LMFDB - Embedded newform 972.2.l.a.755.7

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			755.7
Character	$\chi$	$=$	972.755
Dual form			972.2.l.a.215.7

$q$-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 $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

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

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	0.960142	+	0.279514i	$0.0901735\pi$
$5$	2.38965	+	2.84787i	1.06868	+	1.27361i	0.108541	+	0.994092i	$0.465382\pi$
$6$		0			0
$7$	0.566613	+	1.55676i	0.214159	+	0.588398i	0.999531	−	0.0306266i	$-0.00975027\pi$
$7$	0.566613	+	1.55676i	0.214159	+	0.588398i	−0.785371	+	0.619025i	$0.787528\pi$
$8$	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	0.705209	−	0.708999i	$-0.250853\pi$
$11$	0.429301	+	0.360226i	0.129439	+	0.108612i	−0.575770	+	0.817612i	$0.695298\pi$
$12$		0			0
$13$	0.451135	+	2.55851i	0.125122	+	0.709604i	0.981235	+	0.192815i	$0.0617618\pi$
$13$	0.451135	+	2.55851i	0.125122	+	0.709604i	−0.856113	+	0.516789i	$0.827127\pi$
$14$	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	−0.934521	−	0.355908i	$-0.884172\pi$
$17$	−4.50885	+	2.60318i	−1.09356	+	0.631365i	−0.159035	+	0.987273i	$0.550838\pi$
$18$		0			0
$19$	0.925473	+	0.534322i	0.212318	+	0.122582i	0.602388	−	0.798203i	$-0.294216\pi$
$19$	0.925473	+	0.534322i	0.212318	+	0.122582i	−0.390070	+	0.920785i	$0.627549\pi$
$20$	−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	−0.746562	−	0.665316i	$-0.768297\pi$
$23$	−8.37409	−	3.04792i	−1.74612	−	0.635535i	−0.999556	+	0.0297813i	$0.990519\pi$
$24$		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	0.0728065	−	0.997346i	$-0.476804\pi$
$29$	−1.07644	−	0.189806i	−0.199890	−	0.0352460i	−0.272697	+	0.962100i	$0.587916\pi$
$30$		0			0
$31$	1.10240	−	3.02881i	0.197996	−	0.543990i	−0.800469	−	0.599374i	$-0.795416\pi$
$31$	1.10240	−	3.02881i	0.197996	−	0.543990i	0.998465	+	0.0553841i	$0.0176383\pi$
$32$	−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	0.999656	+	0.0262257i	$0.00834884\pi$
$37$	3.17849	+	5.50530i	0.522540	+	0.905066i	−0.477116	+	0.878840i	$0.658318\pi$
$38$	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	−0.239794	−	0.970824i	$-0.577080\pi$
$41$	−0.852165	+	0.150260i	−0.133086	+	0.0234666i	0.106708	+	0.994290i	$0.465969\pi$
$42$		0			0
$43$	−1.29834	+	1.54730i	−0.197995	+	0.235961i	−0.855902	−	0.517138i	$-0.826997\pi$
$43$	−1.29834	+	1.54730i	−0.197995	+	0.235961i	0.657907	+	0.753099i	$0.271442\pi$
$44$	−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	−0.777136	−	0.629333i	$-0.783328\pi$
$47$	−6.63579	+	2.41523i	−0.967929	+	0.352297i	−0.190793	+	0.981630i	$0.561106\pi$
$48$		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	$0.154797\pi$
$53$			6.80497i			0.934734i	−0.884063	+	0.467367i	$0.845203\pi$
$54$		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	−0.0624814	−	0.998046i	$-0.519901\pi$
$59$	6.98640	−	5.86229i	0.909552	−	0.763205i	0.972034	+	0.234841i	$0.0754570\pi$
$60$		0			0
$61$	−4.50303	+	1.63897i	−0.576554	+	0.209849i	−0.613805	−	0.789457i	$-0.710362\pi$
$61$	−4.50303	+	1.63897i	−0.576554	+	0.209849i	0.0372511	+	0.999306i	$0.488140\pi$
$62$	−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	0.532773	−	0.846258i	$-0.321150\pi$
$67$	10.8280	−	1.90927i	1.32285	−	0.233255i	0.790080	+	0.613004i	$0.210039\pi$
$68$	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	0.526924	−	0.849912i	$-0.323345\pi$
$71$	−3.98206	−	6.89713i	−0.472583	−	0.818538i	−0.999508	+	0.0313737i	$0.990012\pi$
$72$		0			0
$73$	1.92588	−	3.33572i	0.225407	−	0.390416i	−0.731035	−	0.682340i	$-0.760962\pi$
$73$	1.92588	−	3.33572i	0.225407	−	0.390416i	0.956441	+	0.291924i	$0.0942955\pi$
$74$	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	0.687069	−	0.726592i	$-0.258897\pi$
