LMFDB - Embedded newform 675.2.y.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(19,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 27]))

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

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

chi := DirichletCharacter("675.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.y (of order $30$, degree $8$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	675.19
Dual form			675.2.y.a.604.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.454043 + 2.13611i) q^{2} +(-2.52970 - 1.12630i) q^{4} +(-2.10220 - 0.762073i) q^{5} +(2.11102 + 1.21880i) q^{7} +(0.987242 - 1.35882i) q^{8} +O(q^{10})$	\(q+(-0.454043 + 2.13611i) q^{2} +(-2.52970 - 1.12630i) q^{4} +(-2.10220 - 0.762073i) q^{5} +(2.11102 + 1.21880i) q^{7} +(0.987242 - 1.35882i) q^{8} +(2.58236 - 4.14451i) q^{10} +(-3.33285 - 0.708420i) q^{11} +(-0.500440 - 2.35439i) q^{13} +(-3.56198 + 3.95598i) q^{14} +(-1.25145 - 1.38988i) q^{16} +(1.84041 - 2.53310i) q^{17} +(-3.90815 - 2.83944i) q^{19} +(4.45963 + 4.29552i) q^{20} +(3.02652 - 6.79768i) q^{22} +(-5.41181 - 4.87281i) q^{23} +(3.83849 + 3.20406i) q^{25} +5.25644 q^{26} +(-3.96753 - 5.46084i) q^{28} +(0.388288 + 3.69431i) q^{29} +(0.0852569 - 0.811165i) q^{31} +(6.44628 - 3.72176i) q^{32} +(4.57536 + 5.08145i) q^{34} +(-3.50898 - 4.17091i) q^{35} +(-3.75054 - 1.21863i) q^{37} +(7.83982 - 7.05901i) q^{38} +(-3.11090 + 2.10417i) q^{40} +(10.3245 - 2.19454i) q^{41} +(1.56940 + 0.906093i) q^{43} +(7.63324 + 5.54588i) q^{44} +(12.8660 - 9.34773i) q^{46} +(10.9524 - 1.15114i) q^{47} +(-0.529060 - 0.916359i) q^{49} +(-8.58705 + 6.74464i) q^{50} +(-1.38577 + 6.51955i) q^{52} +(-6.00535 - 8.26565i) q^{53} +(6.46646 + 4.02912i) q^{55} +(3.74022 - 1.66525i) q^{56} +(-8.06775 - 0.847954i) q^{58} +(-1.42188 + 0.302230i) q^{59} +(-5.72286 - 1.21643i) q^{61} +(1.69403 + 0.550422i) q^{62} +(3.86730 + 11.9023i) q^{64} +(-0.742188 + 5.33076i) q^{65} +(-3.67886 - 0.386664i) q^{67} +(-7.50872 + 4.33516i) q^{68} +(10.5027 - 5.60177i) q^{70} +(-9.39299 + 6.82441i) q^{71} +(-9.19406 + 2.98733i) q^{73} +(4.30602 - 7.45825i) q^{74} +(6.68842 + 11.5847i) q^{76} +(-6.17230 - 5.55757i) q^{77} +(-0.642822 - 6.11604i) q^{79} +(1.57161 + 3.87549i) q^{80} +23.0506i q^{82} +(-3.90626 - 8.77360i) q^{83} +(-5.79932 + 3.92257i) q^{85} +(-2.64809 + 2.94100i) q^{86} +(-4.25295 + 3.82937i) q^{88} +(3.17776 + 9.78015i) q^{89} +(1.81308 - 5.58010i) q^{91} +(8.20204 + 18.4221i) q^{92} +(-2.51389 + 23.9181i) q^{94} +(6.05186 + 8.94737i) q^{95} +(-15.0146 + 1.57810i) q^{97} +(2.19766 - 0.714062i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.454043	+	2.13611i	−0.321057	+	1.51046i	0.461085	+	0.887356i	$0.347460\pi$
$2$	−0.454043	+	2.13611i	−0.321057	+	1.51046i	−0.782143	+	0.623100i	$0.785873\pi$
$3$		0			0
$3$		0			0
$4$	−2.52970	−	1.12630i	−1.26485	−	0.563149i
$5$	−2.10220	−	0.762073i	−0.940132	−	0.340809i
$5$	−2.10220	−	0.762073i	−0.940132	−	0.340809i
$6$		0			0
$7$	2.11102	+	1.21880i	0.797891	+	0.460663i	0.842733	−	0.538332i	$-0.180945\pi$
$7$	2.11102	+	1.21880i	0.797891	+	0.460663i	−0.0448422	+	0.998994i	$0.514279\pi$
$8$	0.987242	−	1.35882i	0.349043	−	0.480416i
$9$		0			0
$10$	2.58236	−	4.14451i	0.816613	−	1.31061i
$11$	−3.33285	−	0.708420i	−1.00489	−	0.213597i	−0.324061	−	0.946036i	$-0.605048\pi$
$11$	−3.33285	−	0.708420i	−1.00489	−	0.213597i	−0.680832	+	0.732440i	$0.738382\pi$
$12$		0			0
$13$	−0.500440	−	2.35439i	−0.138797	−	0.652989i	−0.991447	−	0.130507i	$-0.958339\pi$
$13$	−0.500440	−	2.35439i	−0.138797	−	0.652989i	0.852650	−	0.522482i	$-0.174994\pi$
$14$	−3.56198	+	3.95598i	−0.951979	+	1.05728i
$15$		0			0
$16$	−1.25145	−	1.38988i	−0.312862	−	0.347469i
$17$	1.84041	−	2.53310i	0.446365	−	0.614368i	−0.525247	−	0.850950i	$-0.676027\pi$
$17$	1.84041	−	2.53310i	0.446365	−	0.614368i	0.971612	+	0.236582i	$0.0760271\pi$
$18$		0			0
$19$	−3.90815	−	2.83944i	−0.896592	−	0.651412i	0.0409962	−	0.999159i	$-0.486947\pi$
$19$	−3.90815	−	2.83944i	−0.896592	−	0.651412i	−0.937588	+	0.347747i	$0.886947\pi$
$20$	4.45963	+	4.29552i	0.997203	+	0.960508i
$21$		0			0
$22$	3.02652	−	6.79768i	0.645256	−	1.44927i
$23$	−5.41181	−	4.87281i	−1.12844	−	1.01605i	−0.999703	−	0.0243730i	$-0.992241\pi$
$23$	−5.41181	−	4.87281i	−1.12844	−	1.01605i	−0.128737	−	0.991679i	$-0.541092\pi$
$24$		0			0
$25$	3.83849	+	3.20406i	0.767698	+	0.640812i
$26$	5.25644			1.03087
$27$		0			0
$28$	−3.96753	−	5.46084i	−0.749793	−	1.03200i
$29$	0.388288	+	3.69431i	0.0721033	+	0.686017i	0.969550	+	0.244894i	$0.0787531\pi$
$29$	0.388288	+	3.69431i	0.0721033	+	0.686017i	−0.897447	+	0.441123i	$0.854580\pi$
$30$		0			0
$31$	0.0852569	−	0.811165i	0.0153126	−	0.145690i	−0.984194	−	0.177092i	$-0.943331\pi$
$31$	0.0852569	−	0.811165i	0.0153126	−	0.145690i	0.999507	+	0.0314029i	$0.00999749\pi$
$32$	6.44628	−	3.72176i	1.13955	−	0.657921i
$33$		0			0
$34$	4.57536	+	5.08145i	0.784667	+	0.871461i
$35$	−3.50898	−	4.17091i	−0.593125	−	0.705012i
$36$		0			0
$37$	−3.75054	−	1.21863i	−0.616586	−	0.200341i	−0.0159619	−	0.999873i	$-0.505081\pi$
$37$	−3.75054	−	1.21863i	−0.616586	−	0.200341i	−0.600624	+	0.799532i	$0.705081\pi$
$38$	7.83982	−	7.05901i	1.27179	−	1.14512i
$39$		0			0
$40$	−3.11090	+	2.10417i	−0.491877	+	0.332698i
$41$	10.3245	−	2.19454i	1.61241	−	0.342729i	0.688473	−	0.725262i	$-0.258281\pi$
$41$	10.3245	−	2.19454i	1.61241	−	0.342729i	0.923942	+	0.382533i	$0.124948\pi$
$42$		0			0
$43$	1.56940	+	0.906093i	0.239331	+	0.138178i	0.614869	−	0.788629i	$-0.289209\pi$
$43$	1.56940	+	0.906093i	0.239331	+	0.138178i	−0.375538	+	0.926807i	$0.622542\pi$
$44$	7.63324	+	5.54588i	1.15075	+	0.836072i
$45$		0			0
$46$	12.8660	−	9.34773i	1.89699	−	1.37825i
$47$	10.9524	−	1.15114i	1.59757	−	0.167911i	0.736512	−	0.676425i	$-0.236472\pi$
$47$	10.9524	−	1.15114i	1.59757	−	0.167911i	0.861054	+	0.508514i	$0.169805\pi$
$48$		0			0
$49$	−0.529060	−	0.916359i	−0.0755800	−	0.130908i
$50$	−8.58705	+	6.74464i	−1.21439	+	0.953837i
$51$		0			0
$52$	−1.38577	+	6.51955i	−0.192172	+	0.904099i
$53$	−6.00535	−	8.26565i	−0.824898	−	1.13537i	−0.988851	−	0.148906i	$-0.952425\pi$
$53$	−6.00535	−	8.26565i	−0.824898	−	1.13537i	0.163954	−	0.986468i	$-0.447575\pi$
$54$		0			0
$55$	6.46646	+	4.02912i	0.871937	+	0.543286i
$56$	3.74022	−	1.66525i	0.499808	−	0.222529i
$57$		0			0
$58$	−8.06775	−	0.847954i	−1.05935	−	0.111342i
$59$	−1.42188	+	0.302230i	−0.185113	+	0.0393470i	−0.299535	−	0.954085i	$-0.596832\pi$
$59$	−1.42188	+	0.302230i	−0.185113	+	0.0393470i	0.114422	+	0.993432i	$0.463498\pi$
$60$		0			0
$61$	−5.72286	−	1.21643i	−0.732737	−	0.155748i	−0.173591	−	0.984818i	$-0.555537\pi$
$61$	−5.72286	−	1.21643i	−0.732737	−	0.155748i	−0.559145	+	0.829070i	$0.688871\pi$
$62$	1.69403	+	0.550422i	0.215141	+	0.0699037i
$63$		0			0
$64$	3.86730	+	11.9023i	0.483413	+	1.48779i
$65$	−0.742188	+	5.33076i	−0.0920570	+	0.661200i
$66$		0			0
$67$	−3.67886	−	0.386664i	−0.449444	−	0.0472385i	−0.122897	−	0.992419i	$-0.539219\pi$
$67$	−3.67886	−	0.386664i	−0.449444	−	0.0472385i	−0.326547	+	0.945181i	$0.605885\pi$
$68$	−7.50872	+	4.33516i	−0.910566	+	0.525715i
$69$		0			0
$70$	10.5027	−	5.60177i	1.25532	−	0.669540i
$71$	−9.39299	+	6.82441i	−1.11474	+	0.809908i	−0.983404	−	0.181430i	$-0.941928\pi$
$71$	−9.39299	+	6.82441i	−1.11474	+	0.809908i	−0.131339	+	0.991338i	$0.541928\pi$
$72$		0			0
$73$	−9.19406	+	2.98733i	−1.07608	+	0.349641i	−0.792854	−	0.609411i	$-0.791406\pi$
$73$	−9.19406	+	2.98733i	−1.07608	+	0.349641i	−0.283229	+	0.959052i	$0.591406\pi$
$74$	4.30602	−	7.45825i	0.500565	−	0.867004i
$75$		0			0
$76$	6.68842	+	11.5847i	0.767215	+	1.32886i
