LMFDB - Embedded newform 810.3.j.a.539.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(269,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("810.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.j (of order $6$, degree $2$, 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:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.81622204416.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 14x^{6} + 165x^{4} - 434x^{2} + 961 $ x^8 - 14x^6 + 165x^4 - 434*x^2 + 961
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			539.4
Root			$2.90379 + 1.67650i$ of defining polynomial
Character	$\chi$	$=$	810.539
Dual form			810.3.j.a.269.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(3.31368 + 3.74426i) q^{5} +(0.704577 - 0.406788i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(3.31368 + 3.74426i) q^{5} +(0.704577 - 0.406788i) q^{7} -2.82843 q^{8} +(-2.24264 + 6.70601i) q^{10} +(-13.3161 + 7.68808i) q^{11} +(-5.10300 - 2.94622i) q^{13} +(0.996422 + 0.575285i) q^{14} +(-2.00000 - 3.46410i) q^{16} -12.8995 q^{17} +1.24264 q^{19} +(-9.79894 + 1.99520i) q^{20} +(-18.8319 - 10.8726i) q^{22} +(2.39949 - 4.15605i) q^{23} +(-3.03902 + 24.8146i) q^{25} -8.33316i q^{26} +1.62715i q^{28} +(-36.9592 + 21.3384i) q^{29} +(-2.10660 + 3.64874i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-9.12132 - 15.7986i) q^{34} +(3.85786 + 1.29016i) q^{35} -70.3144i q^{37} +(0.878680 + 1.52192i) q^{38} +(-9.37251 - 10.5904i) q^{40} +(6.09942 + 3.52150i) q^{41} +(-35.5500 + 20.5248i) q^{43} -30.7523i q^{44} +6.78680 q^{46} +(39.8995 + 69.1080i) q^{47} +(-24.1690 + 41.8620i) q^{49} +(-32.5405 + 13.8245i) q^{50} +(10.2060 - 5.89243i) q^{52} +63.7279 q^{53} +(-72.9117 - 24.3833i) q^{55} +(-1.99284 + 1.15057i) q^{56} +(-52.2682 - 30.1770i) q^{58} +(-31.7353 - 18.3224i) q^{59} +(41.4706 + 71.8291i) q^{61} -5.95837 q^{62} +8.00000 q^{64} +(-5.87830 - 28.8698i) q^{65} +(-77.0786 - 44.5013i) q^{67} +(12.8995 - 22.3426i) q^{68} +(1.14781 + 5.63718i) q^{70} +69.6982i q^{71} -89.6188i q^{73} +(86.1172 - 49.7198i) q^{74} +(-1.24264 + 2.15232i) q^{76} +(-6.25483 + 10.8337i) q^{77} +(-67.0477 - 116.130i) q^{79} +(6.34315 - 18.9675i) q^{80} +9.96031i q^{82} +(-54.5122 - 94.4179i) q^{83} +(-42.7448 - 48.2991i) q^{85} +(-50.2753 - 29.0265i) q^{86} +(37.6638 - 21.7452i) q^{88} +137.514i q^{89} -4.79394 q^{91} +(4.79899 + 8.31209i) q^{92} +(-56.4264 + 97.7334i) q^{94} +(4.11772 + 4.65277i) q^{95} +(-78.4877 + 45.3149i) q^{97} -68.3604 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 12 q^{5}+O(q^{10}) $ 8 * q - 8 * q^4 - 12 * q^5	$ 8 q - 8 q^{4} - 12 q^{5} + 16 q^{10} - 16 q^{16} - 24 q^{17} - 24 q^{19} - 24 q^{20} - 60 q^{23} + 12 q^{25} + 68 q^{31} - 56 q^{34} + 144 q^{35} + 24 q^{38} - 16 q^{40} + 224 q^{46} + 240 q^{47} + 180 q^{49} - 96 q^{50} + 408 q^{53} - 176 q^{55} + 196 q^{61} - 240 q^{62} + 64 q^{64} + 24 q^{65} + 24 q^{68} - 80 q^{70} + 24 q^{76} + 312 q^{77} - 180 q^{79} + 96 q^{80} - 108 q^{83} - 20 q^{85} + 912 q^{91} - 120 q^{92} - 112 q^{94} + 60 q^{95} - 1056 q^{98}+O(q^{100}) $ 8 * q - 8 * q^4 - 12 * q^5 + 16 * q^10 - 16 * q^16 - 24 * q^17 - 24 * q^19 - 24 * q^20 - 60 * q^23 + 12 * q^25 + 68 * q^31 - 56 * q^34 + 144 * q^35 + 24 * q^38 - 16 * q^40 + 224 * q^46 + 240 * q^47 + 180 * q^49 - 96 * q^50 + 408 * q^53 - 176 * q^55 + 196 * q^61 - 240 * q^62 + 64 * q^64 + 24 * q^65 + 24 * q^68 - 80 * q^70 + 24 * q^76 + 312 * q^77 - 180 * q^79 + 96 * q^80 - 108 * q^83 - 20 * q^85 + 912 * q^91 - 120 * q^92 - 112 * q^94 + 60 * q^95 - 1056 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	3.31368	+	3.74426i	0.662736	+	0.748853i
$5$	3.31368	+	3.74426i	0.662736	+	0.748853i
$6$		0			0
$7$	0.704577	−	0.406788i	0.100654	−	0.0581125i	−0.448828	−	0.893618i	$-0.648158\pi$
$7$	0.704577	−	0.406788i	0.100654	−	0.0581125i	0.549482	+	0.835506i	$0.314825\pi$
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−2.24264	+	6.70601i	−0.224264	+	0.670601i
$11$	−13.3161	+	7.68808i	−1.21056	+	0.698917i	−0.962881	−	0.269926i	$-0.913001\pi$
$11$	−13.3161	+	7.68808i	−1.21056	+	0.698917i	−0.247678	+	0.968842i	$0.579667\pi$
$12$		0			0
$13$	−5.10300	−	2.94622i	−0.392538	−	0.226632i	0.290721	−	0.956808i	$-0.406105\pi$
$13$	−5.10300	−	2.94622i	−0.392538	−	0.226632i	−0.683259	+	0.730176i	$0.739438\pi$
$14$	0.996422	+	0.575285i	0.0711730	+	0.0410918i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−12.8995			−0.758794			−0.379397	−	0.925234i	$-0.623869\pi$
$17$	−12.8995			−0.758794			−0.379397	+	0.925234i	$0.623869\pi$
$18$		0			0
$19$	1.24264			0.0654021			0.0327011	−	0.999465i	$-0.489589\pi$
$19$	1.24264			0.0654021			0.0327011	+	0.999465i	$0.489589\pi$
$20$	−9.79894	+	1.99520i	−0.489947	+	0.0997601i
$21$		0			0
$22$	−18.8319	−	10.8726i	−0.855994	−	0.494209i
$23$	2.39949	−	4.15605i	0.104326	−	0.180698i	−0.809137	−	0.587620i	$-0.800065\pi$
$23$	2.39949	−	4.15605i	0.104326	−	0.180698i	0.913463	+	0.406923i	$0.133398\pi$
$24$		0			0
$25$	−3.03902	+	24.8146i	−0.121561	+	0.992584i
$26$		−	8.33316i		−	0.320506i
$27$		0			0
$28$			1.62715i			0.0581125i
$29$	−36.9592	+	21.3384i	−1.27445	+	0.735807i	−0.975823	−	0.218562i	$-0.929863\pi$
$29$	−36.9592	+	21.3384i	−1.27445	+	0.735807i	−0.298631	+	0.954369i	$0.596530\pi$
$30$		0			0
$31$	−2.10660	+	3.64874i	−0.0679549	+	0.117701i	−0.898001	−	0.439994i	$-0.854981\pi$
$31$	−2.10660	+	3.64874i	−0.0679549	+	0.117701i	0.830046	+	0.557695i	$0.188314\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$	−9.12132	−	15.7986i	−0.268274	−	0.464664i
$35$	3.85786	+	1.29016i	0.110225	+	0.0368616i
$36$		0			0
$37$		−	70.3144i		−	1.90039i	−0.311657	−	0.950195i	$-0.600884\pi$
$37$		−	70.3144i		−	1.90039i	0.311657	−	0.950195i	$-0.399116\pi$
$38$	0.878680	+	1.52192i	0.0231231	+	0.0400505i
$39$		0			0
$40$	−9.37251	−	10.5904i	−0.234313	−	0.264759i
$41$	6.09942	+	3.52150i	0.148766	+	0.0858903i	0.572535	−	0.819880i	$-0.305960\pi$
