LMFDB - Embedded newform 605.2.e.c.362.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.3
Character	$\chi$	$=$	605.362
Dual form			605.2.e.c.483.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63660 + 1.63660i) q^{2} +(-0.722598 + 0.722598i) q^{3} -3.35690i q^{4} +(0.360665 + 2.20679i) q^{5} -2.36520i q^{6} +(2.14665 - 2.14665i) q^{7} +(2.22069 + 2.22069i) q^{8} +1.95570i q^{9} +O(q^{10})$	\(q+(-1.63660 + 1.63660i) q^{2} +(-0.722598 + 0.722598i) q^{3} -3.35690i q^{4} +(0.360665 + 2.20679i) q^{5} -2.36520i q^{6} +(2.14665 - 2.14665i) q^{7} +(2.22069 + 2.22069i) q^{8} +1.95570i q^{9} +(-4.20189 - 3.02136i) q^{10} +(2.42569 + 2.42569i) q^{12} +(-2.96163 - 2.96163i) q^{13} +7.02641i q^{14} +(-1.85524 - 1.33401i) q^{15} -0.554967 q^{16} +(-4.75495 + 4.75495i) q^{17} +(-3.20070 - 3.20070i) q^{18} +0.733696 q^{19} +(7.40797 - 1.21071i) q^{20} +3.10233i q^{21} +(-4.96412 + 4.96412i) q^{23} -3.20934 q^{24} +(-4.73984 + 1.59182i) q^{25} +9.69399 q^{26} +(-3.58098 - 3.58098i) q^{27} +(-7.20610 - 7.20610i) q^{28} -4.84873 q^{29} +(5.21950 - 0.853045i) q^{30} +1.08368 q^{31} +(-3.53313 + 3.53313i) q^{32} -15.5639i q^{34} +(5.51143 + 3.96299i) q^{35} +6.56510 q^{36} +(0.0598868 + 0.0598868i) q^{37} +(-1.20076 + 1.20076i) q^{38} +4.28013 q^{39} +(-4.09968 + 5.70153i) q^{40} -5.36272i q^{41} +(-5.07727 - 5.07727i) q^{42} +(1.92858 + 1.92858i) q^{43} +(-4.31583 + 0.705353i) q^{45} -16.2485i q^{46} +(-7.22547 - 7.22547i) q^{47} +(0.401018 - 0.401018i) q^{48} -2.21624i q^{49} +(5.15204 - 10.3624i) q^{50} -6.87184i q^{51} +(-9.94189 + 9.94189i) q^{52} +(1.60548 - 1.60548i) q^{53} +11.7212 q^{54} +9.53412 q^{56} +(-0.530167 + 0.530167i) q^{57} +(7.93542 - 7.93542i) q^{58} -1.19649i q^{59} +(-4.47812 + 6.22784i) q^{60} +7.37123i q^{61} +(-1.77355 + 1.77355i) q^{62} +(4.19822 + 4.19822i) q^{63} -12.6746i q^{64} +(5.46754 - 7.60385i) q^{65} +(3.89698 + 3.89698i) q^{67} +(15.9619 + 15.9619i) q^{68} -7.17412i q^{69} +(-15.5058 + 2.53418i) q^{70} +13.9081 q^{71} +(-4.34302 + 4.34302i) q^{72} +(-1.92573 - 1.92573i) q^{73} -0.196021 q^{74} +(2.27475 - 4.57525i) q^{75} -2.46294i q^{76} +(-7.00485 + 7.00485i) q^{78} -10.3593 q^{79} +(-0.200157 - 1.22470i) q^{80} -0.691896 q^{81} +(8.77660 + 8.77660i) q^{82} +(-1.21373 - 1.21373i) q^{83} +10.4142 q^{84} +(-12.2081 - 8.77824i) q^{85} -6.31262 q^{86} +(3.50368 - 3.50368i) q^{87} -10.9954i q^{89} +(5.90889 - 8.21765i) q^{90} -12.7152 q^{91} +(16.6640 + 16.6640i) q^{92} +(-0.783066 + 0.783066i) q^{93} +23.6504 q^{94} +(0.264618 + 1.61911i) q^{95} -5.10607i q^{96} +(-3.15495 - 3.15495i) q^{97} +(3.62710 + 3.62710i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) $ 40 * q + 8 * q^3 - 4 * q^5	$ 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) $ 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.63660	+	1.63660i	−1.15725	+	1.15725i	−0.172184	+	0.985065i	$0.555082\pi$
$2$	−1.63660	+	1.63660i	−1.15725	+	1.15725i	−0.985065	+	0.172184i	$0.944918\pi$
$3$	−0.722598	+	0.722598i	−0.417192	+	0.417192i	−0.884235	−	0.467043i	$-0.845319\pi$
$3$	−0.722598	+	0.722598i	−0.417192	+	0.417192i	0.467043	+	0.884235i	$0.345319\pi$
$4$		−	3.35690i		−	1.67845i
$5$	0.360665	+	2.20679i	0.161294	+	0.986906i
$5$	0.360665	+	2.20679i	0.161294	+	0.986906i
$6$		−	2.36520i		−	0.965590i
$7$	2.14665	−	2.14665i	0.811359	−	0.811359i	−0.173479	−	0.984838i	$-0.555501\pi$
$7$	2.14665	−	2.14665i	0.811359	−	0.811359i	0.984838	+	0.173479i	$0.0555008\pi$
$8$	2.22069	+	2.22069i	0.785134	+	0.785134i
$9$			1.95570i			0.651902i
$10$	−4.20189	−	3.02136i	−1.32875	−	0.955439i
$11$		0			0
$11$		0			0
$12$	2.42569	+	2.42569i	0.700235	+	0.700235i
$13$	−2.96163	−	2.96163i	−0.821408	−	0.821408i	0.164902	−	0.986310i	$-0.447269\pi$
$13$	−2.96163	−	2.96163i	−0.821408	−	0.821408i	−0.986310	+	0.164902i	$0.947269\pi$
$14$			7.02641i			1.87789i
$15$	−1.85524	−	1.33401i	−0.479020	−	0.344439i
$16$	−0.554967			−0.138742
$17$	−4.75495	+	4.75495i	−1.15325	+	1.15325i	−0.167347	+	0.985898i	$0.553520\pi$
$17$	−4.75495	+	4.75495i	−1.15325	+	1.15325i	−0.985898	+	0.167347i	$0.946480\pi$
$18$	−3.20070	−	3.20070i	−0.754412	−	0.754412i
$19$	0.733696			0.168321			0.0841607	−	0.996452i	$-0.473179\pi$
$19$	0.733696			0.168321			0.0841607	+	0.996452i	$0.473179\pi$
$20$	7.40797	−	1.21071i	1.65647	−	0.270724i
$21$			3.10233i			0.676985i
$22$		0			0
$23$	−4.96412	+	4.96412i	−1.03509	+	1.03509i	−0.0357287	+	0.999362i	$0.511375\pi$
$23$	−4.96412	+	4.96412i	−1.03509	+	1.03509i	−0.999362	+	0.0357287i	$0.988625\pi$
$24$	−3.20934			−0.655103
$25$	−4.73984	+	1.59182i	−0.947968	+	0.318364i
$26$	9.69399			1.90115
$27$	−3.58098	−	3.58098i	−0.689160	−	0.689160i
$28$	−7.20610	−	7.20610i	−1.36182	−	1.36182i
$29$	−4.84873			−0.900387			−0.450194	−	0.892931i	$-0.648645\pi$
$29$	−4.84873			−0.900387			−0.450194	+	0.892931i	$0.648645\pi$
$30$	5.21950	−	0.853045i	0.952947	−	0.155744i
$31$	1.08368			0.194635			0.0973175	−	0.995253i	$-0.468974\pi$
$31$	1.08368			0.194635			0.0973175	+	0.995253i	$0.468974\pi$
$32$	−3.53313	+	3.53313i	−0.624575	+	0.624575i
$33$		0			0
$34$		−	15.5639i		−	2.66918i
$35$	5.51143	+	3.96299i	0.931603	+	0.669868i
$36$	6.56510			1.09418
$37$	0.0598868	+	0.0598868i	0.00984533	+	0.00984533i	0.712012	−	0.702167i	$-0.247784\pi$
$37$	0.0598868	+	0.0598868i	0.00984533	+	0.00984533i	−0.702167	+	0.712012i	$0.747784\pi$
$38$	−1.20076	+	1.20076i	−0.194790	+	0.194790i
$39$	4.28013			0.685370
$40$	−4.09968	+	5.70153i	−0.648216	+	0.901491i
$41$		−	5.36272i		−	0.837515i	−0.908098	−	0.418758i	$-0.862466\pi$
$41$		−	5.36272i		−	0.837515i	0.908098	−	0.418758i	$-0.137534\pi$
$42$	−5.07727	−	5.07727i	−0.783440	−	0.783440i
$43$	1.92858	+	1.92858i	0.294106	+	0.294106i	0.838700	−	0.544594i	$-0.183316\pi$
$43$	1.92858	+	1.92858i	0.294106	+	0.294106i	−0.544594	+	0.838700i	$0.683316\pi$
$44$		0			0
$45$	−4.31583	+	0.705353i	−0.643366	+	0.105148i
$46$		−	16.2485i		−	2.39571i
$47$	−7.22547	−	7.22547i	−1.05394	−	1.05394i	−0.998460	−	0.0554838i	$-0.982330\pi$
$47$	−7.22547	−	7.22547i	−1.05394	−	1.05394i	−0.0554838	−	0.998460i	$-0.517670\pi$
$48$	0.401018	−	0.401018i	0.0578819	−	0.0578819i
$49$		−	2.21624i		−	0.316606i
$50$	5.15204	−	10.3624i	0.728608	−	1.46546i
$51$		−	6.87184i		−	0.962249i
$52$	−9.94189	+	9.94189i	−1.37869	+	1.37869i
$53$	1.60548	−	1.60548i	0.220530	−	0.220530i	−0.588192	−	0.808722i	$-0.700160\pi$
$53$	1.60548	−	1.60548i	0.220530	−	0.220530i	0.808722	+	0.588192i	$0.200160\pi$
$54$	11.7212			1.59506
$55$		0			0
$56$	9.53412			1.27405
$57$	−0.530167	+	0.530167i	−0.0702223	+	0.0702223i
$58$	7.93542	−	7.93542i	1.04197	−	1.04197i
$59$		−	1.19649i		−	0.155770i	−0.996962	−	0.0778850i	$-0.975183\pi$
$59$		−	1.19649i		−	0.155770i	0.996962	−	0.0778850i	$-0.0248167\pi$
$60$	−4.47812	+	6.22784i	−0.578123	+	0.804011i
$61$			7.37123i			0.943790i	0.881655	+	0.471895i	$0.156430\pi$
$61$			7.37123i			0.943790i	−0.881655	+	0.471895i	$0.843570\pi$
$62$	−1.77355	+	1.77355i	−0.225241	+	0.225241i
$63$	4.19822	+	4.19822i	0.528926	+	0.528926i
$64$		−	12.6746i		−	1.58432i
$65$	5.46754	−	7.60385i	0.678165	−	0.943141i
$66$		0			0
$67$	3.89698	+	3.89698i	0.476092	+	0.476092i	0.903879	−	0.427787i	$-0.140707\pi$
$67$	3.89698	+	3.89698i	0.476092	+	0.476092i	−0.427787	+	0.903879i	$0.640707\pi$
$68$	15.9619	+	15.9619i	1.93566	+	1.93566i
$69$		−	7.17412i		−	0.863663i
$70$	−15.5058	+	2.53418i	−1.85330	+	0.302892i
$71$	13.9081			1.65059			0.825297	−	0.564699i	$-0.191008\pi$
$71$	13.9081			1.65059			0.825297	+	0.564699i	$0.191008\pi$
$72$	−4.34302	+	4.34302i	−0.511830	+	0.511830i
$73$	−1.92573	−	1.92573i	−0.225390	−	0.225390i	0.585374	−	0.810764i	$-0.300948\pi$
$73$	−1.92573	−	1.92573i	−0.225390	−	0.225390i	−0.810764	+	0.585374i	$0.800948\pi$
$74$	−0.196021			−0.0227870
$75$	2.27475	−	4.57525i	0.262666	−	0.528304i
$76$		−	2.46294i		−	0.282519i
$77$		0			0
$78$	−7.00485	+	7.00485i	−0.793143	+	0.793143i
