LMFDB - Embedded newform 828.2.u.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [828,2,Mod(19,828)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(828, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 15]))

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

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

chi := DirichletCharacter("828.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.u (of order $22$, degree $10$, 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:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	no (minimal twist has level 92)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	828.19
Dual form			828.2.u.a.523.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.908675 - 1.08366i) q^{2} +(-0.348619 + 1.96938i) q^{4} +(-1.74032 + 2.70799i) q^{5} +(0.439673 + 3.05800i) q^{7} +(2.45091 - 1.41175i) q^{8} +O(q^{10})$	\(q+(-0.908675 - 1.08366i) q^{2} +(-0.348619 + 1.96938i) q^{4} +(-1.74032 + 2.70799i) q^{5} +(0.439673 + 3.05800i) q^{7} +(2.45091 - 1.41175i) q^{8} +(4.51592 - 0.574777i) q^{10} +(-0.0147862 + 0.0323773i) q^{11} +(-0.214704 + 1.49330i) q^{13} +(2.91429 - 3.25518i) q^{14} +(-3.75693 - 1.37313i) q^{16} +(2.81816 - 2.44195i) q^{17} +(-0.225545 + 0.260293i) q^{19} +(-4.72636 - 4.37142i) q^{20} +(0.0485217 - 0.0133973i) q^{22} +(-4.15401 + 2.39670i) q^{23} +(-2.22743 - 4.87740i) q^{25} +(1.81332 - 1.12426i) q^{26} +(-6.17564 - 0.200191i) q^{28} +(0.217665 + 0.251198i) q^{29} +(-1.06260 + 3.61888i) q^{31} +(1.92583 + 5.31895i) q^{32} +(-5.20703 - 0.834977i) q^{34} +(-9.04621 - 4.13126i) q^{35} +(-4.10489 - 6.38734i) q^{37} +(0.487015 + 0.00789152i) q^{38} +(-0.442381 + 9.09395i) q^{40} +(-7.08463 - 4.55301i) q^{41} +(-7.63873 + 2.24293i) q^{43} +(-0.0586085 - 0.0404070i) q^{44} +(6.37185 + 2.32369i) q^{46} +12.4933i q^{47} +(-2.44157 + 0.716911i) q^{49} +(-3.26141 + 6.84575i) q^{50} +(-2.86603 - 0.943427i) q^{52} +(4.98512 - 0.716752i) q^{53} +(-0.0619447 - 0.0963878i) q^{55} +(5.39471 + 6.87418i) q^{56} +(0.0744261 - 0.464131i) q^{58} +(-11.5305 - 1.65784i) q^{59} +(1.07769 - 3.67028i) q^{61} +(4.88718 - 2.13690i) q^{62} +(4.01395 - 6.92013i) q^{64} +(-3.67019 - 3.18024i) q^{65} +(-2.05467 - 4.49910i) q^{67} +(3.82667 + 6.40135i) q^{68} +(3.74319 + 13.5569i) q^{70} +(4.38573 - 2.00290i) q^{71} +(4.95391 - 5.71712i) q^{73} +(-3.19166 + 10.2523i) q^{74} +(-0.433987 - 0.534927i) q^{76} +(-0.105511 - 0.0309807i) q^{77} +(-0.475186 + 3.30499i) q^{79} +(10.2567 - 7.78406i) q^{80} +(1.50373 + 11.8145i) q^{82} +(4.11011 - 2.64141i) q^{83} +(1.70828 + 11.8813i) q^{85} +(9.37170 + 6.23966i) q^{86} +(0.00946875 + 0.100228i) q^{88} +(3.09200 + 10.5304i) q^{89} -4.66091 q^{91} +(-3.27186 - 9.01637i) q^{92} +(13.5385 - 11.3524i) q^{94} +(-0.312350 - 1.06377i) q^{95} +(-5.11806 + 7.96386i) q^{97} +(2.99548 + 1.99439i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 7 q^{2} - 11 q^{4} + 22 q^{5} + 10 q^{8}+O(q^{10}) $ 100 * q + 7 * q^2 - 11 * q^4 + 22 * q^5 + 10 * q^8	$ 100 q + 7 q^{2} - 11 q^{4} + 22 q^{5} + 10 q^{8} - 11 q^{10} - 18 q^{13} + 11 q^{14} + 5 q^{16} + 22 q^{17} + 11 q^{20} - 16 q^{25} - 12 q^{26} - 11 q^{28} + 42 q^{29} + 27 q^{32} + 11 q^{34} - 22 q^{37} - 44 q^{38} + 77 q^{40} + 10 q^{41} - 66 q^{44} + 65 q^{46} - 8 q^{49} - 30 q^{50} + 96 q^{52} + 22 q^{53} - 44 q^{56} + 79 q^{58} - 22 q^{61} + 36 q^{62} + 10 q^{64} + 22 q^{65} + 34 q^{70} - 18 q^{73} + 22 q^{74} - 66 q^{76} - 122 q^{77} + 110 q^{80} - 122 q^{82} + 54 q^{85} + 121 q^{86} - 99 q^{88} - 22 q^{89} + 86 q^{92} - 61 q^{94} + 22 q^{97} + 71 q^{98}+O(q^{100}) $ 100 * q + 7 * q^2 - 11 * q^4 + 22 * q^5 + 10 * q^8 - 11 * q^10 - 18 * q^13 + 11 * q^14 + 5 * q^16 + 22 * q^17 + 11 * q^20 - 16 * q^25 - 12 * q^26 - 11 * q^28 + 42 * q^29 + 27 * q^32 + 11 * q^34 - 22 * q^37 - 44 * q^38 + 77 * q^40 + 10 * q^41 - 66 * q^44 + 65 * q^46 - 8 * q^49 - 30 * q^50 + 96 * q^52 + 22 * q^53 - 44 * q^56 + 79 * q^58 - 22 * q^61 + 36 * q^62 + 10 * q^64 + 22 * q^65 + 34 * q^70 - 18 * q^73 + 22 * q^74 - 66 * q^76 - 122 * q^77 + 110 * q^80 - 122 * q^82 + 54 * q^85 + 121 * q^86 - 99 * q^88 - 22 * q^89 + 86 * q^92 - 61 * q^94 + 22 * q^97 + 71 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$-1$	$1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.908675	−	1.08366i	−0.642530	−	0.766260i
$2$	−0.908675	−	1.08366i	−0.642530	−	0.766260i
$3$		0			0
$3$		0			0
$4$	−0.348619	+	1.96938i	−0.174310	+	0.984691i
$5$	−1.74032	+	2.70799i	−0.778296	+	1.21105i	0.194844	+	0.980834i	$0.437580\pi$
$5$	−1.74032	+	2.70799i	−0.778296	+	1.21105i	−0.973139	+	0.230217i	$0.926056\pi$
$6$		0			0
$7$	0.439673	+	3.05800i	0.166181	+	1.15581i	0.886689	+	0.462367i	$0.153000\pi$
$7$	0.439673	+	3.05800i	0.166181	+	1.15581i	−0.720508	+	0.693447i	$0.756091\pi$
$8$	2.45091	−	1.41175i	0.866529	−	0.499127i
$9$		0			0
$10$	4.51592	−	0.574777i	1.42806	−	0.181760i
$11$	−0.0147862	+	0.0323773i	−0.00445821	+	0.00976211i	−0.911848	−	0.410528i	$-0.865344\pi$
$11$	−0.0147862	+	0.0323773i	−0.00445821	+	0.00976211i	0.907390	+	0.420290i	$0.138072\pi$
$12$		0			0
$13$	−0.214704	+	1.49330i	−0.0595482	+	0.414167i	0.938143	+	0.346249i	$0.112545\pi$
$13$	−0.214704	+	1.49330i	−0.0595482	+	0.414167i	−0.997691	+	0.0679180i	$0.978364\pi$
$14$	2.91429	−	3.25518i	0.778878	−	0.869983i
$15$		0			0
$16$	−3.75693	−	1.37313i	−0.939232	−	0.343282i
$17$	2.81816	−	2.44195i	0.683505	−	0.592260i	−0.242328	−	0.970194i	$-0.577911\pi$
$17$	2.81816	−	2.44195i	0.683505	−	0.592260i	0.925832	+	0.377934i	$0.123365\pi$
$18$		0			0
$19$	−0.225545	+	0.260293i	−0.0517436	+	0.0597153i	−0.781031	−	0.624492i	$-0.785306\pi$
$19$	−0.225545	+	0.260293i	−0.0517436	+	0.0597153i	0.729288	+	0.684207i	$0.239852\pi$
$20$	−4.72636	−	4.37142i	−1.05685	−	0.977478i
$21$		0			0
$22$	0.0485217	−	0.0133973i	0.0103449	−	0.00285631i
$23$	−4.15401	+	2.39670i	−0.866171	+	0.499747i
$23$	−4.15401	+	2.39670i	−0.866171	+	0.499747i
$24$		0			0
$25$	−2.22743	−	4.87740i	−0.445487	−	0.975480i
$26$	1.81332	−	1.12426i	0.355621	−	0.220485i
$27$		0			0
$28$	−6.17564	−	0.200191i	−1.16709	−	0.0378325i
$29$	0.217665	+	0.251198i	0.0404193	+	0.0466464i	0.775599	−	0.631226i	$-0.217448\pi$
$29$	0.217665	+	0.251198i	0.0404193	+	0.0466464i	−0.735180	+	0.677872i	$0.762902\pi$
$30$		0			0
$31$	−1.06260	+	3.61888i	−0.190849	+	0.649970i	0.807356	+	0.590065i	$0.200898\pi$
$31$	−1.06260	+	3.61888i	−0.190849	+	0.649970i	−0.998204	+	0.0599052i	$0.980920\pi$
$32$	1.92583	+	5.31895i	0.340442	+	0.940266i
$33$		0			0
$34$	−5.20703	−	0.834977i	−0.892998	−	0.143197i
$35$	−9.04621	−	4.13126i	−1.52909	−	0.698311i
$36$		0			0
$37$	−4.10489	−	6.38734i	−0.674840	−	1.05007i	−0.994721	−	0.102614i	$-0.967279\pi$
$37$	−4.10489	−	6.38734i	−0.674840	−	1.05007i	0.319881	−	0.947458i	$-0.396357\pi$
$38$	0.487015	+	0.00789152i	0.0790043	+	0.00128017i
$39$		0			0
$40$	−0.442381	+	9.09395i	−0.0699466	+	1.43788i
$41$	−7.08463	−	4.55301i	−1.10643	−	0.711061i	−0.145920	−	0.989296i	$-0.546614\pi$
$41$	−7.08463	−	4.55301i	−1.10643	−	0.711061i	−0.960513	+	0.278235i	$0.910251\pi$
$42$		0			0
$43$	−7.63873	+	2.24293i	−1.16490	+	0.342044i	−0.806333	−	0.591461i	$-0.798551\pi$
$43$	−7.63873	+	2.24293i	−1.16490	+	0.342044i	−0.358563	+	0.933506i	$0.616733\pi$
$44$	−0.0586085	−	0.0404070i	−0.00883556	−	0.00609159i
$45$		0			0
$46$	6.37185	+	2.32369i	0.939478	+	0.342610i
$47$			12.4933i			1.82234i	0.412031	+	0.911170i	$0.364820\pi$
$47$			12.4933i			1.82234i	−0.412031	+	0.911170i	$0.635180\pi$
$48$		0			0
$49$	−2.44157	+	0.716911i	−0.348796	+	0.102416i
$50$	−3.26141	+	6.84575i	−0.461233	+	0.968135i
$51$		0			0
$52$	−2.86603	−	0.943427i	−0.397447	−	0.130830i
$53$	4.98512	−	0.716752i	0.684759	−	0.0984534i	0.208849	−	0.977948i	$-0.433028\pi$
$53$	4.98512	−	0.716752i	0.684759	−	0.0984534i	0.475909	+	0.879494i	$0.342119\pi$
$54$		0			0
$55$	−0.0619447	−	0.0963878i	−0.00835262	−	0.0129969i
$56$	5.39471	+	6.87418i	0.720899	+	0.918600i
$57$		0			0
$58$	0.0744261	−	0.464131i	0.00977263	−	0.0609434i
$59$	−11.5305	−	1.65784i	−1.50114	−	0.215832i	−0.657794	−	0.753198i	$-0.728510\pi$
