LMFDB - Embedded newform 450.2.h.e.361.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$1.66637 - 0.917186i$ of defining polynomial
Character	$\chi$	$=$	450.361
Dual form			450.2.h.e.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-2.02373 - 0.951057i) q^{5} -2.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-2.02373 - 0.951057i) q^{5} -2.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.19625 + 0.420099i) q^{10} +(2.24459 - 1.63079i) q^{11} +(-4.59343 - 3.33732i) q^{13} +(-2.24459 + 1.63079i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-1.59343 - 4.90406i) q^{17} +(0.436451 + 1.34326i) q^{19} +(-1.52988 + 1.63079i) q^{20} +(0.857358 - 2.63868i) q^{22} +(-0.529876 + 0.384978i) q^{23} +(3.19098 + 3.84937i) q^{25} -5.67779 q^{26} +(-0.857358 + 2.63868i) q^{28} +(-1.26594 + 3.89618i) q^{29} +(-2.20239 - 6.77827i) q^{31} -1.00000 q^{32} +(-4.17164 - 3.03088i) q^{34} +(5.61478 + 2.63868i) q^{35} +(0.847416 + 0.615684i) q^{37} +(1.14264 + 0.830178i) q^{38} +(-0.279141 + 2.21858i) q^{40} +(7.36789 + 5.35309i) q^{41} +9.24660 q^{43} +(-0.857358 - 2.63868i) q^{44} +(-0.202395 + 0.622907i) q^{46} +(0.857358 - 2.63868i) q^{47} +0.697669 q^{49} +(4.84416 + 1.23859i) q^{50} +(-4.59343 + 3.33732i) q^{52} +(0.162577 - 0.500362i) q^{53} +(-6.09343 + 1.16555i) q^{55} +(0.857358 + 2.63868i) q^{56} +(1.26594 + 3.89618i) q^{58} +(-3.05975 - 2.22304i) q^{59} +(8.76365 - 6.36716i) q^{61} +(-5.76594 - 4.18920i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(6.12188 + 11.1224i) q^{65} +(-1.33600 - 4.11180i) q^{67} -5.15643 q^{68} +(6.09343 - 1.16555i) q^{70} +(4.09343 - 12.5983i) q^{71} +(-3.40859 + 2.47648i) q^{73} +1.04746 q^{74} +1.41238 q^{76} +(-6.22754 + 4.52458i) q^{77} +(-3.05975 + 9.41695i) q^{79} +(1.07822 + 1.95894i) q^{80} +9.10722 q^{82} +(-1.44497 - 4.44717i) q^{83} +(-1.43937 + 11.4399i) q^{85} +(7.48066 - 5.43502i) q^{86} +(-2.24459 - 1.63079i) q^{88} +(-7.43002 + 5.39823i) q^{89} +(12.7443 + 9.25928i) q^{91} +(0.202395 + 0.622907i) q^{92} +(-0.857358 - 2.63868i) q^{94} +(0.394254 - 3.13348i) q^{95} +(-0.0278640 + 0.0857567i) q^{97} +(0.564426 - 0.410079i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8	$ 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8} - q^{11} - 13 q^{13} + q^{14} - 2 q^{16} + 11 q^{17} + 20 q^{19} - 5 q^{20} + q^{22} + 3 q^{23} + 30 q^{25} - 22 q^{26} - q^{28} + 15 q^{29} - 9 q^{31} - 8 q^{32} - q^{34} + 15 q^{35} - 6 q^{37} + 15 q^{38} - 5 q^{40} + 9 q^{41} + 12 q^{43} - q^{44} + 7 q^{46} + q^{47} - 4 q^{49} + 5 q^{50} - 13 q^{52} - 7 q^{53} - 25 q^{55} + q^{56} - 15 q^{58} - 10 q^{59} + 6 q^{61} - 21 q^{62} - 2 q^{64} + 10 q^{65} - 11 q^{67} - 24 q^{68} + 25 q^{70} + 9 q^{71} - 8 q^{73} - 24 q^{74} - 10 q^{76} - 33 q^{77} - 10 q^{79} + 26 q^{82} - 27 q^{83} + 5 q^{85} + 23 q^{86} + q^{88} + 15 q^{89} + q^{91} - 7 q^{92} - q^{94} + 30 q^{95} - 36 q^{97} + 19 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8 - q^11 - 13 * q^13 + q^14 - 2 * q^16 + 11 * q^17 + 20 * q^19 - 5 * q^20 + q^22 + 3 * q^23 + 30 * q^25 - 22 * q^26 - q^28 + 15 * q^29 - 9 * q^31 - 8 * q^32 - q^34 + 15 * q^35 - 6 * q^37 + 15 * q^38 - 5 * q^40 + 9 * q^41 + 12 * q^43 - q^44 + 7 * q^46 + q^47 - 4 * q^49 + 5 * q^50 - 13 * q^52 - 7 * q^53 - 25 * q^55 + q^56 - 15 * q^58 - 10 * q^59 + 6 * q^61 - 21 * q^62 - 2 * q^64 + 10 * q^65 - 11 * q^67 - 24 * q^68 + 25 * q^70 + 9 * q^71 - 8 * q^73 - 24 * q^74 - 10 * q^76 - 33 * q^77 - 10 * q^79 + 26 * q^82 - 27 * q^83 + 5 * q^85 + 23 * q^86 + q^88 + 15 * q^89 + q^91 - 7 * q^92 - q^94 + 30 * q^95 - 36 * q^97 + 19 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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
$5$	−2.02373	−	0.951057i	−0.905040	−	0.425325i
$5$	−2.02373	−	0.951057i	−0.905040	−	0.425325i
$6$		0			0
$7$	−2.77447			−1.04865			−0.524325	−	0.851518i	$-0.675682\pi$
$7$	−2.77447			−1.04865			−0.524325	+	0.851518i	$0.675682\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$		0			0
$10$	−2.19625	+	0.420099i	−0.694515	+	0.132847i
$11$	2.24459	−	1.63079i	0.676770	−	0.491702i	−0.195515	−	0.980701i	$-0.562638\pi$
$11$	2.24459	−	1.63079i	0.676770	−	0.491702i	0.872284	+	0.488999i	$0.162638\pi$
$12$		0			0
$13$	−4.59343	−	3.33732i	−1.27399	−	0.925606i	−0.274633	−	0.961549i	$-0.588556\pi$
$13$	−4.59343	−	3.33732i	−1.27399	−	0.925606i	−0.999354	+	0.0359433i	$0.988556\pi$
$14$	−2.24459	+	1.63079i	−0.599892	+	0.435847i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.59343	−	4.90406i	−0.386462	−	1.18941i	−0.935414	−	0.353555i	$-0.884973\pi$
$17$	−1.59343	−	4.90406i	−0.386462	−	1.18941i	0.548951	−	0.835854i	$-0.315027\pi$
$18$		0			0
$19$	0.436451	+	1.34326i	0.100129	+	0.308164i	0.988556	−	0.150852i	$-0.0482018\pi$
$19$	0.436451	+	1.34326i	0.100129	+	0.308164i	−0.888428	+	0.459017i	$0.848202\pi$
$20$	−1.52988	+	1.63079i	−0.342091	+	0.364656i
$21$		0			0
$22$	0.857358	−	2.63868i	0.182789	−	0.562567i
$23$	−0.529876	+	0.384978i	−0.110487	+	0.0802734i	−0.641657	−	0.766992i	$-0.721753\pi$
$23$	−0.529876	+	0.384978i	−0.110487	+	0.0802734i	0.531170	+	0.847265i	$0.321753\pi$
$24$		0			0
$25$	3.19098	+	3.84937i	0.638197	+	0.769873i
$26$	−5.67779			−1.11351
$27$		0			0
$28$	−0.857358	+	2.63868i	−0.162025	+	0.498663i
$29$	−1.26594	+	3.89618i	−0.235080	+	0.723502i	0.762031	+	0.647541i	$0.224202\pi$
$29$	−1.26594	+	3.89618i	−0.235080	+	0.723502i	−0.997111	+	0.0759609i	$0.975798\pi$
$30$		0			0
$31$	−2.20239	−	6.77827i	−0.395562	−	1.21741i	−0.928523	−	0.371274i	$-0.878921\pi$
$31$	−2.20239	−	6.77827i	−0.395562	−	1.21741i	0.532961	−	0.846140i	$-0.321079\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−4.17164	−	3.03088i	−0.715431	−	0.519791i
$35$	5.61478	+	2.63868i	0.949071	+	0.446018i
$36$		0			0
$37$	0.847416	+	0.615684i	0.139314	+	0.101218i	0.655260	−	0.755404i	$-0.272559\pi$
$37$	0.847416	+	0.615684i	0.139314	+	0.101218i	−0.515945	+	0.856622i	$0.672559\pi$
$38$	1.14264	+	0.830178i	0.185361	+	0.134673i
$39$		0			0
$40$	−0.279141	+	2.21858i	−0.0441361	+	0.350788i
$41$	7.36789	+	5.35309i	1.15067	+	0.836012i	0.988570	−	0.150762i	$-0.0481728\pi$
$41$	7.36789	+	5.35309i	1.15067	+	0.836012i	0.162101	+	0.986774i	$0.448173\pi$
$42$		0			0
$43$	9.24660			1.41009			0.705047	−	0.709161i	$-0.250926\pi$
$43$	9.24660			1.41009			0.705047	+	0.709161i	$0.250926\pi$
$44$	−0.857358	−	2.63868i	−0.129252	−	0.397795i
$45$		0			0
$46$	−0.202395	+	0.622907i	−0.0298415	+	0.0918426i
$47$	0.857358	−	2.63868i	0.125058	−	0.384890i	−0.868853	−	0.495070i	$-0.835143\pi$
$47$	0.857358	−	2.63868i	0.125058	−	0.384890i	0.993912	+	0.110179i	$0.0351425\pi$
$48$		0			0
$49$	0.697669			0.0996670
$50$	4.84416	+	1.23859i	0.685068	+	0.175163i
$51$		0			0
$52$	−4.59343	+	3.33732i	−0.636994	+	0.462803i
$53$	0.162577	−	0.500362i	0.0223317	−	0.0687299i	−0.939270	−	0.343180i	$-0.888496\pi$
$53$	0.162577	−	0.500362i	0.0223317	−	0.0687299i	0.961601	+	0.274450i	$0.0884959\pi$
$54$		0			0
$55$	−6.09343	+	1.16555i	−0.821637	+	0.157163i
$56$	0.857358	+	2.63868i	0.114569	+	0.352608i
$57$		0			0
$58$	1.26594	+	3.89618i	0.166227	+	0.511593i
$59$	−3.05975	−	2.22304i	−0.398346	−	0.289415i	0.370521	−	0.928824i	$-0.379179\pi$
$59$	−3.05975	−	2.22304i	−0.398346	−	0.289415i	−0.768867	+	0.639409i	$0.779179\pi$
$60$		0			0
$61$	8.76365	−	6.36716i	1.12207	−	0.815232i	0.137549	−	0.990495i	$-0.456078\pi$
$61$	8.76365	−	6.36716i	1.12207	−	0.815232i	0.984522	+	0.175263i	$0.0560776\pi$
$62$	−5.76594	−	4.18920i	−0.732276	−	0.532029i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	6.12188	+	11.1224i	0.759326	+	1.37957i
$66$		0			0
$67$	−1.33600	−	4.11180i	−0.163219	−	0.502336i	0.835682	−	0.549214i	$-0.185073\pi$
$67$	−1.33600	−	4.11180i	−0.163219	−	0.502336i	−0.998901	+	0.0468778i	$0.985073\pi$
