LMFDB - Embedded newform 450.2.l.c.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.3
Root			$3.42137 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	450.19
Dual form			450.2.l.c.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-2.23558 + 0.0466062i) q^{5} -3.52206i q^{7} +(0.587785 - 0.809017i) q^{8} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-2.23558 + 0.0466062i) q^{5} -3.52206i q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.11176 + 0.735158i) q^{10} +(-1.62388 - 4.99779i) q^{11} +(-0.588802 - 0.191313i) q^{13} +(-1.08838 - 3.34968i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-2.02525 + 2.78752i) q^{17} +(1.83995 + 1.33680i) q^{19} +(-1.78123 + 1.35175i) q^{20} +(-3.08880 - 4.25137i) q^{22} +(8.51557 - 2.76688i) q^{23} +(4.99566 - 0.208384i) q^{25} -0.619103 q^{26} +(-2.07022 - 2.84941i) q^{28} +(2.16949 - 1.57623i) q^{29} +(-7.90309 - 5.74193i) q^{31} -1.00000i q^{32} +(-1.06474 + 3.27693i) q^{34} +(0.164150 + 7.87386i) q^{35} +(-0.952702 - 0.309552i) q^{37} +(2.16299 + 0.702799i) q^{38} +(-1.27634 + 1.83602i) q^{40} +(-1.94584 + 5.98868i) q^{41} +1.51251i q^{43} +(-4.25137 - 3.08880i) q^{44} +(7.24378 - 5.26291i) q^{46} +(6.27522 + 8.63710i) q^{47} -5.40494 q^{49} +(4.68676 - 1.74193i) q^{50} +(-0.588802 + 0.191313i) q^{52} +(-0.325260 - 0.447681i) q^{53} +(3.86324 + 11.0973i) q^{55} +(-2.84941 - 2.07022i) q^{56} +(1.57623 - 2.16949i) q^{58} +(0.0861451 - 0.265127i) q^{59} +(1.13786 + 3.50196i) q^{61} +(-9.29064 - 3.01871i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(1.32523 + 0.400255i) q^{65} +(-7.00176 + 9.63710i) q^{67} +3.44557i q^{68} +(2.58927 + 7.43777i) q^{70} +(3.84168 - 2.79115i) q^{71} +(9.35277 - 3.03890i) q^{73} -1.00173 q^{74} +2.27431 q^{76} +(-17.6025 + 5.71941i) q^{77} +(5.27525 - 3.83269i) q^{79} +(-0.646508 + 2.14057i) q^{80} +6.29687i q^{82} +(1.56335 - 2.15177i) q^{83} +(4.39770 - 6.32612i) q^{85} +(0.467392 + 1.43848i) q^{86} +(-4.99779 - 1.62388i) q^{88} +(-4.13649 - 12.7308i) q^{89} +(-0.673818 + 2.07380i) q^{91} +(5.26291 - 7.24378i) q^{92} +(8.63710 + 6.27522i) q^{94} +(-4.17567 - 2.90278i) q^{95} +(-2.56983 - 3.53706i) q^{97} +(-5.14040 + 1.67022i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^4 - 4 * q^5	$ 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37} - 10 q^{38} - 2 q^{40} - 22 q^{41} - 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} - 12 q^{50} + 20 q^{52} - 30 q^{53} + 18 q^{55} + 2 q^{56} - 30 q^{58} - 20 q^{59} + 12 q^{61} - 50 q^{62} + 4 q^{64} + 8 q^{65} - 50 q^{67} - 12 q^{70} + 28 q^{71} + 20 q^{73} - 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{80} + 30 q^{83} - 4 q^{85} + 6 q^{86} - 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} + 30 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^5 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 2 * q^14 - 4 * q^16 + 30 * q^17 + 4 * q^20 - 20 * q^22 + 10 * q^23 + 24 * q^25 - 4 * q^26 + 10 * q^29 - 18 * q^31 + 12 * q^34 + 34 * q^35 + 20 * q^37 - 10 * q^38 - 2 * q^40 - 22 * q^41 - 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 - 12 * q^50 + 20 * q^52 - 30 * q^53 + 18 * q^55 + 2 * q^56 - 30 * q^58 - 20 * q^59 + 12 * q^61 - 50 * q^62 + 4 * q^64 + 8 * q^65 - 50 * q^67 - 12 * q^70 + 28 * q^71 + 20 * q^73 - 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^80 + 30 * q^83 - 4 * q^85 + 6 * q^86 - 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 + 30 * q^95 - 10 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−2.23558	+	0.0466062i	−0.999783	+	0.0208429i
$5$	−2.23558	+	0.0466062i	−0.999783	+	0.0208429i
$6$		0			0
$7$		−	3.52206i		−	1.33122i	−0.746302	−	0.665608i	$-0.768172\pi$
$7$		−	3.52206i		−	1.33122i	0.746302	−	0.665608i	$-0.231828\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$		0			0
$10$	−2.11176	+	0.735158i	−0.667798	+	0.232477i
$11$	−1.62388	−	4.99779i	−0.489618	−	1.50689i	−0.825179	−	0.564871i	$-0.808926\pi$
$11$	−1.62388	−	4.99779i	−0.489618	−	1.50689i	0.335561	−	0.942018i	$-0.391074\pi$
$12$		0			0
$13$	−0.588802	−	0.191313i	−0.163304	−	0.0530608i	0.226224	−	0.974075i	$-0.427362\pi$
$13$	−0.588802	−	0.191313i	−0.163304	−	0.0530608i	−0.389528	+	0.921015i	$0.627362\pi$
$14$	−1.08838	−	3.34968i	−0.290881	−	0.895240i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.02525	+	2.78752i	−0.491196	+	0.676073i	−0.980608	−	0.195979i	$-0.937211\pi$
$17$	−2.02525	+	2.78752i	−0.491196	+	0.676073i	0.489412	+	0.872053i	$0.337211\pi$
$18$		0			0
$19$	1.83995	+	1.33680i	0.422114	+	0.306684i	0.778488	−	0.627660i	$-0.215987\pi$
$19$	1.83995	+	1.33680i	0.422114	+	0.306684i	−0.356374	+	0.934343i	$0.615987\pi$
$20$	−1.78123	+	1.35175i	−0.398295	+	0.302260i
$21$		0			0
$22$	−3.08880	−	4.25137i	−0.658535	−	0.906395i
$23$	8.51557	−	2.76688i	1.77562	−	0.576934i	0.777002	−	0.629498i	$-0.216739\pi$
$23$	8.51557	−	2.76688i	1.77562	−	0.576934i	0.998618	+	0.0525639i	$0.0167393\pi$
$24$		0			0
$25$	4.99566	−	0.208384i	0.999131	−	0.0416768i
$26$	−0.619103			−0.121416
$27$		0			0
$28$	−2.07022	−	2.84941i	−0.391234	−	0.538488i
$29$	2.16949	−	1.57623i	0.402864	−	0.292698i	−0.367843	−	0.929888i	$-0.619904\pi$
$29$	2.16949	−	1.57623i	0.402864	−	0.292698i	0.770706	+	0.637190i	$0.219904\pi$
$30$		0			0
$31$	−7.90309	−	5.74193i	−1.41944	−	1.03128i	−0.991864	−	0.127300i	$-0.959369\pi$
$31$	−7.90309	−	5.74193i	−1.41944	−	1.03128i	−0.427572	−	0.903981i	$-0.640631\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−1.06474	+	3.27693i	−0.182601	+	0.561989i
$35$	0.164150	+	7.87386i	0.0277464	+	1.33093i
$36$		0			0
$37$	−0.952702	−	0.309552i	−0.156623	−	0.0508900i	0.229656	−	0.973272i	$-0.426240\pi$
$37$	−0.952702	−	0.309552i	−0.156623	−	0.0508900i	−0.386279	+	0.922382i	$0.626240\pi$
$38$	2.16299	+	0.702799i	0.350884	+	0.114009i
$39$		0			0
$40$	−1.27634	+	1.83602i	−0.201807	+	0.290300i
$41$	−1.94584	+	5.98868i	−0.303889	+	0.935274i	0.676200	+	0.736718i	$0.263625\pi$
$41$	−1.94584	+	5.98868i	−0.303889	+	0.935274i	−0.980089	+	0.198557i	$0.936375\pi$
$42$		0			0
$43$			1.51251i			0.230656i	0.993327	+	0.115328i	$0.0367919\pi$
$43$			1.51251i			0.230656i	−0.993327	+	0.115328i	$0.963208\pi$
$44$	−4.25137	−	3.08880i	−0.640918	−	0.465654i
$45$		0			0
$46$	7.24378	−	5.26291i	1.06804	−	0.775974i
$47$	6.27522	+	8.63710i	0.915335	+	1.25985i	0.965312	+	0.261100i	$0.0840851\pi$
$47$	6.27522	+	8.63710i	0.915335	+	1.25985i	−0.0499772	+	0.998750i	$0.515915\pi$
$48$		0			0
$49$	−5.40494			−0.772134
$50$	4.68676	−	1.74193i	0.662808	−	0.246346i
$51$		0			0
$52$	−0.588802	+	0.191313i	−0.0816522	+	0.0265304i
$53$	−0.325260	−	0.447681i	−0.0446778	−	0.0614938i	0.786094	−	0.618107i	$-0.212100\pi$
$53$	−0.325260	−	0.447681i	−0.0446778	−	0.0614938i	−0.830771	+	0.556614i	$0.812100\pi$
$54$		0			0
$55$	3.86324	+	11.0973i	0.520920	+	1.49636i
$56$	−2.84941	−	2.07022i	−0.380768	−	0.276644i
$57$		0			0
$58$	1.57623	−	2.16949i	0.206968	−	0.284868i
$59$	0.0861451	−	0.265127i	0.0112151	−	0.0345166i	−0.945292	−	0.326224i	$-0.894223\pi$
$59$	0.0861451	−	0.265127i	0.0112151	−	0.0345166i	0.956507	+	0.291708i	$0.0942235\pi$
$60$		0			0
$61$	1.13786	+	3.50196i	0.145688	+	0.448380i	0.997099	−	0.0761185i	$-0.0242527\pi$
$61$	1.13786	+	3.50196i	0.145688	+	0.448380i	−0.851411	+	0.524499i	$0.824253\pi$
$62$	−9.29064	−	3.01871i	−1.17991	−	0.383377i
$63$		0			0
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	1.32523	+	0.400255i	0.164375	+	0.0496455i
$66$		0			0
$67$	−7.00176	+	9.63710i	−0.855401	+	1.17736i	0.127245	+	0.991871i	$0.459386\pi$
$67$	−7.00176	+	9.63710i	−0.855401	+	1.17736i	−0.982647	+	0.185487i	$0.940614\pi$
$68$			3.44557i			0.417836i
$69$		0			0
$70$	2.58927	+	7.43777i	0.309477	+	0.888983i
