LMFDB - Embedded newform 675.2.y.a.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("675.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	675.19
Dual form			675.2.y.a.604.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.188119 + 0.885029i) q^{2} +(1.07920 + 0.480492i) q^{4} +(0.419997 - 2.19627i) q^{5} +(-3.56731 - 2.05959i) q^{7} +(-1.69193 + 2.32874i) q^{8} +O(q^{10})$	\(q+(-0.188119 + 0.885029i) q^{2} +(1.07920 + 0.480492i) q^{4} +(0.419997 - 2.19627i) q^{5} +(-3.56731 - 2.05959i) q^{7} +(-1.69193 + 2.32874i) q^{8} +(1.86475 + 0.784869i) q^{10} +(-3.60133 - 0.765487i) q^{11} +(-0.555564 - 2.61372i) q^{13} +(2.49387 - 2.76973i) q^{14} +(-0.161781 - 0.179676i) q^{16} +(3.11975 - 4.29397i) q^{17} +(-2.11305 - 1.53522i) q^{19} +(1.50855 - 2.16842i) q^{20} +(1.35496 - 3.04328i) q^{22} +(-0.241422 - 0.217378i) q^{23} +(-4.64720 - 1.84486i) q^{25} +2.41773 q^{26} +(-2.86024 - 3.93678i) q^{28} +(0.419376 + 3.99009i) q^{29} +(0.301239 - 2.86609i) q^{31} +(-4.79621 + 2.76909i) q^{32} +(3.21341 + 3.56885i) q^{34} +(-6.02167 + 6.96976i) q^{35} +(-9.96572 - 3.23806i) q^{37} +(1.75622 - 1.58131i) q^{38} +(4.40393 + 4.69399i) q^{40} +(11.0506 - 2.34887i) q^{41} +(-3.47868 - 2.00842i) q^{43} +(-3.51876 - 2.55653i) q^{44} +(0.237802 - 0.172773i) q^{46} +(0.657409 - 0.0690965i) q^{47} +(4.98380 + 8.63220i) q^{49} +(2.50698 - 3.76586i) q^{50} +(0.656307 - 3.08768i) q^{52} +(-1.02817 - 1.41515i) q^{53} +(-3.19377 + 7.58800i) q^{55} +(10.8319 - 4.82265i) q^{56} +(-3.61024 - 0.379452i) q^{58} +(-3.36772 + 0.715832i) q^{59} +(9.97712 + 2.12070i) q^{61} +(2.47991 + 0.805771i) q^{62} +(-1.69790 - 5.22560i) q^{64} +(-5.97378 + 0.122412i) q^{65} +(5.50254 + 0.578340i) q^{67} +(5.43007 - 3.13505i) q^{68} +(-5.03565 - 6.64050i) q^{70} +(-0.103447 + 0.0751586i) q^{71} +(14.5057 - 4.71320i) q^{73} +(4.74051 - 8.21081i) q^{74} +(-1.54275 - 2.67212i) q^{76} +(11.2705 + 10.1480i) q^{77} +(1.22520 + 11.6570i) q^{79} +(-0.462565 + 0.279851i) q^{80} +10.2220i q^{82} +(-5.80347 - 13.0348i) q^{83} +(-8.12043 - 8.65528i) q^{85} +(2.43191 - 2.70091i) q^{86} +(7.87581 - 7.09141i) q^{88} +(-1.47511 - 4.53994i) q^{89} +(-3.40132 + 10.4682i) q^{91} +(-0.156096 - 0.350596i) q^{92} +(-0.0625186 + 0.594825i) q^{94} +(-4.25924 + 3.99604i) q^{95} +(-4.50262 + 0.473244i) q^{97} +(-8.57729 + 2.78693i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.188119	+	0.885029i	−0.133020	+	0.625810i	0.860239	+	0.509892i	$0.170314\pi$
$2$	−0.188119	+	0.885029i	−0.133020	+	0.625810i	−0.993259	+	0.115918i	$0.963019\pi$
$3$		0			0
$3$		0			0
$4$	1.07920	+	0.480492i	0.539602	+	0.240246i
$5$	0.419997	−	2.19627i	0.187829	−	0.982202i
$5$	0.419997	−	2.19627i	0.187829	−	0.982202i
$6$		0			0
$7$	−3.56731	−	2.05959i	−1.34832	−	0.778451i	−0.360306	−	0.932834i	$-0.617328\pi$
$7$	−3.56731	−	2.05959i	−1.34832	−	0.778451i	−0.988011	+	0.154383i	$0.950661\pi$
$8$	−1.69193	+	2.32874i	−0.598186	+	0.823332i
$9$		0			0
$10$	1.86475	+	0.784869i	0.589687	+	0.248197i
$11$	−3.60133	−	0.765487i	−1.08584	−	0.230803i	−0.369977	−	0.929041i	$-0.620635\pi$
$11$	−3.60133	−	0.765487i	−1.08584	−	0.230803i	−0.715866	+	0.698238i	$0.753968\pi$
$12$		0			0
$13$	−0.555564	−	2.61372i	−0.154086	−	0.724916i	−0.985556	−	0.169348i	$-0.945834\pi$
$13$	−0.555564	−	2.61372i	−0.154086	−	0.724916i	0.831471	−	0.555569i	$-0.187499\pi$
$14$	2.49387	−	2.76973i	0.666516	−	0.740241i
$15$		0			0
$16$	−0.161781	−	0.179676i	−0.0404452	−	0.0449190i
$17$	3.11975	−	4.29397i	0.756651	−	1.04144i	−0.240834	−	0.970566i	$-0.577421\pi$
$17$	3.11975	−	4.29397i	0.756651	−	1.04144i	0.997485	−	0.0708748i	$-0.0225791\pi$
$18$		0			0
$19$	−2.11305	−	1.53522i	−0.484767	−	0.352204i	0.318401	−	0.947956i	$-0.396854\pi$
$19$	−2.11305	−	1.53522i	−0.484767	−	0.352204i	−0.803168	+	0.595752i	$0.796854\pi$
$20$	1.50855	−	2.16842i	0.337323	−	0.484873i
$21$		0			0
$22$	1.35496	−	3.04328i	0.288878	−	0.648830i
$23$	−0.241422	−	0.217378i	−0.0503401	−	0.0453264i	0.643577	−	0.765382i	$-0.277450\pi$
$23$	−0.241422	−	0.217378i	−0.0503401	−	0.0453264i	−0.693917	+	0.720055i	$0.744116\pi$
$24$		0			0
$25$	−4.64720	−	1.84486i	−0.929441	−	0.368971i
$26$	2.41773			0.474156
$27$		0			0
$28$	−2.86024	−	3.93678i	−0.540534	−	0.743981i
$29$	0.419376	+	3.99009i	0.0778761	+	0.740942i	0.961882	+	0.273466i	$0.0881699\pi$
$29$	0.419376	+	3.99009i	0.0778761	+	0.740942i	−0.884006	+	0.467476i	$0.845163\pi$
$30$		0			0
$31$	0.301239	−	2.86609i	0.0541041	−	0.514766i	−0.933587	−	0.358350i	$-0.883339\pi$
$31$	0.301239	−	2.86609i	0.0541041	−	0.514766i	0.987691	−	0.156416i	$-0.0499939\pi$
$32$	−4.79621	+	2.76909i	−0.847859	+	0.489511i
$33$		0			0
$34$	3.21341	+	3.56885i	0.551095	+	0.612052i
$35$	−6.02167	+	6.96976i	−1.01785	+	1.17810i
$36$		0			0
$37$	−9.96572	−	3.23806i	−1.63835	−	0.532334i	−0.662184	−	0.749341i	$-0.730370\pi$
$37$	−9.96572	−	3.23806i	−1.63835	−	0.532334i	−0.976170	+	0.217007i	$0.930370\pi$
$38$	1.75622	−	1.58131i	0.284897	−	0.256522i
$39$		0			0
$40$	4.40393	+	4.69399i	0.696322	+	0.742185i
$41$	11.0506	−	2.34887i	1.72581	−	0.366832i	0.764999	−	0.644032i	$-0.222740\pi$
$41$	11.0506	−	2.34887i	1.72581	−	0.366832i	0.960812	+	0.277200i	$0.0894063\pi$
$42$		0			0
$43$	−3.47868	−	2.00842i	−0.530493	−	0.306281i	0.210724	−	0.977546i	$-0.432418\pi$
$43$	−3.47868	−	2.00842i	−0.530493	−	0.306281i	−0.741217	+	0.671265i	$0.765751\pi$
$44$	−3.51876	−	2.55653i	−0.530473	−	0.385411i
$45$		0			0
$46$	0.237802	−	0.172773i	0.0350620	−	0.0254740i
$47$	0.657409	−	0.0690965i	0.0958930	−	0.0100788i	−0.0564604	−	0.998405i	$-0.517981\pi$
$47$	0.657409	−	0.0690965i	0.0958930	−	0.0100788i	0.152353	+	0.988326i	$0.451315\pi$
$48$		0			0
$49$	4.98380	+	8.63220i	0.711972	+	1.23317i
$50$	2.50698	−	3.76586i	0.354540	−	0.532573i
$51$		0			0
$52$	0.656307	−	3.08768i	0.0910134	−	0.428184i
$53$	−1.02817	−	1.41515i	−0.141230	−	0.194386i	0.732543	−	0.680721i	$-0.238333\pi$
$53$	−1.02817	−	1.41515i	−0.141230	−	0.194386i	−0.873772	+	0.486335i	$0.838333\pi$
$54$		0			0
$55$	−3.19377	+	7.58800i	−0.430648	+	1.02317i
$56$	10.8319	−	4.82265i	1.44747	−	0.644454i
$57$		0			0
$58$	−3.61024	−	0.379452i	−0.474048	−	0.0498244i
$59$	−3.36772	+	0.715832i	−0.438440	+	0.0931933i	−0.421843	−	0.906669i	$-0.638617\pi$
$59$	−3.36772	+	0.715832i	−0.438440	+	0.0931933i	−0.0165972	+	0.999862i	$0.505283\pi$
$60$		0			0
$61$	9.97712	+	2.12070i	1.27744	+	0.271528i	0.796185	−	0.605053i	$-0.206848\pi$
$61$	9.97712	+	2.12070i	1.27744	+	0.271528i	0.481254	+	0.876581i	$0.340181\pi$
$62$	2.47991	+	0.805771i	0.314949	+	0.102333i
$63$		0			0
$64$	−1.69790	−	5.22560i	−0.212237	−	0.653199i
$65$	−5.97378	+	0.122412i	−0.740956	+	0.0151833i
$66$		0			0
$67$	5.50254	+	0.578340i	0.672242	+	0.0706555i	0.434499	−	0.900672i	$-0.356926\pi$
$67$	5.50254	+	0.578340i	0.672242	+	0.0706555i	0.237744	+	0.971328i	$0.423592\pi$
$68$	5.43007	−	3.13505i	0.658492	−	0.380181i
$69$		0			0
$70$	−5.03565	−	6.64050i	−0.601875	−	0.793691i
$71$	−0.103447	+	0.0751586i	−0.0122769	+	0.00891969i	−0.593907	−	0.804534i	$-0.702415\pi$
$71$	−0.103447	+	0.0751586i	−0.0122769	+	0.00891969i	0.581630	+	0.813454i	$0.302415\pi$
$72$		0			0
$73$	14.5057	−	4.71320i	1.69777	−	0.551638i	0.709545	−	0.704660i	$-0.248900\pi$
$73$	14.5057	−	4.71320i	1.69777	−	0.551638i	0.988223	+	0.153021i	$0.0489003\pi$
$74$	4.74051	−	8.21081i	0.551074	−	0.954488i
$75$		0			0
$76$	−1.54275	−	2.67212i	−0.176965	−	0.306513i
$77$	11.2705	+	10.1480i	1.28439	+	1.15647i
$78$		0			0
$79$	1.22520	+	11.6570i	0.137846	+	1.31152i	0.816623	+	0.577172i	$0.195844\pi$
$79$	1.22520	+	11.6570i	0.137846	+	1.31152i	−0.678777	+	0.734345i	$0.737490\pi$
$80$	−0.462565	+	0.279851i	−0.0517163	+	0.0312883i
