LMFDB - Embedded newform 450.2.h.f.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			$-1.38239 + 1.75756i$ of defining polynomial
Character	$\chi$	$=$	450.91
Dual form			450.2.h.f.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.38239 + 1.75756i) q^{5} -0.447412 q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.38239 + 1.75756i) q^{5} -0.447412 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.15144 - 0.609344i) q^{10} +(-4.42816 - 3.21725i) q^{11} +(-0.573372 + 0.416579i) q^{13} +(0.361964 + 0.262982i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-0.133697 + 0.411479i) q^{17} +(2.49304 - 7.67280i) q^{19} +(-2.09872 - 0.771616i) q^{20} +(1.69141 + 5.20561i) q^{22} +(-4.65186 - 3.37978i) q^{23} +(-1.17800 - 4.85925i) q^{25} +0.708727 q^{26} +(-0.138258 - 0.425514i) q^{28} +(-1.03259 - 3.17797i) q^{29} +(-0.407310 + 1.25357i) q^{31} +1.00000 q^{32} +(0.350025 - 0.254308i) q^{34} +(0.618497 - 0.786351i) q^{35} +(-8.14595 + 5.91838i) q^{37} +(-6.52687 + 4.74205i) q^{38} +(1.24435 + 1.85784i) q^{40} +(4.80242 - 3.48916i) q^{41} -7.09283 q^{43} +(1.69141 - 5.20561i) q^{44} +(1.77685 + 5.46859i) q^{46} +(2.83769 + 8.73350i) q^{47} -6.79982 q^{49} +(-1.90317 + 4.62363i) q^{50} +(-0.573372 - 0.416579i) q^{52} +(0.210809 + 0.648802i) q^{53} +(11.7759 - 3.33525i) q^{55} +(-0.138258 + 0.425514i) q^{56} +(-1.03259 + 3.17797i) q^{58} +(-2.75539 + 2.00191i) q^{59} +(4.91755 + 3.57281i) q^{61} +(1.06635 - 0.774750i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(0.0604623 - 1.58361i) q^{65} +(0.528998 - 1.62809i) q^{67} -0.432654 q^{68} +(-0.962580 + 0.272628i) q^{70} +(-0.558490 - 1.71886i) q^{71} +(-10.0932 - 7.33316i) q^{73} +10.0689 q^{74} +8.06766 q^{76} +(1.98121 + 1.43943i) q^{77} +(-2.72171 - 8.37656i) q^{79} +(0.0853112 - 2.23444i) q^{80} -5.93612 q^{82} +(0.545222 - 1.67802i) q^{83} +(-0.538374 - 0.803804i) q^{85} +(5.73822 + 4.16906i) q^{86} +(-4.42816 + 3.21725i) q^{88} +(11.2689 + 8.18730i) q^{89} +(0.256533 - 0.186382i) q^{91} +(1.77685 - 5.46859i) q^{92} +(2.83769 - 8.73350i) q^{94} +(10.0390 + 14.9885i) q^{95} +(4.04585 + 12.4519i) q^{97} +(5.50117 + 3.99684i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.38239	+	1.75756i	−0.618223	+	0.786003i
$5$	−1.38239	+	1.75756i	−0.618223	+	0.786003i
$6$		0			0
$7$	−0.447412			−0.169106			−0.0845529	−	0.996419i	$-0.526946\pi$
$7$	−0.447412			−0.169106			−0.0845529	+	0.996419i	$0.526946\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$		0			0
$10$	2.15144	−	0.609344i	0.680345	−	0.192692i
$11$	−4.42816	−	3.21725i	−1.33514	−	0.970036i	−0.999608	−	0.0280073i	$-0.991084\pi$
$11$	−4.42816	−	3.21725i	−1.33514	−	0.970036i	−0.335532	−	0.942029i	$-0.608916\pi$
$12$		0			0
$13$	−0.573372	+	0.416579i	−0.159025	+	0.115538i	−0.664452	−	0.747331i	$-0.731335\pi$
$13$	−0.573372	+	0.416579i	−0.159025	+	0.115538i	0.505427	+	0.862869i	$0.331335\pi$
$14$	0.361964	+	0.262982i	0.0967389	+	0.0702849i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.133697	+	0.411479i	−0.0324264	+	0.0997982i	−0.965960	−	0.258692i	$-0.916708\pi$
$17$	−0.133697	+	0.411479i	−0.0324264	+	0.0997982i	0.933533	+	0.358490i	$0.116708\pi$
$18$		0			0
$19$	2.49304	−	7.67280i	0.571944	−	1.76026i	−0.0744148	−	0.997227i	$-0.523709\pi$
$19$	2.49304	−	7.67280i	0.571944	−	1.76026i	0.646358	−	0.763034i	$-0.276291\pi$
$20$	−2.09872	−	0.771616i	−0.469287	−	0.172539i
$21$		0			0
$22$	1.69141	+	5.20561i	0.360609	+	1.10984i
$23$	−4.65186	−	3.37978i	−0.969981	−	0.704732i	−0.0145336	−	0.999894i	$-0.504626\pi$
$23$	−4.65186	−	3.37978i	−0.969981	−	0.704732i	−0.955447	+	0.295162i	$0.904626\pi$
$24$		0			0
$25$	−1.17800	−	4.85925i	−0.235600	−	0.971850i
$26$	0.708727			0.138993
$27$		0			0
$28$	−0.138258	−	0.425514i	−0.0261283	−	0.0804145i
$29$	−1.03259	−	3.17797i	−0.191746	−	0.590135i	−0.999999	−	0.00129904i	$-0.999587\pi$
$29$	−1.03259	−	3.17797i	−0.191746	−	0.590135i	0.808253	−	0.588836i	$-0.200413\pi$
$30$		0			0
$31$	−0.407310	+	1.25357i	−0.0731550	+	0.225148i	−0.980948	−	0.194271i	$-0.937766\pi$
$31$	−0.407310	+	1.25357i	−0.0731550	+	0.225148i	0.907793	+	0.419419i	$0.137766\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	0.350025	−	0.254308i	0.0600287	−	0.0436134i
$35$	0.618497	−	0.786351i	0.104545	−	0.132918i
$36$		0			0
$37$	−8.14595	+	5.91838i	−1.33919	+	0.972976i	−0.339713	+	0.940529i	$0.610330\pi$
$37$	−8.14595	+	5.91838i	−1.33919	+	0.972976i	−0.999473	+	0.0324464i	$0.989670\pi$
$38$	−6.52687	+	4.74205i	−1.05880	+	0.769262i
$39$		0			0
$40$	1.24435	+	1.85784i	0.196749	+	0.293751i
$41$	4.80242	−	3.48916i	0.750012	−	0.544916i	−0.145819	−	0.989311i	$-0.546582\pi$
$41$	4.80242	−	3.48916i	0.750012	−	0.544916i	0.895831	+	0.444396i	$0.146582\pi$
$42$		0			0
$43$	−7.09283			−1.08165			−0.540823	−	0.841136i	$-0.681887\pi$
$43$	−7.09283			−1.08165			−0.540823	+	0.841136i	$0.681887\pi$
$44$	1.69141	−	5.20561i	0.254989	−	0.784776i
$45$		0			0
$46$	1.77685	+	5.46859i	0.261983	+	0.806300i
$47$	2.83769	+	8.73350i	0.413919	+	1.27391i	0.913214	+	0.407480i	$0.133592\pi$
$47$	2.83769	+	8.73350i	0.413919	+	1.27391i	−0.499295	+	0.866432i	$0.666408\pi$
$48$		0			0
$49$	−6.79982			−0.971403
$50$	−1.90317	+	4.62363i	−0.269149	+	0.653880i
$51$		0			0
$52$	−0.573372	−	0.416579i	−0.0795124	−	0.0577691i
$53$	0.210809	+	0.648802i	0.0289568	+	0.0891198i	0.964490	−	0.264118i	$-0.0850807\pi$
$53$	0.210809	+	0.648802i	0.0289568	+	0.0891198i	−0.935534	+	0.353238i	$0.885081\pi$
$54$		0			0
$55$	11.7759	−	3.33525i	1.58787	−	0.449725i
$56$	−0.138258	+	0.425514i	−0.0184755	+	0.0568617i
$57$		0			0
$58$	−1.03259	+	3.17797i	−0.135585	+	0.417288i
$59$	−2.75539	+	2.00191i	−0.358721	+	0.260626i	−0.752518	−	0.658571i	$-0.771161\pi$
$59$	−2.75539	+	2.00191i	−0.358721	+	0.260626i	0.393798	+	0.919197i	$0.371161\pi$
$60$		0			0
$61$	4.91755	+	3.57281i	0.629628	+	0.457451i	0.856271	−	0.516527i	$-0.172775\pi$
$61$	4.91755	+	3.57281i	0.629628	+	0.457451i	−0.226644	+	0.973978i	$0.572775\pi$
$62$	1.06635	−	0.774750i	0.135427	−	0.0983933i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.0604623	−	1.58361i	0.00749943	−	0.196422i
$66$		0			0
$67$	0.528998	−	1.62809i	0.0646274	−	0.198903i	−0.913529	−	0.406774i	$-0.866654\pi$
$67$	0.528998	−	1.62809i	0.0646274	−	0.198903i	0.978156	+	0.207871i	$0.0666536\pi$
$68$	−0.432654			−0.0524670
$69$		0			0
$70$	−0.962580	+	0.272628i	−0.115050	+	0.0325852i
$71$	−0.558490	−	1.71886i	−0.0662806	−	0.203991i	0.912431	−	0.409230i	$-0.134203\pi$
$71$	−0.558490	−	1.71886i	−0.0662806	−	0.203991i	−0.978712	+	0.205240i	$0.934203\pi$
$72$		0			0
$73$	−10.0932	−	7.33316i	−1.18132	−	0.858281i	−0.189003	−	0.981977i	$-0.560525\pi$
$73$	−10.0932	−	7.33316i	−1.18132	−	0.858281i	−0.992320	+	0.123695i	$0.960525\pi$
$74$	10.0689			1.17049
$75$		0			0
$76$	8.06766			0.925424
$77$	1.98121	+	1.43943i	0.225780	+	0.164039i
$78$		0			0
$79$	−2.72171	−	8.37656i	−0.306216	−	0.942436i	−0.979221	−	0.202798i	$-0.934997\pi$
$79$	−2.72171	−	8.37656i	−0.306216	−	0.942436i	0.673004	−	0.739638i	$-0.265003\pi$
$80$	0.0853112	−	2.23444i	0.00953808	−	0.249818i
$81$		0			0
$82$	−5.93612			−0.655534
$83$	0.545222	−	1.67802i	0.0598459	−	0.184187i	−0.916664	−	0.399658i	$-0.869129\pi$
$83$	0.545222	−	1.67802i	0.0598459	−	0.184187i	0.976510	+	0.215471i	$0.0691288\pi$
