LMFDB - Embedded newform 405.2.r.a.368.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			368.2
Character	$\chi$	$=$	405.368
Dual form			405.2.r.a.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.08671 - 0.182563i) q^{2} +(2.35140 + 0.414615i) q^{4} +(1.98370 + 1.03196i) q^{5} +(3.38127 + 2.36759i) q^{7} +(-0.784385 - 0.210175i) q^{8} +(-3.95100 - 2.51554i) q^{10} +(-1.66957 + 4.58710i) q^{11} +(-0.223275 - 2.55204i) q^{13} +(-6.62348 - 5.55776i) q^{14} +(-2.88895 - 1.05149i) q^{16} +(2.36120 - 0.632683i) q^{17} +(-4.05431 + 2.34076i) q^{19} +(4.23661 + 3.24902i) q^{20} +(4.32134 - 9.26714i) q^{22} +(-2.13442 - 3.04827i) q^{23} +(2.87013 + 4.09419i) q^{25} +5.36612i q^{26} +(6.96907 + 6.96907i) q^{28} +(-2.44490 + 2.05152i) q^{29} +(-0.272295 + 1.54426i) q^{31} +(7.30837 + 3.40795i) q^{32} +(-5.04264 + 0.889154i) q^{34} +(4.26417 + 8.18590i) q^{35} +(0.592937 + 2.21287i) q^{37} +(8.88750 - 4.14431i) q^{38} +(-1.33909 - 1.22638i) q^{40} +(4.38733 - 5.22862i) q^{41} +(0.553045 + 1.18601i) q^{43} +(-5.82771 + 10.0939i) q^{44} +(3.89741 + 6.75051i) q^{46} +(0.220307 - 0.314631i) q^{47} +(3.43334 + 9.43304i) q^{49} +(-5.24167 - 9.06735i) q^{50} +(0.533107 - 6.09344i) q^{52} +(-0.177802 + 0.177802i) q^{53} +(-8.04562 + 7.37651i) q^{55} +(-2.15461 - 2.56776i) q^{56} +(5.47633 - 3.83457i) q^{58} +(0.797126 - 0.290130i) q^{59} +(1.38646 + 7.86300i) q^{61} +(0.850126 - 3.17272i) q^{62} +(-9.30332 - 5.37128i) q^{64} +(2.19069 - 5.29289i) q^{65} +(8.09911 - 0.708580i) q^{67} +(5.81446 - 0.508699i) q^{68} +(-7.40362 - 17.8601i) q^{70} +(7.83146 + 4.52149i) q^{71} +(3.19228 - 11.9138i) q^{73} +(-0.833296 - 4.72586i) q^{74} +(-10.5038 + 3.82308i) q^{76} +(-16.5056 + 11.5574i) q^{77} +(-6.94728 - 8.27944i) q^{79} +(-4.64572 - 5.06712i) q^{80} +(-10.1096 + 10.1096i) q^{82} +(-0.325084 + 3.71573i) q^{83} +(5.33682 + 1.18161i) q^{85} +(-0.937521 - 2.57582i) q^{86} +(2.27368 - 3.24715i) q^{88} +(-7.58469 - 13.1371i) q^{89} +(5.28723 - 9.15775i) q^{91} +(-3.75502 - 8.05267i) q^{92} +(-0.517156 + 0.616322i) q^{94} +(-10.4581 + 0.459486i) q^{95} +(-1.25036 + 0.583050i) q^{97} +(-5.44226 - 20.3108i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−2.08671	−	0.182563i	−1.47552	−	0.129092i	−0.679196	−	0.733956i	$-0.737672\pi$
$2$	−2.08671	−	0.182563i	−1.47552	−	0.129092i	−0.796328	+	0.604865i	$0.793227\pi$
$3$		0			0
$3$		0			0
$4$	2.35140	+	0.414615i	1.17570	+	0.207308i
$5$	1.98370	+	1.03196i	0.887138	+	0.461505i
$5$	1.98370	+	1.03196i	0.887138	+	0.461505i
$6$		0			0
$7$	3.38127	+	2.36759i	1.27800	+	0.894864i	0.997879	−	0.0651011i	$-0.0207370\pi$
$7$	3.38127	+	2.36759i	1.27800	+	0.894864i	0.280120	+	0.959965i	$0.409626\pi$
$8$	−0.784385	−	0.210175i	−0.277322	−	0.0743082i
$9$		0			0
$10$	−3.95100	−	2.51554i	−1.24942	−	0.795484i
$11$	−1.66957	+	4.58710i	−0.503394	+	1.38306i	0.384546	+	0.923106i	$0.374358\pi$
$11$	−1.66957	+	4.58710i	−0.503394	+	1.38306i	−0.887940	+	0.459958i	$0.847864\pi$
$12$		0			0
$13$	−0.223275	−	2.55204i	−0.0619252	−	0.707809i	−0.962175	−	0.272434i	$-0.912171\pi$
$13$	−0.223275	−	2.55204i	−0.0619252	−	0.707809i	0.900249	−	0.435375i	$-0.143384\pi$
$14$	−6.62348	−	5.55776i	−1.77020	−	1.48537i
$15$		0			0
$16$	−2.88895	−	1.05149i	−0.722238	−	0.262873i
$17$	2.36120	−	0.632683i	0.572676	−	0.153448i	0.0391524	−	0.999233i	$-0.487534\pi$
$17$	2.36120	−	0.632683i	0.572676	−	0.153448i	0.533524	+	0.845785i	$0.320868\pi$
$18$		0			0
$19$	−4.05431	+	2.34076i	−0.930123	+	0.537007i	−0.886850	−	0.462057i	$-0.847112\pi$
$19$	−4.05431	+	2.34076i	−0.930123	+	0.537007i	−0.0432724	+	0.999063i	$0.513778\pi$
$20$	4.23661	+	3.24902i	0.947335	+	0.726502i
$21$		0			0
$22$	4.32134	−	9.26714i	0.921313	−	1.97576i
$23$	−2.13442	−	3.04827i	−0.445058	−	0.635608i	0.532462	−	0.846454i	$-0.321267\pi$
$23$	−2.13442	−	3.04827i	−0.445058	−	0.635608i	−0.977519	+	0.210846i	$0.932378\pi$
$24$		0			0
$25$	2.87013	+	4.09419i	0.574026	+	0.818837i
$26$			5.36612i			1.05238i
$27$		0			0
$28$	6.96907	+	6.96907i	1.31703	+	1.31703i
$29$	−2.44490	+	2.05152i	−0.454007	+	0.380957i	−0.840920	−	0.541159i	$-0.817986\pi$
$29$	−2.44490	+	2.05152i	−0.454007	+	0.380957i	0.386913	+	0.922116i	$0.373541\pi$
$30$		0			0
$31$	−0.272295	+	1.54426i	−0.0489057	+	0.277358i	−0.999447	−	0.0332389i	$-0.989418\pi$
$31$	−0.272295	+	1.54426i	−0.0489057	+	0.277358i	0.950542	+	0.310597i	$0.100529\pi$
$32$	7.30837	+	3.40795i	1.29195	+	0.602446i
$33$		0			0
$34$	−5.04264	+	0.889154i	−0.864806	+	0.152489i
$35$	4.26417	+	8.18590i	0.720776	+	1.38367i
$36$		0			0
$37$	0.592937	+	2.21287i	0.0974782	+	0.363793i	0.997384	−	0.0722918i	$-0.0230313\pi$
$37$	0.592937	+	2.21287i	0.0974782	+	0.363793i	−0.899905	+	0.436085i	$0.856365\pi$
$38$	8.88750	−	4.14431i	1.44174	−	0.672295i
$39$		0			0
$40$	−1.33909	−	1.22638i	−0.211729	−	0.193907i
$41$	4.38733	−	5.22862i	0.685186	−	0.816573i	−0.305579	−	0.952167i	$-0.598850\pi$
$41$	4.38733	−	5.22862i	0.685186	−	0.816573i	0.990764	+	0.135594i	$0.0432944\pi$
$42$		0			0
$43$	0.553045	+	1.18601i	0.0843385	+	0.180865i	0.943954	−	0.330077i	$-0.107075\pi$
$43$	0.553045	+	1.18601i	0.0843385	+	0.180865i	−0.859616	+	0.510941i	$0.829297\pi$
$44$	−5.82771	+	10.0939i	−0.878561	+	1.52171i
$45$		0			0
$46$	3.89741	+	6.75051i	0.574642	+	0.995309i
$47$	0.220307	−	0.314631i	0.0321351	−	0.0458936i	−0.802763	−	0.596298i	$-0.796638\pi$
$47$	0.220307	−	0.314631i	0.0321351	−	0.0458936i	0.834898	+	0.550405i	$0.185527\pi$
$48$		0			0
$49$	3.43334	+	9.43304i	0.490478	+	1.34758i
$50$	−5.24167	−	9.06735i	−0.741284	−	1.28232i
$51$		0			0
$52$	0.533107	−	6.09344i	0.0739287	−	0.845009i
$53$	−0.177802	+	0.177802i	−0.0244229	+	0.0244229i	−0.719213	−	0.694790i	$-0.755497\pi$
$53$	−0.177802	+	0.177802i	−0.0244229	+	0.0244229i	0.694790	+	0.719213i	$0.255497\pi$
$54$		0			0
$55$	−8.04562	+	7.37651i	−1.08487	+	0.994649i
$56$	−2.15461	−	2.56776i	−0.287921	−	0.343131i
$57$		0			0
$58$	5.47633	−	3.83457i	0.719077	−	0.503503i
$59$	0.797126	−	0.290130i	0.103777	−	0.0377717i	−0.289610	−	0.957145i	$-0.593526\pi$