$81$		0			0
$82$			10.2220i			1.12883i
$83$	−5.80347	−	13.0348i	−0.637014	−	1.43076i	−0.886661	−	0.462420i	$-0.846981\pi$
$83$	−5.80347	−	13.0348i	−0.637014	−	1.43076i	0.249647	−	0.968337i	$-0.419685\pi$
$84$		0			0
$85$	−8.12043	−	8.65528i	−0.880785	−	0.938797i
$86$	2.43191	−	2.70091i	0.262240	−	0.291247i
$87$		0			0
$88$	7.87581	−	7.09141i	0.839564	−	0.755947i
$89$	−1.47511	−	4.53994i	−0.156362	−	0.481232i	0.841934	−	0.539580i	$-0.181417\pi$
$89$	−1.47511	−	4.53994i	−0.156362	−	0.481232i	−0.998296	+	0.0583475i	$0.981417\pi$
$90$		0			0
$91$	−3.40132	+	10.4682i	−0.356555	+	1.09736i
$92$	−0.156096	−	0.350596i	−0.0162741	−	0.0365522i
$93$		0			0
$94$	−0.0625186	+	0.594825i	−0.00644830	+	0.0613515i
$95$	−4.25924	+	3.99604i	−0.436988	+	0.409985i
$96$		0			0
$97$	−4.50262	+	0.473244i	−0.457172	+	0.0480507i	−0.330316	−	0.943870i	$-0.607155\pi$
$97$	−4.50262	+	0.473244i	−0.457172	+	0.0480507i	−0.126856	+	0.991921i	$0.540489\pi$
$98$	−8.57729	+	2.78693i	−0.866438	+	0.281523i
$99$		0			0
$100$	−4.12884	−	4.22392i	−0.412884	−	0.422392i
$101$	−1.18616	+	2.05448i	−0.118027	+	0.204429i	−0.918986	−	0.394291i	$-0.870990\pi$
$101$	−1.18616	+	2.05448i	−0.118027	+	0.204429i	0.800959	+	0.598720i	$0.204324\pi$
$102$		0			0
$103$	−2.13554	+	4.79650i	−0.210421	+	0.472613i	−0.987664	−	0.156587i	$-0.949951\pi$
$103$	−2.13554	+	4.79650i	−0.210421	+	0.472613i	0.777243	+	0.629200i	$0.216617\pi$
$104$	7.02664	+	3.12846i	0.689019	+	0.306771i
$105$		0			0
$106$	1.44587	−	0.643741i	0.140435	−	0.0625257i
$107$			11.6339i			1.12469i	0.826902	+	0.562346i	$0.190101\pi$
$107$			11.6339i			1.12469i	−0.826902	+	0.562346i	$0.809899\pi$
$108$		0			0
$109$	1.27084	−	3.91125i	0.121725	−	0.374630i	−0.871565	−	0.490279i	$-0.836895\pi$
$109$	1.27084	−	3.91125i	0.121725	−	0.374630i	0.993290	+	0.115649i	$0.0368948\pi$
$110$	−6.11479	−	4.25402i	−0.583023	−	0.405605i
$111$		0			0
$112$	0.207065	+	0.974162i	0.0195658	+	0.0920497i
$113$	−1.49167	−	7.01775i	−0.140324	−	0.660174i	−0.990931	−	0.134372i	$-0.957098\pi$
$113$	−1.49167	−	7.01775i	−0.140324	−	0.660174i	0.850607	−	0.525803i	$-0.176235\pi$
$114$		0			0
$115$	−0.578817	+	0.438931i	−0.0539750	+	0.0409305i
$116$	−1.46462	+	4.50763i	−0.135986	+	0.418523i
$117$		0			0
$118$		−	3.11519i		−	0.286777i
$119$	−19.9729	+	8.89253i	−1.83092	+	0.815176i
$120$		0			0
$121$	2.33464	+	1.03945i	0.212240	+	0.0944954i
$122$	−3.75377	+	8.43110i	−0.339850	+	0.763316i
$123$		0			0
$124$	1.70223	−	2.94835i	0.152865	−	0.264770i
$125$	−6.00361	+	9.43168i	−0.536980	+	0.843595i
$126$		0			0
$127$	18.4271	−	5.98731i	1.63514	−	0.531288i	0.659692	−	0.751536i	$-0.270687\pi$
$127$	18.4271	−	5.98731i	1.63514	−	0.531288i	0.975444	+	0.220248i	$0.0706866\pi$
$128$	−6.07149	+	0.638140i	−0.536649	+	0.0564041i
$129$		0			0
$130$	1.01544	−	5.30999i	0.0890601	−	0.465717i
$131$	0.737895	−	7.02060i	0.0644702	−	0.613393i	−0.913815	−	0.406130i	$-0.866878\pi$
$131$	0.737895	−	7.02060i	0.0644702	−	0.613393i	0.978285	−	0.207263i	$-0.0664555\pi$
$132$		0			0
$133$	4.37599	+	9.82863i	0.379446	+	0.852250i
$134$	−1.54698	+	4.76111i	−0.133639	+	0.411297i
$135$		0			0
$136$	4.72114	+	14.5302i	0.404834	+	1.24595i
$137$	−2.80582	+	2.52638i	−0.239718	+	0.215843i	−0.780229	−	0.625494i	$-0.784898\pi$
$137$	−2.80582	+	2.52638i	−0.239718	+	0.215843i	0.540511	+	0.841337i	$0.318231\pi$
$138$		0			0
$139$	−9.04974	+	10.0508i	−0.767589	+	0.852494i	−0.992545	−	0.121875i	$-0.961109\pi$
$139$	−9.04974	+	10.0508i	−0.767589	+	0.852494i	0.224956	+	0.974369i	$0.427776\pi$
$140$	−9.84752	+	4.62842i	−0.832267	+	0.391173i
$141$		0			0
$142$	−0.0470573	−	0.105692i	−0.00394896	−	0.00886950i
$143$			9.83817i			0.822709i
$144$		0			0
$145$	8.93946	+	0.754766i	0.742382	+	0.0626799i
$146$	1.44252	+	13.7246i	0.119384	+	1.13586i
$147$		0			0
$148$	−9.19918	−	8.28297i	−0.756168	−	0.680856i
$149$	7.02898	+	12.1745i	0.575836	+	0.997378i	0.995950	+	0.0899065i	$0.0286568\pi$
$149$	7.02898	+	12.1745i	0.575836	+	0.997378i	−0.420114	+	0.907471i	$0.638010\pi$
$150$		0			0
$151$	3.05448	−	5.29052i	0.248570	−	0.430536i	−0.714559	−	0.699575i	$-0.753373\pi$
$151$	3.05448	−	5.29052i	0.248570	−	0.430536i	0.963129	+	0.269039i	$0.0867060\pi$
$152$	7.15025	−	2.32326i	0.579962	−	0.188441i
$153$		0			0
$154$	−11.1015	+	8.06568i	−0.894581	+	0.649951i
$155$	−6.16820	−	1.86535i	−0.495441	−	0.149829i
$156$		0			0
$157$	−16.0589	+	9.27160i	−1.28164	+	0.739954i	−0.977148	−	0.212561i	$-0.931820\pi$
$157$	−16.0589	+	9.27160i	−1.28164	+	0.739954i	−0.304490	+	0.952515i	$0.598486\pi$
$158$	−10.5473	−	1.10856i	−0.839096	−	0.0881926i
$159$		0			0
$160$	4.06728	+	11.6968i	0.321547	+	0.924713i
$161$	0.413520	+	1.27268i	0.0325900	+	0.100302i
$162$		0			0
$163$	6.32194	+	2.05412i	0.495172	+	0.160891i	0.545948	−	0.837819i	$-0.316169\pi$
$163$	6.32194	+	2.05412i	0.495172	+	0.160891i	−0.0507760	+	0.998710i	$0.516169\pi$
$164$	13.0544	+	2.77481i	1.01938	+	0.216676i
$165$		0			0
$166$	12.6279	−	2.68415i	0.980118	−	0.208330i
$167$	−0.441741	−	0.0464289i	−0.0341830	−	0.00359278i	0.0874215	−	0.996171i	$-0.472137\pi$
$167$	−0.441741	−	0.0464289i	−0.0341830	−	0.00359278i	−0.121605	+	0.992579i	$0.538804\pi$
$168$		0			0
$169$	5.35319	−	2.38340i	0.411784	−	0.183338i
$170$	9.18778	−	5.55860i	0.704670	−	0.426325i
$171$		0			0
$172$	−2.78917	−	3.83897i	−0.212672	−	0.292718i
$173$	2.46229	−	11.5842i	0.187205	−	0.880729i	−0.779811	−	0.626014i	$-0.784685\pi$
$173$	2.46229	−	11.5842i	0.187205	−	0.880729i	0.967016	−	0.254715i	$-0.0819816\pi$
$174$		0			0
$175$	12.7784	+	16.1525i	0.965955	+	1.22101i
$176$	0.445088	+	0.770915i	0.0335498	+	0.0581099i
$177$		0			0
$178$	4.29547	−	0.451472i	0.321959	−	0.0338393i
$179$	4.49007	−	3.26223i	0.335604	−	0.243831i	−0.407201	−	0.913339i	$-0.633495\pi$
$179$	4.49007	−	3.26223i	0.335604	−	0.243831i	0.742805	+	0.669508i	$0.233495\pi$
$180$		0			0
$181$	−0.124713	−	0.0906095i	−0.00926987	−	0.00673495i	0.583141	−	0.812371i	$-0.301824\pi$
$181$	−0.124713	−	0.0906095i	−0.00926987	−	0.00673495i	−0.592411	+	0.805636i	$0.701824\pi$
$182$	−8.62480	−	4.97953i	−0.639313	−	0.369108i
$183$		0			0
$184$	0.914684	−	0.194422i	0.0674314	−	0.0143330i
$185$	−11.2972	+	20.5274i	−0.830589	+	1.50921i
$186$		0			0
$187$	−14.5223	+	13.0759i	−1.06197	+	0.956204i
$188$	0.742679	+	0.241311i	0.0541654	+	0.0175994i
$189$		0			0
$190$	−2.73537	−	4.52128i	−0.198445	−	0.328008i
$191$	−9.63013	−	10.6953i	−0.696812	−	0.773888i	0.286054	−	0.958214i	$-0.407656\pi$
$191$	−9.63013	−	10.6953i	−0.696812	−	0.773888i	−0.982865	+	0.184326i	$0.940990\pi$
$192$		0			0
$193$	−5.68308	+	3.28113i	−0.409077	+	0.236181i	−0.690393	−	0.723434i	$-0.742562\pi$
$193$	−5.68308	+	3.28113i	−0.409077	+	0.236181i	0.281316	+	0.959615i	$0.409229\pi$
$194$	0.428192	−	4.07397i	0.0307424	−	0.292494i
$195$		0			0
$196$	1.23083	+	11.7106i	0.0879165	+	0.836470i
$197$	3.99667	+	5.50095i	0.284751	+	0.391926i	0.927300	−	0.374318i	$-0.122123\pi$
$197$	3.99667	+	5.50095i	0.284751	+	0.391926i	−0.642549	+	0.766244i	$0.722123\pi$
$198$		0			0
$199$	−11.8774			−0.841968			−0.420984	−	0.907068i	$-0.638315\pi$
$199$	−11.8774			−0.841968			−0.420984	+	0.907068i	$0.638315\pi$
$200$	12.1589	−	7.70075i	0.859764	−	0.544525i
$201$		0			0
$202$	−1.59514	−	1.43627i	−0.112234	−	0.101056i
$203$	6.72190	−	15.0976i	0.471785	−	1.05965i
$204$		0			0
$205$	−0.517546	−	25.2566i	−0.0361470	−	1.76400i
$206$	−3.84331	−	2.79233i	−0.267776	−	0.194551i
$207$		0			0
$208$	−0.379744	+	0.522672i	−0.0263305	+	0.0362408i
$209$	6.43461	+	7.14636i	0.445091	+	0.494324i
$210$		0			0
$211$	12.9122	−	14.3404i	0.888912	−	0.987236i	−0.111067	−	0.993813i	$-0.535427\pi$
