	−0.661498	−	0.480606i	0.205671	−	0.978621i	$-0.434062\pi$
$883$	−19.6566	−	14.2814i	−0.661498	−	0.480606i	−0.867168	+	0.498015i	$0.834062\pi$
$884$	−11.9764	+	36.8595i	−0.402809	+	1.23972i
$885$		0			0
$886$	10.1197	+	31.1453i	0.339979	+	1.04635i
$887$	11.3071	−	34.7995i	0.379654	−	1.16845i	−0.560631	−	0.828065i	$-0.689442\pi$
$887$	11.3071	−	34.7995i	0.379654	−	1.16845i	0.940285	−	0.340388i	$-0.110558\pi$
$888$		0			0
$889$	−1.21227	−	3.73099i	−0.0406583	−	0.125133i
$890$	15.3779	+	5.62515i	0.515470	+	0.188555i
$891$		0			0
$892$	7.31954	+	5.31796i	0.245076	+	0.178058i
$893$	10.9256			0.365613
$894$		0			0
$895$	34.6843	+	12.6873i	1.15937	+	0.424089i
$896$	2.17046	−	1.57693i	0.0725100	−	0.0526816i
$897$		0			0
$898$	6.34538	+	19.5291i	0.211748	+	0.651694i
$899$	17.9562			0.598871
$900$		0			0
$901$	78.3870			2.61145
$902$	0.924257	+	2.84457i	0.0307744	+	0.0947139i
$903$		0			0
$904$	−1.96044	+	1.42434i	−0.0652034	+	0.0473730i
$905$	1.57580	−	43.1352i	0.0523815	−	1.43386i
$906$		0			0
$907$	30.1732			1.00189			0.500943	−	0.865481i	$-0.332987\pi$
$907$	30.1732			1.00189			0.500943	+	0.865481i	$0.332987\pi$
$908$	17.4384	+	12.6698i	0.578714	+	0.420461i
$909$		0			0
$910$	−16.8558	−	25.0767i	−0.558764	−	0.831284i
$911$	8.21882	+	25.2949i	0.272302	+	0.838059i	0.989921	+	0.141623i	$0.0452320\pi$
$911$	8.21882	+	25.2949i	0.272302	+	0.838059i	−0.717619	+	0.696436i	$0.754768\pi$
$912$		0			0
$913$	0.127755	−	0.393188i	0.00422806	−	0.0130126i
$914$	11.4742	+	35.3139i	0.379532	+	1.16808i
$915$		0			0
$916$	3.80323	−	11.7051i	0.125662	−	0.386748i
$917$	42.7167	+	31.0355i	1.41063	+	1.02488i
$918$		0			0
$919$	−20.9718	−	15.2369i	−0.691796	−	0.502619i	0.185454	−	0.982653i	$-0.440624\pi$
$919$	−20.9718	−	15.2369i	−0.691796	−	0.502619i	−0.877250	+	0.480034i	$0.840624\pi$
$920$	10.5002	−	2.99260i	0.346180	−	0.0986630i
$921$		0			0
$922$	−29.8392	+	21.6795i	−0.982702	+	0.713975i
$923$	13.4566	+	41.4152i	0.442930	+	1.36320i
$924$		0			0
$925$	−13.3177	−	11.2481i	−0.437885	−	0.369837i
$926$	−24.5239			−0.805904
$927$		0			0
$928$	4.62991	−	3.36383i	0.151984	−	0.110423i
$929$	−30.0226	+	21.8127i	−0.985009	+	0.715651i	−0.958822	−	0.284006i	$-0.908336\pi$
$929$	−30.0226	+	21.8127i	−0.985009	+	0.715651i	−0.0261864	+	0.999657i	$0.508336\pi$
$930$		0			0
$931$	−0.999808	−	0.726403i	−0.0327674	−	0.0238069i
$932$	29.0407			0.951260
$933$		0			0
$934$	5.36221	−	16.5032i	0.175457	−	0.540001i
$935$	8.96661	−	2.55553i	0.293239	−	0.0835747i
$936$		0			0
$937$	−2.56078	+	7.88126i	−0.0836569	+	0.257470i	−0.984132	−	0.177438i	$-0.943219\pi$
$937$	−2.56078	+	7.88126i	−0.0836569	+	0.257470i	0.900475	+	0.434908i	$0.143219\pi$
$938$	−11.2904	+	34.7483i	−0.368645	+	1.13457i
$939$		0			0
$940$	−3.75690	+	1.07073i	−0.122536	+	0.0349235i
