LMFDB - Embedded newform 459.2.y.a.368.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(44,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([40, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.44"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.y (of order $48$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			368.4
Character	$\chi$	$=$	459.368
Dual form			459.2.y.a.116.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73496 + 0.228412i) q^{2} +(1.02607 - 0.274934i) q^{4} +(-1.19800 - 2.42931i) q^{5} +(-1.42204 - 0.701273i) q^{7} +(1.51606 - 0.627973i) q^{8} +(2.63338 + 3.94113i) q^{10} +(2.75958 - 0.936750i) q^{11} +(-0.0154499 - 0.0576598i) q^{13} +(2.62737 + 0.891870i) q^{14} +(-4.32677 + 2.49806i) q^{16} +(-3.87687 + 1.40353i) q^{17} +(-1.06733 - 0.442104i) q^{19} +(-1.89714 - 2.16327i) q^{20} +(-4.57380 + 2.25555i) q^{22} +(-4.90225 + 5.58995i) q^{23} +(-1.42254 + 1.85389i) q^{25} +(0.0399752 + 0.0965087i) q^{26} +(-1.65192 - 0.328587i) q^{28} +(0.539809 - 8.23590i) q^{29} +(-0.835738 + 2.46201i) q^{31} +(4.33245 - 3.32441i) q^{32} +(6.40564 - 3.32059i) q^{34} +4.29471i q^{35} +(0.970339 + 4.87822i) q^{37} +(1.95277 + 0.523242i) q^{38} +(-3.34179 - 2.93067i) q^{40} +(-10.7925 + 0.707376i) q^{41} +(-7.37322 - 5.65767i) q^{43} +(2.57397 - 1.71987i) q^{44} +(7.22841 - 10.8181i) q^{46} +(0.0354488 - 0.132297i) q^{47} +(-2.73091 - 3.55900i) q^{49} +(2.04460 - 3.54135i) q^{50} +(-0.0317053 - 0.0549153i) q^{52} +(-3.58381 + 8.65209i) q^{53} +(-5.58164 - 5.58164i) q^{55} +(-2.59628 - 0.170169i) q^{56} +(0.944630 + 14.4123i) q^{58} +(-0.271422 + 2.06166i) q^{59} +(-3.05066 + 6.18613i) q^{61} +(0.887622 - 4.46238i) q^{62} +(0.308284 - 0.308284i) q^{64} +(-0.121565 + 0.106609i) q^{65} +(4.28070 + 2.47146i) q^{67} +(-3.59206 + 2.50600i) q^{68} +(-0.980963 - 7.45116i) q^{70} +(-6.84006 + 1.36057i) q^{71} +(-2.68314 - 1.79281i) q^{73} +(-2.79775 - 8.24189i) q^{74} +(-1.21671 - 0.160183i) q^{76} +(-4.58115 - 0.603120i) q^{77} +(-0.385543 - 1.13577i) q^{79} +(11.2521 + 7.51839i) q^{80} +(18.5629 - 3.69240i) q^{82} +(0.972852 + 7.38954i) q^{83} +(8.05411 + 7.73670i) q^{85} +(14.0845 + 8.13171i) q^{86} +(3.59543 - 3.15311i) q^{88} +(10.1512 - 10.1512i) q^{89} +(-0.0184649 + 0.0928292i) q^{91} +(-3.49318 + 7.08347i) q^{92} +(-0.0312842 + 0.237627i) q^{94} +(0.204661 + 3.12253i) q^{95} +(-12.5228 - 0.820787i) q^{97} +(5.55095 + 5.55095i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{16}\right)$

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 $

$2$	−1.73496	+	0.228412i	−1.22680	+	0.161512i	−0.715947	−	0.698154i	$-0.754005\pi$
$2$	−1.73496	+	0.228412i	−1.22680	+	0.161512i	−0.510856	+	0.859666i	$0.670672\pi$
$3$		0			0
$3$		0			0
$4$	1.02607	−	0.274934i	0.513035	−	0.137467i
$5$	−1.19800	−	2.42931i	−0.535764	−	1.08642i	−0.981536	−	0.191275i	$-0.938738\pi$
$5$	−1.19800	−	2.42931i	−0.535764	−	1.08642i	0.445773	−	0.895146i	$-0.352929\pi$
$6$		0			0
$7$	−1.42204	−	0.701273i	−0.537481	−	0.265056i	0.153226	−	0.988191i	$-0.451034\pi$
$7$	−1.42204	−	0.701273i	−0.537481	−	0.265056i	−0.690707	+	0.723135i	$0.742700\pi$
$8$	1.51606	−	0.627973i	0.536009	−	0.222022i
$9$		0			0
$10$	2.63338	+	3.94113i	0.832747	+	1.24629i
$11$	2.75958	−	0.936750i	0.832044	−	0.282441i	0.127266	−	0.991869i	$-0.459380\pi$
$11$	2.75958	−	0.936750i	0.832044	−	0.282441i	0.704778	+	0.709428i	$0.251047\pi$
$12$		0			0
$13$	−0.0154499	−	0.0576598i	−0.00428503	−	0.0159920i	0.963750	−	0.266806i	$-0.0859683\pi$
$13$	−0.0154499	−	0.0576598i	−0.00428503	−	0.0159920i	−0.968035	+	0.250814i	$0.919302\pi$
$14$	2.62737	+	0.891870i	0.702193	+	0.238362i
$15$		0			0
$16$	−4.32677	+	2.49806i	−1.08169	+	0.624515i
$17$	−3.87687	+	1.40353i	−0.940279	+	0.340405i
$17$	−3.87687	+	1.40353i	−0.940279	+	0.340405i
$18$		0			0
$19$	−1.06733	−	0.442104i	−0.244863	−	0.101426i	0.256877	−	0.966444i	$-0.417307\pi$
$19$	−1.06733	−	0.442104i	−0.244863	−	0.101426i	−0.501740	+	0.865019i	$0.667307\pi$
$20$	−1.89714	−	2.16327i	−0.424213	−	0.483722i
$21$		0			0
$22$	−4.57380	+	2.25555i	−0.975137	+	0.480884i
$23$	−4.90225	+	5.58995i	−1.02219	+	1.16558i	−0.0361041	+	0.999348i	$0.511495\pi$
$23$	−4.90225	+	5.58995i	−1.02219	+	1.16558i	−0.986086	+	0.166236i	$0.946839\pi$
$24$		0			0
$25$	−1.42254	+	1.85389i	−0.284508	+	0.370778i
$26$	0.0399752	+	0.0965087i	0.00783978	+	0.0189269i
$27$		0			0
$28$	−1.65192	−	0.328587i	−0.312183	−	0.0620970i
$29$	0.539809	−	8.23590i	0.100240	−	1.52937i	−0.590958	−	0.806703i	$-0.701250\pi$
$29$	0.539809	−	8.23590i	0.100240	−	1.52937i	0.691198	−	0.722666i	$-0.257083\pi$
$30$		0			0
$31$	−0.835738	+	2.46201i	−0.150103	+	0.442189i	−0.995809	−	0.0914603i	$-0.970847\pi$
$31$	−0.835738	+	2.46201i	−0.150103	+	0.442189i	0.845706	+	0.533650i	$0.179180\pi$
$32$	4.33245	−	3.32441i	0.765876	−	0.587677i
$33$		0			0
$34$	6.40564	−	3.32059i	1.09856	−	0.569476i
$35$			4.29471i			0.725938i
$36$		0			0
$37$	0.970339	+	4.87822i	0.159523	+	0.801975i	0.974831	+	0.222947i	$0.0715677\pi$
$37$	0.970339	+	4.87822i	0.159523	+	0.801975i	−0.815308	+	0.579028i	$0.803432\pi$
$38$	1.95277	+	0.523242i	0.316780	+	0.0848810i
$39$		0			0
$40$	−3.34179	−	2.93067i	−0.528384	−	0.463380i
$41$	−10.7925	+	0.707376i	−1.68550	+	0.110474i	−0.877771	−	0.479080i	$-0.840970\pi$
$41$	−10.7925	+	0.707376i	−1.68550	+	0.110474i	−0.807729	+	0.589554i	$0.799304\pi$
$42$		0			0
$43$	−7.37322	−	5.65767i	−1.12441	−	0.862787i	−0.132680	−	0.991159i	$-0.542358\pi$
$43$	−7.37322	−	5.65767i	−1.12441	−	0.862787i	−0.991726	+	0.128372i	$0.959025\pi$
$44$	2.57397	−	1.71987i	0.388041	−	0.259281i
$45$		0			0
$46$	7.22841	−	10.8181i	1.06577	−	1.59504i
$47$	0.0354488	−	0.132297i	0.00517074	−	0.0192975i	−0.963292	−	0.268455i	$-0.913487\pi$
$47$	0.0354488	−	0.132297i	0.00517074	−	0.0192975i	0.968463	+	0.249157i	$0.0801536\pi$
$48$		0			0
$49$	−2.73091	−	3.55900i	−0.390131	−	0.508428i
$50$	2.04460	−	3.54135i	0.289150	−	0.500823i
$51$		0			0
$52$	−0.0317053	−	0.0549153i	−0.00439674	−	0.00761538i
$53$	−3.58381	+	8.65209i	−0.492275	+	1.18846i	0.461285	+	0.887252i	$0.347389\pi$
$53$	−3.58381	+	8.65209i	−0.492275	+	1.18846i	−0.953560	+	0.301204i	$0.902611\pi$
$54$		0			0
$55$	−5.58164	−	5.58164i	−0.752629	−	0.752629i
$56$	−2.59628	−	0.170169i	−0.346943	−	0.0227398i
$57$		0			0
$58$	0.944630	+	14.4123i	0.124036	+	1.89242i
$59$	−0.271422	+	2.06166i	−0.0353362	+	0.268405i	0.964652	+	0.263527i	$0.0848859\pi$
$59$	−0.271422	+	2.06166i	−0.0353362	+	0.268405i	−0.999988	+	0.00487761i	$0.998447\pi$
$60$		0			0
$61$	−3.05066	+	6.18613i	−0.390597	+	0.792052i	−1.00000		0.000808619i	$-0.999743\pi$
$61$	−3.05066	+	6.18613i	−0.390597	+	0.792052i	0.609403	+	0.792861i	$0.291409\pi$
$62$	0.887622	−	4.46238i	0.112728	−	0.566723i
$63$		0			0
$64$	0.308284	−	0.308284i	0.0385355	−	0.0385355i
$65$	−0.121565	+	0.106609i	−0.0150782	+	0.0132233i
$66$		0			0
$67$	4.28070	+	2.47146i	0.522970	+	0.301937i	0.738149	−	0.674638i	$-0.235700\pi$
$67$	4.28070	+	2.47146i	0.522970	+	0.301937i	−0.215179	+	0.976575i	$0.569033\pi$
$68$	−3.59206	+	2.50600i	−0.435601	+	0.303897i
$69$		0			0
$70$	−0.980963	−	7.45116i	−0.117248	−	0.890584i
$71$	−6.84006	+	1.36057i	−0.811766	+	0.161470i	−0.583484	−	0.812125i	$-0.698311\pi$
$71$	−6.84006	+	1.36057i	−0.811766	+	0.161470i	−0.228282	+	0.973595i	$0.573311\pi$
$72$		0			0
$73$	−2.68314	−	1.79281i	−0.314037	−	0.209833i	0.388555	−	0.921425i	$-0.372974\pi$
$73$	−2.68314	−	1.79281i	−0.314037	−	0.209833i	−0.702592	+	0.711592i	$0.747974\pi$
$74$	−2.79775	−	8.24189i	−0.325231	−	0.958101i
$75$		0			0
$76$	−1.21671	−	0.160183i	−0.139566	−	0.0183742i
$77$	−4.58115	−	0.603120i	−0.522070	−	0.0687319i
$78$		0			0
$79$	−0.385543	−	1.13577i	−0.0433769	−	0.127784i	0.923084	−	0.384599i	$-0.125660\pi$