$59$	−11.5305	−	1.65784i	−1.50114	−	0.215832i	−0.843349	+	0.537366i	$0.819419\pi$
$60$		0			0
$61$	1.07769	−	3.67028i	0.137984	−	0.469931i	−0.861286	−	0.508120i	$-0.830341\pi$
$61$	1.07769	−	3.67028i	0.137984	−	0.469931i	0.999271	+	0.0381888i	$0.0121588\pi$
$62$	4.88718	−	2.13690i	0.620673	−	0.271386i
$63$		0			0
$64$	4.01395	−	6.92013i	0.501744	−	0.865016i
$65$	−3.67019	−	3.18024i	−0.455231	−	0.394460i
$66$		0			0
$67$	−2.05467	−	4.49910i	−0.251018	−	0.549653i	0.741613	−	0.670828i	$-0.234061\pi$
$67$	−2.05467	−	4.49910i	−0.251018	−	0.549653i	−0.992631	+	0.121175i	$0.961334\pi$
$68$	3.82667	+	6.40135i	0.464052	+	0.776277i
$69$		0			0
$70$	3.74319	+	13.5569i	0.447397	+	1.62037i
$71$	4.38573	−	2.00290i	0.520490	−	0.237700i	−0.137805	−	0.990459i	$-0.544005\pi$
$71$	4.38573	−	2.00290i	0.520490	−	0.237700i	0.658296	+	0.752759i	$0.271278\pi$
$72$		0			0
$73$	4.95391	−	5.71712i	0.579812	−	0.669138i	−0.387753	−	0.921763i	$-0.626749\pi$
$73$	4.95391	−	5.71712i	0.579812	−	0.669138i	0.967564	+	0.252625i	$0.0812940\pi$
$74$	−3.19166	+	10.2523i	−0.371023	+	1.19181i
$75$		0			0
$76$	−0.433987	−	0.534927i	−0.0497817	−	0.0613604i
$77$	−0.105511	−	0.0309807i	−0.0120241	−	0.00353058i
$78$		0			0
$79$	−0.475186	+	3.30499i	−0.0534626	+	0.371840i	0.945472	+	0.325702i	$0.105601\pi$
$79$	−0.475186	+	3.30499i	−0.0534626	+	0.371840i	−0.998935	+	0.0461383i	$0.985308\pi$
$80$	10.2567	−	7.78406i	1.14673	−	0.870284i
$81$		0			0
$82$	1.50373	+	11.8145i	0.166059	+	1.30469i
$83$	4.11011	−	2.64141i	0.451143	−	0.289932i	−0.295271	−	0.955413i	$-0.595410\pi$
$83$	4.11011	−	2.64141i	0.451143	−	0.289932i	0.746415	+	0.665481i	$0.231774\pi$
$84$		0			0
$85$	1.70828	+	11.8813i	0.185289	+	1.28871i
$86$	9.37170	+	6.23966i	1.01058	+	0.672840i
$87$		0			0
$88$	0.00946875	+	0.100228i	0.00100937	+	0.0106844i
$89$	3.09200	+	10.5304i	0.327752	+	1.11622i	0.944350	+	0.328942i	$0.106692\pi$
$89$	3.09200	+	10.5304i	0.327752	+	1.11622i	−0.616598	+	0.787278i	$0.711490\pi$
$90$		0			0
$91$	−4.66091			−0.488596
$92$	−3.27186	−	9.01637i	−0.341115	−	0.940022i
$93$		0			0
$94$	13.5385	−	11.3524i	1.39639	−	1.17091i
$95$	−0.312350	−	1.06377i	−0.0320465	−	0.109140i
$96$		0			0
$97$	−5.11806	+	7.96386i	−0.519660	+	0.808607i	−0.997561	−	0.0698070i	$-0.977762\pi$
$97$	−5.11806	+	7.96386i	−0.519660	+	0.808607i	0.477900	+	0.878414i	$0.341398\pi$
$98$	2.99548	+	1.99439i	0.302589	+	0.201464i
$99$		0			0
$100$	10.3820	−	2.68631i	1.03820	−	0.268631i
$101$	−2.95662	+	1.90011i	−0.294195	+	0.189068i	−0.679409	−	0.733760i	$-0.737764\pi$
$101$	−2.95662	+	1.90011i	−0.294195	+	0.189068i	0.385214	+	0.922827i	$0.374127\pi$
$102$		0			0
$103$	1.93240	−	4.23136i	0.190405	−	0.416928i	−0.790220	−	0.612823i	$-0.790034\pi$
$103$	1.93240	−	4.23136i	0.190405	−	0.416928i	0.980625	+	0.195895i	$0.0627612\pi$
$104$	1.58194	+	3.96306i	0.155122	+	0.388610i
$105$		0			0
$106$	−5.30657	−	4.75086i	−0.515419	−	0.461444i
$107$	−2.37791	−	0.698218i	−0.229881	−	0.0674992i	0.164763	−	0.986333i	$-0.447314\pi$
$107$	−2.37791	−	0.698218i	−0.229881	−	0.0674992i	−0.394644	+	0.918834i	$0.629132\pi$
$108$		0			0
$109$	−5.19693	+	4.50317i	−0.497776	+	0.431325i	−0.867218	−	0.497928i	$-0.834094\pi$
$109$	−5.19693	+	4.50317i	−0.497776	+	0.431325i	0.369442	+	0.929254i	$0.379549\pi$
$110$	−0.0481636	+	0.154712i	−0.00459222	+	0.0147512i
$111$		0			0
$112$	2.54720	−	12.0924i	0.240688	−	1.14262i
$113$	7.83329	−	3.57734i	0.736894	−	0.336528i	−0.0113644	−	0.999935i	$-0.503617\pi$
$113$	7.83329	−	3.57734i	0.736894	−	0.336528i	0.748259	+	0.663407i	$0.230890\pi$
$114$		0			0
$115$	0.739056	−	15.4201i	0.0689173	−	1.43793i
$116$	−0.570587	+	0.341092i	−0.0529777	+	0.0316696i
$117$		0			0
$118$	8.68096	+	14.0015i	0.799147	+	1.28894i
$119$	8.70655	+	7.54427i	0.798128	+	0.691582i
$120$		0			0
$121$	7.20264	+	8.31229i	0.654785	+	0.755663i
$122$	−4.95659	+	2.16725i	−0.448749	+	0.196213i
$123$		0			0
$124$	−6.75652	−	3.35428i	−0.606753	−	0.301223i
$125$	1.15326	+	0.165813i	0.103151	+	0.0148308i
$126$		0			0
$127$	−2.50526	−	1.14412i	−0.222306	−	0.101524i	0.301149	−	0.953577i	$-0.402630\pi$
$127$	−2.50526	−	1.14412i	−0.222306	−	0.101524i	−0.523455	+	0.852053i	$0.675357\pi$
$128$	−11.1464	+	1.93841i	−0.985213	+	0.171333i
$129$		0			0
$130$	−0.111272	+	6.86703i	−0.00975924	+	0.602278i
$131$	−5.99257	+	0.861601i	−0.523573	+	0.0752784i	−0.399034	−	0.916936i	$-0.630654\pi$
$131$	−5.99257	+	0.861601i	−0.523573	+	0.0752784i	−0.124539	+	0.992215i	$0.539745\pi$
$132$		0			0
$133$	−0.895141	−	0.575272i	−0.0776185	−	0.0498824i
$134$	−3.00845	+	6.31478i	−0.259891	+	0.545514i
$135$		0			0
$136$	3.45966	−	9.96354i	0.296663	−	0.854366i
$137$		−	13.9104i		−	1.18844i	−0.804302	−	0.594221i	$-0.797461\pi$
$137$		−	13.9104i		−	1.18844i	0.804302	−	0.594221i	$-0.202539\pi$
$138$		0			0
$139$			20.1629i			1.71020i	0.518466	+	0.855098i	$0.326503\pi$
$139$			20.1629i			1.71020i	−0.518466	+	0.855098i	$0.673497\pi$
$140$	11.2897	−	16.3752i	0.954155	−	1.38396i
$141$		0			0
$142$	−6.15565	−	2.93264i	−0.516571	−	0.246102i
$143$	−0.0451743	−	0.0290318i	−0.00377767	−	0.00242776i
$144$		0			0
$145$	−1.05905	+	0.152268i	−0.0879493	+	0.0126452i
$146$	−10.6969	−	0.173331i	−0.885280	−	0.0143450i
$147$		0			0
$148$	14.0101	−	5.85735i	1.15163	−	0.481471i
$149$	−11.5907	−	5.29331i	−0.949549	−	0.433645i	−0.120433	−	0.992721i	$-0.538428\pi$
$149$	−11.5907	−	5.29331i	−0.949549	−	0.433645i	−0.829116	+	0.559077i	$0.811156\pi$
$150$		0			0
$151$	−7.91514	−	1.13802i	−0.644125	−	0.0926112i	−0.187492	−	0.982266i	$-0.560036\pi$
$151$	−7.91514	−	1.13802i	−0.644125	−	0.0926112i	−0.456633	+	0.889655i	$0.650945\pi$
$152$	−0.185324	+	0.956367i	−0.0150318	+	0.0775716i
$153$		0			0
$154$	0.0623025	+	0.142489i	0.00502048	+	0.0114821i
$155$	−7.95065	−	9.17553i	−0.638611	−	0.736997i
$156$		0			0
$157$	6.12526	+	5.30756i	0.488849	+	0.423590i	0.864090	−	0.503337i	$-0.167895\pi$
$157$	6.12526	+	5.30756i	0.488849	+	0.423590i	−0.375241	+	0.926927i	$0.622440\pi$
$158$	4.01326	−	2.48822i	0.319278	−	0.197952i
$159$		0			0
$160$	−17.7552	−	4.04154i	−1.40367	−	0.319512i
$161$	−9.15552	−	11.6492i	−0.721556	−	0.918084i
$162$		0			0
$163$	−2.04513	+	0.933978i	−0.160187	+	0.0731548i	−0.493895	−	0.869522i	$-0.664427\pi$
$163$	−2.04513	+	0.933978i	−0.160187	+	0.0731548i	0.333708	+	0.942676i	$0.391700\pi$
$164$	11.4365	−	12.3651i	0.893037	−	0.965550i
$165$		0			0
$166$	−6.59713	−	2.05376i	−0.512037	−	0.159403i
$167$	−6.40479	+	5.54978i	−0.495617	+	0.429455i	−0.866464	−	0.499239i	$-0.833613\pi$
$167$	−6.40479	+	5.54978i	−0.495617	+	0.429455i	0.370847	+	0.928694i	$0.379067\pi$
$168$		0			0
$169$	10.2896	+	3.02129i	0.791505	+	0.232407i
$170$	11.3230	−	12.6475i	0.868436	−	0.970017i
$171$		0			0
$172$	−1.75419	−	15.8255i	−0.133755	−	1.20668i
$173$	−9.21644	+	20.1812i	−0.700713	+	1.53435i	0.138391	+	0.990378i	$0.455807\pi$
$173$	−9.21644	+	20.1812i	−0.700713	+	1.53435i	−0.839105	+	0.543970i	$0.816920\pi$
$174$		0			0
$175$	13.9357	−	8.95595i	1.05344	−	0.677006i
$176$	0.100009	−	0.101336i	0.00753845	−	0.00763847i
$177$		0			0
$178$	8.60170	−	12.9194i	0.644724	−	0.968348i
$179$	1.82884	−	2.84573i	0.136694	−	0.212700i	−0.766157	−	0.642653i	$-0.777834\pi$
$179$	1.82884	−	2.84573i	0.136694	−	0.212700i	0.902851	+	0.429953i	$0.141470\pi$
$180$		0			0
$181$	−2.75175	−	9.37159i	−0.204536	−	0.696585i	−0.996314	−	0.0857766i	$-0.972663\pi$
$181$	−2.75175	−	9.37159i	−0.204536	−	0.696585i	0.791779	−	0.610808i	$-0.209155\pi$
$182$	4.23525	+	5.05082i	0.313937	+	0.374391i
$183$		0			0
$184$	−6.79758	+	11.7385i	−0.501125	+	0.865375i
$185$	24.4407			1.79692
$186$		0			0
$187$	0.0373938	+	0.127352i	0.00273450	+	0.00931287i
$188$	−24.6041	−	4.35541i	−1.79444	−	0.317651i
$189$		0			0
$190$	−0.868933	+	1.30510i	−0.0630390	+	0.0946819i
$191$	−0.716897	−	4.98613i	−0.0518728	−	0.360784i	−0.999181	−	0.0404603i	$-0.987118\pi$
$191$	−0.716897	−	4.98613i	−0.0518728	−	0.360784i	0.947308	−	0.320323i	$-0.103792\pi$
$192$		0			0
$193$	0.218286	−	0.140284i	0.0157126	−	0.0100979i	−0.532761	−	0.846266i	$-0.678846\pi$
