LMFDB - Embedded newform 441.2.s.d.362.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(362,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("441.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (of order $6$, degree $2$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			362.17
Character	$\chi$	$=$	441.362
Dual form			441.2.s.d.374.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02035 - 0.589100i) q^{2} +(-1.34152 - 1.09560i) q^{3} +(-0.305921 + 0.529871i) q^{4} +4.33202 q^{5} +(-2.01424 - 0.327604i) q^{6} +3.07728i q^{8} +(0.599340 + 2.93952i) q^{9} +O(q^{10})$	\(q+(1.02035 - 0.589100i) q^{2} +(-1.34152 - 1.09560i) q^{3} +(-0.305921 + 0.529871i) q^{4} +4.33202 q^{5} +(-2.01424 - 0.327604i) q^{6} +3.07728i q^{8} +(0.599340 + 2.93952i) q^{9} +(4.42019 - 2.55200i) q^{10} +2.16204i q^{11} +(0.990924 - 0.375666i) q^{12} +(2.25256 - 1.30052i) q^{13} +(-5.81148 - 4.74614i) q^{15} +(1.20098 + 2.08016i) q^{16} +(0.585576 + 1.01425i) q^{17} +(2.34321 + 2.64628i) q^{18} +(-2.09282 - 1.20829i) q^{19} +(-1.32526 + 2.29541i) q^{20} +(1.27366 + 2.20604i) q^{22} -3.65101i q^{23} +(3.37145 - 4.12822i) q^{24} +13.7664 q^{25} +(1.53227 - 2.65397i) q^{26} +(2.41650 - 4.60006i) q^{27} +(0.589262 + 0.340210i) q^{29} +(-8.72571 - 1.41919i) q^{30} +(-5.67723 - 3.27775i) q^{31} +(-2.87915 - 1.66228i) q^{32} +(2.36872 - 2.90042i) q^{33} +(1.19499 + 0.689926i) q^{34} +(-1.74092 - 0.581689i) q^{36} +(2.55346 - 4.42272i) q^{37} -2.84722 q^{38} +(-4.44669 - 0.723230i) q^{39} +13.3308i q^{40} +(-3.68473 - 6.38214i) q^{41} +(-2.12577 + 3.68194i) q^{43} +(-1.14560 - 0.661414i) q^{44} +(2.59635 + 12.7341i) q^{45} +(-2.15081 - 3.72531i) q^{46} +(3.57157 + 6.18614i) q^{47} +(0.667877 - 4.10636i) q^{48} +(14.0466 - 8.10980i) q^{50} +(0.325645 - 2.00219i) q^{51} +1.59142i q^{52} +(-2.79976 + 1.61644i) q^{53} +(-0.244212 - 6.11724i) q^{54} +9.36601i q^{55} +(1.48376 + 3.91383i) q^{57} +0.801672 q^{58} +(2.91810 - 5.05430i) q^{59} +(4.29270 - 1.62739i) q^{60} +(-6.21638 + 3.58903i) q^{61} -7.72370 q^{62} -8.72092 q^{64} +(9.75814 - 5.63387i) q^{65} +(0.708294 - 4.35486i) q^{66} +(-3.32682 + 5.76221i) q^{67} -0.716561 q^{68} +(-4.00003 + 4.89789i) q^{69} -1.95976i q^{71} +(-9.04572 + 1.84433i) q^{72} +(-10.3117 + 5.95345i) q^{73} -6.01697i q^{74} +(-18.4679 - 15.0824i) q^{75} +(1.28048 - 0.739283i) q^{76} +(-4.96324 + 1.88160i) q^{78} +(4.87702 + 8.44725i) q^{79} +(5.20268 + 9.01130i) q^{80} +(-8.28158 + 3.52355i) q^{81} +(-7.51944 - 4.34135i) q^{82} +(0.796736 - 1.37999i) q^{83} +(2.53673 + 4.39374i) q^{85} +5.00916i q^{86} +(-0.417772 - 1.10199i) q^{87} -6.65320 q^{88} +(3.04961 - 5.28207i) q^{89} +(10.1508 + 11.4637i) q^{90} +(1.93456 + 1.11692i) q^{92} +(4.02502 + 10.6171i) q^{93} +(7.28851 + 4.20802i) q^{94} +(-9.06614 - 5.23434i) q^{95} +(2.04125 + 5.38436i) q^{96} +(-2.36387 - 1.36478i) q^{97} +(-6.35537 + 1.29580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 - 8 * q^9	$ 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.02035	−	0.589100i	0.721498	−	0.416557i	−0.0938059	−	0.995591i	$-0.529903\pi$
$2$	1.02035	−	0.589100i	0.721498	−	0.416557i	0.815304	+	0.579034i	$0.196570\pi$
$3$	−1.34152	−	1.09560i	−0.774526	−	0.632542i
$3$	−1.34152	−	1.09560i	−0.774526	−	0.632542i
$4$	−0.305921	+	0.529871i	−0.152961	+	0.264936i
$5$	4.33202			1.93734			0.968670	−	0.248353i	$-0.0798894\pi$
$5$	4.33202			1.93734			0.968670	+	0.248353i	$0.0798894\pi$
$6$	−2.01424	−	0.327604i	−0.822308	−	0.133744i
$7$		0			0
$7$		0			0
$8$			3.07728i			1.08798i
$9$	0.599340	+	2.93952i	0.199780	+	0.979841i
$10$	4.42019	−	2.55200i	1.39779	−	0.807012i
$11$			2.16204i			0.651880i	0.945390	+	0.325940i	$0.105681\pi$
$11$			2.16204i			0.651880i	−0.945390	+	0.325940i	$0.894319\pi$
$12$	0.990924	−	0.375666i	0.286055	−	0.108445i
$13$	2.25256	−	1.30052i	0.624748	−	0.360698i	−0.153967	−	0.988076i	$-0.549205\pi$
$13$	2.25256	−	1.30052i	0.624748	−	0.360698i	0.778715	+	0.627378i	$0.215872\pi$
$14$		0			0
$15$	−5.81148	−	4.74614i	−1.50052	−	1.22545i
$16$	1.20098	+	2.08016i	0.300245	+	0.520040i
$17$	0.585576	+	1.01425i	0.142023	+	0.245991i	0.928258	−	0.371936i	$-0.121306\pi$
$17$	0.585576	+	1.01425i	0.142023	+	0.245991i	−0.786235	+	0.617927i	$0.787973\pi$
$18$	2.34321	+	2.64628i	0.552300	+	0.623733i
$19$	−2.09282	−	1.20829i	−0.480126	−	0.277201i	0.240343	−	0.970688i	$-0.422740\pi$
$19$	−2.09282	−	1.20829i	−0.480126	−	0.277201i	−0.720469	+	0.693487i	$0.756073\pi$
$20$	−1.32526	+	2.29541i	−0.296337	+	0.513270i
$21$		0			0
$22$	1.27366	+	2.20604i	0.271545	+	0.470330i
$23$		−	3.65101i		−	0.761287i	−0.924722	−	0.380644i	$-0.875702\pi$
$23$		−	3.65101i		−	0.761287i	0.924722	−	0.380644i	$-0.124298\pi$
$24$	3.37145	−	4.12822i	0.688194	−	0.842669i
$25$	13.7664			2.75328
$26$	1.53227	−	2.65397i	0.300503	−	0.520486i
$27$	2.41650	−	4.60006i	0.465056	−	0.885281i
$28$		0			0
$29$	0.589262	+	0.340210i	0.109423	+	0.0631755i	0.553713	−	0.832708i	$-0.313211\pi$
$29$	0.589262	+	0.340210i	0.109423	+	0.0631755i	−0.444290	+	0.895883i	$0.646544\pi$
$30$	−8.72571	−	1.41919i	−1.59309	−	0.259107i
$31$	−5.67723	−	3.27775i	−1.01966	−	0.588702i	−0.105655	−	0.994403i	$-0.533694\pi$
$31$	−5.67723	−	3.27775i	−1.01966	−	0.588702i	−0.914006	+	0.405701i	$0.867027\pi$
$32$	−2.87915	−	1.66228i	−0.508967	−	0.293852i
$33$	2.36872	−	2.90042i	0.412342	−	0.504898i
$34$	1.19499	+	0.689926i	0.204939	+	0.118321i
$35$		0			0
$36$	−1.74092	−	0.581689i	−0.290153	−	0.0969482i
$37$	2.55346	−	4.42272i	0.419786	−	0.727090i	−0.576132	−	0.817357i	$-0.695439\pi$
$37$	2.55346	−	4.42272i	0.419786	−	0.727090i	0.995918	+	0.0902663i	$0.0287718\pi$
$38$	−2.84722			−0.461880
$39$	−4.44669	−	0.723230i	−0.712040	−	0.115809i
$40$			13.3308i			2.10779i
$41$	−3.68473	−	6.38214i	−0.575458	−	0.996723i	−0.995992	−	0.0894458i	$-0.971490\pi$
$41$	−3.68473	−	6.38214i	−0.575458	−	0.996723i	0.420534	−	0.907277i	$-0.361843\pi$
$42$		0			0
$43$	−2.12577	+	3.68194i	−0.324176	+	0.561490i	−0.981345	−	0.192253i	$-0.938420\pi$
$43$	−2.12577	+	3.68194i	−0.324176	+	0.561490i	0.657169	+	0.753743i	$0.271754\pi$
$44$	−1.14560	−	0.661414i	−0.172706	−	0.0997120i
$45$	2.59635	+	12.7341i	0.387042	+	1.89828i
$46$	−2.15081	−	3.72531i	−0.317120	−	0.549267i
$47$	3.57157	+	6.18614i	0.520967	+	0.902341i	0.999703	+	0.0243819i	$0.00776176\pi$
$47$	3.57157	+	6.18614i	0.520967	+	0.902341i	−0.478736	+	0.877959i	$0.658905\pi$
$48$	0.667877	−	4.10636i	0.0963998	−	0.592703i
$49$		0			0
$50$	14.0466	−	8.10980i	1.98649	−	1.14690i
$51$	0.325645	−	2.00219i	0.0455994	−	0.280362i
$52$			1.59142i			0.220691i
$53$	−2.79976	+	1.61644i	−0.384577	+	0.222036i	−0.679808	−	0.733390i	$-0.737937\pi$
$53$	−2.79976	+	1.61644i	−0.384577	+	0.222036i	0.295231	+	0.955426i	$0.404603\pi$
$54$	−0.244212	−	6.11724i	−0.0332331	−	0.832451i
$55$			9.36601i			1.26291i
$56$		0			0
$57$	1.48376	+	3.91383i	0.196528	+	0.518399i
$58$	0.801672			0.105265
$59$	2.91810	−	5.05430i	0.379905	−	0.658014i	−0.611143	−	0.791520i	$-0.709290\pi$
$59$	2.91810	−	5.05430i	0.379905	−	0.658014i	0.991048	+	0.133506i	$0.0426234\pi$
$60$	4.29270	−	1.62739i	0.554186	−	0.210095i
$61$	−6.21638	+	3.58903i	−0.795925	+	0.459528i	−0.842044	−	0.539408i	$-0.818648\pi$
$61$	−6.21638	+	3.58903i	−0.795925	+	0.459528i	0.0461190	+	0.998936i	$0.485315\pi$
$62$	−7.72370			−0.980911
$63$		0			0
$64$	−8.72092			−1.09012
$65$	9.75814	−	5.63387i	1.21035	−	0.698795i
$66$	0.708294	−	4.35486i	0.0871850	−	0.536046i
$67$	−3.32682	+	5.76221i	−0.406435	+	0.703966i	−0.994487	−	0.104857i	$-0.966562\pi$
$67$	−3.32682	+	5.76221i	−0.406435	+	0.703966i	0.588052	+	0.808823i	$0.299895\pi$
$68$	−0.716561			−0.0868958
$69$	−4.00003	+	4.89789i	−0.481547	+	0.589637i
$70$		0			0
$71$		−	1.95976i		−	0.232580i	−0.993215	−	0.116290i	$-0.962900\pi$
$71$		−	1.95976i		−	0.232580i	0.993215	−	0.116290i	$-0.0371003\pi$
$72$	−9.04572	+	1.84433i	−1.06605	+	0.217357i
$73$	−10.3117	+	5.95345i	−1.20689	+	0.696799i	−0.962079	−	0.272771i	$-0.912060\pi$
$73$	−10.3117	+	5.95345i	−1.20689	+	0.696799i	−0.244812	+	0.969570i	$0.578726\pi$
$74$		−	6.01697i		−	0.699459i
$75$	−18.4679	−	15.0824i	−2.13249	−	1.74157i
$76$	1.28048	−	0.739283i	0.146881	−	0.0848016i
$77$		0			0
$78$	−4.96324	+	1.88160i	−0.561977	+	0.213049i
