LMFDB - Embedded newform 504.2.bk.c.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.c.451.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.582416 - 1.28872i) q^{2} +(-1.32158 + 1.50114i) q^{4} +(0.128707 - 0.222928i) q^{5} +(-0.623918 + 2.57113i) q^{7} +(2.70425 + 0.828860i) q^{8} +O(q^{10})$	\(q+(-0.582416 - 1.28872i) q^{2} +(-1.32158 + 1.50114i) q^{4} +(0.128707 - 0.222928i) q^{5} +(-0.623918 + 2.57113i) q^{7} +(2.70425 + 0.828860i) q^{8} +(-0.362252 - 0.0360307i) q^{10} +(-1.79412 - 3.10751i) q^{11} -4.57992 q^{13} +(3.67684 - 0.693415i) q^{14} +(-0.506836 - 3.96776i) q^{16} +(-6.92813 + 3.99996i) q^{17} +(0.201988 + 0.116618i) q^{19} +(0.164548 + 0.487825i) q^{20} +(-2.95978 + 4.12198i) q^{22} +(-5.76102 - 3.32613i) q^{23} +(2.46687 + 4.27274i) q^{25} +(2.66742 + 5.90222i) q^{26} +(-3.03507 - 4.33455i) q^{28} +2.80806i q^{29} +(-1.03380 - 1.79060i) q^{31} +(-4.81813 + 2.96405i) q^{32} +(9.18987 + 6.59876i) q^{34} +(0.492874 + 0.470013i) q^{35} +(6.46587 + 3.73307i) q^{37} +(0.0326463 - 0.328225i) q^{38} +(0.532833 - 0.496173i) q^{40} +4.55693i q^{41} -5.42738 q^{43} +(7.03589 + 1.41361i) q^{44} +(-0.931125 + 9.36151i) q^{46} +(1.42355 - 2.46565i) q^{47} +(-6.22145 - 3.20835i) q^{49} +(4.06961 - 5.66761i) q^{50} +(6.05274 - 6.87509i) q^{52} +(1.93137 - 1.11508i) q^{53} -0.923668 q^{55} +(-3.81834 + 6.43586i) q^{56} +(3.61879 - 1.63546i) q^{58} +(-2.14701 + 1.23958i) q^{59} +(4.44251 - 7.69466i) q^{61} +(-1.70547 + 2.37515i) q^{62} +(6.62598 + 4.48289i) q^{64} +(-0.589469 + 1.02099i) q^{65} +(-0.867859 - 1.50318i) q^{67} +(3.15161 - 15.6864i) q^{68} +(0.318656 - 0.908918i) q^{70} +8.97302i q^{71} +(-6.57828 + 3.79797i) q^{73} +(1.04505 - 10.5069i) q^{74} +(-0.442003 + 0.149092i) q^{76} +(9.10921 - 2.67409i) q^{77} +(-7.51791 - 4.34047i) q^{79} +(-0.949757 - 0.397692i) q^{80} +(5.87259 - 2.65403i) q^{82} +3.79017i q^{83} +2.05930i q^{85} +(3.16099 + 6.99435i) q^{86} +(-2.27607 - 9.89058i) q^{88} +(2.25065 + 1.29941i) q^{89} +(2.85749 - 11.7756i) q^{91} +(12.6066 - 4.25234i) q^{92} +(-4.00663 - 0.398512i) q^{94} +(0.0519946 - 0.0300191i) q^{95} +14.6024i q^{97} +(-0.511188 + 9.88629i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.582416	−	1.28872i	−0.411830	−	0.911261i
$2$	−0.582416	−	1.28872i	−0.411830	−	0.911261i
$3$		0			0
$3$		0			0
$4$	−1.32158	+	1.50114i	−0.660792	+	0.750569i
$5$	0.128707	−	0.222928i	0.0575597	−	0.0996963i	−0.835810	−	0.549019i	$-0.815001\pi$
$5$	0.128707	−	0.222928i	0.0575597	−	0.0996963i	0.893369	+	0.449323i	$0.148335\pi$
$6$		0			0
$7$	−0.623918	+	2.57113i	−0.235819	+	0.971797i
$7$	−0.623918	+	2.57113i	−0.235819	+	0.971797i
$8$	2.70425	+	0.828860i	0.956098	+	0.293046i
$9$		0			0
$10$	−0.362252	−	0.0360307i	−0.114554	−	0.0113939i
$11$	−1.79412	−	3.10751i	−0.540948	−	0.936950i	−0.998850	−	0.0479470i	$-0.984732\pi$
$11$	−1.79412	−	3.10751i	−0.540948	−	0.936950i	0.457902	−	0.889003i	$-0.348601\pi$
$12$		0			0
$13$	−4.57992			−1.27024			−0.635120	−	0.772413i	$-0.719049\pi$
$13$	−4.57992			−1.27024			−0.635120	+	0.772413i	$0.719049\pi$
$14$	3.67684	−	0.693415i	0.982678	−	0.185323i
$15$		0			0
$16$	−0.506836	−	3.96776i	−0.126709	−	0.991940i
$17$	−6.92813	+	3.99996i	−1.68032	+	0.970132i	−0.718871	+	0.695143i	$0.755341\pi$
$17$	−6.92813	+	3.99996i	−1.68032	+	0.970132i	−0.961447	+	0.274989i	$0.911326\pi$
$18$		0			0
$19$	0.201988	+	0.116618i	0.0463391	+	0.0267539i	0.522991	−	0.852338i	$-0.324816\pi$
$19$	0.201988	+	0.116618i	0.0463391	+	0.0267539i	−0.476651	+	0.879092i	$0.658150\pi$
$20$	0.164548	+	0.487825i	0.0367941	+	0.109081i
$21$		0			0
$22$	−2.95978	+	4.12198i	−0.631027	+	0.878809i
$23$	−5.76102	−	3.32613i	−1.20126	−	0.693545i	−0.240421	−	0.970669i	$-0.577286\pi$
$23$	−5.76102	−	3.32613i	−1.20126	−	0.693545i	−0.960834	+	0.277124i	$0.910619\pi$
$24$		0			0
$25$	2.46687	+	4.27274i	0.493374	+	0.854548i
$26$	2.66742	+	5.90222i	0.523123	+	1.15752i
$27$		0			0
$28$	−3.03507	−	4.33455i	−0.573574	−	0.819154i
$29$			2.80806i			0.521444i	0.965414	+	0.260722i	$0.0839605\pi$
$29$			2.80806i			0.521444i	−0.965414	+	0.260722i	$0.916039\pi$
$30$		0			0
$31$	−1.03380	−	1.79060i	−0.185676	−	0.321600i	0.758128	−	0.652106i	$-0.226114\pi$
$31$	−1.03380	−	1.79060i	−0.185676	−	0.321600i	−0.943804	+	0.330505i	$0.892781\pi$
$32$	−4.81813	+	2.96405i	−0.851733	+	0.523976i
$33$		0			0
$34$	9.18987	+	6.59876i	1.57605	+	1.13168i
$35$	0.492874	+	0.470013i	0.0833109	+	0.0794466i
$36$		0			0
$37$	6.46587	+	3.73307i	1.06298	+	0.613713i	0.926256	−	0.376896i	$-0.123009\pi$
$37$	6.46587	+	3.73307i	1.06298	+	0.613713i	0.136726	+	0.990609i	$0.456342\pi$
$38$	0.0326463	−	0.328225i	0.00529593	−	0.0532451i
$39$		0			0
$40$	0.532833	−	0.496173i	0.0842484	−	0.0784519i
$41$			4.55693i			0.711673i	0.934548	+	0.355837i	$0.115804\pi$
$41$			4.55693i			0.711673i	−0.934548	+	0.355837i	$0.884196\pi$
$42$		0			0
$43$	−5.42738			−0.827667			−0.413834	−	0.910353i	$-0.635810\pi$
$43$	−5.42738			−0.827667			−0.413834	+	0.910353i	$0.635810\pi$
$44$	7.03589	+	1.41361i	1.06070	+	0.213109i
$45$		0			0
$46$	−0.931125	+	9.36151i	−0.137287	+	1.38028i
$47$	1.42355	−	2.46565i	0.207646	−	0.359653i	−0.743327	−	0.668928i	$-0.766753\pi$
$47$	1.42355	−	2.46565i	0.207646	−	0.359653i	0.950972	+	0.309276i	$0.100087\pi$
$48$		0			0
$49$	−6.22145	−	3.20835i	−0.888779	−	0.458336i
$50$	4.06961	−	5.66761i	0.575530	−	0.801521i
$51$		0			0
$52$	6.05274	−	6.87509i	0.839364	−	0.953404i
$53$	1.93137	−	1.11508i	0.265295	−	0.153168i	−0.361453	−	0.932390i	$-0.617719\pi$
$53$	1.93137	−	1.11508i	0.265295	−	0.153168i	0.626747	+	0.779222i	$0.284386\pi$
$54$		0			0
$55$	−0.923668			−0.124547
$56$	−3.81834	+	6.43586i	−0.510247	+	0.860028i
$57$		0			0
$58$	3.61879	−	1.63546i	0.475171	−	0.214746i
$59$	−2.14701	+	1.23958i	−0.279517	+	0.161379i	−0.633205	−	0.773984i	$-0.718261\pi$
$59$	−2.14701	+	1.23958i	−0.279517	+	0.161379i	0.353688	+	0.935364i	$0.384928\pi$
$60$		0			0
$61$	4.44251	−	7.69466i	0.568806	−	0.985200i	−0.427879	−	0.903836i	$-0.640739\pi$
$61$	4.44251	−	7.69466i	0.568806	−	0.985200i	0.996684	−	0.0813643i	$-0.0259277\pi$
$62$	−1.70547	+	2.37515i	−0.216595	+	0.301644i
$63$		0			0
$64$	6.62598	+	4.48289i	0.828248	+	0.560362i
$65$	−0.589469	+	1.02099i	−0.0731147	+	0.126638i
$66$		0			0
$67$	−0.867859	−	1.50318i	−0.106026	−	0.183642i	0.808131	−	0.589003i	$-0.200479\pi$
$67$	−0.867859	−	1.50318i	−0.106026	−	0.183642i	−0.914157	+	0.405361i	$0.867146\pi$
$68$	3.15161	−	15.6864i	0.382189	−	1.90225i
$69$		0			0
$70$	0.318656	−	0.908918i	0.0380866	−	0.108637i
$71$			8.97302i			1.06490i	0.846461	+	0.532451i	$0.178729\pi$
$71$			8.97302i			1.06490i	−0.846461	+	0.532451i	$0.821271\pi$
$72$		0			0
$73$	−6.57828	+	3.79797i	−0.769929	+	0.444519i	−0.832849	−	0.553500i	$-0.813292\pi$
$73$	−6.57828	+	3.79797i	−0.769929	+	0.444519i	0.0629201	+	0.998019i	$0.479959\pi$
$74$	1.04505	−	10.5069i	0.121484	−	1.22140i
$75$		0			0
$76$	−0.442003	+	0.149092i	−0.0507012	+	0.0171020i
$77$	9.10921	−	2.67409i	1.03809	−	0.304741i
$78$		0			0
$79$	−7.51791	−	4.34047i	−0.845831	−	0.488341i	0.0134112	−	0.999910i	$-0.495731\pi$
$79$	−7.51791	−	4.34047i	−0.845831	−	0.488341i	−0.859242	+	0.511569i	$0.829064\pi$
$80$	−0.949757	−	0.397692i	−0.106186	−	0.0444634i
$81$		0			0
$82$	5.87259	−	2.65403i	0.648520	−	0.293089i
$83$			3.79017i			0.416025i	0.978126	+	0.208012i	$0.0666994\pi$
$83$			3.79017i			0.416025i	−0.978126	+	0.208012i	$0.933301\pi$
$84$		0			0
$85$			2.05930i			0.223362i
$86$	3.16099	+	6.99435i	0.340858	+	0.754220i