$79$	−0.385543	−	1.13577i	−0.0433769	−	0.127784i	−0.966461	+	0.256815i	$0.917327\pi$
$80$	11.2521	+	7.51839i	1.25802	+	0.840581i
$81$		0			0
$82$	18.5629	−	3.69240i	2.04993	−	0.407757i
$83$	0.972852	+	7.38954i	0.106784	+	0.811108i	0.958096	+	0.286447i	$0.0924744\pi$
$83$	0.972852	+	7.38954i	0.106784	+	0.811108i	−0.851312	+	0.524660i	$0.824192\pi$
$84$		0			0
$85$	8.05411	+	7.73670i	0.873591	+	0.839162i
$86$	14.0845	+	8.13171i	1.51878	+	0.876865i
$87$		0			0
$88$	3.59543	−	3.15311i	0.383275	−	0.336123i
$89$	10.1512	−	10.1512i	1.07602	−	1.07602i	0.0791578	−	0.996862i	$-0.474777\pi$
$89$	10.1512	−	10.1512i	1.07602	−	1.07602i	0.996862	−	0.0791578i	$-0.0252231\pi$
$90$		0			0
$91$	−0.0184649	+	0.0928292i	−0.00193565	+	0.00973115i
$92$	−3.49318	+	7.08347i	−0.364189	+	0.738503i
$93$		0			0
$94$	−0.0312842	+	0.237627i	−0.00322672	+	0.0245093i
$95$	0.204661	+	3.12253i	0.0209978	+	0.320365i
$96$		0			0
$97$	−12.5228	−	0.820787i	−1.27150	−	0.0833383i	−0.585337	−	0.810790i	$-0.699038\pi$
$97$	−12.5228	−	0.820787i	−1.27150	−	0.0833383i	−0.686159	+	0.727452i	$0.740705\pi$
$98$	5.55095	+	5.55095i	0.560731	+	0.560731i
$99$		0			0
$100$	−0.949925	+	2.29332i	−0.0949925	+	0.229332i
$101$	6.17752	+	10.6998i	0.614686	+	1.06467i	0.990439	+	0.137948i	$0.0440507\pi$
$101$	6.17752	+	10.6998i	0.614686	+	1.06467i	−0.375753	+	0.926720i	$0.622616\pi$
$102$		0			0
$103$	3.53868	−	6.12918i	0.348677	−	0.603926i	−0.637338	−	0.770584i	$-0.719964\pi$
$103$	3.53868	−	6.12918i	0.348677	−	0.603926i	0.986015	+	0.166659i	$0.0532978\pi$
$104$	−0.0596318	−	0.0777137i	−0.00584738	−	0.00762046i
$105$		0			0
$106$	4.24154	−	15.8296i	0.411975	−	1.53751i
$107$	7.68188	−	11.4967i	0.742635	−	1.11143i	−0.247166	−	0.968973i	$-0.579499\pi$
$107$	7.68188	−	11.4967i	0.742635	−	1.11143i	0.989801	−	0.142459i	$-0.0455008\pi$
$108$		0			0
$109$	7.20324	−	4.81305i	0.689946	−	0.461007i	−0.160523	−	0.987032i	$-0.551318\pi$
$109$	7.20324	−	4.81305i	0.689946	−	0.461007i	0.850469	+	0.526025i	$0.176318\pi$
$110$	10.9589	+	8.40903i	1.04489	+	0.801769i
$111$		0			0
$112$	7.90466	−	0.518099i	0.746921	−	0.0489558i
$113$	−10.3302	−	9.05932i	−0.971781	−	0.852229i	0.0172626	−	0.999851i	$-0.494505\pi$
$113$	−10.3302	−	9.05932i	−0.971781	−	0.852229i	−0.989044	+	0.147622i	$0.952838\pi$
$114$		0			0
$115$	19.4526	+	5.21232i	1.81397	+	0.486051i
$116$	−1.71045	−	8.59901i	−0.158811	−	0.798398i
$117$		0			0
$118$		−	3.63889i		−	0.334987i
$119$	6.49732	+	0.722871i	0.595608	+	0.0662654i
$120$		0			0
$121$	−1.98912	+	1.52631i	−0.180829	+	0.138755i
$122$	3.87979	−	11.4295i	0.351260	−	1.03478i
$123$		0			0
$124$	−0.180635	+	2.75596i	−0.0162215	+	0.247493i
$125$	−7.07513	−	1.40733i	−0.632819	−	0.125876i
$126$		0			0
$127$	8.29944	+	20.0366i	0.736456	+	1.77796i	0.619754	+	0.784796i	$0.287232\pi$
$127$	8.29944	+	20.0366i	0.736456	+	1.77796i	0.116703	+	0.993167i	$0.462768\pi$
$128$	−7.11326	+	9.27018i	−0.628729	+	0.819376i
$129$		0			0
$130$	0.186559	−	0.212730i	0.0163623	−	0.0186577i
$131$	17.6229	−	8.69067i	1.53972	−	0.759308i	0.542965	−	0.839755i	$-0.317302\pi$
$131$	17.6229	−	8.69067i	1.53972	−	0.759308i	0.996759	+	0.0804478i	$0.0256350\pi$
$132$		0			0
$133$	1.20776	+	1.37718i	0.104726	+	0.119417i
$134$	−7.99136	−	3.31013i	−0.690348	−	0.285952i
$135$		0			0
$136$	−4.99619	+	4.56240i	−0.428420	+	0.391223i
$137$	0.365975	−	0.211296i	0.0312673	−	0.0180522i	−0.484285	−	0.874910i	$-0.660920\pi$
$137$	0.365975	−	0.211296i	0.0312673	−	0.0180522i	0.515552	+	0.856858i	$0.327587\pi$
$138$		0			0
$139$	0.803025	+	0.272590i	0.0681117	+	0.0231208i	0.355287	−	0.934757i	$-0.384383\pi$
$139$	0.803025	+	0.272590i	0.0681117	+	0.0231208i	−0.287176	+	0.957878i	$0.592716\pi$
$140$	1.18076	+	4.40667i	0.0997927	+	0.372431i
$141$		0			0
$142$	11.5565	−	3.92290i	0.969798	−	0.329202i
$143$	−0.0966481	−	0.144644i	−0.00808212	−	0.0120957i
$144$		0			0
$145$	−20.6543	+	8.55528i	−1.71524	+	0.710477i
$146$	5.06464	+	2.49760i	0.419152	+	0.206703i
$147$		0			0
$148$	2.33683	+	4.73861i	0.192086	+	0.389512i
$149$	10.8874	−	2.91728i	0.891933	−	0.238993i	0.216384	−	0.976308i	$-0.430574\pi$
$149$	10.8874	−	2.91728i	0.891933	−	0.238993i	0.675549	+	0.737315i	$0.263907\pi$
$150$		0			0
$151$	1.15066	−	0.151488i	0.0936397	−	0.0123279i	−0.0835607	−	0.996503i	$-0.526629\pi$
$151$	1.15066	−	0.151488i	0.0936397	−	0.0123279i	0.177200	+	0.984175i	$0.443296\pi$
$152$	−1.89577			−0.153767
$153$		0			0
$154$	8.08588			0.651579
$155$	6.98220	−	0.919224i	0.560824	−	0.0738339i
$156$		0			0
$157$	−11.7048	+	3.13630i	−0.934146	+	0.250304i	−0.693622	−	0.720339i	$-0.743986\pi$
$157$	−11.7048	+	3.13630i	−0.934146	+	0.250304i	−0.240524	+	0.970643i	$0.577319\pi$
$158$	0.928326	+	1.88246i	0.0738536	+	0.149760i
$159$		0			0
$160$	−13.2663	−	6.54222i	−1.04879	−	0.517208i
$161$	10.8913	−	4.51131i	0.858353	−	0.355541i
$162$		0			0
$163$	−2.09236	−	3.13144i	−0.163886	−	0.245273i	0.740433	−	0.672130i	$-0.234621\pi$
$163$	−2.09236	−	3.13144i	−0.163886	−	0.245273i	−0.904319	+	0.426857i	$0.859621\pi$
$164$	−10.8793	+	3.69304i	−0.849534	+	0.288378i
$165$		0			0
$166$	−3.37572	−	12.5984i	−0.262007	−	0.977823i
$167$	−0.503975	−	0.171077i	−0.0389988	−	0.0132383i	0.301872	−	0.953348i	$-0.402389\pi$
$167$	−0.503975	−	0.171077i	−0.0389988	−	0.0132383i	−0.340871	+	0.940110i	$0.610722\pi$
$168$		0			0
$169$	11.2552	−	6.49822i	0.865788	−	0.499863i
$170$	−15.7407	−	11.5832i	−1.20726	−	0.888392i
$171$		0			0
$172$	−9.12092	−	3.77801i	−0.695464	−	0.288071i
$173$	−6.47250	−	7.38048i	−0.492095	−	0.561127i	0.451482	−	0.892280i	$-0.350896\pi$
$173$	−6.47250	−	7.38048i	−0.492095	−	0.561127i	−0.943577	+	0.331153i	$0.892562\pi$
$174$		0			0
$175$	3.32299	−	1.63872i	0.251194	−	0.123875i
$176$	−9.59999	+	10.9467i	−0.723627	+	0.825138i
$177$		0			0
$178$	−15.2932	+	19.9305i	−1.14628	+	1.49385i
$179$	−4.85593	−	11.7232i	−0.362949	−	0.876236i	−0.994866	−	0.101200i	$-0.967732\pi$
$179$	−4.85593	−	11.7232i	−0.362949	−	0.876236i	0.631917	−	0.775036i	$-0.282268\pi$
$180$		0			0
$181$	−24.9297	−	4.95882i	−1.85301	−	0.368586i	−0.862503	−	0.506052i	$-0.831104\pi$
$181$	−24.9297	−	4.95882i	−1.85301	−	0.368586i	−0.990507	+	0.137466i	$0.956104\pi$
$182$	0.0108325	−	0.165273i	0.000802962	−	0.0122508i
$183$		0			0
$184$	−3.92178	+	11.5532i	−0.289117	+	0.851712i
$185$	10.6883	−	8.20139i	0.785816	−	0.602978i
$186$		0			0
$187$	−9.38376	+	7.50480i	−0.686209	+	0.548805i
$188$		−	0.145492i		−	0.0106111i
$189$		0			0
$190$	−1.06830	−	5.37072i	−0.0775029	−	0.389633i
$191$	−8.97182	−	2.40399i	−0.649178	−	0.173947i	−0.0808210	−	0.996729i	$-0.525754\pi$
$191$	−8.97182	−	2.40399i	−0.649178	−	0.173947i	−0.568357	+	0.822782i	$0.692421\pi$
$192$		0			0
$193$	8.79713	+	7.71488i	0.633231	+	0.555329i	0.914645	−	0.404258i	$-0.132470\pi$
$193$	8.79713	+	7.71488i	0.633231	+	0.555329i	−0.281414	+	0.959586i	$0.590803\pi$
$194$	21.9140	−	1.43632i	1.57334	−	0.103122i
$195$		0			0
$196$	−3.78060	−	2.90095i	−0.270043	−	0.207211i
$197$	−18.8701	+	12.6086i	−1.34444	+	0.898328i	−0.999192	−	0.0401830i	$-0.987206\pi$
$197$	−18.8701	+	12.6086i	−1.34444	+	0.898328i	−0.345250	+	0.938511i	$0.612206\pi$
$198$		0			0
$199$	13.3536	−	19.9851i	0.946611	−	1.41670i	0.0378986	−	0.999282i	$-0.487934\pi$
$199$	13.3536	−	19.9851i	0.946611	−	1.41670i	0.908713	−	0.417422i	$-0.137066\pi$
$200$	−0.992464	+	3.70392i	−0.0701778	+	0.261907i
$201$		0			0
$202$	−13.1617	−	17.1527i	−0.926055	−	1.20686i
$203$	−6.54324	+	11.3332i	−0.459246	+	0.795437i
$204$		0			0
$205$	14.6479	+	25.3708i	1.02305	+	1.77198i
$206$	−4.73950	+	11.4422i	−0.330217	+	0.797213i
$207$		0			0
$208$	0.210886	+	0.210886i	0.0146223	+	0.0146223i
$209$	−3.35953	−	0.220195i	−0.232384	−	0.0152312i