$71$	3.84168	−	2.79115i	0.455924	−	0.331248i	−0.336006	−	0.941860i	$-0.609076\pi$
$71$	3.84168	−	2.79115i	0.455924	−	0.331248i	0.791930	+	0.610612i	$0.209076\pi$
$72$		0			0
$73$	9.35277	−	3.03890i	1.09466	−	0.355676i	0.294614	−	0.955616i	$-0.404809\pi$
$73$	9.35277	−	3.03890i	1.09466	−	0.355676i	0.800045	+	0.599940i	$0.204809\pi$
$74$	−1.00173			−0.116449
$75$		0			0
$76$	2.27431			0.260881
$77$	−17.6025	+	5.71941i	−2.00599	+	0.651787i
$78$		0			0
$79$	5.27525	−	3.83269i	0.593512	−	0.431212i	−0.250058	−	0.968231i	$-0.580450\pi$
$79$	5.27525	−	3.83269i	0.593512	−	0.431212i	0.843570	+	0.537019i	$0.180450\pi$
$80$	−0.646508	+	2.14057i	−0.0722818	+	0.239323i
$81$		0			0
$82$			6.29687i			0.695373i
$83$	1.56335	−	2.15177i	0.171600	−	0.236187i	−0.714551	−	0.699583i	$-0.753369\pi$
$83$	1.56335	−	2.15177i	0.171600	−	0.236187i	0.886151	+	0.463396i	$0.153369\pi$
$84$		0			0
$85$	4.39770	−	6.32612i	0.476998	−	0.686164i
$86$	0.467392	+	1.43848i	0.0504002	+	0.155116i
$87$		0			0
$88$	−4.99779	−	1.62388i	−0.532766	−	0.173106i
$89$	−4.13649	−	12.7308i	−0.438467	−	1.34946i	−0.889491	−	0.456952i	$-0.848941\pi$
$89$	−4.13649	−	12.7308i	−0.438467	−	1.34946i	0.451024	−	0.892512i	$-0.351059\pi$
$90$		0			0
$91$	−0.673818	+	2.07380i	−0.0706353	+	0.217393i
$92$	5.26291	−	7.24378i	0.548697	−	0.755216i
$93$		0			0
$94$	8.63710	+	6.27522i	0.890848	+	0.647239i
$95$	−4.17567	−	2.90278i	−0.428414	−	0.297819i
$96$		0			0
$97$	−2.56983	−	3.53706i	−0.260926	−	0.359134i	0.658374	−	0.752691i	$-0.271244\pi$
$97$	−2.56983	−	3.53706i	−0.260926	−	0.359134i	−0.919300	+	0.393557i	$0.871244\pi$
$98$	−5.14040	+	1.67022i	−0.519259	+	0.168717i
$99$		0			0
$100$	3.91909	−	3.10496i	0.391909	−	0.310496i
$101$	14.2687			1.41979			0.709893	−	0.704309i	$-0.248743\pi$
$101$	14.2687			1.41979			0.709893	+	0.704309i	$0.248743\pi$
$102$		0			0
$103$	10.3852	+	14.2939i	1.02328	+	1.40842i	0.909879	+	0.414875i	$0.136175\pi$
$103$	10.3852	+	14.2939i	1.02328	+	1.40842i	0.113401	+	0.993549i	$0.463825\pi$
$104$	−0.500865	+	0.363900i	−0.0491138	+	0.0356833i
$105$		0			0
$106$	−0.447681	−	0.325260i	−0.0434827	−	0.0315920i
$107$		−	0.723713i		−	0.0699640i	−0.999388	−	0.0349820i	$-0.988863\pi$
$107$		−	0.723713i		−	0.0699640i	0.999388	−	0.0349820i	$-0.0111374\pi$
$108$		0			0
$109$	0.795198	−	2.44737i	0.0761661	−	0.234415i	−0.905724	−	0.423869i	$-0.860672\pi$
$109$	0.795198	−	2.44737i	0.0761661	−	0.234415i	0.981890	+	0.189454i	$0.0606717\pi$
$110$	7.10341	+	9.36033i	0.677284	+	0.892473i
$111$		0			0
$112$	−3.34968	−	1.08838i	−0.316515	−	0.102842i
$113$	14.4448	+	4.69339i	1.35885	+	0.441517i	0.895659	−	0.444741i	$-0.146704\pi$
$113$	14.4448	+	4.69339i	1.35885	+	0.441517i	0.463191	+	0.886258i	$0.346704\pi$
$114$		0			0
$115$	−18.9083	+	6.58246i	−1.76321	+	0.613818i
$116$	0.828671	−	2.55039i	0.0769401	−	0.236797i
$117$		0			0
$118$		−	0.278771i		−	0.0256630i
$119$	9.81783	+	7.13307i	0.899999	+	0.653888i
$120$		0			0
$121$	−13.4417	+	9.76597i	−1.22197	+	0.887815i
$122$	2.16433	+	2.97895i	0.195949	+	0.269701i
$123$		0			0
$124$	−9.76875			−0.877260
$125$	−11.1585	+	0.698687i	−0.998045	+	0.0624925i
$126$		0			0
$127$	4.15027	−	1.34850i	0.368277	−	0.119660i	−0.119031	−	0.992891i	$-0.537979\pi$
$127$	4.15027	−	1.34850i	0.368277	−	0.119660i	0.487308	+	0.873230i	$0.337979\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$		0			0
$130$	1.38406	−	0.0288540i	0.121390	−	0.00253066i
$131$	−0.499797	−	0.363124i	−0.0436675	−	0.0317263i	0.565737	−	0.824585i	$-0.308592\pi$
$131$	−0.499797	−	0.363124i	−0.0436675	−	0.0317263i	−0.609405	+	0.792859i	$0.708592\pi$
$132$		0			0
$133$	4.70831	−	6.48043i	0.408262	−	0.561925i
$134$	−3.68104	+	11.3291i	−0.317994	+	0.978684i
$135$		0			0
$136$	1.06474	+	3.27693i	0.0913006	+	0.280994i
$137$	−8.81784	−	2.86509i	−0.753359	−	0.244781i	−0.0929329	−	0.995672i	$-0.529624\pi$
$137$	−8.81784	−	2.86509i	−0.753359	−	0.244781i	−0.660426	+	0.750891i	$0.729624\pi$
$138$		0			0
$139$	−5.79774	−	17.8436i	−0.491757	−	1.51347i	−0.821950	−	0.569560i	$-0.807114\pi$
$139$	−5.79774	−	17.8436i	−0.491757	−	1.51347i	0.330192	−	0.943914i	$-0.392886\pi$
$140$	4.76094	+	6.27361i	0.402373	+	0.530216i
$141$		0			0
$142$	2.79115	−	3.84168i	0.234228	−	0.322387i
$143$			3.25338i			0.272061i
$144$		0			0
$145$	−4.77661	+	3.62489i	−0.396676	+	0.301031i
$146$	7.95594	−	5.78033i	0.658438	−	0.478383i
$147$		0			0
$148$	−0.952702	+	0.309552i	−0.0783116	+	0.0254450i
$149$	−16.8396			−1.37955			−0.689777	−	0.724022i	$-0.742291\pi$
$149$	−16.8396			−1.37955			−0.689777	+	0.724022i	$0.742291\pi$
$150$		0			0
$151$	16.7932			1.36661			0.683305	−	0.730133i	$-0.260542\pi$
$151$	16.7932			1.36661			0.683305	+	0.730133i	$0.260542\pi$
$152$	2.16299	−	0.702799i	0.175442	−	0.0570045i
$153$		0			0
$154$	−14.9736	+	10.8790i	−1.20661	+	0.876652i
$155$	17.9356	+	12.4682i	1.44062	+	1.00147i
$156$		0			0
$157$			4.55451i			0.363489i	0.983346	+	0.181745i	$0.0581744\pi$
$157$			4.55451i			0.363489i	−0.983346	+	0.181745i	$0.941826\pi$
$158$	3.83269	−	5.27525i	0.304913	−	0.419676i
$159$		0			0
$160$	0.0466062	+	2.23558i	0.00368454	+	0.176738i
$161$	−9.74512	−	29.9924i	−0.768023	−	2.36373i
$162$		0			0
$163$	19.2239	+	6.24624i	1.50574	+	0.489243i	0.941685	−	0.336497i	$-0.109242\pi$
$163$	19.2239	+	6.24624i	1.50574	+	0.489243i	0.564051	+	0.825740i	$0.309242\pi$
$164$	1.94584	+	5.98868i	0.151945	+	0.467637i
$165$		0			0
$166$	0.821902	−	2.52955i	0.0637920	−	0.196331i
$167$	4.22725	−	5.81831i	0.327114	−	0.450234i	−0.613508	−	0.789688i	$-0.710242\pi$
$167$	4.22725	−	5.81831i	0.327114	−	0.450234i	0.940623	+	0.339454i	$0.110242\pi$
$168$		0			0
$169$	−10.2071	−	7.41592i	−0.785164	−	0.570455i
$170$	2.22759	−	7.37547i	0.170848	−	0.565672i
$171$		0			0
$172$	0.889032	+	1.22365i	0.0677881	+	0.0933023i
$173$	−5.83145	+	1.89475i	−0.443357	+	0.144055i	−0.522184	−	0.852833i	$-0.674883\pi$
$173$	−5.83145	+	1.89475i	−0.443357	+	0.144055i	0.0788271	+	0.996888i	$0.474883\pi$
$174$		0			0
$175$	−0.733941	−	17.5950i	−0.0554807	−	1.33006i
$176$	−5.25498			−0.396109
$177$		0			0
$178$	−7.86808	−	10.8295i	−0.589737	−	0.811704i
$179$	−11.5930	+	8.42280i	−0.866501	+	0.629549i	−0.929646	−	0.368455i	$-0.879887\pi$
$179$	−11.5930	+	8.42280i	−0.866501	+	0.629549i	0.0631451	+	0.998004i	$0.479887\pi$
$180$		0			0
$181$	−12.7254	−	9.24554i	−0.945871	−	0.687215i	0.00395575	−	0.999992i	$-0.498741\pi$
$181$	−12.7254	−	9.24554i	−0.945871	−	0.687215i	−0.949827	+	0.312777i	$0.898741\pi$
$182$			2.18052i			0.161631i
$183$		0			0
$184$	2.76688	−	8.51557i	0.203977	−	0.627776i
$185$	2.14427	+	0.647626i	0.157650	+	0.0476144i
$186$		0			0
$187$	17.2202	+	5.59518i	1.25927	+	0.409160i
$188$	10.1535	+	3.29908i	0.740521	+	0.240610i
$189$		0			0
$190$	−4.86830	−	1.47036i	−0.353184	−	0.106671i
$191$	1.11938	−	3.44511i	0.0809958	−	0.249279i	−0.902356	−	0.430992i	$-0.858164\pi$
$191$	1.11938	−	3.44511i	0.0809958	−	0.249279i	0.983352	+	0.181712i	$0.0581639\pi$
$192$		0			0
$193$			9.72486i			0.700010i	0.936748	+	0.350005i	$0.113820\pi$
$193$			9.72486i			0.700010i	−0.936748	+	0.350005i	$0.886180\pi$
$194$	−3.53706	−	2.56983i	−0.253946	−	0.184503i
$195$		0			0
$196$	−4.37269	+	3.17694i	−0.312335	+	0.226925i
$197$	−4.15786	−	5.72280i	−0.296235	−	0.407732i	0.634792	−	0.772683i	$-0.281086\pi$
$197$	−4.15786	−	5.72280i	−0.296235	−	0.407732i	−0.931027	+	0.364951i	$0.881086\pi$
$198$		0			0
$199$	17.6745			1.25291			0.626455	−	0.779457i	$-0.284505\pi$
$199$	17.6745			1.25291			0.626455	+	0.779457i	$0.284505\pi$
$200$	2.76779	−	4.16406i	0.195712	−	0.294443i
$201$		0			0
$202$	13.5703	−	4.40926i	0.954804	−	0.310235i
$203$	−5.55157	−	7.64108i	−0.389644	−	0.536298i
$204$		0			0
$205$	4.07098	−	13.4789i	0.284329	−	0.941405i