$193$	0.218286	−	0.140284i	0.0157126	−	0.0100979i	0.548474	+	0.836168i	$0.315209\pi$
$194$	13.2807	−	1.69034i	0.953501	−	0.121360i
$195$		0			0
$196$	−0.560692	−	5.05832i	−0.0400494	−	0.361309i
$197$	1.16018	−	8.06921i	0.0826592	−	0.574907i	−0.905833	−	0.423635i	$-0.860754\pi$
$197$	1.16018	−	8.06921i	0.0826592	−	0.574907i	0.988492	−	0.151272i	$-0.0483370\pi$
$198$		0			0
$199$	20.9070	+	6.13885i	1.48206	+	0.435172i	0.919998	−	0.391924i	$-0.128190\pi$
$199$	20.9070	+	6.13885i	1.48206	+	0.435172i	0.562061	+	0.827096i	$0.310009\pi$
$200$	−12.3449	−	8.80952i	−0.872916	−	0.622927i
$201$		0			0
$202$	4.74567	+	1.47738i	0.333904	+	0.103948i
$203$	−0.672462	+	0.776063i	−0.0471976	+	0.0544689i
$204$		0			0
$205$	24.6591	−	11.2614i	1.72226	−	0.786531i
$206$	−6.34125	+	1.75088i	−0.441816	+	0.121989i
$207$		0			0
$208$	2.85712	−	5.31541i	0.198106	−	0.368557i
$209$	−0.00509262	−	0.0111513i	−0.000352264	−	0.000771350i
$210$		0			0
$211$	6.22420	+	5.39330i	0.428491	+	0.371290i	0.842241	−	0.539101i	$-0.181236\pi$
$211$	6.22420	+	5.39330i	0.428491	+	0.371290i	−0.413750	+	0.910391i	$0.635781\pi$
$212$	−0.326350	+	10.0675i	−0.0224138	+	0.691437i
$213$		0			0
$214$	1.40412	+	3.21129i	0.0959837	+	0.219519i
$215$	7.22000	−	24.5891i	0.492400	−	1.67696i
$216$		0			0
$217$	−11.5337	−	1.65830i	−0.782960	−	0.112573i
$218$	9.60221	+	1.53977i	0.650343	+	0.104286i
$219$		0			0
$220$	0.211420	−	0.0883901i	0.0142539	−	0.00595926i
$221$	3.04149	+	4.73266i	0.204593	+	0.318353i
$222$		0			0
$223$	12.0942	−	1.73889i	0.809890	−	0.116445i	0.275085	−	0.961420i	$-0.411294\pi$
$223$	12.0942	−	1.73889i	0.809890	−	0.116445i	0.534805	+	0.844975i	$0.320385\pi$
$224$	−15.4186	+	8.22778i	−1.03020	+	0.549742i
$225$		0			0
$226$	−10.9945	−	5.23795i	−0.731345	−	0.348423i
$227$	12.5214	−	3.67661i	0.831073	−	0.244025i	0.161595	−	0.986857i	$-0.448336\pi$
$227$	12.5214	−	3.67661i	0.831073	−	0.244025i	0.669478	+	0.742832i	$0.266518\pi$
$228$		0			0
$229$		−	10.0144i		−	0.661773i	−0.943671	−	0.330887i	$-0.892652\pi$
$229$		−	10.0144i		−	0.661773i	0.943671	−	0.330887i	$-0.107348\pi$
$230$	−17.3816	+	13.2110i	−1.14611	+	0.871105i
$231$		0			0
$232$	0.888105	+	0.308378i	0.0583070	+	0.0202460i
$233$	16.2134	−	4.76067i	1.06217	−	0.311882i	0.296447	−	0.955049i	$-0.404198\pi$
$233$	16.2134	−	4.76067i	1.06217	−	0.311882i	0.765725	+	0.643168i	$0.222380\pi$
$234$		0			0
$235$	−33.8319	−	21.7424i	−2.20695	−	1.41832i
$236$	7.28466	−	22.1300i	0.474191	−	1.44054i
$237$		0			0
$238$	0.263964	−	16.2902i	0.0171102	−	1.05594i
$239$	12.4223	+	19.3294i	0.803529	+	1.25032i	0.964690	+	0.263387i	$0.0848397\pi$
$239$	12.4223	+	19.3294i	0.803529	+	1.25032i	−0.161161	+	0.986928i	$0.551524\pi$
$240$		0			0
$241$	−25.9543	−	11.8530i	−1.67187	−	0.763516i	−0.999734	−	0.0230849i	$-0.992651\pi$
$241$	−25.9543	−	11.8530i	−1.67187	−	0.763516i	−0.672133	−	0.740431i	$-0.734622\pi$
$242$	2.46280	−	15.3583i	0.158315	−	0.987272i
$243$		0			0
$244$	6.85248	+	3.40192i	0.438685	+	0.217785i
$245$	2.30774	−	7.85943i	0.147436	−	0.502120i
$246$		0			0
$247$	−0.340270	−	0.392692i	−0.0216509	−	0.0249864i
$248$	2.50460	+	10.3697i	0.159042	+	0.658476i
$249$		0			0
$250$	−0.868252	−	1.40040i	−0.0549131	−	0.0885694i
$251$	3.24606	+	7.10788i	0.204890	+	0.448645i	0.983983	−	0.178262i	$-0.0570476\pi$
$251$	3.24606	+	7.10788i	0.204890	+	0.448645i	−0.779093	+	0.626908i	$0.784320\pi$
$252$		0			0
$253$	−0.0161767	−	0.169934i	−0.00101702	−	0.0106836i
$254$	1.03664	+	3.75447i	0.0650448	+	0.235577i
$255$		0			0
$256$	12.2290	+	10.3175i	0.764315	+	0.644843i
$257$	4.59844	−	5.30688i	0.286842	−	0.331034i	−0.593981	−	0.804479i	$-0.702444\pi$
$257$	4.59844	−	5.30688i	0.286842	−	0.331034i	0.880823	+	0.473445i	$0.156990\pi$
$258$		0			0
$259$	17.7276	−	15.3611i	1.10154	−	0.954491i
$260$	7.54261	−	6.11932i	0.467773	−	0.379504i
$261$		0			0
$262$	6.37897	+	5.71096i	0.394094	+	0.352824i
$263$	−1.07557	+	7.48075i	−0.0663225	+	0.461283i	0.929414	+	0.369039i	$0.120313\pi$
$263$	−1.07557	+	7.48075i	−0.0663225	+	0.461283i	−0.995736	+	0.0922440i	$0.970596\pi$
$264$		0			0
$265$	−6.73475	+	14.7470i	−0.413713	+	0.905904i
$266$	0.189995	+	1.49276i	0.0116494	+	0.0915270i
$267$		0			0
$268$	9.57675	−	2.47796i	0.584993	−	0.151365i
$269$	2.84640	+	19.7971i	0.173548	+	1.20705i	0.871314	+	0.490726i	$0.163268\pi$
$269$	2.84640	+	19.7971i	0.173548	+	1.20705i	−0.697766	+	0.716326i	$0.745822\pi$
$270$		0			0
$271$	−13.5908	+	21.1477i	−0.825580	+	1.28463i	0.130478	+	0.991451i	$0.458349\pi$
$271$	−13.5908	+	21.1477i	−0.825580	+	1.28463i	−0.956058	+	0.293177i	$0.905287\pi$
$272$	−13.9407	+	5.30454i	−0.845282	+	0.321635i
$273$		0			0
$274$	−15.0740	+	12.6400i	−0.910655	+	0.763610i
$275$	0.190852			0.0115088
$276$		0			0
$277$	15.8515			0.952423			0.476212	−	0.879331i	$-0.342010\pi$
$277$	15.8515			0.952423			0.476212	+	0.879331i	$0.342010\pi$
$278$	21.8497	−	18.3215i	1.31046	−	1.09885i
$279$		0			0
$280$	−28.0038	+	2.64557i	−1.67354	+	0.158103i
$281$	−9.43888	+	14.6872i	−0.563076	+	0.876164i	−0.999725	−	0.0234683i	$-0.992529\pi$
$281$	−9.43888	+	14.6872i	−0.563076	+	0.876164i	0.436648	+	0.899632i	$0.356165\pi$
$282$		0			0
$283$	−3.67235	−	25.5418i	−0.218299	−	1.51830i	−0.744316	−	0.667827i	$-0.767224\pi$
$283$	−3.67235	−	25.5418i	−0.218299	−	1.51830i	0.526017	−	0.850474i	$-0.323685\pi$
$284$	2.41552	+	9.33542i	0.143335	+	0.553955i
$285$		0			0
$286$	0.00958834	+	0.0753339i	0.000566970	+	0.00445458i
$287$	10.8082	−	23.6666i	0.637986	−	1.39700i
$288$		0			0
$289$	−0.440442	+	3.06334i	−0.0259083	+	0.180197i
$290$	1.12734	+	1.00928i	0.0661996	+	0.0592671i
$291$		0			0
$292$	9.53216	+	11.7492i	0.557828	+	0.687572i
$293$	−10.5229	+	9.11810i	−0.614752	+	0.532685i	−0.905627	−	0.424076i	$-0.860599\pi$
$293$	−10.5229	+	9.11810i	−0.614752	+	0.532685i	0.290875	+	0.956761i	$0.406054\pi$
$294$		0			0
$295$	24.5562	−	28.3394i	1.42972	−	1.64998i
$296$	−19.0780	−	9.85975i	−1.10889	−	0.573086i
$297$		0			0
$298$	4.79608	+	17.3703i	0.277830	+	1.00623i
$299$	−2.68712	−	6.71777i	−0.155400	−	0.388499i
$300$		0			0
$301$	−10.2174	−	22.3731i	−0.588923	−	1.28956i
$302$	5.95906	+	9.61138i	0.342905	+	0.553073i
$303$		0			0
$304$	1.20477	−	0.668200i	0.0690984	−	0.0383239i
$305$	8.06357	+	9.30585i	0.461718	+	0.532851i
$306$		0			0
$307$	−5.86566	+	19.9766i	−0.334771	+	1.14013i	0.604402	+	0.796680i	$0.293412\pi$
$307$	−5.86566	+	19.9766i	−0.334771	+	1.14013i	−0.939173	+	0.343445i	$0.888406\pi$
$308$	0.0977959	−	0.196990i	0.00557244	−	0.0112246i
$309$		0			0
$310$	−2.71857	+	16.9533i	−0.154404	+	0.962885i
$311$	−9.51746	−	4.34648i	−0.539685	−	0.246466i	0.126873	−	0.991919i	$-0.459506\pi$
$311$	−9.51746	−	4.34648i	−0.539685	−	0.246466i	−0.666558	+	0.745453i	$0.732233\pi$
$312$		0			0
$313$	11.8653	+	18.4627i	0.670666	+	1.04358i	0.995215	+	0.0977075i	$0.0311510\pi$
$313$	11.8653	+	18.4627i	0.670666	+	1.04358i	−0.324549	+	0.945869i	$0.605213\pi$
$314$	0.185705	−	11.4605i	0.0104799	−	0.646755i
$315$		0			0
$316$	−6.34313	−	2.08800i	−0.356829	−	0.117459i
$317$	7.13318	+	4.58422i	0.400639	+	0.257475i	0.725409	−	0.688318i	$-0.241650\pi$
$317$	7.13318	+	4.58422i	0.400639	+	0.257475i	−0.324770	+	0.945793i	$0.605287\pi$
$318$		0			0
$319$	−0.0113515	+	0.00333312i	−0.000635565	+	0.000186619i
$320$	11.7541	+	22.9130i	0.657074	+	1.28088i
$321$		0			0
$322$	−4.30431	+	20.5068i	−0.239870	+	1.14280i
$323$			1.28432i			0.0714613i
$324$		0			0
$325$	7.76166	−	2.27903i	0.430540	−	0.126418i
$326$	2.87047	+	1.36753i	0.158980	+	0.0757405i
$327$		0			0
$328$	−23.7915	−	1.15735i	−1.31367	−	0.0639041i
$329$	−38.2046	+	5.49299i	−2.10629	+	0.302838i
$330$		0			0
$331$	−8.93643	−	13.9054i	−0.491190	−	0.764307i	0.503849	−	0.863792i	$-0.331917\pi$
$331$	−8.93643	−	13.9054i	−0.491190	−	0.764307i	−0.995039	+	0.0994847i	$0.968281\pi$
$332$	3.76908	+	9.01522i	0.206855	+	0.494775i
$333$		0			0
$334$	11.8339	+	1.89764i	0.647523	+	0.103834i
$335$	15.7593	+	2.26585i	0.861024	+	0.123797i
$336$		0			0
$337$	4.06233	−	13.8350i	0.221289	−	0.753641i	−0.771757	−	0.635917i	$-0.780622\pi$