$79$	9.63652	+	1.69918i	1.08419	+	0.191173i	0.397124	+	0.917765i	$0.370008\pi$
$80$	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	−0.964583	−	0.263780i	$-0.915031\pi$
$83$	0.291958	−	1.65578i	0.0320466	−	0.181745i	0.996629	+	0.0820348i	$0.0261419\pi$
$84$		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	0.950781	−	0.309864i	$-0.100283\pi$
$89$	10.9229	+	6.30632i	1.15782	+	0.668469i	0.207041	+	0.978332i	$0.433617\pi$
$90$		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	0.474296	−	0.880365i	$-0.342703\pi$
$97$	−3.05643	−	2.56465i	−0.310334	−	0.260401i	−0.784630	+	0.619964i	$0.787147\pi$
$98$	−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	0.999029	+	0.0440493i	$0.0140259\pi$
$101$	2.63350	+	7.23547i	0.262043	+	0.719957i	−0.736987	+	0.675907i	$0.763752\pi$
$102$		0			0
$103$	1.92800	+	2.29770i	0.189972	+	0.226399i	0.852620	−	0.522531i	$-0.175012\pi$
$103$	1.92800	+	2.29770i	0.189972	+	0.226399i	−0.662649	+	0.748930i	$0.730568\pi$
$104$	−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	0.909057	−	0.416671i	$-0.136803\pi$
$113$	3.62339	+	4.31819i	0.340860	+	0.406221i	−0.568197	+	0.822893i	$0.692359\pi$
$114$		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	0.778002	−	0.628261i	$-0.216233\pi$
$127$	7.01988	+	4.05293i	0.622914	+	0.359639i	−0.155089	+	0.987901i	$0.549566\pi$
$128$	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	0.693360	−	0.720591i	$-0.256129\pi$
$131$	8.71368	+	3.17152i	0.761318	+	0.277097i	0.0679578	+	0.997688i	$0.478352\pi$
$132$		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	0.0264373	−	0.999650i	$-0.491584\pi$
$137$	−3.40162	−	0.599798i	−0.290620	−	0.0512442i	−0.317058	+	0.948406i	$0.602695\pi$
$138$		0			0
$139$	−1.83675	+	5.04642i	−0.155791	+	0.428031i	−0.992892	−	0.119016i	$-0.962026\pi$
$139$	−1.83675	+	5.04642i	−0.155791	+	0.428031i	0.837102	+	0.547047i	$0.184248\pi$
$140$	−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	−0.615526	−	0.788116i	$-0.711057\pi$
$149$	−11.2835	+	1.98959i	−0.924380	+	0.162993i	−0.308854	+	0.951109i	$0.599945\pi$
$150$		0			0
$151$	−14.6691	+	17.4820i	−1.19376	+	1.42266i	−0.312570	+	0.949895i	$0.601190\pi$
$151$	−14.6691	+	17.4820i	−1.19376	+	1.42266i	−0.881186	+	0.472769i	$0.843255\pi$
$152$	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	−0.352895	−	0.935663i	$-0.614803\pi$
$157$	6.35613	−	5.33342i	0.507274	−	0.425653i	0.860169	+	0.510010i	$0.170358\pi$
$158$	−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	$0.112203\pi$
$163$			8.81551i			0.690484i	−0.938514	+	0.345242i	$0.887797\pi$
$164$	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	−0.354306	+	0.935130i	$0.615283\pi$
$167$	−17.2747	+	14.4952i	−1.33675	+	1.12167i	−0.982447	+	0.186540i	$0.940273\pi$
$168$		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	−0.454748	−	0.890620i	$-0.650271\pi$
$173$	6.59368	−	7.85804i	0.501308	−	0.597436i	0.956056	+	0.293185i	$0.0947150\pi$
$174$		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	−0.998794	−	0.0491053i	$-0.984363\pi$
$179$	−7.25044	−	12.5581i	−0.541923	−	0.938639i	0.456870	−	0.889533i	$-0.348970\pi$
$180$		0			0
$181$	−2.64382	+	4.57923i	−0.196513	+	0.340371i	−0.947396	−	0.320065i	$-0.896295\pi$
$181$	−2.64382	+	4.57923i	−0.196513	+	0.340371i	0.750882	+	0.660436i	$0.229629\pi$
$182$	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	0.817955	+	0.575283i	$0.195108\pi$
$191$	−2.03752	+	11.5553i	−0.147429	+	0.836114i	−0.965384	+	0.260832i	$0.916003\pi$
$192$		0			0
$193$	21.7564	+	7.91869i	1.56606	+	0.570000i	0.972115	−	0.234504i	$-0.0753467\pi$
$193$	21.7564	+	7.91869i	1.56606	+	0.570000i	0.593947	+	0.804504i	$0.297569\pi$
$194$	−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	0.513705	−	0.857967i	$-0.328273\pi$
