LMFDB - Embedded newform 972.2.l.a.215.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [972,2,Mod(107,972)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(972, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("972.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, 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:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			215.7
Character	$\chi$	$=$	972.215
Dual form			972.2.l.a.755.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.408783 + 1.35385i) q^{2} +(-1.66579 - 1.10686i) q^{4} +(2.38965 - 2.84787i) q^{5} +(0.566613 - 1.55676i) q^{7} +(2.17946 - 1.80276i) q^{8} +O(q^{10})$	\(q+(-0.408783 + 1.35385i) q^{2} +(-1.66579 - 1.10686i) q^{4} +(2.38965 - 2.84787i) q^{5} +(0.566613 - 1.55676i) q^{7} +(2.17946 - 1.80276i) q^{8} +(2.87873 + 4.39937i) q^{10} +(0.429301 - 0.360226i) q^{11} +(0.451135 - 2.55851i) q^{13} +(1.87598 + 1.40348i) q^{14} +(1.54974 + 3.68759i) q^{16} +(-4.50885 - 2.60318i) q^{17} +(0.925473 - 0.534322i) q^{19} +(-7.13284 + 2.09897i) q^{20} +(0.312200 + 0.728461i) q^{22} +(-8.37409 + 3.04792i) q^{23} +(-1.53171 - 8.68677i) q^{25} +(3.27942 + 1.65664i) q^{26} +(-2.66696 + 1.96607i) q^{28} +(-1.07644 + 0.189806i) q^{29} +(1.10240 + 3.02881i) q^{31} +(-5.62593 + 0.590682i) q^{32} +(5.36745 - 5.04015i) q^{34} +(-3.07943 - 5.33373i) q^{35} +(3.17849 - 5.50530i) q^{37} +(0.345072 + 1.47137i) q^{38} +(0.0741044 - 10.5148i) q^{40} +(-0.852165 - 0.150260i) q^{41} +(-1.29834 - 1.54730i) q^{43} +(-1.11385 + 0.124888i) q^{44} +(-0.703229 - 12.5832i) q^{46} +(-6.63579 - 2.41523i) q^{47} +(3.25987 + 2.73536i) q^{49} +(12.3867 + 1.47730i) q^{50} +(-3.58341 + 3.76262i) q^{52} -6.80497i q^{53} -2.08341i q^{55} +(-1.57155 - 4.41435i) q^{56} +(0.183063 - 1.53492i) q^{58} +(6.98640 + 5.86229i) q^{59} +(-4.50303 - 1.63897i) q^{61} +(-4.55118 + 0.254350i) q^{62} +(1.50009 - 7.85810i) q^{64} +(-6.20826 - 7.39872i) q^{65} +(10.8280 + 1.90927i) q^{67} +(4.62946 + 9.32702i) q^{68} +(8.47987 - 1.98874i) q^{70} +(-3.98206 + 6.89713i) q^{71} +(1.92588 + 3.33572i) q^{73} +(6.15402 + 6.55365i) q^{74} +(-2.13306 - 0.134296i) q^{76} +(-0.317537 - 0.872425i) q^{77} +(9.63652 - 1.69918i) q^{79} +(14.2051 + 4.39859i) q^{80} +(0.551778 - 1.09228i) q^{82} +(0.291958 + 1.65578i) q^{83} +(-18.1881 + 6.61992i) q^{85} +(2.62554 - 1.12524i) q^{86} +(0.286242 - 1.55903i) q^{88} +(10.9229 - 6.30632i) q^{89} +(-3.72736 - 2.15199i) q^{91} +(17.3231 + 4.19171i) q^{92} +(5.98244 - 7.99653i) q^{94} +(0.689874 - 3.91247i) q^{95} +(-3.05643 + 2.56465i) q^{97} +(-5.03583 + 3.29520i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8	$ 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} - 33 q^{14} + 3 q^{16} + 18 q^{17} + 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} - 30 q^{29} - 33 q^{32} + 15 q^{34} - 6 q^{37} + 63 q^{38} + 33 q^{40} + 24 q^{41} - 63 q^{44} - 3 q^{46} + 6 q^{49} + 21 q^{50} + 57 q^{52} + 18 q^{56} + 57 q^{58} + 6 q^{61} - 90 q^{62} - 3 q^{64} - 30 q^{65} + 102 q^{68} + 51 q^{70} - 6 q^{73} - 75 q^{74} + 27 q^{76} + 42 q^{77} - 12 q^{82} - 24 q^{85} + 111 q^{86} + 27 q^{88} - 147 q^{92} + 30 q^{94} - 12 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 - 33 * q^14 + 3 * q^16 + 18 * q^17 + 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 - 30 * q^29 - 33 * q^32 + 15 * q^34 - 6 * q^37 + 63 * q^38 + 33 * q^40 + 24 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 21 * q^50 + 57 * q^52 + 18 * q^56 + 57 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 - 30 * q^65 + 102 * q^68 + 51 * q^70 - 6 * q^73 - 75 * q^74 + 27 * q^76 + 42 * q^77 - 12 * q^82 - 24 * q^85 + 111 * q^86 + 27 * q^88 - 147 * q^92 + 30 * q^94 - 12 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	−0.408783	+	1.35385i	−0.289053	+	0.957313i
$2$	−0.408783	+	1.35385i	−0.289053	+	0.957313i
$3$		0			0
$3$		0			0
$4$	−1.66579	−	1.10686i	−0.832897	−	0.553428i
$5$	2.38965	−	2.84787i	1.06868	−	1.27361i	0.108541	−	0.994092i	$-0.465382\pi$
$5$	2.38965	−	2.84787i	1.06868	−	1.27361i	0.960142	−	0.279514i	$-0.0901735\pi$
$6$		0			0
$7$	0.566613	−	1.55676i	0.214159	−	0.588398i	−0.785371	−	0.619025i	$-0.787528\pi$
$7$	0.566613	−	1.55676i	0.214159	−	0.588398i	0.999531	+	0.0306266i	$0.00975027\pi$
$8$	2.17946	−	1.80276i	0.770555	−	0.637373i
$9$		0			0
$10$	2.87873	+	4.39937i	0.910334	+	1.39120i
$11$	0.429301	−	0.360226i	0.129439	−	0.108612i	−0.575770	−	0.817612i	$-0.695298\pi$
$11$	0.429301	−	0.360226i	0.129439	−	0.108612i	0.705209	+	0.708999i	$0.250853\pi$
$12$		0			0
$13$	0.451135	−	2.55851i	0.125122	−	0.709604i	−0.856113	−	0.516789i	$-0.827127\pi$
$13$	0.451135	−	2.55851i	0.125122	−	0.709604i	0.981235	−	0.192815i	$-0.0617618\pi$
$14$	1.87598	+	1.40348i	0.501378	+	0.375096i
$15$		0			0
$16$	1.54974	+	3.68759i	0.387434	+	0.921897i
$17$	−4.50885	−	2.60318i	−1.09356	−	0.631365i	−0.159035	−	0.987273i	$-0.550838\pi$
$17$	−4.50885	−	2.60318i	−1.09356	−	0.631365i	−0.934521	+	0.355908i	$0.884172\pi$
$18$		0			0
$19$	0.925473	−	0.534322i	0.212318	−	0.122582i	−0.390070	−	0.920785i	$-0.627549\pi$
$19$	0.925473	−	0.534322i	0.212318	−	0.122582i	0.602388	+	0.798203i	$0.294216\pi$
$20$	−7.13284	+	2.09897i	−1.59495	+	0.469343i
$21$		0			0
$22$	0.312200	+	0.728461i	0.0665612	+	0.155308i
$23$	−8.37409	+	3.04792i	−1.74612	+	0.635535i	−0.999556	−	0.0297813i	$-0.990519\pi$
$23$	−8.37409	+	3.04792i	−1.74612	+	0.635535i	−0.746562	+	0.665316i	$0.768297\pi$
$24$		0			0
$25$	−1.53171	−	8.68677i	−0.306342	−	1.73735i
$26$	3.27942	+	1.65664i	0.643147	+	0.324895i
$27$		0			0
$28$	−2.66696	+	1.96607i	−0.504009	+	0.371553i
$29$	−1.07644	+	0.189806i	−0.199890	+	0.0352460i	−0.272697	−	0.962100i	$-0.587916\pi$
$29$	−1.07644	+	0.189806i	−0.199890	+	0.0352460i	0.0728065	+	0.997346i	$0.476804\pi$
$30$		0			0
$31$	1.10240	+	3.02881i	0.197996	+	0.543990i	0.998465	−	0.0553841i	$-0.0176383\pi$
$31$	1.10240	+	3.02881i	0.197996	+	0.543990i	−0.800469	+	0.599374i	$0.795416\pi$
$32$	−5.62593	+	0.590682i	−0.994533	+	0.104419i
$33$		0			0
$34$	5.36745	−	5.04015i	0.920510	−	0.864378i
$35$	−3.07943	−	5.33373i	−0.520519	−	0.901566i
$36$		0			0
$37$	3.17849	−	5.50530i	0.522540	−	0.905066i	−0.477116	−	0.878840i	$-0.658318\pi$
$37$	3.17849	−	5.50530i	0.522540	−	0.905066i	0.999656	−	0.0262257i	$-0.00834884\pi$
$38$	0.345072	+	1.47137i	0.0559781	+	0.238688i
$39$		0			0
$40$	0.0741044	−	10.5148i	0.0117169	−	1.66253i
$41$	−0.852165	−	0.150260i	−0.133086	−	0.0234666i	0.106708	−	0.994290i	$-0.465969\pi$
$41$	−0.852165	−	0.150260i	−0.133086	−	0.0234666i	−0.239794	+	0.970824i	$0.577080\pi$
$42$		0			0
$43$	−1.29834	−	1.54730i	−0.197995	−	0.235961i	0.657907	−	0.753099i	$-0.271442\pi$
$43$	−1.29834	−	1.54730i	−0.197995	−	0.235961i	−0.855902	+	0.517138i	$0.826997\pi$
$44$	−1.11385	+	0.124888i	−0.167919	+	0.0188276i
$45$		0			0
$46$	−0.703229	−	12.5832i	−0.103685	−	1.85528i
$47$	−6.63579	−	2.41523i	−0.967929	−	0.352297i	−0.190793	−	0.981630i	$-0.561106\pi$
$47$	−6.63579	−	2.41523i	−0.967929	−	0.352297i	−0.777136	+	0.629333i	$0.783328\pi$
$48$		0			0
$49$	3.25987	+	2.73536i	0.465696	+	0.390766i
$50$	12.3867	+	1.47730i	1.75174	+	0.208922i
$51$		0			0
$52$	−3.58341	+	3.76262i	−0.496929	+	0.521781i
$53$		−	6.80497i		−	0.934734i	−0.884063	−	0.467367i	$-0.845203\pi$
$53$		−	6.80497i		−	0.934734i	0.884063	−	0.467367i	$-0.154797\pi$
$54$		0			0
$55$		−	2.08341i		−	0.280926i
$56$	−1.57155	−	4.41435i	−0.210007	−	0.589893i
$57$		0			0
$58$	0.183063	−	1.53492i	0.0240373	−	0.201545i
$59$	6.98640	+	5.86229i	0.909552	+	0.763205i	0.972034	−	0.234841i	$-0.0754570\pi$
$59$	6.98640	+	5.86229i	0.909552	+	0.763205i	−0.0624814	+	0.998046i	$0.519901\pi$
$60$		0			0
$61$	−4.50303	−	1.63897i	−0.576554	−	0.209849i	0.0372511	−	0.999306i	$-0.488140\pi$
$61$	−4.50303	−	1.63897i	−0.576554	−	0.209849i	−0.613805	+	0.789457i	$0.710362\pi$
$62$	−4.55118	+	0.254350i	−0.578000	+	0.0323024i
$63$		0			0
$64$	1.50009	−	7.85810i	0.187511	−	0.982262i
$65$	−6.20826	−	7.39872i	−0.770040	−	0.917699i
$66$		0			0
