LMFDB - Embedded newform 1050.2.j.c.743.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(407,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1050.407");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.j (of order $4$, degree $2$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 $ x^12 + 16x^10 + 86x^8 + 196x^6 + 185x^4 + 60*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			743.6
Root			$-0.678294i$ of defining polynomial
Character	$\chi$	$=$	1050.743
Dual form			1050.2.j.c.407.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.67762 + 0.430811i) q^{3} +1.00000i q^{4} +(0.881625 + 1.49088i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.62880 + 1.44547i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.67762 + 0.430811i) q^{3} +1.00000i q^{4} +(0.881625 + 1.49088i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.62880 + 1.44547i) q^{9} +5.11849i q^{11} +(-0.430811 + 1.67762i) q^{12} +(-2.66102 - 2.66102i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(0.660063 + 0.660063i) q^{17} +(0.836740 + 2.88095i) q^{18} +4.57375i q^{19} +(-1.49088 + 0.881625i) q^{21} +(-3.61932 + 3.61932i) q^{22} +(0.915044 - 0.915044i) q^{23} +(-1.49088 + 0.881625i) q^{24} -3.76325i q^{26} +(3.78740 + 3.55747i) q^{27} +(-0.707107 - 0.707107i) q^{28} +8.71047 q^{29} -9.86542 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.20510 + 8.58686i) q^{33} +0.933471i q^{34} +(-1.44547 + 2.62880i) q^{36} +(8.30181 - 8.30181i) q^{37} +(-3.23413 + 3.23413i) q^{38} +(-3.31778 - 5.61057i) q^{39} +2.55167i q^{41} +(-1.67762 - 0.430811i) q^{42} +(-1.01688 - 1.01688i) q^{43} -5.11849 q^{44} +1.29407 q^{46} +(2.54338 + 2.54338i) q^{47} +(-1.67762 - 0.430811i) q^{48} -1.00000i q^{49} +(0.822971 + 1.39170i) q^{51} +(2.66102 - 2.66102i) q^{52} +(-0.551238 + 0.551238i) q^{53} +(0.162584 + 5.19361i) q^{54} -1.00000i q^{56} +(-1.97043 + 7.67301i) q^{57} +(6.15923 + 6.15923i) q^{58} -1.36204 q^{59} +8.09345 q^{61} +(-6.97590 - 6.97590i) q^{62} +(-2.88095 + 0.836740i) q^{63} -1.00000i q^{64} +(-7.63107 + 4.51259i) q^{66} +(1.67348 - 1.67348i) q^{67} +(-0.660063 + 0.660063i) q^{68} +(1.92931 - 1.14088i) q^{69} +3.62916i q^{71} +(-2.88095 + 0.836740i) q^{72} +(-5.95286 - 5.95286i) q^{73} +11.7405 q^{74} -4.57375 q^{76} +(-3.61932 - 3.61932i) q^{77} +(1.62125 - 6.31330i) q^{78} -7.87966i q^{79} +(4.82121 + 7.59973i) q^{81} +(-1.80431 + 1.80431i) q^{82} +(3.65347 - 3.65347i) q^{83} +(-0.881625 - 1.49088i) q^{84} -1.43808i q^{86} +(14.6128 + 3.75257i) q^{87} +(-3.61932 - 3.61932i) q^{88} +5.65138 q^{89} +3.76325 q^{91} +(0.915044 + 0.915044i) q^{92} +(-16.5504 - 4.25014i) q^{93} +3.59688i q^{94} +(-0.881625 - 1.49088i) q^{96} +(-3.76976 + 3.76976i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-7.39864 + 13.4555i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3}+O(q^{10}) $ 12 * q - 4 * q^3	$ 12 q - 4 q^{3} + 4 q^{12} - 12 q^{14} - 12 q^{16} - 28 q^{17} - 4 q^{21} - 4 q^{22} + 24 q^{23} - 4 q^{24} + 20 q^{27} + 8 q^{29} - 8 q^{31} - 4 q^{33} + 4 q^{36} + 20 q^{37} + 4 q^{38} - 40 q^{39} + 4 q^{42} - 8 q^{43} + 8 q^{44} + 8 q^{46} - 16 q^{47} + 4 q^{48} + 8 q^{51} + 24 q^{53} - 4 q^{54} + 12 q^{57} + 8 q^{58} + 32 q^{59} - 28 q^{62} - 8 q^{63} - 8 q^{66} + 28 q^{68} - 32 q^{69} - 8 q^{72} + 24 q^{73} + 8 q^{74} - 4 q^{77} - 36 q^{81} - 32 q^{82} + 24 q^{83} + 64 q^{87} - 4 q^{88} + 48 q^{89} + 24 q^{91} + 24 q^{92} - 76 q^{93} - 8 q^{97} - 40 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 + 4 * q^12 - 12 * q^14 - 12 * q^16 - 28 * q^17 - 4 * q^21 - 4 * q^22 + 24 * q^23 - 4 * q^24 + 20 * q^27 + 8 * q^29 - 8 * q^31 - 4 * q^33 + 4 * q^36 + 20 * q^37 + 4 * q^38 - 40 * q^39 + 4 * q^42 - 8 * q^43 + 8 * q^44 + 8 * q^46 - 16 * q^47 + 4 * q^48 + 8 * q^51 + 24 * q^53 - 4 * q^54 + 12 * q^57 + 8 * q^58 + 32 * q^59 - 28 * q^62 - 8 * q^63 - 8 * q^66 + 28 * q^68 - 32 * q^69 - 8 * q^72 + 24 * q^73 + 8 * q^74 - 4 * q^77 - 36 * q^81 - 32 * q^82 + 24 * q^83 + 64 * q^87 - 4 * q^88 + 48 * q^89 + 24 * q^91 + 24 * q^92 - 76 * q^93 - 8 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.67762	+	0.430811i	0.968573	+	0.248729i
$3$	1.67762	+	0.430811i	0.968573	+	0.248729i
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	0.881625	+	1.49088i	0.359922	+	0.608651i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.62880	+	1.44547i	0.876268	+	0.481825i
$10$		0			0
$11$			5.11849i			1.54328i	0.636059	+	0.771641i	$0.280564\pi$
$11$			5.11849i			1.54328i	−0.636059	+	0.771641i	$0.719436\pi$
$12$	−0.430811	+	1.67762i	−0.124365	+	0.484287i
$13$	−2.66102	−	2.66102i	−0.738034	−	0.738034i	0.234163	−	0.972197i	$-0.424765\pi$
$13$	−2.66102	−	2.66102i	−0.738034	−	0.738034i	−0.972197	+	0.234163i	$0.924765\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.660063	+	0.660063i	0.160089	+	0.160089i	0.782606	−	0.622517i	$-0.213890\pi$
$17$	0.660063	+	0.660063i	0.160089	+	0.160089i	−0.622517	+	0.782606i	$0.713890\pi$
$18$	0.836740	+	2.88095i	0.197221	+	0.679046i
$19$			4.57375i			1.04929i	0.851321	+	0.524646i	$0.175802\pi$
$19$			4.57375i			1.04929i	−0.851321	+	0.524646i	$0.824198\pi$
$20$		0			0
$21$	−1.49088	+	0.881625i	−0.325338	+	0.192386i
$22$	−3.61932	+	3.61932i	−0.771641	+	0.771641i
$23$	0.915044	−	0.915044i	0.190800	−	0.190800i	−0.605242	−	0.796042i	$-0.706924\pi$
$23$	0.915044	−	0.915044i	0.190800	−	0.190800i	0.796042	+	0.605242i	$0.206924\pi$
$24$	−1.49088	+	0.881625i	−0.304326	+	0.179961i
$25$		0			0
$26$		−	3.76325i		−	0.738034i
$27$	3.78740	+	3.55747i	0.728885	+	0.684636i
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$	8.71047			1.61749			0.808747	−	0.588157i	$-0.200146\pi$
$29$	8.71047			1.61749			0.808747	+	0.588157i	$0.200146\pi$
$30$		0			0
$31$	−9.86542			−1.77188			−0.885941	−	0.463798i	$-0.846486\pi$
$31$	−9.86542			−1.77188			−0.885941	+	0.463798i	$0.846486\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−2.20510	+	8.58686i	−0.383859	+	1.49478i
$34$			0.933471i			0.160089i
$35$		0			0
$36$	−1.44547	+	2.62880i	−0.240912	+	0.438134i
$37$	8.30181	−	8.30181i	1.36481	−	1.36481i	0.497139	−	0.867671i	$-0.334384\pi$
$37$	8.30181	−	8.30181i	1.36481	−	1.36481i	0.867671	−	0.497139i	$-0.165616\pi$
$38$	−3.23413	+	3.23413i	−0.524646	+	0.524646i
$39$	−3.31778	−	5.61057i	−0.531269	−	0.898411i
$40$		0			0
$41$			2.55167i			0.398504i	0.979948	+	0.199252i	$0.0638513\pi$
$41$			2.55167i			0.398504i	−0.979948	+	0.199252i	$0.936149\pi$
$42$	−1.67762	−	0.430811i	−0.258862	−	0.0664757i
$43$	−1.01688	−	1.01688i	−0.155072	−	0.155072i	0.625307	−	0.780379i	$-0.284974\pi$
$43$	−1.01688	−	1.01688i	−0.155072	−	0.155072i	−0.780379	+	0.625307i	$0.784974\pi$
$44$	−5.11849			−0.771641
$45$		0			0
$46$	1.29407			0.190800
$47$	2.54338	+	2.54338i	0.370990	+	0.370990i	0.867838	−	0.496848i	$-0.165509\pi$
$47$	2.54338	+	2.54338i	0.370990	+	0.370990i	−0.496848	+	0.867838i	$0.665509\pi$
$48$	−1.67762	−	0.430811i	−0.242143	−	0.0621823i
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	0.822971	+	1.39170i	0.115239	+	0.194877i
$52$	2.66102	−	2.66102i	0.369017	−	0.369017i
$53$	−0.551238	+	0.551238i	−0.0757184	+	0.0757184i	−0.743952	−	0.668233i	$-0.767051\pi$
$53$	−0.551238	+	0.551238i	−0.0757184	+	0.0757184i	0.668233	+	0.743952i	$0.267051\pi$
$54$	0.162584	+	5.19361i	0.0221249	+	0.706761i
$55$		0			0
$56$		−	1.00000i		−	0.133631i
$57$	−1.97043	+	7.67301i	−0.260989	+	1.01632i
$58$	6.15923	+	6.15923i	0.808747	+	0.808747i
$59$	−1.36204			−0.177323			−0.0886615	−	0.996062i	$-0.528259\pi$
$59$	−1.36204			−0.177323			−0.0886615	+	0.996062i	$0.528259\pi$
$60$		0			0
$61$	8.09345			1.03626			0.518130	−	0.855302i	$-0.326628\pi$
$61$	8.09345			1.03626			0.518130	+	0.855302i	$0.326628\pi$
$62$	−6.97590	−	6.97590i	−0.885941	−	0.885941i
$63$	−2.88095	+	0.836740i	−0.362965	+	0.105419i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−7.63107	+	4.51259i	−0.939320	+	0.555461i