$211$	12.9122	−	14.3404i	0.888912	−	0.987236i	0.999978	+	0.00657654i	$0.00209339\pi$
$212$	−0.429632	−	2.02126i	−0.0295073	−	0.138821i
$213$		0			0
$214$	−10.2963	−	2.18855i	−0.703843	−	0.149607i
$215$	−5.87206	+	6.79659i	−0.400471	+	0.463523i
$216$		0			0
$217$	−6.97758	+	9.60382i	−0.473669	+	0.651950i
$218$	3.22250	+	1.86051i	0.218256	+	0.126010i
$219$		0			0
$220$	−7.09270	+	6.65441i	−0.478190	+	0.448641i
$221$	−12.9565	−	5.76859i	−0.871547	−	0.388038i
$222$		0			0
$223$	0.861696	−	4.05396i	0.0577034	−	0.271473i	−0.939832	−	0.341637i	$-0.889019\pi$
$223$	0.861696	−	4.05396i	0.0577034	−	0.271473i	0.997536	+	0.0701635i	$0.0223521\pi$
$224$	22.8128			1.52424
$225$		0			0
$226$	6.49152			0.431810
$227$	2.43665	−	11.4635i	0.161726	−	0.760861i	−0.820273	−	0.571973i	$-0.806178\pi$
$227$	2.43665	−	11.4635i	0.161726	−	0.760861i	0.981999	−	0.188888i	$-0.0604884\pi$
$228$		0			0
$229$	−7.02698	−	3.12861i	−0.464356	−	0.206744i	0.161203	−	0.986921i	$-0.448462\pi$
$229$	−7.02698	−	3.12861i	−0.464356	−	0.206744i	−0.625559	+	0.780177i	$0.715129\pi$
$230$	−0.279580	−	0.594841i	−0.0184350	−	0.0392227i
$231$		0			0
$232$	−10.0014	−	5.77432i	−0.656626	−	0.379103i
$233$	6.45077	−	8.87872i	0.422604	−	0.581664i	−0.543632	−	0.839324i	$-0.682951\pi$
$233$	6.45077	−	8.87872i	0.422604	−	0.581664i	0.966236	+	0.257659i	$0.0829512\pi$
$234$		0			0
$235$	0.124356	−	1.47287i	0.00811206	−	0.0960794i
$236$	−3.97841	−	0.845637i	−0.258972	−	0.0550463i
$237$		0			0
$238$	−4.11286	−	19.3495i	−0.266597	−	1.25424i
$239$	4.61867	−	5.12956i	0.298757	−	0.331804i	−0.575011	−	0.818145i	$-0.695002\pi$
$239$	4.61867	−	5.12956i	0.298757	−	0.331804i	0.873769	+	0.486342i	$0.161669\pi$
$240$		0			0
$241$	−19.2878	−	21.4212i	−1.24243	−	1.37986i	−0.897368	−	0.441284i	$-0.854523\pi$
$241$	−19.2878	−	21.4212i	−1.24243	−	1.37986i	−0.345066	−	0.938579i	$-0.612143\pi$
$242$	−1.35913	+	1.87069i	−0.0873684	+	0.120252i
$243$		0			0
$244$	9.74836	+	7.08260i	0.624075	+	0.453417i
$245$	21.0518	−	7.32028i	1.34495	−	0.467675i
$246$		0			0
$247$	−2.83871	+	6.37584i	−0.180623	+	0.405685i
$248$	6.16470	+	5.55072i	0.391459	+	0.352471i
$249$		0			0
$250$	−7.21792	−	7.08765i	−0.456501	−	0.448262i
$251$	−12.1822			−0.768934			−0.384467	−	0.923139i	$-0.625615\pi$
$251$	−12.1822			−0.768934			−0.384467	+	0.923139i	$0.625615\pi$
$252$		0			0
$253$	0.703043	+	0.967656i	0.0441999	+	0.0608360i
$254$	1.83247	+	17.4348i	0.114979	+	1.09396i
$255$		0			0
$256$	1.72606	−	16.4223i	0.107879	−	1.02640i
$257$	−9.46811	+	5.46641i	−0.590604	+	0.340986i	−0.765336	−	0.643630i	$-0.777427\pi$
$257$	−9.46811	+	5.46641i	−0.590604	+	0.340986i	0.174732	+	0.984616i	$0.444094\pi$
$258$		0			0
$259$	28.8818	+	32.0764i	1.79462	+	1.99313i
$260$	−6.50574	−	2.73825i	−0.403469	−	0.169819i
$261$		0			0
$262$	6.07463	+	1.97377i	0.375292	+	0.121940i
$263$	−14.5743	+	13.1228i	−0.898690	+	0.809184i	−0.982300	−	0.187314i	$-0.940022\pi$
$263$	−14.5743	+	13.1228i	−0.898690	+	0.809184i	0.0836100	+	0.996499i	$0.473355\pi$
$264$		0			0
$265$	−3.53988	+	1.66377i	−0.217453	+	0.102205i
$266$	−9.52182	+	2.02393i	−0.583820	+	0.124095i
$267$		0			0
$268$	5.66047	+	3.26808i	0.345768	+	0.199629i
$269$	17.0589	+	12.3940i	1.04010	+	0.755675i	0.970304	−	0.241887i	$-0.0777663\pi$
$269$	17.0589	+	12.3940i	1.04010	+	0.755675i	0.0697926	+	0.997562i	$0.477766\pi$
$270$		0			0
$271$	5.95749	−	4.32837i	0.361892	−	0.262930i	−0.391949	−	0.919987i	$-0.628199\pi$
$271$	5.95749	−	4.32837i	0.361892	−	0.262930i	0.753841	+	0.657057i	$0.228199\pi$
$272$	−1.27624	+	0.134138i	−0.0773834	+	0.00813333i
$273$		0			0
$274$	−1.70809	−	2.95850i	−0.103189	−	0.178729i
$275$	15.3239	+	10.2013i	0.924068	+	0.615163i
$276$		0			0
$277$	−6.74036	+	31.7109i	−0.404989	+	1.90532i	0.0193326	+	0.999813i	$0.493846\pi$
$277$	−6.74036	+	31.7109i	−0.404989	+	1.90532i	−0.424322	+	0.905511i	$0.639487\pi$
$278$	−7.19279	−	9.90002i	−0.431395	−	0.593764i
$279$		0			0
$280$	−6.04250	−	25.8152i	−0.361108	−	1.54275i
$281$	−0.915375	+	0.407551i	−0.0546067	+	0.0243125i	−0.433858	−	0.900981i	$-0.642848\pi$
$281$	−0.915375	+	0.407551i	−0.0546067	+	0.0243125i	0.379252	+	0.925294i	$0.376181\pi$
$282$		0			0
$283$	3.00730	+	0.316080i	0.178766	+	0.0187890i	0.193488	−	0.981103i	$-0.438020\pi$
$283$	3.00730	+	0.316080i	0.178766	+	0.0187890i	−0.0147226	+	0.999892i	$0.504687\pi$
$284$	−0.147753	+	0.0314060i	−0.00876755	+	0.00186360i
$285$		0			0
$286$	−8.70707	−	1.85074i	−0.514860	−	0.109437i
$287$	−44.2586	−	14.3805i	−2.61250	−	0.848853i
$288$		0			0
$289$	−3.45205	−	10.6243i	−0.203061	−	0.624959i
$290$	−2.34967	+	7.76969i	−0.137977	+	0.456252i
$291$		0			0
$292$	17.9193	+	1.88339i	1.04865	+	0.110217i
$293$	15.2088	−	8.78080i	0.888508	−	0.512980i	0.0150535	−	0.999887i	$-0.495208\pi$
$293$	15.2088	−	8.78080i	0.888508	−	0.512980i	0.873454	+	0.486907i	$0.161875\pi$
$294$		0			0
$295$	0.157725	+	7.69708i	0.00918309	+	0.448141i
$296$	24.4018	−	17.7290i	1.41833	−	1.03048i
$297$		0			0
$298$	−12.0971	+	3.93059i	−0.700767	+	0.227693i
$299$	−0.434040	+	0.751779i	−0.0251012	+	0.0434765i
$300$		0			0
$301$	8.27302	+	14.3293i	0.476849	+	0.825926i
$302$	4.10766	+	3.69855i	0.236369	+	0.212828i
$303$		0			0
$304$	0.0660091	+	0.628034i	0.00378588	+	0.0360202i
$305$	8.84800	−	21.0218i	0.506635	−	1.20370i
$306$		0			0
$307$		−	22.3085i		−	1.27321i	−0.771188	−	0.636607i	$-0.780337\pi$
$307$		−	22.3085i		−	1.27321i	0.771188	−	0.636607i	$-0.219663\pi$
$308$	7.28712	+	16.3671i	0.415222	+	0.932604i
$309$		0			0
$310$	2.81125	−	5.10813i	0.159668	−	0.290122i
$311$	18.6407	−	20.7026i	1.05702	−	1.17394i	0.0727335	−	0.997351i	$-0.476828\pi$
$311$	18.6407	−	20.7026i	1.05702	−	1.17394i	0.984285	−	0.176587i	$-0.0565056\pi$
$312$		0			0
$313$	12.7215	−	11.4545i	0.719064	−	0.647448i	−0.226078	−	0.974109i	$-0.572590\pi$
$313$	12.7215	−	11.4545i	0.719064	−	0.647448i	0.945142	+	0.326661i	$0.105924\pi$
$314$	−5.18466	−	15.9567i	−0.292587	−	0.900491i
$315$		0			0
$316$	−4.27886	+	13.1690i	−0.240705	+	0.740813i
$317$	8.22835	+	18.4812i	0.462150	+	1.03801i	0.982874	+	0.184281i	$0.0589957\pi$
$317$	8.22835	+	18.4812i	0.462150	+	1.03801i	−0.520723	+	0.853726i	$0.674338\pi$
$318$		0			0
$319$	1.54405	−	14.6907i	0.0864504	−	0.822521i
$320$	−12.1899	+	1.53431i	−0.681438	+	0.0857704i
$321$		0			0
$322$	−1.20415	+	0.126562i	−0.0671049	+	0.00705301i
$323$	−13.1844	+	4.28387i	−0.733599	+	0.238361i
$324$		0			0
$325$	−2.24012	+	13.1714i	−0.124260	+	0.730620i
$326$	−3.00723	+	5.20868i	−0.166555	+	0.288482i
$327$		0			0
$328$	−13.2269	+	29.7080i	−0.730331	+	1.64035i
$329$	−2.48749	−	1.10750i	−0.137140	−	0.0610586i
$330$		0			0
$331$	0.270443	−	0.120409i	0.0148649	−	0.00661827i	−0.399291	−	0.916824i	$-0.630744\pi$
$331$	0.270443	−	0.120409i	0.0148649	−	0.00661827i	0.414156	+	0.910206i	$0.364077\pi$
$332$		−	16.8557i		−	0.925079i
$333$		0			0
$334$	0.124191	−	0.382220i	0.00679542	−	0.0209141i
$335$	3.58124	−	11.8422i	0.195664	−	0.647007i
$336$		0			0
$337$	−4.66633	−	21.9534i	−0.254191	−	1.19588i	−0.901203	−	0.433396i	$-0.857315\pi$
$337$	−4.66633	−	21.9534i	−0.254191	−	1.19588i	0.647012	−	0.762480i	$-0.276018\pi$
$338$	1.10234	+	5.18609i	0.0599593	+	0.282086i
$339$		0			0
$340$	−4.60480	−	13.2426i	−0.249731	−	0.718181i
$341$	−3.27882	+	10.0912i	−0.177558	+	0.546467i
$342$		0			0
$343$		−	12.2241i		−	0.660039i
$344$	10.5627	−	4.70283i	0.569504	−	0.253560i
$345$		0			0
$346$	9.78913	+	4.35840i	0.526267	+	0.234309i
$347$	3.64075	−	8.17725i	0.195445	−	0.438978i	−0.789064	−	0.614312i	$-0.789434\pi$
$347$	3.64075	−	8.17725i	0.195445	−	0.438978i	0.984509	+	0.175334i	$0.0561005\pi$
$348$		0			0
$349$	15.7481	−	27.2765i	0.842977	−	1.46008i	−0.0443893	−	0.999014i	$-0.514134\pi$