$41$	6.09942	+	3.52150i	0.148766	+	0.0858903i	−0.423769	+	0.905770i	$0.639293\pi$
$42$		0			0
$43$	−35.5500	+	20.5248i	−0.826745	+	0.477321i	−0.852737	−	0.522341i	$-0.825059\pi$
$43$	−35.5500	+	20.5248i	−0.826745	+	0.477321i	0.0259920	+	0.999662i	$0.491726\pi$
$44$		−	30.7523i		−	0.698917i
$45$		0			0
$46$	6.78680			0.147539
$47$	39.8995	+	69.1080i	0.848925	+	1.47038i	0.882168	+	0.470935i	$0.156083\pi$
$47$	39.8995	+	69.1080i	0.848925	+	1.47038i	−0.0332427	+	0.999447i	$0.510583\pi$
$48$		0			0
$49$	−24.1690	+	41.8620i	−0.493246	+	0.854327i
$50$	−32.5405	+	13.8245i	−0.650809	+	0.276491i
$51$		0			0
$52$	10.2060	−	5.89243i	0.196269	−	0.113316i
$53$	63.7279			1.20241			0.601207	−	0.799093i	$-0.294687\pi$
$53$	63.7279			1.20241			0.601207	+	0.799093i	$0.294687\pi$
$54$		0			0
$55$	−72.9117	−	24.3833i	−1.32567	−	0.443333i
$56$	−1.99284	+	1.15057i	−0.0355865	+	0.0205459i
$57$		0			0
$58$	−52.2682	−	30.1770i	−0.901175	−	0.520294i
$59$	−31.7353	−	18.3224i	−0.537886	−	0.310549i	0.206336	−	0.978481i	$-0.433846\pi$
$59$	−31.7353	−	18.3224i	−0.537886	−	0.310549i	−0.744222	+	0.667932i	$0.767179\pi$
$60$		0			0
$61$	41.4706	+	71.8291i	0.679845	+	1.17753i	0.975027	+	0.222086i	$0.0712864\pi$
$61$	41.4706	+	71.8291i	0.679845	+	1.17753i	−0.295182	+	0.955441i	$0.595380\pi$
$62$	−5.95837			−0.0961027
$63$		0			0
$64$	8.00000			0.125000
$65$	−5.87830	−	28.8698i	−0.0904354	−	0.444151i
$66$		0			0
$67$	−77.0786	−	44.5013i	−1.15043	−	0.664199i	−0.201435	−	0.979502i	$-0.564561\pi$
$67$	−77.0786	−	44.5013i	−1.15043	−	0.664199i	−0.948991	+	0.315303i	$0.897894\pi$
$68$	12.8995	−	22.3426i	0.189698	−	0.328567i
$69$		0			0
$70$	1.14781	+	5.63718i	0.0163973	+	0.0805311i
$71$			69.6982i			0.981665i	0.871254	+	0.490833i	$0.163307\pi$
$71$			69.6982i			0.981665i	−0.871254	+	0.490833i	$0.836693\pi$
$72$		0			0
$73$		−	89.6188i		−	1.22766i	−0.789440	−	0.613828i	$-0.789629\pi$
$73$		−	89.6188i		−	1.22766i	0.789440	−	0.613828i	$-0.210371\pi$
$74$	86.1172	−	49.7198i	1.16375	−	0.671889i
$75$		0			0
$76$	−1.24264	+	2.15232i	−0.0163505	+	0.0283200i
$77$	−6.25483	+	10.8337i	−0.0812316	+	0.140697i
$78$		0			0
$79$	−67.0477	−	116.130i	−0.848705	−	1.47000i	−0.882364	−	0.470567i	$-0.844049\pi$
$79$	−67.0477	−	116.130i	−0.848705	−	1.47000i	0.0336586	−	0.999433i	$-0.489284\pi$
$80$	6.34315	−	18.9675i	0.0792893	−	0.237093i
$81$		0			0
$82$			9.96031i			0.121467i
$83$	−54.5122	−	94.4179i	−0.656773	−	1.13756i	−0.981446	−	0.191738i	$-0.938587\pi$
$83$	−54.5122	−	94.4179i	−0.656773	−	1.13756i	0.324673	−	0.945826i	$-0.394746\pi$
$84$		0			0
$85$	−42.7448	−	48.2991i	−0.502880	−	0.568225i
$86$	−50.2753	−	29.0265i	−0.584597	−	0.337517i
$87$		0			0
$88$	37.6638	−	21.7452i	0.427997	−	0.247104i
$89$			137.514i			1.54510i	0.634953	+	0.772551i	$0.281020\pi$
$89$			137.514i			1.54510i	−0.634953	+	0.772551i	$0.718980\pi$
$90$		0			0
$91$	−4.79394			−0.0526807
$92$	4.79899	+	8.31209i	0.0521629	+	0.0903489i
$93$		0			0
$94$	−56.4264	+	97.7334i	−0.600281	+	1.03972i
$95$	4.11772	+	4.65277i	0.0433444	+	0.0489766i
$96$		0			0
$97$	−78.4877	+	45.3149i	−0.809152	+	0.467164i	−0.846661	−	0.532132i	$-0.821391\pi$
$97$	−78.4877	+	45.3149i	−0.809152	+	0.467164i	0.0375094	+	0.999296i	$0.488058\pi$
$98$	−68.3604			−0.697555
$99$		0			0
$100$	−39.9411	−	30.0783i	−0.399411	−	0.300783i
$101$	43.0586	−	24.8599i	0.426323	−	0.246138i	−0.271456	−	0.962451i	$-0.587505\pi$
$101$	43.0586	−	24.8599i	0.426323	−	0.246138i	0.697779	+	0.716313i	$0.254172\pi$
$102$		0			0
$103$	−111.582	−	64.4220i	−1.08332	−	0.625456i	−0.151531	−	0.988453i	$-0.548420\pi$
$103$	−111.582	−	64.4220i	−1.08332	−	0.625456i	−0.931790	+	0.362997i	$0.881754\pi$
$104$	14.4335	+	8.33316i	0.138783	+	0.0801265i
$105$		0			0
$106$	45.0624	+	78.0504i	0.425117	+	0.736325i
$107$	6.42641			0.0600599			0.0300299	−	0.999549i	$-0.490440\pi$
$107$	6.42641			0.0600599			0.0300299	+	0.999549i	$0.490440\pi$
$108$		0			0
$109$	108.279			0.993387			0.496694	−	0.867926i	$-0.334547\pi$
$109$	108.279			0.993387			0.496694	+	0.867926i	$0.334547\pi$
$110$	−21.6930	−	106.540i	−0.197209	−	0.968544i
$111$		0			0
$112$	−2.81831	−	1.62715i	−0.0251635	−	0.0145281i
$113$	15.2132	−	26.3500i	0.134630	−	0.233186i	−0.790826	−	0.612041i	$-0.790349\pi$
$113$	15.2132	−	26.3500i	0.134630	−	0.233186i	0.925456	+	0.378855i	$0.123682\pi$
$114$		0			0
$115$	23.5125	−	4.78748i	0.204457	−	0.0416302i
$116$		−	85.3536i		−	0.735807i
$117$		0			0
$118$		−	51.8235i		−	0.439182i
$119$	−9.08869	+	5.24736i	−0.0763755	+	0.0440954i
$120$		0			0
$121$	57.7132	−	99.9622i	0.476969	−	0.826134i
$122$	−58.6482	+	101.582i	−0.480723	+	0.832637i
$123$		0			0
$124$	−4.21320	−	7.29748i	−0.0339774	−	0.0588507i
$125$	−102.983	+	70.8488i	−0.823862	+	0.566790i
$126$		0			0
$127$			133.725i			1.05296i	0.850189	+	0.526478i	$0.176488\pi$
$127$			133.725i			1.05296i	−0.850189	+	0.526478i	$0.823512\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$	31.2015	−	27.6134i	0.240012	−	0.212411i
$131$	53.5064	+	30.8919i	0.408446	+	0.235816i	0.690122	−	0.723693i	$-0.257557\pi$
$131$	53.5064	+	30.8919i	0.408446	+	0.235816i	−0.281676	+	0.959510i	$0.590890\pi$
$132$		0			0
$133$	0.875536	−	0.505491i	0.00658298	−	0.00380068i
$134$		−	125.869i		−	0.939319i
$135$		0			0
$136$	36.4853			0.268274
$137$	81.9594	+	141.958i	0.598244	+	1.03619i	0.993080	+	0.117437i	$0.0374679\pi$
$137$	81.9594	+	141.958i	0.598244	+	1.03619i	−0.394836	+	0.918751i	$0.629199\pi$
$138$		0			0
$139$	−91.1249	+	157.833i	−0.655575	+	1.13549i	0.326175	+	0.945310i	$0.394240\pi$
$139$	−91.1249	+	157.833i	−0.655575	+	1.13549i	−0.981749	+	0.190179i	$0.939093\pi$
$140$	−6.09248	+	5.39186i	−0.0435177	+	0.0385133i
$141$		0			0
$142$	−85.3625	+	49.2841i	−0.601145	+	0.347071i
$143$	90.6030			0.633588
$144$		0			0
$145$	−202.368	−	67.6763i	−1.39564	−	0.466733i
$146$	109.760	−	63.3701i	0.751782	−	0.434042i
$147$		0			0
$148$	121.788	+	70.3144i	0.822893	+	0.475097i
$149$	164.142	+	94.7675i	1.10163	+	0.636023i	0.936647	−	0.350274i	$-0.113911\pi$