$84$		0			0
$85$	−0.538374	−	0.803804i	−0.0583949	−	0.0871848i
$86$	5.73822	+	4.16906i	0.618768	+	0.449561i
$87$		0			0
$88$	−4.42816	+	3.21725i	−0.472043	+	0.342960i
$89$	11.2689	+	8.18730i	1.19450	+	0.867852i	0.993732	−	0.111787i	$-0.0356575\pi$
$89$	11.2689	+	8.18730i	1.19450	+	0.867852i	0.200764	+	0.979640i	$0.435658\pi$
$90$		0			0
$91$	0.256533	−	0.186382i	0.0268920	−	0.0195382i
$92$	1.77685	−	5.46859i	0.185250	−	0.570140i
$93$		0			0
$94$	2.83769	−	8.73350i	0.292685	−	0.900792i
$95$	10.0390	+	14.9885i	1.02998	+	1.53778i
$96$		0			0
$97$	4.04585	+	12.4519i	0.410794	+	1.26429i	0.915959	+	0.401272i	$0.131432\pi$
$97$	4.04585	+	12.4519i	0.410794	+	1.26429i	−0.505165	+	0.863023i	$0.668568\pi$
$98$	5.50117	+	3.99684i	0.555702	+	0.403741i
$99$		0			0
$100$	4.25740	−	2.62194i	0.425740	−	0.262194i
$101$	−11.9062			−1.18471			−0.592354	−	0.805678i	$-0.701801\pi$
$101$	−11.9062			−1.18471			−0.592354	+	0.805678i	$0.701801\pi$
$102$		0			0
$103$	−1.66263	−	5.11705i	−0.163824	−	0.504198i	0.835124	−	0.550062i	$-0.185396\pi$
$103$	−1.66263	−	5.11705i	−0.163824	−	0.504198i	−0.998948	+	0.0458642i	$0.985396\pi$
$104$	0.219009	+	0.674039i	0.0214756	+	0.0660950i
$105$		0			0
$106$	0.210809	−	0.648802i	0.0204755	−	0.0630172i
$107$	13.9215			1.34584			0.672921	−	0.739715i	$-0.265040\pi$
$107$	13.9215			1.34584			0.672921	+	0.739715i	$0.265040\pi$
$108$		0			0
$109$	5.60018	−	4.06877i	0.536400	−	0.389718i	−0.286346	−	0.958126i	$-0.592441\pi$
$109$	5.60018	−	4.06877i	0.536400	−	0.389718i	0.822746	+	0.568409i	$0.192441\pi$
$110$	−11.4873	−	4.22344i	−1.09527	−	0.402689i
$111$		0			0
$112$	0.361964	−	0.262982i	0.0342024	−	0.0248495i
$113$	11.1677	−	8.11381i	1.05057	−	0.763283i	0.0782487	−	0.996934i	$-0.475067\pi$
$113$	11.1677	−	8.11381i	1.05057	−	0.763283i	0.972321	+	0.233651i	$0.0750672\pi$
$114$		0			0
$115$	12.3708	−	3.50374i	1.15359	−	0.326726i
$116$	2.70335	−	1.96410i	0.250999	−	0.182362i
$117$		0			0
$118$	3.40584			0.313533
$119$	0.0598178	−	0.184100i	0.00548349	−	0.0168764i
$120$		0			0
$121$	5.85873	+	18.0313i	0.532612	+	1.63921i
$122$	−1.87834	−	5.78092i	−0.170057	−	0.523380i
$123$		0			0
$124$	−1.31808			−0.118367
$125$	10.1689	+	4.64697i	0.909530	+	0.415638i
$126$		0			0
$127$	8.62222	+	6.26441i	0.765098	+	0.555876i	0.900470	−	0.434919i	$-0.143223\pi$
$127$	8.62222	+	6.26441i	0.765098	+	0.555876i	−0.135372	+	0.990795i	$0.543223\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	−0.979736	+	1.24563i	−0.0859285	+	0.109249i
$131$	3.01855	−	9.29014i	0.263732	−	0.811683i	−0.728251	−	0.685311i	$-0.759666\pi$
$131$	3.01855	−	9.29014i	0.263732	−	0.811683i	0.991983	−	0.126373i	$-0.0403336\pi$
$132$		0			0
$133$	−1.11542	+	3.43290i	−0.0967189	+	0.297670i
$134$	−1.38494	+	1.00621i	−0.119640	+	0.0869237i
$135$		0			0
$136$	0.350025	+	0.254308i	0.0300144	+	0.0218067i
$137$	−12.7881	+	9.29107i	−1.09256	+	0.793790i	−0.979829	−	0.199836i	$-0.935959\pi$
$137$	−12.7881	+	9.29107i	−1.09256	+	0.793790i	−0.112729	+	0.993626i	$0.535959\pi$
$138$		0			0
$139$	−8.10149	−	5.88608i	−0.687159	−	0.499251i	0.188566	−	0.982061i	$-0.439616\pi$
$139$	−8.10149	−	5.88608i	−0.687159	−	0.499251i	−0.875725	+	0.482810i	$0.839616\pi$
$140$	0.938990	+	0.345230i	0.0793591	+	0.0291772i
$141$		0			0
$142$	−0.558490	+	1.71886i	−0.0468674	+	0.144243i
$143$	3.87922			0.324397
$144$		0			0
$145$	7.01290	+	2.57837i	0.582390	+	0.214122i
$146$	3.85527	+	11.8653i	0.319064	+	0.981979i
$147$		0			0
$148$	−8.14595	−	5.91838i	−0.669593	−	0.486488i
$149$	−15.8758			−1.30060			−0.650299	−	0.759678i	$-0.725356\pi$
$149$	−15.8758			−1.30060			−0.650299	+	0.759678i	$0.725356\pi$
$150$		0			0
$151$	17.9787			1.46308			0.731541	−	0.681797i	$-0.238801\pi$
$151$	17.9787			1.46308			0.731541	+	0.681797i	$0.238801\pi$
$152$	−6.52687	−	4.74205i	−0.529399	−	0.384631i
$153$		0			0
$154$	−0.756755	−	2.32905i	−0.0609810	−	0.187680i
$155$	−1.64016	−	2.44879i	−0.131741	−	0.196692i
$156$		0			0
$157$	−20.7997			−1.66000			−0.830000	−	0.557763i	$-0.811660\pi$
$157$	−20.7997			−1.66000			−0.830000	+	0.557763i	$0.811660\pi$
$158$	−2.72171	+	8.37656i	−0.216528	+	0.666403i
$159$		0			0
$160$	−1.38239	+	1.75756i	−0.109287	+	0.138947i
$161$	2.08130	+	1.51215i	0.164029	+	0.119174i
$162$		0			0
$163$	−4.54778	+	3.30416i	−0.356210	+	0.258802i	−0.751469	−	0.659768i	$-0.770655\pi$
$163$	−4.54778	+	3.30416i	−0.356210	+	0.258802i	0.395260	+	0.918569i	$0.370655\pi$
$164$	4.80242	+	3.48916i	0.375006	+	0.272458i
$165$		0			0
$166$	−1.42741	+	1.03707i	−0.110788	+	0.0804925i
$167$	−0.628797	+	1.93524i	−0.0486578	+	0.149753i	−0.972433	−	0.233181i	$-0.925086\pi$
$167$	−0.628797	+	1.93524i	−0.0486578	+	0.149753i	0.923776	+	0.382934i	$0.125086\pi$
$168$		0			0
$169$	−3.86200	+	11.8860i	−0.297077	+	0.914310i
$170$	−0.0369102	+	0.966740i	−0.00283088	+	0.0741455i
$171$		0			0
$172$	−2.19180	−	6.74568i	−0.167124	−	0.514353i
$173$	−3.75509	−	2.72823i	−0.285494	−	0.207424i	0.435816	−	0.900036i	$-0.356460\pi$
$173$	−3.75509	−	2.72823i	−0.285494	−	0.207424i	−0.721310	+	0.692612i	$0.756460\pi$
$174$		0			0
$175$	0.527051	+	2.17409i	0.0398413	+	0.164345i
$176$	5.47350			0.412581
$177$		0			0
$178$	−4.30432	−	13.2473i	−0.322622	−	0.992930i
$179$	−5.14952	−	15.8486i	−0.384893	−	1.18458i	−0.936558	−	0.350514i	$-0.886007\pi$
$179$	−5.14952	−	15.8486i	−0.384893	−	1.18458i	0.551664	−	0.834066i	$-0.313993\pi$
$180$		0			0
$181$	2.03554	−	6.26475i	0.151301	−	0.465655i	−0.846467	−	0.532442i	$-0.821275\pi$
$181$	2.03554	−	6.26475i	0.151301	−	0.465655i	0.997767	+	0.0667863i	$0.0212746\pi$
$182$	−0.317093			−0.0235045
$183$		0			0
$184$	−4.65186	+	3.37978i	−0.342940	+	0.249160i
$185$	0.858994	−	22.4985i	0.0631545	−	1.65412i
$186$		0			0
$187$	1.91586	−	1.39195i	0.140102	−	0.101790i
$188$	−7.42916	+	5.39760i	−0.541827	+	0.393661i
$189$		0			0
$190$	0.688261	−	18.0267i	0.0499317	−	1.30779i
$191$	−7.30988	+	5.31094i	−0.528924	+	0.384286i	−0.819955	−	0.572428i	$-0.806002\pi$
$191$	−7.30988	+	5.31094i	−0.528924	+	0.384286i	0.291031	+	0.956714i	$0.406002\pi$
$192$		0			0
$193$	−16.1970			−1.16589			−0.582944	−	0.812512i	$-0.698099\pi$
$193$	−16.1970			−1.16589			−0.582944	+	0.812512i	$0.698099\pi$
$194$	4.04585	−	12.4519i	0.290475	−	0.893991i
$195$		0			0
$196$	−2.10126	−	6.46702i	−0.150090	−	0.461930i
$197$	2.93651	+	9.03765i	0.209218	+	0.643906i	0.999514	+	0.0311807i	$0.00992672\pi$
$197$	2.93651	+	9.03765i	0.209218	+	0.643906i	−0.790296	+	0.612725i	$0.790073\pi$
$198$		0			0
$199$	17.2676			1.22407			0.612033	−	0.790832i	$-0.290352\pi$
$199$	17.2676			1.22407			0.612033	+	0.790832i	$0.290352\pi$
$200$	−4.98544	−	0.381245i	−0.352524	−	0.0269581i
$201$		0			0
$202$	9.63228	+	6.99826i	0.677725	+	0.492396i
$203$	0.461991	+	1.42186i	0.0324254	+	0.0997952i
$204$		0			0
$205$	−0.506417	+	13.2639i	−0.0353697	+	0.926391i
$206$	−1.66263	+	5.11705i	−0.115841	+	0.356521i
$207$		0			0
$208$	0.219009	−	0.674039i	0.0151855	−	0.0467362i
$209$	−35.7249	+	25.9556i	−2.47114	+	1.79539i
$210$		0			0
$211$	−1.18538	−	0.861229i	−0.0816049	−	0.0592894i	0.546235	−	0.837632i	$-0.316061\pi$
$211$	−1.18538	−	0.861229i	−0.0816049	−	0.0592894i	−0.627840	+	0.778343i	$0.716061\pi$
$212$	−0.551904	+	0.400982i	−0.0379049	+	0.0275395i