$349$	15.7481	−	27.2765i	0.842977	−	1.46008i	0.887366	−	0.461065i	$-0.152532\pi$
$350$	−16.6993	+	8.27065i	−0.892614	+	0.442085i
$351$		0			0
$352$	19.3925	−	6.30100i	1.03362	−	0.335844i
$353$	34.5062	−	3.62675i	1.83658	−	0.193032i	0.878155	−	0.478376i	$-0.158774\pi$
$353$	34.5062	−	3.62675i	1.83658	−	0.193032i	0.958425	+	0.285343i	$0.0921077\pi$
$354$		0			0
$355$	0.121621	+	0.258764i	0.00645498	+	0.0137338i
$356$	0.589456	−	5.60829i	0.0312411	−	0.297239i
$357$		0			0
$358$	2.04250	+	4.58753i	0.107950	+	0.242459i
$359$	2.92332	−	8.99706i	0.154287	−	0.474847i	−0.843801	−	0.536656i	$-0.819687\pi$
$359$	2.92332	−	8.99706i	0.154287	−	0.474847i	0.998088	+	0.0618095i	$0.0196871\pi$
$360$		0			0
$361$	−3.76324	−	11.5821i	−0.198065	−	0.609583i
$362$	0.103653	−	0.0933296i	0.00544788	−	0.00490529i
$363$		0			0
$364$	−8.70060	+	9.66300i	−0.456036	+	0.506479i
$365$	−4.25909	−	33.8381i	−0.222931	−	1.77116i
$366$		0			0
$367$	10.4527	+	23.4771i	0.545626	+	1.22550i	0.950386	+	0.311074i	$0.100689\pi$
$367$	10.4527	+	23.4771i	0.545626	+	1.22550i	−0.404760	+	0.914423i	$0.632645\pi$
$368$			0.0785454i			0.00409446i
$369$		0			0
$370$	−16.0422	−	13.8600i	−0.833992	−	0.720546i
$371$	0.753165	+	7.16588i	0.0391024	+	0.372034i
$372$		0			0
$373$	−0.656237	−	0.590879i	−0.0339787	−	0.0305945i	0.651966	−	0.758248i	$-0.273944\pi$
$373$	−0.656237	−	0.590879i	−0.0339787	−	0.0305945i	−0.685945	+	0.727653i	$0.740611\pi$
$374$	−8.84064	−	15.3124i	−0.457139	−	0.791787i
$375$		0			0
$376$	−0.951380	+	1.64784i	−0.0490637	+	0.0849808i
$377$	10.1960	−	3.31288i	0.525121	−	0.170622i
$378$		0			0
$379$	12.6620	−	9.19945i	0.650401	−	0.472544i	−0.213007	−	0.977051i	$-0.568326\pi$
$379$	12.6620	−	9.19945i	0.650401	−	0.472544i	0.863408	+	0.504507i	$0.168326\pi$
$380$	−6.51665	+	2.26601i	−0.334297	+	0.116244i
$381$		0			0
$382$	11.2773	−	6.51095i	0.576997	−	0.333129i
$383$	−27.7506	−	2.91670i	−1.41799	−	0.149037i	−0.635692	−	0.771943i	$-0.719285\pi$
$383$	−27.7506	−	2.91670i	−1.41799	−	0.149037i	−0.782297	+	0.622906i	$0.785952\pi$
$384$		0			0
$385$	27.0213	−	20.4909i	1.37713	−	1.04431i
$386$	−1.83480	−	5.64693i	−0.0933889	−	0.287421i
$387$		0			0
$388$	−5.08663	−	1.65275i	−0.258235	−	0.0839055i
$389$	−25.8898	−	5.50305i	−1.31267	−	0.279016i	−0.502174	−	0.864767i	$-0.667466\pi$
$389$	−25.8898	−	5.50305i	−1.31267	−	0.279016i	−0.810491	+	0.585751i	$0.800800\pi$
$390$		0			0
$391$	−1.68659	+	0.358496i	−0.0852946	+	0.0181299i
$392$	−28.5343	−	2.99908i	−1.44120	−	0.151476i
$393$		0			0
$394$	−5.62035	+	2.50234i	−0.283149	+	0.126066i
$395$	26.1165	+	2.20504i	1.31407	+	0.110948i
$396$		0			0
$397$	18.3797	+	25.2976i	0.922453	+	1.26965i	0.962731	+	0.270459i	$0.0871755\pi$
$397$	18.3797	+	25.2976i	0.922453	+	1.26965i	−0.0402784	+	0.999188i	$0.512824\pi$
$398$	2.23437	−	10.5119i	0.111999	−	0.526912i
$399$		0			0
$400$	0.420353	+	1.13345i	0.0210177	+	0.0566727i
$401$	−3.80871	−	6.59689i	−0.190198	−	0.329433i	0.755118	−	0.655589i	$-0.227580\pi$
$401$	−3.80871	−	6.59689i	−0.190198	−	0.329433i	−0.945316	+	0.326156i	$0.894246\pi$
$402$		0			0
$403$	−7.65853	+	0.804944i	−0.381499	+	0.0400971i
$404$	−2.26727	+	1.64727i	−0.112801	+	0.0819545i
$405$		0			0
$406$	12.0973	+	8.78923i	0.600381	+	0.436202i
$407$	33.4112	+	19.2900i	1.65613	+	0.956168i
$408$		0			0
$409$	16.0238	−	3.40596i	0.792324	−	0.168414i	0.206066	−	0.978538i	$-0.433934\pi$
$409$	16.0238	−	3.40596i	0.792324	−	0.168414i	0.586258	+	0.810124i	$0.300600\pi$
$410$	22.4502	+	4.29319i	1.10873	+	0.212026i
$411$		0			0
$412$	−4.60936	+	4.15029i	−0.227087	+	0.204470i
$413$	13.4880	+	4.38253i	0.663703	+	0.215650i
$414$		0			0
$415$	−31.0654	+	7.27141i	−1.52494	+	0.356939i
$416$	9.90225	+	10.9976i	0.485498	+	0.539200i
$417$		0			0
$418$	−7.53521	+	4.35045i	−0.368559	+	0.212788i
$419$	−0.853915	+	8.12446i	−0.0417165	+	0.396906i	0.953662	+	0.300879i	$0.0972800\pi$
$419$	−0.853915	+	8.12446i	−0.0417165	+	0.396906i	−0.995379	+	0.0960266i	$0.969387\pi$
$420$		0			0
$421$	0.513409	+	4.88476i	0.0250220	+	0.238068i	0.999884	+	0.0152572i	$0.00485670\pi$
$421$	0.513409	+	4.88476i	0.0250220	+	0.238068i	−0.974862	+	0.222811i	$0.928477\pi$
$422$	10.2627	+	14.1254i	0.499579	+	0.687612i
$423$		0			0
$424$	5.03509			0.244526
$425$	−22.4199	+	14.1995i	−1.08752	+	0.688776i
$426$		0			0
$427$	−31.2237	−	28.1140i	−1.51102	−	1.36053i
$428$	−5.59000	+	12.5553i	−0.270203	+	0.606885i
$429$		0			0
$430$	−4.91053	−	6.47551i	−0.236807	−	0.312277i
$431$	15.7930	+	11.4743i	0.760720	+	0.552695i	0.899131	−	0.437679i	$-0.144200\pi$
$431$	15.7930	+	11.4743i	0.760720	+	0.552695i	−0.138411	+	0.990375i	$0.544200\pi$
$432$		0			0
$433$	9.07208	−	12.4866i	0.435976	−	0.600070i	−0.533336	−	0.845904i	$-0.679062\pi$
$433$	9.07208	−	12.4866i	0.435976	−	0.600070i	0.969312	+	0.245834i	$0.0790618\pi$
$434$	−7.18705	−	7.98202i	−0.344989	−	0.383149i
$435$		0			0
$436$	3.25083	−	3.61041i	0.155686	−	0.172907i
$437$	0.176415	+	0.829967i	0.00843907	+	0.0397027i
$438$		0			0
$439$	−35.3673	−	7.51755i	−1.68799	−	0.358793i	−0.738904	−	0.673811i	$-0.764656\pi$
$439$	−35.3673	−	7.51755i	−1.68799	−	0.358793i	−0.949086	+	0.315018i	$0.897990\pi$
$440$	−12.2668	−	20.2758i	−0.584798	−	0.966610i
$441$		0			0
$442$	7.54273	−	10.3817i	0.358771	−	0.493806i
$443$	3.61415	+	2.08663i	0.171713	+	0.0991388i	0.583393	−	0.812190i	$-0.301725\pi$
$443$	3.61415	+	2.08663i	0.171713	+	0.0991388i	−0.411680	+	0.911328i	$0.635058\pi$
$444$		0			0
$445$	−10.5905	+	1.33299i	−0.502036	+	0.0631897i
$446$	3.42577	+	1.52525i	0.162215	+	0.0722227i
$447$		0			0
$448$	−4.70564	+	22.1383i	−0.222321	+	1.04594i
$449$	8.79746			0.415178			0.207589	−	0.978216i	$-0.433438\pi$
$449$	8.79746			0.415178			0.207589	+	0.978216i	$0.433438\pi$
$450$		0			0
$451$	−41.5949			−1.95863
$452$	1.76216	−	8.29031i	0.0828850	−	0.389943i
$453$		0			0
$454$	9.68718	+	4.31301i	0.454642	+	0.202420i
$455$	21.5624	+	11.8668i	1.01086	+	0.556326i
$456$		0			0
$457$	−16.6943	−	9.63843i	−0.780924	−	0.450867i	0.0558334	−	0.998440i	$-0.482218\pi$
$457$	−16.6943	−	9.63843i	−0.780924	−	0.450867i	−0.836758	+	0.547573i	$0.815552\pi$
$458$	4.09082	−	5.63053i	0.191151	−	0.263097i
$459$		0			0
$460$	−0.835564	+	0.195578i	−0.0389584	+	0.00911889i
$461$	−4.42914	−	0.941443i	−0.206286	−	0.0438474i	0.103610	−	0.994618i	$-0.466961\pi$
$461$	−4.42914	−	0.941443i	−0.206286	−	0.0438474i	−0.309895	+	0.950771i	$0.600294\pi$
$462$		0			0
$463$	2.10589	+	9.90745i	0.0978691	+	0.460438i	0.999604	+	0.0281481i	$0.00896099\pi$
$463$	2.10589	+	9.90745i	0.0978691	+	0.460438i	−0.901735	+	0.432290i	$0.857706\pi$
$464$	0.649077	−	0.720873i	0.0301326	−	0.0334657i
$465$		0			0
$466$	6.64442	+	7.37937i	0.307797	+	0.341843i
$467$	3.94322	−	5.42737i	0.182470	−	0.251149i	−0.707977	−	0.706236i	$-0.750392\pi$
$467$	3.94322	−	5.42737i	0.182470	−	0.251149i	0.890447	+	0.455087i	$0.150392\pi$
$468$		0			0
$469$	−18.4381	−	13.3961i	−0.851394	−	0.618574i
$470$	1.28014	+	0.387132i	0.0590484	+	0.0178571i
$471$		0			0
$472$	4.03095	−	9.05367i	0.185540	−	0.416729i
$473$	10.9905	+	9.89586i	0.505342	+	0.455012i
$474$		0			0
$475$	6.98752	+	11.0328i	0.320609	+	0.506218i
$476$	−25.8276			−1.18381
$477$		0			0
$478$	3.67095	+	5.05263i	0.167905	+	0.231102i
$479$	−0.732324	−	6.96759i	−0.0334607	−	0.318357i	−0.998431	−	0.0559979i	$-0.982166\pi$
$479$	−0.732324	−	6.96759i	−0.0334607	−	0.318357i	0.964970	−	0.262360i	$-0.0845007\pi$
$480$		0			0
$481$	−2.92679	+	27.8466i	−0.133450	+	1.26969i
$482$	22.5868	−	13.0405i	1.02880	−	0.593978i
$483$		0			0
$484$	2.02011	+	2.24356i	0.0918230	+	0.101980i
$485$	−0.851716	+	10.0877i	−0.0386744	+	0.458060i