$79$	−10.3593			−1.16551			−0.582757	−	0.812647i	$-0.698026\pi$
$79$	−10.3593			−1.16551			−0.582757	+	0.812647i	$0.698026\pi$
$80$	−0.200157	−	1.22470i	−0.0223782	−	0.136925i
$81$	−0.691896			−0.0768773
$82$	8.77660	+	8.77660i	0.969214	+	0.969214i
$83$	−1.21373	−	1.21373i	−0.133224	−	0.133224i	0.637350	−	0.770574i	$-0.280031\pi$
$83$	−1.21373	−	1.21373i	−0.133224	−	0.133224i	−0.770574	+	0.637350i	$0.780031\pi$
$84$	10.4142			1.13628
$85$	−12.2081	−	8.77824i	−1.32416	−	0.952133i
$86$	−6.31262			−0.680707
$87$	3.50368	−	3.50368i	0.375634	−	0.375634i
$88$		0			0
$89$		−	10.9954i		−	1.16551i	−0.812647	−	0.582756i	$-0.801974\pi$
$89$		−	10.9954i		−	1.16551i	0.812647	−	0.582756i	$-0.198026\pi$
$90$	5.90889	−	8.21765i	0.622852	−	0.866217i
$91$	−12.7152			−1.33291
$92$	16.6640	+	16.6640i	1.73735	+	1.73735i
$93$	−0.783066	+	0.783066i	−0.0812001	+	0.0812001i
$94$	23.6504			2.43935
$95$	0.264618	+	1.61911i	0.0271492	+	0.166117i
$96$		−	5.10607i		−	0.521136i
$97$	−3.15495	−	3.15495i	−0.320337	−	0.320337i	0.528559	−	0.848896i	$-0.322732\pi$
$97$	−3.15495	−	3.15495i	−0.320337	−	0.320337i	−0.848896	+	0.528559i	$0.822732\pi$
$98$	3.62710	+	3.62710i	0.366392	+	0.366392i
$99$		0			0
$100$	5.34358	+	15.9112i	0.534358	+	1.59112i
$101$			13.8415i			1.37728i	0.725102	+	0.688642i	$0.241793\pi$
$101$			13.8415i			1.37728i	−0.725102	+	0.688642i	$0.758207\pi$
$102$	11.2464	+	11.2464i	1.11356	+	1.11356i
$103$	−5.94662	+	5.94662i	−0.585938	+	0.585938i	−0.936529	−	0.350591i	$-0.885981\pi$
$103$	−5.94662	+	5.94662i	−0.585938	+	0.585938i	0.350591	+	0.936529i	$0.385981\pi$
$104$		−	13.1537i		−	1.28983i
$105$	−6.84620	+	1.11890i	−0.668121	+	0.109194i
$106$			5.25505i			0.510416i
$107$	2.00202	−	2.00202i	0.193543	−	0.193543i	−0.603682	−	0.797225i	$-0.706300\pi$
$107$	2.00202	−	2.00202i	0.193543	−	0.193543i	0.797225	+	0.603682i	$0.206300\pi$
$108$	−12.0210	+	12.0210i	−1.15672	+	1.15672i
$109$	−3.06400			−0.293478			−0.146739	−	0.989175i	$-0.546878\pi$
$109$	−3.06400			−0.293478			−0.146739	+	0.989175i	$0.546878\pi$
$110$		0			0
$111$	−0.0865481			−0.00821478
$112$	−1.19132	+	1.19132i	−0.112569	+	0.112569i
$113$	−5.32678	+	5.32678i	−0.501101	+	0.501101i	−0.911780	−	0.410679i	$-0.865292\pi$
$113$	−5.32678	+	5.32678i	−0.501101	+	0.501101i	0.410679	+	0.911780i	$0.365292\pi$
$114$		−	1.73534i		−	0.162529i
$115$	−12.7451	−	9.16438i	−1.18849	−	0.854583i
$116$			16.2767i			1.51125i
$117$	5.79207	−	5.79207i	0.535477	−	0.535477i
$118$	1.95817	+	1.95817i	0.180265	+	0.180265i
$119$			20.4145i			1.87139i
$120$	−1.15749	−	7.08233i	−0.105664	−	0.646526i
$121$		0			0
$122$	−12.0637	−	12.0637i	−1.09220	−	1.09220i
$123$	3.87509	+	3.87509i	0.349405	+	0.349405i
$124$		−	3.63781i		−	0.326685i
$125$	−5.22231	−	9.88572i	−0.467098	−	0.884206i
$126$	−13.7416			−1.22420
$127$	−1.62438	+	1.62438i	−0.144140	+	0.144140i	−0.775495	−	0.631354i	$-0.782499\pi$
$127$	−1.62438	+	1.62438i	−0.144140	+	0.144140i	0.631354	+	0.775495i	$0.282499\pi$
$128$	13.6769	+	13.6769i	1.20888	+	1.20888i
$129$	−2.78718			−0.245397
$130$	3.49628	+	21.3926i	0.306644	+	1.87625i
$131$			2.05576i			0.179613i	0.995959	+	0.0898063i	$0.0286248\pi$
$131$			2.05576i			0.179613i	−0.995959	+	0.0898063i	$0.971375\pi$
$132$		0			0
$133$	1.57499	−	1.57499i	0.136569	−	0.136569i
$134$	−12.7556			−1.10191
$135$	6.61094	−	9.19401i	0.568979	−	0.791294i
$136$	−21.1186			−1.81090
$137$	−3.55311	−	3.55311i	−0.303562	−	0.303562i	0.538844	−	0.842406i	$-0.318861\pi$
$137$	−3.55311	−	3.55311i	−0.303562	−	0.303562i	−0.842406	+	0.538844i	$0.818861\pi$
$138$	11.7411	+	11.7411i	0.999473	+	0.999473i
$139$	−1.95822			−0.166094			−0.0830472	−	0.996546i	$-0.526465\pi$
$139$	−1.95822			−0.166094			−0.0830472	+	0.996546i	$0.526465\pi$
$140$	13.3034	−	18.5013i	1.12434	−	1.56365i
$141$	10.4422			0.879394
$142$	−22.7620	+	22.7620i	−1.91015	+	1.91015i
$143$		0			0
$144$		−	1.08535i		−	0.0904460i
$145$	−1.74877	−	10.7001i	−0.145227	−	0.888598i
$146$	6.30330			0.521665
$147$	1.60145	+	1.60145i	0.132086	+	0.132086i
$148$	0.201034	−	0.201034i	0.0165249	−	0.0165249i
$149$	−10.7180			−0.878050			−0.439025	−	0.898475i	$-0.644676\pi$
$149$	−10.7180			−0.878050			−0.439025	+	0.898475i	$0.644676\pi$
$150$	3.76498	+	11.2107i	0.307409	+	0.915349i
$151$			18.4137i			1.49848i	0.662297	+	0.749241i	$0.269582\pi$
$151$			18.4137i			1.49848i	−0.662297	+	0.749241i	$0.730418\pi$
$152$	1.62931	+	1.62931i	0.132155	+	0.132155i
$153$	−9.29928	−	9.29928i	−0.751802	−	0.751802i
$154$		0			0
$155$	0.390845	+	2.39146i	0.0313935	+	0.192086i
$156$		−	14.3680i		−	1.15036i
$157$	12.4571	+	12.4571i	0.994188	+	0.994188i	0.999983	−	0.00579537i	$-0.00184473\pi$
$157$	12.4571	+	12.4571i	0.994188	+	0.994188i	−0.00579537	+	0.999983i	$0.501845\pi$
$158$	16.9540	−	16.9540i	1.34879	−	1.34879i
$159$			2.32023i			0.184007i
$160$	−9.07115	−	6.52260i	−0.717138	−	0.515657i
$161$			21.3125i			1.67966i
$162$	1.13235	−	1.13235i	0.0889662	−	0.0889662i
$163$	−9.88201	+	9.88201i	−0.774018	+	0.774018i	−0.978806	−	0.204788i	$-0.934350\pi$
$163$	−9.88201	+	9.88201i	−0.774018	+	0.774018i	0.204788	+	0.978806i	$0.434350\pi$
$164$	−18.0021			−1.40573
$165$		0			0
$166$	3.97278			0.308348
$167$	−1.06313	+	1.06313i	−0.0822675	+	0.0822675i	−0.747043	−	0.664776i	$-0.768527\pi$
$167$	−1.06313	+	1.06313i	−0.0822675	+	0.0822675i	0.664776	+	0.747043i	$0.268527\pi$
$168$	−6.88934	+	6.88934i	−0.531524	+	0.531524i
$169$			4.54250i			0.349423i
$170$	34.3462	−	5.61334i	2.63423	−	0.430523i
$171$			1.43489i			0.109729i
$172$	6.47405	−	6.47405i	0.493642	−	0.493642i
$173$	1.85447	+	1.85447i	0.140993	+	0.140993i	0.774080	−	0.633088i	$-0.218213\pi$
$173$	1.85447	+	1.85447i	0.140993	+	0.140993i	−0.633088	+	0.774080i	$0.718213\pi$
$174$			11.4682i			0.869405i
$175$	−6.75771	+	13.5919i	−0.510835	+	1.02745i
$176$		0			0
$177$	0.864582	+	0.864582i	0.0649860	+	0.0649860i
$178$	17.9951	+	17.9951i	1.34879	+	1.34879i
$179$			4.79768i			0.358596i	0.983795	+	0.179298i	$0.0573825\pi$
$179$			4.79768i			0.358596i	−0.983795	+	0.179298i	$0.942617\pi$
$180$	2.36780	+	14.4878i	0.176485	+	1.07986i
$181$	−0.951554			−0.0707284			−0.0353642	−	0.999374i	$-0.511259\pi$
$181$	−0.951554			−0.0707284			−0.0353642	+	0.999374i	$0.511259\pi$
$182$	20.8096	−	20.8096i	1.54251	−	1.54251i
$183$	−5.32644	−	5.32644i	−0.393742	−	0.393742i
$184$	−22.0476			−1.62537
$185$	−0.110559	+	0.153757i	−0.00812842	+	0.0113044i
$186$		−	2.56313i		−	0.187937i
$187$		0			0
$188$	−24.2552	+	24.2552i	−1.76899	+	1.76899i
$189$	−15.3743			−1.11831
$190$	−3.08291	−	2.21676i	−0.223658	−	0.160821i
$191$	10.5175			0.761020			0.380510	−	0.924777i	$-0.375748\pi$
$191$	10.5175			0.761020			0.380510	+	0.924777i	$0.375748\pi$
$192$	9.15861	+	9.15861i	0.660966	+	0.660966i
$193$	9.02409	+	9.02409i	0.649569	+	0.649569i	0.952889	−	0.303320i	$-0.0980952\pi$
$193$	9.02409	+	9.02409i	0.649569	+	0.649569i	−0.303320	+	0.952889i	$0.598095\pi$
$194$	10.3268			0.741419
$195$	1.54369	+	9.44536i	0.110546	+	0.676396i
$196$	−7.43970			−0.531407
$197$	7.07191	−	7.07191i	0.503853	−	0.503853i	−0.408780	−	0.912633i	$-0.634046\pi$
$197$	7.07191	−	7.07191i	0.503853	−	0.503853i	0.912633	+	0.408780i	$0.134046\pi$
$198$		0			0
$199$			19.7573i			1.40056i	0.713870	+	0.700278i	$0.246941\pi$
$199$			19.7573i			1.40056i	−0.713870	+	0.700278i	$0.753059\pi$
$200$	−14.0607	−	6.99079i	−0.994241	−	0.494324i
$201$	−5.63190			−0.397244
$202$	−22.6530	−	22.6530i	−1.59386	−	1.59386i
$203$	−10.4085	+	10.4085i	−0.730537	+	0.730537i
$204$	−23.0680			−1.61509
$205$	11.8344	−	1.93414i	0.826549	−	0.135086i
$206$		−	19.4644i		−	1.35615i
$207$	−9.70835	−	9.70835i	−0.674777	−	0.674777i
$208$	1.64361	+	1.64361i	0.113964	+	0.113964i
$209$		0			0
$210$	9.37328	−	13.0357i	0.646817	−	0.899546i
$211$			15.5818i			1.07269i	0.843997	+	0.536347i	$0.180196\pi$
$211$			15.5818i			1.07269i	−0.843997	+	0.536347i	$0.819804\pi$
$212$	−5.38944	−	5.38944i	−0.370148	−	0.370148i