$59$	0.797126	−	0.290130i	0.103777	−	0.0377717i	0.393387	+	0.919373i	$0.371303\pi$
$60$		0			0
$61$	1.38646	+	7.86300i	0.177518	+	1.00675i	0.935197	+	0.354127i	$0.115222\pi$
$61$	1.38646	+	7.86300i	0.177518	+	1.00675i	−0.757679	+	0.652627i	$0.773667\pi$
$62$	0.850126	−	3.17272i	0.107966	−	0.402935i
$63$		0			0
$64$	−9.30332	−	5.37128i	−1.16292	−	0.671410i
$65$	2.19069	−	5.29289i	0.271721	−	0.656502i
$66$		0			0
$67$	8.09911	−	0.708580i	0.989463	−	0.0865668i	0.419083	−	0.907948i	$-0.362351\pi$
$67$	8.09911	−	0.708580i	0.989463	−	0.0865668i	0.570380	+	0.821381i	$0.306796\pi$
$68$	5.81446	−	0.508699i	0.705106	−	0.0616888i
$69$		0			0
$70$	−7.40362	−	17.8601i	−0.884902	−	2.13469i
$71$	7.83146	+	4.52149i	0.929423	+	0.536603i	0.886629	−	0.462481i	$-0.153041\pi$
$71$	7.83146	+	4.52149i	0.929423	+	0.536603i	0.0427939	+	0.999084i	$0.486374\pi$
$72$		0			0
$73$	3.19228	−	11.9138i	0.373628	−	1.39440i	−0.481710	−	0.876330i	$-0.659984\pi$
$73$	3.19228	−	11.9138i	0.373628	−	1.39440i	0.855339	−	0.518069i	$-0.173349\pi$
$74$	−0.833296	−	4.72586i	−0.0968687	−	0.549370i
$75$		0			0
$76$	−10.5038	+	3.82308i	−1.20487	+	0.438537i
$77$	−16.5056	+	11.5574i	−1.88099	+	1.31708i
$78$		0			0
$79$	−6.94728	−	8.27944i	−0.781630	−	0.931510i	0.217376	−	0.976088i	$-0.430250\pi$
$79$	−6.94728	−	8.27944i	−0.781630	−	0.931510i	−0.999006	+	0.0445777i	$0.985806\pi$
$80$	−4.64572	−	5.06712i	−0.519407	−	0.566521i
$81$		0			0
$82$	−10.1096	+	10.1096i	−1.11642	+	1.11642i
$83$	−0.325084	+	3.71573i	−0.0356826	+	0.407854i	0.957257	+	0.289237i	$0.0934016\pi$
$83$	−0.325084	+	3.71573i	−0.0356826	+	0.407854i	−0.992940	+	0.118617i	$0.962154\pi$
$84$		0			0
$85$	5.33682	+	1.18161i	0.578859	+	0.128163i
$86$	−0.937521	−	2.57582i	−0.101095	−	0.277758i
$87$		0			0
$88$	2.27368	−	3.24715i	0.242375	−	0.346148i
$89$	−7.58469	−	13.1371i	−0.803975	−	1.39253i	−0.916981	−	0.398932i	$-0.869381\pi$
$89$	−7.58469	−	13.1371i	−0.803975	−	1.39253i	0.113006	−	0.993594i	$-0.463952\pi$
$90$		0			0
$91$	5.28723	−	9.15775i	0.554252	−	0.959993i
$92$	−3.75502	−	8.05267i	−0.391488	−	0.839549i
$93$		0			0
$94$	−0.517156	+	0.616322i	−0.0533406	+	0.0635688i
$95$	−10.4581	+	0.459486i	−1.07298	+	0.0471422i
$96$		0			0
$97$	−1.25036	+	0.583050i	−0.126954	+	0.0591998i	−0.485058	−	0.874482i	$-0.661201\pi$
$97$	−1.25036	+	0.583050i	−0.126954	+	0.0591998i	0.358103	+	0.933682i	$0.383424\pi$
$98$	−5.44226	−	20.3108i	−0.549751	−	2.05170i
$99$		0			0
$100$	5.05131	+	10.8171i	0.505131	+	1.08171i
$101$	−0.515416	+	0.0908818i	−0.0512858	+	0.00904308i	−0.199232	−	0.979952i	$-0.563845\pi$
$101$	−0.515416	+	0.0908818i	−0.0512858	+	0.00904308i	0.147946	+	0.988995i	$0.452734\pi$
$102$		0			0
$103$	3.14419	+	1.46616i	0.309806	+	0.144465i	0.571303	−	0.820739i	$-0.306438\pi$
$103$	3.14419	+	1.46616i	0.309806	+	0.144465i	−0.261496	+	0.965204i	$0.584216\pi$
$104$	−0.361243	+	2.04871i	−0.0354228	+	0.200892i
$105$		0			0
$106$	0.403480	−	0.338560i	0.0391894	−	0.0328838i
$107$	4.07064	+	4.07064i	0.393524	+	0.393524i	0.875941	−	0.482418i	$-0.160241\pi$
$107$	4.07064	+	4.07064i	0.393524	+	0.393524i	−0.482418	+	0.875941i	$0.660241\pi$
$108$		0			0
$109$		−	10.3288i		−	0.989319i	−0.869087	−	0.494660i	$-0.835293\pi$
$109$		−	10.3288i		−	0.989319i	0.869087	−	0.494660i	$-0.164707\pi$
$110$	18.1355	−	13.9238i	1.72916	−	1.32758i
$111$		0			0
$112$	−7.27881	−	10.3952i	−0.687783	−	0.982256i
$113$	2.31072	−	4.95536i	0.217375	−	0.466161i	−0.767136	−	0.641484i	$-0.778319\pi$
$113$	2.31072	−	4.95536i	0.217375	−	0.466161i	0.984511	+	0.175323i	$0.0560969\pi$
$114$		0			0
$115$	−1.08837	−	8.24948i	−0.101491	−	0.769268i
$116$	−6.59954	+	3.81025i	−0.612752	+	0.353773i
$117$		0			0
$118$	−1.71634	+	0.459891i	−0.158001	+	0.0423364i
$119$	9.48179	+	3.45109i	0.869194	+	0.316361i
$120$		0			0
$121$	−9.82758	−	8.24632i	−0.893416	−	0.749665i
$122$	−1.45764	−	16.6609i	−0.131968	−	1.50841i
$123$		0			0
$124$	−1.28055	+	3.51829i	−0.114997	+	0.315951i
$125$	1.46845	+	11.0835i	0.131342	+	0.991337i
$126$		0			0
$127$	6.98435	+	1.87145i	0.619760	+	0.166064i	0.555019	−	0.831838i	$-0.312711\pi$
$127$	6.98435	+	1.87145i	0.619760	+	0.166064i	0.0647416	+	0.997902i	$0.479378\pi$
$128$	5.22160	+	3.65620i	0.461528	+	0.323166i
$129$		0			0
$130$	−5.53761	+	10.6448i	−0.485680	+	0.933608i
$131$	−7.48308	−	1.31947i	−0.653800	−	0.115283i	−0.163098	−	0.986610i	$-0.552149\pi$
$131$	−7.48308	−	1.31947i	−0.653800	−	0.115283i	−0.490702	+	0.871327i	$0.663260\pi$
$132$		0			0
$133$	−19.2507	−	1.68421i	−1.66924	−	0.146040i
$134$	−17.0298			−1.47115
$135$		0			0
$136$	−1.98507			−0.170218
$137$	−8.77434	−	0.767656i	−0.749643	−	0.0655852i	−0.294070	−	0.955784i	$-0.595010\pi$
$137$	−8.77434	−	0.767656i	−0.749643	−	0.0655852i	−0.455573	+	0.890199i	$0.650565\pi$
$138$		0			0
$139$	0.637180	+	0.112352i	0.0540449	+	0.00952958i	0.200605	−	0.979672i	$-0.435709\pi$
$139$	0.637180	+	0.112352i	0.0540449	+	0.00952958i	−0.146560	+	0.989202i	$0.546820\pi$
$140$	6.63277	+	21.0163i	0.560571	+	1.77620i
$141$		0			0
$142$	−15.5165	−	10.8648i	−1.30212	−	0.911751i
$143$	12.0792	+	3.23662i	1.01012	+	0.270660i
$144$		0			0
$145$	−6.96703	+	1.54656i	−0.578581	+	0.128435i
$146$	−8.83637	+	24.2777i	−0.731303	+	2.00924i
$147$		0			0
$148$	0.476742	+	5.44918i	0.0391879	+	0.447920i
$149$	14.2896	+	11.9904i	1.17065	+	0.982290i	0.999995	−	0.00304137i	$-0.000968099\pi$
$149$	14.2896	+	11.9904i	1.17065	+	0.982290i	0.170652	+	0.985331i	$0.445413\pi$
$150$		0			0
$151$	11.1465	+	4.05701i	0.907092	+	0.330155i	0.753091	−	0.657916i	$-0.228562\pi$
$151$	11.1465	+	4.05701i	0.907092	+	0.330155i	0.154001	+	0.988071i	$0.450784\pi$
$152$	3.67211	−	0.983939i	0.297847	−	0.0798080i
$153$		0			0
$154$	36.5524	−	21.1035i	2.94547	−	1.70057i
$155$	−2.13377	+	2.78236i	−0.171388	+	0.223484i
$156$		0			0
$157$	0.402710	−	0.863615i	0.0321398	−	0.0689240i	−0.889582	−	0.456775i	$-0.849005\pi$
$157$	0.402710	−	0.863615i	0.0321398	−	0.0689240i	0.921722	+	0.387851i	$0.126782\pi$
$158$	12.9854	+	18.5451i	1.03306	+	1.47537i
$159$		0			0
$160$	10.9808	+	14.3023i	0.868105	+	1.13069i
$161$		−	15.3604i		−	1.21057i
$162$		0			0