$486$		0			0
$487$	−3.68447	−	1.19716i	−0.166959	−	0.0542483i	0.224345	−	0.974510i	$-0.427976\pi$
$487$	−3.68447	−	1.19716i	−0.166959	−	0.0542483i	−0.391304	+	0.920262i	$0.627976\pi$
$488$	−21.8191	+	19.6460i	−0.987705	+	0.889333i
$489$		0			0
$490$	2.51841	+	20.0086i	0.113770	+	0.903895i
$491$	2.24217	−	0.476588i	0.101188	−	0.0215081i	−0.157040	−	0.987592i	$-0.550195\pi$
$491$	2.24217	−	0.476588i	0.101188	−	0.0215081i	0.258227	+	0.966084i	$0.416862\pi$
$492$		0			0
$493$	18.4417	+	10.6473i	0.830572	+	0.479531i
$494$	−5.10879	−	3.71175i	−0.229855	−	0.167000i
$495$		0			0
$496$	−0.563703	+	0.409554i	−0.0253110	+	0.0183895i
$497$	0.523823	−	0.0550560i	0.0234967	−	0.00246960i
$498$		0			0
$499$	−1.86581	−	3.23167i	−0.0835250	−	0.144670i	0.821237	−	0.570588i	$-0.193285\pi$
$499$	−1.86581	−	3.23167i	−0.0835250	−	0.144670i	−0.904762	+	0.425918i	$0.859951\pi$
$500$	−11.0110	+	7.29401i	−0.492425	+	0.326198i
$501$		0			0
$502$	2.29170	−	10.7816i	0.102284	−	0.481207i
$503$	23.9511	+	32.9658i	1.06792	+	1.46987i	0.872160	+	0.489221i	$0.162719\pi$
$503$	23.9511	+	32.9658i	1.06792	+	1.46987i	0.195765	+	0.980651i	$0.437281\pi$
$504$		0			0
$505$	4.01402	+	3.46800i	0.178621	+	0.154324i
$506$	−0.988659	+	0.440179i	−0.0439513	+	0.0195684i
$507$		0			0
$508$	22.7634	+	2.39253i	1.00996	+	0.106151i
$509$	−17.5363	+	3.72745i	−0.777282	+	0.165216i	−0.579437	−	0.815017i	$-0.696728\pi$
$509$	−17.5363	+	3.72745i	−0.777282	+	0.165216i	−0.197845	+	0.980233i	$0.563394\pi$
$510$		0			0
$511$	−61.4537	−	13.0624i	−2.71855	−	0.577846i
$512$	2.59725	+	0.843899i	0.114784	+	0.0372954i
$513$		0			0
$514$	−3.05681	−	9.40788i	−0.134830	−	0.414964i
$515$	9.63749	+	6.70474i	0.424679	+	0.295446i
$516$		0			0
$517$	−2.42044	−	0.254399i	−0.106451	−	0.0111884i
$518$	−33.8218	+	19.5270i	−1.48604	+	0.857968i
$519$		0			0
$520$	9.82212	−	14.1185i	0.430728	−	0.619135i
$521$	23.3109	−	16.9363i	1.02127	−	0.741995i	0.0547257	−	0.998501i	$-0.482572\pi$
$521$	23.3109	−	16.9363i	1.02127	−	0.741995i	0.966542	+	0.256507i	$0.0825716\pi$
$522$		0			0
$523$	21.2772	−	6.91337i	0.930385	−	0.302300i	0.195665	−	0.980671i	$-0.437313\pi$
$523$	21.2772	−	6.91337i	0.930385	−	0.302300i	0.734720	+	0.678370i	$0.237313\pi$
$524$	4.16968	−	7.22211i	0.182154	−	0.315499i
$525$		0			0
$526$	−8.87233	−	15.3673i	−0.386852	−	0.670047i
$527$	−11.3671	−	10.2350i	−0.495160	−	0.445844i
$528$		0			0
$529$	−2.39312	−	22.7690i	−0.104049	−	0.989958i
$530$	−0.806570	−	3.44588i	−0.0350352	−	0.149680i
$531$		0			0
$532$			12.7097i			0.551036i
$533$	−12.2786	−	27.5782i	−0.531846	−	1.19454i
$534$		0			0
$535$	25.5512	+	4.88621i	1.10467	+	0.211249i
$536$	−10.6567	+	11.8355i	−0.460299	+	0.511214i
$537$		0			0
$538$	−14.1781	+	12.7660i	−0.611263	+	0.550383i
$539$	−11.3405	−	34.9025i	−0.488470	−	1.50336i
$540$		0			0
$541$	−3.03790	+	9.34969i	−0.130609	+	0.401975i	−0.994881	−	0.101050i	$-0.967780\pi$
$541$	−3.03790	+	9.34969i	−0.130609	+	0.401975i	0.864272	+	0.503025i	$0.167780\pi$
$542$	2.71002	+	6.08680i	0.116405	+	0.261450i
$543$		0			0
$544$	−3.07259	+	29.2337i	−0.131736	+	1.25338i
$545$	−8.05642	−	4.43383i	−0.345099	−	0.189925i
$546$		0			0
$547$	27.4562	−	2.88577i	1.17394	−	0.123386i	0.502591	−	0.864524i	$-0.332380\pi$
$547$	27.4562	−	2.88577i	1.17394	−	0.123386i	0.671353	+	0.741138i	$0.265714\pi$
$548$	−4.24196	+	1.37830i	−0.181208	+	0.0588779i
$549$		0			0
$550$	−11.9112	+	11.6431i	−0.507894	+	0.496462i
$551$	5.23951	−	9.07510i	0.223211	−	0.386612i
$552$		0			0
$553$	19.6380	−	44.1076i	0.835091	−	1.87565i
$554$	−26.7971	−	11.9308i	−1.13850	−	0.506893i
$555$		0			0
$556$	−14.5958	+	6.49848i	−0.619001	+	0.275597i
$557$		−	28.1811i		−	1.19407i	−0.802214	−	0.597036i	$-0.796345\pi$
$557$		−	28.1811i		−	1.19407i	0.802214	−	0.597036i	$-0.203655\pi$
$558$		0			0
$559$	−3.31681	+	10.2081i	−0.140286	+	0.431757i
$560$	2.22649	−	0.0456242i	0.0940864	−	0.00192797i
$561$		0			0
$562$	−0.188496	−	0.886802i	−0.00795120	−	0.0374075i
$563$	−1.62108	−	7.62657i	−0.0683203	−	0.321422i	0.930695	−	0.365797i	$-0.119204\pi$
$563$	−1.62108	−	7.62657i	−0.0683203	−	0.321422i	−0.999015	+	0.0443754i	$0.985870\pi$
$564$		0			0
$565$	−16.0394	+	0.328671i	−0.674781	+	0.0138273i
$566$	−0.845471	+	2.60209i	−0.0355378	+	0.109374i
$567$		0			0
$568$		−	0.368063i		−	0.0154436i
$569$	19.8548	−	8.83994i	0.832358	−	0.370590i	0.0541009	−	0.998535i	$-0.482771\pi$
$569$	19.8548	−	8.83994i	0.832358	−	0.370590i	0.778257	+	0.627946i	$0.216104\pi$
$570$		0			0
$571$	−2.12985	−	0.948272i	−0.0891316	−	0.0396839i	0.361687	−	0.932300i	$-0.382201\pi$
$571$	−2.12985	−	0.948272i	−0.0891316	−	0.0396839i	−0.450818	+	0.892616i	$0.648868\pi$
$572$	−4.72716	+	10.6174i	−0.197653	+	0.443935i
$573$		0			0
$574$	21.0530	−	36.4649i	0.878736	−	1.52201i
$575$	0.720909	+	1.45559i	0.0300640	+	0.0607022i
$576$		0			0
$577$	−27.2147	+	8.84261i	−1.13296	+	0.368123i	−0.814702	−	0.579880i	$-0.803099\pi$
$577$	−27.2147	+	8.84261i	−1.13296	+	0.368123i	−0.318263	+	0.948003i	$0.603099\pi$
$578$	10.0522	−	1.05653i	0.418117	−	0.0439459i
$579$		0			0
$580$	9.28483	+	5.10989i	0.385532	+	0.212176i
$581$	−6.14355	+	58.4520i	−0.254878	+	2.42500i
$582$		0			0
$583$	2.61949	+	5.88348i	0.108488	+	0.243669i
$584$	−13.5668	+	41.7544i	−0.561399	+	1.72781i
$585$		0			0
$586$	4.91021	+	15.1121i	0.202839	+	0.624274i
$587$	−23.7934	+	21.4236i	−0.982057	+	0.884248i	−0.993286	−	0.115689i	$-0.963093\pi$
$587$	−23.7934	+	21.4236i	−0.982057	+	0.884248i	0.0112282	+	0.999937i	$0.496426\pi$
$588$		0			0
$589$	−5.03662	+	5.59373i	−0.207530	+	0.230486i
$590$	−6.84181	−	1.30837i	−0.281673	−	0.0538649i
$591$		0			0
$592$	1.03046	+	2.31446i	0.0423518	+	0.0951236i
$593$		−	23.1107i		−	0.949044i	−0.880244	−	0.474522i	$-0.842621\pi$
$593$		−	23.1107i		−	0.949044i	0.880244	−	0.474522i	$-0.157379\pi$
$594$		0			0
$595$	11.1418	+	47.6008i	0.456770	+	1.95144i
$596$	1.73592	+	16.5162i	0.0711061	+	0.676529i
$597$		0			0
$598$	−0.583695	−	0.525561i	−0.0238691	−	0.0214918i
$599$	13.5846	+	23.5292i	0.555051	+	0.961377i	0.997900	+	0.0647805i	$0.0206347\pi$
$599$	13.5846	+	23.5292i	0.555051	+	0.961377i	−0.442848	+	0.896597i	$0.646032\pi$
$600$		0			0
$601$	15.1138	−	26.1780i	0.616507	−	1.06782i	−0.373611	−	0.927585i	$-0.621881\pi$
$601$	15.1138	−	26.1780i	0.616507	−	1.06782i	0.990118	−	0.140236i	$-0.0447860\pi$
$602$	−14.2381	+	4.62625i	−0.580303	+	0.188552i
$603$		0			0
$604$	5.83846	−	4.24189i	0.237564	−	0.172600i
$605$	3.26346	−	4.69094i	0.132678	−	0.190714i
$606$		0			0
$607$	−11.3751	+	6.56741i	−0.461701	+	0.266563i	−0.712759	−	0.701409i	$-0.752555\pi$
$607$	−11.3751	+	6.56741i	−0.461701	+	0.266563i	0.251058	+	0.967972i	$0.419221\pi$
$608$	14.3858	+	1.51201i	0.583422	+	0.0613201i
$609$		0			0
$610$	16.9404	+	11.7853i	0.685897	+	0.477174i
$611$	−0.545832	−	1.67990i	−0.0220820	−	0.0679614i
$612$		0			0
$613$	−9.49264	−	3.08435i	−0.383404	−	0.124576i	0.110972	−	0.993824i	$-0.464604\pi$
$613$	−9.49264	−	3.08435i	−0.383404	−	0.124576i	−0.494376	+	0.869248i	$0.664604\pi$
$614$	19.7437	+	4.19665i	0.796790	+	0.169363i
$615$		0			0
$616$	−42.7008	+	9.07634i	−1.72047	+	0.365696i
$617$	−5.85622	−	0.615513i	−0.235762	−	0.0247796i	−0.0140896	−	0.999901i	$-0.504485\pi$
$617$	−5.85622	−	0.615513i	−0.235762	−	0.0247796i	−0.221673	+	0.975121i	$0.571152\pi$
$618$		0			0
$619$	14.3741	−	6.39976i	0.577743	−	0.257228i	−0.0969950	−	0.995285i	$-0.530923\pi$
$619$	14.3741	−	6.39976i	0.577743	−	0.257228i	0.674738	+	0.738057i	$0.264256\pi$
$620$	−5.76045	−	4.97687i	−0.231345	−	0.199876i
$621$		0			0
$622$	14.8158	+	20.3921i	0.594058	+	0.817650i
$623$	−4.08820	+	19.2335i	−0.163790	+	0.770573i
$624$		0			0