$197$	0.386490	+	0.223140i	0.0275363	+	0.0158981i	−0.486169	+	0.873865i	$0.661606\pi$
$198$		0			0
$199$	9.88191	−	5.70532i	0.700510	−	0.404440i	−0.107027	−	0.994256i	$-0.534133\pi$
$199$	9.88191	−	5.70532i	0.700510	−	0.404440i	0.807537	+	0.589816i	$0.200800\pi$
$200$	−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	0.622032	−	0.782992i	$-0.286307\pi$
$211$	−3.73428	−	4.45035i	−0.257079	−	0.306374i	−0.879111	+	0.476617i	$0.841863\pi$
$212$	−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	0.974981	−	0.222287i	$-0.0713523\pi$
$223$	1.27259	+	3.49640i	0.0852186	+	0.234136i	−0.889763	+	0.456424i	$0.849130\pi$
$224$	−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	0.458917	−	0.888479i	$-0.348237\pi$
$227$	−5.06798	−	4.25254i	−0.336373	−	0.282251i	−0.795291	+	0.606228i	$0.792682\pi$
$228$		0			0
$229$	0.200719	+	1.13833i	0.0132639	+	0.0752232i	0.990721	−	0.135910i	$-0.0433958\pi$
$229$	0.200719	+	1.13833i	0.0132639	+	0.0752232i	−0.977457	+	0.211133i	$0.932285\pi$
$230$	−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	0.0679527	−	0.997689i	$-0.478353\pi$
$233$	14.7446	−	8.51281i	0.965953	−	0.557693i	0.898000	+	0.439996i	$0.145020\pi$
$234$		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	0.305093	−	0.952322i	$-0.401312\pi$
$239$	−1.13370	−	0.412633i	−0.0733329	−	0.0266910i	−0.378426	+	0.925632i	$0.623535\pi$
$240$		0			0
$241$	−1.73549	+	9.84245i	−0.111793	+	0.634008i	0.876496	+	0.481410i	$0.159875\pi$
$241$	−1.73549	+	9.84245i	−0.111793	+	0.634008i	−0.988288	+	0.152598i	$0.951236\pi$
$242$	−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	−0.995937	−	0.0900521i	$-0.971297\pi$
$251$	−6.65375	+	11.5246i	−0.419981	+	0.727429i	0.575956	+	0.817481i	$0.304630\pi$
$252$		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	0.269429	−	0.963020i	$-0.413165\pi$
$257$	13.6583	−	2.40833i	0.851982	−	0.150227i	0.582553	+	0.812793i	$0.302054\pi$
$258$		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	−0.411983	−	0.911192i	$-0.635164\pi$
$263$	−2.30086	+	0.837443i	−0.141877	+	0.0516389i	0.270106	+	0.962831i	$0.412941\pi$
$264$		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	$-0.959904\pi$
$269$		−	4.12106i		−	0.251266i	0.992077	−	0.125633i	$-0.0400961\pi$
$270$		0			0
$271$		−	11.9859i		−	0.728089i	−0.931382	−	0.364044i	$-0.881396\pi$
$271$		−	11.9859i		−	0.728089i	0.931382	−	0.364044i	$-0.118604\pi$
$272$	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	0.700404	−	0.713747i	$-0.253003\pi$
$277$	28.2226	−	10.2722i	1.69573	−	0.617196i	0.995328	+	0.0965505i	$0.0307809\pi$
$278$	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	−0.882362	−	0.470572i	$-0.844048\pi$
$281$	−4.45426	+	5.30838i	−0.265719	+	0.316671i	0.616643	+	0.787243i	$0.288492\pi$
$282$		0			0
$283$	−18.5824	+	3.27657i	−1.10461	+	0.194772i	−0.696073	−	0.717971i	$-0.745071\pi$
$283$	−18.5824	+	3.27657i	−1.10461	+	0.194772i	−0.408534	+	0.912743i	$0.633960\pi$
$284$	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	−0.528186	−	0.849128i	$-0.677128\pi$
$293$	7.22753	−	19.8575i	0.422237	−	1.16009i	0.950424	−	0.310958i	$-0.100650\pi$
$294$		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	−0.906253	−	0.422736i	$-0.861070\pi$
$307$	−17.4037	+	10.0480i	−0.993279	+	0.573470i	−0.0870262	+	0.996206i	$0.527736\pi$
$308$	−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	−0.791928	−	0.610614i	$-0.790923\pi$
$311$	−4.52522	−	25.6638i	−0.256602	−	1.45526i	0.535326	−	0.844645i	$-0.320189\pi$
$312$		0			0
$313$	−18.6039	−	15.6105i	−1.05155	−	0.882358i	−0.0582968	−	0.998299i	$-0.518567\pi$
$313$	−18.6039	−	15.6105i	−1.05155	−	0.882358i	−0.993256	+	0.115942i	$0.963011\pi$
$314$	−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	0.984760	−	0.173919i	$-0.0556432\pi$
$317$	2.11156	+	5.80146i	0.118597	+	0.325842i	−0.866163	+	0.499762i	$0.833421\pi$