$210$		0			0
$211$	−1.57208	−	23.9852i	−0.108226	−	1.65121i	−0.614557	−	0.788873i	$-0.710665\pi$
$211$	−1.57208	−	23.9852i	−0.108226	−	1.65121i	0.506331	−	0.862340i	$-0.331002\pi$
$212$	−1.29848	+	9.86296i	−0.0891802	+	0.677391i
$213$		0			0
$214$	−10.7018	+	21.7010i	−0.731558	+	1.48345i
$215$	−4.91110	+	24.6898i	−0.334934	+	1.68383i
$216$		0			0
$217$	2.91499	−	2.91499i	0.197883	−	0.197883i
$218$	−11.3980	+	9.99577i	−0.771970	+	0.676999i
$219$		0			0
$220$	−7.26174	−	4.19257i	−0.489586	−	0.282663i
$221$	0.140824	+	0.201855i	0.00947287	+	0.0135783i
$222$		0			0
$223$	−0.882741	−	6.70508i	−0.0591127	−	0.449006i	−0.995249	−	0.0973670i	$-0.968958\pi$
$223$	−0.882741	−	6.70508i	−0.0591127	−	0.449006i	0.936136	−	0.351639i	$-0.114375\pi$
$224$	−8.49223	+	1.68921i	−0.567411	+	0.112865i
$225$		0			0
$226$	19.9917	+	13.3580i	1.32983	+	0.888564i
$227$	−8.58329	−	25.2856i	−0.569693	−	1.67826i	−0.723636	−	0.690182i	$-0.757531\pi$
$227$	−8.58329	−	25.2856i	−0.569693	−	1.67826i	0.153943	−	0.988080i	$-0.450803\pi$
$228$		0			0
$229$	−6.76991	−	0.891276i	−0.447368	−	0.0588972i	−0.0965234	−	0.995331i	$-0.530772\pi$
$229$	−6.76991	−	0.891276i	−0.447368	−	0.0588972i	−0.350845	+	0.936434i	$0.614106\pi$
$230$	−34.9402	−	4.59996i	−2.30389	−	0.303312i
$231$		0			0
$232$	−4.35354	−	12.8251i	−0.285824	−	0.842010i
$233$	−0.901442	−	0.602324i	−0.0590554	−	0.0394596i	0.525692	−	0.850675i	$-0.323806\pi$
$233$	−0.901442	−	0.602324i	−0.0590554	−	0.0394596i	−0.584747	+	0.811215i	$0.698806\pi$
$234$		0			0
$235$	−0.363858	+	0.0723759i	−0.0237355	+	0.00472128i
$236$	0.288323	+	2.19003i	0.0187682	+	0.142559i
$237$		0			0
$238$	−11.4377	+	0.229913i	−0.741397	+	0.0149031i
$239$	2.06984	+	1.19502i	0.133887	+	0.0772995i	0.565447	−	0.824784i	$-0.308704\pi$
$239$	2.06984	+	1.19502i	0.133887	+	0.0772995i	−0.431561	+	0.902084i	$0.642037\pi$
$240$		0			0
$241$	−2.18057	+	1.91231i	−0.140463	+	0.123183i	−0.726694	−	0.686961i	$-0.758944\pi$
$241$	−2.18057	+	1.91231i	−0.140463	+	0.123183i	0.586231	+	0.810144i	$0.300611\pi$
$242$	3.10242	−	3.10242i	0.199431	−	0.199431i
$243$		0			0
$244$	−1.42941	+	7.18612i	−0.0915085	+	0.460044i
$245$	−5.37427	+	10.8979i	−0.343349	+	0.696244i
$246$		0			0
$247$	−0.00900144	+	0.0683727i	−0.000572748	+	0.00435045i
$248$	0.279043	+	4.25737i	0.0177193	+	0.270344i
$249$		0			0
$250$	12.5965	+	0.825620i	0.796675	+	0.0522168i
$251$	−5.69148	−	5.69148i	−0.359243	−	0.359243i	0.504291	−	0.863534i	$-0.331754\pi$
$251$	−5.69148	−	5.69148i	−0.359243	−	0.359243i	−0.863534	+	0.504291i	$0.831754\pi$
$252$		0			0
$253$	−8.29176	+	20.0181i	−0.521298	+	1.25853i
$254$	−18.9758	−	32.8671i	−1.19065	−	2.06226i
$255$		0			0
$256$	9.78783	−	16.9530i	0.611739	−	1.05956i
$257$	−4.32173	−	5.63218i	−0.269582	−	0.351326i	0.638870	−	0.769314i	$-0.279402\pi$
$257$	−4.32173	−	5.63218i	−0.269582	−	0.351326i	−0.908452	+	0.417988i	$0.862735\pi$
$258$		0			0
$259$	2.04110	−	7.61750i	0.126828	−	0.473329i
$260$	−0.0954232	+	0.142811i	−0.00591790	+	0.00885676i
$261$		0			0
$262$	−28.5901	+	19.1033i	−1.76630	+	1.18020i
$263$	4.47813	+	3.43619i	0.276133	+	0.211885i	0.737539	−	0.675305i	$-0.235988\pi$
$263$	4.47813	+	3.43619i	0.276133	+	0.211885i	−0.461405	+	0.887189i	$0.652655\pi$
$264$		0			0
$265$	25.3121	−	1.65904i	1.55491	−	0.101914i
$266$	−2.40998	−	2.11349i	−0.147765	−	0.129587i
$267$		0			0
$268$	5.07178	+	1.35898i	0.309808	+	0.0830129i
$269$	1.22383	+	6.15259i	0.0746180	+	0.375130i	0.999992	−	0.00392470i	$-0.00124927\pi$
$269$	1.22383	+	6.15259i	0.0746180	+	0.375130i	−0.925374	+	0.379055i	$0.876249\pi$
$270$		0			0
$271$		−	16.0106i		−	0.972576i	−0.873799	−	0.486288i	$-0.838351\pi$
$271$		−	16.0106i		−	0.972576i	0.873799	−	0.486288i	$-0.161649\pi$
$272$	13.2682	−	15.7574i	0.804504	−	0.955432i
$273$		0			0
$274$	−0.586690	+	0.450183i	−0.0354432	+	0.0271966i
$275$	−2.18897	+	6.44851i	−0.132000	+	0.388860i
$276$		0			0
$277$	−0.190047	+	2.89956i	−0.0114188	+	0.174218i	0.988340	+	0.152262i	$0.0486559\pi$
$277$	−0.190047	+	2.89956i	−0.0114188	+	0.174218i	−0.999759	+	0.0219554i	$0.993011\pi$
$278$	−1.45548	−	0.289513i	−0.0872939	−	0.0173638i
$279$		0			0
$280$	2.69696	+	6.51104i	0.161174	+	0.389109i
$281$	2.72194	−	3.54730i	0.162377	−	0.211614i	−0.705077	−	0.709130i	$-0.749088\pi$
$281$	2.72194	−	3.54730i	0.162377	−	0.211614i	0.867455	+	0.497516i	$0.165754\pi$
$282$		0			0
$283$	−0.776633	+	0.885580i	−0.0461660	+	0.0526422i	−0.774462	−	0.632621i	$-0.781979\pi$
$283$	−0.776633	+	0.885580i	−0.0461660	+	0.0526422i	0.728296	+	0.685263i	$0.240313\pi$
$284$	−6.64431	+	3.27661i	−0.394267	+	0.194431i
$285$		0			0
$286$	0.200719	+	0.228876i	0.0118688	+	0.0135337i
$287$	15.8434	+	6.56255i	0.935206	+	0.387375i
$288$		0			0
$289$	13.0602	−	10.8826i	0.768249	−	0.640152i
$290$	33.8802	−	19.5608i	1.98952	−	1.14865i
$291$		0			0
$292$	−3.24599	−	1.10186i	−0.189957	−	0.0644818i
$293$	−6.45324	−	24.0838i	−0.377002	−	1.40699i	−0.850397	−	0.526141i	$-0.823638\pi$
$293$	−6.45324	−	24.0838i	−0.377002	−	1.40699i	0.473395	−	0.880850i	$-0.343028\pi$
$294$		0			0
$295$	5.33358	−	1.81051i	0.310533	−	0.105412i
$296$	4.53449	+	6.78634i	0.263562	+	0.394448i
$297$		0			0
$298$	−18.2229	+	7.54819i	−1.05563	+	0.437255i
$299$	0.398055	+	0.196299i	0.0230201	+	0.0113523i
$300$		0			0
$301$	6.51745	+	13.2161i	0.375660	+	0.761762i
$302$	−1.96176	+	0.525651i	−0.112886	+	0.0302478i
$303$		0			0
$304$	5.72251	−	0.753383i	0.328208	−	0.0432095i
$305$	18.6827			1.06977
$306$		0			0
$307$	−5.12708			−0.292618			−0.146309	−	0.989239i	$-0.546739\pi$
$307$	−5.12708			−0.292618			−0.146309	+	0.989239i	$0.546739\pi$
$308$	−4.86639	+	0.640673i	−0.277288	+	0.0365057i
$309$		0			0
$310$	−11.9039	+	3.18964i	−0.676095	+	0.181159i
$311$	5.66806	+	11.4937i	0.321406	+	0.651748i	0.996279	−	0.0861867i	$-0.0274681\pi$
$311$	5.66806	+	11.4937i	0.321406	+	0.651748i	−0.674873	+	0.737934i	$0.735801\pi$
$312$		0			0
$313$	−15.1705	−	7.48129i	−0.857490	−	0.422867i	−0.0402672	−	0.999189i	$-0.512821\pi$
$313$	−15.1705	−	7.48129i	−0.857490	−	0.422867i	−0.817223	+	0.576322i	$0.804488\pi$
$314$	19.5910	−	8.11488i	1.10559	−	0.457949i
$315$		0			0
$316$	−0.707856	−	1.05938i	−0.0398200	−	0.0595949i
$317$	1.72745	−	0.586389i	0.0970231	−	0.0329349i	−0.272506	−	0.962154i	$-0.587852\pi$
$317$	1.72745	−	0.586389i	0.0970231	−	0.0329349i	0.369529	+	0.929219i	$0.379519\pi$
$318$		0			0
$319$	−6.22534	−	23.2333i	−0.348552	−	1.30081i
$320$	−1.11824	−	0.379593i	−0.0625118	−	0.0212199i
$321$		0			0
$322$	−17.8655	+	10.3147i	−0.995606	+	0.574813i
$323$	4.75842	+	0.215948i	0.264765	+	0.0120157i
$324$		0			0
$325$	0.128873	+	0.0533809i	0.00714859	+	0.00296104i
$326$	4.34542	+	4.95500i	0.240671	+	0.274432i
$327$		0			0
$328$	−15.9178	+	7.84981i	−0.878915	+	0.433433i
$329$	−0.143186	+	0.163272i	−0.00789409	+	0.00900148i
$330$		0			0
$331$	−0.0970129	+	0.126430i	−0.00533231	+	0.00694920i	−0.796012	−	0.605281i	$-0.793061\pi$
$331$	−0.0970129	+	0.126430i	−0.00533231	+	0.00694920i	0.790680	+	0.612230i	$0.209727\pi$
$332$	3.02985	+	7.31471i	0.166285	+	0.401447i
$333$		0			0
$334$	0.913454	+	0.181697i	0.0499820	+	0.00994203i
$335$	0.875659	−	13.3600i	0.0478424	−	0.729933i
$336$		0			0
$337$	1.32080	−	3.89096i	0.0719487	−	0.211954i	−0.905007	−	0.425397i	$-0.860134\pi$
$337$	1.32080	−	3.89096i	0.0719487	−	0.211954i	0.976956	+	0.213443i	$0.0684678\pi$
$338$	−18.0431	+	13.8450i	−0.981418	+	0.753068i
$339$		0			0
$340$	10.3912	+	5.72403i	0.563540	+	0.310429i
$341$			7.57697i			0.410316i
$342$		0			0
$343$	3.55293	+	17.8618i	0.191840	+	0.964445i
$344$	−14.7311	−	3.94719i	−0.794249	−	0.212818i
$345$		0			0
$346$	12.9153	+	11.3264i	0.694333	+	0.608914i
$347$	12.3796	−	0.811402i	0.664572	−	0.0435584i	0.270616	−	0.962687i	$-0.412773\pi$