$625$	18.1930	+	17.1468i	0.727721	+	0.685874i
$626$	7.74443	+	13.4137i	0.309530	+	0.536121i
$627$		0			0
$628$	−21.7857	+	2.28977i	−0.869345	+	0.0913719i
$629$	−44.9947	+	32.6906i	−1.79406	+	1.30346i
$630$		0			0
$631$	11.9212	+	8.66123i	0.474574	+	0.344798i	0.799221	−	0.601037i	$-0.205246\pi$
$631$	11.9212	+	8.66123i	0.474574	+	0.344798i	−0.324647	+	0.945835i	$0.605246\pi$
$632$	−29.2190	−	16.8696i	−1.16227	−	0.671038i
$633$		0			0
$634$	−17.9043	+	3.80567i	−0.711070	+	0.151143i
$635$	−5.41044	−	42.9854i	−0.214707	−	1.70582i
$636$		0			0
$637$	19.7934	−	17.8220i	0.784241	−	0.706134i
$638$	12.7112	+	4.13013i	0.503242	+	0.163513i
$639$		0			0
$640$	−1.14848	+	13.6027i	−0.0453978	+	0.537692i
$641$	−24.0727	−	26.7354i	−0.950814	−	1.05599i	−0.998368	−	0.0571168i	$-0.981809\pi$
$641$	−24.0727	−	26.7354i	−0.950814	−	1.05599i	0.0475539	−	0.998869i	$-0.484857\pi$
$642$		0			0
$643$	−17.0530	+	9.84554i	−0.672504	+	0.388270i	−0.797025	−	0.603947i	$-0.793594\pi$
$643$	−17.0530	+	9.84554i	−0.672504	+	0.388270i	0.124521	+	0.992217i	$0.460261\pi$
$644$	−0.165243	+	1.57218i	−0.00651147	+	0.0619525i
$645$		0			0
$646$	−1.31112	−	12.4744i	−0.0515852	−	0.490801i
$647$	26.9791	+	37.1335i	1.06066	+	1.45987i	0.879189	+	0.476473i	$0.158085\pi$
$647$	26.9791	+	37.1335i	1.06066	+	1.45987i	0.181469	+	0.983397i	$0.441915\pi$
$648$		0			0
$649$	12.6763			0.497587
$650$	−11.2357	−	4.46037i	−0.440700	−	0.174950i
$651$		0			0
$652$	5.83567	+	5.25446i	0.228542	+	0.205780i
$653$	−9.11562	+	20.4740i	−0.356722	+	0.801210i	0.642663	+	0.766149i	$0.277829\pi$
$653$	−9.11562	+	20.4740i	−0.356722	+	0.801210i	−0.999385	+	0.0350615i	$0.988837\pi$
$654$		0			0
$655$	−15.1092	−	4.56925i	−0.590366	−	0.178535i
$656$	−2.20981	−	1.60552i	−0.0862786	−	0.0626851i
$657$		0			0
$658$	1.44812	−	1.99316i	0.0564535	−	0.0777015i
$659$	12.5963	+	13.9896i	0.490681	+	0.544956i	0.936730	−	0.350052i	$-0.113836\pi$
$659$	12.5963	+	13.9896i	0.490681	+	0.544956i	−0.446050	+	0.895008i	$0.647169\pi$
$660$		0			0
$661$	21.3856	−	23.7511i	0.831804	−	0.923812i	−0.166255	−	0.986083i	$-0.553167\pi$
$661$	21.3856	−	23.7511i	0.831804	−	0.923812i	0.998059	+	0.0622705i	$0.0198342\pi$
$662$	0.0556900	+	0.262001i	0.00216445	+	0.0101830i
$663$		0			0
$664$	40.1737	+	8.53918i	1.55904	+	0.331384i
$665$	23.4242	−	5.48285i	0.908352	−	0.212616i
$666$		0			0
$667$	0.766111	−	1.05446i	0.0296639	−	0.0408289i
$668$	−0.454420	−	0.262360i	−0.0175820	−	0.0101510i
$669$		0			0
$670$	9.80696	+	5.39724i	0.378876	+	0.208514i
$671$	−34.3076	−	15.2747i	−1.32443	−	0.589674i
$672$		0			0
$673$	−7.84189	+	36.8932i	−0.302283	+	1.42213i	0.520544	+	0.853835i	$0.325729\pi$
$673$	−7.84189	+	36.8932i	−0.302283	+	1.42213i	−0.822826	+	0.568293i	$0.807604\pi$
$674$	20.3072			0.782204
$675$		0			0
$676$	6.92239			0.266246
$677$	4.62758	−	21.7711i	0.177852	−	0.836730i	−0.795236	−	0.606299i	$-0.792653\pi$
$677$	4.62758	−	21.7711i	0.177852	−	0.836730i	0.973089	−	0.230430i	$-0.0740134\pi$
$678$		0			0
$679$	17.0369	+	7.58533i	0.653817	+	0.291098i
$680$	33.8950	−	4.26626i	1.29981	−	0.163604i
$681$		0			0
$682$	−8.31417	−	4.80019i	−0.318366	−	0.183809i
$683$	−12.8808	+	17.7289i	−0.492869	+	0.678376i	−0.980914	−	0.194443i	$-0.937710\pi$
$683$	−12.8808	+	17.7289i	−0.492869	+	0.678376i	0.488045	+	0.872818i	$0.337710\pi$
$684$		0			0
$685$	4.37016	+	7.22342i	0.166975	+	0.275993i
$686$	10.8187	+	2.29958i	0.413059	+	0.0877984i
$687$		0			0
$688$	0.201920	+	0.949958i	0.00769812	+	0.0362168i
$689$	−3.12760	+	3.47355i	−0.119152	+	0.132332i
$690$		0			0
$691$	18.6614	+	20.7255i	0.709911	+	0.788436i	0.984921	−	0.173005i	$-0.0553477\pi$
$691$	18.6614	+	20.7255i	0.709911	+	0.788436i	−0.275010	+	0.961441i	$0.588681\pi$
$692$	8.22343	−	11.3186i	0.312608	−	0.430268i
$693$		0			0
$694$	6.55221	+	4.76046i	0.248718	+	0.180705i
$695$	18.2733	+	24.0970i	0.693146	+	0.914050i
$696$		0			0
$697$	24.3891	−	54.7788i	0.923803	−	2.07489i
$698$	21.1780	+	19.0688i	0.801599	+	0.721763i
$699$		0			0
$700$	6.02932	+	23.5717i	0.227887	+	0.890928i
$701$	17.1956			0.649469			0.324734	−	0.945805i	$-0.394725\pi$
$701$	17.1956			0.649469			0.324734	+	0.945805i	$0.394725\pi$
$702$		0			0
$703$	16.0869	+	22.1418i	0.606730	+	0.835093i
$704$	2.11458	+	20.1188i	0.0796961	+	0.758257i
$705$		0			0
$706$	−3.28149	+	31.2213i	−0.123500	+	1.17503i
$707$	8.46277	−	4.88599i	0.318275	−	0.183756i
$708$		0			0
$709$	−0.0856962	−	0.0951753i	−0.00321839	−	0.00357438i	0.741533	−	0.670916i	$-0.234099\pi$
$709$	−0.0856962	−	0.0951753i	−0.00321839	−	0.00357438i	−0.744752	+	0.667341i	$0.767432\pi$
$710$	−0.251893	+	0.0589599i	−0.00945337	+	0.00221273i
$711$		0			0
$712$	13.0681	+	4.24608i	0.489748	+	0.159129i
$713$	−0.695751	+	0.626457i	−0.0260561	+	0.0234610i
$714$		0			0
$715$	21.6073	+	4.13200i	0.808066	+	0.154528i
$716$	6.41318	−	1.36316i	0.239672	−	0.0509438i
$717$		0			0
$718$	7.41273	+	4.27974i	0.276641	+	0.159719i
$719$	−25.4872	−	18.5176i	−0.950513	−	0.690588i	0.000415006	−	1.00000i	$-0.499868\pi$
$719$	−25.4872	−	18.5176i	−0.950513	−	0.690588i	−0.950928	+	0.309412i	$0.899868\pi$
$720$		0			0
$721$	17.4969	−	12.7123i	0.651620	−	0.473430i
$722$	10.9584	−	1.15177i	0.407830	−	0.0428646i
$723$		0			0
$724$	−0.0910538	−	0.157710i	−0.00338399	−	0.00586124i
$725$	5.41222	−	19.3165i	0.201005	−	0.717395i
$726$		0			0
$727$	2.65171	−	12.4753i	0.0983465	−	0.462684i	−0.901223	−	0.433355i	$-0.857330\pi$
$727$	2.65171	−	12.4753i	0.0983465	−	0.462684i	0.999570	−	0.0293289i	$-0.00933703\pi$
$728$	−18.6229	−	25.6322i	−0.690210	−	0.949992i
$729$		0			0
$730$	30.7489	+	2.59615i	1.13807	+	0.0960880i
$731$	−19.4767	+	8.67158i	−0.720372	+	0.320730i
$732$		0			0
$733$	−32.5619	−	3.42239i	−1.20270	−	0.126409i	−0.518096	−	0.855323i	$-0.673359\pi$
$733$	−32.5619	−	3.42239i	−1.20270	−	0.126409i	−0.684606	+	0.728914i	$0.740026\pi$
$734$	−22.7443	+	4.83445i	−0.839507	+	0.178443i
$735$		0			0
$736$	1.75985	+	0.374068i	0.0648691	+	0.0137883i
$737$	−19.3738	−	6.29492i	−0.713642	−	0.231876i
$738$		0			0
$739$	−4.71375	−	14.5074i	−0.173398	−	0.533665i	0.826158	−	0.563438i	$-0.190522\pi$
$739$	−4.71375	−	14.5074i	−0.173398	−	0.533665i	−0.999557	+	0.0297729i	$0.990522\pi$
$740$	−22.0553	+	16.7250i	−0.810768	+	0.614825i
$741$		0			0
$742$	−6.48370	−	0.681464i	−0.238024	−	0.0250173i
$743$	11.8000	−	6.81274i	0.432901	−	0.249935i	−0.267681	−	0.963508i	$-0.586257\pi$
$743$	11.8000	−	6.81274i	0.432901	−	0.249935i	0.700582	+	0.713572i	$0.252924\pi$
$744$		0			0
$745$	29.6908	−	10.3243i	1.08778	−	0.378252i
$746$	0.646395	−	0.469634i	0.0236662	−	0.0171945i
$747$		0			0
$748$	−21.9553	+	7.13372i	−0.802766	+	0.260835i
$749$	23.9610	−	41.5017i	0.875517	−	1.51644i
$750$		0			0
$751$	−1.10797	−	1.91906i	−0.0404303	−	0.0700273i	0.845102	−	0.534605i	$-0.179540\pi$
$751$	−1.10797	−	1.91906i	−0.0404303	−	0.0700273i	−0.885532	+	0.464578i	$0.846206\pi$
$752$	−0.118771	−	0.106942i	−0.00433114	−	0.00389978i
$753$		0			0
$754$	1.01394	+	9.64698i	0.0369255	+	0.351322i
$755$	−10.3365	−	8.93048i	−0.376185	−	0.325013i
$756$		0			0
$757$		−	8.94324i		−	0.325048i	−0.986705	−	0.162524i	$-0.948037\pi$
$757$		−	8.94324i		−	0.325048i	0.986705	−	0.162524i	$-0.0519634\pi$
$758$	5.75983	+	12.9368i	0.209206	+	0.469885i
$759$		0			0
$760$	−2.09941	−	16.6796i	−0.0761537	−	0.605034i
$761$	−20.0344	+	22.2505i	−0.726246	+	0.806578i	−0.987320	−	0.158740i	$-0.949257\pi$
$761$	−20.0344	+	22.2505i	−0.726246	+	0.806578i	0.261074	+	0.965319i	$0.415923\pi$
$762$		0			0
$763$	−12.5891	+	11.3352i	−0.455755	+	0.410363i
$764$	−5.25384	−	16.1696i	−0.190077	−	0.584997i
$765$		0			0
$766$	7.80177	−	24.0114i	0.281890	−	0.867567i