$163$	12.1885	+	12.1885i	0.954673	+	0.954673i	0.999016	−	0.0443429i	$-0.0141194\pi$
$163$	12.1885	+	12.1885i	0.954673	+	0.954673i	−0.0443429	+	0.999016i	$0.514119\pi$
$164$	12.4842	−	10.4755i	0.974855	−	0.818001i
$165$		0			0
$166$	1.35671	−	7.69429i	0.105301	−	0.597193i
$167$	4.59936	+	2.14472i	0.355909	+	0.165963i	0.592346	−	0.805684i	$-0.298202\pi$
$167$	4.59936	+	2.14472i	0.355909	+	0.165963i	−0.236437	+	0.971647i	$0.575980\pi$
$168$		0			0
$169$	6.33944	−	1.11781i	0.487649	−	0.0859858i
$170$	−10.9207	−	3.43998i	−0.837577	−	0.263834i
$171$		0			0
$172$	0.808693	+	3.01808i	0.0616622	+	0.230127i
$173$	1.51516	−	0.706530i	0.115195	−	0.0537164i	−0.364166	−	0.931334i	$-0.618646\pi$
$173$	1.51516	−	0.706530i	0.115195	−	0.0537164i	0.479362	+	0.877617i	$0.340868\pi$
$174$		0			0
$175$	0.0113268	+	20.6388i	0.000856228	+	1.56015i
$176$	9.64661	−	11.4964i	0.727140	−	0.866572i
$177$		0			0
$178$	13.4287	+	28.7979i	1.00652	+	2.15849i
$179$	−7.16939	+	12.4178i	−0.535866	+	0.928147i	0.463255	+	0.886225i	$0.346681\pi$
$179$	−7.16939	+	12.4178i	−0.535866	+	0.928147i	−0.999121	+	0.0419217i	$0.986652\pi$
$180$		0			0
$181$	−10.7361	−	18.5955i	−0.798011	−	1.38220i	−0.920910	−	0.389776i	$-0.872552\pi$
$181$	−10.7361	−	18.5955i	−0.798011	−	1.38220i	0.122899	−	0.992419i	$-0.460781\pi$
$182$	−12.7048	+	18.1443i	−0.941740	+	1.34494i
$183$		0			0
$184$	1.03354	+	2.83962i	0.0761933	+	0.209339i
$185$	−1.10738	+	5.00155i	−0.0814160	+	0.367722i
$186$		0			0
$187$	−1.04001	+	11.8874i	−0.0760532	+	0.869292i
$188$	0.648481	−	0.648481i	0.0472953	−	0.0472953i
$189$		0			0
$190$	21.9069	+	0.950452i	1.58929	+	0.0689530i
$191$	7.60498	+	9.06326i	0.550277	+	0.655794i	0.967459	−	0.253029i	$-0.0814267\pi$
$191$	7.60498	+	9.06326i	0.550277	+	0.655794i	−0.417182	+	0.908823i	$0.636982\pi$
$192$		0			0
$193$	−13.1725	+	9.22349i	−0.948178	+	0.663922i	−0.941841	−	0.336058i	$-0.890906\pi$
$193$	−13.1725	+	9.22349i	−0.948178	+	0.663922i	−0.00633721	+	0.999980i	$0.502017\pi$
$194$	2.71557	−	0.988386i	0.194967	−	0.0709620i
$195$		0			0
$196$	4.16209	+	23.6044i	0.297292	+	1.68603i
$197$	7.15409	−	26.6994i	0.509708	−	1.90225i	0.0864206	−	0.996259i	$-0.472457\pi$
$197$	7.15409	−	26.6994i	0.509708	−	1.90225i	0.423287	−	0.905996i	$-0.360876\pi$
$198$		0			0
$199$	−17.2147	−	9.93892i	−1.22032	−	0.704551i	−0.255332	−	0.966853i	$-0.582185\pi$
$199$	−17.2147	−	9.93892i	−1.22032	−	0.704551i	−0.964986	+	0.262302i	$0.915518\pi$
$200$	−1.39079	−	3.81465i	−0.0983437	−	0.269736i
$201$		0			0
$202$	1.09211	−	0.0955476i	0.0768409	−	0.00672271i
$203$	−13.1240	+	1.14820i	−0.921126	+	0.0805881i
$204$		0			0
$205$	14.0988	−	5.84447i	0.984706	−	0.408195i
$206$	−6.29334	−	3.63346i	−0.438478	−	0.253155i
$207$		0			0
$208$	−2.03842	+	7.60749i	−0.141339	+	0.527484i
$209$	−3.96835	−	22.5056i	−0.274496	−	1.55675i
$210$		0			0
$211$	21.2772	−	7.74427i	1.46478	−	0.533137i	0.518105	−	0.855317i	$-0.326638\pi$
$211$	21.2772	−	7.74427i	1.46478	−	0.533137i	0.946678	+	0.322180i	$0.104416\pi$
$212$	−0.491802	+	0.344364i	−0.0337771	+	0.0236510i
$213$		0			0
$214$	−7.75108	−	9.23738i	−0.529853	−	0.631454i
$215$	−0.126835	+	2.92340i	−0.00865006	+	0.199374i
$216$		0			0
$217$	−4.57688	+	4.57688i	−0.310699	+	0.310699i
$218$	−1.88566	+	21.5532i	−0.127713	+	1.45976i
$219$		0			0
$220$	−21.9769	+	14.0093i	−1.48168	+	0.944507i
$221$	−2.14183	−	5.88462i	−0.144075	−	0.395843i
$222$		0			0
$223$	5.78878	−	8.26723i	0.387645	−	0.553615i	−0.577143	−	0.816643i	$-0.695832\pi$
$223$	5.78878	−	8.26723i	0.387645	−	0.553615i	0.964788	+	0.263029i	$0.0847213\pi$
$224$	16.6429	+	28.8264i	1.11200	+	1.92604i
$225$		0			0
$226$	−5.72647	+	9.91853i	−0.380919	+	0.659771i
$227$	−10.3017	−	22.0920i	−0.683745	−	1.46630i	−0.874684	−	0.484694i	$-0.838931\pi$
$227$	−10.3017	−	22.0920i	−0.683745	−	1.46630i	0.190939	−	0.981602i	$-0.438847\pi$
$228$		0			0
$229$	−5.75242	+	6.85547i	−0.380131	+	0.453022i	−0.921855	−	0.387534i	$-0.873327\pi$
$229$	−5.75242	+	6.85547i	−0.380131	+	0.453022i	0.541725	+	0.840556i	$0.317771\pi$
$230$	0.765053	+	17.4129i	0.0504461	+	1.14818i
$231$		0			0
$232$	2.34892	−	1.09532i	0.154214	−	0.0719114i
$233$	−4.94285	−	18.4470i	−0.323817	−	1.20850i	−0.915496	−	0.402328i	$-0.868201\pi$
$233$	−4.94285	−	18.4470i	−0.323817	−	1.20850i	0.591679	−	0.806174i	$-0.298465\pi$
$234$		0			0
$235$	0.761708	−	0.396786i	0.0496884	−	0.0258835i
$236$	1.99466	−	0.351712i	0.129841	−	0.0228945i
$237$		0			0
$238$	−19.1557	−	8.93244i	−1.24168	−	0.579004i
$239$	0.434105	−	2.46193i	0.0280799	−	0.159249i	−0.967544	−	0.252704i	$-0.918680\pi$
$239$	0.434105	−	2.46193i	0.0280799	−	0.159249i	0.995623	+	0.0934552i	$0.0297912\pi$
$240$		0			0
$241$	16.4029	−	13.7637i	1.05660	−	0.886595i	0.0628307	−	0.998024i	$-0.479987\pi$
$241$	16.4029	−	13.7637i	1.05660	−	0.886595i	0.993772	+	0.111429i	$0.0355428\pi$
$242$	19.0018	+	19.0018i	1.22148	+	1.22148i
$243$		0			0
$244$			19.0639i			1.22044i
$245$	−2.92376	+	22.2554i	−0.186792	+	1.42184i
$246$		0			0
$247$	6.87893	+	9.82413i	0.437696	+	0.625095i
$248$	0.538151	−	1.15407i	0.0341726	−	0.0732834i
$249$		0			0
$250$	−1.04079	−	23.3961i	−0.0658255	−	1.47970i
$251$	−13.6587	+	7.88585i	−0.862129	+	0.497751i	−0.864725	−	0.502246i	$-0.832507\pi$
$251$	−13.6587	+	7.88585i	−0.862129	+	0.497751i	0.00259539	+	0.999997i	$0.499174\pi$
$252$		0			0
$253$	17.5463	−	4.70152i	1.10313	−	0.295582i
$254$	−14.2326	−	5.18025i	−0.893034	−	0.325038i
$255$		0			0
$256$	6.23009	+	5.22767i	0.389381	+	0.326729i
$257$	0.121306	+	1.38654i	0.00756687	+	0.0864897i	0.999039	−	0.0438287i	$-0.0139556\pi$
$257$	0.121306	+	1.38654i	0.00756687	+	0.0864897i	−0.991472	+	0.130318i	$0.958400\pi$
$258$		0			0
$259$	−3.23429	+	8.88613i	−0.200969	+	0.552157i
$260$	7.34570	−	11.5374i	0.455561	−	0.715520i
$261$		0			0
$262$	15.3741	+	4.11948i	0.949816	+	0.254502i
$263$	−20.2750	−	14.1967i	−1.25021	−	0.875405i	−0.254420	−	0.967094i	$-0.581884\pi$
$263$	−20.2750	−	14.1967i	−1.25021	−	0.875405i	−0.995788	+	0.0916894i	$0.970773\pi$
$264$		0			0
$265$	−0.536189	+	0.169221i	−0.0329378	+	0.0103952i