$213$		0			0
$214$	−11.2627	−	8.18285i	−0.769904	−	0.559368i
$215$	9.80505	−	12.4660i	0.668699	−	0.850177i
$216$		0			0
$217$	0.182235	−	0.560863i	0.0123709	−	0.0380738i
$218$	−6.92221			−0.468831
$219$		0			0
$220$	6.81097	+	10.1689i	0.459196	+	0.685589i
$221$	−0.0947550	−	0.291626i	−0.00637391	−	0.0196169i
$222$		0			0
$223$	13.5522	+	9.84622i	0.907520	+	0.659352i	0.940386	−	0.340108i	$-0.110464\pi$
$223$	13.5522	+	9.84622i	0.907520	+	0.659352i	−0.0328667	+	0.999460i	$0.510464\pi$
$224$	−0.447412			−0.0298940
$225$		0			0
$226$	−13.8040			−0.918231
$227$	−17.3999	−	12.6418i	−1.15487	−	0.839064i	−0.165752	−	0.986167i	$-0.553005\pi$
$227$	−17.3999	−	12.6418i	−1.15487	−	0.839064i	−0.989121	+	0.147103i	$0.953005\pi$
$228$		0			0
$229$	−5.13908	−	15.8165i	−0.339600	−	1.04518i	−0.964412	−	0.264406i	$-0.914824\pi$
$229$	−5.13908	−	15.8165i	−0.339600	−	1.04518i	0.624812	−	0.780775i	$-0.285176\pi$
$230$	−12.0677	−	4.43681i	−0.795718	−	0.292554i
$231$		0			0
$232$	−3.34152			−0.219381
$233$	6.74920	−	20.7719i	0.442155	−	1.36081i	−0.443420	−	0.896314i	$-0.646235\pi$
$233$	6.74920	−	20.7719i	0.442155	−	1.36081i	0.885574	−	0.464498i	$-0.153765\pi$
$234$		0			0
$235$	−19.2724	−	7.08571i	−1.25719	−	0.462221i
$236$	−2.75539	−	2.00191i	−0.179360	−	0.130313i
$237$		0			0
$238$	−0.156605	+	0.113780i	−0.0101512	+	0.00737528i
$239$	5.25729	+	3.81964i	0.340066	+	0.247072i	0.744690	−	0.667411i	$-0.232598\pi$
$239$	5.25729	+	3.81964i	0.340066	+	0.247072i	−0.404624	+	0.914483i	$0.632598\pi$
$240$		0			0
$241$	−16.3804	+	11.9011i	−1.05515	+	0.766614i	−0.973186	−	0.230021i	$-0.926121\pi$
$241$	−16.3804	+	11.9011i	−1.05515	+	0.766614i	−0.0819684	+	0.996635i	$0.526121\pi$
$242$	5.85873	−	18.0313i	0.376614	−	1.15910i
$243$		0			0
$244$	−1.87834	+	5.78092i	−0.120248	+	0.370086i
$245$	9.40000	−	11.9511i	0.600544	−	0.763525i
$246$		0			0
$247$	1.76689	+	5.43792i	0.112424	+	0.346007i
$248$	1.06635	+	0.774750i	0.0677134	+	0.0491967i
$249$		0			0
$250$	−5.49536	−	9.73658i	−0.347557	−	0.615796i
$251$	−2.36756			−0.149439			−0.0747196	−	0.997205i	$-0.523806\pi$
$251$	−2.36756			−0.149439			−0.0747196	+	0.997205i	$0.523806\pi$
$252$		0			0
$253$	9.72562	+	29.9324i	0.611444	+	1.88183i
$254$	−3.29339	−	10.1360i	−0.206646	−	0.635991i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−13.0993			−0.817115			−0.408557	−	0.912733i	$-0.633968\pi$
$257$	−13.0993			−0.817115			−0.408557	+	0.912733i	$0.633968\pi$
$258$		0			0
$259$	3.64459	−	2.64795i	0.226464	−	0.164536i
$260$	1.52478	−	0.431859i	0.0945631	−	0.0267827i
$261$		0			0
$262$	−7.90267	+	5.74162i	−0.488228	+	0.354719i
$263$	−5.88793	+	4.27783i	−0.363065	+	0.263782i	−0.754330	−	0.656496i	$-0.772038\pi$
$263$	−5.88793	+	4.27783i	−0.363065	+	0.263782i	0.391264	+	0.920278i	$0.372038\pi$
$264$		0			0
$265$	−1.43172	−	0.526389i	−0.0879501	−	0.0323358i
$266$	2.92020	−	2.12165i	0.179049	−	0.130087i
$267$		0			0
$268$	1.71187			0.104569
$269$	0.236058	−	0.726511i	0.0143927	−	0.0442962i	−0.943602	−	0.331081i	$-0.892587\pi$
$269$	0.236058	−	0.726511i	0.0143927	−	0.0442962i	0.957995	+	0.286785i	$0.0925866\pi$
$270$		0			0
$271$	0.744584	+	2.29159i	0.0452303	+	0.139204i	0.971121	−	0.238586i	$-0.0766839\pi$
$271$	0.744584	+	2.29159i	0.0452303	+	0.139204i	−0.925891	+	0.377791i	$0.876684\pi$
$272$	−0.133697	−	0.411479i	−0.00810660	−	0.0249496i
$273$		0			0
$274$	15.8069			0.954931
$275$	−10.4170	+	25.3074i	−0.628170	+	1.52610i
$276$		0			0
$277$	8.52655	+	6.19490i	0.512311	+	0.372215i	0.813699	−	0.581286i	$-0.197450\pi$
$277$	8.52655	+	6.19490i	0.512311	+	0.372215i	−0.301389	+	0.953501i	$0.597450\pi$
$278$	3.09449	+	9.52387i	0.185595	+	0.571204i
$279$		0			0
$280$	−0.556738	−	0.831221i	−0.0332715	−	0.0496750i
$281$	−5.62518	+	17.3125i	−0.335570	+	1.03278i	0.630870	+	0.775888i	$0.282698\pi$
$281$	−5.62518	+	17.3125i	−0.335570	+	1.03278i	−0.966440	+	0.256891i	$0.917302\pi$
$282$		0			0
$283$	8.09320	−	24.9083i	0.481091	−	1.48064i	−0.356473	−	0.934305i	$-0.616021\pi$
$283$	8.09320	−	24.9083i	0.481091	−	1.48064i	0.837564	−	0.546339i	$-0.183979\pi$
$284$	1.46215	−	1.06231i	0.0867624	−	0.0630366i
$285$		0			0
$286$	−3.13835	−	2.28015i	−0.185575	−	0.134828i
$287$	−2.14866	+	1.56109i	−0.126831	+	0.0921483i
$288$		0			0
$289$	13.6018	+	9.88232i	0.800109	+	0.581313i
$290$	−4.15803	−	6.20802i	−0.244168	−	0.364548i
$291$		0			0
$292$	3.85527	−	11.8653i	0.225613	−	0.694364i
$293$	23.8637			1.39413			0.697067	−	0.717006i	$-0.254488\pi$
$293$	23.8637			1.39413			0.697067	+	0.717006i	$0.254488\pi$
$294$		0			0
$295$	0.290557	−	7.61015i	0.0169169	−	0.443080i
$296$	3.11148	+	9.57614i	0.180851	+	0.556602i
$297$		0			0
$298$	12.8438	+	9.33157i	0.744022	+	0.540563i
$299$	4.07519			0.235675
$300$		0			0
$301$	3.17341			0.182913
$302$	−14.5450	−	10.5676i	−0.836973	−	0.608097i
$303$		0			0
$304$	2.49304	+	7.67280i	0.142986	+	0.440065i
$305$	−13.0774	+	3.70385i	−0.748808	+	0.212082i
$306$		0			0
$307$	−18.8333			−1.07487			−0.537436	−	0.843304i	$-0.680607\pi$
$307$	−18.8333			−1.07487			−0.537436	+	0.843304i	$0.680607\pi$
$308$	−0.756755	+	2.32905i	−0.0431201	+	0.132710i
$309$		0			0
$310$	−0.112447	+	2.94518i	−0.00638657	+	0.167275i
$311$	−24.9160	−	18.1025i	−1.41285	−	1.02650i	−0.992900	−	0.118954i	$-0.962046\pi$
$311$	−24.9160	−	18.1025i	−1.41285	−	1.02650i	−0.419955	−	0.907545i	$-0.637954\pi$
$312$		0			0
$313$	13.8105	−	10.0339i	0.780616	−	0.567151i	−0.124548	−	0.992214i	$-0.539748\pi$
$313$	13.8105	−	10.0339i	0.780616	−	0.567151i	0.905164	+	0.425063i	$0.139748\pi$
$314$	16.8273	+	12.2258i	0.949622	+	0.689941i
$315$		0			0
$316$	7.12553	−	5.17700i	0.400842	−	0.291229i
$317$	8.42991	−	25.9446i	0.473471	−	1.45719i	−0.374538	−	0.927212i	$-0.622199\pi$
$317$	8.42991	−	25.9446i	0.473471	−	1.45719i	0.848009	−	0.529982i	$-0.177801\pi$
$318$		0			0
$319$	−5.65186	+	17.3946i	−0.316444	+	0.973913i
$320$	2.15144	−	0.609344i	0.120269	−	0.0340634i
$321$		0			0
$322$	−0.794985	−	2.44671i	−0.0443028	−	0.136350i
$323$	2.82388	+	2.05167i	0.157125	+	0.114158i
$324$		0			0
$325$	2.69970	+	2.29543i	0.149752	+	0.127327i
$326$	5.62137			0.311339
$327$		0			0
$328$	−1.83436	−	5.64558i	−0.101286	−	0.311725i
$329$	−1.26961	−	3.90747i	−0.0699961	−	0.215426i
$330$		0			0
$331$	3.85194	−	11.8551i	0.211722	−	0.651613i	−0.787648	−	0.616125i	$-0.788701\pi$
$331$	3.85194	−	11.8551i	0.211722	−	0.651613i	0.999370	−	0.0354879i	$-0.0112985\pi$
$332$	1.76437			0.0968327
$333$		0			0
$334$	1.64621	−	1.19604i	0.0900768	−	0.0654446i
$335$	2.13018	+	3.18040i	0.116384	+	0.173764i
$336$		0			0
$337$	25.2892	−	18.3737i	1.37759	−	1.00088i	0.380487	−	0.924786i	$-0.375756\pi$
$337$	25.2892	−	18.3737i	1.37759	−	1.00088i	0.997101	−	0.0760905i	$-0.0242438\pi$
$338$	10.1109	−	7.34597i	0.549958	−	0.399568i
$339$		0			0
$340$	0.598096	−	0.760414i	0.0324363	−	0.0412392i
$341$	5.83668	−	4.24060i	0.316074	−	0.229641i
$342$		0			0
$343$	6.17420			0.333376
$344$	−2.19180	+	6.74568i	−0.118174	+	0.363703i
$345$		0			0
$346$	1.43432	+	4.41438i	0.0771094	+	0.237318i
$347$	8.23487	+	25.3443i	0.442071	+	1.36056i	0.885664	+	0.464327i	$0.153704\pi$
$347$	8.23487	+	25.3443i	0.442071	+	1.36056i	−0.443593	+	0.896228i	$0.646296\pi$
$348$		0			0
