LMFDB - Embedded newform 507.2.q.b.55.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			55.3
Character	$\chi$	$=$	507.55
Dual form			507.2.q.b.295.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21429 + 1.48724i) q^{2} +(-0.996757 - 0.0804666i) q^{3} +(-0.337321 - 1.65231i) q^{4} +(-0.0596193 - 0.491009i) q^{5} +(1.33003 - 1.38471i) q^{6} +(0.351566 - 0.222317i) q^{7} +(-0.533160 - 0.279824i) q^{8} +(0.987050 + 0.160411i) q^{9} +(0.802643 + 0.507561i) q^{10} +(-0.655329 + 0.106501i) q^{11} +(0.203272 + 1.67409i) q^{12} +(3.60021 - 0.196167i) q^{13} +(-0.0962657 + 0.792820i) q^{14} +(0.0199161 + 0.494214i) q^{15} +(4.16647 - 1.77517i) q^{16} +(1.53745 - 0.972226i) q^{17} +(-1.43714 + 1.27319i) q^{18} +(-3.32336 + 5.75624i) q^{19} +(-0.791188 + 0.264137i) q^{20} +(-0.368315 + 0.193306i) q^{21} +(0.637369 - 1.10396i) q^{22} +(1.79357 + 3.10655i) q^{23} +(0.508915 + 0.321818i) q^{24} +(4.61717 - 1.13803i) q^{25} +(-4.07996 + 5.59258i) q^{26} +(-0.970942 - 0.239316i) q^{27} +(-0.485926 - 0.505903i) q^{28} +(-3.20355 + 3.92364i) q^{29} +(-0.759199 - 0.570501i) q^{30} +(9.76630 + 2.40718i) q^{31} +(-2.08417 + 7.19539i) q^{32} +(0.661774 - 0.0534239i) q^{33} +(-0.420986 + 3.46713i) q^{34} +(-0.130119 - 0.159367i) q^{35} +(-0.0679041 - 1.68502i) q^{36} +(-1.40651 - 4.85582i) q^{37} +(-4.52536 - 11.9324i) q^{38} +(-3.60432 - 0.0941653i) q^{39} +(-0.105609 + 0.278469i) q^{40} +(-11.9008 - 0.960731i) q^{41} +(0.159749 - 0.782503i) q^{42} +(-2.78040 + 9.59906i) q^{43} +(0.397030 + 1.04688i) q^{44} +(0.0199161 - 0.494214i) q^{45} +(-6.79810 - 1.10480i) q^{46} +(7.97158 + 7.06221i) q^{47} +(-4.29580 + 1.43415i) q^{48} +(-2.92667 + 6.16784i) q^{49} +(-3.91408 + 8.24875i) q^{50} +(-1.61070 + 0.845360i) q^{51} +(-1.53856 - 5.88249i) q^{52} +(7.81874 + 4.10359i) q^{53} +(1.53493 - 1.15342i) q^{54} +(0.0913634 + 0.315423i) q^{55} +(-0.249650 + 0.0201538i) q^{56} +(3.77577 - 5.47015i) q^{57} +(-1.94534 - 9.52890i) q^{58} +(-5.70977 - 2.43271i) q^{59} +(0.809876 - 0.199617i) q^{60} +(0.350414 - 8.69542i) q^{61} +(-15.4392 + 11.6018i) q^{62} +(0.382675 - 0.163043i) q^{63} +(-3.02509 - 4.38260i) q^{64} +(-0.310962 - 1.75604i) q^{65} +(-0.724134 + 1.04909i) q^{66} +(0.0907319 - 0.444434i) q^{67} +(-2.12503 - 2.21240i) q^{68} +(-1.53778 - 3.24080i) q^{69} +0.395021 q^{70} +(-0.299260 - 0.630677i) q^{71} +(-0.481369 - 0.361725i) q^{72} +(1.99522 - 5.26095i) q^{73} +(8.92968 + 3.80458i) q^{74} +(-4.69378 + 0.762813i) q^{75} +(10.6321 + 3.54952i) q^{76} +(-0.206714 + 0.183133i) q^{77} +(4.51675 - 5.24614i) q^{78} +(4.53713 + 4.01954i) q^{79} +(-1.12002 - 1.93994i) q^{80} +(0.948536 + 0.316668i) q^{81} +(15.8799 - 16.5327i) q^{82} +(4.76899 + 6.90907i) q^{83} +(0.443642 + 0.543363i) q^{84} +(-0.569034 - 0.696940i) q^{85} +(-10.8999 - 15.7912i) q^{86} +(3.50889 - 3.65314i) q^{87} +(0.379197 + 0.126595i) q^{88} +(2.35043 + 4.07107i) q^{89} +(0.710831 + 0.629741i) q^{90} +(1.22210 - 0.869352i) q^{91} +(4.52797 - 4.01143i) q^{92} +(-9.54093 - 3.18523i) q^{93} +(-20.1830 + 3.28006i) q^{94} +(3.02450 + 1.28862i) q^{95} +(2.65640 - 7.00435i) q^{96} +(10.4127 + 7.82461i) q^{97} +(-5.61921 - 11.8422i) q^{98} -0.663927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{28}{39}\right)$

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 $

$2$	−1.21429	+	1.48724i	−0.858635	+	1.05164i	0.139477	+	0.990225i	$0.455458\pi$
$2$	−1.21429	+	1.48724i	−0.858635	+	1.05164i	−0.998113	+	0.0614119i	$0.980440\pi$
$3$	−0.996757	−	0.0804666i	−0.575478	−	0.0464574i
$3$	−0.996757	−	0.0804666i	−0.575478	−	0.0464574i
$4$	−0.337321	−	1.65231i	−0.168661	−	0.826155i
$5$	−0.0596193	−	0.491009i	−0.0266626	−	0.219586i	0.973287	−	0.229590i	$-0.0737386\pi$
$5$	−0.0596193	−	0.491009i	−0.0266626	−	0.219586i	−0.999950	+	0.0100043i	$0.996815\pi$
$6$	1.33003	−	1.38471i	0.542982	−	0.565304i
$7$	0.351566	−	0.222317i	0.132879	−	0.0840278i	−0.466372	−	0.884589i	$-0.654439\pi$
$7$	0.351566	−	0.222317i	0.132879	−	0.0840278i	0.599252	+	0.800561i	$0.295465\pi$
$8$	−0.533160	−	0.279824i	−0.188501	−	0.0989327i
$9$	0.987050	+	0.160411i	0.329017	+	0.0534704i
$10$	0.802643	+	0.507561i	0.253818	+	0.160505i
$11$	−0.655329	+	0.106501i	−0.197589	+	0.0321114i	−0.258400	−	0.966038i	$-0.583195\pi$
$11$	−0.655329	+	0.106501i	−0.197589	+	0.0321114i	0.0608112	+	0.998149i	$0.480631\pi$
$12$	0.203272	+	1.67409i	0.0586795	+	0.483269i
$13$	3.60021	−	0.196167i	0.998519	−	0.0544071i
$13$	3.60021	−	0.196167i	0.998519	−	0.0544071i
$14$	−0.0962657	+	0.792820i	−0.0257281	+	0.211890i
$15$	0.0199161	+	0.494214i	0.00514233	+	0.127606i
$16$	4.16647	−	1.77517i	1.04162	−	0.443791i
$17$	1.53745	−	0.972226i	0.372887	−	0.235800i	−0.334856	−	0.942269i	$-0.608688\pi$
$17$	1.53745	−	0.972226i	0.372887	−	0.235800i	0.707743	+	0.706470i	$0.249713\pi$
$18$	−1.43714	+	1.27319i	−0.338737	+	0.300095i
$19$	−3.32336	+	5.75624i	−0.762432	+	1.32057i	0.179161	+	0.983820i	$0.442662\pi$
$19$	−3.32336	+	5.75624i	−0.762432	+	1.32057i	−0.941594	+	0.336751i	$0.890672\pi$
$20$	−0.791188	+	0.264137i	−0.176915	+	0.0590629i
$21$	−0.368315	+	0.193306i	−0.0803728	+	0.0421829i
$22$	0.637369	−	1.10396i	0.135887	−	0.235364i
$23$	1.79357	+	3.10655i	0.373985	+	0.647761i	0.990175	−	0.139837i	$-0.0446579\pi$
$23$	1.79357	+	3.10655i	0.373985	+	0.647761i	−0.616190	+	0.787598i	$0.711325\pi$
$24$	0.508915	+	0.321818i	0.103882	+	0.0656909i
$25$	4.61717	−	1.13803i	0.923435	−	0.227606i
$26$	−4.07996	+	5.59258i	−0.800147	+	1.09680i
$27$	−0.970942	−	0.239316i	−0.186858	−	0.0460563i
$28$	−0.485926	−	0.505903i	−0.0918314	−	0.0956066i
$29$	−3.20355	+	3.92364i	−0.594885	+	0.728602i	−0.981034	−	0.193834i	$-0.937908\pi$
$29$	−3.20355	+	3.92364i	−0.594885	+	0.728602i	0.386149	+	0.922436i	$0.373805\pi$
$30$	−0.759199	−	0.570501i	−0.138610	−	0.104159i
$31$	9.76630	+	2.40718i	1.75408	+	0.432342i	0.979715	−	0.200398i	$-0.0642236\pi$
$31$	9.76630	+	2.40718i	1.75408	+	0.432342i	0.774364	+	0.632740i	$0.218070\pi$
$32$	−2.08417	+	7.19539i	−0.368433	+	1.27198i
$33$	0.661774	−	0.0534239i	0.115200	−	0.00929991i
$34$	−0.420986	+	3.46713i	−0.0721985	+	0.594608i
$35$	−0.130119	−	0.159367i	−0.0219942	−	0.0269380i
$36$	−0.0679041	−	1.68502i	−0.0113173	−	0.280837i
$37$	−1.40651	−	4.85582i	−0.231228	−	0.798292i	−0.989272	−	0.146088i	$-0.953332\pi$
$37$	−1.40651	−	4.85582i	−0.231228	−	0.798292i	0.758044	−	0.652204i	$-0.226155\pi$
$38$	−4.52536	−	11.9324i	−0.734111	−	1.93569i
$39$	−3.60432	−	0.0941653i	−0.577153	−	0.0150785i
$40$	−0.105609	+	0.278469i	−0.0166983	+	0.0440299i
$41$	−11.9008	−	0.960731i	−1.85859	−	0.150041i	−0.900196	−	0.435485i	$-0.856577\pi$
$41$	−11.9008	−	0.960731i	−1.85859	−	0.150041i	−0.958395	+	0.285444i	$0.907859\pi$
$42$	0.159749	−	0.782503i	0.0246498	−	0.120743i
$43$	−2.78040	+	9.59906i	−0.424007	+	1.46384i	0.409998	+	0.912086i	$0.365529\pi$
$43$	−2.78040	+	9.59906i	−0.424007	+	1.46384i	−0.834005	+	0.551756i	$0.813958\pi$
$44$	0.397030	+	1.04688i	0.0598545	+	0.157823i
$45$	0.0199161	−	0.494214i	0.00296892	−	0.0736731i
$46$	−6.79810	−	1.10480i	−1.00233	−	0.162894i
$47$	7.97158	+	7.06221i	1.16277	+	1.03013i	0.999048	+	0.0436230i	$0.0138900\pi$
$47$	7.97158	+	7.06221i	1.16277	+	1.03013i	0.163727	+	0.986506i	$0.447648\pi$
$48$	−4.29580	+	1.43415i	−0.620045	+	0.207001i
$49$	−2.92667	+	6.16784i	−0.418096	+	0.881119i
$50$	−3.91408	+	8.24875i	−0.553534	+	1.16655i
$51$	−1.61070	+	0.845360i	−0.225543	+	0.118374i
$52$	−1.53856	−	5.88249i	−0.213359	−	0.815755i