$318$		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	0.998408	+	0.0563994i	$0.0179620\pi$
$331$	4.90924	+	13.4880i	0.269836	+	0.741368i	−0.728572	+	0.684969i	$0.759816\pi$
$332$	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	−0.929672	−	0.368388i	$-0.879910\pi$
$337$	−3.34222	−	18.9547i	−0.182062	−	1.03253i	0.747610	−	0.664138i	$-0.231201\pi$
$338$	−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	0.979984	−	0.199077i	$-0.0637945\pi$
$347$	29.8556	+	10.8665i	1.60273	+	0.583346i	0.622747	+	0.782423i	$0.286017\pi$
$348$		0			0
$349$	3.00735	−	17.0555i	0.160980	−	0.912962i	−0.792134	−	0.610348i	$-0.791030\pi$
$349$	3.00735	−	17.0555i	0.160980	−	0.912962i	0.953113	−	0.302614i	$-0.0978592\pi$
$350$	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	0.0675442	−	0.997716i	$-0.478484\pi$
$353$	−3.94975	−	0.696448i	−0.210224	−	0.0370682i	−0.277768	+	0.960648i	$0.589595\pi$
$354$		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	−0.661010	−	0.750377i	$-0.729872\pi$
$359$	6.05065	−	10.4800i	0.319341	−	0.553115i	0.980351	+	0.197262i	$0.0632051\pi$
$360$		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	−0.705260	−	0.708949i	$-0.749170\pi$
$367$	2.21046	−	2.63433i	0.115385	−	0.137511i	0.820645	+	0.571438i	$0.193614\pi$
$368$	−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	−0.521908	−	0.853002i	$-0.674779\pi$
$373$	4.39389	−	3.68691i	0.227507	−	0.190901i	0.749415	+	0.662101i	$0.230335\pi$
$374$	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	$-0.775461\pi$
$379$		−	25.2439i		−	1.29669i	0.761346	−	0.648346i	$-0.224539\pi$
$380$	−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	−0.432234	−	0.901761i	$-0.642275\pi$
$383$	7.45183	−	6.25283i	0.380771	−	0.319505i	0.813005	+	0.582257i	$0.197830\pi$
$384$		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	−0.600665	−	0.799501i	$-0.705097\pi$
$389$	5.73930	−	6.83983i	0.290994	−	0.346793i	0.891659	+	0.452708i	$0.149542\pi$
$390$		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	−0.890821	−	0.454354i	$-0.849870\pi$
$397$	−1.03466	+	1.79209i	−0.0519283	+	0.0899424i	0.838893	+	0.544297i	$0.183203\pi$
$398$	−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	−0.349013	−	0.937118i	$-0.613483\pi$
$401$	10.4273	−	28.6488i	0.520714	−	1.43065i	0.869727	−	0.493533i	$-0.164295\pi$
$402$		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	0.989031	−	0.147708i	$-0.0471896\pi$
$409$	33.4041	+	12.1581i	1.65173	+	0.601180i	0.662697	+	0.748888i	$0.269412\pi$
$410$	−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	0.991411	+	0.130786i	$0.0417500\pi$
$419$	2.13949	+	12.1336i	0.104521	+	0.592766i	−0.886890	+	0.461981i	$0.847139\pi$
$420$		0			0
$421$	−13.3302	−	11.1854i	−0.649674	−	0.545141i	0.257298	−	0.966332i	$-0.417168\pi$
$421$	−13.3302	−	11.1854i	−0.649674	−	0.545141i	−0.906972	+	0.421191i	$0.861612\pi$
$422$	−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	−0.976670	−	0.214744i	$-0.931108\pi$
$439$	−7.67971	−	21.0998i	−0.366532	−	1.00704i	0.610138	−	0.792295i	$-0.291114\pi$
$440$	−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	0.436055	−	0.899920i	$-0.356375\pi$
$443$	−7.88175	−	6.61357i	−0.374473	−	0.314220i	−0.810528	+	0.585700i	$0.800820\pi$
$444$		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	−0.305086	−	0.952325i	$-0.598685\pi$
$449$	7.77889	−	4.49114i	0.367109	−	0.211950i	0.672194	+	0.740375i	$0.265352\pi$
$450$		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	−0.998034	−	0.0626714i	$-0.980038\pi$
$457$	−0.828465	+	4.69846i	−0.0387540	+	0.219785i	0.959280	+	0.282456i	$0.0911491\pi$
$458$	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	−0.525897	−	0.850548i	$-0.676270\pi$
$461$	−28.1480	−	4.96325i	−1.31098	−	0.231162i	−0.785086	+	0.619386i	$0.787381\pi$