$77$	−6.17230	−	5.55757i	−0.703399	−	0.633343i
$78$		0			0
$79$	−0.642822	−	6.11604i	−0.0723231	−	0.688108i	−0.969275	−	0.245980i	$-0.920890\pi$
$79$	−0.642822	−	6.11604i	−0.0723231	−	0.688108i	0.896952	−	0.442128i	$-0.145776\pi$
$80$	1.57161	+	3.87549i	0.175712	+	0.433293i
$81$		0			0
$82$			23.0506i			2.54552i
$83$	−3.90626	−	8.77360i	−0.428768	−	0.963028i	−0.990728	−	0.135864i	$-0.956619\pi$
$83$	−3.90626	−	8.77360i	−0.428768	−	0.963028i	0.561960	−	0.827165i	$-0.310048\pi$
$84$		0			0
$85$	−5.79932	+	3.92257i	−0.629024	+	0.425462i
$86$	−2.64809	+	2.94100i	−0.285551	+	0.317136i
$87$		0			0
$88$	−4.25295	+	3.82937i	−0.453366	+	0.408213i
$89$	3.17776	+	9.78015i	0.336842	+	1.03669i	0.965807	+	0.259260i	$0.0834788\pi$
$89$	3.17776	+	9.78015i	0.336842	+	1.03669i	−0.628965	+	0.777433i	$0.716521\pi$
$90$		0			0
$91$	1.81308	−	5.58010i	0.190063	−	0.584953i
$92$	8.20204	+	18.4221i	0.855122	+	1.92063i
$93$		0			0
$94$	−2.51389	+	23.9181i	−0.259288	+	2.46696i
$95$	6.05186	+	8.94737i	0.620908	+	0.917981i
$96$		0			0
$97$	−15.0146	+	1.57810i	−1.52450	+	0.160232i	−0.829391	−	0.558668i	$-0.811313\pi$
$97$	−15.0146	+	1.57810i	−1.52450	+	0.160232i	−0.695113	+	0.718900i	$0.744646\pi$
$98$	2.19766	−	0.714062i	0.221997	−	0.0721311i
$99$		0			0
$100$	−6.10153	−	12.4286i	−0.610153	−	1.24286i
$101$	−1.86456	+	3.22952i	−0.185531	+	0.321349i	−0.943755	−	0.330645i	$-0.892734\pi$
$101$	−1.86456	+	3.22952i	−0.185531	+	0.321349i	0.758224	+	0.651994i	$0.226067\pi$
$102$		0			0
$103$	7.39425	−	16.6078i	0.728577	−	1.63641i	−0.0420430	−	0.999116i	$-0.513387\pi$
$103$	7.39425	−	16.6078i	0.728577	−	1.63641i	0.770620	−	0.637295i	$-0.219947\pi$
$104$	−3.69325	−	1.64434i	−0.362153	−	0.161241i
$105$		0			0
$106$	20.3830	−	9.07509i	1.97977	−	0.881451i
$107$		−	13.0017i		−	1.25692i	−0.777840	−	0.628462i	$-0.783685\pi$
$107$		−	13.0017i		−	1.25692i	0.777840	−	0.628462i	$-0.216315\pi$
$108$		0			0
$109$	−2.54643	+	7.83710i	−0.243904	+	0.750658i	0.751911	+	0.659264i	$0.229132\pi$
$109$	−2.54643	+	7.83710i	−0.243904	+	0.750658i	−0.995815	+	0.0913936i	$0.970868\pi$
$110$	−11.5427	+	11.9836i	−1.10055	+	1.14260i
$111$		0			0
$112$	−0.947858	−	4.45932i	−0.0895642	−	0.421366i
$113$	2.30241	+	10.8320i	0.216593	+	1.01899i	0.943274	+	0.332014i	$0.107728\pi$
$113$	2.30241	+	10.8320i	0.216593	+	1.01899i	−0.726682	+	0.686974i	$0.758939\pi$
$114$		0			0
$115$	7.66327	+	14.3678i	0.714603	+	1.33981i
$116$	3.17864	−	9.78285i	0.295129	−	0.908315i
$117$		0			0
$118$		−	3.17451i		−	0.292238i
$119$	6.97249	−	3.10435i	0.639167	−	0.284575i
$120$		0			0
$121$	0.557053	+	0.248016i	0.0506411	+	0.0225469i
$122$	5.19685	−	11.6723i	0.470501	−	1.05676i
$123$		0			0
$124$	−1.12929	+	1.95598i	−0.101413	+	0.175653i
$125$	−5.62755	−	9.66078i	−0.503344	−	0.864086i
$126$		0			0
$127$	0.113262	−	0.0368011i	0.0100504	−	0.00326557i	−0.303987	−	0.952676i	$-0.598318\pi$
$127$	0.113262	−	0.0368011i	0.0100504	−	0.00326557i	0.314038	+	0.949410i	$0.398318\pi$
$128$	−12.3751	+	1.30067i	−1.09381	+	0.114964i
$129$		0			0
$130$	−11.0501	−	4.00579i	−0.969157	−	0.351331i
$131$	0.286083	−	2.72190i	0.0249952	−	0.237813i	−0.974890	−	0.222685i	$-0.928518\pi$
$131$	0.286083	−	2.72190i	0.0249952	−	0.237813i	0.999886	−	0.0151279i	$-0.00481554\pi$
$132$		0			0
$133$	−4.78949	−	10.7574i	−0.415302	−	0.932783i
$134$	2.49632	−	7.68287i	0.215649	−	0.663699i
$135$		0			0
$136$	−1.62511	−	5.00158i	−0.139352	−	0.428882i
$137$	−11.4072	+	10.2711i	−0.974583	+	0.877518i	−0.992491	−	0.122321i	$-0.960966\pi$
$137$	−11.4072	+	10.2711i	−0.974583	+	0.877518i	0.0179078	+	0.999840i	$0.494299\pi$
$138$		0			0
$139$	−2.48049	+	2.75486i	−0.210392	+	0.233664i	−0.839100	−	0.543978i	$-0.816918\pi$
$139$	−2.48049	+	2.75486i	−0.210392	+	0.233664i	0.628707	+	0.777642i	$0.283584\pi$
$140$	4.17899	+	14.5033i	0.353189	+	1.22575i
$141$		0			0
$142$	−10.3128	−	23.1630i	−0.865434	−	1.94380i
$143$			8.20135i			0.685831i
$144$		0			0
$145$	1.99908	−	8.06209i	0.166014	−	0.669520i
$146$	−2.20676	−	20.9959i	−0.182632	−	1.73763i
$147$		0			0
$148$	8.11524	+	7.30699i	0.667068	+	0.600631i
$149$	−6.07849	−	10.5283i	−0.497969	−	0.862508i	0.502028	−	0.864851i	$-0.332588\pi$
$149$	−6.07849	−	10.5283i	−0.497969	−	0.862508i	−0.999997	+	0.00234309i	$0.999254\pi$
$150$		0			0
$151$	−5.37350	+	9.30718i	−0.437289	+	0.757407i	−0.997479	−	0.0709567i	$-0.977395\pi$
$151$	−5.37350	+	9.30718i	−0.437289	+	0.757407i	0.560190	+	0.828364i	$0.310728\pi$
$152$	−7.71659	+	2.50727i	−0.625898	+	0.203367i
$153$		0			0
$154$	14.6740	−	10.6613i	1.18247	−	0.859114i
$155$	−0.797394	+	1.64026i	−0.0640482	+	0.131749i
$156$		0			0
$157$	7.67250	−	4.42972i	0.612332	−	0.353530i	−0.161546	−	0.986865i	$-0.551648\pi$
$157$	7.67250	−	4.42972i	0.612332	−	0.353530i	0.773878	+	0.633335i	$0.218315\pi$
$158$	13.3564	+	1.40381i	1.06258	+	0.111681i
$159$		0			0
$160$	−16.3876	+	2.91136i	−1.29556	+	0.230163i
$161$	−5.48546	−	16.8825i	−0.432315	−	1.33053i
$162$		0			0
$163$	−1.12812	−	0.366548i	−0.0883610	−	0.0287102i	0.264503	−	0.964385i	$-0.414792\pi$
$163$	−1.12812	−	0.366548i	−0.0883610	−	0.0287102i	−0.352864	+	0.935675i	$0.614792\pi$
$164$	−28.5896	−	6.07691i	−2.23247	−	0.474527i
$165$		0			0
$166$	20.5150	−	4.36059i	1.59227	−	0.338447i
$167$	−23.0367	−	2.42125i	−1.78263	−	0.187362i	−0.844946	−	0.534851i	$-0.820368\pi$
$167$	−23.0367	−	2.42125i	−1.78263	−	0.187362i	−0.937684	+	0.347489i	$0.887034\pi$
$168$		0			0
$169$	6.58340	−	2.93112i	0.506415	−	0.225470i
$170$	−5.74588	−	14.1690i	−0.440689	−	1.08671i
$171$		0			0
$172$	−2.94959	−	4.05976i	−0.224904	−	0.309554i
$173$	−1.80160	+	8.47586i	−0.136973	+	0.644407i	0.855070	+	0.518512i	$0.173514\pi$
$173$	−1.80160	+	8.47586i	−0.136973	+	0.644407i	−0.992043	+	0.125896i	$0.959820\pi$
$174$		0			0
$175$	4.19803	+	11.4422i	0.317342	+	0.864948i
$176$	3.18628	+	5.51880i	0.240175	+	0.415996i
$177$		0			0
$178$	−22.3343	+	2.34743i	−1.67403	+	0.175947i
$179$	−10.1931	+	7.40570i	−0.761866	+	0.553528i	−0.899482	−	0.436958i	$-0.856056\pi$
$179$	−10.1931	+	7.40570i	−0.761866	+	0.553528i	0.137616	+	0.990486i	$0.456056\pi$
$180$		0			0
$181$	16.8867	+	12.2689i	1.25518	+	0.911941i	0.998511	−	0.0545582i	$-0.0173750\pi$
$181$	16.8867	+	12.2689i	1.25518	+	0.911941i	0.256669	+	0.966499i	$0.417375\pi$
$182$	11.0965	+	6.40654i	0.822524	+	0.474885i
$183$		0			0
$184$	−11.9640	+	2.54304i	−0.882001	+	0.187475i
$185$	6.95571	+	5.41998i	0.511394	+	0.398485i
$186$		0			0
$187$	−7.92831	+	7.13869i	−0.579776	+	0.522032i
$188$	−29.0027	−	9.42356i	−2.11524	−	0.687284i
$189$		0			0
$190$	−21.8603	+	8.86493i	−1.58592	+	0.643130i
$191$	−5.12494	−	5.69182i	−0.370828	−	0.411846i	0.528631	−	0.848852i	$-0.322706\pi$
$191$	−5.12494	−	5.69182i	−0.370828	−	0.411846i	−0.899459	+	0.437006i	$0.856039\pi$
$192$		0			0
$193$	21.3642	−	12.3347i	1.53783	−	0.887868i	0.538866	−	0.842391i	$-0.318853\pi$
$193$	21.3642	−	12.3347i	1.53783	−	0.887868i	0.998965	−	0.0454765i	$-0.0144806\pi$
$194$	3.44630	−	32.7894i	0.247430	−	2.35414i
$195$		0			0
$196$	0.306273	+	2.91400i	0.0218767	+	0.208143i
$197$	7.71150	+	10.6140i	0.549422	+	0.756214i	0.989934	−	0.141533i	$-0.0452031\pi$
$197$	7.71150	+	10.6140i	0.549422	+	0.756214i	−0.440512	+	0.897747i	$0.645203\pi$
$198$		0			0
$199$	−1.68893			−0.119725			−0.0598627	−	0.998207i	$-0.519066\pi$
$199$	−1.68893			−0.119725			−0.0598627	+	0.998207i	$0.519066\pi$
$200$	8.14326	−	2.05265i	0.575816	−	0.145144i
$201$		0			0
$202$	−6.05200	−	5.44924i	−0.425817	−	0.383407i
$203$	−3.68294	+	8.27202i	−0.258492	+	0.580582i
$204$		0			0
$205$	−23.3765	−	3.25465i	−1.63269	−	0.227315i
$206$	32.1186	+	23.3355i	2.23781	+	1.62586i
$207$		0			0