$53$	7.81874	+	4.10359i	1.07399	+	0.563672i	0.906502	−	0.422203i	$-0.138743\pi$
$53$	7.81874	+	4.10359i	1.07399	+	0.563672i	0.167486	+	0.985875i	$0.446435\pi$
$54$	1.53493	−	1.15342i	0.208877	−	0.156961i
$55$	0.0913634	+	0.315423i	0.0123194	+	0.0425316i
$56$	−0.249650	+	0.0201538i	−0.0333609	+	0.00269317i
$57$	3.77577	−	5.47015i	0.500113	−	0.724539i
$58$	−1.94534	−	9.52890i	−0.255436	−	1.25121i
$59$	−5.70977	−	2.43271i	−0.743349	−	0.316712i	−0.0131203	−	0.999914i	$-0.504176\pi$
$59$	−5.70977	−	2.43271i	−0.743349	−	0.316712i	−0.730229	+	0.683202i	$0.760587\pi$
$60$	0.809876	−	0.199617i	0.104555	−	0.0257704i
$61$	0.350414	−	8.69542i	0.0448659	−	1.11334i	−0.807326	−	0.590106i	$-0.799086\pi$
$61$	0.350414	−	8.69542i	0.0448659	−	1.11334i	0.852192	−	0.523229i	$-0.175273\pi$
$62$	−15.4392	+	11.6018i	−1.96078	+	1.47343i
$63$	0.382675	−	0.163043i	0.0482125	−	0.0205414i
$64$	−3.02509	−	4.38260i	−0.378137	−	0.547825i
$65$	−0.310962	−	1.75604i	−0.0385701	−	0.217810i
$66$	−0.724134	+	1.04909i	−0.0891347	+	0.129134i
$67$	0.0907319	−	0.444434i	0.0110847	−	0.0542963i	−0.973872	−	0.227097i	$-0.927077\pi$
$67$	0.0907319	−	0.444434i	0.0110847	−	0.0542963i	0.984957	+	0.172801i	$0.0552817\pi$
$68$	−2.12503	−	2.21240i	−0.257698	−	0.268292i
$69$	−1.53778	−	3.24080i	−0.185127	−	0.390146i
$70$	0.395021			0.0472140
$71$	−0.299260	−	0.630677i	−0.0355156	−	0.0748476i	0.884917	−	0.465748i	$-0.154215\pi$
$71$	−0.299260	−	0.630677i	−0.0355156	−	0.0748476i	−0.920433	+	0.390901i	$0.872164\pi$
$72$	−0.481369	−	0.361725i	−0.0567299	−	0.0426297i
$73$	1.99522	−	5.26095i	0.233522	−	0.615748i	−0.766114	−	0.642704i	$-0.777812\pi$
$73$	1.99522	−	5.26095i	0.233522	−	0.615748i	0.999637	+	0.0269567i	$0.00858163\pi$
$74$	8.92968	+	3.80458i	1.03805	+	0.442273i
$75$	−4.69378	+	0.762813i	−0.541990	+	0.0880820i
$76$	10.6321	+	3.54952i	1.21959	+	0.407158i
$77$	−0.206714	+	0.183133i	−0.0235573	+	0.0208699i
$78$	4.51675	−	5.24614i	0.511421	−	0.594009i
$79$	4.53713	+	4.01954i	0.510467	+	0.452234i	0.878613	−	0.477534i	$-0.158469\pi$
$79$	4.53713	+	4.01954i	0.510467	+	0.452234i	−0.368147	+	0.929768i	$0.620008\pi$
$80$	−1.12002	−	1.93994i	−0.125222	−	0.216892i
$81$	0.948536	+	0.316668i	0.105393	+	0.0351853i
$82$	15.8799	−	16.5327i	1.75364	−	1.82573i
$83$	4.76899	+	6.90907i	0.523465	+	0.758369i	0.992158	−	0.124992i	$-0.0398904\pi$
$83$	4.76899	+	6.90907i	0.523465	+	0.758369i	−0.468693	+	0.883361i	$0.655275\pi$
$84$	0.443642	+	0.543363i	0.0484053	+	0.0592858i
$85$	−0.569034	−	0.696940i	−0.0617204	−	0.0755937i
$86$	−10.8999	−	15.7912i	−1.17536	−	1.70281i
$87$	3.50889	−	3.65314i	0.376192	−	0.391658i
$88$	0.379197	+	0.126595i	0.0404225	+	0.0134950i
$89$	2.35043	+	4.07107i	0.249145	+	0.431533i	0.963289	−	0.268467i	$-0.0865169\pi$
$89$	2.35043	+	4.07107i	0.249145	+	0.431533i	−0.714143	+	0.699999i	$0.753184\pi$
$90$	0.710831	+	0.629741i	0.0749281	+	0.0663805i
$91$	1.22210	−	0.869352i	0.128111	−	0.0911329i
$92$	4.52797	−	4.01143i	0.472074	−	0.418221i
$93$	−9.54093	−	3.18523i	−0.989349	−	0.330293i
$94$	−20.1830	+	3.28006i	−2.08172	+	0.338313i
$95$	3.02450	+	1.28862i	0.310307	+	0.132210i
$96$	2.65640	−	7.00435i	0.271118	−	0.714879i
$97$	10.4127	+	7.82461i	1.05725	+	0.794469i	0.979285	−	0.202487i	$-0.0649025\pi$
$97$	10.4127	+	7.82461i	1.05725	+	0.794469i	0.0779614	+	0.996956i	$0.475159\pi$
$98$	−5.61921	−	11.8422i	−0.567626	−	1.19625i
$99$	−0.663927			−0.0667272
$100$	−3.43785	−	7.24512i	−0.343785	−	0.724512i
$101$	13.3002	+	13.8469i	1.32341	+	1.37782i	0.875098	+	0.483946i	$0.160797\pi$
$101$	13.3002	+	13.8469i	1.32341	+	1.37782i	0.448317	+	0.893875i	$0.352024\pi$
$102$	0.698609	−	3.42201i	0.0691726	−	0.338830i
$103$	4.78244	−	6.92856i	0.471228	−	0.682691i	−0.513243	−	0.858244i	$-0.671556\pi$
$103$	4.78244	−	6.92856i	0.471228	−	0.682691i	0.984470	+	0.175553i	$0.0561712\pi$
$104$	−1.97438	−	0.902837i	−0.193604	−	0.0885304i
$105$	0.116874	+	0.169321i	0.0114057	+	0.0165240i
$106$	−15.5973	+	6.64538i	−1.51494	+	0.645456i
$107$	13.9280	−	10.4662i	1.34647	−	1.01181i	0.349271	−	0.937022i	$-0.386429\pi$
$107$	13.9280	−	10.4662i	1.34647	−	1.01181i	0.997200	−	0.0747848i	$-0.0238270\pi$
$108$	−0.0679041	+	1.68502i	−0.00653407	+	0.162141i
$109$	−6.89701	+	1.69996i	−0.660614	+	0.162827i	−0.555349	−	0.831618i	$-0.687415\pi$
$109$	−6.89701	+	1.69996i	−0.660614	+	0.162827i	−0.105265	+	0.994444i	$0.533569\pi$
$110$	−0.580051	−	0.247137i	−0.0553057	−	0.0235636i
$111$	1.01121	+	4.95325i	0.0959801	+	0.470142i
$112$	1.07014	−	1.55036i	0.101118	−	0.146495i
$113$	13.9210	−	1.12382i	1.30958	−	0.105720i	0.594121	−	0.804376i	$-0.297500\pi$
$113$	13.9210	−	1.12382i	1.30958	−	0.105720i	0.715458	+	0.698656i	$0.246218\pi$
$114$	3.55053	+	12.2578i	0.332537	+	1.14805i
$115$	1.41841	−	1.06587i	0.132268	−	0.0993927i
$116$	7.56370	+	3.96973i	0.702272	+	0.368581i
$117$	3.58506	+	0.383887i	0.331439	+	0.0354904i
$118$	10.5514	−	5.53778i	0.971332	−	0.509794i
$119$	0.324373	−	0.683603i	0.0297353	−	0.0626657i
$120$	0.127674	−	0.269068i	0.0116550	−	0.0245625i
$121$	−10.0158	+	3.34376i	−0.910526	+	0.303978i
$122$	12.5067	+	11.0799i	1.13230	+	1.00313i
$123$	11.7849	+	1.91523i	1.06261	+	0.172691i
$124$	0.683019	−	16.9489i	0.0613369	−	1.52206i
$125$	−1.71102	−	4.51159i	−0.153038	−	0.403529i
$126$	−0.222196	+	0.767111i	−0.0197948	+	0.0683397i
$127$	1.24788	−	6.11252i	0.110731	−	0.542398i	−0.886144	−	0.463410i	$-0.846626\pi$
$127$	1.24788	−	6.11252i	0.110731	−	0.542398i	0.996876	−	0.0789885i	$-0.0251691\pi$
$128$	−4.74240	−	0.382846i	−0.419173	−	0.0338391i
$129$	3.54379	−	9.34420i	0.312013	−	0.822711i
$130$	2.98925	+	1.66987i	0.262175	+	0.146458i
$131$	−3.54498	−	9.34734i	−0.309726	−	0.816681i	−0.996001	−	0.0893387i	$-0.971525\pi$
$131$	−3.54498	−	9.34734i	−0.309726	−	0.816681i	0.686275	−	0.727342i	$-0.259245\pi$
$132$	−0.311503	−	1.07543i	−0.0271129	−	0.0936045i
$133$	0.111326	+	2.76253i	0.00965321	+	0.239542i
$134$	0.550805	+	0.674614i	0.0475823	+	0.0582778i
$135$	−0.0596193	+	0.491009i	−0.00513121	+	0.0422593i
$136$	−1.09176	+	0.0881361i	−0.0936177	+	0.00755760i
$137$	3.72955	−	12.8759i	0.318637	−	1.10006i	−0.628120	−	0.778116i	$-0.716175\pi$
$137$	3.72955	−	12.8759i	0.318637	−	1.10006i	0.946758	−	0.321947i	$-0.104337\pi$
$138$	6.68716	+	1.64824i	0.569249	+	0.140307i
$139$	5.97012	+	4.48625i	0.506379	+	0.380519i	0.823007	−	0.568031i	$-0.192294\pi$
$139$	5.97012	+	4.48625i	0.506379	+	0.380519i	−0.316629	+	0.948550i	$0.602551\pi$
$140$	−0.219432	+	0.268756i	−0.0185454	+	0.0227140i
$141$	−7.37746	−	7.68075i	−0.621294	−	0.646836i
$142$	1.30136	+	0.320756i	0.109207	+	0.0269172i
$143$	−2.33843	+	0.511982i	−0.195549	+	0.0428140i
$144$	4.39727	−	1.08383i	0.366439	−	0.0903191i
$145$	2.11754	+	1.33905i	0.175852	+	0.111202i
$146$	5.40152	+	9.35570i	0.447033	+	0.774283i
$147$	3.41349	−	5.91234i	0.281540	−	0.487641i
$148$	−7.54887	+	3.96195i	−0.620513	+	0.325671i
$149$	−3.43766	+	1.14766i	−0.281624	+	0.0940199i	−0.453971	−	0.891016i	$-0.649993\pi$
$149$	−3.43766	+	1.14766i	−0.281624	+	0.0940199i	0.172347	+	0.985036i	$0.444865\pi$
$150$	4.56514	−	7.90705i	0.372742	−	0.645608i
$151$	−3.88156	+	3.43876i	−0.315877	+	0.279842i	−0.806131	−	0.591737i	$-0.798442\pi$
$151$	−3.88156	+	3.43876i	−0.315877	+	0.279842i	0.490254	+	0.871579i	$0.336904\pi$
$152$	3.38262	−	2.13904i	0.274367	−	0.173499i
$153$	1.67350	−	0.713012i	0.135294	−	0.0576436i
$154$	−0.0213506	−	0.529810i	−0.00172048	−	0.0426933i
$155$	0.599685	−	4.93885i	0.0481679	−	0.396698i