$68$	−5.15643			−0.625309
$69$		0			0
$70$	6.09343	−	1.16555i	0.728304	−	0.139310i
$71$	4.09343	−	12.5983i	0.485800	−	1.49514i	−0.345018	−	0.938596i	$-0.612127\pi$
$71$	4.09343	−	12.5983i	0.485800	−	1.49514i	0.830819	−	0.556543i	$-0.187873\pi$
$72$		0			0
$73$	−3.40859	+	2.47648i	−0.398945	+	0.289850i	−0.769111	−	0.639115i	$-0.779301\pi$
$73$	−3.40859	+	2.47648i	−0.398945	+	0.289850i	0.370166	+	0.928966i	$0.379301\pi$
$74$	1.04746			0.121765
$75$		0			0
$76$	1.41238			0.162012
$77$	−6.22754	+	4.52458i	−0.709695	+	0.515623i
$78$		0			0
$79$	−3.05975	+	9.41695i	−0.344249	+	1.05949i	0.617736	+	0.786386i	$0.288050\pi$
$79$	−3.05975	+	9.41695i	−0.344249	+	1.05949i	−0.961985	+	0.273104i	$0.911950\pi$
$80$	1.07822	+	1.95894i	0.120548	+	0.219016i
$81$		0			0
$82$	9.10722			1.00572
$83$	−1.44497	−	4.44717i	−0.158606	−	0.488141i	0.839902	−	0.542738i	$-0.182612\pi$
$83$	−1.44497	−	4.44717i	−0.158606	−	0.488141i	−0.998508	+	0.0545976i	$0.982612\pi$
$84$		0			0
$85$	−1.43937	+	11.4399i	−0.156122	+	1.24084i
$86$	7.48066	−	5.43502i	0.806660	−	0.586073i
$87$		0			0
$88$	−2.24459	−	1.63079i	−0.239274	−	0.173843i
$89$	−7.43002	+	5.39823i	−0.787581	+	0.572211i	−0.907245	−	0.420603i	$-0.861818\pi$
$89$	−7.43002	+	5.39823i	−0.787581	+	0.572211i	0.119664	+	0.992814i	$0.461818\pi$
$90$		0			0
$91$	12.7443	+	9.25928i	1.33597	+	0.970637i
$92$	0.202395	+	0.622907i	0.0211011	+	0.0649425i
$93$		0			0
$94$	−0.857358	−	2.63868i	−0.0884297	−	0.272159i
$95$	0.394254	−	3.13348i	0.0404496	−	0.321488i
$96$		0			0
$97$	−0.0278640	+	0.0857567i	−0.00282917	+	0.00870727i	−0.952461	−	0.304660i	$-0.901457\pi$
$97$	−0.0278640	+	0.0857567i	−0.00282917	+	0.00870727i	0.949632	+	0.313367i	$0.101457\pi$
$98$	0.564426	−	0.410079i	0.0570156	−	0.0414243i
$99$		0			0
$100$	4.64703	−	1.84529i	0.464703	−	0.184529i
$101$	7.90632			0.786709			0.393354	−	0.919387i	$-0.371315\pi$
$101$	7.90632			0.786709			0.393354	+	0.919387i	$0.371315\pi$
$102$		0			0
$103$	2.42091	−	7.45079i	0.238539	−	0.734148i	−0.758093	−	0.652146i	$-0.773869\pi$
$103$	2.42091	−	7.45079i	0.238539	−	0.734148i	0.996632	−	0.0820014i	$-0.0261312\pi$
$104$	−1.75453	+	5.39990i	−0.172046	+	0.529503i
$105$		0			0
$106$	−0.162577	−	0.500362i	−0.0157909	−	0.0485994i
$107$	10.2220			0.988194			0.494097	−	0.869407i	$-0.335499\pi$
$107$	10.2220			0.988194			0.494097	+	0.869407i	$0.335499\pi$
$108$		0			0
$109$	−3.16400	−	2.29878i	−0.303056	−	0.220183i	0.425855	−	0.904791i	$-0.359973\pi$
$109$	−3.16400	−	2.29878i	−0.303056	−	0.220183i	−0.728911	+	0.684608i	$0.759973\pi$
$110$	−4.24459	+	4.52458i	−0.404706	+	0.431401i
$111$		0			0
$112$	2.24459	+	1.63079i	0.212094	+	0.154095i
$113$	−5.15785	−	3.74740i	−0.485210	−	0.352526i	0.318129	−	0.948047i	$-0.396945\pi$
$113$	−5.15785	−	3.74740i	−0.485210	−	0.352526i	−0.803339	+	0.595522i	$0.796945\pi$
$114$		0			0
$115$	1.43846	−	0.275149i	0.134137	−	0.0256578i
$116$	3.31428	+	2.40797i	0.307724	+	0.223574i
$117$		0			0
$118$	−3.78206			−0.348167
$119$	4.42091	+	13.6062i	0.405264	+	1.24727i
$120$		0			0
$121$	−1.02048	+	3.14070i	−0.0927706	+	0.285519i
$122$	3.34742	−	10.3023i	0.303061	−	0.932725i
$123$		0			0
$124$	−7.12710			−0.640032
$125$	−2.79673	−	10.8249i	−0.250147	−	0.968208i
$126$		0			0
$127$	−7.72525	+	5.61272i	−0.685505	+	0.498049i	−0.875179	−	0.483798i	$-0.839257\pi$
$127$	−7.72525	+	5.61272i	−0.685505	+	0.498049i	0.189674	+	0.981847i	$0.439257\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$		0			0
$130$	11.4903	+	5.39990i	1.00777	+	0.473602i
$131$	−1.73026	−	5.32519i	−0.151173	−	0.465264i	0.846580	−	0.532262i	$-0.178658\pi$
$131$	−1.73026	−	5.32519i	−0.151173	−	0.465264i	−0.997753	+	0.0669981i	$0.978658\pi$
$132$		0			0
$133$	−1.21092	−	3.72682i	−0.105000	−	0.323156i
$134$	−3.49771	−	2.54123i	−0.302156	−	0.219529i
$135$		0			0
$136$	−4.17164	+	3.03088i	−0.357715	+	0.259895i
$137$	6.45931	+	4.69296i	0.551856	+	0.400947i	0.828469	−	0.560035i	$-0.189212\pi$
$137$	6.45931	+	4.69296i	0.551856	+	0.400947i	−0.276613	+	0.960981i	$0.589212\pi$
$138$		0			0
$139$	17.8699	−	12.9832i	1.51571	−	1.10122i	0.552140	−	0.833751i	$-0.313811\pi$
$139$	17.8699	−	12.9832i	1.51571	−	1.10122i	0.963565	−	0.267473i	$-0.0861887\pi$
$140$	4.24459	−	4.52458i	0.358733	−	0.382396i
$141$		0			0
$142$	−4.09343	−	12.5983i	−0.343513	−	1.05722i
$143$	−15.7528			−1.31732
$144$		0			0
$145$	6.26741	−	6.68083i	0.520480	−	0.554813i
$146$	−1.30196	+	4.00703i	−0.107751	+	0.331624i
$147$		0			0
$148$	0.847416	−	0.615684i	0.0696572	−	0.0506089i
$149$	−4.18401			−0.342768			−0.171384	−	0.985204i	$-0.554824\pi$
$149$	−4.18401			−0.342768			−0.171384	+	0.985204i	$0.554824\pi$
$150$		0			0
$151$	−0.331561			−0.0269821			−0.0134910	−	0.999909i	$-0.504294\pi$
$151$	−0.331561			−0.0269821			−0.0134910	+	0.999909i	$0.504294\pi$
$152$	1.14264	−	0.830178i	0.0926805	−	0.0673364i
$153$		0			0
$154$	−2.37871	+	7.32092i	−0.191682	+	0.589936i
$155$	−1.98946	+	15.8120i	−0.159798	+	1.27005i
$156$		0			0
$157$	3.60750			0.287910			0.143955	−	0.989584i	$-0.454018\pi$
$157$	3.60750			0.287910			0.143955	+	0.989584i	$0.454018\pi$
$158$	3.05975	+	9.41695i	0.243421	+	0.749172i
$159$		0			0
$160$	2.02373	+	0.951057i	0.159990	+	0.0751876i
$161$	1.47012	−	1.06811i	0.115862	−	0.0841787i
$162$		0			0
$163$	−4.12101	−	2.99409i	−0.322782	−	0.234515i	0.414580	−	0.910013i	$-0.363929\pi$
$163$	−4.12101	−	2.99409i	−0.322782	−	0.234515i	−0.737362	+	0.675498i	$0.763929\pi$
$164$	7.36789	−	5.35309i	0.575336	−	0.418006i
$165$		0			0
$166$	−3.78299	−	2.74850i	−0.293617	−	0.213325i
$167$	−6.44699	−	19.8418i	−0.498883	−	1.53540i	−0.810817	−	0.585300i	$-0.800977\pi$
$167$	−6.44699	−	19.8418i	−0.498883	−	1.53540i	0.311934	−	0.950104i	$-0.399023\pi$
$168$		0			0
$169$	5.94464	+	18.2957i	0.457280	+	1.40736i
$170$	5.55975	+	10.1011i	0.426414	+	0.774723i
$171$		0			0
$172$	2.85736	−	8.79404i	0.217871	−	0.670539i
$173$	−9.69826	+	7.04620i	−0.737345	+	0.535713i	−0.891879	−	0.452275i	$-0.850613\pi$
$173$	−9.69826	+	7.04620i	−0.737345	+	0.535713i	0.154533	+	0.987988i	$0.450613\pi$
$174$		0			0
$175$	−8.85328	−	10.6799i	−0.669245	−	0.807328i
$176$	−2.77447			−0.209133
$177$		0			0
$178$	−2.83802	+	8.73452i	−0.212718	+	0.654680i
$179$	2.63942	−	8.12330i	0.197279	−	0.607164i	−0.802663	−	0.596433i	$-0.796584\pi$
$179$	2.63942	−	8.12330i	0.197279	−	0.607164i	0.999942	−	0.0107309i	$-0.00341581\pi$
$180$		0			0
$181$	2.41912	+	7.44529i	0.179812	+	0.553404i	0.999820	−	0.0189471i	$-0.00603140\pi$
$181$	2.41912	+	7.44529i	0.179812	+	0.553404i	−0.820009	+	0.572351i	$0.806031\pi$
$182$	15.7528			1.16768
$183$		0			0
$184$	0.529876	+	0.384978i	0.0390630	+	0.0283809i
$185$	−1.12939	−	2.05192i	−0.0830346	−	0.150860i
$186$		0			0
$187$	−11.5741	−	8.40906i	−0.846381	−	0.614932i
$188$	−2.24459	−	1.63079i	−0.163704	−	0.118938i
$189$		0			0
$190$	−1.52286	−	2.76678i	−0.110480	−	0.200723i
$191$	2.72324	+	1.97855i	0.197047	+	0.143163i	0.681934	−	0.731414i	$-0.261139\pi$
$191$	2.72324	+	1.97855i	0.197047	+	0.143163i	−0.484887	+	0.874577i	$0.661139\pi$
$192$		0			0
$193$	−15.4211			−1.11004			−0.555018	−	0.831839i	$-0.687288\pi$
$193$	−15.4211			−1.11004			−0.555018	+	0.831839i	$0.687288\pi$
$194$	0.0278640	+	0.0857567i	0.00200052	+	0.00615697i
$195$		0			0
$196$	0.215591	−	0.663522i	0.0153994	−	0.0473945i
$197$	−2.72086	+	8.37394i	−0.193853	+	0.596619i	0.806135	+	0.591732i	$0.201556\pi$
$197$	−2.72086	+	8.37394i	−0.193853	+	0.596619i	−0.999988	+	0.00488692i	$0.998444\pi$
$198$		0			0
$199$	−17.6222			−1.24920			−0.624601	−	0.780944i	$-0.714738\pi$
$199$	−17.6222			−1.24920			−0.624601	+	0.780944i	$0.714738\pi$
$200$	2.67490	−	4.22433i	0.189144	−	0.298705i
$201$		0			0
$202$	6.39635	−	4.64722i	0.450046	−	0.326977i