$347$	12.3796	−	0.811402i	0.664572	−	0.0435584i	0.393956	+	0.919129i	$0.371106\pi$
$348$		0			0
$349$	15.5355	+	11.9208i	0.831595	+	0.638105i	0.934253	−	0.356612i	$-0.116068\pi$
$349$	15.5355	+	11.9208i	0.831595	+	0.638105i	−0.102658	+	0.994717i	$0.532735\pi$
$350$	−5.39096	+	3.60212i	−0.288159	+	0.192541i
$351$		0			0
$352$	8.84159	−	13.2324i	0.471258	−	0.705288i
$353$	−9.11017	+	33.9996i	−0.484885	+	1.80962i	0.0956908	+	0.995411i	$0.469494\pi$
$353$	−9.11017	+	33.9996i	−0.484885	+	1.80962i	−0.580576	+	0.814206i	$0.697173\pi$
$354$		0			0
$355$	11.4997	+	14.9867i	0.610340	+	0.795410i
$356$	7.62488	−	13.2067i	0.404118	−	0.699953i
$357$		0			0
$358$	11.1026	+	19.2302i	0.586790	+	1.01635i
$359$	4.36840	−	10.5462i	0.230555	−	0.556609i	−0.765688	−	0.643212i	$-0.777601\pi$
$359$	4.36840	−	10.5462i	0.230555	−	0.556609i	0.996243	+	0.0866031i	$0.0276012\pi$
$360$		0			0
$361$	−12.4913	−	12.4913i	−0.657436	−	0.657436i
$362$	44.3847	+	2.90913i	2.33281	+	0.152900i
$363$		0			0
$364$	0.00657570	+	0.100326i	0.000344660	+	0.00525850i
$365$	−1.14090	+	8.66597i	−0.0597173	+	0.453598i
$366$		0			0
$367$	−4.23405	+	8.58579i	−0.221015	+	0.448175i	−0.978935	−	0.204173i	$-0.934549\pi$
$367$	−4.23405	+	8.58579i	−0.221015	+	0.448175i	0.757919	+	0.652348i	$0.226216\pi$
$368$	7.24688	−	36.4325i	0.377770	−	1.89918i
$369$		0			0
$370$	−16.6704	+	16.6704i	−0.866654	+	0.866654i
$371$	11.1638	−	9.79039i	0.579596	−	0.508292i
$372$		0			0
$373$	14.4471	+	8.34104i	0.748043	+	0.431883i	0.824986	−	0.565153i	$-0.191183\pi$
$373$	14.4471	+	8.34104i	0.748043	+	0.431883i	−0.0769434	+	0.997035i	$0.524516\pi$
$374$	14.5663	−	15.1639i	0.753205	−	0.784107i
$375$		0			0
$376$	−0.0293363	−	0.222831i	−0.00151290	−	0.0114916i
$377$	−0.483221	+	0.0961186i	−0.0248871	+	0.00495036i
$378$		0			0
$379$	16.8002	+	11.2256i	0.862970	+	0.576618i	0.906391	−	0.422439i	$-0.138826\pi$
$379$	16.8002	+	11.2256i	0.862970	+	0.576618i	−0.0434215	+	0.999057i	$0.513826\pi$
$380$	1.06849	+	3.14766i	0.0548123	+	0.161472i
$381$		0			0
$382$	16.1149	+	2.12156i	0.824509	+	0.108549i
$383$	1.74146	+	0.229268i	0.0889845	+	0.0117150i	0.174887	−	0.984589i	$-0.444044\pi$
$383$	1.74146	+	0.229268i	0.0889845	+	0.0117150i	−0.0859025	+	0.996304i	$0.527377\pi$
$384$		0			0
$385$	4.02307	+	11.8516i	0.205035	+	0.604012i
$386$	−17.0249	−	11.3756i	−0.866542	−	0.579005i
$387$		0			0
$388$	−13.0749	+	2.60076i	−0.663778	+	0.132034i
$389$	1.50614	+	11.4403i	0.0763643	+	0.580045i	0.986259	+	0.165206i	$0.0528288\pi$
$389$	1.50614	+	11.4403i	0.0763643	+	0.580045i	−0.909895	+	0.414839i	$0.863838\pi$
$390$		0			0
$391$	11.1597	−	28.5519i	0.564373	−	1.44393i
$392$	−6.37519	−	3.68072i	−0.321996	−	0.185904i
$393$		0			0
$394$	29.8590	−	26.1857i	1.50428	−	1.31921i
$395$	−2.29726	+	2.29726i	−0.115588	+	0.115588i
$396$		0			0
$397$	2.52247	−	12.6813i	0.126599	−	0.636457i	−0.864424	−	0.502764i	$-0.832316\pi$
$397$	2.52247	−	12.6813i	0.126599	−	0.636457i	0.991023	−	0.133693i	$-0.0426836\pi$
$398$	−18.6031	+	37.7235i	−0.932492	+	1.89091i
$399$		0			0
$400$	1.52387	−	11.5749i	0.0761934	−	0.578747i
$401$	2.29851	+	35.0685i	0.114782	+	1.75124i	0.535947	+	0.844252i	$0.319955\pi$
$401$	2.29851	+	35.0685i	0.114782	+	1.75124i	−0.421165	+	0.906984i	$0.638379\pi$
$402$		0			0
$403$	0.154871	+	0.0101508i	0.00771467	+	0.000505646i
$404$	9.28030	+	9.28030i	0.461712	+	0.461712i
$405$		0			0
$406$	8.76363	−	21.1573i	0.434932	−	1.05002i
$407$	7.24740	+	12.5529i	0.359240	+	0.622223i
$408$		0			0
$409$	−2.34951	+	4.06948i	−0.116176	+	0.201223i	−0.918249	−	0.396003i	$-0.870397\pi$
$409$	−2.34951	+	4.06948i	−0.116176	+	0.201223i	0.802073	+	0.597226i	$0.203730\pi$
$410$	−31.2085	−	40.6717i	−1.54128	−	2.00863i
$411$		0			0
$412$	1.94581	−	7.26186i	0.0958632	−	0.357766i
$413$	1.83176	−	2.74142i	0.0901349	−	0.134896i
$414$		0			0
$415$	16.7860	−	11.2161i	0.823994	−	0.550575i
$416$	−0.258621	−	0.198447i	−0.0126799	−	0.00972964i
$417$		0			0
$418$	5.87895	−	0.385327i	0.287549	−	0.0188470i
$419$	1.50546	+	1.32025i	0.0735466	+	0.0644987i	0.695330	−	0.718691i	$-0.255258\pi$
$419$	1.50546	+	1.32025i	0.0735466	+	0.0644987i	−0.621783	+	0.783189i	$0.713592\pi$
$420$		0			0
$421$	−13.3323	−	3.57239i	−0.649778	−	0.174108i	−0.0811497	−	0.996702i	$-0.525859\pi$
$421$	−13.3323	−	3.57239i	−0.649778	−	0.174108i	−0.568629	+	0.822594i	$0.692526\pi$
$422$	8.20601	+	41.2544i	0.399462	+	2.00823i
$423$		0			0
$424$			15.3676i			0.746319i
$425$	2.91301	−	9.18385i	0.141302	−	0.445482i
$426$		0			0
$427$	8.67632	−	6.65758i	0.419877	−	0.322183i
$428$	4.72129	−	13.9085i	0.228212	−	0.672291i
$429$		0			0
$430$	2.88113	−	43.9576i	0.138941	−	2.11982i
$431$	19.9058	+	3.95950i	0.958827	+	0.190722i	0.649609	−	0.760269i	$-0.274933\pi$
$431$	19.9058	+	3.95950i	0.958827	+	0.190722i	0.309218	+	0.950991i	$0.399933\pi$
$432$		0			0
$433$	−9.44212	−	22.7953i	−0.453759	−	1.09547i	−0.970882	−	0.239560i	$-0.922997\pi$
$433$	−9.44212	−	22.7953i	−0.453759	−	1.09547i	0.517122	−	0.855912i	$-0.327003\pi$
$434$	−4.39158	+	5.72322i	−0.210803	+	0.274723i
$435$		0			0
$436$	6.06775	−	6.91895i	0.290593	−	0.331357i
$437$	7.70368	−	3.79903i	0.368517	−	0.181732i
$438$		0			0
$439$	−8.45940	−	9.64610i	−0.403745	−	0.460383i	0.513861	−	0.857873i	$-0.328215\pi$
$439$	−8.45940	−	9.64610i	−0.403745	−	0.460383i	−0.917606	+	0.397490i	$0.869881\pi$
$440$	−11.9672	−	4.95699i	−0.570516	−	0.236315i
$441$		0			0
$442$	−0.290431	−	0.318045i	−0.0138144	−	0.0151279i
$443$	18.7164	−	10.8059i	0.889241	−	0.513404i	0.0155470	−	0.999879i	$-0.495051\pi$
$443$	18.7164	−	10.8059i	0.889241	−	0.513404i	0.873694	+	0.486475i	$0.161718\pi$
$444$		0			0
$445$	−36.8214	−	12.4992i	−1.74550	−	0.592519i
$446$	3.06304	+	11.4314i	0.145039	+	0.541294i
$447$		0			0
$448$	−0.654584	+	0.222201i	−0.0309262	+	0.0104980i
$449$	−11.8403	−	17.7202i	−0.558778	−	0.836270i	0.439294	−	0.898343i	$-0.355229\pi$
$449$	−11.8403	−	17.7202i	−0.558778	−	0.836270i	−0.998072	+	0.0620736i	$0.980229\pi$
$450$		0			0
$451$	−29.1200	+	12.0619i	−1.37121	+	0.567973i
$452$	−13.0902	−	6.45537i	−0.615711	−	0.303635i
$453$		0			0
$454$	20.6672	+	41.9090i	0.969960	+	1.96688i
$455$	0.247632	−	0.0663528i	0.0116092	−	0.00311067i
$456$		0			0
$457$	14.0614	−	1.85122i	0.657765	−	0.0865964i	0.205747	−	0.978605i	$-0.434038\pi$
$457$	14.0614	−	1.85122i	0.657765	−	0.0865964i	0.452018	+	0.892009i	$0.350704\pi$
$458$	11.9491			0.558346
$459$		0			0
$460$	21.3928			0.997445
$461$	−27.1781	+	3.57807i	−1.26581	+	0.166647i	−0.733376	−	0.679823i	$-0.762057\pi$
$461$	−27.1781	+	3.57807i	−1.26581	+	0.166647i	−0.532436	+	0.846470i	$0.678723\pi$
$462$		0			0
$463$	4.10532	−	1.10002i	0.190790	−	0.0511221i	−0.162159	−	0.986765i	$-0.551846\pi$
$463$	4.10532	−	1.10002i	0.190790	−	0.0511221i	0.352949	+	0.935643i	$0.385179\pi$
$464$	18.2382	+	36.9833i	0.846685	+	1.71691i
$465$		0			0
$466$	1.70154	+	0.839109i	0.0788225	+	0.0388710i
$467$	−17.7184	+	7.33920i	−0.819910	+	0.339618i	−0.752900	−	0.658135i	$-0.771346\pi$
$467$	−17.7184	+	7.33920i	−0.819910	+	0.339618i	−0.0670094	+	0.997752i	$0.521346\pi$
$468$		0			0
$469$	−4.35416	−	6.51645i	−0.201056	−	0.300902i
$470$	0.614748	−	0.208679i	0.0283562	−	0.00962564i
$471$		0			0
$472$	0.883173	+	3.29605i	0.0406513	+	0.151713i
$473$	−25.6468	−	8.70592i	−1.17924	−	0.400298i
$474$		0			0
$475$	2.33793	−	1.34981i	0.107272	−	0.0619334i
$476$	6.86544	−	1.04462i	0.314677	−	0.0478802i
$477$		0			0
$478$	−3.86405	−	1.60054i	−0.176737	−	0.0732071i
$479$	−5.51358	−	6.28703i	−0.251922	−	0.287262i	0.612032	−	0.790833i	$-0.290352\pi$
$479$	−5.51358	−	6.28703i	−0.251922	−	0.287262i	−0.863954	+	0.503571i	$0.832019\pi$
$480$		0			0
$481$	0.266286	−	0.131318i	0.0121416	−	0.00598757i