$156$	1.06022	+	5.98722i	0.0848859	+	0.479361i
$157$	1.64318	+	13.5328i	0.131140	+	1.08003i	0.898548	+	0.438875i	$0.144623\pi$
$157$	1.64318	+	13.5328i	0.131140	+	1.08003i	−0.767409	+	0.641158i	$0.778454\pi$
$158$	−11.4874	+	1.86689i	−0.913891	+	0.148522i
$159$	−7.46319	−	4.71943i	−0.591869	−	0.374276i
$160$	3.65726	+	0.594362i	0.289132	+	0.0469885i
$161$	1.32119	+	0.693416i	0.104125	+	0.0546489i
$162$	−1.62276	+	1.02617i	−0.127496	+	0.0806238i
$163$	−10.4847	+	10.9157i	−0.821225	+	0.854985i	−0.991459	−	0.130418i	$-0.958368\pi$
$163$	−10.4847	+	10.9157i	−0.821225	+	0.854985i	0.170234	+	0.985404i	$0.445547\pi$
$164$	2.42697	+	19.9879i	0.189514	+	1.56079i
$165$	−0.0656861	−	0.321752i	−0.00511366	−	0.0250483i
$166$	−16.0664	−	1.29701i	−1.24699	−	0.100668i
$167$	−3.58604	+	4.39210i	−0.277496	+	0.339871i	−0.894483	−	0.447103i	$-0.852456\pi$
$167$	−3.58604	+	4.39210i	−0.277496	+	0.339871i	0.616987	+	0.786974i	$0.288353\pi$
$168$	0.250462			0.0193236
$169$	12.9230	−	1.41249i	0.994080	−	0.108653i
$170$	1.72749			0.132492
$171$	−4.20369	+	5.14859i	−0.321464	+	0.393722i
$172$	16.7985	+	1.35612i	1.28087	+	0.103403i
$173$	−5.11164	−	25.0385i	−0.388631	−	1.90364i	−0.426754	−	0.904368i	$-0.640343\pi$
$173$	−5.11164	−	25.0385i	−0.388631	−	1.90364i	0.0381224	−	0.999273i	$-0.487862\pi$
$174$	1.17227	+	9.65454i	0.0888698	+	0.731909i
$175$	1.37024	−	1.42657i	0.103580	−	0.107838i
$176$	−2.54135	+	1.60705i	−0.191561	+	0.121136i
$177$	5.49551	+	2.88427i	0.413068	+	0.216795i
$178$	−8.90877	−	1.44782i	−0.667741	−	0.108518i
$179$	−6.26436	−	3.96134i	−0.468220	−	0.296084i	0.279444	−	0.960162i	$-0.409850\pi$
$179$	−6.26436	−	3.96134i	−0.468220	−	0.296084i	−0.747664	+	0.664078i	$0.768824\pi$
$180$	−0.823313	+	0.133801i	−0.0613661	+	0.00997296i
$181$	−2.76209	−	22.7478i	−0.205304	−	1.69083i	−0.622981	−	0.782237i	$-0.714079\pi$
$181$	−2.76209	−	22.7478i	−0.205304	−	1.69083i	0.417677	−	0.908596i	$-0.362844\pi$
$182$	−0.191052	+	2.87320i	−0.0141617	+	0.212976i
$183$	−1.04897	+	8.63903i	−0.0775420	+	0.638616i
$184$	−0.0869714	−	2.15817i	−0.00641161	−	0.159103i
$185$	−2.30040	+	0.980107i	−0.169128	+	0.0720589i
$186$	16.3227	−	10.3218i	1.19684	−	0.756834i
$187$	−0.903994	+	0.800869i	−0.0661066	+	0.0585654i
$188$	8.97996	−	15.5538i	0.654931	−	1.13437i
$189$	−0.394554	+	0.131721i	−0.0286995	+	0.00958132i
$190$	−5.58912	+	2.93339i	−0.405477	+	0.212811i
$191$	2.76415	−	4.78764i	0.200007	−	0.346422i	−0.748524	−	0.663108i	$-0.769237\pi$
$191$	2.76415	−	4.78764i	0.200007	−	0.346422i	0.948530	+	0.316686i	$0.102570\pi$
$192$	2.66263	+	4.61181i	0.192159	+	0.332829i
$193$	−16.6004	−	10.4974i	−1.19492	−	0.755622i	−0.219422	−	0.975630i	$-0.570417\pi$
$193$	−16.6004	−	10.4974i	−1.19492	−	0.755622i	−0.975498	+	0.220008i	$0.929391\pi$
$194$	−24.2811	+	5.98476i	−1.74328	+	0.429680i
$195$	0.168651	+	1.77537i	0.0120774	+	0.127137i
$196$	11.1784	+	2.75523i	0.798457	+	0.196802i
$197$	4.58084	+	4.76916i	0.326372	+	0.339789i	0.864092	−	0.503335i	$-0.167894\pi$
$197$	4.58084	+	4.76916i	0.326372	+	0.339789i	−0.537720	+	0.843123i	$0.680714\pi$
$198$	0.806202	−	0.987418i	0.0572943	−	0.0701728i
$199$	6.07252	+	4.56320i	0.430470	+	0.323477i	0.793795	−	0.608185i	$-0.208102\pi$
$199$	6.07252	+	4.56320i	0.430470	+	0.323477i	−0.363325	+	0.931662i	$0.618359\pi$
$200$	−2.78014	−	0.685243i	−0.196586	−	0.0484540i
$201$	−0.126200	+	0.435692i	−0.00890145	+	0.0307314i
$202$	−36.7440	+	2.96628i	−2.58530	+	0.208707i
$203$	−0.253969	+	2.09162i	−0.0178251	+	0.146803i
$204$	1.94012	+	2.37622i	0.135836	+	0.166368i
$205$	0.237789	+	5.90067i	0.0166079	+	0.412121i
$206$	4.49714	+	15.5259i	0.313331	+	1.08174i
$207$	1.27202	+	3.35403i	0.0884112	+	0.233121i
$208$	14.6519	−	7.20829i	1.01593	−	0.499805i
$209$	1.56485	−	4.12617i	0.108243	−	0.285413i
$210$	−0.393740	−	0.0317860i	−0.0271706	−	0.00219344i
$211$	−1.00324	+	4.91421i	−0.0690661	+	0.338308i	−0.999612	−	0.0278681i	$-0.991128\pi$
$211$	−1.00324	+	4.91421i	−0.0690661	+	0.338308i	0.930545	+	0.366176i	$0.119333\pi$
$212$	4.14298	−	14.3032i	0.284541	−	0.982349i
$213$	0.247541	+	0.652712i	0.0169612	+	0.0447231i
$214$	−1.34691	+	33.4233i	−0.0920731	+	2.28477i
$215$	4.87899	+	0.792913i	0.332744	+	0.0540762i
$216$	0.450701	+	0.399286i	0.0306663	+	0.0271680i
$217$	3.96865	−	1.32493i	0.269409	−	0.0899421i
$218$	5.84674	−	12.3218i	0.395992	−	0.834534i
$219$	−2.41208	+	5.08334i	−0.162993	+	0.343500i
$220$	0.490357	−	0.257359i	0.0330599	−	0.0173512i
$221$	5.34444	−	3.80182i	0.359506	−	0.255738i
$222$	−8.59458	−	4.51078i	−0.576830	−	0.302744i
$223$	−18.0174	+	13.5392i	−1.20653	+	0.906652i	−0.997459	−	0.0712473i	$-0.977302\pi$
$223$	−18.0174	+	13.5392i	−1.20653	+	0.906652i	−0.209076	+	0.977899i	$0.567046\pi$
$224$	0.866932	+	2.99300i	0.0579243	+	0.199978i
$225$	4.73994	−	0.382647i	0.315996	−	0.0255098i
$226$	−15.2328	+	22.0685i	−1.01327	+	1.46798i
$227$	1.93863	+	9.49606i	0.128672	+	0.630276i	0.992063	+	0.125741i	$0.0401308\pi$
$227$	1.93863	+	9.49606i	0.128672	+	0.630276i	−0.863391	+	0.504535i	$0.831664\pi$
$228$	−10.3120	−	4.39354i	−0.682931	−	0.290970i
$229$	−14.8137	+	3.65124i	−0.978916	+	0.241281i	−0.696141	−	0.717905i	$-0.745101\pi$
$229$	−14.8137	+	3.65124i	−0.978916	+	0.241281i	−0.282775	+	0.959186i	$0.591255\pi$
$230$	−0.137168	+	3.40380i	−0.00904461	+	0.224440i
$231$	0.220780	−	0.165905i	0.0145262	−	0.0109158i
$232$	2.80594	−	1.19550i	0.184219	−	0.0784883i
$233$	−11.1883	−	16.2090i	−0.732970	−	1.06189i	−0.995293	−	0.0969101i	$-0.969104\pi$
$233$	−11.1883	−	16.2090i	−0.732970	−	1.06189i	0.262323	−	0.964980i	$-0.415511\pi$
$234$	−4.92424	+	4.86569i	−0.321908	+	0.318080i
$235$	2.99235	−	4.33516i	0.195199	−	0.282795i
$236$	−2.09356	+	10.2549i	−0.136279	+	0.667538i
$237$	−4.19898	−	4.37160i	−0.272753	−	0.283966i
$238$	0.622796	+	1.31252i	0.0403699	+	0.0850777i
$239$	−12.3006			−0.795661			−0.397830	−	0.917459i	$-0.630237\pi$
$239$	−12.3006			−0.795661			−0.397830	+	0.917459i	$0.630237\pi$
$240$	0.960292	+	2.02377i	0.0619866	+	0.130634i
$241$	−16.0551	−	12.0646i	−1.03420	−	0.777149i	−0.0589490	−	0.998261i	$-0.518775\pi$
$241$	−16.0551	−	12.0646i	−1.03420	−	0.777149i	−0.975248	+	0.221112i	$0.929031\pi$
$242$	7.18913	−	18.9562i	0.462135	−	1.21855i
$243$	−0.919979	−	0.391967i	−0.0590167	−	0.0251447i
$244$	−14.4857	+	2.35416i	−0.927354	+	0.150710i
$245$	3.20295	+	1.06930i	0.204629	+	0.0683152i
$246$	−17.1587	+	15.2013i	−1.09400	+	0.969200i
$247$	−10.8356	+	21.3756i	−0.689454	+	1.36010i
$248$	−4.53341	−	4.01625i	−0.287872	−	0.255032i
$249$	−4.19758	−	7.27041i	−0.266011	−	0.460744i
$250$	8.78750	+	2.93370i	0.555770	+	0.185543i
$251$	−15.5808	+	16.2213i	−0.983451	+	1.02388i	0.0162603	+	0.999868i	$0.494824\pi$
$251$	−15.5808	+	16.2213i	−0.983451	+	1.02388i	−0.999712	+	0.0240135i	$0.992356\pi$
$252$	−0.398481	−	0.577300i	−0.0251019	−	0.0363665i
$253$	−1.50623	−	1.84480i	−0.0946958	−	0.115981i
$254$	7.57549	+	9.27829i	0.475328	+	0.582171i
$255$	0.511108	+	0.740468i	0.0320068	+	0.0463699i
$256$	13.7059	−	14.2694i	0.856620	−	0.891836i
$257$	−0.574721	−	0.191870i	−0.0358501	−	0.0119685i	0.298686	−	0.954351i	$-0.403452\pi$
$257$	−0.574721	−	0.191870i	−0.0358501	−	0.0119685i	−0.334536	+	0.942383i	$0.608580\pi$
$258$	9.59387	+	16.6171i	0.597288	+	1.03453i
$259$	−1.57401	−	1.39445i	−0.0978041	−	0.0866469i
$260$	−2.79663	+	1.10616i	−0.173439	+	0.0686008i
$261$	−3.79147	+	3.35895i	−0.234686	+	0.207913i
$262$	18.2064	+	6.07818i	1.12479	+	0.375511i