$87$		0			0
$88$	−2.27607	−	9.89058i	−0.242630	−	1.05434i
$89$	2.25065	+	1.29941i	0.238569	+	0.137738i	0.614519	−	0.788902i	$-0.289350\pi$
$89$	2.25065	+	1.29941i	0.238569	+	0.137738i	−0.375950	+	0.926640i	$0.622684\pi$
$90$		0			0
$91$	2.85749	−	11.7756i	0.299547	−	1.23442i
$92$	12.6066	−	4.25234i	1.31433	−	0.443337i
$93$		0			0
$94$	−4.00663	−	0.398512i	−0.413252	−	0.0411033i
$95$	0.0519946	−	0.0300191i	0.00533454	−	0.00307990i
$96$		0			0
$97$			14.6024i			1.48265i	0.671146	+	0.741325i	$0.265802\pi$
$97$			14.6024i			1.48265i	−0.671146	+	0.741325i	$0.734198\pi$
$98$	−0.511188	+	9.88629i	−0.0516378	+	0.998666i
$99$		0			0
$100$	−9.67415	−	1.94367i	−0.967415	−	0.194367i
$101$	−0.709937	−	1.22965i	−0.0706414	−	0.122354i	0.828541	−	0.559928i	$-0.189171\pi$
$101$	−0.709937	−	1.22965i	−0.0706414	−	0.122354i	−0.899183	+	0.437574i	$0.855838\pi$
$102$		0			0
$103$	−4.42816	+	7.66981i	−0.436320	+	0.755728i	−0.997402	−	0.0720316i	$-0.977052\pi$
$103$	−4.42816	+	7.66981i	−0.436320	+	0.755728i	0.561082	+	0.827760i	$0.310385\pi$
$104$	−12.3853	−	3.79611i	−1.21447	−	0.372239i
$105$		0			0
$106$	−2.56189	−	1.83955i	−0.248832	−	0.178673i
$107$	6.00175	−	10.3953i	0.580211	−	1.00496i	−0.415243	−	0.909711i	$-0.636303\pi$
$107$	6.00175	−	10.3953i	0.580211	−	1.00496i	0.995454	−	0.0952445i	$-0.0303633\pi$
$108$		0			0
$109$	10.8275	−	6.25126i	1.03709	−	0.598762i	0.118080	−	0.993004i	$-0.462326\pi$
$109$	10.8275	−	6.25126i	1.03709	−	0.598762i	0.919007	+	0.394242i	$0.128993\pi$
$110$	0.537959	+	1.19035i	0.0512924	+	0.113495i
$111$		0			0
$112$	10.5179	+	1.17242i	0.993845	+	0.110783i
$113$	−0.143571			−0.0135061			−0.00675303	−	0.999977i	$-0.502150\pi$
$113$	−0.143571			−0.0135061			−0.00675303	+	0.999977i	$0.502150\pi$
$114$		0			0
$115$	−1.48297	+	0.856194i	−0.138288	+	0.0798405i
$116$	−4.21529	−	3.71108i	−0.391380	−	0.344566i
$117$		0			0
$118$	2.84792	+	2.04494i	0.262172	+	0.188252i
$119$	−5.96184	−	20.3088i	−0.546521	−	1.86170i
$120$		0			0
$121$	−0.937751	+	1.62423i	−0.0852501	+	0.147657i
$122$	−12.5036	−	1.24365i	−1.13203	−	0.112595i
$123$		0			0
$124$	4.05419	+	0.814542i	0.364077	+	0.0731481i
$125$	2.55709			0.228713
$126$		0			0
$127$		−	18.5252i		−	1.64385i	−0.569597	−	0.821924i	$-0.692901\pi$
$127$		−	18.5252i		−	1.64385i	0.569597	−	0.821924i	$-0.307099\pi$
$128$	1.91810	−	11.1499i	0.169538	−	0.985524i
$129$		0			0
$130$	1.65908	+	0.165018i	0.145511	+	0.0144730i
$131$	−11.3578	−	6.55743i	−0.992336	−	0.572925i	−0.0863640	−	0.996264i	$-0.527525\pi$
$131$	−11.3578	−	6.55743i	−0.992336	−	0.572925i	−0.905972	+	0.423338i	$0.860858\pi$
$132$		0			0
$133$	−0.425863	+	0.446577i	−0.0369270	+	0.0387232i
$134$	−1.43171	+	1.99390i	−0.123681	+	0.172247i
$135$		0			0
$136$	−22.0508	+	5.07446i	−1.89084	+	0.435131i
$137$	−1.26333	−	2.18816i	−0.107934	−	0.186947i	0.806999	−	0.590552i	$-0.201090\pi$
$137$	−1.26333	−	2.18816i	−0.107934	−	0.186947i	−0.914933	+	0.403606i	$0.867757\pi$
$138$		0			0
$139$		−	16.8020i		−	1.42512i	−0.701609	−	0.712562i	$-0.747535\pi$
$139$		−	16.8020i		−	1.42512i	0.701609	−	0.712562i	$-0.252465\pi$
$140$	−1.35693	+	0.118712i	−0.114681	+	0.0100330i
$141$		0			0
$142$	11.5637	−	5.22603i	0.970403	−	0.438559i
$143$	8.21693	+	14.2321i	0.687134	+	1.19015i
$144$		0			0
$145$	0.625995	+	0.361418i	0.0519860	+	0.0300141i
$146$	8.72580	+	6.26554i	0.722153	+	0.518540i
$147$		0			0
$148$	−14.1490	+	4.77260i	−1.16304	+	0.392305i
$149$	−20.1564	−	11.6373i	−1.65128	−	0.953366i	−0.976547	−	0.215303i	$-0.930926\pi$
$149$	−20.1564	−	11.6373i	−1.65128	−	0.953366i	−0.674731	−	0.738064i	$-0.735740\pi$
$150$		0			0
$151$	10.6125	−	6.12714i	0.863634	−	0.498619i	−0.00159368	−	0.999999i	$-0.500507\pi$
$151$	10.6125	−	6.12714i	0.863634	−	0.498619i	0.865227	+	0.501380i	$0.167174\pi$
$152$	0.449566	+	0.482783i	0.0364646	+	0.0391589i
$153$		0			0
$154$	−8.75150	−	10.1818i	−0.705216	−	0.820470i
$155$	−0.532231			−0.0427498
$156$		0			0
$157$	10.3040	+	17.8471i	0.822352	+	1.42436i	0.903926	+	0.427688i	$0.140672\pi$
$157$	10.3040	+	17.8471i	0.822352	+	1.42436i	−0.0815741	+	0.996667i	$0.525995\pi$
$158$	−1.21508	+	12.2164i	−0.0966668	+	0.971886i
$159$		0			0
$160$	0.0406410	+	1.45559i	0.00321295	+	0.115075i
$161$	12.1463	−	12.7371i	0.957264	−	1.00383i
$162$		0			0
$163$	7.21136	−	12.4904i	0.564837	−	0.978326i	−0.432228	−	0.901764i	$-0.642272\pi$
$163$	7.21136	−	12.4904i	0.564837	−	0.978326i	0.997065	−	0.0765619i	$-0.0243943\pi$
$164$	−6.84059	−	6.02236i	−0.534160	−	0.470268i
$165$		0			0
$166$	4.88445	−	2.20745i	0.379107	−	0.171332i
$167$	−7.63662			−0.590939			−0.295470	−	0.955352i	$-0.595476\pi$
$167$	−7.63662			−0.590939			−0.295470	+	0.955352i	$0.595476\pi$
$168$		0			0
$169$	7.97564			0.613510
$170$	2.65385	−	1.19937i	0.203541	−	0.0919873i
$171$		0			0
$172$	7.17273	−	8.14725i	0.546916	−	0.621222i
$173$	−7.89966	+	13.6826i	−0.600600	+	1.04027i	0.392130	+	0.919910i	$0.371738\pi$
$173$	−7.89966	+	13.6826i	−0.600600	+	1.04027i	−0.992730	+	0.120360i	$0.961595\pi$
$174$		0			0
$175$	−12.5249	+	3.67681i	−0.946794	+	0.277940i
$176$	−11.4205	+	8.69364i	−0.860855	+	0.655308i
$177$		0			0
$178$	0.363762	−	3.65725i	0.0272651	−	0.274123i
$179$	11.4726	+	19.8711i	0.857500	+	1.48523i	0.874306	+	0.485374i	$0.161317\pi$
$179$	11.4726	+	19.8711i	0.857500	+	1.48523i	−0.0168065	+	0.999859i	$0.505350\pi$
$180$		0			0
$181$	−15.1773			−1.12812			−0.564060	−	0.825734i	$-0.690761\pi$
$181$	−15.1773			−1.12812			−0.564060	+	0.825734i	$0.690761\pi$
$182$	−16.8396	+	3.17578i	−1.24824	+	0.235405i
$183$		0			0
$184$	−12.8224	−	13.7698i	−0.945278	−	1.01512i
$185$	1.66441	−	0.960948i	0.122370	−	0.0706503i
$186$		0			0
$187$	24.8598	+	14.3528i	1.81793	+	1.04958i
$188$	1.81995	+	5.39551i	0.132734	+	0.393508i
$189$		0			0
$190$	−0.0689686	−	0.0495227i	−0.00500351	−	0.00359276i
$191$	18.5980	+	10.7376i	1.34571	+	0.776944i	0.987638	−	0.156751i	$-0.0501020\pi$
$191$	18.5980	+	10.7376i	1.34571	+	0.776944i	0.358069	+	0.933695i	$0.383435\pi$
$192$		0			0
$193$	3.58036	+	6.20137i	0.257720	+	0.446384i	0.965631	−	0.259918i	$-0.0836954\pi$
$193$	3.58036	+	6.20137i	0.257720	+	0.446384i	−0.707911	+	0.706302i	$0.750362\pi$
$194$	18.8184	−	8.50468i	1.35108	−	0.610600i
$195$		0			0
$196$	13.0384	−	5.09915i	0.931311	−	0.364225i
$197$			9.29594i			0.662309i	0.943577	+	0.331154i	$0.107438\pi$
$197$			9.29594i			0.662309i	−0.943577	+	0.331154i	$0.892562\pi$
$198$		0			0
$199$	10.3895	+	17.9951i	0.736491	+	1.27564i	0.954066	+	0.299596i	$0.0968518\pi$
$199$	10.3895	+	17.9951i	0.736491	+	1.27564i	−0.217575	+	0.976043i	$0.569815\pi$
$200$	3.12954	+	13.5993i	0.221292	+	0.961614i
$201$		0			0
$202$	−1.17119	+	1.63107i	−0.0824045	+	0.114762i
$203$	−7.21989	−	1.75200i	−0.506737	−	0.122966i
$204$		0			0
$205$	1.01587	+	0.586511i	0.0709512	+	0.0409637i
$206$	12.4632	+	1.23963i	0.868355	+	0.0863694i
$207$		0			0
$208$	2.32126	+	18.1720i	0.160951	+	1.26000i
$209$		−	0.836905i		−	0.0578899i
$210$		0			0
$211$	5.13459			0.353480			0.176740	−	0.984258i	$-0.443445\pi$
$211$	5.13459			0.353480			0.176740	+	0.984258i	$0.443445\pi$
$212$	−0.878583	+	4.37293i	−0.0603413	+	0.300334i
$213$		0			0
$214$	−16.8922	−	1.68015i	−1.15472	−	0.114853i
$215$	−0.698544	+	1.20991i	−0.0476403	+	0.0825154i
$216$		0			0
$217$	5.24887	−	1.54085i	0.356316	−	0.104600i
$218$	−14.3622	−	10.3128i	−0.972732	−	0.698468i
$219$		0			0
$220$	1.22070	−	1.38655i	0.0822998	−	0.0934814i
$221$	31.7303	−	18.3195i	2.13441	−	1.23230i
$222$		0			0