$337$	4.06233	−	13.8350i	0.221289	−	0.753641i	0.993046	−	0.117724i	$-0.0375599\pi$
$338$	−6.07583	−	13.8957i	−0.330482	−	0.755827i
$339$		0			0
$340$	−23.9944	−	0.777810i	−1.30128	−	0.0421826i
$341$	−0.101458	−	0.0879136i	−0.00549424	−	0.00476079i
$342$		0			0
$343$	5.71800	+	12.5207i	0.308743	+	0.676052i
$344$	−15.5554	+	16.2812i	−0.838692	+	0.877823i
$345$		0			0
$346$	30.2442	−	8.35070i	1.62594	−	0.448936i
$347$	7.08801	−	3.23699i	0.380505	−	0.173771i	−0.215975	−	0.976399i	$-0.569293\pi$
$347$	7.08801	−	3.23699i	0.380505	−	0.173771i	0.596480	+	0.802628i	$0.296566\pi$
$348$		0			0
$349$	5.76898	−	6.65776i	0.308807	−	0.356382i	−0.580039	−	0.814589i	$-0.696963\pi$
$349$	5.76898	−	6.65776i	0.308807	−	0.356382i	0.888846	+	0.458207i	$0.151508\pi$
$350$	−22.3682	−	6.96348i	−1.19563	−	0.372214i
$351$		0			0
$352$	−0.200689	−	0.0162939i	−0.0106967	−	0.000868468i
$353$	22.1233	+	6.49597i	1.17750	+	0.345746i	0.811210	−	0.584754i	$-0.198809\pi$
$353$	22.1233	+	6.49597i	1.17750	+	0.345746i	0.366292	+	0.930500i	$0.380627\pi$
$354$		0			0
$355$	−2.20875	+	15.3622i	−0.117228	+	0.815342i
$356$	−21.8163	+	2.41824i	−1.15626	+	0.128166i
$357$		0			0
$358$	−4.74562	+	0.604012i	−0.250814	+	0.0319230i
$359$	−23.1888	+	14.9026i	−1.22386	+	0.786527i	−0.982924	−	0.184014i	$-0.941091\pi$
$359$	−23.1888	+	14.9026i	−1.22386	+	0.786527i	−0.240937	+	0.970541i	$0.577455\pi$
$360$		0			0
$361$	2.68710	+	18.6892i	0.141426	+	0.983642i
$362$	−7.65513	+	11.4977i	−0.402345	+	0.604304i
$363$		0			0
$364$	1.62488	−	9.17910i	0.0851669	−	0.481116i
$365$	6.86052	+	23.3648i	0.359096	+	1.22297i
$366$		0			0
$367$	20.9251			1.09228			0.546141	−	0.837693i	$-0.316096\pi$
$367$	20.9251			1.09228			0.546141	+	0.837693i	$0.316096\pi$
$368$	18.8973	−	3.30026i	0.985090	−	0.172038i
$369$		0			0
$370$	−22.2087	−	26.4853i	−1.15457	−	1.37691i
$371$	4.38365	+	14.9293i	0.227588	+	0.775093i
$372$		0			0
$373$	−9.39615	+	14.6207i	−0.486514	+	0.757031i	−0.994545	−	0.104308i	$-0.966737\pi$
$373$	−9.39615	+	14.6207i	−0.486514	+	0.757031i	0.508031	+	0.861339i	$0.330374\pi$
$374$	0.104026	−	0.156243i	0.00537908	−	0.00807914i
$375$		0			0
$376$	17.6374	+	30.6201i	0.909579	+	1.57911i
$377$	−0.421848	+	0.271105i	−0.0217263	+	0.0139626i
$378$		0			0
$379$	−15.7381	+	34.4616i	−0.808411	+	1.77017i	−0.194319	+	0.980938i	$0.562250\pi$
$379$	−15.7381	+	34.4616i	−0.808411	+	1.77017i	−0.614092	+	0.789235i	$0.710478\pi$
$380$	2.20386	−	0.244287i	0.113055	−	0.0125317i
$381$		0			0
$382$	−4.75182	+	5.30764i	−0.243124	+	0.271562i
$383$	33.2874	+	9.77407i	1.70091	+	0.499431i	0.980896	−	0.194531i	$-0.0623186\pi$
$383$	33.2874	+	9.77407i	1.70091	+	0.499431i	0.720011	+	0.693963i	$0.244137\pi$
$384$		0			0
$385$	0.267518	−	0.231806i	0.0136340	−	0.0118139i
$386$	−0.350371	−	0.109074i	−0.0178334	−	0.00555174i
$387$		0			0
$388$	−13.8996	−	12.8558i	−0.705646	−	0.652653i
$389$	6.31175	−	2.88248i	0.320019	−	0.146148i	−0.248928	−	0.968522i	$-0.580078\pi$
$389$	6.31175	−	2.88248i	0.320019	−	0.146148i	0.568947	+	0.822374i	$0.307351\pi$
$390$		0			0
$391$	−5.85404	+	16.8982i	−0.296052	+	0.854578i
$392$	−4.97199	+	5.20397i	−0.251124	+	0.262840i
$393$		0			0
$394$	−9.79847	+	6.07506i	−0.493640	+	0.306057i
$395$	−8.12291	−	7.03854i	−0.408708	−	0.354148i
$396$		0			0
$397$	5.12145	+	5.91047i	0.257038	+	0.296638i	0.869572	−	0.493807i	$-0.164395\pi$
$397$	5.12145	+	5.91047i	0.257038	+	0.296638i	−0.612533	+	0.790445i	$0.709850\pi$
$398$	−12.3453	−	28.2342i	−0.618813	−	1.41525i
$399$		0			0
$400$	1.67102	+	21.3826i	0.0835508	+	1.06913i
$401$	−31.7183	−	4.56040i	−1.58394	−	0.227735i	−0.706600	−	0.707613i	$-0.749772\pi$
$401$	−31.7183	−	4.56040i	−1.58394	−	0.227735i	−0.877335	+	0.479878i	$0.840681\pi$
$402$		0			0
$403$	−5.17593	−	2.36377i	−0.257832	−	0.117748i
$404$	−2.71130	−	6.48513i	−0.134892	−	0.322647i
$405$		0			0
$406$	1.45203	+	0.0235286i	0.0720633	+	0.00116770i
$407$	0.267500	−	0.0384607i	0.0132595	−	0.00190643i
$408$		0			0
$409$	7.81430	+	5.02195i	0.386392	+	0.248319i	0.719387	−	0.694609i	$-0.244423\pi$
$409$	7.81430	+	5.02195i	0.386392	+	0.248319i	−0.332995	+	0.942929i	$0.608059\pi$
$410$	−34.6106	−	16.4890i	−1.70929	−	0.814332i
$411$		0			0
$412$	7.65949	+	5.28076i	0.377356	+	0.260164i
$413$		−	35.9891i		−	1.77091i
$414$		0			0
$415$			15.7271i			0.772011i
$416$	−8.35627	+	1.73384i	−0.409700	+	0.0850086i
$417$		0			0
$418$	−0.00745661	+	0.0156515i	−0.000364715	+	0.000765541i
$419$	32.4769	+	20.8716i	1.58660	+	1.01965i	0.973225	+	0.229855i	$0.0738251\pi$
$419$	32.4769	+	20.8716i	1.58660	+	1.01965i	0.613375	+	0.789792i	$0.289811\pi$
$420$		0			0
$421$	−34.9440	+	5.02419i	−1.70307	+	0.244864i	−0.924086	−	0.382183i	$-0.875172\pi$
$421$	−34.9440	+	5.02419i	−1.70307	+	0.244864i	−0.778981	+	0.627048i	$0.784263\pi$
$422$	0.188704	−	11.6456i	0.00918598	−	0.566901i
$423$		0			0
$424$	11.2062	−	8.79441i	0.544222	−	0.427094i
$425$	−18.1876	−	8.30602i	−0.882230	−	0.402901i
$426$		0			0
$427$	11.6975	+	1.68185i	0.566083	+	0.0813905i
$428$	2.20404	−	4.43960i	0.106536	−	0.214596i
$429$		0			0
$430$	−33.2067	+	14.5195i	−1.60137	+	0.700192i
$431$	−13.1453	−	15.1704i	−0.633185	−	0.730734i	0.344970	−	0.938614i	$-0.387889\pi$
$431$	−13.1453	−	15.1704i	−0.633185	−	0.730734i	−0.978154	+	0.207880i	$0.933344\pi$
$432$		0			0
$433$	−19.1716	−	16.6123i	−0.921330	−	0.798337i	0.0584754	−	0.998289i	$-0.481376\pi$
$433$	−19.1716	−	16.6123i	−0.921330	−	0.798337i	−0.979806	+	0.199952i	$0.935922\pi$
$434$	8.68338	+	14.0054i	0.416816	+	0.672283i
$435$		0			0
$436$	−7.05671	−	11.8046i	−0.337955	−	0.565339i
$437$	0.313072	−	1.62182i	0.0149762	−	0.0775824i
$438$		0			0
$439$	20.7654	−	9.48324i	0.991079	−	0.452610i	0.147178	−	0.989110i	$-0.452981\pi$
$439$	20.7654	−	9.48324i	0.991079	−	0.452610i	0.843901	+	0.536500i	$0.180254\pi$
$440$	−0.287896	−	0.148788i	−0.0137249	−	0.00709319i
$441$		0			0
$442$	2.36484	−	7.59638i	0.112484	−	0.361323i
$443$	4.50488	−	3.90350i	0.214033	−	0.185461i	−0.541245	−	0.840865i	$-0.682047\pi$
$443$	4.50488	−	3.90350i	0.214033	−	0.185461i	0.755279	+	0.655404i	$0.227502\pi$
$444$		0			0
$445$	−33.8973	−	9.95315i	−1.60689	−	0.471825i
$446$	−12.8741	−	11.5259i	−0.609606	−	0.545767i
$447$		0			0
$448$	22.9266	+	9.23205i	1.08318	+	0.436173i
$449$	−11.6766	+	25.5682i	−0.551054	+	1.20664i	0.405234	+	0.914213i	$0.367190\pi$
$449$	−11.6766	+	25.5682i	−0.551054	+	1.20664i	−0.956288	+	0.292427i	$0.905537\pi$
$450$		0			0
$451$	0.252169	−	0.162059i	0.0118742	−	0.00763107i
$452$	4.31432	+	16.6739i	0.202929	+	0.784273i
$453$		0			0
$454$	−15.3620	−	10.2280i	−0.720976	−	0.480025i
$455$	8.11148	−	12.6217i	0.380272	−	0.591714i
$456$		0			0
$457$	11.4987	+	39.1611i	0.537889	+	1.83188i	0.554742	+	0.832022i	$0.312817\pi$
$457$	11.4987	+	39.1611i	0.537889	+	1.83188i	−0.0168539	+	0.999858i	$0.505365\pi$
$458$	−10.8522	+	9.09988i	−0.507090	+	0.425209i
$459$		0			0
$460$	30.1104	+	6.83122i	1.40390	+	0.318507i
$461$	13.4775			0.627710			0.313855	−	0.949471i	$-0.398379\pi$
$461$	13.4775			0.627710			0.313855	+	0.949471i	$0.398379\pi$
$462$		0			0
$463$	3.12666	+	10.6484i	0.145308	+	0.494874i	0.999693	−	0.0247663i	$-0.00788418\pi$
$463$	3.12666	+	10.6484i	0.145308	+	0.494874i	−0.854385	+	0.519640i	$0.826066\pi$
$464$	−0.472823	−	1.24262i	−0.0219503	−	0.0576870i
$465$		0			0
$466$	−19.8916	−	13.2438i	−0.921460	−	0.613507i
$467$	−0.809679	−	5.63144i	−0.0374675	−	0.260592i	0.962474	−	0.271372i	$-0.0874775\pi$
$467$	−0.809679	−	5.63144i	−0.0374675	−	0.260592i	−0.999942	+	0.0107805i	$0.996568\pi$
$468$		0			0
$469$	12.8549	−	8.26131i	0.593582	−	0.381472i
$470$	7.18088	+	56.4189i	0.331229	+	2.60241i
$471$		0			0
$472$	−30.6007	+	12.2149i	−1.40851	+	0.562237i
$473$	0.0403278	−	0.280486i	0.00185427	−	0.0128968i
$474$		0			0
$475$	1.77194	+	0.520288i	0.0813022	+	0.0238725i
$476$	−17.8928	+	14.5164i	−0.820115	+	0.665360i
$477$		0			0
$478$	9.65863	−	31.0256i	0.441775	−	1.41908i
$479$	15.8016	−	18.2361i	0.721995	−	0.833227i	−0.269551	−	0.962986i	$-0.586875\pi$