$263$	13.1323	−	2.13420i	0.809770	−	0.131600i	0.258591	−	0.965987i	$-0.416742\pi$
$263$	13.1323	−	2.13420i	0.809770	−	0.131600i	0.551180	+	0.834387i	$0.314178\pi$
$264$	−0.367781	−	0.156697i	−0.0226353	−	0.00964402i
$265$	1.54875	−	4.08373i	0.0951392	−	0.250861i
$266$	−4.24373	−	3.18896i	−0.260200	−	0.195528i
$267$	−2.01523	−	4.24700i	−0.123330	−	0.259912i
$268$	−0.764949			−0.0467267
$269$	9.00991	+	18.9880i	0.549344	+	1.15772i	0.968318	+	0.249720i	$0.0803385\pi$
$269$	9.00991	+	18.9880i	0.549344	+	1.15772i	−0.418974	+	0.907998i	$0.637610\pi$
$270$	−0.657853	−	0.684897i	−0.0400356	−	0.0416815i
$271$	2.40547	−	11.7828i	0.146122	−	0.715753i	−0.839032	−	0.544081i	$-0.816878\pi$
$271$	2.40547	−	11.7828i	0.146122	−	0.715753i	0.985154	−	0.171671i	$-0.0549166\pi$
$272$	4.67988	−	6.77998i	0.283760	−	0.411097i
$273$	−1.28809	+	0.768195i	−0.0779587	+	0.0464933i
$274$	14.6208	+	21.1819i	0.883275	+	1.27964i
$275$	−2.90457	+	1.23752i	−0.175152	+	0.0746253i
$276$	−4.83608	+	3.63408i	−0.291098	+	0.218746i
$277$	0.593061	−	14.7167i	0.0356336	−	0.884238i	−0.878235	−	0.478229i	$-0.841279\pi$
$277$	0.593061	−	14.7167i	0.0356336	−	0.884238i	0.913869	−	0.406009i	$-0.133080\pi$
$278$	−13.9216	+	3.43137i	−0.834963	+	0.205800i
$279$	9.25369	+	3.94263i	0.554004	+	0.236039i
$280$	0.0247797	+	0.121379i	0.00148087	+	0.00725378i
$281$	9.11527	−	13.2058i	0.543772	−	0.787789i	−0.450713	−	0.892669i	$-0.648830\pi$
$281$	9.11527	−	13.2058i	0.543772	−	0.787789i	0.994485	+	0.104880i	$0.0334457\pi$
$282$	20.3815	−	1.64537i	1.21370	−	0.0979802i
$283$	2.73534	+	9.44348i	0.162599	+	0.561357i	0.999893	+	0.0146044i	$0.00464888\pi$
$283$	2.73534	+	9.44348i	0.162599	+	0.561357i	−0.837294	+	0.546752i	$0.815864\pi$
$284$	−0.941126	+	0.707210i	−0.0558456	+	0.0419652i
$285$	−2.91100	−	1.52781i	−0.172433	−	0.0904997i
$286$	2.07810	−	4.09950i	0.122881	−	0.242409i
$287$	−4.39749	+	2.30798i	−0.259576	+	0.136236i
$288$	−3.21140	+	6.76789i	−0.189234	+	0.398802i
$289$	−5.86924	+	12.3692i	−0.345249	+	0.727597i
$290$	−4.56280	+	1.52329i	−0.267937	+	0.0894504i
$291$	−9.74928	−	8.63711i	−0.571513	−	0.506316i
$292$	−9.36574	−	1.52208i	−0.548089	−	0.0890731i
$293$	−0.420547	+	10.4358i	−0.0245686	+	0.609664i	0.939270	+	0.343178i	$0.111504\pi$
$293$	−0.420547	+	10.4358i	−0.0245686	+	0.609664i	−0.963839	+	0.266486i	$0.914138\pi$
$294$	4.64808	+	12.2560i	0.271082	+	0.714784i
$295$	−0.854069	+	2.94859i	−0.0497258	+	0.171673i
$296$	−0.608882	+	2.98250i	−0.0353906	+	0.173354i
$297$	0.661774	+	0.0534239i	0.0384000	+	0.00309997i
$298$	2.46748	−	6.50622i	0.142937	−	0.376895i
$299$	7.06663	+	10.8324i	0.408674	+	0.626454i
$300$	2.84371	+	7.49825i	0.164182	+	0.432912i
$301$	1.15654	+	3.99283i	0.0666617	+	0.230143i
$302$	−0.400910	−	9.94847i	−0.0230698	−	0.572470i
$303$	−12.1428	−	14.8722i	−0.697586	−	0.854388i
$304$	−3.62841	+	29.8827i	−0.208104	+	1.71389i
$305$	−4.29042	+	0.346359i	−0.245669	+	0.0198324i
$306$	−0.971701	+	3.35470i	−0.0555484	+	0.191775i
$307$	−20.7077	−	5.10399i	−1.18185	−	0.291300i	−0.401035	−	0.916063i	$-0.631350\pi$
$307$	−20.7077	−	5.10399i	−1.18185	−	0.291300i	−0.780815	+	0.624763i	$0.785196\pi$
$308$	0.372321	+	0.279781i	0.0212150	+	0.0159420i
$309$	−5.32445	+	6.52126i	−0.302897	+	0.370982i
$310$	6.61706	+	6.88909i	0.375824	+	0.391274i
$311$	−2.28669	−	0.563618i	−0.129666	−	0.0319599i	0.173948	−	0.984755i	$-0.444347\pi$
$311$	−2.28669	−	0.563618i	−0.129666	−	0.0319599i	−0.303615	+	0.952795i	$0.598194\pi$
$312$	1.89533	+	1.05878i	0.107302	+	0.0599417i
$313$	1.68587	−	0.415531i	0.0952913	−	0.0234872i	−0.191382	−	0.981516i	$-0.561297\pi$
$313$	1.68587	−	0.415531i	0.0952913	−	0.0234872i	0.286673	+	0.958028i	$0.407451\pi$
$314$	−22.1218	−	13.9890i	−1.24840	−	0.789443i
$315$	−0.102870	−	0.178176i	−0.00579608	−	0.0100391i
$316$	5.11106	−	8.85261i	0.287520	−	0.497998i
$317$	17.9935	−	9.44373i	1.01062	−	0.530413i	0.123689	−	0.992321i	$-0.460527\pi$
$317$	17.9935	−	9.44373i	1.01062	−	0.530413i	0.886928	+	0.461908i	$0.152835\pi$
$318$	16.0814	−	5.36877i	0.901802	−	0.301066i
$319$	1.68151	−	2.91246i	0.0941464	−	0.163066i
$320$	−1.97154	+	1.74664i	−0.110213	+	0.0976399i
$321$	−14.7250	+	9.31153i	−0.821870	+	0.519719i
$322$	−2.63559	+	1.12292i	−0.146876	+	0.0625780i
$323$	0.486848	+	12.0810i	0.0270889	+	0.672205i
$324$	0.203272	−	1.67409i	0.0112929	−	0.0930052i
$325$	16.3996	−	5.00289i	0.909684	−	0.277510i
$326$	−3.50280	−	28.8481i	−0.194002	−	1.59775i
$327$	7.01143	−	1.13947i	0.387733	−	0.0630128i
$328$	6.07619	+	3.84235i	0.335501	+	0.212158i
$329$	4.37258	+	0.710613i	0.241068	+	0.0391774i
$330$	0.558284	+	0.293010i	0.0307325	+	0.0161297i
$331$	15.5191	−	9.81366i	0.853004	−	0.539407i	−0.0349234	−	0.999390i	$-0.511119\pi$
$331$	15.5191	−	9.81366i	0.853004	−	0.539407i	0.887928	+	0.459983i	$0.152144\pi$
$332$	9.80724	−	10.2104i	0.538242	−	0.560370i
$333$	−0.609363	−	5.01856i	−0.0333929	−	0.275015i
$334$	−2.17760	−	10.6666i	−0.119153	−	0.583650i
$335$	−0.223631	−	0.0180533i	−0.0122182	−	0.000986359i
$336$	−1.19142	+	1.45922i	−0.0649973	+	0.0796072i
$337$	20.9130			1.13921			0.569603	−	0.821920i	$-0.307097\pi$
$337$	20.9130			1.13921			0.569603	+	0.821920i	$0.307097\pi$
$338$	−13.5917	+	20.9348i	−0.739288	+	1.13870i
$339$	−13.9663			−0.758546
$340$	−0.959613	+	1.17531i	−0.0520423	+	0.0637403i
$341$	−6.65651	−	0.537369i	−0.360470	−	0.0291002i
$342$	−2.55267	−	12.5038i	−0.138032	−	0.676128i
$343$	0.693264	+	5.70954i	0.0374327	+	0.308286i
$344$	4.16845	−	4.33981i	0.224748	−	0.233987i
$345$	−1.49958	+	0.948277i	−0.0807347	+	0.0510535i
$346$	43.4453	+	22.8018i	2.33563	+	1.22583i
$347$	−6.70618	−	1.08986i	−0.360007	−	0.0585068i	−0.0222820	−	0.999752i	$-0.507093\pi$
$347$	−6.70618	−	1.08986i	−0.360007	−	0.0585068i	−0.337725	+	0.941245i	$0.609657\pi$
$348$	−7.21974	−	4.56549i	−0.387019	−	0.244736i
$349$	−0.582664	+	0.0946920i	−0.0311893	+	0.00506875i	−0.175986	−	0.984393i	$-0.556311\pi$
$349$	−0.582664	+	0.0946920i	−0.0311893	+	0.00506875i	0.144797	+	0.989461i	$0.453747\pi$
$350$	0.457778	+	3.77014i	0.0244693	+	0.201522i
$351$	−3.54254	−	0.671120i	−0.189087	−	0.0358217i
$352$	0.599499	−	4.93732i	0.0319534	−	0.263160i
$353$	−0.930146	−	23.0813i	−0.0495067	−	1.22850i	−0.812839	−	0.582489i	$-0.802079\pi$
$353$	−0.930146	−	23.0813i	−0.0495067	−	1.22850i	0.763332	−	0.646006i	$-0.223562\pi$
$354$	−10.9628	+	4.67079i	−0.582664	+	0.248250i
$355$	−0.291826	+	0.184540i	−0.0154885	+	0.00979435i
$356$	5.93382	−	5.25690i	0.314492	−	0.278615i
$357$	−0.378329	+	0.655285i	−0.0200233	+	0.0346813i
$358$	13.4982	−	4.50637i	0.713403	−	0.238169i
$359$	18.8550	−	9.89586i	0.995128	−	0.522284i	0.113152	−	0.993578i	$-0.463905\pi$
$359$	18.8550	−	9.89586i	0.995128	−	0.522284i	0.881976	+	0.471294i	$0.156213\pi$
$360$	−0.148911	+	0.257922i	−0.00784832	+	0.0135937i
$361$	−12.5895	−	21.8057i	−0.662605	−	1.14767i
$362$	37.1854	+	23.5146i	1.95442	+	1.23590i
$363$	10.2524	−	2.52698i	0.538110	−	0.132632i
$364$	−1.84868	−	1.72603i	−0.0968971	−	0.0904688i
$365$	−2.70213	−	0.666014i	−0.141436	−	0.0348608i
$366$	−11.5746	−	12.0504i	−0.605012	−	0.629884i
$367$	−19.7000	+	24.1282i	−1.02833	+	1.25948i	−0.0631235	+	0.998006i	$0.520106\pi$
$367$	−19.7000	+	24.1282i	−1.02833	+	1.25948i	−0.965210	+	0.261475i	$0.915791\pi$
$368$	12.9875	+	9.75946i	0.677019	+	0.508747i
$369$	−11.5926	−	2.85731i	−0.603485	−	0.148746i
$370$	1.33570	−	4.61138i	0.0694398	−	0.239734i
$371$	3.66110	−	0.295554i	0.190075	−	0.0153444i