$462$		0			0
$463$	−14.5089	+	39.8630i	−0.674287	+	1.85259i	−0.179029	+	0.983844i	$0.557296\pi$
$463$	−14.5089	+	39.8630i	−0.674287	+	1.85259i	−0.495258	+	0.868746i	$0.664927\pi$
$464$	−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	−0.930991	−	0.365043i	$-0.881054\pi$
$467$	−3.22767	+	5.59048i	−0.149359	+	0.258697i	0.781632	+	0.623740i	$0.214388\pi$
$468$		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	0.568778	−	0.822491i	$-0.307416\pi$
$479$	33.5552	−	12.2131i	1.53317	−	0.558030i	0.964396	+	0.264461i	$0.0851939\pi$
$480$		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	$0.372823\pi$
$487$			40.6600i			1.84248i	−0.388993	+	0.921241i	$0.627177\pi$
$488$	−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	−0.0107111	−	0.999943i	$-0.503410\pi$
$491$	21.5421	−	18.0759i	0.972180	−	0.815756i	0.982891	+	0.184187i	$0.0589651\pi$
$492$		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	−0.846574	−	0.532272i	$-0.821339\pi$
$499$	−32.6149	+	5.75089i	−1.46005	+	0.257445i	−0.613471	+	0.789717i	$0.710227\pi$
$500$	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	0.992875	+	0.119159i	$0.0380200\pi$
$503$	13.4484	+	23.2932i	0.599633	+	1.03859i	−0.393242	+	0.919435i	$0.628647\pi$
$504$		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	−0.990529	−	0.137303i	$-0.956157\pi$
$509$	−3.23712	+	8.89393i	−0.143483	+	0.394216i	0.847046	+	0.531519i	$0.178379\pi$
$510$		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	0.115070	−	0.993357i	$-0.463291\pi$
$521$	−15.6963	−	9.06226i	−0.687667	−	0.397025i	−0.802737	+	0.596333i	$0.796624\pi$
$522$		0			0
$523$	31.7246	−	18.3162i	1.38722	−	0.800912i	0.394219	−	0.919017i	$-0.371015\pi$
$523$	31.7246	−	18.3162i	1.38722	−	0.800912i	0.993001	+	0.118105i	$0.0376819\pi$
$524$	−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	−0.925003	−	0.379961i	$-0.875938\pi$
$547$	−10.7735	−	29.6001i	−0.460644	−	1.26561i	0.464359	−	0.885647i	$-0.346285\pi$
$548$	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	−0.173662	−	0.984805i	$-0.555560\pi$
$557$	13.9805	−	8.07165i	0.592373	−	0.342007i	0.766035	+	0.642799i	$0.222227\pi$
$558$		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	−0.319687	−	0.947523i	$-0.603578\pi$
$563$	−27.8476	−	10.1357i	−1.17364	−	0.427169i	−0.853951	+	0.520354i	$0.825800\pi$
$564$		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	0.870071	−	0.492926i	$-0.164073\pi$
$569$	36.2357	+	6.38933i	1.51908	+	0.267855i	0.649009	+	0.760781i	$0.275184\pi$
$570$		0			0
$571$	0.343099	−	0.942656i	0.0143582	−	0.0394489i	−0.932306	−	0.361669i	$-0.882207\pi$
$571$	0.343099	−	0.942656i	0.0143582	−	0.0394489i	0.946665	+	0.322220i	$0.104429\pi$
$572$	−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	0.996326	−	0.0856433i	$-0.0272945\pi$
$577$	10.1847	+	17.6404i	0.423994	+	0.734379i	−0.572332	+	0.820022i	$0.693961\pi$
$578$	−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	−0.791655	−	0.610968i	$-0.790780\pi$
$587$	−24.3583	+	8.86571i	−1.00538	+	0.365927i	−0.213721	+	0.976895i	$0.568558\pi$
$588$		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	$0.323361\pi$
$593$			41.3947i			1.69988i	−0.526881	+	0.849939i	$0.676639\pi$
$594$		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	−0.229393	−	0.973334i	$-0.573674\pi$
$599$	16.8708	−	14.1563i	0.689321	−	0.578409i	0.918713	+	0.394925i	$0.129230\pi$
$600$		0			0
$601$	−6.20868	+	2.25978i	−0.253257	+	0.0921782i	−0.465529	−	0.885033i	$-0.654136\pi$
$601$	−6.20868	+	2.25978i	−0.253257	+	0.0921782i	0.212272	+	0.977211i	$0.431914\pi$
$602$	−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	−0.297053	−	0.954861i	$-0.596004\pi$
$607$	−6.14972	+	1.08436i	−0.249610	+	0.0440129i	0.0474433	+	0.998874i	$0.484893\pi$
$608$	−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	−0.891232	−	0.453548i	$-0.850158\pi$