$67$	1.67348	−	1.67348i	0.204448	−	0.204448i	−0.597455	−	0.801903i	$-0.703821\pi$
$67$	1.67348	−	1.67348i	0.204448	−	0.204448i	0.801903	+	0.597455i	$0.203821\pi$
$68$	−0.660063	+	0.660063i	−0.0800444	+	0.0800444i
$69$	1.92931	−	1.14088i	0.232261	−	0.137346i
$70$		0			0
$71$			3.62916i			0.430702i	0.976537	+	0.215351i	$0.0690896\pi$
$71$			3.62916i			0.430702i	−0.976537	+	0.215351i	$0.930910\pi$
$72$	−2.88095	+	0.836740i	−0.339523	+	0.0986107i
$73$	−5.95286	−	5.95286i	−0.696729	−	0.696729i	0.266974	−	0.963704i	$-0.413976\pi$
$73$	−5.95286	−	5.95286i	−0.696729	−	0.696729i	−0.963704	+	0.266974i	$0.913976\pi$
$74$	11.7405			1.36481
$75$		0			0
$76$	−4.57375			−0.524646
$77$	−3.61932	−	3.61932i	−0.412459	−	0.412459i
$78$	1.62125	−	6.31330i	0.183571	−	0.714840i
$79$		−	7.87966i		−	0.886531i	−0.896390	−	0.443265i	$-0.853820\pi$
$79$		−	7.87966i		−	0.886531i	0.896390	−	0.443265i	$-0.146180\pi$
$80$		0			0
$81$	4.82121	+	7.59973i	0.535690	+	0.844415i
$82$	−1.80431	+	1.80431i	−0.199252	+	0.199252i
$83$	3.65347	−	3.65347i	0.401020	−	0.401020i	−0.477572	−	0.878592i	$-0.658483\pi$
$83$	3.65347	−	3.65347i	0.401020	−	0.401020i	0.878592	+	0.477572i	$0.158483\pi$
$84$	−0.881625	−	1.49088i	−0.0961932	−	0.162669i
$85$		0			0
$86$		−	1.43808i		−	0.155072i
$87$	14.6128	+	3.75257i	1.56666	+	0.402318i
$88$	−3.61932	−	3.61932i	−0.385820	−	0.385820i
$89$	5.65138			0.599045			0.299523	−	0.954089i	$-0.403173\pi$
$89$	5.65138			0.599045			0.299523	+	0.954089i	$0.403173\pi$
$90$		0			0
$91$	3.76325			0.394496
$92$	0.915044	+	0.915044i	0.0953999	+	0.0953999i
$93$	−16.5504	−	4.25014i	−1.71620	−	0.440719i
$94$			3.59688i			0.370990i
$95$		0			0
$96$	−0.881625	−	1.49088i	−0.0899805	−	0.152163i
$97$	−3.76976	+	3.76976i	−0.382761	+	0.382761i	−0.872096	−	0.489335i	$-0.837240\pi$
$97$	−3.76976	+	3.76976i	−0.382761	+	0.382761i	0.489335	+	0.872096i	$0.337240\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$	−7.39864	+	13.4555i	−0.743591	+	1.35233i
$100$		0			0
$101$		−	9.35180i		−	0.930539i	−0.885169	−	0.465269i	$-0.845957\pi$
$101$		−	9.35180i		−	0.930539i	0.885169	−	0.465269i	$-0.154043\pi$
$102$	−0.402150	+	1.56601i	−0.0398188	+	0.155058i
$103$	−4.21956	−	4.21956i	−0.415766	−	0.415766i	0.467975	−	0.883741i	$-0.344984\pi$
$103$	−4.21956	−	4.21956i	−0.415766	−	0.415766i	−0.883741	+	0.467975i	$0.844984\pi$
$104$	3.76325			0.369017
$105$		0			0
$106$	−0.779568			−0.0757184
$107$	−9.84339	−	9.84339i	−0.951597	−	0.951597i	0.0472848	−	0.998881i	$-0.484943\pi$
$107$	−9.84339	−	9.84339i	−0.951597	−	0.951597i	−0.998881	+	0.0472848i	$0.984943\pi$
$108$	−3.55747	+	3.78740i	−0.342318	+	0.364443i
$109$		−	11.0771i		−	1.06100i	−0.847686	−	0.530498i	$-0.822005\pi$
$109$		−	11.0771i		−	1.06100i	0.847686	−	0.530498i	$-0.177995\pi$
$110$		0			0
$111$	17.5038	−	10.3508i	1.66139	−	0.982450i
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	6.81822	−	6.81822i	0.641404	−	0.641404i	−0.309496	−	0.950901i	$-0.600160\pi$
$113$	6.81822	−	6.81822i	0.641404	−	0.641404i	0.950901	+	0.309496i	$0.100160\pi$
$114$	−6.81894	+	4.03234i	−0.638652	+	0.377663i
$115$		0			0
$116$			8.71047i			0.808747i
$117$	−3.14886	−	10.8417i	−0.291112	−	1.00232i
$118$	−0.963111	−	0.963111i	−0.0886615	−	0.0886615i
$119$	−0.933471			−0.0855711
$120$		0			0
$121$	−15.1989			−1.38172
$122$	5.72293	+	5.72293i	0.518130	+	0.518130i
$123$	−1.09929	+	4.28073i	−0.0991196	+	0.385981i
$124$		−	9.86542i		−	0.885941i
$125$		0			0
$126$	−2.62880	−	1.44547i	−0.234192	−	0.128773i
$127$	−2.49131	+	2.49131i	−0.221068	+	0.221068i	−0.808948	−	0.587880i	$-0.799963\pi$
$127$	−2.49131	+	2.49131i	−0.221068	+	0.221068i	0.587880	+	0.808948i	$0.299963\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−1.26785	−	2.14402i	−0.111628	−	0.188770i
$130$		0			0
$131$			2.05511i			0.179556i	0.995962	+	0.0897778i	$0.0286157\pi$
$131$			2.05511i			0.179556i	−0.995962	+	0.0897778i	$0.971384\pi$
$132$	−8.58686	−	2.20510i	−0.747391	−	0.191930i
$133$	−3.23413	−	3.23413i	−0.280435	−	0.280435i
$134$	2.36666			0.204448
$135$		0			0
$136$	−0.933471			−0.0800444
$137$	8.74776	+	8.74776i	0.747371	+	0.747371i	0.973985	−	0.226613i	$-0.0727654\pi$
$137$	8.74776	+	8.74776i	0.747371	+	0.747371i	−0.226613	+	0.973985i	$0.572765\pi$
$138$	2.17095	+	0.557499i	0.184804	+	0.0474575i
$139$			0.0502116i			0.00425889i	0.999998	+	0.00212945i	$0.000677824\pi$
$139$			0.0502116i			0.00425889i	−0.999998	+	0.00212945i	$0.999322\pi$
$140$		0			0
$141$	3.17110	+	5.36253i	0.267055	+	0.451607i
$142$	−2.56620	+	2.56620i	−0.215351	+	0.215351i
$143$	13.6204	−	13.6204i	1.13899	−	1.13899i
$144$	−2.62880	−	1.44547i	−0.219067	−	0.120456i
$145$		0			0
$146$		−	8.41861i		−	0.696729i
$147$	0.430811	−	1.67762i	0.0355327	−	0.138368i
$148$	8.30181	+	8.30181i	0.682405	+	0.682405i
$149$	11.7819			0.965211			0.482605	−	0.875838i	$-0.339691\pi$
$149$	11.7819			0.965211			0.482605	+	0.875838i	$0.339691\pi$
$150$		0			0
$151$	13.0407			1.06123			0.530617	−	0.847612i	$-0.321960\pi$
$151$	13.0407			1.06123			0.530617	+	0.847612i	$0.321960\pi$
$152$	−3.23413	−	3.23413i	−0.262323	−	0.262323i
$153$	0.781072	+	2.68928i	0.0631459	+	0.217415i
$154$		−	5.11849i		−	0.412459i
$155$		0			0
$156$	5.61057	−	3.31778i	0.449205	−	0.265635i
$157$	−8.84559	+	8.84559i	−0.705955	+	0.705955i	−0.965682	−	0.259727i	$-0.916367\pi$
$157$	−8.84559	+	8.84559i	−0.705955	+	0.705955i	0.259727	+	0.965682i	$0.416367\pi$
$158$	5.57176	−	5.57176i	0.443265	−	0.443265i
$159$	−1.16225	+	0.687287i	−0.0921721	+	0.0545054i
$160$		0			0
$161$			1.29407i			0.101987i
$162$	−1.96471	+	8.78293i	−0.154362	+	0.690052i
$163$	9.97183	+	9.97183i	0.781054	+	0.781054i	0.980009	−	0.198955i	$-0.0637546\pi$
$163$	9.97183	+	9.97183i	0.781054	+	0.781054i	−0.198955	+	0.980009i	$0.563755\pi$
$164$	−2.55167			−0.199252
$165$		0			0
$166$	5.16678			0.401020
$167$	−1.53541	−	1.53541i	−0.118814	−	0.118814i	0.645200	−	0.764014i	$-0.276774\pi$
$167$	−1.53541	−	1.53541i	−0.118814	−	0.118814i	−0.764014	+	0.645200i	$0.776774\pi$
$168$	0.430811	−	1.67762i	0.0332378	−	0.129431i
$169$			1.16205i			0.0893887i
$170$		0			0
$171$	−6.61124	+	12.0235i	−0.505574	+	0.919460i
$172$	1.01688	−	1.01688i	0.0775362	−	0.0775362i
$173$	6.82152	−	6.82152i	0.518631	−	0.518631i	−0.398526	−	0.917157i	$-0.630478\pi$
$173$	6.82152	−	6.82152i	0.518631	−	0.518631i	0.917157	+	0.398526i	$0.130478\pi$
$174$	7.67937	+	12.9863i	0.582172	+	0.984489i
$175$		0			0
$176$		−	5.11849i		−	0.385820i
$177$	−2.28499	−	0.586784i	−0.171750	−	0.0441054i
$178$	3.99613	+	3.99613i	0.299523	+	0.299523i
$179$	−9.67016			−0.722782			−0.361391	−	0.932414i	$-0.617698\pi$
$179$	−9.67016			−0.722782			−0.361391	+	0.932414i	$0.617698\pi$
$180$		0			0
$181$	−20.0487			−1.49020			−0.745102	−	0.666950i	$-0.767599\pi$
$181$	−20.0487			−1.49020			−0.745102	+	0.666950i	$0.767599\pi$
$182$	2.66102	+	2.66102i	0.197248	+	0.197248i
$183$	13.5777	+	3.48675i	1.00369	+	0.257748i
$184$			1.29407i			0.0953999i
$185$		0			0
$186$	−8.69760	−	14.7082i	−0.637739	−	1.07846i
$187$	−3.37853	+	3.37853i	−0.247062	+	0.247062i
$188$	−2.54338	+	2.54338i	−0.185495	+	0.185495i
$189$	−5.19361	+	0.162584i	−0.377779	+	0.0118262i
$190$		0			0
$191$		−	20.5852i		−	1.48950i	−0.667346	−	0.744748i	$-0.732570\pi$
$191$		−	20.5852i		−	1.48950i	0.667346	−	0.744748i	$-0.267430\pi$
$192$	0.430811	−	1.67762i	0.0310911	−	0.121072i
$193$	3.33427	+	3.33427i	0.240006	+	0.240006i	0.816852	−	0.576847i	$-0.195717\pi$
$193$	3.33427	+	3.33427i	0.240006	+	0.240006i	−0.576847	+	0.816852i	$0.695717\pi$
$194$	−5.33124			−0.382761
$195$		0			0
$196$	1.00000			0.0714286
$197$	12.0863	+	12.0863i	0.861114	+	0.861114i	0.991468	−	0.130354i	$-0.0416113\pi$
$197$	12.0863	+	12.0863i	0.861114	+	0.861114i	−0.130354	+	0.991468i	$0.541611\pi$