$372$	−2.04463	+	16.8390i	−0.106009	+	0.873062i
$373$	−16.9473	−	20.7567i	−0.877498	−	1.07474i	−0.996644	−	0.0818628i	$-0.973913\pi$
$373$	−16.9473	−	20.7567i	−0.877498	−	1.07474i	0.119146	−	0.992877i	$-0.461984\pi$
$374$	−0.0933697	−	2.31695i	−0.00482803	−	0.119806i
$375$	1.34244	+	4.63464i	0.0693233	+	0.239332i
$376$	−2.27396	−	5.99593i	−0.117270	−	0.309216i
$377$	−10.7638	+	14.7544i	−0.554363	+	0.759889i
$378$	0.283203	−	0.746744i	0.0145664	−	0.0384084i
$379$	8.13466	+	0.656697i	0.417849	+	0.0337323i	0.287604	−	0.957750i	$-0.407141\pi$
$379$	8.13466	+	0.656697i	0.417849	+	0.0337323i	0.130245	+	0.991482i	$0.458423\pi$
$380$	1.10897	−	5.43209i	0.0568889	−	0.278660i
$381$	−1.73569	+	5.99228i	−0.0889219	+	0.306994i
$382$	3.76389	+	9.92455i	0.192577	+	0.507784i
$383$	0.381416	−	9.46474i	0.0194894	−	0.483626i	−0.959742	−	0.280882i	$-0.909373\pi$
$383$	0.381416	−	9.46474i	0.0194894	−	0.483626i	0.979232	−	0.202744i	$-0.0649859\pi$
$384$	4.69621	+	0.763209i	0.239653	+	0.0389473i
$385$	0.102244	+	0.0905802i	0.00521083	+	0.00461640i
$386$	35.7699	−	11.9417i	1.82064	−	0.607819i
$387$	−4.28419	+	9.02875i	−0.217778	+	0.458957i
$388$	9.41626	−	19.8444i	0.478038	−	1.00744i
$389$	−2.11342	+	1.10921i	−0.107155	+	0.0562391i	−0.517449	−	0.855714i	$-0.673118\pi$
$389$	−2.11342	+	1.10921i	−0.107155	+	0.0562391i	0.410294	+	0.911953i	$0.365426\pi$
$390$	−2.84519	−	1.90499i	−0.144072	−	0.0964631i
$391$	5.77780	+	3.03242i	0.292196	+	0.153356i
$392$	3.28629	−	2.46949i	0.165983	−	0.124728i
$393$	2.78133	+	9.60228i	0.140300	+	0.484371i
$394$	−12.6554	+	1.02165i	−0.637568	+	0.0514698i
$395$	1.70313	−	2.46741i	0.0856939	−	0.124149i
$396$	0.223957	+	1.09701i	0.0112542	+	0.0551269i
$397$	−17.6541	−	7.52173i	−0.886036	−	0.377505i	−0.0994915	−	0.995038i	$-0.531722\pi$
$397$	−17.6541	−	7.52173i	−0.886036	−	0.377505i	−0.786544	+	0.617534i	$0.788132\pi$
$398$	−14.1604	+	3.49022i	−0.709797	+	0.174949i
$399$	0.111326	−	2.76253i	0.00557328	−	0.138300i
$400$	17.2171	−	12.9378i	0.860855	−	0.646891i
$401$	−13.1002	+	5.58148i	−0.654193	+	0.278726i	−0.693451	−	0.720503i	$-0.743911\pi$
$401$	−13.1002	+	5.58148i	−0.654193	+	0.278726i	0.0392582	+	0.999229i	$0.487501\pi$
$402$	−0.494735	−	0.716748i	−0.0246751	−	0.0357481i
$403$	35.6329	+	6.75051i	1.77500	+	0.336267i
$404$	18.3930	−	26.6468i	0.915085	−	1.32573i
$405$	0.0989358	−	0.484619i	0.00491616	−	0.0240809i
$406$	−2.80235	−	2.91755i	−0.139078	−	0.144796i
$407$	1.43888	+	3.03237i	0.0713224	+	0.150309i
$408$	1.09531			0.0542261
$409$	−0.253218	−	0.533646i	−0.0125208	−	0.0263871i	0.897094	−	0.441840i	$-0.145674\pi$
$409$	−0.253218	−	0.533646i	−0.0125208	−	0.0263871i	−0.909615	+	0.415453i	$0.863623\pi$
$410$	−9.06446	−	6.81150i	−0.447662	−	0.336396i
$411$	−4.75354	+	12.5341i	−0.234475	+	0.618260i
$412$	−13.0613	−	5.56491i	−0.643486	−	0.274164i
$413$	−2.54819	+	0.414121i	−0.125388	+	0.0203776i
$414$	−6.53285	−	2.18098i	−0.321072	−	0.107190i
$415$	3.10809	−	2.75353i	0.152570	−	0.135165i
$416$	−6.09195	+	26.3138i	−0.298682	+	1.29014i
$417$	−5.58977	−	4.95210i	−0.273732	−	0.242505i
$418$	4.23642	+	7.33769i	0.207210	+	0.358898i
$419$	17.2167	+	5.74776i	0.841089	+	0.280797i	0.704387	−	0.709816i	$-0.251222\pi$
$419$	17.2167	+	5.74776i	0.841089	+	0.280797i	0.136701	+	0.990612i	$0.456350\pi$
$420$	0.240347	−	0.250227i	0.0117277	−	0.0122098i
$421$	−0.434846	−	0.629983i	−0.0211931	−	0.0307035i	0.812244	−	0.583318i	$-0.198246\pi$
$421$	−0.434846	−	0.629983i	−0.0211931	−	0.0307035i	−0.833437	+	0.552614i	$0.813630\pi$
$422$	−6.09038	−	7.45936i	−0.296475	−	0.363116i
$423$	6.73550	+	8.24948i	0.327491	+	0.401104i
$424$	−3.02036	−	4.37575i	−0.146682	−	0.212505i
$425$	5.99226	−	6.23861i	0.290668	−	0.302617i
$426$	−1.27133	−	0.424431i	−0.0615960	−	0.0205638i
$427$	−1.80994	−	3.13491i	−0.0875893	−	0.151709i
$428$	−21.9916	−	19.4829i	−1.06301	−	0.941741i
$429$	2.37205	−	0.322156i	0.114523	−	0.0155538i
$430$	−7.10378	+	6.29340i	−0.342574	+	0.303495i
$431$	9.76314	+	3.25942i	0.470274	+	0.157001i	0.541921	−	0.840429i	$-0.317697\pi$
$431$	9.76314	+	3.25942i	0.470274	+	0.157001i	−0.0716468	+	0.997430i	$0.522825\pi$
$432$	−4.47022	+	0.726482i	−0.215074	+	0.0349529i
$433$	19.0985	+	8.13710i	0.917814	+	0.391044i	0.798626	−	0.601828i	$-0.205561\pi$
$433$	19.0985	+	8.13710i	0.917814	+	0.391044i	0.119188	+	0.992872i	$0.461971\pi$
$434$	−2.84862	+	7.51118i	−0.136738	+	0.360548i
$435$	−2.00292	−	1.50510i	−0.0960327	−	0.0721639i
$436$	5.13537	+	10.8226i	0.245939	+	0.518306i
$437$	−23.8427			−1.14055
$438$	−4.63118	−	9.76000i	−0.221286	−	0.466351i
$439$	−17.2706	−	17.9806i	−0.824281	−	0.858168i	0.167532	−	0.985867i	$-0.446420\pi$
$439$	−17.2706	−	17.9806i	−0.824281	−	0.858168i	−0.991813	+	0.127699i	$0.959241\pi$
$440$	0.0395516	−	0.193737i	0.00188555	−	0.00923603i
$441$	−3.87816	+	5.61849i	−0.184675	+	0.267547i
$442$	−0.835499	+	12.5650i	−0.0397407	+	0.597655i
$443$	5.83416	+	8.45224i	0.277189	+	0.401578i	0.936709	−	0.350109i	$-0.113856\pi$
$443$	5.83416	+	8.45224i	0.277189	+	0.401578i	−0.659519	+	0.751687i	$0.729240\pi$
$444$	7.84320	−	3.34167i	0.372222	−	0.158589i
$445$	1.85880	−	1.39680i	0.0881156	−	0.0662146i
$446$	1.74238	−	43.2368i	0.0825042	−	2.04732i
$447$	3.51886	−	0.867321i	0.166436	−	0.0410229i
$448$	−2.03784	−	0.868244i	−0.0962791	−	0.0410207i
$449$	4.33495	+	21.2340i	0.204579	+	1.00209i	0.944276	+	0.329154i	$0.106764\pi$
$449$	4.33495	+	21.2340i	0.204579	+	1.00209i	−0.739697	+	0.672940i	$0.765031\pi$
$450$	−5.18658	+	7.51407i	−0.244498	+	0.354216i
$451$	7.90125	−	0.637855i	0.372055	−	0.0300354i
$452$	−6.55275	−	22.6227i	−0.308216	−	1.06408i
$453$	4.14568	−	3.11527i	0.194781	−	0.146368i
$454$	−16.4770	−	8.64779i	−0.773303	−	0.405861i
$455$	−0.499720	−	0.548231i	−0.0234273	−	0.0257015i
$456$	−3.54377	+	1.85991i	−0.165952	+	0.0870985i
$457$	7.46723	−	15.7369i	0.349302	−	0.736139i	−0.650423	−	0.759572i	$-0.725408\pi$
$457$	7.46723	−	15.7369i	0.349302	−	0.736139i	0.999725	+	0.0234331i	$0.00745965\pi$
$458$	12.5579	−	26.4652i	0.586791	−	1.23664i
$459$	−1.72545	+	0.576039i	−0.0805369	+	0.0268872i
$460$	−2.23960	−	1.98412i	−0.104422	−	0.0925099i
$461$	12.9220	+	2.10003i	0.601839	+	0.0978083i	0.453694	−	0.891157i	$-0.350106\pi$
$461$	12.9220	+	2.10003i	0.601839	+	0.0978083i	0.148145	+	0.988966i	$0.452670\pi$
$462$	−0.0213506	+	0.529810i	−0.000993321	+	0.0246490i
$463$	1.62065	+	4.27331i	0.0753181	+	0.198597i	0.967388	−	0.253301i	$-0.0815162\pi$
$463$	1.62065	+	4.27331i	0.0753181	+	0.198597i	−0.892069	+	0.451898i	$0.850747\pi$
$464$	−6.38239	+	22.0346i	−0.296295	+	1.02293i
$465$	−0.995153	+	4.87458i	−0.0461491	+	0.226053i
$466$	37.6926	+	3.04286i	1.74608	+	0.140958i
$467$	8.66325	−	22.8431i	0.400887	−	1.05705i	−0.570864	−	0.821045i	$-0.693392\pi$
$467$	8.66325	−	22.8431i	0.400887	−	1.05705i	0.971751	−	0.236008i	$-0.0758392\pi$
$468$	−0.575016	−	6.05311i	−0.0265801	−	0.279805i
$469$	−0.0669069	−	0.176419i	−0.00308947	−	0.00814627i
$470$	2.81384	+	9.71449i	0.129793	+	0.448096i
$471$	−0.548912	−	13.6211i	−0.0252925	−	0.627628i
$472$	2.36349	+	2.89475i	0.108789	+	0.133242i
$473$	0.799765	−	6.58666i	0.0367732	−	0.302855i
$474$	11.6004	−	0.936481i	0.532824	−	0.0430140i
$475$	−8.79378	+	30.3596i	−0.403486	+	1.39300i
$476$	−1.23894	−	0.305372i	−0.0567868	−	0.0139967i
$477$	7.05923	+	5.30467i	0.323220	+	0.242884i
$478$	14.9366	−	18.2940i	0.683182	−	0.836746i
$479$	−8.06476	−	8.39631i	−0.368488	−	0.383637i	0.510981	−	0.859592i	$-0.329282\pi$