$482$	3.34641	−	3.81585i	0.152425	−	0.173807i
$483$		0			0
$484$	−1.62134	+	2.11297i	−0.0736974	+	0.0960443i
$485$	13.0084	+	31.4051i	0.590681	+	1.42603i
$486$		0			0
$487$	−0.136538	−	0.0271590i	−0.00618712	−	0.00123069i	0.191996	−	0.981396i	$-0.438504\pi$
$487$	−0.136538	−	0.0271590i	−0.00618712	−	0.00123069i	−0.198183	+	0.980165i	$0.563504\pi$
$488$	−0.740266	+	11.2943i	−0.0335103	+	0.511268i
$489$		0			0
$490$	6.83493	−	20.1351i	0.308771	−	0.909609i
$491$	19.5906	−	15.0324i	0.884110	−	0.678401i	−0.0634481	−	0.997985i	$-0.520210\pi$
$491$	19.5906	−	15.0324i	0.884110	−	0.678401i	0.947558	+	0.319584i	$0.103543\pi$
$492$		0			0
$493$	9.46654	+	32.6871i	0.426351	+	1.47215i
$494$		−	0.120680i		−	0.00542966i
$495$		0			0
$496$	−2.53419	−	12.7403i	−0.113789	−	0.572054i
$497$	10.6810	+	2.86196i	0.479107	+	0.128376i
$498$		0			0
$499$	−22.4043	−	19.6481i	−1.00296	−	0.879569i	−0.0102282	−	0.999948i	$-0.503256\pi$
$499$	−22.4043	−	19.6481i	−1.00296	−	0.879569i	−0.992728	+	0.120379i	$0.961589\pi$
$500$	−7.64650	+	0.501178i	−0.341962	+	0.0224134i
$501$		0			0
$502$	11.1745	+	8.57451i	0.498743	+	0.382699i
$503$	36.3824	−	24.3099i	1.62221	−	1.08393i	0.688897	−	0.724859i	$-0.258095\pi$
$503$	36.3824	−	24.3099i	1.62221	−	1.08393i	0.933312	−	0.359067i	$-0.116905\pi$
$504$		0			0
$505$	18.5924	−	27.8255i	0.827351	−	1.23822i
$506$	9.81351	−	36.6245i	0.436264	−	1.62816i
$507$		0			0
$508$	14.0246	+	18.2772i	0.622239	+	0.810918i
$509$	−16.9628	+	29.3804i	−0.751861	+	1.30226i	0.195059	+	0.980792i	$0.437510\pi$
$509$	−16.9628	+	29.3804i	−0.751861	+	1.30226i	−0.946920	+	0.321470i	$0.895823\pi$
$510$		0			0
$511$	2.55828	+	4.43106i	0.113171	+	0.196019i
$512$	−4.16608	+	10.0578i	−0.184116	+	0.444496i
$513$		0			0
$514$	8.78449	+	8.78449i	0.387467	+	0.387467i
$515$	−19.1290	−	1.25378i	−0.842926	−	0.0552483i
$516$		0			0
$517$	−0.0261053	−	0.398290i	−0.00114811	−	0.0175168i
$518$	−1.80131	+	13.6823i	−0.0791449	+	0.601165i
$519$		0			0
$520$	−0.117352	+	0.237966i	−0.00514621	+	0.0104355i
$521$	−2.83039	+	14.2293i	−0.124002	+	0.623399i	0.867936	+	0.496675i	$0.165446\pi$
$521$	−2.83039	+	14.2293i	−0.124002	+	0.623399i	−0.991938	+	0.126723i	$0.959554\pi$
$522$		0			0
$523$	−20.3511	+	20.3511i	−0.889890	+	0.889890i	−0.994512	−	0.104622i	$-0.966637\pi$
$523$	−20.3511	+	20.3511i	−0.889890	+	0.889890i	0.104622	+	0.994512i	$0.466637\pi$
$524$	15.6930	−	13.7624i	0.685552	−	0.601213i
$525$		0			0
$526$	−8.55426	−	4.93880i	−0.372983	−	0.215342i
$527$	−0.215443	−	10.7179i	−0.00938486	−	0.466877i
$528$		0			0
$529$	−4.21333	−	32.0034i	−0.183188	−	1.39145i
$530$	−43.5365	+	8.65995i	−1.89111	+	0.376164i
$531$		0			0
$532$	1.61788	+	1.08103i	0.0701438	+	0.0468686i
$533$	0.207530	+	0.611363i	0.00898911	+	0.0264811i
$534$		0			0
$535$	−37.1321	−	4.88853i	−1.60536	−	0.211350i
$536$	8.04181	+	1.05872i	0.347353	+	0.0457299i
$537$		0			0
$538$	−3.52862	−	10.3950i	−0.152129	−	0.448159i
$539$	−10.8701	−	7.26314i	−0.468207	−	0.312846i
$540$		0			0
$541$	−4.10266	+	0.816069i	−0.176387	+	0.0350856i	−0.282493	−	0.959269i	$-0.591162\pi$
$541$	−4.10266	+	0.816069i	−0.176387	+	0.0350856i	0.106106	+	0.994355i	$0.466162\pi$
$542$	3.65702	+	27.7778i	0.157082	+	1.19316i
$543$		0			0
$544$	−12.1304	+	18.9690i	−0.520089	+	0.813289i
$545$	−20.3219	−	11.7329i	−0.870496	−	0.502581i
$546$		0			0
$547$	30.7552	−	26.9716i	1.31500	−	1.15322i	0.337725	−	0.941245i	$-0.390343\pi$
$547$	30.7552	−	26.9716i	1.31500	−	1.15322i	0.977274	−	0.211979i	$-0.0679907\pi$
$548$	0.317423	−	0.317423i	0.0135596	−	0.0135596i
$549$		0			0
$550$	2.32487	−	11.6879i	0.0991328	−	0.498374i
$551$	−4.21728	+	8.55180i	−0.179662	+	0.364319i
$552$		0			0
$553$	−0.248229	+	1.88548i	−0.0105558	+	0.0801790i
$554$	−0.332570	−	5.07404i	−0.0141295	−	0.215575i
$555$		0			0
$556$	0.898903	+	0.0589172i	0.0381220	+	0.00249865i
$557$	−4.82152	−	4.82152i	−0.204294	−	0.204294i	0.597543	−	0.801837i	$-0.296144\pi$
$557$	−4.82152	−	4.82152i	−0.204294	−	0.204294i	−0.801837	+	0.597543i	$0.796144\pi$
$558$		0			0
$559$	−0.212305	+	0.512549i	−0.00897954	+	0.0216785i
$560$	−10.7284	−	18.5822i	−0.453360	−	0.785242i
$561$		0			0
$562$	−3.91222	+	6.77616i	−0.165027	+	0.285835i
$563$	20.5528	+	26.7849i	0.866196	+	1.12885i	0.990624	+	0.136619i	$0.0436237\pi$
$563$	20.5528	+	26.7849i	0.866196	+	1.12885i	−0.124428	+	0.992229i	$0.539710\pi$
$564$		0			0
$565$	−9.63233	+	35.9483i	−0.405235	+	1.51236i
$566$	1.14515	−	1.71384i	0.0481343	−	0.0720380i
$567$		0			0
$568$	−9.51555	+	6.35809i	−0.399264	+	0.266780i
$569$	6.61491	+	5.07580i	0.277312	+	0.212789i	0.738048	−	0.674749i	$-0.235748\pi$
$569$	6.61491	+	5.07580i	0.277312	+	0.212789i	−0.460736	+	0.887537i	$0.652415\pi$
$570$		0			0
$571$	−10.2497	+	0.671801i	−0.428937	+	0.0281140i	−0.278343	−	0.960482i	$-0.589785\pi$
$571$	−10.2497	+	0.671801i	−0.428937	+	0.0281140i	−0.150594	+	0.988596i	$0.548119\pi$
$572$	−0.138935	−	0.121843i	−0.00580917	−	0.00509451i
$573$		0			0
$574$	−28.9866	−	7.76695i	−1.20988	−	0.324186i
$575$	−3.38949	−	17.0401i	−0.141352	−	0.710623i
$576$		0			0
$577$		−	4.76545i		−	0.198388i	−0.995068	−	0.0991942i	$-0.968373\pi$
$577$		−	4.76545i		−	0.198388i	0.995068	−	0.0991942i	$-0.0316265\pi$
$578$	−20.1733	+	21.8640i	−0.839098	+	0.909421i
$579$		0			0
$580$	−18.8406	+	14.4569i	−0.782312	+	0.600289i
$581$	3.79865	−	11.1905i	0.157595	−	0.464259i
$582$		0			0
$583$	−1.78496	+	27.2332i	−0.0739255	+	1.12789i
$584$	−5.19364	−	1.03308i	−0.214914	−	0.0427491i
$585$		0			0
$586$	16.6972	+	40.3105i	0.689753	+	1.66521i
$587$	2.79948	−	3.64835i	0.115547	−	0.150584i	−0.731999	−	0.681306i	$-0.761412\pi$
$587$	2.79948	−	3.64835i	0.115547	−	0.150584i	0.847546	+	0.530722i	$0.178079\pi$
$588$		0			0
$589$	1.98047	−	2.25830i	0.0816040	−	0.0930516i
$590$	−8.84001	+	4.35941i	−0.363937	+	0.179474i
$591$		0			0
$592$	−16.3845	−	18.6830i	−0.673400	−	0.767866i
$593$	−22.8624	−	9.46991i	−0.938846	−	0.388883i	−0.139818	−	0.990177i	$-0.544652\pi$
$593$	−22.8624	−	9.46991i	−0.938846	−	0.388883i	−0.799027	+	0.601295i	$0.794652\pi$
$594$		0			0
$595$	−6.02774	−	16.6500i	−0.247113	−	0.682584i
$596$	10.3692	−	5.98666i	0.424739	−	0.245223i
$597$		0			0
$598$	−0.735447	−	0.249651i	−0.0300747	−	0.0102090i
$599$	4.05692	+	15.1406i	0.165761	+	0.618629i	0.997942	+	0.0641245i	$0.0204255\pi$
$599$	4.05692	+	15.1406i	0.165761	+	0.618629i	−0.832181	+	0.554504i	$0.812908\pi$
$600$		0			0
$601$	−3.00197	+	1.01903i	−0.122453	+	0.0415672i	−0.381993	−	0.924165i	$-0.624762\pi$
$601$	−3.00197	+	1.01903i	−0.122453	+	0.0415672i	0.259540	+	0.965732i	$0.416429\pi$
$602$	−14.3262	−	21.4407i	−0.583894	−	0.873859i
$603$		0			0
$604$	1.13901	−	0.471794i	0.0463457	−	0.0191970i
$605$	6.09085	+	3.00368i	0.247628	+	0.122117i
$606$		0			0
$607$	−10.2835	−	20.8528i	−0.417393	−	0.846389i	−0.999447	−	0.0332394i	$-0.989418\pi$
$607$	−10.2835	−	20.8528i	−0.417393	−	0.846389i	0.582054	−	0.813150i	$-0.302249\pi$
$608$	−6.09390	+	1.63286i	−0.247140	+	0.0662211i
$609$		0			0
$610$	−32.4138	+	4.26736i	−1.31240	+	0.172780i
$611$	−0.00817589			−0.000330761
$612$		0			0
$613$	−7.68237			−0.310288			−0.155144	−	0.987892i	$-0.549584\pi$
$613$	−7.68237			−0.310288			−0.155144	+	0.987892i	$0.549584\pi$
$614$	8.89529	−	1.17109i	0.358985	−	0.0472612i
$615$		0			0
$616$	−7.32405	+	1.96247i	−0.295094	+	0.0790703i
$617$	−9.74308	−	19.7570i	−0.392241	−	0.795387i	−0.999999	−	0.00126452i	$-0.999597\pi$
$617$	−9.74308	−	19.7570i	−0.392241	−	0.795387i	0.607758	−	0.794122i	$-0.292069\pi$
$618$		0			0
$619$	15.7721	+	7.77793i	0.633934	+	0.312621i	0.730713	−	0.682684i	$-0.239188\pi$
$619$	15.7721	+	7.77793i	0.633934	+	0.312621i	−0.0967798	+	0.995306i	$0.530854\pi$
$620$	6.91149	−	2.86283i	0.277572	−	0.114974i