$67$	10.8280	+	1.90927i	1.32285	+	0.233255i	0.790080	−	0.613004i	$-0.210039\pi$
$67$	10.8280	+	1.90927i	1.32285	+	0.233255i	0.532773	+	0.846258i	$0.321150\pi$
$68$	4.62946	+	9.32702i	0.561404	+	1.13107i
$69$		0			0
$70$	8.47987	−	1.98874i	1.01354	−	0.237700i
$71$	−3.98206	+	6.89713i	−0.472583	+	0.818538i	−0.999508	−	0.0313737i	$-0.990012\pi$
$71$	−3.98206	+	6.89713i	−0.472583	+	0.818538i	0.526924	+	0.849912i	$0.323345\pi$
$72$		0			0
$73$	1.92588	+	3.33572i	0.225407	+	0.390416i	0.956441	−	0.291924i	$-0.0942955\pi$
$73$	1.92588	+	3.33572i	0.225407	+	0.390416i	−0.731035	+	0.682340i	$0.760962\pi$
$74$	6.15402	+	6.55365i	0.715390	+	0.761846i
$75$		0			0
$76$	−2.13306	−	0.134296i	−0.244679	−	0.0154048i
$77$	−0.317537	−	0.872425i	−0.0361867	−	0.0994221i
$78$		0			0
$79$	9.63652	−	1.69918i	1.08419	−	0.191173i	0.397124	−	0.917765i	$-0.370008\pi$
$79$	9.63652	−	1.69918i	1.08419	−	0.191173i	0.687069	+	0.726592i	$0.258897\pi$
$80$	14.2051	+	4.39859i	1.58818	+	0.491777i
$81$		0			0
$82$	0.551778	−	1.09228i	0.0609337	−	0.120622i
$83$	0.291958	+	1.65578i	0.0320466	+	0.181745i	0.996629	−	0.0820348i	$-0.0261419\pi$
$83$	0.291958	+	1.65578i	0.0320466	+	0.181745i	−0.964583	+	0.263780i	$0.915031\pi$
$84$		0			0
$85$	−18.1881	+	6.61992i	−1.97278	+	0.718031i
$86$	2.62554	−	1.12524i	0.283120	−	0.121338i
$87$		0			0
$88$	0.286242	−	1.55903i	0.0305135	−	0.166193i
$89$	10.9229	−	6.30632i	1.15782	−	0.668469i	0.207041	−	0.978332i	$-0.433617\pi$
$89$	10.9229	−	6.30632i	1.15782	−	0.668469i	0.950781	+	0.309864i	$0.100283\pi$
$90$		0			0
$91$	−3.72736	−	2.15199i	−0.390734	−	0.225590i
$92$	17.3231	+	4.19171i	1.80606	+	0.437016i
$93$		0			0
$94$	5.98244	−	7.99653i	0.617042	−	0.824779i
$95$	0.689874	−	3.91247i	0.0707795	−	0.401411i
$96$		0			0
$97$	−3.05643	+	2.56465i	−0.310334	+	0.260401i	−0.784630	−	0.619964i	$-0.787147\pi$
$97$	−3.05643	+	2.56465i	−0.310334	+	0.260401i	0.474296	+	0.880365i	$0.342703\pi$
$98$	−5.03583	+	3.29520i	−0.508696	+	0.332865i
$99$		0			0
$100$	−7.06349	+	16.1658i	−0.706349	+	1.61658i
$101$	2.63350	−	7.23547i	0.262043	−	0.719957i	−0.736987	−	0.675907i	$-0.763752\pi$
$101$	2.63350	−	7.23547i	0.262043	−	0.719957i	0.999029	−	0.0440493i	$-0.0140259\pi$
$102$		0			0
$103$	1.92800	−	2.29770i	0.189972	−	0.226399i	−0.662649	−	0.748930i	$-0.730568\pi$
$103$	1.92800	−	2.29770i	0.189972	−	0.226399i	0.852620	+	0.522531i	$0.175012\pi$
$104$	−3.62916	−	6.38947i	−0.355869	−	0.626539i
$105$		0			0
$106$	9.21288	+	2.78175i	0.894834	+	0.270188i
$107$	11.8919			1.14963			0.574815	−	0.818283i	$-0.305074\pi$
$107$	11.8919			1.14963			0.574815	+	0.818283i	$0.305074\pi$
$108$		0			0
$109$	9.26570			0.887493			0.443747	−	0.896152i	$-0.353649\pi$
$109$	9.26570			0.887493			0.443747	+	0.896152i	$0.353649\pi$
$110$	2.82061	+	0.851660i	0.268935	+	0.0812026i
$111$		0			0
$112$	6.61877	−	0.323126i	0.625415	−	0.0305326i
$113$	3.62339	−	4.31819i	0.340860	−	0.406221i	−0.568197	−	0.822893i	$-0.692359\pi$
$113$	3.62339	−	4.31819i	0.340860	−	0.406221i	0.909057	+	0.416671i	$0.136803\pi$
$114$		0			0
$115$	−11.3310	+	31.1318i	−1.05662	+	2.90305i
$116$	2.00322	+	0.875289i	0.185994	+	0.0812686i
$117$		0			0
$118$	−10.7926	+	7.06211i	−0.993535	+	0.650120i
$119$	−6.60729	+	5.54418i	−0.605689	+	0.508234i
$120$		0			0
$121$	−1.85559	+	10.5236i	−0.168690	+	0.956690i
$122$	4.05967	−	5.42643i	0.367546	−	0.491286i
$123$		0			0
$124$	1.51609	−	6.26557i	0.136149	−	0.562664i
$125$	−12.3012	−	7.10212i	−1.10026	−	0.635233i
$126$		0			0
$127$	7.01988	−	4.05293i	0.622914	−	0.359639i	−0.155089	−	0.987901i	$-0.549566\pi$
$127$	7.01988	−	4.05293i	0.622914	−	0.359639i	0.778002	+	0.628261i	$0.216233\pi$
$128$	10.0254	+	5.24315i	0.886132	+	0.463433i
$129$		0			0
$130$	12.5546	−	5.38056i	1.10111	−	0.471906i
$131$	8.71368	−	3.17152i	0.761318	−	0.277097i	0.0679578	−	0.997688i	$-0.478352\pi$
$131$	8.71368	−	3.17152i	0.761318	−	0.277097i	0.693360	+	0.720591i	$0.256129\pi$
$132$		0			0
$133$	−0.307424	−	1.74349i	−0.0266570	−	0.151180i
$134$	−7.01116	+	13.8790i	−0.605672	+	1.19896i
$135$		0			0
$136$	−14.5198	+	2.45485i	−1.24506	+	0.210501i
$137$	−3.40162	+	0.599798i	−0.290620	+	0.0512442i	−0.317058	−	0.948406i	$-0.602695\pi$
$137$	−3.40162	+	0.599798i	−0.290620	+	0.0512442i	0.0264373	+	0.999650i	$0.491584\pi$
$138$		0			0
$139$	−1.83675	−	5.04642i	−0.155791	−	0.428031i	0.837102	−	0.547047i	$-0.184248\pi$
$139$	−1.83675	−	5.04642i	−0.155791	−	0.428031i	−0.992892	+	0.119016i	$0.962026\pi$
$140$	−0.773979	+	12.2934i	−0.0654132	+	1.03898i
$141$		0			0
$142$	−7.70985	−	8.21052i	−0.646996	−	0.689011i
$143$	−0.727971	−	1.26088i	−0.0608760	−	0.105440i
$144$		0			0
$145$	−2.03177	+	3.51913i	−0.168730	+	0.292248i
$146$	−5.30331	+	1.24376i	−0.438905	+	0.102934i
$147$		0			0
$148$	−11.3883	+	5.65257i	−0.936111	+	0.464638i
$149$	−11.2835	−	1.98959i	−0.924380	−	0.162993i	−0.308854	−	0.951109i	$-0.599945\pi$
$149$	−11.2835	−	1.98959i	−0.924380	−	0.162993i	−0.615526	+	0.788116i	$0.711057\pi$
$150$		0			0
$151$	−14.6691	−	17.4820i	−1.19376	−	1.42266i	−0.881186	−	0.472769i	$-0.843255\pi$
$151$	−14.6691	−	17.4820i	−1.19376	−	1.42266i	−0.312570	−	0.949895i	$-0.601190\pi$
$152$	1.05378	−	2.83294i	0.0854725	−	0.229782i
$153$		0			0
$154$	1.31093	−	0.0732635i	0.105638	−	0.00590374i
$155$	11.2600	+	4.09830i	0.904425	+	0.329184i
$156$		0			0
$157$	6.35613	+	5.33342i	0.507274	+	0.425653i	0.860169	−	0.510010i	$-0.170358\pi$
$157$	6.35613	+	5.33342i	0.507274	+	0.425653i	−0.352895	+	0.935663i	$0.614803\pi$
$158$	−1.63882	+	13.7409i	−0.130377	+	1.09317i
$159$		0			0
$160$	−11.7618	+	17.4334i	−0.929852	+	1.37823i
$161$			14.7634i			1.16352i
$162$		0			0
$163$		−	8.81551i		−	0.690484i	−0.938514	−	0.345242i	$-0.887797\pi$
$163$		−	8.81551i		−	0.690484i	0.938514	−	0.345242i	$-0.112203\pi$
$164$	1.25321	+	1.19353i	0.0978596	+	0.0931987i
$165$		0			0
$166$	−2.36101	−	0.281586i	−0.183250	−	0.0218554i
$167$	−17.2747	−	14.4952i	−1.33675	−	1.12167i	−0.982447	−	0.186540i	$-0.940273\pi$
$167$	−17.2747	−	14.4952i	−1.33675	−	1.12167i	−0.354306	−	0.935130i	$-0.615283\pi$
$168$		0			0
$169$	5.87353	+	2.13779i	0.451810	+	0.164445i
$170$	−1.52738	−	27.3300i	−0.117144	−	2.09611i
$171$		0			0
$172$	0.450126	+	4.01456i	0.0343218	+	0.306107i
$173$	6.59368	+	7.85804i	0.501308	+	0.597436i	0.956056	−	0.293185i	$-0.0947150\pi$
$173$	6.59368	+	7.85804i	0.501308	+	0.597436i	−0.454748	+	0.890620i	$0.650271\pi$
$174$		0			0
$175$	−14.3911	−	2.53753i	−1.08786	−	0.191819i
$176$	1.99367	+	1.02483i	0.150279	+	0.0772494i
$177$		0			0
$178$	4.07270	+	17.3658i	0.305262	+	1.30162i
$179$	−7.25044	+	12.5581i	−0.541923	+	0.938639i	0.456870	+	0.889533i	$0.348970\pi$
$179$	−7.25044	+	12.5581i	−0.541923	+	0.938639i	−0.998794	+	0.0491053i	$0.984363\pi$
$180$		0			0
$181$	−2.64382	−	4.57923i	−0.196513	−	0.340371i	0.750882	−	0.660436i	$-0.229629\pi$
$181$	−2.64382	−	4.57923i	−0.196513	−	0.340371i	−0.947396	+	0.320065i	$0.896295\pi$
$182$	4.43715	−	4.16657i	0.328903	−	0.308847i
$183$		0			0
$184$	−12.7563	+	21.7393i	−0.940408	+	1.60264i
$185$	−8.08292	−	22.2076i	−0.594268	−	1.63274i
$186$		0			0
$187$	−2.87339	+	0.506656i	−0.210123	+	0.0370503i
$188$	8.38054	+	11.3681i	0.611214	+	0.829107i
$189$		0			0
$190$	5.01487	+	2.53333i	0.363817	+	0.183787i
$191$	−2.03752	−	11.5553i	−0.147429	−	0.836114i	−0.965384	−	0.260832i	$-0.916003\pi$
$191$	−2.03752	−	11.5553i	−0.147429	−	0.836114i	0.817955	−	0.575283i	$-0.195108\pi$
$192$		0			0
$193$	21.7564	−	7.91869i	1.56606	−	0.570000i	0.593947	−	0.804504i	$-0.297569\pi$
$193$	21.7564	−	7.91869i	1.56606	−	0.570000i	0.972115	+	0.234504i	$0.0753467\pi$
$194$	−2.22273	−	5.18632i	−0.159582	−	0.372356i
$195$		0			0
$196$	−2.40263	−	8.16476i	−0.171616	−	0.583197i
$197$	0.386490	−	0.223140i	0.0275363	−	0.0158981i	−0.486169	−	0.873865i	$-0.661606\pi$
$197$	0.386490	−	0.223140i	0.0275363	−	0.0158981i	0.513705	+	0.857967i	$0.328273\pi$
$198$		0			0
$199$	9.88191	+	5.70532i	0.700510	+	0.404440i	0.807537	−	0.589816i	$-0.200800\pi$
$199$	9.88191	+	5.70532i	0.700510	+	0.404440i	−0.107027	+	0.994256i	$0.534133\pi$