$206$	14.2939	+	10.3852i	0.995906	+	0.723568i
$207$		0			0
$208$	−0.363900	+	0.500865i	−0.0252319	+	0.0347287i
$209$	3.69320	−	11.3665i	0.255464	−	0.786237i
$210$		0			0
$211$	−3.63522	−	11.1881i	−0.250259	−	0.770218i	−0.994727	−	0.102559i	$-0.967297\pi$
$211$	−3.63522	−	11.1881i	−0.250259	−	0.770218i	0.744468	−	0.667658i	$-0.232703\pi$
$212$	−0.526281	−	0.170999i	−0.0361451	−	0.0117443i
$213$		0			0
$214$	−0.223640	−	0.688292i	−0.0152877	−	0.0470507i
$215$	−0.0704924	−	3.38135i	−0.00480754	−	0.230606i
$216$		0			0
$217$	−20.2234	+	27.8352i	−1.37286	+	1.88958i
$218$		−	2.57331i		−	0.174287i
$219$		0			0
$220$	9.64825	+	6.70713i	0.650485	+	0.452195i
$221$	1.72576	−	1.25384i	0.116087	−	0.0843424i
$222$		0			0
$223$	−12.0789	+	3.92466i	−0.808860	+	0.262815i	−0.684115	−	0.729374i	$-0.739811\pi$
$223$	−12.0789	+	3.92466i	−0.808860	+	0.262815i	−0.124745	+	0.992189i	$0.539811\pi$
$224$	−3.52206			−0.235328
$225$		0			0
$226$	15.1881			1.01030
$227$	−13.5679	+	4.40848i	−0.900533	+	0.292601i	−0.722457	−	0.691416i	$-0.756987\pi$
$227$	−13.5679	+	4.40848i	−0.900533	+	0.292601i	−0.178076	+	0.984017i	$0.556987\pi$
$228$		0			0
$229$	7.12184	−	5.17432i	0.470625	−	0.341929i	−0.327060	−	0.945004i	$-0.606058\pi$
$229$	7.12184	−	5.17432i	0.470625	−	0.341929i	0.797685	+	0.603075i	$0.206058\pi$
$230$	−15.9488	+	12.1033i	−1.05163	+	0.798067i
$231$		0			0
$232$		−	2.68163i		−	0.176058i
$233$	−8.86158	+	12.1969i	−0.580542	+	0.799047i	−0.993755	−	0.111587i	$-0.964406\pi$
$233$	−8.86158	+	12.1969i	−0.580542	+	0.799047i	0.413213	+	0.910634i	$0.364406\pi$
$234$		0			0
$235$	−14.4313	−	19.0165i	−0.941395	−	1.24050i
$236$	−0.0861451	−	0.265127i	−0.00560757	−	0.0172583i
$237$		0			0
$238$	11.5416	+	3.75008i	0.748128	+	0.243081i
$239$	−1.93007	−	5.94013i	−0.124846	−	0.384235i	0.869027	−	0.494764i	$-0.164746\pi$
$239$	−1.93007	−	5.94013i	−0.124846	−	0.384235i	−0.993873	+	0.110529i	$0.964746\pi$
$240$		0			0
$241$	−4.57636	+	14.0846i	−0.294790	+	0.907269i	0.688503	+	0.725234i	$0.258268\pi$
$241$	−4.57636	+	14.0846i	−0.294790	+	0.907269i	−0.983292	+	0.182035i	$0.941732\pi$
$242$	−9.76597	+	13.4417i	−0.627780	+	0.864065i
$243$		0			0
$244$	2.97895	+	2.16433i	0.190708	+	0.138557i
$245$	12.0832	−	0.251903i	0.771966	−	0.0160935i
$246$		0			0
$247$	−0.827619	−	1.13912i	−0.0526601	−	0.0724805i
$248$	−9.29064	+	3.01871i	−0.589956	+	0.191688i
$249$		0			0
$250$	−10.3964	+	4.11265i	−0.657529	+	0.260107i
$251$	−18.2744			−1.15347			−0.576735	−	0.816931i	$-0.695673\pi$
$251$	−18.2744			−1.15347			−0.576735	+	0.816931i	$0.695673\pi$
$252$		0			0
$253$	−27.6565	−	38.0659i	−1.73875	−	2.39319i
$254$	3.53043	−	2.56501i	0.221519	−	0.160943i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$			1.80149i			0.112374i	0.998420	+	0.0561868i	$0.0178942\pi$
$257$			1.80149i			0.112374i	−0.998420	+	0.0561868i	$0.982106\pi$
$258$		0			0
$259$	−1.09026	+	3.35548i	−0.0677455	+	0.208499i
$260$	1.30740	−	0.455139i	0.0810814	−	0.0282265i
$261$		0			0
$262$	−0.587547	−	0.190905i	−0.0362987	−	0.0117942i
$263$	13.5087	+	4.38923i	0.832981	+	0.270652i	0.694300	−	0.719685i	$-0.255714\pi$
$263$	13.5087	+	4.38923i	0.832981	+	0.270652i	0.138680	+	0.990337i	$0.455714\pi$
$264$		0			0
$265$	0.748009	+	0.985670i	0.0459498	+	0.0605492i
$266$	2.47530	−	7.61820i	0.151771	−	0.467102i
$267$		0			0
$268$			11.9121i			0.727648i
$269$	5.05075	+	3.66959i	0.307950	+	0.223739i	0.731016	−	0.682360i	$-0.239046\pi$
$269$	5.05075	+	3.66959i	0.307950	+	0.223739i	−0.423066	+	0.906099i	$0.639046\pi$
$270$		0			0
$271$	19.2926	−	14.0169i	1.17194	−	0.851464i	0.180700	−	0.983538i	$-0.442164\pi$
$271$	19.2926	−	14.0169i	1.17194	−	0.851464i	0.991240	+	0.132074i	$0.0421637\pi$
$272$	2.02525	+	2.78752i	0.122799	+	0.169018i
$273$		0			0
$274$	−9.27162			−0.560119
$275$	−9.15380	−	24.6288i	−0.551995	−	1.48517i
$276$		0			0
$277$	6.63226	−	2.15495i	0.398494	−	0.129478i	−0.102913	−	0.994690i	$-0.532816\pi$
$277$	6.63226	−	2.15495i	0.398494	−	0.129478i	0.501406	+	0.865212i	$0.332816\pi$
$278$	−11.0279	−	15.1787i	−0.661412	−	0.910356i
$279$		0			0
$280$	6.46658	+	4.49534i	0.386452	+	0.268648i
$281$	9.41192	+	6.83816i	0.561468	+	0.407931i	0.831996	−	0.554782i	$-0.187198\pi$
$281$	9.41192	+	6.83816i	0.561468	+	0.407931i	−0.270528	+	0.962712i	$0.587198\pi$
$282$		0			0
$283$	−5.64568	+	7.77061i	−0.335601	+	0.461915i	−0.943150	−	0.332367i	$-0.892153\pi$
$283$	−5.64568	+	7.77061i	−0.335601	+	0.461915i	0.607549	+	0.794282i	$0.292153\pi$
$284$	1.46739	−	4.51617i	0.0870737	−	0.267985i
$285$		0			0
$286$	1.00535	+	3.09415i	0.0594475	+	0.182961i
$287$	21.0925	+	6.85337i	1.24505	+	0.404542i
$288$		0			0
$289$	1.58466	+	4.87709i	0.0932154	+	0.286888i
$290$	−3.42267	+	4.92353i	−0.200986	+	0.289120i
$291$		0			0
$292$	5.78033	−	7.95594i	0.338268	−	0.465586i
$293$		−	8.52716i		−	0.498162i	−0.968483	−	0.249081i	$-0.919871\pi$
$293$		−	8.52716i		−	0.498162i	0.968483	−	0.249081i	$-0.0801286\pi$
$294$		0			0
$295$	−0.180228	+	0.596729i	−0.0104933	+	0.0347429i
$296$	−0.810416	+	0.588802i	−0.0471045	+	0.0342234i
$297$		0			0
$298$	−16.0154	+	5.20372i	−0.927748	+	0.301444i
$299$	−5.54333			−0.320579
$300$		0			0
$301$	5.32717			0.307053
$302$	15.9713	−	5.18938i	0.919043	−	0.298615i
$303$		0			0
$304$	1.83995	−	1.33680i	0.105528	−	0.0766709i
$305$	−2.70698	−	7.77589i	−0.155001	−	0.445246i
$306$		0			0
$307$		−	2.85794i		−	0.163111i	−0.996669	−	0.0815557i	$-0.974011\pi$
$307$		−	2.85794i		−	0.163111i	0.996669	−	0.0815557i	$-0.0259889\pi$
$308$	−10.8790	+	14.9736i	−0.619886	+	0.853200i
$309$		0			0
$310$	20.9107	+	6.31558i	1.18765	+	0.358701i
$311$	3.14017	+	9.66444i	0.178063	+	0.548020i	0.999760	−	0.0219035i	$-0.00697267\pi$
$311$	3.14017	+	9.66444i	0.178063	+	0.548020i	−0.821697	+	0.569924i	$0.806973\pi$
$312$		0			0
$313$	17.3127	+	5.62523i	0.978570	+	0.317957i	0.754271	−	0.656564i	$-0.227991\pi$
$313$	17.3127	+	5.62523i	0.978570	+	0.317957i	0.224299	+	0.974520i	$0.427991\pi$
$314$	1.40742	+	4.33159i	0.0794253	+	0.244446i
$315$		0			0
$316$	2.01497	−	6.20143i	0.113351	−	0.348857i
$317$	18.3838	−	25.3031i	1.03254	−	1.42116i	0.129510	−	0.991578i	$-0.458660\pi$
$317$	18.3838	−	25.3031i	1.03254	−	1.42116i	0.903026	−	0.429586i	$-0.141340\pi$
$318$		0			0
$319$	−11.4006	−	8.28304i	−0.638312	−	0.463761i
$320$	0.735158	+	2.11176i	0.0410966	+	0.118051i
$321$		0			0
$322$	−18.5363	−	25.5131i	−1.03299	−	1.42179i
$323$	−7.45274	+	2.42154i	−0.414681	+	0.134738i
$324$		0			0
$325$	−2.98132	−	0.833039i	−0.165374	−	0.0462087i
$326$	20.2133			1.11951
$327$		0			0
$328$	3.70121	+	5.09427i	0.204365	+	0.281284i
$329$	30.4204	−	22.1017i	1.67713	−	1.21851i
$330$		0			0
$331$	−2.77650	−	2.01724i	−0.152610	−	0.110878i	0.508860	−	0.860849i	$-0.330067\pi$
$331$	−2.77650	−	2.01724i	−0.152610	−	0.110878i	−0.661470	+	0.749972i	$0.730067\pi$
$332$		−	2.65973i		−	0.145972i
$333$		0			0
$334$	2.22240	−	6.83983i	0.121604	−	0.374259i
$335$	15.2039	−	21.8708i	0.830676	−	1.19493i
$336$		0			0
$337$	−11.1497	−	3.62277i	−0.607365	−	0.197345i	−0.0108427	−	0.999941i	$-0.503451\pi$
$337$	−11.1497	−	3.62277i	−0.607365	−	0.197345i	−0.596523	+	0.802596i	$0.703451\pi$
$338$	−11.9992	−	3.89878i	−0.652671	−	0.212066i
$339$		0			0
$340$	−0.160585	−	7.70285i	−0.00870892	−	0.417746i
$341$	−15.8633	+	48.8221i	−0.859045	+	2.64387i
$342$		0			0
$343$		−	5.61791i		−	0.303339i
$344$	1.22365	+	0.889032i	0.0659747	+	0.0479334i
$345$		0			0
$346$	−4.96053	+	3.60403i	−0.266680	+	0.193754i
$347$	19.0502	+	26.2204i	1.02267	+	1.40758i	0.910315	+	0.413916i	$0.135839\pi$
$347$	19.0502	+	26.2204i	1.02267	+	1.40758i	0.112355	+	0.993668i	$0.464161\pi$
$348$		0			0
$349$	11.3708			0.608665			0.304333	−	0.952566i	$-0.401567\pi$