$198$	−14.7461	+	4.28284i	−1.04796	+	0.304368i
$199$			13.4749i			0.955210i	0.878575	+	0.477605i	$0.158495\pi$
$199$			13.4749i			0.955210i	−0.878575	+	0.477605i	$0.841505\pi$
$200$		0			0
$201$	3.52841	−	2.08651i	0.248875	−	0.147171i
$202$	6.61272	−	6.61272i	0.465269	−	0.465269i
$203$	−6.15923	+	6.15923i	−0.432293	+	0.432293i
$204$	−1.39170	+	0.822971i	−0.0974383	+	0.0576195i
$205$		0			0
$206$		−	5.96736i		−	0.415766i
$207$	3.72814	−	1.08280i	0.259124	−	0.0752596i
$208$	2.66102	+	2.66102i	0.184509	+	0.184509i
$209$	−23.4107			−1.61935
$210$		0			0
$211$	−20.9033			−1.43904			−0.719521	−	0.694471i	$-0.755638\pi$
$211$	−20.9033			−1.43904			−0.719521	+	0.694471i	$0.755638\pi$
$212$	−0.551238	−	0.551238i	−0.0378592	−	0.0378592i
$213$	−1.56348	+	6.08834i	−0.107128	+	0.417166i
$214$		−	13.9207i		−	0.951597i
$215$		0			0
$216$	−5.19361	+	0.162584i	−0.353380	+	0.0110624i
$217$	6.97590	−	6.97590i	0.473555	−	0.473555i
$218$	7.83271	−	7.83271i	0.530498	−	0.530498i
$219$	−7.42206	−	12.5512i	−0.501537	−	0.848130i
$220$		0			0
$221$		−	3.51288i		−	0.236302i
$222$	19.6961	+	5.05796i	1.32192	+	0.339468i
$223$	3.30682	+	3.30682i	0.221441	+	0.221441i	0.809105	−	0.587664i	$-0.199952\pi$
$223$	3.30682	+	3.30682i	0.221441	+	0.221441i	−0.587664	+	0.809105i	$0.699952\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	9.64242			0.641404
$227$	−19.6412	−	19.6412i	−1.30363	−	1.30363i	−0.925926	−	0.377706i	$-0.876713\pi$
$227$	−19.6412	−	19.6412i	−1.30363	−	1.30363i	−0.377706	−	0.925926i	$-0.623287\pi$
$228$	−7.67301	−	1.97043i	−0.508158	−	0.130495i
$229$			1.41048i			0.0932069i	0.998913	+	0.0466034i	$0.0148397\pi$
$229$			1.41048i			0.0932069i	−0.998913	+	0.0466034i	$0.985160\pi$
$230$		0			0
$231$	−4.51259	−	7.63107i	−0.296906	−	0.502088i
$232$	−6.15923	+	6.15923i	−0.404373	+	0.404373i
$233$	9.42431	−	9.42431i	0.617407	−	0.617407i	−0.327459	−	0.944866i	$-0.606192\pi$
$233$	9.42431	−	9.42431i	0.617407	−	0.617407i	0.944866	+	0.327459i	$0.106192\pi$
$234$	5.43968	−	9.89284i	0.355603	−	0.646715i
$235$		0			0
$236$		−	1.36204i		−	0.0886615i
$237$	3.39465	−	13.2191i	0.220506	−	0.858670i
$238$	−0.660063	−	0.660063i	−0.0427856	−	0.0427856i
$239$	23.5817			1.52538			0.762688	−	0.646767i	$-0.223879\pi$
$239$	23.5817			1.52538			0.762688	+	0.646767i	$0.223879\pi$
$240$		0			0
$241$	24.3495			1.56849			0.784245	−	0.620451i	$-0.213050\pi$
$241$	24.3495			1.56849			0.784245	+	0.620451i	$0.213050\pi$
$242$	−10.7472	−	10.7472i	−0.690859	−	0.690859i
$243$	4.81409	+	14.8265i	0.308824	+	0.951119i
$244$			8.09345i			0.518130i
$245$		0			0
$246$	−3.80425	+	2.24962i	−0.242550	+	0.143430i
$247$	12.1709	−	12.1709i	0.774413	−	0.774413i
$248$	6.97590	−	6.97590i	0.442970	−	0.442970i
$249$	7.70308	−	4.55517i	0.488163	−	0.288672i
$250$		0			0
$251$		−	16.0687i		−	1.01425i	−0.861873	−	0.507123i	$-0.830709\pi$
$251$		−	16.0687i		−	1.01425i	0.861873	−	0.507123i	$-0.169291\pi$
$252$	−0.836740	−	2.88095i	−0.0527097	−	0.181483i
$253$	4.68364	+	4.68364i	0.294458	+	0.294458i
$254$	−3.52325			−0.221068
$255$		0			0
$256$	1.00000			0.0625000
$257$	−13.3686	−	13.3686i	−0.833912	−	0.833912i	0.154138	−	0.988049i	$-0.450740\pi$
$257$	−13.3686	−	13.3686i	−0.833912	−	0.833912i	−0.988049	+	0.154138i	$0.950740\pi$
$258$	0.619543	−	2.41255i	0.0385710	−	0.150199i
$259$			11.7405i			0.729522i
$260$		0			0
$261$	22.8981	+	12.5908i	1.41736	+	0.779348i
$262$	−1.45318	+	1.45318i	−0.0897778	+	0.0897778i
$263$	−16.6109	+	16.6109i	−1.02427	+	1.02427i	−0.0245723	+	0.999698i	$0.507822\pi$
$263$	−16.6109	+	16.6109i	−1.02427	+	1.02427i	−0.999698	+	0.0245723i	$0.992178\pi$
$264$	−4.51259	−	7.63107i	−0.277730	−	0.469660i
$265$		0			0
$266$		−	4.57375i		−	0.280435i
$267$	9.48086	+	2.43468i	0.580219	+	0.149000i
$268$	1.67348	+	1.67348i	0.102224	+	0.102224i
$269$	1.05024			0.0640340			0.0320170	−	0.999487i	$-0.489807\pi$
$269$	1.05024			0.0640340			0.0320170	+	0.999487i	$0.489807\pi$
$270$		0			0
$271$	25.6890			1.56050			0.780249	−	0.625469i	$-0.215093\pi$
$271$	25.6890			1.56050			0.780249	+	0.625469i	$0.215093\pi$
$272$	−0.660063	−	0.660063i	−0.0400222	−	0.0400222i
$273$	6.31330	+	1.62125i	0.382098	+	0.0981226i
$274$			12.3712i			0.747371i
$275$		0			0
$276$	1.14088	+	1.92931i	0.0686730	+	0.116131i
$277$	−1.71978	+	1.71978i	−0.103332	+	0.103332i	−0.756883	−	0.653551i	$-0.773279\pi$
$277$	−1.71978	+	1.71978i	−0.103332	+	0.103332i	0.653551	+	0.756883i	$0.273279\pi$
$278$	−0.0355050	+	0.0355050i	−0.00212945	+	0.00212945i
$279$	−25.9342	−	14.2602i	−1.55264	−	0.853736i
$280$		0			0
$281$			29.3325i			1.74983i	0.484275	+	0.874916i	$0.339083\pi$
$281$			29.3325i			1.74983i	−0.484275	+	0.874916i	$0.660917\pi$
$282$	−1.54958	+	6.03419i	−0.0922760	+	0.359331i
$283$	0.440015	+	0.440015i	0.0261562	+	0.0261562i	0.720064	−	0.693908i	$-0.244112\pi$
$283$	0.440015	+	0.440015i	0.0261562	+	0.0261562i	−0.693908	+	0.720064i	$0.744112\pi$
$284$	−3.62916			−0.215351
$285$		0			0
$286$	19.2621			1.13899
$287$	−1.80431	−	1.80431i	−0.106505	−	0.106505i
$288$	−0.836740	−	2.88095i	−0.0493054	−	0.169762i
$289$		−	16.1286i		−	0.948743i
$290$		0			0
$291$	−7.94827	+	4.70016i	−0.465936	+	0.275528i
$292$	5.95286	−	5.95286i	0.348365	−	0.348365i
$293$	−6.16657	+	6.16657i	−0.360255	+	0.360255i	−0.863907	−	0.503652i	$-0.831989\pi$
$293$	−6.16657	+	6.16657i	−0.360255	+	0.360255i	0.503652	+	0.863907i	$0.331989\pi$
$294$	1.49088	−	0.881625i	0.0869502	−	0.0514174i
$295$		0			0
$296$			11.7405i			0.682405i
$297$	−18.2089	+	19.3858i	−1.05659	+	1.12488i
$298$	8.33106	+	8.33106i	0.482605	+	0.482605i
$299$	−4.86990			−0.281634
$300$		0			0
$301$	1.43808			0.0828897
$302$	9.22114	+	9.22114i	0.530617	+	0.530617i
$303$	4.02886	−	15.6887i	0.231452	−	0.901295i
$304$		−	4.57375i		−	0.262323i
$305$		0			0
$306$	−1.34931	+	2.45391i	−0.0771348	+	0.140281i
$307$	11.9319	−	11.9319i	0.680991	−	0.680991i	−0.279232	−	0.960224i	$-0.590080\pi$
$307$	11.9319	−	11.9319i	0.680991	−	0.680991i	0.960224	+	0.279232i	$0.0900800\pi$
$308$	3.61932	−	3.61932i	0.206230	−	0.206230i
$309$	−5.26098	−	8.89665i	−0.299287	−	0.506113i
$310$		0			0
$311$			11.6450i			0.660328i	0.943924	+	0.330164i	$0.107104\pi$
$311$			11.6450i			0.660328i	−0.943924	+	0.330164i	$0.892896\pi$
$312$	6.31330	+	1.62125i	0.357420	+	0.0917853i
$313$	−21.4297	−	21.4297i	−1.21128	−	1.21128i	−0.970606	−	0.240672i	$-0.922632\pi$
$313$	−21.4297	−	21.4297i	−1.21128	−	1.21128i	−0.240672	−	0.970606i	$-0.577368\pi$
$314$	−12.5096			−0.705955
$315$		0			0
$316$	7.87966			0.443265
$317$	10.2198	+	10.2198i	0.574002	+	0.574002i	0.933244	−	0.359242i	$-0.116965\pi$
$317$	10.2198	+	10.2198i	0.574002	+	0.574002i	−0.359242	+	0.933244i	$0.616965\pi$
$318$	−1.30782	−	0.335847i	−0.0733388	−	0.0188334i
$319$			44.5844i			2.49625i
$320$		0			0
$321$	−12.2728	−	20.7541i	−0.685001	−	1.15838i
$322$	−0.915044	+	0.915044i	−0.0509934	+	0.0509934i
$323$	−3.01897	+	3.01897i	−0.167980	+	0.167980i
$324$	−7.59973	+	4.82121i	−0.422207	+	0.267845i
$325$		0			0
$326$			14.1023i			0.781054i
$327$	4.77215	−	18.5832i	0.263901	−	1.02765i
$328$	−1.80431	−	1.80431i	−0.0996261	−	0.0996261i
$329$	−3.59688			−0.198302
$330$		0			0
$331$	8.10042			0.445240			0.222620	−	0.974905i	$-0.428539\pi$
$331$	8.10042			0.445240			0.222620	+	0.974905i	$0.428539\pi$
$332$	3.65347	+	3.65347i	0.200510	+	0.200510i
$333$	33.8239	−	9.82378i	1.85354	−	0.538340i
$334$		−	2.17140i		−	0.118814i
$335$		0			0
$336$	1.49088	−	0.881625i	0.0813344	−	0.0480966i
$337$	−0.775056	+	0.775056i	−0.0422200	+	0.0422200i	−0.727902	−	0.685682i	$-0.759504\pi$
$337$	−0.775056	+	0.775056i	−0.0422200	+	0.0422200i	0.685682	+	0.727902i	$0.259504\pi$
$338$	−0.821696	+	0.821696i	−0.0446944	+	0.0446944i
$339$	14.3757	−	8.50100i	0.780783	−	0.461711i
$340$		0			0
$341$		−	50.4960i		−	2.73451i
$342$	−13.1768	+	3.82704i	−0.712517	+	0.206943i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	1.43808			0.0775362