$613$	−1.30807	+	2.26564i	−0.0528323	+	0.0915083i	0.838400	+	0.545056i	$0.183492\pi$
$614$	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	−0.812837	−	0.582491i	$-0.802078\pi$
$617$	4.57669	−	12.5744i	0.184251	−	0.506224i	0.997087	+	0.0762671i	$0.0243002\pi$
$618$		0			0
$619$	26.4425	+	4.66253i	1.06281	+	0.187403i	0.677605	−	0.735426i	$-0.263018\pi$
$619$	26.4425	+	4.66253i	1.06281	+	0.187403i	0.385210	+	0.922829i	$0.374129\pi$
$620$	−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	−0.905790	−	0.423727i	$-0.860722\pi$
$631$	−24.9119	+	14.3829i	−0.991726	+	0.572573i	−0.0859365	+	0.996301i	$0.527388\pi$
$632$	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	0.952305	−	0.305149i	$-0.0987062\pi$
$641$	0.674751	+	1.85386i	0.0266510	+	0.0732231i	−0.925654	+	0.378372i	$0.876484\pi$
$642$		0			0
$643$	−24.5026	−	29.2010i	−0.966286	−	1.15158i	−0.988408	−	0.151820i	$-0.951487\pi$
$643$	−24.5026	−	29.2010i	−0.966286	−	1.15158i	0.0221217	−	0.999755i	$-0.492958\pi$
$644$	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	0.887733	−	0.460359i	$-0.152279\pi$
$653$	7.16057	+	8.53364i	0.280215	+	0.333947i	−0.607518	+	0.794306i	$0.707835\pi$
$654$		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	−0.117228	−	0.993105i	$-0.537401\pi$
$659$	−28.6386	−	24.0307i	−1.11560	−	0.936102i	−0.998374	+	0.0570034i	$0.981845\pi$
$660$		0			0
$661$	0.973924	+	5.52340i	0.0378812	+	0.214835i	0.997873	−	0.0651945i	$-0.0207668\pi$
$661$	0.973924	+	5.52340i	0.0378812	+	0.214835i	−0.959991	+	0.280030i	$0.909656\pi$
$662$	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	−0.546164	−	0.837678i	$-0.683913\pi$
$673$	6.57805	−	37.3060i	0.253565	−	1.43804i	0.799729	−	0.600361i	$-0.204976\pi$
$674$	−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	−0.595238	−	0.803549i	$-0.702942\pi$
$677$	−37.1921	−	6.55797i	−1.42941	−	0.252043i	−0.834171	+	0.551506i	$0.814053\pi$
$678$		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	0.466431	+	0.884558i	$0.345540\pi$
$683$	−13.9252	+	24.1192i	−0.532834	+	0.922895i	−0.999265	+	0.0383376i	$0.987794\pi$
$684$		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	−0.815769	−	0.578378i	$-0.803686\pi$
$691$	−2.74753	+	3.27438i	−0.104521	+	0.124563i	0.711248	+	0.702941i	$0.248130\pi$
$692$	−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	$0.129530\pi$
$701$			20.9584i			0.791586i	−0.918340	+	0.395793i	$0.870470\pi$
$702$		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	−0.196792	−	0.980445i	$-0.563053\pi$
$709$	7.52677	−	2.73952i	0.282674	−	0.102885i	0.479466	+	0.877560i	$0.340830\pi$
$710$	−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	0.775227	−	0.631683i	$-0.217636\pi$
$719$	−4.27525	−	7.40496i	−0.159440	−	0.276158i	−0.934667	+	0.355525i	$0.884302\pi$
$720$		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	−0.330852	−	0.943683i	$-0.607336\pi$
$727$	−26.0060	−	4.58556i	−0.964509	−	0.170069i	−0.633657	+	0.773614i	$0.718447\pi$
$728$	−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	−0.437542	−	0.899198i	$-0.644151\pi$
$733$	−36.5691	−	13.3101i	−1.35071	−	0.491619i	−0.913170	+	0.407579i	$0.866373\pi$
$734$	−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	−0.291505	−	0.956569i	$-0.594156\pi$
$739$	10.6334	−	6.13920i	0.391156	−	0.225834i	0.682661	+	0.730735i	$0.260823\pi$
$740$	−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	0.981554	+	0.191187i	$0.0612338\pi$
$743$	3.39594	+	19.2593i	0.124585	+	0.706556i	−0.856969	+	0.515368i	$0.827655\pi$
$744$		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	0.779649	−	0.626216i	$-0.215397\pi$
$751$	0.755319	+	0.900154i	0.0275620	+	0.0328471i	−0.752087	+	0.659063i	$0.770953\pi$
$752$	−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	0.576462	−	0.817124i	$-0.304433\pi$