$79$	4.87702	+	8.44725i	0.548708	+	0.950390i	0.998363	+	0.0571879i	$0.0182134\pi$
$79$	4.87702	+	8.44725i	0.548708	+	0.950390i	−0.449656	+	0.893202i	$0.648453\pi$
$80$	5.20268	+	9.01130i	0.581677	+	1.00749i
$81$	−8.28158	+	3.52355i	−0.920176	+	0.391505i
$82$	−7.51944	−	4.34135i	−0.830384	−	0.479422i
$83$	0.796736	−	1.37999i	0.0874531	−	0.151473i	−0.818981	−	0.573821i	$-0.805461\pi$
$83$	0.796736	−	1.37999i	0.0874531	−	0.151473i	0.906434	+	0.422348i	$0.138794\pi$
$84$		0			0
$85$	2.53673	+	4.39374i	0.275147	+	0.476568i
$86$			5.00916i			0.540152i
$87$	−0.417772	−	1.10199i	−0.0447899	−	0.118146i
$88$	−6.65320			−0.709233
$89$	3.04961	−	5.28207i	0.323258	−	0.559899i	−0.657901	−	0.753105i	$-0.728555\pi$
$89$	3.04961	−	5.28207i	0.323258	−	0.559899i	0.981158	+	0.193206i	$0.0618886\pi$
$90$	10.1508	+	11.4637i	1.06999	+	1.20838i
$91$		0			0
$92$	1.93456	+	1.11692i	0.201692	+	0.116447i
$93$	4.02502	+	10.6171i	0.417375	+	1.10094i
$94$	7.28851	+	4.20802i	0.751753	+	0.434025i
$95$	−9.06614	−	5.23434i	−0.930166	−	0.537032i
$96$	2.04125	+	5.38436i	0.208334	+	0.549539i
$97$	−2.36387	−	1.36478i	−0.240014	−	0.138572i	0.375169	−	0.926956i	$-0.377585\pi$
$97$	−2.36387	−	1.36478i	−0.240014	−	0.138572i	−0.615183	+	0.788384i	$0.710918\pi$
$98$		0			0
$99$	−6.35537	+	1.29580i	−0.638738	+	0.130233i
$100$	−4.21144	+	7.29443i	−0.421144	+	0.729443i
$101$	−15.9970			−1.59176			−0.795880	−	0.605455i	$-0.792991\pi$
$101$	−15.9970			−1.59176			−0.795880	+	0.605455i	$0.792991\pi$
$102$	−0.847217	−	2.23477i	−0.0838870	−	0.221275i
$103$		−	3.01667i		−	0.297241i	−0.988894	−	0.148621i	$-0.952517\pi$
$103$		−	3.01667i		−	0.297241i	0.988894	−	0.148621i	$-0.0474834\pi$
$104$	4.00205	+	6.93175i	0.392433	+	0.679714i
$105$		0			0
$106$	−1.90450	+	3.29868i	−0.184981	+	0.320397i
$107$	−10.2611	−	5.92422i	−0.991973	−	0.572716i	−0.0861099	−	0.996286i	$-0.527444\pi$
$107$	−10.2611	−	5.92422i	−0.991973	−	0.572716i	−0.905864	+	0.423569i	$0.860777\pi$
$108$	1.69818	+	2.68769i	0.163407	+	0.258623i
$109$	−3.58078	−	6.20210i	−0.342977	−	0.594053i	0.642007	−	0.766699i	$-0.278102\pi$
$109$	−3.58078	−	6.20210i	−0.342977	−	0.594053i	−0.984984	+	0.172645i	$0.944769\pi$
$110$	5.51752	+	9.55662i	0.526075	+	0.911188i
$111$	−8.27102	+	3.13560i	−0.785051	+	0.297618i
$112$		0			0
$113$	2.46102	−	1.42087i	0.231514	−	0.133664i	−0.379756	−	0.925086i	$-0.623992\pi$
$113$	2.46102	−	1.42087i	0.231514	−	0.133664i	0.611270	+	0.791422i	$0.290659\pi$
$114$	3.81959	+	3.11940i	0.357738	+	0.292158i
$115$		−	15.8162i		−	1.47487i
$116$	−0.360535	+	0.208155i	−0.0334749	+	0.0193267i
$117$	5.17295	+	5.84200i	0.478239	+	0.540093i
$118$		−	6.87623i		−	0.633008i
$119$		0			0
$120$	14.6052	−	17.8835i	1.33327	−	1.63254i
$121$	6.32558			0.575053
$122$	−4.22859	+	7.32414i	−0.382839	+	0.663096i
$123$	−2.04911	+	12.5987i	−0.184762	+	1.13599i
$124$	3.47357	−	2.00547i	0.311936	−	0.180096i
$125$	37.9763			3.39670
$126$		0			0
$127$	18.5344			1.64466			0.822332	−	0.569009i	$-0.192673\pi$
$127$	18.5344			1.64466			0.822332	+	0.569009i	$0.192673\pi$
$128$	−3.14011	+	1.81294i	−0.277549	+	0.160243i
$129$	6.88567	−	2.61040i	0.606249	−	0.229833i
$130$	6.63783	−	11.4971i	0.582176	−	1.00836i
$131$	−6.70441			−0.585767			−0.292884	−	0.956148i	$-0.594615\pi$
$131$	−6.70441			−0.585767			−0.292884	+	0.956148i	$0.594615\pi$
$132$	0.812205	+	2.14242i	0.0706933	+	0.186474i
$133$		0			0
$134$			7.83931i			0.677214i
$135$	10.4683	−	19.9275i	0.900971	−	1.71509i
$136$	−3.12112	+	1.80198i	−0.267634	+	0.154518i
$137$		−	13.6463i		−	1.16588i	−0.812514	−	0.582942i	$-0.801901\pi$
$137$		−	13.6463i		−	1.16588i	0.812514	−	0.582942i	$-0.198099\pi$
$138$	−1.19609	+	7.35399i	−0.101818	+	0.626013i
$139$	7.74126	−	4.46942i	0.656605	−	0.379091i	−0.134377	−	0.990930i	$-0.542903\pi$
$139$	7.74126	−	4.46942i	0.656605	−	0.379091i	0.790982	+	0.611839i	$0.209570\pi$
$140$		0			0
$141$	1.98618	−	12.2118i	0.167267	−	1.02842i
$142$	−1.15449	−	1.99964i	−0.0968830	−	0.167806i
$143$	2.81177	+	4.87013i	0.235132	+	0.407261i
$144$	−5.39488	+	4.77704i	−0.449574	+	0.398086i
$145$	2.55269	+	1.47380i	0.211990	+	0.122392i
$146$	−7.01436	+	12.1492i	−0.580513	+	1.00548i
$147$		0			0
$148$	1.56231	+	2.70601i	0.128421	+	0.222432i
$149$		−	3.79900i		−	0.311227i	−0.987818	−	0.155613i	$-0.950265\pi$
$149$		−	3.79900i		−	0.311227i	0.987818	−	0.155613i	$-0.0497354\pi$
$150$	−27.7288	−	4.50994i	−2.26405	−	0.368235i
$151$	−3.82166			−0.311002			−0.155501	−	0.987836i	$-0.549699\pi$
$151$	−3.82166			−0.311002			−0.155501	+	0.987836i	$0.549699\pi$
$152$	3.71824	−	6.44018i	0.301589	−	0.522368i
$153$	−2.63044	+	2.32919i	−0.212659	+	0.188304i
$154$		0			0
$155$	−24.5939	−	14.1993i	−1.97543	−	1.14051i
$156$	1.74356	−	2.13492i	0.139596	−	0.170931i
$157$	18.6081	+	10.7434i	1.48509	+	0.857417i	0.999856	−	0.0169675i	$-0.00540117\pi$
$157$	18.6081	+	10.7434i	1.48509	+	0.857417i	0.485234	+	0.874384i	$0.338735\pi$
$158$	9.95256	+	5.74611i	0.791783	+	0.457136i
$159$	5.52690	+	0.898920i	0.438312	+	0.0712890i
$160$	−12.4725	−	7.20102i	−0.986041	−	0.569291i
$161$		0			0
$162$	−6.37441	+	8.47394i	−0.500821	+	0.665776i
$163$	−6.25875	+	10.8405i	−0.490223	+	0.849092i	−0.999937	−	0.0112525i	$-0.996418\pi$
$163$	−6.25875	+	10.8405i	−0.490223	+	0.849092i	0.509713	+	0.860344i	$0.329751\pi$
$164$	4.50895			0.352090
$165$	10.2614	−	12.5647i	0.798846	−	0.978158i
$166$		−	1.87743i		−	0.145717i
$167$	−7.70819	−	13.3510i	−0.596477	−	1.03313i	−0.993337	−	0.115250i	$-0.963233\pi$
$167$	−7.70819	−	13.3510i	−0.596477	−	1.03313i	0.396859	−	0.917880i	$-0.370100\pi$
$168$		0			0
$169$	−3.11731	+	5.39935i	−0.239793	+	0.415334i
$170$	5.17671	+	2.98878i	0.397036	+	0.229229i
$171$	2.29748	−	6.87607i	0.175693	−	0.525826i
$172$	−1.30063	−	2.25277i	−0.0991725	−	0.171772i
$173$	−4.30737	−	7.46059i	−0.327483	−	0.567218i	0.654528	−	0.756037i	$-0.272867\pi$
$173$	−4.30737	−	7.46059i	−0.327483	−	0.567218i	−0.982012	+	0.188820i	$0.939534\pi$
$174$	−1.07546	−	0.878309i	−0.0815302	−	0.0665844i
$175$		0			0
$176$	−4.49739	+	2.59657i	−0.339004	+	0.195724i
$177$	−9.45216	+	3.58338i	−0.710468	+	0.269343i
$178$		−	7.18610i		−	0.538621i
$179$	16.5744	−	9.56922i	1.23883	−	0.715237i	0.269972	−	0.962868i	$-0.412985\pi$
$179$	16.5744	−	9.56922i	1.23883	−	0.715237i	0.968854	+	0.247631i	$0.0796521\pi$
$180$	−7.54170	−	2.51989i	−0.562125	−	0.187822i
$181$		−	7.69817i		−	0.572200i	−0.958200	−	0.286100i	$-0.907641\pi$
$181$		−	7.69817i		−	0.572200i	0.958200	−	0.286100i	$-0.0923590\pi$
$182$		0			0
$183$	12.2715	+	1.99589i	0.907135	+	0.147541i
$184$	11.2352			0.828266
$185$	11.0616	−	19.1593i	0.813268	−	1.40862i
$186$	10.3615	+	8.46205i	0.759741	+	0.620468i
$187$	−2.19285	+	1.26604i	−0.160357	+	0.0925820i
$188$	−4.37047			−0.318750
$189$		0			0
$190$	−12.3342			−0.894817
$191$	−16.1203	+	9.30704i	−1.16642	+	0.673433i	−0.952834	−	0.303491i	$-0.901848\pi$
$191$	−16.1203	+	9.30704i	−1.16642	+	0.673433i	−0.213587	+	0.976924i	$0.568515\pi$
$192$	11.6993	+	9.55460i	0.844322	+	0.689544i
$193$	−9.05721	+	15.6875i	−0.651952	+	1.12921i	0.330696	+	0.943737i	$0.392716\pi$
$193$	−9.05721	+	15.6875i	−0.651952	+	1.12921i	−0.982649	+	0.185477i	$0.940617\pi$
$194$	−3.21597			−0.230893
$195$	−19.2632	−	3.13305i	−1.37946	−	0.224362i
$196$		0			0
$197$			16.5945i			1.18231i	0.806559	+	0.591154i	$0.201328\pi$
$197$			16.5945i			1.18231i	−0.806559	+	0.591154i	$0.798672\pi$
$198$	−5.72136	+	5.06612i	−0.406599	+	0.360033i
$199$	−2.35461	+	1.35943i	−0.166914	+	0.0963677i	−0.581130	−	0.813811i	$-0.697389\pi$
$199$	−2.35461	+	1.35943i	−0.166914	+	0.0963677i	0.414216	+	0.910179i	$0.364056\pi$
$200$			42.3630i			2.99552i
$201$	10.7760	−	4.08527i	0.760083	−	0.288153i
$202$	−16.3225	+	9.42383i	−1.14845	+	0.663058i
$203$		0			0
$204$	0.961279	+	0.785061i	0.0673030	+	0.0549653i
$205$	−15.9623	−	27.6476i	−1.11486	−	1.93099i
$206$	−1.77712	−	3.07807i	−0.123818	−	0.214459i
$207$	10.7322	−	2.18819i	0.745940	−	0.152090i
$208$	5.41057	+	3.12379i	0.375155	+	0.216596i
$209$	2.61237	−	4.52476i	0.180702	−	0.312984i
$210$		0			0
$211$	−13.9445	−	24.1526i	−0.959979	−	1.66273i	−0.722539	−	0.691330i	$-0.757025\pi$
$211$	−13.9445	−	24.1526i	−0.959979	−	1.66273i	−0.237440	−	0.971402i	$-0.576308\pi$