$149$	164.142	+	94.7675i	1.10163	+	0.636023i	0.164978	+	0.986297i	$0.447245\pi$
$150$		0			0
$151$	56.6690	+	98.1537i	0.375292	+	0.650024i	0.990371	−	0.138441i	$-0.0442092\pi$
$151$	56.6690	+	98.1537i	0.375292	+	0.650024i	−0.615079	+	0.788466i	$0.710876\pi$
$152$	−3.51472			−0.0231231
$153$		0			0
$154$	−17.6913			−0.114879
$155$	−20.6425	+	4.20310i	−0.133177	+	0.0271167i
$156$		0			0
$157$	98.0242	+	56.5943i	0.624358	+	0.360473i	0.778564	−	0.627566i	$-0.215949\pi$
$157$	98.0242	+	56.5943i	0.624358	+	0.360473i	−0.154206	+	0.988039i	$0.549282\pi$
$158$	94.8198	−	164.233i	0.600125	−	1.03945i
$159$		0			0
$160$	27.7156	−	5.64328i	0.173222	−	0.0352705i
$161$		−	3.90434i		−	0.0242506i
$162$		0			0
$163$			152.414i			0.935053i	0.883979	+	0.467527i	$0.154855\pi$
$163$			152.414i			0.935053i	−0.883979	+	0.467527i	$0.845145\pi$
$164$	−12.1988	+	7.04300i	−0.0743832	+	0.0429451i
$165$		0			0
$166$	77.0919	−	133.527i	0.464409	−	0.804380i
$167$	−52.9264	+	91.6712i	−0.316925	+	0.548929i	−0.979845	−	0.199761i	$-0.935984\pi$
$167$	−52.9264	+	91.6712i	−0.316925	+	0.548929i	0.662920	+	0.748690i	$0.269317\pi$
$168$		0			0
$169$	−67.1396	−	116.289i	−0.397276	−	0.688102i
$170$	28.9289	−	86.5041i	0.170170	−	0.508848i
$171$		0			0
$172$		−	82.0993i		−	0.477321i
$173$	−55.0061	−	95.2734i	−0.317954	−	0.550713i	0.662107	−	0.749410i	$-0.269663\pi$
$173$	−55.0061	−	95.2734i	−0.317954	−	0.550713i	−0.980061	+	0.198697i	$0.936329\pi$
$174$		0			0
$175$	7.95305	+	18.7200i	0.0454460	+	0.106972i
$176$	53.2646	+	30.7523i	0.302640	+	0.174729i
$177$		0			0
$178$	−168.420	+	97.2371i	−0.946178	+	0.546276i
$179$		−	118.407i		−	0.661492i	−0.943720	−	0.330746i	$-0.892700\pi$
$179$		−	118.407i		−	0.661492i	0.943720	−	0.330746i	$-0.107300\pi$
$180$		0			0
$181$	172.397			0.952469			0.476235	−	0.879318i	$-0.342001\pi$
$181$	172.397			0.952469			0.476235	+	0.879318i	$0.342001\pi$
$182$	−3.38983	−	5.87135i	−0.0186254	−	0.0322602i
$183$		0			0
$184$	−6.78680	+	11.7551i	−0.0368848	+	0.0638863i
$185$	263.276	−	233.000i	1.42311	−	1.25946i
$186$		0			0
$187$	171.772	−	99.1724i	0.918565	−	0.530334i
$188$	−159.598			−0.848925
$189$		0			0
$190$	−2.78680	+	8.33316i	−0.0146674	+	0.0438587i
$191$	−250.622	+	144.697i	−1.31216	+	0.757574i	−0.982453	−	0.186510i	$-0.940282\pi$
$191$	−250.622	+	144.697i	−1.31216	+	0.757574i	−0.329704	+	0.944084i	$0.606949\pi$
$192$		0			0
$193$	110.707	+	63.9165i	0.573609	+	0.331173i	0.758590	−	0.651569i	$-0.225889\pi$
$193$	110.707	+	63.9165i	0.573609	+	0.331173i	−0.184980	+	0.982742i	$0.559222\pi$
$194$	−110.998	−	64.0850i	−0.572157	−	0.330335i
$195$		0			0
$196$	−48.3381	−	83.7240i	−0.246623	−	0.427163i
$197$	280.414			1.42342			0.711711	−	0.702472i	$-0.247920\pi$
$197$	280.414			1.42342			0.711711	+	0.702472i	$0.247920\pi$
$198$		0			0
$199$	156.426			0.786062			0.393031	−	0.919525i	$-0.371426\pi$
$199$	156.426			0.786062			0.393031	+	0.919525i	$0.371426\pi$
$200$	8.59565	−	70.1863i	0.0429783	−	0.350931i
$201$		0			0
$202$	60.8941	+	35.1572i	0.301456	+	0.174046i
$203$	−17.3604	+	30.0691i	−0.0855192	+	0.148124i
$204$		0			0
$205$	7.02611	+	34.5070i	0.0342737	+	0.168327i
$206$		−	182.213i		−	0.884528i
$207$		0			0
$208$			23.5697i			0.113316i
$209$	−16.5472	+	9.55352i	−0.0791731	+	0.0457106i
$210$		0			0
$211$	−11.2538	+	19.4921i	−0.0533355	+	0.0923798i	−0.891460	−	0.453098i	$-0.850319\pi$
$211$	−11.2538	+	19.4921i	−0.0533355	+	0.0923798i	0.838125	+	0.545478i	$0.183652\pi$
$212$	−63.7279	+	110.380i	−0.300603	+	0.520660i
$213$		0			0
$214$	4.54416	+	7.87071i	0.0212344	+	0.0367790i
$215$	−194.652	−	65.0959i	−0.905357	−	0.302772i
$216$		0			0
$217$			3.42776i			0.0157961i
$218$	76.5650	+	132.614i	0.351215	+	0.608323i
$219$		0			0
$220$	115.145	−	101.903i	0.523386	−	0.463197i
$221$	65.8261	+	38.0047i	0.297856	+	0.171967i
$222$		0			0
$223$	307.289	−	177.413i	1.37798	−	0.795575i	0.386060	−	0.922474i	$-0.373836\pi$
$223$	307.289	−	177.413i	1.37798	−	0.795575i	0.991916	+	0.126899i	$0.0405024\pi$
$224$		−	4.60228i		−	0.0205459i
$225$		0			0
$226$	43.0294			0.190396
$227$	207.549	+	359.485i	0.914312	+	1.58363i	0.807906	+	0.589312i	$0.200601\pi$
$227$	207.549	+	359.485i	0.914312	+	1.58363i	0.106406	+	0.994323i	$0.466066\pi$
$228$		0			0
$229$	110.110	−	190.716i	0.480830	−	0.832823i	−0.518928	−	0.854818i	$-0.673669\pi$
$229$	110.110	−	190.716i	0.480830	−	0.832823i	0.999758	+	0.0219954i	$0.00700192\pi$
$230$	22.4893	+	25.4116i	0.0977795	+	0.110485i
$231$		0			0
$232$	104.536	−	60.3541i	0.450588	−	0.260147i
$233$	10.0345			0.0430665			0.0215332	−	0.999768i	$-0.493145\pi$
$233$	10.0345			0.0430665			0.0215332	+	0.999768i	$0.493145\pi$
$234$		0			0
$235$	−126.544	+	378.396i	−0.538486	+	1.61020i
$236$	63.4706	−	36.6448i	0.268943	−	0.155274i
$237$		0			0
$238$	−12.8533	−	7.42088i	−0.0540056	−	0.0311802i
$239$	−99.0414	−	57.1816i	−0.414399	−	0.239253i	0.278279	−	0.960500i	$-0.410236\pi$
$239$	−99.0414	−	57.1816i	−0.414399	−	0.239253i	−0.692678	+	0.721247i	$0.743569\pi$
$240$		0			0
$241$	31.8604	+	55.1838i	0.132201	+	0.228978i	0.924525	−	0.381122i	$-0.124462\pi$
$241$	31.8604	+	55.1838i	0.132201	+	0.228978i	−0.792324	+	0.610101i	$0.791129\pi$
$242$	163.238			0.674535
$243$		0			0
$244$	−165.882			−0.679845
$245$	−236.831	+	48.2221i	−0.966657	+	0.196825i
$246$		0			0
$247$	−6.34119	−	3.66109i	−0.0256728	−	0.0148222i
$248$	5.95837	−	10.3202i	0.0240257	−	0.0416137i
$249$		0			0
$250$	−159.592	−	76.0299i	−0.638366	−	0.304120i
$251$			229.631i			0.914866i	0.889244	+	0.457433i	$0.151231\pi$
$251$			229.631i			0.914866i	−0.889244	+	0.457433i	$0.848769\pi$
$252$		0			0
$253$			73.7901i			0.291660i
$254$	−163.779	+	94.5581i	−0.644801	+	0.372276i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−194.114	+	336.215i	−0.755306	+	1.30823i	0.189915	+	0.981800i	$0.439179\pi$
$257$	−194.114	+	336.215i	−0.755306	+	1.30823i	−0.945222	+	0.326429i	$0.894155\pi$
$258$		0			0