$208$	−2.64603	+	3.64195i	−0.183469	+	0.252524i
$209$	11.0138	+	12.2321i	0.761840	+	0.846109i
$210$		0			0
$211$	−3.61787	+	4.01805i	−0.249064	+	0.276614i	−0.854693	−	0.519133i	$-0.826255\pi$
$211$	−3.61787	+	4.01805i	−0.249064	+	0.276614i	0.605629	+	0.795747i	$0.292922\pi$
$212$	5.88217	+	27.6735i	0.403989	+	1.90062i
$213$		0			0
$214$	27.7731	+	5.90335i	1.89853	+	0.403545i
$215$	−2.60868	−	3.10079i	−0.177911	−	0.211472i
$216$		0			0
$217$	1.16863	−	1.60848i	0.0793315	−	0.109190i
$218$	−15.5847	−	8.99782i	−1.05553	−	0.609409i
$219$		0			0
$220$	−11.8202	−	17.4756i	−0.796921	−	1.17821i
$221$	−6.88492	−	3.06537i	−0.463130	−	0.206199i
$222$		0			0
$223$	−1.54087	+	7.24923i	−0.103184	+	0.485444i	0.895962	+	0.444131i	$0.146487\pi$
$223$	−1.54087	+	7.24923i	−0.103184	+	0.485444i	−0.999146	+	0.0413133i	$0.986846\pi$
$224$	18.1443			1.21232
$225$		0			0
$226$	−24.1837			−1.60867
$227$	1.62588	−	7.64916i	0.107913	−	0.507693i	−0.890678	−	0.454635i	$-0.849770\pi$
$227$	1.62588	−	7.64916i	0.107913	−	0.507693i	0.998591	−	0.0530581i	$-0.0168969\pi$
$228$		0			0
$229$	8.41750	+	3.74771i	0.556244	+	0.247656i	0.665551	−	0.746352i	$-0.268197\pi$
$229$	8.41750	+	3.74771i	0.556244	+	0.247656i	−0.109307	+	0.994008i	$0.534863\pi$
$230$	−34.1706	+	9.84594i	−2.25315	+	0.649222i
$231$		0			0
$232$	5.40325	+	3.11957i	0.354741	+	0.204810i
$233$	9.19639	−	12.6577i	0.602475	−	0.829236i	−0.393457	−	0.919343i	$-0.628721\pi$
$233$	9.19639	−	12.6577i	0.602475	−	0.829236i	0.995932	+	0.0901069i	$0.0287209\pi$
$234$		0			0
$235$	−23.9013	−	5.92656i	−1.55915	−	0.386606i
$236$	3.93734	+	0.836907i	0.256299	+	0.0544780i
$237$		0			0
$238$	3.46541	+	16.3035i	0.224629	+	1.05680i
$239$	−0.941074	+	1.04517i	−0.0608730	+	0.0676063i	−0.772812	−	0.634635i	$-0.781151\pi$
$239$	−0.941074	+	1.04517i	−0.0608730	+	0.0676063i	0.711939	+	0.702241i	$0.247817\pi$
$240$		0			0
$241$	−12.6439	−	14.0425i	−0.814466	−	0.904556i	0.182435	−	0.983218i	$-0.441602\pi$
$241$	−12.6439	−	14.0425i	−0.814466	−	0.904556i	−0.996901	+	0.0786614i	$0.974935\pi$
$242$	−0.782714	+	1.07731i	−0.0503148	+	0.0692523i
$243$		0			0
$244$	13.1071	+	9.52285i	0.839094	+	0.609638i
$245$	0.413858	+	2.32955i	0.0264404	+	0.148830i
$246$		0			0
$247$	−4.72934	+	10.6223i	−0.300921	+	0.675879i
$248$	−1.01806	−	0.916666i	−0.0646469	−	0.0582083i
$249$		0			0
$250$	23.1916	−	7.63464i	1.46677	−	0.482857i
$251$	−14.7510			−0.931078			−0.465539	−	0.885027i	$-0.654139\pi$
$251$	−14.7510			−0.931078			−0.465539	+	0.885027i	$0.654139\pi$
$252$		0			0
$253$	14.5848	+	20.0742i	0.916936	+	1.26205i
$254$	0.0271851	+	0.258649i	0.00170575	+	0.0162291i
$255$		0			0
$256$	0.224131	−	2.13246i	0.0140082	−	0.133279i
$257$	−12.4883	+	7.21012i	−0.778998	+	0.449755i	−0.836075	−	0.548615i	$-0.815155\pi$
$257$	−12.4883	+	7.21012i	−0.778998	+	0.449755i	0.0570768	+	0.998370i	$0.481822\pi$
$258$		0			0
$259$	−6.43222	−	7.14370i	−0.399679	−	0.443888i
$260$	7.88154	−	12.6493i	0.488792	−	0.784478i
$261$		0			0
$262$	5.68436	+	1.84696i	0.351181	+	0.114106i
$263$	19.5824	−	17.6321i	1.20751	−	1.08724i	0.213609	−	0.976919i	$-0.431478\pi$
$263$	19.5824	−	17.6321i	1.20751	−	1.08724i	0.993896	−	0.110323i	$-0.0351886\pi$
$264$		0			0
$265$	6.32541	+	21.9526i	0.388567	+	1.34853i
$266$	25.1535	−	5.34655i	1.54226	−	0.327818i
$267$		0			0
$268$	8.87093	+	5.12163i	0.541878	+	0.312854i
$269$	2.86489	+	2.08146i	0.174675	+	0.126909i	0.671688	−	0.740834i	$-0.265570\pi$
$269$	2.86489	+	2.08146i	0.174675	+	0.126909i	−0.497012	+	0.867743i	$0.665570\pi$
$270$		0			0
$271$	−11.1459	+	8.09799i	−0.677067	+	0.491918i	−0.872383	−	0.488823i	$-0.837427\pi$
$271$	−11.1459	+	8.09799i	−0.677067	+	0.491918i	0.195317	+	0.980740i	$0.437427\pi$
$272$	−5.82388	+	0.612114i	−0.353125	+	0.0371149i
$273$		0			0
$274$	−16.7608	−	29.0305i	−1.01256	−	1.75380i
$275$	−10.5233	−	13.3979i	−0.634579	−	0.807925i
$276$		0			0
$277$	2.97430	−	13.9930i	0.178708	−	0.840756i	−0.793853	−	0.608110i	$-0.791928\pi$
$277$	2.97430	−	13.9930i	0.178708	−	0.840756i	0.972561	−	0.232647i	$-0.0747385\pi$
$278$	−4.75843	−	6.54941i	−0.285392	−	0.392808i
$279$		0			0
$280$	−9.13173	+	0.650377i	−0.545725	+	0.0388674i
$281$	14.9802	−	6.66960i	0.893642	−	0.397875i	0.0920555	−	0.995754i	$-0.470656\pi$
$281$	14.9802	−	6.66960i	0.893642	−	0.397875i	0.801587	+	0.597879i	$0.203990\pi$
$282$		0			0
$283$	3.09412	+	0.325205i	0.183926	+	0.0193314i	0.196044	−	0.980595i	$-0.437191\pi$
$283$	3.09412	+	0.325205i	0.183926	+	0.0193314i	−0.0121174	+	0.999927i	$0.503857\pi$
$284$	31.4478	−	6.68444i	1.86608	−	0.396648i
$285$		0			0
$286$	−17.5190	−	3.72377i	−1.03592	−	0.220191i
$287$	24.4699	+	7.95076i	1.44441	+	0.469319i
$288$		0			0
$289$	2.22377	+	6.84407i	0.130810	+	0.402592i
$290$	16.3138	+	7.93078i	0.957980	+	0.465711i
$291$		0			0
$292$	26.6229	+	2.79818i	1.55799	+	0.163751i
$293$	5.52683	−	3.19092i	0.322881	−	0.186415i	−0.329795	−	0.944053i	$-0.606980\pi$
$293$	5.52683	−	3.19092i	0.322881	−	0.186415i	0.652676	+	0.757637i	$0.273646\pi$
$294$		0			0
$295$	3.21940	+	0.448228i	0.187441	+	0.0260969i
$296$	−5.35859	+	3.89324i	−0.311462	+	0.226290i
$297$		0			0
$298$	25.2494	−	8.20402i	1.46266	−	0.475246i
$299$	−8.76420	+	15.1800i	−0.506847	+	0.877884i
$300$		0			0
$301$	2.20869	+	3.82556i	0.127307	+	0.220502i
$302$	−17.4413	−	15.7042i	−1.00364	−	0.903677i
$303$		0			0
$304$	0.944390	+	8.98527i	0.0541645	+	0.515340i
$305$	11.1036	+	6.91841i	0.635789	+	0.396147i
$306$		0			0
$307$			30.1115i			1.71855i	0.511510	+	0.859277i	$0.329086\pi$
$307$			30.1115i			1.71855i	−0.511510	+	0.859277i	$0.670914\pi$
$308$	9.35463	+	21.0108i	0.533030	+	1.19720i
$309$		0			0
$310$	−3.14172	−	2.44807i	−0.178438	−	0.139041i
$311$	−13.1659	+	14.6222i	−0.746567	+	0.829147i	−0.990044	−	0.140760i	$-0.955045\pi$
$311$	−13.1659	+	14.6222i	−0.746567	+	0.829147i	0.243476	+	0.969907i	$0.421712\pi$
$312$		0			0
$313$	7.48539	−	6.73988i	0.423099	−	0.380960i	−0.429896	−	0.902878i	$-0.641450\pi$
$313$	7.48539	−	6.73988i	0.423099	−	0.380960i	0.852996	+	0.521918i	$0.174783\pi$
$314$	5.97870	+	18.4006i	0.337398	+	1.03840i
$315$		0			0
$316$	−5.26233	+	16.1958i	−0.296029	+	0.911084i
$317$	0.262837	+	0.590342i	0.0147624	+	0.0331569i	0.920776	−	0.390091i	$-0.127557\pi$
$317$	0.262837	+	0.590342i	0.0147624	+	0.0331569i	−0.906014	+	0.423248i	$0.860890\pi$
$318$		0			0
$319$	1.32302	−	12.5877i	0.0740748	−	0.704775i
$320$	0.940598	−	27.9683i	0.0525810	−	1.56347i
$321$		0			0
$322$	38.5535	−	4.05213i	2.14850	−	0.225817i
$323$	−14.3852	+	4.67404i	−0.800414	+	0.260070i
$324$		0			0
$325$	5.62266	−	10.6407i	0.311889	−	0.590242i
$326$	1.29520	−	2.24335i	0.0717345	−	0.124248i
$327$		0			0
$328$	7.21079	−	16.1957i	0.398149	−	0.894257i
$329$	24.5237	+	10.9186i	1.35203	+	0.601964i
$330$		0			0
$331$	16.5533	−	7.37000i	0.909851	−	0.405092i	0.102208	−	0.994763i	$-0.467409\pi$
$331$	16.5533	−	7.37000i	0.909851	−	0.405092i	0.807643	+	0.589671i	$0.200743\pi$
$332$			26.5942i			1.45955i
$333$		0			0
$334$	15.6317	−	48.1094i	0.855328	−	2.63243i
$335$	7.43903	+	3.61640i	0.406438	+	0.197585i
$336$		0			0
$337$	4.00550	+	18.8444i	0.218193	+	1.02652i	0.941766	+	0.336270i	$0.109165\pi$
$337$	4.00550	+	18.8444i	0.218193	+	1.02652i	−0.723572	+	0.690249i	$0.757501\pi$
$338$	3.27203	+	15.3937i	0.177975	+	0.837306i
$339$		0			0
$340$	19.0885	−	3.39119i	1.03522	−	0.183913i
$341$	−0.858794	+	2.64310i	−0.0465063	+	0.143132i
$342$		0			0
$343$		−	19.6425i		−	1.06059i
$344$	2.78060	−	1.23800i	0.149920	−	0.0667486i
$345$		0			0
$346$	−17.2873	−	7.69681i	−0.929373	−	0.413783i
$347$	5.85858	−	13.1586i	0.314505	−	0.706390i	−0.685255	−	0.728304i	$-0.740309\pi$