$941$	3.57339	−	10.9978i	0.116489	−	0.358517i	−0.875766	−	0.482737i	$-0.839643\pi$
$941$	3.57339	−	10.9978i	0.116489	−	0.358517i	0.992255	+	0.124220i	$0.0396428\pi$
$942$		0			0
$943$	26.9510			0.877645
$944$	0.643726	+	0.467694i	0.0209515	+	0.0152222i
$945$		0			0
$946$	5.65534	−	4.10884i	0.183871	−	0.133590i
$947$	−25.6584	+	18.6420i	−0.833787	+	0.605782i	−0.920628	−	0.390440i	$-0.872323\pi$
$947$	−25.6584	+	18.6420i	−0.833787	+	0.605782i	0.0868408	+	0.996222i	$0.472323\pi$
$948$		0			0
$949$	−6.55396			−0.212751
$950$	23.8887	+	20.1763i	0.775051	+	0.654606i
$951$		0			0
$952$	−6.37930	−	19.6335i	−0.206754	−	0.636324i
$953$	−21.7191	+	15.7799i	−0.703551	+	0.511160i	−0.881087	−	0.472954i	$-0.843188\pi$
$953$	−21.7191	+	15.7799i	−0.703551	+	0.511160i	0.177535	+	0.984114i	$0.443188\pi$
$954$		0			0
$955$	−55.3041	+	15.7619i	−1.78960	+	0.510045i
$956$	−8.27354	−	6.01108i	−0.267585	−	0.194412i
$957$		0			0
$958$	−12.4299	−	9.03087i	−0.401593	−	0.291774i
$959$	−4.89754	+	15.0731i	−0.158150	+	0.486735i
$960$		0			0
$961$	−6.53739	−	20.1200i	−0.210884	−	0.649033i
$962$	5.42640	−	16.7007i	0.174954	−	0.538453i
$963$		0			0
$964$	−2.55006	−	7.84827i	−0.0821318	−	0.252776i
$965$	−11.1498	−	16.5877i	−0.358924	−	0.533978i
$966$		0			0
$967$	21.0325	+	15.2810i	0.676361	+	0.491405i	0.872148	−	0.489241i	$-0.162726\pi$
$967$	21.0325	+	15.2810i	0.676361	+	0.491405i	−0.195787	+	0.980646i	$0.562726\pi$
$968$	−10.7064			−0.344116
$969$		0			0
$970$	−0.932530	+	25.5266i	−0.0299417	+	0.819610i
$971$	23.0178	−	16.7234i	0.738678	−	0.536681i	−0.153619	−	0.988130i	$-0.549093\pi$
$971$	23.0178	−	16.7234i	0.738678	−	0.536681i	0.892297	+	0.451449i	$0.149093\pi$
$972$		0			0
$973$	14.4356	+	44.4281i	0.462783	+	1.42430i
$974$	−38.6355			−1.23796
$975$		0			0
$976$	−1.71734			−0.0549708
$977$	3.45996	+	10.6487i	0.110694	+	0.340681i	0.991025	−	0.133680i	$-0.0426793\pi$
$977$	3.45996	+	10.6487i	0.110694	+	0.340681i	−0.880331	+	0.474361i	$0.842679\pi$
$978$		0			0
$979$	3.21030	−	2.33242i	0.102602	−	0.0745444i
$980$	0.414983	+	0.151798i	0.0132561	+	0.00484901i
$981$		0			0
$982$	−41.8590			−1.33577
$983$	32.2607	+	23.4388i	1.02896	+	0.747580i	0.968099	−	0.250566i	$-0.0806168\pi$
$983$	32.2607	+	23.4388i	1.02896	+	0.747580i	0.0608564	+	0.998147i	$0.480617\pi$
$984$		0			0
$985$	27.0661	+	9.90061i	0.862398	+	0.315460i
$986$	−13.6080	−	41.8811i	−0.433367	−	1.33377i
$987$		0			0
$988$	−9.73359	+	29.9569i	−0.309667	+	0.953056i
$989$	−19.4647	−	59.9061i	−0.618941	−	1.90490i
$990$		0			0
$991$	9.09055	−	27.9778i	0.288771	−	0.888745i	−0.696472	−	0.717584i	$-0.745248\pi$
$991$	9.09055	−	27.9778i	0.288771	−	0.888745i	0.985243	−	0.171161i	$-0.0547519\pi$
$992$	2.53838	+	1.84424i	0.0805935	+	0.0585546i
$993$		0			0
$994$	−18.7655	−	13.6339i	−0.595204	−	0.432441i
$995$	−20.6664	−	30.7458i	−0.655169	−	0.974708i