$259$	−28.6030	−	49.5419i	−0.110436	−	0.191281i
$260$	55.8823	+	18.6883i	0.214932	+	0.0718780i
$261$		0			0
$262$			87.3755i			0.333494i
$263$	−113.439	−	196.481i	−0.431325	−	0.747078i	0.565662	−	0.824637i	$-0.308621\pi$
$263$	−113.439	−	196.481i	−0.431325	−	0.747078i	−0.996988	+	0.0775594i	$0.975287\pi$
$264$		0			0
$265$	211.174	+	238.614i	0.796883	+	0.900431i
$266$	1.23819	+	0.714872i	0.00465487	+	0.00268749i
$267$		0			0
$268$	154.157	−	89.0027i	0.575213	−	0.332100i
$269$			226.772i			0.843019i	0.906824	+	0.421509i	$0.138500\pi$
$269$			226.772i			0.843019i	−0.906824	+	0.421509i	$0.861500\pi$
$270$		0			0
$271$	322.889			1.19147			0.595737	−	0.803180i	$-0.296860\pi$
$271$	322.889			1.19147			0.595737	+	0.803180i	$0.296860\pi$
$272$	25.7990	+	44.6852i	0.0948492	+	0.164284i
$273$		0			0
$274$	−115.908	+	200.759i	−0.423022	+	0.732696i
$275$	−150.309	−	353.799i	−0.546577	−	1.28654i
$276$		0			0
$277$	173.694	−	100.282i	0.627053	−	0.362029i	−0.152557	−	0.988295i	$-0.548751\pi$
$277$	173.694	−	100.282i	0.627053	−	0.362029i	0.779610	+	0.626266i	$0.215417\pi$
$278$	−257.740			−0.927123
$279$		0			0
$280$	−10.9117	−	3.64911i	−0.0389703	−	0.0130326i
$281$	110.878	−	64.0152i	0.394582	−	0.227812i	−0.289562	−	0.957159i	$-0.593510\pi$
$281$	110.878	−	64.0152i	0.394582	−	0.227812i	0.684144	+	0.729347i	$0.260176\pi$
$282$		0			0
$283$	363.934	+	210.118i	1.28599	+	0.742465i	0.977936	−	0.208905i	$-0.0669898\pi$
$283$	363.934	+	210.118i	1.28599	+	0.742465i	0.308051	+	0.951370i	$0.400323\pi$
$284$	−120.721	−	69.6982i	−0.425073	−	0.245416i
$285$		0			0
$286$	64.0660	+	110.966i	0.224007	+	0.387992i
$287$	5.73001			0.0199652
$288$		0			0
$289$	−122.603			−0.424232
$290$	−60.2093	−	295.703i	−0.207618	−	1.01967i
$291$		0			0
$292$	155.224	+	89.6188i	0.531590	+	0.306914i
$293$	−68.7168	+	119.021i	−0.234528	+	0.406215i	−0.959135	−	0.282947i	$-0.908688\pi$
$293$	−68.7168	+	119.021i	−0.234528	+	0.406215i	0.724607	+	0.689162i	$0.242021\pi$
$294$		0			0
$295$	−36.5569	−	179.540i	−0.123922	−	0.608610i
$296$			198.879i			0.671889i
$297$		0			0
$298$			268.043i			0.899473i
$299$	−24.4892	+	14.1389i	−0.0819038	+	0.0472872i
$300$		0			0
$301$	−16.6985	+	28.9226i	−0.0554767	+	0.0960885i
$302$	−80.1421	+	138.810i	−0.265371	+	0.459637i
$303$		0			0
$304$	−2.48528	−	4.30463i	−0.00817527	−	0.0141600i
$305$	−131.527	+	393.296i	−0.431236	+	1.28949i
$306$		0			0
$307$		−	117.849i		−	0.383872i	−0.981407	−	0.191936i	$-0.938523\pi$
$307$		−	117.849i		−	0.383872i	0.981407	−	0.191936i	$-0.0614766\pi$
$308$	−12.5097	−	21.6674i	−0.0406158	−	0.0703486i
$309$		0			0
$310$	−19.7441	−	22.3097i	−0.0636908	−	0.0719668i
$311$	−432.429	−	249.663i	−1.39045	−	0.802774i	−0.397081	−	0.917783i	$-0.629977\pi$
$311$	−432.429	−	249.663i	−1.39045	−	0.802774i	−0.993364	+	0.115009i	$0.963310\pi$
$312$		0			0
$313$	−425.916	+	245.903i	−1.36076	+	0.785633i	−0.989724	−	0.142988i	$-0.954329\pi$
$313$	−425.916	+	245.903i	−1.36076	+	0.785633i	−0.371031	+	0.928620i	$0.620996\pi$
$314$			160.073i			0.509786i
$315$		0			0
$316$	268.191			0.848705
$317$	120.700	+	209.058i	0.380756	+	0.659488i	0.991170	−	0.132594i	$-0.0423306\pi$
$317$	120.700	+	209.058i	0.380756	+	0.659488i	−0.610415	+	0.792082i	$0.708997\pi$
$318$		0			0
$319$	328.103	−	568.290i	1.02853	−	1.78147i
$320$	26.5095	+	29.9541i	0.0828421	+	0.0936066i
$321$		0			0
$322$	4.78182	−	2.76079i	0.0148504	−	0.00857387i
$323$	−16.0294			−0.0496267
$324$		0			0
$325$	88.6173	−	117.675i	0.272669	−	0.362078i
$326$	−186.668	+	107.773i	−0.572601	+	0.330591i
$327$		0			0
$328$	−17.2518	−	9.96031i	−0.0525968	−	0.0303668i
$329$	56.2245	+	32.4612i	0.170895	+	0.0986664i
$330$		0			0
$331$	43.9045	+	76.0449i	0.132642	+	0.229743i	0.924694	−	0.380711i	$-0.124321\pi$
$331$	43.9045	+	76.0449i	0.132642	+	0.229743i	−0.792052	+	0.610453i	$0.790987\pi$
$332$	218.049			0.656773
$333$		0			0
$334$	−149.698			−0.448199
$335$	−88.7892	−	436.066i	−0.265042	−	1.30169i
$336$		0			0
$337$	391.563	+	226.069i	1.16191	+	0.670828i	0.951761	−	0.306841i	$-0.0992721\pi$
$337$	391.563	+	226.069i	1.16191	+	0.670828i	0.210148	+	0.977670i	$0.432605\pi$
$338$	94.9497	−	164.458i	0.280916	−	0.486561i
$339$		0			0
$340$	126.401	−	25.7371i	0.371769	−	0.0756974i
$341$		−	64.7829i		−	0.189979i
$342$		0			0
$343$			79.1919i			0.230880i
$344$	100.551	−	58.0529i	0.292298	−	0.168759i
$345$		0			0
$346$	77.7904	−	134.737i	0.224828	−	0.389413i
$347$	−94.7056	+	164.035i	−0.272927	+	0.472723i	−0.969610	−	0.244656i	$-0.921325\pi$
$347$	−94.7056	+	164.035i	−0.272927	+	0.472723i	0.696683	+	0.717379i	$0.254658\pi$
$348$		0			0
$349$	77.8970	+	134.922i	0.223200	+	0.386595i	0.955778	−	0.294089i	$-0.0950162\pi$
$349$	77.8970	+	134.922i	0.223200	+	0.386595i	−0.732578	+	0.680684i	$0.761683\pi$
$350$	−17.3036	+	22.9775i	−0.0494389	+	0.0656500i
$351$		0			0
$352$			86.9807i			0.247104i
$353$	−131.693	−	228.100i	−0.373069	−	0.646175i	0.616967	−	0.786989i	$-0.288361\pi$
$353$	−131.693	−	228.100i	−0.373069	−	0.646175i	−0.990036	+	0.140814i	$0.955028\pi$
$354$		0			0
$355$	−260.969	+	230.958i	−0.735123	+	0.650585i
$356$	−238.181	−	137.514i	−0.669049	−	0.386275i
$357$		0			0
$358$	145.018	−	83.7264i	0.405079	−	0.233873i
$359$		−	79.6346i		−	0.221823i	−0.993830	−	0.110912i	$-0.964623\pi$
$359$		−	79.6346i		−	0.221823i	0.993830	−	0.110912i	$-0.0353771\pi$
$360$		0			0
$361$	−359.456			−0.995723
$362$	121.903	+	211.142i	0.336749	+	0.583266i
$363$		0			0
$364$	4.79394	−	8.30335i	0.0131702	−	0.0228114i
$365$	335.557	−	296.968i	0.919333	−	0.813612i
$366$		0			0
$367$	−412.188	+	237.977i	−1.12313	+	0.648438i	−0.942197	−	0.335058i	$-0.891244\pi$
$367$	−412.188	+	237.977i	−1.12313	+	0.648438i	−0.180930	+	0.983496i	$0.557911\pi$
$368$	−19.1960			−0.0521629
$369$		0			0
$370$	471.529	+	157.690i	1.27440	+	0.426189i
$371$	44.9012	−	25.9237i	0.121028	−	0.0698753i
$372$		0			0
$373$	53.5064	+	30.8919i	0.143449	+	0.0828201i	0.570007	−	0.821640i	$-0.306941\pi$