$213$	−10.0500	+	10.0500i	−0.688615	+	0.688615i
$214$			6.55301i			0.447955i
$215$	−3.56040	+	4.95155i	−0.242817	+	0.337693i
$216$		−	15.9045i		−	1.08217i
$217$	2.32629	−	2.32629i	0.157919	−	0.157919i
$218$	5.01454	−	5.01454i	0.339627	−	0.339627i
$219$	2.78306			0.188062
$220$		0			0
$221$	28.1648			1.89457
$222$	0.141644	−	0.141644i	0.00950655	−	0.00950655i
$223$	14.7523	−	14.7523i	0.987890	−	0.987890i	−0.0120377	−	0.999928i	$-0.503832\pi$
$223$	14.7523	−	14.7523i	0.987890	−	0.987890i	0.999928	+	0.0120377i	$0.00383182\pi$
$224$			15.1688i			1.01351i
$225$	−3.11313	−	9.26973i	−0.207542	−	0.617982i
$226$		−	17.4356i		−	1.15980i
$227$	4.72921	−	4.72921i	0.313889	−	0.313889i	−0.532525	−	0.846414i	$-0.678757\pi$
$227$	4.72921	−	4.72921i	0.313889	−	0.313889i	0.846414	+	0.532525i	$0.178757\pi$
$228$	1.77972	+	1.77972i	0.117865	+	0.117865i
$229$		−	28.4289i		−	1.87863i	−0.343054	−	0.939316i	$-0.611461\pi$
$229$		−	28.4289i		−	1.87863i	0.343054	−	0.939316i	$-0.388539\pi$
$230$	35.8571	−	5.86027i	2.36434	−	0.386414i
$231$		0			0
$232$	−10.7676	−	10.7676i	−0.706925	−	0.706925i
$233$	−17.5703	−	17.5703i	−1.15107	−	1.15107i	−0.986339	−	0.164731i	$-0.947324\pi$
$233$	−17.5703	−	17.5703i	−1.15107	−	1.15107i	−0.164731	−	0.986339i	$-0.552676\pi$
$234$			18.9586i			1.23936i
$235$	13.3391	−	18.5511i	0.870149	−	1.21014i
$236$	−4.01650			−0.261452
$237$	7.48562	−	7.48562i	0.486243	−	0.486243i
$238$	−33.4103	−	33.4103i	−2.16566	−	2.16566i
$239$	−13.4336			−0.868947			−0.434473	−	0.900685i	$-0.643065\pi$
$239$	−13.4336			−0.868947			−0.434473	+	0.900685i	$0.643065\pi$
$240$	1.02960	+	0.740329i	0.0664601	+	0.0477880i
$241$		−	10.8836i		−	0.701075i	−0.936549	−	0.350537i	$-0.885999\pi$
$241$		−	10.8836i		−	0.701075i	0.936549	−	0.350537i	$-0.114001\pi$
$242$		0			0
$243$	11.2429	−	11.2429i	0.721233	−	0.721233i
$244$	24.7445			1.58410
$245$	4.89078	−	0.799320i	0.312461	−	0.0510667i
$246$	−12.6839			−0.808696
$247$	−2.17294	−	2.17294i	−0.138261	−	0.138261i
$248$	2.40653	+	2.40653i	0.152814	+	0.152814i
$249$	1.75408			0.111160
$250$	24.7258	+	7.63212i	1.56379	+	0.482698i
$251$	6.92712			0.437236			0.218618	−	0.975811i	$-0.429845\pi$
$251$	6.92712			0.437236			0.218618	+	0.975811i	$0.429845\pi$
$252$	14.0930	−	14.0930i	0.887775	−	0.887775i
$253$		0			0
$254$		−	5.31691i		−	0.333612i
$255$	15.1647	−	2.47843i	0.949650	−	0.155205i
$256$	−19.4179			−1.21362
$257$	8.75919	+	8.75919i	0.546383	+	0.546383i	0.925393	−	0.379010i	$-0.123735\pi$
$257$	8.75919	+	8.75919i	0.546383	+	0.546383i	−0.379010	+	0.925393i	$0.623735\pi$
$258$	4.56149	−	4.56149i	0.283986	−	0.283986i
$259$	0.257112			0.0159762
$260$	−25.5253	−	18.3540i	−1.58301	−	1.13826i
$261$		−	9.48269i		−	0.586964i
$262$	−3.36445	−	3.36445i	−0.207856	−	0.207856i
$263$	10.5123	+	10.5123i	0.648216	+	0.648216i	0.952562	−	0.304346i	$-0.0984378\pi$
$263$	10.5123	+	10.5123i	0.648216	+	0.648216i	−0.304346	+	0.952562i	$0.598438\pi$
$264$		0			0
$265$	4.12200	+	2.96392i	0.253212	+	0.182072i
$266$			5.15525i			0.316089i
$267$	7.94526	+	7.94526i	0.486242	+	0.486242i
$268$	13.0818	−	13.0818i	0.799096	−	0.799096i
$269$			7.12439i			0.434382i	0.976129	+	0.217191i	$0.0696894\pi$
$269$			7.12439i			0.434382i	−0.976129	+	0.217191i	$0.930311\pi$
$270$	4.22744	+	25.8663i	0.257274	+	1.57417i
$271$			25.4315i			1.54485i	0.635106	+	0.772425i	$0.280957\pi$
$271$			25.4315i			1.54485i	−0.635106	+	0.772425i	$0.719043\pi$
$272$	2.63884	−	2.63884i	0.160003	−	0.160003i
$273$	9.18797	−	9.18797i	0.556081	−	0.556081i
$274$	11.6300			0.702594
$275$		0			0
$276$	−24.0828			−1.44961
$277$	−2.18052	+	2.18052i	−0.131015	+	0.131015i	−0.769573	−	0.638559i	$-0.779531\pi$
$277$	−2.18052	+	2.18052i	−0.131015	+	0.131015i	0.638559	+	0.769573i	$0.279531\pi$
$278$	3.20482	−	3.20482i	0.192213	−	0.192213i
$279$			2.11936i			0.126883i
$280$	3.43862	+	21.0398i	0.205497	+	1.25737i
$281$		−	28.5493i		−	1.70311i	−0.524268	−	0.851554i	$-0.675661\pi$
$281$		−	28.5493i		−	1.70311i	0.524268	−	0.851554i	$-0.324339\pi$
$282$	−17.0897	+	17.0897i	−1.01768	+	1.01768i
$283$	18.8323	+	18.8323i	1.11947	+	1.11947i	0.991820	+	0.127646i	$0.0407423\pi$
$283$	18.8323	+	18.8323i	1.11947	+	1.11947i	0.127646	+	0.991820i	$0.459258\pi$
$284$		−	46.6882i		−	2.77044i
$285$	−1.36118	−	0.978755i	−0.0806293	−	0.0579764i
$286$		0			0
$287$	−11.5119	−	11.5119i	−0.679525	−	0.679525i
$288$	−6.90976	−	6.90976i	−0.407162	−	0.407162i
$289$		−	28.2191i		−	1.65995i
$290$	20.3738	+	14.6498i	1.19639	+	0.860265i
$291$	4.55952			0.267284
$292$	−6.46450	+	6.46450i	−0.378306	+	0.378306i
$293$	10.7750	+	10.7750i	0.629480	+	0.629480i	0.947937	−	0.318457i	$-0.103165\pi$
$293$	10.7750	+	10.7750i	0.629480	+	0.629480i	−0.318457	+	0.947937i	$0.603165\pi$
$294$	−5.24186			−0.305712
$295$	2.64041	−	0.431532i	0.153730	−	0.0251248i
$296$			0.265981i			0.0154598i
$297$		0			0
$298$	17.5410	−	17.5410i	1.01612	−	1.01612i
$299$	29.4038			1.70046
$300$	−15.3586	−	7.63611i	−0.886731	−	0.440871i
$301$	8.27999			0.477251
$302$	−30.1357	−	30.1357i	−1.73412	−	1.73412i
$303$	−10.0019	−	10.0019i	−0.574592	−	0.574592i
$304$	−0.407177			−0.0233532
$305$	−16.2668	+	2.65854i	−0.931432	+	0.152228i
$306$	30.4383			1.74004
$307$	16.7363	−	16.7363i	0.955194	−	0.955194i	−0.0438445	−	0.999038i	$-0.513961\pi$
$307$	16.7363	−	16.7363i	0.955194	−	0.955194i	0.999038	+	0.0438445i	$0.0139606\pi$
$308$		0			0
$309$		−	8.59403i		−	0.488897i
$310$	−4.55351	−	3.27419i	−0.258622	−	0.185962i
$311$	−0.487252			−0.0276295			−0.0138148	−	0.999905i	$-0.504398\pi$
$311$	−0.487252			−0.0276295			−0.0138148	+	0.999905i	$0.504398\pi$
$312$	9.50487	+	9.50487i	0.538107	+	0.538107i
$313$	−3.51069	+	3.51069i	−0.198436	+	0.198436i	−0.799329	−	0.600893i	$-0.794812\pi$
$313$	−3.51069	+	3.51069i	−0.198436	+	0.198436i	0.600893	+	0.799329i	$0.294812\pi$
$314$	−40.7746			−2.30105
$315$	−7.75044	+	10.7787i	−0.436688	+	0.607313i
$316$			34.7752i			1.95626i
$317$	18.2251	+	18.2251i	1.02362	+	1.02362i	0.999714	+	0.0239077i	$0.00761078\pi$
$317$	18.2251	+	18.2251i	1.02362	+	1.02362i	0.0239077	+	0.999714i	$0.492389\pi$
$318$	−3.79729	−	3.79729i	−0.212941	−	0.212941i
$319$		0			0
$320$	27.9701	−	4.57126i	1.56358	−	0.255541i
$321$			2.89332i			0.161489i
$322$	−34.8799	−	34.8799i	−1.94378	−	1.94378i
$323$	−3.48869	+	3.48869i	−0.194116	+	0.194116i
$324$			2.32262i			0.129035i
$325$	18.7520	+	9.32327i	1.04018	+	0.517162i
$326$		−	32.3457i		−	1.79146i
$327$	2.21404	−	2.21404i	0.122437	−	0.122437i
$328$	11.9090	−	11.9090i	0.657562	−	0.657562i
$329$	−31.0212			−1.71025
$330$		0			0
$331$	−30.1887			−1.65932			−0.829660	−	0.558270i	$-0.811465\pi$
$331$	−30.1887			−1.65932			−0.829660	+	0.558270i	$0.811465\pi$
$332$	−4.07438	+	4.07438i	−0.223610	+	0.223610i
$333$	−0.117121	+	0.117121i	−0.00641819	+	0.00641819i
$334$		−	3.47983i		−	0.190408i
$335$	−7.19432	+	10.0053i	−0.393068	+	0.546649i
$336$		−	1.72169i		−	0.0939260i
$337$	−9.61794	+	9.61794i	−0.523923	+	0.523923i	−0.918754	−	0.394831i	$-0.870803\pi$
$337$	−9.61794	+	9.61794i	−0.523923	+	0.523923i	0.394831	+	0.918754i	$0.370803\pi$
$338$	−7.43424	−	7.43424i	−0.404369	−	0.404369i
$339$		−	7.69824i		−	0.418111i
$340$	−29.4676	+	40.9814i	−1.59811	+	2.22253i
$341$		0			0
$342$	−2.34834	−	2.34834i	−0.126984	−	0.126984i
$343$	10.2691	+	10.2691i	0.554478	+	0.554478i
$344$			8.56558i			0.461825i
$345$	15.8318	−	2.58745i	0.852354	−	0.139304i
$346$	−6.07003			−0.326327
$347$	−17.1449	+	17.1449i	−0.920386	+	0.920386i	−0.997056	−	0.0766709i	$-0.975571\pi$
$347$	−17.1449	+	17.1449i	−0.920386	+	0.920386i	0.0766709	+	0.997056i	$0.475571\pi$
$348$	−11.7615	−	11.7615i	−0.630483	−	0.630483i
$349$	10.5166			0.562938			0.281469	−	0.959570i	$-0.409178\pi$
$349$	10.5166			0.562938			0.281469	+	0.959570i	$0.409178\pi$
$350$	−11.1848	−	33.3041i	−0.597853	−	1.78018i
$351$			21.2111i			1.13216i
$352$		0			0
$353$	7.93178	−	7.93178i	0.422166	−	0.422166i	−0.463783	−	0.885949i	$-0.653508\pi$