$479$	−8.06476	−	8.39631i	−0.368488	−	0.383637i	−0.879470	+	0.475955i	$0.842103\pi$
$480$	−3.59757	−	0.886722i	−0.164206	−	0.0404731i
$481$	−6.01627	−	17.2061i	−0.274318	−	0.784529i
$482$	37.4385	−	9.22776i	1.70528	−	0.420313i
$483$	−1.26111	−	0.797480i	−0.0573826	−	0.0362866i
$484$	8.90347	+	15.4213i	0.404703	+	0.700966i
$485$	3.22116	−	5.57921i	0.146265	−	0.253339i
$486$	1.70007	−	0.892267i	0.0771169	−	0.0404741i
$487$	29.2512	−	9.76547i	1.32550	−	0.442516i	0.436201	−	0.899849i	$-0.356324\pi$
$487$	29.2512	−	9.76547i	1.32550	−	0.442516i	0.889295	+	0.457333i	$0.151195\pi$
$488$	−2.62002	+	4.53800i	−0.118603	+	0.205426i
$489$	11.3290	−	10.0367i	0.512317	−	0.453873i
$490$	−5.47963	+	3.46511i	−0.247544	+	0.156538i
$491$	−27.8705	+	11.8745i	−1.25778	+	0.535889i	−0.914972	−	0.403517i	$-0.867787\pi$
$491$	−27.8705	+	11.8745i	−1.25778	+	0.535889i	−0.342806	+	0.939406i	$0.611377\pi$
$492$	−0.810741	−	20.1183i	−0.0365510	−	0.907004i
$493$	−1.11065	+	9.14700i	−0.0500210	+	0.411960i
$494$	−18.6330	−	42.0714i	−0.838339	−	1.89288i
$495$	0.0395828	+	0.325994i	0.00177912	+	0.0146523i
$496$	44.9641	−	7.30738i	2.01895	−	0.328111i
$497$	−0.245419	−	0.155194i	−0.0110086	−	0.00696139i
$498$	15.9099	+	2.58562i	0.712941	+	0.115864i
$499$	−31.3031	−	16.4292i	−1.40132	−	0.735470i	−0.416515	−	0.909129i	$-0.636749\pi$
$499$	−31.3031	−	16.4292i	−1.40132	−	0.735470i	−0.984806	+	0.173659i	$0.944441\pi$
$500$	−6.87738	+	4.34899i	−0.307566	+	0.194493i
$501$	3.92783	−	4.08930i	0.175482	−	0.182696i
$502$	−5.20534	−	42.8698i	−0.232326	−	1.91337i
$503$	0.514512	+	2.52025i	0.0229409	+	0.112372i	0.989649	−	0.143510i	$-0.0458391\pi$
$503$	0.514512	+	2.52025i	0.0229409	+	0.112372i	−0.966708	+	0.255883i	$0.917634\pi$
$504$	−0.249650	−	0.0201538i	−0.0111203	−	0.000897724i
$505$	6.00602	−	7.35604i	0.267264	−	0.327339i
$506$	4.57266			0.203279
$507$	−12.9948	+	0.368036i	−0.577119	+	0.0163450i
$508$	−10.5207			−0.466781
$509$	−18.3132	+	22.4295i	−0.811716	+	0.994172i	0.188211	+	0.982129i	$0.439731\pi$
$509$	−18.3132	+	22.4295i	−0.811716	+	0.994172i	−0.999927	+	0.0120436i	$0.996166\pi$
$510$	−1.72189	−	0.139005i	−0.0762465	−	0.00615525i
$511$	−0.468147	−	2.29314i	−0.0207096	−	0.101442i
$512$	3.43198	+	28.2649i	0.151674	+	1.24914i
$513$	4.60435	−	4.79364i	0.203287	−	0.211644i
$514$	0.983236	−	0.621761i	0.0433687	−	0.0274247i
$515$	−3.68711	−	1.93514i	−0.162473	−	0.0852726i
$516$	−16.6349	−	2.70344i	−0.732311	−	0.119012i
$517$	−5.97615	−	3.77909i	−0.262831	−	0.166204i
$518$	3.98519	−	0.647656i	0.175099	−	0.0284564i
$519$	3.08031	+	25.3686i	0.135210	+	1.11356i
$520$	−0.325590	+	1.02327i	−0.0142781	+	0.0448731i
$521$	0.646577	−	5.32504i	0.0283270	−	0.233294i	−0.971668	−	0.236349i	$-0.924049\pi$
$521$	0.646577	−	5.32504i	0.0283270	−	0.233294i	0.999995	+	0.00305459i	$0.000972309\pi$
$522$	−0.391604	−	9.71756i	−0.0171401	−	0.425326i
$523$	−0.160485	+	0.0683763i	−0.00701752	+	0.00298988i	−0.395473	−	0.918478i	$-0.629419\pi$
$523$	−0.160485	+	0.0683763i	−0.00701752	+	0.00298988i	0.388455	+	0.921468i	$0.373009\pi$
$524$	−14.2489	+	9.01045i	−0.622466	+	0.393624i
$525$	−1.48058	+	1.31168i	−0.0646180	+	0.0572465i
$526$	−12.7724	+	22.1224i	−0.556901	+	0.964581i
$527$	17.3555	−	5.79413i	0.756019	−	0.252396i
$528$	2.66242	−	1.39735i	0.115867	−	0.0608117i
$529$	5.06623	−	8.77497i	0.220271	−	0.381520i
$530$	4.19284	+	7.26221i	0.182125	+	0.315450i
$531$	−5.24560	−	3.31712i	−0.227640	−	0.143951i
$532$	4.52701	−	1.11581i	0.196271	−	0.0483764i
$533$	−43.0338	−	1.12429i	−1.86400	−	0.0486983i
$534$	8.76338	+	2.15998i	0.379229	+	0.0934715i
$535$	−5.96938	−	6.21478i	−0.258079	−	0.268688i
$536$	−0.172738	+	0.211566i	−0.00746115	+	0.00913825i
$537$	5.92529	+	4.45257i	0.255695	+	0.192142i
$538$	−39.1804	−	9.65709i	−1.68919	−	0.416347i
$539$	1.26105	−	4.35366i	0.0543174	−	0.187525i
$540$	0.831409	−	0.0671183i	0.0357782	−	0.00288831i
$541$	−3.51887	+	28.9805i	−0.151288	+	1.24597i	0.697247	+	0.716830i	$0.254408\pi$
$541$	−3.51887	+	28.9805i	−0.151288	+	1.24597i	−0.848536	+	0.529138i	$0.822515\pi$
$542$	14.6029	+	17.8853i	0.627247	+	0.768238i
$543$	0.922690	+	22.8963i	0.0395964	+	0.982575i
$544$	3.79123	+	13.0889i	0.162548	+	0.561180i
$545$	1.24589	+	3.28514i	0.0533681	+	0.140720i
$546$	0.421629	−	2.84851i	0.0180440	−	0.121905i
$547$	8.28160	−	21.8368i	0.354096	−	0.933673i	−0.633087	−	0.774080i	$-0.718213\pi$
$547$	8.28160	−	21.8368i	0.354096	−	0.933673i	0.987183	−	0.159593i	$-0.0510182\pi$
$548$	−22.5331	−	1.81906i	−0.962564	−	0.0777062i
$549$	1.74072	−	8.52661i	0.0742921	−	0.363907i
$550$	1.68651	−	5.82250i	0.0719129	−	0.248272i
$551$	−11.9388	−	31.4801i	−0.508611	−	1.34110i
$552$	−0.0869714	+	2.15817i	−0.00370175	+	0.0918579i
$553$	2.48871	+	0.404455i	0.105831	+	0.0171992i
$554$	21.1670	+	18.7524i	0.899301	+	0.796711i
$555$	2.37180	−	0.791824i	0.100677	−	0.0336111i
$556$	5.39883	−	11.3778i	0.228961	−	0.482526i
$557$	2.07839	−	4.38011i	0.0880640	−	0.185591i	−0.854640	−	0.519221i	$-0.826222\pi$
$557$	2.07839	−	4.38011i	0.0880640	−	0.185591i	0.942704	+	0.333630i	$0.108274\pi$
$558$	−17.1003	+	8.97494i	−0.723915	+	0.379940i
$559$	−8.12701	+	35.1041i	−0.343736	+	1.48474i
$560$	−0.825042	−	0.433015i	−0.0348644	−	0.0182982i
$561$	0.965506	−	0.725531i	0.0407637	−	0.0306319i
$562$	8.57150	+	29.5922i	0.361567	+	1.24827i
$563$	−40.4368	+	3.26439i	−1.70421	+	0.137578i	−0.893852	−	0.448362i	$-0.852008\pi$
$563$	−40.4368	+	3.26439i	−1.70421	+	0.137578i	−0.810355	+	0.585940i	$0.800726\pi$
$564$	−10.2024	+	14.7807i	−0.429599	+	0.622381i
$565$	−1.38177	−	6.76834i	−0.0581314	−	0.284746i
$566$	−17.3662	−	7.39905i	−0.729957	−	0.311005i
$567$	0.403873	−	0.0995458i	0.0169611	−	0.00418053i
$568$	−0.0169251	+	0.419992i	−0.000710161	+	0.0176225i
$569$	17.1975	−	12.9231i	0.720956	−	0.541763i	−0.175726	−	0.984439i	$-0.556227\pi$
$569$	17.1975	−	12.9231i	0.720956	−	0.541763i	0.896682	+	0.442676i	$0.145971\pi$
$570$	5.80703	−	2.47414i	0.243230	−	0.103631i
$571$	3.23171	+	4.68195i	0.135243	+	0.195933i	0.884754	−	0.466059i	$-0.154327\pi$
$571$	3.23171	+	4.68195i	0.135243	+	0.195933i	−0.749511	+	0.661992i	$0.769711\pi$
$572$	1.63475	+	3.69111i	0.0683525	+	0.154333i
$573$	−3.14043	+	4.54970i	−0.131193	+	0.190066i
$574$	1.90732	−	9.34269i	0.0796102	−	0.389957i
$575$	11.8166	+	12.3023i	0.492785	+	0.513043i
$576$	−2.28290	−	4.81111i	−0.0951208	−	0.200463i
$577$	−15.7138			−0.654174			−0.327087	−	0.944994i	$-0.606067\pi$
$577$	−15.7138			−0.654174			−0.327087	+	0.944994i	$0.606067\pi$
$578$	−11.2689	−	23.7487i	−0.468725	−	0.987817i
$579$	15.7018	+	11.7992i	0.652546	+	0.490357i
$580$	1.49823	−	3.95051i	0.0622107	−	0.164036i
$581$	3.21261	+	1.36877i	0.133282	+	0.0567860i
$582$	24.6839	−	4.01153i	1.02318	−	0.166283i
$583$	−5.56089	−	1.85650i	−0.230309	−	0.0768883i
$584$	−2.53591	+	2.24662i	−0.104937	+	0.0929658i
$585$	−0.0252464	−	1.78318i	−0.00104381	−	0.0737255i
$586$	−15.0098	−	13.2975i	−0.620050	−	0.549316i
$587$	−7.10107	−	12.2994i	−0.293093	−	0.507651i	0.681447	−	0.731868i	$-0.261351\pi$
$587$	−7.10107	−	12.2994i	−0.293093	−	0.507651i	−0.974539	+	0.224216i	$0.928018\pi$
$588$	−10.9204	−	3.64578i	−0.450352	−	0.150349i
$589$	−46.3132	+	48.2172i	−1.90830	+	1.98675i
$590$	−3.34816	−	4.85065i	−0.137842	−	0.199698i
$591$	−4.18223	−	5.12230i	−0.172034	−	0.210703i
$592$	−14.4800	−	17.7348i	−0.595126	−	0.728897i
$593$	22.8797	+	33.1470i	0.939556	+	1.36118i	0.932486	+	0.361207i	$0.117635\pi$
$593$	22.8797	+	33.1470i	0.939556	+	1.36118i	0.00707066	+	0.999975i	$0.497749\pi$