$223$	−8.76372			−0.586862			−0.293431	−	0.955980i	$-0.594797\pi$
$223$	−8.76372			−0.586862			−0.293431	+	0.955980i	$0.594797\pi$
$224$	−4.61486	−	14.2374i	−0.308343	−	0.951275i
$225$		0			0
$226$	0.0836182	+	0.185023i	0.00556220	+	0.0123075i
$227$	5.09712	−	2.94282i	0.338308	−	0.195322i	−0.321216	−	0.947006i	$-0.604091\pi$
$227$	5.09712	−	2.94282i	0.338308	−	0.195322i	0.659523	+	0.751684i	$0.270758\pi$
$228$		0			0
$229$	7.90278	−	13.6880i	0.522230	−	0.904529i	−0.477435	−	0.878667i	$-0.658434\pi$
$229$	7.90278	−	13.6880i	0.522230	−	0.904529i	0.999666	−	0.0258624i	$-0.00823316\pi$
$230$	1.96710	+	1.41247i	0.129707	+	0.0931355i
$231$		0			0
$232$	−2.32749	+	7.59371i	−0.152807	+	0.498551i
$233$	0.159081	−	0.275536i	0.0104217	−	0.0180510i	−0.860768	−	0.508998i	$-0.830016\pi$
$233$	0.159081	−	0.275536i	0.0104217	−	0.0180510i	0.871189	+	0.490947i	$0.163349\pi$
$234$		0			0
$235$	−0.366442	−	0.634696i	−0.0239040	−	0.0414030i
$236$	0.976675	−	4.86116i	0.0635761	−	0.316435i
$237$		0			0
$238$	−22.7000	+	19.5113i	−1.47142	+	1.26473i
$239$			1.46820i			0.0949697i	0.998872	+	0.0474849i	$0.0151206\pi$
$239$			1.46820i			0.0949697i	−0.998872	+	0.0474849i	$0.984879\pi$
$240$		0			0
$241$	−12.8350	+	7.41030i	−0.826776	+	0.477339i	−0.852748	−	0.522323i	$-0.825065\pi$
$241$	−12.8350	+	7.41030i	−0.826776	+	0.477339i	0.0259714	+	0.999663i	$0.491732\pi$
$242$	2.63934	+	0.262517i	0.169663	+	0.0168752i
$243$		0			0
$244$	5.67960	+	16.8380i	0.363599	+	1.07794i
$245$	−1.51598	+	0.973995i	−0.0968523	+	0.0622263i
$246$		0			0
$247$	−0.925087	−	0.534099i	−0.0588619	−	0.0339839i
$248$	−1.31151	−	5.69910i	−0.0832808	−	0.361893i
$249$		0			0
$250$	−1.48929	−	3.29537i	−0.0941910	−	0.208417i
$251$		−	10.0773i		−	0.636074i	−0.948078	−	0.318037i	$-0.896976\pi$
$251$		−	10.0773i		−	0.636074i	0.948078	−	0.318037i	$-0.103024\pi$
$252$		0			0
$253$			23.8699i			1.50069i
$254$	−23.8738	+	10.7894i	−1.49797	+	0.676986i
$255$		0			0
$256$	−15.4862	+	4.02200i	−0.967890	+	0.251375i
$257$	15.8763	+	9.16617i	0.990334	+	0.571770i	0.905374	−	0.424615i	$-0.139590\pi$
$257$	15.8763	+	9.16617i	0.990334	+	0.571770i	0.0849601	+	0.996384i	$0.472924\pi$
$258$		0			0
$259$	−13.6324	+	14.2955i	−0.847076	+	0.888278i
$260$	−0.753616	−	2.23420i	−0.0467373	−	0.138559i
$261$		0			0
$262$	−1.83571	+	18.4561i	−0.113410	+	1.14022i
$263$	−2.62507	+	1.51558i	−0.161869	+	0.0934549i	−0.578746	−	0.815508i	$-0.696458\pi$
$263$	−2.62507	+	1.51558i	−0.161869	+	0.0934549i	0.416877	+	0.908963i	$0.363124\pi$
$264$		0			0
$265$		−	0.574076i		−	0.0352652i
$266$	0.823541	+	0.288724i	0.0504946	+	0.0177028i
$267$		0			0
$268$	3.40342	+	0.683795i	0.207897	+	0.0417694i
$269$	12.7236	+	22.0380i	0.775774	+	1.34368i	0.934358	+	0.356335i	$0.115974\pi$
$269$	12.7236	+	22.0380i	0.775774	+	1.34368i	−0.158584	+	0.987345i	$0.550693\pi$
$270$		0			0
$271$	−10.4445	+	18.0904i	−0.634458	+	1.09891i	0.352172	+	0.935935i	$0.385443\pi$
$271$	−10.4445	+	18.0904i	−0.634458	+	1.09891i	−0.986630	+	0.162978i	$0.947890\pi$
$272$	19.3823	+	25.4618i	1.17522	+	1.54385i
$273$		0			0
$274$	−2.08413	+	2.90250i	−0.125907	+	0.175346i
$275$	8.85173	−	15.3316i	0.533779	−	0.924533i
$276$		0			0
$277$	−15.4661	+	8.92934i	−0.929266	+	0.536512i	−0.886579	−	0.462576i	$-0.846925\pi$
$277$	−15.4661	+	8.92934i	−0.929266	+	0.536512i	−0.0426868	+	0.999089i	$0.513592\pi$
$278$	−21.6530	+	9.78573i	−1.29866	+	0.586909i
$279$		0			0
$280$	0.943283	+	1.67956i	0.0563719	+	0.100373i
$281$	−3.12507			−0.186426			−0.0932132	−	0.995646i	$-0.529714\pi$
$281$	−3.12507			−0.186426			−0.0932132	+	0.995646i	$0.529714\pi$
$282$		0			0
$283$	−13.3128	+	7.68615i	−0.791364	+	0.456894i	−0.840442	−	0.541901i	$-0.817705\pi$
$283$	−13.3128	+	7.68615i	−0.791364	+	0.456894i	0.0490788	+	0.998795i	$0.484371\pi$
$284$	−13.4697	−	11.8586i	−0.799282	−	0.703678i
$285$		0			0
$286$	13.5555	−	18.8783i	0.801555	−	1.11630i
$287$	−11.7165	−	2.84315i	−0.691602	−	0.167826i
$288$		0			0
$289$	23.4993	−	40.7020i	1.38231	−	2.39424i
$290$	0.101176	−	1.01723i	0.00594129	−	0.0597335i
$291$		0			0
$292$	2.99246	−	14.8942i	0.175121	−	0.871620i
$293$	−23.0311			−1.34549			−0.672746	−	0.739873i	$-0.734885\pi$
$293$	−23.0311			−1.34549			−0.672746	+	0.739873i	$0.734885\pi$
$294$		0			0
$295$			0.638171i			0.0371557i
$296$	14.3912	+	15.4545i	0.836469	+	0.898273i
$297$		0			0
$298$	−3.25778	+	32.7537i	−0.188718	+	1.89737i
$299$	26.3850	+	15.2334i	1.52588	+	0.880969i
$300$		0			0
$301$	3.38624	−	13.9545i	0.195180	−	0.804325i
$302$	−14.0770	−	10.1080i	−0.810043	−	0.581649i
$303$		0			0
$304$	0.360336	−	0.860544i	0.0206667	−	0.0493556i
$305$	−1.14357	−	1.98072i	−0.0654806	−	0.113416i
$306$		0			0
$307$			4.16830i			0.237898i	0.992900	+	0.118949i	$0.0379524\pi$
$307$			4.16830i			0.237898i	−0.992900	+	0.118949i	$0.962048\pi$
$308$	−8.02439	+	17.2082i	−0.457232	+	0.980530i
$309$		0			0
$310$	0.309980	+	0.685896i	0.0176057	+	0.0389563i
$311$	0.255482	+	0.442507i	0.0144870	+	0.0250923i	0.873178	−	0.487401i	$-0.162055\pi$
$311$	0.255482	+	0.442507i	0.0144870	+	0.0250923i	−0.858691	+	0.512494i	$0.828722\pi$
$312$		0			0
$313$	−12.1966	−	7.04172i	−0.689393	−	0.398021i	0.113991	−	0.993482i	$-0.463636\pi$
$313$	−12.1966	−	7.04172i	−0.689393	−	0.398021i	−0.803385	+	0.595460i	$0.796970\pi$
$314$	16.9987	−	23.6734i	0.959290	−	1.33597i
$315$		0			0
$316$	16.4512	−	5.54914i	0.925451	−	0.312163i
$317$	−4.17009	−	2.40760i	−0.234216	−	0.135224i	0.378300	−	0.925683i	$-0.376509\pi$
$317$	−4.17009	−	2.40760i	−0.234216	−	0.135224i	−0.612515	+	0.790459i	$0.709842\pi$
$318$		0			0
$319$	8.72608	−	5.03800i	0.488566	−	0.282074i
$320$	1.85218	−	0.900134i	0.103540	−	0.0503190i
$321$		0			0
$322$	−23.4887	−	8.23487i	−1.30898	−	0.458911i
$323$	−1.86586			−0.103819
$324$		0			0
$325$	−11.2981	−	19.5688i	−0.626703	−	1.08548i
$326$	−20.2966	−	2.01877i	−1.12413	−	0.111809i
$327$		0			0
$328$	−3.77706	+	12.3231i	−0.208553	+	0.680429i
$329$	5.45135	+	5.19849i	0.300543	+	0.286602i
$330$		0			0
$331$	−10.5895	+	18.3415i	−0.582049	+	1.00814i	0.413187	+	0.910646i	$0.364416\pi$
$331$	−10.5895	+	18.3415i	−0.582049	+	1.00814i	−0.995236	+	0.0974930i	$0.968918\pi$
$332$	−5.68957	−	5.00902i	−0.312255	−	0.274906i
$333$		0			0
$334$	4.44769	+	9.84144i	0.243367	+	0.538500i
$335$	−0.446800			−0.0244113
$336$		0			0
$337$	13.0422			0.710454			0.355227	−	0.934780i	$-0.384404\pi$
$337$	13.0422			0.710454			0.355227	+	0.934780i	$0.384404\pi$
$338$	−4.64514	−	10.2783i	−0.252662	−	0.559068i
$339$		0			0
$340$	−3.09129	−	2.72153i	−0.167649	−	0.147596i
$341$	−3.70953	+	6.42509i	−0.200882	+	0.347938i
$342$		0			0
$343$	12.1308	−	13.9944i	0.655001	−	0.755628i
$344$	−14.6770	−	4.49853i	−0.791331	−	0.242545i
$345$		0			0
$346$	22.2339	+	2.21146i	1.19530	+	0.118889i
$347$	2.51166	+	4.35032i	0.134833	+	0.233537i	0.925534	−	0.378665i	$-0.123617\pi$
$347$	2.51166	+	4.35032i	0.134833	+	0.233537i	−0.790701	+	0.612203i	$0.790284\pi$
$348$		0			0
$349$	−13.9823			−0.748455			−0.374227	−	0.927337i	$-0.622092\pi$
$349$	−13.9823			−0.748455			−0.374227	+	0.927337i	$0.622092\pi$
$350$	12.0331	+	13.9996i	0.643195	+	0.748312i
$351$		0			0
$352$	17.8551	+	9.65452i	0.951683	+	0.514588i
$353$	2.00338	−	1.15665i	0.106629	−	0.0615622i	−0.445737	−	0.895164i	$-0.647058\pi$
$353$	2.00338	−	1.15665i	0.106629	−	0.0615622i	0.552366	+	0.833602i	$0.313725\pi$
$354$		0			0
$355$	2.00034	+	1.15489i	0.106167	+	0.0612954i
$356$	−4.92503	+	1.66126i	−0.261026	+	0.0880464i
$357$		0			0
$358$	18.9264	−	26.3581i	1.00029	−	1.39307i