$353$	7.93178	−	7.93178i	0.422166	−	0.422166i	0.885949	+	0.463783i	$0.153508\pi$
$354$	−2.82995			−0.150410
$355$	5.01618	+	30.6924i	0.266231	+	1.62898i
$356$	−36.9105			−1.95625
$357$	−14.7514	−	14.7514i	−0.780729	−	0.780729i
$358$	−7.85187	−	7.85187i	−0.414984	−	0.414984i
$359$	−32.7114			−1.72644			−0.863222	−	0.504824i	$-0.831557\pi$
$359$	−32.7114			−1.72644			−0.863222	+	0.504824i	$0.831557\pi$
$360$	−11.1505	−	8.01776i	−0.587684	−	0.422573i
$361$	−18.4617			−0.971668
$362$	1.55731	−	1.55731i	0.0818504	−	0.0818504i
$363$		0			0
$364$			42.6836i			2.23723i
$365$	3.55515	−	4.94424i	0.186085	−	0.258793i
$366$	17.4345			0.911314
$367$	−20.7693	−	20.7693i	−1.08415	−	1.08415i	−0.996118	−	0.0880284i	$-0.971943\pi$
$367$	−20.7693	−	20.7693i	−1.08415	−	1.08415i	−0.0880284	−	0.996118i	$-0.528057\pi$
$368$	2.75492	−	2.75492i	0.143610	−	0.143610i
$369$	10.4879			0.545978
$370$	−0.0706979	−	0.432577i	−0.00367541	−	0.0224886i
$371$		−	6.89282i		−	0.357858i
$372$	2.62867	+	2.62867i	0.136290	+	0.136290i
$373$	22.9546	+	22.9546i	1.18854	+	1.18854i	0.977470	+	0.211074i	$0.0676963\pi$
$373$	22.9546	+	22.9546i	1.18854	+	1.18854i	0.211074	+	0.977470i	$0.432304\pi$
$374$		0			0
$375$	10.9170	+	3.36977i	0.563753	+	0.174014i
$376$		−	32.0911i		−	1.65497i
$377$	14.3602	+	14.3602i	0.739585	+	0.739585i
$378$	25.1615	−	25.1615i	1.29417	−	1.29417i
$379$			26.1879i			1.34518i	0.740015	+	0.672590i	$0.234818\pi$
$379$			26.1879i			1.34518i	−0.740015	+	0.672590i	$0.765182\pi$
$380$	5.43520	−	0.888296i	0.278820	−	0.0455686i
$381$		−	2.34755i		−	0.120268i
$382$	−17.2129	+	17.2129i	−0.880689	+	0.880689i
$383$	−24.5679	+	24.5679i	−1.25536	+	1.25536i	−0.302081	+	0.953282i	$0.597681\pi$
$383$	−24.5679	+	24.5679i	−1.25536	+	1.25536i	−0.953282	+	0.302081i	$0.902319\pi$
$384$	−19.7658			−1.00867
$385$		0			0
$386$	−29.5376			−1.50342
$387$	−3.77174	+	3.77174i	−0.191728	+	0.191728i
$388$	−10.5909	+	10.5909i	−0.537669	+	0.537669i
$389$			17.0667i			0.865317i	0.901558	+	0.432659i	$0.142424\pi$
$389$			17.0667i			0.865317i	−0.901558	+	0.432659i	$0.857576\pi$
$390$	−17.9846	−	12.9318i	−0.910688	−	0.654829i
$391$		−	47.2083i		−	2.38743i
$392$	4.92160	−	4.92160i	0.248578	−	0.248578i
$393$	−1.48549	−	1.48549i	−0.0749330	−	0.0749330i
$394$			23.1477i			1.16617i
$395$	−3.73624	−	22.8608i	−0.187990	−	1.15025i
$396$		0			0
$397$	3.11088	+	3.11088i	0.156130	+	0.156130i	0.780850	−	0.624719i	$-0.214787\pi$
$397$	3.11088	+	3.11088i	0.156130	+	0.156130i	−0.624719	+	0.780850i	$0.714787\pi$
$398$	−32.3347	−	32.3347i	−1.62079	−	1.62079i
$399$			2.27617i			0.113951i
$400$	2.63046	−	0.883408i	0.131523	−	0.0441704i
$401$	25.9754			1.29715			0.648576	−	0.761150i	$-0.275365\pi$
$401$	25.9754			1.29715			0.648576	+	0.761150i	$0.275365\pi$
$402$	9.21715	−	9.21715i	0.459710	−	0.459710i
$403$	−3.20946	−	3.20946i	−0.159875	−	0.159875i
$404$	46.4646			2.31170
$405$	−0.249542	−	1.52687i	−0.0123999	−	0.0758707i
$406$		−	34.0692i		−	1.69083i
$407$		0			0
$408$	15.2602	−	15.2602i	0.755495	−	0.755495i
$409$	−5.76537			−0.285079			−0.142540	−	0.989789i	$-0.545527\pi$
$409$	−5.76537			−0.285079			−0.142540	+	0.989789i	$0.545527\pi$
$410$	−16.2027	+	22.5335i	−0.800195	+	1.11285i
$411$	5.13493			0.253288
$412$	19.9622	+	19.9622i	0.983467	+	0.983467i
$413$	−2.56845	−	2.56845i	−0.126385	−	0.126385i
$414$	31.7773			1.56177
$415$	2.24070	−	3.11620i	0.109992	−	0.152968i
$416$	20.9277			1.02606
$417$	1.41501	−	1.41501i	0.0692933	−	0.0692933i
$418$		0			0
$419$			15.1605i			0.740637i	0.928905	+	0.370318i	$0.120751\pi$
$419$			15.1605i			0.740637i	−0.928905	+	0.370318i	$0.879249\pi$
$420$	3.75604	+	22.9820i	0.183276	+	1.12141i
$421$	−7.49994			−0.365525			−0.182762	−	0.983157i	$-0.558504\pi$
$421$	−7.49994			−0.365525			−0.182762	+	0.983157i	$0.558504\pi$
$422$	−25.5011	−	25.5011i	−1.24137	−	1.24137i
$423$	14.1309	−	14.1309i	0.687067	−	0.687067i
$424$	7.13057			0.346291
$425$	14.9687	−	30.1068i	0.726088	−	1.46039i
$426$		−	32.8956i		−	1.59380i
$427$	15.8235	+	15.8235i	0.765752	+	0.765752i
$428$	−6.72059	−	6.72059i	−0.324852	−	0.324852i
$429$		0			0
$430$	−2.27674	−	13.9306i	−0.109794	−	0.671794i
$431$			1.92476i			0.0927124i	0.998925	+	0.0463562i	$0.0147609\pi$
$431$			1.92476i			0.0927124i	−0.998925	+	0.0463562i	$0.985239\pi$
$432$	1.98733	+	1.98733i	0.0956153	+	0.0956153i
$433$	−1.69314	+	1.69314i	−0.0813672	+	0.0813672i	−0.746619	−	0.665252i	$-0.768324\pi$
$433$	−1.69314	+	1.69314i	−0.0813672	+	0.0813672i	0.665252	+	0.746619i	$0.268324\pi$
$434$			7.61439i			0.365503i
$435$	8.99555	+	6.46824i	0.431303	+	0.310128i
$436$			10.2855i			0.492588i
$437$	−3.64215	+	3.64215i	−0.174228	+	0.174228i
$438$	−4.55475	+	4.55475i	−0.217635	+	0.217635i
$439$	−4.93496			−0.235533			−0.117767	−	0.993041i	$-0.537573\pi$
$439$	−4.93496			−0.235533			−0.117767	+	0.993041i	$0.537573\pi$
$440$		0			0
$441$	4.33432			0.206396
$442$	−46.0944	+	46.0944i	−2.19249	+	2.19249i
$443$	8.89908	−	8.89908i	0.422808	−	0.422808i	−0.463361	−	0.886169i	$-0.653357\pi$
$443$	8.89908	−	8.89908i	0.422808	−	0.422808i	0.886169	+	0.463361i	$0.153357\pi$
$444$			0.290533i			0.0137881i
$445$	24.2646	−	3.96566i	1.15025	−	0.187990i
$446$			48.2873i			2.28647i
$447$	7.74478	−	7.74478i	0.366315	−	0.366315i
$448$	−27.2079	−	27.2079i	−1.28545	−	1.28545i
$449$			15.0054i			0.708150i	0.935217	+	0.354075i	$0.115204\pi$
$449$			15.0054i			0.708150i	−0.935217	+	0.354075i	$0.884796\pi$
$450$	20.2658	+	10.0759i	0.955337	+	0.474981i
$451$		0			0
$452$	17.8815	+	17.8815i	0.841073	+	0.841073i
$453$	−13.3057	−	13.3057i	−0.625155	−	0.625155i
$454$			15.4796i			0.726494i
$455$	−4.58592	−	28.0597i	−0.214991	−	1.31546i
$456$	−2.35468			−0.110268
$457$	0.633937	−	0.633937i	0.0296543	−	0.0296543i	−0.692124	−	0.721778i	$-0.743325\pi$
$457$	0.633937	−	0.633937i	0.0296543	−	0.0296543i	0.721778	+	0.692124i	$0.243325\pi$
$458$	46.5266	+	46.5266i	2.17404	+	2.17404i
$459$	34.0548			1.58954
$460$	−30.7639	+	42.7842i	−1.43437	+	1.99482i
$461$		−	4.51026i		−	0.210064i	−0.994469	−	0.105032i	$-0.966506\pi$
$461$		−	4.51026i		−	0.210064i	0.994469	−	0.105032i	$-0.0334945\pi$
$462$		0			0
$463$	−16.0636	+	16.0636i	−0.746539	+	0.746539i	−0.973827	−	0.227289i	$-0.927014\pi$
$463$	−16.0636	+	16.0636i	−0.746539	+	0.746539i	0.227289	+	0.973827i	$0.427014\pi$
$464$	2.69089			0.124921
$465$	−2.01049	−	1.44564i	−0.0932340	−	0.0670398i
$466$	57.5110			2.66415
$467$	13.3301	+	13.3301i	0.616842	+	0.616842i	0.944720	−	0.327878i	$-0.106334\pi$
$467$	13.3301	+	13.3301i	0.616842	+	0.616842i	−0.327878	+	0.944720i	$0.606334\pi$
$468$	−19.4434	−	19.4434i	−0.898771	−	0.898771i
$469$	16.7309			0.772563
$470$	8.52985	+	52.1914i	0.393453	+	2.40741i
$471$	−18.0030			−0.829534
$472$	2.65704	−	2.65704i	0.122300	−	0.122300i
$473$		0			0
$474$			24.5019i			1.12541i
$475$	−3.47760	+	1.16791i	−0.159563	+	0.0535875i
$476$	68.5293			3.14103
$477$	3.13985	+	3.13985i	0.143764	+	0.143764i
$478$	21.9854	−	21.9854i	1.00559	−	1.00559i
$479$	16.9039			0.772360			0.386180	−	0.922423i	$-0.373794\pi$
$479$	16.9039			0.772360			0.386180	+	0.922423i	$0.373794\pi$
$480$	11.2680	−	1.84158i	0.514312	−	0.0840561i
$481$		−	0.354725i		−	0.0161741i
$482$	17.8121	+	17.8121i	0.811318	+	0.811318i
$483$	−15.4004	−	15.4004i	−0.700740	−	0.700740i
$484$		0			0
$485$	5.82444	−	8.10020i	0.264474	−	0.367811i
$486$			36.8002i			1.66929i
$487$	7.62190	+	7.62190i	0.345381	+	0.345381i	0.858386	−	0.513005i	$-0.171468\pi$
$487$	7.62190	+	7.62190i	0.345381	+	0.345381i	−0.513005	+	0.858386i	$0.671468\pi$
$488$	−16.3693	+	16.3693i	−0.741001	+	0.741001i
$489$		−	14.2814i		−	0.645829i
$490$	−6.69607	+	9.31240i	−0.302498	+	0.420691i
$491$		−	27.1196i		−	1.22389i	−0.790901	−	0.611944i	$-0.790388\pi$
$491$		−	27.1196i		−	1.22389i	0.790901	−	0.611944i	$-0.209612\pi$
$492$	13.0083	−	13.0083i	0.586458	−	0.586458i
$493$	23.0555	−	23.0555i	1.03837	−	1.03837i