$349$	−17.1736			−0.919283			−0.459642	−	0.888104i	$-0.652022\pi$
$349$	−17.1736			−0.919283			−0.459642	+	0.888104i	$0.652022\pi$
$350$	0.851502	−	2.06867i	0.0455147	−	0.110575i
$351$		0			0
$352$	−4.42816	−	3.21725i	−0.236022	−	0.171480i
$353$	−1.75506	−	5.40152i	−0.0934124	−	0.287494i	0.893424	−	0.449214i	$-0.148296\pi$
$353$	−1.75506	−	5.40152i	−0.0934124	−	0.287494i	−0.986837	+	0.161720i	$0.948296\pi$
$354$		0			0
$355$	3.79303	+	1.39455i	0.201313	+	0.0740150i
$356$	−4.30432	+	13.2473i	−0.228128	+	0.702107i
$357$		0			0
$358$	−5.14952	+	15.8486i	−0.272161	+	0.837625i
$359$	−24.1874	+	17.5731i	−1.27656	+	0.927475i	−0.999443	−	0.0333611i	$-0.989379\pi$
$359$	−24.1874	+	17.5731i	−1.27656	+	0.927475i	−0.277117	+	0.960836i	$0.589379\pi$
$360$		0			0
$361$	−37.2853	−	27.0893i	−1.96238	−	1.42576i
$362$	−5.32912	+	3.87183i	−0.280092	+	0.203499i
$363$		0			0
$364$	0.256533	+	0.186382i	0.0134460	+	0.00976909i
$365$	26.8412	−	7.60213i	1.40493	−	0.397913i
$366$		0			0
$367$	8.81431	−	27.1277i	0.460103	−	1.41605i	−0.404935	−	0.914346i	$-0.632706\pi$
$367$	8.81431	−	27.1277i	0.460103	−	1.41605i	0.865038	−	0.501706i	$-0.167294\pi$
$368$	5.75002			0.299741
$369$		0			0
$370$	−13.9192	+	17.6967i	−0.723625	+	0.920009i
$371$	−0.0943182	−	0.290282i	−0.00489676	−	0.0150707i
$372$		0			0
$373$	2.60399	+	1.89191i	0.134830	+	0.0979595i	0.653156	−	0.757224i	$-0.273445\pi$
$373$	2.60399	+	1.89191i	0.134830	+	0.0979595i	−0.518326	+	0.855183i	$0.673445\pi$
$374$	−2.36813			−0.122453
$375$		0			0
$376$	9.18295			0.473574
$377$	1.91593	+	1.39201i	0.0986756	+	0.0716920i
$378$		0			0
$379$	6.54435	+	20.1414i	0.336161	+	1.03460i	0.966147	+	0.257990i	$0.0830603\pi$
$379$	6.54435	+	20.1414i	0.336161	+	1.03460i	−0.629987	+	0.776606i	$0.716940\pi$
$380$	−11.1526	+	14.1794i	−0.572119	+	0.727386i
$381$		0			0
$382$	9.03551			0.462297
$383$	−1.68003	+	5.17061i	−0.0858456	+	0.264206i	−0.984760	−	0.173919i	$-0.944357\pi$
$383$	−1.68003	+	5.17061i	−0.0858456	+	0.264206i	0.898914	+	0.438124i	$0.144357\pi$
$384$		0			0
$385$	−5.26869	+	1.49223i	−0.268517	+	0.0760510i
$386$	13.1037	+	9.52038i	0.666960	+	0.484575i
$387$		0			0
$388$	−10.5922	+	7.69567i	−0.537737	+	0.390689i
$389$	21.4966	+	15.6182i	1.08992	+	0.791873i	0.979386	−	0.201999i	$-0.0647439\pi$
$389$	21.4966	+	15.6182i	1.08992	+	0.791873i	0.110534	+	0.993872i	$0.464744\pi$
$390$		0			0
$391$	2.01265	−	1.46227i	0.101784	−	0.0739504i
$392$	−2.10126	+	6.46702i	−0.106130	+	0.326634i
$393$		0			0
$394$	2.93651	−	9.03765i	0.147939	−	0.455310i
$395$	18.4847	+	6.79611i	0.930067	+	0.341949i
$396$		0			0
$397$	0.315674	+	0.971546i	0.0158432	+	0.0487605i	0.958666	−	0.284535i	$-0.0918393\pi$
$397$	0.315674	+	0.971546i	0.0158432	+	0.0487605i	−0.942822	+	0.333296i	$0.891839\pi$
$398$	−13.9698	−	10.1496i	−0.700241	−	0.508755i
$399$		0			0
$400$	3.80922	+	3.23880i	0.190461	+	0.161940i
$401$	22.2689			1.11205			0.556027	−	0.831164i	$-0.312325\pi$
$401$	22.2689			1.11205			0.556027	+	0.831164i	$0.312325\pi$
$402$		0			0
$403$	−0.288672	−	0.888440i	−0.0143798	−	0.0442563i
$404$	−3.67921	−	11.3234i	−0.183047	−	0.563362i
$405$		0			0
$406$	0.461991	−	1.42186i	0.0229282	−	0.0705658i
$407$	55.1124			2.73182
$408$		0			0
$409$	−2.27376	+	1.65198i	−0.112430	+	0.0816852i	−0.642580	−	0.766219i	$-0.722136\pi$
$409$	−2.27376	+	1.65198i	−0.112430	+	0.0816852i	0.530150	+	0.847904i	$0.322136\pi$
$410$	8.20602	−	10.4331i	0.405267	−	0.515252i
$411$		0			0
$412$	4.35282	−	3.16251i	0.214448	−	0.155806i
$413$	1.23279	−	0.895676i	0.0606617	−	0.0440733i
$414$		0			0
$415$	2.19550	+	3.27793i	0.107773	+	0.160907i
$416$	−0.573372	+	0.416579i	−0.0281119	+	0.0204245i
$417$		0			0
$418$	44.1584			2.15986
$419$	11.9334	−	36.7271i	0.582983	−	1.79424i	−0.0242384	−	0.999706i	$-0.507716\pi$
$419$	11.9334	−	36.7271i	0.582983	−	1.79424i	0.607222	−	0.794532i	$-0.292284\pi$
$420$		0			0
$421$	−6.31871	−	19.4470i	−0.307955	−	0.947788i	−0.978558	−	0.205971i	$-0.933965\pi$
$421$	−6.31871	−	19.4470i	−0.307955	−	0.947788i	0.670603	−	0.741816i	$-0.266035\pi$
$422$	0.452775	+	1.39350i	0.0220407	+	0.0678344i
$423$		0			0
$424$	0.682191			0.0331301
$425$	2.15697	+	0.164947i	0.104629	+	0.00800112i
$426$		0			0
$427$	−2.20017	−	1.59852i	−0.106474	−	0.0773576i
$428$	4.30198	+	13.2401i	0.207944	+	0.639985i
$429$		0			0
$430$	−15.2598	+	4.32197i	−0.735893	+	0.208424i
$431$	6.40476	−	19.7118i	0.308506	−	0.949485i	−0.669839	−	0.742506i	$-0.733637\pi$
$431$	6.40476	−	19.7118i	0.308506	−	0.949485i	0.978345	−	0.206979i	$-0.0663631\pi$
$432$		0			0
$433$	0.302540	−	0.931123i	0.0145392	−	0.0447469i	−0.943524	−	0.331305i	$-0.892511\pi$
$433$	0.302540	−	0.931123i	0.0145392	−	0.0447469i	0.958063	+	0.286558i	$0.0925111\pi$
$434$	−0.477098	+	0.346632i	−0.0229014	+	0.0166389i
$435$		0			0
$436$	5.60018	+	4.06877i	0.268200	+	0.194859i
$437$	−37.5297	+	27.2669i	−1.79529	+	1.30435i
$438$		0			0
$439$	24.2110	+	17.5904i	1.15553	+	0.839542i	0.989206	−	0.146529i	$-0.0468103\pi$
$439$	24.2110	+	17.5904i	1.15553	+	0.839542i	0.166324	+	0.986071i	$0.446810\pi$
$440$	0.466951	−	12.2302i	0.0222610	−	0.583053i
$441$		0			0
$442$	−0.0947550	+	0.291626i	−0.00450704	+	0.0138712i
$443$	−24.4581			−1.16204			−0.581020	−	0.813889i	$-0.697346\pi$
$443$	−24.4581			−1.16204			−0.581020	+	0.813889i	$0.697346\pi$
$444$		0			0
$445$	−29.9676	+	8.48760i	−1.42060	+	0.402351i
$446$	−5.17646	−	15.9315i	−0.245113	−	0.754379i
$447$		0			0
$448$	0.361964	+	0.262982i	0.0171012	+	0.0124247i
$449$	14.0251			0.661886			0.330943	−	0.943651i	$-0.392633\pi$
$449$	14.0251			0.661886			0.330943	+	0.943651i	$0.392633\pi$
$450$		0			0
$451$	−32.4914			−1.52996
$452$	11.1677	+	8.11381i	0.525285	+	0.381642i
$453$		0			0
$454$	6.64618	+	20.4548i	0.311921	+	0.959993i
$455$	−0.0270515	+	0.708525i	−0.00126820	+	0.0332161i
$456$		0			0
$457$	17.2858			0.808595			0.404298	−	0.914627i	$-0.367516\pi$
$457$	17.2858			0.808595			0.404298	+	0.914627i	$0.367516\pi$
$458$	−5.13908	+	15.8165i	−0.240133	+	0.739055i
$459$		0			0
$460$	7.15505	+	10.6826i	0.333606	+	0.498081i
$461$	29.2840	+	21.2761i	1.36389	+	0.990925i	0.998187	+	0.0601941i	$0.0191720\pi$
$461$	29.2840	+	21.2761i	1.36389	+	0.990925i	0.365705	+	0.930731i	$0.380828\pi$
$462$		0			0
$463$	15.6981	−	11.4054i	0.729554	−	0.530052i	−0.159868	−	0.987138i	$-0.551107\pi$
$463$	15.6981	−	11.4054i	0.729554	−	0.530052i	0.889422	+	0.457086i	$0.151107\pi$
$464$	2.70335	+	1.96410i	0.125500	+	0.0911808i
$465$		0			0
$466$	−17.6696	+	12.8377i	−0.818530	+	0.594697i
$467$	−2.20831	+	6.79649i	−0.102189	+	0.314504i	−0.989060	−	0.147512i	$-0.952874\pi$
$467$	−2.20831	+	6.79649i	−0.102189	+	0.314504i	0.886872	+	0.462016i	$0.152874\pi$
$468$		0			0
$469$	−0.236680	+	0.728426i	−0.0109289	+	0.0336356i
$470$	11.4268	+	17.0605i	0.527080	+	0.786942i
$471$		0			0
$472$	1.05246	+	3.23915i	0.0484436	+	0.149094i
$473$	31.4082	+	22.8194i	1.44415	+	1.04924i
$474$		0			0
$475$	−40.2209	−	3.07576i	−1.84546	−	0.141125i
$476$	0.193575			0.00887247
$477$		0			0
$478$	−2.00811	−	6.18031i	−0.0918486	−	0.282681i
$479$	−5.88784	−	18.1209i	−0.269022	−	0.827965i	−0.990739	−	0.135777i	$-0.956647\pi$
$479$	−5.88784	−	18.1209i	−0.269022	−	0.827965i	0.721717	−	0.692188i	$-0.243353\pi$
$480$		0			0
$481$	2.20519	−	6.78687i	0.100548	−	0.309455i