$347$	5.85858	−	13.1586i	0.314505	−	0.706390i	0.999760	+	0.0219132i	$0.00697574\pi$
$348$		0			0
$349$	−5.17386	+	8.96139i	−0.276951	+	0.479692i	−0.970625	−	0.240596i	$-0.922657\pi$
$349$	−5.17386	+	8.96139i	−0.276951	+	0.479692i	0.693675	+	0.720288i	$0.255990\pi$
$350$	−26.3478	+	3.77220i	−1.40835	+	0.201633i
$351$		0			0
$352$	−24.1211	+	7.83741i	−1.28566	+	0.417736i
$353$	25.4170	−	2.67144i	1.35281	−	0.142186i	0.599778	−	0.800167i	$-0.295256\pi$
$353$	25.4170	−	2.67144i	1.35281	−	0.142186i	0.753035	+	0.657980i	$0.228589\pi$
$354$		0			0
$355$	24.9466	−	7.18813i	1.32403	−	0.381506i
$356$	2.97655	−	28.3200i	0.157757	−	1.50096i
$357$		0			0
$358$	−11.1913	−	25.1360i	−0.591477	−	1.32848i
$359$	3.97075	−	12.2207i	0.209568	−	0.644984i	−0.789927	−	0.613201i	$-0.789881\pi$
$359$	3.97075	−	12.2207i	0.209568	−	0.644984i	0.999495	−	0.0317829i	$-0.0101185\pi$
$360$		0			0
$361$	1.33993	+	4.12388i	0.0705225	+	0.217046i
$362$	−33.8750	+	30.5012i	−1.78043	+	1.60311i
$363$		0			0
$364$	−10.8714	+	12.0739i	−0.569817	+	0.632846i
$365$	21.6043	+	0.726573i	1.13082	+	0.0380306i
$366$		0			0
$367$	−6.53875	−	14.6863i	−0.341320	−	0.766617i	−0.999900	−	0.0141067i	$-0.995510\pi$
$367$	−6.53875	−	14.6863i	−0.341320	−	0.766617i	0.658581	−	0.752510i	$-0.271157\pi$
$368$			13.6198i			0.709982i
$369$		0			0
$370$	−14.7359	+	12.3972i	−0.766081	+	0.644502i
$371$	−2.60325	−	24.7683i	−0.135154	−	1.28590i
$372$		0			0
$373$	−15.1999	−	13.6860i	−0.787019	−	0.708635i	0.174113	−	0.984726i	$-0.444294\pi$
$373$	−15.1999	−	13.6860i	−0.787019	−	0.708635i	−0.961131	+	0.276091i	$0.910961\pi$
$374$	−11.6492	−	20.1770i	−0.602365	−	1.04333i
$375$		0			0
$376$	9.24843	−	16.0188i	0.476951	−	0.826104i
$377$	8.50353	−	2.76296i	0.437954	−	0.142300i
$378$		0			0
$379$	6.64402	−	4.82716i	0.341280	−	0.247955i	−0.403922	−	0.914794i	$-0.632353\pi$
$379$	6.64402	−	4.82716i	0.341280	−	0.247955i	0.745202	+	0.666839i	$0.232353\pi$
$380$	−5.23203	−	29.4504i	−0.268398	−	1.51077i
$381$		0			0
$382$	14.4853	−	8.36308i	0.741131	−	0.427892i
$383$	35.3271	+	3.71303i	1.80513	+	0.189727i	0.946464	−	0.322810i	$-0.104627\pi$
$383$	35.3271	+	3.71303i	1.80513	+	0.189727i	0.858665	+	0.512536i	$0.171294\pi$
$384$		0			0
$385$	8.74015	+	16.3869i	0.445439	+	0.835152i
$386$	16.6478	+	51.2368i	0.847352	+	2.60788i
$387$		0			0
$388$	39.7600	+	12.9188i	2.01851	+	0.655853i
$389$	19.0206	+	4.04294i	0.964380	+	0.204985i	0.663084	−	0.748545i	$-0.269247\pi$
$389$	19.0206	+	4.04294i	0.964380	+	0.204985i	0.301297	+	0.953530i	$0.402581\pi$
$390$		0			0
$391$	−22.3033	+	4.74071i	−1.12793	+	0.239748i
$392$	−1.76748	−	0.185770i	−0.0892712	−	0.00938278i
$393$		0			0
$394$	−26.1739	+	11.6534i	−1.31862	+	0.587089i
$395$	−3.30953	+	13.3470i	−0.166520	+	0.671561i
$396$		0			0
$397$	7.95571	+	10.9501i	0.399286	+	0.549570i	0.960565	−	0.278057i	$-0.0896904\pi$
$397$	7.95571	+	10.9501i	0.399286	+	0.549570i	−0.561279	+	0.827627i	$0.689690\pi$
$398$	0.766850	−	3.60774i	0.0384387	−	0.180840i
$399$		0			0
$400$	−0.350436	−	9.34474i	−0.0175218	−	0.467237i
$401$	7.07920	+	12.2615i	0.353519	+	0.612312i	0.986863	−	0.161558i	$-0.0516518\pi$
$401$	7.07920	+	12.2615i	0.353519	+	0.612312i	−0.633345	+	0.773870i	$0.718318\pi$
$402$		0			0
$403$	−1.95246	+	0.205212i	−0.0972591	+	0.0102223i
$404$	8.35418	−	6.06967i	0.415636	−	0.301977i
$405$		0			0
$406$	−15.9977	−	11.6230i	−0.793952	−	0.576840i
$407$	11.6367	+	6.71846i	0.576811	+	0.333022i
$408$		0			0
$409$	15.7538	−	3.34858i	0.778976	−	0.165576i	0.198770	−	0.980046i	$-0.436305\pi$
$409$	15.7538	−	3.34858i	0.778976	−	0.165576i	0.580206	+	0.814470i	$0.302972\pi$
$410$	17.5663	−	48.4570i	0.867535	−	2.39312i
$411$		0			0
$412$	−37.4105	+	33.6846i	−1.84308	+	1.65952i
$413$	−3.36998	−	1.09497i	−0.165826	−	0.0538801i
$414$		0			0
$415$	1.52562	+	21.4207i	0.0748897	+	1.05150i
$416$	−11.9884	−	13.3145i	−0.587782	−	0.652798i
$417$		0			0
$418$	−31.1297	+	17.9727i	−1.52260	+	0.879076i
$419$	−2.91352	+	27.7203i	−0.142335	+	1.35423i	0.657250	+	0.753673i	$0.271720\pi$
$419$	−2.91352	+	27.7203i	−0.142335	+	1.35423i	−0.799584	+	0.600554i	$0.794947\pi$
$420$		0			0
$421$	0.704150	+	6.69954i	0.0343182	+	0.326516i	0.998190	+	0.0601474i	$0.0191571\pi$
$421$	0.704150	+	6.69954i	0.0343182	+	0.326516i	−0.963871	+	0.266368i	$0.914176\pi$
$422$	−6.94031	−	9.55252i	−0.337849	−	0.465009i
$423$		0			0
$424$	−17.1603			−0.833377
$425$	15.1806	−	3.82652i	0.736368	−	0.185614i
$426$		0			0
$427$	−10.5985	−	9.54292i	−0.512897	−	0.461814i
$428$	−14.6438	+	32.8905i	−0.707835	+	1.58982i
$429$		0			0
$430$	7.80807	−	4.16453i	0.376538	−	0.200832i
$431$	−20.8642	−	15.1587i	−1.00499	−	0.730169i	−0.0418387	−	0.999124i	$-0.513322\pi$
$431$	−20.8642	−	15.1587i	−1.00499	−	0.730169i	−0.963153	+	0.268955i	$0.913322\pi$
$432$		0			0
$433$	14.1286	−	19.4463i	0.678976	−	0.934531i	−0.320945	−	0.947098i	$-0.604000\pi$
$433$	14.1286	−	19.4463i	0.678976	−	0.934531i	0.999921	+	0.0125674i	$0.00400042\pi$
$434$	2.90527	+	3.22663i	0.139457	+	0.154883i
$435$		0			0
$436$	15.2686	−	16.9575i	0.731234	−	0.812117i
$437$	7.31412	+	34.4102i	0.349882	+	1.64606i
$438$		0			0
$439$	−4.95500	−	1.05322i	−0.236489	−	0.0502674i	0.0881422	−	0.996108i	$-0.471907\pi$
$439$	−4.95500	−	1.05322i	−0.236489	−	0.0502674i	−0.324632	+	0.945841i	$0.605240\pi$
$440$	11.8588	−	4.80905i	0.565347	−	0.229263i
$441$		0			0
$442$	9.67400	−	13.3151i	0.460145	−	0.633336i
$443$	−21.9747	−	12.6871i	−1.04405	−	0.602783i	−0.123072	−	0.992398i	$-0.539275\pi$
$443$	−21.9747	−	12.6871i	−1.04405	−	0.602783i	−0.920978	+	0.389615i	$0.872608\pi$
$444$		0			0
$445$	0.772889	−	22.9815i	0.0366385	−	1.08943i
$446$	−14.7855	−	6.58293i	−0.700114	−	0.311711i
$447$		0			0
$448$	−6.34259	+	29.8395i	−0.299659	+	1.40979i
$449$	6.58126			0.310589			0.155295	−	0.987868i	$-0.450367\pi$
$449$	6.58126			0.310589			0.155295	+	0.987868i	$0.450367\pi$
$450$		0			0
$451$	−35.9647			−1.69351
$452$	6.37562	−	29.9949i	0.299884	−	1.41084i
$453$		0			0
$454$	15.6012	+	6.94611i	0.732201	+	0.325997i
$455$	−8.06390	+	10.3488i	−0.378042	+	0.485158i
$456$		0			0
$457$	21.4902	+	12.4074i	1.00527	+	0.580393i	0.909803	−	0.415040i	$-0.136232\pi$
$457$	21.4902	+	12.4074i	1.00527	+	0.580393i	0.0954663	+	0.995433i	$0.469566\pi$
$458$	−11.8274	+	16.2791i	−0.552659	+	0.760670i
$459$		0			0
$460$	−3.20337	−	44.9774i	−0.149358	−	2.09708i
$461$	−35.8394	−	7.61791i	−1.66921	−	0.354801i	−0.726178	−	0.687506i	$-0.758705\pi$
$461$	−35.8394	−	7.61791i	−1.66921	−	0.354801i	−0.943031	+	0.332705i	$0.892039\pi$
$462$		0			0
$463$	−1.69953	−	7.99564i	−0.0789837	−	0.371589i	0.920848	−	0.389921i	$-0.127498\pi$
$463$	−1.69953	−	7.99564i	−0.0789837	−	0.371589i	−0.999832	+	0.0183321i	$0.994164\pi$
$464$	4.64871	−	5.16292i	0.215811	−	0.239683i
$465$		0			0
$466$	22.8627	+	25.3916i	1.05910	+	1.17624i
$467$	9.09752	−	12.5217i	0.420983	−	0.579433i	−0.544871	−	0.838520i	$-0.683421\pi$
$467$	9.09752	−	12.5217i	0.420983	−	0.579433i	0.965854	+	0.259087i	$0.0834215\pi$
$468$		0			0
$469$	−7.29489	−	5.30004i	−0.336847	−	0.244733i
$470$	23.5120	−	48.3648i	1.08453	−	2.23090i
$471$		0			0
$472$	−0.993064	+	2.23046i	−0.0457095	+	0.102665i
$473$	−4.58869	−	4.13167i	−0.210988	−	0.189974i
$474$		0			0
$475$	−5.90368	−	23.4211i	−0.270880	−	1.07463i
$476$	−21.1348			−0.968710
$477$		0			0
$478$	−1.80530	−	2.48479i	−0.0825726	−	0.113651i
$479$	−1.25195	−	11.9115i	−0.0572029	−	0.544249i	−0.985169	−	0.171585i	$-0.945111\pi$
$479$	−1.25195	−	11.9115i	−0.0572029	−	0.544249i	0.927966	−	0.372664i	$-0.121556\pi$
$480$		0			0
$481$	−0.992193	+	9.44008i	−0.0452401	+	0.430431i
$482$	35.7371	−	20.6329i	1.62778	−	0.939801i