$266$	39.8630	+	7.02892i	2.44416	+	0.430971i
$267$		0			0
$268$	19.3380	+	1.69186i	1.18126	+	0.103347i
$269$	30.2129			1.84212			0.921058	−	0.389426i	$-0.127327\pi$
$269$	30.2129			1.84212			0.921058	+	0.389426i	$0.127327\pi$
$270$		0			0
$271$	−30.1849			−1.83360			−0.916802	−	0.399341i	$-0.869239\pi$
$271$	−30.1849			−1.83360			−0.916802	+	0.399341i	$0.869239\pi$
$272$	−7.48666	−	0.654998i	−0.453946	−	0.0397151i
$273$		0			0
$274$	18.1693	+	3.20374i	1.09765	+	0.193545i
$275$	−23.5723	+	6.33006i	−1.42147	+	0.381717i
$276$		0			0
$277$	−4.74942	−	3.32558i	−0.285365	−	0.199815i	0.422126	−	0.906537i	$-0.361284\pi$
$277$	−4.74942	−	3.32558i	−0.285365	−	0.199815i	−0.707491	+	0.706723i	$0.750173\pi$
$278$	−1.30910	−	0.350772i	−0.0785144	−	0.0210379i
$279$		0			0
$280$	−1.62427	−	7.31712i	−0.0970689	−	0.437282i
$281$	5.21843	−	14.3375i	0.311305	−	0.855304i	−0.681089	−	0.732201i	$-0.738493\pi$
$281$	5.21843	−	14.3375i	0.311305	−	0.855304i	0.992394	−	0.123103i	$-0.0392846\pi$
$282$		0			0
$283$	−2.06765	−	23.6334i	−0.122909	−	1.40486i	−0.767852	−	0.640627i	$-0.778674\pi$
$283$	−2.06765	−	23.6334i	−0.122909	−	1.40486i	0.644943	−	0.764231i	$-0.276881\pi$
$284$	16.5402	+	13.8789i	0.981481	+	0.823561i
$285$		0			0
$286$	−24.6150	−	8.95911i	−1.45551	−	0.529764i
$287$	27.2139	−	7.29195i	1.60639	−	0.430430i
$288$		0			0
$289$	−9.54744	+	5.51222i	−0.561614	+	0.324248i
$290$	14.8205	−	1.95529i	0.870290	−	0.114819i
$291$		0			0
$292$	12.4460	−	26.6905i	0.728345	−	1.56194i
$293$	−4.78492	−	6.83357i	−0.279538	−	0.399221i	0.654690	−	0.755897i	$-0.272799\pi$
$293$	−4.78492	−	6.83357i	−0.279538	−	0.399221i	−0.934228	+	0.356676i	$0.883910\pi$
$294$		0			0
$295$	1.88066	+	0.247069i	0.109496	+	0.0143849i
$296$		−	1.86036i		−	0.108131i
$297$		0			0
$298$	−27.6292	−	27.6292i	−1.60051	−	1.60051i
$299$	−7.30274	+	6.12773i	−0.422329	+	0.354376i
$300$		0			0
$301$	−0.937987	+	5.31959i	−0.0540647	+	0.306616i
$302$	−22.5189	−	10.5007i	−1.29582	−	0.604249i
$303$		0			0
$304$	14.1740	−	2.49926i	0.812934	−	0.143342i
$305$	−5.36396	+	17.0286i	−0.307139	+	0.975055i
$306$		0			0
$307$	−5.72891	−	21.3806i	−0.326966	−	1.22025i	−0.912321	−	0.409476i	$-0.865711\pi$
$307$	−5.72891	−	21.3806i	−0.326966	−	1.22025i	0.585355	−	0.810777i	$-0.300955\pi$
$308$	−43.6032	+	20.3325i	−2.48452	+	1.15855i
$309$		0			0
$310$	4.96050	−	5.41642i	0.281738	−	0.307632i
$311$	−17.1260	+	20.4100i	−0.971128	+	1.15735i	0.0163937	+	0.999866i	$0.494781\pi$
$311$	−17.1260	+	20.4100i	−0.971128	+	1.15735i	−0.987522	+	0.157480i	$0.949663\pi$
$312$		0			0
$313$	−0.188967	−	0.405241i	−0.0106810	−	0.0229056i	0.900895	−	0.434037i	$-0.142911\pi$
$313$	−0.188967	−	0.405241i	−0.0106810	−	0.0229056i	−0.911576	+	0.411132i	$0.865134\pi$
$314$	−0.998003	+	1.72859i	−0.0563206	+	0.0975501i
$315$		0			0
$316$	−12.9031	−	22.3487i	−0.725853	−	1.25722i
$317$	−0.491526	+	0.701972i	−0.0276069	+	0.0394267i	−0.832718	−	0.553697i	$-0.813217\pi$
$317$	−0.491526	+	0.701972i	−0.0276069	+	0.0394267i	0.805111	+	0.593124i	$0.202105\pi$
$318$		0			0
$319$	−5.32859	−	14.6402i	−0.298344	−	0.819693i
$320$	−12.9121	−	20.2556i	−0.721807	−	1.13232i
$321$		0			0
$322$	−2.80425	+	32.0527i	−0.156275	+	1.78623i
$323$	−8.09210	+	8.09210i	−0.450256	+	0.450256i
$324$		0			0
$325$	9.80770	−	8.23881i	0.544033	−	0.457007i
$326$	−23.2086	−	27.6589i	−1.28540	−	1.53188i
$327$		0			0
$328$	−4.54028	+	3.17914i	−0.250695	+	0.175539i
$329$	1.48983	−	0.542255i	0.0821371	−	0.0298955i
$330$		0			0
$331$	4.97884	+	28.2364i	0.273662	+	1.55201i	0.743181	+	0.669091i	$0.233316\pi$
$331$	4.97884	+	28.2364i	0.273662	+	1.55201i	−0.469519	+	0.882922i	$0.655573\pi$
$332$	−2.30500	+	8.60238i	−0.126503	+	0.472117i
$333$		0			0
$334$	−9.20598	−	5.31507i	−0.503729	−	0.290828i
$335$	16.7974	+	6.95232i	0.917741	+	0.379846i
$336$		0			0
$337$	−7.49834	+	0.656020i	−0.408461	+	0.0357357i	−0.289535	−	0.957167i	$-0.593501\pi$
$337$	−7.49834	+	0.656020i	−0.408461	+	0.0357357i	−0.118926	+	0.992903i	$0.537945\pi$
$338$	−13.4326	+	1.17520i	−0.730639	+	0.0639226i
$339$		0			0
$340$	12.0591	+	4.99116i	0.653996	+	0.270684i
$341$	−6.62908	−	3.82730i	−0.358985	−	0.207260i
$342$		0			0
$343$	−3.24609	+	12.1146i	−0.175272	+	0.654125i
$344$	−0.184530	−	1.04652i	−0.00994921	−	0.0564248i
$345$		0			0
$346$	−3.29068	+	1.19771i	−0.176908	+	0.0643892i
$347$	21.2589	−	14.8856i	1.14124	−	0.799103i	0.159099	−	0.987263i	$-0.449141\pi$
$347$	21.2589	−	14.8856i	1.14124	−	0.799103i	0.982138	+	0.188160i	$0.0602524\pi$
$348$		0			0
$349$	11.2260	+	13.3786i	0.600915	+	0.716143i	0.977664	−	0.210173i	$-0.0674026\pi$
$349$	11.2260	+	13.3786i	0.600915	+	0.716143i	−0.376749	+	0.926315i	$0.622958\pi$
$350$	3.74425	−	43.0692i	0.200139	−	2.30215i
$351$		0			0
$352$	−27.8345	+	27.8345i	−1.48358	+	1.48358i
$353$	0.785720	−	8.98082i	0.0418196	−	0.478001i	−0.946190	−	0.323611i	$-0.895103\pi$
$353$	0.785720	−	8.98082i	0.0418196	−	0.478001i	0.988010	−	0.154390i	$-0.0493413\pi$
$354$		0			0
$355$	10.8693	+	17.0510i	0.576881	+	0.904974i
$356$	−12.3878	−	34.0352i	−0.656553	−	1.80386i
$357$		0			0
$358$	17.2275	−	24.6033i	0.910499	−	1.30033i
$359$	−7.90716	−	13.6956i	−0.417324	−	0.722827i	0.578345	−	0.815792i	$-0.303699\pi$
$359$	−7.90716	−	13.6956i	−0.417324	−	0.722827i	−0.995669	+	0.0929655i	$0.970365\pi$
$360$		0			0
$361$	1.45829	−	2.52584i	0.0767523	−	0.132939i
$362$	19.0083	+	40.7635i	0.999055	+	2.14248i
$363$		0			0
$364$	16.2293	−	19.3414i	0.850648	−	1.01376i
$365$	18.6270	−	20.3390i	0.974982	−	1.06459i
$366$		0			0
$367$	19.6260	−	9.15174i	1.02447	−	0.477717i	0.163589	−	0.986529i	$-0.447693\pi$
$367$	19.6260	−	9.15174i	1.02447	−	0.477717i	0.860878	+	0.508812i	$0.169915\pi$
$368$	2.96101	+	11.0506i	0.154353	+	0.576054i
$369$		0			0
$370$	3.22387	−	10.2346i	0.167601	−	0.532072i
$371$	−1.02216	+	0.180234i	−0.0530677	+	0.00935726i
$372$		0			0
$373$	−22.0287	−	10.2722i	−1.14060	−	0.531873i	−0.241845	−	0.970315i	$-0.577753\pi$
$373$	−22.0287	−	10.2722i	−1.14060	−	0.531873i	−0.898760	+	0.438442i	$0.855530\pi$
$374$	4.34040	−	24.6156i	0.224437	−	1.27284i