$200$	−18.9985	−	16.1712i	−1.34340	−	1.14347i
$201$		0			0
$202$	8.71918	+	6.52308i	0.613480	+	0.458963i
$203$	−0.314444	+	1.78330i	−0.0220697	+	0.125163i
$204$		0			0
$205$	−2.46429	+	2.06779i	−0.172114	+	0.144420i
$206$	2.32260	+	3.54947i	0.161823	+	0.247304i
$207$		0			0
$208$	10.1339	−	2.30142i	0.702659	−	0.159575i
$209$	0.204830	−	0.562765i	0.0141684	−	0.0389272i
$210$		0			0
$211$	−3.73428	+	4.45035i	−0.257079	+	0.306374i	−0.879111	−	0.476617i	$-0.841863\pi$
$211$	−3.73428	+	4.45035i	−0.257079	+	0.306374i	0.622032	+	0.782992i	$0.286307\pi$
$212$	−7.53213	+	11.3357i	−0.517309	+	0.778537i
$213$		0			0
$214$	−4.86119	+	16.0998i	−0.332304	+	1.10056i
$215$	−7.50908			−0.512115
$216$		0			0
$217$	5.33975			0.362486
$218$	−3.78766	+	12.5443i	−0.256533	+	0.849609i
$219$		0			0
$220$	−2.30603	+	3.47053i	−0.155473	+	0.233983i
$221$	−8.69439	+	10.3616i	−0.584848	+	0.696994i
$222$		0			0
$223$	1.27259	−	3.49640i	0.0852186	−	0.234136i	−0.889763	−	0.456424i	$-0.849130\pi$
$223$	1.27259	−	3.49640i	0.0852186	−	0.234136i	0.974981	+	0.222287i	$0.0713523\pi$
$224$	−2.26818	+	9.09288i	−0.151549	+	0.607544i
$225$		0			0
$226$	4.36498	+	6.67072i	0.290354	+	0.443729i
$227$	−5.06798	+	4.25254i	−0.336373	+	0.282251i	−0.795291	−	0.606228i	$-0.792682\pi$
$227$	−5.06798	+	4.25254i	−0.336373	+	0.282251i	0.458917	+	0.888479i	$0.348237\pi$
$228$		0			0
$229$	0.200719	−	1.13833i	0.0132639	−	0.0752232i	−0.977457	−	0.211133i	$-0.932285\pi$
$229$	0.200719	−	1.13833i	0.0132639	−	0.0752232i	0.990721	+	0.135910i	$0.0433958\pi$
$230$	−37.5157	−	28.0666i	−2.47371	−	1.85066i
$231$		0			0
$232$	−2.00389	+	2.35424i	−0.131562	+	0.154564i
$233$	14.7446	+	8.51281i	0.965953	+	0.557693i	0.898000	−	0.439996i	$-0.145020\pi$
$233$	14.7446	+	8.51281i	0.965953	+	0.557693i	0.0679527	+	0.997689i	$0.478353\pi$
$234$		0			0
$235$	−22.7355	+	13.1263i	−1.48310	+	0.856267i
$236$	−5.14919	−	17.4983i	−0.335184	−	1.13904i
$237$		0			0
$238$	−4.80501	−	11.2116i	−0.311463	−	0.726741i
$239$	−1.13370	+	0.412633i	−0.0733329	+	0.0266910i	−0.378426	−	0.925632i	$-0.623535\pi$
$239$	−1.13370	+	0.412633i	−0.0733329	+	0.0266910i	0.305093	+	0.952322i	$0.401312\pi$
$240$		0			0
$241$	−1.73549	−	9.84245i	−0.111793	−	0.634008i	−0.988288	−	0.152598i	$-0.951236\pi$
$241$	−1.73549	−	9.84245i	−0.111793	−	0.634008i	0.876496	−	0.481410i	$-0.159875\pi$
$242$	−13.4888	−	6.81405i	−0.867092	−	0.438024i
$243$		0			0
$244$	5.68702	+	7.71440i	0.364074	+	0.493864i
$245$	15.5799	−	2.74716i	0.995363	−	0.175509i
$246$		0			0
$247$	−0.949558	−	2.60889i	−0.0604189	−	0.166000i
$248$	7.86285	+	4.61381i	0.499292	+	0.292977i
$249$		0			0
$250$	14.6437	−	13.7507i	0.926149	−	0.869674i
$251$	−6.65375	−	11.5246i	−0.419981	−	0.727429i	0.575956	−	0.817481i	$-0.304630\pi$
$251$	−6.65375	−	11.5246i	−0.419981	−	0.727429i	−0.995937	+	0.0900521i	$0.971297\pi$
$252$		0			0
$253$	−2.49706	+	4.32504i	−0.156989	+	0.271913i
$254$	2.61743	+	11.1606i	0.164232	+	0.700278i
$255$		0			0
$256$	−11.1966	+	11.4296i	−0.699789	+	0.714349i
$257$	13.6583	+	2.40833i	0.851982	+	0.150227i	0.582553	−	0.812793i	$-0.302054\pi$
$257$	13.6583	+	2.40833i	0.851982	+	0.150227i	0.269429	+	0.963020i	$0.413165\pi$
$258$		0			0
$259$	−6.76944	−	8.06750i	−0.420632	−	0.501290i
$260$	2.15236	+	19.1964i	0.133484	+	1.19051i
$261$		0			0
$262$	0.731747	+	13.0934i	0.0452075	+	0.808916i
$263$	−2.30086	−	0.837443i	−0.141877	−	0.0516389i	0.270106	−	0.962831i	$-0.412941\pi$
$263$	−2.30086	−	0.837443i	−0.141877	−	0.0516389i	−0.411983	+	0.911192i	$0.635164\pi$
$264$		0			0
$265$	−19.3797	−	16.2615i	−1.19048	−	0.998934i
$266$	2.48608	+	0.296503i	0.152432	+	0.0181798i
$267$		0			0
$268$	−15.9240	−	15.1655i	−0.972710	−	0.926381i
$269$			4.12106i			0.251266i	0.992077	+	0.125633i	$0.0400961\pi$
$269$			4.12106i			0.251266i	−0.992077	+	0.125633i	$0.959904\pi$
$270$		0			0
$271$			11.9859i			0.728089i	0.931382	+	0.364044i	$0.118604\pi$
$271$			11.9859i			0.728089i	−0.931382	+	0.364044i	$0.881396\pi$
$272$	2.61195	−	20.6610i	0.158373	−	1.25276i
$273$		0			0
$274$	0.578491	−	4.85046i	0.0349479	−	0.293027i
$275$	−3.78677	−	3.17748i	−0.228351	−	0.191609i
$276$		0			0
$277$	28.2226	+	10.2722i	1.69573	+	0.617196i	0.995328	−	0.0965505i	$-0.0307809\pi$
$277$	28.2226	+	10.2722i	1.69573	+	0.617196i	0.700404	+	0.713747i	$0.253003\pi$
$278$	7.58289	−	0.423782i	0.454792	−	0.0254167i
$279$		0			0
$280$	−16.3270	−	6.07317i	−0.975722	−	0.362941i
$281$	−4.45426	−	5.30838i	−0.265719	−	0.316671i	0.616643	−	0.787243i	$-0.288492\pi$
$281$	−4.45426	−	5.30838i	−0.265719	−	0.316671i	−0.882362	+	0.470572i	$0.844048\pi$
$282$		0			0
$283$	−18.5824	−	3.27657i	−1.10461	−	0.194772i	−0.408534	−	0.912743i	$-0.633960\pi$
$283$	−18.5824	−	3.27657i	−1.10461	−	0.194772i	−0.696073	+	0.717971i	$0.745071\pi$
$284$	14.2674	−	7.08162i	0.846616	−	0.420217i
$285$		0			0
$286$	2.00462	−	0.470133i	0.118536	−	0.0277996i
$287$	−0.716765	+	1.24147i	−0.0423093	+	0.0732818i
$288$		0			0
$289$	5.05314	+	8.75230i	0.297244	+	0.514841i
$290$	−3.93381	−	4.18927i	−0.231001	−	0.246002i
$291$		0			0
$292$	0.484047	−	7.68828i	0.0283267	−	0.449923i
$293$	7.22753	+	19.8575i	0.422237	+	1.16009i	0.950424	+	0.310958i	$0.100650\pi$
$293$	7.22753	+	19.8575i	0.422237	+	1.16009i	−0.528186	+	0.849128i	$0.677128\pi$
$294$		0			0
$295$	33.3901	−	5.88757i	1.94405	−	0.342788i
$296$	−2.99737	−	17.7286i	−0.174218	−	1.03046i
$297$		0			0
$298$	7.30609	−	14.4628i	0.423230	−	0.837808i
$299$	4.02030	+	22.8003i	0.232500	+	1.31857i
$300$		0			0
$301$	−3.14442	+	1.14448i	−0.181242	+	0.0659665i
$302$	29.6644	−	12.7134i	1.70699	−	0.731574i
$303$		0			0
$304$	3.40460	+	2.58471i	0.195267	+	0.148243i
$305$	−15.4282	+	8.90750i	−0.883418	+	0.510042i
$306$		0			0
$307$	−17.4037	−	10.0480i	−0.993279	−	0.573470i	−0.0870262	−	0.996206i	$-0.527736\pi$
$307$	−17.4037	−	10.0480i	−0.993279	−	0.573470i	−0.906253	+	0.422736i	$0.861070\pi$
$308$	−0.436699	+	1.80475i	−0.0248832	+	0.102835i
$309$		0			0
$310$	−10.1514	+	13.5690i	−0.576558	+	0.770666i
$311$	−4.52522	+	25.6638i	−0.256602	+	1.45526i	0.535326	+	0.844645i	$0.320189\pi$
$311$	−4.52522	+	25.6638i	−0.256602	+	1.45526i	−0.791928	+	0.610614i	$0.790923\pi$
$312$		0			0
$313$	−18.6039	+	15.6105i	−1.05155	+	0.882358i	−0.993256	−	0.115942i	$-0.963011\pi$
$313$	−18.6039	+	15.6105i	−1.05155	+	0.882358i	−0.0582968	+	0.998299i	$0.518567\pi$
$314$	−9.81890	+	6.42500i	−0.554113	+	0.362584i
$315$		0			0
$316$	−17.9332	−	7.83576i	−1.00882	−	0.440796i
$317$	2.11156	−	5.80146i	0.118597	−	0.325842i	−0.866163	−	0.499762i	$-0.833421\pi$
$317$	2.11156	−	5.80146i	0.118597	−	0.325842i	0.984760	+	0.173919i	$0.0556432\pi$
$318$		0			0
$319$	−0.393744	+	0.469246i	−0.0220454	+	0.0262727i
$320$	−18.7942	−	23.0501i	−1.05063	−	1.28854i
$321$		0			0
$322$	−19.9874	−	6.03502i	−1.11385	−	0.336318i
$323$	−5.56376			−0.309576
$324$		0			0
$325$	−22.9162			−1.27116
$326$	11.9348	+	3.60363i	0.661010	+	0.199586i
$327$		0			0
$328$	−2.12814	+	1.20877i	−0.117507	+	0.0667429i
$329$	−7.51984	+	8.96180i	−0.414582	+	0.494080i
$330$		0			0
$331$	4.90924	−	13.4880i	0.269836	−	0.741368i	−0.728572	−	0.684969i	$-0.759816\pi$
$331$	4.90924	−	13.4880i	0.269836	−	0.741368i	0.998408	−	0.0563994i	$-0.0179620\pi$
$332$	1.34637	−	3.08134i	0.0738914	−	0.169110i
$333$		0			0
$334$	26.6858	−	17.4618i	1.46018	−	0.955470i
$335$	31.3125	−	26.2743i	1.71078	−	1.43552i
$336$		0			0
$337$	−3.34222	+	18.9547i	−0.182062	+	1.03253i	0.747610	+	0.664138i	$0.231201\pi$
$337$	−3.34222	+	18.9547i	−0.182062	+	1.03253i	−0.929672	+	0.368388i	$0.879910\pi$
$338$	−5.29523	+	7.07796i	−0.288023	+	0.384990i
$339$		0			0
$340$	37.6249	+	9.10418i	2.04050	+	0.493744i
$341$	1.56432	+	0.903158i	0.0847125	+	0.0489088i
$342$		0			0
$343$	16.1484	−	9.32326i	0.871930	−	0.503409i
$344$	−5.61910	−	1.03168i	−0.302961	−	0.0556245i
$345$		0			0
$346$	−13.3340	+	5.71459i	−0.716838	+	0.307218i
$347$	29.8556	−	10.8665i	1.60273	−	0.583346i	0.622747	−	0.782423i	$-0.286017\pi$
$347$	29.8556	−	10.8665i	1.60273	−	0.583346i	0.979984	+	0.199077i	$0.0637945\pi$