$373$	53.5064	+	30.8919i	0.143449	+	0.0828201i	−0.426558	+	0.904460i	$0.640274\pi$
$374$	242.922	+	140.251i	0.649523	+	0.375002i
$375$		0			0
$376$	−112.853	−	195.467i	−0.300140	−	0.519859i
$377$	251.470			0.667030
$378$		0			0
$379$	−142.345			−0.375581			−0.187791	−	0.982209i	$-0.560133\pi$
$379$	−142.345			−0.375581			−0.187791	+	0.982209i	$0.560133\pi$
$380$	−12.1766	+	2.47932i	−0.0320436	+	0.00652452i
$381$		0			0
$382$	−354.433	−	204.632i	−0.927835	−	0.535686i
$383$	−178.760	+	309.621i	−0.466736	+	0.808410i	−0.999278	−	0.0379931i	$-0.987904\pi$
$383$	−178.760	+	309.621i	−0.466736	+	0.808410i	0.532542	+	0.846404i	$0.321237\pi$
$384$		0			0
$385$	−61.2907	+	12.4797i	−0.159197	+	0.0324147i
$386$			180.783i			0.468350i
$387$		0			0
$388$		−	181.260i		−	0.467164i
$389$	356.005	−	205.539i	0.915179	−	0.528379i	0.0330850	−	0.999453i	$-0.489467\pi$
$389$	356.005	−	205.539i	0.915179	−	0.528379i	0.882094	+	0.471074i	$0.156133\pi$
$390$		0			0
$391$	−30.9523	+	53.6109i	−0.0791618	+	0.137112i
$392$	68.3604	−	118.404i	0.174389	−	0.302050i
$393$		0			0
$394$	198.283	+	343.436i	0.503256	+	0.871665i
$395$	212.647	−	635.863i	0.538346	−	1.60978i
$396$		0			0
$397$			457.462i			1.15230i	0.817345	+	0.576149i	$0.195445\pi$
$397$			457.462i			1.15230i	−0.817345	+	0.576149i	$0.804555\pi$
$398$	110.610	+	191.582i	0.277915	+	0.481363i
$399$		0			0
$400$	92.0383	−	39.1017i	0.230096	−	0.0977543i
$401$	404.679	+	233.642i	1.00917	+	0.582647i	0.910950	−	0.412517i	$-0.135350\pi$
$401$	404.679	+	233.642i	1.00917	+	0.582647i	0.0982247	+	0.995164i	$0.468684\pi$
$402$		0			0
$403$	21.5000	−	12.4130i	0.0533498	−	0.0308015i
$404$			99.4396i			0.246138i
$405$		0			0
$406$	−49.1026			−0.120942
$407$	540.583	+	936.317i	1.32821	+	2.30053i
$408$		0			0
$409$	224.287	−	388.476i	0.548378	−	0.949819i	−0.450007	−	0.893025i	$-0.648579\pi$
$409$	224.287	−	388.476i	0.548378	−	0.949819i	0.998386	−	0.0567946i	$-0.0180880\pi$
$410$	−37.2940	+	33.0053i	−0.0909611	+	0.0805007i
$411$		0			0
$412$	223.164	−	128.844i	0.541661	−	0.312728i
$413$	−29.8133			−0.0721871
$414$		0			0
$415$	172.889	−	516.979i	0.416601	−	1.24573i
$416$	−28.8669	+	16.6663i	−0.0693916	+	0.0400633i
$417$		0			0
$418$	−23.4013	−	13.5107i	−0.0559839	−	0.0323223i
$419$	−312.492	−	180.417i	−0.745804	−	0.430590i	0.0783720	−	0.996924i	$-0.475028\pi$
$419$	−312.492	−	180.417i	−0.745804	−	0.430590i	−0.824176	+	0.566334i	$0.808361\pi$
$420$		0			0
$421$	−178.529	−	309.222i	−0.424060	−	0.734494i	0.572272	−	0.820064i	$-0.306062\pi$
$421$	−178.529	−	309.222i	−0.424060	−	0.734494i	−0.996332	+	0.0855699i	$0.972729\pi$
$422$	−31.8305			−0.0754278
$423$		0			0
$424$	−180.250			−0.425117
$425$	39.2018	−	320.096i	0.0922396	−	0.753167i
$426$		0			0
$427$	58.4384	+	33.7394i	0.136858	+	0.0790151i
$428$	−6.42641	+	11.1309i	−0.0150150	+	0.0260067i
$429$		0			0
$430$	−57.9137	−	284.429i	−0.134683	−	0.661462i
$431$		−	655.947i		−	1.52192i	−0.648800	−	0.760959i	$-0.724729\pi$
$431$		−	655.947i		−	1.52192i	0.648800	−	0.760959i	$-0.275271\pi$
$432$		0			0
$433$		−	164.372i		−	0.379612i	−0.981822	−	0.189806i	$-0.939214\pi$
$433$		−	164.372i		−	0.379612i	0.981822	−	0.189806i	$-0.0607859\pi$
$434$	−4.19813	+	2.42379i	−0.00967311	+	0.00558477i
$435$		0			0
$436$	−108.279	+	187.545i	−0.248347	+	0.430149i
$437$	2.98171	−	5.16447i	0.00682314	−	0.0118180i
$438$		0			0
$439$	66.1432	+	114.563i	0.150668	+	0.260964i	0.931473	−	0.363810i	$-0.118524\pi$
$439$	66.1432	+	114.563i	0.150668	+	0.260964i	−0.780805	+	0.624774i	$0.785191\pi$
$440$	206.225	+	68.9664i	0.468694	+	0.156742i
$441$		0			0
$442$			107.494i			0.243198i
$443$	−227.743	−	394.462i	−0.514092	−	0.890433i	−0.999866	−	0.0163489i	$-0.994796\pi$
$443$	−227.743	−	394.462i	−0.514092	−	0.890433i	0.485775	−	0.874084i	$-0.338538\pi$
$444$		0			0
$445$	−514.889	+	455.678i	−1.15705	+	1.02400i
$446$	434.572	+	250.900i	0.974376	+	0.562556i
$447$		0			0
$448$	5.63662	−	3.25430i	0.0125817	−	0.00726407i
$449$		−	415.749i		−	0.925944i	−0.886373	−	0.462972i	$-0.846783\pi$
$449$		−	415.749i		−	0.925944i	0.886373	−	0.462972i	$-0.153217\pi$
$450$		0			0
$451$	−108.294			−0.240121
$452$	30.4264	+	52.7001i	0.0673151	+	0.116593i
$453$		0			0
$454$	−293.518	+	508.389i	−0.646516	+	1.11980i
$455$	−15.8856	−	17.9498i	−0.0349134	−	0.0394501i
$456$		0			0
$457$	−262.962	+	151.821i	−0.575410	+	0.332213i	−0.759307	−	0.650732i	$-0.774462\pi$
$457$	−262.962	+	151.821i	−0.575410	+	0.332213i	0.183897	+	0.982946i	$0.441129\pi$
$458$	311.439			0.679997
$459$		0			0
$460$	−15.2203	+	45.5123i	−0.0330877	+	0.0989398i
$461$	371.343	−	214.395i	0.805516	−	0.465065i	−0.0398803	−	0.999204i	$-0.512698\pi$
$461$	371.343	−	214.395i	0.805516	−	0.465065i	0.845396	+	0.534140i	$0.179364\pi$
$462$		0			0
$463$	−705.364	−	407.242i	−1.52346	−	0.879572i	−0.999615	−	0.0277616i	$-0.991162\pi$
$463$	−705.364	−	407.242i	−1.52346	−	0.879572i	−0.523850	−	0.851811i	$-0.675505\pi$
$464$	147.837	+	85.3536i	0.318614	+	0.183952i
$465$		0			0
$466$	7.09545	+	12.2897i	0.0152263	+	0.0263727i
$467$	−607.118			−1.30004			−0.650019	−	0.759918i	$-0.725239\pi$
$467$	−607.118			−1.30004			−0.650019	+	0.759918i	$0.725239\pi$
$468$		0			0
$469$	−72.4104			−0.154393
$470$	−552.919	+	112.582i	−1.17642	+	0.239536i
$471$		0			0
$472$	89.7610	+	51.8235i	0.190172	+	0.109796i
$473$	315.593	−	546.623i	0.667215	−	1.15565i
$474$		0			0
$475$	−3.77641	+	30.8356i	−0.00795034	+	0.0649171i
$476$		−	20.9894i		−	0.0440954i
$477$		0			0
$478$		−	161.734i		−	0.338355i
$479$	−297.816	+	171.944i	−0.621746	+	0.358965i	−0.777549	−	0.628823i	$-0.783537\pi$
$479$	−297.816	+	171.944i	−0.621746	+	0.358965i	0.155802	+	0.987788i	$0.450204\pi$
$480$		0			0
$481$	−207.161	+	358.814i	−0.430689	+	0.745975i
$482$	−45.0574	+	78.0417i	−0.0934801	+	0.161912i
$483$		0			0
$484$	115.426	+	199.924i	0.238484	+	0.413067i
$485$	−429.754	−	143.720i	−0.886092	−	0.296329i
$486$		0			0