$375$		0			0
$376$	−0.238933	+	0.200489i	−0.0123220	+	0.0103394i
$377$	5.78144	+	5.78144i	0.297759	+	0.297759i
$378$		0			0
$379$		−	18.5170i		−	0.951157i	−0.879673	−	0.475578i	$-0.842239\pi$
$379$		−	18.5170i		−	0.951157i	0.879673	−	0.475578i	$-0.157761\pi$
$380$	−24.7817	−	3.25565i	−1.27127	−	0.167012i
$381$		0			0
$382$	−14.2147	−	20.3008i	−0.727289	−	1.03868i
$383$	0.998023	−	2.14027i	0.0509966	−	0.109363i	−0.879158	−	0.476530i	$-0.841895\pi$
$383$	0.998023	−	2.14027i	0.0509966	−	0.109363i	0.930155	+	0.367167i	$0.119672\pi$
$384$		0			0
$385$	−44.6689	+	5.89325i	−2.27654	+	0.300348i
$386$	29.1711	−	16.8419i	1.48477	−	0.857231i
$387$		0			0
$388$	−3.18183	+	0.852569i	−0.161533	+	0.0432826i
$389$	−9.90399	−	3.60476i	−0.502152	−	0.182768i	0.0785096	−	0.996913i	$-0.474984\pi$
$389$	−9.90399	−	3.60476i	−0.502152	−	0.182768i	−0.580662	+	0.814145i	$0.697206\pi$
$390$		0			0
$391$	−6.96839	−	5.84717i	−0.352407	−	0.295704i
$392$	−0.710472	−	8.12074i	−0.0358843	−	0.410159i
$393$		0			0
$394$	−19.8028	+	54.4078i	−0.997651	+	2.74102i
$395$	−5.23728	−	23.5932i	−0.263516	−	1.18710i
$396$		0			0
$397$	−7.52877	−	2.01733i	−0.377858	−	0.101247i	0.0648910	−	0.997892i	$-0.479330\pi$
$397$	−7.52877	−	2.01733i	−0.377858	−	0.101247i	−0.442749	+	0.896646i	$0.645997\pi$
$398$	34.1076	+	23.8824i	1.70966	+	1.19712i
$399$		0			0
$400$	−3.98666	−	14.8458i	−0.199333	−	0.742291i
$401$	28.6980	+	5.06024i	1.43311	+	0.252696i	0.835677	−	0.549222i	$-0.185076\pi$
$401$	28.6980	+	5.06024i	1.43311	+	0.252696i	0.597434	+	0.801918i	$0.296187\pi$
$402$		0			0
$403$	4.00182	+	0.350114i	0.199345	+	0.0174404i
$404$	−1.24963			−0.0621715
$405$		0			0
$406$	27.5956			1.36955
$407$	−11.1406	−	0.974677i	−0.552220	−	0.0483130i
$408$		0			0
$409$	−10.1037	−	1.78155i	−0.499594	−	0.0880918i	−0.0818277	−	0.996646i	$-0.526076\pi$
$409$	−10.1037	−	1.78155i	−0.499594	−	0.0880918i	−0.417766	+	0.908555i	$0.637187\pi$
$410$	−30.4872	+	9.62176i	−1.50565	+	0.475185i
$411$		0			0
$412$	6.78536	+	4.75116i	0.334291	+	0.234073i
$413$	3.38220	+	0.906258i	0.166427	+	0.0445941i
$414$		0			0
$415$	−4.47934	+	7.03542i	−0.219882	+	0.345355i
$416$	7.06545	−	19.4122i	0.346412	−	0.951760i
$417$		0			0
$418$	4.17208	+	47.6871i	0.204063	+	2.33245i
$419$	14.0240	+	11.7675i	0.685117	+	0.574881i	0.917496	−	0.397744i	$-0.130207\pi$
$419$	14.0240	+	11.7675i	0.685117	+	0.574881i	−0.232380	+	0.972625i	$0.574651\pi$
$420$		0			0
$421$	−28.8617	−	10.5048i	−1.40664	−	0.511973i	−0.476495	−	0.879177i	$-0.658093\pi$
$421$	−28.8617	−	10.5048i	−1.40664	−	0.511973i	−0.930140	+	0.367204i	$0.880315\pi$
$422$	−45.8131	+	12.2756i	−2.23015	+	0.597566i
$423$		0			0
$424$	0.176834	−	0.102095i	0.00858784	−	0.00495819i
$425$	9.36728	+	7.85132i	0.454380	+	0.380845i
$426$		0			0
$427$	−13.9284	+	29.8695i	−0.674040	+	1.44548i
$428$	7.88396	+	11.2595i	0.381085	+	0.544246i
$429$		0			0
$430$	0.798373	−	6.07713i	0.0385010	−	0.293065i
$431$			13.0253i			0.627407i	0.949521	+	0.313703i	$0.101570\pi$
$431$			13.0253i			0.627407i	−0.949521	+	0.313703i	$0.898430\pi$
$432$		0			0
$433$	24.3815	+	24.3815i	1.17170	+	1.17170i	0.981804	+	0.189896i	$0.0608150\pi$
$433$	24.3815	+	24.3815i	1.17170	+	1.17170i	0.189896	+	0.981804i	$0.439185\pi$
$434$	10.3862	−	8.71504i	0.498553	−	0.418335i
$435$		0			0
$436$	4.28248	−	24.2871i	0.205093	−	1.16314i
$437$	15.7889	+	7.36247i	0.755284	+	0.352195i
$438$		0			0
$439$	21.0657	−	3.71446i	1.00541	−	0.177281i	0.353386	−	0.935477i	$-0.385030\pi$
$439$	21.0657	−	3.71446i	1.00541	−	0.177281i	0.652027	+	0.758196i	$0.273919\pi$
$440$	7.86122	−	4.09504i	0.374769	−	0.195223i
$441$		0			0
$442$	3.39505	+	12.6705i	0.161486	+	0.602674i
$443$	24.5747	−	11.4594i	1.16758	−	0.544452i	0.260527	−	0.965466i	$-0.416104\pi$
$443$	24.5747	−	11.4594i	1.16758	−	0.544452i	0.907054	+	0.421014i	$0.138326\pi$
$444$		0			0
$445$	−1.48886	−	33.8871i	−0.0705786	−	1.60640i
$446$	−13.5888	+	16.1945i	−0.643447	+	0.766830i
$447$		0			0
$448$	−18.7400	−	40.1882i	−0.885384	−	1.89871i
$449$	−1.17379	+	2.03306i	−0.0553944	+	0.0959459i	−0.892393	−	0.451259i	$-0.850975\pi$
$449$	−1.17379	+	2.03306i	−0.0553944	+	0.0959459i	0.836998	+	0.547205i	$0.184308\pi$
$450$		0			0
$451$	16.6593	+	28.8547i	0.784454	+	1.35871i
$452$	7.48801	−	10.6940i	0.352206	−	0.503003i
$453$		0			0
$454$	17.4634	+	47.9802i	0.819596	+	2.25182i
$455$	19.9387	−	12.7100i	0.934740	−	0.595855i
$456$		0			0
$457$	0.0458303	−	0.523843i	0.00214385	−	0.0245043i	−0.995047	−	0.0994013i	$-0.968307\pi$
$457$	0.0458303	−	0.523843i	0.00214385	−	0.0245043i	0.997191	+	0.0748970i	$0.0238628\pi$
$458$	13.2552	−	13.2552i	0.619374	−	0.619374i
$459$		0			0
$460$	0.861173	−	19.8491i	0.0401524	−	0.925469i
$461$	5.97585	+	7.12174i	0.278323	+	0.331693i	0.887038	−	0.461696i	$-0.152759\pi$
$461$	5.97585	+	7.12174i	0.278323	+	0.331693i	−0.608715	+	0.793389i	$0.708315\pi$
$462$		0			0
$463$	−18.1131	+	12.6829i	−0.841787	+	0.589426i	−0.912965	−	0.408038i	$-0.866213\pi$
$463$	−18.1131	+	12.6829i	−0.841787	+	0.589426i	0.0711780	+	0.997464i	$0.477324\pi$
$464$	9.22036	−	3.35594i	0.428045	−	0.155795i
$465$		0			0
$466$	6.94655	+	39.3958i	0.321793	+	1.82498i
$467$	−6.61375	+	24.6828i	−0.306048	+	1.14219i	0.625992	+	0.779830i	$0.284694\pi$
$467$	−6.61375	+	24.6828i	−0.306048	+	1.14219i	−0.932040	+	0.362356i	$0.881972\pi$
$468$		0			0
$469$	29.0629	+	16.7794i	1.34200	+	0.774803i
$470$	−1.66190	+	0.688916i	−0.0766577	+	0.0317773i
$471$		0			0
$472$	−0.686232	+	0.0600375i	−0.0315864	+	0.00276345i
$473$	−6.36369	+	0.556751i	−0.292603	+	0.0255994i
$474$		0			0
$475$	−21.2199	−	9.88083i	−0.973636	−	0.453363i
$476$	20.8646	+	12.0462i	0.956328	+	0.552136i
$477$		0			0
$478$	−1.35531	+	5.05807i	−0.0619903	+	0.231351i
$479$	−2.14579	−	12.1694i	−0.0980435	−	0.556032i	−0.993772	−	0.111431i	$-0.964457\pi$
$479$	−2.14579	−	12.1694i	−0.0980435	−	0.556032i	0.895729	−	0.444601i	$-0.146655\pi$
$480$		0			0
$481$	5.51494	−	2.00728i	0.251460	−	0.0915239i
$482$	−36.7408	+	25.7262i	−1.67350	+	1.17179i
$483$		0			0
$484$	−19.6895	−	23.4651i	−0.894979	−	1.06659i