$345$		0			0
$346$	9.64709			0.518631
$347$	6.04424	+	6.04424i	0.324472	+	0.324472i	0.850480	−	0.526008i	$-0.176312\pi$
$347$	6.04424	+	6.04424i	0.324472	+	0.324472i	−0.526008	+	0.850480i	$0.676312\pi$
$348$	−3.75257	+	14.6128i	−0.201159	+	0.783331i
$349$		−	11.2187i		−	0.600525i	−0.953857	−	0.300263i	$-0.902926\pi$
$349$		−	11.2187i		−	0.600525i	0.953857	−	0.300263i	$-0.0970744\pi$
$350$		0			0
$351$	−0.611844	−	19.5448i	−0.0326578	−	1.04323i
$352$	3.61932	−	3.61932i	0.192910	−	0.192910i
$353$	13.1367	−	13.1367i	0.699198	−	0.699198i	−0.265040	−	0.964238i	$-0.585385\pi$
$353$	13.1367	−	13.1367i	0.699198	−	0.699198i	0.964238	+	0.265040i	$0.0853850\pi$
$354$	−1.20081	−	2.03065i	−0.0638225	−	0.107928i
$355$		0			0
$356$			5.65138i			0.299523i
$357$	−1.56601	−	0.402150i	−0.0828819	−	0.0212840i
$358$	−6.83784	−	6.83784i	−0.361391	−	0.361391i
$359$	−4.10021			−0.216401			−0.108200	−	0.994129i	$-0.534509\pi$
$359$	−4.10021			−0.216401			−0.108200	+	0.994129i	$0.534509\pi$
$360$		0			0
$361$	−1.91923			−0.101012
$362$	−14.1765	−	14.1765i	−0.745102	−	0.745102i
$363$	−25.4979	−	6.54786i	−1.33829	−	0.343674i
$364$			3.76325i			0.197248i
$365$		0			0
$366$	7.13539	+	12.0664i	0.372973	+	0.630721i
$367$	−22.3293	+	22.3293i	−1.16558	+	1.16558i	−0.182348	+	0.983234i	$0.558370\pi$
$367$	−22.3293	+	22.3293i	−1.16558	+	1.16558i	−0.983234	+	0.182348i	$0.941630\pi$
$368$	−0.915044	+	0.915044i	−0.0477000	+	0.0477000i
$369$	−3.68838	+	6.70785i	−0.192009	+	0.349196i
$370$		0			0
$371$		−	0.779568i		−	0.0404732i
$372$	4.25014	−	16.5504i	0.220359	−	0.858098i
$373$	−16.1487	−	16.1487i	−0.836148	−	0.836148i	0.152202	−	0.988349i	$-0.451364\pi$
$373$	−16.1487	−	16.1487i	−0.836148	−	0.836148i	−0.988349	+	0.152202i	$0.951364\pi$
$374$	−4.77796			−0.247062
$375$		0			0
$376$	−3.59688			−0.185495
$377$	−23.1787	−	23.1787i	−1.19377	−	1.19377i
$378$	−3.78740	−	3.55747i	−0.194803	−	0.182977i
$379$			17.9824i			0.923694i	0.886960	+	0.461847i	$0.152813\pi$
$379$			17.9824i			0.923694i	−0.886960	+	0.461847i	$0.847187\pi$
$380$		0			0
$381$	−5.25275	+	3.10618i	−0.269107	+	0.159135i
$382$	14.5560	−	14.5560i	0.744748	−	0.744748i
$383$	−12.8721	+	12.8721i	−0.657733	+	0.657733i	−0.954843	−	0.297110i	$-0.903977\pi$
$383$	−12.8721	+	12.8721i	−0.657733	+	0.657733i	0.297110	+	0.954843i	$0.403977\pi$
$384$	1.49088	−	0.881625i	0.0760814	−	0.0449902i
$385$		0			0
$386$			4.71537i			0.240006i
$387$	−1.20330	−	4.14304i	−0.0611672	−	0.210603i
$388$	−3.76976	−	3.76976i	−0.191380	−	0.191380i
$389$	7.82278			0.396631			0.198315	−	0.980138i	$-0.436453\pi$
$389$	7.82278			0.396631			0.198315	+	0.980138i	$0.436453\pi$
$390$		0			0
$391$	1.20797			0.0610899
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$	−0.885364	+	3.44768i	−0.0446607	+	0.173913i
$394$			17.0926i			0.861114i
$395$		0			0
$396$	−13.4555	−	7.39864i	−0.676164	−	0.371796i
$397$	−15.1217	+	15.1217i	−0.758937	+	0.758937i	−0.976129	−	0.217192i	$-0.930310\pi$
$397$	−15.1217	+	15.1217i	−0.758937	+	0.758937i	0.217192	+	0.976129i	$0.430310\pi$
$398$	−9.52819	+	9.52819i	−0.477605	+	0.477605i
$399$	−4.03234	−	6.81894i	−0.201869	−	0.341374i
$400$		0			0
$401$		−	17.0712i		−	0.852493i	−0.904607	−	0.426246i	$-0.859836\pi$
$401$		−	17.0712i		−	0.852493i	0.904607	−	0.426246i	$-0.140164\pi$
$402$	3.97035	+	1.01958i	0.198023	+	0.0508522i
$403$	26.2521	+	26.2521i	1.30771	+	1.30771i
$404$	9.35180			0.465269
$405$		0			0
$406$	−8.71047			−0.432293
$407$	42.4927	+	42.4927i	2.10629	+	2.10629i
$408$	−1.56601	−	0.402150i	−0.0775289	−	0.0199094i
$409$			1.08737i			0.0537671i	0.999639	+	0.0268836i	$0.00855834\pi$
$409$			1.08737i			0.0537671i	−0.999639	+	0.0268836i	$0.991442\pi$
$410$		0			0
$411$	10.9068	+	18.4440i	0.537991	+	0.909777i
$412$	4.21956	−	4.21956i	0.207883	−	0.207883i
$413$	0.963111	−	0.963111i	0.0473916	−	0.0473916i
$414$	3.40185	+	1.87054i	0.167192	+	0.0919321i
$415$		0			0
$416$			3.76325i			0.184509i
$417$	−0.0216317	+	0.0842359i	−0.00105931	+	0.00412505i
$418$	−16.5539	−	16.5539i	−0.809676	−	0.809676i
$419$	35.7634			1.74715			0.873577	−	0.486685i	$-0.161794\pi$
$419$	35.7634			1.74715			0.873577	+	0.486685i	$0.161794\pi$
$420$		0			0
$421$	−36.8504			−1.79598			−0.897989	−	0.440018i	$-0.854972\pi$
$421$	−36.8504			−1.79598			−0.897989	+	0.440018i	$0.854972\pi$
$422$	−14.7809	−	14.7809i	−0.719521	−	0.719521i
$423$	3.00965	+	10.3624i	0.146334	+	0.503839i
$424$		−	0.779568i		−	0.0378592i
$425$		0			0
$426$	−5.41066	+	3.19956i	−0.262147	+	0.155019i
$427$	−5.72293	+	5.72293i	−0.276952	+	0.276952i
$428$	9.84339	−	9.84339i	0.475798	−	0.475798i
$429$	28.7176	−	16.9820i	1.38650	−	0.819898i
$430$		0			0
$431$		−	8.14190i		−	0.392181i	−0.980586	−	0.196091i	$-0.937175\pi$
$431$		−	8.14190i		−	0.392181i	0.980586	−	0.196091i	$-0.0628247\pi$
$432$	−3.78740	−	3.55747i	−0.182221	−	0.171159i
$433$	−3.87199	−	3.87199i	−0.186076	−	0.186076i	0.607921	−	0.793997i	$-0.292004\pi$
$433$	−3.87199	−	3.87199i	−0.186076	−	0.186076i	−0.793997	+	0.607921i	$0.792004\pi$
$434$	9.86542			0.473555
$435$		0			0
$436$	11.0771			0.530498
$437$	4.18519	+	4.18519i	0.200205	+	0.200205i
$438$	3.62684	−	14.1232i	0.173297	−	0.674833i
$439$		−	24.4939i		−	1.16903i	−0.811383	−	0.584515i	$-0.801285\pi$
$439$		−	24.4939i		−	1.16903i	0.811383	−	0.584515i	$-0.198715\pi$
$440$		0			0
$441$	1.44547	−	2.62880i	0.0688321	−	0.125181i
$442$	2.48398	−	2.48398i	0.118151	−	0.118151i
$443$	−16.7488	+	16.7488i	−0.795760	+	0.795760i	−0.982424	−	0.186664i	$-0.940232\pi$
$443$	−16.7488	+	16.7488i	−0.795760	+	0.795760i	0.186664	+	0.982424i	$0.440232\pi$
$444$	10.3508	+	17.5038i	0.491225	+	0.830693i
$445$		0			0
$446$			4.67655i			0.221441i
$447$	19.7655	+	5.07578i	0.934877	+	0.240076i
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	−14.5848			−0.688297			−0.344149	−	0.938915i	$-0.611832\pi$
$449$	−14.5848			−0.688297			−0.344149	+	0.938915i	$0.611832\pi$
$450$		0			0
$451$	−13.0607			−0.615004
$452$	6.81822	+	6.81822i	0.320702	+	0.320702i
$453$	21.8773	+	5.61807i	1.02788	+	0.263960i
$454$		−	27.7768i		−	1.30363i
$455$		0			0
$456$	−4.03234	−	6.81894i	−0.188831	−	0.319326i
$457$	−8.72594	+	8.72594i	−0.408182	+	0.408182i	−0.881104	−	0.472922i	$-0.843199\pi$
$457$	−8.72594	+	8.72594i	−0.408182	+	0.408182i	0.472922	+	0.881104i	$0.343199\pi$
$458$	−0.997357	+	0.997357i	−0.0466034	+	0.0466034i
$459$	0.151767	+	4.84808i	0.00708389	+	0.226289i
$460$		0			0
$461$			19.9418i			0.928784i	0.885630	+	0.464392i	$0.153727\pi$
$461$			19.9418i			0.928784i	−0.885630	+	0.464392i	$0.846273\pi$
$462$	2.20510	−	8.58686i	0.102591	−	0.399497i
$463$	−9.70556	−	9.70556i	−0.451055	−	0.451055i	0.444649	−	0.895705i	$-0.353328\pi$
$463$	−9.70556	−	9.70556i	−0.451055	−	0.451055i	−0.895705	+	0.444649i	$0.853328\pi$
$464$	−8.71047			−0.404373
$465$		0			0
$466$	13.3280			0.617407
$467$	−5.73494	−	5.73494i	−0.265382	−	0.265382i	0.561854	−	0.827236i	$-0.310088\pi$
$467$	−5.73494	−	5.73494i	−0.265382	−	0.265382i	−0.827236	+	0.561854i	$0.810088\pi$
$468$	10.8417	−	3.14886i	0.501159	−	0.145556i
$469$			2.36666i			0.109282i
$470$		0			0
$471$	−18.6503	+	11.0287i	−0.859360	+	0.508177i
$472$	0.963111	−	0.963111i	0.0443308	−	0.0443308i
$473$	5.20488	−	5.20488i	0.239320	−	0.239320i
$474$	11.7477	−	6.94691i	0.539588	−	0.319082i
$475$		0			0
$476$		−	0.933471i		−	0.0427856i
$477$	−2.24590	+	0.652296i	−0.102833	+	0.0298666i
$478$	16.6748	+	16.6748i	0.762688	+	0.762688i
$479$	−9.59046			−0.438199			−0.219100	−	0.975702i	$-0.570312\pi$
$479$	−9.59046			−0.438199			−0.219100	+	0.975702i	$0.570312\pi$
$480$		0			0
$481$	−44.1826			−2.01455
$482$	17.2177	+	17.2177i	0.784245	+	0.784245i
$483$	−0.557499	+	2.17095i	−0.0253671	+	0.0987817i
$484$		−	15.1989i		−	0.690859i
$485$		0			0
$486$	−7.07983	+	13.8880i	−0.321147	+	0.629972i