$203$	3.51232	−	10.8098i	0.246517	−	0.758700i
$204$		0			0
$205$	−9.81955	−	17.8405i	−0.685827	−	1.24603i
$206$	−2.42091	−	7.45079i	−0.168673	−	0.519121i
$207$		0			0
$208$	1.75453	+	5.39990i	0.121655	+	0.374415i
$209$	3.17022	+	2.30330i	0.219289	+	0.159323i
$210$		0			0
$211$	−4.93617	+	3.58634i	−0.339820	+	0.246894i	−0.744586	−	0.667527i	$-0.767353\pi$
$211$	−4.93617	+	3.58634i	−0.339820	+	0.246894i	0.404766	+	0.914420i	$0.367353\pi$
$212$	−0.425633	−	0.309240i	−0.0292326	−	0.0212387i
$213$		0			0
$214$	8.26974	−	6.00832i	0.565308	−	0.410720i
$215$	−18.7126	−	8.79404i	−1.27619	−	0.599749i
$216$		0			0
$217$	6.11047	+	18.8061i	0.414806	+	1.27664i
$218$	−3.91091			−0.264880
$219$		0			0
$220$	−0.774467	+	6.15537i	−0.0522146	+	0.414995i
$221$	−9.04713	+	27.8442i	−0.608576	+	1.87300i
$222$		0			0
$223$	4.06828	−	2.95578i	0.272432	−	0.197933i	−0.443178	−	0.896434i	$-0.646149\pi$
$223$	4.06828	−	2.95578i	0.272432	−	0.197933i	0.715610	+	0.698500i	$0.246149\pi$
$224$	2.77447			0.185377
$225$		0			0
$226$	−6.37545			−0.424089
$227$	−14.4314	+	10.4851i	−0.957848	+	0.695918i	−0.952650	−	0.304069i	$-0.901655\pi$
$227$	−14.4314	+	10.4851i	−0.957848	+	0.695918i	−0.00519840	+	0.999986i	$0.501655\pi$
$228$		0			0
$229$	−6.66137	+	20.5016i	−0.440195	+	1.35478i	0.447472	+	0.894298i	$0.352324\pi$
$229$	−6.66137	+	20.5016i	−0.440195	+	1.35478i	−0.887668	+	0.460485i	$0.847676\pi$
$230$	1.00201	−	1.06811i	0.0660707	−	0.0704289i
$231$		0			0
$232$	4.09668			0.268960
$233$	−4.54454	−	13.9867i	−0.297723	−	0.916297i	−0.982293	−	0.187350i	$-0.940010\pi$
$233$	−4.54454	−	13.9867i	−0.297723	−	0.916297i	0.684570	−	0.728947i	$-0.259990\pi$
$234$		0			0
$235$	−4.24459	+	4.52458i	−0.276887	+	0.295151i
$236$	−3.05975	+	2.22304i	−0.199173	+	0.144708i
$237$		0			0
$238$	11.5741	+	8.40906i	0.750236	+	0.545079i
$239$	5.61478	−	4.07938i	0.363190	−	0.263873i	−0.391192	−	0.920309i	$-0.627937\pi$
$239$	5.61478	−	4.07938i	0.363190	−	0.263873i	0.754381	+	0.656436i	$0.227937\pi$
$240$		0			0
$241$	−2.67787	−	1.94559i	−0.172497	−	0.125326i	0.498187	−	0.867070i	$-0.333999\pi$
$241$	−2.67787	−	1.94559i	−0.172497	−	0.125326i	−0.670684	+	0.741743i	$0.733999\pi$
$242$	1.02048	+	3.14070i	0.0655987	+	0.201892i
$243$		0			0
$244$	−3.34742	−	10.3023i	−0.214296	−	0.659536i
$245$	−1.41189	−	0.663522i	−0.0902026	−	0.0423909i
$246$		0			0
$247$	2.47807	−	7.62672i	0.157676	−	0.485277i
$248$	−5.76594	+	4.18920i	−0.366138	+	0.266015i
$249$		0			0
$250$	−8.62531	−	7.11365i	−0.545513	−	0.449906i
$251$	9.46454			0.597397			0.298698	−	0.954348i	$-0.403448\pi$
$251$	9.46454			0.597397			0.298698	+	0.954348i	$0.403448\pi$
$252$		0			0
$253$	−0.561537	+	1.72823i	−0.0353036	+	0.108653i
$254$	−2.95078	+	9.08158i	−0.185149	+	0.569829i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	7.07963			0.441615			0.220808	−	0.975317i	$-0.429131\pi$
$257$	7.07963			0.441615			0.220808	+	0.975317i	$0.429131\pi$
$258$		0			0
$259$	−2.35113	−	1.70820i	−0.146092	−	0.106142i
$260$	12.4698	−	2.38523i	0.773347	−	0.147926i
$261$		0			0
$262$	−4.52988	−	3.29115i	−0.279857	−	0.203328i
$263$	1.15969	+	0.842563i	0.0715095	+	0.0519547i	0.622966	−	0.782249i	$-0.285928\pi$
$263$	1.15969	+	0.842563i	0.0715095	+	0.0519547i	−0.551456	+	0.834204i	$0.685928\pi$
$264$		0			0
$265$	−0.804885	+	0.857977i	−0.0494437	+	0.0527051i
$266$	−3.17022	−	2.30330i	−0.194379	−	0.141225i
$267$		0			0
$268$	−4.32340			−0.264094
$269$	4.41368	+	13.5839i	0.269107	+	0.828226i	0.990719	+	0.135928i	$0.0434015\pi$
$269$	4.41368	+	13.5839i	0.269107	+	0.828226i	−0.721612	+	0.692298i	$0.756598\pi$
$270$		0			0
$271$	9.51325	−	29.2788i	0.577889	−	1.77856i	−0.0482363	−	0.998836i	$-0.515360\pi$
$271$	9.51325	−	29.2788i	0.577889	−	1.77856i	0.626125	−	0.779723i	$-0.284640\pi$
$272$	−1.59343	+	4.90406i	−0.0966156	+	0.297352i
$273$		0			0
$274$	7.98414			0.482340
$275$	13.4400	+	3.43643i	0.810460	+	0.207224i
$276$		0			0
$277$	−2.58051	+	1.87485i	−0.155048	+	0.112649i	−0.662604	−	0.748970i	$-0.730549\pi$
$277$	−2.58051	+	1.87485i	−0.155048	+	0.112649i	0.507556	+	0.861619i	$0.330549\pi$
$278$	6.82570	−	21.0073i	0.409378	−	1.25994i
$279$		0			0
$280$	0.774467	−	6.15537i	0.0462833	−	0.367854i
$281$	−6.30053	−	19.3910i	−0.375858	−	1.15677i	−0.942898	−	0.333081i	$-0.891912\pi$
$281$	−6.30053	−	19.3910i	−0.375858	−	1.15677i	0.567040	−	0.823690i	$-0.308088\pi$
$282$		0			0
$283$	−4.10897	−	12.6461i	−0.244253	−	0.751733i	−0.995758	−	0.0920063i	$-0.970672\pi$
$283$	−4.10897	−	12.6461i	−0.244253	−	0.751733i	0.751506	−	0.659727i	$-0.229328\pi$
$284$	−10.7167	−	7.78616i	−0.635921	−	0.462023i
$285$		0			0
$286$	−12.7443	+	9.25928i	−0.753587	+	0.547513i
$287$	−20.4420	−	14.8520i	−1.20665	−	0.876684i
$288$		0			0
$289$	−7.75751	+	5.63616i	−0.456324	+	0.331539i
$290$	1.14355	−	9.08880i	0.0671516	−	0.533713i
$291$		0			0
$292$	1.30196	+	4.00703i	0.0761917	+	0.234494i
$293$	26.0420			1.52139			0.760696	−	0.649108i	$-0.224858\pi$
$293$	26.0420			1.52139			0.760696	+	0.649108i	$0.224858\pi$
$294$		0			0
$295$	4.07788	+	7.40883i	0.237423	+	0.431359i
$296$	0.323684	−	0.996198i	0.0188138	−	0.0579028i
$297$		0			0
$298$	−3.38494	+	2.45930i	−0.196084	+	0.142464i
$299$	3.71874			0.215060
$300$		0			0
$301$	−25.6544			−1.47869
$302$	−0.268239	+	0.194887i	−0.0154354	+	0.0112145i
$303$		0			0
$304$	0.436451	−	1.34326i	0.0250322	−	0.0770411i
$305$	−23.7908	+	4.55071i	−1.36226	+	0.260573i
$306$		0			0
$307$	25.1000			1.43253			0.716267	−	0.697826i	$-0.245849\pi$
$307$	25.1000			1.43253			0.716267	+	0.697826i	$0.245849\pi$
$308$	2.37871	+	7.32092i	0.135540	+	0.417148i
$309$		0			0
$310$	7.68456	+	13.9616i	0.436453	+	0.792964i
$311$	0.585185	−	0.425162i	0.0331828	−	0.0241087i	−0.571070	−	0.820901i	$-0.693472\pi$
$311$	0.585185	−	0.425162i	0.0331828	−	0.0241087i	0.604253	+	0.796792i	$0.293472\pi$
$312$		0			0
$313$	−17.4879	−	12.7057i	−0.988477	−	0.718170i	−0.0288898	−	0.999583i	$-0.509197\pi$
$313$	−17.4879	−	12.7057i	−0.988477	−	0.718170i	−0.959587	+	0.281412i	$0.909197\pi$
$314$	2.91853	−	2.12043i	0.164702	−	0.119663i
$315$		0			0
$316$	8.01054	+	5.81999i	0.450628	+	0.327400i
$317$	5.81992	+	17.9119i	0.326879	+	1.00603i	0.970585	+	0.240758i	$0.0773960\pi$
$317$	5.81992	+	17.9119i	0.326879	+	1.00603i	−0.643706	+	0.765273i	$0.722604\pi$
$318$		0			0
$319$	3.51232	+	10.8098i	0.196652	+	0.605233i
$320$	2.19625	−	0.420099i	0.122774	−	0.0234842i
$321$		0			0
$322$	0.561537	−	1.72823i	0.0312933	−	0.0963107i
$323$	5.89196	−	4.28076i	0.327837	−	0.238188i
$324$		0			0
$325$	−1.81098	−	28.3311i	−0.100455	−	1.57153i
$326$	−5.09385			−0.282122
$327$		0			0
$328$	2.81428	−	8.66148i	0.155393	−	0.478250i
$329$	−2.37871	+	7.32092i	−0.131143	+	0.403615i
$330$		0			0
$331$	5.21494	+	16.0499i	0.286639	+	0.882185i	0.985903	+	0.167320i	$0.0535115\pi$
$331$	5.21494	+	16.0499i	0.286639	+	0.882185i	−0.699263	+	0.714864i	$0.746489\pi$
$332$	−4.67603			−0.256631
$333$		0			0
$334$	−16.8784	−	12.2629i	−0.923546	−	0.670996i
$335$	−1.20684	+	9.59180i	−0.0659366	+	0.524056i
$336$		0			0
$337$	−15.6562	−	11.3749i	−0.852845	−	0.619628i	0.0730841	−	0.997326i	$-0.476716\pi$
$337$	−15.6562	−	11.3749i	−0.852845	−	0.619628i	−0.925929	+	0.377698i	$0.876716\pi$
$338$	15.5633	+	11.3074i	0.846530	+	0.615040i
$339$		0			0
$340$	10.4352	+	4.90406i	0.565930	+	0.265960i
$341$	−15.9974	−	11.6228i	−0.866309	−	0.629410i
$342$		0			0
$343$	17.4856			0.944134
$344$	−2.85736	−	8.79404i	−0.154058	−	0.474143i
$345$		0			0
$346$	−3.70441	+	11.4010i	−0.199150	+	0.612921i
$347$	2.79311	−	8.59630i	0.149942	−	0.461473i	−0.847672	−	0.530521i	$-0.821996\pi$
$347$	2.79311	−	8.59630i	0.149942	−	0.461473i	0.997613	+	0.0690480i	$0.0219962\pi$
$348$		0			0
$349$	36.7305			1.96614			0.983068	−	0.183240i	$-0.0586584\pi$