$483$		0			0
$484$	−1.12984	−	1.25481i	−0.0513563	−	0.0570370i
$485$	32.7664	+	8.12475i	1.48784	+	0.368926i
$486$		0			0
$487$	−9.67177	−	3.14255i	−0.438270	−	0.142402i	0.0815675	−	0.996668i	$-0.474007\pi$
$487$	−9.67177	−	3.14255i	−0.438270	−	0.142402i	−0.519837	+	0.854265i	$0.674007\pi$
$488$	−7.30276	+	6.57543i	−0.330580	+	0.297656i
$489$		0			0
$490$	−5.16408	−	0.173673i	−0.233289	−	0.00784573i
$491$	−23.0020	+	4.88922i	−1.03807	+	0.220648i	−0.695260	−	0.718759i	$-0.744711\pi$
$491$	−23.0020	+	4.88922i	−1.03807	+	0.220648i	−0.342806	+	0.939406i	$0.611377\pi$
$492$		0			0
$493$	10.0727	+	5.81547i	0.453651	+	0.261916i
$494$	−20.5430	−	14.9254i	−0.924273	−	0.671524i
$495$		0			0
$496$	−1.23411	+	0.896636i	−0.0554134	+	0.0402602i
$497$	−28.1464	+	2.95830i	−1.26254	+	0.132698i
$498$		0			0
$499$	−6.92481	−	11.9941i	−0.309997	−	0.536930i	0.668364	−	0.743834i	$-0.266995\pi$
$499$	−6.92481	−	11.9941i	−0.309997	−	0.536930i	−0.978361	+	0.206904i	$0.933661\pi$
$500$	3.35514	+	30.7772i	0.150046	+	1.37640i
$501$		0			0
$502$	6.69762	−	31.5098i	0.298929	−	1.40635i
$503$	16.3579	+	22.5148i	0.729364	+	1.00388i	0.999161	+	0.0409659i	$0.0130435\pi$
$503$	16.3579	+	22.5148i	0.729364	+	1.00388i	−0.269797	+	0.962917i	$0.586957\pi$
$504$		0			0
$505$	6.38081	−	5.36816i	0.283942	−	0.238880i
$506$	−49.5028	+	22.0400i	−2.20067	+	0.979800i
$507$		0			0
$508$	−0.327968	−	0.0344709i	−0.0145512	−	0.00152940i
$509$	−13.8192	+	2.93737i	−0.612526	+	0.130196i	−0.503721	−	0.863867i	$-0.668036\pi$
$509$	−13.8192	+	2.93737i	−0.612526	+	0.130196i	−0.108805	+	0.994063i	$0.534703\pi$
$510$		0			0
$511$	−23.0498	−	4.89939i	−1.01966	−	0.216736i
$512$	−19.2151	−	6.24335i	−0.849194	−	0.275920i
$513$		0			0
$514$	−9.73136	−	29.9500i	−0.429232	−	1.32104i
$515$	−28.2005	+	29.2779i	−1.24266	+	1.29014i
$516$		0			0
$517$	−37.3181	−	3.92229i	−1.64125	−	0.172502i
$518$	18.1802	−	10.4964i	0.798793	−	0.461183i
$519$		0			0
$520$	6.51084	+	6.27125i	0.285519	+	0.275013i
$521$	−19.0531	+	13.8429i	−0.834732	+	0.606468i	−0.920894	−	0.389813i	$-0.872540\pi$
$521$	−19.0531	+	13.8429i	−0.834732	+	0.606468i	0.0861620	+	0.996281i	$0.472540\pi$
$522$		0			0
$523$	12.9841	−	4.21880i	0.567757	−	0.184475i	−0.0110517	−	0.999939i	$-0.503518\pi$
$523$	12.9841	−	4.21880i	0.567757	−	0.184475i	0.578808	+	0.815464i	$0.303518\pi$
$524$	−3.78937	+	6.56338i	−0.165539	+	0.286722i
$525$		0			0
$526$	28.7728	+	49.8359i	1.25455	+	2.17295i
$527$	−1.89786	−	1.70884i	−0.0826721	−	0.0744383i
$528$		0			0
$529$	3.13920	+	29.8674i	0.136487	+	1.29858i
$530$	−49.7650	+	3.54434i	−2.16165	+	0.153956i
$531$		0			0
$532$			32.6074i			1.41371i
$533$	−10.3336	−	23.2096i	−0.447597	−	1.00532i
$534$		0			0
$535$	−9.90826	+	27.3322i	−0.428372	+	1.18168i
$536$	−4.15733	+	4.61719i	−0.179569	+	0.199432i
$537$		0			0
$538$	−5.74701	+	5.17463i	−0.247771	+	0.223094i
$539$	1.11411	+	3.42889i	0.0479882	+	0.147693i
$540$		0			0
$541$	1.48266	−	4.56314i	0.0637443	−	0.196185i	−0.914112	−	0.405461i	$-0.867111\pi$
$541$	1.48266	−	4.56314i	0.0637443	−	0.196185i	0.977857	+	0.209276i	$0.0671109\pi$
$542$	−12.2374	−	27.4857i	−0.525643	−	1.18061i
$543$		0			0
$544$	2.43618	−	23.1787i	0.104450	−	0.993777i
$545$	11.3255	−	14.5346i	0.485133	−	0.622593i
$546$		0			0
$547$	3.01495	−	0.316884i	0.128910	−	0.0135490i	−0.0398538	−	0.999206i	$-0.512689\pi$
$547$	3.01495	−	0.316884i	0.128910	−	0.0135490i	0.168764	+	0.985657i	$0.446023\pi$
$548$	40.4251	−	13.1349i	1.72688	−	0.561096i
$549$		0			0
$550$	33.3974	−	16.3957i	1.42407	−	0.699114i
$551$	8.97230	−	15.5405i	0.382233	−	0.662046i
$552$		0			0
$553$	6.09721	−	13.6946i	0.259280	−	0.582352i
$554$	28.5400	+	12.7068i	1.21255	+	0.539862i
$555$		0			0
$556$	9.37770	−	4.17522i	0.397703	−	0.177069i
$557$		−	16.2016i		−	0.686484i	−0.939247	−	0.343242i	$-0.888475\pi$
$557$		−	16.2016i		−	0.686484i	0.939247	−	0.343242i	$-0.111525\pi$
$558$		0			0
$559$	1.34790	−	4.14842i	0.0570102	−	0.175459i
$560$	−1.40574	+	10.0967i	−0.0594033	+	0.426665i
$561$		0			0
$562$	7.44533	+	35.0275i	0.314062	+	1.47755i
$563$	−0.934405	−	4.39603i	−0.0393805	−	0.185271i	0.954061	−	0.299613i	$-0.0968574\pi$
$563$	−0.934405	−	4.39603i	−0.0393805	−	0.185271i	−0.993441	+	0.114342i	$0.963524\pi$
$564$		0			0
$565$	3.41464	−	24.5256i	0.143655	−	1.03180i
$566$	−2.09954	+	6.46172i	−0.0882502	+	0.271606i
$567$		0			0
$568$			19.5007i			0.818233i
$569$	−13.5447	+	6.03047i	−0.567821	+	0.252810i	−0.670507	−	0.741904i	$-0.733923\pi$
$569$	−13.5447	+	6.03047i	−0.567821	+	0.252810i	0.102685	+	0.994714i	$0.467257\pi$
$570$		0			0
$571$	−0.696880	−	0.310271i	−0.0291635	−	0.0129844i	0.392103	−	0.919921i	$-0.371748\pi$
$571$	−0.696880	−	0.310271i	−0.0291635	−	0.0129844i	−0.421267	+	0.906937i	$0.638414\pi$
$572$	9.23715	−	20.7470i	0.386225	−	0.867475i
$573$		0			0
$574$	−28.0941	+	48.6604i	−1.17262	+	2.03104i
$575$	−5.16040	−	36.0440i	−0.215203	−	1.50314i
$576$		0			0
$577$	34.9503	−	11.3560i	1.45500	−	0.472758i	0.528461	−	0.848958i	$-0.322769\pi$
$577$	34.9503	−	11.3560i	1.45500	−	0.472758i	0.926538	+	0.376200i	$0.122769\pi$
$578$	−15.6293	+	1.64271i	−0.650095	+	0.0683277i
$579$		0			0
$580$	−14.1374	+	18.1432i	−0.587023	+	0.753354i
$581$	2.44706	−	23.2822i	0.101521	−	0.965909i
$582$		0			0
$583$	14.1594	+	31.8025i	0.586422	+	1.31713i
$584$	−5.01751	+	15.4423i	−0.207626	+	0.639008i
$585$		0			0
$586$	4.30672	+	13.2547i	0.177909	+	0.547548i
$587$	21.9524	−	19.7661i	0.906074	−	0.815833i	−0.0773780	−	0.997002i	$-0.524655\pi$
$587$	21.9524	−	19.7661i	0.906074	−	0.815833i	0.983452	+	0.181169i	$0.0579881\pi$
$588$		0			0
$589$	−2.63645	+	2.92808i	−0.108633	+	0.120649i
$590$	−2.41921	+	6.67346i	−0.0995973	+	0.274742i
$591$		0			0
$592$	2.99988	+	6.73784i	0.123294	+	0.276924i
$593$		−	0.848920i		−	0.0348610i	−0.999848	−	0.0174305i	$-0.994451\pi$
$593$		−	0.848920i		−	0.0348610i	0.999848	−	0.0174305i	$-0.00554858\pi$
$594$		0			0
$595$	−17.0233	+	1.21243i	−0.697887	+	0.0497046i
$596$	3.51884	+	33.4796i	0.144137	+	1.37138i
$597$		0			0
$598$	−28.4469	−	25.6137i	−1.16328	−	1.04742i
$599$	−14.9750	−	25.9375i	−0.611863	−	1.05978i	−0.990926	−	0.134407i	$-0.957087\pi$
$599$	−14.9750	−	25.9375i	−0.611863	−	1.05978i	0.379063	−	0.925371i	$-0.376246\pi$
$600$		0			0
$601$	16.7732	−	29.0520i	0.684192	−	1.18506i	−0.289498	−	0.957179i	$-0.593488\pi$
$601$	16.7732	−	29.0520i	0.684192	−	1.18506i	0.973690	−	0.227877i	$-0.0731783\pi$
$602$	−9.17466	+	2.98103i	−0.373931	+	0.121498i
$603$		0			0
$604$	24.0760	−	17.4923i	0.979639	−	0.711750i
$605$	−0.982030	−	0.945893i	−0.0399252	−	0.0384560i
$606$		0			0
$607$	−12.8646	+	7.42741i	−0.522160	+	0.301469i	−0.737818	−	0.675000i	$-0.764144\pi$
$607$	−12.8646	+	7.42741i	−0.522160	+	0.301469i	0.215658	+	0.976469i	$0.430810\pi$
$608$	−35.7608	−	3.75861i	−1.45029	−	0.152432i
$609$		0			0
$610$	−19.8200	+	20.5772i	−0.802487	+	0.833145i
$611$	−8.19123	−	25.2100i	−0.331382	−	1.01989i
$612$		0			0
$613$	−19.5860	−	6.36389i	−0.791073	−	0.257035i	−0.114512	−	0.993422i	$-0.536530\pi$
$613$	−19.5860	−	6.36389i	−0.791073	−	0.257035i	−0.676561	+	0.736387i	$0.736530\pi$
$614$	−64.3214	−	13.6719i	−2.59580	−	0.551754i
$615$		0			0
$616$	−13.6453	+	2.90040i	−0.549785	+	0.116860i
$617$	−11.7432	−	1.23426i	−0.472762	−	0.0496893i	−0.134848	−	0.990866i	$-0.543055\pi$
$617$	−11.7432	−	1.23426i	−0.472762	−	0.0496893i	−0.337914	+	0.941177i	$0.609721\pi$
$618$		0			0
$619$	28.8243	−	12.8334i	1.15855	−	0.515819i	0.264763	−	0.964314i	$-0.414706\pi$
$619$	28.8243	−	12.8334i	1.15855	−	0.515819i	0.893785	+	0.448495i	$0.148040\pi$
$620$	3.86459	−	3.25127i	0.155206	−	0.130574i
$621$		0			0