$479$	15.8016	−	18.2361i	0.721995	−	0.833227i	0.991545	+	0.129760i	$0.0414206\pi$
$480$		0			0
$481$	10.4195	−	4.75845i	0.475090	−	0.216967i
$482$	10.7395	+	38.8961i	0.489173	+	1.77167i
$483$		0			0
$484$	−18.8810	+	11.2869i	−0.858229	+	0.513042i
$485$	−12.6590	−	27.7193i	−0.574816	−	1.25867i
$486$		0			0
$487$	2.07401	+	1.79714i	0.0939824	+	0.0814362i	0.700585	−	0.713569i	$-0.252923\pi$
$487$	2.07401	+	1.79714i	0.0939824	+	0.0814362i	−0.606602	+	0.795005i	$0.707468\pi$
$488$	−2.54017	−	10.5170i	−0.114988	−	0.476081i
$489$		0			0
$490$	−10.6139	+	4.64087i	−0.479487	+	0.209653i
$491$	−10.7149	+	36.4915i	−0.483556	+	1.64684i	0.250774	+	0.968046i	$0.419315\pi$
$491$	−10.7149	+	36.4915i	−0.483556	+	1.64684i	−0.734329	+	0.678793i	$0.762503\pi$
$492$		0			0
$493$	1.22683	+	0.176391i	0.0552536	+	0.00794426i
$494$	−0.116349	+	0.725565i	−0.00523477	+	0.0326447i
$495$		0			0
$496$	8.96130	−	12.1368i	0.402374	−	0.544958i
$497$	8.05314	+	12.5309i	0.361232	+	0.562089i
$498$		0			0
$499$	−3.74529	+	0.538491i	−0.167662	+	0.0241062i	−0.225635	−	0.974212i	$-0.572446\pi$
$499$	−3.74529	+	0.538491i	−0.167662	+	0.0241062i	0.0579724	+	0.998318i	$0.481536\pi$
$500$	−0.728598	+	2.21340i	−0.0325839	+	0.0989862i
$501$		0			0
$502$	4.75288	−	9.97637i	0.212131	−	0.445267i
$503$	17.3591	−	5.09708i	0.774003	−	0.227268i	0.129202	−	0.991618i	$-0.458758\pi$
$503$	17.3591	−	5.09708i	0.774003	−	0.227268i	0.644801	+	0.764351i	$0.276940\pi$
$504$		0			0
$505$		−	11.3133i		−	0.503436i
$506$	−0.169450	+	0.171944i	−0.00753298	+	0.00764386i
$507$		0			0
$508$	3.12658	−	4.53496i	0.138720	−	0.201206i
$509$	−0.683452	+	0.200680i	−0.0302935	+	0.00889497i	−0.296844	−	0.954926i	$-0.595934\pi$
$509$	−0.683452	+	0.200680i	−0.0302935	+	0.00889497i	0.266551	+	0.963821i	$0.414116\pi$
$510$		0			0
$511$	19.6610	+	12.6354i	0.869753	+	0.558956i
$512$	0.0683880	−	22.6273i	0.00302235	−	0.999995i
$513$		0			0
$514$	−9.92931	−	0.160893i	−0.437963	−	0.00709670i
$515$	8.09550	+	12.5968i	0.356730	+	0.555083i
$516$		0			0
$517$	−0.404500	−	0.184729i	−0.0177899	−	0.00812437i
$518$	−32.7548	−	5.25242i	−1.43916	−	0.230778i
$519$		0			0
$520$	−13.4850	−	2.61312i	−0.591357	−	0.114593i
$521$	4.41957	−	15.0517i	0.193625	−	0.659426i	−0.804251	−	0.594289i	$-0.797433\pi$
$521$	4.41957	−	15.0517i	0.193625	−	0.659426i	0.997876	−	0.0651366i	$-0.0207483\pi$
$522$		0			0
$523$	−8.66514	−	10.0001i	−0.378900	−	0.437274i	0.533983	−	0.845495i	$-0.320695\pi$
$523$	−8.66514	−	10.0001i	−0.378900	−	0.437274i	−0.912883	+	0.408221i	$0.866149\pi$
$524$	0.392302	−	12.1020i	0.0171378	−	0.528679i
$525$		0			0
$526$	9.08390	−	5.63203i	0.396077	−	0.245568i
$527$	5.84256	+	12.7934i	0.254506	+	0.557290i
$528$		0			0
$529$	11.5116	−	19.9119i	0.500505	−	0.865734i
$530$	22.1004	−	6.10212i	0.959981	−	0.265059i
$531$		0			0
$532$	1.44499	−	1.56232i	0.0626484	−	0.0677353i
$533$	8.32011	−	9.60192i	0.360384	−	0.415905i
$534$		0			0
$535$	6.02910	−	5.22424i	0.260661	−	0.225864i
$536$	−11.3874	−	8.12624i	−0.491861	−	0.351000i
$537$		0			0
$538$	18.8668	−	21.0737i	0.813406	−	0.908550i
$539$	0.0128900	−	0.0896519i	0.000555212	−	0.00386158i
$540$		0			0
$541$	−8.42338	+	18.4446i	−0.362149	+	0.792996i	0.637595	+	0.770372i	$0.279929\pi$
$541$	−8.42338	+	18.4446i	−0.362149	+	0.792996i	−0.999744	+	0.0226243i	$0.992798\pi$
$542$	35.2664	−	4.48863i	1.51482	−	0.192803i
$543$		0			0
$544$	18.4159	+	10.2869i	0.789575	+	0.441046i
$545$	−3.15021	−	21.9102i	−0.134940	−	0.938531i
$546$		0			0
$547$	3.56889	−	5.55330i	0.152595	−	0.237442i	−0.756537	−	0.653951i	$-0.773110\pi$
$547$	3.56889	−	5.55330i	0.152595	−	0.237442i	0.909132	+	0.416509i	$0.136747\pi$
$548$	27.3948	+	4.84941i	1.17025	+	0.207157i
$549$		0			0
$550$	−0.173423	−	0.206818i	−0.00739477	−	0.00881875i
$551$	−0.114478			−0.00487694
$552$		0			0
$553$	−10.3156			−0.438663
$554$	−14.4039	−	17.1776i	−0.611961	−	0.729804i
$555$		0			0
$556$	−39.7085	−	7.02918i	−1.68401	−	0.298104i
$557$	7.54329	−	11.7376i	0.319620	−	0.497338i	−0.643851	−	0.765151i	$-0.722665\pi$
$557$	7.54329	−	11.7376i	0.319620	−	0.497338i	0.963471	+	0.267813i	$0.0863009\pi$
$558$		0			0
$559$	−1.70931	−	11.8885i	−0.0722960	−	0.502830i
$560$	28.3132	+	27.9425i	1.19645	+	1.18078i
$561$		0			0
$562$	24.4927	−	3.11738i	1.03316	−	0.131499i
$563$	4.99550	−	10.9386i	0.210535	−	0.461008i	−0.774674	−	0.632360i	$-0.782086\pi$
$563$	4.99550	−	10.9386i	0.210535	−	0.461008i	0.985210	+	0.171352i	$0.0548135\pi$
$564$		0			0
$565$	−3.94502	+	27.4382i	−0.165968	+	1.15434i
$566$	−24.3415	+	27.1887i	−1.02315	+	1.14283i
$567$		0			0
$568$	7.92146	−	11.1005i	0.332377	−	0.465765i
$569$	16.3119	−	14.1343i	0.683830	−	0.592542i	−0.242094	−	0.970253i	$-0.577834\pi$
$569$	16.3119	−	14.1343i	0.683830	−	0.592542i	0.925924	+	0.377711i	$0.123289\pi$
$570$		0			0
$571$	−23.5159	+	27.1388i	−0.984111	+	1.13572i	0.00663307	+	0.999978i	$0.497889\pi$
$571$	−23.5159	+	27.1388i	−0.984111	+	1.13572i	−0.990744	+	0.135746i	$0.956657\pi$
$572$	0.0729233	−	0.0788445i	0.00304908	−	0.00329665i
$573$		0			0
$574$	−35.4676	+	9.79291i	−1.48039	+	0.408748i
$575$	20.9425	+	14.9223i	0.873362	+	0.622302i
$576$		0			0
$577$	11.5340	+	25.2560i	0.480167	+	1.05142i	0.982417	+	0.186697i	$0.0597784\pi$
$577$	11.5340	+	25.2560i	0.480167	+	1.05142i	−0.502250	+	0.864722i	$0.667494\pi$
$578$	3.71982	−	2.30629i	0.154724	−	0.0959292i
$579$		0			0
$580$	0.0693305	−	2.13876i	0.00287879	−	0.0888071i
$581$	9.88452	+	11.4073i	0.410079	+	0.473256i
$582$		0			0
$583$	−0.0505045	+	0.172003i	−0.00209168	+	0.00712362i
$584$	4.07049	−	21.0058i	0.168438	−	0.869227i
$585$		0			0
$586$	19.4427	+	3.11776i	0.803172	+	0.128793i
$587$	−28.8385	−	13.1701i	−1.19029	−	0.543589i	−0.280985	−	0.959712i	$-0.590661\pi$
$587$	−28.8385	−	13.1701i	−1.19029	−	0.543589i	−0.909308	+	0.416123i	$0.863389\pi$
$588$		0			0
$589$	−0.702305	−	1.09281i	−0.0289380	−	0.0450284i
$590$	−53.0237	−	0.859189i	−2.18295	−	0.0353722i
$591$		0			0
$592$	6.65116	+	29.6333i	0.273361	+	1.21792i
$593$	38.0769	+	24.4705i	1.56363	+	1.00488i	0.981426	+	0.191840i	$0.0614456\pi$
$593$	38.0769	+	24.4705i	1.56363	+	1.00488i	0.582203	+	0.813043i	$0.302191\pi$
$594$		0			0
$595$	−35.5820	+	10.4478i	−1.45872	+	0.428319i
$596$	14.4653	−	20.9812i	0.592521	−	0.859424i
$597$		0			0
$598$	−4.83803	+	9.01618i	−0.197842	+	0.368699i
$599$			0.227769i			0.00930639i	0.999989	+	0.00465320i	$0.00148116\pi$
$599$			0.227769i			0.00930639i	−0.999989	+	0.00465320i	$0.998519\pi$
$600$		0			0
$601$	−17.3126	+	5.08344i	−0.706196	+	0.207358i	−0.615059	−	0.788481i	$-0.710868\pi$
$601$	−17.3126	+	5.08344i	−0.706196	+	0.207358i	−0.0911361	+	0.995838i	$0.529050\pi$
$602$	−14.9604	+	31.4020i	−0.609739	+	1.27985i
$603$		0			0
$604$	5.00057	−	15.1912i	0.203470	−	0.618121i
$605$	−35.0445	+	5.03864i	−1.42476	+	0.204850i
$606$		0			0
$607$	−20.9697	−	32.6294i	−0.851132	−	1.32439i	−0.944418	−	0.328748i	$-0.893373\pi$
$607$	−20.9697	−	32.6294i	−0.851132	−	1.32439i	0.0932857	−	0.995639i	$-0.470263\pi$
$608$	−1.81884	−	0.698382i	−0.0737639	−	0.0283231i
$609$		0			0
$610$	2.75718	−	17.1941i	0.111635	−	0.696170i
$611$	−18.6563	−	2.68237i	−0.754753	−	0.108517i
$612$		0			0
$613$	6.99907	−	23.8366i	0.282690	−	0.962752i	−0.688657	−	0.725087i	$-0.741800\pi$
$613$	6.99907	−	23.8366i	0.282690	−	0.962752i	0.971347	−	0.237666i	$-0.0763822\pi$
$614$	26.9777	−	11.7959i	1.08873	−	0.476043i
$615$		0			0
$616$	−0.302334	+	0.0730231i	−0.0121814	+	0.00294218i
$617$	3.66690	+	3.17739i	0.147624	+	0.127917i	0.725542	−	0.688178i	$-0.241589\pi$
$617$	3.66690	+	3.17739i	0.147624	+	0.127917i	−0.577918	+	0.816095i	$0.696135\pi$
$618$		0			0
$619$	9.10370	+	19.9343i	0.365908	+	0.801228i	0.999617	+	0.0276562i	$0.00880438\pi$
$619$	9.10370	+	19.9343i	0.365908	+	0.801228i	−0.633709	+	0.773571i	$0.718468\pi$
$620$	20.8419	−	12.4591i	0.837030	−	0.500369i
$621$		0			0
$622$	3.93819	+	14.2632i	0.157907	+	0.571901i
$623$	−30.8424	+	14.0853i	−1.23568	+	0.564314i
$624$		0			0
$625$	15.1006	−	17.4270i	0.604024	−	0.697080i
$626$	9.22557	−	29.6345i	0.368728	−	1.18443i
$627$		0			0