$594$	−0.883042	+	0.919344i	−0.0362316	+	0.0377211i
$595$	−0.354994	−	0.118514i	−0.0145533	−	0.00485862i
$596$	3.05588	+	5.29294i	0.125174	+	0.216807i
$597$	−5.68564	−	5.03704i	−0.232698	−	0.206152i
$598$	−24.6913	−	2.64394i	−1.00970	−	0.108119i
$599$	−15.6732	+	13.8852i	−0.640389	+	0.567335i	−0.919581	−	0.392900i	$-0.871472\pi$
$599$	−15.6732	+	13.8852i	−0.640389	+	0.567335i	0.279192	+	0.960235i	$0.409933\pi$
$600$	2.71599	+	0.906730i	0.110880	+	0.0370171i
$601$	29.1163	−	4.73186i	1.18768	−	0.193017i	0.465707	−	0.884939i	$-0.345800\pi$
$601$	29.1163	−	4.73186i	1.18768	−	0.193017i	0.721972	+	0.691922i	$0.243236\pi$
$602$	−7.34267	−	3.12842i	−0.299265	−	0.127505i
$603$	0.160849	−	0.424125i	0.00655029	−	0.0172717i
$604$	6.99123	+	5.25357i	0.284469	+	0.213765i
$605$	2.23895	+	4.71849i	0.0910263	+	0.191834i
$606$	36.8635			1.49748
$607$	−15.6478	−	32.9771i	−0.635125	−	1.33850i	−0.924463	−	0.381271i	$-0.875486\pi$
$607$	−15.6478	−	32.9771i	−0.635125	−	1.33850i	0.289338	−	0.957227i	$-0.406565\pi$
$608$	−34.4919	−	35.9099i	−1.39883	−	1.45634i
$609$	0.421451	−	2.06440i	0.0170780	−	0.0836538i
$610$	4.69471	−	6.80147i	0.190083	−	0.275383i
$611$	30.0848	+	23.8617i	1.21710	+	0.965340i
$612$	−1.74262	−	2.52462i	−0.0704413	−	0.102052i
$613$	12.1072	−	5.15842i	0.489007	−	0.208346i	−0.133366	−	0.991067i	$-0.542579\pi$
$613$	12.1072	−	5.15842i	0.489007	−	0.208346i	0.622374	+	0.782720i	$0.286168\pi$
$614$	32.7361	−	24.5995i	1.32112	−	0.992757i
$615$	0.237789	−	5.90067i	0.00958858	−	0.237938i
$616$	0.161457	−	0.0397955i	0.00650527	−	0.00160341i
$617$	33.2718	+	14.1758i	1.33947	+	0.570696i	0.938464	−	0.345378i	$-0.112249\pi$
$617$	33.2718	+	14.1758i	1.33947	+	0.570696i	0.401009	+	0.916074i	$0.368660\pi$
$618$	−3.23324	−	15.8375i	−0.130060	−	0.637076i
$619$	−20.4513	+	29.6288i	−0.822008	+	1.19088i	0.157108	+	0.987581i	$0.449783\pi$
$619$	−20.4513	+	29.6288i	−0.822008	+	1.19088i	−0.979116	+	0.203302i	$0.934833\pi$
$620$	−8.36280	+	0.675115i	−0.335858	+	0.0271133i
$621$	−0.998004	−	3.44551i	−0.0400485	−	0.138263i
$622$	3.61495	−	2.71646i	0.144946	−	0.108920i
$623$	1.73140	+	0.908708i	0.0693670	+	0.0364066i
$624$	−15.1844	+	6.00593i	−0.607864	+	0.240430i
$625$	18.9401	−	9.94052i	0.757603	−	0.397621i
$626$	−1.42915	+	3.01188i	−0.0571204	+	0.120379i
$627$	−1.89180	+	3.98687i	−0.0755510	+	0.159220i
$628$	21.8060	−	7.27993i	0.870156	−	0.290501i
$629$	−6.88339	−	6.09815i	−0.274459	−	0.243149i
$630$	0.389905	+	0.0633658i	0.0155342	+	0.00252455i
$631$	−0.313634	+	7.78274i	−0.0124856	+	0.309826i	0.980864	+	0.194692i	$0.0623708\pi$
$631$	−0.313634	+	7.78274i	−0.0124856	+	0.309826i	−0.993350	+	0.115134i	$0.963270\pi$
$632$	−1.29425	−	3.41266i	−0.0514825	−	0.135748i
$633$	1.39542	−	4.81755i	0.0554630	−	0.191480i
$634$	−7.80433	+	38.2281i	−0.309950	+	1.51823i
$635$	−3.07570	−	0.248296i	−0.122055	−	0.00985333i
$636$	−5.28047	+	13.9235i	−0.209384	+	0.552101i
$637$	−9.32672	+	22.7796i	−0.369538	+	0.902562i
$638$	2.28968	+	6.03739i	0.0906493	+	0.239022i
$639$	−0.194217	−	0.670514i	−0.00768310	−	0.0265251i
$640$	0.0947575	+	2.35138i	0.00374562	+	0.0929466i
$641$	5.93002	+	7.26296i	0.234222	+	0.286870i	0.878320	−	0.478073i	$-0.158665\pi$
$641$	5.93002	+	7.26296i	0.234222	+	0.286870i	−0.644098	+	0.764943i	$0.722767\pi$
$642$	4.03201	−	33.2066i	0.159131	−	1.31056i
$643$	−38.2449	+	3.08744i	−1.50823	+	0.121757i	−0.806733	−	0.590916i	$-0.798767\pi$
$643$	−38.2449	+	3.08744i	−1.50823	+	0.121757i	−0.701497	+	0.712672i	$0.747485\pi$
$644$	0.700071	−	2.41693i	0.0275867	−	0.0952402i
$645$	−4.79936	−	1.18294i	−0.188975	−	0.0465781i
$646$	−18.5585	−	13.9458i	−0.730175	−	0.548691i
$647$	7.36308	−	9.01814i	0.289473	−	0.354540i	−0.609312	−	0.792931i	$-0.708554\pi$
$647$	7.36308	−	9.01814i	0.289473	−	0.354540i	0.898784	+	0.438391i	$0.144452\pi$
$648$	−0.417110	−	0.434258i	−0.0163856	−	0.0170593i
$649$	4.00087	+	0.986125i	0.157048	+	0.0387088i
$650$	−12.4734	+	30.4650i	−0.489246	+	1.19494i
$651$	−4.06239	+	1.00129i	−0.159218	+	0.0392436i
$652$	21.5729	+	13.6418i	0.844858	+	0.534256i
$653$	−2.00524	−	3.47317i	−0.0784710	−	0.135916i	0.824119	−	0.566416i	$-0.191670\pi$
$653$	−2.00524	−	3.47317i	−0.0784710	−	0.135916i	−0.902590	+	0.430500i	$0.858337\pi$
$654$	−6.81927	+	11.8113i	−0.266655	+	0.461860i
$655$	−4.37828	+	2.29790i	−0.171073	+	0.0897863i
$656$	−51.2897	+	17.1230i	−2.00253	+	0.668541i
$657$	2.81329	−	4.87277i	0.109757	−	0.190105i
$658$	−6.36645	+	5.64018i	−0.248190	+	0.219877i
$659$	−0.860334	+	0.544042i	−0.0335139	+	0.0211929i	−0.551118	−	0.834428i	$-0.685798\pi$
$659$	−0.860334	+	0.544042i	−0.0335139	+	0.0211929i	0.517604	+	0.855620i	$0.326824\pi$
$660$	−0.509476	+	0.217067i	−0.0198313	+	0.00844934i
$661$	−2.02555	−	50.2635i	−0.0787848	−	1.95503i	−0.246389	−	0.969171i	$-0.579244\pi$
$661$	−2.02555	−	50.2635i	−0.0787848	−	1.95503i	0.167604	−	0.985854i	$-0.446397\pi$
$662$	−4.24943	+	34.9972i	−0.165159	+	1.36021i
$663$	−5.63303	+	3.35944i	−0.218769	+	0.130470i
$664$	−0.609310	−	5.01812i	−0.0236458	−	0.194741i
$665$	1.34979	−	0.219362i	0.0523427	−	0.00850651i
$666$	8.20374	+	5.18773i	0.317889	+	0.201021i
$667$	−17.9348	−	2.91469i	−0.694438	−	0.112857i
$668$	8.46675	+	4.44369i	0.327589	+	0.171932i
$669$	19.0484	−	12.0455i	0.736455	−	0.465706i
$670$	0.298403	−	0.310670i	0.0115283	−	0.0120022i
$671$	0.696438	+	5.73568i	0.0268857	+	0.221424i
$672$	−0.623285	−	3.05305i	−0.0240437	−	0.117774i
$673$	12.0987	+	0.976708i	0.466370	+	0.0376493i	0.311419	−	0.950273i	$-0.399196\pi$
$673$	12.0987	+	0.976708i	0.466370	+	0.0376493i	0.154952	+	0.987922i	$0.450478\pi$
$674$	−25.3946	+	31.1027i	−0.978162	+	1.19803i
$675$	−4.75536			−0.183034
$676$	−6.69308	−	20.8764i	−0.257426	−	0.802938i
$677$	−38.5403			−1.48123			−0.740613	−	0.671932i	$-0.765465\pi$
$677$	−38.5403			−1.48123			−0.740613	+	0.671932i	$0.765465\pi$
$678$	16.9592	−	20.7712i	0.651314	−	0.797715i
$679$	5.40028	+	0.435955i	0.207244	+	0.0167304i
$680$	0.108366	+	0.530810i	0.00415563	+	0.0203556i
$681$	−1.16823	−	9.62126i	−0.0447668	−	0.368688i
$682$	8.88215	−	9.24730i	0.340115	−	0.354097i
$683$	19.6156	−	12.4042i	0.750571	−	0.474632i	−0.103604	−	0.994619i	$-0.533037\pi$
$683$	19.6156	−	12.4042i	0.750571	−	0.474632i	0.854175	+	0.519986i	$0.174063\pi$
$684$	9.92506	+	5.20907i	0.379494	+	0.199174i
$685$	−6.54454	−	1.06359i	−0.250054	−	0.0406378i
$686$	−9.33328	−	5.90201i	−0.356346	−	0.225340i
$687$	15.0594	−	2.44740i	0.574554	−	0.0933741i
$688$	5.45547	+	44.9298i	0.207988	+	1.71293i
$689$	28.9541	+	13.2400i	1.10306	+	0.504405i
$690$	0.410615	−	3.38172i	0.0156319	−	0.128740i
$691$	−1.04630	−	25.9637i	−0.0398032	−	0.987707i	−0.888514	−	0.458850i	$-0.848262\pi$
$691$	−1.04630	−	25.9637i	−0.0398032	−	0.987707i	0.848711	−	0.528857i	$-0.177379\pi$
$692$	−39.6471	+	16.8920i	−1.50715	+	0.642139i
$693$	−0.233414	+	0.147602i	−0.00886666	+	0.00560693i
$694$	9.76416	−	8.65029i	0.370642	−	0.328360i
$695$	1.84686	−	3.19885i	0.0700553	−	0.121339i
$696$	−2.89304	+	0.965837i	−0.109660	+	0.0366100i
$697$	−19.2310	+	10.0932i	−0.728424	+	0.382307i
$698$	0.566695	−	0.981544i	0.0214497	−	0.0371520i
$699$	9.84773	+	17.0568i	0.372475	+	0.645146i
$700$	−2.81934	−	1.78284i	−0.106561	−	0.0673851i
$701$	−6.85011	+	1.68840i	−0.258725	+	0.0637700i	−0.366545	−	0.930400i	$-0.619459\pi$
$701$	−6.85011	+	1.68840i	−0.258725	+	0.0637700i	0.107819	+	0.994170i	$0.465613\pi$
$702$	5.29980	−	4.45367i	0.200028	−	0.168093i