$767$	3.74197	+	8.40460i	0.135115	+	0.303473i
$768$		0			0
$769$	−1.82003	+	17.3164i	−0.0656319	+	0.624446i	0.911425	+	0.411467i	$0.134983\pi$
$769$	−1.82003	+	17.3164i	−0.0656319	+	0.624446i	−0.977057	+	0.212979i	$0.931683\pi$
$770$	13.0518	+	27.7694i	0.470356	+	1.00074i
$771$		0			0
$772$	−7.70976	+	0.810328i	−0.277480	+	0.0291643i
$773$	15.2151	−	4.94368i	0.547248	−	0.177812i	−0.0223274	−	0.999751i	$-0.507108\pi$
$773$	15.2151	−	4.94368i	0.547248	−	0.177812i	0.569576	+	0.821939i	$0.307108\pi$
$774$		0			0
$775$	−6.68745	+	12.7636i	−0.240220	+	0.458481i
$776$	6.51603	−	11.2861i	0.233912	−	0.405147i
$777$		0			0
$778$	9.74071	−	21.8780i	0.349221	−	0.784364i
$779$	−26.9565	−	12.0018i	−0.965816	−	0.430009i
$780$		0			0
$781$	0.430080	−	0.191484i	0.0153895	−	0.00685184i
$782$		−	1.56012i		−	0.0557899i
$783$		0			0
$784$	0.744715	−	2.29200i	0.0265969	−	0.0818570i
$785$	13.6182	+	39.1637i	0.486056	+	1.39781i
$786$		0			0
$787$	1.33959	+	6.30227i	0.0477512	+	0.224652i	0.995552	−	0.0942104i	$-0.0300327\pi$
$787$	1.33959	+	6.30227i	0.0477512	+	0.224652i	−0.947801	+	0.318862i	$0.896699\pi$
$788$	1.67006	+	7.85701i	0.0594934	+	0.279895i
$789$		0			0
$790$	−6.86453	+	22.6991i	−0.244229	+	0.807597i
$791$	−9.13242	+	28.1067i	−0.324712	+	0.999360i
$792$		0			0
$793$		−	27.2556i		−	0.967876i
$794$	−25.8466	+	11.5077i	−0.917263	+	0.408392i
$795$		0			0
$796$	−12.8182	−	5.70701i	−0.454328	−	0.202280i
$797$	12.2495	−	27.5128i	0.433899	−	0.974554i	−0.555790	−	0.831323i	$-0.687584\pi$
$797$	12.2495	−	27.5128i	0.433899	−	0.974554i	0.989689	−	0.143231i	$-0.0457492\pi$
$798$		0			0
$799$	1.75426	−	3.03846i	0.0620611	−	0.107493i
$800$	27.3976	−	4.02023i	0.968650	−	0.142137i
$801$		0			0
$802$	6.55493	−	2.12983i	0.231463	−	0.0752067i
$803$	−55.8479	+	5.86985i	−1.97083	+	0.207143i
$804$		0			0
$805$	2.96884	−	0.373678i	0.104638	−	0.0131704i
$806$	0.728314	−	6.92945i	0.0256538	−	0.244079i
$807$		0			0
$808$	−2.77746	−	6.23828i	−0.0977107	−	0.219462i
$809$	−15.0501	+	46.3195i	−0.529134	+	1.62851i	0.226858	+	0.973928i	$0.427155\pi$
$809$	−15.0501	+	46.3195i	−0.529134	+	1.62851i	−0.755993	+	0.654580i	$0.772845\pi$
$810$		0			0
$811$	−1.33531	−	4.10967i	−0.0468891	−	0.144310i	0.924871	−	0.380281i	$-0.124173\pi$
$811$	−1.33531	−	4.10967i	−0.0468891	−	0.144310i	−0.971760	+	0.235971i	$0.924173\pi$
$812$	14.5086	−	13.0636i	0.509152	−	0.458442i
$813$		0			0
$814$	−23.3575	+	25.9411i	−0.818678	+	0.909234i
$815$	7.16660	−	13.0220i	0.251035	−	0.456139i
$816$		0			0
$817$	4.26726	+	9.58443i	0.149293	+	0.335317i
$818$			14.8222i			0.518247i
$819$		0			0
$820$	11.5771	−	27.5057i	0.404288	−	0.960539i
$821$	−2.49972	−	23.7833i	−0.0872409	−	0.830042i	−0.947408	−	0.320029i	$-0.896307\pi$
$821$	−2.49972	−	23.7833i	−0.0872409	−	0.830042i	0.860167	−	0.510013i	$-0.170359\pi$
$822$		0			0
$823$	−21.9352	−	19.7505i	−0.764612	−	0.688459i	0.191490	−	0.981495i	$-0.438668\pi$
$823$	−21.9352	−	19.7505i	−0.764612	−	0.688459i	−0.956102	+	0.293035i	$0.905335\pi$
$824$	−7.55661	−	13.0884i	−0.263247	−	0.455957i
$825$		0			0
$826$	−6.41601	+	11.1129i	−0.223242	+	0.386666i
$827$	32.0673	−	10.4193i	1.11509	−	0.362315i	0.307199	−	0.951645i	$-0.400608\pi$
$827$	32.0673	−	10.4193i	1.11509	−	0.362315i	0.807892	+	0.589330i	$0.200608\pi$
$828$		0			0
$829$	−28.9771	+	21.0531i	−1.00642	+	0.731204i	−0.963454	−	0.267873i	$-0.913679\pi$
$829$	−28.9771	+	21.0531i	−1.00642	+	0.731204i	−0.0429613	+	0.999077i	$0.513679\pi$
$830$	−0.591420	−	28.8617i	−0.0205285	−	1.00180i
$831$		0			0
$832$	−12.7150	+	7.34099i	−0.440812	+	0.254503i
$833$	52.6147	+	5.53002i	1.82299	+	0.191604i
$834$		0			0
$835$	−0.287501	+	0.950684i	−0.00994937	+	0.0328998i
$836$	3.51048	+	10.8042i	0.121413	+	0.373670i
$837$		0			0
$838$	−7.02974	−	2.28410i	−0.242838	−	0.0789030i
$839$	−52.2463	−	11.1053i	−1.80374	−	0.383397i	−0.821379	−	0.570382i	$-0.806795\pi$
$839$	−52.2463	−	11.1053i	−1.80374	−	0.383397i	−0.982363	+	0.186985i	$0.940128\pi$
$840$		0			0
$841$	12.6213	−	2.68274i	0.435218	−	0.0925084i
$842$	−4.41973	−	0.464533i	−0.152314	−	0.0160089i
$843$		0			0
$844$	20.8253	−	9.27204i	0.716838	−	0.319157i
$845$	−2.98625	−	12.7581i	−0.102730	−	0.438891i
$846$		0			0
$847$	−6.18756	−	8.51644i	−0.212607	−	0.292628i
$848$	−0.0879307	+	0.413681i	−0.00301955	+	0.0142059i
$849$		0			0
$850$	−8.34934	−	22.5134i	−0.286380	−	0.772205i
$851$	1.70207	+	2.94807i	0.0583461	+	0.101058i
$852$		0			0
$853$	−26.1707	+	2.75065i	−0.896068	+	0.0941806i	−0.541355	−	0.840794i	$-0.682088\pi$
$853$	−26.1707	+	2.75065i	−0.896068	+	0.0941806i	−0.354714	+	0.934975i	$0.615422\pi$
$854$	30.7554	−	22.3451i	1.05243	−	0.764635i
$855$		0			0
$856$	−27.0923	−	19.6837i	−0.925995	−	0.672775i
$857$	13.6272	+	7.86766i	0.465496	+	0.268754i	0.714352	−	0.699786i	$-0.246721\pi$
$857$	13.6272	+	7.86766i	0.465496	+	0.268754i	−0.248856	+	0.968540i	$0.580055\pi$
$858$		0			0
$859$	−29.6447	+	6.30117i	−1.01146	+	0.214993i	−0.683697	−	0.729766i	$-0.739629\pi$
$859$	−29.6447	+	6.30117i	−1.01146	+	0.214993i	−0.327766	+	0.944759i	$0.606296\pi$
$860$	−9.60285	+	4.51342i	−0.327455	+	0.153906i
$861$		0			0
$862$	−13.1260	+	11.8187i	−0.447073	+	0.402547i
$863$	8.32256	+	2.70416i	0.283303	+	0.0920508i	0.447222	−	0.894423i	$-0.352413\pi$
$863$	8.32256	+	2.70416i	0.283303	+	0.0920508i	−0.163919	+	0.986474i	$0.552413\pi$
$864$		0			0
$865$	−24.4078	−	10.2732i	−0.829891	−	0.349299i
$866$	9.34442	+	10.3780i	0.317536	+	0.352660i
$867$		0			0
$868$	−12.1448	+	7.01180i	−0.412221	+	0.237996i
$869$	4.51093	−	42.9187i	0.153023	−	1.45592i
$870$		0			0
$871$	−1.54539	−	14.7034i	−0.0523636	−	0.498207i
$872$	6.95811	+	9.57701i	0.235631	+	0.324318i
$873$		0			0
$874$	−0.767732			−0.0259689
$875$	40.8421	−	21.2808i	1.38072	−	0.719421i
$876$		0			0
$877$	6.09724	+	5.48998i	0.205889	+	0.185384i	0.765624	−	0.643288i	$-0.222430\pi$
$877$	6.09724	+	5.48998i	0.205889	+	0.185384i	−0.559735	+	0.828672i	$0.689097\pi$
$878$	13.3065	−	29.8869i	0.449073	−	1.00863i
$879$		0			0
$880$	1.88007	−	0.653751i	0.0633772	−	0.0220379i
$881$	−14.6130	−	10.6169i	−0.492323	−	0.357694i	0.313754	−	0.949504i	$-0.398413\pi$
$881$	−14.6130	−	10.6169i	−0.492323	−	0.357694i	−0.806077	+	0.591811i	$0.798413\pi$
$882$		0			0
$883$	−1.06733	+	1.46905i	−0.0359185	+	0.0494375i	−0.826599	−	0.562792i	$-0.809727\pi$
$883$	−1.06733	+	1.46905i	−0.0359185	+	0.0494375i	0.790680	+	0.612230i	$0.209727\pi$
$884$	−11.2109	−	12.4510i	−0.377064	−	0.418771i
$885$		0			0
$886$	−2.52662	+	2.80609i	−0.0848834	+	0.0942725i
$887$	−3.41036	−	16.0445i	−0.114509	−	0.538721i	−0.997583	−	0.0694876i	$-0.977864\pi$
$887$	−3.41036	−	16.0445i	−0.114509	−	0.538721i	0.883074	−	0.469234i	$-0.155470\pi$
$888$		0			0
$889$	−78.0664	−	16.5935i	−2.61826	−	0.556529i
$890$	0.812532	−	9.62363i	0.0272361	−	0.322585i
$891$		0			0
$892$	2.87784	−	3.96101i	0.0963572	−	0.132624i
$893$	−1.49522	−	0.863264i	−0.0500356	−	0.0288880i
$894$		0			0
$895$	−5.27892	−	11.2315i	−0.176455	−	0.375429i
$896$	22.9732	+	10.2283i	0.767481	+	0.341704i
$897$		0			0
$898$	−1.65497	+	7.78600i	−0.0552269	+	0.259822i
$899$	11.5623			0.385625
$900$		0			0
$901$	−9.28424			−0.309303
$902$	7.82478	−	36.8127i	0.260537	−	1.22573i
$903$		0			0
$904$	18.8663	+	8.39981i	0.627483	+	0.279373i
$905$	−0.251382	+	0.235848i	−0.00835623	+	0.00783986i
$906$		0			0
$907$	10.9332	+	6.31231i	0.363033	+	0.209597i	0.670410	−	0.741991i	$-0.266118\pi$
$907$	10.9332	+	6.31231i	0.363033	+	0.209597i	−0.307378	+	0.951588i	$0.599451\pi$
$908$	8.13778	−	11.2007i	0.270062	−	0.371708i
$909$		0			0
$910$	−14.5588	+	16.8510i	−0.482619	+	0.558605i
$911$	0.0232378	+	0.00493935i	0.000769904	+	0.000163648i	0.208297	−	0.978066i	$-0.433208\pi$