$628$	−12.5880	+	10.2126i	−0.502316	+	0.407529i
$629$	−27.1658	−	7.97660i	−1.08317	−	0.318048i
$630$		0			0
$631$	2.58950	−	18.0104i	0.103086	−	0.716982i	−0.871079	−	0.491144i	$-0.836579\pi$
$631$	2.58950	−	18.0104i	0.103086	−	0.716982i	0.974165	−	0.225838i	$-0.0725120\pi$
$632$	3.50116	+	8.77108i	0.139269	+	0.348895i
$633$		0			0
$634$	−1.51403	−	11.8955i	−0.0601299	−	0.472430i
$635$	7.45822	−	4.79311i	0.295971	−	0.190209i
$636$		0			0
$637$	−0.546347	−	3.79993i	−0.0216471	−	0.150559i
$638$	0.0139268	+	0.00927245i	0.000551368	+	0.000367100i
$639$		0			0
$640$	14.1492	−	33.5579i	0.559294	−	1.32649i
$641$	3.51165	+	11.9596i	0.138702	+	0.472375i	0.999320	−	0.0368759i	$-0.0117406\pi$
$641$	3.51165	+	11.9596i	0.138702	+	0.472375i	−0.860618	+	0.509251i	$0.829922\pi$
$642$		0			0
$643$	34.7765			1.37145			0.685726	−	0.727860i	$-0.259485\pi$
$643$	34.7765			1.37145			0.685726	+	0.727860i	$0.259485\pi$
$644$	26.1335	−	13.9696i	1.02980	−	0.550479i
$645$		0			0
$646$	1.39176	−	1.16703i	0.0547580	−	0.0459161i
$647$	−3.60657	−	12.2828i	−0.141789	−	0.482888i	0.857724	−	0.514111i	$-0.171878\pi$
$647$	−3.60657	−	12.2828i	−0.141789	−	0.482888i	−0.999512	+	0.0312227i	$0.990060\pi$
$648$		0			0
$649$	0.224169	−	0.348813i	0.00879938	−	0.0136921i
$650$	−9.52251	−	6.34007i	−0.373504	−	0.248678i
$651$		0			0
$652$	−1.12639	−	4.35324i	−0.0441128	−	0.170486i
$653$	17.9373	−	11.5276i	0.701942	−	0.451111i	−0.140371	−	0.990099i	$-0.544830\pi$
$653$	17.9373	−	11.5276i	0.701942	−	0.451111i	0.842313	+	0.538988i	$0.181193\pi$
$654$		0			0
$655$	8.09578	−	17.7273i	0.316328	−	0.692663i
$656$	20.3646	+	26.8335i	0.795103	+	1.04767i
$657$		0			0
$658$	40.6680	+	36.4092i	1.58541	+	1.41938i
$659$	−5.15581	−	1.51388i	−0.200842	−	0.0589725i	0.179764	−	0.983710i	$-0.442467\pi$
$659$	−5.15581	−	1.51388i	−0.200842	−	0.0589725i	−0.380606	+	0.924737i	$0.624285\pi$
$660$		0			0
$661$	15.0791	−	13.0661i	0.586507	−	0.508212i	−0.310296	−	0.950640i	$-0.600428\pi$
$661$	15.0791	−	13.0661i	0.586507	−	0.508212i	0.896804	+	0.442428i	$0.145883\pi$
$662$	−6.94830	+	22.3195i	−0.270053	+	0.867470i
$663$		0			0
$664$	6.34453	−	12.2763i	0.246216	−	0.476412i
$665$	3.11567	−	1.42288i	0.120820	−	0.0551768i
$666$		0			0
$667$	−1.50623	−	0.521803i	−0.0583214	−	0.0202043i
$668$	−8.69680	−	14.5482i	−0.336489	−	0.562888i
$669$		0			0
$670$	−11.8647	−	19.1366i	−0.458374	−	0.739312i
$671$	0.102899	+	0.0891622i	0.00397236	+	0.00344207i
$672$		0			0
$673$	−11.7294	−	13.5365i	−0.452136	−	0.521793i	0.483221	−	0.875499i	$-0.339467\pi$
$673$	−11.7294	−	13.5365i	−0.452136	−	0.521793i	−0.935357	+	0.353706i	$0.884921\pi$
$674$	−18.6837	+	8.16937i	−0.719670	+	0.314672i
$675$		0			0
$676$	−9.53721	+	19.2108i	−0.366816	+	0.738877i
$677$	21.6422	+	3.11168i	0.831778	+	0.119592i	0.545032	−	0.838415i	$-0.316517\pi$
$677$	21.6422	+	3.11168i	0.831778	+	0.119592i	0.286746	+	0.958007i	$0.407426\pi$
$678$		0			0
$679$	−26.6037	−	12.1495i	−1.02096	−	0.466255i
$680$	20.9603	+	26.7085i	0.803790	+	1.02422i
$681$		0			0
$682$	−0.00307598	+	0.189830i	−0.000117785	+	0.00726897i
$683$	−50.9829	+	7.33023i	−1.95081	+	0.280484i	−0.999605	−	0.0280901i	$-0.991057\pi$
$683$	−50.9829	+	7.33023i	−1.95081	+	0.280484i	−0.951200	+	0.308574i	$0.900148\pi$
$684$		0			0
$685$	37.6691	+	24.2085i	1.43926	+	0.924959i
$686$	8.37229	−	17.5736i	0.319656	−	0.670962i
$687$		0			0
$688$	31.7780	+	2.06242i	1.21153	+	0.0786289i
$689$			7.59817i			0.289467i
$690$		0			0
$691$		−	23.2234i		−	0.883459i	−0.897148	−	0.441730i	$-0.854365\pi$
$691$		−	23.2234i		−	0.883459i	0.897148	−	0.441730i	$-0.145635\pi$
$692$	−36.5314	−	25.1862i	−1.38872	−	0.957437i
$693$		0			0
$694$	−9.94848	−	4.73960i	−0.377639	−	0.179913i
$695$	−54.6010	−	35.0900i	−2.07114	−	1.33104i
$696$		0			0
$697$	−31.0839	+	4.46918i	−1.17739	+	0.169282i
$698$	−12.4569	−	0.201849i	−0.471499	−	0.00764010i
$699$		0			0
$700$	12.7794	+	30.5670i	0.483017	+	1.15532i
$701$	9.20084	+	4.20188i	0.347511	+	0.158703i	0.581521	−	0.813531i	$-0.302458\pi$
$701$	9.20084	+	4.20188i	0.347511	+	0.158703i	−0.234010	+	0.972234i	$0.575185\pi$
$702$		0			0
$703$	2.58842	+	0.372158i	0.0976240	+	0.0140362i
$704$	0.164704	+	0.232283i	0.00620751	+	0.00875450i
$705$		0			0
$706$	−13.0635	−	29.8767i	−0.491650	−	1.12443i
$707$	−7.11046	−	8.20591i	−0.267416	−	0.308615i
$708$		0			0
$709$	5.96392	+	5.16777i	0.223980	+	0.194080i	0.759621	−	0.650366i	$-0.225385\pi$
$709$	5.96392	+	5.16777i	0.223980	+	0.194080i	−0.535641	+	0.844446i	$0.679930\pi$
$710$	18.6544	−	11.5657i	0.700087	−	0.434054i
$711$		0			0
$712$	22.4445	+	21.4440i	0.841142	+	0.803647i
$713$	−4.25934	−	17.5796i	−0.159514	−	0.658362i
$714$		0			0
$715$	0.157236	−	0.0718071i	0.00588028	−	0.00268544i
$716$	4.96676	+	4.59376i	0.185617	+	0.171677i
$717$		0			0
$718$	37.2204	+	11.5871i	1.38905	+	0.432428i
$719$	−3.49955	+	3.03238i	−0.130511	+	0.113089i	−0.717671	−	0.696383i	$-0.754792\pi$
$719$	−3.49955	+	3.03238i	−0.130511	+	0.113089i	0.587159	+	0.809471i	$0.300246\pi$
$720$		0			0
$721$	13.7891	+	4.04884i	0.513533	+	0.150787i
$722$	17.8109	−	19.8943i	0.662855	−	0.740389i
$723$		0			0
$724$	19.4155	−	2.15212i	0.721573	−	0.0799831i
$725$	0.740361	−	1.62117i	0.0274963	−	0.0602086i
$726$		0			0
$727$	15.3981	−	9.89574i	0.571083	−	0.367013i	−0.223004	−	0.974818i	$-0.571586\pi$
$727$	15.3981	−	9.89574i	0.571083	−	0.367013i	0.794086	+	0.607805i	$0.207950\pi$
$728$	−11.4235	+	6.58001i	−0.423382	+	0.243871i
$729$		0			0
$730$	19.0854	−	28.6654i	0.706382	−	1.06096i
$731$	−16.0501	+	24.9744i	−0.593633	+	0.923710i
$732$		0			0
$733$	−6.22211	−	21.1906i	−0.229819	−	0.782692i	−0.990966	−	0.134112i	$-0.957182\pi$
$733$	−6.22211	−	21.1906i	−0.229819	−	0.782692i	0.761147	−	0.648579i	$-0.224636\pi$
$734$	−19.0141	−	22.6756i	−0.701824	−	0.836973i
$735$		0			0
$736$	−20.7479	−	17.4793i	−0.764776	−	0.644296i
$737$	0.176050			0.00648487
$738$		0			0
$739$	−7.18128	−	24.4572i	−0.264168	−	0.899672i	−0.979594	−	0.200985i	$-0.935586\pi$
$739$	−7.18128	−	24.4572i	−0.264168	−	0.899672i	0.715427	−	0.698688i	$-0.246232\pi$
$740$	−8.52050	+	48.1331i	−0.313220	+	1.76941i
$741$		0			0
$742$	12.1949	−	18.3163i	0.447691	−	0.672412i
$743$	−5.21572	−	36.2761i	−0.191346	−	1.33084i	−0.828450	−	0.560063i	$-0.810777\pi$
$743$	−5.21572	−	36.2761i	−0.191346	−	1.33084i	0.637104	−	0.770778i	$-0.280132\pi$
$744$		0			0
$745$	34.5058	−	22.1756i	1.26420	−	0.812450i
$746$	24.3818	−	3.10327i	0.892683	−	0.113619i
$747$		0			0
$748$	−0.263840	+	0.0292455i	−0.00964695	+	0.00106932i
$749$	1.08964	−	7.57863i	0.0398147	−	0.276917i
$750$		0			0
$751$	−49.1188	−	14.4226i	−1.79237	−	0.526288i	−0.795546	−	0.605894i	$-0.792816\pi$
$751$	−49.1188	−	14.4226i	−1.79237	−	0.526288i	−0.996826	+	0.0796059i	$0.974634\pi$
$752$	17.1549	−	46.9366i	0.625577	−	1.71160i
$753$		0			0
$754$	0.677107	+	0.210791i	0.0246588	+	0.00767657i
$755$	16.8567	−	19.4536i	0.613476	−	0.707989i
$756$		0			0
$757$	−31.3442	+	14.3144i	−1.13922	+	0.520266i	−0.893496	−	0.449072i	$-0.851755\pi$
$757$	−31.3442	+	14.3144i	−1.13922	+	0.520266i	−0.245729	+	0.969339i	$0.579027\pi$
$758$	51.6453	−	14.2597i	1.87584	−	0.517937i
$759$		0			0
$760$	−2.26731	−	2.16624i	−0.0822441	−	0.0785779i
$761$	−5.45157	−	11.9373i	−0.197619	−	0.432726i	0.784716	−	0.619855i	$-0.212809\pi$
$761$	−5.45157	−	11.9373i	−0.197619	−	0.432726i	−0.982335	+	0.187130i	$0.940081\pi$
$762$		0			0
$763$	−16.0556	−	13.9123i	−0.581253	−	0.503658i
$764$	10.0695	+	0.326416i	0.364302	+	0.0118093i
$765$		0			0
$766$	−19.6557	−	44.9535i	−0.710190	−	1.62424i
$767$	4.95129	−	16.8626i	0.178781	−	0.608871i
$768$		0			0
$769$	−8.77875	−	1.26219i	−0.316570	−	0.0455159i	−0.0178015	−	0.999842i	$-0.505667\pi$
$769$	−8.77875	−	1.26219i	−0.316570	−	0.0455159i	−0.298768	+	0.954326i	$0.596576\pi$
$770$	−0.494285	−	0.0792614i	−0.0178128	−	0.00285638i
$771$		0			0
$772$	0.200174	+	0.478795i	0.00720442	+	0.0172322i
$773$	10.5244	+	16.3762i	0.378535	+	0.589012i	0.977286	−	0.211923i	$-0.0679726\pi$
$773$	10.5244	+	16.3762i	0.378535	+	0.589012i	−0.598751	+	0.800935i	$0.704336\pi$