$212$		−	1.97802i		−	0.135851i
$213$	−2.14710	+	2.62905i	−0.147117	+	0.180140i
$214$	−13.9598			−0.954276
$215$	−9.20887	+	15.9502i	−0.628040	+	1.08780i
$216$	14.1556	+	7.43624i	0.963169	+	0.505972i
$217$		0			0
$218$	−7.30732	−	4.21888i	−0.494914	−	0.285739i
$219$	20.3559	+	3.31077i	1.37552	+	0.223721i
$220$	−4.96278	−	2.86526i	−0.334590	−	0.193176i
$221$	2.63809	+	1.52310i	0.177457	+	0.102455i
$222$	−6.59217	+	8.07188i	−0.442437	+	0.541749i
$223$	6.64349	+	3.83562i	0.444881	+	0.256852i	0.705666	−	0.708545i	$-0.250648\pi$
$223$	6.64349	+	3.83562i	0.444881	+	0.256852i	−0.260785	+	0.965397i	$0.583981\pi$
$224$		0			0
$225$	8.25076	+	40.4667i	0.550051	+	2.69778i
$226$	1.67407	−	2.89958i	0.111358	−	0.192877i
$227$	−2.32877			−0.154566			−0.0772829	−	0.997009i	$-0.524624\pi$
$227$	−2.32877			−0.154566			−0.0772829	+	0.997009i	$0.524624\pi$
$228$	−2.52774	−	0.411123i	−0.167404	−	0.0272273i
$229$		−	11.9689i		−	0.790925i	−0.918482	−	0.395463i	$-0.870584\pi$
$229$		−	11.9689i		−	0.790925i	0.918482	−	0.395463i	$-0.129416\pi$
$230$	−9.31735	−	16.1381i	−0.614368	−	1.06412i
$231$		0			0
$232$	−1.04692	+	1.81332i	−0.0687337	+	0.119050i
$233$	−2.18913	−	1.26390i	−0.143415	−	0.0828007i	0.426576	−	0.904452i	$-0.359720\pi$
$233$	−2.18913	−	1.26390i	−0.143415	−	0.0828007i	−0.569991	+	0.821651i	$0.693053\pi$
$234$	8.71975	+	2.91351i	0.570028	+	0.190462i
$235$	15.4721	+	26.7985i	1.00929	+	1.74814i
$236$	1.78542	+	3.09244i	0.116221	+	0.201301i
$237$	2.71216	−	16.6754i	0.176174	−	1.08318i
$238$		0			0
$239$	17.4587	−	10.0798i	1.12931	−	0.652006i	0.185546	−	0.982636i	$-0.440595\pi$
$239$	17.4587	−	10.0798i	1.12931	−	0.652006i	0.943761	+	0.330630i	$0.107261\pi$
$240$	2.89326	−	17.7889i	0.186759	−	1.14827i
$241$			20.9294i			1.34818i	0.738649	+	0.674091i	$0.235464\pi$
$241$			20.9294i			1.34818i	−0.738649	+	0.674091i	$0.764536\pi$
$242$	6.45432	−	3.72640i	0.414899	−	0.239542i
$243$	14.9703	+	4.34636i	0.960344	+	0.278819i
$244$		−	4.39184i		−	0.281159i
$245$		0			0
$246$	5.33110	+	14.0623i	0.339899	+	0.896578i
$247$	−6.28560			−0.399943
$248$	10.0865	−	17.4704i	0.640496	−	1.10937i
$249$	−2.58074	+	0.978377i	−0.163548	+	0.0620021i
$250$	38.7492	−	22.3718i	2.45071	−	1.41492i
$251$	−25.5747			−1.61426			−0.807130	−	0.590374i	$-0.798980\pi$
$251$	−25.5747			−1.61426			−0.807130	+	0.590374i	$0.798980\pi$
$252$		0			0
$253$	7.89363			0.496268
$254$	18.9116	−	10.9186i	1.18662	−	0.685096i
$255$	1.41070	−	8.67352i	0.0883414	−	0.543157i
$256$	6.58491	−	11.4054i	0.411557	−	0.712837i
$257$	−11.8745			−0.740711			−0.370355	−	0.928890i	$-0.620764\pi$
$257$	−11.8745			−0.740711			−0.370355	+	0.928890i	$0.620764\pi$
$258$	5.48801	−	6.71988i	0.341669	−	0.418361i
$259$		0			0
$260$			6.89408i			0.427553i
$261$	−0.646888	+	1.93605i	−0.0400414	+	0.119838i
$262$	−6.84086	+	3.94957i	−0.422630	+	0.244005i
$263$		−	22.3671i		−	1.37922i	−0.724183	−	0.689608i	$-0.757783\pi$
$263$		−	22.3671i		−	1.37922i	0.724183	−	0.689608i	$-0.242217\pi$
$264$	8.92538	+	7.28921i	0.549319	+	0.448620i
$265$	−12.1286	+	7.00247i	−0.745056	+	0.430158i
$266$		0			0
$267$	−9.87812	+	3.74486i	−0.604531	+	0.229182i
$268$	−2.03549	−	3.52557i	−0.124337	−	0.215358i
$269$	−2.11335	−	3.66043i	−0.128853	−	0.223180i	0.794379	−	0.607422i	$-0.207796\pi$
$269$	−2.11335	−	3.66043i	−0.128853	−	0.223180i	−0.923232	+	0.384242i	$0.874463\pi$
$270$	−1.05793	−	26.5000i	−0.0643837	−	1.61274i
$271$	19.3941	+	11.1972i	1.17811	+	0.680179i	0.955576	−	0.294746i	$-0.0952352\pi$
$271$	19.3941	+	11.1972i	1.17811	+	0.680179i	0.222530	+	0.974926i	$0.428568\pi$
$272$	−1.40653	+	2.43619i	−0.0852836	+	0.147715i
$273$		0			0
$274$	−8.03905	−	13.9240i	−0.485657	−	0.841183i
$275$			29.7635i			1.79481i
$276$	−1.37156	−	3.61787i	−0.0825581	−	0.217770i
$277$	11.3846			0.684034			0.342017	−	0.939694i	$-0.388890\pi$
$277$	11.3846			0.684034			0.342017	+	0.939694i	$0.388890\pi$
$278$	5.26587	−	9.12076i	0.315826	−	0.547027i
$279$	6.23243	−	18.6528i	0.373126	−	1.11672i
$280$		0			0
$281$	−0.702700	−	0.405704i	−0.0419196	−	0.0242023i	0.478894	−	0.877873i	$-0.341038\pi$
$281$	−0.702700	−	0.405704i	−0.0419196	−	0.0242023i	−0.520813	+	0.853671i	$0.674371\pi$
$282$	−5.16738	−	13.6304i	−0.307713	−	0.811679i
$283$	−15.8740	−	9.16486i	−0.943611	−	0.544794i	−0.0525206	−	0.998620i	$-0.516726\pi$
$283$	−15.8740	−	9.16486i	−0.943611	−	0.544794i	−0.891090	+	0.453826i	$0.850059\pi$
$284$	1.03842	+	0.599532i	0.0616188	+	0.0355757i
$285$	6.42767	+	16.9548i	0.380742	+	1.00431i
$286$	5.73799	+	3.31283i	0.339294	+	0.195892i
$287$		0			0
$288$	3.16071	−	9.45959i	0.186247	−	0.557412i
$289$	7.81420	−	13.5346i	0.459659	−	0.796153i
$290$	3.47286			0.203933
$291$	1.67592	+	4.42072i	0.0982444	+	0.259147i
$292$		−	7.28515i		−	0.426331i
$293$	6.23639	+	10.8017i	0.364334	+	0.631044i	0.988669	−	0.150112i	$-0.0479634\pi$
$293$	6.23639	+	10.8017i	0.364334	+	0.631044i	−0.624335	+	0.781156i	$0.714630\pi$
$294$		0			0
$295$	12.6413	−	21.8954i	0.736004	−	1.27480i
$296$	13.6099	+	7.85769i	0.791061	+	0.456719i
$297$	9.94551	+	5.22458i	0.577097	+	0.303161i
$298$	−2.23800	−	3.87632i	−0.129644	−	0.224549i
$299$	−4.74819	−	8.22411i	−0.274595	−	0.475613i
$300$	13.6415	−	5.17157i	0.787590	−	0.298581i
$301$		0			0
$302$	−3.89943	+	2.25134i	−0.224387	+	0.129550i
$303$	21.4602	+	17.5262i	1.23286	+	1.00686i
$304$		−	5.80454i		−	0.332913i
$305$	−26.9295	+	15.5477i	−1.54198	+	0.890261i
$306$	−1.31185	+	3.92619i	−0.0749935	+	0.224446i
$307$			21.3241i			1.21703i	0.793543	+	0.608514i	$0.208234\pi$
$307$			21.3241i			1.21703i	−0.793543	+	0.608514i	$0.791766\pi$
$308$		0			0
$309$	−3.30505	+	4.04692i	−0.188018	+	0.230221i
$310$	−33.4592			−1.90036
$311$	−3.92094	+	6.79126i	−0.222336	+	0.385097i	−0.955517	−	0.294936i	$-0.904702\pi$
$311$	−3.92094	+	6.79126i	−0.222336	+	0.385097i	0.733181	+	0.680034i	$0.238035\pi$
$312$	2.22558	−	13.6837i	0.125998	−	0.774686i
$313$	−8.57593	+	4.95131i	−0.484740	+	0.279865i	−0.722390	−	0.691486i	$-0.756956\pi$
$313$	−8.57593	+	4.95131i	−0.484740	+	0.279865i	0.237650	+	0.971351i	$0.423623\pi$
$314$	25.3158			1.42865
$315$		0			0
$316$	−5.96794			−0.335723
$317$	−20.8358	+	12.0296i	−1.17025	+	0.675647i	−0.953740	−	0.300632i	$-0.902802\pi$
$317$	−20.8358	+	12.0296i	−1.17025	+	0.675647i	−0.216515	+	0.976279i	$0.569469\pi$
$318$	6.16894	−	2.33869i	0.345937	−	0.131147i
$319$	−0.735549	+	1.27401i	−0.0411828	+	0.0713308i
$320$	−37.7792			−2.11192
$321$	7.27483	+	19.1894i	0.406042	+	1.07105i
$322$		0			0
$323$		−	2.83018i		−	0.157476i
$324$	0.666486	−	5.46610i	0.0370270	−	0.303672i
$325$	31.0097	−	17.9034i	1.72011	−	0.993104i
$326$			14.7481i			0.816824i
$327$	−1.99131	+	12.2433i	−0.110120	+	0.677057i
$328$	19.6396	−	11.3389i	1.08442	−	0.626088i
$329$		0			0
$330$	3.06835	−	18.8654i	0.168907	−	1.03850i
$331$	4.53686	+	7.85807i	0.249368	+	0.431918i	0.963351	−	0.268245i	$-0.0864437\pi$
$331$	4.53686	+	7.85807i	0.249368	+	0.431918i	−0.713982	+	0.700164i	$0.753110\pi$
$332$	0.487477	+	0.844335i	0.0267538	+	0.0463389i
$333$	14.5311	+	4.85523i	0.796298	+	0.266065i
$334$	−15.7301	−	9.08179i	−0.860714	−	0.496934i
$335$	−14.4118	+	24.9620i	−0.787403	+	1.36382i
$336$		0			0
$337$	4.02012	+	6.96304i	0.218990	+	0.379301i	0.954499	−	0.298213i	$-0.0963906\pi$
$337$	4.02012	+	6.96304i	0.218990	+	0.379301i	−0.735510	+	0.677514i	$0.763057\pi$
$338$			7.34565i			0.399550i
$339$	−4.85821	−	0.790161i	−0.263862	−	0.0429157i
$340$	−3.10416			−0.168347
$341$	7.08663	−	12.2744i	0.383763	−	0.664696i
$342$	−1.70645	−	8.36946i	−0.0922743	−	0.452568i
$343$		0			0
$344$	−11.3303	−	6.54157i	−0.610891	−	0.352698i
$345$	−17.3282	+	21.2178i	−0.932919	+	1.14233i
$346$	−8.79007	−	5.07495i	−0.472557	−	0.272831i
$347$	30.6345	+	17.6868i	1.64454	+	0.949478i	0.979189	+	0.202952i	$0.0650536\pi$
$347$	30.6345	+	17.6868i	1.64454	+	0.949478i	0.665356	+	0.746526i	$0.268280\pi$
$348$	0.711719	+	0.115757i	0.0381521	+	0.00620523i
$349$	21.1868	+	12.2322i	1.13411	+	0.654776i	0.944964	−	0.327174i	$-0.106096\pi$
$349$	21.1868	+	12.2322i	1.13411	+	0.654776i	0.189141	+	0.981950i	$0.439430\pi$
$350$		0			0
$351$	−0.539130	−	13.5046i	−0.0287766	−	0.720823i
$352$	3.59391	−	6.22484i	0.191556	−	0.331785i