$349$	36.7305			1.96614			0.983068	+	0.183240i	$0.0586584\pi$
$350$	−13.4400	−	3.43643i	−0.718396	−	0.183685i
$351$		0			0
$352$	−2.24459	+	1.63079i	−0.119637	+	0.0869214i
$353$	−5.67779	+	17.4744i	−0.302198	+	0.930070i	0.678510	+	0.734591i	$0.262626\pi$
$353$	−5.67779	+	17.4744i	−0.302198	+	0.930070i	−0.980708	+	0.195479i	$0.937374\pi$
$354$		0			0
$355$	−20.2657	+	21.6024i	−1.07559	+	1.14654i
$356$	2.83802	+	8.73452i	0.150415	+	0.462928i
$357$		0			0
$358$	−2.63942	−	8.12330i	−0.139498	−	0.429330i
$359$	−19.7609	−	14.3572i	−1.04294	−	0.757742i	−0.0720846	−	0.997399i	$-0.522965\pi$
$359$	−19.7609	−	14.3572i	−1.04294	−	0.757742i	−0.970858	+	0.239657i	$0.922965\pi$
$360$		0			0
$361$	13.7575	−	9.99539i	0.724078	−	0.526073i
$362$	6.33334	+	4.60144i	0.332873	+	0.241846i
$363$		0			0
$364$	12.7443	−	9.25928i	0.667983	−	0.485318i
$365$	9.25334	−	1.76998i	0.484342	−	0.0926450i
$366$		0			0
$367$	4.48768	+	13.8117i	0.234255	+	0.720963i	0.997219	+	0.0745221i	$0.0237431\pi$
$367$	4.48768	+	13.8117i	0.234255	+	0.720963i	−0.762964	+	0.646441i	$0.776257\pi$
$368$	0.654963			0.0341423
$369$		0			0
$370$	−2.11979	−	0.996198i	−0.110202	−	0.0517898i
$371$	−0.451065	+	1.38824i	−0.0234182	+	0.0720737i
$372$		0			0
$373$	18.8410	−	13.6888i	0.975549	−	0.708778i	0.0188399	−	0.999823i	$-0.494003\pi$
$373$	18.8410	−	13.6888i	0.975549	−	0.708778i	0.956710	+	0.291044i	$0.0940027\pi$
$374$	−14.3064			−0.739764
$375$		0			0
$376$	−2.77447			−0.143082
$377$	18.8178	−	13.6719i	0.969166	−	0.704140i
$378$		0			0
$379$	8.84332	−	27.2169i	0.454251	−	1.39804i	−0.417762	−	0.908556i	$-0.637185\pi$
$379$	8.84332	−	27.2169i	0.454251	−	1.39804i	0.872013	−	0.489483i	$-0.162815\pi$
$380$	−2.85829	−	1.34326i	−0.146627	−	0.0689076i
$381$		0			0
$382$	3.36611			0.172225
$383$	5.13454	+	15.8025i	0.262363	+	0.807469i	0.992289	+	0.123944i	$0.0395542\pi$
$383$	5.13454	+	15.8025i	0.262363	+	0.807469i	−0.729927	+	0.683526i	$0.760446\pi$
$384$		0			0
$385$	16.9060	−	3.23378i	0.861610	−	0.164809i
$386$	−12.4759	+	9.06430i	−0.635008	+	0.461361i
$387$		0			0
$388$	0.0729490	+	0.0530006i	0.00370343	+	0.00269070i
$389$	21.3392	−	15.5039i	1.08194	−	0.786077i	0.103922	−	0.994585i	$-0.466861\pi$
$389$	21.3392	−	15.5039i	1.08194	−	0.786077i	0.978021	+	0.208508i	$0.0668609\pi$
$390$		0			0
$391$	2.73227	+	1.98511i	0.138177	+	0.100391i
$392$	−0.215591	−	0.663522i	−0.0108890	−	0.0335129i
$393$		0			0
$394$	2.72086	+	8.37394i	0.137075	+	0.421873i
$395$	15.1482	−	16.1474i	0.762187	−	0.812463i
$396$		0			0
$397$	−5.53406	+	17.0321i	−0.277747	+	0.854816i	0.710733	+	0.703462i	$0.248363\pi$
$397$	−5.53406	+	17.0321i	−0.277747	+	0.854816i	−0.988480	+	0.151354i	$0.951637\pi$
$398$	−14.2566	+	10.3580i	−0.714620	+	0.519202i
$399$		0			0
$400$	−0.318958	−	4.98982i	−0.0159479	−	0.249491i
$401$	−32.0164			−1.59882			−0.799411	−	0.600785i	$-0.794855\pi$
$401$	−32.0164			−1.59882			−0.799411	+	0.600785i	$0.794855\pi$
$402$		0			0
$403$	−12.5047	+	38.4856i	−0.622905	+	1.91710i
$404$	2.44319	−	7.51936i	0.121553	−	0.374102i
$405$		0			0
$406$	−3.51232	−	10.8098i	−0.174314	−	0.536482i
$407$	2.90615			0.144053
$408$		0			0
$409$	−14.5901	−	10.6003i	−0.721435	−	0.524153i	0.165407	−	0.986225i	$-0.447106\pi$
$409$	−14.5901	−	10.6003i	−0.721435	−	0.524153i	−0.886842	+	0.462072i	$0.847106\pi$
$410$	−18.4306	−	8.66148i	−0.910221	−	0.427760i
$411$		0			0
$412$	−6.33802	−	4.60484i	−0.312252	−	0.226864i
$413$	8.48918	+	6.16775i	0.417725	+	0.303495i
$414$		0			0
$415$	−1.30527	+	10.3741i	−0.0640733	+	0.509246i
$416$	4.59343	+	3.33732i	0.225211	+	0.163626i
$417$		0			0
$418$	3.91861			0.191666
$419$	6.03511	+	18.5742i	0.294834	+	0.907407i	0.983277	+	0.182116i	$0.0582947\pi$
$419$	6.03511	+	18.5742i	0.294834	+	0.907407i	−0.688443	+	0.725291i	$0.741705\pi$
$420$		0			0
$421$	−6.04242	+	18.5967i	−0.294490	+	0.906346i	0.688903	+	0.724854i	$0.258093\pi$
$421$	−6.04242	+	18.5967i	−0.294490	+	0.906346i	−0.983392	+	0.181492i	$0.941907\pi$
$422$	−1.88545	+	5.80281i	−0.0917822	+	0.282477i
$423$		0			0
$424$	−0.526111			−0.0255502
$425$	13.7929	−	21.7825i	0.669055	−	1.05660i
$426$		0			0
$427$	−24.3145	+	17.6655i	−1.17666	+	0.854893i
$428$	3.15876	−	9.72166i	0.152684	−	0.469914i
$429$		0			0
$430$	−20.3079	+	3.88449i	−0.979332	+	0.187327i
$431$	6.55002	+	20.1589i	0.315503	+	0.971019i	0.975547	+	0.219792i	$0.0705378\pi$
$431$	6.55002	+	20.1589i	0.315503	+	0.971019i	−0.660044	+	0.751227i	$0.729462\pi$
$432$		0			0
$433$	2.64199	+	8.13122i	0.126966	+	0.390761i	0.994254	−	0.107045i	$-0.0341389\pi$
$433$	2.64199	+	8.13122i	0.126966	+	0.390761i	−0.867288	+	0.497807i	$0.834139\pi$
$434$	15.9974	+	11.6228i	0.767901	+	0.557913i
$435$		0			0
$436$	−3.16400	+	2.29878i	−0.151528	+	0.110091i
$437$	−0.748388	−	0.543736i	−0.0358003	−	0.0260104i
$438$		0			0
$439$	22.7102	−	16.4999i	1.08390	−	0.787499i	0.105541	−	0.994415i	$-0.466343\pi$
$439$	22.7102	−	16.4999i	1.08390	−	0.787499i	0.978359	+	0.206916i	$0.0663427\pi$
$440$	2.99148	+	5.43502i	0.142613	+	0.259104i
$441$		0			0
$442$	9.04713	+	27.8442i	0.430328	+	1.32441i
$443$	33.0546			1.57047			0.785236	−	0.619197i	$-0.212542\pi$
$443$	33.0546			1.57047			0.785236	+	0.619197i	$0.212542\pi$
$444$		0			0
$445$	20.1704	−	3.85820i	0.956169	−	0.182896i
$446$	1.55394	−	4.78254i	0.0735813	−	0.226460i
$447$		0			0
$448$	2.24459	−	1.63079i	0.106047	−	0.0770476i
$449$	37.1628			1.75382			0.876911	−	0.480652i	$-0.159600\pi$
$449$	37.1628			1.75382			0.876911	+	0.480652i	$0.159600\pi$
$450$		0			0
$451$	25.2677			1.18981
$452$	−5.15785	+	3.74740i	−0.242605	+	0.176263i
$453$		0			0
$454$	−5.51232	+	16.9652i	−0.258706	+	0.796215i
$455$	−16.9850	−	30.8589i	−0.796267	−	1.44669i
$456$		0			0
$457$	29.3139			1.37125			0.685624	−	0.727956i	$-0.259529\pi$
$457$	29.3139			1.37125			0.685624	+	0.727956i	$0.259529\pi$
$458$	6.66137	+	20.5016i	0.311265	+	0.957976i
$459$		0			0
$460$	0.182827	−	1.45309i	0.00852435	−	0.0677504i
$461$	7.20624	−	5.23564i	0.335628	−	0.243848i	−0.407187	−	0.913345i	$-0.633490\pi$
$461$	7.20624	−	5.23564i	0.335628	−	0.243848i	0.742815	+	0.669497i	$0.233490\pi$
$462$		0			0
$463$	14.7865	+	10.7430i	0.687187	+	0.499271i	0.875734	−	0.482793i	$-0.160378\pi$
$463$	14.7865	+	10.7430i	0.687187	+	0.499271i	−0.188547	+	0.982064i	$0.560378\pi$
$464$	3.31428	−	2.40797i	0.153862	−	0.111787i
$465$		0			0
$466$	−11.8978	−	8.64424i	−0.551154	−	0.400436i
$467$	11.3360	+	34.8886i	0.524568	+	1.61445i	0.765169	+	0.643829i	$0.222655\pi$
$467$	11.3360	+	34.8886i	0.524568	+	1.61445i	−0.240601	+	0.970624i	$0.577345\pi$
$468$		0			0
$469$	3.70670	+	11.4081i	0.171160	+	0.526775i
$470$	−0.774467	+	6.15537i	−0.0357235	+	0.283926i
$471$		0			0
$472$	−1.16872	+	3.59695i	−0.0537948	+	0.165563i
$473$	20.7548	−	15.0793i	0.954309	−	0.693346i
$474$		0			0
$475$	−3.77798	+	5.96637i	−0.173346	+	0.273756i
$476$	14.3064			0.655731
$477$		0			0
$478$	2.14465	−	6.60057i	0.0980942	−	0.301903i
$479$	3.89046	−	11.9736i	0.177760	−	0.547088i	−0.821989	−	0.569503i	$-0.807136\pi$
$479$	3.89046	−	11.9736i	0.177760	−	0.547088i	0.999749	+	0.0224155i	$0.00713568\pi$
$480$		0			0
$481$	−1.83781	−	5.65620i	−0.0837969	−	0.257900i
$482$	−3.31003			−0.150768
$483$		0			0
$484$	2.67164	+	1.94106i	0.121438	+	0.0882301i
$485$	0.137949	−	0.147048i	0.00626393	−	0.00667712i
$486$		0			0
$487$	14.8257	+	10.7715i	0.671816	+	0.488103i	0.870633	−	0.491934i	$-0.163710\pi$
$487$	14.8257	+	10.7715i	0.671816	+	0.488103i	−0.198816	+	0.980037i	$0.563710\pi$
$488$	−8.76365	−	6.36716i	−0.396712	−	0.288228i
$489$		0			0
$490$	−1.53226	+	0.293090i	−0.0692202	+	0.0132405i
$491$	17.5595	+	12.7577i	0.792448	+	0.575747i	0.908689	−	0.417474i	$-0.137085\pi$