$487$		−	300.759i		−	0.617576i	−0.951131	−	0.308788i	$-0.900077\pi$
$487$		−	300.759i		−	0.617576i	0.951131	−	0.308788i	$-0.0999233\pi$
$488$	−117.296	−	203.163i	−0.240362	−	0.416319i
$489$		0			0
$490$	−226.525	−	255.959i	−0.462295	−	0.522366i
$491$	150.614	+	86.9568i	0.306749	+	0.177101i	0.645471	−	0.763785i	$-0.276661\pi$
$491$	150.614	+	86.9568i	0.306749	+	0.177101i	−0.338722	+	0.940886i	$0.609995\pi$
$492$		0			0
$493$	476.755	−	275.254i	0.967048	−	0.558326i
$494$		−	10.3551i		−	0.0209618i
$495$		0			0
$496$	16.8528			0.0339774
$497$	28.3524	+	49.1078i	0.0570470	+	0.0988084i
$498$		0			0
$499$	380.805	−	659.574i	0.763136	−	1.32179i	−0.178090	−	0.984014i	$-0.556992\pi$
$499$	380.805	−	659.574i	0.763136	−	1.32179i	0.941226	−	0.337777i	$-0.109675\pi$
$500$	−19.7310	−	249.220i	−0.0394619	−	0.498440i
$501$		0			0
$502$	−281.240	+	162.374i	−0.560239	+	0.323454i
$503$	−280.632			−0.557917			−0.278959	−	0.960303i	$-0.589989\pi$
$503$	−280.632			−0.557917			−0.278959	+	0.960303i	$0.589989\pi$
$504$		0			0
$505$	235.765	+	78.8450i	0.466860	+	0.156129i
$506$	−90.3740	+	52.1774i	−0.178605	+	0.103117i
$507$		0			0
$508$	−231.619	−	133.725i	−0.455943	−	0.263239i
$509$	548.347	+	316.588i	1.07730	+	0.621981i	0.930167	−	0.367136i	$-0.119662\pi$
$509$	548.347	+	316.588i	1.07730	+	0.621981i	0.147135	+	0.989116i	$0.452995\pi$
$510$		0			0
$511$	−36.4558	−	63.1434i	−0.0713422	−	0.123568i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	−549.037			−1.06816
$515$	−128.535	−	631.267i	−0.249582	−	1.22576i
$516$		0			0
$517$	−1062.62	−	613.501i	−2.05535	−	1.18666i
$518$	40.4508	−	70.0628i	0.0780903	−	0.135256i
$519$		0			0
$520$	16.6263	+	81.6561i	0.0319737	+	0.157031i
$521$			92.3966i			0.177345i	0.996061	+	0.0886723i	$0.0282624\pi$
$521$			92.3966i			0.177345i	−0.996061	+	0.0886723i	$0.971738\pi$
$522$		0			0
$523$		−	818.552i		−	1.56511i	−0.622582	−	0.782554i	$-0.713916\pi$
$523$		−	818.552i		−	1.56511i	0.622582	−	0.782554i	$-0.286084\pi$
$524$	−107.013	+	61.7838i	−0.204223	+	0.117908i
$525$		0			0
$526$	160.426	−	277.867i	0.304993	−	0.528264i
$527$	27.1741	−	47.0669i	0.0515638	−	0.0893110i
$528$		0			0
$529$	252.985	+	438.183i	0.478232	+	0.828323i
$530$	−142.919	+	427.360i	−0.269658	+	0.806340i
$531$		0			0
$532$			2.02196i			0.00380068i
$533$	−20.7502	−	35.9404i	−0.0389310	−	0.0674304i
$534$		0			0
$535$	21.2951	+	24.0622i	0.0398039	+	0.0449760i
$536$	218.011	+	125.869i	0.406737	+	0.234830i
$537$		0			0
$538$	−277.738	+	160.352i	−0.516241	+	0.298052i
$539$		−	743.254i		−	1.37895i
$540$		0			0
$541$	−376.985			−0.696830			−0.348415	−	0.937340i	$-0.613280\pi$
$541$	−376.985			−0.696830			−0.348415	+	0.937340i	$0.613280\pi$
$542$	228.317	+	395.457i	0.421250	+	0.729626i
$543$		0			0
$544$	−36.4853	+	63.1944i	−0.0670685	+	0.116166i
$545$	358.803	+	405.426i	0.658354	+	0.743901i
$546$		0			0
$547$	292.151	−	168.673i	0.534096	−	0.308360i	−0.208587	−	0.978004i	$-0.566886\pi$
$547$	292.151	−	168.673i	0.534096	−	0.308360i	0.742683	+	0.669643i	$0.233553\pi$
$548$	−327.838			−0.598244
$549$		0			0
$550$	327.029	−	434.263i	0.594599	−	0.789570i
$551$	−45.9270	+	26.5160i	−0.0833520	+	0.0481233i
$552$		0			0
$553$	−94.4806	−	54.5484i	−0.170851	−	0.0986408i
$554$	245.640	+	141.820i	0.443393	+	0.255993i
$555$		0			0
$556$	−182.250	−	315.666i	−0.327787	−	0.567744i
$557$	303.338			0.544593			0.272296	−	0.962213i	$-0.412217\pi$
$557$	303.338			0.544593			0.272296	+	0.962213i	$0.412217\pi$
$558$		0			0
$559$	241.882			0.432705
$560$	−3.24649	−	15.9443i	−0.00579731	−	0.0284720i
$561$		0			0
$562$	156.805	+	90.5311i	0.279012	+	0.161087i
$563$	−117.047	+	202.731i	−0.207898	+	0.360090i	−0.951052	−	0.309030i	$-0.899996\pi$
$563$	−117.047	+	202.731i	−0.207898	+	0.360090i	0.743154	+	0.669120i	$0.233329\pi$
$564$		0			0
$565$	149.073	−	30.3534i	0.263846	−	0.0537229i
$566$			594.302i			1.05000i
$567$		0			0
$568$		−	197.136i		−	0.347071i
$569$	−57.6129	+	33.2628i	−0.101253	+	0.0584584i	−0.549771	−	0.835315i	$-0.685285\pi$
$569$	−57.6129	+	33.2628i	−0.101253	+	0.0584584i	0.448518	+	0.893774i	$0.351952\pi$
$570$		0			0
$571$	−557.768	+	966.082i	−0.976826	+	1.69191i	−0.303053	+	0.952974i	$0.598006\pi$
$571$	−557.768	+	966.082i	−0.976826	+	1.69191i	−0.673773	+	0.738939i	$0.735327\pi$
$572$	−90.6030	+	156.929i	−0.158397	+	0.274351i
$573$		0			0
$574$	4.05173	+	7.01781i	0.00705877	+	0.0122261i
$575$	95.8385	+	72.1728i	0.166676	+	0.125518i
$576$		0			0
$577$		−	957.356i		−	1.65920i	−0.558361	−	0.829598i	$-0.688570\pi$
$577$		−	957.356i		−	1.65920i	0.558361	−	0.829598i	$-0.311430\pi$
$578$	−86.6934	−	150.157i	−0.149989	−	0.259788i
$579$		0			0
$580$	319.586	−	282.835i	0.551011	−	0.487646i
$581$	−76.8161	−	44.3498i	−0.132214	−	0.0763335i
$582$		0			0
$583$	−848.610	+	489.945i	−1.45559	+	0.840387i
$584$			253.480i			0.434042i
$585$		0			0
$586$	−194.360			−0.331673
$587$	39.9487	+	69.1932i	0.0680557	+	0.117876i	0.898045	−	0.439903i	$-0.144987\pi$
$587$	39.9487	+	69.1932i	0.0680557	+	0.117876i	−0.829990	+	0.557779i	$0.811654\pi$
$588$		0			0
$589$	−2.61775	+	4.53407i	−0.00444440	+	0.00769792i
$590$	194.041	−	171.727i	0.328883	−	0.291062i
$591$		0			0
$592$	−243.576	+	140.629i	−0.411446	+	0.237549i
$593$	−213.831			−0.360593			−0.180296	−	0.983612i	$-0.557706\pi$
$593$	−213.831			−0.360593			−0.180296	+	0.983612i	$0.557706\pi$
$594$		0			0
$595$	−49.7645	−	16.6424i	−0.0836378	−	0.0279704i
$596$	−328.284	+	189.535i	−0.550813	+	0.318012i
$597$		0			0
$598$	−34.6330	−	19.9954i	−0.0579147	−	0.0334371i
$599$	−792.840	−	457.746i	−1.32361	−	0.764184i	−0.339304	−	0.940677i	$-0.610192\pi$
$599$	−792.840	−	457.746i	−1.32361	−	0.764184i	−0.984302	+	0.176492i	$0.943525\pi$
$600$		0			0
$601$	−239.713	−	415.195i	−0.398857	−	0.690841i	0.594728	−	0.803927i	$-0.297260\pi$
$601$	−239.713	−	415.195i	−0.398857	−	0.690841i	−0.993585	+	0.113086i	$0.963926\pi$
$602$	−47.2304			−0.0784559
$603$		0			0
$604$	−226.676			−0.375292