$349$	11.3708			0.608665			0.304333	+	0.952566i	$0.401567\pi$
$350$	−6.13518	−	16.5071i	−0.327939	−	0.882339i
$351$		0			0
$352$	−4.99779	+	1.62388i	−0.266383	+	0.0865531i
$353$	−1.22685	−	1.68861i	−0.0652984	−	0.0898756i	0.775119	−	0.631816i	$-0.217690\pi$
$353$	−1.22685	−	1.68861i	−0.0652984	−	0.0898756i	−0.840417	+	0.541940i	$0.817690\pi$
$354$		0			0
$355$	−8.45831	+	6.41888i	−0.448921	+	0.340679i
$356$	−10.8295	−	7.86808i	−0.573961	−	0.417007i
$357$		0			0
$358$	−8.42280	+	11.5930i	−0.445159	+	0.612708i
$359$	2.10507	−	6.47874i	0.111101	−	0.341935i	−0.880013	−	0.474950i	$-0.842466\pi$
$359$	2.10507	−	6.47874i	0.111101	−	0.341935i	0.991114	+	0.133015i	$0.0424660\pi$
$360$		0			0
$361$	−4.27294	−	13.1508i	−0.224892	−	0.692146i
$362$	−14.9596	−	4.86067i	−0.786259	−	0.255471i
$363$		0			0
$364$	0.673818	+	2.07380i	0.0353177	+	0.108697i
$365$	−20.7673	+	7.22961i	−1.08701	+	0.378415i
$366$		0			0
$367$	−0.0913045	+	0.125670i	−0.00476606	+	0.00655991i	−0.811393	−	0.584500i	$-0.801291\pi$
$367$	−0.0913045	+	0.125670i	−0.00476606	+	0.00655991i	0.806627	+	0.591060i	$0.201291\pi$
$368$		−	8.95380i		−	0.466749i
$369$		0			0
$370$	2.23945	−	0.0466868i	0.116423	−	0.00242713i
$371$	−1.57676	+	1.14559i	−0.0818615	+	0.0594758i
$372$		0			0
$373$	−28.2902	+	9.19203i	−1.46481	+	0.475945i	−0.929535	−	0.368733i	$-0.879792\pi$
$373$	−28.2902	+	9.19203i	−1.46481	+	0.475945i	−0.535274	+	0.844679i	$0.679792\pi$
$374$	18.1064			0.936259
$375$		0			0
$376$	10.6760			0.550575
$377$	−1.57895	+	0.513032i	−0.0813201	+	0.0264225i
$378$		0			0
$379$	−13.4962	+	9.80558i	−0.693254	+	0.503679i	−0.877728	−	0.479159i	$-0.840942\pi$
$379$	−13.4962	+	9.80558i	−0.693254	+	0.503679i	0.184474	+	0.982837i	$0.440942\pi$
$380$	−5.08440	+	0.105997i	−0.260824	+	0.00543751i
$381$		0			0
$382$		−	3.62240i		−	0.185338i
$383$	−6.62972	+	9.12503i	−0.338763	+	0.466267i	−0.944080	−	0.329718i	$-0.893046\pi$
$383$	−6.62972	+	9.12503i	−0.338763	+	0.466267i	0.605317	+	0.795985i	$0.293046\pi$
$384$		0			0
$385$	39.0853	−	13.6066i	1.99197	−	0.693456i
$386$	3.00515	+	9.24889i	0.152958	+	0.470756i
$387$		0			0
$388$	−4.15806	−	1.35104i	−0.211094	−	0.0685885i
$389$	2.05849	+	6.33537i	0.104369	+	0.321216i	0.989582	−	0.143971i	$-0.0459872\pi$
$389$	2.05849	+	6.33537i	0.104369	+	0.321216i	−0.885213	+	0.465187i	$0.845987\pi$
$390$		0			0
$391$	−9.53346	+	29.3410i	−0.482128	+	1.48384i
$392$	−3.17694	+	4.37269i	−0.160460	+	0.220854i
$393$		0			0
$394$	−5.72280	−	4.15786i	−0.288310	−	0.209470i
$395$	−11.6146	+	8.81416i	−0.584395	+	0.443488i
$396$		0			0
$397$	21.8794	+	30.1144i	1.09810	+	1.51140i	0.837884	+	0.545849i	$0.183793\pi$
$397$	21.8794	+	30.1144i	1.09810	+	1.51140i	0.260213	+	0.965551i	$0.416207\pi$
$398$	16.8094	−	5.46171i	0.842580	−	0.273771i
$399$		0			0
$400$	1.34556	−	4.81555i	0.0672779	−	0.240777i
$401$	−19.6891			−0.983228			−0.491614	−	0.870813i	$-0.663593\pi$
$401$	−19.6891			−0.983228			−0.491614	+	0.870813i	$0.663593\pi$
$402$		0			0
$403$	3.55485	+	4.89283i	0.177080	+	0.243729i
$404$	11.5436	−	8.38692i	0.574316	−	0.417265i
$405$		0			0
$406$	−7.64108	−	5.55157i	−0.379220	−	0.275520i
$407$			5.26407i			0.260930i
$408$		0			0
$409$	−9.13460	+	28.1134i	−0.451677	+	1.39012i	0.423316	+	0.905982i	$0.360866\pi$
$409$	−9.13460	+	28.1134i	−0.451677	+	1.39012i	−0.874993	+	0.484136i	$0.839134\pi$
$410$	−0.293473	−	14.0772i	−0.0144936	−	0.695222i
$411$		0			0
$412$	16.8035	+	5.45980i	0.827851	+	0.268985i
$413$	−0.933796	−	0.303409i	−0.0459491	−	0.0149298i
$414$		0			0
$415$	−3.39471	+	4.88331i	−0.166640	+	0.239712i
$416$	−0.191313	+	0.588802i	−0.00937991	+	0.0288684i
$417$		0			0
$418$		−	11.9514i		−	0.584564i
$419$	0.946768	+	0.687867i	0.0462526	+	0.0336045i	0.610671	−	0.791884i	$-0.290900\pi$
$419$	0.946768	+	0.687867i	0.0462526	+	0.0336045i	−0.564419	+	0.825489i	$0.690900\pi$
$420$		0			0
$421$	−6.73922	+	4.89633i	−0.328449	+	0.238632i	−0.739772	−	0.672857i	$-0.765067\pi$
$421$	−6.73922	+	4.89633i	−0.328449	+	0.238632i	0.411323	+	0.911490i	$0.365067\pi$
$422$	−6.91460	−	9.51713i	−0.336597	−	0.463287i
$423$		0			0
$424$	−0.553365			−0.0268738
$425$	−9.53659	+	14.3475i	−0.462593	+	0.695957i
$426$		0			0
$427$	12.3341	−	4.00760i	0.596891	−	0.193942i
$428$	−0.425388	−	0.585496i	−0.0205619	−	0.0283010i
$429$		0			0
$430$	−1.11194	−	3.19407i	−0.0536223	−	0.154032i
$431$	−15.1227	−	10.9873i	−0.728435	−	0.529239i	0.160633	−	0.987014i	$-0.448646\pi$
$431$	−15.1227	−	10.9873i	−0.728435	−	0.529239i	−0.889068	+	0.457775i	$0.848646\pi$
$432$		0			0
$433$	11.1140	−	15.2972i	0.534107	−	0.735135i	−0.453643	−	0.891184i	$-0.649876\pi$
$433$	11.1140	−	15.2972i	0.534107	−	0.735135i	0.987749	+	0.156049i	$0.0498758\pi$
$434$	−10.6321	+	32.7222i	−0.510357	+	1.57072i
$435$		0			0
$436$	−0.795198	−	2.44737i	−0.0380831	−	0.117208i
$437$	19.3670	+	6.29273i	0.926450	+	0.301022i
$438$		0			0
$439$	12.6264	+	38.8602i	0.602627	+	1.85469i	0.512348	+	0.858778i	$0.328776\pi$
$439$	12.6264	+	38.8602i	0.602627	+	1.85469i	0.0902783	+	0.995917i	$0.471224\pi$
$440$	11.2486	+	3.39739i	0.536258	+	0.161964i
$441$		0			0
$442$	1.25384	−	1.72576i	0.0596391	−	0.0820862i
$443$			5.99083i			0.284633i	0.989821	+	0.142317i	$0.0454551\pi$
$443$			5.99083i			0.284633i	−0.989821	+	0.142317i	$0.954545\pi$
$444$		0			0
$445$	9.84080	+	28.2680i	0.466499	+	1.34003i
$446$	−10.2749	+	7.46514i	−0.486530	+	0.353485i
$447$		0			0
$448$	−3.34968	+	1.08838i	−0.158258	+	0.0514210i
$449$	12.4505			0.587574			0.293787	−	0.955871i	$-0.405084\pi$
$449$	12.4505			0.587574			0.293787	+	0.955871i	$0.405084\pi$
$450$		0			0
$451$	33.0899			1.55814
$452$	14.4448	−	4.69339i	0.679425	−	0.220759i
$453$		0			0
$454$	−11.5415	+	8.38543i	−0.541672	+	0.393548i
$455$	1.40972	−	4.66755i	0.0660889	−	0.218818i
$456$		0			0
$457$			1.11807i			0.0523011i	0.999658	+	0.0261506i	$0.00832493\pi$
$457$			1.11807i			0.0523011i	−0.999658	+	0.0261506i	$0.991675\pi$
$458$	5.17432	−	7.12184i	0.241780	−	0.332782i
$459$		0			0
$460$	−11.4281	+	16.4393i	−0.532837	+	0.766489i
$461$	9.29974	+	28.6216i	0.433132	+	1.33304i	0.894989	+	0.446089i	$0.147183\pi$
$461$	9.29974	+	28.6216i	0.433132	+	1.33304i	−0.461857	+	0.886954i	$0.652817\pi$
$462$		0			0
$463$	20.0062	+	6.50042i	0.929768	+	0.302100i	0.734468	−	0.678644i	$-0.237432\pi$
$463$	20.0062	+	6.50042i	0.929768	+	0.302100i	0.195300	+	0.980743i	$0.437432\pi$
$464$	−0.828671	−	2.55039i	−0.0384701	−	0.118399i
$465$		0			0
$466$	−4.65881	+	14.3383i	−0.215815	+	0.664211i
$467$	2.07849	−	2.86080i	0.0961812	−	0.132382i	−0.758214	−	0.652006i	$-0.773928\pi$
$467$	2.07849	−	2.86080i	0.0961812	−	0.132382i	0.854395	+	0.519624i	$0.173928\pi$
$468$		0			0
$469$	33.9425	+	24.6607i	1.56732	+	1.13872i
$470$	−19.6014	−	13.6262i	−0.904145	−	0.628531i
$471$		0			0
$472$	−0.163858	−	0.225531i	−0.00754216	−	0.0103809i
$473$	7.55921	−	2.45614i	0.347573	−	0.112933i
$474$		0			0
$475$	9.47034	+	6.29479i	0.434529	+	0.288825i
$476$	12.1355			0.556230
$477$		0			0
$478$	−3.67120	−	5.05298i	−0.167917	−	0.231118i
$479$	−32.7132	+	23.7675i	−1.49470	+	1.08597i	−0.522272	+	0.852779i	$0.674915\pi$
$479$	−32.7132	+	23.7675i	−1.49470	+	1.08597i	−0.972432	+	0.233187i	$0.925085\pi$
$480$		0			0
$481$	0.501731	+	0.364529i	0.0228770	+	0.0166211i
$482$			14.8094i			0.674551i
$483$		0			0
$484$	−5.13427	+	15.8017i	−0.233376	+	0.718258i
$485$	5.90990	+	7.78762i	0.268355	+	0.353618i
$486$		0			0
$487$	−25.3973	−	8.25208i	−1.15086	−	0.373938i	−0.329394	−	0.944193i	$-0.606844\pi$
$487$	−25.3973	−	8.25208i	−1.15086	−	0.373938i	−0.821468	+	0.570255i	$0.806844\pi$
$488$	3.50196	+	1.13786i	0.158526	+	0.0515083i
$489$		0			0
$490$	11.4139	−	3.97348i	0.515630	−	0.179504i