$485$	−3.08201	−	0.133716i	−0.139947	−	0.00607174i
$486$		0			0
$487$	16.4134	−	16.4134i	0.743762	−	0.743762i	−0.229538	−	0.973300i	$-0.573722\pi$
$487$	16.4134	−	16.4134i	0.743762	−	0.743762i	0.973300	+	0.229538i	$0.0737215\pi$
$488$	0.565091	−	6.45902i	0.0255805	−	0.292386i
$489$		0			0
$490$	10.1641	−	45.9067i	0.459165	−	2.07385i
$491$	−3.53191	−	9.70384i	−0.159393	−	0.437928i	0.834129	−	0.551569i	$-0.185971\pi$
$491$	−3.53191	−	9.70384i	−0.159393	−	0.437928i	−0.993522	+	0.113641i	$0.963749\pi$
$492$		0			0
$493$	−4.47496	+	6.39090i	−0.201542	+	0.287832i
$494$	−12.5608	−	21.7559i	−0.565137	−	0.978846i
$495$		0			0
$496$	2.41043	−	4.17499i	0.108231	−	0.187462i
$497$	15.7752	+	33.8300i	0.707615	+	1.51748i
$498$		0			0
$499$	−21.3906	+	25.4924i	−0.957576	+	1.14119i	0.0323314	+	0.999477i	$0.489707\pi$
$499$	−21.3906	+	25.4924i	−0.957576	+	1.14119i	−0.989907	+	0.141717i	$0.954738\pi$
$500$	−1.14247	+	26.6706i	−0.0510926	+	1.19274i
$501$		0			0
$502$	29.9414	−	13.9619i	1.33635	−	0.623150i
$503$	7.47831	+	27.9094i	0.333441	+	1.24442i	0.905549	+	0.424241i	$0.139459\pi$
$503$	7.47831	+	27.9094i	0.333441	+	1.24442i	−0.572108	+	0.820178i	$0.693874\pi$
$504$		0			0
$505$	−1.11622	−	0.351605i	−0.0496710	−	0.0156462i
$506$	−37.4723	+	6.60738i	−1.66585	+	0.293734i
$507$		0			0
$508$	15.6471	+	7.29635i	0.694226	+	0.323723i
$509$	−2.41068	+	13.6717i	−0.106852	+	0.605986i	0.883613	+	0.468218i	$0.155104\pi$
$509$	−2.41068	+	13.6717i	−0.106852	+	0.605986i	−0.990465	+	0.137768i	$0.956007\pi$
$510$		0			0
$511$	39.0008	−	32.7256i	1.72529	−	1.44769i
$512$	−21.0607	−	21.0607i	−0.930762	−	0.930762i
$513$		0			0
$514$		−	2.91544i		−	0.128594i
$515$	4.72412	+	6.15309i	0.208169	+	0.271138i
$516$		0			0
$517$	1.07543	+	1.53587i	0.0472972	+	0.0675474i
$518$	8.37129	−	17.9523i	0.367813	−	0.788778i
$519$		0			0
$520$	−2.83078	+	3.69124i	−0.124138	+	0.161871i
$521$	−4.10889	+	2.37227i	−0.180014	+	0.103931i	−0.587299	−	0.809370i	$-0.699809\pi$
$521$	−4.10889	+	2.37227i	−0.180014	+	0.103931i	0.407285	+	0.913301i	$0.366475\pi$
$522$		0			0
$523$	−39.4721	+	10.5765i	−1.72599	+	0.462478i	−0.979254	−	0.202638i	$-0.935048\pi$
$523$	−39.4721	+	10.5765i	−1.72599	+	0.462478i	−0.746739	+	0.665117i	$0.768382\pi$
$524$	−17.0487	−	6.20521i	−0.744774	−	0.271076i
$525$		0			0
$526$	39.7161	+	33.3258i	1.73170	+	1.45307i
$527$	0.334084	+	3.81860i	0.0145529	+	0.166341i
$528$		0			0
$529$	3.13027	−	8.60035i	0.136099	−	0.373928i
$530$	1.14976	−	0.255227i	0.0499425	−	0.0110864i
$531$		0			0
$532$	−44.5677	−	11.9419i	−1.93226	−	0.517746i
$533$	−14.3232	−	10.0292i	−0.620407	−	0.434414i
$534$		0			0
$535$	3.87420	+	12.2757i	0.167496	+	0.530723i
$536$	−6.50174	−	1.14643i	−0.280833	−	0.0495184i
$537$		0			0
$538$	−63.0456	−	5.51577i	−2.71809	−	0.237802i
$539$	−49.0025			−2.11069
$540$		0			0
$541$	−14.7870			−0.635743			−0.317871	−	0.948134i	$-0.602968\pi$
$541$	−14.7870			−0.635743			−0.317871	+	0.948134i	$0.602968\pi$
$542$	62.9871	+	5.51066i	2.70553	+	0.236703i
$543$		0			0
$544$	19.4127	+	3.42298i	0.832313	+	0.146759i
$545$	10.6589	−	20.4892i	0.456576	−	0.877662i
$546$		0			0
$547$	19.2746	+	13.4962i	0.824123	+	0.577057i	0.907784	−	0.419437i	$-0.137773\pi$
$547$	19.2746	+	13.4962i	0.824123	+	0.577057i	−0.0836614	+	0.996494i	$0.526661\pi$
$548$	−20.3137	−	5.44304i	−0.867759	−	0.232515i
$549$		0			0
$550$	50.3442	−	8.90553i	2.14668	−	0.379733i
$551$	5.11030	−	14.0404i	0.217706	−	0.598142i
$552$		0			0
$553$	−3.88828	−	44.4433i	−0.165347	−	1.88992i
$554$	9.30352	+	7.80658i	0.395269	+	0.331670i
$555$		0			0
$556$	1.45168	+	0.528370i	0.0615651	+	0.0224079i
$557$	23.7629	−	6.36725i	1.00687	−	0.269789i	0.282547	−	0.959253i	$-0.408821\pi$
$557$	23.7629	−	6.36725i	1.00687	−	0.269789i	0.724320	+	0.689464i	$0.242154\pi$
$558$		0			0
$559$	2.90326	−	1.67620i	0.122795	−	0.0708956i
$560$	−3.71156	−	28.1324i	−0.156842	−	1.18881i
$561$		0			0
$562$	−13.5068	+	28.9655i	−0.569751	+	1.22184i
$563$	7.57539	+	10.8188i	0.319265	+	0.455957i	0.946421	−	0.322936i	$-0.104670\pi$
$563$	7.57539	+	10.8188i	0.319265	+	0.455957i	−0.627156	+	0.778894i	$0.715781\pi$
$564$		0			0
$565$	9.69750	−	7.44538i	0.407977	−	0.313230i
$566$			49.6934i			2.08877i
$567$		0			0
$568$	−5.19257	−	5.19257i	−0.217875	−	0.217875i
$569$	−9.80603	+	8.22824i	−0.411090	+	0.344946i	−0.824762	−	0.565481i	$-0.808691\pi$
$569$	−9.80603	+	8.22824i	−0.411090	+	0.344946i	0.413671	+	0.910426i	$0.364246\pi$
$570$		0			0
$571$	1.27813	−	7.24862i	0.0534879	−	0.303345i	−0.946314	−	0.323249i	$-0.895225\pi$
$571$	1.27813	−	7.24862i	0.0534879	−	0.303345i	0.999802	+	0.0199038i	$0.00633599\pi$
$572$	27.0612	+	12.6188i	1.13149	+	0.527620i
$573$		0			0
$574$	−58.1187	+	10.2479i	−2.42583	+	0.427739i
$575$	6.35412	−	17.4876i	0.264985	−	0.729285i
$576$		0			0
$577$	6.02067	+	22.4695i	0.250644	+	0.935416i	0.970462	+	0.241253i	$0.0775585\pi$
$577$	6.02067	+	22.4695i	0.250644	+	0.935416i	−0.719818	+	0.694163i	$0.755775\pi$
$578$	20.9290	−	9.75937i	0.870533	−	0.405936i
$579$		0			0
$580$	−17.0235	+	0.747943i	−0.706863	+	0.0310567i
$581$	−9.89651	+	11.7942i	−0.410576	+	0.489306i
$582$		0			0
$583$	−0.518743	−	1.11245i	−0.0214841	−	0.0460729i
$584$	−5.00795	+	8.67403i	−0.207231	+	0.358934i
$585$		0			0
$586$	8.73716	+	15.1332i	0.360929	+	0.625147i
$587$	6.11631	−	8.73500i	0.252447	−	0.360532i	−0.672847	−	0.739781i	$-0.734929\pi$
$587$	6.11631	−	8.73500i	0.252447	−	0.360532i	0.925294	+	0.379249i	$0.123818\pi$
$588$		0			0
$589$	−2.51078	−	6.89830i	−0.103455	−	0.284240i
$590$	−3.87928	−	0.858899i	−0.159707	−	0.0353603i
$591$		0			0
$592$	0.613850	−	7.01634i	0.0252291	−	0.288370i
$593$	−30.2299	+	30.2299i	−1.24139	+	1.24139i	−0.281969	+	0.959424i	$0.590987\pi$
$593$	−30.2299	+	30.2299i	−1.24139	+	1.24139i	−0.959424	+	0.281969i	$0.909013\pi$
$594$		0			0
$595$	15.2476	+	16.6307i	0.625093	+	0.681793i
$596$	28.6291	+	34.1189i	1.17269	+	1.39756i
$597$		0			0
$598$	16.3574	−	11.4536i	0.668903	−	0.468371i
$599$	−18.4157	+	6.70275i	−0.752444	+	0.273867i	−0.689634	−	0.724158i	$-0.742228\pi$