$482$	20.2473			0.922239
$483$		0			0
$484$	−15.3384	+	11.1440i	−0.697198	+	0.506544i
$485$	−27.4778	−	10.1025i	−1.24770	−	0.458731i
$486$		0			0
$487$	−20.0136	+	14.5407i	−0.906903	+	0.658904i	−0.940230	−	0.340541i	$-0.889390\pi$
$487$	−20.0136	+	14.5407i	−0.906903	+	0.658904i	0.0333265	+	0.999445i	$0.489390\pi$
$488$	4.91755	−	3.57281i	0.222607	−	0.161733i
$489$		0			0
$490$	−14.6294	+	4.14343i	−0.660890	+	0.187181i
$491$	−8.43327	+	6.12713i	−0.380588	+	0.276513i	−0.761588	−	0.648062i	$-0.775580\pi$
$491$	−8.43327	+	6.12713i	−0.380588	+	0.276513i	0.381000	+	0.924575i	$0.375580\pi$
$492$		0			0
$493$	1.44572			0.0651120
$494$	1.76689	−	5.43792i	0.0794960	−	0.244664i
$495$		0			0
$496$	−0.407310	−	1.25357i	−0.0182888	−	0.0562870i
$497$	0.249875	+	0.769036i	0.0112084	+	0.0344960i
$498$		0			0
$499$	−43.6293			−1.95311			−0.976557	−	0.215259i	$-0.930940\pi$
$499$	−43.6293			−1.95311			−0.976557	+	0.215259i	$0.930940\pi$
$500$	−1.27718	+	11.1072i	−0.0571174	+	0.496727i
$501$		0			0
$502$	1.91540	+	1.39162i	0.0854884	+	0.0621110i
$503$	−8.61533	−	26.5153i	−0.384139	−	1.18226i	−0.937103	−	0.349052i	$-0.886504\pi$
$503$	−8.61533	−	26.5153i	−0.384139	−	1.18226i	0.552965	−	0.833205i	$-0.313496\pi$
$504$		0			0
$505$	16.4589	−	20.9257i	0.732413	−	0.931183i
$506$	9.72562	−	29.9324i	0.432357	−	1.33066i
$507$		0			0
$508$	−3.29339	+	10.1360i	−0.146121	+	0.449713i
$509$	−21.3896	+	15.5405i	−0.948078	+	0.688819i	−0.950352	−	0.311178i	$-0.899276\pi$
$509$	−21.3896	+	15.5405i	−0.948078	+	0.688819i	0.00227352	+	0.999997i	$0.499276\pi$
$510$		0			0
$511$	4.51583	+	3.28094i	0.199768	+	0.145140i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	10.5976	+	7.69960i	0.467440	+	0.339615i
$515$	11.2919	+	4.15159i	0.497580	+	0.182941i
$516$		0			0
$517$	15.5321	−	47.8029i	0.683101	−	2.10237i
$518$	−4.50497			−0.197937
$519$		0			0
$520$	−1.48742	−	0.546865i	−0.0652275	−	0.0239816i
$521$	−3.63782	−	11.1961i	−0.159376	−	0.490509i	0.839202	−	0.543820i	$-0.183023\pi$
$521$	−3.63782	−	11.1961i	−0.159376	−	0.490509i	−0.998578	+	0.0533110i	$0.983023\pi$
$522$		0			0
$523$	4.22035	+	3.06626i	0.184543	+	0.134078i	0.676221	−	0.736699i	$-0.263616\pi$
$523$	4.22035	+	3.06626i	0.184543	+	0.134078i	−0.491678	+	0.870777i	$0.663616\pi$
$524$	9.76823			0.426727
$525$		0			0
$526$	7.27788			0.317331
$527$	−0.461361	−	0.335199i	−0.0200972	−	0.0146015i
$528$		0			0
$529$	3.10956	+	9.57023i	0.135198	+	0.416097i
$530$	0.848886	+	1.26740i	0.0368732	+	0.0550525i
$531$		0			0
$532$	−3.60957			−0.156495
$533$	−1.30006	+	4.00118i	−0.0563119	+	0.173310i
$534$		0			0
$535$	−19.2449	+	24.4678i	−0.832030	+	1.05783i
$536$	−1.38494	−	1.00621i	−0.0598201	−	0.0434619i
$537$		0			0
$538$	−0.618008	+	0.449009i	−0.0266442	+	0.0193581i
$539$	30.1107	+	21.8767i	1.29696	+	0.942296i
$540$		0			0
$541$	9.91189	−	7.20141i	0.426145	−	0.309613i	−0.353960	−	0.935260i	$-0.615165\pi$
$541$	9.91189	−	7.20141i	0.426145	−	0.309613i	0.780106	+	0.625648i	$0.215165\pi$
$542$	0.744584	−	2.29159i	0.0319826	−	0.0984324i
$543$		0			0
$544$	−0.133697	+	0.411479i	−0.00573223	+	0.0176420i
$545$	−0.590541	+	15.4673i	−0.0252960	+	0.662544i
$546$		0			0
$547$	−10.7782	−	33.1719i	−0.460842	−	1.41833i	−0.864137	−	0.503256i	$-0.832135\pi$
$547$	−10.7782	−	33.1719i	−0.460842	−	1.41833i	0.403295	−	0.915070i	$-0.367865\pi$
$548$	−12.7881	−	9.29107i	−0.546279	−	0.396895i
$549$		0			0
$550$	23.3029	−	14.3512i	0.993639	−	0.611936i
$551$	−26.9582			−1.14846
$552$		0			0
$553$	1.21772	+	3.74777i	0.0517829	+	0.159371i
$554$	−3.25685	−	10.0236i	−0.138370	−	0.425860i
$555$		0			0
$556$	3.09449	−	9.52387i	0.131236	−	0.403902i
$557$	−9.78468			−0.414590			−0.207295	−	0.978278i	$-0.566466\pi$
$557$	−9.78468			−0.414590			−0.207295	+	0.978278i	$0.566466\pi$
$558$		0			0
$559$	4.06683	−	2.95472i	0.172009	−	0.124972i
$560$	−0.0381692	+	0.999715i	−0.00161294	+	0.0422456i
$561$		0			0
$562$	14.7269	−	10.6997i	0.621218	−	0.451341i
$563$	−15.8610	+	11.5237i	−0.668460	+	0.485665i	−0.869510	−	0.493916i	$-0.835565\pi$
$563$	−15.8610	+	11.5237i	−0.668460	+	0.485665i	0.201049	+	0.979581i	$0.435565\pi$
$564$		0			0
$565$	−1.17764	+	30.8443i	−0.0495436	+	1.29763i
$566$	−21.1883	+	15.3942i	−0.890609	+	0.647065i
$567$		0			0
$568$	−1.80731			−0.0758331
$569$	4.27880	−	13.1688i	0.179377	−	0.552064i	−0.820430	−	0.571747i	$-0.806266\pi$
$569$	4.27880	−	13.1688i	0.179377	−	0.552064i	0.999806	+	0.0196831i	$0.00626572\pi$
$570$		0			0
$571$	−6.28381	−	19.3396i	−0.262969	−	0.809336i	−0.992154	−	0.125020i	$-0.960101\pi$
$571$	−6.28381	−	19.3396i	−0.262969	−	0.809336i	0.729185	−	0.684317i	$-0.239899\pi$
$572$	1.19874	+	3.68936i	0.0501220	+	0.154260i
$573$		0			0
$574$	2.65589			0.110855
$575$	−10.9433	+	26.5860i	−0.456366	+	1.10871i
$576$		0			0
$577$	−25.3717	−	18.4337i	−1.05624	−	0.767403i	−0.0828507	−	0.996562i	$-0.526402\pi$
$577$	−25.3717	−	18.4337i	−1.05624	−	0.767403i	−0.973389	+	0.229159i	$0.926402\pi$
$578$	−5.19544	−	15.9899i	−0.216102	−	0.665094i
$579$		0			0
$580$	−0.285069	+	7.46642i	−0.0118368	+	0.310026i
$581$	−0.243939	+	0.750766i	−0.0101203	+	0.0311470i
$582$		0			0
$583$	1.15386	−	3.55122i	0.0477881	−	0.147077i
$584$	−10.0932	+	7.33316i	−0.417661	+	0.303448i
$585$		0			0
$586$	−19.3062	−	14.0267i	−0.797530	−	0.579439i
$587$	18.9945	−	13.8003i	0.783985	−	0.569598i	−0.122187	−	0.992507i	$-0.538991\pi$
$587$	18.9945	−	13.8003i	0.783985	−	0.569598i	0.906172	+	0.422909i	$0.138991\pi$
$588$		0			0
$589$	8.60296	+	6.25042i	0.354479	+	0.257544i
$590$	−4.70820	+	5.98596i	−0.193834	+	0.246438i
$591$		0			0
$592$	3.11148	−	9.57614i	0.127881	−	0.393577i
$593$	−21.9658			−0.902025			−0.451013	−	0.892518i	$-0.648937\pi$
$593$	−21.9658			−0.902025			−0.451013	+	0.892518i	$0.648937\pi$
$594$		0			0
$595$	0.240875	+	0.359631i	0.00987491	+	0.0147434i
$596$	−4.90590	−	15.0988i	−0.200953	−	0.618471i
$597$		0			0
$598$	−3.29690	−	2.39534i	−0.134820	−	0.0979527i
$599$	19.6941			0.804680			0.402340	−	0.915490i	$-0.368197\pi$
$599$	19.6941			0.804680			0.402340	+	0.915490i	$0.368197\pi$
$600$		0			0
$601$	13.4764			0.549715			0.274857	−	0.961485i	$-0.411369\pi$
$601$	13.4764			0.549715			0.274857	+	0.961485i	$0.411369\pi$
$602$	−2.56735	−	1.86529i	−0.104637	−	0.0760234i
$603$		0			0
$604$	5.55571	+	17.0987i	0.226059	+	0.695737i
$605$	−39.7901	−	14.6293i	−1.61770	−	0.594764i
$606$		0			0
$607$	46.7224			1.89641			0.948203	−	0.317666i	$-0.102899\pi$
$607$	46.7224			1.89641			0.948203	+	0.317666i	$0.102899\pi$
$608$	2.49304	−	7.67280i	0.101106	−	0.311173i
$609$		0			0
$610$	12.7569	+	4.69021i	0.516511	+	0.189901i
$611$	−5.26525	−	3.82543i	−0.213009	−	0.154760i
$612$		0			0
$613$	20.9461	−	15.2182i	0.846006	−	0.614659i	−0.0780360	−	0.996951i	$-0.524865\pi$
$613$	20.9461	−	15.2182i	0.846006	−	0.614659i	0.924042	+	0.382291i	$0.124865\pi$
$614$	15.2364	+	11.0699i	0.614893	+	0.446746i
$615$		0			0
$616$	1.98121	−	1.43943i	0.0798252	−	0.0579964i
$617$	11.0219	−	33.9219i	0.443725	−	1.36565i	−0.440150	−	0.897924i	$-0.645075\pi$
$617$	11.0219	−	33.9219i	0.443725	−	1.36565i	0.883876	−	0.467722i	$-0.154925\pi$
$618$		0			0
$619$	−3.57307	+	10.9968i	−0.143614	+	0.441998i	−0.996830	−	0.0795594i	$-0.974649\pi$