$774$		0			0
$775$	20.0176	−	2.87810i	0.719054	−	0.103384i
$776$	−1.30099	+	26.7441i	−0.0467026	+	0.960058i
$777$		0			0
$778$	−8.85895	−	4.22053i	−0.317609	−	0.151313i
$779$	2.78302	−	0.817168i	0.0997120	−	0.0292781i
$780$		0			0
$781$			0.171613i			0.00614080i
$782$	23.6312	−	9.01120i	0.845051	−	0.322240i
$783$		0			0
$784$	10.1572	+	0.659211i	0.362758	+	0.0235433i
$785$	−25.0328	+	7.35028i	−0.893458	+	0.262343i
$786$		0			0
$787$	−17.3049	−	11.1212i	−0.616851	−	0.396426i	0.194569	−	0.980889i	$-0.437669\pi$
$787$	−17.3049	−	11.1212i	−0.616851	−	0.396426i	−0.811421	+	0.584462i	$0.801305\pi$
$788$	15.4869	+	5.09791i	0.551698	+	0.181606i
$789$		0			0
$790$	−0.246269	+	15.1982i	−0.00876187	+	0.540727i
$791$	14.3836	+	22.3813i	0.511422	+	0.795788i
$792$		0			0
$793$	5.24944	+	2.39734i	0.186413	+	0.0851321i
$794$	1.75118	−	10.9206i	0.0621470	−	0.387557i
$795$		0			0
$796$	−19.3783	+	39.0338i	−0.686847	+	1.38352i
$797$	−15.0814	+	51.3625i	−0.534210	+	1.81935i	0.0380428	+	0.999276i	$0.487888\pi$
$797$	−15.0814	+	51.3625i	−0.534210	+	1.81935i	−0.572253	+	0.820077i	$0.693930\pi$
$798$		0			0
$799$	30.5081	+	35.2082i	1.07930	+	1.24558i
$800$	21.6530	−	21.2406i	0.765548	−	0.750970i
$801$		0			0
$802$	23.8797	+	38.5156i	0.843222	+	1.36003i
$803$	0.111855	+	0.244929i	0.00394728	+	0.00864334i
$804$		0			0
$805$	47.4795	−	4.51977i	1.67343	−	0.159301i
$806$	2.14173	+	7.75683i	0.0754392	+	0.273223i
$807$		0			0
$808$	−4.56396	+	8.83099i	−0.160559	+	0.310673i
$809$	−12.7815	+	14.7506i	−0.449372	+	0.518603i	−0.934559	−	0.355807i	$-0.884206\pi$
$809$	−12.7815	+	14.7506i	−0.449372	+	0.518603i	0.485187	+	0.874410i	$0.338752\pi$
$810$		0			0
$811$	−18.7689	+	16.2634i	−0.659067	+	0.571085i	−0.918862	−	0.394579i	$-0.870890\pi$
$811$	−18.7689	+	16.2634i	−0.659067	+	0.571085i	0.259795	+	0.965664i	$0.416345\pi$
$812$	−1.29393	−	1.59488i	−0.0454081	−	0.0559695i
$813$		0			0
$814$	−0.284749	−	0.254930i	−0.00998045	−	0.00893529i
$815$	1.02997	−	7.16361i	0.0360783	−	0.250930i
$816$		0			0
$817$	1.13906	−	2.49419i	0.0398506	−	0.0872607i
$818$	−1.65860	−	13.0313i	−0.0579916	−	0.455630i
$819$		0			0
$820$	13.5814	+	52.4891i	0.474283	+	1.83300i
$821$	−4.14794	−	28.8495i	−0.144764	−	1.00686i	−0.924618	−	0.380895i	$-0.875616\pi$
$821$	−4.14794	−	28.8495i	−0.144764	−	1.00686i	0.779854	−	0.625961i	$-0.215293\pi$
$822$		0			0
$823$	−7.39377	+	11.5049i	−0.257731	+	0.401036i	−0.945872	−	0.324540i	$-0.894790\pi$
$823$	−7.39377	+	11.5049i	−0.257731	+	0.401036i	0.688141	+	0.725577i	$0.258427\pi$
$824$	−1.23746	−	13.0987i	−0.0431091	−	0.456316i
$825$		0			0
$826$	−38.9998	+	32.7024i	−1.35698	+	1.13786i
$827$	−5.74191			−0.199666			−0.0998328	−	0.995004i	$-0.531831\pi$
$827$	−5.74191			−0.199666			−0.0998328	+	0.995004i	$0.531831\pi$
$828$		0			0
$829$	−10.9254			−0.379453			−0.189727	−	0.981837i	$-0.560760\pi$
$829$	−10.9254			−0.379453			−0.189727	+	0.981837i	$0.560760\pi$
$830$	17.0427	−	14.2908i	0.591561	−	0.496040i
$831$		0			0
$832$	9.47202	+	7.47981i	0.328383	+	0.259316i
$833$	−5.13009	+	7.98258i	−0.177747	+	0.276580i
$834$		0			0
$835$	−3.88238	−	27.0025i	−0.134355	−	0.934461i
$836$	0.0237365	−	0.00614176i	0.000820944	−	0.000212417i
$837$		0			0
$838$	−6.89328	−	54.1593i	−0.238125	−	1.87090i
$839$	−5.25663	+	11.5104i	−0.181479	+	0.397383i	−0.978406	−	0.206692i	$-0.933730\pi$
$839$	−5.25663	+	11.5104i	−0.181479	+	0.397383i	0.796927	+	0.604075i	$0.206457\pi$
$840$		0			0
$841$	4.11141	−	28.5955i	0.141773	−	0.986051i
$842$	37.1973	+	33.3019i	1.28190	+	1.14766i
$843$		0			0
$844$	−12.7913	+	10.3776i	−0.440296	+	0.357212i
$845$	−26.0888	+	22.6061i	−0.897481	+	0.777672i
$846$		0			0
$847$	−22.2521	+	25.6803i	−0.764592	+	0.882387i
$848$	−19.7129	−	4.15242i	−0.676945	−	0.142595i
$849$		0			0
$850$	7.52580	+	27.2566i	0.258133	+	0.934894i
$851$	32.3603	+	16.6949i	1.10930	+	0.572292i
$852$		0			0
$853$	18.4378	+	40.3732i	0.631299	+	1.38235i	0.907009	+	0.421111i	$0.138360\pi$
$853$	18.4378	+	40.3732i	0.631299	+	1.38235i	−0.275710	+	0.961241i	$0.588913\pi$
$854$	−8.80671	−	14.2044i	−0.301359	−	0.486063i
$855$		0			0
$856$	−6.81376	+	1.64573i	−0.232889	+	0.0562500i
$857$	−16.2036	−	18.6999i	−0.553503	−	0.638776i	0.408193	−	0.912896i	$-0.366159\pi$
$857$	−16.2036	−	18.6999i	−0.553503	−	0.638776i	−0.961696	+	0.274119i	$0.911614\pi$
$858$		0			0
$859$	3.06616	−	10.4424i	0.104616	−	0.356290i	−0.890502	−	0.454979i	$-0.849647\pi$
$859$	3.06616	−	10.4424i	0.104616	−	0.356290i	0.995118	+	0.0986892i	$0.0314650\pi$
$860$	45.9082	+	22.7912i	1.56546	+	0.777172i
$861$		0			0
$862$	−4.49476	+	28.0299i	−0.153092	+	0.954703i
$863$	17.6366	+	8.05438i	0.600358	+	0.274174i	0.692323	−	0.721588i	$-0.256587\pi$
$863$	17.6366	+	8.05438i	0.600358	+	0.274174i	−0.0919649	+	0.995762i	$0.529315\pi$
$864$		0			0
$865$	−38.6110	−	60.0798i	−1.31281	−	2.04278i
$866$	−0.581243	+	35.8707i	−0.0197515	+	1.21893i
$867$		0			0
$868$	7.28670	−	22.1362i	0.247327	−	0.751351i
$869$	−0.0999803	−	0.0642535i	−0.00339160	−	0.00217965i
$870$		0			0
$871$	7.15966	−	2.10227i	0.242596	−	0.0712325i
$872$	−6.37991	+	18.3736i	−0.216051	+	0.622209i
$873$		0			0
$874$	−2.04198	+	1.13445i	−0.0690710	+	0.0383733i
$875$			3.59956i			0.121687i
$876$		0			0
$877$	23.1334	−	6.79259i	0.781160	−	0.229369i	0.133246	−	0.991083i	$-0.457460\pi$
$877$	23.1334	−	6.79259i	0.781160	−	0.229369i	0.647914	+	0.761714i	$0.275642\pi$
$878$	−29.1456	−	13.8854i	−0.983616	−	0.468608i
$879$		0			0
$880$	0.100369	+	0.447180i	0.00338344	+	0.0150744i
$881$	10.0629	−	1.44683i	0.339028	−	0.0487449i	0.0293018	−	0.999571i	$-0.490672\pi$
$881$	10.0629	−	1.44683i	0.339028	−	0.0487449i	0.309726	+	0.950826i	$0.399763\pi$
$882$		0			0
$883$	19.3974	+	30.1830i	0.652775	+	1.01574i	0.997041	+	0.0768656i	$0.0244912\pi$
$883$	19.3974	+	30.1830i	0.652775	+	1.01574i	−0.344267	+	0.938872i	$0.611872\pi$
$884$	−10.3807	+	4.33997i	−0.349142	+	0.145969i
$885$		0			0
$886$	−8.32352	−	1.33472i	−0.279634	−	0.0448409i
$887$	−17.0557	−	2.45224i	−0.572676	−	0.0823383i	−0.150108	−	0.988670i	$-0.547962\pi$
$887$	−17.0557	−	2.45224i	−0.572676	−	0.0823383i	−0.422568	+	0.906331i	$0.638871\pi$
$888$		0			0
$889$	2.39720	−	8.16412i	0.0803996	−	0.273816i
$890$	20.0159	+	45.7772i	0.670933	+	1.53446i
$891$		0			0
$892$	−0.791747	+	24.4244i	−0.0265096	+	0.817789i
$893$	−3.25192	−	2.81781i	−0.108822	−	0.0942944i
$894$		0			0
$895$	4.52345	+	9.90498i	0.151202	+	0.331087i
$896$	−10.8284	−	33.2334i	−0.361752	−	1.11025i
$897$		0			0
$898$	38.3174	−	10.5798i	1.27867	−	0.353052i
$899$	−1.14035	+	0.520779i	−0.0380327	+	0.0173690i
$900$		0			0
$901$	12.2986	−	14.1933i	0.409726	−	0.472849i
$902$	−0.404756	−	0.126005i	−0.0134769	−	0.00419551i
$903$		0			0
$904$	14.1484	−	19.8264i	0.470570	−	0.659415i
$905$	30.1671	+	8.85787i	1.00279	+	0.294446i
$906$		0			0
$907$	0.865985	−	6.02306i	0.0287545	−	0.199992i	−0.970380	−	0.241583i	$-0.922333\pi$
$907$	0.865985	−	6.02306i	0.0287545	−	0.199992i	0.999135	+	0.0415906i	$0.0132425\pi$
$908$	2.87545	+	25.9411i	0.0954253	+	0.860886i
$909$		0			0
$910$	−21.0483	+	2.67898i	−0.697743	+	0.0888073i
$911$	−37.1111	+	23.8499i	−1.22955	+	0.790182i	−0.983820	−	0.179157i	$-0.942663\pi$
$911$	−37.1111	+	23.8499i	−1.22955	+	0.790182i	−0.245726	+	0.969339i	$0.579027\pi$
$912$		0			0
$913$	0.0247486	+	0.172131i	0.000819060	+	0.00569669i
$914$	31.9886	−	48.0454i	1.05809	−	1.58920i
$915$		0			0
$916$	19.7223	+	3.49123i	0.651642	+	0.115353i
$917$	−5.26954	−	17.9464i	−0.174016	−	0.592643i
$918$		0			0
$919$	9.53477			0.314523			0.157262	−	0.987557i	$-0.449733\pi$
$919$	9.53477			0.314523			0.157262	+	0.987557i	$0.449733\pi$
$920$	−19.9579	−	38.8366i	−0.657991	−	1.28041i
$921$		0			0
$922$	−12.2467	−	14.6050i	−0.403323	−	0.480990i
$923$	2.04929	+	6.97924i	0.0674532	+	0.229724i
$924$		0			0
$925$	−22.0102	+	34.2486i	−0.723692	+	1.12609i
$926$	8.69810	−	13.0642i	0.285837	−	0.429315i
$927$		0			0
$928$	−0.916925	+	1.64151i	−0.0300995	+	0.0538853i
$929$	−4.26906	+	2.74356i	−0.140063	+	0.0900131i	−0.608796	−	0.793327i	$-0.708347\pi$