$621$		0			0
$622$	−12.4592	−	18.6465i	−0.499567	−	0.747655i
$623$	−21.5541	+	7.31662i	−0.863546	+	0.293134i
$624$		0			0
$625$	8.08120	+	30.1594i	0.323248	+	1.20638i
$626$	28.0291	+	9.51461i	1.12027	+	0.380280i
$627$		0			0
$628$	−11.1477	+	6.43611i	−0.444841	+	0.256829i
$629$	−10.6086	−	17.5503i	−0.422992	−	0.699778i
$630$		0			0
$631$	33.4430	+	13.8525i	1.33134	+	0.551460i	0.931038	−	0.364922i	$-0.118904\pi$
$631$	33.4430	+	13.8525i	1.33134	+	0.551460i	0.400305	+	0.916382i	$0.368904\pi$
$632$	−1.29774	−	1.47979i	−0.0516214	−	0.0588629i
$633$		0			0
$634$	−2.86312	+	1.41193i	−0.113709	+	0.0560750i
$635$	38.7325	−	44.1659i	1.53705	−	1.75267i
$636$		0			0
$637$	−0.163019	+	0.212450i	−0.00645904	+	0.00841758i
$638$	16.1075	+	38.8869i	0.637701	+	1.53955i
$639$		0			0
$640$	31.0419	+	6.17461i	1.22704	+	0.244073i
$641$	1.42453	−	21.7341i	0.0562656	−	0.858447i	−0.872694	−	0.488267i	$-0.837629\pi$
$641$	1.42453	−	21.7341i	0.0562656	−	0.858447i	0.928960	−	0.370180i	$-0.120704\pi$
$642$		0			0
$643$	−8.48429	+	24.9939i	−0.334588	+	0.985663i	0.641281	+	0.767306i	$0.278403\pi$
$643$	−8.48429	+	24.9939i	−0.334588	+	0.985663i	−0.975869	+	0.218357i	$0.929930\pi$
$644$	9.93489	−	7.62331i	0.391489	−	0.300400i
$645$		0			0
$646$	−8.30500	+	0.712218i	−0.326756	+	0.0280219i
$647$		−	8.74993i		−	0.343995i	−0.985097	−	0.171998i	$-0.944978\pi$
$647$		−	8.74993i		−	0.343995i	0.985097	−	0.171998i	$-0.0550221\pi$
$648$		0			0
$649$	1.18225	+	5.94356i	0.0464073	+	0.233305i
$650$	−0.235783	−	0.0631777i	−0.00924815	−	0.00247803i
$651$		0			0
$652$	−3.00784	−	2.63781i	−0.117796	−	0.103305i
$653$	12.4054	−	0.813095i	0.485462	−	0.0318189i	0.179292	−	0.983796i	$-0.442619\pi$
$653$	12.4054	−	0.813095i	0.485462	−	0.0318189i	0.306170	+	0.951977i	$0.400952\pi$
$654$		0			0
$655$	−42.2247	−	32.4002i	−1.64986	−	1.26598i
$656$	44.9295	−	30.0209i	1.75420	−	1.17212i
$657$		0			0
$658$	0.211129	−	0.315976i	0.00823065	−	0.0123180i
$659$	−6.73100	+	25.1204i	−0.262202	+	0.978553i	0.701738	+	0.712435i	$0.252408\pi$
$659$	−6.73100	+	25.1204i	−0.262202	+	0.978553i	−0.963941	+	0.266118i	$0.914259\pi$
$660$		0			0
$661$	20.2785	+	26.4275i	0.788742	+	1.02791i	0.998739	+	0.0502068i	$0.0159880\pi$
$661$	20.2785	+	26.4275i	0.788742	+	1.02791i	−0.209997	+	0.977702i	$0.567345\pi$
$662$	0.139436	−	0.241510i	0.00541932	−	0.00938654i
$663$		0			0
$664$	6.11534	+	10.5921i	0.237321	+	0.411052i
$665$	1.89871	−	4.58389i	0.0736287	−	0.177756i
$666$		0			0
$667$	43.3920	+	43.3920i	1.68014	+	1.68014i
$668$	−0.564148	−	0.0369762i	−0.0218276	−	0.00143065i
$669$		0			0
$670$	1.53234	+	23.3791i	0.0591996	+	0.903212i
$671$	−2.62368	+	19.9288i	−0.101286	+	0.769343i
$672$		0			0
$673$	1.72440	−	3.49675i	0.0664709	−	0.134790i	−0.861102	−	0.508433i	$-0.830225\pi$
$673$	1.72440	−	3.49675i	0.0664709	−	0.134790i	0.927572	+	0.373643i	$0.121892\pi$
$674$	−1.40280	+	7.05236i	−0.0540339	+	0.271647i
$675$		0			0
$676$	9.76208	−	9.76208i	0.375464	−	0.375464i
$677$	−5.77320	+	5.06296i	−0.221882	+	0.194585i	−0.763069	−	0.646317i	$-0.776308\pi$
$677$	−5.77320	+	5.06296i	−0.221882	+	0.194585i	0.541187	+	0.840902i	$0.317975\pi$
$678$		0			0
$679$	17.2323	+	9.94908i	0.661316	+	0.381811i
$680$	17.0690	+	6.67154i	0.654565	+	0.255842i
$681$		0			0
$682$	−1.73067	−	13.1458i	−0.0662709	−	0.503377i
$683$	−24.0653	+	4.78690i	−0.920835	+	0.183165i	−0.632676	−	0.774417i	$-0.718043\pi$
$683$	−24.0653	+	4.78690i	−0.920835	+	0.183165i	−0.288159	+	0.957582i	$0.593043\pi$
$684$		0			0
$685$	−0.951743	−	0.635934i	−0.0363642	−	0.0242978i
$686$	−10.2440	−	30.1780i	−0.391119	−	1.15220i
$687$		0			0
$688$	46.0354	+	6.06068i	1.75508	+	0.231061i
$689$	0.554248	+	0.0729681i	0.0211152	+	0.00277986i
$690$		0			0
$691$	−7.12811	−	20.9987i	−0.271166	−	0.798829i	−0.994154	−	0.107969i	$-0.965565\pi$
$691$	−7.12811	−	20.9987i	−0.271166	−	0.798829i	0.722988	−	0.690860i	$-0.242768\pi$
$692$	−8.67038	−	5.79337i	−0.329599	−	0.220231i
$693$		0			0
$694$	−21.2928	+	4.23540i	−0.808264	+	0.160774i
$695$	−0.299820	−	2.27736i	−0.0113728	−	0.0863853i
$696$		0			0
$697$	40.8482	−	17.8899i	1.54723	−	0.677629i
$698$	−29.6763	−	17.1336i	−1.12326	−	0.648517i
$699$		0			0
$700$	2.95908	−	2.59504i	0.111843	−	0.0980833i
$701$	15.9461	−	15.9461i	0.602276	−	0.602276i	−0.338640	−	0.940916i	$-0.609967\pi$
$701$	15.9461	−	15.9461i	0.602276	−	0.602276i	0.940916	+	0.338640i	$0.109967\pi$
$702$		0			0
$703$	1.12101	−	5.63568i	0.0422796	−	0.212554i
$704$	0.561949	−	1.13952i	0.0211792	−	0.0429472i
$705$		0			0
$706$	8.03987	−	61.0689i	0.302585	−	2.29836i
$707$	−1.28122	−	19.5476i	−0.0481852	−	0.735165i
$708$		0			0
$709$	−36.6046	−	2.39919i	−1.37471	−	0.0901036i	−0.639945	−	0.768421i	$-0.721043\pi$
$709$	−36.6046	−	2.39919i	−1.37471	−	0.0901036i	−0.734769	+	0.678317i	$0.762710\pi$
$710$	−23.3747	−	23.3747i	−0.877235	−	0.877235i
$711$		0			0
$712$	9.01512	−	21.7644i	0.337856	−	0.815656i
$713$	−9.66548	−	16.7411i	−0.361975	−	0.626959i
$714$		0			0
$715$	−0.235601	+	0.408073i	−0.00881097	+	0.0152610i
$716$	−8.20564	−	10.6938i	−0.306659	−	0.399646i
$717$		0			0
$718$	−5.17011	+	19.2951i	−0.192947	+	0.720088i
$719$	−9.54937	+	14.2916i	−0.356131	+	0.532988i	−0.965671	−	0.259767i	$-0.916354\pi$
$719$	−9.54937	+	14.2916i	−0.356131	+	0.532988i	0.609540	+	0.792755i	$0.291354\pi$
$720$		0			0
$721$	−9.33037	+	6.23436i	−0.347481	+	0.232180i
$722$	24.5251	+	18.8187i	0.912728	+	0.700361i
$723$		0			0
$724$	−26.9429	+	1.76593i	−1.00133	+	0.0656304i
$725$	14.5005	+	12.7166i	0.538536	+	0.472284i
$726$		0			0
$727$	6.85734	+	1.83742i	0.254325	+	0.0681461i	0.383729	−	0.923446i	$-0.374640\pi$
$727$	6.85734	+	1.83742i	0.254325	+	0.0681461i	−0.129404	+	0.991592i	$0.541306\pi$
$728$	0.0303004	+	0.152330i	0.00112301	+	0.00564574i
$729$		0			0
$730$		−	15.2957i		−	0.566120i
$731$	36.5257	+	11.5855i	1.35095	+	0.428507i
$732$		0			0
$733$	−13.3482	+	10.2424i	−0.493027	+	0.378313i	−0.825142	−	0.564926i	$-0.808905\pi$
$733$	−13.3482	+	10.2424i	−0.493027	+	0.378313i	0.332114	+	0.943239i	$0.392238\pi$
$734$	5.38481	−	15.8631i	0.198757	−	0.585519i
$735$		0			0
$736$	−2.65551	+	40.5152i	−0.0978833	+	1.49341i
$737$	14.1281	+	2.81024i	0.520414	+	0.103517i
$738$		0			0
$739$	9.59552	+	23.1656i	0.352977	+	0.852162i	0.996250	+	0.0865247i	$0.0275761\pi$
$739$	9.59552	+	23.1656i	0.352977	+	0.852162i	−0.643273	+	0.765637i	$0.722424\pi$
$740$	8.71205	−	11.3538i	0.320261	−	0.417373i
$741$		0			0
$742$	−17.1325	+	19.5359i	−0.628955	+	0.717186i
$743$	−19.8209	+	9.77456i	−0.727157	+	0.358594i	−0.767895	−	0.640576i	$-0.778696\pi$
$743$	−19.8209	+	9.77456i	−0.727157	+	0.358594i	0.0407383	+	0.999170i	$0.487029\pi$
$744$		0			0
$745$	−20.1302	−	22.9541i	−0.737512	−	0.840972i
$746$	−26.9704	−	11.1715i	−0.987456	−	0.409018i
$747$		0			0
$748$	−7.56506	+	10.2804i	−0.276606	+	0.375887i
$749$	−18.9863	+	10.9617i	−0.693744	+	0.400533i
$750$		0			0
$751$	37.4892	+	12.7259i	1.36800	+	0.464374i	0.906290	−	0.422657i	$-0.138903\pi$
$751$	37.4892	+	12.7259i	1.36800	+	0.464374i	0.461711	+	0.887031i	$0.347236\pi$
$752$	0.177107	+	0.660971i	0.00645842	+	0.0241031i
$753$		0			0
$754$	0.816415	−	0.277135i	0.0297321	−	0.0100927i
$755$	−1.74651	−	2.61384i	−0.0635621	−	0.0951274i
$756$		0			0
$757$	48.2630	−	19.9912i	1.75415	−	0.726592i	0.756815	−	0.653630i	$-0.226755\pi$
$757$	48.2630	−	19.9912i	1.75415	−	0.726592i	0.997335	−	0.0729628i	$-0.0232454\pi$
$758$	−31.7118	−	15.6385i	−1.15183	−	0.568017i
$759$		0			0
$760$	2.27114	+	4.60543i	0.0823831	+	0.167056i
$761$	21.4694	−	5.75270i	0.778264	−	0.208535i	0.152245	−	0.988343i	$-0.451350\pi$
$761$	21.4694	−	5.75270i	0.778264	−	0.208535i	0.626019	+	0.779807i	$0.284683\pi$
$762$		0			0