$605$	565.528	−	115.150i	0.934757	−	0.190330i
$606$		0			0
$607$	−190.433	−	109.946i	−0.313727	−	0.181131i	0.334866	−	0.942266i	$-0.391309\pi$
$607$	−190.433	−	109.946i	−0.313727	−	0.181131i	−0.648593	+	0.761135i	$0.724642\pi$
$608$	3.51472	−	6.08767i	0.00578079	−	0.0100126i
$609$		0			0
$610$	−574.690	+	117.015i	−0.942115	+	0.191828i
$611$		−	470.210i		−	0.769575i
$612$		0			0
$613$			862.066i			1.40631i	0.711038	+	0.703154i	$0.248225\pi$
$613$			862.066i			1.40631i	−0.711038	+	0.703154i	$0.751775\pi$
$614$	144.335	−	83.3316i	0.235073	−	0.135719i
$615$		0			0
$616$	17.6913	−	30.6423i	0.0287197	−	0.0497440i
$617$	−347.712	+	602.254i	−0.563552	+	0.976101i	0.433631	+	0.901091i	$0.357232\pi$
$617$	−347.712	+	602.254i	−0.563552	+	0.976101i	−0.997183	+	0.0750103i	$0.976101\pi$
$618$		0			0
$619$	256.037	+	443.468i	0.413629	+	0.716427i	0.995283	−	0.0970091i	$-0.0309276\pi$
$619$	256.037	+	443.468i	0.413629	+	0.716427i	−0.581654	+	0.813436i	$0.697594\pi$
$620$	13.3625	−	39.9569i	0.0215524	−	0.0644466i
$621$		0			0
$622$		−	706.153i		−	1.13529i
$623$	55.9390	+	96.8892i	0.0897898	+	0.155520i
$624$		0			0
$625$	−606.529	−	150.824i	−0.970446	−	0.241319i
$626$	−602.337	−	347.759i	−0.962199	−	0.555526i
$627$		0			0
$628$	−196.048	+	113.189i	−0.312179	+	0.180237i
$629$			907.020i			1.44200i
$630$		0			0
$631$	−643.375			−1.01961			−0.509806	−	0.860290i	$-0.670283\pi$
$631$	−643.375			−1.01961			−0.509806	+	0.860290i	$0.670283\pi$
$632$	189.640	+	328.465i	0.300063	+	0.519724i
$633$		0			0
$634$	−170.695	+	295.652i	−0.269235	+	0.466328i
$635$	−500.703	+	443.123i	−0.788509	+	0.697832i
$636$		0			0
$637$	246.669	−	142.415i	0.387236	−	0.223571i
$638$	928.014			1.45457
$639$		0			0
$640$	−17.9411	+	53.6481i	−0.0280330	+	0.0838251i
$641$	170.542	−	98.4625i	0.266056	−	0.153608i	−0.361038	−	0.932551i	$-0.617578\pi$
$641$	170.542	−	98.4625i	0.266056	−	0.153608i	0.627094	+	0.778944i	$0.284244\pi$
$642$		0			0
$643$	205.208	+	118.477i	0.319141	+	0.184256i	0.651010	−	0.759069i	$-0.274346\pi$
$643$	205.208	+	118.477i	0.319141	+	0.184256i	−0.331868	+	0.943326i	$0.607679\pi$
$644$	6.76252	+	3.90434i	0.0105008	+	0.00606264i
$645$		0			0
$646$	−11.3345	−	19.6320i	−0.0175457	−	0.0303900i
$647$	17.3818			0.0268653			0.0134326	−	0.999910i	$-0.495724\pi$
$647$	17.3818			0.0268653			0.0134326	+	0.999910i	$0.495724\pi$
$648$		0			0
$649$	563.456			0.868191
$650$	206.784	+	25.3247i	0.318129	+	0.0389610i
$651$		0			0
$652$	−263.988	−	152.414i	−0.404890	−	0.233763i
$653$	392.852	−	680.439i	0.601611	−	1.04202i	−0.390967	−	0.920405i	$-0.627859\pi$
$653$	392.852	−	680.439i	0.601611	−	1.04202i	0.992577	−	0.121615i	$-0.0388074\pi$
$654$		0			0
$655$	61.6356	+	302.708i	0.0941002	+	0.462150i
$656$		−	28.1720i		−	0.0429451i
$657$		0			0
$658$			91.8143i			0.139535i
$659$	431.945	−	249.384i	0.655455	−	0.378427i	−0.135088	−	0.990834i	$-0.543132\pi$
$659$	431.945	−	249.384i	0.655455	−	0.378427i	0.790543	+	0.612406i	$0.209798\pi$
$660$		0			0
$661$	−151.566	+	262.521i	−0.229299	+	0.397157i	−0.957600	−	0.288100i	$-0.906977\pi$
$661$	−151.566	+	262.521i	−0.229299	+	0.397157i	0.728302	+	0.685257i	$0.240310\pi$
$662$	−62.0904	+	107.544i	−0.0937922	+	0.162453i
$663$		0			0
$664$	154.184	+	267.054i	0.232204	+	0.402190i
$665$	4.79394	+	1.60320i	0.00720893	+	0.00241083i
$666$		0			0
$667$			204.805i			0.307055i
$668$	−105.853	−	183.342i	−0.158462	−	0.274465i
$669$		0			0
$670$	471.286	−	417.089i	0.703412	−	0.622521i
$671$	−1104.46	−	637.658i	−1.64599	−	0.950310i
$672$		0			0
$673$	401.085	−	231.567i	0.595966	−	0.344081i	−0.171487	−	0.985186i	$-0.554857\pi$
$673$	401.085	−	231.567i	0.595966	−	0.344081i	0.767453	+	0.641105i	$0.221524\pi$
$674$			639.420i			0.948694i
$675$		0			0
$676$	268.558			0.397276
$677$	−155.532	−	269.389i	−0.229737	−	0.397916i	0.727993	−	0.685584i	$-0.240453\pi$
$677$	−155.532	−	269.389i	−0.229737	−	0.397916i	−0.957730	+	0.287668i	$0.907120\pi$
$678$		0			0
$679$	−36.8671	+	63.8557i	−0.0542962	+	0.0940437i
$680$	120.901	+	136.611i	0.177795	+	0.200898i
$681$		0			0
$682$	79.3425	−	45.8084i	0.116338	−	0.0671678i
$683$	232.009			0.339691			0.169846	−	0.985471i	$-0.445673\pi$
$683$	232.009			0.339691			0.169846	+	0.985471i	$0.445673\pi$
$684$		0			0
$685$	−259.940	+	777.281i	−0.379475	+	1.13472i
$686$	−96.9898	+	55.9971i	−0.141385	+	0.0816284i
$687$		0			0
$688$	142.200	+	82.0993i	0.206686	+	0.119330i
$689$	−325.203	−	187.756i	−0.471993	−	0.272506i
$690$		0			0
$691$	276.452	+	478.829i	0.400075	+	0.692950i	0.993735	−	0.111766i	$-0.0356507\pi$
$691$	276.452	+	478.829i	0.400075	+	0.692950i	−0.593660	+	0.804716i	$0.702317\pi$
$692$	220.024			0.317954
$693$		0			0
$694$	−267.868			−0.385977
$695$	−892.927	+	181.813i	−1.28479	+	0.261601i
$696$		0			0
$697$	−78.6794	−	45.4256i	−0.112883	−	0.0651730i
$698$	−110.163	+	190.808i	−0.157827	+	0.273364i
$699$		0			0
$700$	−40.3771	−	4.94495i	−0.0576816	−	0.00706421i
$701$			250.274i			0.357024i	0.983938	+	0.178512i	$0.0571284\pi$
$701$			250.274i			0.357024i	−0.983938	+	0.178512i	$0.942872\pi$
$702$		0			0
$703$		−	87.3755i		−	0.124290i
$704$	−106.529	+	61.5047i	−0.151320	+	0.0873646i
$705$		0			0
$706$	186.243	−	322.582i	0.263800	−	0.456915i
$707$	20.2254	−	35.0314i	0.0286074	−	0.0495494i
$708$		0			0
$709$	−585.286	−	1013.75i	−0.825510	−	1.42982i	−0.901529	−	0.432718i	$-0.857554\pi$
$709$	−585.286	−	1013.75i	−0.825510	−	1.42982i	0.0760195	−	0.997106i	$-0.475779\pi$
$710$	−467.397	−	156.308i	−0.658306	−	0.220152i
$711$		0			0
$712$		−	388.949i		−	0.546276i
$713$	10.1096	+	17.5103i	0.0141789	+	0.0245586i
$714$		0			0
$715$	300.230	+	339.242i	0.419902	+	0.474464i
$716$	205.087	+	118.407i	0.286434	+	0.165373i
$717$		0			0
$718$	97.5321	−	56.3102i	0.135839	−	0.0784264i
$719$		−	168.127i		−	0.233834i	−0.993142	−	0.116917i	$-0.962699\pi$
$719$		−	168.127i		−	0.233834i	0.993142	−	0.116917i	$-0.0373012\pi$
$720$		0			0
$721$	−104.824			−0.145387