$619$	−3.57307	+	10.9968i	−0.143614	+	0.441998i	0.853216	+	0.521557i	$0.174649\pi$
$620$	1.82210	−	2.31660i	0.0731774	−	0.0930370i
$621$		0			0
$622$	9.51705	+	29.2905i	0.381599	+	1.17444i
$623$	−5.04182	−	3.66309i	−0.201996	−	0.146759i
$624$		0			0
$625$	−22.2246	+	11.4484i	−0.888985	+	0.457936i
$626$	−17.0707			−0.682283
$627$		0			0
$628$	−6.42747	−	19.7817i	−0.256484	−	0.789377i
$629$	−1.34619	−	4.14316i	−0.0536762	−	0.165198i
$630$		0			0
$631$	−0.207791	+	0.639515i	−0.00827202	+	0.0254587i	−0.955107	−	0.296260i	$-0.904261\pi$
$631$	−0.207791	+	0.639515i	−0.00827202	+	0.0254587i	0.946835	+	0.321719i	$0.104261\pi$
$632$	−8.80763			−0.350349
$633$		0			0
$634$	−22.0698	+	16.0346i	−0.876504	+	0.636817i
$635$	−22.9293	+	6.49417i	−0.909921	+	0.257713i
$636$		0			0
$637$	3.89883	−	2.83266i	0.154477	−	0.112234i
$638$	14.7968	−	10.7505i	0.585810	−	0.425616i
$639$		0			0
$640$	−2.09872	−	0.771616i	−0.0829590	−	0.0305008i
$641$	−3.29243	+	2.39209i	−0.130043	+	0.0944820i	−0.650905	−	0.759159i	$-0.725611\pi$
$641$	−3.29243	+	2.39209i	−0.130043	+	0.0944820i	0.520862	+	0.853641i	$0.325611\pi$
$642$		0			0
$643$	−23.9998			−0.946458			−0.473229	−	0.880939i	$-0.656912\pi$
$643$	−23.9998			−0.946458			−0.473229	+	0.880939i	$0.656912\pi$
$644$	−0.794985	+	2.44671i	−0.0313268	+	0.0964140i
$645$		0			0
$646$	−1.07863	−	3.31967i	−0.0424380	−	0.130611i
$647$	5.10597	+	15.7146i	0.200737	+	0.617804i	0.999862	+	0.0166387i	$0.00529651\pi$
$647$	5.10597	+	15.7146i	0.200737	+	0.617804i	−0.799125	+	0.601165i	$0.794703\pi$
$648$		0			0
$649$	18.6419			0.731759
$650$	−0.834881	−	3.44388i	−0.0327467	−	0.135080i
$651$		0			0
$652$	−4.54778	−	3.30416i	−0.178105	−	0.129401i
$653$	−7.91588	−	24.3626i	−0.309772	−	0.953381i	−0.977853	−	0.209292i	$-0.932884\pi$
$653$	−7.91588	−	24.3626i	−0.309772	−	0.953381i	0.668081	−	0.744089i	$-0.267116\pi$
$654$		0			0
$655$	12.1551	+	18.1479i	0.474940	+	0.709095i
$656$	−1.83436	+	5.64558i	−0.0716198	+	0.220423i
$657$		0			0
$658$	−1.26961	+	3.90747i	−0.0494947	+	0.152329i
$659$	12.5375	−	9.10904i	0.488392	−	0.354838i	−0.316173	−	0.948701i	$-0.602398\pi$
$659$	12.5375	−	9.10904i	0.488392	−	0.354838i	0.804566	+	0.593864i	$0.202398\pi$
$660$		0			0
$661$	12.2492	+	8.89955i	0.476438	+	0.346152i	0.799945	−	0.600073i	$-0.204862\pi$
$661$	12.2492	+	8.89955i	0.476438	+	0.346152i	−0.323507	+	0.946226i	$0.604862\pi$
$662$	−10.0845	+	7.32683i	−0.391946	+	0.284765i
$663$		0			0
$664$	−1.42741	−	1.03707i	−0.0553942	−	0.0402463i
$665$	−4.49157	−	6.70601i	−0.174176	−	0.260048i
$666$		0			0
$667$	−5.93739	+	18.2734i	−0.229897	+	0.707549i
$668$	−2.03483			−0.0787300
$669$		0			0
$670$	0.146042	−	3.82508i	0.00564210	−	0.147776i
$671$	−10.2811	−	31.6419i	−0.396897	−	1.22152i
$672$		0			0
$673$	22.8814	+	16.6243i	0.882012	+	0.640819i	0.933783	−	0.357840i	$-0.116487\pi$
$673$	22.8814	+	16.6243i	0.882012	+	0.640819i	−0.0517712	+	0.998659i	$0.516487\pi$
$674$	−31.2591			−1.20406
$675$		0			0
$676$	−12.4977			−0.480681
$677$	−32.8594	−	23.8737i	−1.26289	−	0.917542i	−0.263992	−	0.964525i	$-0.585039\pi$
$677$	−32.8594	−	23.8737i	−1.26289	−	0.917542i	−0.998896	+	0.0469832i	$0.985039\pi$
$678$		0			0
$679$	−1.81016	−	5.57111i	−0.0694677	−	0.213799i
$680$	−0.930830	+	0.263635i	−0.0356957	+	0.0101100i
$681$		0			0
$682$	−7.21453			−0.276259
$683$	−10.4076	+	32.0312i	−0.398235	+	1.22564i	0.528179	+	0.849133i	$0.322875\pi$
$683$	−10.4076	+	32.0312i	−0.398235	+	1.22564i	−0.926414	+	0.376507i	$0.877125\pi$
$684$		0			0
$685$	1.34851	−	35.3196i	0.0515238	−	1.34949i
$686$	−4.99503	−	3.62910i	−0.190711	−	0.138560i
$687$		0			0
$688$	5.73822	−	4.16906i	0.218768	−	0.158944i
$689$	−0.391149	−	0.284186i	−0.0149016	−	0.0108266i
$690$		0			0
$691$	−9.02540	+	6.55734i	−0.343342	+	0.249453i	−0.746071	−	0.665867i	$-0.768062\pi$
$691$	−9.02540	+	6.55734i	−0.343342	+	0.249453i	0.402728	+	0.915320i	$0.368062\pi$
$692$	1.43432	−	4.41438i	0.0545246	−	0.167809i
$693$		0			0
$694$	8.23487	−	25.3443i	0.312592	−	0.962058i
$695$	21.5445	−	6.10197i	0.817230	−	0.231461i
$696$		0			0
$697$	0.793644	+	2.44258i	0.0300614	+	0.0925195i
$698$	13.8938	+	10.0944i	0.525886	+	0.382079i
$699$		0			0
$700$	−1.90481	+	1.17309i	−0.0719951	+	0.0443384i
$701$	11.1999			0.423014			0.211507	−	0.977377i	$-0.432163\pi$
$701$	11.1999			0.423014			0.211507	+	0.977377i	$0.432163\pi$
$702$		0			0
$703$	25.1023	+	77.2570i	0.946753	+	2.91380i
$704$	1.69141	+	5.20561i	0.0637473	+	0.196194i
$705$		0			0
$706$	−1.75506	+	5.40152i	−0.0660526	+	0.203289i
$707$	5.32695			0.200341
$708$		0			0
$709$	10.8595	−	7.88987i	0.407836	−	0.296310i	−0.364889	−	0.931051i	$-0.618893\pi$
$709$	10.8595	−	7.88987i	0.407836	−	0.296310i	0.772725	+	0.634741i	$0.218893\pi$
$710$	−2.24893	−	3.35770i	−0.0844009	−	0.126012i
$711$		0			0
$712$	11.2689	−	8.18730i	0.422318	−	0.306832i
$713$	6.13154	−	4.45483i	0.229628	−	0.166835i
$714$		0			0
$715$	−5.36259	+	6.81794i	−0.200550	+	0.254977i
$716$	13.4816	−	9.79497i	0.503832	−	0.366055i
$717$		0			0
$718$	29.8972			1.11575
$719$	13.5053	−	41.5652i	0.503664	−	1.55012i	−0.299340	−	0.954147i	$-0.596766\pi$
$719$	13.5053	−	41.5652i	0.503664	−	1.55012i	0.803004	−	0.595973i	$-0.203234\pi$
$720$		0			0
$721$	0.743880	+	2.28943i	0.0277035	+	0.0852627i
$722$	14.2417	+	43.8315i	0.530022	+	1.63124i
$723$		0			0
$724$	6.58715			0.244809
$725$	−14.2262	+	8.76125i	−0.528347	+	0.325385i
$726$		0			0
$727$	15.3509	+	11.1531i	0.569334	+	0.413646i	0.834863	−	0.550457i	$-0.185547\pi$
$727$	15.3509	+	11.1531i	0.569334	+	0.413646i	−0.265529	+	0.964103i	$0.585547\pi$
$728$	−0.0979870	−	0.301573i	−0.00363164	−	0.0111770i
$729$		0			0
$730$	−26.1834	−	9.62661i	−0.969091	−	0.356297i
$731$	0.948293	−	2.91855i	0.0350739	−	0.107946i
$732$		0			0
$733$	13.8676	−	42.6802i	0.512213	−	1.57643i	−0.276085	−	0.961133i	$-0.589037\pi$
$733$	13.8676	−	42.6802i	0.512213	−	1.57643i	0.788297	−	0.615295i	$-0.210963\pi$
$734$	−23.0762	+	16.7658i	−0.851757	+	0.618837i
$735$		0			0
$736$	−4.65186	−	3.37978i	−0.171470	−	0.124580i
$737$	−7.58045	+	5.50752i	−0.279230	+	0.202872i
$738$		0			0
$739$	5.55621	+	4.03683i	0.204389	+	0.148497i	0.685271	−	0.728288i	$-0.259684\pi$
$739$	5.55621	+	4.03683i	0.204389	+	0.148497i	−0.480883	+	0.876785i	$0.659684\pi$
$740$	21.6628	−	6.13546i	0.796339	−	0.225544i
$741$		0			0
$742$	−0.0943182	+	0.290282i	−0.00346253	+	0.0106566i
$743$	−35.5994			−1.30602			−0.653008	−	0.757351i	$-0.726493\pi$
$743$	−35.5994			−1.30602			−0.653008	+	0.757351i	$0.726493\pi$
$744$		0			0
$745$	21.9466	−	27.9026i	0.804060	−	1.02227i
$746$	−0.994637	−	3.06118i	−0.0364162	−	0.112078i
$747$		0			0
$748$	1.91586	+	1.39195i	0.0700508	+	0.0508949i
$749$	−6.22864			−0.227589
$750$		0			0
$751$	−20.1261			−0.734414			−0.367207	−	0.930139i	$-0.619686\pi$
$751$	−20.1261			−0.734414			−0.367207	+	0.930139i	$0.619686\pi$
$752$	−7.42916	−	5.39760i	−0.270914	−	0.196830i
$753$		0			0
$754$	−0.731821	−	2.25231i	−0.0266514	−	0.0820245i
$755$	−24.8535	+	31.5985i	−0.904512	+	1.14999i
$756$		0			0
$757$	−20.7503			−0.754183			−0.377091	−	0.926176i	$-0.623076\pi$
$757$	−20.7503			−0.754183			−0.377091	+	0.926176i	$0.623076\pi$
$758$	6.54435	−	20.1414i	0.237702	−	0.731570i
$759$		0			0
$760$	17.3571	−	4.91598i	0.629608	−	0.178321i