$763$	−13.6186	+	1.79292i	−0.493025	+	0.0649080i
$764$	−9.86665			−0.356963
$765$		0			0
$766$	−3.07374			−0.111059
$767$	0.123068	−	0.0162022i	0.00444374	−	0.000585029i
$768$		0			0
$769$	12.8921	−	3.45443i	0.464901	−	0.124570i	−0.0187621	−	0.999824i	$-0.505973\pi$
$769$	12.8921	−	3.45443i	0.464901	−	0.124570i	0.483664	+	0.875254i	$0.339306\pi$
$770$	−9.68692	−	19.6431i	−0.349092	−	0.707889i
$771$		0			0
$772$	11.1475	+	5.49736i	0.401209	+	0.197854i
$773$	−14.7654	+	6.11601i	−0.531073	+	0.219978i	−0.632073	−	0.774909i	$-0.717796\pi$
$773$	−14.7654	+	6.11601i	−0.531073	+	0.219978i	0.101000	+	0.994886i	$0.467796\pi$
$774$		0			0
$775$	−3.37541	−	5.05166i	−0.121248	−	0.181461i
$776$	−19.5008	+	6.61961i	−0.700036	+	0.237630i
$777$		0			0
$778$	−5.22619	−	19.5044i	−0.187368	−	0.699267i
$779$	11.8319	+	4.01639i	0.423922	+	0.143902i
$780$		0			0
$781$	−17.6012	+	10.1620i	−0.629819	+	0.363626i
$782$	−12.8401	+	52.0855i	−0.459162	+	1.86257i
$783$		0			0
$784$	20.7066	+	8.57697i	0.739522	+	0.306320i
$785$	21.6415	+	24.6774i	0.772417	+	0.880773i
$786$		0			0
$787$	−38.0440	+	18.7612i	−1.35612	+	0.668766i	−0.967557	−	0.252654i	$-0.918697\pi$
$787$	−38.0440	+	18.7612i	−1.35612	+	0.668766i	−0.388567	+	0.921420i	$0.627030\pi$
$788$	−15.8955	+	18.1254i	−0.566255	+	0.645690i
$789$		0			0
$790$	3.46094	−	4.51039i	0.123135	−	0.160472i
$791$	8.33687	+	20.1270i	0.296425	+	0.715634i
$792$		0			0
$793$	0.403823	+	0.0803255i	0.0143402	+	0.00285244i
$794$	−1.47983	+	22.5778i	−0.0525170	+	0.801255i
$795$		0			0
$796$	8.20713	−	24.1774i	0.290894	−	0.856946i
$797$	−22.8595	+	17.5407i	−0.809727	+	0.621325i	−0.928389	−	0.371610i	$-0.878806\pi$
$797$	−22.8595	+	17.5407i	−0.809727	+	0.621325i	0.118662	+	0.992935i	$0.462139\pi$
$798$		0			0
$799$	0.0482517	+	0.562651i	0.00170702	+	0.0199052i
$800$			12.7610i			0.451168i
$801$		0			0
$802$	−11.9979	−	60.3175i	−0.423660	−	2.12988i
$803$	−9.08374	−	2.43398i	−0.320558	−	0.0858933i
$804$		0			0
$805$	−24.0072	−	21.0537i	−0.846142	−	0.742047i
$806$	−0.271014	+	0.0177632i	−0.00954605	+	0.000625681i
$807$		0			0
$808$	16.0847	+	12.3422i	0.565857	+	0.434197i
$809$	20.5769	−	13.7490i	0.723444	−	0.483390i	−0.138520	−	0.990360i	$-0.544234\pi$
$809$	20.5769	−	13.7490i	0.723444	−	0.483390i	0.861964	+	0.506970i	$0.169234\pi$
$810$		0			0
$811$	−24.5341	+	36.7178i	−0.861507	+	1.28934i	0.0943601	+	0.995538i	$0.469920\pi$
$811$	−24.5341	+	36.7178i	−0.861507	+	1.28934i	−0.955867	+	0.293799i	$0.905080\pi$
$812$	−3.59793	+	13.4276i	−0.126262	+	0.471218i
$813$		0			0
$814$	−15.4412	−	20.1234i	−0.541213	−	0.705323i
$815$	−5.10058	+	8.83447i	−0.178666	+	0.309458i
$816$		0			0
$817$	5.36841	+	9.29836i	0.187817	+	0.325308i
$818$	3.14680	−	7.59704i	0.110025	−	0.265624i
$819$		0			0
$820$	22.0050	+	22.0050i	0.768449	+	0.768449i
$821$	−50.6515	−	3.31987i	−1.76775	−	0.115864i	−0.853519	−	0.521061i	$-0.825536\pi$
$821$	−50.6515	−	3.31987i	−1.76775	−	0.115864i	−0.914230	+	0.405197i	$0.867203\pi$
$822$		0			0
$823$	1.88308	+	28.7302i	0.0656399	+	1.00147i	0.895946	+	0.444163i	$0.146499\pi$
$823$	1.88308	+	28.7302i	0.0656399	+	1.00147i	−0.830306	+	0.557308i	$0.811834\pi$
$824$	1.51590	−	11.5144i	0.0528089	−	0.401123i
$825$		0			0
$826$	−2.55186	+	5.17465i	−0.0887905	+	0.180049i
$827$	−2.52147	+	12.6763i	−0.0876800	+	0.440797i	0.911861	+	0.410499i	$0.134646\pi$
$827$	−2.52147	+	12.6763i	−0.0876800	+	0.440797i	−0.999541	+	0.0302977i	$0.990354\pi$
$828$		0			0
$829$	6.58216	−	6.58216i	0.228608	−	0.228608i	−0.583503	−	0.812111i	$-0.698318\pi$
$829$	6.58216	−	6.58216i	0.228608	−	0.228608i	0.812111	+	0.583503i	$0.198318\pi$
$830$	−26.5612	+	23.2936i	−0.921954	+	0.808532i
$831$		0			0
$832$	−0.0225386	−	0.0130127i	−0.000781384	−	0.000451132i
$833$	15.5825	+	9.96485i	0.539903	+	0.345262i
$834$		0			0
$835$	0.188166	+	1.42926i	0.00651176	+	0.0494617i
$836$	−3.50765	+	0.697715i	−0.121315	+	0.0241310i
$837$		0			0
$838$	−2.91348	−	1.94673i	−0.100645	−	0.0672485i
$839$	−1.65670	−	4.88049i	−0.0571958	−	0.168493i	0.914577	−	0.404411i	$-0.132524\pi$
$839$	−1.65670	−	4.88049i	−0.0571958	−	0.168493i	−0.971773	+	0.235918i	$0.924190\pi$
$840$		0			0
$841$	−38.7867	−	5.10637i	−1.33747	−	0.176082i
$842$	23.9471	+	3.15269i	0.825271	+	0.108649i
$843$		0			0
$844$	−8.20743	−	24.1783i	−0.282511	−	0.832251i
$845$	−29.2700	−	19.5576i	−1.00692	−	0.672802i
$846$		0			0
$847$	3.89897	−	0.775553i	0.133970	−	0.0266483i
$848$	−6.10712	−	46.3882i	−0.209719	−	1.59298i
$849$		0			0
$850$	−2.95626	+	16.5990i	−0.101399	+	0.569341i
$851$	−32.0258	−	18.4901i	−1.09783	−	0.633834i
$852$		0			0
$853$	24.7501	−	21.7053i	0.847428	−	0.743174i	−0.120951	−	0.992658i	$-0.538594\pi$
$853$	24.7501	−	21.7053i	0.847428	−	0.743174i	0.968379	+	0.249484i	$0.0802611\pi$
$854$	−13.5324	+	13.5324i	−0.463070	+	0.463070i
$855$		0			0
$856$	4.42655	−	22.2538i	0.151296	−	0.760619i
$857$	6.19656	−	12.5654i	0.211671	−	0.429225i	−0.764982	−	0.644052i	$-0.777252\pi$
$857$	6.19656	−	12.5654i	0.211671	−	0.429225i	0.976652	+	0.214827i	$0.0689187\pi$
$858$		0			0
$859$	−2.15156	+	16.3428i	−0.0734104	+	0.557608i	0.914731	+	0.404063i	$0.132402\pi$
$859$	−2.15156	+	16.3428i	−0.0734104	+	0.557608i	−0.988142	+	0.153545i	$0.950931\pi$
$860$	1.74894	+	26.6837i	0.0596383	+	0.909905i
$861$		0			0
$862$	−35.4401	−	2.32287i	−1.20710	−	0.0791172i
$863$	−15.8984	−	15.8984i	−0.541189	−	0.541189i	0.382688	−	0.923878i	$-0.374998\pi$
$863$	−15.8984	−	15.8984i	−0.541189	−	0.541189i	−0.923878	+	0.382688i	$0.874998\pi$
$864$		0			0
$865$	−10.1754	+	24.5656i	−0.345974	+	0.835255i
$866$	21.5884	+	37.3923i	0.733605	+	1.27064i
$867$		0			0
$868$	2.18955	−	3.79241i	0.0743182	−	0.128723i
$869$	−2.12787	−	2.77309i	−0.0721830	−	0.0940708i
$870$		0			0
$871$	0.0763677	−	0.285008i	0.00258762	−	0.00965713i
$872$	7.89809	−	11.8203i	0.267463	−	0.400287i
$873$		0			0
$874$	−12.4978	+	8.35079i	−0.422746	+	0.282470i
$875$	9.07420	+	6.96288i	0.306764	+	0.235388i
$876$		0			0
$877$	9.03011	−	0.591864i	0.304925	−	0.0199858i	0.0878273	−	0.996136i	$-0.472008\pi$
$877$	9.03011	−	0.591864i	0.304925	−	0.0199858i	0.217098	+	0.976150i	$0.430341\pi$
$878$	16.8800	+	14.8034i	0.569673	+	0.499590i
$879$		0			0
$880$	38.0938	+	10.2072i	1.28414	+	0.344085i
$881$	−7.06742	−	35.5303i	−0.238107	−	1.19705i	−0.896041	−	0.443971i	$-0.853569\pi$
$881$	−7.06742	−	35.5303i	−0.238107	−	1.19705i	0.657934	−	0.753076i	$-0.271431\pi$
$882$		0			0
$883$		−	27.9322i		−	0.939993i	−0.882668	−	0.469997i	$-0.844255\pi$
$883$		−	27.9322i		−	0.939993i	0.882668	−	0.469997i	$-0.155745\pi$
$884$	0.199993	+	0.168400i	0.00672648	+	0.00566390i
$885$		0			0
$886$	−30.0040	+	23.0229i	−1.00800	+	0.773468i
$887$	10.7714	−	31.7314i	0.361667	−	1.06544i	−0.602038	−	0.798467i	$-0.705644\pi$
$887$	10.7714	−	31.7314i	0.361667	−	1.06544i	0.963705	−	0.266969i	$-0.0860222\pi$
$888$		0			0
$889$	2.24900	−	34.3131i	0.0754290	−	1.15082i
$890$	66.7388	+	13.2752i	2.23709	+	0.444985i
$891$		0			0
$892$	−2.74921	−	6.63718i	−0.0920504	−	0.222229i
$893$	−0.0963247	+	0.125533i	−0.00322338	+	0.00420079i
$894$		0			0
$895$	−22.6620	+	25.8411i	−0.757507	+	0.863772i
$896$	16.6163	−	8.19423i	0.555110	−	0.273750i
$897$		0			0
$898$	24.5900	+	28.0395i	0.820578	+	0.935689i
$899$	19.8257	+	8.21207i	0.661224	+	0.273888i
$900$		0			0
$901$	1.75053	−	38.5730i	0.0583187	−	1.28505i
$902$	47.7670	−	27.5783i	1.59047	−	0.918257i
$903$		0			0
$904$	−21.3502	−	7.24742i	−0.710097	−	0.241045i
$905$	17.8193	+	66.5027i	0.592335	+	2.21062i
$906$		0			0
$907$	−13.3178	+	4.52080i	−0.442211	+	0.150111i	−0.533660	−	0.845699i	$-0.679184\pi$
$907$	−13.3178	+	4.52080i	−0.442211	+	0.150111i	0.0914483	+	0.995810i	$0.470850\pi$
$908$	−15.7589	−	23.5849i	−0.522978	−	0.782692i