$929$	−4.26906	+	2.74356i	−0.140063	+	0.0900131i	0.468733	+	0.883340i	$0.344711\pi$
$930$		0			0
$931$	0.364078	−	0.797220i	0.0119322	−	0.0261278i
$932$	3.72329	+	33.5899i	0.121960	+	1.10028i
$933$		0			0
$934$	−5.36681	+	5.99456i	−0.175607	+	0.196148i
$935$	−0.409944	−	0.120371i	−0.0134066	−	0.00393654i
$936$		0			0
$937$	−2.72871	+	2.36444i	−0.0891431	+	0.0772429i	−0.698292	−	0.715813i	$-0.746056\pi$
$937$	−2.72871	+	2.36444i	−0.0891431	+	0.0772429i	0.609149	+	0.793056i	$0.291511\pi$
$938$	−20.6333	−	6.42339i	−0.673701	−	0.209731i
$939$		0			0
$940$	54.6136	−	59.0480i	1.78130	−	1.92593i
$941$	43.5770	−	19.9009i	1.42057	−	0.648752i	0.450766	−	0.892642i	$-0.351151\pi$
$941$	43.5770	−	19.9009i	1.42057	−	0.648752i	0.969803	+	0.243890i	$0.0784237\pi$
$942$		0			0
$943$	40.3418	+	1.93351i	1.31371	+	0.0629638i
$944$	41.0429	+	22.0612i	1.33583	+	0.718032i
$945$		0			0
$946$	−0.340595	+	0.211169i	−0.0110737	+	0.00686570i
$947$	−19.4905	−	16.8886i	−0.633356	−	0.548806i	0.277919	−	0.960605i	$-0.410355\pi$
$947$	−19.4905	−	16.8886i	−0.633356	−	0.548806i	−0.911275	+	0.411798i	$0.864901\pi$
$948$		0			0
$949$	7.47375	+	8.62517i	0.242608	+	0.279985i
$950$	−1.04630	−	2.39295i	−0.0339466	−	0.0776374i
$951$		0			0
$952$	31.9896	+	6.19892i	1.03679	+	0.200908i
$953$	7.41943	+	1.06675i	0.240339	+	0.0345555i	0.261432	−	0.965222i	$-0.415805\pi$
$953$	7.41943	+	1.06675i	0.240339	+	0.0345555i	−0.0210927	+	0.999778i	$0.506715\pi$
$954$		0			0
$955$	14.7500	+	6.73611i	0.477300	+	0.217976i
$956$	−42.3976	+	17.7256i	−1.37124	+	0.573286i
$957$		0			0
$958$	−34.1202	−	0.552878i	−1.10237	−	0.0178627i
$959$	42.5378	−	6.11601i	1.37362	−	0.197496i
$960$		0			0
$961$	14.1117	+	9.06902i	0.455215	+	0.292549i
$962$	−14.6245	−	6.96732i	−0.471513	−	0.224635i
$963$		0			0
$964$	32.3912	−	46.9818i	1.04325	−	1.51318i
$965$			0.835257i			0.0268879i
$966$		0			0
$967$		−	26.1514i		−	0.840972i	−0.907299	−	0.420486i	$-0.861860\pi$
$967$		−	26.1514i		−	0.840972i	0.907299	−	0.420486i	$-0.138140\pi$
$968$	29.3879	+	10.2044i	0.944562	+	0.327982i
$969$		0			0
$970$	−18.5353	+	38.9059i	−0.595133	+	1.24919i
$971$	−9.65741	−	6.20644i	−0.309921	−	0.199174i	0.376429	−	0.926445i	$-0.377152\pi$
$971$	−9.65741	−	6.20644i	−0.309921	−	0.199174i	−0.686350	+	0.727271i	$0.740788\pi$
$972$		0			0
$973$	−61.6581	+	8.86510i	−1.97667	+	0.284202i
$974$	0.0628796	−	3.88053i	0.00201479	−	0.124340i
$975$		0			0
$976$	−9.08858	+	12.3092i	−0.290918	+	0.394007i
$977$	−12.1989	−	5.57103i	−0.390276	−	0.178233i	0.210606	−	0.977571i	$-0.432456\pi$
$977$	−12.1989	−	5.57103i	−0.390276	−	0.178233i	−0.600882	+	0.799338i	$0.705184\pi$
$978$		0			0
$979$	−0.386664	−	0.0555940i	−0.0123578	−	0.00177679i
$980$	14.6737	+	7.28476i	0.468734	+	0.232703i
$981$		0			0
$982$	49.2806	−	21.5477i	1.57261	−	0.687615i
$983$	28.4637	+	32.8489i	0.907851	+	1.04772i	0.998655	+	0.0518471i	$0.0165108\pi$
$983$	28.4637	+	32.8489i	0.907851	+	1.04772i	−0.0908041	+	0.995869i	$0.528944\pi$
$984$		0			0
$985$	19.8323	+	17.1848i	0.631909	+	0.547552i
$986$	−0.923641	−	1.48974i	−0.0294147	−	0.0474430i
$987$		0			0
$988$	0.891986	−	0.533221i	0.0283778	−	0.0169640i
$989$	26.3557	−	27.6250i	0.838064	−	0.878423i
$990$		0			0
$991$	−8.38396	+	3.82883i	−0.266325	+	0.121627i	−0.544102	−	0.839019i	$-0.683130\pi$
$991$	−8.38396	+	3.82883i	−0.266325	+	0.121627i	0.277777	+	0.960646i	$0.410402\pi$
$992$	−21.2950	+	1.31744i	−0.676118	+	0.0418288i
$993$		0			0
$994$	6.26152	−	20.1134i	0.198603	−	0.637957i
$995$	−53.0089	+	45.9325i	−1.68050	+	1.45616i
$996$		0			0
$997$	−35.5705	−	10.4444i	−1.12653	−	0.330779i	−0.335186	−	0.942152i	$-0.608799\pi$
$997$	−35.5705	−	10.4444i	−1.12653	−	0.330779i	−0.791342	+	0.611373i	$0.790617\pi$
$998$	3.98679	+	3.56929i	0.126200	+	0.112984i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.u.a.19.3		100
3.2	odd	2		92.2.h.a.19.8	yes	100
4.3	odd	2	inner	828.2.u.a.19.5		100
12.11	even	2		92.2.h.a.19.6	✓	100
23.17	odd	22	inner	828.2.u.a.523.5		100
69.17	even	22		92.2.h.a.63.6	yes	100
92.63	even	22	inner	828.2.u.a.523.3		100
276.155	odd	22		92.2.h.a.63.8	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.h.a.19.6	✓	100	12.11	even	2
92.2.h.a.19.8	yes	100	3.2	odd	2
92.2.h.a.63.6	yes	100	69.17	even	22
92.2.h.a.63.8	yes	100	276.155	odd	22
828.2.u.a.19.3		100	1.1	even	1	trivial
828.2.u.a.19.5		100	4.3	odd	2	inner
828.2.u.a.523.3		100	92.63	even	22	inner
828.2.u.a.523.5		100	23.17	odd	22	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:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.908675 - 1.08366i) q^{2} +(-0.348619 + 1.96938i) q^{4} +(-1.74032 + 2.70799i) q^{5} +(0.439673 + 3.05800i) q^{7} +(2.45091 - 1.41175i) q^{8} +O(q^{10})\)	\(q+(-0.908675 - 1.08366i) q^{2} +(-0.348619 + 1.96938i) q^{4} +(-1.74032 + 2.70799i) q^{5} +(0.439673 + 3.05800i) q^{7} +(2.45091 - 1.41175i) q^{8} +(4.51592 - 0.574777i) q^{10} +(-0.0147862 + 0.0323773i) q^{11} +(-0.214704 + 1.49330i) q^{13} +(2.91429 - 3.25518i) q^{14} +(-3.75693 - 1.37313i) q^{16} +(2.81816 - 2.44195i) q^{17} +(-0.225545 + 0.260293i) q^{19} +(-4.72636 - 4.37142i) q^{20} +(0.0485217 - 0.0133973i) q^{22} +(-4.15401 + 2.39670i) q^{23} +(-2.22743 - 4.87740i) q^{25} +(1.81332 - 1.12426i) q^{26} +(-6.17564 - 0.200191i) q^{28} +(0.217665 + 0.251198i) q^{29} +(-1.06260 + 3.61888i) q^{31} +(1.92583 + 5.31895i) q^{32} +(-5.20703 - 0.834977i) q^{34} +(-9.04621 - 4.13126i) q^{35} +(-4.10489 - 6.38734i) q^{37} +(0.487015 + 0.00789152i) q^{38} +(-0.442381 + 9.09395i) q^{40} +(-7.08463 - 4.55301i) q^{41} +(-7.63873 + 2.24293i) q^{43} +(-0.0586085 - 0.0404070i) q^{44} +(6.37185 + 2.32369i) q^{46} +12.4933i q^{47} +(-2.44157 + 0.716911i) q^{49} +(-3.26141 + 6.84575i) q^{50} +(-2.86603 - 0.943427i) q^{52} +(4.98512 - 0.716752i) q^{53} +(-0.0619447 - 0.0963878i) q^{55} +(5.39471 + 6.87418i) q^{56} +(0.0744261 - 0.464131i) q^{58} +(-11.5305 - 1.65784i) q^{59} +(1.07769 - 3.67028i) q^{61} +(4.88718 - 2.13690i) q^{62} +(4.01395 - 6.92013i) q^{64} +(-3.67019 - 3.18024i) q^{65} +(-2.05467 - 4.49910i) q^{67} +(3.82667 + 6.40135i) q^{68} +(3.74319 + 13.5569i) q^{70} +(4.38573 - 2.00290i) q^{71} +(4.95391 - 5.71712i) q^{73} +(-3.19166 + 10.2523i) q^{74} +(-0.433987 - 0.534927i) q^{76} +(-0.105511 - 0.0309807i) q^{77} +(-0.475186 + 3.30499i) q^{79} +(10.2567 - 7.78406i) q^{80} +(1.50373 + 11.8145i) q^{82} +(4.11011 - 2.64141i) q^{83} +(1.70828 + 11.8813i) q^{85} +(9.37170 + 6.23966i) q^{86} +(0.00946875 + 0.100228i) q^{88} +(3.09200 + 10.5304i) q^{89} -4.66091 q^{91} +(-3.27186 - 9.01637i) q^{92} +(13.5385 - 11.3524i) q^{94} +(-0.312350 - 1.06377i) q^{95} +(-5.11806 + 7.96386i) q^{97} +(2.99548 + 1.99439i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 7 q^{2} - 11 q^{4} + 22 q^{5} + 10 q^{8}+O(q^{10}) \) 100 * q + 7 * q^2 - 11 * q^4 + 22 * q^5 + 10 * q^8	\( 100 q + 7 q^{2} - 11 q^{4} + 22 q^{5} + 10 q^{8} - 11 q^{10} - 18 q^{13} + 11 q^{14} + 5 q^{16} + 22 q^{17} + 11 q^{20} - 16 q^{25} - 12 q^{26} - 11 q^{28} + 42 q^{29} + 27 q^{32} + 11 q^{34} - 22 q^{37} - 44 q^{38} + 77 q^{40} + 10 q^{41} - 66 q^{44} + 65 q^{46} - 8 q^{49} - 30 q^{50} + 96 q^{52} + 22 q^{53} - 44 q^{56} + 79 q^{58} - 22 q^{61} + 36 q^{62} + 10 q^{64} + 22 q^{65} + 34 q^{70} - 18 q^{73} + 22 q^{74} - 66 q^{76} - 122 q^{77} + 110 q^{80} - 122 q^{82} + 54 q^{85} + 121 q^{86} - 99 q^{88} - 22 q^{89} + 86 q^{92} - 61 q^{94} + 22 q^{97} + 71 q^{98}+O(q^{100}) \) 100 * q + 7 * q^2 - 11 * q^4 + 22 * q^5 + 10 * q^8 - 11 * q^10 - 18 * q^13 + 11 * q^14 + 5 * q^16 + 22 * q^17 + 11 * q^20 - 16 * q^25 - 12 * q^26 - 11 * q^28 + 42 * q^29 + 27 * q^32 + 11 * q^34 - 22 * q^37 - 44 * q^38 + 77 * q^40 + 10 * q^41 - 66 * q^44 + 65 * q^46 - 8 * q^49 - 30 * q^50 + 96 * q^52 + 22 * q^53 - 44 * q^56 + 79 * q^58 - 22 * q^61 + 36 * q^62 + 10 * q^64 + 22 * q^65 + 34 * q^70 - 18 * q^73 + 22 * q^74 - 66 * q^76 - 122 * q^77 + 110 * q^80 - 122 * q^82 + 54 * q^85 + 121 * q^86 - 99 * q^88 - 22 * q^89 + 86 * q^92 - 61 * q^94 + 22 * q^97 + 71 * q^98

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