$348$		0			0
$349$	3.00735	+	17.0555i	0.160980	+	0.912962i	0.953113	+	0.302614i	$0.0978592\pi$
$349$	3.00735	+	17.0555i	0.160980	+	0.912962i	−0.792134	+	0.610348i	$0.791030\pi$
$350$	9.31824	−	18.4460i	0.498081	−	0.985979i
$351$		0			0
$352$	−2.20244	+	2.28019i	−0.117390	+	0.121534i
$353$	−3.94975	+	0.696448i	−0.210224	+	0.0370682i	−0.277768	−	0.960648i	$-0.589595\pi$
$353$	−3.94975	+	0.696448i	−0.210224	+	0.0370682i	0.0675442	+	0.997716i	$0.478484\pi$
$354$		0			0
$355$	10.1264	+	27.8221i	0.537454	+	1.47664i
$356$	−25.1754	−	1.58502i	−1.33430	−	0.0840059i
$357$		0			0
$358$	−14.0379	−	14.9495i	−0.741927	−	0.790106i
$359$	6.05065	+	10.4800i	0.319341	+	0.553115i	0.980351	−	0.197262i	$-0.0632051\pi$
$359$	6.05065	+	10.4800i	0.319341	+	0.553115i	−0.661010	+	0.750377i	$0.729872\pi$
$360$		0			0
$361$	−8.92900	+	15.4655i	−0.469947	+	0.813973i
$362$	7.28031	−	1.70741i	0.382645	−	0.0897396i
$363$		0			0
$364$	3.82707	+	7.71043i	0.200593	+	0.404137i
$365$	14.1019	+	2.48654i	0.738125	+	0.130151i
$366$		0			0
$367$	2.21046	+	2.63433i	0.115385	+	0.137511i	0.820645	−	0.571438i	$-0.193614\pi$
$367$	2.21046	+	2.63433i	0.115385	+	0.137511i	−0.705260	+	0.708949i	$0.749170\pi$
$368$	−24.2171	−	26.1567i	−1.26240	−	1.36351i
$369$		0			0
$370$	33.3699	−	1.86493i	1.73482	−	0.0969529i
$371$	−10.5937	−	3.85578i	−0.549996	−	0.200182i
$372$		0			0
$373$	4.39389	+	3.68691i	0.227507	+	0.190901i	0.749415	−	0.662101i	$-0.230335\pi$
$373$	4.39389	+	3.68691i	0.227507	+	0.190901i	−0.521908	+	0.853002i	$0.674779\pi$
$374$	0.488657	−	4.09723i	0.0252679	−	0.211863i
$375$		0			0
$376$	−18.8165	+	6.69886i	−0.970388	+	0.345467i
$377$			2.83972i			0.146253i
$378$		0			0
$379$			25.2439i			1.29669i	0.761346	+	0.648346i	$0.224539\pi$
$379$			25.2439i			1.29669i	−0.761346	+	0.648346i	$0.775461\pi$
$380$	−5.47973	+	5.75377i	−0.281104	+	0.295162i
$381$		0			0
$382$	16.4770	+	1.96514i	0.843038	+	0.100545i
$383$	7.45183	+	6.25283i	0.380771	+	0.319505i	0.813005	−	0.582257i	$-0.197830\pi$
$383$	7.45183	+	6.25283i	0.380771	+	0.319505i	−0.432234	+	0.901761i	$0.642275\pi$
$384$		0			0
$385$	−3.24335	−	1.18048i	−0.165297	−	0.0601631i
$386$	1.82703	+	32.6919i	0.0929936	+	1.66397i
$387$		0			0
$388$	7.93009	−	0.889148i	0.402589	−	0.0451396i
$389$	5.73930	+	6.83983i	0.290994	+	0.346793i	0.891659	−	0.452708i	$-0.149542\pi$
$389$	5.73930	+	6.83983i	0.290994	+	0.346793i	−0.600665	+	0.799501i	$0.705097\pi$
$390$		0			0
$391$	45.6918	+	8.05670i	2.31073	+	0.407445i
$392$	12.0360	+	0.0848252i	0.607908	+	0.00428432i
$393$		0			0
$394$	0.144107	+	0.614464i	0.00726000	+	0.0309562i
$395$	18.1888	−	31.5040i	0.915180	−	1.58514i
$396$		0			0
$397$	−1.03466	−	1.79209i	−0.0519283	−	0.0899424i	0.838893	−	0.544297i	$-0.183203\pi$
$397$	−1.03466	−	1.79209i	−0.0519283	−	0.0899424i	−0.890821	+	0.454354i	$0.849870\pi$
$398$	−11.7637	+	11.0463i	−0.589660	+	0.553703i
$399$		0			0
$400$	29.6595	−	19.1105i	1.48297	−	0.955527i
$401$	10.4273	+	28.6488i	0.520714	+	1.43065i	0.869727	+	0.493533i	$0.164295\pi$
$401$	10.4273	+	28.6488i	0.520714	+	1.43065i	−0.349013	+	0.937118i	$0.613483\pi$
$402$		0			0
$403$	8.24658	−	1.45410i	0.410792	−	0.0724336i
$404$	−12.3955	+	9.13790i	−0.616699	+	0.454628i
$405$		0			0
$406$	−2.28578	−	1.15469i	−0.113441	−	0.0573064i
$407$	−0.618626	−	3.50841i	−0.0306642	−	0.173905i
$408$		0			0
$409$	33.4041	−	12.1581i	1.65173	−	0.601180i	0.662697	−	0.748888i	$-0.269412\pi$
$409$	33.4041	−	12.1581i	1.65173	−	0.601180i	0.989031	+	0.147708i	$0.0471896\pi$
$410$	−1.79210	−	4.18155i	−0.0885057	−	0.206512i
$411$		0			0
$412$	−5.75488	+	1.69348i	−0.283522	+	0.0834316i
$413$	13.0847	−	7.55447i	0.643858	−	0.371731i
$414$		0			0
$415$	5.41311	+	3.12526i	0.265719	+	0.153413i
$416$	−1.02679	+	14.6605i	−0.0503424	+	0.718790i
$417$		0			0
$418$	0.678165	+	0.507356i	0.0331701	+	0.0248156i
$419$	2.13949	−	12.1336i	0.104521	−	0.592766i	−0.886890	−	0.461981i	$-0.847139\pi$
$419$	2.13949	−	12.1336i	0.104521	−	0.592766i	0.991411	−	0.130786i	$-0.0417500\pi$
$420$		0			0
$421$	−13.3302	+	11.1854i	−0.649674	+	0.545141i	−0.906972	−	0.421191i	$-0.861612\pi$
$421$	−13.3302	+	11.1854i	−0.649674	+	0.545141i	0.257298	+	0.966332i	$0.417168\pi$
$422$	−4.49857	−	6.87487i	−0.218987	−	0.334663i
$423$		0			0
$424$	−12.2677	−	14.8312i	−0.595774	−	0.720265i
$425$	−15.7070	+	43.1547i	−0.761902	+	2.09331i
$426$		0			0
$427$	−5.10295	+	6.08146i	−0.246949	+	0.294302i
$428$	−19.8094	−	13.1626i	−0.957524	−	0.636238i
$429$		0			0
$430$	3.06958	−	10.1661i	0.148028	−	0.490255i
$431$	19.0526			0.917729			0.458865	−	0.888506i	$-0.348256\pi$
$431$	19.0526			0.917729			0.458865	+	0.888506i	$0.348256\pi$
$432$		0			0
$433$	−37.4918			−1.80174			−0.900870	−	0.434088i	$-0.857071\pi$
$433$	−37.4918			−1.80174			−0.900870	+	0.434088i	$0.857071\pi$
$434$	−2.18280	+	7.22919i	−0.104778	+	0.347012i
$435$		0			0
$436$	−15.4348	−	10.2558i	−0.739191	−	0.491164i
$437$	−6.12142	+	7.29523i	−0.292827	+	0.348978i
$438$		0			0
$439$	−7.67971	+	21.0998i	−0.366532	+	1.00704i	0.610138	+	0.792295i	$0.291114\pi$
$439$	−7.67971	+	21.0998i	−0.366532	+	1.00704i	−0.976670	+	0.214744i	$0.931108\pi$
$440$	−3.75589	−	4.54070i	−0.179055	−	0.216469i
$441$		0			0
$442$	−10.4738	−	16.0065i	−0.498190	−	0.761351i
$443$	−7.88175	+	6.61357i	−0.374473	+	0.314220i	−0.810528	−	0.585700i	$-0.800820\pi$
$443$	−7.88175	+	6.61357i	−0.374473	+	0.314220i	0.436055	+	0.899920i	$0.356375\pi$
$444$		0			0
$445$	8.14221	−	46.1768i	0.385978	−	2.18899i
$446$	4.21337	+	3.15215i	0.199509	+	0.149259i
$447$		0			0
$448$	−11.3832	−	6.78777i	−0.537804	−	0.320692i
$449$	7.77889	+	4.49114i	0.367109	+	0.211950i	0.672194	−	0.740375i	$-0.265352\pi$
$449$	7.77889	+	4.49114i	0.367109	+	0.211950i	−0.305086	+	0.952325i	$0.598685\pi$
$450$		0			0
$451$	−0.419962	+	0.242465i	−0.0197753	+	0.0114172i
$452$	−10.8154	+	3.18264i	−0.508716	+	0.149699i
$453$		0			0
$454$	−3.68558	−	8.59962i	−0.172973	−	0.403600i
$455$	−15.0357	+	5.47254i	−0.704884	+	0.256557i
$456$		0			0
$457$	−0.828465	−	4.69846i	−0.0387540	−	0.219785i	0.959280	−	0.282456i	$-0.0911491\pi$
$457$	−0.828465	−	4.69846i	−0.0387540	−	0.219785i	−0.998034	+	0.0626714i	$0.980038\pi$
$458$	1.45908	+	0.737074i	0.0681782	+	0.0344412i
$459$		0			0
$460$	53.3336	−	39.3173i	2.48669	−	1.83318i
$461$	−28.1480	+	4.96325i	−1.31098	+	0.231162i	−0.785086	−	0.619386i	$-0.787381\pi$
$461$	−28.1480	+	4.96325i	−1.31098	+	0.231162i	−0.525897	+	0.850548i	$0.676270\pi$
$462$		0			0
$463$	−14.5089	−	39.8630i	−0.674287	−	1.85259i	−0.495258	−	0.868746i	$-0.664927\pi$
$463$	−14.5089	−	39.8630i	−0.674287	−	1.85259i	−0.179029	−	0.983844i	$-0.557296\pi$
$464$	−2.36813	−	3.67533i	−0.109938	−	0.170623i
$465$		0			0
$466$	−17.5524	+	16.4821i	−0.813098	+	0.763516i
$467$	−3.22767	−	5.59048i	−0.149359	−	0.258697i	0.781632	−	0.623740i	$-0.214388\pi$
$467$	−3.22767	−	5.59048i	−0.149359	−	0.258697i	−0.930991	+	0.365043i	$0.881054\pi$
$468$		0			0
$469$	9.10756	−	15.7748i	0.420548	−	0.728410i
$470$	−8.47715	−	36.1461i	−0.391022	−	1.66730i
$471$		0			0
$472$	25.7949	+	0.181793i	1.18731	+	0.00836771i
$473$	−1.11476	−	0.196562i	−0.0512566	−	0.00903791i
$474$		0			0
$475$	−6.05909	−	7.22094i	−0.278010	−	0.331320i
$476$	17.1430	−	1.92213i	0.785748	−	0.0881006i
$477$		0			0
$478$	−0.0952044	−	1.70353i	−0.00435455	−	0.0779176i
$479$	33.5552	+	12.2131i	1.53317	+	0.558030i	0.964396	−	0.264461i	$-0.0851939\pi$
$479$	33.5552	+	12.2131i	1.53317	+	0.558030i	0.568778	+	0.822491i	$0.307416\pi$
$480$		0			0
$481$	−12.6515	−	10.6158i	−0.576857	−	0.484041i
$482$	14.0346	+	1.67384i	0.639258	+	0.0762412i
$483$		0			0
$484$	14.7391	−	15.4763i	0.669961	−	0.703466i
$485$			14.8329i			0.673529i
$486$		0			0
$487$		−	40.6600i		−	1.84248i	−0.388993	−	0.921241i	$-0.627177\pi$
$487$		−	40.6600i		−	1.84248i	0.388993	−	0.921241i	$-0.372823\pi$
$488$	−12.7689	+	4.54583i	−0.578019	+	0.205780i
$489$		0			0
$490$	−2.64957	+	22.2158i	−0.119695	+	1.00361i
$491$	21.5421	+	18.0759i	0.972180	+	0.815756i	0.982891	−	0.184187i	$-0.0589651\pi$