$487$	−14.2720	+	14.2720i	−0.646725	+	0.646725i	−0.952200	−	0.305475i	$-0.901185\pi$
$487$	−14.2720	+	14.2720i	−0.646725	+	0.646725i	0.305475	+	0.952200i	$0.401185\pi$
$488$	−5.72293	+	5.72293i	−0.259065	+	0.259065i
$489$	12.4329	+	21.0249i	0.562237	+	0.950779i
$490$		0			0
$491$			28.6728i			1.29398i	0.762497	+	0.646992i	$0.223973\pi$
$491$			28.6728i			1.29398i	−0.762497	+	0.646992i	$0.776027\pi$
$492$	−4.28073	−	1.09929i	−0.192990	−	0.0495598i
$493$	5.74946	+	5.74946i	0.258943	+	0.258943i
$494$	17.2122			0.774413
$495$		0			0
$496$	9.86542			0.442970
$497$	−2.56620	−	2.56620i	−0.115110	−	0.115110i
$498$	8.66789	+	2.22591i	0.388417	+	0.0997454i
$499$			14.3520i			0.642483i	0.946997	+	0.321242i	$0.104100\pi$
$499$			14.3520i			0.642483i	−0.946997	+	0.321242i	$0.895900\pi$
$500$		0			0
$501$	−1.91436	−	3.23730i	−0.0855273	−	0.144632i
$502$	11.3623	−	11.3623i	0.507123	−	0.507123i
$503$	−23.0425	+	23.0425i	−1.02741	+	1.02741i	−0.0277992	+	0.999614i	$0.508850\pi$
$503$	−23.0425	+	23.0425i	−1.02741	+	1.02741i	−0.999614	+	0.0277992i	$0.991150\pi$
$504$	1.44547	−	2.62880i	0.0643865	−	0.117096i
$505$		0			0
$506$			6.62367i			0.294458i
$507$	−0.500626	+	1.94948i	−0.0222336	+	0.0865795i
$508$	−2.49131	−	2.49131i	−0.110534	−	0.110534i
$509$	−36.0312			−1.59706			−0.798528	−	0.601957i	$-0.794388\pi$
$509$	−36.0312			−1.59706			−0.798528	+	0.601957i	$0.794388\pi$
$510$		0			0
$511$	8.41861			0.372418
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−16.2710	+	17.3226i	−0.718382	+	0.764813i
$514$		−	18.9061i		−	0.833912i
$515$		0			0
$516$	2.14402	−	1.26785i	0.0943850	−	0.0558140i
$517$	−13.0182	+	13.0182i	−0.572542	+	0.572542i
$518$	−8.30181	+	8.30181i	−0.364761	+	0.364761i
$519$	14.3827	−	8.50512i	0.631331	−	0.373333i
$520$		0			0
$521$		−	6.46917i		−	0.283420i	−0.989908	−	0.141710i	$-0.954740\pi$
$521$		−	6.46917i		−	0.283420i	0.989908	−	0.141710i	$-0.0452600\pi$
$522$	7.28840	+	25.0944i	0.319005	+	1.09835i
$523$	7.55711	+	7.55711i	0.330449	+	0.330449i	0.852757	−	0.522308i	$-0.174929\pi$
$523$	7.55711	+	7.55711i	0.330449	+	0.330449i	−0.522308	+	0.852757i	$0.674929\pi$
$524$	−2.05511			−0.0897778
$525$		0			0
$526$	−23.4913			−1.02427
$527$	−6.51180	−	6.51180i	−0.283659	−	0.283659i
$528$	2.20510	−	8.58686i	0.0959648	−	0.373695i
$529$			21.3254i			0.927191i
$530$		0			0
$531$	−3.58055	−	1.96880i	−0.155382	−	0.0854386i
$532$	3.23413	−	3.23413i	0.140217	−	0.140217i
$533$	6.79005	−	6.79005i	0.294110	−	0.294110i
$534$	4.98240	+	8.42556i	0.215609	+	0.364609i
$535$		0			0
$536$			2.36666i			0.102224i
$537$	−16.2228	−	4.16602i	−0.700067	−	0.179777i
$538$	0.742629	+	0.742629i	0.0320170	+	0.0320170i
$539$	5.11849			0.220469
$540$		0			0
$541$	−23.7219			−1.01988			−0.509942	−	0.860209i	$-0.670333\pi$
$541$	−23.7219			−1.01988			−0.509942	+	0.860209i	$0.670333\pi$
$542$	18.1649	+	18.1649i	0.780249	+	0.780249i
$543$	−33.6340	−	8.63719i	−1.44337	−	0.370657i
$544$		−	0.933471i		−	0.0400222i
$545$		0			0
$546$	3.31778	+	5.61057i	0.141988	+	0.240110i
$547$	−17.2270	+	17.2270i	−0.736574	+	0.736574i	−0.971913	−	0.235339i	$-0.924380\pi$
$547$	−17.2270	+	17.2270i	−0.736574	+	0.736574i	0.235339	+	0.971913i	$0.424380\pi$
$548$	−8.74776	+	8.74776i	−0.373686	+	0.373686i
$549$	21.2761	+	11.6989i	0.908041	+	0.499295i
$550$		0			0
$551$			39.8396i			1.69722i
$552$	−0.557499	+	2.17095i	−0.0237287	+	0.0924018i
$553$	5.57176	+	5.57176i	0.236935	+	0.236935i
$554$	−2.43214			−0.103332
$555$		0			0
$556$	−0.0502116			−0.00212945
$557$	7.02290	+	7.02290i	0.297570	+	0.297570i	0.840061	−	0.542491i	$-0.182519\pi$
$557$	7.02290	+	7.02290i	0.297570	+	0.297570i	−0.542491	+	0.840061i	$0.682519\pi$
$558$	−8.25479	−	28.4218i	−0.349453	−	1.20319i
$559$			5.41187i			0.228898i
$560$		0			0
$561$	−7.12338	+	4.21237i	−0.300749	+	0.177846i
$562$	−20.7412	+	20.7412i	−0.874916	+	0.874916i
$563$	16.2207	−	16.2207i	0.683621	−	0.683621i	−0.277194	−	0.960814i	$-0.589404\pi$
$563$	16.2207	−	16.2207i	0.683621	−	0.683621i	0.960814	+	0.277194i	$0.0894043\pi$
$564$	−5.36253	+	3.17110i	−0.225803	+	0.133527i
$565$		0			0
$566$			0.622275i			0.0261562i
$567$	−8.78293	−	1.96471i	−0.368848	−	0.0825102i
$568$	−2.56620	−	2.56620i	−0.107675	−	0.107675i
$569$	−15.0582			−0.631272			−0.315636	−	0.948880i	$-0.602218\pi$
$569$	−15.0582			−0.631272			−0.315636	+	0.948880i	$0.602218\pi$
$570$		0			0
$571$	−11.1090			−0.464896			−0.232448	−	0.972609i	$-0.574674\pi$
$571$	−11.1090			−0.464896			−0.232448	+	0.972609i	$0.574674\pi$
$572$	13.6204	+	13.6204i	0.569497	+	0.569497i
$573$	8.86836	−	34.5342i	0.370481	−	1.44269i
$574$		−	2.55167i		−	0.106505i
$575$		0			0
$576$	1.44547	−	2.62880i	0.0602281	−	0.109533i
$577$	12.2383	−	12.2383i	0.509487	−	0.509487i	−0.404882	−	0.914369i	$-0.632687\pi$
$577$	12.2383	−	12.2383i	0.509487	−	0.509487i	0.914369	+	0.404882i	$0.132687\pi$
$578$	11.4047	−	11.4047i	0.474372	−	0.474372i
$579$	4.15719	+	7.03007i	0.172767	+	0.292160i
$580$		0			0
$581$			5.16678i			0.214354i
$582$	−8.94379	−	2.29676i	−0.370732	−	0.0952038i
$583$	−2.82150	−	2.82150i	−0.116855	−	0.116855i
$584$	8.41861			0.348365
$585$		0			0
$586$	−8.72085			−0.360255
$587$	−1.80620	−	1.80620i	−0.0745497	−	0.0745497i	0.668849	−	0.743398i	$-0.266787\pi$
$587$	−1.80620	−	1.80620i	−0.0745497	−	0.0745497i	−0.743398	+	0.668849i	$0.766787\pi$
$588$	1.67762	+	0.430811i	0.0691838	+	0.0177664i
$589$		−	45.1220i		−	1.85922i
$590$		0			0
$591$	15.0693	+	25.4831i	0.619868	+	1.04824i
$592$	−8.30181	+	8.30181i	−0.341202	+	0.341202i
$593$	−28.3207	+	28.3207i	−1.16299	+	1.16299i	−0.179175	+	0.983817i	$0.557343\pi$
$593$	−28.3207	+	28.3207i	−1.16299	+	1.16299i	−0.983817	+	0.179175i	$0.942657\pi$
$594$	−26.5834	+	0.832183i	−1.09073	+	0.0341449i
$595$		0			0
$596$			11.7819i			0.482605i
$597$	−5.80514	+	22.6057i	−0.237589	+	0.925191i
$598$	−3.44354	−	3.44354i	−0.140817	−	0.140817i
$599$	8.99206			0.367405			0.183703	−	0.982982i	$-0.441192\pi$
$599$	8.99206			0.367405			0.183703	+	0.982982i	$0.441192\pi$
$600$		0			0
$601$	1.77419			0.0723709			0.0361855	−	0.999345i	$-0.488479\pi$
$601$	1.77419			0.0723709			0.0361855	+	0.999345i	$0.488479\pi$
$602$	1.01688	+	1.01688i	0.0414449	+	0.0414449i
$603$	6.81822	−	1.98028i	0.277659	−	0.0806431i
$604$			13.0407i			0.530617i
$605$		0			0
$606$	13.9425	−	8.24478i	0.566374	−	0.334921i
$607$	22.9565	−	22.9565i	0.931777	−	0.931777i	−0.0660402	−	0.997817i	$-0.521037\pi$
$607$	22.9565	−	22.9565i	0.931777	−	0.931777i	0.997817	+	0.0660402i	$0.0210365\pi$
$608$	3.23413	−	3.23413i	0.131161	−	0.131161i
$609$	−12.9863	+	7.67937i	−0.526232	+	0.311184i
$610$		0			0
$611$		−	13.5360i		−	0.547606i
$612$	−2.68928	+	0.781072i	−0.108708	+	0.0315730i
$613$	−17.8179	−	17.8179i	−0.719657	−	0.719657i	0.248878	−	0.968535i	$-0.419938\pi$
$613$	−17.8179	−	17.8179i	−0.719657	−	0.719657i	−0.968535	+	0.248878i	$0.919938\pi$
$614$	16.8743			0.680991
$615$		0			0
$616$	5.11849			0.206230
$617$	−22.3285	−	22.3285i	−0.898910	−	0.898910i	0.0964302	−	0.995340i	$-0.469258\pi$
$617$	−22.3285	−	22.3285i	−0.898910	−	0.898910i	−0.995340	+	0.0964302i	$0.969258\pi$
$618$	2.57081	−	10.0110i	0.103413	−	0.402700i
$619$			44.8213i			1.80152i	0.434319	+	0.900759i	$0.356989\pi$
$619$			44.8213i			1.80152i	−0.434319	+	0.900759i	$0.643011\pi$
$620$		0			0
$621$	6.72088	−	0.210394i	0.269700	−	0.00844284i
$622$	−8.23427	+	8.23427i	−0.330164	+	0.330164i
$623$	−3.99613	+	3.99613i	−0.160102	+	0.160102i
$624$	3.31778	+	5.61057i	0.132817	+	0.224603i
$625$		0			0
$626$		−	30.3062i		−	1.21128i
$627$	−39.2742	−	10.0856i	−1.56846	−	0.402780i
$628$	−8.84559	−	8.84559i	−0.352977	−	0.352977i
$629$	10.9594			0.436982
$630$		0			0
$631$	30.1896			1.20183			0.600914	−	0.799314i	$-0.294804\pi$
$631$	30.1896			1.20183			0.600914	+	0.799314i	$0.294804\pi$
$632$	5.57176	+	5.57176i	0.221633	+	0.221633i