$761$	−9.05794	−	10.7948i	−0.328350	−	0.391313i	−0.904812	+	0.425812i	$0.859989\pi$
$762$		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	−0.957640	−	0.287968i	$-0.907020\pi$
$769$	−4.33277	−	24.5724i	−0.156244	−	0.886102i	0.801396	−	0.598134i	$-0.204091\pi$
$770$	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	−0.253550	−	0.967322i	$-0.581598\pi$
$773$	12.7170	−	7.34218i	0.457400	−	0.264080i	0.710950	+	0.703242i	$0.248265\pi$
$774$		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	−0.972991	−	0.230844i	$-0.925851\pi$
$787$	−2.22332	+	6.10852i	−0.0792528	+	0.217745i	0.893738	+	0.448589i	$0.148073\pi$
$788$	−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	−0.593290	−	0.804989i	$-0.702171\pi$
$797$	−24.7158	+	4.35806i	−0.875477	+	0.154370i	−0.282188	+	0.959359i	$0.591060\pi$
$798$		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	$-0.896830\pi$
$809$		−	18.1165i		−	0.636944i	0.947932	−	0.318472i	$-0.103170\pi$
$810$		0			0
$811$		−	6.98634i		−	0.245324i	−0.992449	−	0.122662i	$-0.960857\pi$
$811$		−	6.98634i		−	0.245324i	0.992449	−	0.122662i	$-0.0391430\pi$
$812$	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	−0.999831	−	0.0183987i	$-0.994143\pi$
$821$	−23.1544	+	27.5943i	−0.808093	+	0.963047i	0.191738	+	0.981446i	$0.438588\pi$
$822$		0			0
$823$	22.5108	−	3.96925i	0.784676	−	0.138359i	0.233065	−	0.972461i	$-0.425125\pi$
$823$	22.5108	−	3.96925i	0.784676	−	0.138359i	0.551611	+	0.834102i	$0.314013\pi$
$824$	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	0.992782	+	0.119929i	$0.0382667\pi$
$827$	17.2618	+	29.8984i	0.600253	+	1.03967i	−0.392530	+	0.919739i	$0.628400\pi$
$828$		0			0
$829$	11.3276	−	19.6199i	0.393423	−	0.681429i	−0.599475	−	0.800393i	$-0.704624\pi$
$829$	11.3276	−	19.6199i	0.393423	−	0.681429i	0.992899	+	0.118964i	$0.0379574\pi$
$830$	−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	0.935184	+	0.354161i	$0.115234\pi$
$839$	−1.87499	+	10.6336i	−0.0647317	+	0.367112i	−0.999916	+	0.0129506i	$0.995878\pi$
$840$		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	0.376491	−	0.926420i	$-0.377131\pi$
$853$	−13.7409	−	11.5299i	−0.470478	−	0.394778i	−0.846969	+	0.531643i	$0.821575\pi$
$854$	−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	0.968585	−	0.248682i	$-0.0799973\pi$
$857$	1.95427	+	5.36930i	0.0667564	+	0.183412i	−0.901829	+	0.432093i	$0.857775\pi$
$858$		0			0
$859$	−12.2892	−	14.6457i	−0.419302	−	0.499704i	0.514502	−	0.857489i	$-0.327977\pi$
$859$	−12.2892	−	14.6457i	−0.419302	−	0.499704i	−0.933804	+	0.357785i	$0.883532\pi$
$860$	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	−0.955240	−	0.295831i	$-0.904403\pi$
$877$	−4.70239	−	26.6686i	−0.158788	−	0.900533i	0.796452	−	0.604702i	$-0.206708\pi$
$878$	−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	−0.609532	−	0.792761i	$-0.708643\pi$
$881$	−6.75989	+	3.90282i	−0.227746	+	0.131489i	0.381786	+	0.924251i	$0.375309\pi$
$882$		0			0
$883$	−43.9985	−	25.4025i	−1.48067	−	0.854864i	−0.480907	−	0.876772i	$-0.659693\pi$
$883$	−43.9985	−	25.4025i	−1.48067	−	0.854864i	−0.999760	+	0.0219080i	$0.993026\pi$
$884$	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	0.263652	−	0.964618i	$-0.415073\pi$
$887$	−4.59913	−	1.67395i	−0.154424	−	0.0562056i	−0.418075	+	0.908412i	$0.637295\pi$
$888$		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	−0.421077	−	0.907025i	$-0.638348\pi$
$907$	16.4221	−	19.5711i	0.545288	−	0.649849i	0.966365	+	0.257176i	$0.0827921\pi$
$908$	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	0.437107	−	0.899410i	$-0.356003\pi$
$911$	40.7491	−	14.8315i	1.35008	−	0.491389i	0.912973	+	0.408021i	$0.133781\pi$
$912$		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	$0.174865\pi$
$919$			31.6571i			1.04427i	−0.852862	+	0.522136i	$0.825135\pi$