$494$	7.11244			0.320004
$495$		0			0
$496$	−0.601407			−0.0270040
$497$	29.8560	−	29.8560i	1.33922	−	1.33922i
$498$	−2.87072	+	2.87072i	−0.128640	+	0.128640i
$499$			22.7394i			1.01795i	0.860780	+	0.508977i	$0.169976\pi$
$499$			22.7394i			1.01795i	−0.860780	+	0.508977i	$0.830024\pi$
$500$	−33.1854	+	17.5308i	−1.48409	+	0.783999i
$501$		−	1.53643i		−	0.0686427i
$502$	−11.3369	+	11.3369i	−0.505991	+	0.505991i
$503$	−4.25456	−	4.25456i	−0.189701	−	0.189701i	0.605866	−	0.795567i	$-0.292827\pi$
$503$	−4.25456	−	4.25456i	−0.189701	−	0.189701i	−0.795567	+	0.605866i	$0.792827\pi$
$504$			18.6459i			0.830556i
$505$	−30.5453	+	4.99215i	−1.35925	+	0.222148i
$506$		0			0
$507$	−3.28240	−	3.28240i	−0.145777	−	0.145777i
$508$	5.45288	+	5.45288i	0.241932	+	0.241932i
$509$			30.2574i			1.34114i	0.741848	+	0.670568i	$0.233949\pi$
$509$			30.2574i			1.34114i	−0.741848	+	0.670568i	$0.766051\pi$
$510$	−20.7623	+	28.8747i	−0.919370	+	1.27859i
$511$	−8.26777			−0.365745
$512$	4.42560	−	4.42560i	0.195586	−	0.195586i
$513$	−2.62735	−	2.62735i	−0.116000	−	0.116000i
$514$	−28.6705			−1.26460
$515$	−15.2677	−	10.9782i	−0.672774	−	0.483758i
$516$			9.35627i			0.411887i
$517$		0			0
$518$	−0.420789	+	0.420789i	−0.0184884	+	0.0184884i
$519$	−2.68007			−0.117642
$520$	29.0276	−	4.74409i	1.27294	−	0.208042i
$521$	−38.4122			−1.68287			−0.841433	−	0.540361i	$-0.818288\pi$
$521$	−38.4122			−1.68287			−0.841433	+	0.540361i	$0.818288\pi$
$522$	15.5193	+	15.5193i	0.679263	+	0.679263i
$523$	13.1985	+	13.1985i	0.577132	+	0.577132i	0.934112	−	0.356980i	$-0.116194\pi$
$523$	13.1985	+	13.1985i	0.577132	+	0.577132i	−0.356980	+	0.934112i	$0.616194\pi$
$524$	6.90098			0.301471
$525$	−4.93836	−	14.7046i	−0.215528	−	0.641760i
$526$	−34.4088			−1.50029
$527$	−5.15285	+	5.15285i	−0.224462	+	0.224462i
$528$		0			0
$529$		−	26.2849i		−	1.14282i
$530$	−11.5968	+	1.89531i	−0.503732	+	0.0823270i
$531$	2.33999			0.101547
$532$	−5.28708	−	5.28708i	−0.229224	−	0.229224i
$533$	−15.8824	+	15.8824i	−0.687942	+	0.687942i
$534$	−26.0064			−1.12541
$535$	5.14010	+	3.69599i	0.222226	+	0.159791i
$536$			17.3080i			0.747592i
$537$	−3.46679	−	3.46679i	−0.149603	−	0.149603i
$538$	−11.6597	−	11.6597i	−0.502687	−	0.502687i
$539$		0			0
$540$	−30.8633	−	22.1922i	−1.32815	−	0.955002i
$541$		−	30.4015i		−	1.30706i	−0.756900	−	0.653531i	$-0.773287\pi$
$541$		−	30.4015i		−	1.30706i	0.756900	−	0.653531i	$-0.226713\pi$
$542$	−41.6210	−	41.6210i	−1.78778	−	1.78778i
$543$	0.687591	−	0.687591i	0.0295073	−	0.0295073i
$544$		−	33.5997i		−	1.44058i
$545$	−1.10508	−	6.76161i	−0.0473363	−	0.289636i
$546$			30.0740i			1.28705i
$547$	30.2121	−	30.2121i	1.29178	−	1.29178i	0.358091	−	0.933687i	$-0.383428\pi$
$547$	30.2121	−	30.2121i	1.29178	−	1.29178i	0.933687	−	0.358091i	$-0.116572\pi$
$548$	−11.9274	+	11.9274i	−0.509514	+	0.509514i
$549$	−14.4160			−0.615258
$550$		0			0
$551$	−3.55750			−0.151554
$552$	15.9315	−	15.9315i	0.678091	−	0.678091i
$553$	−22.2379	+	22.2379i	−0.945650	+	0.945650i
$554$		−	7.13726i		−	0.303233i
$555$	−0.0312148	−	0.190994i	−0.00132500	−	0.00810722i
$556$			6.57356i			0.278781i
$557$	1.60744	−	1.60744i	0.0681094	−	0.0681094i	−0.672232	−	0.740341i	$-0.734664\pi$
$557$	1.60744	−	1.60744i	0.0681094	−	0.0681094i	0.740341	+	0.672232i	$0.234664\pi$
$558$	−3.46854	−	3.46854i	−0.146835	−	0.146835i
$559$		−	11.4235i		−	0.483162i
$560$	−3.05866	−	2.19933i	−0.129252	−	0.0929386i
$561$		0			0
$562$	46.7237	+	46.7237i	1.97092	+	1.97092i
$563$	5.17531	+	5.17531i	0.218114	+	0.218114i	0.807703	−	0.589590i	$-0.200710\pi$
$563$	5.17531	+	5.17531i	0.218114	+	0.218114i	−0.589590	+	0.807703i	$0.700710\pi$
$564$		−	35.0535i		−	1.47602i
$565$	−13.6763	−	9.83390i	−0.575365	−	0.413715i
$566$	−61.6419			−2.59100
$567$	−1.48526	+	1.48526i	−0.0623751	+	0.0623751i
$568$	30.8857	+	30.8857i	1.29594	+	1.29594i
$569$	−26.8384			−1.12513			−0.562563	−	0.826754i	$-0.690185\pi$
$569$	−26.8384			−1.12513			−0.562563	+	0.826754i	$0.690185\pi$
$570$	3.82953	−	0.625875i	0.160401	−	0.0262150i
$571$			26.2105i			1.09687i	0.836192	+	0.548437i	$0.184777\pi$
$571$			26.2105i			1.09687i	−0.836192	+	0.548437i	$0.815223\pi$
$572$		0			0
$573$	−7.59993	+	7.59993i	−0.317492	+	0.317492i
$574$	37.6806			1.57276
$575$	15.6271	−	31.4311i	0.651697	−	1.31077i
$576$	24.7877			1.03282
$577$	−7.99392	−	7.99392i	−0.332791	−	0.332791i	0.520854	−	0.853646i	$-0.325613\pi$
$577$	−7.99392	−	7.99392i	−0.332791	−	0.332791i	−0.853646	+	0.520854i	$0.825613\pi$
$578$	46.1833	+	46.1833i	1.92097	+	1.92097i
$579$	−13.0416			−0.541990
$580$	−35.9193	+	5.87043i	−1.49147	+	0.243756i
$581$	−5.21093			−0.216186
$582$	−7.46210	+	7.46210i	−0.309314	+	0.309314i
$583$		0			0
$584$		−	8.55294i		−	0.353923i
$585$	14.8709	+	10.6929i	0.614835	+	0.442097i
$586$	−35.2686			−1.45693
$587$	26.4761	+	26.4761i	1.09279	+	1.09279i	0.995230	+	0.0975577i	$0.0311031\pi$
$587$	26.4761	+	26.4761i	1.09279	+	1.09279i	0.0975577	+	0.995230i	$0.468897\pi$
$588$	5.37591	−	5.37591i	0.221699	−	0.221699i
$589$	0.795093			0.0327612
$590$	−3.61504	+	5.02752i	−0.148829	+	0.206980i
$591$			10.2203i			0.420407i
$592$	−0.0332352	−	0.0332352i	−0.00136596	−	0.00136596i
$593$	19.3337	+	19.3337i	0.793940	+	0.793940i	0.982132	−	0.188192i	$-0.0602627\pi$
$593$	19.3337	+	19.3337i	0.793940	+	0.793940i	−0.188192	+	0.982132i	$0.560263\pi$
$594$		0			0
$595$	−45.0504	+	7.36278i	−1.84689	+	0.301844i
$596$			35.9791i			1.47376i
$597$	−14.2766	−	14.2766i	−0.584301	−	0.584301i
$598$	−48.1221	+	48.1221i	−1.96786	+	1.96786i
$599$			1.13930i			0.0465504i	0.999729	+	0.0232752i	$0.00740939\pi$
$599$			1.13930i			0.0465504i	−0.999729	+	0.0232752i	$0.992591\pi$
$600$	15.2118	−	5.10869i	0.621017	−	0.208562i
$601$			26.8026i			1.09330i	0.837360	+	0.546651i	$0.184098\pi$
$601$			26.8026i			1.09330i	−0.837360	+	0.546651i	$0.815902\pi$
$602$	−13.5510	+	13.5510i	−0.552298	+	0.552298i
$603$	−7.62135	+	7.62135i	−0.310365	+	0.310365i
$604$	61.8128			2.51513
$605$		0			0
$606$	32.7380			1.32989
$607$	10.2358	−	10.2358i	0.415457	−	0.415457i	−0.468178	−	0.883634i	$-0.655089\pi$
$607$	10.2358	−	10.2358i	0.415457	−	0.415457i	0.883634	+	0.468178i	$0.155089\pi$
$608$	−2.59224	+	2.59224i	−0.105129	+	0.105129i
$609$		−	15.0424i		−	0.609548i
$610$	22.2712	−	30.9731i	0.901733	−	1.25406i
$611$			42.7983i			1.73144i
$612$	−31.2167	+	31.2167i	−1.26186	+	1.26186i
$613$	−18.2601	−	18.2601i	−0.737517	−	0.737517i	0.234580	−	0.972097i	$-0.424629\pi$
$613$	−18.2601	−	18.2601i	−0.737517	−	0.737517i	−0.972097	+	0.234580i	$0.924629\pi$
$614$			54.7813i			2.21079i
$615$	−7.15389	+	9.94911i	−0.288473	+	0.401187i
$616$		0			0
$617$	−33.8317	−	33.8317i	−1.36201	−	1.36201i	−0.871348	−	0.490665i	$-0.836754\pi$
$617$	−33.8317	−	33.8317i	−1.36201	−	1.36201i	−0.490665	−	0.871348i	$-0.663246\pi$
$618$	14.0650	+	14.0650i	0.565776	+	0.565776i
$619$		−	35.4561i		−	1.42510i	−0.701620	−	0.712551i	$-0.747540\pi$
$619$		−	35.4561i		−	1.42510i	0.701620	−	0.712551i	$-0.252460\pi$
$620$	8.02788	−	1.31203i	0.322407	−	0.0526923i
$621$	35.5528			1.42669
$622$	0.797435	−	0.797435i	0.0319742	−	0.0319742i
$623$	−23.6033	−	23.6033i	−0.945648	−	0.945648i
$624$	−2.37533			−0.0950894
$625$	19.9322	−	15.0900i	0.797288	−	0.603599i
$626$		−	11.4912i		−	0.459280i
$627$		0			0
$628$	41.8173	−	41.8173i	1.66869	−	1.66869i
$629$	−0.569518			−0.0227082
$630$	−4.95610	−	30.3248i	−0.197456	−	1.20817i
$631$	14.7401			0.586793			0.293397	−	0.955991i	$-0.405214\pi$
$631$	14.7401			0.586793			0.293397	+	0.955991i	$0.405214\pi$
$632$	−23.0049	−	23.0049i	−0.915084	−	0.915084i
$633$	−11.2594	−	11.2594i	−0.447520	−	0.447520i
$634$	−59.6542			−2.36917
$635$	−4.17052	−	2.99881i	−0.165502	−	0.119004i
$636$	7.78879			0.308846
$637$	−6.56369	+	6.56369i	−0.260063	+	0.260063i
$638$		0			0
$639$			27.2002i			1.07602i
$640$	−25.2492	+	35.1148i	−0.998063	+	1.38803i
$641$	−17.3243			−0.684269			−0.342134	−	0.939651i	$-0.611150\pi$