$491$	−10.2314	+	31.4891i	−0.461738	+	1.42108i	0.401302	+	0.915946i	$0.368558\pi$
$491$	−10.2314	+	31.4891i	−0.461738	+	1.42108i	−0.863040	+	0.505136i	$0.831442\pi$
$492$		0			0
$493$			9.23975i			0.416137i
$494$	−1.13912	−	0.827619i	−0.0512514	−	0.0372363i
$495$		0			0
$496$	−7.90309	+	5.74193i	−0.354859	+	0.257820i
$497$	−9.83059	−	13.5307i	−0.440962	−	0.606933i
$498$		0			0
$499$	−6.01303			−0.269180			−0.134590	−	0.990901i	$-0.542972\pi$
$499$	−6.01303			−0.269180			−0.134590	+	0.990901i	$0.542972\pi$
$500$	−8.61673	+	7.12404i	−0.385352	+	0.318597i
$501$		0			0
$502$	−17.3800	+	5.64710i	−0.775707	+	0.252042i
$503$	−3.91890	−	5.39391i	−0.174735	−	0.240502i	0.712662	−	0.701507i	$-0.247489\pi$
$503$	−3.91890	−	5.39391i	−0.174735	−	0.240502i	−0.887398	+	0.461005i	$0.847489\pi$
$504$		0			0
$505$	−31.8988	+	0.665008i	−1.41948	+	0.0295925i
$506$	−38.0659	−	27.6565i	−1.69224	−	1.22948i
$507$		0			0
$508$	2.56501	−	3.53043i	0.113804	−	0.156638i
$509$	−5.43941	+	16.7408i	−0.241098	+	0.742022i	0.755156	+	0.655545i	$0.227561\pi$
$509$	−5.43941	+	16.7408i	−0.241098	+	0.742022i	−0.996254	+	0.0864773i	$0.972439\pi$
$510$		0			0
$511$	−10.7032	−	32.9411i	−0.473482	−	1.45723i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$		0			0
$514$	0.556690	+	1.71331i	0.0245545	+	0.0755711i
$515$	−23.8831	−	31.4713i	−1.05241	−	1.38679i
$516$		0			0
$517$	32.9762	−	45.3878i	1.45029	−	1.99615i
$518$			3.52816i			0.155018i
$519$		0			0
$520$	1.10276	−	0.836871i	0.0483594	−	0.0366992i
$521$	14.9188	−	10.8391i	0.653605	−	0.474872i	−0.210892	−	0.977509i	$-0.567637\pi$
$521$	14.9188	−	10.8391i	0.653605	−	0.474872i	0.864497	+	0.502638i	$0.167637\pi$
$522$		0			0
$523$	−9.81016	+	3.18752i	−0.428968	+	0.139380i	−0.515540	−	0.856865i	$-0.672409\pi$
$523$	−9.81016	+	3.18752i	−0.428968	+	0.139380i	0.0865719	+	0.996246i	$0.472409\pi$
$524$	−0.617783			−0.0269880
$525$		0			0
$526$	14.2039			0.619318
$527$	32.0115	−	10.4012i	1.39444	−	0.453082i
$528$		0			0
$529$	46.2520	−	33.6040i	2.01096	−	1.46105i
$530$	1.01599	+	0.706280i	0.0441317	+	0.0306788i
$531$		0			0
$532$		−	8.01025i		−	0.347288i
$533$	2.29143	−	3.15388i	0.0992528	−	0.136610i
$534$		0			0
$535$	0.0337295	+	1.61792i	0.00145825	+	0.0699488i
$536$	3.68104	+	11.3291i	0.158997	+	0.489342i
$537$		0			0
$538$	5.93752	+	1.92922i	0.255985	+	0.0831744i
$539$	8.77697	+	27.0127i	0.378051	+	1.16352i
$540$		0			0
$541$	−11.5756	+	35.6262i	−0.497676	+	1.53169i	0.315069	+	0.949069i	$0.397972\pi$
$541$	−11.5756	+	35.6262i	−0.497676	+	1.53169i	−0.812745	+	0.582620i	$0.802028\pi$
$542$	14.0169	−	19.2926i	0.602076	−	0.828687i
$543$		0			0
$544$	2.78752	+	2.02525i	0.119514	+	0.0868320i
$545$	−1.66367	+	5.50835i	−0.0712637	+	0.235952i
$546$		0			0
$547$	−6.49261	−	8.93631i	−0.277604	−	0.382089i	0.647334	−	0.762206i	$-0.275884\pi$
$547$	−6.49261	−	8.93631i	−0.277604	−	0.382089i	−0.924938	+	0.380117i	$0.875884\pi$
$548$	−8.81784	+	2.86509i	−0.376679	+	0.122391i
$549$		0			0
$550$	−16.3165	−	20.5947i	−0.695738	−	0.878162i
$551$	6.09886			0.259820
$552$		0			0
$553$	−13.4990	−	18.5798i	−0.574035	−	0.790092i
$554$	5.64173	−	4.09896i	0.239694	−	0.174148i
$555$		0			0
$556$	−15.1787	−	11.0279i	−0.643719	−	0.467689i
$557$		−	29.7087i		−	1.25880i	−0.777082	−	0.629400i	$-0.783301\pi$
$557$		−	29.7087i		−	1.25880i	0.777082	−	0.629400i	$-0.216699\pi$
$558$		0			0
$559$	0.289364	−	0.890570i	0.0122388	−	0.0376671i
$560$	7.53922	+	2.27704i	0.318590	+	0.0962226i
$561$		0			0
$562$	11.0644	+	3.59504i	0.466723	+	0.151647i
$563$	17.4332	+	5.66439i	0.734722	+	0.238726i	0.652394	−	0.757880i	$-0.273765\pi$
$563$	17.4332	+	5.66439i	0.734722	+	0.238726i	0.0823274	+	0.996605i	$0.473765\pi$
$564$		0			0
$565$	−32.5112	−	9.81925i	−1.36776	−	0.413099i
$566$	−2.96811	+	9.13490i	−0.124759	+	0.383969i
$567$		0			0
$568$		−	4.74858i		−	0.199246i
$569$	17.7915	+	12.9263i	0.745859	+	0.541898i	0.894541	−	0.446987i	$-0.147503\pi$
$569$	17.7915	+	12.9263i	0.745859	+	0.541898i	−0.148681	+	0.988885i	$0.547503\pi$
$570$		0			0
$571$	−20.2890	+	14.7408i	−0.849069	+	0.616885i	−0.924889	−	0.380237i	$-0.875843\pi$
$571$	−20.2890	+	14.7408i	−0.849069	+	0.616885i	0.0758199	+	0.997122i	$0.475843\pi$
$572$	1.91229	+	2.63204i	0.0799567	+	0.110051i
$573$		0			0
$574$	22.1780			0.925691
$575$	41.9643	−	15.5969i	1.75003	−	0.650435i
$576$		0			0
$577$	−33.2751	+	10.8117i	−1.38526	+	0.450099i	−0.904395	−	0.426695i	$-0.859678\pi$
$577$	−33.2751	+	10.8117i	−1.38526	+	0.450099i	−0.480866	+	0.876794i	$0.659678\pi$
$578$	3.01421	+	4.14870i	0.125374	+	0.172563i
$579$		0			0
$580$	−1.73370	+	5.74022i	−0.0719879	+	0.238350i
$581$	−7.57866	−	5.50622i	−0.314416	−	0.228437i
$582$		0			0
$583$	−1.70923	+	2.35256i	−0.0707892	+	0.0974330i
$584$	3.03890	−	9.35277i	0.125751	−	0.387020i
$585$		0			0
$586$	−2.63504	−	8.10981i	−0.108852	−	0.335013i
$587$	−9.87738	−	3.20936i	−0.407683	−	0.132464i	0.0979941	−	0.995187i	$-0.468757\pi$
$587$	−9.87738	−	3.20936i	−0.407683	−	0.132464i	−0.505677	+	0.862723i	$0.668757\pi$
$588$		0			0
$589$	−6.86547	−	21.1298i	−0.282887	−	0.870636i
$590$	0.0129925	+	0.623216i	0.000534891	+	0.0256574i
$591$		0			0
$592$	−0.588802	+	0.810416i	−0.0241996	+	0.0333079i
$593$		−	0.948200i		−	0.0389379i	−0.999810	−	0.0194690i	$-0.993802\pi$
$593$		−	0.948200i		−	0.0389379i	0.999810	−	0.0194690i	$-0.00619755\pi$
$594$		0			0
$595$	−22.2810	−	15.4890i	−0.913433	−	0.634987i
$596$	−13.6235	+	9.89807i	−0.558041	+	0.405441i
$597$		0			0
$598$	−5.27202	+	1.71298i	−0.215589	+	0.0700491i
$599$	25.4901			1.04150			0.520748	−	0.853710i	$-0.325653\pi$
$599$	25.4901			1.04150			0.520748	+	0.853710i	$0.325653\pi$
$600$		0			0
$601$	−16.6409			−0.678797			−0.339399	−	0.940643i	$-0.610224\pi$
$601$	−16.6409			−0.678797			−0.339399	+	0.940643i	$0.610224\pi$
$602$	5.06644	−	1.64618i	0.206492	−	0.0670935i
$603$		0			0
$604$	13.5860	−	9.87079i	0.552805	−	0.401637i
$605$	29.5949	−	22.4591i	1.20320	−	0.913092i
$606$		0			0
$607$		−	33.2662i		−	1.35023i	−0.737712	−	0.675116i	$-0.764094\pi$
$607$		−	33.2662i		−	1.35023i	0.737712	−	0.675116i	$-0.235906\pi$
$608$	1.33680	−	1.83995i	0.0542145	−	0.0746199i
$609$		0			0
$610$	−4.97738	−	6.55881i	−0.201528	−	0.265558i
$611$	−2.04247	−	6.28607i	−0.0826295	−	0.254307i
$612$		0			0
$613$	−15.4852	−	5.03144i	−0.625440	−	0.203218i	−0.0208859	−	0.999782i	$-0.506649\pi$
$613$	−15.4852	−	5.03144i	−0.625440	−	0.203218i	−0.604554	+	0.796564i	$0.706649\pi$
$614$	−0.883153	−	2.71807i	−0.0356412	−	0.109692i
$615$		0			0
$616$	−5.71941	+	17.6025i	−0.230442	+	0.709226i
$617$	−28.5243	+	39.2603i	−1.14834	+	1.58056i	−0.401063	+	0.916050i	$0.631359\pi$
$617$	−28.5243	+	39.2603i	−1.14834	+	1.58056i	−0.747280	+	0.664509i	$0.768641\pi$
$618$		0			0
$619$	−19.9552	−	14.4983i	−0.802066	−	0.582735i	0.109454	−	0.993992i	$-0.465090\pi$
$619$	−19.9552	−	14.4983i	−0.802066	−	0.582735i	−0.911519	+	0.411257i	$0.865090\pi$
$620$	21.8389	−	0.455284i	0.877069	−	0.0182847i
$621$		0			0
$622$	5.97296	+	8.22107i	0.239494	+	0.329635i
$623$	−44.8388	+	14.5690i	−1.79643	+	0.583694i
$624$		0			0
$625$	24.9132	−	2.08203i	0.996526	−	0.0832811i
$626$	18.2036			0.727563
$627$		0			0
$628$	2.67707	+	3.68467i	0.106827	+	0.147034i
$629$	2.79234	−	2.02876i	0.111338	−	0.0808918i
$630$		0			0
$631$	9.54099	+	6.93194i	0.379821	+	0.275956i	0.761272	−	0.648433i	$-0.224575\pi$
$631$	9.54099	+	6.93194i	0.379821	+	0.275956i	−0.381451	+	0.924389i	$0.624575\pi$
$632$		−	6.52057i		−	0.259374i
$633$		0			0
$634$	9.66493	−	29.7456i	0.383843	−	1.18135i
$635$	−9.21542	+	3.20812i	−0.365703	+	0.127310i
$636$		0			0
$637$	3.18244	+	1.03404i	0.126093	+	0.0409700i
$638$	−13.4022	−	4.35465i	−0.530600	−	0.172402i
$639$		0			0