$599$	−18.4157	+	6.70275i	−0.752444	+	0.273867i	−0.0628100	+	0.998026i	$0.520006\pi$
$600$		0			0
$601$	−5.44723	−	30.8927i	−0.222197	−	1.26014i	−0.867972	−	0.496614i	$-0.834577\pi$
$601$	−5.44723	−	30.8927i	−0.222197	−	1.26014i	0.645775	−	0.763528i	$-0.276534\pi$
$602$	2.92847	−	10.9292i	0.119355	−	0.445440i
$603$		0			0
$604$	24.5279	+	14.1612i	0.998025	+	0.576210i
$605$	−10.9851	−	26.4999i	−0.446609	−	1.07737i
$606$		0			0
$607$	−14.5354	+	1.27168i	−0.589972	+	0.0516159i	−0.378233	−	0.925710i	$-0.623468\pi$
$607$	−14.5354	+	1.27168i	−0.589972	+	0.0516159i	−0.211739	+	0.977326i	$0.567913\pi$
$608$	−37.6076	+	3.29024i	−1.52519	+	0.133437i
$609$		0			0
$610$	14.3018	−	34.5544i	0.579063	−	1.39907i
$611$	−0.852139	−	0.491983i	−0.0344739	−	0.0199035i
$612$		0			0
$613$	3.72795	−	13.9129i	0.150571	−	0.561937i	−0.848873	−	0.528596i	$-0.822719\pi$
$613$	3.72795	−	13.9129i	0.150571	−	0.561937i	0.999444	−	0.0333409i	$-0.0106147\pi$
$614$	8.05124	+	45.6609i	0.324922	+	1.84272i
$615$		0			0
$616$	15.3758	−	5.59635i	0.619510	−	0.225483i
$617$	2.15631	−	1.50986i	0.0868096	−	0.0607847i	−0.529366	−	0.848394i	$-0.677570\pi$
$617$	2.15631	−	1.50986i	0.0868096	−	0.0607847i	0.616175	+	0.787609i	$0.288681\pi$
$618$		0			0
$619$	−14.0882	−	16.7897i	−0.566254	−	0.674836i	0.404603	−	0.914492i	$-0.367410\pi$
$619$	−14.0882	−	16.7897i	−0.566254	−	0.674836i	−0.970858	+	0.239657i	$0.922965\pi$
$620$	−6.17095	+	5.65775i	−0.247831	+	0.227221i
$621$		0			0
$622$	39.4631	−	39.4631i	1.58233	−	1.58233i
$623$	5.45731	−	62.3773i	0.218642	−	2.49909i
$624$		0			0
$625$	−8.52471	+	23.5017i	−0.340989	+	0.940067i
$626$	0.320337	+	0.880118i	0.0128032	+	0.0351766i
$627$		0			0
$628$	1.30500	−	1.86374i	0.0520753	−	0.0743712i
$629$	2.80009	+	4.84989i	0.111647	+	0.193378i
$630$		0			0
$631$	−12.3536	+	21.3971i	−0.491790	+	0.851805i	−0.999955	−	0.00945434i	$-0.996991\pi$
$631$	−12.3536	+	21.3971i	−0.491790	+	0.851805i	0.508165	+	0.861260i	$0.330324\pi$
$632$	3.70921	+	7.95442i	0.147544	+	0.316410i
$633$		0			0
$634$	1.15383	−	1.37508i	0.0458243	−	0.0546112i
$635$	11.9236	+	10.9199i	0.473173	+	0.433345i
$636$		0			0
$637$	23.3069	−	10.8682i	0.923453	−	0.430613i
$638$	8.44645	+	31.5226i	0.334398	+	1.24799i
$639$		0			0
$640$	6.58504	+	12.6413i	0.260297	+	0.499690i
$641$	1.07217	−	0.189053i	0.0423482	−	0.00746712i	−0.152434	−	0.988314i	$-0.548711\pi$
$641$	1.07217	−	0.189053i	0.0423482	−	0.00746712i	0.194782	+	0.980847i	$0.437600\pi$
$642$		0			0
$643$	38.6292	+	18.0131i	1.52339	+	0.710367i	0.990715	−	0.135954i	$-0.0434099\pi$
$643$	38.6292	+	18.0131i	1.52339	+	0.710367i	0.532673	+	0.846321i	$0.321188\pi$
$644$	6.36868	−	36.1186i	0.250961	−	1.42327i
$645$		0			0
$646$	18.3632	−	15.4085i	0.722489	−	0.606240i
$647$	−8.11871	−	8.11871i	−0.319179	−	0.319179i	0.529273	−	0.848452i	$-0.322465\pi$
$647$	−8.11871	−	8.11871i	−0.319179	−	0.319179i	−0.848452	+	0.529273i	$0.822465\pi$
$648$		0			0
$649$			4.14089i			0.162544i
$650$	−21.9699	+	15.4015i	−0.861730	+	0.604095i
$651$		0			0
$652$	23.6064	+	33.7135i	0.924499	+	1.32032i
$653$	−20.7963	+	44.5979i	−0.813823	+	1.74525i	−0.162125	+	0.986770i	$0.551835\pi$
$653$	−20.7963	+	44.5979i	−0.813823	+	1.74525i	−0.651698	+	0.758479i	$0.725943\pi$
$654$		0			0
$655$	−13.4826	−	10.3397i	−0.526807	−	0.404004i
$656$	−18.1726	+	10.4920i	−0.709522	+	0.409643i
$657$		0			0
$658$	−3.20784	+	0.859538i	−0.125055	+	0.0335083i
$659$	15.4676	+	5.62976i	0.602534	+	0.219304i	0.625233	−	0.780438i	$-0.285004\pi$
$659$	15.4676	+	5.62976i	0.602534	+	0.219304i	−0.0226995	+	0.999742i	$0.507226\pi$
$660$		0			0
$661$	5.35212	+	4.49096i	0.208173	+	0.174678i	0.740913	−	0.671601i	$-0.234393\pi$
$661$	5.35212	+	4.49096i	0.208173	+	0.174678i	−0.532740	+	0.846279i	$0.678838\pi$
$662$	−5.23445	−	59.8301i	−0.203443	−	2.32536i
$663$		0			0
$664$	1.03595	−	2.84624i	0.0402025	−	0.110455i
$665$	−36.4495	−	23.2068i	−1.41345	−	0.899922i
$666$		0			0
$667$	11.4720	+	3.07392i	0.444199	+	0.119023i
$668$	9.92571	+	6.95006i	0.384037	+	0.268906i
$669$		0			0
$670$	−33.7821	−	17.5740i	−1.30511	−	0.678945i
$671$	−38.3832	−	6.76799i	−1.48177	−	0.261276i
$672$		0			0
$673$	−6.71205	−	0.587229i	−0.258731	−	0.0226360i	−0.0429476	−	0.999077i	$-0.513675\pi$
$673$	−6.71205	−	0.587229i	−0.258731	−	0.0226360i	−0.215783	+	0.976441i	$0.569230\pi$
$674$	15.7666			0.607307
$675$		0			0
$676$	15.3700			0.591155
$677$	−5.61594	−	0.491331i	−0.215838	−	0.0188834i	−0.0212762	−	0.999774i	$-0.506773\pi$
$677$	−5.61594	−	0.491331i	−0.215838	−	0.0188834i	−0.194562	+	0.980890i	$0.562328\pi$
$678$		0			0
$679$	−5.60821	−	0.988878i	−0.215223	−	0.0379497i
$680$	−3.93778	−	2.04850i	−0.151007	−	0.0785565i
$681$		0			0
$682$	13.1342	+	9.19669i	0.502936	+	0.352159i
$683$	17.2898	+	4.63280i	0.661577	+	0.177269i	0.573958	−	0.818885i	$-0.305407\pi$
$683$	17.2898	+	4.63280i	0.661577	+	0.177269i	0.0876196	+	0.996154i	$0.472074\pi$
$684$		0			0
$685$	−16.6135	−	10.5775i	−0.634768	−	0.404147i
$686$	8.98530	−	24.6869i	0.343060	−	0.942551i
$687$		0			0
$688$	−0.350641	−	4.00784i	−0.0133681	−	0.152798i
$689$	0.493456	+	0.414058i	0.0187992	+	0.0157744i
$690$		0			0
$691$	−27.1342	−	9.87603i	−1.03223	−	0.375702i	−0.230302	−	0.973119i	$-0.573971\pi$
$691$	−27.1342	−	9.87603i	−1.03223	−	0.375702i	−0.801930	+	0.597417i	$0.796194\pi$
$692$	3.85568	−	1.03313i	0.146571	−	0.0392736i
$693$		0			0
$694$	−47.0786	+	27.1809i	−1.78708	+	1.03177i
$695$	1.14803	+	0.880416i	0.0435473	+	0.0333961i
$696$		0			0
$697$	7.05132	−	15.1216i	0.267088	−	0.572772i
$698$	−20.9830	−	29.9668i	−0.794217	−	1.13426i
$699$		0			0
$700$	−8.53054	+	48.5348i	−0.322424	+	1.83444i
$701$		−	20.6819i		−	0.781145i	−0.920572	−	0.390573i	$-0.872277\pi$
$701$		−	20.6819i		−	0.781145i	0.920572	−	0.390573i	$-0.127723\pi$
$702$		0			0
$703$	−7.58374	−	7.58374i	−0.286026	−	0.286026i
$704$	40.1712	−	33.7076i	1.51401	−	1.27040i
$705$		0			0
$706$	−3.27913	+	18.5969i	−0.123412	+	0.699903i
$707$	−1.95793	−	0.912998i	−0.0736355	−	0.0343368i
$708$		0			0
$709$	−18.9529	+	3.34191i	−0.711791	+	0.125508i	−0.517808	−	0.855497i	$-0.673252\pi$