$359$	−8.33838	−	4.81417i	−0.440083	−	0.254082i	0.263550	−	0.964646i	$-0.415107\pi$
$359$	−8.33838	−	4.81417i	−0.440083	−	0.254082i	−0.703633	+	0.710564i	$0.748440\pi$
$360$		0			0
$361$	−9.47280	−	16.4074i	−0.498568	−	0.863546i
$362$	8.83950	+	19.5592i	0.464594	+	1.02801i
$363$		0			0
$364$	13.9004	+	19.8519i	0.728577	+	1.04052i
$365$			1.95531i			0.102346i
$366$		0			0
$367$	3.79729	+	6.57711i	0.198217	+	0.343322i	0.947950	−	0.318418i	$-0.103152\pi$
$367$	3.79729	+	6.57711i	0.198217	+	0.343322i	−0.749733	+	0.661740i	$0.769818\pi$
$368$	−10.2774	+	24.5441i	−0.535745	+	1.27945i
$369$		0			0
$370$	−2.20777	−	1.58528i	−0.114776	−	0.0824149i
$371$	1.66200	+	5.66154i	0.0862866	+	0.293932i
$372$		0			0
$373$	−17.6547	−	10.1929i	−0.914124	−	0.527769i	−0.0323679	−	0.999476i	$-0.510305\pi$
$373$	−17.6547	−	10.1929i	−0.914124	−	0.527769i	−0.881756	+	0.471707i	$0.843638\pi$
$374$	4.01797	−	40.3966i	0.207764	−	2.08886i
$375$		0			0
$376$	5.89331	−	5.48784i	0.303924	−	0.283014i
$377$		−	12.8607i		−	0.662359i
$378$		0			0
$379$	−35.3247			−1.81451			−0.907253	−	0.420584i	$-0.861825\pi$
$379$	−35.3247			−1.81451			−0.907253	+	0.420584i	$0.861825\pi$
$380$	−0.0236524	+	0.117724i	−0.00121334	+	0.00603911i
$381$		0			0
$382$	3.00591	−	30.2214i	0.153796	−	1.54626i
$383$	−7.06305	+	12.2336i	−0.360905	+	0.625106i	−0.988110	−	0.153748i	$-0.950866\pi$
$383$	−7.06305	+	12.2336i	−0.360905	+	0.625106i	0.627205	+	0.778854i	$0.284199\pi$
$384$		0			0
$385$	0.576293	−	2.37487i	0.0293706	−	0.121035i
$386$	5.90655	−	8.22585i	0.300636	−	0.418685i
$387$		0			0
$388$	−21.9203	−	19.2983i	−1.11283	−	0.979723i
$389$	−1.66609	+	0.961919i	−0.0844743	+	0.0487712i	−0.541642	−	0.840609i	$-0.682197\pi$
$389$	−1.66609	+	0.961919i	−0.0844743	+	0.0487712i	0.457168	+	0.889380i	$0.348864\pi$
$390$		0			0
$391$	53.2175			2.69132
$392$	−14.1651	−	13.8329i	−0.715446	−	0.698668i
$393$		0			0
$394$	11.9798	−	5.41411i	0.603536	−	0.272759i
$395$	−1.93522	+	1.11730i	−0.0973715	+	0.0562175i
$396$		0			0
$397$	5.33766	−	9.24510i	0.267890	−	0.463998i	−0.700427	−	0.713724i	$-0.747007\pi$
$397$	5.33766	−	9.24510i	0.267890	−	0.463998i	0.968317	+	0.249726i	$0.0803404\pi$
$398$	17.1396	−	23.8697i	0.859131	−	1.19648i
$399$		0			0
$400$	15.7029	−	11.9535i	0.785146	−	0.597676i
$401$	−6.90465	+	11.9592i	−0.344802	+	0.597214i	−0.985318	−	0.170731i	$-0.945387\pi$
$401$	−6.90465	+	11.9592i	−0.344802	+	0.597214i	0.640516	+	0.767945i	$0.278720\pi$
$402$		0			0
$403$	4.73472	+	8.20078i	0.235853	+	0.408510i
$404$	2.78411	+	0.559367i	0.138515	+	0.0278295i
$405$		0			0
$406$	1.94715	+	10.3248i	0.0966354	+	0.512411i
$407$		−	26.7903i		−	1.32795i
$408$		0			0
$409$	19.5725	−	11.3002i	0.967797	−	0.558758i	0.0692334	−	0.997600i	$-0.477945\pi$
$409$	19.5725	−	11.3002i	0.967797	−	0.558758i	0.898564	+	0.438842i	$0.144611\pi$
$410$	0.164190	−	1.65076i	0.00810875	−	0.0815251i
$411$		0			0
$412$	−5.66126	−	16.7836i	−0.278910	−	0.826867i
$413$	−1.84756	−	6.29364i	−0.0909124	−	0.309690i
$414$		0			0
$415$	0.844933	+	0.487823i	0.0414762	+	0.0239463i
$416$	22.0666	−	13.5751i	1.08191	−	0.665575i
$417$		0			0
$418$	−1.07853	+	0.487427i	−0.0527528	+	0.0238408i
$419$		−	18.9813i		−	0.927299i	−0.886019	−	0.463650i	$-0.846540\pi$
$419$		−	18.9813i		−	0.927299i	0.886019	−	0.463650i	$-0.153460\pi$
$420$		0			0
$421$			18.7332i			0.912999i	0.889724	+	0.456499i	$0.150897\pi$
$421$			18.7332i			0.912999i	−0.889724	+	0.456499i	$0.849103\pi$
$422$	−2.99047	−	6.61704i	−0.145574	−	0.322112i
$423$		0			0
$424$	6.14717	−	1.41462i	0.298533	−	0.0687000i
$425$	−34.1816	−	19.7347i	−1.65805	−	0.957276i
$426$		0			0
$427$	17.0122	+	16.2231i	0.823280	+	0.785093i
$428$	7.67303	+	22.7478i	0.370890	+	1.09955i
$429$		0			0
$430$	1.96608	+	0.195552i	0.0948127	+	0.00943037i
$431$	22.2380	−	12.8391i	1.07117	−	0.618439i	0.142668	−	0.989771i	$-0.454432\pi$
$431$	22.2380	−	12.8391i	1.07117	−	0.618439i	0.928500	+	0.371331i	$0.121099\pi$
$432$		0			0
$433$		−	9.18476i		−	0.441392i	−0.975343	−	0.220696i	$-0.929167\pi$
$433$		−	9.18476i		−	0.441392i	0.975343	−	0.220696i	$-0.0708328\pi$
$434$	−5.04275	−	5.86689i	−0.242060	−	0.281620i
$435$		0			0
$436$	−4.92543	+	24.5151i	−0.235885	+	1.17406i
$437$	−0.775770	−	1.34367i	−0.0371101	−	0.0642766i
$438$		0			0
$439$	−9.86253	+	17.0824i	−0.470713	+	0.815298i	−0.999439	−	0.0334941i	$-0.989336\pi$
$439$	−9.86253	+	17.0824i	−0.470713	+	0.815298i	0.528726	+	0.848792i	$0.322670\pi$
$440$	−2.49783	−	0.765591i	−0.119079	−	0.0364981i
$441$		0			0
$442$	−42.0888	−	30.2218i	−2.00196	−	1.43750i
$443$	−13.0143	+	22.5415i	−0.618330	+	1.07098i	0.371460	+	0.928449i	$0.378857\pi$
$443$	−13.0143	+	22.5415i	−0.618330	+	1.07098i	−0.989790	+	0.142531i	$0.954476\pi$
$444$		0			0
$445$	0.579351	−	0.334489i	0.0274639	−	0.0158563i
$446$	5.10413	+	11.2939i	0.241687	+	0.534784i
$447$		0			0
$448$	−15.6602	+	14.2393i	−0.739874	+	0.672745i
$449$	−10.8554			−0.512297			−0.256148	−	0.966637i	$-0.582454\pi$
$449$	−10.8554			−0.512297			−0.256148	+	0.966637i	$0.582454\pi$
$450$		0			0
$451$	14.1607	−	8.17569i	0.666802	−	0.384978i
$452$	0.189741	−	0.215521i	0.00892469	−	0.0101372i
$453$		0			0
$454$	−6.76111	−	4.85480i	−0.317315	−	0.227847i
$455$	−2.25732	−	2.15262i	−0.105825	−	0.100916i
$456$		0			0
$457$	−15.0321	+	26.0363i	−0.703171	+	1.21793i	0.264177	+	0.964474i	$0.414900\pi$
$457$	−15.0321	+	26.0363i	−0.703171	+	1.21793i	−0.967348	+	0.253453i	$0.918434\pi$
$458$	−22.2427	−	2.21233i	−1.03933	−	0.103375i
$459$		0			0
$460$	0.674604	−	3.35768i	0.0314536	−	0.156553i
$461$	−9.23630			−0.430177			−0.215089	−	0.976595i	$-0.569004\pi$
$461$	−9.23630			−0.430177			−0.215089	+	0.976595i	$0.569004\pi$
$462$		0			0
$463$		−	17.3618i		−	0.806869i	−0.915008	−	0.403435i	$-0.867816\pi$
$463$		−	17.3618i		−	0.806869i	0.915008	−	0.403435i	$-0.132184\pi$
$464$	11.1417	−	1.42322i	0.517241	−	0.0660715i
$465$		0			0
$466$	−0.447739	−	0.0445335i	−0.0207411	−	0.00206298i
$467$	−18.8961	−	10.9097i	−0.874408	−	0.504840i	−0.00559766	−	0.999984i	$-0.501782\pi$
$467$	−18.8961	−	10.9097i	−0.874408	−	0.504840i	−0.868811	+	0.495144i	$0.835115\pi$
$468$		0			0
$469$	4.40634	−	1.29352i	0.203466	−	0.0597293i
$470$	−0.604522	+	0.841897i	−0.0278845	+	0.0388338i
$471$		0			0
$472$	−6.83349	+	1.57256i	−0.314537	+	0.0723830i
$473$	9.73738	+	16.8656i	0.447725	+	0.775483i
$474$		0			0
$475$			1.15072i			0.0527987i
$476$	38.3654	+	17.8902i	1.75847	+	0.819997i
$477$		0			0
$478$	1.89209	−	0.855101i	0.0865422	−	0.0391114i
$479$	10.2056	+	17.6766i	0.466306	+	0.807665i	0.999259	−	0.0384791i	$-0.0122513\pi$
$479$	10.2056	+	17.6766i	0.466306	+	0.807665i	−0.532954	+	0.846144i	$0.678918\pi$
$480$		0			0
$481$	−29.6131	−	17.0972i	−1.35024	−	0.779563i
$482$	17.0251	+	12.2248i	0.775472	+	0.556826i
$483$		0			0
$484$	−1.19888	−	3.55425i	−0.0544946	−	0.161557i
$485$	3.25528	+	1.87944i	0.147815	+	0.0853409i
$486$		0			0
$487$	−7.32382	+	4.22841i	−0.331874	+	0.191608i	−0.656673	−	0.754176i	$-0.728037\pi$
$487$	−7.32382	+	4.22841i	−0.331874	+	0.191608i	0.324799	+	0.945783i	$0.394703\pi$
$488$	18.3915	−	17.1261i	0.832543	−	0.775262i
$489$		0			0
$490$	2.13813	+	1.38640i	0.0965911	+	0.0626310i
$491$	−37.4822			−1.69155			−0.845774	−	0.533541i	$-0.820861\pi$
$491$	−37.4822			−1.69155			−0.845774	+	0.533541i	$0.820861\pi$
$492$		0			0
$493$	−11.2321	−	19.4546i	−0.505869	−	0.876191i
$494$	−0.149517	+	1.50324i	−0.00672710	+	0.0676341i
$495$		0			0
$496$	−6.58069	+	5.00941i	−0.295481	+	0.224929i