$761$	6.20460	+	4.50791i	0.224917	+	0.163412i	0.694537	−	0.719457i	$-0.255609\pi$
$761$	6.20460	+	4.50791i	0.224917	+	0.163412i	−0.469620	+	0.882868i	$0.655609\pi$
$762$		0			0
$763$	−2.50559	+	1.82042i	−0.0907083	+	0.0659035i
$764$	−7.30988	−	5.31094i	−0.264462	−	0.192143i
$765$		0			0
$766$	4.39838	−	3.19561i	0.158920	−	0.115462i
$767$	0.745909	−	2.29567i	0.0269332	−	0.0828919i
$768$		0			0
$769$	−0.130256	+	0.400887i	−0.00469715	+	0.0144563i	−0.953378	−	0.301780i	$-0.902419\pi$
$769$	−0.130256	+	0.400887i	−0.00469715	+	0.0144563i	0.948680	+	0.316236i	$0.102419\pi$
$770$	5.13957	+	1.88962i	0.185217	+	0.0680971i
$771$		0			0
$772$	−5.00516	−	15.4043i	−0.180140	−	0.554413i
$773$	−30.4631	−	22.1327i	−1.09568	−	0.796059i	−0.115332	−	0.993327i	$-0.536793\pi$
$773$	−30.4631	−	22.1327i	−1.09568	−	0.796059i	−0.980350	+	0.197268i	$0.936793\pi$
$774$		0			0
$775$	6.57123	+	0.502513i	0.236046	+	0.0180508i
$776$	13.0927			0.469999
$777$		0			0
$778$	−8.21096	−	25.2707i	−0.294377	−	0.906000i
$779$	−14.7990	−	45.5466i	−0.530229	−	1.63188i
$780$		0			0
$781$	−3.05690	+	9.40816i	−0.109384	+	0.336651i
$782$	−2.48777			−0.0889625
$783$		0			0
$784$	5.50117	−	3.99684i	0.196470	−	0.142744i
$785$	28.7533	−	36.5567i	1.02625	−	1.30476i
$786$		0			0
$787$	−3.58854	+	2.60723i	−0.127918	+	0.0929377i	−0.649904	−	0.760016i	$-0.725191\pi$
$787$	−3.58854	+	2.60723i	−0.127918	+	0.0929377i	0.521987	+	0.852954i	$0.325191\pi$
$788$	−7.68788	+	5.58557i	−0.273870	+	0.198978i
$789$		0			0
$790$	−10.9598	−	16.3632i	−0.389932	−	0.582177i
$791$	−4.99656	+	3.63021i	−0.177657	+	0.129076i
$792$		0			0
$793$	−4.30794			−0.152980
$794$	0.315674	−	0.971546i	0.0112029	−	0.0344789i
$795$		0			0
$796$	5.33598	+	16.4224i	0.189129	+	0.582078i
$797$	3.51514	+	10.8185i	0.124513	+	0.383211i	0.993812	−	0.111075i	$-0.0354295\pi$
$797$	3.51514	+	10.8185i	0.124513	+	0.383211i	−0.869299	+	0.494286i	$0.835429\pi$
$798$		0			0
$799$	−3.97304			−0.140556
$800$	−1.17800	−	4.85925i	−0.0416486	−	0.171800i
$801$		0			0
$802$	−18.0159	−	13.0893i	−0.636163	−	0.462200i
$803$	21.1018	+	64.9448i	0.744668	+	2.29185i
$804$		0			0
$805$	−5.53485	+	1.56761i	−0.195078	+	0.0552512i
$806$	−0.288672	+	0.888440i	−0.0101680	+	0.0312940i
$807$		0			0
$808$	−3.67921	+	11.3234i	−0.129434	+	0.398357i
$809$	−15.2356	+	11.0693i	−0.535655	+	0.389176i	−0.822469	−	0.568810i	$-0.807404\pi$
$809$	−15.2356	+	11.0693i	−0.535655	+	0.389176i	0.286814	+	0.957986i	$0.407404\pi$
$810$		0			0
$811$	−3.52006	−	2.55748i	−0.123606	−	0.0898051i	0.524265	−	0.851555i	$-0.324340\pi$
$811$	−3.52006	−	2.55748i	−0.123606	−	0.0898051i	−0.647871	+	0.761750i	$0.724340\pi$
$812$	−1.20951	+	0.878759i	−0.0424454	+	0.0308384i
$813$		0			0
$814$	−44.5869	−	32.3943i	−1.56277	−	1.13542i
$815$	0.479565	−	12.5606i	0.0167984	−	0.439979i
$816$		0			0
$817$	−17.6827	+	54.4219i	−0.618641	+	1.90398i
$818$	2.81052			0.0982674
$819$		0			0
$820$	−12.7712	+	3.61714i	−0.445990	+	0.126316i
$821$	14.6214	+	45.0000i	0.510290	+	1.57051i	0.791692	+	0.610921i	$0.209201\pi$
$821$	14.6214	+	45.0000i	0.510290	+	1.57051i	−0.281402	+	0.959590i	$0.590799\pi$
$822$		0			0
$823$	−29.8018	−	21.6523i	−1.03882	−	0.754750i	−0.0687689	−	0.997633i	$-0.521907\pi$
$823$	−29.8018	−	21.6523i	−1.03882	−	0.754750i	−0.970056	+	0.242882i	$0.921907\pi$
$824$	−5.38038			−0.187434
$825$		0			0
$826$	−1.52381			−0.0530203
$827$	−4.98478	−	3.62165i	−0.173338	−	0.125937i	0.497734	−	0.867330i	$-0.334166\pi$
$827$	−4.98478	−	3.62165i	−0.173338	−	0.125937i	−0.671072	+	0.741393i	$0.734166\pi$
$828$		0			0
$829$	3.41535	+	10.5114i	0.118620	+	0.365074i	0.992685	−	0.120735i	$-0.0385250\pi$
$829$	3.41535	+	10.5114i	0.118620	+	0.365074i	−0.874065	+	0.485809i	$0.838525\pi$
$830$	0.150521	−	3.94239i	0.00522466	−	0.136842i
$831$		0			0
$832$	0.708727			0.0245707
$833$	0.909119	−	2.79798i	0.0314991	−	0.0969443i
$834$		0			0
$835$	−2.53205	−	3.78040i	−0.0876251	−	0.130826i
$836$	−35.7249	−	25.9556i	−1.23557	−	0.897695i
$837$		0			0
$838$	−31.2420	+	22.6986i	−1.07924	+	0.784111i
$839$	23.7557	+	17.2596i	0.820139	+	0.595866i	0.916752	−	0.399456i	$-0.130801\pi$
$839$	23.7557	+	17.2596i	0.820139	+	0.595866i	−0.0966132	+	0.995322i	$0.530801\pi$
$840$		0			0
$841$	14.4282	−	10.4827i	0.497525	−	0.361473i
$842$	−6.31871	+	19.4470i	−0.217757	+	0.670187i
$843$		0			0
$844$	0.452775	−	1.39350i	0.0155852	−	0.0479662i
$845$	−15.5516	−	23.2188i	−0.534990	−	0.798751i
$846$		0			0
$847$	−2.62127	−	8.06742i	−0.0900677	−	0.277200i
$848$	−0.551904	−	0.400982i	−0.0189525	−	0.0137698i
$849$		0			0
$850$	−1.64807	−	1.40128i	−0.0565285	−	0.0480636i
$851$	57.8967			1.98467
$852$		0			0
$853$	−8.97089	−	27.6096i	−0.307157	−	0.945333i	−0.978863	−	0.204515i	$-0.934438\pi$
$853$	−8.97089	−	27.6096i	−0.307157	−	0.945333i	0.671706	−	0.740818i	$-0.265562\pi$
$854$	0.840390	+	2.58645i	0.0287575	+	0.0885066i
$855$		0			0
$856$	4.30198	−	13.2401i	0.147039	−	0.452538i
$857$	11.5950			0.396076			0.198038	−	0.980194i	$-0.436543\pi$
$857$	11.5950			0.396076			0.198038	+	0.980194i	$0.436543\pi$
$858$		0			0
$859$	−2.87734	+	2.09051i	−0.0981737	+	0.0713274i	−0.635789	−	0.771863i	$-0.719325\pi$
$859$	−2.87734	+	2.09051i	−0.0981737	+	0.0713274i	0.537615	+	0.843190i	$0.319325\pi$
$860$	14.8858	+	5.47294i	0.507603	+	0.186626i
$861$		0			0
$862$	−16.7679	+	12.1826i	−0.571116	+	0.414940i
$863$	−14.3646	+	10.4365i	−0.488975	+	0.355261i	−0.804790	−	0.593559i	$-0.797722\pi$
$863$	−14.3646	+	10.4365i	−0.488975	+	0.355261i	0.315815	+	0.948821i	$0.397722\pi$
$864$		0			0
$865$	9.98602	−	2.82830i	0.339535	−	0.0961651i
$866$	−0.792061	+	0.575466i	−0.0269153	+	0.0195551i
$867$		0			0
$868$	0.589726			0.0200166
$869$	−14.8973	+	45.8491i	−0.505356	+	1.55533i
$870$		0			0
$871$	0.374915	+	1.15387i	0.0127035	+	0.0390974i
$872$	−2.13908	−	6.58341i	−0.0724384	−	0.222942i
$873$		0			0
$874$	46.3892			1.56914
$875$	−4.54967	−	2.07911i	−0.153807	−	0.0702867i
$876$		0			0
$877$	19.1476	+	13.9115i	0.646568	+	0.469759i	0.862100	−	0.506737i	$-0.169149\pi$
$877$	19.1476	+	13.9115i	0.646568	+	0.469759i	−0.215532	+	0.976497i	$0.569149\pi$
$878$	−9.24780	−	28.4618i	−0.312098	−	0.960539i
$879$		0			0
$880$	−7.56651	+	9.61999i	−0.255067	+	0.324290i
$881$	−8.46021	+	26.0378i	−0.285032	+	0.877237i	0.701358	+	0.712810i	$0.252578\pi$
$881$	−8.46021	+	26.0378i	−0.285032	+	0.877237i	−0.986389	+	0.164427i	$0.947422\pi$
$882$		0			0
$883$	−14.2222	+	43.7714i	−0.478615	+	1.47303i	0.362404	+	0.932021i	$0.381956\pi$
$883$	−14.2222	+	43.7714i	−0.478615	+	1.47303i	−0.841020	+	0.541005i	$0.818044\pi$
$884$	0.248072	−	0.180235i	0.00834356	−	0.00606195i
$885$		0			0
$886$	19.7870	+	14.3761i	0.664758	+	0.482975i
$887$	5.80575	−	4.21812i	0.194938	−	0.141631i	−0.486035	−	0.873939i	$-0.661557\pi$
$887$	5.80575	−	4.21812i	0.194938	−	0.141631i	0.680973	+	0.732309i	$0.261557\pi$
$888$		0			0
$889$	−3.85768	−	2.80277i	−0.129382	−	0.0940018i
$890$	29.2332	+	10.7479i	0.979898	+	0.360270i
$891$		0			0
$892$	−5.17646	+	15.9315i	−0.173321	+	0.533427i
$893$	74.0849			2.47916
$894$		0			0
$895$	34.9734	+	12.8584i	1.16903	+	0.429808i
$896$	−0.138258	−	0.425514i	−0.00461887	−	0.0142154i
$897$		0			0
$898$	−11.3466	−	8.24376i	−0.378640	−	0.275098i
$899$	4.40440			0.146895
$900$		0			0