$633$	−35.0677	−	9.00537i	−1.39382	−	0.357931i
$634$			14.4530i			0.574002i
$635$		0			0
$636$	−0.687287	−	1.16225i	−0.0272527	−	0.0460861i
$637$	−2.66102	+	2.66102i	−0.105433	+	0.105433i
$638$	−31.5259	+	31.5259i	−1.24812	+	1.24812i
$639$	−5.24586	+	9.54034i	−0.207523	+	0.377410i
$640$		0			0
$641$			45.9893i			1.81647i	0.418462	+	0.908234i	$0.362569\pi$
$641$			45.9893i			1.81647i	−0.418462	+	0.908234i	$0.637431\pi$
$642$	5.99718	−	23.3535i	0.236690	−	0.921691i
$643$	6.36667	+	6.36667i	0.251077	+	0.251077i	0.821412	−	0.570335i	$-0.193187\pi$
$643$	6.36667	+	6.36667i	0.251077	+	0.251077i	−0.570335	+	0.821412i	$0.693187\pi$
$644$	−1.29407			−0.0509934
$645$		0			0
$646$	−4.26947			−0.167980
$647$	8.36361	+	8.36361i	0.328808	+	0.328808i	0.852133	−	0.523325i	$-0.175309\pi$
$647$	8.36361	+	8.36361i	0.328808	+	0.328808i	−0.523325	+	0.852133i	$0.675309\pi$
$648$	−8.78293	−	1.96471i	−0.345026	−	0.0771812i
$649$		−	6.97160i		−	0.273659i
$650$		0			0
$651$	14.7082	−	8.69760i	0.576460	−	0.340886i
$652$	−9.97183	+	9.97183i	−0.390527	+	0.390527i
$653$	12.5810	−	12.5810i	0.492334	−	0.492334i	−0.416707	−	0.909041i	$-0.636816\pi$
$653$	12.5810	−	12.5810i	0.492334	−	0.492334i	0.909041	+	0.416707i	$0.136816\pi$
$654$	16.5147	−	9.76588i	0.645777	−	0.381876i
$655$		0			0
$656$		−	2.55167i		−	0.0996261i
$657$	−7.04419	−	24.2536i	−0.274820	−	0.946223i
$658$	−2.54338	−	2.54338i	−0.0991512	−	0.0991512i
$659$	−9.08235			−0.353798			−0.176899	−	0.984229i	$-0.556607\pi$
$659$	−9.08235			−0.353798			−0.176899	+	0.984229i	$0.556607\pi$
$660$		0			0
$661$	4.47568			0.174084			0.0870420	−	0.996205i	$-0.472259\pi$
$661$	4.47568			0.174084			0.0870420	+	0.996205i	$0.472259\pi$
$662$	5.72786	+	5.72786i	0.222620	+	0.222620i
$663$	1.51339	−	5.89328i	0.0587752	−	0.228876i
$664$			5.16678i			0.200510i
$665$		0			0
$666$	30.8636	+	16.9706i	1.19594	+	0.657599i
$667$	7.97046	−	7.97046i	0.308618	−	0.308618i
$668$	1.53541	−	1.53541i	0.0594068	−	0.0594068i
$669$	4.12297	+	6.97220i	0.159403	+	0.269561i
$670$		0			0
$671$			41.4262i			1.59924i
$672$	1.67762	+	0.430811i	0.0647155	+	0.0166189i
$673$	11.5712	+	11.5712i	0.446035	+	0.446035i	0.894034	−	0.447999i	$-0.147863\pi$
$673$	11.5712	+	11.5712i	0.446035	+	0.446035i	−0.447999	+	0.894034i	$0.647863\pi$
$674$	−1.09609			−0.0422200
$675$		0			0
$676$	−1.16205			−0.0446944
$677$	−12.8813	−	12.8813i	−0.495067	−	0.495067i	0.414831	−	0.909898i	$-0.363841\pi$
$677$	−12.8813	−	12.8813i	−0.495067	−	0.495067i	−0.909898	+	0.414831i	$0.863841\pi$
$678$	16.1763	+	4.15406i	0.621247	+	0.159536i
$679$		−	5.33124i		−	0.204594i
$680$		0			0
$681$	−24.4888	−	41.4121i	−0.938411	−	1.58691i
$682$	35.7061	−	35.7061i	1.36726	−	1.36726i
$683$	−4.66122	+	4.66122i	−0.178357	+	0.178357i	−0.790639	−	0.612282i	$-0.790252\pi$
$683$	−4.66122	+	4.66122i	−0.178357	+	0.178357i	0.612282	+	0.790639i	$0.290252\pi$
$684$	−12.0235	−	6.61124i	−0.459730	−	0.252787i
$685$		0			0
$686$			1.00000i			0.0381802i
$687$	−0.607649	+	2.36624i	−0.0231833	+	0.0902777i
$688$	1.01688	+	1.01688i	0.0387681	+	0.0387681i
$689$	2.93371			0.111765
$690$		0			0
$691$	−15.2567			−0.580393			−0.290197	−	0.956967i	$-0.593721\pi$
$691$	−15.2567			−0.580393			−0.290197	+	0.956967i	$0.593721\pi$
$692$	6.82152	+	6.82152i	0.259315	+	0.259315i
$693$	−4.28284	−	14.7461i	−0.162692	−	0.560158i
$694$			8.54785i			0.324472i
$695$		0			0
$696$	−12.9863	+	7.67937i	−0.492245	+	0.291086i
$697$	−1.68427	+	1.68427i	−0.0637961	+	0.0637961i
$698$	7.93285	−	7.93285i	0.300263	−	0.300263i
$699$	19.8705	−	11.7503i	0.751571	−	0.444437i
$700$		0			0
$701$			22.5053i			0.850012i	0.905190	+	0.425006i	$0.139728\pi$
$701$			22.5053i			0.850012i	−0.905190	+	0.425006i	$0.860272\pi$
$702$	13.3877	−	14.2529i	0.505285	−	0.537942i
$703$	37.9705	+	37.9705i	1.43208	+	1.43208i
$704$	5.11849			0.192910
$705$		0			0
$706$	18.5782			0.699198
$707$	6.61272	+	6.61272i	0.248697	+	0.248697i
$708$	0.586784	−	2.28499i	0.0220527	−	0.0858752i
$709$			2.18889i			0.0822055i	0.999155	+	0.0411028i	$0.0130871\pi$
$709$			2.18889i			0.0822055i	−0.999155	+	0.0411028i	$0.986913\pi$
$710$		0			0
$711$	11.3898	−	20.7141i	0.427152	−	0.776838i
$712$	−3.99613	+	3.99613i	−0.149761	+	0.149761i
$713$	−9.02729	+	9.02729i	−0.338075	+	0.338075i
$714$	−0.822971	−	1.39170i	−0.0307989	−	0.0520830i
$715$		0			0
$716$		−	9.67016i		−	0.361391i
$717$	39.5611	+	10.1593i	1.47744	+	0.379405i
$718$	−2.89929	−	2.89929i	−0.108200	−	0.108200i
$719$	−36.4233			−1.35836			−0.679179	−	0.733972i	$-0.737664\pi$
$719$	−36.4233			−1.35836			−0.679179	+	0.733972i	$0.737664\pi$
$720$		0			0
$721$	5.96736			0.222236
$722$	−1.35710	−	1.35710i	−0.0505061	−	0.0505061i
$723$	40.8492	+	10.4901i	1.51920	+	0.390129i
$724$		−	20.0487i		−	0.745102i
$725$		0			0
$726$	−13.3997	−	22.6598i	−0.497311	−	0.840984i
$727$	18.7018	−	18.7018i	0.693611	−	0.693611i	−0.269414	−	0.963025i	$-0.586830\pi$
$727$	18.7018	−	18.7018i	0.693611	−	0.693611i	0.963025	+	0.269414i	$0.0868299\pi$
$728$	−2.66102	+	2.66102i	−0.0986240	+	0.0986240i
$729$	1.68879	+	26.9471i	0.0625479	+	0.998042i
$730$		0			0
$731$		−	1.34241i		−	0.0496508i
$732$	−3.48675	+	13.5777i	−0.128874	+	0.501847i
$733$	−16.9813	−	16.9813i	−0.627217	−	0.627217i	0.320150	−	0.947367i	$-0.396267\pi$
$733$	−16.9813	−	16.9813i	−0.627217	−	0.627217i	−0.947367	+	0.320150i	$0.896267\pi$
$734$	−31.5785			−1.16558
$735$		0			0
$736$	−1.29407			−0.0477000
$737$	8.56568	+	8.56568i	0.315521	+	0.315521i
$738$	−7.35124	+	2.13509i	−0.270603	+	0.0785936i
$739$		−	38.3267i		−	1.40987i	−0.709272	−	0.704935i	$-0.750976\pi$
$739$		−	38.3267i		−	1.40987i	0.709272	−	0.704935i	$-0.249024\pi$
$740$		0			0
$741$	25.6614	−	15.1747i	0.942694	−	0.557456i
$742$	0.551238	−	0.551238i	0.0202366	−	0.0202366i
$743$	−4.74090	+	4.74090i	−0.173927	+	0.173927i	−0.788702	−	0.614775i	$-0.789247\pi$
$743$	−4.74090	+	4.74090i	−0.173927	+	0.173927i	0.614775	+	0.788702i	$0.289247\pi$
$744$	14.7082	−	8.69760i	0.539229	−	0.318870i
$745$		0			0
$746$		−	22.8377i		−	0.836148i
$747$	14.8852	−	4.32325i	0.544623	−	0.158180i
$748$	−3.37853	−	3.37853i	−0.123531	−	0.123531i
$749$	13.9207			0.508650
$750$		0			0
$751$	11.1768			0.407846			0.203923	−	0.978987i	$-0.434631\pi$
$751$	11.1768			0.407846			0.203923	+	0.978987i	$0.434631\pi$
$752$	−2.54338	−	2.54338i	−0.0927475	−	0.0927475i
$753$	6.92258	−	26.9571i	0.252273	−	0.982372i
$754$		−	32.7797i		−	1.19377i
$755$		0			0
$756$	−0.162584	−	5.19361i	−0.00591312	−	0.188890i
$757$	−3.45116	+	3.45116i	−0.125435	+	0.125435i	−0.767037	−	0.641603i	$-0.778270\pi$
$757$	−3.45116	+	3.45116i	−0.125435	+	0.125435i	0.641603	+	0.767037i	$0.278270\pi$
$758$	−12.7155	+	12.7155i	−0.461847	+	0.461847i
$759$	5.83959	+	9.87512i	0.211964	+	0.358444i
$760$		0			0
$761$		−	10.4354i		−	0.378283i	−0.981950	−	0.189141i	$-0.939430\pi$
$761$		−	10.4354i		−	0.378283i	0.981950	−	0.189141i	$-0.0605704\pi$
$762$	−5.91066	−	1.51785i	−0.214121	−	0.0549861i
$763$	7.83271	+	7.83271i	0.283563	+	0.283563i
$764$	20.5852			0.744748
$765$		0			0
$766$	−18.2039			−0.657733
$767$	3.62443	+	3.62443i	0.130870	+	0.130870i
$768$	1.67762	+	0.430811i	0.0605358	+	0.0155456i
$769$		−	32.5260i		−	1.17292i	−0.809978	−	0.586460i	$-0.800521\pi$
$769$		−	32.5260i		−	1.17292i	0.809978	−	0.586460i	$-0.199479\pi$
$770$		0			0
$771$	−16.6681	−	28.1868i	−0.600286	−	1.01512i
$772$	−3.33427	+	3.33427i	−0.120003	+	0.120003i
$773$	−37.7224	+	37.7224i	−1.35678	+	1.35678i	−0.478920	+	0.877858i	$0.658972\pi$
$773$	−37.7224	+	37.7224i	−1.35678	+	1.35678i	−0.877858	+	0.478920i	$0.841028\pi$
$774$	2.07871	−	3.78044i	0.0747177	−	0.135885i
$775$		0			0
$776$		−	5.33124i		−	0.191380i
$777$	−5.05796	+	19.6961i	−0.181453	+	0.706595i
$778$	5.53154	+	5.53154i	0.198315	+	0.198315i
$779$	−11.6707			−0.418147
$780$		0			0
$781$	−18.5758			−0.664694