$909$		0			0
$910$	−0.414477	+	0.171682i	−0.0137398	+	0.00569120i
$911$	−22.9359	−	11.3107i	−0.759899	−	0.374741i	0.0206898	−	0.999786i	$-0.493414\pi$
$911$	−22.9359	−	11.3107i	−0.759899	−	0.374741i	−0.780588	+	0.625045i	$0.785080\pi$
$912$		0			0
$913$	9.60682	+	19.4807i	0.317939	+	0.644717i
$914$	−23.9732	+	6.42359i	−0.792962	+	0.212473i
$915$		0			0
$916$	−7.19144	+	0.946771i	−0.237612	+	0.0312822i
$917$	−31.1551			−1.02883
$918$		0			0
$919$	−59.7459			−1.97083			−0.985417	−	0.170156i	$-0.945573\pi$
$919$	−59.7459			−1.97083			−0.985417	+	0.170156i	$0.945573\pi$
$920$	32.7646	−	4.31354i	1.08022	−	0.142213i
$921$		0			0
$922$	46.3358	−	12.4156i	1.52599	−	0.408887i
$923$	0.184129	+	0.373376i	0.00606067	+	0.0122898i
$924$		0			0
$925$	−10.4240	−	5.14056i	−0.342740	−	0.169021i
$926$	−6.87131	+	2.84619i	−0.225805	+	0.0935317i
$927$		0			0
$928$	−25.0408	−	37.4762i	−0.822004	−	1.23022i
$929$	23.6629	−	8.03247i	0.776354	−	0.263537i	0.0949870	−	0.995479i	$-0.469719\pi$
$929$	23.6629	−	8.03247i	0.776354	−	0.263537i	0.681367	+	0.731942i	$0.261386\pi$
$930$		0			0
$931$	1.34135	+	5.00598i	0.0439610	+	0.164065i
$932$	−1.09054	−	0.370189i	−0.0357219	−	0.0121259i
$933$		0			0
$934$	29.0644	−	16.7803i	0.951016	−	0.549069i
$935$	29.4733	+	13.8053i	0.963880	+	0.451482i
$936$		0			0
$937$	−26.8876	−	11.1372i	−0.878381	−	0.363837i	−0.102512	−	0.994732i	$-0.532688\pi$
$937$	−26.8876	−	11.1372i	−0.878381	−	0.363837i	−0.775869	+	0.630894i	$0.782688\pi$
$938$	9.04273	+	10.3113i	0.295256	+	0.336675i
$939$		0			0
$940$	−0.353445	+	0.174300i	−0.0115281	+	0.00568503i
$941$	18.3308	−	20.9022i	0.597566	−	0.681394i	−0.371432	−	0.928460i	$-0.621133\pi$
$941$	18.3308	−	20.9022i	0.597566	−	0.681394i	0.968999	+	0.247066i	$0.0794666\pi$
$942$		0			0
$943$	48.9532	−	63.7971i	1.59414	−	2.07752i
$944$	−3.97577	−	9.59835i	−0.129400	−	0.312400i
$945$		0			0
$946$	46.4848	+	9.24639i	1.51135	+	0.300626i
$947$	1.88439	−	28.7503i	0.0612346	−	0.934259i	−0.851149	−	0.524924i	$-0.824094\pi$
$947$	1.88439	−	28.7503i	0.0612346	−	0.934259i	0.912384	−	0.409336i	$-0.134239\pi$
$948$		0			0
$949$	−0.0619192	+	0.182408i	−0.00200998	+	0.00592121i
$950$	−3.74791	+	2.87588i	−0.121598	+	0.0933057i
$951$		0			0
$952$	10.3043	−	2.98423i	0.333964	−	0.0967194i
$953$			8.00428i			0.259284i	0.991561	+	0.129642i	$0.0413828\pi$
$953$			8.00428i			0.259284i	−0.991561	+	0.129642i	$0.958617\pi$
$954$		0			0
$955$	4.90823	+	24.6754i	0.158827	+	0.798476i
$956$	2.45235	+	0.657105i	0.0793147	+	0.0212523i
$957$		0			0
$958$	11.0019	+	9.64839i	0.355455	+	0.311725i
$959$	−0.668607	+	0.0438228i	−0.0215904	+	0.00141511i
$960$		0			0
$961$	19.2309	+	14.7564i	0.620353	+	0.476014i
$962$	−0.432001	+	0.288654i	−0.0139283	+	0.00930658i
$963$		0			0
$964$	−1.71166	+	2.56168i	−0.0551287	+	0.0825060i
$965$	8.20284	−	30.6134i	0.264059	−	0.985481i
$966$		0			0
$967$	−17.1874	−	22.3990i	−0.552708	−	0.720303i	0.430541	−	0.902571i	$-0.358323\pi$
$967$	−17.1874	−	22.3990i	−0.552708	−	0.720303i	−0.983249	+	0.182268i	$0.941656\pi$
$968$	−2.05715	+	3.56309i	−0.0661193	+	0.114522i
$969$		0			0
$970$	−29.7424	−	51.5153i	−0.954971	−	1.65406i
$971$	−22.6404	+	54.6588i	−0.726565	+	1.75408i	−0.0728496	+	0.997343i	$0.523209\pi$
$971$	−22.6404	+	54.6588i	−0.726565	+	1.75408i	−0.653716	+	0.756740i	$0.726791\pi$
$972$		0			0
$973$	−0.950774	−	0.950774i	−0.0304804	−	0.0304804i
$974$	0.243091	+	0.0159330i	0.00778915	+	0.000510528i
$975$		0			0
$976$	−2.25382	−	34.3867i	−0.0721431	−	1.10069i
$977$	−1.00991	+	7.67102i	−0.0323098	+	0.245418i	−0.999977	−	0.00681378i	$-0.997831\pi$
$977$	−1.00991	+	7.67102i	−0.0323098	+	0.245418i	0.967667	+	0.252231i	$0.0811644\pi$
$978$		0			0
$979$	18.5038	−	37.5220i	0.591384	−	1.19921i
$980$	−2.51815	+	12.6596i	−0.0804394	+	0.404396i
$981$		0			0
$982$	−30.5553	+	30.5553i	−0.975059	+	0.975059i
$983$	16.0891	−	14.1098i	0.513163	−	0.450032i	−0.363181	−	0.931719i	$-0.618309\pi$
$983$	16.0891	−	14.1098i	0.513163	−	0.450032i	0.876343	+	0.481687i	$0.159976\pi$
$984$		0			0
$985$	53.2368	+	30.7363i	1.69627	+	0.979340i
$986$	−23.8902	−	54.5487i	−0.760820	−	1.73718i
$987$		0			0
$988$	0.00956192	+	0.0726300i	0.000304205	+	0.00231067i
$989$	67.7715	−	13.4806i	2.15501	−	0.428658i
$990$		0			0
$991$	20.4059	+	13.6348i	0.648216	+	0.433124i	0.835732	−	0.549138i	$-0.185044\pi$
$991$	20.4059	+	13.6348i	0.648216	+	0.433124i	−0.187516	+	0.982261i	$0.560044\pi$
$992$	4.56391	+	13.4448i	0.144904	+	0.426874i
$993$		0			0
$994$	−19.1848	−	2.52573i	−0.608505	−	0.0801112i
$995$	−64.5476	−	8.49786i	−2.04630	−	0.269400i
$996$		0			0
$997$	9.54455	+	28.1173i	0.302279	+	0.890485i	0.986864	+	0.161552i	$0.0516500\pi$
$997$	9.54455	+	28.1173i	0.302279	+	0.890485i	−0.684585	+	0.728933i	$0.740017\pi$
$998$	43.3585	+	28.9713i	1.37249	+	0.917069i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.y.a.368.4		256
3.2	odd	2		153.2.s.a.113.13	yes	256
9.2	odd	6	inner	459.2.y.a.62.4		256
9.7	even	3		153.2.s.a.11.13	✓	256
17.14	odd	16	inner	459.2.y.a.422.4		256
51.14	even	16		153.2.s.a.14.13	yes	256
153.65	even	48	inner	459.2.y.a.116.4		256
153.133	odd	48		153.2.s.a.65.13	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.13	✓	256	9.7	even	3
153.2.s.a.14.13	yes	256	51.14	even	16
153.2.s.a.65.13	yes	256	153.133	odd	48
153.2.s.a.113.13	yes	256	3.2	odd	2
459.2.y.a.62.4		256	9.2	odd	6	inner
459.2.y.a.116.4		256	153.65	even	48	inner
459.2.y.a.368.4		256	1.1	even	1	trivial
459.2.y.a.422.4		256	17.14	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.y (of order \(48\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73496 + 0.228412i) q^{2} +(1.02607 - 0.274934i) q^{4} +(-1.19800 - 2.42931i) q^{5} +(-1.42204 - 0.701273i) q^{7} +(1.51606 - 0.627973i) q^{8} +(2.63338 + 3.94113i) q^{10} +(2.75958 - 0.936750i) q^{11} +(-0.0154499 - 0.0576598i) q^{13} +(2.62737 + 0.891870i) q^{14} +(-4.32677 + 2.49806i) q^{16} +(-3.87687 + 1.40353i) q^{17} +(-1.06733 - 0.442104i) q^{19} +(-1.89714 - 2.16327i) q^{20} +(-4.57380 + 2.25555i) q^{22} +(-4.90225 + 5.58995i) q^{23} +(-1.42254 + 1.85389i) q^{25} +(0.0399752 + 0.0965087i) q^{26} +(-1.65192 - 0.328587i) q^{28} +(0.539809 - 8.23590i) q^{29} +(-0.835738 + 2.46201i) q^{31} +(4.33245 - 3.32441i) q^{32} +(6.40564 - 3.32059i) q^{34} +4.29471i q^{35} +(0.970339 + 4.87822i) q^{37} +(1.95277 + 0.523242i) q^{38} +(-3.34179 - 2.93067i) q^{40} +(-10.7925 + 0.707376i) q^{41} +(-7.37322 - 5.65767i) q^{43} +(2.57397 - 1.71987i) q^{44} +(7.22841 - 10.8181i) q^{46} +(0.0354488 - 0.132297i) q^{47} +(-2.73091 - 3.55900i) q^{49} +(2.04460 - 3.54135i) q^{50} +(-0.0317053 - 0.0549153i) q^{52} +(-3.58381 + 8.65209i) q^{53} +(-5.58164 - 5.58164i) q^{55} +(-2.59628 - 0.170169i) q^{56} +(0.944630 + 14.4123i) q^{58} +(-0.271422 + 2.06166i) q^{59} +(-3.05066 + 6.18613i) q^{61} +(0.887622 - 4.46238i) q^{62} +(0.308284 - 0.308284i) q^{64} +(-0.121565 + 0.106609i) q^{65} +(4.28070 + 2.47146i) q^{67} +(-3.59206 + 2.50600i) q^{68} +(-0.980963 - 7.45116i) q^{70} +(-6.84006 + 1.36057i) q^{71} +(-2.68314 - 1.79281i) q^{73} +(-2.79775 - 8.24189i) q^{74} +(-1.21671 - 0.160183i) q^{76} +(-4.58115 - 0.603120i) q^{77} +(-0.385543 - 1.13577i) q^{79} +(11.2521 + 7.51839i) q^{80} +(18.5629 - 3.69240i) q^{82} +(0.972852 + 7.38954i) q^{83} +(8.05411 + 7.73670i) q^{85} +(14.0845 + 8.13171i) q^{86} +(3.59543 - 3.15311i) q^{88} +(10.1512 - 10.1512i) q^{89} +(-0.0184649 + 0.0928292i) q^{91} +(-3.49318 + 7.08347i) q^{92} +(-0.0312842 + 0.237627i) q^{94} +(0.204661 + 3.12253i) q^{95} +(-12.5228 - 0.820787i) q^{97} +(5.55095 + 5.55095i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Introduction

L-functions

Modular forms

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