$901$	−0.295153			−0.00983296
$902$	26.2861	+	19.0979i	0.875230	+	0.635892i
$903$		0			0
$904$	−4.26568	−	13.1284i	−0.141875	−	0.436645i
$905$	8.19674	+	12.2379i	0.272469	+	0.406802i
$906$		0			0
$907$	−5.56195			−0.184682			−0.0923408	−	0.995727i	$-0.529435\pi$
$907$	−5.56195			−0.184682			−0.0923408	+	0.995727i	$0.529435\pi$
$908$	6.64618	−	20.4548i	0.220561	−	0.678817i
$909$		0			0
$910$	0.438345	−	0.557308i	0.0145310	−	0.0184746i
$911$	8.66550	+	6.29585i	0.287101	+	0.208591i	0.722009	−	0.691884i	$-0.243219\pi$
$911$	8.66550	+	6.29585i	0.287101	+	0.208591i	−0.434908	+	0.900475i	$0.643219\pi$
$912$		0			0
$913$	−7.81293	+	5.67643i	−0.258570	+	0.187862i
$914$	−13.9845	−	10.1603i	−0.462566	−	0.336074i
$915$		0			0
$916$	13.4543	−	9.77511i	0.444542	−	0.322979i
$917$	−1.35053	+	4.15652i	−0.0445986	+	0.137260i
$918$		0			0
$919$	−7.39033	+	22.7451i	−0.243785	+	0.750292i	0.752049	+	0.659107i	$0.229065\pi$
$919$	−7.39033	+	22.7451i	−0.243785	+	0.750292i	−0.995834	+	0.0911851i	$0.970935\pi$
$920$	0.490541	−	12.8481i	0.0161727	−	0.423589i
$921$		0			0
$922$	−11.1855	−	34.4254i	−0.368374	−	1.13374i
$923$	1.03626	+	0.752888i	0.0341090	+	0.0247816i
$924$		0			0
$925$	38.3548	+	32.6114i	1.26110	+	1.07225i
$926$	−19.4040			−0.637654
$927$		0			0
$928$	−1.03259	−	3.17797i	−0.0338963	−	0.104322i
$929$	6.00826	+	18.4915i	0.197124	+	0.606687i	0.999945	+	0.0104663i	$0.00333159\pi$
$929$	6.00826	+	18.4915i	0.197124	+	0.606687i	−0.802821	+	0.596220i	$0.796668\pi$
$930$		0			0
$931$	−16.9523	+	52.1737i	−0.555588	+	1.70992i
$932$	21.8409			0.715421
$933$		0			0
$934$	5.78144	−	4.20046i	0.189175	−	0.137443i
$935$	−0.202028	+	5.29145i	−0.00660703	+	0.173049i
$936$		0			0
$937$	13.3009	−	9.66370i	0.434523	−	0.315699i	−0.348932	−	0.937148i	$-0.613456\pi$
$937$	13.3009	−	9.66370i	0.434523	−	0.315699i	0.783455	+	0.621449i	$0.213456\pi$
$938$	0.619637	−	0.450192i	0.0202318	−	0.0146993i
$939$		0			0
$940$	0.783408	−	20.5187i	0.0255519	−	0.669248i
$941$	5.92599	−	4.30548i	0.193182	−	0.140355i	−0.486990	−	0.873408i	$-0.661905\pi$
$941$	5.92599	−	4.30548i	0.193182	−	0.140355i	0.680172	+	0.733053i	$0.261905\pi$
$942$		0			0
$943$	−34.1328			−1.11152
$944$	1.05246	−	3.23915i	0.0342548	−	0.105425i
$945$		0			0
$946$	−11.9969	−	36.9225i	−0.390051	−	1.20045i
$947$	−13.0142	−	40.0535i	−0.422903	−	1.30156i	−0.904988	−	0.425438i	$-0.860120\pi$
$947$	−13.0142	−	40.0535i	−0.422903	−	1.30156i	0.482085	−	0.876125i	$-0.339880\pi$
$948$		0			0
$949$	8.84201			0.287024
$950$	30.7315	+	26.1296i	0.997061	+	0.847755i
$951$		0			0
$952$	−0.156605	−	0.113780i	−0.00507560	−	0.00368764i
$953$	11.4876	+	35.3551i	0.372119	+	1.14526i	0.945402	+	0.325907i	$0.105669\pi$
$953$	11.4876	+	35.3551i	0.372119	+	1.14526i	−0.573283	+	0.819357i	$0.694331\pi$
$954$		0			0
$955$	0.770830	−	20.1893i	0.0249435	−	0.653310i
$956$	−2.00811	+	6.18031i	−0.0649468	+	0.199886i
$957$		0			0
$958$	−5.88784	+	18.1209i	−0.190227	+	0.585460i
$959$	5.72153	−	4.15693i	0.184758	−	0.134234i
$960$		0			0
$961$	23.6740	+	17.2002i	0.763677	+	0.554844i
$962$	−5.77325	+	4.19451i	−0.186137	+	0.135237i
$963$		0			0
$964$	−16.3804	−	11.9011i	−0.527577	−	0.383307i
$965$	22.3906	−	28.4672i	0.720779	−	0.916391i
$966$		0			0
$967$	−18.0263	+	55.4791i	−0.579685	+	1.78409i	0.0399536	+	0.999202i	$0.487279\pi$
$967$	−18.0263	+	55.4791i	−0.579685	+	1.78409i	−0.619639	+	0.784887i	$0.712721\pi$
$968$	18.9593			0.609374
$969$		0			0
$970$	16.2919	+	24.3241i	0.523101	+	0.781001i
$971$	1.77798	+	5.47205i	0.0570579	+	0.175606i	0.975524	−	0.219894i	$-0.0705712\pi$
$971$	1.77798	+	5.47205i	0.0570579	+	0.175606i	−0.918466	+	0.395500i	$0.870571\pi$
$972$		0			0
$973$	3.62470	+	2.63350i	0.116203	+	0.0844261i
$974$	24.7382			0.792663
$975$		0			0
$976$	−6.07842			−0.194566
$977$	−38.3212	−	27.8420i	−1.22600	−	0.890744i	−0.229420	−	0.973327i	$-0.573683\pi$
$977$	−38.3212	−	27.8420i	−1.22600	−	0.890744i	−0.996584	+	0.0825830i	$0.973683\pi$
$978$		0			0
$979$	−23.5597	−	72.5093i	−0.752972	−	2.31741i
$980$	14.2709	+	5.24685i	0.455867	+	0.167604i
$981$		0			0
$982$	10.4241			0.332646
$983$	2.26705	−	6.97726i	0.0723077	−	0.222540i	−0.908371	−	0.418165i	$-0.862673\pi$
$983$	2.26705	−	6.97726i	0.0723077	−	0.222540i	0.980679	+	0.195625i	$0.0626734\pi$
$984$		0			0
$985$	−19.9436	−	7.33247i	−0.635455	−	0.233632i
$986$	−1.16961	−	0.849774i	−0.0372481	−	0.0270623i
$987$		0			0
$988$	−4.62577	+	3.36082i	−0.147165	+	0.106922i
$989$	32.9949	+	23.9722i	1.04918	+	0.762271i
$990$		0			0
$991$	0.714712	−	0.519269i	0.0227036	−	0.0164951i	−0.576376	−	0.817185i	$-0.695533\pi$
$991$	0.714712	−	0.519269i	0.0227036	−	0.0164951i	0.599079	+	0.800690i	$0.295533\pi$
$992$	−0.407310	+	1.25357i	−0.0129321	+	0.0398009i
$993$		0			0
$994$	0.249875	−	0.769036i	0.00792555	−	0.0243923i
$995$	−23.8705	+	30.3487i	−0.756746	+	0.962119i
$996$		0			0
$997$	8.50456	+	26.1743i	0.269342	+	0.828950i	0.990661	+	0.136347i	$0.0435361\pi$
$997$	8.50456	+	26.1743i	0.269342	+	0.828950i	−0.721319	+	0.692603i	$0.756464\pi$
$998$	35.2968	+	25.6446i	1.11730	+	0.811767i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.38239 + 1.75756i) q^{5} -0.447412 q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.38239 + 1.75756i) q^{5} -0.447412 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.15144 - 0.609344i) q^{10} +(-4.42816 - 3.21725i) q^{11} +(-0.573372 + 0.416579i) q^{13} +(0.361964 + 0.262982i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-0.133697 + 0.411479i) q^{17} +(2.49304 - 7.67280i) q^{19} +(-2.09872 - 0.771616i) q^{20} +(1.69141 + 5.20561i) q^{22} +(-4.65186 - 3.37978i) q^{23} +(-1.17800 - 4.85925i) q^{25} +0.708727 q^{26} +(-0.138258 - 0.425514i) q^{28} +(-1.03259 - 3.17797i) q^{29} +(-0.407310 + 1.25357i) q^{31} +1.00000 q^{32} +(0.350025 - 0.254308i) q^{34} +(0.618497 - 0.786351i) q^{35} +(-8.14595 + 5.91838i) q^{37} +(-6.52687 + 4.74205i) q^{38} +(1.24435 + 1.85784i) q^{40} +(4.80242 - 3.48916i) q^{41} -7.09283 q^{43} +(1.69141 - 5.20561i) q^{44} +(1.77685 + 5.46859i) q^{46} +(2.83769 + 8.73350i) q^{47} -6.79982 q^{49} +(-1.90317 + 4.62363i) q^{50} +(-0.573372 - 0.416579i) q^{52} +(0.210809 + 0.648802i) q^{53} +(11.7759 - 3.33525i) q^{55} +(-0.138258 + 0.425514i) q^{56} +(-1.03259 + 3.17797i) q^{58} +(-2.75539 + 2.00191i) q^{59} +(4.91755 + 3.57281i) q^{61} +(1.06635 - 0.774750i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(0.0604623 - 1.58361i) q^{65} +(0.528998 - 1.62809i) q^{67} -0.432654 q^{68} +(-0.962580 + 0.272628i) q^{70} +(-0.558490 - 1.71886i) q^{71} +(-10.0932 - 7.33316i) q^{73} +10.0689 q^{74} +8.06766 q^{76} +(1.98121 + 1.43943i) q^{77} +(-2.72171 - 8.37656i) q^{79} +(0.0853112 - 2.23444i) q^{80} -5.93612 q^{82} +(0.545222 - 1.67802i) q^{83} +(-0.538374 - 0.803804i) q^{85} +(5.73822 + 4.16906i) q^{86} +(-4.42816 + 3.21725i) q^{88} +(11.2689 + 8.18730i) q^{89} +(0.256533 - 0.186382i) q^{91} +(1.77685 - 5.46859i) q^{92} +(2.83769 - 8.73350i) q^{94} +(10.0390 + 14.9885i) q^{95} +(4.04585 + 12.4519i) q^{97} +(5.50117 + 3.99684i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + q^{5} - 2 q^{7} - 3 q^{8}+O(q^{10}) \) 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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