$911$	0.0232378	+	0.00493935i	0.000769904	+	0.000163648i	−0.207527	+	0.978229i	$0.566541\pi$
$912$		0			0
$913$	10.9223	+	51.3852i	0.361474	+	1.70060i
$914$	11.6708	−	12.9617i	0.386036	−	0.428736i
$915$		0			0
$916$	−6.08026	−	6.75282i	−0.200898	−	0.223119i
$917$	−17.0919	+	23.5249i	−0.564423	+	0.776861i
$918$		0			0
$919$	−42.2094	−	30.6669i	−1.39236	−	1.01161i	−0.995602	−	0.0936857i	$-0.970135\pi$
$919$	−42.2094	−	30.6669i	−1.39236	−	1.01161i	−0.396758	−	0.917923i	$-0.629865\pi$
$920$	−0.0428385	−	2.09055i	−0.00141235	−	0.0689234i
$921$		0			0
$922$	1.66641	−	3.74282i	0.0548803	−	0.123263i
$923$	0.253915	+	0.228626i	0.00835772	+	0.00752533i
$924$		0			0
$925$	40.3390	+	33.4332i	1.32634	+	1.09928i
$926$	−9.16454			−0.301165
$927$		0			0
$928$	−13.0604	−	17.9760i	−0.428727	−	0.590093i
$929$	0.458308	+	4.36050i	0.0150366	+	0.143064i	0.999464	−	0.0327260i	$-0.0104189\pi$
$929$	0.458308	+	4.36050i	0.0150366	+	0.143064i	−0.984428	+	0.175789i	$0.943752\pi$
$930$		0			0
$931$	2.72131	−	25.8915i	0.0891873	−	0.848560i
$932$	11.2278	−	6.48240i	0.367780	−	0.212338i
$933$		0			0
$934$	4.06159	+	4.51085i	0.132899	+	0.147600i
$935$	22.6189	+	37.3866i	0.739717	+	1.22267i
$936$		0			0
$937$	41.1125	+	13.3583i	1.34309	+	0.436395i	0.890361	−	0.455255i	$-0.150452\pi$
$937$	41.1125	+	13.3583i	1.34309	+	0.436395i	0.452725	+	0.891650i	$0.350452\pi$
$938$	15.3245	−	13.7982i	0.500362	−	0.450528i
$939$		0			0
$940$	0.841907	−	1.52977i	0.0274600	−	0.0498957i
$941$	6.25975	−	1.33055i	0.204062	−	0.0433747i	−0.104746	−	0.994499i	$-0.533403\pi$
$941$	6.25975	−	1.33055i	0.204062	−	0.0433747i	0.308809	+	0.951124i	$0.400070\pi$
$942$		0			0
$943$	−3.17845	−	1.83508i	−0.103505	−	0.0597584i
$944$	0.673451	+	0.489291i	0.0219190	+	0.0159251i
$945$		0			0
$946$	−10.8256	+	7.86529i	−0.351972	+	0.255723i
$947$	−53.3522	+	5.60754i	−1.73371	+	0.182221i	−0.918093	−	0.396365i	$-0.870271\pi$
$947$	−53.3522	+	5.60754i	−1.73371	+	0.182221i	−0.815621	+	0.578586i	$0.803605\pi$
$948$		0			0
$949$	−20.3779	−	35.2955i	−0.661493	−	1.14574i
$950$	−11.0788	+	4.10869i	−0.359444	+	0.133303i
$951$		0			0
$952$	13.0844	−	61.5572i	0.424067	−	1.99508i
$953$	3.66908	+	5.05006i	0.118853	+	0.163587i	0.864298	−	0.502980i	$-0.167763\pi$
$953$	3.66908	+	5.05006i	0.118853	+	0.163587i	−0.745445	+	0.666567i	$0.767763\pi$
$954$		0			0
$955$	−27.5345	+	16.6583i	−0.890995	+	0.539051i
$956$	7.44920	−	3.31660i	0.240924	−	0.107266i
$957$		0			0
$958$	6.30429	+	0.662607i	0.203682	+	0.0214079i
$959$	15.2125	−	3.23353i	0.491239	−	0.104416i
$960$		0			0
$961$	22.1988	+	4.71851i	0.716091	+	0.152210i
$962$	−24.0944	−	7.82876i	−0.776836	−	0.252409i
$963$		0			0
$964$	−10.5227	−	32.3855i	−0.338913	−	1.04307i
$965$	4.81937	+	13.8596i	0.155141	+	0.446158i
$966$		0			0
$967$	27.0112	+	2.83899i	0.868621	+	0.0912957i	0.528345	−	0.849030i	$-0.322813\pi$
$967$	27.0112	+	2.83899i	0.868621	+	0.0912957i	0.340276	+	0.940326i	$0.389479\pi$
$968$	−6.37064	+	3.67809i	−0.204760	+	0.118218i
$969$		0			0
$970$	−8.76771	−	2.65148i	−0.281514	−	0.0851340i
$971$	−39.0168	+	28.3474i	−1.25211	+	0.909711i	−0.998342	−	0.0575544i	$-0.981670\pi$
$971$	−39.0168	+	28.3474i	−1.25211	+	0.909711i	−0.253767	+	0.967265i	$0.581670\pi$
$972$		0			0
$973$	52.9837	−	17.2154i	1.69858	−	0.551902i
$974$	1.75264	−	3.03565i	0.0561581	−	0.0972686i
$975$		0			0
$976$	−1.23307	−	2.13574i	−0.0394696	−	0.0683633i
$977$	27.7857	+	25.0184i	0.888943	+	0.800408i	0.980729	−	0.195371i	$-0.0625910\pi$
$977$	27.7857	+	25.0184i	0.888943	+	0.800408i	−0.0917862	+	0.995779i	$0.529258\pi$
$978$		0			0
$979$	1.83712	+	17.4790i	0.0587146	+	0.558632i
$980$	26.2365	+	2.21517i	0.838095	+	0.0707611i
$981$		0			0
$982$			2.07404i			0.0661853i
$983$	17.6949	+	39.7434i	0.564380	+	1.26762i	0.940104	+	0.340887i	$0.110727\pi$
$983$	17.6949	+	39.7434i	0.564380	+	1.26762i	−0.375725	+	0.926731i	$0.622606\pi$
$984$		0			0
$985$	13.7602	−	6.46739i	0.438435	−	0.206068i
$986$	−12.8924	+	14.3185i	−0.410578	+	0.455993i
$987$		0			0
$988$	−6.12709	+	5.51685i	−0.194929	+	0.175514i
$989$	0.403246	+	1.24106i	0.0128225	+	0.0394635i
$990$		0			0
$991$	16.4345	−	50.5803i	0.522061	−	1.60674i	−0.247996	−	0.968761i	$-0.579772\pi$
$991$	16.4345	−	50.5803i	0.522061	−	1.60674i	0.770056	−	0.637976i	$-0.220228\pi$
$992$	6.49168	+	14.5806i	0.206111	+	0.462933i
$993$		0			0
$994$	−0.0498148	+	0.473956i	−0.00158003	+	0.0150330i
$995$	−4.98849	+	26.0860i	−0.158146	+	0.826983i
$996$		0			0
$997$	10.7738	−	1.13237i	0.341208	−	0.0358624i	0.0676251	−	0.997711i	$-0.478458\pi$
$997$	10.7738	−	1.13237i	0.341208	−	0.0358624i	0.273583	+	0.961848i	$0.411791\pi$
$998$	3.21112	−	1.04336i	0.101646	−	0.0330268i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.y.a.19.10		224
3.2	odd	2		225.2.u.a.169.19	yes	224
9.4	even	3	inner	675.2.y.a.469.10		224
9.5	odd	6		225.2.u.a.94.19	yes	224
25.4	even	10	inner	675.2.y.a.154.10		224
75.29	odd	10		225.2.u.a.79.19	yes	224
225.4	even	30	inner	675.2.y.a.604.10		224
225.104	odd	30		225.2.u.a.4.19	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.19	✓	224	225.104	odd	30
225.2.u.a.79.19	yes	224	75.29	odd	10
225.2.u.a.94.19	yes	224	9.5	odd	6
225.2.u.a.169.19	yes	224	3.2	odd	2
675.2.y.a.19.10		224	1.1	even	1	trivial
675.2.y.a.154.10		224	25.4	even	10	inner
675.2.y.a.469.10		224	9.4	even	3	inner
675.2.y.a.604.10		224	225.4	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.188119 + 0.885029i) q^{2} +(1.07920 + 0.480492i) q^{4} +(0.419997 - 2.19627i) q^{5} +(-3.56731 - 2.05959i) q^{7} +(-1.69193 + 2.32874i) q^{8} +O(q^{10})\)	\(q+(-0.188119 + 0.885029i) q^{2} +(1.07920 + 0.480492i) q^{4} +(0.419997 - 2.19627i) q^{5} +(-3.56731 - 2.05959i) q^{7} +(-1.69193 + 2.32874i) q^{8} +(1.86475 + 0.784869i) q^{10} +(-3.60133 - 0.765487i) q^{11} +(-0.555564 - 2.61372i) q^{13} +(2.49387 - 2.76973i) q^{14} +(-0.161781 - 0.179676i) q^{16} +(3.11975 - 4.29397i) q^{17} +(-2.11305 - 1.53522i) q^{19} +(1.50855 - 2.16842i) q^{20} +(1.35496 - 3.04328i) q^{22} +(-0.241422 - 0.217378i) q^{23} +(-4.64720 - 1.84486i) q^{25} +2.41773 q^{26} +(-2.86024 - 3.93678i) q^{28} +(0.419376 + 3.99009i) q^{29} +(0.301239 - 2.86609i) q^{31} +(-4.79621 + 2.76909i) q^{32} +(3.21341 + 3.56885i) q^{34} +(-6.02167 + 6.96976i) q^{35} +(-9.96572 - 3.23806i) q^{37} +(1.75622 - 1.58131i) q^{38} +(4.40393 + 4.69399i) q^{40} +(11.0506 - 2.34887i) q^{41} +(-3.47868 - 2.00842i) q^{43} +(-3.51876 - 2.55653i) q^{44} +(0.237802 - 0.172773i) q^{46} +(0.657409 - 0.0690965i) q^{47} +(4.98380 + 8.63220i) q^{49} +(2.50698 - 3.76586i) q^{50} +(0.656307 - 3.08768i) q^{52} +(-1.02817 - 1.41515i) q^{53} +(-3.19377 + 7.58800i) q^{55} +(10.8319 - 4.82265i) q^{56} +(-3.61024 - 0.379452i) q^{58} +(-3.36772 + 0.715832i) q^{59} +(9.97712 + 2.12070i) q^{61} +(2.47991 + 0.805771i) q^{62} +(-1.69790 - 5.22560i) q^{64} +(-5.97378 + 0.122412i) q^{65} +(5.50254 + 0.578340i) q^{67} +(5.43007 - 3.13505i) q^{68} +(-5.03565 - 6.64050i) q^{70} +(-0.103447 + 0.0751586i) q^{71} +(14.5057 - 4.71320i) q^{73} +(4.74051 - 8.21081i) q^{74} +(-1.54275 - 2.67212i) q^{76} +(11.2705 + 10.1480i) q^{77} +(1.22520 + 11.6570i) q^{79} +(-0.462565 + 0.279851i) q^{80} +10.2220i q^{82} +(-5.80347 - 13.0348i) q^{83} +(-8.12043 - 8.65528i) q^{85} +(2.43191 - 2.70091i) q^{86} +(7.87581 - 7.09141i) q^{88} +(-1.47511 - 4.53994i) q^{89} +(-3.40132 + 10.4682i) q^{91} +(-0.156096 - 0.350596i) q^{92} +(-0.0625186 + 0.594825i) q^{94} +(-4.25924 + 3.99604i) q^{95} +(-4.50262 + 0.473244i) q^{97} +(-8.57729 + 2.78693i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Introduction

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