$491$	21.5421	+	18.0759i	0.972180	+	0.815756i	−0.0107111	+	0.999943i	$0.503410\pi$
$492$		0			0
$493$	5.34761	+	1.94637i	0.240844	+	0.0876601i
$494$	3.92019	−	0.219086i	0.176378	−	0.00985715i
$495$		0			0
$496$	−9.46058	+	8.75904i	−0.424793	+	0.393293i
$497$	8.48085	+	10.1071i	0.380418	+	0.453365i
$498$		0			0
$499$	−32.6149	−	5.75089i	−1.46005	−	0.257445i	−0.613471	−	0.789717i	$-0.710227\pi$
$499$	−32.6149	−	5.75089i	−1.46005	−	0.257445i	−0.846574	+	0.532272i	$0.821339\pi$
$500$	12.6303	+	25.4464i	0.564844	+	1.13800i
$501$		0			0
$502$	18.3225	−	4.29708i	0.817774	−	0.191788i
$503$	13.4484	−	23.2932i	0.599633	−	1.03859i	−0.393242	−	0.919435i	$-0.628647\pi$
$503$	13.4484	−	23.2932i	0.599633	−	1.03859i	0.992875	−	0.119159i	$-0.0380200\pi$
$504$		0			0
$505$	−14.3126	−	24.7901i	−0.636901	−	1.10314i
$506$	−4.83468	−	5.14864i	−0.214928	−	0.228885i
$507$		0			0
$508$	−16.1797	−	1.01866i	−0.717857	−	0.0451956i
$509$	−3.23712	−	8.89393i	−0.143483	−	0.394216i	0.847046	−	0.531519i	$-0.178379\pi$
$509$	−3.23712	−	8.89393i	−0.143483	−	0.394216i	−0.990529	+	0.137303i	$0.956157\pi$
$510$		0			0
$511$	6.28412	−	1.10806i	0.277993	−	0.0490177i
$512$	−10.8969	−	19.8307i	−0.481580	−	0.876402i
$513$		0			0
$514$	−8.84379	+	17.5068i	−0.390083	+	0.772190i
$515$	−1.93632	−	10.9814i	−0.0853242	−	0.483898i
$516$		0			0
$517$	−3.71878	+	1.35352i	−0.163552	+	0.0595280i
$518$	13.6894	−	5.86692i	0.601477	−	0.257777i
$519$		0			0
$520$	−26.8688	−	4.93319i	−1.17828	−	0.216335i
$521$	−15.6963	+	9.06226i	−0.687667	+	0.397025i	−0.802737	−	0.596333i	$-0.796624\pi$
$521$	−15.6963	+	9.06226i	−0.687667	+	0.397025i	0.115070	+	0.993357i	$0.463291\pi$
$522$		0			0
$523$	31.7246	+	18.3162i	1.38722	+	0.800912i	0.993001	−	0.118105i	$-0.0376819\pi$
$523$	31.7246	+	18.3162i	1.38722	+	0.800912i	0.394219	+	0.919017i	$0.371015\pi$
$524$	−18.0256	−	4.36170i	−0.787453	−	0.190542i
$525$		0			0
$526$	2.07432	−	2.77267i	0.0904446	−	0.120894i
$527$	2.91401	−	16.5262i	0.126936	−	0.719892i
$528$		0			0
$529$	43.2165	−	36.2630i	1.87898	−	1.57665i
$530$	29.9376	−	19.5897i	1.30041	−	0.850921i
$531$		0			0
$532$	−1.41769	+	3.24457i	−0.0614645	+	0.140670i
$533$	−0.768883	+	2.11249i	−0.0333040	+	0.0915020i
$534$		0			0
$535$	28.4174	−	33.8665i	1.22859	−	1.46418i
$536$	27.0412	−	15.3592i	1.16800	−	0.663415i
$537$		0			0
$538$	−5.57928	−	1.68462i	−0.240540	−	0.0726291i
$539$	2.38481			0.102721
$540$		0			0
$541$	31.5175			1.35504			0.677521	−	0.735504i	$-0.263054\pi$
$541$	31.5175			1.35504			0.677521	+	0.735504i	$0.263054\pi$
$542$	−16.2270	−	4.89961i	−0.697009	−	0.210456i
$543$		0			0
$544$	26.9041	+	11.9820i	1.15350	+	0.513726i
$545$	22.1418	−	26.3875i	0.948449	−	1.13032i
$546$		0			0
$547$	−10.7735	+	29.6001i	−0.460644	+	1.26561i	0.464359	+	0.885647i	$0.346285\pi$
$547$	−10.7735	+	29.6001i	−0.460644	+	1.26561i	−0.925003	+	0.379961i	$0.875938\pi$
$548$	6.33029	+	2.76597i	0.270417	+	0.118156i
$549$		0			0
$550$	5.84977	−	3.82780i	0.249435	−	0.163218i
$551$	−0.894800	+	0.750826i	−0.0381198	+	0.0319863i
$552$		0			0
$553$	2.81497	−	15.9645i	0.119705	−	0.678879i
$554$	−25.4439	+	34.0100i	−1.08101	+	1.44494i
$555$		0			0
$556$	−2.52602	+	10.4393i	−0.107127	+	0.442725i
$557$	13.9805	+	8.07165i	0.592373	+	0.342007i	0.766035	−	0.642799i	$-0.222227\pi$
$557$	13.9805	+	8.07165i	0.592373	+	0.342007i	−0.173662	+	0.984805i	$0.555560\pi$
$558$		0			0
$559$	−4.54452	+	2.62378i	−0.192213	+	0.110974i
$560$	14.8963	−	19.6216i	0.629484	−	0.829163i
$561$		0			0
$562$	9.00754	−	3.86040i	0.379960	−	0.162841i
$563$	−27.8476	+	10.1357i	−1.17364	+	0.427169i	−0.853951	−	0.520354i	$-0.825800\pi$
$563$	−27.8476	+	10.1357i	−1.17364	+	0.427169i	−0.319687	+	0.947523i	$0.603578\pi$
$564$		0			0
$565$	−3.63902	−	20.6379i	−0.153095	−	0.868244i
$566$	12.0321	−	23.8182i	0.505748	−	1.00116i
$567$		0			0
$568$	3.75515	+	22.2107i	0.157563	+	0.931941i
$569$	36.2357	−	6.38933i	1.51908	−	0.267855i	0.649009	−	0.760781i	$-0.275184\pi$
$569$	36.2357	−	6.38933i	1.51908	−	0.267855i	0.870071	+	0.492926i	$0.164073\pi$
$570$		0			0
$571$	0.343099	+	0.942656i	0.0143582	+	0.0394489i	0.946665	−	0.322220i	$-0.104429\pi$
$571$	0.343099	+	0.942656i	0.0143582	+	0.0394489i	−0.932306	+	0.361669i	$0.882207\pi$
$572$	−0.182967	+	2.90613i	−0.00765024	+	0.121511i
$573$		0			0
$574$	−1.38776	−	1.47788i	−0.0579240	−	0.0616855i
$575$	39.3033	+	68.0753i	1.63906	+	2.83893i
$576$		0			0
$577$	10.1847	−	17.6404i	0.423994	−	0.734379i	−0.572332	−	0.820022i	$-0.693961\pi$
$577$	10.1847	−	17.6404i	0.423994	−	0.734379i	0.996326	+	0.0856433i	$0.0272945\pi$
$578$	−13.9149	+	3.26339i	−0.578783	+	0.135739i
$579$		0			0
$580$	7.27969	−	3.61327i	0.302273	−	0.150033i
$581$	2.74307	+	0.483676i	0.113802	+	0.0200663i
$582$		0			0
$583$	−2.45133	−	2.92138i	−0.101524	−	0.120991i
$584$	10.2109	+	3.79816i	0.422529	+	0.157169i
$585$		0			0
$586$	−29.8385	+	1.66757i	−1.23262	+	0.0688866i
$587$	−24.3583	−	8.86571i	−1.00538	−	0.365927i	−0.213721	−	0.976895i	$-0.568558\pi$
$587$	−24.3583	−	8.86571i	−1.00538	−	0.365927i	−0.791655	+	0.610968i	$0.790780\pi$
$588$		0			0
$589$	2.63860	+	2.21405i	0.108722	+	0.0912282i
$590$	−5.67842	+	47.6117i	−0.233777	+	1.96014i
$591$		0			0
$592$	25.2271	+	3.18919i	1.03683	+	0.131075i
$593$		−	41.3947i		−	1.69988i	−0.526881	−	0.849939i	$-0.676639\pi$
$593$		−	41.3947i		−	1.69988i	0.526881	−	0.849939i	$-0.323361\pi$
$594$		0			0
$595$			32.0653i			1.31455i
$596$	16.5938	+	15.8035i	0.679708	+	0.647335i
$597$		0			0
$598$	−32.5114	−	3.87748i	−1.32949	−	0.158562i
$599$	16.8708	+	14.1563i	0.689321	+	0.578409i	0.918713	−	0.394925i	$-0.129230\pi$
$599$	16.8708	+	14.1563i	0.689321	+	0.578409i	−0.229393	+	0.973334i	$0.573674\pi$
$600$		0			0
$601$	−6.20868	−	2.25978i	−0.253257	−	0.0921782i	0.212272	−	0.977211i	$-0.431914\pi$
$601$	−6.20868	−	2.25978i	−0.253257	−	0.0921782i	−0.465529	+	0.885033i	$0.654136\pi$
$602$	−0.264059	−	4.72491i	−0.0107622	−	0.192573i
$603$		0			0
$604$	5.08569	+	45.3580i	0.206934	+	1.84559i
$605$	25.5356	+	30.4322i	1.03817	+	1.23724i
$606$		0			0
$607$	−6.14972	−	1.08436i	−0.249610	−	0.0440129i	0.0474433	−	0.998874i	$-0.484893\pi$
$607$	−6.14972	−	1.08436i	−0.249610	−	0.0440129i	−0.297053	+	0.954861i	$0.596004\pi$
$608$	−4.89103	+	3.55272i	−0.198358	+	0.144082i
$609$		0			0
$610$	−5.75258	−	24.5287i	−0.232915	−	0.993137i
$611$	−9.17304	+	15.8882i	−0.371101	+	0.642767i
$612$		0			0
$613$	−1.30807	−	2.26564i	−0.0528323	−	0.0915083i	0.838400	−	0.545056i	$-0.183492\pi$
$613$	−1.30807	−	2.26564i	−0.0528323	−	0.0915083i	−0.891232	+	0.453548i	$0.850158\pi$
$614$	20.7178	−	19.4544i	0.836101	−	0.785116i
$615$		0			0
$616$	−2.26483	−	1.32897i	−0.0912528	−	0.0535458i
$617$	4.57669	+	12.5744i	0.184251	+	0.506224i	0.997087	−	0.0762671i	$-0.0243002\pi$
$617$	4.57669	+	12.5744i	0.184251	+	0.506224i	−0.812837	+	0.582491i	$0.802078\pi$
$618$		0			0
$619$	26.4425	−	4.66253i	1.06281	−	0.187403i	0.385210	−	0.922829i	$-0.374129\pi$
$619$	26.4425	−	4.66253i	1.06281	−	0.187403i	0.677605	+	0.735426i	$0.263018\pi$
$620$	−14.2206	−	19.2901i	−0.571113	−	0.774710i
$621$		0			0
$622$	−32.8950	−	16.6174i	−1.31897	−	0.666295i
$623$	−3.62836	−	20.5775i	−0.145367	−	0.824419i
$624$		0			0
$625$	−8.17743	+	2.97634i	−0.327097	+	0.119054i
$626$	−13.5293	−	31.5681i	−0.540738	−	1.26171i
$627$		0			0
$628$	−4.68466	−	15.9197i	−0.186938	−	0.635265i
$629$	−28.6626	+	16.5484i	−1.14285	+	0.659827i
$630$		0			0
$631$	−24.9119	−	14.3829i	−0.991726	−	0.572573i	−0.0859365	−	0.996301i	$-0.527388\pi$
$631$	−24.9119	−	14.3829i	−0.991726	−	0.572573i	−0.905790	+	0.423727i	$0.860722\pi$
$632$	17.9392	−	21.0757i	0.713583	−	0.838344i
$633$		0			0
$634$	6.99111	+	5.23026i	0.277652	+	0.207720i
$635$	5.23282	−	29.6768i	0.207658	−	1.17769i
$636$		0			0
$637$	8.46910	−	7.10642i	0.335558	−	0.281567i
$638$	−0.474331	−	0.724888i	−0.0187789	−	0.0286986i
$639$		0			0
$640$	38.8891	−	16.0219i	1.53722	−	0.633321i
$641$	0.674751	−	1.85386i	0.0266510	−	0.0732231i	−0.925654	−	0.378372i	$-0.876484\pi$