$497$	−23.0708	−	5.59843i	−1.03487	−	0.251124i
$498$		0			0
$499$	−6.23338	+	10.7965i	−0.279045	+	0.483319i	−0.971148	−	0.238479i	$-0.923351\pi$
$499$	−6.23338	+	10.7965i	−0.279045	+	0.483319i	0.692103	+	0.721799i	$0.256684\pi$
$500$	−3.37941	+	3.83855i	−0.151132	+	0.171665i
$501$		0			0
$502$	−12.9868	+	5.86919i	−0.579629	+	0.261955i
$503$	13.8883			0.619250			0.309625	−	0.950859i	$-0.399797\pi$
$503$	13.8883			0.619250			0.309625	+	0.950859i	$0.399797\pi$
$504$		0			0
$505$	−0.365497			−0.0162644
$506$	30.7616	−	13.9022i	1.36752	−	0.618029i
$507$		0			0
$508$	27.8089	+	24.4826i	1.23382	+	1.08624i
$509$	19.5215	−	33.8121i	0.865273	−	1.49870i	−0.00150245	−	0.999999i	$-0.500478\pi$
$509$	19.5215	−	33.8121i	0.865273	−	1.49870i	0.866776	−	0.498698i	$-0.166188\pi$
$510$		0			0
$511$	−5.66078	−	19.2833i	−0.250418	−	0.853041i
$512$	14.2027	+	17.6149i	0.627675	+	0.778476i
$513$		0			0
$514$	2.56600	−	25.7985i	0.113182	−	1.13792i
$515$	1.13988	+	1.97432i	0.0502289	+	0.0869990i
$516$		0			0
$517$	−10.2161			−0.449302
$518$	26.3625	+	9.24239i	1.15830	+	0.406087i
$519$		0			0
$520$	−2.44033	+	2.27243i	−0.107016	+	0.0996527i
$521$	−12.2354	+	7.06409i	−0.536041	+	0.309483i	−0.743473	−	0.668766i	$-0.766823\pi$
$521$	−12.2354	+	7.06409i	−0.536041	+	0.309483i	0.207432	+	0.978249i	$0.433489\pi$
$522$		0			0
$523$	9.63976	+	5.56552i	0.421517	+	0.243363i	0.695726	−	0.718307i	$-0.255083\pi$
$523$	9.63976	+	5.56552i	0.421517	+	0.243363i	−0.274209	+	0.961670i	$0.588416\pi$
$524$	24.8539	−	8.38345i	1.08575	−	0.366233i
$525$		0			0
$526$	3.48204	+	2.50027i	0.151824	+	0.109017i
$527$	14.3246	+	8.27032i	0.623990	+	0.360261i
$528$		0			0
$529$	10.6262	+	18.4052i	0.462010	+	0.800224i
$530$	−0.739822	+	0.334351i	−0.0321358	+	0.0145233i
$531$		0			0
$532$	−0.107561	−	1.22947i	−0.00466335	−	0.0533042i
$533$		−	20.8704i		−	0.903996i
$534$		0			0
$535$	−1.54494	−	2.67591i	−0.0667936	−	0.115690i
$536$	−1.10099	−	4.78430i	−0.0475555	−	0.206650i
$537$		0			0
$538$	20.9903	−	29.2325i	0.904955	−	1.26030i
$539$	1.19205	+	25.0894i	0.0513451	+	1.08068i
$540$		0			0
$541$	11.0648	+	6.38829i	0.475715	+	0.274654i	0.718629	−	0.695394i	$-0.244770\pi$
$541$	11.0648	+	6.38829i	0.475715	+	0.274654i	−0.242914	+	0.970048i	$0.578103\pi$
$542$	29.3964	+	2.92386i	1.26268	+	0.125591i
$543$		0			0
$544$	21.5245	−	39.8077i	0.922857	−	1.70674i
$545$		−	3.21833i		−	0.137858i
$546$		0			0
$547$	−20.6852			−0.884437			−0.442218	−	0.896907i	$-0.645808\pi$
$547$	−20.6852			−0.884437			−0.442218	+	0.896907i	$0.645808\pi$
$548$	4.95433	+	0.995393i	0.211638	+	0.0425211i
$549$		0			0
$550$	−24.9135	−	2.47798i	−1.06232	−	0.105661i
$551$	−0.327469	+	0.567193i	−0.0139507	+	0.0241632i
$552$		0			0
$553$	15.8505	−	16.6214i	0.674031	−	0.706816i
$554$	20.5151	+	14.7308i	0.871602	+	0.625852i
$555$		0			0
$556$	25.2221	+	22.2052i	1.06965	+	0.941710i
$557$	4.75011	−	2.74248i	0.201268	−	0.116202i	−0.395979	−	0.918260i	$-0.629595\pi$
$557$	4.75011	−	2.74248i	0.201268	−	0.116202i	0.597247	+	0.802057i	$0.296261\pi$
$558$		0			0
$559$	24.8569			1.05134
$560$	1.61509	−	2.19383i	0.0682501	−	0.0927060i
$561$		0			0
$562$	1.82009	+	4.02734i	0.0767760	+	0.169883i
$563$	−35.0039	+	20.2095i	−1.47524	+	0.851730i	−0.999610	−	0.0279158i	$-0.991113\pi$
$563$	−35.0039	+	20.2095i	−1.47524	+	0.851730i	−0.475629	+	0.879646i	$0.657780\pi$
$564$		0			0
$565$	−0.0184787	+	0.0320060i	−0.000777405	+	0.00134650i
$566$	17.6589	+	12.6799i	0.742257	+	0.532976i
$567$		0			0
$568$	−7.43737	+	24.2653i	−0.312065	+	1.01815i
$569$	8.93137	−	15.4696i	0.374422	−	0.648519i	−0.615818	−	0.787888i	$-0.711174\pi$
$569$	8.93137	−	15.4696i	0.374422	−	0.648519i	0.990240	+	0.139370i	$0.0445077\pi$
$570$		0			0
$571$	4.38717	+	7.59881i	0.183597	+	0.318000i	0.943103	−	0.332501i	$-0.107892\pi$
$571$	4.38717	+	7.59881i	0.183597	+	0.318000i	−0.759506	+	0.650501i	$0.774559\pi$
$572$	−32.2238	−	6.47421i	−1.34734	−	0.270700i
$573$		0			0
$574$	3.15984	+	16.7551i	0.131889	+	0.699345i
$575$		−	32.8205i		−	1.36871i
$576$		0			0
$577$	−3.76090	+	2.17135i	−0.156568	+	0.0903947i	−0.576237	−	0.817283i	$-0.695480\pi$
$577$	−3.76090	+	2.17135i	−0.156568	+	0.0903947i	0.419669	+	0.907677i	$0.362146\pi$
$578$	−66.1398	−	6.57847i	−2.75105	−	0.273628i
$579$		0			0
$580$	−1.36984	+	0.462061i	−0.0568796	+	0.0191860i
$581$	−9.74502	−	2.36475i	−0.404292	−	0.0981065i
$582$		0			0
$583$	−6.93024	−	4.00118i	−0.287021	−	0.165712i
$584$	−20.9373	+	4.81821i	−0.866393	+	0.199379i
$585$		0			0
$586$	13.4137	+	29.6806i	0.554114	+	1.22609i
$587$			10.5208i			0.434239i	0.976145	+	0.217119i	$0.0696661\pi$
$587$			10.5208i			0.434239i	−0.976145	+	0.217119i	$0.930334\pi$
$588$		0			0
$589$		−	0.482238i		−	0.0198703i
$590$	0.822422	−	0.371681i	0.0338586	−	0.0153019i
$591$		0			0
$592$	11.5348	−	27.5471i	0.474077	−	1.13218i
$593$	13.0551	+	7.53735i	0.536107	+	0.309522i	0.743500	−	0.668736i	$-0.233164\pi$
$593$	13.0551	+	7.53735i	0.536107	+	0.309522i	−0.207392	+	0.978258i	$0.566498\pi$
$594$		0			0
$595$	−5.29473	−	1.28483i	−0.217063	−	0.0526730i
$596$	44.1076	−	14.8779i	1.80672	−	0.609423i
$597$		0			0
$598$	4.26448	−	42.8749i	0.174387	−	1.75329i
$599$	−6.10386	+	3.52407i	−0.249397	+	0.143989i	−0.619488	−	0.785006i	$-0.712660\pi$
$599$	−6.10386	+	3.52407i	−0.249397	+	0.143989i	0.370091	+	0.928995i	$0.379326\pi$
$600$		0			0
$601$			0.706153i			0.0288046i	0.999896	+	0.0144023i	$0.00458455\pi$
$601$			0.706153i			0.0288046i	−0.999896	+	0.0144023i	$0.995415\pi$
$602$	−19.9556	+	3.76342i	−0.813330	+	0.153386i
$603$		0			0
$604$	−4.82763	+	24.0284i	−0.196434	+	0.977700i
$605$	0.241391	+	0.418101i	0.00981394	+	0.0169982i
$606$		0			0
$607$	−3.09824	+	5.36632i	−0.125754	+	0.217812i	−0.922027	−	0.387125i	$-0.873468\pi$
$607$	−3.09824	+	5.36632i	−0.125754	+	0.217812i	0.796273	+	0.604937i	$0.206802\pi$
$608$	−1.31886	+	0.0368234i	−0.0534870	+	0.00149339i
$609$		0			0
$610$	−1.88655	+	2.62734i	−0.0763844	+	0.106378i
$611$	−6.51972	+	11.2925i	−0.263760	+	0.456845i
$612$		0			0
$613$	9.94156	−	5.73976i	0.401536	−	0.231827i	−0.285611	−	0.958346i	$-0.592196\pi$
$613$	9.94156	−	5.73976i	0.401536	−	0.231827i	0.687146	+	0.726519i	$0.258863\pi$
$614$	5.37176	−	2.42769i	0.216787	−	0.0979734i
$615$		0			0
$616$	26.8501	+	0.318826i	1.08182	+	0.0128459i
$617$	48.1839			1.93981			0.969905	−	0.243485i	$-0.0782908\pi$
$617$	48.1839			1.93981			0.969905	+	0.243485i	$0.0782908\pi$
$618$		0			0
$619$	10.6872	−	6.17027i	0.429556	−	0.248004i	−0.269602	−	0.962972i	$-0.586892\pi$
$619$	10.6872	−	6.17027i	0.429556	−	0.248004i	0.699157	+	0.714968i	$0.253559\pi$
$620$	0.703388	−	0.798953i	0.0282487	−	0.0320867i
$621$		0			0
$622$	0.421470	−	0.586966i	0.0168994	−	0.0235352i
$623$	−4.74519	+	4.97600i	−0.190112	+	0.199359i
$624$		0			0
$625$	−12.0052	+	20.7937i	−0.480209	+	0.831747i
$626$	−1.97128	+	19.8192i	−0.0787882	+	0.792134i
$627$		0			0
$628$	−40.4087	−	8.11866i	−1.61248	−	0.323970i
$629$	−59.7285			−2.38153
$630$		0			0
$631$		−	2.33444i		−	0.0929326i	−0.998920	−	0.0464663i	$-0.985204\pi$
$631$		−	2.33444i		−	0.0929326i	0.998920	−	0.0464663i	$-0.0147960\pi$
$632$	−16.7327	−	17.9690i	−0.665591	−	0.714769i
$633$		0			0
$634$	−0.673991	+	6.77629i	−0.0267676	+	0.269121i
$635$	−4.12979	−	2.38433i	−0.163886	−	0.0946194i
$636$		0			0
$637$	28.4937	+	14.6940i	1.12896	+	0.582197i
$638$	−11.5748	−	8.31123i	−0.458249	−	0.329045i
$639$		0			0
$640$	−2.23875	−	1.86268i	−0.0884945	−	0.0736288i