$641$	−17.3243			−0.684269			−0.342134	+	0.939651i	$0.611150\pi$
$642$	−4.73519	−	4.73519i	−0.186883	−	0.186883i
$643$	14.2891	−	14.2891i	0.563506	−	0.563506i	−0.366796	−	0.930302i	$-0.619545\pi$
$643$	14.2891	−	14.2891i	0.563506	−	0.563506i	0.930302	+	0.366796i	$0.119545\pi$
$644$	71.5438			2.81922
$645$	−1.00524	−	6.15071i	−0.0395811	−	0.242184i
$646$		−	11.4192i		−	0.449281i
$647$	−24.1484	−	24.1484i	−0.949372	−	0.949372i	0.0494070	−	0.998779i	$-0.484267\pi$
$647$	−24.1484	−	24.1484i	−0.949372	−	0.949372i	−0.998779	+	0.0494070i	$0.984267\pi$
$648$	−1.53649	−	1.53649i	−0.0603590	−	0.0603590i
$649$		0			0
$650$	−45.9480	+	15.4311i	−1.80223	+	0.605258i
$651$			3.36194i			0.131765i
$652$	33.1729	+	33.1729i	1.29915	+	1.29915i
$653$	−26.0653	+	26.0653i	−1.02001	+	1.02001i	−0.0202168	+	0.999796i	$0.506436\pi$
$653$	−26.0653	+	26.0653i	−1.02001	+	1.02001i	−0.999796	+	0.0202168i	$0.993564\pi$
$654$			7.24699i			0.283380i
$655$	−4.53663	+	0.741440i	−0.177261	+	0.0289705i
$656$			2.97613i			0.116198i
$657$	3.76617	−	3.76617i	0.146932	−	0.146932i
$658$	50.7691	−	50.7691i	1.97919	−	1.97919i
$659$	42.3793			1.65086			0.825432	−	0.564501i	$-0.190931\pi$
$659$	42.3793			1.65086			0.825432	+	0.564501i	$0.190931\pi$
$660$		0			0
$661$	1.78019			0.0692412			0.0346206	−	0.999401i	$-0.488978\pi$
$661$	1.78019			0.0692412			0.0346206	+	0.999401i	$0.488978\pi$
$662$	49.4067	−	49.4067i	1.92024	−	1.92024i
$663$	−20.3518	+	20.3518i	−0.790400	+	0.790400i
$664$		−	5.39066i		−	0.209198i
$665$	4.04372	+	2.90763i	0.156809	+	0.112753i
$666$		−	0.383359i		−	0.0148549i
$667$	24.0697	−	24.0697i	0.931982	−	0.931982i
$668$	3.56882	+	3.56882i	0.138082	+	0.138082i
$669$			21.3200i			0.824280i
$670$	−4.60049	−	28.1489i	−0.177732	−	1.08749i
$671$		0			0
$672$	−10.9610	−	10.9610i	−0.422828	−	0.422828i
$673$	−6.31995	−	6.31995i	−0.243616	−	0.243616i	0.574728	−	0.818344i	$-0.305108\pi$
$673$	−6.31995	−	6.31995i	−0.243616	−	0.243616i	−0.818344	+	0.574728i	$0.805108\pi$
$674$		−	31.4814i		−	1.21262i
$675$	22.6736	+	11.2730i	0.872706	+	0.433898i
$676$	15.2487			0.586489
$677$	8.35228	−	8.35228i	0.321004	−	0.321004i	−0.528148	−	0.849152i	$-0.677113\pi$
$677$	8.35228	−	8.35228i	0.321004	−	0.321004i	0.849152	+	0.528148i	$0.177113\pi$
$678$	12.5989	+	12.5989i	0.483858	+	0.483858i
$679$	−13.5452			−0.519816
$680$	−7.61673	−	46.6043i	−0.292088	−	1.78719i
$681$			6.83463i			0.261904i
$682$		0			0
$683$	12.1989	−	12.1989i	0.466779	−	0.466779i	−0.434090	−	0.900869i	$-0.642930\pi$
$683$	12.1989	−	12.1989i	0.466779	−	0.466779i	0.900869	+	0.434090i	$0.142930\pi$
$684$	4.81679			0.184174
$685$	6.55948	−	9.12244i	0.250625	−	0.348550i
$686$	−33.6127			−1.28334
$687$	20.5426	+	20.5426i	0.783750	+	0.783750i
$688$	−1.07030	−	1.07030i	−0.0408048	−	0.0408048i
$689$	−9.50968			−0.362290
$690$	−21.6756	+	30.1449i	−0.825177	+	1.14759i
$691$	12.2552			0.466210			0.233105	−	0.972452i	$-0.425111\pi$
$691$	12.2552			0.466210			0.233105	+	0.972452i	$0.425111\pi$
$692$	6.22526	−	6.22526i	0.236649	−	0.236649i
$693$		0			0
$694$		−	56.1185i		−	2.13023i
$695$	−0.706262	−	4.32139i	−0.0267901	−	0.163920i
$696$	15.5612			0.589847
$697$	25.4995	+	25.4995i	0.965861	+	0.965861i
$698$	−17.2114	+	17.2114i	−0.651459	+	0.651459i
$699$	25.3925			0.960434
$700$	45.6266	+	22.6849i	1.72452	+	0.857410i
$701$			8.29787i			0.313406i	0.987646	+	0.156703i	$0.0500866\pi$
$701$			8.29787i			0.313406i	−0.987646	+	0.156703i	$0.949913\pi$
$702$	−34.7140	−	34.7140i	−1.31020	−	1.31020i
$703$	0.0439387	+	0.0439387i	0.00165718	+	0.00165718i
$704$		0			0
$705$	3.76614	+	23.0438i	0.141841	+	0.867879i
$706$			25.9622i			0.977102i
$707$	29.7130	+	29.7130i	1.11747	+	1.11747i
$708$	2.90231	−	2.90231i	0.109076	−	0.109076i
$709$			37.6735i			1.41486i	0.706784	+	0.707430i	$0.250145\pi$
$709$			37.6735i			1.41486i	−0.706784	+	0.707430i	$0.749855\pi$
$710$	−58.4405	−	42.0216i	−2.19323	−	1.57704i
$711$		−	20.2598i		−	0.759800i
$712$	24.4175	−	24.4175i	0.915083	−	0.915083i
$713$	−5.37952	+	5.37952i	−0.201465	+	0.201465i
$714$	48.2843			1.80700
$715$		0			0
$716$	16.1053			0.601884
$717$	9.70708	−	9.70708i	0.362518	−	0.362518i
$718$	53.5354	−	53.5354i	1.99793	−	1.99793i
$719$		−	50.3250i		−	1.87680i	−0.345545	−	0.938402i	$-0.612306\pi$
$719$		−	50.3250i		−	1.87680i	0.345545	−	0.938402i	$-0.387694\pi$
$720$	2.39514	−	0.391448i	0.0892617	−	0.0145884i
$721$			25.5307i			0.950812i
$722$	30.2143	−	30.2143i	1.12446	−	1.12446i
$723$	7.86447	+	7.86447i	0.292483	+	0.292483i
$724$			3.19427i			0.118714i
$725$	22.9822	−	7.71832i	0.853538	−	0.286651i
$726$		0			0
$727$	12.0396	+	12.0396i	0.446524	+	0.446524i	0.894197	−	0.447673i	$-0.147747\pi$
$727$	12.0396	+	12.0396i	0.446524	+	0.446524i	−0.447673	+	0.894197i	$0.647747\pi$
$728$	−28.2365	−	28.2365i	−1.04652	−	1.04652i
$729$			14.1725i			0.524908i
$730$	2.27338	+	13.9101i	0.0841415	+	0.514835i
$731$	−18.3406			−0.678352
$732$	−17.8803	+	17.8803i	−0.660875	+	0.660875i
$733$	13.1556	+	13.1556i	0.485915	+	0.485915i	0.907014	−	0.421100i	$-0.138356\pi$
$733$	13.1556	+	13.1556i	0.485915	+	0.485915i	−0.421100	+	0.907014i	$0.638356\pi$
$734$	67.9818			2.50925
$735$	−2.95648	+	4.11165i	−0.109051	+	0.151661i
$736$		−	35.0778i		−	1.29298i
$737$		0			0
$738$	−17.1644	+	17.1644i	−0.631832	+	0.631832i
$739$	1.70288			0.0626416			0.0313208	−	0.999509i	$-0.490029\pi$
$739$	1.70288			0.0626416			0.0313208	+	0.999509i	$0.490029\pi$
$740$	0.516145	+	0.371134i	0.0189739	+	0.0136431i
$741$	3.14032			0.115362
$742$	11.2808	+	11.2808i	0.414130	+	0.414130i
$743$	−8.95229	−	8.95229i	−0.328428	−	0.328428i	0.523561	−	0.851988i	$-0.324603\pi$
$743$	−8.95229	−	8.95229i	−0.328428	−	0.328428i	−0.851988	+	0.523561i	$0.824603\pi$
$744$	−3.47790			−0.127506
$745$	−3.86559	−	23.6523i	−0.141624	−	0.866553i
$746$	−75.1349			−2.75088
$747$	2.37370	−	2.37370i	0.0868492	−	0.0868492i
$748$		0			0
$749$		−	8.59530i		−	0.314065i
$750$	−23.3817	+	12.3518i	−0.853780	+	0.451025i
$751$	−33.3301			−1.21623			−0.608116	−	0.793848i	$-0.708075\pi$
$751$	−33.3301			−1.21623			−0.608116	+	0.793848i	$0.708075\pi$
$752$	4.00990	+	4.00990i	0.146226	+	0.146226i
$753$	−5.00552	+	5.00552i	−0.182411	+	0.182411i
$754$	−47.0036			−1.71177
$755$	−40.6351	+	6.64116i	−1.47886	+	0.241696i
$756$			51.6098i			1.87703i
$757$	−17.1101	−	17.1101i	−0.621878	−	0.621878i	0.324133	−	0.946011i	$-0.394927\pi$
$757$	−17.1101	−	17.1101i	−0.621878	−	0.621878i	−0.946011	+	0.324133i	$0.894927\pi$
$758$	−42.8590	−	42.8590i	−1.55671	−	1.55671i
$759$		0			0
$760$	−3.00792	+	4.18319i	−0.109109	+	0.151740i
$761$			15.4727i			0.560886i	0.959871	+	0.280443i	$0.0904813\pi$
$761$			15.4727i			0.560886i	−0.959871	+	0.280443i	$0.909519\pi$
$762$	3.84199	+	3.84199i	0.139180	+	0.139180i
$763$	−6.57735	+	6.57735i	−0.238116	+	0.238116i
$764$		−	35.3062i		−	1.27733i
$765$	17.1676	−	23.8755i	0.620697	−	0.863220i
$766$		−	80.4156i		−	2.90554i
$767$	−3.54357	+	3.54357i	−0.127951	+	0.127951i
$768$	14.0314	−	14.0314i	0.506313	−	0.506313i
$769$	16.4515			0.593255			0.296627	−	0.954993i	$-0.404138\pi$
$769$	16.4515			0.593255			0.296627	+	0.954993i	$0.404138\pi$
$770$		0			0
$771$	−12.6587			−0.455894
$772$	30.2930	−	30.2930i	1.09027	−	1.09027i
$773$	−16.4382	+	16.4382i	−0.591239	+	0.591239i	−0.937966	−	0.346727i	$-0.887293\pi$
$773$	−16.4382	+	16.4382i	−0.591239	+	0.591239i	0.346727	+	0.937966i	$0.387293\pi$
$774$		−	12.3456i		−	0.443754i
$775$	−5.13648	+	1.72503i	−0.184508	+	0.0619648i
$776$		−	14.0124i		−	0.503015i
$777$	−0.185789	+	0.185789i	−0.00666514	+	0.00666514i
$778$	−27.9313	−	27.9313i	−1.00139	−	1.00139i
$779$		−	3.93460i		−	0.140972i
$780$	31.7071	−	5.18202i	1.13530	−	0.185546i
$781$		0			0
$782$	77.2609	+	77.2609i	2.76284	+	2.76284i
$783$	17.3632	+	17.3632i	0.620511	+	0.620511i
$784$			1.22994i			0.0439265i
$785$	−22.9974	+	31.9831i	−0.820814	+	1.14153i
$786$	4.86229			0.173432