$622$	−25.2566	−	34.7628i	−1.01270	−	1.39386i
$623$	−5.21171	+	24.5192i	−0.208803	+	0.982339i
$624$		0			0
$625$	4.46803	+	24.5975i	0.178721	+	0.983900i
$626$	10.9984	+	19.0498i	0.439585	+	0.761383i
$627$		0			0
$628$	−24.3983	+	2.56437i	−0.973600	+	0.102329i
$629$	−9.98944	+	7.25775i	−0.398305	+	0.289386i
$630$		0			0
$631$	−19.9001	−	14.4583i	−0.792210	−	0.575574i	0.116409	−	0.993201i	$-0.462862\pi$
$631$	−19.9001	−	14.4583i	−0.792210	−	0.575574i	−0.908618	+	0.417627i	$0.862862\pi$
$632$	−8.94523	−	5.16453i	−0.355822	−	0.205434i
$633$		0			0
$634$	−1.38037	+	0.293407i	−0.0548216	+	0.0116527i
$635$	−0.266145	−	0.00895068i	−0.0105616	−	0.000355197i
$636$		0			0
$637$	−1.89270	+	1.70420i	−0.0749915	+	0.0675227i
$638$	26.2879	+	8.54146i	1.04075	+	0.338160i
$639$		0			0
$640$	27.0061	+	6.69643i	1.06751	+	0.264700i
$641$	27.2249	+	30.2363i	1.07532	+	1.19426i	0.980038	+	0.198812i	$0.0637083\pi$
$641$	27.2249	+	30.2363i	1.07532	+	1.19426i	0.0952811	+	0.995450i	$0.469625\pi$
$642$		0			0
$643$	−17.8361	+	10.2977i	−0.703389	+	0.406102i	−0.808608	−	0.588347i	$-0.799779\pi$
$643$	−17.8361	+	10.2977i	−0.703389	+	0.406102i	0.105220	+	0.994449i	$0.466445\pi$
$644$	−5.13813	+	48.8860i	−0.202471	+	1.92638i
$645$		0			0
$646$	−3.45273	−	32.8505i	−0.135846	−	1.29249i
$647$	−0.642724	−	0.884634i	−0.0252681	−	0.0347786i	0.796196	−	0.605039i	$-0.206842\pi$
$647$	−0.642724	−	0.884634i	−0.0252681	−	0.0347786i	−0.821464	+	0.570260i	$0.806842\pi$
$648$		0			0
$649$	4.95303			0.194423
$650$	20.1768	+	16.8419i	0.791399	+	0.660595i
$651$		0			0
$652$	2.44096	+	2.19785i	0.0955955	+	0.0860746i
$653$	12.1483	−	27.2856i	0.475400	−	1.06777i	−0.503606	−	0.863934i	$-0.667994\pi$
$653$	12.1483	−	27.2856i	0.475400	−	1.06777i	0.979006	−	0.203833i	$-0.0653398\pi$
$654$		0			0
$655$	−2.67568	+	5.50395i	−0.104548	+	0.215057i
$656$	−15.9707	−	11.6034i	−0.623552	−	0.453037i
$657$		0			0
$658$	−34.4582	+	47.4276i	−1.34332	+	1.84892i
$659$	23.9839	+	26.6368i	0.934281	+	1.03762i	0.999210	+	0.0397341i	$0.0126511\pi$
$659$	23.9839	+	26.6368i	0.934281	+	1.03762i	−0.0649294	+	0.997890i	$0.520682\pi$
$660$		0			0
$661$	9.55804	−	10.6153i	0.371764	−	0.412886i	−0.528012	−	0.849237i	$-0.677063\pi$
$661$	9.55804	−	10.6153i	0.371764	−	0.412886i	0.899777	+	0.436350i	$0.143729\pi$
$662$	8.22719	+	38.7059i	0.319759	+	1.50435i
$663$		0			0
$664$	−15.7782	−	3.35376i	−0.612313	−	0.130151i
$665$	1.87057	+	26.2641i	0.0725376	+	1.01848i
$666$		0			0
$667$	15.9004	−	21.8850i	0.615664	−	0.847389i
$668$	55.5489	+	32.0712i	2.14925	+	1.24087i
$669$		0			0
$670$	−11.1027	+	14.2486i	−0.428933	+	0.550470i
$671$	18.2117	+	8.10837i	0.703055	+	0.313020i
$672$		0			0
$673$	−1.48756	+	6.99842i	−0.0573412	+	0.269769i	−0.997473	−	0.0710407i	$-0.977368\pi$
$673$	−1.48756	+	6.99842i	−0.0573412	+	0.269769i	0.940132	+	0.340810i	$0.110701\pi$
$674$	−42.0723			−1.62056
$675$		0			0
$676$	−19.9554			−0.767514
$677$	−1.79160	+	8.42881i	−0.0688567	+	0.323945i	−0.999072	−	0.0430687i	$-0.986287\pi$
$677$	−1.79160	+	8.42881i	−0.0688567	+	0.323945i	0.930215	+	0.367014i	$0.119620\pi$
$678$		0			0
$679$	−33.6196	−	14.9684i	−1.29020	−	0.574435i
$680$	−0.395256	+	11.7528i	−0.0151574	+	0.450698i
$681$		0			0
$682$	−5.25601	−	3.03456i	−0.201263	−	0.116199i
$683$	4.10816	−	5.65440i	0.157195	−	0.216360i	−0.723154	−	0.690686i	$-0.757308\pi$
$683$	4.10816	−	5.65440i	0.157195	−	0.216360i	0.880349	+	0.474327i	$0.157308\pi$
$684$		0			0
$685$	31.8075	−	12.8988i	1.21530	−	0.492837i
$686$	41.9584	+	8.91853i	1.60198	+	0.340511i
$687$		0			0
$688$	−0.704668	−	3.31520i	−0.0268652	−	0.126391i
$689$	−16.4552	+	18.2754i	−0.626894	+	0.696236i
$690$		0			0
$691$	30.8484	+	34.2606i	1.17353	+	1.30334i	0.943966	+	0.330041i	$0.107063\pi$
$691$	30.8484	+	34.2606i	1.17353	+	1.30334i	0.229562	+	0.973294i	$0.426271\pi$
$692$	14.1038	−	19.4123i	0.536148	−	0.737944i
$693$		0			0
$694$	25.4481	+	18.4891i	0.965997	+	0.701838i
$695$	7.31389	−	3.90096i	0.277432	−	0.147972i
$696$		0			0
$697$	13.4423	−	30.1919i	0.509163	−	1.14360i
$698$	−16.7933	−	15.1208i	−0.635637	−	0.572330i
$699$		0			0
$700$	2.26751	−	33.6736i	0.0857038	−	1.27274i
$701$	28.6050			1.08040			0.540199	−	0.841537i	$-0.318349\pi$
$701$	28.6050			1.08040			0.540199	+	0.841537i	$0.318349\pi$
$702$		0			0
$703$	11.1975	+	15.4120i	0.422321	+	0.581276i
$704$	−4.45730	−	42.4084i	−0.167991	−	1.59833i
$705$		0			0
$706$	−5.83397	+	55.5065i	−0.219564	+	2.08901i
$707$	−7.87226	+	4.54505i	−0.296067	+	0.170934i
$708$		0			0
$709$	−23.4158	−	26.0058i	−0.879397	−	0.976669i	0.120474	−	0.992716i	$-0.461559\pi$
$709$	−23.4158	−	26.0058i	−0.879397	−	0.976669i	−0.999871	+	0.0160471i	$0.994892\pi$
$710$	4.02775	+	56.5524i	0.151159	+	2.12237i
$711$		0			0
$712$	16.4267	+	5.33736i	0.615617	+	0.200026i
$713$	−4.41405	+	3.97443i	−0.165308	+	0.148844i
$714$		0			0
$715$	6.25002	−	17.2409i	0.233738	−	0.644772i
$716$	34.1265	−	7.25381i	1.27537	−	0.271087i
$717$		0			0
$718$	24.3018	+	14.0307i	0.906936	+	0.523620i
$719$	−23.5102	−	17.0812i	−0.876783	−	0.637020i	0.0556153	−	0.998452i	$-0.482288\pi$
$719$	−23.5102	−	17.0812i	−0.876783	−	0.637020i	−0.932398	+	0.361432i	$0.882288\pi$
$720$		0			0
$721$	35.8509	−	26.0472i	1.33516	−	0.970049i
$722$	−9.41742	+	0.989811i	−0.350480	+	0.0368370i
$723$		0			0
$724$	−28.9000	−	50.0562i	−1.07406	−	1.86032i
$725$	−10.3464	+	15.4247i	−0.384254	+	0.572859i
$726$		0			0
$727$	0.751438	−	3.53524i	0.0278693	−	0.131115i	−0.962014	−	0.273002i	$-0.911984\pi$
$727$	0.751438	−	3.53524i	0.0278693	−	0.131115i	0.989883	+	0.141887i	$0.0453169\pi$
$728$	−5.79241	−	7.97256i	−0.214681	−	0.295483i
$729$		0			0
$730$	−11.3613	+	45.8192i	−0.420502	+	1.69585i
$731$	5.18357	−	2.30787i	0.191721	−	0.0853598i
$732$		0			0
$733$	13.9131	+	1.46233i	0.513893	+	0.0540123i	0.357926	−	0.933750i	$-0.383484\pi$
$733$	13.9131	+	1.46233i	0.513893	+	0.0540123i	0.155967	+	0.987762i	$0.450151\pi$
$734$	34.3403	−	7.29926i	1.26752	−	0.269420i
$735$		0			0
$736$	−53.0215	−	11.2701i	−1.95440	−	0.415420i
$737$	11.9872	+	3.89487i	0.441553	+	0.143469i
$738$		0			0
$739$	7.55293	+	23.2455i	0.277839	+	0.855100i	0.988454	+	0.151520i	$0.0484167\pi$
$739$	7.55293	+	23.2455i	0.277839	+	0.855100i	−0.710615	+	0.703581i	$0.751583\pi$
$740$	−11.4914	−	21.5452i	−0.422432	−	0.792016i
$741$		0			0
$742$	54.0896	+	5.68505i	1.98569	+	0.208705i
$743$	19.5845	−	11.3071i	0.718486	−	0.414818i	−0.0957094	−	0.995409i	$-0.530512\pi$
$743$	19.5845	−	11.3071i	0.718486	−	0.414818i	0.814195	+	0.580591i	$0.197179\pi$
$744$		0			0
$745$	4.75491	+	26.7648i	0.174206	+	0.980585i
$746$	36.1362	−	26.2545i	1.32304	−	0.961244i
$747$		0			0
$748$	28.0966	−	9.12913i	1.02731	−	0.333794i
$749$	15.8465	−	27.4469i	0.579018	−	1.00289i
$750$		0			0
$751$	−9.87040	−	17.0960i	−0.360176	−	0.623843i	0.627814	−	0.778364i	$-0.283950\pi$
$751$	−9.87040	−	17.0960i	−0.360176	−	0.623843i	−0.987990	+	0.154521i	$0.950617\pi$
$752$	−15.3063	−	13.7818i	−0.558162	−	0.502571i
$753$		0			0
$754$	2.04101	+	19.4189i	0.0743293	+	0.707196i
$755$	18.3889	−	15.4706i	0.669241	−	0.563031i
$756$		0			0
$757$		−	26.5162i		−	0.963748i	−0.876240	−	0.481874i	$-0.839956\pi$
$757$		−	26.5162i		−	0.963748i	0.876240	−	0.481874i	$-0.160044\pi$
$758$	7.29466	+	16.3841i	0.264954	+	0.595096i
$759$		0			0
$760$	18.1325	+	0.609813i	0.657736	+	0.0221203i
$761$	1.99288	−	2.21331i	0.0722417	−	0.0802326i	−0.705940	−	0.708271i	$-0.749475\pi$
$761$	1.99288	−	2.21331i	0.0722417	−	0.0802326i	0.778182	+	0.628039i	$0.216142\pi$
$762$		0			0
$763$	−14.9274	+	13.4407i	−0.540408	+	0.486586i
$764$	6.55390	+	20.1708i	0.237112	+	0.729755i
$765$		0			0