$641$	−22.0146	−	38.1304i	−0.869525	−	1.50606i	−0.862483	−	0.506086i	$-0.831092\pi$
$641$	−22.0146	−	38.1304i	−0.869525	−	1.50606i	−0.00704191	−	0.999975i	$-0.502242\pi$
$642$		0			0
$643$		−	0.391635i		−	0.0154446i	−0.999970	−	0.00772228i	$-0.997542\pi$
$643$		−	0.391635i		−	0.0154446i	0.999970	−	0.00772228i	$-0.00245810\pi$
$644$	3.06781	+	35.0665i	0.120889	+	1.38181i
$645$		0			0
$646$	1.08671	+	2.40457i	0.0427560	+	0.0946065i
$647$	13.1914	+	22.8482i	0.518608	+	0.898256i	0.999766	+	0.0216222i	$0.00688310\pi$
$647$	13.1914	+	22.8482i	0.518608	+	0.898256i	−0.481158	+	0.876634i	$0.659784\pi$
$648$		0			0
$649$	7.70400	+	4.44790i	0.302408	+	0.174596i
$650$	−18.6385	+	25.9572i	−0.731061	+	1.01812i
$651$		0			0
$652$	9.21947	+	27.3324i	0.361062	+	1.07042i
$653$	33.2271	+	19.1837i	1.30028	+	0.750715i	0.980451	−	0.196762i	$-0.0630426\pi$
$653$	33.2271	+	19.1837i	1.30028	+	0.750715i	0.319825	+	0.947477i	$0.396376\pi$
$654$		0			0
$655$	−2.92367	+	1.68798i	−0.114237	+	0.0659548i
$656$	18.0808	−	2.30961i	0.705937	−	0.0901753i
$657$		0			0
$658$	3.52444	−	10.0529i	0.137397	−	0.391904i
$659$	27.8445			1.08467			0.542334	−	0.840163i	$-0.317541\pi$
$659$	27.8445			1.08467			0.542334	+	0.840163i	$0.317541\pi$
$660$		0			0
$661$	10.0199	+	17.3549i	0.389728	+	0.675029i	0.992413	−	0.122951i	$-0.0392357\pi$
$661$	10.0199	+	17.3549i	0.389728	+	0.675029i	−0.602685	+	0.797979i	$0.705902\pi$
$662$	29.8045	+	2.96445i	1.15838	+	0.115216i
$663$		0			0
$664$	−3.14152	+	10.2496i	−0.121914	+	0.397761i
$665$	0.0447427	+	0.152415i	0.00173505	+	0.00591038i
$666$		0			0
$667$	9.33996	−	16.1773i	0.361645	−	0.626387i
$668$	10.0924	−	11.4636i	0.390488	−	0.443541i
$669$		0			0
$670$	0.260223	+	0.575798i	0.0100533	+	0.0222450i
$671$	−31.8817			−1.23078
$672$		0			0
$673$	−2.90485			−0.111974			−0.0559868	−	0.998432i	$-0.517830\pi$
$673$	−2.90485			−0.111974			−0.0559868	+	0.998432i	$0.517830\pi$
$674$	−7.59599	−	16.8077i	−0.292586	−	0.647409i
$675$		0			0
$676$	−10.5405	+	11.9725i	−0.405403	+	0.460482i
$677$	−14.6961	+	25.4545i	−0.564819	+	0.978295i	0.432248	+	0.901755i	$0.357721\pi$
$677$	−14.6961	+	25.4545i	−0.564819	+	0.978295i	−0.997067	+	0.0765400i	$0.975613\pi$
$678$		0			0
$679$	−37.5448	−	9.11071i	−1.44084	−	0.349637i
$680$	−1.70687	+	5.56886i	−0.0654554	+	0.213556i
$681$		0			0
$682$	10.4406	+	1.03846i	0.399792	+	0.0397646i
$683$	0.120445	+	0.208616i	0.00460868	+	0.00798247i	0.868321	−	0.496003i	$-0.165200\pi$
$683$	0.120445	+	0.208616i	0.00460868	+	0.00798247i	−0.863712	+	0.503986i	$0.831866\pi$
$684$		0			0
$685$	−0.650401			−0.0248506
$686$	−25.1000	−	7.48257i	−0.958323	−	0.285686i
$687$		0			0
$688$	2.75079	+	21.5345i	0.104873	+	0.820996i
$689$	−8.84553	+	5.10697i	−0.336988	+	0.194560i
$690$		0			0
$691$	−26.5759	−	15.3436i	−1.01099	−	0.583698i	−0.0995117	−	0.995036i	$-0.531728\pi$
$691$	−26.5759	−	15.3436i	−1.01099	−	0.583698i	−0.911483	+	0.411339i	$0.865061\pi$
$692$	−10.0994	−	29.9412i	−0.383923	−	1.13819i
$693$		0			0
$694$	4.14350	−	5.77052i	0.157285	−	0.219046i
$695$	−3.74563	−	2.16254i	−0.142080	−	0.0820297i
$696$		0			0
$697$	−18.2275	−	31.5710i	−0.690417	−	1.19584i
$698$	8.14351	+	18.0192i	0.308236	+	0.682037i
$699$		0			0
$700$	11.0333	−	23.6608i	0.417020	−	0.894296i
$701$			1.90784i			0.0720581i	0.999351	+	0.0360290i	$0.0114709\pi$
$701$			1.90784i			0.0720581i	−0.999351	+	0.0360290i	$0.988529\pi$
$702$		0			0
$703$	0.870684	+	1.50807i	0.0328385	+	0.0568779i
$704$	2.04282	−	28.6332i	0.0769916	−	1.07915i
$705$		0			0
$706$	−2.65739	−	1.90813i	−0.100012	−	0.0718136i
$707$	3.60453	−	1.05814i	0.135562	−	0.0397956i
$708$		0			0
$709$	−29.0031	−	16.7450i	−1.08923	−	0.628870i	−0.155862	−	0.987779i	$-0.549816\pi$
$709$	−29.0031	−	16.7450i	−1.08923	−	0.628870i	−0.933373	+	0.358909i	$0.883149\pi$
$710$	0.323304	−	3.25050i	0.0121334	−	0.121989i
$711$		0			0
$712$	5.00930	+	5.37942i	0.187732	+	0.201602i
$713$			13.7542i			0.515099i
$714$		0			0
$715$	4.23032			0.158205
$716$	−44.9912	−	9.03935i	−1.68140	−	0.337817i
$717$		0			0
$718$	−1.34769	+	13.5497i	−0.0502954	+	0.505669i
$719$	0.0121575	−	0.0210575i	0.000453399	−	0.000785311i	−0.865799	−	0.500393i	$-0.833189\pi$
$719$	0.0121575	−	0.0210575i	0.000453399	−	0.000785311i	0.866252	+	0.499607i	$0.166522\pi$
$720$		0			0
$721$	−16.9573	−	16.1707i	−0.631522	−	0.602230i
$722$	−15.6273	+	21.7637i	−0.581590	+	0.809960i
$723$		0			0
$724$	20.0581	−	22.7832i	0.745452	−	0.846732i
$725$	−11.9981	+	6.92711i	−0.445599	+	0.257267i
$726$		0			0
$727$	−16.6521			−0.617593			−0.308797	−	0.951128i	$-0.599926\pi$
$727$	−16.6521			−0.617593			−0.308797	+	0.951128i	$0.599926\pi$
$728$	17.4877	−	29.4757i	0.648137	−	1.09244i
$729$		0			0
$730$	2.51984	−	1.13880i	0.0932634	−	0.0421490i
$731$	37.6016	−	21.7093i	1.39074	−	0.802947i
$732$		0			0
$733$	−13.1766	+	22.8226i	−0.486691	+	0.842973i	−0.999883	−	0.0153008i	$-0.995129\pi$
$733$	−13.1766	+	22.8226i	−0.486691	+	0.842973i	0.513192	+	0.858274i	$0.328463\pi$
$734$	6.26442	−	8.72425i	0.231224	−	0.322018i
$735$		0			0
$736$	37.6162	−	1.05027i	1.38655	−	0.0387133i
$737$	−3.11409	+	5.39376i	−0.114709	+	0.198682i
$738$		0			0
$739$	2.67874	+	4.63971i	0.0985390	+	0.170675i	0.911080	−	0.412229i	$-0.135250\pi$
$739$	2.67874	+	4.63971i	0.0985390	+	0.170675i	−0.812541	+	0.582904i	$0.801916\pi$
$740$	−0.757141	+	3.76848i	−0.0278330	+	0.138532i
$741$		0			0
$742$	6.32815	−	5.43922i	0.232314	−	0.199680i
$743$			33.1321i			1.21550i	0.794129	+	0.607749i	$0.207927\pi$
$743$			33.1321i			1.21550i	−0.794129	+	0.607749i	$0.792073\pi$
$744$		0			0
$745$	−5.18856	+	2.99562i	−0.190094	+	0.109751i
$746$	−2.85344	+	28.6884i	−0.104472	+	1.05036i
$747$		0			0
$748$	−54.3999	+	18.3496i	−1.98906	+	0.670928i
$749$	22.9832	+	21.9171i	0.839788	+	0.800835i
$750$		0			0
$751$	13.6288	+	7.86861i	0.497323	+	0.287130i	0.727607	−	0.685994i	$-0.240632\pi$
$751$	13.6288	+	7.86861i	0.497323	+	0.287130i	−0.230284	+	0.973123i	$0.573966\pi$
$752$	−10.5046	−	4.39861i	−0.383064	−	0.160401i
$753$		0			0
$754$	−16.5738	+	7.49026i	−0.603581	+	0.272779i
$755$		−	3.15443i		−	0.114802i
$756$		0			0
$757$			17.9229i			0.651418i	0.945470	+	0.325709i	$0.105603\pi$
$757$			17.9229i			0.651418i	−0.945470	+	0.325709i	$0.894397\pi$
$758$	20.5737	+	45.5235i	0.747269	+	1.65349i
$759$		0			0
$760$	0.165488	−	0.0380831i	0.00600289	−	0.00138142i
$761$	−15.7934	−	9.11832i	−0.572510	−	0.330539i	0.185641	−	0.982618i	$-0.440564\pi$
$761$	−15.7934	−	9.11832i	−0.572510	−	0.330539i	−0.758151	+	0.652079i	$0.773897\pi$
$762$		0			0
$763$	9.31735	+	31.7392i	0.337311	+	1.14904i
$764$	−40.6975	+	13.7276i	−1.47238	+	0.496648i
$765$		0			0
$766$	19.8792	+	1.97725i	0.718266	+	0.0714410i
$767$	9.83312	−	5.67716i	0.355054	−	0.204990i
$768$		0			0
$769$			41.7710i			1.50630i	0.657847	+	0.753151i	$0.271467\pi$
$769$			41.7710i			1.50630i	−0.657847	+	0.753151i	$0.728533\pi$
$770$	−3.39618	+	0.640485i	−0.122390	+	0.0230815i
$771$		0			0
$772$	−14.0409	−	2.82101i	−0.505342	−	0.101530i
$773$	−22.1831	−	38.4222i	−0.797870	−	1.38195i	−0.921001	−	0.389561i	$-0.872627\pi$
$773$	−22.1831	−	38.4222i	−0.797870	−	1.38195i	0.123131	−	0.992390i	$-0.460706\pi$
$774$		0			0
$775$	5.10050	−	8.83433i	0.183215	−	0.317338i
$776$	−12.1034	+	39.4886i	−0.434485	+	1.41756i
$777$		0			0
$778$	2.21000	+	1.58689i	0.0792324	+	0.0568926i
$779$	−0.531419	+	0.920444i	−0.0190400	+	0.0329783i
$780$		0			0
$781$	27.8838	−	16.0987i	0.997759	−	0.576057i
$782$	−30.9947	−	68.5822i	−1.10837	−	2.45250i
$783$		0			0