$491$	17.5595	+	12.7577i	0.792448	+	0.575747i	−0.116241	+	0.993221i	$0.537085\pi$
$492$		0			0
$493$	21.1243			0.951389
$494$	−2.47807	−	7.62672i	−0.111494	−	0.343143i
$495$		0			0
$496$	−2.20239	+	6.77827i	−0.0988904	+	0.304353i
$497$	−11.3571	+	34.9535i	−0.509434	+	1.56788i
$498$		0			0
$499$	15.8391			0.709055			0.354527	−	0.935046i	$-0.384642\pi$
$499$	15.8391			0.709055			0.354527	+	0.935046i	$0.384642\pi$
$500$	−11.1593	−	0.685229i	−0.499060	−	0.0306444i
$501$		0			0
$502$	7.65697	−	5.56312i	0.341748	−	0.248294i
$503$	−8.51433	+	26.2044i	−0.379635	+	1.16840i	0.560662	+	0.828044i	$0.310547\pi$
$503$	−8.51433	+	26.2044i	−0.379635	+	1.16840i	−0.940298	+	0.340353i	$0.889453\pi$
$504$		0			0
$505$	−16.0003	−	7.51936i	−0.712003	−	0.334607i
$506$	0.561537	+	1.72823i	0.0249634	+	0.0768294i
$507$		0			0
$508$	2.95078	+	9.08158i	0.130920	+	0.402930i
$509$	−22.3386	−	16.2300i	−0.990142	−	0.719380i	−0.0301894	−	0.999544i	$-0.509611\pi$
$509$	−22.3386	−	16.2300i	−0.990142	−	0.719380i	−0.959952	+	0.280164i	$0.909611\pi$
$510$		0			0
$511$	9.45701	−	6.87092i	0.418354	−	0.303952i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$		0			0
$514$	5.72754	−	4.16130i	0.252631	−	0.183547i
$515$	−11.9854	+	12.7760i	−0.528139	+	0.562977i
$516$		0			0
$517$	−2.37871	−	7.32092i	−0.104616	−	0.321974i
$518$	−2.90615			−0.127689
$519$		0			0
$520$	8.68631	−	9.25928i	0.380920	−	0.406046i
$521$	−5.28084	+	16.2527i	−0.231358	+	0.712046i	0.766226	+	0.642571i	$0.222132\pi$
$521$	−5.28084	+	16.2527i	−0.231358	+	0.712046i	−0.997584	+	0.0694747i	$0.977868\pi$
$522$		0			0
$523$	−29.3796	+	21.3456i	−1.28468	+	0.933376i	−0.999684	−	0.0251516i	$-0.991993\pi$
$523$	−29.3796	+	21.3456i	−1.28468	+	0.933376i	−0.284999	+	0.958528i	$0.591993\pi$
$524$	−5.59923			−0.244604
$525$		0			0
$526$	1.43345			0.0625016
$527$	−29.7317	+	21.6013i	−1.29513	+	0.940970i
$528$		0			0
$529$	−6.97483	+	21.4663i	−0.303253	+	0.933318i
$530$	−0.146859	+	1.16722i	−0.00637915	+	0.0507007i
$531$		0			0
$532$	−3.91861			−0.169893
$533$	−15.9789	−	49.1780i	−0.692123	−	2.13014i
$534$		0			0
$535$	−20.6865	−	9.72166i	−0.894356	−	0.420304i
$536$	−3.49771	+	2.54123i	−0.151078	+	0.109764i
$537$		0			0
$538$	11.5552	+	8.39532i	0.498178	+	0.361948i
$539$	1.56598	−	1.13775i	0.0674516	−	0.0490064i
$540$		0			0
$541$	−20.1742	−	14.6574i	−0.867355	−	0.630170i	0.0625209	−	0.998044i	$-0.480086\pi$
$541$	−20.1742	−	14.6574i	−0.867355	−	0.630170i	−0.929876	+	0.367873i	$0.880086\pi$
$542$	−9.51325	−	29.2788i	−0.408629	−	1.25763i
$543$		0			0
$544$	1.59343	+	4.90406i	0.0683176	+	0.210260i
$545$	4.21681	+	7.66125i	0.180628	+	0.328172i
$546$		0			0
$547$	2.06176	−	6.34546i	0.0881547	−	0.271312i	−0.897255	−	0.441513i	$-0.854442\pi$
$547$	2.06176	−	6.34546i	0.0881547	−	0.271312i	0.985409	+	0.170201i	$0.0544418\pi$
$548$	6.45931	−	4.69296i	0.275928	−	0.200473i
$549$		0			0
$550$	12.8930	−	5.11968i	0.549761	−	0.218304i
$551$	−5.78609			−0.246496
$552$		0			0
$553$	8.48918	−	26.1270i	0.360997	−	1.11103i
$554$	−0.985668	+	3.03357i	−0.0418770	+	0.128884i
$555$		0			0
$556$	−6.82570	−	21.0073i	−0.289474	−	0.890909i
$557$	20.4328			0.865765			0.432882	−	0.901450i	$-0.357497\pi$
$557$	20.4328			0.865765			0.432882	+	0.901450i	$0.357497\pi$
$558$		0			0
$559$	−42.4736	−	30.8589i	−1.79644	−	1.30519i
$560$	−2.99148	−	5.43502i	−0.126413	−	0.229671i
$561$		0			0
$562$	−16.4950	−	11.9843i	−0.695799	−	0.505528i
$563$	−0.487680	−	0.354320i	−0.0205532	−	0.0149328i	0.577461	−	0.816418i	$-0.304043\pi$
$563$	−0.487680	−	0.354320i	−0.0205532	−	0.0149328i	−0.598014	+	0.801485i	$0.704043\pi$
$564$		0			0
$565$	6.87412	+	12.4891i	0.289196	+	0.525422i
$566$	−10.7574	−	7.81572i	−0.452168	−	0.328519i
$567$		0			0
$568$	−13.2466			−0.555815
$569$	−10.4688	−	32.2195i	−0.438873	−	1.35071i	−0.889065	−	0.457781i	$-0.848644\pi$
$569$	−10.4688	−	32.2195i	−0.438873	−	1.35071i	0.450192	−	0.892932i	$-0.351356\pi$
$570$		0			0
$571$	−1.92521	+	5.92520i	−0.0805677	+	0.247962i	−0.983225	−	0.182399i	$-0.941614\pi$
$571$	−1.92521	+	5.92520i	−0.0805677	+	0.247962i	0.902657	+	0.430361i	$0.141614\pi$
$572$	−4.86789	+	14.9818i	−0.203537	+	0.626422i
$573$		0			0
$574$	−25.2677			−1.05465
$575$	−3.17275	−	0.811231i	−0.132313	−	0.0338307i
$576$		0			0
$577$	−3.05893	+	2.22244i	−0.127345	+	0.0925214i	−0.649634	−	0.760247i	$-0.725078\pi$
$577$	−3.05893	+	2.22244i	−0.127345	+	0.0925214i	0.522290	+	0.852768i	$0.325078\pi$
$578$	−2.96310	+	9.11949i	−0.123249	+	0.379321i
$579$		0			0
$580$	−4.41711	−	8.02516i	−0.183410	−	0.333226i
$581$	4.00903	+	12.3385i	0.166323	+	0.511889i
$582$		0			0
$583$	−0.451065	−	1.38824i	−0.0186812	−	0.0574949i
$584$	3.40859	+	2.47648i	0.141048	+	0.102478i
$585$		0			0
$586$	21.0684	−	15.3071i	0.870330	−	0.632332i
$587$	13.2296	+	9.61184i	0.546042	+	0.396723i	0.826324	−	0.563195i	$-0.190428\pi$
$587$	13.2296	+	9.61184i	0.546042	+	0.396723i	−0.280282	+	0.959918i	$0.590428\pi$
$588$		0			0
$589$	8.14373	−	5.91676i	0.335556	−	0.243796i
$590$	7.65388	+	3.59695i	0.315105	+	0.148084i
$591$		0			0
$592$	−0.323684	−	0.996198i	−0.0133033	−	0.0409435i
$593$	−9.53314			−0.391479			−0.195740	−	0.980656i	$-0.562711\pi$
$593$	−9.53314			−0.391479			−0.195740	+	0.980656i	$0.562711\pi$
$594$		0			0
$595$	3.99349	−	31.7397i	0.163717	−	1.30120i
$596$	−1.29293	+	3.97923i	−0.0529605	+	0.162996i
$597$		0			0
$598$	3.00852	−	2.18582i	0.123028	−	0.0893848i
$599$	16.0682			0.656528			0.328264	−	0.944586i	$-0.393536\pi$
$599$	16.0682			0.656528			0.328264	+	0.944586i	$0.393536\pi$
$600$		0			0
$601$	15.0380			0.613413			0.306707	−	0.951804i	$-0.400773\pi$
$601$	15.0380			0.613413			0.306707	+	0.951804i	$0.400773\pi$
$602$	−20.7548	+	15.0793i	−0.845904	+	0.614585i
$603$		0			0
$604$	−0.102458	+	0.315333i	−0.00416896	+	0.0128307i
$605$	5.05216	−	5.38541i	0.205399	−	0.218948i
$606$		0			0
$607$	−44.8348			−1.81979			−0.909894	−	0.414840i	$-0.863837\pi$
$607$	−44.8348			−1.81979			−0.909894	+	0.414840i	$0.863837\pi$
$608$	−0.436451	−	1.34326i	−0.0177004	−	0.0544763i
$609$		0			0
$610$	−16.5723	+	17.6655i	−0.670994	+	0.715255i
$611$	−12.7443	+	9.25928i	−0.515580	+	0.374590i
$612$		0			0
$613$	12.5793	+	9.13937i	0.508072	+	0.369136i	0.812092	−	0.583530i	$-0.198329\pi$
$613$	12.5793	+	9.13937i	0.508072	+	0.369136i	−0.304020	+	0.952666i	$0.598329\pi$
$614$	20.3064	−	14.7534i	0.819498	−	0.595400i
$615$		0			0
$616$	6.22754	+	4.52458i	0.250915	+	0.182300i
$617$	−5.43852	−	16.7380i	−0.218946	−	0.673848i	−0.998850	−	0.0479478i	$-0.984732\pi$
$617$	−5.43852	−	16.7380i	−0.218946	−	0.673848i	0.779903	−	0.625900i	$-0.215268\pi$
$618$		0			0
$619$	−11.5229	−	35.4637i	−0.463143	−	1.42541i	−0.861303	−	0.508091i	$-0.830351\pi$
$619$	−11.5229	−	35.4637i	−0.463143	−	1.42541i	0.398161	−	0.917316i	$-0.369649\pi$
$620$	14.4233	+	6.77827i	0.579255	+	0.272222i
$621$		0			0
$622$	0.223521	−	0.687926i	0.00896236	−	0.0275833i
$623$	20.6144	−	14.9772i	0.825897	−	0.600049i
$624$		0			0
$625$	−4.63525	+	24.5665i	−0.185410	+	0.982661i
$626$	−21.6163			−0.863960
$627$		0			0
$628$	1.11478	−	3.43094i	0.0444845	−	0.136909i
$629$	1.66906	−	5.13683i	0.0665496	−	0.204819i
$630$		0			0
$631$	2.64380	+	8.13677i	0.105248	+	0.323920i	0.989789	−	0.142543i	$-0.0455280\pi$
$631$	2.64380	+	8.13677i	0.105248	+	0.323920i	−0.884541	+	0.466463i	$0.845528\pi$
$632$	9.90157			0.393863
$633$		0			0
$634$	15.2367	+	11.0701i	0.605129	+	0.439652i
$635$	20.9719	−	4.01150i	0.832243	−	0.159191i
$636$		0			0
$637$	−3.20469	−	2.32834i	−0.126974	−	0.0922523i
$638$	9.19537	+	6.68083i	0.364048	+	0.264497i
$639$		0			0
$640$	1.52988	−	1.63079i	0.0604737	−	0.0644627i
$641$	−18.4582	−	13.4107i	−0.729055	−	0.529690i	0.160209	−	0.987083i	$-0.448783\pi$
$641$	−18.4582	−	13.4107i	−0.729055	−	0.529690i	−0.889264	+	0.457394i	$0.848783\pi$