$766$	−23.9714	+	73.7765i	−0.866124	+	2.66565i
$767$	1.42313	+	3.19641i	0.0513864	+	0.115416i
$768$		0			0
$769$	−1.31451	+	12.5067i	−0.0474025	+	0.451005i	0.944918	+	0.327308i	$0.106142\pi$
$769$	−1.31451	+	12.5067i	−0.0474025	+	0.451005i	−0.992320	+	0.123697i	$0.960525\pi$
$770$	−38.9725	+	11.2295i	−1.40447	+	0.404684i
$771$		0			0
$772$	−67.9377	+	7.14054i	−2.44513	+	0.256994i
$773$	10.4435	−	3.39331i	0.375628	−	0.122049i	−0.115117	−	0.993352i	$-0.536724\pi$
$773$	10.4435	−	3.39331i	0.375628	−	0.122049i	0.490746	+	0.871303i	$0.336724\pi$
$774$		0			0
$775$	2.92628	−	2.84048i	0.105115	−	0.102033i
$776$	−12.6787	+	21.9602i	−0.455139	+	0.788324i
$777$		0			0
$778$	−17.2723	+	38.7943i	−0.619243	+	1.39084i
$779$	−46.5810	−	20.7392i	−1.66894	−	0.743059i
$780$		0			0
$781$	36.1400	−	16.0906i	1.29319	−	0.575766i
$782$		−	49.7947i		−	1.78065i
$783$		0			0
$784$	−0.611533	+	1.88211i	−0.0218405	+	0.0672180i
$785$	−19.5049	+	3.46516i	−0.696160	+	0.123677i
$786$		0			0
$787$	1.80503	+	8.49201i	0.0643425	+	0.302708i	0.998538	−	0.0540538i	$-0.0172142\pi$
$787$	1.80503	+	8.49201i	0.0643425	+	0.302708i	−0.934196	+	0.356761i	$0.883881\pi$
$788$	−7.55333	−	35.5356i	−0.269076	−	1.26590i
$789$		0			0
$790$	−27.0080	−	13.1296i	−0.960901	−	0.467131i
$791$	−8.34158	+	25.6727i	−0.296592	+	0.912818i
$792$		0			0
$793$			14.0826i			0.500087i
$794$	−27.0028	+	12.0224i	−0.958294	+	0.426660i
$795$		0			0
$796$	4.27251	+	1.90224i	0.151435	+	0.0674232i
$797$	−0.921963	+	2.07076i	−0.0326576	+	0.0733502i	−0.929138	−	0.369734i	$-0.879449\pi$
$797$	−0.921963	+	2.07076i	−0.0326576	+	0.0733502i	0.896480	+	0.443084i	$0.146116\pi$
$798$		0			0
$799$	17.2409	−	29.8620i	0.609937	−	1.05644i
$800$	36.6687	+	6.36831i	1.29644	+	0.225154i
$801$		0			0
$802$	−29.4062	+	9.55466i	−1.03837	+	0.337387i
$803$	32.7587	−	3.44308i	1.15603	−	0.121504i
$804$		0			0
$805$	−1.33416	+	39.6707i	−0.0470231	+	1.39821i
$806$	0.448148	−	4.26384i	0.0157853	−	0.150188i
$807$		0			0
$808$	2.54756	+	5.72192i	0.0896230	+	0.201296i
$809$	1.98856	−	6.12016i	0.0699141	−	0.215173i	−0.909995	−	0.414620i	$-0.863914\pi$
$809$	1.98856	−	6.12016i	0.0699141	−	0.215173i	0.979909	+	0.199447i	$0.0639145\pi$
$810$		0			0
$811$	10.2116	+	31.4280i	0.358577	+	1.10359i	0.953906	+	0.300104i	$0.0970215\pi$
$811$	10.2116	+	31.4280i	0.358577	+	1.10359i	−0.595330	+	0.803482i	$0.702979\pi$
$812$	18.6335	−	16.7777i	0.653908	−	0.588781i
$813$		0			0
$814$	−19.6349	+	21.8068i	−0.688204	+	0.764328i
$815$	2.09219	+	1.63026i	0.0732863	+	0.0571057i
$816$		0			0
$817$	−3.56066	−	7.99737i	−0.124572	−	0.279793i
$818$			35.1722i			1.22977i
$819$		0			0
$820$	55.4701	+	34.5622i	1.93710	+	1.20697i
$821$	4.98269	+	47.4071i	0.173897	+	1.65452i	0.638959	+	0.769241i	$0.279365\pi$
$821$	4.98269	+	47.4071i	0.173897	+	1.65452i	−0.465062	+	0.885278i	$0.653968\pi$
$822$		0			0
$823$	−30.4257	−	27.3955i	−1.06057	−	0.954946i	−0.0615065	−	0.998107i	$-0.519590\pi$
$823$	−30.4257	−	27.3955i	−1.06057	−	0.954946i	−0.999068	+	0.0431610i	$0.986257\pi$
$824$	−15.2671	−	26.4433i	−0.531854	−	0.921197i
$825$		0			0
$826$	3.86909	−	6.70147i	0.134623	−	0.233174i
$827$	−31.7854	+	10.3277i	−1.10529	+	0.359130i	−0.804136	−	0.594446i	$-0.797371\pi$
$827$	−31.7854	+	10.3277i	−1.10529	+	0.359130i	−0.301153	+	0.953576i	$0.597371\pi$
$828$		0			0
$829$	−16.8299	+	12.2277i	−0.584528	+	0.424684i	−0.840354	−	0.542039i	$-0.817653\pi$
$829$	−16.8299	+	12.2277i	−0.584528	+	0.424684i	0.255826	+	0.966723i	$0.417653\pi$
$830$	−46.4496	−	6.46706i	−1.61229	−	0.224475i
$831$		0			0
$832$	26.0873	−	15.0615i	0.904416	−	0.522165i
$833$	−3.29492	−	0.346310i	−0.114162	−	0.0119989i
$834$		0			0
$835$	46.5825	+	22.6456i	1.61205	+	0.783682i
$836$	−14.0847	−	43.3483i	−0.487130	−	1.49923i
$837$		0			0
$838$	−57.8907	−	18.8098i	−1.99980	−	0.649775i
$839$	7.82598	+	1.66346i	0.270183	+	0.0574291i	0.341011	−	0.940059i	$-0.389231\pi$
$839$	7.82598	+	1.66346i	0.270183	+	0.0574291i	−0.0708279	+	0.997489i	$0.522564\pi$
$840$		0			0
$841$	14.8691	−	3.16052i	0.512727	−	0.108984i
$842$	−14.6306	−	1.53774i	−0.504205	−	0.0529941i
$843$		0			0
$844$	13.6777	−	6.08968i	0.470804	−	0.209616i
$845$	−16.0733	+	1.14477i	−0.552940	+	0.0393812i
$846$		0			0
$847$	0.873668	+	1.20250i	0.0300196	+	0.0413184i
$848$	−3.97284	+	18.6907i	−0.136428	+	0.641842i
$849$		0			0
$850$	1.28121	+	34.1648i	0.0439451	+	1.17184i
$851$	14.3591	+	24.8707i	0.492223	+	0.852556i
$852$		0			0
$853$	44.4971	−	4.67683i	1.52355	−	0.160132i	0.694577	−	0.719419i	$-0.255592\pi$
$853$	44.4971	−	4.67683i	1.52355	−	0.160132i	0.828974	+	0.559287i	$0.188925\pi$
$854$	25.1969	−	18.3066i	0.862219	−	0.626439i
$855$		0			0
$856$	−17.6670	−	12.8359i	−0.603847	−	0.438721i
$857$	−3.48544	−	2.01232i	−0.119060	−	0.0687396i	0.439287	−	0.898347i	$-0.355231\pi$
$857$	−3.48544	−	2.01232i	−0.119060	−	0.0687396i	−0.558348	+	0.829607i	$0.688564\pi$
$858$		0			0
$859$	18.6107	−	3.95582i	0.634988	−	0.134971i	0.120839	−	0.992672i	$-0.461441\pi$
$859$	18.6107	−	3.95582i	0.634988	−	0.134971i	0.514148	+	0.857701i	$0.328108\pi$
$860$	3.10679	+	10.7822i	0.105941	+	0.367671i
$861$		0			0
$862$	41.8538	−	37.6854i	1.42555	−	1.28357i
$863$	−36.6196	−	11.8984i	−1.24655	−	0.405028i	−0.389865	−	0.920872i	$-0.627478\pi$
$863$	−36.6196	−	11.8984i	−1.24655	−	0.405028i	−0.856682	+	0.515845i	$0.827478\pi$
$864$		0			0
$865$	10.2465	−	16.4450i	0.348393	−	0.559147i
$866$	35.1244	+	39.0096i	1.19358	+	1.32560i
$867$		0			0
$868$	−4.76790	+	2.75275i	−0.161833	+	0.0934344i
$869$	−2.19029	+	20.8393i	−0.0743006	+	0.706923i
$870$		0			0
$871$	0.930694	+	8.85496i	0.0315354	+	0.300039i
$872$	8.13528	+	11.1973i	0.275495	+	0.379187i
$873$		0			0
$874$	−76.8248			−2.59864
$875$	−0.105336	−	27.2530i	−0.00356099	−	0.921318i
$876$		0			0
$877$	0.586917	+	0.528462i	0.0198188	+	0.0178449i	0.678981	−	0.734156i	$-0.262422\pi$
$877$	0.586917	+	0.528462i	0.0198188	+	0.0178449i	−0.659162	+	0.752001i	$0.729089\pi$
$878$	4.49957	−	10.1062i	0.151853	−	0.341068i
$879$		0			0
$880$	−2.49248	−	14.0298i	−0.0840213	−	0.472945i
$881$	−18.5788	−	13.4983i	−0.625937	−	0.454770i	0.229053	−	0.973414i	$-0.426437\pi$
$881$	−18.5788	−	13.4983i	−0.625937	−	0.454770i	−0.854990	+	0.518644i	$0.826437\pi$
$882$		0			0
$883$	−11.8992	+	16.3779i	−0.400442	+	0.551160i	−0.960855	−	0.277053i	$-0.910642\pi$
$883$	−11.8992	+	16.3779i	−0.400442	+	0.551160i	0.560413	+	0.828213i	$0.310642\pi$
$884$	13.9643	+	15.5089i	0.469671	+	0.521622i
$885$		0			0
$886$	37.0785	−	41.1798i	1.24568	−	1.38346i
$887$	−5.90799	−	27.7949i	−0.198371	−	0.933261i	−0.958853	−	0.283903i	$-0.908371\pi$
$887$	−5.90799	−	27.7949i	−0.198371	−	0.933261i	0.760482	−	0.649359i	$-0.224963\pi$
$888$		0			0
$889$	0.283952	+	0.0603558i	0.00952343	+	0.00202427i
$890$	48.7401	+	12.0856i	1.63377	+	0.405110i
$891$		0			0
$892$	12.0627	−	16.6029i	0.403890	−	0.555907i
$893$	−46.0721	−	26.5997i	−1.54174	−	0.890126i
$894$		0			0
$895$	27.0716	−	7.80040i	0.904902	−	0.260739i
$896$	−27.7093	−	12.3370i	−0.925703	−	0.412150i
$897$		0			0
$898$	−2.98818	+	14.0583i	−0.0997169	+	0.469131i
$899$	3.02980			0.101050
$900$		0			0
$901$	−31.9900			−1.06574
$902$	16.3295	−	76.8244i	0.543714	−	2.55797i
$903$		0			0
$904$	16.9918	+	7.56523i	0.565138	+	0.251616i
$905$	−26.1494	−	38.6606i	−0.869237	−	1.28512i
$906$		0			0
$907$	−3.21141	−	1.85411i	−0.106633	−	0.0615646i	0.445735	−	0.895165i	$-0.352942\pi$
$907$	−3.21141	−	1.85411i	−0.106633	−	0.0615646i	−0.552368	+	0.833600i	$0.686276\pi$
$908$	−12.7282	+	17.5189i	−0.422401	+	0.581385i
$909$		0			0
$910$	−18.4447	−	21.9241i	−0.611437	−	0.726778i
$911$	33.2039	+	7.05771i	1.10009	+	0.233832i	0.721972	−	0.691923i	$-0.243236\pi$