$722$	−254.174	−	440.242i	−0.352041	−	0.609753i
$723$		0			0
$724$	−172.397	+	298.600i	−0.238117	+	0.412431i
$725$	−417.184	−	981.975i	−0.575426	−	1.35445i
$726$		0			0
$727$	331.545	−	191.417i	0.456045	−	0.263298i	−0.254335	−	0.967116i	$-0.581857\pi$
$727$	331.545	−	191.417i	0.456045	−	0.263298i	0.710380	+	0.703819i	$0.248523\pi$
$728$	13.5593			0.0186254
$729$		0			0
$730$	600.985	+	200.983i	0.823267	+	0.275319i
$731$	458.577	−	264.760i	0.627329	−	0.362188i
$732$		0			0
$733$	−1215.10	−	701.541i	−1.65771	−	0.957082i	−0.973766	−	0.227550i	$-0.926928\pi$
$733$	−1215.10	−	701.541i	−1.65771	−	0.957082i	−0.683948	−	0.729531i	$-0.739738\pi$
$734$	−582.921	−	336.550i	−0.794171	−	0.458515i
$735$		0			0
$736$	−13.5736	−	23.5102i	−0.0184424	−	0.0319431i
$737$	1368.52			1.85688
$738$		0			0
$739$	899.125			1.21668			0.608339	−	0.793677i	$-0.291836\pi$
$739$	899.125			1.21668			0.608339	+	0.793677i	$0.291836\pi$
$740$	140.291	+	689.006i	0.189583	+	0.931090i
$741$		0			0
$742$	63.4999	+	36.6617i	0.0855794	+	0.0494093i
$743$	158.294	−	274.172i	0.213046	−	0.369007i	−0.739620	−	0.673025i	$-0.764995\pi$
$743$	158.294	−	274.172i	0.213046	−	0.369007i	0.952666	+	0.304017i	$0.0983281\pi$
$744$		0			0
$745$	189.080	+	928.621i	0.253799	+	1.24647i
$746$			87.3755i			0.117125i
$747$		0			0
$748$			396.689i			0.530334i
$749$	4.52790	−	2.61418i	0.00604526	−	0.00349023i
$750$		0			0
$751$	143.216	−	248.058i	0.190701	−	0.330304i	−0.754782	−	0.655976i	$-0.772257\pi$
$751$	143.216	−	248.058i	0.190701	−	0.330304i	0.945483	+	0.325672i	$0.105591\pi$
$752$	159.598	−	276.432i	0.212231	−	0.367595i
$753$		0			0
$754$	177.816	+	307.987i	0.235831	+	0.408470i
$755$	−179.730	+	537.434i	−0.238053	+	0.711833i
$756$		0			0
$757$			783.221i			1.03464i	0.855793	+	0.517319i	$0.173070\pi$
$757$			783.221i			1.03464i	−0.855793	+	0.517319i	$0.826930\pi$
$758$	−100.653	−	174.337i	−0.132788	−	0.229996i
$759$		0			0
$760$	−11.6467	−	13.1600i	−0.0153246	−	0.0173158i
$761$	893.662	+	515.956i	1.17433	+	0.677997i	0.954695	−	0.297586i	$-0.0961814\pi$
$761$	893.662	+	515.956i	1.17433	+	0.677997i	0.219631	+	0.975583i	$0.429515\pi$
$762$		0			0
$763$	76.2910	−	44.0467i	0.0999883	−	0.0577282i
$764$		−	578.787i		−	0.757574i
$765$		0			0
$766$	−505.609			−0.660064
$767$	107.963	+	186.998i	0.140761	+	0.243805i
$768$		0			0
$769$	415.625	−	719.883i	0.540475	−	0.936129i	−0.458402	−	0.888745i	$-0.651578\pi$
$769$	415.625	−	719.883i	0.540475	−	0.936129i	0.998877	−	0.0473845i	$-0.0150886\pi$
$770$	−58.6235	−	66.2411i	−0.0761344	−	0.0860273i
$771$		0			0
$772$	−221.413	+	127.833i	−0.286805	+	0.165587i
$773$	−395.360			−0.511462			−0.255731	−	0.966748i	$-0.582316\pi$
$773$	−395.360			−0.511462			−0.255731	+	0.966748i	$0.582316\pi$
$774$		0			0
$775$	−84.1400	−	63.3631i	−0.108568	−	0.0817588i
$776$	221.997	−	128.170i	0.286078	−	0.165167i
$777$		0			0
$778$	503.466	+	290.676i	0.647129	+	0.373620i
$779$	7.57939	+	4.37596i	0.00972964	+	0.00561741i
$780$		0			0
$781$	−535.846	−	928.112i

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(3.31368 + 3.74426i) q^{5} +(0.704577 - 0.406788i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(3.31368 + 3.74426i) q^{5} +(0.704577 - 0.406788i) q^{7} -2.82843 q^{8} +(-2.24264 + 6.70601i) q^{10} +(-13.3161 + 7.68808i) q^{11} +(-5.10300 - 2.94622i) q^{13} +(0.996422 + 0.575285i) q^{14} +(-2.00000 - 3.46410i) q^{16} -12.8995 q^{17} +1.24264 q^{19} +(-9.79894 + 1.99520i) q^{20} +(-18.8319 - 10.8726i) q^{22} +(2.39949 - 4.15605i) q^{23} +(-3.03902 + 24.8146i) q^{25} -8.33316i q^{26} +1.62715i q^{28} +(-36.9592 + 21.3384i) q^{29} +(-2.10660 + 3.64874i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-9.12132 - 15.7986i) q^{34} +(3.85786 + 1.29016i) q^{35} -70.3144i q^{37} +(0.878680 + 1.52192i) q^{38} +(-9.37251 - 10.5904i) q^{40} +(6.09942 + 3.52150i) q^{41} +(-35.5500 + 20.5248i) q^{43} -30.7523i q^{44} +6.78680 q^{46} +(39.8995 + 69.1080i) q^{47} +(-24.1690 + 41.8620i) q^{49} +(-32.5405 + 13.8245i) q^{50} +(10.2060 - 5.89243i) q^{52} +63.7279 q^{53} +(-72.9117 - 24.3833i) q^{55} +(-1.99284 + 1.15057i) q^{56} +(-52.2682 - 30.1770i) q^{58} +(-31.7353 - 18.3224i) q^{59} +(41.4706 + 71.8291i) q^{61} -5.95837 q^{62} +8.00000 q^{64} +(-5.87830 - 28.8698i) q^{65} +(-77.0786 - 44.5013i) q^{67} +(12.8995 - 22.3426i) q^{68} +(1.14781 + 5.63718i) q^{70} +69.6982i q^{71} -89.6188i q^{73} +(86.1172 - 49.7198i) q^{74} +(-1.24264 + 2.15232i) q^{76} +(-6.25483 + 10.8337i) q^{77} +(-67.0477 - 116.130i) q^{79} +(6.34315 - 18.9675i) q^{80} +9.96031i q^{82} +(-54.5122 - 94.4179i) q^{83} +(-42.7448 - 48.2991i) q^{85} +(-50.2753 - 29.0265i) q^{86} +(37.6638 - 21.7452i) q^{88} +137.514i q^{89} -4.79394 q^{91} +(4.79899 + 8.31209i) q^{92} +(-56.4264 + 97.7334i) q^{94} +(4.11772 + 4.65277i) q^{95} +(-78.4877 + 45.3149i) q^{97} -68.3604 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 12 q^{5}+O(q^{10}) \) 8 * q - 8 * q^4 - 12 * q^5	\( 8 q - 8 q^{4} - 12 q^{5} + 16 q^{10} - 16 q^{16} - 24 q^{17} - 24 q^{19} - 24 q^{20} - 60 q^{23} + 12 q^{25} + 68 q^{31} - 56 q^{34} + 144 q^{35} + 24 q^{38} - 16 q^{40} + 224 q^{46} + 240 q^{47} + 180 q^{49} - 96 q^{50} + 408 q^{53} - 176 q^{55} + 196 q^{61} - 240 q^{62} + 64 q^{64} + 24 q^{65} + 24 q^{68} - 80 q^{70} + 24 q^{76} + 312 q^{77} - 180 q^{79} + 96 q^{80} - 108 q^{83} - 20 q^{85} + 912 q^{91} - 120 q^{92} - 112 q^{94} + 60 q^{95} - 1056 q^{98}+O(q^{100}) \) 8 * q - 8 * q^4 - 12 * q^5 + 16 * q^10 - 16 * q^16 - 24 * q^17 - 24 * q^19 - 24 * q^20 - 60 * q^23 + 12 * q^25 + 68 * q^31 - 56 * q^34 + 144 * q^35 + 24 * q^38 - 16 * q^40 + 224 * q^46 + 240 * q^47 + 180 * q^49 - 96 * q^50 + 408 * q^53 - 176 * q^55 + 196 * q^61 - 240 * q^62 + 64 * q^64 + 24 * q^65 + 24 * q^68 - 80 * q^70 + 24 * q^76 + 312 * q^77 - 180 * q^79 + 96 * q^80 - 108 * q^83 - 20 * q^85 + 912 * q^91 - 120 * q^92 - 112 * q^94 + 60 * q^95 - 1056 * q^98

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