$642$		0			0
$643$	34.7745			1.37137			0.685686	−	0.727898i	$-0.259503\pi$
$643$	34.7745			1.37137			0.685686	+	0.727898i	$0.259503\pi$
$644$	−0.561537	−	1.72823i	−0.0221277	−	0.0681020i
$645$		0			0
$646$	2.25053	−	6.92641i	0.0885459	−	0.272516i
$647$	5.08583	−	15.6526i	0.199945	−	0.615366i	−0.799939	−	0.600082i	$-0.795135\pi$
$647$	5.08583	−	15.6526i	0.199945	−	0.615366i	0.999883	−	0.0152844i	$-0.00486537\pi$
$648$		0			0
$649$	−10.4932			−0.411894
$650$	−18.1177	−	21.8559i	−0.710635	−	0.857258i
$651$		0			0
$652$	−4.12101	+	2.99409i	−0.161391	+	0.117257i
$653$	−9.33515	+	28.7306i	−0.365313	+	1.12432i	0.584473	+	0.811414i	$0.301301\pi$
$653$	−9.33515	+	28.7306i	−0.365313	+	1.12432i	−0.949785	+	0.312903i	$0.898699\pi$
$654$		0			0
$655$	−1.56298	+	12.4223i	−0.0610705	+	0.485381i
$656$	−2.81428	−	8.66148i	−0.109879	−	0.338174i
$657$		0			0
$658$	2.37871	+	7.32092i	0.0927318	+	0.285399i
$659$	−23.0523	−	16.7485i	−0.897991	−	0.652428i	0.0399585	−	0.999201i	$-0.487277\pi$
$659$	−23.0523	−	16.7485i	−0.897991	−	0.652428i	−0.937949	+	0.346773i	$0.887277\pi$
$660$		0			0
$661$	−41.0448	+	29.8208i	−1.59646	+	1.15990i	−0.702562	+	0.711622i	$0.747961\pi$
$661$	−41.0448	+	29.8208i	−1.59646	+	1.15990i	−0.893897	+	0.448273i	$0.852039\pi$
$662$	13.6529	+	9.91941i	0.530635	+	0.385529i
$663$		0			0
$664$	−3.78299	+	2.74850i	−0.146809	+	0.106663i
$665$	−1.09385	+	8.69374i	−0.0424175	+	0.337129i
$666$		0			0
$667$	−0.829146	−	2.55185i	−0.0321047	−	0.0988080i
$668$	−20.8629			−0.807209
$669$		0			0
$670$	4.66156	+	8.46929i	0.180092	+	0.327197i
$671$	9.28730	−	28.5834i	0.358532	−	1.10345i
$672$		0			0
$673$	16.5401	−	12.0171i	0.637573	−	0.463224i	−0.221442	−	0.975173i	$-0.571077\pi$
$673$	16.5401	−	12.0171i	0.637573	−	0.463224i	0.859016	+	0.511949i	$0.171077\pi$
$674$	−19.3521			−0.745414
$675$		0			0
$676$	19.2373			0.739894
$677$	6.90383	−	5.01592i	0.265336	−	0.192778i	−0.447160	−	0.894454i	$-0.647565\pi$
$677$	6.90383	−	5.01592i	0.265336	−	0.192778i	0.712496	+	0.701676i	$0.247565\pi$
$678$		0			0
$679$	0.0773079	−	0.237929i	0.00296680	−	0.00913088i
$680$	11.3248	−	2.16621i	0.434287	−	0.0830705i
$681$		0			0
$682$	−19.7739			−0.757182
$683$	15.0085	+	46.1913i	0.574283	+	1.76746i	0.638608	+	0.769532i	$0.279511\pi$
$683$	15.0085	+	46.1913i	0.574283	+	1.76746i	−0.0643246	+	0.997929i	$0.520489\pi$
$684$		0			0
$685$	−8.60863	−	15.6405i	−0.328919	−	0.597591i
$686$	14.1462	−	10.2778i	0.540103	−	0.392408i
$687$		0			0
$688$	−7.48066	−	5.43502i	−0.285197	−	0.207208i
$689$	−2.41665	+	1.75580i	−0.0920671	+	0.0668907i
$690$		0			0
$691$	−36.2501	−	26.3373i	−1.37902	−	1.00192i	−0.996971	−	0.0777740i	$-0.975219\pi$
$691$	−36.2501	−	26.3373i	−1.37902	−	1.00192i	−0.382048	−	0.924142i	$-0.624781\pi$
$692$	3.70441	+	11.4010i	0.140820	+	0.433401i
$693$		0			0
$694$	−2.79311	−	8.59630i	−0.106025	−	0.326311i
$695$	−48.5117	+	9.27932i	−1.84015	+	0.351985i
$696$		0			0
$697$	14.5117	−	44.6623i	0.549669	−	1.69171i
$698$	29.7156	−	21.5896i	1.12475	−	0.817179i
$699$		0			0
$700$	−12.8930	+	5.11968i	−0.487311	+	0.193506i
$701$	−2.21913			−0.0838152			−0.0419076	−	0.999121i	$-0.513344\pi$
$701$	−2.21913			−0.0838152			−0.0419076	+	0.999121i	$0.513344\pi$
$702$		0			0
$703$	−0.457166	+	1.40701i	−0.0172424	+	0.0530665i
$704$	−0.857358	+	2.63868i	−0.0323129	+	0.0994488i
$705$		0			0
$706$	5.67779	+	17.4744i	0.213686	+	0.657659i
$707$	−21.9358			−0.824982
$708$		0			0
$709$	−27.7968	−	20.1955i	−1.04393	−	0.758459i	−0.0728805	−	0.997341i	$-0.523219\pi$
$709$	−27.7968	−	20.1955i	−1.04393	−	0.758459i	−0.971049	+	0.238882i	$0.923219\pi$
$710$	−3.69767	+	29.3886i	−0.138771	+	1.10293i
$711$		0			0
$712$	7.43002	+	5.39823i	0.278452	+	0.202307i
$713$	3.77648	+	2.74377i	0.141430	+	0.102755i
$714$		0			0
$715$	31.8795	+	14.9818i	1.19223	+	0.560289i
$716$	−6.91009	−	5.02047i	−0.258242	−	0.187624i
$717$		0			0
$718$	−24.4259			−0.911565
$719$	−3.70511	−	11.4032i	−0.138177	−	0.425266i	0.857893	−	0.513828i	$-0.171773\pi$
$719$	−3.70511	−	11.4032i	−0.138177	−	0.425266i	−0.996071	+	0.0885618i	$0.971773\pi$
$720$		0			0
$721$	−6.71673	+	20.6720i	−0.250144	+	0.769864i
$722$	5.25489	−	16.1729i	0.195567	−	0.601892i
$723$		0			0
$724$	7.82844			0.290942
$725$	−19.0374	+	7.55955i	−0.707032	+	0.280754i
$726$		0			0
$727$	−34.1265	+	24.7944i	−1.26568	+	0.919573i	−0.999022	−	0.0442177i	$-0.985920\pi$
$727$	−34.1265	+	24.7944i	−1.26568	+	0.919573i	−0.266661	+	0.963790i	$0.585920\pi$
$728$	4.86789	−	14.9818i	0.180416	−	0.555264i
$729$		0			0
$730$	6.44574	−	6.87092i	0.238568	−	0.254304i
$731$	−14.7338	−	45.3459i	−0.544948	−	1.67718i
$732$		0			0
$733$	−0.0996219	−	0.306605i	−0.00367962	−	0.0113247i	0.949200	−	0.314674i	$-0.101895\pi$
$733$	−0.0996219	−	0.306605i	−0.00367962	−	0.0113247i	−0.952879	+	0.303349i	$0.901895\pi$
$734$	11.7489	+	8.53607i	0.433660	+	0.315072i
$735$		0			0
$736$	0.529876	−	0.384978i	0.0195315	−	0.0141905i
$737$	−9.70427	−	7.05056i	−0.357461	−	0.259711i
$738$		0			0
$739$	4.44942	−	3.23269i	0.163674	−	0.118916i	−0.502933	−	0.864325i	$-0.667746\pi$
$739$	4.44942	−	3.23269i	0.163674	−	0.118916i	0.666607	+	0.745409i	$0.267746\pi$
$740$	−2.30049	+	0.440039i	−0.0845678	+	0.0161761i
$741$		0			0
$742$	0.451065	+	1.38824i	0.0165591	+	0.0509638i
$743$	6.03812			0.221517			0.110759	−	0.993847i	$-0.464672\pi$
$743$	6.03812			0.221517			0.110759	+	0.993847i	$0.464672\pi$
$744$		0			0
$745$	8.46733	+	3.97923i	0.310219	+	0.145788i
$746$	7.19662	−	22.1489i	0.263487	−	0.810929i
$747$		0			0
$748$	−11.5741	+	8.40906i	−0.423190	+	0.307466i
$749$	−28.3605			−1.03627
$750$		0			0
$751$	−13.5719			−0.495244			−0.247622	−	0.968857i	$-0.579649\pi$
$751$	−13.5719			−0.495244			−0.247622	+	0.968857i	$0.579649\pi$
$752$	−2.24459	+	1.63079i	−0.0818518	+	0.0594688i
$753$		0			0
$754$	7.18776	−	22.1216i	0.261763	−	0.805623i
$755$	0.670991	+	0.315333i	0.0244199	+	0.0114762i
$756$		0			0
$757$	33.0661			1.20181			0.600904	−	0.799321i	$-0.294807\pi$
$757$	33.0661			1.20181			0.600904	+	0.799321i	$0.294807\pi$
$758$	−8.84332	−	27.2169i	−0.321204	−	0.988563i
$759$		0			0
$760$	−3.10195	+	0.593341i	−0.112520	+	0.0215227i
$761$	4.19767	−	3.04978i	0.152165	−	0.110555i	−0.509098	−	0.860709i	$-0.670021\pi$
$761$	4.19767	−	3.04978i	0.152165	−	0.110555i	0.661263	+	0.750154i	$0.270021\pi$
$762$		0			0
$763$	8.77840	+	6.37788i	0.317799	+	0.230895i
$764$	2.72324	−	1.97855i	0.0985233	−	0.0715814i
$765$		0			0
$766$	13.4424	+	9.76647i	0.485694	+	0.352877i
$767$	6.63575	+	20.4227i	0.239603	+	0.737422i
$768$		0			0
$769$	10.2191	+	31.4512i	0.368511	+	1.13416i	0.947753	+	0.319005i	$0.103349\pi$
$769$	10.2191	+	31.4512i	0.368511	+	1.13416i	−0.579242	+	0.815156i	$0.696651\pi$
$770$	11.7765	−	12.5533i	0.424395	−	0.452389i
$771$		0			0
$772$	−4.76538	+	14.6663i	−0.171510	+	0.527853i
$773$	−0.914961	+	0.664758i	−0.0329088	+	0.0239097i	−0.604118	−	0.796895i	$-0.706474\pi$
$773$	−0.914961	+	0.664758i	−0.0329088	+	0.0239097i	0.571209	+	0.820804i	$0.306474\pi$
$774$		0			0
$775$	19.0643	−	30.1072i	0.684808	−	1.08148i
$776$	0.0901699			0.00323691
$777$		0			0
$778$	8.15086	−	25.0858i	0.292223	−	0.899369i
$779$	−3.97485	+	12.2333i	−0.142414	+	0.438305i
$780$		0			0
$781$	−11.3571	−	34.9535i	−0.406388	−	1.25073i
$782$	3.37727			0.120771
$783$		0			0
$784$	−0.564426	−	0.410079i	−0.0201581	−	0.0146457i
$785$	−7.30061	−	3.43094i	−0.260570	−	0.122455i
$786$		0			0
$787$	−12.7509	−	9.26408i	−0.454521	−	0.330229i	0.336857	−	0.941556i	$-0.390636\pi$
$787$	−12.7509	−	9.26408i	−0.454521	−	0.330229i	−0.791378	+	0.611327i	$0.790636\pi$
$788$	7.12330	+	5.17538i	0.253757	+	0.184365i
$789$		0			0
$790$	2.76393	−	21.9674i	0.0983363	−	0.781564i