$784$	−9.57673	+	26.3113i	−0.342026	+	0.939690i
$785$	5.30483			0.189337
$786$		0			0
$787$	25.7940	−	14.8922i	0.919458	−	0.530849i	0.0359959	−	0.999352i	$-0.488540\pi$
$787$	25.7940	−	14.8922i	0.919458	−	0.530849i	0.883462	+	0.468503i	$0.155206\pi$
$788$	−13.9545	−	12.2854i	−0.497109	−	0.437648i
$789$		0			0
$790$	2.56699	+	1.84322i	0.0913293	+	0.0655788i
$791$	0.0895768	−	0.369141i	0.00318498	−	0.0131251i
$792$		0			0
$793$	−20.3463	+	35.2409i	−0.722520	+	1.25144i
$794$	−15.0231	−	1.49424i	−0.533148	−	0.0530286i
$795$		0			0
$796$	−40.7437	−	8.18598i	−1.44412	−	0.290144i
$797$	34.1552			1.20984			0.604920	−	0.796286i	$-0.293205\pi$
$797$	34.1552			1.20984			0.604920	+	0.796286i	$0.293205\pi$
$798$		0			0
$799$			22.7765i			0.805775i
$800$	−24.5503	−	13.2747i	−0.867985	−	0.469331i
$801$		0			0
$802$	19.4334	+	1.93291i	0.686217	+	0.0682533i
$803$	23.6045	+	13.6280i	0.832984	+	0.480923i
$804$		0			0
$805$	−1.27614	−	4.34711i	−0.0449779	−	0.153216i
$806$	7.81090	−	10.8780i	0.275127	−	0.383160i
$807$		0			0
$808$	−0.900646	−	3.91372i	−0.0316846	−	0.137684i
$809$	13.4152	+	23.2358i	0.471653	+	0.816928i	0.999474	−	0.0324281i	$-0.0103240\pi$
$809$	13.4152	+	23.2358i	0.471653	+	0.816928i	−0.527821	+	0.849356i	$0.676991\pi$
$810$		0			0
$811$		−	45.1596i		−	1.58577i	−0.609372	−	0.792885i	$-0.708578\pi$
$811$		−	45.1596i		−	1.58577i	0.609372	−	0.792885i	$-0.291422\pi$
$812$	12.1717	−	8.52265i	0.427142	−	0.299086i
$813$		0			0
$814$	−34.5252	+	15.6031i	−1.21011	+	0.546889i
$815$	−1.85631	−	3.21522i	−0.0650237	−	0.112624i
$816$		0			0
$817$	−1.09626	−	0.632928i	−0.0383534	−	0.0221433i
$818$	−25.9621	−	18.6420i	−0.907743	−	0.651802i
$819$		0			0
$820$	−2.22299	+	0.749834i	−0.0776301	+	0.0261853i
$821$	−17.5238	−	10.1174i	−0.611585	−	0.353099i	0.162000	−	0.986791i	$-0.448205\pi$
$821$	−17.5238	−	10.1174i	−0.611585	−	0.353099i	−0.773586	+	0.633692i	$0.781539\pi$
$822$		0			0
$823$	−40.5392	+	23.4053i	−1.41311	+	0.815858i	−0.995680	−	0.0928521i	$-0.970402\pi$
$823$	−40.5392	+	23.4053i	−1.41311	+	0.815858i	−0.417428	+	0.908710i	$0.637068\pi$
$824$	−18.3321	+	17.0708i	−0.638628	+	0.594689i
$825$		0			0
$826$	−7.03468	+	6.04650i	−0.244768	+	0.210385i
$827$	17.0446			0.592700			0.296350	−	0.955079i	$-0.404231\pi$
$827$	17.0446			0.592700			0.296350	+	0.955079i	$0.404231\pi$
$828$		0			0
$829$	−6.94700	−	12.0325i	−0.241279	−	0.417908i	0.719800	−	0.694182i	$-0.244234\pi$
$829$	−6.94700	−	12.0325i	−0.241279	−	0.417908i	−0.961079	+	0.276274i	$0.910900\pi$
$830$	0.136562	−	1.37300i	0.00474015	−	0.0476574i
$831$		0			0
$832$	−30.3465	−	20.5313i	−1.05207	−	0.711794i
$833$	55.9363	−	2.65765i	1.93808	−	0.0920820i
$834$		0			0
$835$	−0.982890	+	1.70242i	−0.0340143	+	0.0589145i
$836$	1.25631	+	1.10604i	0.0434504	+	0.0382532i
$837$		0			0
$838$	−24.4616	+	11.0550i	−0.845011	+	0.381890i
$839$	34.7647			1.20021			0.600105	−	0.799921i	$-0.295125\pi$
$839$	34.7647			1.20021			0.600105	+	0.799921i	$0.295125\pi$
$840$		0			0
$841$	21.1148			0.728097
$842$	24.1418	−	10.9105i	0.831980	−	0.376001i
$843$		0			0
$844$	−6.78579	+	7.70773i	−0.233577	+	0.265311i
$845$	1.02652	−	1.77799i	0.0353135	−	0.0611648i
$846$		0			0
$847$	−3.59104	−	3.42447i	−0.123389	−	0.117666i
$848$	−5.40326	−	7.09807i	−0.185549	−	0.243749i
$849$		0			0
$850$	−5.52460	+	55.5442i	−0.189492	+	1.90515i
$851$	−24.8333	−	43.0126i	−0.851275	−	1.47445i
$852$		0			0
$853$	−39.5354			−1.35367			−0.676834	−	0.736136i	$-0.736648\pi$
$853$	−39.5354			−1.35367			−0.676834	+	0.736136i	$0.736648\pi$
$854$	10.9988	−	31.3726i	0.376373	−	1.07355i
$855$		0			0
$856$	24.8465	−	23.1370i	0.849237	−	0.790807i
$857$	17.9608	−	10.3697i	0.613530	−	0.354221i	−0.160816	−	0.986984i	$-0.551413\pi$
$857$	17.9608	−	10.3697i	0.613530	−	0.354221i	0.774346	+	0.632763i	$0.218079\pi$
$858$		0			0
$859$	−41.7159	−	24.0847i	−1.42333	−	0.821759i	−0.426746	−	0.904371i	$-0.640340\pi$
$859$	−41.7159	−	24.0847i	−1.42333	−	0.821759i	−0.996582	+	0.0826128i	$0.973674\pi$
$860$	−0.893064	−	2.64761i	−0.0304532	−	0.0902828i
$861$		0			0
$862$	−29.4978	−	21.1808i	−1.00470	−	0.721421i
$863$	−38.2263	−	22.0700i	−1.30124	−	0.751271i	−0.320622	−	0.947207i	$-0.603892\pi$
$863$	−38.2263	−	22.0700i	−1.30124	−	0.751271i	−0.980617	+	0.195937i	$0.937225\pi$
$864$		0			0
$865$	2.03349	+	3.52211i	0.0691408	+	0.119755i
$866$	−11.8366	+	5.34935i	−0.402223	+	0.181778i
$867$		0			0
$868$	−4.62378	+	9.91564i	−0.156941	+	0.336559i
$869$			31.1493i			1.05667i
$870$		0			0
$871$	3.97472	+	6.88442i	0.134678	+	0.233270i
$872$	34.4617	−	7.93052i	1.16702	−	0.268561i
$873$		0			0
$874$	−1.27979	+	1.78232i	−0.0432896	+	0.0602880i
$875$	−1.59542	+	6.57462i	−0.0539349	+	0.222263i
$876$		0			0
$877$	1.21231	+	0.699930i	0.0409369	+	0.0236350i	0.520329	−	0.853966i	$-0.325809\pi$
$877$	1.21231	+	0.699930i	0.0409369	+	0.0236350i	−0.479392	+	0.877601i	$0.659143\pi$
$878$	27.7585	+	2.76094i	0.936803	+	0.0931774i
$879$		0			0
$880$	0.468148	+	3.66489i	0.0157813	+	0.123543i
$881$		−	0.164680i		−	0.00554821i	−0.999996	−	0.00277410i	$-0.999117\pi$
$881$		−	0.164680i		−	0.00554821i	0.999996	−	0.00277410i	$-0.000883026\pi$
$882$		0			0
$883$	28.9462			0.974116			0.487058	−	0.873370i	$-0.338070\pi$
$883$	28.9462			0.974116			0.487058	+	0.873370i	$0.338070\pi$
$884$	−14.4341	+	71.8422i	−0.485472	+	2.41632i
$885$		0			0
$886$	36.6294	+	3.64328i	1.23059	+	0.122398i
$887$	−20.3345	+	35.2204i	−0.682766	+	1.18258i	0.291368	+	0.956611i	$0.405890\pi$
$887$	−20.3345	+	35.2204i	−0.682766	+	1.18258i	−0.974133	+	0.225974i	$0.927444\pi$
$888$		0			0
$889$	47.6308	+	11.5582i	1.59749	+	0.387651i
$890$	−0.768485	−	0.551808i	−0.0257597	−	0.0184967i
$891$		0			0
$892$	11.5820	−	13.1556i	0.387793	−	0.440481i
$893$	0.575078	−	0.332021i	0.0192442	−	0.0111107i
$894$		0			0
$895$	5.90642			0.197430
$896$	27.4712	+	11.8883i	0.917749	+	0.397162i
$897$		0			0
$898$	6.32234	+	13.9895i	0.210979	+	0.466836i
$899$	5.02810	−	2.90297i	0.167696	−	0.0968196i
$900$		0			0
$901$	−8.92054	+	15.4508i	−0.297186	+	0.514742i
$902$	−18.7836	−	13.4875i	−0.625425	−	0.449085i
$903$		0			0
$904$	−0.388253	−	0.119000i	−0.0129131	−	0.00395790i
$905$	−1.95343	+	3.38344i	−0.0649343	+	0.112469i
$906$		0			0
$907$	6.57673	+	11.3912i	0.218377	+	0.378240i	0.954312	−	0.298813i	$-0.0965905\pi$
$907$	6.57673	+	11.3912i	0.218377	+	0.378240i	−0.735935	+	0.677052i	$0.763257\pi$
$908$	−2.31868	+	11.5407i	−0.0769482	+	0.382991i
$909$		0			0
$910$	−1.45942	+	4.16277i	−0.0483792	+	0.137994i
$911$		−	4.58131i		−	0.151785i	−0.997116	−	0.0758927i	$-0.975819\pi$
$911$		−	4.58131i		−	0.151785i	0.997116	−	0.0758927i	$-0.0241806\pi$
$912$		0			0
$913$	11.7780	−	6.80002i	0.389794	−	0.225048i
$914$	42.3084	+	4.20812i	1.39944	+	0.139192i
$915$		0			0
$916$	10.1034	+	29.9530i	0.333827	+	0.989675i
$917$	23.9464	−	25.1111i	0.790779	−	0.829242i
$918$		0			0
$919$	22.6967	+	13.1039i	0.748694	+	0.432259i	0.825222	−	0.564809i	$-0.191050\pi$
$919$	22.6967	+	13.1039i	0.748694	+	0.432259i	−0.0765280	+	0.997067i	$0.524383\pi$
$920$	−4.72000	+	1.08619i	−0.155614	+	0.0358107i
$921$		0			0
$922$	5.37937	+	11.9030i	0.177160	+	0.392004i
$923$		−	41.0957i		−	1.35268i
$924$		0			0
$925$			36.8360i			1.21116i
$926$	−22.3744	+	10.1118i	−0.735268	+	0.332293i
$927$		0			0
$928$	−8.32324	−	13.5296i	−0.273224	−	0.444131i
$929$	−4.55350	−	2.62897i	−0.149396	−	0.0862536i	0.423439	−	0.905925i	$-0.360823\pi$
$929$	−4.55350	−	2.62897i	−0.149396	−	0.0862536i	−0.572834	+	0.819671i	$0.694156\pi$
$930$		0			0