$782$	0.854166	+	0.854166i	0.0305449	+	0.0305449i
$783$	32.9900	+	30.9873i	1.17897	+	1.10739i
$784$			1.00000i			0.0357143i
$785$		0			0
$786$	−3.06393	+	1.81183i	−0.109287	+	0.0646260i
$787$	4.83658	−	4.83658i	0.172406	−	0.172406i	−0.615630	−	0.788035i	$-0.711098\pi$
$787$	4.83658	−	4.83658i	0.172406	−	0.172406i	0.788035	+	0.615630i	$0.211098\pi$
$788$	−12.0863	+	12.0863i	−0.430557	+	0.430557i
$789$	−35.0229	+	20.7105i	−1.24685	+	0.737315i
$790$		0			0
$791$			9.64242i			0.342845i
$792$	−4.28284	−	14.7461i	−0.152184	−	0.523980i
$793$	−21.5368	−	21.5368i	−0.764795	−	0.764795i
$794$	−21.3853			−0.758937
$795$		0			0
$796$	−13.4749			−0.477605
$797$	21.5354	+	21.5354i	0.762822	+	0.762822i	0.976832	−	0.214009i	$-0.0686523\pi$
$797$	21.5354	+	21.5354i	0.762822	+	0.762822i	−0.214009	+	0.976832i	$0.568652\pi$
$798$	1.97043	−	7.67301i	0.0697523	−	0.271622i
$799$			3.35758i			0.118783i
$800$		0			0
$801$	14.8564	+	8.16892i	0.524924	+	0.288635i
$802$	12.0711	−	12.0711i	0.426246	−	0.426246i
$803$	30.4696	−	30.4696i	1.07525	−	1.07525i
$804$	2.08651	+	3.52841i	0.0735854	+	0.124438i
$805$		0			0
$806$			37.1260i			1.30771i
$807$	1.76190	+	0.452454i	0.0620217	+	0.0159271i
$808$	6.61272	+	6.61272i	0.232635	+	0.232635i
$809$	−8.89737			−0.312815			−0.156407	−	0.987693i	$-0.549991\pi$
$809$	−8.89737			−0.312815			−0.156407	+	0.987693i	$0.549991\pi$
$810$		0			0
$811$	16.6237			0.583738			0.291869	−	0.956458i	$-0.405723\pi$
$811$	16.6237			0.583738			0.291869	+	0.956458i	$0.405723\pi$
$812$	−6.15923	−	6.15923i	−0.216147	−	0.216147i
$813$	43.0964	+	11.0671i	1.51146	+	0.388141i
$814$			60.0938i			2.10629i
$815$		0			0
$816$	−0.822971	−	1.39170i	−0.0288098	−	0.0487191i
$817$	4.65095	−	4.65095i	0.162716	−	0.162716i
$818$	−0.768889	+	0.768889i	−0.0268836	+	0.0268836i
$819$	9.89284	+	5.43968i	0.345684	+	0.190078i
$820$		0			0
$821$		−	28.2027i		−	0.984281i	−0.870516	−	0.492140i	$-0.836215\pi$
$821$		−	28.2027i		−	0.984281i	0.870516	−	0.492140i	$-0.163785\pi$
$822$	−5.32965	+	20.7541i	−0.185893	+	0.723884i
$823$	−15.1141	−	15.1141i	−0.526846	−	0.526846i	0.392785	−	0.919630i	$-0.371512\pi$
$823$	−15.1141	−	15.1141i	−0.526846	−	0.526846i	−0.919630	+	0.392785i	$0.871512\pi$
$824$	5.96736			0.207883
$825$		0			0
$826$	1.36204			0.0473916
$827$	−17.4527	−	17.4527i	−0.606889	−	0.606889i	0.335243	−	0.942132i	$-0.391182\pi$
$827$	−17.4527	−	17.4527i	−0.606889	−	0.606889i	−0.942132	+	0.335243i	$0.891182\pi$
$828$	1.08280	+	3.72814i	0.0376298	+	0.129562i
$829$			9.48644i			0.329478i	0.986337	+	0.164739i	$0.0526782\pi$
$829$			9.48644i			0.329478i	−0.986337	+	0.164739i	$0.947322\pi$
$830$		0			0
$831$	−3.62604	+	2.14424i	−0.125786	+	0.0743828i
$832$	−2.66102	+	2.66102i	−0.0922543	+	0.0922543i
$833$	0.660063	−	0.660063i	0.0228698	−	0.0228698i
$834$	−0.0748597	+	0.0442678i	−0.00259218	+	0.00153287i
$835$		0			0
$836$		−	23.4107i		−	0.809676i
$837$	−37.3643	−	35.0959i	−1.29150	−	1.21309i
$838$	25.2885	+	25.2885i	0.873577	+	0.873577i
$839$	15.0379			0.519165			0.259582	−	0.965721i	$-0.416415\pi$
$839$	15.0379			0.519165			0.259582	+	0.965721i	$0.416415\pi$
$840$		0			0
$841$	46.8723			1.61629
$842$	−26.0572	−	26.0572i	−0.897989	−	0.897989i
$843$	−12.6368	+	49.2088i	−0.435234	+	1.69484i
$844$		−	20.9033i		−	0.719521i
$845$		0			0
$846$	−5.19920	+	9.45549i	−0.178752	+	0.325086i
$847$	10.7472	−	10.7472i	0.369280	−	0.369280i
$848$	0.551238	−	0.551238i	0.0189296	−	0.0189296i
$849$	0.548614	+	0.927741i	0.0188284	+	0.0318400i
$850$		0			0
$851$		−	15.1930i		−	0.520811i
$852$	−6.08834	−	1.56348i	−0.208583	−	0.0535641i
$853$	−10.4909	−	10.4909i	−0.359202	−	0.359202i	0.504317	−	0.863519i	$-0.331744\pi$
$853$	−10.4909	−	10.4909i	−0.359202	−	0.359202i	−0.863519	+	0.504317i	$0.831744\pi$
$854$	−8.09345			−0.276952
$855$		0			0
$856$	13.9207			0.475798
$857$	4.66985	+	4.66985i	0.159519	+	0.159519i	0.782354	−	0.622834i	$-0.214019\pi$
$857$	4.66985	+	4.66985i	0.159519	+	0.159519i	−0.622834	+	0.782354i	$0.714019\pi$
$858$	32.3145	+	8.29835i	1.10320	+	0.283301i
$859$			12.9895i			0.443195i	0.975138	+	0.221598i	$0.0711271\pi$
$859$			12.9895i			0.443195i	−0.975138	+	0.221598i	$0.928873\pi$
$860$		0			0
$861$	−2.24962	−	3.80425i	−0.0766668	−	0.129649i
$862$	5.75719	−	5.75719i	0.196091	−	0.196091i
$863$	−1.91455	+	1.91455i	−0.0651719	+	0.0651719i	−0.738941	−	0.673770i	$-0.764674\pi$
$863$	−1.91455	+	1.91455i	−0.0651719	+	0.0651719i	0.673770	+	0.738941i	$0.264674\pi$
$864$	−0.162584	−	5.19361i	−0.00553121	−	0.176690i
$865$		0			0
$866$		−	5.47583i		−	0.186076i
$867$	6.94840	−	27.0577i	0.235980	−	0.918927i
$868$	6.97590	+	6.97590i	0.236778	+	0.236778i
$869$	40.3319			1.36817
$870$		0			0
$871$	−8.90633			−0.301779
$872$	7.83271	+	7.83271i	0.265249	+	0.265249i
$873$	−15.3590	+	4.46086i	−0.519825	+	0.150977i
$874$			5.91875i			0.200205i
$875$		0			0
$876$	12.5512	−	7.42206i	0.424065	−	0.250768i
$877$	34.9916	−	34.9916i	1.18158	−	1.18158i	0.202248	−	0.979334i	$-0.435175\pi$
$877$	34.9916	−	34.9916i	1.18158	−	1.18158i	0.979334	−	0.202248i	$-0.0648247\pi$
$878$	17.3198	−	17.3198i	0.584515	−	0.584515i
$879$	−13.0018	+	7.68852i	−0.438539	+	0.259327i
$880$		0			0
$881$		−	2.67655i		−	0.0901753i	−0.998983	−	0.0450877i	$-0.985643\pi$
$881$		−	2.67655i		−	0.0901753i	0.998983	−	0.0450877i	$-0.0143567\pi$
$882$	2.88095	−	0.836740i	0.0970066	−	0.0281745i
$883$	−23.3569	−	23.3569i	−0.786024	−	0.786024i	0.194816	−	0.980840i	$-0.437589\pi$
$883$	−23.3569	−	23.3569i	−0.786024	−	0.786024i	−0.980840	+	0.194816i	$0.937589\pi$
$884$	3.51288			0.118151
$885$		0			0
$886$	−23.6864			−0.795760
$887$	27.7866	+	27.7866i	0.932983	+	0.932983i	0.997891	−	0.0649087i	$-0.0206756\pi$
$887$	27.7866	+	27.7866i	0.932983	+	0.932983i	−0.0649087	+	0.997891i	$0.520676\pi$
$888$	−5.05796	+	19.6961i	−0.169734	+	0.660959i
$889$		−	3.52325i		−	0.118166i
$890$		0			0
$891$	−38.8991	+	24.6773i	−1.30317	+	0.826720i
$892$	−3.30682	+	3.30682i	−0.110721	+	0.110721i
$893$	−11.6328	+	11.6328i	−0.389276	+	0.389276i
$894$	10.3872	+	17.5654i	0.347400	+	0.587476i
$895$		0			0
$896$			1.00000i			0.0334077i
$897$	−8.16983	−	2.09801i	−0.272783	−	0.0700505i
$898$	−10.3130	−	10.3130i	−0.344149	−	0.344149i
$899$	−85.9324			−2.86601
$900$		0			0
$901$	−0.727704			−0.0242433
$902$	−9.23531	−	9.23531i	−0.307502	−	0.307502i
$903$	2.41255	+	0.619543i	0.0802847	+	0.0206171i
$904$			9.64242i			0.320702i
$905$		0			0
$906$	11.4970	+	19.4421i	0.381962	+	0.645922i
$907$	−25.5557	+	25.5557i	−0.848564	+	0.848564i	−0.989954	−	0.141390i	$-0.954843\pi$
$907$	−25.5557	+	25.5557i	−0.848564	+	0.848564i	0.141390	+	0.989954i	$0.454843\pi$
$908$	19.6412	−	19.6412i	0.651816	−	0.651816i
$909$	13.5178	−	24.5840i	0.448357	−	0.815401i
$910$		0			0
$911$		−	40.2447i		−	1.33337i	−0.745341	−	0.666683i	$-0.767713\pi$
$911$		−	40.2447i		−	1.33337i	0.745341	−	0.666683i	$-0.232287\pi$
$912$	1.97043	−	7.67301i	0.0652473	−	0.254079i
$913$	18.7002	+	18.7002i	0.618887	+	0.618887i
$914$	−12.3403			−0.408182
$915$		0			0
$916$	−1.41048			−0.0466034
$917$	−1.45318	−	1.45318i	−0.0479882	−	0.0479882i
$918$	−3.32080	+	3.53543i	−0.109603	+	0.116686i
$919$		−	56.3005i		−	1.85718i	−0.371107	−	0.928590i	$-0.621022\pi$
$919$		−	56.3005i		−	1.85718i	0.371107	−	0.928590i	$-0.378978\pi$
$920$		0			0
$921$	25.1576	−	14.8768i	0.828972	−	0.490207i
$922$	−14.1010	+	14.1010i	−0.464392	+	0.464392i
$923$	9.65726	−	9.65726i	0.317873	−	0.317873i
$924$	7.63107	−	4.51259i	0.251044	−	0.148453i
$925$		0			0
$926$		−	13.7257i		−	0.451055i
$927$	−4.99313	−	17.1917i	−0.163996	−	0.564649i
$928$	−6.15923	−	6.15923i	−0.202187	−	0.202187i
$929$	23.0895			0.757541			0.378770	−	0.925491i	$-0.376347\pi$
$929$	23.0895			0.757541			0.378770	+	0.925491i	$0.376347\pi$
$930$		0			0
$931$	4.57375			0.149899
$932$	9.42431	+	9.42431i	0.308704	+	0.308704i