$791$	14.3103	+	10.3970i	0.508815	+	0.369676i
$792$		0			0
$793$	−61.5044			−2.18409
$794$	5.53406	+	17.0321i	0.196396	+	0.604446i
$795$		0			0
$796$	−5.44555	+	16.7597i	−0.193012	+	0.594031i
$797$	7.15055	−	22.0071i	0.253285	−	0.779532i	−0.740877	−	0.671640i	$-0.765590\pi$
$797$	7.15055	−	22.0071i	0.253285	−	0.779532i	0.994163	−	0.107892i	$-0.0344100\pi$
$798$		0			0
$799$	−14.3064			−0.506122
$800$	−3.19098	−	3.84937i	−0.112818	−	0.136096i
$801$		0			0
$802$	−25.9018	+	18.8188i	−0.914624	+	0.664513i
$803$	−3.61226	+	11.1174i	−0.127474	+	0.392324i
$804$		0			0
$805$	−3.99097	+	0.763393i	−0.140663	+	0.0269061i
$806$	12.5047	+	38.4856i	0.440460	+	1.35560i
$807$		0			0
$808$	−2.44319	−	7.51936i	−0.0859511	−	0.264530i
$809$	27.1345	+	19.7143i	0.953997	+	0.693119i	0.951749	−	0.306878i	$-0.0992844\pi$
$809$	27.1345	+	19.7143i	0.953997	+	0.693119i	0.00224811	+	0.999997i	$0.499284\pi$
$810$		0			0
$811$	9.67796	−	7.03145i	0.339839	−	0.246907i	−0.404755	−	0.914425i	$-0.632643\pi$
$811$	9.67796	−	7.03145i	0.339839	−	0.246907i	0.744594	+	0.667518i	$0.232643\pi$
$812$	−9.19537	−	6.68083i	−0.322694	−	0.234451i
$813$		0			0
$814$	2.35113	−	1.70820i	0.0824070	−	0.0598722i
$815$	5.49227	+	9.97854i	0.192386	+	0.349533i
$816$		0			0
$817$	4.03569	+	12.4206i	0.141191	+	0.434540i
$818$	−18.0344			−0.630557
$819$		0			0
$820$	−20.0017	+	3.82593i	−0.698491	+	0.133607i
$821$	3.30466	−	10.1707i	0.115333	−	0.354960i	−0.876683	−	0.481068i	$-0.840249\pi$
$821$	3.30466	−	10.1707i	0.115333	−	0.354960i	0.992016	+	0.126109i	$0.0402489\pi$
$822$		0			0
$823$	9.72525	−	7.06581i	0.339001	−	0.246299i	−0.405239	−	0.914211i	$-0.632812\pi$
$823$	9.72525	−	7.06581i	0.339001	−	0.246299i	0.744240	+	0.667912i	$0.232812\pi$
$824$	−7.83422			−0.272918
$825$		0			0
$826$	10.4932			0.365105
$827$	−3.34912	+	2.43328i	−0.116460	+	0.0846133i	−0.644491	−	0.764612i	$-0.722931\pi$
$827$	−3.34912	+	2.43328i	−0.116460	+	0.0846133i	0.528031	+	0.849225i	$0.322931\pi$
$828$		0			0
$829$	−6.28859	+	19.3543i	−0.218412	+	0.672203i	0.780482	+	0.625178i	$0.214974\pi$
$829$	−6.28859	+	19.3543i	−0.218412	+	0.672203i	−0.998894	+	0.0470242i	$0.985026\pi$
$830$	5.04178	+	9.16007i	0.175003	+	0.317951i
$831$		0			0
$832$	5.67779			0.196842
$833$	−1.11168	−	3.42141i	−0.0385175	−	0.118545i
$834$		0			0
$835$	−5.82368	+	46.2859i	−0.201537	+	1.60179i
$836$	3.17022	−	2.30330i	0.109644	−	0.0796614i
$837$		0			0
$838$	15.8001	+	11.4795i	0.545806	+	0.396552i
$839$	2.53639	−	1.84279i	0.0875658	−	0.0636203i	−0.543141	−	0.839642i	$-0.682765\pi$
$839$	2.53639	−	1.84279i	0.0875658	−	0.0636203i	0.630707	+	0.776021i	$0.282765\pi$
$840$		0			0
$841$	9.88393	+	7.18109i	0.340825	+	0.247624i
$842$	6.04242	+	18.5967i	0.208236	+	0.640883i
$843$		0			0
$844$	1.88545	+	5.80281i	0.0648998	+	0.199741i
$845$	5.36990	−	42.6793i	0.184730	−	1.46821i
$846$		0			0
$847$	2.83128	−	8.71378i	0.0972839	−	0.299409i
$848$	−0.425633	+	0.309240i	−0.0146163	+	0.0106194i
$849$		0			0
$850$	−1.64469	−	25.7297i	−0.0564123	−	0.882520i
$851$	−0.686050			−0.0235175
$852$		0			0
$853$	7.21464	−	22.2044i	0.247025	−	0.760263i	−0.748272	−	0.663392i	$-0.769116\pi$
$853$	7.21464	−	22.2044i	0.247025	−	0.760263i	0.995297	−	0.0968717i	$-0.0308837\pi$
$854$	−9.28730	+	28.5834i	−0.317805	+	0.978102i
$855$		0			0
$856$	−3.15876	−	9.72166i	−0.107964	−	0.332280i
$857$	−15.3036			−0.522762			−0.261381	−	0.965236i	$-0.584178\pi$
$857$	−15.3036			−0.522762			−0.261381	+	0.965236i	$0.584178\pi$
$858$		0			0
$859$	2.39576	+	1.74062i	0.0817422	+	0.0593892i	0.627906	−	0.778289i	$-0.283912\pi$
$859$	2.39576	+	1.74062i	0.0817422	+	0.0593892i	−0.546164	+	0.837679i	$0.683912\pi$
$860$	−14.1462	+	15.0793i	−0.482380	+	0.514199i
$861$		0			0
$862$	17.1482	+	12.4589i	0.584069	+	0.424351i
$863$	−30.5987	−	22.2312i	−1.04159	−	0.756760i	−0.0709954	−	0.997477i	$-0.522618\pi$
$863$	−30.5987	−	22.2312i	−1.04159	−	0.756760i	−0.970595	+	0.240717i	$0.922618\pi$
$864$		0			0
$865$	26.3280	−	5.03603i	0.895180	−	0.171230i
$866$	6.91683	+	5.02537i	0.235043	+	0.170769i
$867$		0			0
$868$	19.7739			0.671170
$869$	8.48918	+	26.1270i	0.287976	+	0.886298i
$870$		0			0
$871$	−7.58555	+	23.3459i	−0.257027	+	0.791046i
$872$	−1.20854	+	3.71950i	−0.0409263	+	0.125958i
$873$		0			0
$874$	−0.925059			−0.0312906
$875$	7.75943	+	30.0333i	0.262317	+	1.01531i
$876$		0			0
$877$	12.6215	−	9.17007i	0.426198	−	0.309651i	−0.353929	−	0.935272i	$-0.615154\pi$
$877$	12.6215	−	9.17007i	0.426198	−	0.309651i	0.780127	+	0.625621i	$0.215154\pi$
$878$	8.67453	−	26.6975i	0.292751	−	0.900996i
$879$		0			0
$880$	5.61478	+	2.63868i	0.189274	+	0.0889497i
$881$	−0.359812	−	1.10739i	−0.0121224	−	0.0373089i	0.944812	−	0.327612i	$-0.106244\pi$
$881$	−0.359812	−	1.10739i	−0.0121224	−	0.0373089i	−0.956935	+	0.290303i	$0.906244\pi$
$882$		0			0
$883$	15.1063	+	46.4925i	0.508368	+	1.56460i	0.795033	+	0.606566i	$0.207453\pi$
$883$	15.1063	+	46.4925i	0.508368	+	1.56460i	−0.286665	+	0.958031i	$0.592547\pi$
$884$	23.6857	+	17.2087i	0.796636	+	0.578790i
$885$		0			0
$886$	26.7417	−	19.4290i	0.898406	−	0.652730i
$887$	6.98094	+	5.07195i	0.234397	+	0.170299i	0.698783	−	0.715333i	$-0.253725\pi$
$887$	6.98094	+	5.07195i	0.234397	+	0.170299i	−0.464386	+	0.885633i	$0.653725\pi$
$888$		0			0
$889$	21.4335	−	15.5723i	0.718855	−	0.522279i
$890$	14.0504	−	14.9772i	0.470971	−	0.502037i
$891$		0			0
$892$	−1.55394	−	4.78254i	−0.0520299	−	0.160131i
$893$	3.91861			0.131131
$894$		0			0
$895$	−13.0672	+	13.9291i	−0.436788	+	0.465600i
$896$	0.857358	−	2.63868i	0.0286423	−	0.0881520i
$897$		0			0
$898$	30.0654	−	21.8438i	1.00329	−	0.728936i
$899$	29.1975			0.973790
$900$		0			0
$901$	−2.71286			−0.0903784
$902$	20.4420	−	14.8520i	0.680643	−	0.494516i
$903$		0			0
$904$	−1.97012	+	6.06342i	−0.0655253	+	0.201666i
$905$	2.18524	−	17.3680i	0.0726398	−	0.577332i
$906$		0			0
$907$	29.5085			0.979815			0.489907	−	0.871774i	$-0.337031\pi$
$907$	29.5085			0.979815			0.489907	+	0.871774i	$0.337031\pi$
$908$	5.51232	+	16.9652i	0.182933	+	0.563009i
$909$		0			0
$910$	−31.8795	−	14.9818i	−1.05680	−	0.496643i
$911$	−31.0734	+	22.5761i	−1.02951	+	0.747981i	−0.968210	−	0.250139i	$-0.919524\pi$
$911$	−31.0734	+	22.5761i	−1.02951	+	0.747981i	−0.0612971	+	0.998120i	$0.519524\pi$
$912$		0			0
$913$	−10.4958	−	7.62563i	−0.347360	−	0.252372i
$914$	23.7155	−	17.2303i	0.784438	−	0.569928i
$915$		0			0
$916$	17.4397	+	12.6707i	0.576223	+	0.418651i
$917$	4.80055	+	14.7746i	0.158528	+	0.487899i
$918$		0			0
$919$	12.8831	+	39.6500i	0.424974	+	1.30793i	0.903020	+	0.429600i	$0.141345\pi$
$919$	12.8831	+	39.6500i	0.424974	+	1.30793i	−0.478046	+	0.878335i	$0.658655\pi$
$920$	−0.706192	−	1.28303i	−0.0232825	−	0.0423004i
$921$		0			0
$922$	2.75254	−	8.47145i	0.0906501	−	0.278992i
$923$	−60.8473	+	44.2081i	−2.00281	+	1.45513i
$924$		0			0
$925$	0.334097	+	5.22665i	0.0109851	+	0.171851i
$926$	18.2771			0.600624
$927$		0			0
$928$	1.26594	−	3.89618i	0.0415567	−	0.127898i
$929$	−8.68484	+	26.7292i	−0.284940	+	0.876956i	0.701476	+	0.712693i	$0.252525\pi$
$929$	−8.68484	+	26.7292i	−0.284940	+	0.876956i	−0.986417	+	0.164263i	$0.947475\pi$
$930$		0			0
$931$	0.304498	+	0.937148i	0.00997952	+	0.0307138i
$932$	−14.7065			−0.481726
$933$		0			0
$934$	29.6780	+	21.5624i	0.971095	+	0.705542i
$935$	15.4254	+	28.0253i	0.504463	+	0.916525i
$936$		0			0
$937$	10.4164	+	7.56796i	0.340289	+	0.247234i	0.744784	−	0.667306i	$-0.232553\pi$
$937$	10.4164	+	7.56796i	0.340289	+	0.247234i	−0.404495	+	0.914540i	$0.632553\pi$
$938$	9.70427	+	7.05056i	0.316856	+	0.230209i
$939$		0			0
$940$	2.99148	+	5.43502i	0.0975712	+	0.177271i
$941$	8.21234	+	5.96661i	0.267714	+	0.194506i	0.713541	−	0.700613i	$-0.247090\pi$
$941$	8.21234	+	5.96661i	0.267714	+	0.194506i	−0.445827	+	0.895119i	$0.647090\pi$