$353$	0.971897			0.0517289			0.0258644	−	0.999665i	$-0.491766\pi$
$353$	0.971897			0.0517289			0.0258644	+	0.999665i	$0.491766\pi$
$354$	−7.53356	+	9.22458i	−0.400404	+	0.490281i
$355$		−	8.48971i		−	0.450587i
$356$	1.86588	+	3.23180i	0.0988914	+	0.171285i
$357$		0			0
$358$	11.2745	−	19.5279i	0.595874	−	1.03208i
$359$	13.7879	+	7.96048i	0.727700	+	0.420138i	0.817580	−	0.575815i	$-0.195315\pi$
$359$	13.7879	+	7.96048i	0.727700	+	0.420138i	−0.0898801	+	0.995953i	$0.528648\pi$
$360$	−39.1863	+	7.98970i	−2.06530	+	0.421094i
$361$	−6.58007	−	11.3970i	−0.346319	−	0.599843i
$362$	−4.53499	−	7.85484i	−0.238354	−	0.412841i
$363$	−8.48588	−	6.93028i	−0.445393	−	0.363745i
$364$		0			0
$365$	−44.6704	+	25.7905i	−2.33816	+	1.34994i
$366$	13.6970	−	5.19263i	0.715955	−	0.271423i
$367$			24.7087i			1.28978i	0.764274	+	0.644891i	$0.223097\pi$
$367$			24.7087i			1.28978i	−0.764274	+	0.644891i	$0.776903\pi$
$368$	7.59468	−	4.38479i	0.395900	−	0.228573i
$369$	16.5520	−	14.6564i	0.861665	−	0.762983i
$370$		−	26.0657i		−	1.35509i
$371$		0			0
$372$	−6.85704	−	1.11526i	−0.355521	−	0.0578235i
$373$	−9.43621			−0.488588			−0.244294	−	0.969701i	$-0.578556\pi$
$373$	−9.43621			−0.488588			−0.244294	+	0.969701i	$0.578556\pi$
$374$	−1.49165	+	2.58361i	−0.0771314	+	0.133595i
$375$	−50.9459	−	41.6067i	−2.63083	−	2.14856i
$376$	−19.0364	+	10.9907i	−0.981730	+	0.566802i
$377$	1.76980			0.0911492
$378$		0			0
$379$	20.8031			1.06858			0.534292	−	0.845300i	$-0.320578\pi$
$379$	20.8031			1.06858			0.534292	+	0.845300i	$0.320578\pi$
$380$	5.54705	−	3.20259i	0.284558	−	0.164289i
$381$	−24.8642	−	20.3062i	−1.27383	−	1.04032i
$382$	−10.9656	+	18.9929i	−0.561047	+	0.971761i
$383$	6.46017			0.330099			0.165050	−	0.986285i	$-0.447222\pi$
$383$	6.46017			0.330099			0.165050	+	0.986285i	$0.447222\pi$
$384$	6.19876	+	1.00819i	0.316329	+	0.0514492i
$385$		0			0
$386$			21.3424i			1.08630i
$387$	−12.0972	−	4.04201i	−0.614935	−	0.205467i
$388$	1.44632	−	0.835031i	0.0734255	−	0.0423923i
$389$			0.0514818i			0.00261023i	0.999999	+	0.00130512i	$0.000415431\pi$
$389$			0.0514818i			0.00261023i	−0.999999	+	0.00130512i	$0.999585\pi$
$390$	−21.5009	+	8.15113i	−1.08874	+	0.412748i
$391$	3.70303	−	2.13794i	0.187270	−	0.108120i
$392$		0			0
$393$	8.99409	+	7.34533i	0.453692	+	0.370523i
$394$	9.77582	+	16.9322i	0.492499	+	0.853033i
$395$	21.1274	+	36.5937i	1.06303	+	1.84123i
$396$	1.25764	−	3.76394i	0.0631986	−	0.189145i
$397$	−11.0099	−	6.35655i	−0.552569	−	0.319026i	0.197588	−	0.980285i	$-0.436689\pi$
$397$	−11.0099	−	6.35655i	−0.552569	−	0.319026i	−0.750158	+	0.661259i	$0.770022\pi$
$398$	−1.60169	+	2.77420i	−0.0802853	+	0.139058i
$399$		0			0
$400$	16.5332	+	28.6364i	0.826660	+	1.43182i
$401$		−	2.53716i		−	0.126700i	−0.997991	−	0.0633500i	$-0.979822\pi$
$401$		−	2.53716i		−	0.126700i	0.997991	−	0.0633500i	$-0.0201784\pi$
$402$	8.58872	−	10.5166i	0.428366	−	0.524519i
$403$	−17.0511			−0.849375
$404$	4.89382	−	8.47634i	0.243477	−	0.421714i
$405$	−35.8760	+	15.2641i	−1.78269	+	0.758478i
$406$		0			0
$407$	9.56210	+	5.52068i	0.473976	+	0.273650i
$408$	6.16128	+	1.00210i	0.305029	+	0.0496112i
$409$	0.0495655	+	0.0286167i	0.00245086	+	0.00141500i	0.501225	−	0.865317i	$-0.332883\pi$
$409$	0.0495655	+	0.0286167i	0.00245086	+	0.00141500i	−0.498774	+	0.866732i	$0.666216\pi$
$410$	−32.5744	−	18.8068i	−1.60873	−	0.928803i
$411$	−14.9509	+	18.3068i	−0.737471	+	0.903007i
$412$	1.59845	+	0.922864i	0.0787499	+	0.0454663i
$413$		0			0
$414$	9.66157	−	8.55508i	0.474840	−	0.420459i
$415$	3.45148	−	5.97813i	0.169426	−	0.293455i
$416$	−8.64728			−0.423968
$417$	−15.2817	−	2.48549i	−0.748349	−	0.121715i
$418$		−	6.15580i		−	0.301090i
$419$	3.08007	+	5.33484i	0.150471	+	0.260624i	0.931401	−	0.363995i	$-0.118588\pi$
$419$	3.08007	+	5.33484i	0.150471	+	0.260624i	−0.780930	+	0.624619i	$0.785254\pi$
$420$		0			0
$421$	15.0693	−	26.1007i	0.734431	−	1.27207i	−0.220542	−	0.975378i	$-0.570783\pi$
$421$	15.0693	−	26.1007i	0.734431	−	1.27207i	0.954973	−	0.296694i	$-0.0958842\pi$
$422$	−28.4566	−	16.4294i	−1.38525	−	0.799772i
$423$	−16.0437	+	14.2063i	−0.780072	+	0.690734i
$424$	−4.97424	−	8.61564i	−0.241571	−	0.418413i
$425$	8.06128	+	13.9626i	0.391030	+	0.677283i
$426$	−0.642025	+	3.94741i	−0.0311062	+	0.191253i
$427$		0			0
$428$	6.27815	−	3.62469i	0.303466	−	0.175206i
$429$	1.56365	−	9.61393i	0.0754938	−	0.464165i
$430$			21.6998i			1.04646i
$431$	−6.99003	+	4.03570i	−0.336698	+	0.194393i	−0.658811	−	0.752309i	$-0.728940\pi$
$431$	−6.99003	+	4.03570i	−0.336698	+	0.194393i	0.322113	+	0.946701i	$0.395607\pi$
$432$	12.4710	−	0.497868i	0.600013	−	0.0239537i
$433$			28.4938i			1.36933i	0.728860	+	0.684663i	$0.240051\pi$
$433$			28.4938i			1.36933i	−0.728860	+	0.684663i	$0.759949\pi$
$434$		0			0
$435$	−1.80980	−	4.77385i	−0.0867731	−	0.228889i
$436$	4.38175			0.209848
$437$	−4.41147	+	7.64090i	−0.211029	+	0.365514i
$438$	22.7205	−	8.61351i	1.08563	−	0.411569i
$439$	−1.77067	+	1.02230i	−0.0845096	+	0.0487916i	−0.541659	−	0.840598i	$-0.682204\pi$
$439$	−1.77067	+	1.02230i	−0.0845096	+	0.0487916i	0.457150	+	0.889390i	$0.348870\pi$
$440$	−28.8218			−1.37402
$441$		0			0
$442$	3.58904			0.170713
$443$	21.1324	−	12.2008i	1.00403	−	0.579677i	0.0945924	−	0.995516i	$-0.469845\pi$
$443$	21.1324	−	12.2008i	1.00403	−	0.579677i	0.909438	+	0.415839i	$0.136512\pi$
$444$	0.868818	−	5.34182i	0.0412323	−	0.253512i
$445$	13.2110	−	22.8821i	0.626260	−	1.08471i
$446$	9.03827			0.427974
$447$	−4.16217	+	5.09643i	−0.196864	+	0.241053i
$448$		0			0
$449$		−	0.293539i		−	0.0138529i	−0.999976	−	0.00692647i	$-0.997795\pi$
$449$		−	0.293539i		−	0.0138529i	0.999976	−	0.00692647i	$-0.00220478\pi$
$450$	32.2576	+	36.4297i	1.52064	+	1.71731i
$451$	13.7984	−	7.96654i	0.649744	−	0.375130i
$452$			1.73870i			0.0817816i
$453$	5.12682	+	4.18699i	0.240879	+	0.196722i
$454$	−2.37616	+	1.37188i	−0.111519	+	0.0643855i
$455$		0			0
$456$	−12.0439	+	4.56593i	−0.564008	+	0.213819i
$457$	−8.27470	−	14.3322i	−0.387074	−	0.670432i	0.604981	−	0.796240i	$-0.293181\pi$
$457$	−8.27470	−	14.3322i	−0.387074	−	0.670432i	−0.992055	+	0.125808i	$0.959848\pi$
$458$	−7.05087	−	12.2125i	−0.329465	−	0.570651i
$459$	6.08064	−	0.242751i	0.283820	−	0.0113307i
$460$	8.38057	+	4.83852i	0.390746	+	0.225597i
$461$	10.0560	−	17.4175i	0.468354	−	0.811213i	−0.530992	−	0.847377i	$-0.678180\pi$
$461$	10.0560	−	17.4175i	0.468354	−	0.811213i	0.999346	+	0.0361638i	$0.0115138\pi$
$462$		0			0
$463$	9.34602	+	16.1878i	0.434346	+	0.752310i	0.997242	−	0.0742181i	$-0.0236461\pi$
$463$	9.34602	+	16.1878i	0.434346	+	0.752310i	−0.562896	+	0.826528i	$0.690313\pi$
$464$			1.63435i			0.0758726i
$465$	17.4365	+	45.9936i	0.808597	+	2.13290i
$466$	−2.97825			−0.137965
$467$	−14.6803	+	25.4270i	−0.679322	+	1.17662i	0.295864	+	0.955230i	$0.404393\pi$
$467$	−14.6803	+	25.4270i	−0.679322	+	1.17662i	−0.975185	+	0.221390i	$0.928941\pi$
$468$	−4.67802	+	0.953804i	−0.216242	+	0.0440896i
$469$		0			0
$470$	31.5740	+	18.2293i	1.45640	+	0.840853i
$471$	−13.1927	−	34.7994i	−0.607888	−	1.60347i
$472$	15.5535	+	8.97981i	0.715907	+	0.413329i
$473$	−7.96050	−	4.59599i	−0.366024	−	0.211324i
$474$	−7.05612	−	18.6125i	−0.324098	−	0.854900i
$475$	−28.8106	−	16.6338i	−1.32192	−	0.763212i
$476$		0			0
$477$	−6.42958	−	7.26117i	−0.294390	−	0.332466i
$478$	11.8760	−	20.5698i	0.543195	−	0.940841i
$479$	−21.9321			−1.00210			−0.501051	−	0.865417i	$-0.667053\pi$
$479$	−21.9321			−1.00210			−0.501051	+	0.865417i	$0.667053\pi$
$480$	8.84272	+	23.3252i	0.403613	+	1.06464i
$481$		−	13.2833i		−	0.605664i
$482$	12.3295	+	21.3554i	0.561594	+	0.972710i
$483$		0			0
$484$	−1.93513	+	3.35174i	−0.0879604	+	0.152352i
$485$	−10.2403	−	5.91226i	−0.464989	−	0.268462i
$486$	17.8354	−	4.38417i	0.809030	−	0.198870i
$487$	−0.538896	−	0.933395i	−0.0244197	−	0.0422962i	0.853557	−	0.520999i	$-0.174440\pi$
$487$	−0.538896	−	0.933395i	−0.0244197	−	0.0422962i	−0.877977	+	0.478703i	$0.841107\pi$
$488$	−11.0444	−	19.1295i	−0.499957	−	0.865952i
$489$	20.2730	−	7.68563i	0.916777	−	0.347556i
$490$		0			0
$491$	16.3708	−	9.45168i	0.738804	−	0.426549i	−0.0828305	−	0.996564i	$-0.526396\pi$
$491$	16.3708	−	9.45168i	0.738804	−	0.426549i	0.821634	+	0.570015i	$0.193063\pi$