$996$		0			0
$997$	7.81998	−	5.68155i	0.247661	−	0.179936i	−0.457028	−	0.889452i	$-0.651086\pi$
$997$	7.81998	−	5.68155i	0.247661	−	0.179936i	0.704690	+	0.709516i	$0.251086\pi$
$998$	−1.56172	−	4.80648i	−0.0494354	−	0.152147i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.f.181.1	✓	12
3.2	odd	2		450.2.h.g.181.3	yes	12
25.21	even	5	inner	450.2.h.f.271.1	yes	12
75.71	odd	10		450.2.h.g.271.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.h.f.181.1	✓	12	1.1	even	1	trivial
450.2.h.f.271.1	yes	12	25.21	even	5	inner
450.2.h.g.181.3	yes	12	3.2	odd	2
450.2.h.g.271.3	yes	12	75.71	odd	10

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)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-1.24741 - 1.85579i) q^{5} -2.68284 q^{7} +(-0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-1.24741 - 1.85579i) q^{5} -2.68284 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.37949 - 1.75983i) q^{10} +(-0.167451 - 0.515361i) q^{11} +(-1.55643 + 4.79019i) q^{13} +(-0.829042 - 2.55153i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-6.22521 - 4.52288i) q^{17} +(-5.05944 - 3.67590i) q^{19} +(2.09998 + 0.768160i) q^{20} +(0.438392 - 0.318511i) q^{22} +(-1.50887 - 4.64382i) q^{23} +(-1.88794 + 4.62987i) q^{25} -5.03670 q^{26} +(2.17046 - 1.57693i) q^{28} +(4.62991 - 3.36383i) q^{29} +(2.53838 + 1.84424i) q^{31} +1.00000 q^{32} +(2.37782 - 7.31818i) q^{34} +(3.34660 + 4.97879i) q^{35} +(-1.07737 + 3.31581i) q^{37} +(1.93253 - 5.94772i) q^{38} +(-0.0816329 + 2.23458i) q^{40} +(-1.70564 + 5.24942i) q^{41} +12.9002 q^{43} +(0.438392 + 0.318511i) q^{44} +(3.95027 - 2.87004i) q^{46} +(-1.41338 + 1.02688i) q^{47} +0.197613 q^{49} +(-4.98667 - 0.364830i) q^{50} +(-1.55643 - 4.79019i) q^{52} +(-8.24147 + 5.98778i) q^{53} +(-0.747524 + 0.953620i) q^{55} +(2.17046 + 1.57693i) q^{56} +(4.62991 + 3.36383i) q^{58} +(-0.245881 + 0.756745i) q^{59} +(-0.530688 - 1.63329i) q^{61} +(-0.969573 + 2.98404i) q^{62} +(0.309017 + 0.951057i) q^{64} +(10.8311 - 3.08692i) q^{65} +(-11.0177 - 8.00483i) q^{67} +7.69479 q^{68} +(-3.70096 + 4.72133i) q^{70} +(6.99463 - 5.08190i) q^{71} +(0.402106 + 1.23755i) q^{73} -3.48645 q^{74} +6.25381 q^{76} +(0.449244 + 1.38263i) q^{77} +(2.61562 - 1.90036i) q^{79} +(-2.15044 + 0.612885i) q^{80} -5.51957 q^{82} +(0.617229 + 0.448443i) q^{83} +(-0.628147 + 17.1946i) q^{85} +(3.98637 + 12.2688i) q^{86} +(-0.167451 + 0.515361i) q^{88} +(2.26290 + 6.96448i) q^{89} +(4.17564 - 12.8513i) q^{91} +(3.95027 + 2.87004i) q^{92} +(-1.41338 - 1.02688i) q^{94} +(-0.510516 + 13.9746i) q^{95} +(-9.24177 + 6.71454i) q^{97} +(0.0610656 + 0.187941i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + q^{5} - 2 q^{7} - 3 q^{8}+O(q^{10}) \) 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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