$933$	−5.01680	+	19.5359i	−0.164243	+	0.639576i
$934$		−	8.11044i		−	0.265382i
$935$		0			0
$936$	9.89284	+	5.43968i	0.323358	+	0.177802i
$937$	9.64496	−	9.64496i	0.315087	−	0.315087i	−0.531790	−	0.846877i	$-0.678480\pi$
$937$	9.64496	−	9.64496i	0.315087	−	0.315087i	0.846877	+	0.531790i	$0.178480\pi$
$938$	−1.67348	+	1.67348i	−0.0546411	+	0.0546411i
$939$	−26.7187	−	45.1830i	−0.871932	−	1.47449i
$940$		0			0
$941$		−	51.3926i		−	1.67535i	−0.546167	−	0.837676i	$-0.683914\pi$
$941$		−	51.3926i		−	1.67535i	0.546167	−	0.837676i	$-0.316086\pi$
$942$	−20.9862	−	5.38926i	−0.683769	−	0.175592i
$943$	2.33489	+	2.33489i	0.0760346	+	0.0760346i
$944$	1.36204			0.0443308
$945$		0			0
$946$	7.36081			0.239320
$947$	36.6347	+	36.6347i	1.19047	+	1.19047i	0.976936	+	0.213531i	$0.0684965\pi$
$947$	36.6347	+	36.6347i	1.19047	+	1.19047i	0.213531	+	0.976936i	$0.431503\pi$
$948$	13.2191	+	3.39465i	0.429335	+	0.110253i
$949$			31.6814i			1.02842i
$950$		0			0
$951$	12.7421	+	21.5478i	0.413192	+	0.698734i
$952$	0.660063	−	0.660063i	0.0213928	−	0.0213928i
$953$	−6.87447	+	6.87447i	−0.222686	+	0.222686i	−0.809629	−	0.586943i	$-0.800331\pi$
$953$	−6.87447	+	6.87447i	−0.222686	+	0.222686i	0.586943	+	0.809629i	$0.300331\pi$
$954$	−2.04933	−	1.12685i	−0.0663495	−	0.0364830i
$955$		0			0
$956$			23.5817i			0.762688i
$957$	−19.2075	+	74.7956i	−0.620890	+	2.41780i
$958$	−6.78148	−	6.78148i	−0.219100	−	0.219100i
$959$	−12.3712			−0.399487
$960$		0			0
$961$	66.3265			2.13956
$962$	−31.2418	−	31.2418i	−1.00728	−	1.00728i
$963$	−11.6480	−	40.1047i	−0.375351	−	1.29236i
$964$			24.3495i			0.784245i
$965$		0			0
$966$	−1.92931	+	1.14088i	−0.0620744	+	0.0367073i
$967$	11.2771	−	11.2771i	0.362647	−	0.362647i	−0.502140	−	0.864787i	$-0.667454\pi$
$967$	11.2771	−	11.2771i	0.362647	−	0.362647i	0.864787	+	0.502140i	$0.167454\pi$
$968$	10.7472	−	10.7472i	0.345430	−	0.345430i
$969$	−6.36528	+	3.76407i	−0.204482	+	0.120919i
$970$		0			0
$971$		−	22.4417i		−	0.720189i	−0.932916	−	0.360094i	$-0.882744\pi$
$971$		−	22.4417i		−	0.720189i	0.932916	−	0.360094i	$-0.117256\pi$
$972$	−14.8265	+	4.81409i	−0.475560	+	0.154412i
$973$	−0.0355050	−	0.0355050i	−0.00113824	−	0.00113824i
$974$	−20.1836			−0.646725
$975$		0			0
$976$	−8.09345			−0.259065
$977$	12.4873	+	12.4873i	0.399505	+	0.399505i	0.878058	−	0.478553i	$-0.158839\pi$
$977$	12.4873	+	12.4873i	0.399505	+	0.399505i	−0.478553	+	0.878058i	$0.658839\pi$
$978$	−6.07543	+	23.6583i	−0.194271	+	0.756508i
$979$			28.9265i			0.924495i
$980$		0			0
$981$	16.0117	−	29.1196i	0.511214	−	0.929717i
$982$	−20.2747	+	20.2747i	−0.646992	+	0.646992i
$983$	26.0926	−	26.0926i	0.832224	−	0.832224i	−0.155597	−	0.987821i	$-0.549730\pi$
$983$	26.0926	−	26.0926i	0.832224	−	0.832224i	0.987821	+	0.155597i	$0.0497301\pi$
$984$	−2.24962	−	3.80425i	−0.0717152	−	0.121275i
$985$		0			0
$986$			8.13097i			0.258943i
$987$	−6.03419	−	1.54958i	−0.192070	−	0.0493236i
$988$	12.1709	+	12.1709i	0.387206	+	0.387206i
$989$	−1.86098			−0.0591756
$990$		0			0
$991$	3.54343			0.112561			0.0562804	−	0.998415i	$-0.482076\pi$
$991$	3.54343			0.112561			0.0562804	+	0.998415i	$0.482076\pi$
$992$	6.97590	+	6.97590i	0.221485	+	0.221485i
$993$	13.5894	+	3.48976i	0.431247	+	0.110744i
$994$		−	3.62916i		−	0.115110i
$995$		0			0
$996$	4.55517	+	7.70308i	0.144336	+	0.244081i
$997$	33.4928	−	33.4928i	1.06073	−	1.06073i	0.0626944	−	0.998033i	$-0.480031\pi$
$997$	33.4928	−	33.4928i	1.06073	−	1.06073i	0.998033	−	0.0626944i	$-0.0199693\pi$
$998$	−10.1484	+	10.1484i	−0.321242	+	0.321242i
$999$	60.9758	−	1.90882i	1.92919	−	0.0603924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.j.c.743.6		12
3.2	odd	2		1050.2.j.d.743.2		12
5.2	odd	4		1050.2.j.d.407.2		12
5.3	odd	4		210.2.j.b.197.5	yes	12
5.4	even	2		210.2.j.a.113.1	✓	12
15.2	even	4	inner	1050.2.j.c.407.6		12
15.8	even	4		210.2.j.a.197.1	yes	12
15.14	odd	2		210.2.j.b.113.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.j.a.113.1	✓	12	5.4	even	2
210.2.j.a.197.1	yes	12	15.8	even	4
210.2.j.b.113.5	yes	12	15.14	odd	2
210.2.j.b.197.5	yes	12	5.3	odd	4
1050.2.j.c.407.6		12	15.2	even	4	inner
1050.2.j.c.743.6		12	1.1	even	1	trivial
1050.2.j.d.407.2		12	5.2	odd	4
1050.2.j.d.743.2		12	3.2	odd	2

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.67762 + 0.430811i) q^{3} +1.00000i q^{4} +(0.881625 + 1.49088i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.62880 + 1.44547i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.67762 + 0.430811i) q^{3} +1.00000i q^{4} +(0.881625 + 1.49088i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.62880 + 1.44547i) q^{9} +5.11849i q^{11} +(-0.430811 + 1.67762i) q^{12} +(-2.66102 - 2.66102i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(0.660063 + 0.660063i) q^{17} +(0.836740 + 2.88095i) q^{18} +4.57375i q^{19} +(-1.49088 + 0.881625i) q^{21} +(-3.61932 + 3.61932i) q^{22} +(0.915044 - 0.915044i) q^{23} +(-1.49088 + 0.881625i) q^{24} -3.76325i q^{26} +(3.78740 + 3.55747i) q^{27} +(-0.707107 - 0.707107i) q^{28} +8.71047 q^{29} -9.86542 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.20510 + 8.58686i) q^{33} +0.933471i q^{34} +(-1.44547 + 2.62880i) q^{36} +(8.30181 - 8.30181i) q^{37} +(-3.23413 + 3.23413i) q^{38} +(-3.31778 - 5.61057i) q^{39} +2.55167i q^{41} +(-1.67762 - 0.430811i) q^{42} +(-1.01688 - 1.01688i) q^{43} -5.11849 q^{44} +1.29407 q^{46} +(2.54338 + 2.54338i) q^{47} +(-1.67762 - 0.430811i) q^{48} -1.00000i q^{49} +(0.822971 + 1.39170i) q^{51} +(2.66102 - 2.66102i) q^{52} +(-0.551238 + 0.551238i) q^{53} +(0.162584 + 5.19361i) q^{54} -1.00000i q^{56} +(-1.97043 + 7.67301i) q^{57} +(6.15923 + 6.15923i) q^{58} -1.36204 q^{59} +8.09345 q^{61} +(-6.97590 - 6.97590i) q^{62} +(-2.88095 + 0.836740i) q^{63} -1.00000i q^{64} +(-7.63107 + 4.51259i) q^{66} +(1.67348 - 1.67348i) q^{67} +(-0.660063 + 0.660063i) q^{68} +(1.92931 - 1.14088i) q^{69} +3.62916i q^{71} +(-2.88095 + 0.836740i) q^{72} +(-5.95286 - 5.95286i) q^{73} +11.7405 q^{74} -4.57375 q^{76} +(-3.61932 - 3.61932i) q^{77} +(1.62125 - 6.31330i) q^{78} -7.87966i q^{79} +(4.82121 + 7.59973i) q^{81} +(-1.80431 + 1.80431i) q^{82} +(3.65347 - 3.65347i) q^{83} +(-0.881625 - 1.49088i) q^{84} -1.43808i q^{86} +(14.6128 + 3.75257i) q^{87} +(-3.61932 - 3.61932i) q^{88} +5.65138 q^{89} +3.76325 q^{91} +(0.915044 + 0.915044i) q^{92} +(-16.5504 - 4.25014i) q^{93} +3.59688i q^{94} +(-0.881625 - 1.49088i) q^{96} +(-3.76976 + 3.76976i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-7.39864 + 13.4555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3}+O(q^{10}) \) 12 * q - 4 * q^3	\( 12 q - 4 q^{3} + 4 q^{12} - 12 q^{14} - 12 q^{16} - 28 q^{17} - 4 q^{21} - 4 q^{22} + 24 q^{23} - 4 q^{24} + 20 q^{27} + 8 q^{29} - 8 q^{31} - 4 q^{33} + 4 q^{36} + 20 q^{37} + 4 q^{38} - 40 q^{39} + 4 q^{42} - 8 q^{43} + 8 q^{44} + 8 q^{46} - 16 q^{47} + 4 q^{48} + 8 q^{51} + 24 q^{53} - 4 q^{54} + 12 q^{57} + 8 q^{58} + 32 q^{59} - 28 q^{62} - 8 q^{63} - 8 q^{66} + 28 q^{68} - 32 q^{69} - 8 q^{72} + 24 q^{73} + 8 q^{74} - 4 q^{77} - 36 q^{81} - 32 q^{82} + 24 q^{83} + 64 q^{87} - 4 q^{88} + 48 q^{89} + 24 q^{91} + 24 q^{92} - 76 q^{93} - 8 q^{97} - 40 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 + 4 * q^12 - 12 * q^14 - 12 * q^16 - 28 * q^17 - 4 * q^21 - 4 * q^22 + 24 * q^23 - 4 * q^24 + 20 * q^27 + 8 * q^29 - 8 * q^31 - 4 * q^33 + 4 * q^36 + 20 * q^37 + 4 * q^38 - 40 * q^39 + 4 * q^42 - 8 * q^43 + 8 * q^44 + 8 * q^46 - 16 * q^47 + 4 * q^48 + 8 * q^51 + 24 * q^53 - 4 * q^54 + 12 * q^57 + 8 * q^58 + 32 * q^59 - 28 * q^62 - 8 * q^63 - 8 * q^66 + 28 * q^68 - 32 * q^69 - 8 * q^72 + 24 * q^73 + 8 * q^74 - 4 * q^77 - 36 * q^81 - 32 * q^82 + 24 * q^83 + 64 * q^87 - 4 * q^88 + 48 * q^89 + 24 * q^91 + 24 * q^92 - 76 * q^93 - 8 * q^97 - 40 * q^99

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