$641$	0.674751	−	1.85386i	0.0266510	−	0.0732231i	0.952305	+	0.305149i	$0.0987062\pi$
$642$		0			0
$643$	−24.5026	+	29.2010i	−0.966286	+	1.15158i	0.0221217	+	0.999755i	$0.492958\pi$
$643$	−24.5026	+	29.2010i	−0.966286	+	1.15158i	−0.988408	+	0.151820i	$0.951487\pi$
$644$	16.3410	−	24.5928i	0.643924	−	0.969091i
$645$		0			0
$646$	2.27437	−	7.53246i	0.0894838	−	0.296361i
$647$	−7.03763			−0.276678			−0.138339	−	0.990385i	$-0.544176\pi$
$647$	−7.03763			−0.276678			−0.138339	+	0.990385i	$0.544176\pi$
$648$		0			0
$649$	5.11102			0.200625
$650$	9.36776	−	31.0250i	0.367434	−	1.21690i
$651$		0			0
$652$	−9.75751	+	14.6848i	−0.382134	+	0.575102i
$653$	7.16057	−	8.53364i	0.280215	−	0.333947i	−0.607518	−	0.794306i	$-0.707835\pi$
$653$	7.16057	−	8.53364i	0.280215	−	0.333947i	0.887733	+	0.460359i	$0.152279\pi$
$654$		0			0
$655$	11.7905	−	32.3943i	0.460695	−	1.26575i
$656$	−0.766535	−	3.37530i	−0.0299282	−	0.131783i
$657$		0			0
$658$	−9.05891	−	13.8441i	−0.353153	−	0.539700i
$659$	−28.6386	+	24.0307i	−1.11560	+	0.936102i	−0.998374	−	0.0570034i	$-0.981845\pi$
$659$	−28.6386	+	24.0307i	−1.11560	+	0.936102i	−0.117228	+	0.993105i	$0.537401\pi$
$660$		0			0
$661$	0.973924	−	5.52340i	0.0378812	−	0.214835i	−0.959991	−	0.280030i	$-0.909656\pi$
$661$	0.973924	−	5.52340i	0.0378812	−	0.214835i	0.997873	+	0.0651945i	$0.0207668\pi$
$662$	16.2539	+	12.1600i	0.631725	+	0.472612i
$663$		0			0
$664$	3.62128	+	3.08237i	0.140533	+	0.119619i
$665$	−5.69986	−	3.29082i	−0.221031	−	0.127612i
$666$		0			0
$667$	8.43570	−	4.87036i	0.326632	−	0.188581i
$668$	12.7320	+	43.2665i	0.492614	+	1.67403i
$669$		0			0
$670$	22.7713	+	53.1328i	0.879734	+	2.05270i
$671$	−2.52356	+	0.918499i	−0.0974208	+	0.0354583i
$672$		0			0
$673$	6.57805	+	37.3060i	0.253565	+	1.43804i	0.799729	+	0.600361i	$0.204976\pi$
$673$	6.57805	+	37.3060i	0.253565	+	1.43804i	−0.546164	+	0.837678i	$0.683913\pi$
$674$	−24.2955	−	12.2732i	−0.935826	−	0.472746i
$675$		0			0
$676$	−7.41786	−	10.0623i	−0.285302	−	0.387010i
$677$	−37.1921	+	6.55797i	−1.42941	+	0.252043i	−0.834171	−	0.551506i	$-0.814053\pi$
$677$	−37.1921	+	6.55797i	−1.42941	+	0.252043i	−0.595238	+	0.803549i	$0.702942\pi$
$678$		0			0
$679$	2.26072	+	6.21128i	0.0867586	+	0.238367i
$680$	−27.7061	+	47.2167i	−1.06248	+	1.81068i
$681$		0			0
$682$	−1.86220	+	1.74865i	−0.0713074	+	0.0669591i
$683$	−13.9252	−	24.1192i	−0.532834	−	0.922895i	−0.999265	−	0.0383376i	$-0.987794\pi$
$683$	−13.9252	−	24.1192i	−0.532834	−	0.922895i	0.466431	−	0.884558i	$-0.345540\pi$
$684$		0			0
$685$	−6.42053	+	11.1207i	−0.245316	+	0.424900i
$686$	6.02108	+	25.6736i	0.229886	+	0.980222i
$687$		0			0
$688$	3.69373	−	7.18565i	0.140822	−	0.273950i
$689$	−17.4106	−	3.06996i	−0.663292	−	0.116956i
$690$		0			0
$691$	−2.74753	−	3.27438i	−0.104521	−	0.124563i	0.711248	−	0.702941i	$-0.248130\pi$
$691$	−2.74753	−	3.27438i	−0.104521	−	0.124563i	−0.815769	+	0.578378i	$0.803686\pi$
$692$	−2.28598	−	20.3881i	−0.0869001	−	0.775040i
$693$		0			0
$694$	2.50717	+	44.8619i	0.0951710	+	1.70293i
$695$	−18.7607	−	6.82834i	−0.711634	−	0.259014i
$696$		0			0
$697$	3.45113	+	2.89584i	0.130721	+	0.109688i
$698$	−24.3199	−	2.90052i	−0.920522	−	0.109786i
$699$		0			0
$700$	21.1639	+	20.1558i	0.799919	+	0.761820i
$701$		−	20.9584i		−	0.791586i	−0.918340	−	0.395793i	$-0.870470\pi$
$701$		−	20.9584i		−	0.791586i	0.918340	−	0.395793i	$-0.129530\pi$
$702$		0			0
$703$		−	6.79334i		−	0.256216i
$704$	−2.18670	−	3.91386i	−0.0824145	−	0.147509i
$705$		0			0
$706$	0.671707	−	5.63205i	0.0252800	−	0.211965i
$707$	−9.77169	−	8.19942i	−0.367502	−	0.308371i
$708$		0			0
$709$	7.52677	+	2.73952i	0.282674	+	0.102885i	0.479466	−	0.877560i	$-0.340830\pi$
$709$	7.52677	+	2.73952i	0.282674	+	0.102885i	−0.196792	+	0.980445i	$0.563053\pi$
$710$	−41.8063	+	2.33641i	−1.56896	+	0.0876839i
$711$		0			0
$712$	12.4372	−	33.4357i	0.466102	−	1.25306i
$713$	−18.4631	−	22.0035i	−0.691450	−	0.824038i
$714$		0			0
$715$	−5.33043	−	0.939898i	−0.199347	−	0.0351502i
$716$	25.9778	−	12.8941i	0.970835	−	0.481873i
$717$		0			0
$718$	−16.6617	+	3.90759i	−0.621811	+	0.145830i
$719$	−4.27525	+	7.40496i	−0.159440	+	0.276158i	−0.934667	−	0.355525i	$-0.884302\pi$
$719$	−4.27525	+	7.40496i	−0.159440	+	0.276158i	0.775227	+	0.631683i	$0.217636\pi$
$720$		0			0
$721$	−2.48453	−	4.30333i	−0.0925287	−	0.160264i
$722$	−17.2878	−	18.4105i	−0.643387	−	0.685168i
$723$		0			0
$724$	−0.664492	+	10.5544i	−0.0246957	+	0.392250i
$725$	3.29760	+	9.06007i	0.122470	+	0.336483i
$726$		0			0
$727$	−26.0060	+	4.58556i	−0.964509	+	0.170069i	−0.633657	−	0.773614i	$-0.718447\pi$
$727$	−26.0060	+	4.58556i	−0.964509	+	0.170069i	−0.330852	+	0.943683i	$0.607336\pi$
$728$	−12.0032	+	2.02937i	−0.444867	+	0.0752134i
$729$		0			0
$730$	−9.13098	+	18.0753i	−0.337953	+	0.668996i
$731$	1.82611	+	10.3564i	0.0675410	+	0.383044i
$732$		0			0
$733$	−36.5691	+	13.3101i	−1.35071	+	0.491619i	−0.913170	−	0.407579i	$-0.866373\pi$
$733$	−36.5691	+	13.3101i	−1.35071	+	0.491619i	−0.437542	+	0.899198i	$0.644151\pi$
$734$	−4.47007	+	1.91576i	−0.164993	+	0.0707119i
$735$		0			0
$736$	45.3117	−	22.0938i	1.67021	−	0.814388i
$737$	5.33625	−	3.08088i	0.196563	−	0.113486i
$738$		0			0
$739$	10.6334	+	6.13920i	0.391156	+	0.225834i	0.682661	−	0.730735i	$-0.260823\pi$
$739$	10.6334	+	6.13920i	0.391156	+	0.225834i	−0.291505	+	0.956569i	$0.594156\pi$
$740$	−11.1162	+	45.9400i	−0.408640	+	1.68879i
$741$		0			0
$742$	9.55064	−	12.7660i	0.350615	−	0.468655i
$743$	3.39594	−	19.2593i	0.124585	−	0.706556i	−0.856969	−	0.515368i	$-0.827655\pi$
$743$	3.39594	−	19.2593i	0.124585	−	0.706556i	0.981554	−	0.191187i	$-0.0612338\pi$
$744$		0			0
$745$	−32.6297	+	27.3795i	−1.19546	+	1.00311i
$746$	−6.78766	+	4.44151i	−0.248514	+	0.162615i
$747$		0			0
$748$	5.34727	+	2.33644i	0.195515	+	0.0854289i
$749$	6.73808	−	18.5127i	0.246204	−	0.676440i
$750$		0			0
$751$	0.755319	−	0.900154i	0.0275620	−	0.0328471i	−0.752087	−	0.659063i	$-0.770953\pi$
$751$	0.755319	−	0.900154i	0.0275620	−	0.0328471i	0.779649	+	0.626216i	$0.215397\pi$
$752$	−1.37735	−	28.2130i	−0.0502268	−	1.02882i
$753$		0			0
$754$	−3.84454	−	1.16083i	−0.140010	−	0.0422749i
$755$	−84.8405			−3.08766
$756$		0			0
$757$	−15.1258			−0.549756			−0.274878	−	0.961479i	$-0.588638\pi$
$757$	−15.1258			−0.549756			−0.274878	+	0.961479i	$0.588638\pi$
$758$	−34.1763	−	10.3193i	−1.24134	−	0.374812i
$759$		0			0
$760$	−5.54970	−	9.77075i	−0.201309	−	0.354422i
$761$	−9.05794	+	10.7948i	−0.328350	+	0.391313i	−0.904812	−	0.425812i	$-0.859989\pi$
$761$	−9.05794	+	10.7948i	−0.328350	+	0.391313i	0.576462	+	0.817124i	$0.304433\pi$
$762$		0			0
$763$	5.25006	−	14.4244i	0.190065	−	0.522200i
$764$	−9.39601	+	21.5040i	−0.339936	+	0.777989i
$765$		0			0
$766$	−11.5115	+	7.53258i	−0.415929	+	0.272163i
$767$	18.1506	−	15.2301i	0.655379	−	0.549928i
$768$		0			0
$769$	−4.33277	+	24.5724i	−0.156244	+	0.886102i	0.801396	+	0.598134i	$0.204091\pi$
$769$	−4.33277	+	24.5724i	−0.156244	+	0.886102i	−0.957640	+	0.287968i	$0.907020\pi$
$770$	2.92402	−	3.90844i	0.105374	−	0.140850i
$771$		0			0
$772$	−45.0066	−	10.8903i	−1.61982	−	0.391952i
$773$	12.7170	+	7.34218i	0.457400	+	0.264080i	0.710950	−	0.703242i	$-0.248265\pi$
$773$	12.7170	+	7.34218i	0.457400	+	0.264080i	−0.253550	+	0.967322i	$0.581598\pi$
$774$		0			0
$775$	24.6220	−	14.2155i	0.884449	−	0.510637i
$776$	−2.03791	+	11.0996i	−0.0731569	+	0.398452i
$777$		0			0
$778$	−11.6062	+	4.97412i	−0.416102	+	0.178331i
$779$	−0.868942	+	0.316269i	−0.0311331	+	0.0113315i
$780$		0			0
$781$	0.775025	+	4.39538i	0.0277326	+	0.157279i
$782$	−29.5855	+	58.5662i	−1.05798	+	2.09432i
$783$		0			0
$784$	−5.03493	+	16.2602i	−0.179819	+	0.580720i
$785$	30.3778	−	5.35642i	1.08423	−	0.191179i
$786$		0			0
$787$	−2.22332	−	6.10852i	−0.0792528	−	0.217745i	0.893738	−	0.448589i	$-0.148073\pi$
$787$	−2.22332	−	6.10852i	−0.0792528	−	0.217745i	−0.972991	+	0.230844i	$0.925851\pi$
$788$	−0.890797	−	0.0560837i	−0.0317333	−	0.00199790i
$789$		0			0
$790$	35.2163	+	37.5032i	1.25294	+	1.33430i