$492$	−6.04884	−	4.93999i	−0.272703	−	0.222712i
$493$			0.796877i			0.0358895i
$494$	−6.41353	+	3.70285i	−0.288558	+	0.166599i
$495$	−27.5316	+	5.61342i	−1.23745	+	0.252305i
$496$		−	15.7461i		−	0.707020i
$497$		0			0
$498$	−2.05690	+	2.51860i	−0.0921721	+	0.112861i
$499$	−16.6858			−0.746959			−0.373479	−	0.927639i	$-0.621835\pi$
$499$	−16.6858			−0.746959			−0.373479	+	0.927639i	$0.621835\pi$
$500$	−11.6178	+	20.1225i	−0.519562	+	0.899908i
$501$	−4.28660	+	26.3556i	−0.191511	+	1.17748i
$502$	−26.0952	+	15.0661i	−1.16468	+	0.672431i
$503$	21.2386			0.946981			0.473491	−	0.880799i	$-0.342994\pi$
$503$	21.2386			0.946981			0.473491	+	0.880799i	$0.342994\pi$
$504$		0			0
$505$	−69.2993			−3.08378
$506$	8.05428	−	4.65014i	0.358056	−	0.206724i
$507$	10.0974	−	3.82800i	0.448443	−	0.170008i
$508$	−5.67007	+	9.82085i	−0.251569	+	0.435730i
$509$	11.4450			0.507293			0.253646	−	0.967297i	$-0.418370\pi$
$509$	11.4450			0.507293			0.253646	+	0.967297i	$0.418370\pi$
$510$	−3.67016	−	9.68108i	−0.162517	−	0.428685i
$511$		0			0
$512$		−	22.7685i		−	1.00623i
$513$	−10.6155	+	6.70725i	−0.468686	+	0.296132i
$514$	−12.1162	+	6.99527i	−0.534421	+	0.308548i
$515$		−	13.0683i		−	0.575858i
$516$	−0.723295	+	4.44710i	−0.0318413	+	0.195772i
$517$	−13.3747	+	7.72188i	−0.588218	+	0.339608i
$518$		0			0
$519$	−2.39537	+	14.7276i	−0.105145	+	0.646472i
$520$	17.3370	+	30.0285i	0.760276	+	1.31684i
$521$	−10.3999	−	18.0131i	−0.455627	−	0.789169i	0.543097	−	0.839670i	$-0.317252\pi$
$521$	−10.3999	−	18.0131i	−0.455627	−	0.789169i	−0.998724	+	0.0505007i	$0.983918\pi$
$522$	0.480474	+	2.35653i	0.0210298	+	0.103143i
$523$	12.9330	+	7.46690i	0.565523	+	0.326505i	0.755359	−	0.655311i	$-0.227462\pi$
$523$	12.9330	+	7.46690i	0.565523	+	0.326505i	−0.189836	+	0.981816i	$0.560796\pi$
$524$	2.05102	−	3.55248i	0.0895994	−	0.155191i
$525$		0			0
$526$	−13.1765	−	22.8223i	−0.574522	−	0.995101i
$527$		−	7.67749i		−	0.334437i
$528$	8.87813	+	1.44398i	0.386371	+	0.0628411i
$529$	9.67015			0.420441
$530$	−8.25032	+	14.2900i	−0.358371	+	0.620717i
$531$	16.6062	+	5.54858i	0.720647	+	0.240788i
$532$		0			0
$533$	−16.6002	−	9.58410i	−0.719033	−	0.415134i
$534$	−7.87306	+	9.64028i	−0.340701	+	0.417176i
$535$	−44.4511	−	25.6639i	−1.92179	−	1.10955i
$536$	−17.7319	−	10.2375i	−0.765902	−	0.442194i
$537$	−32.7188	−	5.32153i	−1.41192	−	0.229641i
$538$	−4.31272	−	2.48995i	−0.185934	−	0.107349i
$539$		0			0
$540$	7.35654	+	11.6431i	0.316575	+	0.501041i
$541$	−15.5838	+	26.9920i	−0.670002	+	1.16048i	0.307902	+	0.951418i	$0.400373\pi$
$541$	−15.5838	+	26.9920i	−0.670002	+	1.16048i	−0.977903	+	0.209058i	$0.932960\pi$
$542$	26.3850			1.13333
$543$	−8.43408	+	10.3272i	−0.361941	+	0.443184i
$544$		−	3.89356i		−	0.166935i
$545$	−15.5120	−	26.8676i	−0.664462	−	1.15088i
$546$		0			0
$547$	−15.7410	+	27.2642i	−0.673035	+	1.16573i	0.304004	+	0.952671i	$0.401677\pi$
$547$	−15.7410	+	27.2642i	−0.673035	+	1.16573i	−0.977039	+	0.213061i	$0.931657\pi$
$548$	7.23079	+	4.17470i	0.308884	+	0.178334i
$549$	−14.2757	−	16.1221i	−0.609274	−	0.688076i
$550$	17.5337	+	30.3693i	0.747640	+	1.29495i
$551$	−0.822146	−	1.42400i	−0.0350246	−	0.0606644i
$552$	−15.0722	−	12.3092i	−0.641514	−	0.523914i
$553$		0			0
$554$	11.6163	−	6.70667i	0.493529	−	0.284939i
$555$	−35.8302	+	13.5835i	−1.52091	+	0.576587i
$556$			5.46916i			0.231944i
$557$	23.5896	−	13.6194i	0.999522	−	0.577074i	0.0914153	−	0.995813i	$-0.470861\pi$
$557$	23.5896	−	13.6194i	0.999522	−	0.577074i	0.908107	+	0.418738i	$0.137528\pi$
$558$	−4.62912	−	22.7040i	−0.195966	−	0.961136i
$559$			11.0584i			0.467720i
$560$		0			0
$561$	4.32881	+	0.704057i	0.182762	+	0.0297253i
$562$	−0.956002			−0.0403265
$563$	14.1871	−	24.5728i	0.597916	−	1.03562i	−0.395212	−	0.918590i	$-0.629329\pi$
$563$	14.1871	−	24.5728i	0.597916	−	1.03562i	0.993128	−	0.117031i	$-0.0373377\pi$
$564$	5.86307	+	4.78827i	0.246880	+	0.201623i
$565$	10.6612	−	6.15525i	0.448521	−	0.258953i
$566$	−21.5961			−0.907751
$567$		0			0
$568$	6.03071			0.253043
$569$	−29.4616	+	17.0097i	−1.23509	+	0.713082i	−0.968087	−	0.250613i	$-0.919368\pi$
$569$	−29.4616	+	17.0097i	−1.23509	+	0.713082i	−0.267007	+	0.963695i	$0.586035\pi$
$570$	16.5466	+	13.5133i	0.693059	+	0.566010i
$571$	22.3455	−	38.7035i	0.935130	−	1.61969i	0.160727	−	0.986999i	$-0.448616\pi$
$571$	22.3455	−	38.7035i	0.935130	−	1.61969i	0.774402	−	0.632693i	$-0.218051\pi$
$572$	−3.44072			−0.143864
$573$	31.8224	+	5.17573i	1.32940	+	0.216219i
$574$		0			0
$575$		−	50.2613i		−	2.09604i
$576$	−5.22680	−	25.6353i	−0.217783	−	1.06814i
$577$	6.36301	−	3.67369i	0.264896	−	0.152938i	−0.361670	−	0.932306i	$-0.617793\pi$
$577$	6.36301	−	3.67369i	0.264896	−	0.152938i	0.626566	+	0.779369i	$0.284460\pi$
$578$		−	18.4134i		−	0.765896i
$579$	29.3376	−	11.1221i	1.21923	−	0.462218i
$580$	−1.56185	+	0.901733i	−0.0648522	+	0.0374424i
$581$		0			0
$582$	4.31428	+	3.52340i	0.178833	+	0.146050i
$583$	−3.49482	−	6.05320i	−0.144741	−	0.250698i
$584$	−18.3204	−	31.7319i	−0.758104	−	1.31307i
$585$	22.4093	+	25.3077i	0.926511	+	1.04634i
$586$	12.7266	+	7.34772i	0.525732	+	0.303531i
$587$	13.1328	−	22.7466i	0.542048	−	0.938855i	−0.456738	−	0.889601i	$-0.650982\pi$
$587$	13.1328	−	22.7466i	0.542048	−	0.938855i	0.998786	−	0.0492535i	$-0.0156842\pi$
$588$		0			0
$589$	7.92095	+	13.7195i	0.326377	+	0.565302i
$590$		−	29.7880i		−	1.22635i
$591$	18.1809	−	22.2618i	0.747860	−	0.915728i
$592$	12.2666			0.504155
$593$	−4.56209	+	7.90178i	−0.187343	+	0.324487i	−0.944363	−	0.328904i	$-0.893321\pi$
$593$	−4.56209	+	7.90178i	−0.187343	+	0.324487i	0.757021	+	0.653391i	$0.226654\pi$
$594$	13.2257	−	0.527997i	0.542658	−	0.0216640i
$595$		0			0
$596$	2.01298	+	1.16220i	0.0824550	+	0.0476054i
$597$	4.64814	+	0.755994i	0.190236	+	0.0309408i
$598$	−9.68966	−	5.59433i	−0.396240	−	0.228769i
$599$	20.0987	+	11.6040i	0.821210	+	0.474126i	0.850834	−	0.525435i	$-0.176097\pi$
$599$	20.0987	+	11.6040i	0.821210	+	0.474126i	−0.0296234	+	0.999561i	$0.509431\pi$
$600$	46.4128	−	56.8308i	1.89479	−	2.32011i
$601$	19.0021	+	10.9709i	0.775111	+	0.447510i	0.834695	−	0.550713i	$-0.185644\pi$
$601$	19.0021	+	10.9709i	0.775111	+	0.447510i	−0.0595840	+	0.998223i	$0.518977\pi$
$602$		0			0
$603$	−18.9320	−	6.32572i	−0.770973	−	0.257603i
$604$	1.16913	−	2.02499i	0.0475711	−	0.0823955i
$605$	27.4025			1.11407
$606$	32.2217	+	5.24068i	1.30892	+	0.212888i
$607$			44.6048i			1.81045i	0.424929	+	0.905226i	$0.360299\pi$
$607$			44.6048i			1.81045i	−0.424929	+	0.905226i	$0.639701\pi$
$608$	4.01703	+	6.95770i	0.162912	+	0.282172i
$609$		0			0
$610$	−18.3184	+	31.7283i	−0.741689	+	1.28464i
$611$	16.0903	+	9.28976i	0.650946	+	0.375824i
$612$	−0.429464	−	2.10635i	−0.0173600	−	0.0851440i
$613$	−5.82799	−	10.0944i	−0.235390	−	0.407708i	0.723996	−	0.689804i	$-0.242303\pi$
$613$	−5.82799	−	10.0944i	−0.235390	−	0.407708i	−0.959386	+	0.282097i	$0.908970\pi$
$614$	12.5620	+	21.7580i	0.506961	+	0.878083i
$615$	−8.87681	+	54.5780i	−0.357947	+	2.20080i
$616$		0			0
$617$	36.6143	−	21.1393i	1.47403	−	0.851034i	0.474462	−	0.880276i	$-0.342643\pi$
$617$	36.6143	−	21.1393i	1.47403	−	0.851034i	0.999572	+	0.0292416i	$0.00930923\pi$
$618$	−0.988275	+	6.07629i	−0.0397542	+	0.244424i
$619$		−	34.7141i		−	1.39528i	−0.716449	−	0.697640i	$-0.754234\pi$
$619$		−	34.7141i		−	1.39528i	0.716449	−	0.697640i	$-0.245766\pi$
$620$	15.0476	−	8.68773i	0.604326	−	0.348908i
$621$	−16.7948	−	8.82267i	−0.673953	−	0.354041i
$622$			9.23930i			0.370462i
$623$		0			0
$624$	−3.83596	−	10.1184i	−0.153561	−	0.405061i
$625$	95.6821			3.82728
$626$	−5.83364	+	10.1042i	−0.233159	+	0.403844i
$627$	−8.46185	+	3.20794i	−0.337934	+	0.128113i
$628$	−11.3852	+	6.57327i	−0.454321	+	0.262302i
$629$	5.98098			0.238477
$630$		0			0
$631$	−12.8860			−0.512982			−0.256491	−	0.966547i	$-0.582566\pi$
$631$	−12.8860			−0.512982			−0.256491	+	0.966547i	$0.582566\pi$
$632$	−25.9945	+	15.0079i	−1.03401	+	0.596984i
$633$	−7.75467	+	47.6787i	−0.308220	+	1.89506i
$634$	−14.1732	+	24.5488i	−0.562891	+	0.974956i
$635$	80.2915			3.18627
$636$	−2.16711	+	2.65355i	−0.0859315	+	0.105220i
$637$		0			0
$638$			1.73325i			0.0686200i
$639$	5.76075	−	1.17456i	0.227892	−	0.0464649i
$640$	−13.6030	+	7.85371i	−0.537707	+	0.310445i