$920$	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	−0.0360286	+	0.999351i	$0.511471\pi$
$929$	−30.9044	+	36.8304i	−1.01394	+	1.20837i	−0.977912	+	0.209017i	$0.932974\pi$
$930$		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	0.119681	−	0.992812i	$-0.461813\pi$
$937$	28.1506	−	48.7583i	0.919641	−	1.59287i	0.799961	−	0.600053i	$-0.204854\pi$
$938$	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	0.110809	+	0.993842i	$0.464656\pi$
$941$	−18.8013	+	51.6561i	−0.612905	+	1.68394i	−0.723714	+	0.690100i	$0.757566\pi$
$942$		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	−0.496192	−	0.868213i	$-0.665269\pi$
$947$	8.21717	−	46.6019i	0.267022	−	1.51436i	0.763214	−	0.646145i	$-0.223620\pi$
$948$		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	0.896783	−	0.442470i	$-0.145898\pi$
$953$	29.6972	+	17.1457i	0.961985	+	0.555402i	0.0652018	+	0.997872i	$0.479231\pi$
$954$		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	0.956339	−	0.292261i	$-0.0944075\pi$
$967$	15.6245	+	18.6206i	0.502452	+	0.598799i	−0.453887	+	0.891059i	$0.649963\pi$
$968$	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	−0.989807	−	0.142413i	$-0.954514\pi$
$977$	−29.9498	−	35.6928i	−0.958179	−	1.14191i	0.0316286	−	0.999500i	$-0.489931\pi$
$978$		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	0.762848	−	0.646578i	$-0.223800\pi$
$983$	8.10659	+	6.80224i	0.258560	+	0.216958i	−0.504288	+	0.863536i	$0.668245\pi$
$984$		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	0.144312	−	0.989532i	$-0.453903\pi$
$991$	−20.1628	−	11.6410i	−0.640492	−	0.369788i	−0.784804	+	0.619744i	$0.787236\pi$
$992$	−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	0.253497	+	0.967336i	$0.418419\pi$
$997$	−9.96393	+	56.5082i	−0.315561	+	1.78963i	−0.569057	+	0.822298i	$0.692692\pi$
$998$	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.755.7		96
3.2	odd	2		972.2.l.d.755.10		96
4.3	odd	2	inner	972.2.l.a.755.5		96
9.2	odd	6		972.2.l.c.431.12		96
9.4	even	3		324.2.l.a.35.16		96
9.5	odd	6		108.2.l.a.11.1	✓	96
9.7	even	3		972.2.l.b.431.5		96
12.11	even	2		972.2.l.d.755.12		96
27.4	even	9		108.2.l.a.59.11	yes	96
27.5	odd	18		972.2.l.b.539.15		96
27.13	even	9		972.2.l.d.215.12		96
27.14	odd	18	inner	972.2.l.a.215.5		96
27.22	even	9		972.2.l.c.539.2		96
27.23	odd	18		324.2.l.a.287.6		96
36.7	odd	6		972.2.l.b.431.15		96
36.11	even	6		972.2.l.c.431.2		96
36.23	even	6		108.2.l.a.11.11	yes	96
36.31	odd	6		324.2.l.a.35.6		96
108.23	even	18		324.2.l.a.287.16		96
108.31	odd	18		108.2.l.a.59.1	yes	96
108.59	even	18		972.2.l.b.539.5		96
108.67	odd	18		972.2.l.d.215.10		96
108.95	even	18	inner	972.2.l.a.215.7		96
108.103	odd	18		972.2.l.c.539.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.1	✓	96	9.5	odd	6
108.2.l.a.11.11	yes	96	36.23	even	6
108.2.l.a.59.1	yes	96	108.31	odd	18
108.2.l.a.59.11	yes	96	27.4	even	9
324.2.l.a.35.6		96	36.31	odd	6
324.2.l.a.35.16		96	9.4	even	3
324.2.l.a.287.6		96	27.23	odd	18
324.2.l.a.287.16		96	108.23	even	18
972.2.l.a.215.5		96	27.14	odd	18	inner
972.2.l.a.215.7		96	108.95	even	18	inner
972.2.l.a.755.5		96	4.3	odd	2	inner
972.2.l.a.755.7		96	1.1	even	1	trivial
972.2.l.b.431.5		96	9.7	even	3
972.2.l.b.431.15		96	36.7	odd	6
972.2.l.b.539.5		96	108.59	even	18
972.2.l.b.539.15		96	27.5	odd	18
972.2.l.c.431.2		96	36.11	even	6
972.2.l.c.431.12		96	9.2	odd	6
972.2.l.c.539.2		96	27.22	even	9
972.2.l.c.539.12		96	108.103	odd	18
972.2.l.d.215.10		96	108.67	odd	18
972.2.l.d.215.12		96	27.13	even	9
972.2.l.d.755.10		96	3.2	odd	2
972.2.l.d.755.12		96	12.11	even	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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
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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