$640$	1.35175	+	1.78123i	0.0534325	+	0.0704093i
$641$	4.20359	−	12.9373i	0.166032	−	0.510994i	−0.833079	−	0.553154i	$-0.813424\pi$
$641$	4.20359	−	12.9373i	0.166032	−	0.510994i	0.999111	+	0.0421603i	$0.0134240\pi$
$642$		0			0
$643$			20.9102i			0.824617i	0.911044	+	0.412308i	$0.135277\pi$
$643$			20.9102i			0.824617i	−0.911044	+	0.412308i	$0.864723\pi$
$644$	−25.5131	−	18.5363i	−1.00536	−	0.730433i
$645$		0			0
$646$	−6.33968	+	4.60604i	−0.249431	+	0.181222i
$647$	−26.9722	−	37.1240i	−1.06039	−	1.45950i	−0.879444	−	0.476002i	$-0.842086\pi$
$647$	−26.9722	−	37.1240i	−1.06039	−	1.45950i	−0.180941	−	0.983494i	$-0.557914\pi$
$648$		0			0
$649$	−1.46494			−0.0575039
$650$	−3.09283	+	0.129011i	−0.121311	+	0.00506023i
$651$		0			0
$652$	19.2239	−	6.24624i	0.752868	−	0.244622i
$653$	1.53183	+	2.10838i	0.0599450	+	0.0825072i	0.837937	−	0.545767i	$-0.183762\pi$
$653$	1.53183	+	2.10838i	0.0599450	+	0.0825072i	−0.777992	+	0.628274i	$0.783762\pi$
$654$		0			0
$655$	1.13426	+	0.788499i	0.0443192	+	0.0308092i
$656$	5.09427	+	3.70121i	0.198898	+	0.144508i
$657$		0			0
$658$	22.1017	−	30.4204i	0.861615	−	1.18591i
$659$	7.39977	−	22.7742i	0.288254	−	0.887155i	−0.697150	−	0.716925i	$-0.745549\pi$
$659$	7.39977	−	22.7742i	0.288254	−	0.887155i	0.985404	−	0.170230i	$-0.0544511\pi$
$660$		0			0
$661$	8.01908	+	24.6802i	0.311906	+	0.959948i	0.977009	+	0.213196i	$0.0683874\pi$
$661$	8.01908	+	24.6802i	0.311906	+	0.959948i	−0.665103	+	0.746751i	$0.731613\pi$
$662$	−3.26397	−	1.06053i	−0.126858	−	0.0412186i
$663$		0			0
$664$	−0.821902	−	2.52955i	−0.0318960	−	0.0981657i
$665$	−10.2238	+	14.7070i	−0.396461	+	0.570312i
$666$		0			0
$667$	14.1132	−	19.4252i	0.546466	−	0.752145i
$668$		−	7.19183i		−	0.278260i
$669$		0			0
$670$	7.70127	−	25.4987i	0.297526	−	0.985099i
$671$	15.6543	−	11.3735i	0.604328	−	0.439070i
$672$		0			0
$673$	14.0845	−	4.57632i	0.542916	−	0.176404i	−0.0247037	−	0.999695i	$-0.507864\pi$
$673$	14.0845	−	4.57632i	0.542916	−	0.176404i	0.567620	+	0.823291i	$0.307864\pi$
$674$	−11.7235			−0.451574
$675$		0			0
$676$	−12.6167			−0.485258
$677$	−33.2224	+	10.7946i	−1.27684	+	0.414870i	−0.867466	−	0.497497i	$-0.834253\pi$
$677$	−33.2224	+	10.7946i	−1.27684	+	0.414870i	−0.409373	+	0.912367i	$0.634253\pi$
$678$		0			0
$679$	−12.4578	+	9.05109i	−0.478085	+	0.347349i
$680$	−2.53304	−	7.27622i	−0.0971375	−	0.279030i
$681$		0			0
$682$			51.3346i			1.96571i
$683$	12.3485	−	16.9963i	0.472504	−	0.650346i	−0.504539	−	0.863389i	$-0.668338\pi$
$683$	12.3485	−	16.9963i	0.472504	−	0.650346i	0.977043	+	0.213043i	$0.0683375\pi$
$684$		0			0
$685$	19.8465	+	5.99418i	0.758297	+	0.229026i
$686$	−1.73603	−	5.34295i	−0.0662819	−	0.203995i
$687$		0			0
$688$	1.43848	+	0.467392i	0.0548417	+	0.0178192i
$689$	0.105866	+	0.325822i	0.00403318	+	0.0124128i
$690$		0			0
$691$	−7.23231	+	22.2588i	−0.275130	+	0.846763i	0.714055	+	0.700090i	$0.246857\pi$
$691$	−7.23231	+	22.2588i	−0.275130	+	0.846763i	−0.989185	+	0.146673i	$0.953143\pi$
$692$	−3.60403	+	4.96053i	−0.137005	+	0.188571i
$693$		0			0
$694$	26.2204	+	19.0502i	0.995312	+	0.723137i
$695$	13.7929	+	39.6206i	0.523196	+	1.50290i
$696$		0			0
$697$	−12.7528	−	17.5527i	−0.483045	−	0.664854i
$698$	10.8143	−	3.51377i	0.409326	−	0.132998i
$699$		0			0
$700$	−10.9359	−	13.8033i	−0.413337	−	0.521715i
$701$	43.2849			1.63485			0.817424	−	0.576037i	$-0.195402\pi$
$701$	43.2849			1.63485			0.817424	+	0.576037i	$0.195402\pi$
$702$		0			0
$703$	−1.33912	−	1.84314i	−0.0505057	−	0.0695152i
$704$	−4.25137	+	3.08880i	−0.160230	+	0.116414i
$705$		0			0
$706$	−1.68861	−	1.22685i	−0.0635516	−	0.0461730i
$707$		−	50.2552i		−	1.89004i
$708$		0			0
$709$	7.72993	−	23.7903i	0.290303	−	0.893462i	−0.694455	−	0.719536i	$-0.744355\pi$
$709$	7.72993	−	23.7903i	0.290303	−	0.893462i	0.984759	−	0.173926i	$-0.0556454\pi$
$710$	−6.06079	+	8.71848i	−0.227457	+	0.327199i
$711$		0			0
$712$	−12.7308	−	4.13649i	−0.477108	−	0.155022i
$713$	−83.1865	−	27.0289i	−3.11536	−	1.01224i
$714$		0			0
$715$	−0.151627	−	7.27319i	−0.00567054	−	0.272002i
$716$	−4.42813	+	13.6284i	−0.165487	+	0.509316i
$717$		0			0
$718$		−	6.81215i		−	0.254227i
$719$	24.9533	+	18.1296i	0.930601	+	0.676121i	0.946140	−	0.323758i	$-0.104946\pi$
$719$	24.9533	+	18.1296i	0.930601	+	0.676121i	−0.0155391	+	0.999879i	$0.504946\pi$
$720$		0			0
$721$	50.3442	−	36.5772i	1.87492	−	1.36221i
$722$	−8.12762	−	11.1867i	−0.302479	−	0.416326i
$723$		0			0
$724$	−15.7294			−0.584580
$725$	10.5096	−	8.32636i	0.390315	−	0.309233i
$726$		0			0
$727$	0.623458	−	0.202574i	0.0231228	−	0.00751304i	−0.297433	−	0.954743i	$-0.596130\pi$
$727$	0.623458	−	0.202574i	0.0231228	−	0.00751304i	0.320556	+	0.947230i	$0.396130\pi$
$728$	1.28168	+	1.76408i	0.0475022	+	0.0653811i
$729$		0			0
$730$	−17.5168	+	13.2932i	−0.648324	+	0.492003i
$731$	−4.21616	−	3.06322i	−0.155940	−	0.113297i
$732$		0			0
$733$	8.05975	−	11.0933i	0.297694	−	0.409740i	−0.633800	−	0.773497i	$-0.718506\pi$
$733$	8.05975	−	11.0933i	0.297694	−	0.409740i	0.931494	+	0.363756i	$0.118506\pi$
$734$	−0.0480016	+	0.147734i	−0.00177177	+	0.00545295i
$735$		0			0
$736$	−2.76688	−	8.51557i	−0.101988	−	0.313888i
$737$	59.5342	+	19.3438i	2.19297	+	0.712539i
$738$		0			0
$739$	3.38589	+	10.4207i	0.124552	+	0.383332i	0.993819	−	0.111011i	$-0.0354088\pi$
$739$	3.38589	+	10.4207i	0.124552	+	0.383332i	−0.869267	+	0.494343i	$0.835409\pi$
$740$	2.11542	−	0.736430i	0.0777642	−	0.0270717i
$741$		0			0
$742$	−1.14559	+	1.57676i	−0.0420558	+	0.0578848i
$743$		−	5.67053i		−	0.208032i	−0.994576	−	0.104016i	$-0.966831\pi$
$743$		−	5.67053i		−	0.208032i	0.994576	−	0.104016i	$-0.0331692\pi$
$744$		0			0
$745$	37.6463	−	0.784829i	1.37925	−	0.0287539i
$746$	−24.0650	+	17.4843i	−0.881084	+	0.640145i
$747$		0			0
$748$	17.2202	−	5.59518i	0.629633	−	0.204580i
$749$	−2.54896			−0.0931371
$750$		0			0
$751$	−22.2909			−0.813408			−0.406704	−	0.913560i	$-0.633322\pi$
$751$	−22.2909			−0.813408			−0.406704	+	0.913560i	$0.633322\pi$
$752$	10.1535	−	3.29908i	0.370261	−	0.120305i
$753$		0			0
$754$	−1.34314	+	0.975846i	−0.0489141	+	0.0355382i
$755$	−37.5426	+	0.782666i	−1.36631	+	0.0284841i
$756$		0			0
$757$			17.3894i			0.632030i	0.948754	+	0.316015i	$0.102345\pi$
$757$			17.3894i			0.632030i	−0.948754	+	0.316015i	$0.897655\pi$
$758$	−9.80558	+	13.4962i	−0.356155	+	0.490205i
$759$		0			0
$760$	−4.80279	+	1.67197i	−0.174216	+	0.0606489i
$761$	−4.78812	−	14.7363i	−0.173569	−	0.534191i	0.825996	−	0.563676i	$-0.190613\pi$
$761$	−4.78812	−	14.7363i	−0.173569	−	0.534191i	−0.999565	+	0.0294850i	$0.990613\pi$
$762$		0			0
$763$	−8.61978	−	2.80074i	−0.312057	−	0.101393i
$764$	−1.11938	−	3.44511i	−0.0404979	−	0.124640i
$765$		0			0
$766$	−3.48545	+	10.7271i	−0.125934	+	0.387586i
$767$	−0.101445	+	0.139627i	−0.00366296	+	0.00504163i
$768$		0			0
$769$	−39.5215	−	28.7140i	−1.42518	−	1.03545i	−0.990889	−	0.134683i	$-0.956998\pi$
$769$	−39.5215	−	28.7140i	−1.42518	−	1.03545i	−0.434292	−	0.900772i	$-0.643002\pi$
$770$	32.9677	−	25.0187i	1.18807	−	0.901610i
$771$		0			0
$772$	5.71613	+	7.86757i	0.205728	+	0.283160i
$773$	1.02281	−	0.332330i	0.0367878	−	0.0119531i	−0.290565	−	0.956855i	$-0.593843\pi$
$773$	1.02281	−	0.332330i	0.0367878	−	0.0119531i	0.327353	+	0.944902i	$0.393843\pi$
$774$		0			0
$775$	−40.6776	−	27.0378i	−1.46118	−	0.971227i
$776$	−4.37205			−0.156947
$777$		0			0
$778$	3.91547	+	5.38919i	0.140377	+	0.193212i
$779$	−11.5859	+	8.41768i	−0.415109	+	0.301595i
$780$		0			0
$781$	−20.1880	−	14.6674i	−0.722383	−	0.524842i
$782$			30.8509i			1.10323i
$783$		0			0
$784$	−1.67022	+	5.14040i	−0.0596506	+	0.183586i
$785$	−0.212268	−	10.1820i	−0.00757617	−	0.363410i
$786$		0			0