$641$			19.1295i			0.755569i	0.925893	+	0.377785i	$0.123314\pi$
$641$			19.1295i			0.755569i	−0.925893	+	0.377785i	$0.876686\pi$
$642$	18.7274	+	15.2943i	0.739111	+	0.603620i
$643$	9.77521	−	5.64372i	0.385497	−	0.222567i	−0.294710	−	0.955587i	$-0.595223\pi$
$643$	9.77521	−	5.64372i	0.385497	−	0.222567i	0.680207	+	0.733020i	$0.261890\pi$
$644$		0			0
$645$	29.8289	−	11.3083i	1.17451	−	0.445265i
$646$	−1.66726	−	2.88778i	−0.0655976	−	0.113618i
$647$	−2.54339	−	4.40528i	−0.0999909	−	0.173189i	0.811690	−	0.584089i	$-0.198548\pi$
$647$	−2.54339	−	4.40528i	−0.0999909	−	0.173189i	−0.911681	+	0.410900i	$0.865215\pi$
$648$	−10.8429	−	25.4847i	−0.425950	−	1.00113i
$649$	10.9276	+	6.30906i	0.428946	+	0.247652i
$650$	21.0939	−	36.5356i	0.827369	−	1.43305i
$651$		0			0
$652$	−3.82937	−	6.63267i	−0.149970	−	0.259755i
$653$		−	37.9947i		−	1.48685i	−0.668820	−	0.743424i	$-0.733200\pi$
$653$		−	37.9947i		−	1.48685i	0.668820	−	0.743424i	$-0.266800\pi$
$654$	5.18071	+	13.6656i	0.202582	+	0.534366i
$655$	−29.0437			−1.13483
$656$	8.85059	−	15.3297i	0.345557	−	0.598523i
$657$	−23.6805	−	26.7433i	−0.923865	−	1.04335i
$658$		0			0
$659$	9.97949	+	5.76166i	0.388746	+	0.224442i	0.681617	−	0.731710i	$-0.261277\pi$
$659$	9.97949	+	5.76166i	0.388746	+	0.224442i	−0.292871	+	0.956152i	$0.594611\pi$
$660$	3.51849	+	9.28100i	0.136957	+	0.361262i
$661$	38.0928	+	21.9929i	1.48164	+	0.855424i	0.999783	−	0.0208274i	$-0.00663005\pi$
$661$	38.0928	+	21.9929i	1.48164	+	0.855424i	0.481854	+	0.876251i	$0.339963\pi$
$662$	9.25838	+	5.34533i	0.359837	+	0.207752i
$663$	−1.87034	−	4.93355i	−0.0726381	−	0.191603i
$664$	4.24660	+	2.45178i	0.164800	+	0.0951473i
$665$		0			0
$666$	17.6870	−	3.60621i	0.685358	−	0.139738i
$667$	1.24211	−	2.15140i	0.0480947	−	0.0833025i
$668$	9.43240			0.364950
$669$	−4.71007	−	12.4241i	−0.182102	−	0.480345i
$670$			33.9601i			1.31199i
$671$	−7.75962	−	13.4401i	−0.299557	−	0.518848i
$672$		0			0
$673$	−21.9316	+	37.9866i	−0.845400	+	1.46428i	0.0398735	+	0.999205i	$0.487305\pi$
$673$	−21.9316	+	37.9866i	−0.845400	+	1.46428i	−0.885273	+	0.465071i	$0.846029\pi$
$674$	8.20387	+	4.73650i	0.316001	+	0.182443i
$675$	33.2666	−	63.3263i	1.28043	−	2.43743i
$676$	−1.90731	−	3.30355i	−0.0733579	−	0.127060i
$677$	0.738999	+	1.27998i	0.0284020	+	0.0491938i	0.879877	−	0.475201i	$-0.157625\pi$
$677$	0.738999	+	1.27998i	0.0284020	+	0.0491938i	−0.851475	+	0.524395i	$0.824291\pi$
$678$	−5.42257	+	2.05573i	−0.208252	+	0.0789499i
$679$		0			0
$680$	−13.5208	+	7.80621i	−0.518497	+	0.299355i
$681$	3.12409	+	2.55139i	0.119715	+	0.0977695i
$682$		−	16.6990i		−	0.639436i
$683$	−8.94252	+	5.16296i	−0.342176	+	0.197555i	−0.661234	−	0.750180i	$-0.729967\pi$
$683$	−8.94252	+	5.16296i	−0.342176	+	0.197555i	0.319058	+	0.947735i	$0.396634\pi$
$684$	2.94058	+	3.32091i	0.112436	+	0.126978i
$685$		−	59.1162i		−	2.25871i
$686$		0			0
$687$	−13.1130	+	16.0565i	−0.500294	+	0.612592i
$688$	−10.2120			−0.389330
$689$	−4.20442	+	7.28228i	−0.160176	+	0.277433i
$690$	−5.18147	+	31.8576i	−0.197255	+	1.21280i
$691$	−6.58166	+	3.79992i	−0.250378	+	0.144556i	−0.619937	−	0.784651i	$-0.712842\pi$
$691$	−6.58166	+	3.79992i	−0.250378	+	0.144556i	0.369559	+	0.929207i	$0.379509\pi$
$692$	5.27087			0.200368
$693$		0			0
$694$	41.6773			1.58205
$695$	33.5353	−	19.3616i	1.27207	−	0.734428i
$696$	3.39113	−	1.28560i	0.128540	−	0.0487305i
$697$	4.31538	−	7.47446i	0.163457	−	0.283115i
$698$	28.8240			1.09101
$699$	1.55204	+	4.09395i	0.0587036	+	0.154847i
$700$		0			0
$701$			6.35907i			0.240179i	0.992763	+	0.120089i	$0.0383181\pi$
$701$			6.35907i			0.240179i	−0.992763	+	0.120089i	$0.961682\pi$
$702$	−8.50567	−	13.4618i	−0.321026	−	0.508085i
$703$	−10.6879	+	6.17064i	−0.403100	+	0.232730i
$704$		−	18.8550i		−	0.710624i
$705$	8.60419	−	52.9018i	0.324052	−	1.99240i
$706$	0.991677	−	0.572545i	0.0373223	−	0.0215480i
$707$		0			0
$708$	0.992890	−	6.10466i	0.0373151	−	0.229427i
$709$	23.8048	+	41.2311i	0.894007	+	1.54847i	0.835029	+	0.550206i	$0.185451\pi$
$709$	23.8048	+	41.2311i	0.894007	+	1.54847i	0.0589776	+	0.998259i	$0.481216\pi$
$710$	−5.00129	−	8.66249i	−0.187695	−	0.325098i
$711$	−21.9079	+	19.3989i	−0.821610	+	0.727515i
$712$	16.2544	+	9.38448i	0.609159	+	0.351698i
$713$	−11.9671	+	20.7276i	−0.448171	+	0.776255i
$714$		0			0
$715$	12.1806	+	21.0975i	0.455530	+	0.789002i
$716$			11.7097i			0.437612i
$717$	−34.4644	−	5.60545i	−1.28710	−	0.209339i
$718$	18.7581			0.700045
$719$	7.07350	−	12.2517i	0.263797	−	0.456910i	−0.703451	−	0.710744i	$-0.748358\pi$
$719$	7.07350	−	12.2517i	0.263797	−	0.456910i	0.967248	+	0.253834i	$0.0816917\pi$
$720$	−23.3708	+	20.6942i	−0.870977	+	0.771228i
$721$		0			0
$722$	−13.4280	−	7.75264i	−0.499737	−	0.288524i
$723$	22.9302	−	28.0772i	0.852782	−	1.04420i
$724$	4.07904	+	2.35503i	0.151596	+	0.0875241i
$725$	8.11202	+	4.68348i	0.301273	+	0.173940i
$726$	−12.7412	−	2.07229i	−0.472871	−	0.0769098i
$727$	−40.1828	−	23.1996i	−1.49030	−	0.860424i	−0.490360	−	0.871520i	$-0.663135\pi$
$727$	−40.1828	−	23.1996i	−1.49030	−	0.860424i	−0.999938	+	0.0110955i	$0.996468\pi$
$728$		0			0
$729$	−15.3210	−	22.2321i	−0.567446	−	0.823411i
$730$	−30.3864	+	52.6307i	−1.12465	+	1.94795i
$731$	−4.97919			−0.184162
$732$	−4.81168	+	5.89173i	−0.177845	+	0.217765i
$733$		−	26.4303i		−	0.976225i	−0.872781	−	0.488112i	$-0.837686\pi$
$733$		−	26.4303i		−	0.976225i	0.872781	−	0.488112i	$-0.162314\pi$
$734$	14.5559	+	25.2115i	0.537268	+	0.930575i
$735$		0			0
$736$	−6.06899	+	10.5118i	−0.223706	+	0.387470i
$737$	−12.4581	−	7.19271i	−0.458902	−	0.264947i
$738$	8.25480	−	24.7055i	0.303863	−	0.909423i
$739$	23.1335	+	40.0684i	0.850979	+	1.47394i	0.880326	+	0.474370i	$0.157324\pi$
$739$	23.1335	+	40.0684i	0.850979	+	1.47394i	−0.0293467	+	0.999569i	$0.509343\pi$
$740$	6.76798	+	11.7225i	0.248796	+	0.430927i
$741$	8.43225	+	6.88648i	0.309766	+	0.252981i
$742$		0			0
$743$	−36.5640	+	21.1102i	−1.34140	+	0.774458i	−0.987013	−	0.160640i	$-0.948644\pi$
$743$	−36.5640	+	21.1102i	−1.34140	+	0.774458i	−0.354388	+	0.935098i	$0.615311\pi$
$744$	−32.6718	+	12.3861i	−1.19781	+	0.454096i
$745$		−	16.4574i		−	0.602951i
$746$	−9.62825	+	5.55887i	−0.352515	+	0.203525i
$747$	4.53402	+	1.51494i	0.165891	+	0.0554288i
$748$		−	1.54923i		−	0.0566456i
$749$		0			0
$750$	−76.4932	−	12.4412i	−2.79314	−	0.454288i
$751$	−16.0464			−0.585542			−0.292771	−	0.956183i	$-0.594577\pi$
$751$	−16.0464			−0.585542			−0.292771	+	0.956183i	$0.594577\pi$
$752$	−8.57877	+	14.8589i	−0.312836	+	0.541847i
$753$	34.3089	+	28.0195i	1.25029	+	1.02109i
$754$	1.80582	−	1.04259i	0.0657639	−	0.0379688i
$755$	−16.5555			−0.602516
$756$		0			0
$757$	25.0149			0.909183			0.454591	−	0.890700i	$-0.349785\pi$
$757$	25.0149			0.909183			0.454591	+	0.890700i	$0.349785\pi$
$758$	21.2265	−	12.2551i	0.770981	−	0.445126i
$759$	−10.5894	−	8.64822i	−0.384372	−	0.313911i
$760$	16.1075	−	27.8990i	0.584281	−	1.01200i
$761$	6.00729			0.217764			0.108882	−	0.994055i	$-0.465273\pi$
$761$	6.00729			0.217764			0.108882	+	0.994055i	$0.465273\pi$
$762$	−37.3327	−	6.07196i	−1.35242	−	0.219964i
$763$		0			0
$764$		−	11.3889i		−	0.412035i
$765$	−11.3951	+	10.0901i	−0.411992	+	0.364809i
$766$	6.59165	−	3.80569i	0.238166	−	0.137505i
$767$		−	15.1802i		−	0.548124i
$768$	−21.3295	+	8.08615i	−0.769661	+	0.291784i
$769$	−28.9946	+	16.7400i	−1.04557	+	0.603661i	−0.921406	−	0.388600i	$-0.872959\pi$
$769$	−28.9946	+	16.7400i	−1.04557	+	0.603661i	−0.124166	+	0.992262i	$0.539625\pi$
$770$		0			0
$771$	15.9298	+	13.0096i	0.573699	+	0.468531i
$772$	−5.54159	−	9.59831i	−0.199446	−	0.345451i
$773$	18.1008	+	31.3515i	0.651040	+	1.12763i	0.982871	+	0.184296i	$0.0590004\pi$
$773$	18.1008	+	31.3515i	0.651040	+	1.12763i	−0.331831	+	0.943339i	$0.607666\pi$
$774$	−14.7245	+	3.00219i	−0.529263	+	0.107912i
$775$	−78.1551	−	45.1229i	−2.80741	−	1.62086i
$776$	4.19980	−	7.27427i	0.150764	−	0.261131i
$777$		0			0
$778$	0.0303280	+	0.0525296i	0.00108731	+	0.00188328i
$779$			17.8089i			0.638070i
$780$	7.55312	−	9.24853i	0.270445	−	0.331150i
$781$	4.23708			0.151615
$782$	2.51893	−	4.36291i	0.0900766	−	0.156017i
$783$	2.98894	−	1.88852i	0.106816	−	0.0674901i
$784$		0			0
$785$	80.6108	+	46.5407i	2.87712	+	1.66111i