$911$	33.2039	+	7.05771i	1.10009	+	0.233832i	0.378123	+	0.925755i	$0.376569\pi$
$912$		0			0
$913$	6.80360	+	32.0084i	0.225166	+	1.05932i
$914$	−36.2610	+	40.2719i	−1.19941	+	1.33208i
$915$		0			0
$916$	−17.0728	−	18.9612i	−0.564100	−	0.626496i
$917$	3.92137	−	5.39730i	0.129495	−	0.178235i
$918$		0			0
$919$	−28.2405	−	20.5179i	−0.931569	−	0.676825i	0.0148073	−	0.999890i	$-0.495287\pi$
$919$	−28.2405	−	20.5179i	−0.931569	−	0.676825i	−0.946377	+	0.323066i	$0.895287\pi$
$920$	27.0888	+	3.77150i	0.893091	+	0.124343i
$921$		0			0
$922$	32.5453	−	73.0980i	1.07182	−	2.40735i
$923$	20.7679	+	18.6995i	0.683584	+	0.615502i
$924$		0			0
$925$	−10.4919	−	16.6946i	−0.344971	−	0.548917i
$926$	17.8512			0.586627
$927$		0			0
$928$	16.2524	+	22.3695i	0.533510	+	0.734314i
$929$	2.85749	+	27.1872i	0.0937513	+	0.891984i	0.935788	+	0.352564i	$0.114690\pi$
$929$	2.85749	+	27.1872i	0.0937513	+	0.891984i	−0.842037	+	0.539420i	$0.818643\pi$
$930$		0			0
$931$	−0.534298	+	5.08351i	−0.0175109	+	0.166605i
$932$	−37.5205	+	21.6625i	−1.22903	+	0.709578i
$933$		0			0
$934$	22.6169	+	25.1186i	0.740048	+	0.821907i
$935$	22.1071	−	8.96500i	0.722979	−	0.293187i
$936$		0			0
$937$	−31.5506	−	10.2514i	−1.03071	−	0.334899i	−0.255640	−	0.966772i	$-0.582286\pi$
$937$	−31.5506	−	10.2514i	−1.03071	−	0.334899i	−0.775072	+	0.631873i	$0.782286\pi$
$938$	14.6337	−	13.1762i	0.477806	−	0.430218i
$939$		0			0
$940$	53.7881	+	41.9124i	1.75438	+	1.36703i
$941$	13.0500	−	2.77387i	0.425419	−	0.0904256i	0.00977338	−	0.999952i	$-0.496889\pi$
$941$	13.0500	−	2.77387i	0.425419	−	0.0904256i	0.415646	+	0.909527i	$0.363556\pi$
$942$		0			0
$943$	−66.5677	−	38.4329i	−2.16774	−	1.25155i
$944$	2.19947	+	1.59801i	0.0715868	+	0.0520109i
$945$		0			0
$946$	10.9092	−	7.92596i	0.354687	−	0.257695i
$947$	34.5098	−	3.62713i	1.12142	−	0.117866i	0.474377	−	0.880322i	$-0.342673\pi$
$947$	34.5098	−	3.62713i	1.12142	−	0.117866i	0.647040	+	0.762456i	$0.276007\pi$
$948$		0			0
$949$	11.6344	+	20.1514i	0.377669	+	0.654142i
$950$	52.7105	−	1.97669i	1.71016	−	0.0641323i
$951$		0			0
$952$	2.66527	−	12.5391i	0.0863819	−	0.406395i
$953$	−4.18311	−	5.75755i	−0.135504	−	0.186505i	0.735872	−	0.677120i	$-0.236772\pi$
$953$	−4.18311	−	5.75755i	−0.135504	−	0.186505i	−0.871377	+	0.490615i	$0.836772\pi$
$954$		0			0
$955$	6.43607	+	15.8709i	0.208266	+	0.513571i
$956$	3.55781	−	1.58404i	0.115068	−	0.0512315i
$957$		0			0
$958$	26.0126	+	2.73404i	0.840430	+	0.0883327i
$959$	−36.5992	+	7.77941i	−1.18185	+	0.251210i
$960$		0			0
$961$	29.6719	+	6.30695i	0.957157	+	0.203450i
$962$	−19.7145	−	6.40564i	−0.635622	−	0.206526i
$963$		0			0
$964$	16.1694	+	49.7642i	0.520780	+	1.60280i
$965$	−54.3118	+	9.64880i	−1.74836	+	0.310606i
$966$		0			0
$967$	32.5628	+	3.42249i	1.04715	+	0.110060i	0.612444	−	0.790514i	$-0.290186\pi$
$967$	32.5628	+	3.42249i	1.04715	+	0.110060i	0.434704	+	0.900573i	$0.356853\pi$
$968$	0.886955	−	0.512084i	0.0285078	−	0.0164590i
$969$		0			0
$970$	−32.2327	+	66.3035i	−1.03493	+	2.12888i
$971$	24.0211	−	17.4523i	0.770872	−	0.560072i	−0.131353	−	0.991336i	$-0.541932\pi$
$971$	24.0211	−	17.4523i	0.770872	−	0.560072i	0.902226	+	0.431264i	$0.141932\pi$
$972$		0			0
$973$	−8.59398	+	2.79235i	−0.275510	+	0.0895188i
$974$	11.1042	−	19.2331i	0.355802	−	0.616267i
$975$		0			0
$976$	5.47118	+	9.47636i	0.175128	+	0.303331i
$977$	20.2720	+	18.2530i	0.648559	+	0.583965i	0.926344	−	0.376678i	$-0.122934\pi$
$977$	20.2720	+	18.2530i	0.648559	+	0.583965i	−0.277785	+	0.960643i	$0.589600\pi$
$978$		0			0
$979$	−3.66257	−	34.8470i	−0.117056	−	1.11371i
$980$	1.57683	−	6.35921i	0.0503699	−	0.203137i
$981$		0			0
$982$		−	51.3546i		−	1.63879i
$983$	2.49269	+	5.59868i	0.0795046	+	0.178570i	0.948924	−	0.315504i	$-0.102174\pi$
$983$	2.49269	+	5.59868i	0.0795046	+	0.178570i	−0.869420	+	0.494074i	$0.835507\pi$
$984$		0			0
$985$	−8.12250	−	28.1894i	−0.258804	−	0.898189i
$986$	−16.9959	+	18.8759i	−0.541260	+	0.601130i
$987$		0			0
$988$	23.9277	−	21.5446i	0.761241	−	0.685424i
$989$	−4.07807	−	12.5510i	−0.129675	−	0.399098i
$990$		0			0
$991$	16.5883	−	51.0535i	0.526945	−	1.62177i	−0.233493	−	0.972359i	$-0.575016\pi$
$991$	16.5883	−	51.0535i	0.526945	−	1.62177i	0.760438	−	0.649411i	$-0.224984\pi$
$992$	−2.46937	−	5.54631i	−0.0784027	−	0.176095i
$993$		0			0
$994$	6.46043	−	61.4669i	0.204912	−	1.94961i
$995$	3.55048	+	1.28709i	0.112558	+	0.0408035i
$996$		0			0
$997$	−42.7438	+	4.49255i	−1.35371	+	0.142281i	−0.753440	−	0.657517i	$-0.771607\pi$
$997$	−42.7438	+	4.49255i	−1.35371	+	0.142281i	−0.600270	+	0.799798i	$0.704940\pi$
$998$	28.7649	−	9.34627i	0.910536	−	0.295851i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.y.a.19.4		224
3.2	odd	2		225.2.u.a.169.25	yes	224
9.4	even	3	inner	675.2.y.a.469.4		224
9.5	odd	6		225.2.u.a.94.25	yes	224
25.4	even	10	inner	675.2.y.a.154.4		224
75.29	odd	10		225.2.u.a.79.25	yes	224
225.4	even	30	inner	675.2.y.a.604.4		224
225.104	odd	30		225.2.u.a.4.25	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.25	✓	224	225.104	odd	30
225.2.u.a.79.25	yes	224	75.29	odd	10
225.2.u.a.94.25	yes	224	9.5	odd	6
225.2.u.a.169.25	yes	224	3.2	odd	2
675.2.y.a.19.4		224	1.1	even	1	trivial
675.2.y.a.154.4		224	25.4	even	10	inner
675.2.y.a.469.4		224	9.4	even	3	inner
675.2.y.a.604.4		224	225.4	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.y (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.454043 + 2.13611i) q^{2} +(-2.52970 - 1.12630i) q^{4} +(-2.10220 - 0.762073i) q^{5} +(2.11102 + 1.21880i) q^{7} +(0.987242 - 1.35882i) q^{8} +O(q^{10})\)	\(q+(-0.454043 + 2.13611i) q^{2} +(-2.52970 - 1.12630i) q^{4} +(-2.10220 - 0.762073i) q^{5} +(2.11102 + 1.21880i) q^{7} +(0.987242 - 1.35882i) q^{8} +(2.58236 - 4.14451i) q^{10} +(-3.33285 - 0.708420i) q^{11} +(-0.500440 - 2.35439i) q^{13} +(-3.56198 + 3.95598i) q^{14} +(-1.25145 - 1.38988i) q^{16} +(1.84041 - 2.53310i) q^{17} +(-3.90815 - 2.83944i) q^{19} +(4.45963 + 4.29552i) q^{20} +(3.02652 - 6.79768i) q^{22} +(-5.41181 - 4.87281i) q^{23} +(3.83849 + 3.20406i) q^{25} +5.25644 q^{26} +(-3.96753 - 5.46084i) q^{28} +(0.388288 + 3.69431i) q^{29} +(0.0852569 - 0.811165i) q^{31} +(6.44628 - 3.72176i) q^{32} +(4.57536 + 5.08145i) q^{34} +(-3.50898 - 4.17091i) q^{35} +(-3.75054 - 1.21863i) q^{37} +(7.83982 - 7.05901i) q^{38} +(-3.11090 + 2.10417i) q^{40} +(10.3245 - 2.19454i) q^{41} +(1.56940 + 0.906093i) q^{43} +(7.63324 + 5.54588i) q^{44} +(12.8660 - 9.34773i) q^{46} +(10.9524 - 1.15114i) q^{47} +(-0.529060 - 0.916359i) q^{49} +(-8.58705 + 6.74464i) q^{50} +(-1.38577 + 6.51955i) q^{52} +(-6.00535 - 8.26565i) q^{53} +(6.46646 + 4.02912i) q^{55} +(3.74022 - 1.66525i) q^{56} +(-8.06775 - 0.847954i) q^{58} +(-1.42188 + 0.302230i) q^{59} +(-5.72286 - 1.21643i) q^{61} +(1.69403 + 0.550422i) q^{62} +(3.86730 + 11.9023i) q^{64} +(-0.742188 + 5.33076i) q^{65} +(-3.67886 - 0.386664i) q^{67} +(-7.50872 + 4.33516i) q^{68} +(10.5027 - 5.60177i) q^{70} +(-9.39299 + 6.82441i) q^{71} +(-9.19406 + 2.98733i) q^{73} +(4.30602 - 7.45825i) q^{74} +(6.68842 + 11.5847i) q^{76} +(-6.17230 - 5.55757i) q^{77} +(-0.642822 - 6.11604i) q^{79} +(1.57161 + 3.87549i) q^{80} +23.0506i q^{82} +(-3.90626 - 8.77360i) q^{83} +(-5.79932 + 3.92257i) q^{85} +(-2.64809 + 2.94100i) q^{86} +(-4.25295 + 3.82937i) q^{88} +(3.17776 + 9.78015i) q^{89} +(1.81308 - 5.58010i) q^{91} +(8.20204 + 18.4221i) q^{92} +(-2.51389 + 23.9181i) q^{94} +(6.05186 + 8.94737i) q^{95} +(-15.0146 + 1.57810i) q^{97} +(2.19766 - 0.714062i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Introduction

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