$787$	10.4702	−	10.4702i	0.373223	−	0.373223i	−0.495427	−	0.868650i	$-0.664988\pi$
$787$	10.4702	−	10.4702i	0.373223	−	0.373223i	0.868650	+	0.495427i	$0.164988\pi$
$788$	−23.7397	−	23.7397i	−0.845691	−	0.845691i
$789$	−15.1923			−0.540861
$790$	43.5287	+	31.2992i	1.54868	+	1.11358i
$791$			22.8695i			0.813146i
$792$		0			0
$793$	21.8309	−	21.8309i	0.775237	−	0.775237i
$794$	−10.1825			−0.361363
$795$	−5.12027	+	0.836826i	−0.181597	+	0.0296792i
$796$	66.3231			2.35076
$797$	13.2315	+	13.2315i	0.468683	+	0.468683i	0.901488	−	0.432805i	$-0.142476\pi$
$797$	13.2315	+	13.2315i	0.468683	+	0.468683i	−0.432805	+	0.901488i	$0.642476\pi$
$798$	−3.72517	−	3.72517i	−0.131870	−	0.131870i
$799$	68.7135			2.43091
$800$	11.1224	−	22.3706i	0.393235	−	0.790920i
$801$	21.5038			0.759799
$802$	−42.5113	+	42.5113i	−1.50113	+	1.50113i
$803$		0			0
$804$			18.9057i			0.666753i
$805$	−47.0322	+	7.68666i	−1.65767	+	0.270919i
$806$	10.5052			0.370030
$807$	−5.14807	−	5.14807i	−0.181221	−	0.181221i
$808$	−30.7378	+	30.7378i	−1.08135	+	1.08135i
$809$	−16.6913			−0.586836			−0.293418	−	0.955984i	$-0.594793\pi$
$809$	−16.6913			−0.586836			−0.293418	+	0.955984i	$0.594793\pi$
$810$	2.90727	+	2.09047i	0.102151	+	0.0734516i
$811$		−	22.7924i		−	0.800348i	−0.916439	−	0.400174i	$-0.868950\pi$
$811$		−	22.7924i		−	0.800348i	0.916439	−	0.400174i	$-0.131050\pi$
$812$	34.9404	+	34.9404i	1.22617	+	1.22617i
$813$	−18.3767	−	18.3767i	−0.644499	−	0.644499i
$814$		0			0
$815$	−25.3716	−	18.2434i	−0.888728	−	0.639039i
$816$			3.81364i			0.133504i
$817$	1.41499	+	1.41499i	0.0495043	+	0.0495043i
$818$	9.43558	−	9.43558i	0.329907	−	0.329907i
$819$		−	24.8671i		−	0.868929i
$820$	−6.49271	−	39.7268i	−0.226735	−	1.38732i
$821$			2.07713i			0.0724924i	0.999343	+	0.0362462i	$0.0115401\pi$
$821$			2.07713i			0.0724924i	−0.999343	+	0.0362462i	$0.988460\pi$
$822$	−8.40381	+	8.40381i	−0.293117	+	0.293117i
$823$	16.8222	−	16.8222i	0.586385	−	0.586385i	−0.350266	−	0.936650i	$-0.613909\pi$
$823$	16.8222	−	16.8222i	0.586385	−	0.586385i	0.936650	+	0.350266i	$0.113909\pi$
$824$	−26.4113			−0.920080
$825$		0			0
$826$	8.40705			0.292519
$827$	−6.91347	+	6.91347i	−0.240405	+	0.240405i	−0.817018	−	0.576613i	$-0.804374\pi$
$827$	−6.91347	+	6.91347i	−0.240405	+	0.240405i	0.576613	+	0.817018i	$0.304374\pi$
$828$	−32.5899	+	32.5899i	−1.13258	+	1.13258i
$829$		−	48.4415i		−	1.68244i	−0.540690	−	0.841222i	$-0.681837\pi$
$829$		−	48.4415i		−	1.68244i	0.540690	−	0.841222i	$-0.318163\pi$
$830$	1.43284	+	8.76709i	0.0497346	+	0.304310i
$831$		−	3.15128i		−	0.109317i
$832$	−37.5373	+	37.5373i	−1.30137	+	1.30137i
$833$	10.5381	+	10.5381i	0.365124	+	0.365124i
$834$			4.63160i			0.160379i
$835$	−2.72954	−	1.96267i	−0.0944596	−	0.0679211i
$836$		0			0
$837$	−3.88064	−	3.88064i	−0.134135	−	0.134135i
$838$	−24.8116	−	24.8116i	−0.857101	−	0.857101i
$839$			8.88082i			0.306600i	0.988180	+	0.153300i	$0.0489901\pi$
$839$			8.88082i			0.306600i	−0.988180	+	0.153300i	$0.951010\pi$
$840$	−17.6881	−	12.7186i	−0.610296	−	0.438833i
$841$	−5.48979			−0.189303
$842$	12.2744	−	12.2744i	0.423003	−	0.423003i
$843$	20.6296	+	20.6296i	0.710523	+	0.710523i
$844$	52.3065			1.80046
$845$	−10.0243	+	1.63832i	−0.344848	+	0.0563599i
$846$			46.2531i			1.59022i
$847$		0			0
$848$	−0.890989	+	0.890989i	−0.0305967	+	0.0305967i
$849$	−27.2164			−0.934065
$850$	24.7749	+	73.7703i	0.849773	+	2.53030i
$851$	−0.594570			−0.0203816
$852$	33.7368	+	33.7368i	1.15580	+	1.15580i
$853$	−17.3297	−	17.3297i	−0.593358	−	0.593358i	0.345179	−	0.938537i	$-0.387818\pi$
$853$	−17.3297	−	17.3297i	−0.593358	−	0.593358i	−0.938537	+	0.345179i	$0.887818\pi$
$854$	−51.7933			−1.77233
$855$	−3.16651	+	0.517515i	−0.108292	+	0.0176986i
$856$	8.89176			0.303914
$857$	−13.2386	+	13.2386i	−0.452221	+	0.452221i	−0.896091	−	0.443870i	$-0.853605\pi$
$857$	−13.2386	+	13.2386i	−0.452221	+	0.452221i	0.443870	+	0.896091i	$0.353605\pi$
$858$		0			0
$859$		−	9.57133i		−	0.326569i	−0.986579	−	0.163285i	$-0.947791\pi$
$859$		−	9.57133i		−	0.326569i	0.986579	−	0.163285i	$-0.0522089\pi$
$860$	16.6218	+	11.9519i	0.566800	+	0.407557i
$861$	16.6369			0.566985
$862$	−3.15005	−	3.15005i	−0.107291	−	0.107291i
$863$	25.2259	−	25.2259i	0.858700	−	0.858700i	−0.132485	−	0.991185i	$-0.542296\pi$
$863$	25.2259	−	25.2259i	0.858700	−	0.858700i	0.991185	+	0.132485i	$0.0422956\pi$
$864$	25.3042			0.860865
$865$	−3.42358	+	4.76126i	−0.116405	+	0.161888i
$866$		−	5.54198i		−	0.188324i
$867$	20.3911	+	20.3911i	0.692517	+	0.692517i
$868$	−7.80911	−	7.80911i	−0.265059	−	0.265059i
$869$		0			0
$870$	−25.3080	+	4.13619i	−0.858021	+	0.140230i
$871$		−	23.0828i		−	0.782132i
$872$	−6.80421	−	6.80421i	−0.230420	−	0.230420i
$873$	6.17016	−	6.17016i	0.208828	−	0.208828i
$874$		−	11.9215i		−	0.403250i
$875$	−32.4317	−	10.0107i	−1.09639	−	0.338424i
$876$		−	9.34246i		−	0.315652i
$877$	8.11470	−	8.11470i	0.274014	−	0.274014i	−0.556700	−	0.830714i	$-0.687933\pi$
$877$	8.11470	−	8.11470i	0.274014	−	0.274014i	0.830714	+	0.556700i	$0.187933\pi$
$878$	8.07655	−	8.07655i	0.272570	−	0.272570i
$879$	−15.5719			−0.525228
$880$		0			0
$881$	−16.7047			−0.562795			−0.281397	−	0.959591i	$-0.590798\pi$
$881$	−16.7047			−0.562795			−0.281397	+	0.959591i	$0.590798\pi$
$882$	−7.09353	+	7.09353i	−0.238851	+	0.238851i
$883$	6.12619	−	6.12619i	0.206163	−	0.206163i	−0.596472	−	0.802634i	$-0.703431\pi$
$883$	6.12619	−	6.12619i	0.206163	−	0.206163i	0.802634	+	0.596472i	$0.203431\pi$
$884$		−	94.5464i		−	3.17994i
$885$	−1.59613	+	2.21978i	−0.0536532	+	0.0746170i
$886$			29.1284i			0.978589i
$887$	−13.0392	+	13.0392i	−0.437815	+	0.437815i	−0.891276	−	0.453461i	$-0.850189\pi$
$887$	−13.0392	+	13.0392i	−0.437815	+	0.437815i	0.453461	+	0.891276i	$0.350189\pi$
$888$	−0.192197	−	0.192197i	−0.00644971	−	0.00644971i
$889$			6.97396i			0.233899i
$890$	−33.2211	+	46.2015i	−1.11357	+	1.54868i
$891$		0			0
$892$	−49.5221	−	49.5221i	−1.65812	−	1.65812i
$893$	−5.30130	−	5.30130i	−0.177401	−	0.177401i
$894$			25.3502i			0.847836i
$895$	−10.5875	+	1.73035i	−0.353900	+	0.0578393i
$896$	58.7190			1.96167
$897$	−21.2471	+	21.2471i	−0.709420	+	0.709420i
$898$	−24.5578	−	24.5578i	−0.819505	−	0.819505i
$899$	−5.25448			−0.175247
$900$	−31.1175	+	10.4505i	−1.03725	+	0.348349i
$901$			15.2680i			0.508650i
$902$		0			0
$903$	−5.98310	+	5.98310i	−0.199105	+	0.199105i
$904$	−23.6583			−0.786863
$905$	−0.343192	−	2.09988i	−0.0114081	−	0.0698023i
$906$	43.5520			1.44692
$907$	−32.3568	−	32.3568i	−1.07439	−	1.07439i	−0.997001	−	0.0773890i	$-0.975342\pi$
$907$	−32.3568	−	32.3568i	−1.07439	−	1.07439i	−0.0773890	−	0.997001i	$-0.524658\pi$
$908$	−15.8755	−	15.8755i	−0.526846	−	0.526846i
$909$	−27.0699			−0.897853
$910$	53.4278	+	38.4172i	1.77111	+	1.27352i
$911$	26.2463			0.869578			0.434789	−	0.900532i	$-0.356823\pi$
$911$	26.2463			0.869578			0.434789	+	0.900532i	$0.356823\pi$
$912$	0.294225	−	0.294225i	0.00974277	−	0.00974277i
$913$		0			0
$914$			2.07500i			0.0686348i
$915$	9.83327	−	13.6754i	0.325078	−	0.452094i
$916$	−95.4328			−3.15319
$917$	4.41301	+	4.41301i	0.145730	+	0.145730i
$918$	−55.7340	+	55.7340i	−1.83949	+	1.83949i
$919$	35.8494			1.18256			0.591282	−	0.806465i	$-0.298622\pi$
$919$	35.8494			1.18256			0.591282	+	0.806465i	$0.298622\pi$
$920$	−7.95178	−	48.6544i	−0.262162	−	1.60409i
$921$			24.1873i			0.796999i
$922$	7.38148	+	7.38148i	0.243096	+	0.243096i
$923$	−41.1908	−	41.1908i	−1.35581	−	1.35581i
$924$		0			0
$925$	−0.379183	−	0.188525i	−0.0124675	−	0.00619866i
$926$		−	52.5793i		−	1.72786i
$927$	−11.6298	−	11.6298i	−0.381974	−	0.381974i
$928$	17.1312	−	17.1312i	0.562360	−	0.562360i
$929$		−	27.4649i		−	0.901095i	−0.892752	−	0.450547i	$-0.851229\pi$
$929$		−	27.4649i		−	0.901095i	0.892752	−	0.450547i	$-0.148771\pi$
$930$	5.65628	−	0.924429i	0.185477	−	0.0303132i
$931$		−	1.62605i		−	0.0532916i
$932$	−58.9817	+	58.9817i	−1.93201	+	1.93201i