$703$	32.6256	+	8.04148i	1.23050	+	0.303290i
$704$	2.44918	+	2.54987i	0.0923071	+	0.0961019i
$705$	−3.33148	+	4.08032i	−0.125471	+	0.153674i
$706$	35.4569	+	26.6442i	1.33444	+	1.00277i
$707$	7.75428	+	1.91126i	0.291630	+	0.0718802i
$708$	2.91195	−	10.0532i	0.109438	−	0.377822i
$709$	−0.745219	+	0.0601603i	−0.0279873	+	0.00225937i	−0.0944523	−	0.995529i	$-0.530110\pi$
$709$	−0.745219	+	0.0601603i	−0.0279873	+	0.00225937i	0.0664650	+	0.997789i	$0.478828\pi$
$710$	0.0799079	−	0.658101i	0.00299889	−	0.0246981i
$711$	3.83359	+	4.69530i	0.143771	+	0.176087i
$712$	−0.113974	−	2.82824i	−0.00427136	−	0.105993i
$713$	10.0385	+	34.6569i	0.375945	+	1.29791i
$714$	−0.515163	−	1.35837i	−0.0192795	−	0.0508358i
$715$	0.390803	+	1.11767i	0.0146152	+	0.0417984i
$716$	−4.43226	+	11.6869i	−0.165641	+	0.436760i
$717$	12.2607	+	0.989788i	0.457885	+	0.0369643i
$718$	−8.17797	+	40.0584i	−0.305199	+	1.49496i
$719$	5.19809	−	17.9459i	0.193856	−	0.669268i	−0.803414	−	0.595421i	$-0.796985\pi$
$719$	5.19809	−	17.9459i	0.193856	−	0.669268i	0.997270	−	0.0738470i	$-0.0235276\pi$
$720$	−0.794332	−	2.09448i	−0.0296030	−	0.0780567i
$721$	0.141007	−	3.49906i	0.00525138	−	0.130312i
$722$	47.7176	+	7.75486i	1.77586	+	0.288606i
$723$	15.0322	+	13.3174i	0.559054	+	0.495278i
$724$	−36.6547	+	12.2371i	−1.36226	+	0.454790i
$725$	−10.3261	+	21.7619i	−0.383503	+	0.808216i
$726$	−8.69116	+	18.3162i	−0.322559	+	0.679779i
$727$	−25.0618	+	13.1535i	−0.929492	+	0.487835i	−0.860311	−	0.509769i	$-0.829731\pi$
$727$	−25.0618	+	13.1535i	−0.929492	+	0.487835i	−0.0691805	+	0.997604i	$0.522038\pi$
$728$	−0.894840	+	0.121531i	−0.0331650	+	0.00450425i
$729$	0.885456	+	0.464723i	0.0327947	+	0.0172120i
$730$	4.27170	−	3.20997i	0.158103	−	0.118806i
$731$	5.05772	+	17.4613i	0.187067	+	0.645829i
$732$	14.6282	−	1.18091i	0.540673	−	0.0436477i
$733$	5.87740	−	8.51489i	0.217087	−	0.314505i	−0.699277	−	0.714851i	$-0.746495\pi$
$733$	5.87740	−	8.51489i	0.217087	−	0.314505i	0.916364	+	0.400346i	$0.131110\pi$
$734$	−11.9627	−	58.5974i	−0.441553	−	2.16287i
$735$	−3.10652	−	1.32356i	−0.114586	−	0.0488204i
$736$	−26.0909	+	6.43084i	−0.961725	+	0.237044i
$737$	−0.0121264	+	0.300914i	−0.000446682	+	0.0110843i
$738$	18.3263	−	13.7713i	0.674600	−	0.506929i
$739$	22.8734	−	9.74545i	0.841412	−	0.358492i	0.0721253	−	0.997396i	$-0.477022\pi$
$739$	22.8734	−	9.74545i	0.841412	−	0.358492i	0.769287	+	0.638903i	$0.220612\pi$
$740$	2.39541	+	3.47035i	0.0880571	+	0.127573i
$741$	12.5205	−	20.4344i	0.459952	−	0.750676i
$742$	−4.00609	+	5.80382i	−0.147068	+	0.213065i
$743$	2.50947	−	12.2922i	0.0920635	−	0.450957i	−0.907461	−	0.420135i	$-0.861983\pi$
$743$	2.50947	−	12.2922i	0.0920635	−	0.450957i	0.999525	−	0.0308213i	$-0.00981227\pi$
$744$	4.19554	+	4.36802i	0.153816	+	0.160139i
$745$	0.768461	+	1.61950i	0.0281543	+	0.0593338i
$746$	51.4491			1.88369
$747$	3.59894	+	7.58460i	0.131678	+	0.277506i
$748$	1.62822	+	1.22353i	0.0595336	+	0.0447366i
$749$	2.56979	−	6.77598i	0.0938981	−	0.247589i
$750$	−8.52294	−	3.63128i	−0.311214	−	0.132596i
$751$	−5.47064	+	0.889065i	−0.199626	+	0.0324424i	−0.259402	−	0.965769i	$-0.583526\pi$
$751$	−5.47064	+	0.889065i	−0.199626	+	0.0324424i	0.0597758	+	0.998212i	$0.480961\pi$
$752$	45.7499	+	15.2736i	1.66833	+	0.556970i
$753$	16.8356	−	14.9150i	0.613522	−	0.543533i
$754$	−8.87289	−	33.9245i	−0.323132	−	1.23546i
$755$	1.91988	+	1.70086i	0.0698715	+	0.0619007i
$756$	0.350736	+	0.607492i	0.0127561	+	0.0220943i
$757$	−23.8817	−	7.97290i	−0.867997	−	0.289780i	−0.152421	−	0.988316i	$-0.548707\pi$
$757$	−23.8817	−	7.97290i	−0.867997	−	0.289780i	−0.715575	+	0.698536i	$0.753835\pi$
$758$	−10.8545	+	11.3008i	−0.394254	+	0.410462i
$759$	1.35290	+	1.96001i	0.0491072	+	0.0711440i
$760$	−1.25196	−	1.53337i	−0.0454132	−	0.0556211i
$761$	31.5985	+	38.7011i	1.14544	+	1.40291i	0.901312	+	0.433171i	$0.142605\pi$
$761$	31.5985	+	38.7011i	1.14544	+	1.40291i	0.244131	+	0.969742i	$0.421497\pi$
$762$	−6.80433	−	9.85777i	−0.246495	−	0.357109i
$763$	−2.04682	+	2.13097i	−0.0740999	+	0.0771462i
$764$	−8.84307	−	2.95225i	−0.319931	−	0.106809i
$765$	−0.449868	−	0.779194i	−0.0162650	−	0.0281718i
$766$	13.6132	+	12.0602i	0.491864	+	0.435754i
$767$	−21.0336	−	7.63819i	−0.759480	−	0.275799i
$768$	−14.8097	+	13.1202i	−0.534398	+	0.473436i
$769$

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21429 + 1.48724i) q^{2} +(-0.996757 - 0.0804666i) q^{3} +(-0.337321 - 1.65231i) q^{4} +(-0.0596193 - 0.491009i) q^{5} +(1.33003 - 1.38471i) q^{6} +(0.351566 - 0.222317i) q^{7} +(-0.533160 - 0.279824i) q^{8} +(0.987050 + 0.160411i) q^{9} +(0.802643 + 0.507561i) q^{10} +(-0.655329 + 0.106501i) q^{11} +(0.203272 + 1.67409i) q^{12} +(3.60021 - 0.196167i) q^{13} +(-0.0962657 + 0.792820i) q^{14} +(0.0199161 + 0.494214i) q^{15} +(4.16647 - 1.77517i) q^{16} +(1.53745 - 0.972226i) q^{17} +(-1.43714 + 1.27319i) q^{18} +(-3.32336 + 5.75624i) q^{19} +(-0.791188 + 0.264137i) q^{20} +(-0.368315 + 0.193306i) q^{21} +(0.637369 - 1.10396i) q^{22} +(1.79357 + 3.10655i) q^{23} +(0.508915 + 0.321818i) q^{24} +(4.61717 - 1.13803i) q^{25} +(-4.07996 + 5.59258i) q^{26} +(-0.970942 - 0.239316i) q^{27} +(-0.485926 - 0.505903i) q^{28} +(-3.20355 + 3.92364i) q^{29} +(-0.759199 - 0.570501i) q^{30} +(9.76630 + 2.40718i) q^{31} +(-2.08417 + 7.19539i) q^{32} +(0.661774 - 0.0534239i) q^{33} +(-0.420986 + 3.46713i) q^{34} +(-0.130119 - 0.159367i) q^{35} +(-0.0679041 - 1.68502i) q^{36} +(-1.40651 - 4.85582i) q^{37} +(-4.52536 - 11.9324i) q^{38} +(-3.60432 - 0.0941653i) q^{39} +(-0.105609 + 0.278469i) q^{40} +(-11.9008 - 0.960731i) q^{41} +(0.159749 - 0.782503i) q^{42} +(-2.78040 + 9.59906i) q^{43} +(0.397030 + 1.04688i) q^{44} +(0.0199161 - 0.494214i) q^{45} +(-6.79810 - 1.10480i) q^{46} +(7.97158 + 7.06221i) q^{47} +(-4.29580 + 1.43415i) q^{48} +(-2.92667 + 6.16784i) q^{49} +(-3.91408 + 8.24875i) q^{50} +(-1.61070 + 0.845360i) q^{51} +(-1.53856 - 5.88249i) q^{52} +(7.81874 + 4.10359i) q^{53} +(1.53493 - 1.15342i) q^{54} +(0.0913634 + 0.315423i) q^{55} +(-0.249650 + 0.0201538i) q^{56} +(3.77577 - 5.47015i) q^{57} +(-1.94534 - 9.52890i) q^{58} +(-5.70977 - 2.43271i) q^{59} +(0.809876 - 0.199617i) q^{60} +(0.350414 - 8.69542i) q^{61} +(-15.4392 + 11.6018i) q^{62} +(0.382675 - 0.163043i) q^{63} +(-3.02509 - 4.38260i) q^{64} +(-0.310962 - 1.75604i) q^{65} +(-0.724134 + 1.04909i) q^{66} +(0.0907319 - 0.444434i) q^{67} +(-2.12503 - 2.21240i) q^{68} +(-1.53778 - 3.24080i) q^{69} +0.395021 q^{70} +(-0.299260 - 0.630677i) q^{71} +(-0.481369 - 0.361725i) q^{72} +(1.99522 - 5.26095i) q^{73} +(8.92968 + 3.80458i) q^{74} +(-4.69378 + 0.762813i) q^{75} +(10.6321 + 3.54952i) q^{76} +(-0.206714 + 0.183133i) q^{77} +(4.51675 - 5.24614i) q^{78} +(4.53713 + 4.01954i) q^{79} +(-1.12002 - 1.93994i) q^{80} +(0.948536 + 0.316668i) q^{81} +(15.8799 - 16.5327i) q^{82} +(4.76899 + 6.90907i) q^{83} +(0.443642 + 0.543363i) q^{84} +(-0.569034 - 0.696940i) q^{85} +(-10.8999 - 15.7912i) q^{86} +(3.50889 - 3.65314i) q^{87} +(0.379197 + 0.126595i) q^{88} +(2.35043 + 4.07107i) q^{89} +(0.710831 + 0.629741i) q^{90} +(1.22210 - 0.869352i) q^{91} +(4.52797 - 4.01143i) q^{92} +(-9.54093 - 3.18523i) q^{93} +(-20.1830 + 3.28006i) q^{94} +(3.02450 + 1.28862i) q^{95} +(2.65640 - 7.00435i) q^{96} +(10.4127 + 7.82461i) q^{97} +(-5.61921 - 11.8422i) q^{98} -0.663927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

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