$791$	−4.66931	−	8.08748i	−0.166021	−	0.287558i
$792$		0			0
$793$	−6.22481	+	10.7817i	−0.221049	+	0.382869i
$794$	2.84916	−	0.668199i	0.101113	−	0.0237135i
$795$		0			0
$796$	−10.1462	−	20.4417i	−0.359624	−	0.724539i
$797$	−24.7158	−	4.35806i	−0.875477	−	0.154370i	−0.282188	−	0.959359i	$-0.591060\pi$
$797$	−24.7158	−	4.35806i	−0.875477	−	0.154370i	−0.593290	+	0.804989i	$0.702171\pi$
$798$		0			0
$799$	23.6325	+	28.1641i	0.836057	+	0.996374i
$800$	13.7484	+	47.9664i	0.486080	+	1.69587i
$801$		0			0
$802$	−43.0485	+	2.40583i	−1.52010	+	0.0849529i
$803$	2.02839	+	0.738275i	0.0715804	+	0.0260531i
$804$		0			0
$805$	42.0442	+	35.2793i	1.48186	+	1.24343i
$806$	−1.40244	+	11.7590i	−0.0493988	+	0.414193i
$807$		0			0
$808$	−7.30424	−	20.5170i	−0.256962	−	0.721786i
$809$			18.1165i			0.636944i	0.947932	+	0.318472i	$0.103170\pi$
$809$			18.1165i			0.636944i	−0.947932	+	0.318472i	$0.896830\pi$
$810$		0			0
$811$			6.98634i			0.245324i	0.992449	+	0.122662i	$0.0391430\pi$
$811$			6.98634i			0.245324i	−0.992449	+	0.122662i	$0.960857\pi$
$812$	2.49766	−	2.62257i	0.0876506	−	0.0920341i
$813$		0			0
$814$	5.00272	+	0.596650i	0.175345	+	0.0209126i
$815$	−25.1054	−	21.0660i	−0.879405	−	0.737909i
$816$		0			0
$817$	−2.02833	−	0.738254i	−0.0709625	−	0.0258282i
$818$	2.80517	+	50.1940i	0.0980805	+	1.75499i
$819$		0			0
$820$	6.39375	−	0.716888i	0.223279	−	0.0250348i
$821$	−23.1544	−	27.5943i	−0.808093	−	0.963047i	0.191738	−	0.981446i	$-0.438588\pi$
$821$	−23.1544	−	27.5943i	−0.808093	−	0.963047i	−0.999831	+	0.0183987i	$0.994143\pi$
$822$		0			0
$823$	22.5108	+	3.96925i	0.784676	+	0.138359i	0.551611	−	0.834102i	$-0.314013\pi$
$823$	22.5108	+	3.96925i	0.784676	+	0.138359i	0.233065	+	0.972461i	$0.425125\pi$
$824$	0.0597885	−	8.48348i	0.00208283	−	0.295536i
$825$		0			0
$826$	4.87878	+	20.8028i	0.169754	+	0.723823i
$827$	17.2618	−	29.8984i	0.600253	−	1.03967i	−0.392530	−	0.919739i	$-0.628400\pi$
$827$	17.2618	−	29.8984i	0.600253	−	1.03967i	0.992782	−	0.119929i	$-0.0382667\pi$
$828$		0			0
$829$	11.3276	+	19.6199i	0.393423	+	0.681429i	0.992899	−	0.118964i	$-0.0379574\pi$
$829$	11.3276	+	19.6199i	0.393423	+	0.681429i	−0.599475	+	0.800393i	$0.704624\pi$
$830$	−6.44391	+	6.05096i	−0.223671	+	0.210032i
$831$		0			0
$832$	−19.4283	−	7.38307i	−0.673556	−	0.255962i
$833$	−7.57763	−	20.8194i	−0.262549	−	0.721349i
$834$		0			0
$835$	−82.5607	+	14.5577i	−2.85713	+	0.503789i
$836$	−0.964103	+	0.710733i	−0.0333442	+	0.0245812i
$837$		0			0
$838$	15.5525	+	7.85655i	0.537251	+	0.271400i
$839$	−1.87499	−	10.6336i	−0.0647317	−	0.367112i	−0.999916	−	0.0129506i	$-0.995878\pi$
$839$	−1.87499	−	10.6336i	−0.0647317	−	0.367112i	0.935184	−	0.354161i	$-0.115234\pi$
$840$		0			0
$841$	−26.1284	+	9.50995i	−0.900979	+	0.327929i
$842$	−9.69409	−	22.6194i	−0.334080	−	0.779516i
$843$		0			0
$844$	11.1464	−	3.28004i	0.383676	−	0.112904i
$845$	20.1238	−	11.6185i	0.692280	−	0.399688i
$846$		0			0
$847$	15.3313	+	8.85151i	0.526788	+	0.304141i
$848$	25.0939	−	10.5459i	0.861729	−	0.362148i
$849$		0			0
$850$	−52.0040	−	38.9057i	−1.78372	−	1.33446i
$851$	−9.83722	+	55.7897i	−0.337216	+	1.91244i
$852$		0			0
$853$	−13.7409	+	11.5299i	−0.470478	+	0.394778i	−0.846969	−	0.531643i	$-0.821575\pi$
$853$	−13.7409	+	11.5299i	−0.470478	+	0.394778i	0.376491	+	0.926420i	$0.377131\pi$
$854$	−6.14736	−	9.39460i	−0.210358	−	0.321477i
$855$		0			0
$856$	25.9179	−	21.4382i	0.885854	−	0.732743i
$857$	1.95427	−	5.36930i	0.0667564	−	0.183412i	−0.901829	−	0.432093i	$-0.857775\pi$
$857$	1.95427	−	5.36930i	0.0667564	−	0.183412i	0.968585	+	0.248682i	$0.0799973\pi$
$858$		0			0
$859$	−12.2892	+	14.6457i	−0.419302	+	0.499704i	−0.933804	−	0.357785i	$-0.883532\pi$
$859$	−12.2892	+	14.6457i	−0.419302	+	0.499704i	0.514502	+	0.857489i	$0.327977\pi$
$860$	12.5086	+	8.31148i	0.426539	+	0.283419i
$861$		0			0
$862$	−7.78835	+	25.7942i	−0.265272	+	0.878554i
$863$	42.9009			1.46036			0.730181	−	0.683254i	$-0.239436\pi$
$863$	42.9009			1.46036			0.730181	+	0.683254i	$0.239436\pi$
$864$		0			0
$865$	38.1352			1.29664
$866$	15.3260	−	50.7581i	0.520798	−	1.72483i
$867$		0			0
$868$	−8.89492	−	5.91033i	−0.301913	−	0.200610i
$869$	3.52488	−	4.20079i	0.119573	−	0.142502i
$870$		0			0
$871$	9.76980	−	26.8423i	0.331037	−	0.909517i
$872$	20.1942	−	16.7039i	0.683863	−	0.565664i
$873$		0			0
$874$	−7.37428	−	11.2696i	−0.249439	−	0.381201i
$875$	−18.0263	+	15.1259i	−0.609400	+	0.511347i
$876$		0			0
$877$	−4.70239	+	26.6686i	−0.158788	+	0.900533i	0.796452	+	0.604702i	$0.206708\pi$
$877$	−4.70239	+	26.6686i	−0.158788	+	0.900533i	−0.955240	+	0.295831i	$0.904403\pi$
$878$	−25.4266	−	19.0224i	−0.858105	−	0.641974i
$879$		0			0
$880$	7.68275	−	3.22873i	0.258985	−	0.108841i
$881$	−6.75989	−	3.90282i	−0.227746	−	0.131489i	0.381786	−	0.924251i	$-0.375309\pi$
$881$	−6.75989	−	3.90282i	−0.227746	−	0.131489i	−0.609532	+	0.792761i	$0.708643\pi$
$882$		0			0
$883$	−43.9985	+	25.4025i	−1.48067	+	0.854864i	−0.999760	−	0.0219080i	$-0.993026\pi$
$883$	−43.9985	+	25.4025i	−1.48067	+	0.854864i	−0.480907	+	0.876772i	$0.659693\pi$
$884$	25.9518	−	7.63679i	0.872854	−	0.256853i
$885$		0			0
$886$	−5.73183	−	13.3742i	−0.192565	−	0.449314i
$887$	−4.59913	+	1.67395i	−0.154424	+	0.0562056i	−0.418075	−	0.908412i	$-0.637295\pi$
$887$	−4.59913	+	1.67395i	−0.154424	+	0.0562056i	0.263652	+	0.964618i	$0.415073\pi$
$888$		0			0
$889$	−2.33187	−	13.2247i	−0.0782083	−	0.443541i
$890$	59.1878	+	29.8996i	1.98398	+	1.00224i
$891$		0			0
$892$	−5.98988	+	4.41571i	−0.200556	+	0.147849i
$893$	−7.43175	+	1.31042i	−0.248694	+	0.0438515i
$894$		0			0
$895$	18.4379	+	50.6578i	0.616312	+	1.69330i
$896$	13.8428	−	12.6363i	0.462457	−	0.422150i
$897$		0			0
$898$	−9.26019	+	8.69551i	−0.309017	+	0.290173i
$899$	−1.76155	−	3.05109i	−0.0587510	−	0.101760i
$900$		0			0
$901$	−17.7146	+	30.6826i	−0.590159	+	1.02218i
$902$	−0.156587	−	0.667680i	−0.00521379	−	0.0222313i
$903$		0			0
$904$	0.112364	−	15.9434i	0.00373716	−	0.530271i
$905$	−19.3588	−	3.41348i	−0.643509	−	0.113468i
$906$		0			0
$907$	16.4221	+	19.5711i	0.545288	+	0.649849i	0.966365	−	0.257176i	$-0.0827921\pi$
$907$	16.4221	+	19.5711i	0.545288	+	0.649849i	−0.421077	+	0.907025i	$0.638348\pi$
$908$	13.1492	−	1.47433i	0.436370	−	0.0489272i
$909$		0			0
$910$	−1.26265	−	22.5931i	−0.0418564	−	0.748953i
$911$	40.7491	+	14.8315i	1.35008	+	0.491389i	0.912973	−	0.408021i	$-0.133781\pi$
$911$	40.7491	+	14.8315i	1.35008	+	0.491389i	0.437107	+	0.899410i	$0.356003\pi$
$912$		0			0
$913$	0.721792	+	0.605655i	0.0238878	+	0.0200443i
$914$	6.69965	+	0.799034i	0.221605	+	0.0264297i
$915$		0			0
$916$	−1.59433	+	1.67406i	−0.0526781	+	0.0553126i
$917$		−	15.3621i		−	0.507301i
$918$		0			0
$919$		−	31.6571i		−	1.04427i	−0.852862	−	0.522136i	$-0.825135\pi$
$919$		−	31.6571i		−	1.04427i	0.852862	−	0.522136i	$-0.174865\pi$
$920$	31.4277	+	88.2776i	1.03614	+	2.91043i
$921$		0			0
$922$	4.78694	−	40.1369i	0.157649	−	1.32184i
$923$	15.8500	+	13.2997i	0.521708	+	0.437765i
$924$		0			0
$925$	−52.6918	−	19.1783i	−1.73250	−	0.630577i
$926$	59.8993	−	3.34756i	1.96841	−	0.110008i
$927$		0			0
$928$	5.94387	−	1.70367i	0.195117	−	0.0559256i
$929$	−30.9044	−	36.8304i	−1.01394	−	1.20837i	−0.977912	−	0.209017i	$-0.932974\pi$
$929$	−30.9044	−	36.8304i	−1.01394	−	1.20837i	−0.0360286	−	0.999351i	$-0.511471\pi$
$930$		0			0
$931$	4.47849	+	0.789678i	0.146777	+	0.0258807i
$932$	−15.1390	−	30.5008i	−0.495896	−	0.999086i
$933$		0			0
$934$	8.88806	−	2.08447i	0.290826	−	0.0682059i
$935$	−5.42349	+	9.39376i	−0.177367	+	0.307209i
$936$		0			0
$937$	28.1506	+	48.7583i	0.919641	+	1.59287i	0.799961	+	0.600053i	$0.204854\pi$
$937$	28.1506	+	48.7583i	0.919641	+	1.59287i	0.119681	+	0.992812i	$0.461813\pi$
$938$	17.6336	+	18.7787i	0.575756	+	0.613145i
$939$		0			0
$940$	52.4015	+	3.29915i	1.70915	+	0.107606i
$941$	−18.8013	−	51.6561i	−0.612905	−	1.68394i	−0.723714	−	0.690100i	$-0.757566\pi$
$941$	−18.8013	−	51.6561i	−0.612905	−	1.68394i	0.110809	−	0.993842i	$-0.464656\pi$
$942$		0			0
$943$	7.59408	−	1.33904i	0.247297	−	0.0436052i