$933$	0.352087	−	0.352087i	0.0115268	−	0.0115268i
$934$	−43.6319			−1.42768
$935$		0			0
$936$	25.7249			0.840843
$937$	−25.7737	+	25.7737i	−0.841991	+	0.841991i	−0.989118	−	0.147127i	$-0.952997\pi$
$937$	−25.7737	+	25.7737i	−0.841991	+	0.841991i	0.147127	+	0.989118i	$0.452997\pi$
$938$	−27.3818	+	27.3818i	−0.894048	+	0.894048i
$939$		−	5.07364i		−	0.165572i
$940$	−62.2740	−	44.7781i	−2.03116	−	1.46050i
$941$			11.6379i			0.379384i	0.981844	+	0.189692i	$0.0607490\pi$
$941$			11.6379i			0.379384i	−0.981844	+	0.189692i	$0.939251\pi$
$942$	29.4637	−	29.4637i	0.959978	−	0.959978i
$943$	26.6212	+	26.6212i	0.866904	+	0.866904i
$944$			0.664013i			0.0216118i
$945$	−5.54495	−	33.9277i	−0.180377	−	1.10367i
$946$		0			0
$947$	19.6094	+	19.6094i	0.637221	+	0.637221i	0.949869	−	0.312648i	$-0.101216\pi$
$947$	19.6094	+	19.6094i	0.637221	+	0.637221i	−0.312648	+	0.949869i	$0.601216\pi$
$948$	−25.1284	−	25.1284i	−0.816134	−	0.816134i
$949$			11.4066i			0.370275i
$950$	3.78003	−	7.60284i	0.122640	−	0.246669i
$951$	−26.3388			−0.854094
$952$	−45.3343	+	45.3343i	−1.46929	+	1.46929i
$953$	2.17771	+	2.17771i	0.0705429	+	0.0705429i	0.741498	−	0.670955i	$-0.234116\pi$
$953$	2.17771	+	2.17771i	0.0705429	+	0.0705429i	−0.670955	+	0.741498i	$0.734116\pi$
$954$	−10.2773			−0.332741
$955$	3.79329	+	23.2099i	0.122748	+	0.751056i
$956$			45.0952i			1.45848i
$957$		0			0
$958$	−27.6649	+	27.6649i	−0.893813	+	0.893813i
$959$	−15.2546			−0.492596
$960$	−16.9079	+	23.5143i	−0.545701	+	0.758921i
$961$	−29.8256			−0.962117
$962$	0.580542	+	0.580542i	0.0187174	+	0.0187174i
$963$	3.91537	+	3.91537i	0.126171	+	0.126171i
$964$	−36.5352			−1.17672
$965$	−16.6596	+	23.1690i	−0.536292	+	0.745835i
$966$	50.4083			1.62186
$967$	8.85124	−	8.85124i	0.284637	−	0.284637i	−0.550318	−	0.834955i	$-0.685494\pi$
$967$	8.85124	−	8.85124i	0.284637	−	0.284637i	0.834955	+	0.550318i	$0.185494\pi$
$968$		0			0
$969$		−	5.04184i		−	0.161967i
$970$	3.72450	+	22.7890i	0.119587	+	0.731711i
$971$	37.8412			1.21438			0.607191	−	0.794556i	$-0.292296\pi$
$971$	37.8412			1.21438			0.607191	+	0.794556i	$0.292296\pi$
$972$	−37.7413	−	37.7413i	−1.21055	−	1.21055i
$973$	−4.20363	+	4.20363i	−0.134762	+	0.134762i
$974$	−24.9480			−0.799384
$975$	−20.2872	+	6.81321i	−0.649709	+	0.218197i
$976$		−	4.09079i		−	0.130943i
$977$	17.1923	+	17.1923i	0.550031	+	0.550031i	0.926450	−	0.376419i	$-0.122845\pi$
$977$	17.1923	+	17.1923i	0.550031	+	0.550031i	−0.376419	+	0.926450i	$0.622845\pi$
$978$	23.3729	+	23.3729i	0.747384	+	0.747384i
$979$		0			0
$980$	−2.68324	−	16.4179i	−0.0857128	−	0.524449i
$981$		−	5.99229i		−	0.191319i
$982$	44.3838	+	44.3838i	1.41634	+	1.41634i
$983$	10.5538	−	10.5538i	0.336613	−	0.336613i	−0.518478	−	0.855091i	$-0.673501\pi$
$983$	10.5538	−	10.5538i	0.336613	−	0.336613i	0.855091	+	0.518478i	$0.173501\pi$
$984$			17.2108i			0.548659i
$985$	18.1568	+	13.0556i	0.578524	+	0.415987i
$986$			75.4651i			2.40330i
$987$	22.4158	−	22.4158i	0.713504	−	0.713504i
$988$	−7.29432	+	7.29432i	−0.232063	+	0.232063i
$989$	−19.1474			−0.608852
$990$		0			0
$991$	53.6555			1.70442			0.852212	−	0.523197i	$-0.175261\pi$
$991$	53.6555			1.70442			0.852212	+	0.523197i	$0.175261\pi$
$992$	−3.82879	+	3.82879i	−0.121564	+	0.121564i
$993$	21.8143	−	21.8143i	0.692255	−	0.692255i
$994$			97.7244i			3.09963i
$995$	−43.6001	+	7.12575i	−1.38222	+	0.225901i
$996$		−	5.88827i		−	0.186577i
$997$	−8.41562	+	8.41562i	−0.266525	+	0.266525i	−0.827699	−	0.561173i	$-0.810350\pi$
$997$	−8.41562	+	8.41562i	−0.266525	+	0.266525i	0.561173	+	0.827699i	$0.310350\pi$
$998$	−37.2152	−	37.2152i	−1.17803	−	1.17803i
$999$		−	0.428907i		−	0.0135700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.c.362.3	✓	40
5.3	odd	4	inner	605.2.e.c.483.18	yes	40
11.2	odd	10		605.2.m.g.282.3		160
11.3	even	5		605.2.m.g.112.18		160
11.4	even	5		605.2.m.g.457.3		160
11.5	even	5		605.2.m.g.602.18		160
11.6	odd	10		605.2.m.g.602.3		160
11.7	odd	10		605.2.m.g.457.18		160
11.8	odd	10		605.2.m.g.112.3		160
11.9	even	5		605.2.m.g.282.18		160
11.10	odd	2	inner	605.2.e.c.362.18	yes	40
55.3	odd	20		605.2.m.g.233.18		160
55.8	even	20		605.2.m.g.233.3		160
55.13	even	20		605.2.m.g.403.18		160
55.18	even	20		605.2.m.g.578.18		160
55.28	even	20		605.2.m.g.118.18		160
55.38	odd	20		605.2.m.g.118.3		160
55.43	even	4	inner	605.2.e.c.483.3	yes	40
55.48	odd	20		605.2.m.g.578.3		160
55.53	odd	20		605.2.m.g.403.3		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.c.362.3	✓	40	1.1	even	1	trivial
605.2.e.c.362.18	yes	40	11.10	odd	2	inner
605.2.e.c.483.3	yes	40	55.43	even	4	inner
605.2.e.c.483.18	yes	40	5.3	odd	4	inner
605.2.m.g.112.3		160	11.8	odd	10
605.2.m.g.112.18		160	11.3	even	5
605.2.m.g.118.3		160	55.38	odd	20
605.2.m.g.118.18		160	55.28	even	20
605.2.m.g.233.3		160	55.8	even	20
605.2.m.g.233.18		160	55.3	odd	20
605.2.m.g.282.3		160	11.2	odd	10
605.2.m.g.282.18		160	11.9	even	5
605.2.m.g.403.3		160	55.53	odd	20
605.2.m.g.403.18		160	55.13	even	20
605.2.m.g.457.3		160	11.4	even	5
605.2.m.g.457.18		160	11.7	odd	10
605.2.m.g.578.3		160	55.48	odd	20
605.2.m.g.578.18		160	55.18	even	20
605.2.m.g.602.3		160	11.6	odd	10
605.2.m.g.602.18		160	11.5	even	5

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63660 + 1.63660i) q^{2} +(-0.722598 + 0.722598i) q^{3} -3.35690i q^{4} +(0.360665 + 2.20679i) q^{5} -2.36520i q^{6} +(2.14665 - 2.14665i) q^{7} +(2.22069 + 2.22069i) q^{8} +1.95570i q^{9} +O(q^{10})\)	\(q+(-1.63660 + 1.63660i) q^{2} +(-0.722598 + 0.722598i) q^{3} -3.35690i q^{4} +(0.360665 + 2.20679i) q^{5} -2.36520i q^{6} +(2.14665 - 2.14665i) q^{7} +(2.22069 + 2.22069i) q^{8} +1.95570i q^{9} +(-4.20189 - 3.02136i) q^{10} +(2.42569 + 2.42569i) q^{12} +(-2.96163 - 2.96163i) q^{13} +7.02641i q^{14} +(-1.85524 - 1.33401i) q^{15} -0.554967 q^{16} +(-4.75495 + 4.75495i) q^{17} +(-3.20070 - 3.20070i) q^{18} +0.733696 q^{19} +(7.40797 - 1.21071i) q^{20} +3.10233i q^{21} +(-4.96412 + 4.96412i) q^{23} -3.20934 q^{24} +(-4.73984 + 1.59182i) q^{25} +9.69399 q^{26} +(-3.58098 - 3.58098i) q^{27} +(-7.20610 - 7.20610i) q^{28} -4.84873 q^{29} +(5.21950 - 0.853045i) q^{30} +1.08368 q^{31} +(-3.53313 + 3.53313i) q^{32} -15.5639i q^{34} +(5.51143 + 3.96299i) q^{35} +6.56510 q^{36} +(0.0598868 + 0.0598868i) q^{37} +(-1.20076 + 1.20076i) q^{38} +4.28013 q^{39} +(-4.09968 + 5.70153i) q^{40} -5.36272i q^{41} +(-5.07727 - 5.07727i) q^{42} +(1.92858 + 1.92858i) q^{43} +(-4.31583 + 0.705353i) q^{45} -16.2485i q^{46} +(-7.22547 - 7.22547i) q^{47} +(0.401018 - 0.401018i) q^{48} -2.21624i q^{49} +(5.15204 - 10.3624i) q^{50} -6.87184i q^{51} +(-9.94189 + 9.94189i) q^{52} +(1.60548 - 1.60548i) q^{53} +11.7212 q^{54} +9.53412 q^{56} +(-0.530167 + 0.530167i) q^{57} +(7.93542 - 7.93542i) q^{58} -1.19649i q^{59} +(-4.47812 + 6.22784i) q^{60} +7.37123i q^{61} +(-1.77355 + 1.77355i) q^{62} +(4.19822 + 4.19822i) q^{63} -12.6746i q^{64} +(5.46754 - 7.60385i) q^{65} +(3.89698 + 3.89698i) q^{67} +(15.9619 + 15.9619i) q^{68} -7.17412i q^{69} +(-15.5058 + 2.53418i) q^{70} +13.9081 q^{71} +(-4.34302 + 4.34302i) q^{72} +(-1.92573 - 1.92573i) q^{73} -0.196021 q^{74} +(2.27475 - 4.57525i) q^{75} -2.46294i q^{76} +(-7.00485 + 7.00485i) q^{78} -10.3593 q^{79} +(-0.200157 - 1.22470i) q^{80} -0.691896 q^{81} +(8.77660 + 8.77660i) q^{82} +(-1.21373 - 1.21373i) q^{83} +10.4142 q^{84} +(-12.2081 - 8.77824i) q^{85} -6.31262 q^{86} +(3.50368 - 3.50368i) q^{87} -10.9954i q^{89} +(5.90889 - 8.21765i) q^{90} -12.7152 q^{91} +(16.6640 + 16.6640i) q^{92} +(-0.783066 + 0.783066i) q^{93} +23.6504 q^{94} +(0.264618 + 1.61911i) q^{95} -5.10607i q^{96} +(-3.15495 - 3.15495i) q^{97} +(3.62710 + 3.62710i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) \) 40 * q + 8 * q^3 - 4 * q^5	\( 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) \) 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

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