$786$	13.5043	+	2.19640i	0.481682	+	0.0783428i
$787$	14.1930	+	8.19433i	0.505926	+	0.292096i	0.731157	−	0.682209i	$-0.238981\pi$
$787$	14.1930	+	8.19433i	0.505926	+	0.292096i	−0.225232	+	0.974305i	$0.572314\pi$
$788$	−8.79294	−	5.07661i	−0.313236	−	0.180847i
$789$	−24.5053	+	30.0059i	−0.872413	+	1.06824i
$790$	43.1147	+	24.8923i	1.53395	+	0.885628i
$791$		0			0
$792$	−3.98753	−	19.5572i	−0.141691	−	0.694935i
$793$	−9.33517	+	16.1690i	−0.331502	+	0.574178i
$794$	−14.9786			−0.531570
$795$	23.9427	+	3.89414i	0.849159	+	0.138111i
$796$		−	1.66352i		−	0.0589619i
$797$	23.3328	+	40.4137i	0.826492	+	1.43153i	0.900774	+	0.434288i	$0.143000\pi$
$797$	23.3328	+	40.4137i	0.826492	+	1.43153i	−0.0742821	+	0.997237i	$0.523667\pi$
$798$		0			0
$799$	−4.18285	+	7.24491i	−0.147979	+	0.256306i
$800$	−39.6356	−	22.8836i	−1.40133	−	0.809057i
$801$	17.3545	+	5.79863i	0.613192	+	0.204884i
$802$	−1.49464	−	2.58880i	−0.0527777	−	0.0914137i
$803$	−12.8716	−	22.2943i	−0.454229	−	0.786748i
$804$	−1.13195	+	6.95968i	−0.0399209	+	0.245449i
$805$		0			0
$806$	−17.3981	+	10.0448i	−0.612822	+	0.353813i
$807$	−1.17525	+	7.22590i	−0.0413709	+	0.254364i
$808$		−	49.2271i		−	1.73180i
$809$	−25.8925	+	14.9490i	−0.910330	+	0.525580i	−0.880537	−	0.473977i	$-0.842818\pi$
$809$	−25.8925	+	14.9490i	−0.910330	+	0.525580i	−0.0297930	+	0.999556i	$0.509485\pi$
$810$	−27.6141	+	36.7093i	−0.970259	+	1.28983i
$811$		−	25.3404i		−	0.889821i	−0.895575	−	0.444911i	$-0.853235\pi$
$811$		−	25.3404i		−	0.889821i	0.895575	−	0.444911i	$-0.146765\pi$
$812$		0			0
$813$	−13.7499	−	36.2693i	−0.482230	−	1.27202i
$814$	13.0089			0.455963
$815$	−27.1131	+	46.9612i	−0.949729	+	1.64498i
$816$	4.55596	−	1.72720i	0.159491	−	0.0604640i
$817$	8.89769	−	5.13709i	0.311291	−	0.179724i
$818$	0.0674323			0.00235772
$819$		0			0
$820$	19.5329			0.682117
$821$	−9.23012	+	5.32901i	−0.322133	+	0.185984i	−0.652343	−	0.757924i	$-0.726214\pi$
$821$	−9.23012	+	5.32901i	−0.322133	+	0.185984i	0.330210	+	0.943908i	$0.392881\pi$
$822$	−4.47060	+	27.4869i	−0.155930	+	0.958716i
$823$	−8.55239	+	14.8132i	−0.298118	+	0.516355i	−0.975705	−	0.219087i	$-0.929692\pi$
$823$	−8.55239	+	14.8132i	−0.298118	+	0.516355i	0.677588	+	0.735442i	$0.263025\pi$
$824$	9.28313			0.323393
$825$	32.6088	−	39.9283i	1.13529	−	1.39013i
$826$		0			0
$827$		−	18.3221i		−	0.637121i	−0.947903	−	0.318560i	$-0.896801\pi$
$827$		−	18.3221i		−	0.637121i	0.947903	−	0.318560i	$-0.103199\pi$
$828$	−2.12375	+	6.35611i	−0.0738055	+	0.220890i
$829$	6.69733	−	3.86670i	0.232608	−	0.134296i	−0.379167	−	0.925328i	$-0.623789\pi$
$829$	6.69733	−	3.86670i	0.232608	−	0.134296i	0.611775	+	0.791032i	$0.290456\pi$
$830$		−	8.13306i		−	0.282303i
$831$	−15.2726	−	12.4729i	−0.529802	−	0.432681i
$832$	−19.6444	+	11.3417i	−0.681047	+	0.393203i
$833$		0			0
$834$	−17.0569	+	6.46639i	−0.590633	+	0.223913i
$835$	−33.3920	−	57.8367i	−1.15558	−	2.00152i
$836$	1.59836	+	2.76844i	0.0552805	+	0.0957486i
$837$	−28.7969	+	18.1949i	−0.995366	+	0.628907i
$838$	6.28551	+	3.62894i	0.217129	+	0.125360i
$839$	9.73588	−	16.8630i	0.336120	−	0.582177i	−0.647579	−	0.761998i	$-0.724219\pi$
$839$	9.73588	−	16.8630i	0.336120	−	0.582177i	0.983699	+	0.179821i	$0.0575519\pi$
$840$		0			0
$841$	−14.2685	−	24.7138i	−0.492018	−	0.852200i
$842$		−	35.5092i		−	1.22373i
$843$	0.498197	+	1.31413i	0.0171588	+	0.0452612i
$844$	17.0637			0.587356
$845$	−13.5043	+	23.3901i	−0.464561	+	0.804643i
$846$	−8.00128	+	23.9468i	−0.275090	+	0.823307i
$847$		0			0
$848$	−6.72493	−	3.88264i	−0.230935	−	0.133330i
$849$	11.2543	+	29.6863i	0.386246	+	1.01883i
$850$	16.4507	+	9.49781i	0.564254	+	0.325772i
$851$	−16.1474	−	9.32269i	−0.553525	−	0.319578i
$852$	−0.736214	−	1.94197i	−0.0252223	−	0.0665308i
$853$	0.812274	+	0.468967i	0.0278117	+	0.0160571i	0.513841	−	0.857885i	$-0.328222\pi$
$853$	0.812274	+	0.468967i	0.0278117	+	0.0160571i	−0.486030	+	0.873942i	$0.661555\pi$
$854$		0			0
$855$	9.95275	−	29.7873i	0.340377	−	1.01870i
$856$	18.2305	−	31.5761i	0.623104	−	1.07925i
$857$	−18.0017			−0.614927			−0.307464	−	0.951560i	$-0.599480\pi$
$857$	−18.0017			−0.614927			−0.307464	+	0.951560i	$0.599480\pi$
$858$	−4.06809	−	10.7307i	−0.138882	−	0.366341i
$859$			26.6921i			0.910723i	0.890307	+	0.455361i	$0.150490\pi$
$859$			26.6921i			0.910723i	−0.890307	+	0.455361i	$0.849510\pi$
$860$	−5.63438	−	9.75903i	−0.192131	−	0.332780i
$861$		0			0
$862$	−4.75486	+	8.23566i	−0.161951	+	0.280508i
$863$	24.0405	+	13.8798i	0.818348	+	0.472473i	0.849846	−	0.527031i	$-0.176695\pi$
$863$	24.0405	+	13.8798i	0.818348	+	0.472473i	−0.0314987	+	0.999504i	$0.510028\pi$
$864$	−14.6040	+	9.22735i	−0.496840	+	0.313921i
$865$	−18.6596	−	32.3194i	−0.634446	−	1.09889i
$866$	16.7857	+	29.0737i	0.570402	+	0.987966i
$867$	−25.3113	+	9.59569i	−0.859618	+	0.325887i
$868$		0			0
$869$	−18.2633	+	10.5443i	−0.619540	+	0.357692i
$870$	−4.65891	−	3.80485i	−0.157952	−	0.128997i
$871$			17.3063i			0.586402i
$872$	19.0856	−	11.0191i	0.646319	−	0.373152i
$873$	2.59504	−	7.76661i	0.0878288	−	0.262860i
$874$			10.3952i			0.351623i
$875$		0			0
$876$	−7.98158	+	9.77316i	−0.269673	+	0.330205i
$877$	13.8196			0.466654			0.233327	−	0.972398i	$-0.425039\pi$
$877$	13.8196			0.466654			0.233327	+	0.972398i	$0.425039\pi$
$878$	−1.20447	+	2.08621i	−0.0406490	+	0.0704061i
$879$	3.46812	−	21.3233i	0.116977	−	0.719217i
$880$	−19.4828	+	11.2484i	−0.656765	+	0.379184i
$881$	−43.9006			−1.47905			−0.739525	−	0.673129i	$-0.764950\pi$
$881$	−43.9006			−1.47905			−0.739525	+	0.673129i	$0.764950\pi$
$882$		0			0
$883$	7.96743			0.268125			0.134063	−	0.990973i	$-0.457198\pi$
$883$	7.96743			0.268125			0.134063	+	0.990973i	$0.457198\pi$
$884$	−1.61410	+	0.931899i	−0.0542880	+	0.0313432i
$885$	−40.9470	+	15.5233i	−1.37642	+	0.521809i
$886$	14.3750	−	24.8982i	0.482937	−	0.836472i
$887$	−21.2160			−0.712362			−0.356181	−	0.934417i	$-0.615921\pi$
$887$	−21.2160			−0.712362			−0.356181	+	0.934417i	$0.615921\pi$
$888$	−9.64910	−	25.4522i	−0.323803	−	0.854120i
$889$		0			0
$890$		−	31.1303i		−	1.04349i
$891$	−7.61805	−	17.9051i	−0.255214	−	0.599844i
$892$	−4.06477	+	2.34680i	−0.136099	+	0.0785766i
$893$		−	17.2620i		−	0.577649i
$894$	−1.24457	+	7.65209i	−0.0416247	+	0.255924i
$895$	71.8005	−	41.4541i	2.40003	−	1.38566i
$896$		0			0
$897$	−2.64052	+	16.2349i	−0.0881643	+	0.542067i
$898$	−0.172924	−	0.299513i	−0.00577054	−	0.00999487i
$899$	−2.23025	−	3.86291i	−0.0743830	−	0.128835i
$900$	−23.9662	−	8.00778i	−0.798874	−	0.266926i
$901$	−3.27895	−	1.89310i	−0.109238	−	0.0630684i
$902$	9.38618	−	16.2573i	0.312526	−	0.541310i
$903$		0			0
$904$	4.37242	+	7.57325i	0.145424	+	0.251883i
$905$		−	33.3486i		−	1.10855i
$906$	7.69772	+	1.25199i	0.255739	+	0.0415946i
$907$	3.76688			0.125077			0.0625385	−	0.998043i	$-0.480080\pi$
$907$	3.76688			0.125077			0.0625385	+	0.998043i	$0.480080\pi$
$908$	0.712420	−	1.23395i	0.0236425	−	0.0409500i
$909$	−9.58763	−	47.0235i	−0.318002	−	1.55967i
$910$		0			0
$911$	40.0013	+	23.0947i	1.32530	+	0.765163i	0.984569	−	0.174998i	$-0.0559917\pi$
$911$	40.0013	+	23.0947i	1.32530	+	0.765163i	0.340732	+	0.940160i	$0.389325\pi$
$912$	−6.35943	+	7.78689i	−0.210582	+	0.257850i
$913$	2.98359	+	1.72258i	0.0987423	+	0.0570089i
$914$	−16.8862	−	9.74926i	−0.558546	−	0.322477i
$915$	53.1604	+	8.64625i	1.75743	+	0.285836i
$916$	6.34196	+	3.66153i	0.209544	+	0.120980i
$917$		0			0
$918$	6.06139	−	3.82980i	0.200056	−	0.126402i
$919$	−0.607610	+	1.05241i	−0.0200432	+	0.0347158i	−0.875873	−	0.482542i	$-0.839714\pi$
$919$	−0.607610	+	1.05241i	−0.0200432	+	0.0347158i	0.855830	+	0.517257i	$0.173047\pi$
$920$	48.6709			1.60463
$921$	23.3625	−	28.6066i	0.769822	−	0.942620i
$922$		−	23.6960i		−	0.780385i
$923$	−2.54870	−	4.41447i	−0.0838914	−	0.145304i
$924$		0			0
$925$	35.1520	−	60.8850i	1.15579	−	2.00189i
$926$	19.0725	+	11.0115i	0.626760	+	0.361860i
$927$	8.86757	−	1.80801i	0.291249	−	0.0593829i
$928$	−1.13105	−	1.95903i	−0.0371285	−	0.0643084i
$929$	−9.44516	−	16.3595i	−0.309886	−	0.536737i	0.668452	−	0.743756i	$-0.266957\pi$
$929$	−9.44516	−	16.3595i	−0.309886	−	0.536737i	−0.978337	+	0.207018i	$0.933624\pi$
$930$	44.8862	+	36.6578i	1.47188	+	1.20206i
$931$		0			0
$932$	1.33941	−	0.773306i	0.0438737	−	0.0253305i