$944$	−10.7906	+	34.8480i	−0.351205	+	1.13421i
$945$		0			0
$946$	0.721807	−	1.42886i	0.0234680	−	0.0464561i
$947$	8.21717	+	46.6019i	0.267022	+	1.51436i	0.763214	+	0.646145i	$0.223620\pi$
$947$	8.21717	+	46.6019i	0.267022	+	1.51436i	−0.496192	+	0.868213i	$0.665269\pi$
$948$		0			0
$949$	9.40331	−	3.42252i	0.305244	−	0.111100i
$950$	12.2529	−	5.25128i	0.397536	−	0.170374i
$951$		0			0
$952$	−4.40549	+	23.9947i	−0.142783	+	0.777672i
$953$	29.6972	−	17.1457i	0.961985	−	0.555402i	0.0652018	−	0.997872i	$-0.479231\pi$
$953$	29.6972	−	17.1457i	0.961985	−	0.555402i	0.896783	+	0.442470i	$0.145898\pi$
$954$		0			0
$955$	−37.7770	−	21.8106i	−1.22244	−	0.705774i
$956$	2.34523	+	0.567481i	0.0758503	+	0.0183537i
$957$		0			0
$958$	−30.2514	+	40.4360i	−0.977378	+	1.30643i
$959$	−0.993664	+	5.63535i	−0.0320871	+	0.181975i
$960$		0			0
$961$	15.7890	−	13.2485i	0.509322	−	0.427372i
$962$	19.5439	−	12.7886i	0.630121	−	0.412320i
$963$		0			0
$964$	−8.00321	+	18.3164i	−0.257766	+	0.589932i
$965$	29.4388	−	80.8824i	0.947668	−	2.60370i
$966$		0			0
$967$	15.6245	−	18.6206i	0.502452	−	0.598799i	−0.453887	−	0.891059i	$-0.649963\pi$
$967$	15.6245	−	18.6206i	0.502452	−	0.598799i	0.956339	+	0.292261i	$0.0944075\pi$
$968$	14.9274	+	26.2809i	0.479783	+	0.844702i
$969$		0			0
$970$	−20.0815	−	6.06345i	−0.644778	−	0.194686i
$971$	−39.8444			−1.27867			−0.639334	−	0.768929i	$-0.720790\pi$
$971$	−39.8444			−1.27867			−0.639334	+	0.768929i	$0.720790\pi$
$972$		0			0
$973$	−8.89676			−0.285217
$974$	55.0474	+	16.6211i	1.76383	+	0.532575i
$975$		0			0
$976$	−0.934668	−	19.1453i	−0.0299180	−	0.612826i
$977$	−29.9498	+	35.6928i	−0.958179	+	1.14191i	0.0316286	+	0.999500i	$0.489931\pi$
$977$	−29.9498	+	35.6928i	−0.958179	+	1.14191i	−0.989807	+	0.142413i	$0.954514\pi$
$978$		0			0
$979$	2.41749	−	6.64201i	0.0772635	−	0.212280i
$980$	−28.9936	−	12.6685i	−0.926167	−	0.404681i
$981$		0			0
$982$	−33.2781	+	21.7755i	−1.06195	+	0.694884i
$983$	8.10659	−	6.80224i	0.258560	−	0.216958i	−0.504288	−	0.863536i	$-0.668245\pi$
$983$	8.10659	−	6.80224i	0.258560	−	0.216958i	0.762848	+	0.646578i	$0.223800\pi$
$984$		0			0
$985$	0.288101	−	1.63390i	0.00917965	−	0.0520604i
$986$	−4.82109	+	6.44419i	−0.153535	+	0.205225i
$987$		0			0
$988$	−1.30590	+	5.39689i	−0.0415461	+	0.171698i
$989$	15.5885	+	9.00000i	0.495684	+	0.286183i
$990$		0			0
$991$	−20.1628	+	11.6410i	−0.640492	+	0.369788i	−0.784804	−	0.619744i	$-0.787236\pi$
$991$	−20.1628	+	11.6410i	−0.640492	+	0.369788i	0.144312	+	0.989532i	$0.453903\pi$
$992$	−7.99107	−	16.3887i	−0.253717	−	0.520342i
$993$		0			0
$994$	−17.1503	+	7.35016i	−0.543973	+	0.233133i
$995$	39.8623	−	14.5087i	1.26372	−	0.459956i
$996$		0			0
$997$	−9.96393	−	56.5082i	−0.315561	−	1.78963i	−0.569057	−	0.822298i	$-0.692692\pi$
$997$	−9.96393	−	56.5082i	−0.315561	−	1.78963i	0.253497	−	0.967336i	$-0.418419\pi$
$998$	21.1182	−	41.8047i	0.668486	−	1.32330i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.a.215.7		96
3.2	odd	2		972.2.l.d.215.10		96
4.3	odd	2	inner	972.2.l.a.215.5		96
9.2	odd	6		108.2.l.a.59.1	yes	96
9.4	even	3		972.2.l.b.539.5		96
9.5	odd	6		972.2.l.c.539.12		96
9.7	even	3		324.2.l.a.287.16		96
12.11	even	2		972.2.l.d.215.12		96
27.2	odd	18	inner	972.2.l.a.755.5		96
27.7	even	9		108.2.l.a.11.11	yes	96
27.11	odd	18		972.2.l.b.431.15		96
27.16	even	9		972.2.l.c.431.2		96
27.20	odd	18		324.2.l.a.35.6		96
27.25	even	9		972.2.l.d.755.12		96
36.7	odd	6		324.2.l.a.287.6		96
36.11	even	6		108.2.l.a.59.11	yes	96
36.23	even	6		972.2.l.c.539.2		96
36.31	odd	6		972.2.l.b.539.15		96
108.7	odd	18		108.2.l.a.11.1	✓	96
108.11	even	18		972.2.l.b.431.5		96
108.43	odd	18		972.2.l.c.431.12		96
108.47	even	18		324.2.l.a.35.16		96
108.79	odd	18		972.2.l.d.755.10		96
108.83	even	18	inner	972.2.l.a.755.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.1	✓	96	108.7	odd	18
108.2.l.a.11.11	yes	96	27.7	even	9
108.2.l.a.59.1	yes	96	9.2	odd	6
108.2.l.a.59.11	yes	96	36.11	even	6
324.2.l.a.35.6		96	27.20	odd	18
324.2.l.a.35.16		96	108.47	even	18
324.2.l.a.287.6		96	36.7	odd	6
324.2.l.a.287.16		96	9.7	even	3
972.2.l.a.215.5		96	4.3	odd	2	inner
972.2.l.a.215.7		96	1.1	even	1	trivial
972.2.l.a.755.5		96	27.2	odd	18	inner
972.2.l.a.755.7		96	108.83	even	18	inner
972.2.l.b.431.5		96	108.11	even	18
972.2.l.b.431.15		96	27.11	odd	18
972.2.l.b.539.5		96	9.4	even	3
972.2.l.b.539.15		96	36.31	odd	6
972.2.l.c.431.2		96	27.16	even	9
972.2.l.c.431.12		96	108.43	odd	18
972.2.l.c.539.2		96	36.23	even	6
972.2.l.c.539.12		96	9.5	odd	6
972.2.l.d.215.10		96	3.2	odd	2
972.2.l.d.215.12		96	12.11	even	2
972.2.l.d.755.10		96	108.79	odd	18
972.2.l.d.755.12		96	27.25	even	9

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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.408783 + 1.35385i) q^{2} +(-1.66579 - 1.10686i) q^{4} +(2.38965 - 2.84787i) q^{5} +(0.566613 - 1.55676i) q^{7} +(2.17946 - 1.80276i) q^{8} +O(q^{10})\)	\(q+(-0.408783 + 1.35385i) q^{2} +(-1.66579 - 1.10686i) q^{4} +(2.38965 - 2.84787i) q^{5} +(0.566613 - 1.55676i) q^{7} +(2.17946 - 1.80276i) q^{8} +(2.87873 + 4.39937i) q^{10} +(0.429301 - 0.360226i) q^{11} +(0.451135 - 2.55851i) q^{13} +(1.87598 + 1.40348i) q^{14} +(1.54974 + 3.68759i) q^{16} +(-4.50885 - 2.60318i) q^{17} +(0.925473 - 0.534322i) q^{19} +(-7.13284 + 2.09897i) q^{20} +(0.312200 + 0.728461i) q^{22} +(-8.37409 + 3.04792i) q^{23} +(-1.53171 - 8.68677i) q^{25} +(3.27942 + 1.65664i) q^{26} +(-2.66696 + 1.96607i) q^{28} +(-1.07644 + 0.189806i) q^{29} +(1.10240 + 3.02881i) q^{31} +(-5.62593 + 0.590682i) q^{32} +(5.36745 - 5.04015i) q^{34} +(-3.07943 - 5.33373i) q^{35} +(3.17849 - 5.50530i) q^{37} +(0.345072 + 1.47137i) q^{38} +(0.0741044 - 10.5148i) q^{40} +(-0.852165 - 0.150260i) q^{41} +(-1.29834 - 1.54730i) q^{43} +(-1.11385 + 0.124888i) q^{44} +(-0.703229 - 12.5832i) q^{46} +(-6.63579 - 2.41523i) q^{47} +(3.25987 + 2.73536i) q^{49} +(12.3867 + 1.47730i) q^{50} +(-3.58341 + 3.76262i) q^{52} -6.80497i q^{53} -2.08341i q^{55} +(-1.57155 - 4.41435i) q^{56} +(0.183063 - 1.53492i) q^{58} +(6.98640 + 5.86229i) q^{59} +(-4.50303 - 1.63897i) q^{61} +(-4.55118 + 0.254350i) q^{62} +(1.50009 - 7.85810i) q^{64} +(-6.20826 - 7.39872i) q^{65} +(10.8280 + 1.90927i) q^{67} +(4.62946 + 9.32702i) q^{68} +(8.47987 - 1.98874i) q^{70} +(-3.98206 + 6.89713i) q^{71} +(1.92588 + 3.33572i) q^{73} +(6.15402 + 6.55365i) q^{74} +(-2.13306 - 0.134296i) q^{76} +(-0.317537 - 0.872425i) q^{77} +(9.63652 - 1.69918i) q^{79} +(14.2051 + 4.39859i) q^{80} +(0.551778 - 1.09228i) q^{82} +(0.291958 + 1.65578i) q^{83} +(-18.1881 + 6.61992i) q^{85} +(2.62554 - 1.12524i) q^{86} +(0.286242 - 1.55903i) q^{88} +(10.9229 - 6.30632i) q^{89} +(-3.72736 - 2.15199i) q^{91} +(17.3231 + 4.19171i) q^{92} +(5.98244 - 7.99653i) q^{94} +(0.689874 - 3.91247i) q^{95} +(-3.05643 + 2.56465i) q^{97} +(-5.03583 + 3.29520i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} - 33 q^{14} + 3 q^{16} + 18 q^{17} + 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} - 30 q^{29} - 33 q^{32} + 15 q^{34} - 6 q^{37} + 63 q^{38} + 33 q^{40} + 24 q^{41} - 63 q^{44} - 3 q^{46} + 6 q^{49} + 21 q^{50} + 57 q^{52} + 18 q^{56} + 57 q^{58} + 6 q^{61} - 90 q^{62} - 3 q^{64} - 30 q^{65} + 102 q^{68} + 51 q^{70} - 6 q^{73} - 75 q^{74} + 27 q^{76} + 42 q^{77} - 12 q^{82} - 24 q^{85} + 111 q^{86} + 27 q^{88} - 147 q^{92} + 30 q^{94} - 12 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 - 33 * q^14 + 3 * q^16 + 18 * q^17 + 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 - 30 * q^29 - 33 * q^32 + 15 * q^34 - 6 * q^37 + 63 * q^38 + 33 * q^40 + 24 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 21 * q^50 + 57 * q^52 + 18 * q^56 + 57 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 - 30 * q^65 + 102 * q^68 + 51 * q^70 - 6 * q^73 - 75 * q^74 + 27 * q^76 + 42 * q^77 - 12 * q^82 - 24 * q^85 + 111 * q^86 + 27 * q^88 - 147 * q^92 + 30 * q^94 - 12 * q^97 + 180 * q^98

Introduction

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