$942$		0			0
$943$	−5.96489			−0.194243
$944$	1.16872	+	3.59695i	0.0380386	+	0.117071i
$945$		0			0
$946$	7.92764	−	24.3988i	0.257750	−	0.793273i
$947$	17.7298	−	54.5669i	0.576143	−	1.77318i	−0.0561124	−	0.998424i	$-0.517871\pi$
$947$	17.7298	−	54.5669i	0.576143	−	1.77318i	0.632255	−	0.774760i	$-0.282129\pi$
$948$		0			0
$949$	23.9219			0.776538
$950$	0.450491	+	7.04754i	0.0146159	+	0.228652i
$951$		0			0
$952$	11.5741	−	8.40906i	0.375118	−	0.272539i
$953$	−1.59843	+	4.91947i	−0.0517784	+	0.159357i	−0.973602	−	0.228252i	$-0.926699\pi$
$953$	−1.59843	+	4.91947i	−0.0517784	+	0.159357i	0.921824	+	0.387609i	$0.126699\pi$
$954$		0			0
$955$	−3.62939	−	6.59401i	−0.117444	−	0.213377i
$956$	−2.14465	−	6.60057i	−0.0693631	−	0.213478i
$957$		0			0
$958$	−3.89046	−	11.9736i	−0.125695	−	0.386849i
$959$	−17.9211	−	13.0205i	−0.578704	−	0.420453i
$960$		0			0
$961$	−16.0149	+	11.6355i	−0.516611	+	0.375340i
$962$	−4.81145	−	3.49572i	−0.155127	−	0.112707i
$963$		0			0
$964$	−2.67787	+	1.94559i	−0.0862484	+	0.0626631i
$965$	31.2082	+	14.6663i	1.00463	+	0.472126i
$966$		0			0
$967$	−12.7927	−	39.3718i	−0.411384	−	1.26611i	−0.915445	−	0.402443i	$-0.868161\pi$
$967$	−12.7927	−	39.3718i	−0.411384	−	1.26611i	0.504061	−	0.863668i	$-0.331839\pi$
$968$	3.30233			0.106141
$969$		0			0
$970$	0.0251701	−	0.200049i	0.000808164	−	0.00642318i
$971$	−13.3139	+	40.9761i	−0.427265	+	1.31499i	0.473544	+	0.880770i	$0.342975\pi$
$971$	−13.3139	+	40.9761i	−0.427265	+	1.31499i	−0.900809	+	0.434216i	$0.857025\pi$
$972$		0			0
$973$	−49.5795	+	36.0216i	−1.58944	+	1.15480i
$974$	18.3256			0.587189
$975$		0			0
$976$	−10.8325			−0.346739
$977$	32.7340	−	23.7826i	1.04725	−	0.760874i	0.0755652	−	0.997141i	$-0.475924\pi$
$977$	32.7340	−	23.7826i	1.04725	−	0.760874i	0.971688	+	0.236267i	$0.0759239\pi$
$978$		0			0
$979$	−7.87398	+	24.2336i	−0.251654	+	0.774510i
$980$	−1.06735	+	1.13775i	−0.0340951	+	0.0363441i
$981$		0			0
$982$	21.7047			0.692625
$983$	−12.4777	−	38.4023i	−0.397976	−	1.22484i	−0.926620	−	0.376000i	$-0.877299\pi$
$983$	−12.4777	−	38.4023i	−0.397976	−	1.22484i	0.528644	−	0.848844i	$-0.322701\pi$
$984$		0			0
$985$	13.4704	−	14.3589i	0.429202	−	0.457513i
$986$	17.0899	−	12.4165i	0.544253	−	0.395423i
$987$		0			0
$988$	−6.48768	−	4.71358i	−0.206401	−	0.149959i
$989$	−4.89955	+	3.55973i	−0.155797	+	0.113193i
$990$		0			0
$991$	47.0391	+	34.1759i	1.49424	+	1.08563i	0.972604	+	0.232467i	$0.0746798\pi$
$991$	47.0391	+	34.1759i	1.49424	+	1.08563i	0.521641	+	0.853165i	$0.325320\pi$
$992$	2.20239	+	6.77827i	0.0699261	+	0.215210i
$993$		0			0
$994$	11.3571	+	34.9535i	0.360225	+	1.10866i
$995$	35.6625	+	16.7597i	1.13058	+	0.531317i
$996$		0			0
$997$	12.1434	−	37.3735i	0.384585	−	1.18363i	−0.552197	−	0.833714i	$-0.686210\pi$
$997$	12.1434	−	37.3735i	0.384585	−	1.18363i	0.936781	−	0.349916i	$-0.113790\pi$
$998$	12.8141	−	9.30998i	0.405623	−	0.294702i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.e.361.1		8
3.2	odd	2		50.2.d.b.11.2	✓	8
12.11	even	2		400.2.u.d.161.1		8
15.2	even	4		250.2.e.c.199.1		16
15.8	even	4		250.2.e.c.199.4		16
15.14	odd	2		250.2.d.d.51.1		8
25.16	even	5	inner	450.2.h.e.91.1		8
75.29	odd	10		1250.2.a.f.1.2		4
75.38	even	20		250.2.e.c.49.1		16
75.41	odd	10		50.2.d.b.41.2	yes	8
75.47	even	20		1250.2.b.e.1249.6		8
75.53	even	20		1250.2.b.e.1249.3		8
75.59	odd	10		250.2.d.d.201.1		8
75.62	even	20		250.2.e.c.49.4		16
75.71	odd	10		1250.2.a.l.1.3		4
300.71	even	10		10000.2.a.t.1.2		4
300.179	even	10		10000.2.a.x.1.3		4
300.191	even	10		400.2.u.d.241.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.11.2	✓	8	3.2	odd	2
50.2.d.b.41.2	yes	8	75.41	odd	10
250.2.d.d.51.1		8	15.14	odd	2
250.2.d.d.201.1		8	75.59	odd	10
250.2.e.c.49.1		16	75.38	even	20
250.2.e.c.49.4		16	75.62	even	20
250.2.e.c.199.1		16	15.2	even	4
250.2.e.c.199.4		16	15.8	even	4
400.2.u.d.161.1		8	12.11	even	2
400.2.u.d.241.1		8	300.191	even	10
450.2.h.e.91.1		8	25.16	even	5	inner
450.2.h.e.361.1		8	1.1	even	1	trivial
1250.2.a.f.1.2		4	75.29	odd	10
1250.2.a.l.1.3		4	75.71	odd	10
1250.2.b.e.1249.3		8	75.53	even	20
1250.2.b.e.1249.6		8	75.47	even	20
10000.2.a.t.1.2		4	300.71	even	10
10000.2.a.x.1.3		4	300.179	even	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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-2.02373 - 0.951057i) q^{5} -2.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-2.02373 - 0.951057i) q^{5} -2.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.19625 + 0.420099i) q^{10} +(2.24459 - 1.63079i) q^{11} +(-4.59343 - 3.33732i) q^{13} +(-2.24459 + 1.63079i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-1.59343 - 4.90406i) q^{17} +(0.436451 + 1.34326i) q^{19} +(-1.52988 + 1.63079i) q^{20} +(0.857358 - 2.63868i) q^{22} +(-0.529876 + 0.384978i) q^{23} +(3.19098 + 3.84937i) q^{25} -5.67779 q^{26} +(-0.857358 + 2.63868i) q^{28} +(-1.26594 + 3.89618i) q^{29} +(-2.20239 - 6.77827i) q^{31} -1.00000 q^{32} +(-4.17164 - 3.03088i) q^{34} +(5.61478 + 2.63868i) q^{35} +(0.847416 + 0.615684i) q^{37} +(1.14264 + 0.830178i) q^{38} +(-0.279141 + 2.21858i) q^{40} +(7.36789 + 5.35309i) q^{41} +9.24660 q^{43} +(-0.857358 - 2.63868i) q^{44} +(-0.202395 + 0.622907i) q^{46} +(0.857358 - 2.63868i) q^{47} +0.697669 q^{49} +(4.84416 + 1.23859i) q^{50} +(-4.59343 + 3.33732i) q^{52} +(0.162577 - 0.500362i) q^{53} +(-6.09343 + 1.16555i) q^{55} +(0.857358 + 2.63868i) q^{56} +(1.26594 + 3.89618i) q^{58} +(-3.05975 - 2.22304i) q^{59} +(8.76365 - 6.36716i) q^{61} +(-5.76594 - 4.18920i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(6.12188 + 11.1224i) q^{65} +(-1.33600 - 4.11180i) q^{67} -5.15643 q^{68} +(6.09343 - 1.16555i) q^{70} +(4.09343 - 12.5983i) q^{71} +(-3.40859 + 2.47648i) q^{73} +1.04746 q^{74} +1.41238 q^{76} +(-6.22754 + 4.52458i) q^{77} +(-3.05975 + 9.41695i) q^{79} +(1.07822 + 1.95894i) q^{80} +9.10722 q^{82} +(-1.44497 - 4.44717i) q^{83} +(-1.43937 + 11.4399i) q^{85} +(7.48066 - 5.43502i) q^{86} +(-2.24459 - 1.63079i) q^{88} +(-7.43002 + 5.39823i) q^{89} +(12.7443 + 9.25928i) q^{91} +(0.202395 + 0.622907i) q^{92} +(-0.857358 - 2.63868i) q^{94} +(0.394254 - 3.13348i) q^{95} +(-0.0278640 + 0.0857567i) q^{97} +(0.564426 - 0.410079i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8	\( 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8} - q^{11} - 13 q^{13} + q^{14} - 2 q^{16} + 11 q^{17} + 20 q^{19} - 5 q^{20} + q^{22} + 3 q^{23} + 30 q^{25} - 22 q^{26} - q^{28} + 15 q^{29} - 9 q^{31} - 8 q^{32} - q^{34} + 15 q^{35} - 6 q^{37} + 15 q^{38} - 5 q^{40} + 9 q^{41} + 12 q^{43} - q^{44} + 7 q^{46} + q^{47} - 4 q^{49} + 5 q^{50} - 13 q^{52} - 7 q^{53} - 25 q^{55} + q^{56} - 15 q^{58} - 10 q^{59} + 6 q^{61} - 21 q^{62} - 2 q^{64} + 10 q^{65} - 11 q^{67} - 24 q^{68} + 25 q^{70} + 9 q^{71} - 8 q^{73} - 24 q^{74} - 10 q^{76} - 33 q^{77} - 10 q^{79} + 26 q^{82} - 27 q^{83} + 5 q^{85} + 23 q^{86} + q^{88} + 15 q^{89} + q^{91} - 7 q^{92} - q^{94} + 30 q^{95} - 36 q^{97} + 19 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8 - q^11 - 13 * q^13 + q^14 - 2 * q^16 + 11 * q^17 + 20 * q^19 - 5 * q^20 + q^22 + 3 * q^23 + 30 * q^25 - 22 * q^26 - q^28 + 15 * q^29 - 9 * q^31 - 8 * q^32 - q^34 + 15 * q^35 - 6 * q^37 + 15 * q^38 - 5 * q^40 + 9 * q^41 + 12 * q^43 - q^44 + 7 * q^46 + q^47 - 4 * q^49 + 5 * q^50 - 13 * q^52 - 7 * q^53 - 25 * q^55 + q^56 - 15 * q^58 - 10 * q^59 + 6 * q^61 - 21 * q^62 - 2 * q^64 + 10 * q^65 - 11 * q^67 - 24 * q^68 + 25 * q^70 + 9 * q^71 - 8 * q^73 - 24 * q^74 - 10 * q^76 - 33 * q^77 - 10 * q^79 + 26 * q^82 - 27 * q^83 + 5 * q^85 + 23 * q^86 + q^88 + 15 * q^89 + q^91 - 7 * q^92 - q^94 + 30 * q^95 - 36 * q^97 + 19 * q^98

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