$787$	35.9953	+	11.6956i	1.28310	+	0.416903i	0.869669	−	0.493635i	$-0.164332\pi$
$787$	35.9953	+	11.6956i	1.28310	+	0.416903i	0.413426	+	0.910538i	$0.364332\pi$
$788$	−6.72755	−	2.18591i	−0.239659	−	0.0778700i
$789$		0			0
$790$	−8.32244	+	11.9719i	−0.296099	+	0.425940i
$791$	16.5304	−	50.8755i	0.587755	−	1.80892i
$792$		0			0
$793$		−	2.27965i		−	0.0809527i
$794$	30.1144	+	21.8794i	1.06872	+	0.776471i
$795$		0			0
$796$	14.2990	−	10.3888i	0.506813	−	0.368221i
$797$	−6.79344	−	9.35037i	−0.240636	−	0.331207i	0.671568	−	0.740943i	$-0.265621\pi$
$797$	−6.79344	−	9.35037i	−0.240636	−	0.331207i	−0.912204	+	0.409736i	$0.865621\pi$
$798$		0			0
$799$	−36.7850			−1.30136
$800$	−0.208384	−	4.99566i	−0.00736748	−	0.176623i
$801$		0			0
$802$	−18.7255	+	6.08427i	−0.661219	+	0.214843i
$803$	−30.3755	−	41.8083i	−1.07193	−	1.47538i
$804$		0			0
$805$	23.1839	+	66.5963i	0.817123	+	2.34721i
$806$	4.89283	+	3.55485i	0.172342	+	0.125214i
$807$		0			0
$808$	8.38692	−	11.5436i	0.295051	−	0.406103i
$809$	−6.24192	+	19.2106i	−0.219454	+	0.675410i	0.779353	+	0.626585i	$0.215548\pi$
$809$	−6.24192	+	19.2106i	−0.219454	+	0.675410i	−0.998807	+	0.0488254i	$0.984452\pi$
$810$		0			0
$811$	−12.8802	−	39.6412i	−0.452285	−	1.39199i	−0.874293	−	0.485399i	$-0.838674\pi$
$811$	−12.8802	−	39.6412i	−0.452285	−	1.39199i	0.422008	−	0.906592i	$-0.361326\pi$
$812$	−8.98262	−	2.91863i	−0.315228	−	0.102424i
$813$		0			0
$814$	1.62669	+	5.00643i	0.0570154	+	0.175475i
$815$	−43.2678	−	13.0680i	−1.51561	−	0.457753i
$816$		0			0
$817$	−2.02193	+	2.78295i	−0.0707384	+	0.0973631i
$818$			29.5602i			1.03355i
$819$		0			0
$820$	−4.62919	−	13.2975i	−0.161658	−	0.464369i
$821$	−26.4710	+	19.2323i	−0.923844	+	0.671212i	−0.944478	−	0.328575i	$-0.893432\pi$
$821$	−26.4710	+	19.2323i	−0.923844	+	0.671212i	0.0206340	+	0.999787i	$0.493432\pi$
$822$		0			0
$823$	31.8460	−	10.3474i	1.11008	−	0.360687i	0.304107	−	0.952638i	$-0.401642\pi$
$823$	31.8460	−	10.3474i	1.11008	−	0.360687i	0.805974	+	0.591950i	$0.201642\pi$
$824$	17.6683			0.615504
$825$		0			0
$826$	−0.981851			−0.0341630
$827$	−8.32052	+	2.70350i	−0.289333	+	0.0940100i	−0.450088	−	0.892984i	$-0.648607\pi$
$827$	−8.32052	+	2.70350i	−0.289333	+	0.0940100i	0.160755	+	0.986994i	$0.448607\pi$
$828$		0			0
$829$	15.3302	−	11.1381i	0.532441	−	0.386841i	−0.288829	−	0.957381i	$-0.593266\pi$
$829$	15.3302	−	11.1381i	0.532441	−	0.386841i	0.821270	+	0.570539i	$0.193266\pi$
$830$	−1.71954	+	5.69333i	−0.0596860	+	0.197618i
$831$		0			0
$832$			0.619103i			0.0214635i
$833$	10.9464	−	15.0664i	0.379269	−	0.522019i
$834$		0			0
$835$	−9.17919	+	13.2043i	−0.317659	+	0.456955i
$836$	−3.69320	−	11.3665i	−0.127732	−	0.393118i
$837$		0			0
$838$	1.11299	+	0.361633i	0.0384477	+	0.0124924i
$839$	−3.54657	−	10.9152i	−0.122441	−	0.376835i	0.870985	−	0.491309i	$-0.163482\pi$
$839$	−3.54657	−	10.9152i	−0.122441	−	0.376835i	−0.993426	+	0.114474i	$0.963482\pi$
$840$		0			0
$841$	−6.73930	+	20.7414i	−0.232390	+	0.715222i
$842$	−4.89633	+	6.73922i	−0.168739	+	0.232249i
$843$		0			0
$844$	−9.51713	−	6.91460i	−0.327593	−	0.238010i
$845$	23.1645	+	16.1032i	0.796884	+	0.553966i
$846$		0			0
$847$	34.3964	+	47.3425i	1.18187	+	1.62671i
$848$	−0.526281	+	0.170999i	−0.0180726	+	0.00587213i
$849$		0			0
$850$	−4.63621	+	16.5923i	−0.159021	+	0.569110i
$851$	−8.96929			−0.307463
$852$		0			0
$853$	−6.10223	−	8.39899i	−0.208936	−	0.287576i	0.691668	−	0.722215i	$-0.256876\pi$
$853$	−6.10223	−	8.39899i	−0.208936	−	0.287576i	−0.900605	+	0.434639i	$0.856876\pi$
$854$	10.4920	−	7.62292i	0.359030	−	0.260851i
$855$		0			0
$856$	−0.585496	−	0.425388i	−0.0200119	−	0.0145395i
$857$			32.7252i			1.11787i	0.829211	+	0.558936i	$0.188790\pi$
$857$			32.7252i			1.11787i	−0.829211	+	0.558936i	$0.811210\pi$
$858$		0			0
$859$	−6.38693	+	19.6569i	−0.217919	+	0.670686i	0.781014	+	0.624513i	$0.214703\pi$
$859$	−6.38693	+	19.6569i	−0.217919	+	0.670686i	−0.998933	+	0.0461730i	$0.985297\pi$
$860$	−2.04453	−	2.69413i	−0.0697180	−	0.0918691i
$861$		0			0
$862$	−17.7778	−	5.77636i	−0.605515	−	0.196744i
$863$	53.5643	+	17.4041i	1.82335	+	0.592443i	0.999678	+	0.0253777i	$0.00807885\pi$
$863$	53.5643	+	17.4041i	1.82335	+	0.592443i	0.823673	+	0.567065i	$0.191921\pi$
$864$		0			0
$865$	12.9484	−	4.50766i	0.440258	−	0.153265i
$866$	5.84299	−	17.9829i	0.198553	−	0.611083i
$867$		0			0
$868$			34.4062i			1.16782i
$869$	−27.7213	−	20.1407i	−0.940382	−	0.683228i
$870$		0			0
$871$	5.96636	−	4.33481i	0.202162	−	0.146879i
$872$	−1.51256	−	2.08185i	−0.0512216	−	0.0705005i
$873$		0			0
$874$	20.3637			0.688812
$875$	2.46082	+	39.3009i	0.0831910	+	1.32861i
$876$		0			0
$877$	−42.8777	+	13.9318i	−1.44788	+	0.470443i	−0.924343	−	0.381562i	$-0.875386\pi$
$877$	−42.8777	+	13.9318i	−1.44788	+	0.470443i	−0.523533	+	0.852006i	$0.675386\pi$
$878$	24.0169	+	33.0564i	0.810531	+	1.11560i
$879$		0			0
$880$	11.7479	−	0.244915i	0.396023	−	0.00825607i
$881$	25.2754	+	18.3636i	0.851550	+	0.618687i	0.925573	−	0.378569i	$-0.123584\pi$
$881$	25.2754	+	18.3636i	0.851550	+	0.618687i	−0.0740232	+	0.997257i	$0.523584\pi$
$882$		0			0
$883$	15.7843	−	21.7253i	0.531185	−	0.731113i	−0.456126	−	0.889915i	$-0.650763\pi$
$883$	15.7843	−	21.7253i	0.531185	−	0.731113i	0.987310	+	0.158802i	$0.0507633\pi$
$884$	0.659183	−	2.02876i	0.0221707	−	0.0682345i
$885$		0			0
$886$	1.85127	+	5.69762i	0.0621946	+	0.191415i
$887$	−13.8750	−	4.50825i	−0.465876	−	0.151372i	0.0666671	−	0.997775i	$-0.478763\pi$
$887$	−13.8750	−	4.50825i	−0.465876	−	0.151372i	−0.532543	+	0.846403i	$0.678763\pi$
$888$		0			0
$889$	−4.74952	−	14.6175i	−0.159294	−	0.490256i
$890$	18.0945	+	23.8435i	0.606527	+	0.799236i
$891$		0			0
$892$	−7.46514	+	10.2749i	−0.249952	+	0.344029i
$893$			24.2806i			0.812519i
$894$		0			0
$895$	25.5245	−	19.3702i	0.853191	−	0.647473i
$896$	−2.84941	+	2.07022i	−0.0951921	+	0.0691611i
$897$		0			0
$898$	11.8411	−	3.84740i	0.395142	−	0.128390i
$899$	−26.1962			−0.873693
$900$		0			0
$901$	1.90665			0.0635199
$902$	31.4704	−	10.2254i	1.04785	−	0.340467i
$903$		0			0
$904$	12.2875	−	8.92737i	0.408675	−	0.296920i
$905$	28.8796	+	20.0761i	0.959989	+	0.667351i
$906$		0			0
$907$		−	29.5506i		−	0.981211i	−0.871382	−	0.490606i	$-0.836776\pi$
$907$		−	29.5506i		−	0.981211i	0.871382	−	0.490606i	$-0.163224\pi$
$908$	−8.38543	+	11.5415i	−0.278280	+	0.383020i
$909$		0			0
$910$	−0.101626	−	4.87473i	−0.00336886	−	0.161596i
$911$	−1.30316	−	4.01073i	−0.0431757	−	0.132881i	0.927145	−	0.374703i	$-0.122255\pi$
$911$	−1.30316	−	4.01073i	−0.0431757	−	0.132881i	−0.970321	+	0.241821i	$0.922255\pi$
$912$		0			0
$913$	−13.2928	−	4.31908i	−0.439926	−	0.142941i
$914$	0.345503	+	1.06335i	0.0114282	+	0.0351724i
$915$		0			0
$916$	2.72030	−	8.37223i	0.0898813	−	0.276626i
$917$	−1.27895	+	1.76032i	−0.0422345	+	0.0581308i
$918$		0			0
$919$	23.0230	+	16.7272i	0.759459	+	0.551779i	0.898744	−	0.438473i	$-0.144481\pi$
$919$	23.0230	+	16.7272i	0.759459	+	0.551779i	−0.139286	+	0.990252i	$0.544481\pi$
$920$	−5.78870	+	19.1662i	−0.190848	+	0.631892i
$921$		0			0
$922$	17.6892	+	24.3470i	0.582561	+	0.801827i
$923$	−2.79597	+	0.908467i	−0.0920306	+	0.0299026i
$924$		0			0
$925$	−4.82388	−	1.34789i	−0.158608	−	0.0443182i
$926$	21.0358			0.691279
$927$		0			0
$928$	−1.57623	−	2.16949i	−0.0517421	−	0.0712169i
$929$	21.2379	−	15.4302i	0.696792	−	0.506249i	−0.182094	−	0.983281i	$-0.558288\pi$
$929$	21.2379	−	15.4302i	0.696792	−	0.506249i	0.878886	+	0.477032i	$0.158288\pi$
$930$		0			0
$931$	−9.94483	−	7.22534i	−0.325929	−	0.236801i
$932$			15.0762i			0.493838i
$933$		0			0
$934$	1.09273	−	3.36307i	0.0357552	−	0.110043i
$935$	−38.7580	−	11.7059i	−1.26752	−	0.382825i
$936$		0			0
$937$	5.07121	+	1.64774i	0.165669	+	0.0538292i	0.390677	−	0.920528i	$-0.372241\pi$