$933$	12.7005	−	4.81484i	0.415795	−	0.157631i
$934$			34.5926i			1.13190i
$935$	−9.49945	+	5.48451i	−0.310665	+	0.179363i
$936$	−17.9774	+	15.9186i	−0.587611	+	0.520315i
$937$			27.0448i			0.883516i	0.897134	+	0.441758i	$0.145645\pi$
$937$			27.0448i			0.883516i	−0.897134	+	0.441758i	$0.854355\pi$
$938$		0			0
$939$	16.9294	+	2.75347i	0.552470	+	0.0898562i
$940$	−18.9330			−0.617526
$941$	−8.16024	+	14.1339i	−0.266016	+	0.460754i	−0.967829	−	0.251607i	$-0.919041\pi$
$941$	−8.16024	+	14.1339i	−0.266016	+	0.460754i	0.701813	+	0.712361i	$0.252374\pi$
$942$	−33.9616	−	27.7359i	−1.10653	−	0.903683i
$943$	−23.3012	+	13.4530i	−0.758793	+	0.438089i
$944$	14.0184			0.456259
$945$		0			0
$946$	−10.8300			−0.352114
$947$	24.8567	−	14.3510i	0.807734	−	0.466345i	−0.0384343	−	0.999261i	$-0.512237\pi$
$947$	24.8567	−	14.3510i	0.807734	−	0.466345i	0.846168	+	0.532916i	$0.178904\pi$
$948$	8.00610	+	6.53845i	0.260026	+	0.212359i
$949$	−15.4851	+	26.8210i	−0.502668	+	0.870647i
$950$	−39.1960			−1.27168
$951$	41.1311	+	6.68975i	1.33377	+	0.216930i
$952$		0			0
$953$		−	34.5757i		−	1.12002i	−0.828486	−	0.560009i	$-0.810798\pi$
$953$		−	34.5757i		−	1.12002i	0.828486	−	0.560009i	$-0.189202\pi$
$954$	−10.8380	−	3.62127i	−0.350893	−	0.117243i
$955$	−69.8333	+	40.3183i	−2.25975	+	1.30467i
$956$			12.3345i			0.398925i
$957$	2.38255	−	0.903240i	0.0770169	−	0.0291976i
$958$	−22.3785	+	12.9202i	−0.723015	+	0.417433i
$959$		0			0
$960$	50.6815	+	41.3907i	1.63574	+	1.33588i
$961$	5.98731	+	10.3703i	0.193139	+	0.334527i
$962$	−7.82517	−	13.5536i	−0.252294	−	0.436985i
$963$	11.2645	−	33.7132i	0.362994	−	1.08639i
$964$	−11.0899	−	6.40275i	−0.357181	−	0.206219i
$965$	−39.2360	+	67.9588i	−1.26305	+	2.18767i
$966$		0			0
$967$	−5.25000	−	9.09327i	−0.168829	−	0.292420i	0.769180	−	0.639033i	$-0.220665\pi$
$967$	−5.25000	−	9.09327i	−0.168829	−	0.292420i	−0.938008	+	0.346613i	$0.887332\pi$
$968$			19.4655i			0.625646i
$969$	−3.10074	+	3.79674i	−0.0996100	+	0.121969i
$970$	−13.9317			−0.447318
$971$	11.4156	−	19.7724i	0.366345	−	0.634527i	−0.622646	−	0.782503i	$-0.713942\pi$
$971$	11.4156	−	19.7724i	0.366345	−	0.634527i	0.988991	+	0.147976i	$0.0472758\pi$
$972$	−6.88274	+	6.60267i	−0.220764	+	0.211781i
$973$		0			0
$974$	−1.09973	−	0.634927i	−0.0352375	−	0.0203444i
$975$	−61.2150	−	9.95628i	−1.96045	−	0.318856i
$976$	−14.9315	−	8.62071i	−0.477946	−	0.275942i
$977$	8.88551	+	5.13005i	0.284273	+	0.164125i	0.635356	−	0.772219i	$-0.280853\pi$
$977$	8.88551	+	5.13005i	0.284273	+	0.164125i	−0.351083	+	0.936344i	$0.614187\pi$
$978$	16.1580	−	19.7849i	0.516676	−	0.632651i
$979$	11.4201	+	6.59337i	0.364987	+	0.210725i
$980$		0			0
$981$	16.0851	−	14.2430i	0.513558	−	0.454743i
$982$	11.1360	−	19.2881i	0.355363	−	0.615508i
$983$	33.9198			1.08187			0.540937	−	0.841063i	$-0.318070\pi$
$983$	33.9198			1.08187			0.540937	+	0.841063i	$0.318070\pi$
$984$	−38.7698	−	6.30569i	−1.23593	−	0.201018i
$985$			71.8877i			2.29053i
$986$	0.469440	+	0.813095i	0.0149500	+	0.0258942i
$987$		0			0
$988$	1.92290	−	3.33056i	0.0611756	−	0.105959i
$989$	13.4428	+	7.76119i	0.427455	+	0.246791i
$990$	−24.7850	+	21.9465i	−0.787720	+	0.697507i
$991$	−11.4278	−	19.7935i	−0.363015	−	0.628761i	0.625440	−	0.780272i	$-0.284919\pi$
$991$	−11.4278	−	19.7935i	−0.363015	−	0.628761i	−0.988456	+	0.151511i	$0.951586\pi$
$992$	10.8971	+	18.8743i	0.345982	+	0.599259i
$993$	2.52299	−	15.5123i	0.0800647	−	0.492268i
$994$		0			0
$995$	−10.2002	+	5.88910i	−0.323369	+	0.186697i
$996$	0.271091	−	1.66677i	0.00858983	−	0.0528136i
$997$			6.53407i			0.206936i	0.994633	+	0.103468i	$0.0329940\pi$
$997$			6.53407i			0.206936i	−0.994633	+	0.103468i	$0.967006\pi$
$998$	−17.0254	+	9.82961i	−0.538929	+	0.311151i
$999$	−14.1743	−	22.4336i	−0.448456	−	0.709766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.s.d.362.17		48
3.2	odd	2		1323.2.s.d.656.7		48
7.2	even	3		441.2.o.e.146.8	yes	48
7.3	odd	6		441.2.i.d.227.18		48
7.4	even	3		441.2.i.d.227.17		48
7.5	odd	6		441.2.o.e.146.7	✓	48
7.6	odd	2	inner	441.2.s.d.362.18		48
9.4	even	3		1323.2.i.d.1097.20		48
9.5	odd	6		441.2.i.d.68.8		48
21.2	odd	6		1323.2.o.e.440.18		48
21.5	even	6		1323.2.o.e.440.17		48
21.11	odd	6		1323.2.i.d.521.1		48
21.17	even	6		1323.2.i.d.521.20		48
21.20	even	2		1323.2.s.d.656.8		48
63.4	even	3		1323.2.s.d.962.8		48
63.5	even	6		441.2.o.e.293.8	yes	48
63.13	odd	6		1323.2.i.d.1097.1		48
63.23	odd	6		441.2.o.e.293.7	yes	48
63.31	odd	6		1323.2.s.d.962.7		48
63.32	odd	6	inner	441.2.s.d.374.18		48
63.40	odd	6		1323.2.o.e.881.18		48
63.41	even	6		441.2.i.d.68.7		48
63.58	even	3		1323.2.o.e.881.17		48
63.59	even	6	inner	441.2.s.d.374.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.7		48	63.41	even	6
441.2.i.d.68.8		48	9.5	odd	6
441.2.i.d.227.17		48	7.4	even	3
441.2.i.d.227.18		48	7.3	odd	6
441.2.o.e.146.7	✓	48	7.5	odd	6
441.2.o.e.146.8	yes	48	7.2	even	3
441.2.o.e.293.7	yes	48	63.23	odd	6
441.2.o.e.293.8	yes	48	63.5	even	6
441.2.s.d.362.17		48	1.1	even	1	trivial
441.2.s.d.362.18		48	7.6	odd	2	inner
441.2.s.d.374.17		48	63.59	even	6	inner
441.2.s.d.374.18		48	63.32	odd	6	inner
1323.2.i.d.521.1		48	21.11	odd	6
1323.2.i.d.521.20		48	21.17	even	6
1323.2.i.d.1097.1		48	63.13	odd	6
1323.2.i.d.1097.20		48	9.4	even	3
1323.2.o.e.440.17		48	21.5	even	6
1323.2.o.e.440.18		48	21.2	odd	6
1323.2.o.e.881.17		48	63.58	even	3
1323.2.o.e.881.18		48	63.40	odd	6
1323.2.s.d.656.7		48	3.2	odd	2
1323.2.s.d.656.8		48	21.20	even	2
1323.2.s.d.962.7		48	63.31	odd	6
1323.2.s.d.962.8		48	63.4	even	3

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02035 - 0.589100i) q^{2} +(-1.34152 - 1.09560i) q^{3} +(-0.305921 + 0.529871i) q^{4} +4.33202 q^{5} +(-2.01424 - 0.327604i) q^{6} +3.07728i q^{8} +(0.599340 + 2.93952i) q^{9} +O(q^{10})\)	\(q+(1.02035 - 0.589100i) q^{2} +(-1.34152 - 1.09560i) q^{3} +(-0.305921 + 0.529871i) q^{4} +4.33202 q^{5} +(-2.01424 - 0.327604i) q^{6} +3.07728i q^{8} +(0.599340 + 2.93952i) q^{9} +(4.42019 - 2.55200i) q^{10} +2.16204i q^{11} +(0.990924 - 0.375666i) q^{12} +(2.25256 - 1.30052i) q^{13} +(-5.81148 - 4.74614i) q^{15} +(1.20098 + 2.08016i) q^{16} +(0.585576 + 1.01425i) q^{17} +(2.34321 + 2.64628i) q^{18} +(-2.09282 - 1.20829i) q^{19} +(-1.32526 + 2.29541i) q^{20} +(1.27366 + 2.20604i) q^{22} -3.65101i q^{23} +(3.37145 - 4.12822i) q^{24} +13.7664 q^{25} +(1.53227 - 2.65397i) q^{26} +(2.41650 - 4.60006i) q^{27} +(0.589262 + 0.340210i) q^{29} +(-8.72571 - 1.41919i) q^{30} +(-5.67723 - 3.27775i) q^{31} +(-2.87915 - 1.66228i) q^{32} +(2.36872 - 2.90042i) q^{33} +(1.19499 + 0.689926i) q^{34} +(-1.74092 - 0.581689i) q^{36} +(2.55346 - 4.42272i) q^{37} -2.84722 q^{38} +(-4.44669 - 0.723230i) q^{39} +13.3308i q^{40} +(-3.68473 - 6.38214i) q^{41} +(-2.12577 + 3.68194i) q^{43} +(-1.14560 - 0.661414i) q^{44} +(2.59635 + 12.7341i) q^{45} +(-2.15081 - 3.72531i) q^{46} +(3.57157 + 6.18614i) q^{47} +(0.667877 - 4.10636i) q^{48} +(14.0466 - 8.10980i) q^{50} +(0.325645 - 2.00219i) q^{51} +1.59142i q^{52} +(-2.79976 + 1.61644i) q^{53} +(-0.244212 - 6.11724i) q^{54} +9.36601i q^{55} +(1.48376 + 3.91383i) q^{57} +0.801672 q^{58} +(2.91810 - 5.05430i) q^{59} +(4.29270 - 1.62739i) q^{60} +(-6.21638 + 3.58903i) q^{61} -7.72370 q^{62} -8.72092 q^{64} +(9.75814 - 5.63387i) q^{65} +(0.708294 - 4.35486i) q^{66} +(-3.32682 + 5.76221i) q^{67} -0.716561 q^{68} +(-4.00003 + 4.89789i) q^{69} -1.95976i q^{71} +(-9.04572 + 1.84433i) q^{72} +(-10.3117 + 5.95345i) q^{73} -6.01697i q^{74} +(-18.4679 - 15.0824i) q^{75} +(1.28048 - 0.739283i) q^{76} +(-4.96324 + 1.88160i) q^{78} +(4.87702 + 8.44725i) q^{79} +(5.20268 + 9.01130i) q^{80} +(-8.28158 + 3.52355i) q^{81} +(-7.51944 - 4.34135i) q^{82} +(0.796736 - 1.37999i) q^{83} +(2.53673 + 4.39374i) q^{85} +5.00916i q^{86} +(-0.417772 - 1.10199i) q^{87} -6.65320 q^{88} +(3.04961 - 5.28207i) q^{89} +(10.1508 + 11.4637i) q^{90} +(1.93456 + 1.11692i) q^{92} +(4.02502 + 10.6171i) q^{93} +(7.28851 + 4.20802i) q^{94} +(-9.06614 - 5.23434i) q^{95} +(2.04125 + 5.38436i) q^{96} +(-2.36387 - 1.36478i) q^{97} +(-6.35537 + 1.29580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 - 8 * q^9	\( 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more