$709$	−18.9529	+	3.34191i	−0.711791	+	0.125508i	−0.193983	+	0.981005i	$0.562141\pi$
$710$	−19.5681	−	37.5648i	−0.734378	−	1.40978i
$711$		0			0
$712$	3.18823	+	11.8986i	0.119484	+	0.445920i
$713$	5.28853	−	2.46608i	0.198057	−	0.0923554i
$714$		0			0
$715$	20.6215	+	18.8858i	0.771202	+	0.706287i
$716$	−22.0067	+	26.2266i	−0.822430	+	0.980133i
$717$		0			0
$718$	13.9996	+	30.0223i	0.522461	+	1.12042i
$719$	4.55209	−	7.88446i	0.169764	−	0.294041i	−0.768573	−	0.639763i	$-0.779033\pi$
$719$	4.55209	−	7.88446i	0.169764	−	0.294041i	0.938337	+	0.345722i	$0.112366\pi$
$720$		0			0
$721$	7.16008	+	12.4016i	0.266655	+	0.461861i
$722$	−3.50416	+	5.00446i	−0.130411	+	0.186247i
$723$		0			0
$724$	−17.5350	−	48.1769i	−0.651682	−	1.79048i
$725$	−15.4165	−	4.12177i	−0.572554	−	0.153079i
$726$		0			0
$727$	−1.02733	+	11.7425i	−0.0381017	+	0.435505i	0.953054	+	0.302801i	$0.0979216\pi$
$727$	−1.02733	+	11.7425i	−0.0381017	+	0.435505i	−0.991156	+	0.132704i	$0.957634\pi$
$728$	−6.07195	+	6.07195i	−0.225042	+	0.225042i
$729$		0			0
$730$	−42.5823	+	39.0410i	−1.57604	+	1.44497i
$731$	2.05622	+	2.45051i	0.0760520	+	0.0906352i
$732$		0			0
$733$	37.0503	−	25.9429i	1.36848	−	0.958222i	0.368896	−	0.929471i	$-0.379736\pi$
$733$	37.0503	−	25.9429i	1.36848	−	0.958222i	0.999587	−	0.0287512i	$-0.00915305\pi$
$734$	−42.6244	+	15.5140i	−1.57330	+	0.572633i
$735$		0			0
$736$	−5.21080	−	29.5519i	−0.192072	−	1.08930i
$737$	−10.2717	+	38.3345i	−0.378363	+	1.41207i
$738$		0			0
$739$	36.6974	+	21.1872i	1.34994	+	0.779385i	0.988240	−	0.152911i	$-0.0488648\pi$
$739$	36.6974	+	21.1872i	1.34994	+	0.779385i	0.361695	+	0.932296i	$0.382198\pi$
$740$	−4.67761	+	11.3015i	−0.171952	+	0.415452i
$741$		0			0
$742$	2.16584	−	0.189487i	0.0795106	−	0.00695628i
$743$	−11.6932	+	1.02302i	−0.428982	+	0.0375311i	−0.299603	−	0.954064i	$-0.596854\pi$
$743$	−11.6932	+	1.02302i	−0.428982	+	0.0375311i	−0.129379	+	0.991595i	$0.541299\pi$
$744$		0			0
$745$	15.9727	+	38.5315i	0.585193	+	1.41169i
$746$	44.0922	+	25.4566i	1.61433	+	0.932034i
$747$		0			0
$748$	−7.37418	+	27.5208i	−0.269627	+	1.00626i
$749$	4.12632	+	23.4015i	0.150772	+	0.855073i
$750$		0			0
$751$	31.3803	−	11.4215i	1.14509	−	0.416777i	0.301338	−	0.953517i	$-0.402567\pi$
$751$	31.3803	−	11.4215i	1.14509	−	0.416777i	0.843747	+	0.536741i	$0.180345\pi$
$752$	−0.967287	+	0.677302i	−0.0352733	+	0.0246987i
$753$		0			0
$754$	−11.0087	−	13.1197i	−0.400913	−	0.477790i
$755$	17.9247	+	19.5506i	0.652348	+	0.711520i
$756$		0			0
$757$	16.3480	−	16.3480i	0.594177	−	0.594177i	−0.344580	−	0.938757i	$-0.611979\pi$
$757$	16.3480	−	16.3480i	0.594177	−	0.594177i	0.938757	+	0.344580i	$0.111979\pi$
$758$	−3.38053	+	38.6396i	−0.122786	+	1.40345i
$759$		0			0
$760$	8.29975	+	1.83762i	0.301063	+	0.0666575i
$761$	−5.25702	−	14.4435i	−0.190567	−	0.523578i	0.807207	−	0.590269i	$-0.200978\pi$
$761$	−5.25702	−	14.4435i	−0.190567	−	0.523578i	−0.997774	+	0.0666905i	$0.978756\pi$
$762$		0			0
$763$	24.4543	−	34.9244i	0.885306	−	1.26435i
$764$	14.1246	+	24.4645i	0.511010	+	0.885095i
$765$		0			0
$766$	−2.47331	+	4.28391i	−0.0893645	+	0.154784i
$767$	−0.918402	−	1.96952i	−0.0331616	−	0.0711152i
$768$		0			0
$769$	18.6937	−	22.2783i	0.674112	−	0.803376i	−0.315225	−	0.949017i	$-0.602080\pi$
$769$	18.6937	−	22.2783i	0.674112	−	0.803376i	0.989337	+	0.145641i	$0.0465246\pi$
$770$	94.2868	−	4.14257i	3.39786	−	0.149288i
$771$		0			0
$772$	−34.7981	+	16.2266i	−1.25241	+	0.584008i
$773$	−2.50707	−	9.35650i	−0.0901729	−	0.336530i	0.906071	−	0.423127i	$-0.139067\pi$
$773$	−2.50707	−	9.35650i	−0.0901729	−	0.336530i	−0.996243	+	0.0865969i	$0.972401\pi$
$774$		0			0
$775$	−7.10403	+	3.31741i	−0.255184	+	0.119165i
$776$	1.10330	−	0.194542i	0.0396063	−	0.00698365i
$777$		0			0
$778$	20.0086	+	9.33018i	0.717344	+	0.334503i
$779$	−5.54868	+	31.4681i	−0.198802	+	1.12746i
$780$		0			0
$781$	−33.8157	+	28.3748i	−1.21002	+	1.01533i
$782$	13.4735	+	13.4735i	0.481812	+	0.481812i
$783$		0			0
$784$		−

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.08671 - 0.182563i) q^{2} +(2.35140 + 0.414615i) q^{4} +(1.98370 + 1.03196i) q^{5} +(3.38127 + 2.36759i) q^{7} +(-0.784385 - 0.210175i) q^{8} +(-3.95100 - 2.51554i) q^{10} +(-1.66957 + 4.58710i) q^{11} +(-0.223275 - 2.55204i) q^{13} +(-6.62348 - 5.55776i) q^{14} +(-2.88895 - 1.05149i) q^{16} +(2.36120 - 0.632683i) q^{17} +(-4.05431 + 2.34076i) q^{19} +(4.23661 + 3.24902i) q^{20} +(4.32134 - 9.26714i) q^{22} +(-2.13442 - 3.04827i) q^{23} +(2.87013 + 4.09419i) q^{25} +5.36612i q^{26} +(6.96907 + 6.96907i) q^{28} +(-2.44490 + 2.05152i) q^{29} +(-0.272295 + 1.54426i) q^{31} +(7.30837 + 3.40795i) q^{32} +(-5.04264 + 0.889154i) q^{34} +(4.26417 + 8.18590i) q^{35} +(0.592937 + 2.21287i) q^{37} +(8.88750 - 4.14431i) q^{38} +(-1.33909 - 1.22638i) q^{40} +(4.38733 - 5.22862i) q^{41} +(0.553045 + 1.18601i) q^{43} +(-5.82771 + 10.0939i) q^{44} +(3.89741 + 6.75051i) q^{46} +(0.220307 - 0.314631i) q^{47} +(3.43334 + 9.43304i) q^{49} +(-5.24167 - 9.06735i) q^{50} +(0.533107 - 6.09344i) q^{52} +(-0.177802 + 0.177802i) q^{53} +(-8.04562 + 7.37651i) q^{55} +(-2.15461 - 2.56776i) q^{56} +(5.47633 - 3.83457i) q^{58} +(0.797126 - 0.290130i) q^{59} +(1.38646 + 7.86300i) q^{61} +(0.850126 - 3.17272i) q^{62} +(-9.30332 - 5.37128i) q^{64} +(2.19069 - 5.29289i) q^{65} +(8.09911 - 0.708580i) q^{67} +(5.81446 - 0.508699i) q^{68} +(-7.40362 - 17.8601i) q^{70} +(7.83146 + 4.52149i) q^{71} +(3.19228 - 11.9138i) q^{73} +(-0.833296 - 4.72586i) q^{74} +(-10.5038 + 3.82308i) q^{76} +(-16.5056 + 11.5574i) q^{77} +(-6.94728 - 8.27944i) q^{79} +(-4.64572 - 5.06712i) q^{80} +(-10.1096 + 10.1096i) q^{82} +(-0.325084 + 3.71573i) q^{83} +(5.33682 + 1.18161i) q^{85} +(-0.937521 - 2.57582i) q^{86} +(2.27368 - 3.24715i) q^{88} +(-7.58469 - 13.1371i) q^{89} +(5.28723 - 9.15775i) q^{91} +(-3.75502 - 8.05267i) q^{92} +(-0.517156 + 0.616322i) q^{94} +(-10.4581 + 0.459486i) q^{95} +(-1.25036 + 0.583050i) q^{97} +(-5.44226 - 20.3108i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

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