$931$	−0.882506	−	1.37358i	−0.0289230	−	0.0450172i
$932$	0.203379	+	0.602946i	0.00666191	+	0.0197501i
$933$		0			0
$934$	−3.05409	+	30.7057i	−0.0999328	+	1.00472i
$935$	6.39929	−	3.69463i	0.209279	−	0.120827i
$936$		0			0
$937$			4.17839i			0.136502i	0.997668	+	0.0682510i	$0.0217419\pi$
$937$			4.17839i			0.136502i	−0.997668	+	0.0682510i	$0.978258\pi$
$938$	−4.23331	−	4.92516i	−0.138222	−	0.160812i
$939$		0			0
$940$	1.43705	+	0.288723i	0.0468714	+	0.00941712i
$941$	9.55498	+	16.5497i	0.311483	+	0.539505i	0.978684	−	0.205373i	$-0.0658409\pi$
$941$	9.55498	+	16.5497i	0.311483	+	0.539505i	−0.667200	+	0.744878i	$0.732508\pi$
$942$		0			0
$943$	15.1569	−	26.2526i	0.493577	−	0.854901i
$944$	6.00652	+	7.89056i	0.195496	+	0.256816i
$945$		0			0
$946$	16.0638	−	22.3715i	0.522280	−	0.727362i
$947$	−1.20797	+	2.09227i	−0.0392539	+	0.0679897i	−0.884985	−	0.465620i	$-0.845831\pi$
$947$	−1.20797	+	2.09227i	−0.0392539	+	0.0679897i	0.845731	+	0.533610i	$0.179165\pi$
$948$		0			0
$949$	30.1280	−	17.3944i	0.977995	−	0.564646i
$950$	1.48295	−	0.670199i	0.0481134	−	0.0217441i
$951$		0			0
$952$	0.710815	−	59.8617i	0.0230377	−	1.94013i
$953$	−9.71810			−0.314800			−0.157400	−	0.987535i	$-0.550311\pi$
$953$	−9.71810			−0.314800			−0.157400	+	0.987535i	$0.550311\pi$
$954$		0			0
$955$	4.78741	−	2.76401i	0.154917	−	0.0894414i
$956$	−2.20397	−	1.94034i	−0.0712814	−	0.0627552i
$957$		0			0
$958$	16.8363	−	23.4473i	0.543955	−	0.757547i
$959$	6.41426	−	1.88297i	0.207127	−	0.0608041i
$960$		0			0
$961$	13.3625	−	23.1446i	0.431049	−	0.746598i
$962$	−4.78623	+	48.1206i	−0.154314	+	1.55147i
$963$		0			0
$964$	5.83865	−	29.0605i	0.188050	−	0.935975i
$965$	1.84328			0.0593372
$966$		0			0
$967$		−	46.0680i		−	1.48145i	−0.671809	−	0.740724i	$-0.734483\pi$
$967$		−	46.0680i		−	1.48145i	0.671809	−	0.740724i	$-0.265517\pi$
$968$	−3.88218	+	3.61507i	−0.124778	+	0.116193i
$969$		0			0
$970$	0.526136	−	5.28976i	0.0168932	−	0.169844i
$971$	−10.3074	−	5.95095i	−0.330779	−	0.190975i	0.325408	−	0.945574i	$-0.394498\pi$
$971$	−10.3074	−	5.95095i	−0.330779	−	0.190975i	−0.656187	+	0.754599i	$0.727832\pi$
$972$		0			0
$973$	43.2001	+	10.4831i	1.38493	+	0.336071i
$974$	9.71474	+	6.97564i	0.311280	+	0.223514i
$975$		0			0
$976$	−32.7822	−	13.7269i	−1.04933	−	0.439387i
$977$	16.1299	+	27.9379i	0.516042	+	0.893811i	0.999827	+	0.0186241i	$0.00592857\pi$
$977$	16.1299	+	27.9379i	0.516042	+	0.893811i	−0.483784	+	0.875187i	$0.660738\pi$
$978$		0			0
$979$		−	9.32524i		−	0.298036i
$980$	0.541389	−	3.56291i	0.0172940	−	0.113813i
$981$		0			0
$982$	21.8302	+	48.3040i	0.696631	+	1.54144i
$983$	−25.6985	−	44.5110i	−0.819653	−	1.41968i	−0.905938	−	0.423411i	$-0.860833\pi$
$983$	−25.6985	−	44.5110i	−0.819653	−	1.41968i	0.0862842	−	0.996271i	$-0.472501\pi$
$984$		0			0
$985$	2.07232	+	1.19646i	0.0660297	+	0.0381223i
$986$	−18.5297	+	25.8057i	−0.590106	+	0.821821i
$987$		0			0
$988$	2.02434	−	0.682827i	0.0644027	−	0.0217236i
$989$	31.2672	+	18.0521i	0.994240	+	0.574025i
$990$		0			0
$991$	−10.5357	+	6.08280i	−0.334678	+	0.193226i	−0.657916	−	0.753091i	$-0.728562\pi$
$991$	−10.5357	+	6.08280i	−0.334678	+	0.193226i	0.323238	+	0.946318i	$0.395229\pi$
$992$	10.2884	+	5.56308i	0.326657	+	0.176628i
$993$		0			0
$994$	6.22202	+	32.9924i	0.197351	+	1.04645i
$995$	5.34881			0.169569
$996$		0			0
$997$	−7.92001	−	13.7179i	−0.250829	−	0.434449i	0.712925	−	0.701240i	$-0.247370\pi$
$997$	−7.92001	−	13.7179i	−0.250829	−	0.434449i	−0.963754	+	0.266791i	$0.914037\pi$
$998$	17.5441	+	1.74499i	0.555349	+	0.0552368i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.c.19.6		32
3.2	odd	2		168.2.t.a.19.11	yes	32
4.3	odd	2		2016.2.bs.c.271.9		32
7.3	odd	6	inner	504.2.bk.c.451.15		32
8.3	odd	2	inner	504.2.bk.c.19.15		32
8.5	even	2		2016.2.bs.c.271.8		32
12.11	even	2		672.2.bb.a.271.12		32
21.2	odd	6		1176.2.p.a.979.22		32
21.5	even	6		1176.2.p.a.979.21		32
21.17	even	6		168.2.t.a.115.2	yes	32
24.5	odd	2		672.2.bb.a.271.13		32
24.11	even	2		168.2.t.a.19.2	✓	32
28.3	even	6		2016.2.bs.c.1711.8		32
56.3	even	6	inner	504.2.bk.c.451.6		32
56.45	odd	6		2016.2.bs.c.1711.9		32
84.23	even	6		4704.2.p.a.3919.28		32
84.47	odd	6		4704.2.p.a.3919.31		32
84.59	odd	6		672.2.bb.a.367.13		32
168.5	even	6		4704.2.p.a.3919.27		32
168.59	odd	6		168.2.t.a.115.11	yes	32
168.101	even	6		672.2.bb.a.367.12		32
168.107	even	6		1176.2.p.a.979.23		32
168.131	odd	6		1176.2.p.a.979.24		32
168.149	odd	6		4704.2.p.a.3919.32		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.2	✓	32	24.11	even	2
168.2.t.a.19.11	yes	32	3.2	odd	2
168.2.t.a.115.2	yes	32	21.17	even	6
168.2.t.a.115.11	yes	32	168.59	odd	6
504.2.bk.c.19.6		32	1.1	even	1	trivial
504.2.bk.c.19.15		32	8.3	odd	2	inner
504.2.bk.c.451.6		32	56.3	even	6	inner
504.2.bk.c.451.15		32	7.3	odd	6	inner
672.2.bb.a.271.12		32	12.11	even	2
672.2.bb.a.271.13		32	24.5	odd	2
672.2.bb.a.367.12		32	168.101	even	6
672.2.bb.a.367.13		32	84.59	odd	6
1176.2.p.a.979.21		32	21.5	even	6
1176.2.p.a.979.22		32	21.2	odd	6
1176.2.p.a.979.23		32	168.107	even	6
1176.2.p.a.979.24		32	168.131	odd	6
2016.2.bs.c.271.8		32	8.5	even	2
2016.2.bs.c.271.9		32	4.3	odd	2
2016.2.bs.c.1711.8		32	28.3	even	6
2016.2.bs.c.1711.9		32	56.45	odd	6
4704.2.p.a.3919.27		32	168.5	even	6
4704.2.p.a.3919.28		32	84.23	even	6
4704.2.p.a.3919.31		32	84.47	odd	6
4704.2.p.a.3919.32		32	168.149	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.582416 - 1.28872i) q^{2} +(-1.32158 + 1.50114i) q^{4} +(0.128707 - 0.222928i) q^{5} +(-0.623918 + 2.57113i) q^{7} +(2.70425 + 0.828860i) q^{8} +O(q^{10})\)	\(q+(-0.582416 - 1.28872i) q^{2} +(-1.32158 + 1.50114i) q^{4} +(0.128707 - 0.222928i) q^{5} +(-0.623918 + 2.57113i) q^{7} +(2.70425 + 0.828860i) q^{8} +(-0.362252 - 0.0360307i) q^{10} +(-1.79412 - 3.10751i) q^{11} -4.57992 q^{13} +(3.67684 - 0.693415i) q^{14} +(-0.506836 - 3.96776i) q^{16} +(-6.92813 + 3.99996i) q^{17} +(0.201988 + 0.116618i) q^{19} +(0.164548 + 0.487825i) q^{20} +(-2.95978 + 4.12198i) q^{22} +(-5.76102 - 3.32613i) q^{23} +(2.46687 + 4.27274i) q^{25} +(2.66742 + 5.90222i) q^{26} +(-3.03507 - 4.33455i) q^{28} +2.80806i q^{29} +(-1.03380 - 1.79060i) q^{31} +(-4.81813 + 2.96405i) q^{32} +(9.18987 + 6.59876i) q^{34} +(0.492874 + 0.470013i) q^{35} +(6.46587 + 3.73307i) q^{37} +(0.0326463 - 0.328225i) q^{38} +(0.532833 - 0.496173i) q^{40} +4.55693i q^{41} -5.42738 q^{43} +(7.03589 + 1.41361i) q^{44} +(-0.931125 + 9.36151i) q^{46} +(1.42355 - 2.46565i) q^{47} +(-6.22145 - 3.20835i) q^{49} +(4.06961 - 5.66761i) q^{50} +(6.05274 - 6.87509i) q^{52} +(1.93137 - 1.11508i) q^{53} -0.923668 q^{55} +(-3.81834 + 6.43586i) q^{56} +(3.61879 - 1.63546i) q^{58} +(-2.14701 + 1.23958i) q^{59} +(4.44251 - 7.69466i) q^{61} +(-1.70547 + 2.37515i) q^{62} +(6.62598 + 4.48289i) q^{64} +(-0.589469 + 1.02099i) q^{65} +(-0.867859 - 1.50318i) q^{67} +(3.15161 - 15.6864i) q^{68} +(0.318656 - 0.908918i) q^{70} +8.97302i q^{71} +(-6.57828 + 3.79797i) q^{73} +(1.04505 - 10.5069i) q^{74} +(-0.442003 + 0.149092i) q^{76} +(9.10921 - 2.67409i) q^{77} +(-7.51791 - 4.34047i) q^{79} +(-0.949757 - 0.397692i) q^{80} +(5.87259 - 2.65403i) q^{82} +3.79017i q^{83} +2.05930i q^{85} +(3.16099 + 6.99435i) q^{86} +(-2.27607 - 9.89058i) q^{88} +(2.25065 + 1.29941i) q^{89} +(2.85749 - 11.7756i) q^{91} +(12.6066 - 4.25234i) q^{92} +(-4.00663 - 0.398512i) q^{94} +(0.0519946 - 0.0300191i) q^{95} +14.6024i q^{97} +(-0.511188 + 9.88629i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more