$937$	5.07121	+	1.64774i	0.165669	+	0.0538292i	−0.225008	+	0.974357i	$0.572241\pi$
$938$	39.9018	+	12.9649i	1.30284	+	0.423318i
$939$		0			0
$940$	−22.8528	−	6.90214i	−0.745375	−	0.225123i
$941$	2.62746	−	8.08650i	0.0856529	−	0.263612i	−0.899052	−	0.437841i	$-0.855743\pi$
$941$	2.62746	−	8.08650i	0.0856529	−	0.263612i	0.984705	+	0.174229i	$0.0557432\pi$
$942$		0			0
$943$			56.3809i			1.83602i
$944$	−0.225531	−	0.163858i	−0.00734040	−	0.00533311i
$945$		0			0
$946$	6.43025	−	4.67185i	0.209065	−	0.151895i
$947$	13.1250	+	18.0650i	0.426504	+	0.587033i	0.967146	−	0.254220i	$-0.0818187\pi$
$947$	13.1250	+	18.0650i	0.426504	+	0.587033i	−0.540642	+	0.841253i	$0.681819\pi$
$948$		0			0
$949$	−6.08831			−0.197635
$950$	10.9520	+	3.06021i	0.355331	+	0.0992863i
$951$		0			0
$952$	11.5416	−	3.75008i	0.374064	−	0.121541i
$953$	8.02894	+	11.0509i	0.260083	+	0.357973i	0.919011	−	0.394233i	$-0.128990\pi$
$953$	8.02894	+	11.0509i	0.260083	+	0.357973i	−0.658928	+	0.752206i	$0.728990\pi$
$954$		0			0
$955$	−2.34191	+	7.75400i	−0.0757825	+	0.250913i
$956$	−5.05298	−	3.67120i	−0.163425	−	0.118735i
$957$		0			0
$958$	−23.7675	+	32.7132i	−0.767894	+	1.05692i
$959$	−10.0910	+	31.0570i	−0.325856	+	1.00288i
$960$		0			0
$961$	19.9095	+	61.2752i	0.642243	+	1.97662i
$962$	0.589821	+	0.191644i	0.0190166	+	0.00617886i
$963$		0			0
$964$	4.57636	+	14.0846i	0.147395	+	0.453634i
$965$	−0.453238	−	21.7407i	−0.0145903	−	0.699858i
$966$		0			0
$967$	18.4843	−	25.4414i	0.594414	−	0.818141i	−0.400769	−	0.916179i	$-0.631257\pi$
$967$	18.4843	−	25.4414i	0.594414	−	0.818141i	0.995183	+	0.0980386i	$0.0312569\pi$
$968$			16.6149i			0.534022i
$969$		0			0
$970$	8.02716	+	5.58021i	0.257737	+	0.179170i
$971$	−3.40793	+	2.47601i	−0.109366	+	0.0794589i	−0.641124	−	0.767437i	$-0.721532\pi$
$971$	−3.40793	+	2.47601i	−0.109366	+	0.0794589i	0.531758	+	0.846896i	$0.321532\pi$
$972$		0			0
$973$	−62.8463	+	20.4200i	−2.01476	+	0.654635i
$974$	−26.7043			−0.855661
$975$		0			0
$976$	3.68218			0.117864
$977$	13.5077	−	4.38892i	0.432149	−	0.140414i	−0.0848613	−	0.996393i	$-0.527045\pi$
$977$	13.5077	−	4.38892i	0.432149	−	0.140414i	0.517011	+	0.855979i	$0.327045\pi$
$978$		0			0
$979$	−56.9087	+	41.3466i	−1.81881	+	1.32144i
$980$	9.62744	−	7.30611i	0.307537	−	0.233385i
$981$		0			0
$982$			33.1096i			1.05657i
$983$	18.9158	−	26.0353i	0.603319	−	0.830398i	−0.392688	−	0.919672i	$-0.628455\pi$
$983$	18.9158	−	26.0353i	0.603319	−	0.830398i	0.996007	+	0.0892742i	$0.0284547\pi$
$984$		0			0
$985$	9.56194	+	12.6000i	0.304669	+	0.401469i
$986$	2.85524	+	8.78752i	0.0909293	+	0.279852i
$987$		0			0
$988$	−1.33912	−	0.435105i	−0.0426030	−	0.0138425i
$989$	4.18494	+	12.8799i	0.133073	+	0.409557i
$990$		0			0
$991$	12.2198	−	37.6086i	0.388174	−	1.19468i	−0.545978	−	0.837799i	$-0.683842\pi$
$991$	12.2198	−	37.6086i	0.388174	−	1.19468i	0.934152	−	0.356876i	$-0.116158\pi$
$992$	−5.74193	+	7.90309i	−0.182306	+	0.250923i
$993$		0			0
$994$	−13.5307	−	9.83059i	−0.429166	−	0.311808i
$995$	−39.5127	+	0.823740i	−1.25264	+	0.0261143i
$996$		0			0
$997$	−1.66750	−	2.29512i	−0.0528104	−	0.0726873i	0.781795	−	0.623535i	$-0.214304\pi$
$997$	−1.66750	−	2.29512i	−0.0528104	−	0.0726873i	−0.834605	+	0.550848i	$0.814304\pi$
$998$	−5.71873	+	1.85813i	−0.181023	+	0.0588181i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.c.19.3		16
3.2	odd	2		150.2.h.b.19.2	✓	16
15.2	even	4		750.2.g.g.151.4		16
15.8	even	4		750.2.g.f.151.1		16
15.14	odd	2		750.2.h.d.349.4		16
25.4	even	10	inner	450.2.l.c.379.3		16
75.2	even	20		3750.2.a.u.1.7		8
75.11	odd	10		3750.2.c.k.1249.10		16
75.14	odd	10		3750.2.c.k.1249.7		16
75.23	even	20		3750.2.a.v.1.2		8
75.29	odd	10		150.2.h.b.79.2	yes	16
75.47	even	20		750.2.g.g.601.4		16
75.53	even	20		750.2.g.f.601.1		16
75.71	odd	10		750.2.h.d.649.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.19.2	✓	16	3.2	odd	2
150.2.h.b.79.2	yes	16	75.29	odd	10
450.2.l.c.19.3		16	1.1	even	1	trivial
450.2.l.c.379.3		16	25.4	even	10	inner
750.2.g.f.151.1		16	15.8	even	4
750.2.g.f.601.1		16	75.53	even	20
750.2.g.g.151.4		16	15.2	even	4
750.2.g.g.601.4		16	75.47	even	20
750.2.h.d.349.4		16	15.14	odd	2
750.2.h.d.649.3		16	75.71	odd	10
3750.2.a.u.1.7		8	75.2	even	20
3750.2.a.v.1.2		8	75.23	even	20
3750.2.c.k.1249.7		16	75.14	odd	10
3750.2.c.k.1249.10		16	75.11	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-2.23558 + 0.0466062i) q^{5} -3.52206i q^{7} +(0.587785 - 0.809017i) q^{8} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-2.23558 + 0.0466062i) q^{5} -3.52206i q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.11176 + 0.735158i) q^{10} +(-1.62388 - 4.99779i) q^{11} +(-0.588802 - 0.191313i) q^{13} +(-1.08838 - 3.34968i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-2.02525 + 2.78752i) q^{17} +(1.83995 + 1.33680i) q^{19} +(-1.78123 + 1.35175i) q^{20} +(-3.08880 - 4.25137i) q^{22} +(8.51557 - 2.76688i) q^{23} +(4.99566 - 0.208384i) q^{25} -0.619103 q^{26} +(-2.07022 - 2.84941i) q^{28} +(2.16949 - 1.57623i) q^{29} +(-7.90309 - 5.74193i) q^{31} -1.00000i q^{32} +(-1.06474 + 3.27693i) q^{34} +(0.164150 + 7.87386i) q^{35} +(-0.952702 - 0.309552i) q^{37} +(2.16299 + 0.702799i) q^{38} +(-1.27634 + 1.83602i) q^{40} +(-1.94584 + 5.98868i) q^{41} +1.51251i q^{43} +(-4.25137 - 3.08880i) q^{44} +(7.24378 - 5.26291i) q^{46} +(6.27522 + 8.63710i) q^{47} -5.40494 q^{49} +(4.68676 - 1.74193i) q^{50} +(-0.588802 + 0.191313i) q^{52} +(-0.325260 - 0.447681i) q^{53} +(3.86324 + 11.0973i) q^{55} +(-2.84941 - 2.07022i) q^{56} +(1.57623 - 2.16949i) q^{58} +(0.0861451 - 0.265127i) q^{59} +(1.13786 + 3.50196i) q^{61} +(-9.29064 - 3.01871i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(1.32523 + 0.400255i) q^{65} +(-7.00176 + 9.63710i) q^{67} +3.44557i q^{68} +(2.58927 + 7.43777i) q^{70} +(3.84168 - 2.79115i) q^{71} +(9.35277 - 3.03890i) q^{73} -1.00173 q^{74} +2.27431 q^{76} +(-17.6025 + 5.71941i) q^{77} +(5.27525 - 3.83269i) q^{79} +(-0.646508 + 2.14057i) q^{80} +6.29687i q^{82} +(1.56335 - 2.15177i) q^{83} +(4.39770 - 6.32612i) q^{85} +(0.467392 + 1.43848i) q^{86} +(-4.99779 - 1.62388i) q^{88} +(-4.13649 - 12.7308i) q^{89} +(-0.673818 + 2.07380i) q^{91} +(5.26291 - 7.24378i) q^{92} +(8.63710 + 6.27522i) q^{94} +(-4.17567 - 2.90278i) q^{95} +(-2.56983 - 3.53706i) q^{97} +(-5.14040 + 1.67022i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^4 - 4 * q^5	\( 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37} - 10 q^{38} - 2 q^{40} - 22 q^{41} - 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} - 12 q^{50} + 20 q^{52} - 30 q^{53} + 18 q^{55} + 2 q^{56} - 30 q^{58} - 20 q^{59} + 12 q^{61} - 50 q^{62} + 4 q^{64} + 8 q^{65} - 50 q^{67} - 12 q^{70} + 28 q^{71} + 20 q^{73} - 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{80} + 30 q^{83} - 4 q^{85} + 6 q^{86} - 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} + 30 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^5 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 2 * q^14 - 4 * q^16 + 30 * q^17 + 4 * q^20 - 20 * q^22 + 10 * q^23 + 24 * q^25 - 4 * q^26 + 10 * q^29 - 18 * q^31 + 12 * q^34 + 34 * q^35 + 20 * q^37 - 10 * q^38 - 2 * q^40 - 22 * q^41 - 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 - 12 * q^50 + 20 * q^52 - 30 * q^53 + 18 * q^55 + 2 * q^56 - 30 * q^58 - 20 * q^59 + 12 * q^61 - 50 * q^62 + 4 * q^64 + 8 * q^65 - 50 * q^67 - 12 * q^70 + 28 * q^71 + 20 * q^73 - 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^80 + 30 * q^83 - 4 * q^85 + 6 * q^86 - 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 + 30 * q^95 - 10 * q^97 - 60 * q^98

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