LMFDB - Embedded newform 841.2.e.k.236.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			236.4
Character	$\chi$	$=$	841.236
Dual form			841.2.e.k.196.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.35368 + 0.537213i) q^{2} +(-1.04749 - 2.17513i) q^{3} +(3.44929 + 1.66109i) q^{4} +(-0.222521 + 0.974928i) q^{5} +(-1.29695 - 5.68230i) q^{6} +(2.54832 - 1.22721i) q^{7} +(3.45117 + 2.75222i) q^{8} +(-1.76350 + 2.21135i) q^{9} +O(q^{10})$	\(q+(2.35368 + 0.537213i) q^{2} +(-1.04749 - 2.17513i) q^{3} +(3.44929 + 1.66109i) q^{4} +(-0.222521 + 0.974928i) q^{5} +(-1.29695 - 5.68230i) q^{6} +(2.54832 - 1.22721i) q^{7} +(3.45117 + 2.75222i) q^{8} +(-1.76350 + 2.21135i) q^{9} +(-1.04749 + 2.17513i) q^{10} +(0.323845 - 0.258258i) q^{11} -9.24264i q^{12} +(2.38699 + 2.99318i) q^{13} +(6.65722 - 1.51947i) q^{14} +(2.35368 - 0.537213i) q^{15} +(1.87047 + 2.34549i) q^{16} +0.828427i q^{17} +(-5.33868 + 4.25745i) q^{18} +(2.60330 - 5.40581i) q^{19} +(-2.38699 + 2.99318i) q^{20} +(-5.33868 - 4.25745i) q^{21} +(0.900969 - 0.433884i) q^{22} +(-0.813727 - 3.56517i) q^{23} +(2.37137 - 10.3897i) q^{24} +(3.60388 + 1.73553i) q^{25} +(4.01023 + 8.32733i) q^{26} +(-0.403828 - 0.0921712i) q^{27} +10.8284 q^{28} +5.82843 q^{30} +(-9.81857 - 2.24102i) q^{31} +(-0.688047 - 1.42874i) q^{32} +(-0.900969 - 0.433884i) q^{33} +(-0.445042 + 1.94986i) q^{34} +(0.629384 + 2.75751i) q^{35} +(-9.75608 + 4.69828i) q^{36} +(3.12733 + 2.49396i) q^{37} +(9.03143 - 11.3250i) q^{38} +(4.01023 - 8.32733i) q^{39} +(-3.45117 + 2.75222i) q^{40} +4.48528i q^{41} +(-10.2784 - 12.8887i) q^{42} +(3.49588 - 0.797913i) q^{43} +(1.54603 - 0.352871i) q^{44} +(-1.76350 - 2.21135i) q^{45} -8.82843i q^{46} +(-2.53520 + 2.02175i) q^{47} +(3.14246 - 6.52539i) q^{48} +(0.623490 - 0.781831i) q^{49} +(7.55003 + 6.02095i) q^{50} +(1.80194 - 0.867767i) q^{51} +(3.26146 + 14.2894i) q^{52} +(-2.11067 + 9.24747i) q^{53} +(-0.900969 - 0.433884i) q^{54} +(0.179721 + 0.373194i) q^{55} +(12.1722 + 2.77824i) q^{56} -14.4853 q^{57} -3.65685 q^{59} +(9.01091 + 2.05668i) q^{60} +(2.09498 + 4.35026i) q^{61} +(-21.9059 - 10.5493i) q^{62} +(-1.78017 + 7.79942i) q^{63} +(-2.18703 - 9.58201i) q^{64} +(-3.44929 + 1.66109i) q^{65} +(-1.88751 - 1.50524i) q^{66} +(-3.52699 + 4.42271i) q^{67} +(-1.37609 + 2.85749i) q^{68} +(-6.90234 + 5.50443i) q^{69} +6.82843i q^{70} +(5.50443 + 6.90234i) q^{71} +(-12.1722 + 2.77824i) q^{72} +(-3.89971 + 0.890084i) q^{73} +(6.02095 + 7.55003i) q^{74} -9.65685i q^{75} +(17.9591 - 14.3219i) q^{76} +(0.508326 - 1.05555i) q^{77} +(13.9124 - 17.4456i) q^{78} +(-1.88751 - 1.50524i) q^{79} +(-2.70291 + 1.30165i) q^{80} +(2.11067 + 9.24747i) q^{81} +(-2.40955 + 10.5569i) q^{82} +(-6.89859 - 3.32218i) q^{83} +(-11.3426 - 23.5533i) q^{84} +(-0.807657 - 0.184342i) q^{85} +8.65685 q^{86} +1.82843 q^{88} +(12.1722 + 2.77824i) q^{89} +(-2.96274 - 6.15220i) q^{90} +(9.75608 + 4.69828i) q^{91} +(3.11529 - 13.6490i) q^{92} +(5.41031 + 23.7041i) q^{93} +(-7.05317 + 3.39663i) q^{94} +(4.69099 + 3.74094i) q^{95} +(-2.38699 + 2.99318i) q^{96} +(-1.94609 + 4.04110i) q^{97} +(1.88751 - 1.50524i) q^{98} +1.17157i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6}+O(q^{10}) $ 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6	$ 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6} - 4 q^{13} - 12 q^{16} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{24} + 16 q^{25} + 192 q^{28} + 72 q^{30} - 4 q^{33} - 8 q^{34} - 32 q^{36} - 24 q^{38} + 32 q^{42} - 4 q^{49} + 8 q^{51} + 36 q^{52} - 4 q^{53} - 4 q^{54} - 144 q^{57} + 48 q^{59} - 52 q^{62} - 32 q^{63} - 28 q^{64} - 4 q^{65} - 24 q^{71} - 16 q^{74} - 44 q^{78} - 12 q^{80} + 4 q^{81} - 32 q^{82} - 8 q^{83} + 72 q^{86} - 24 q^{88} + 32 q^{91} + 56 q^{92} + 52 q^{93} - 20 q^{94} + 4 q^{96}+O(q^{100}) $ 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6 - 4 * q^13 - 12 * q^16 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 20 * q^24 + 16 * q^25 + 192 * q^28 + 72 * q^30 - 4 * q^33 - 8 * q^34 - 32 * q^36 - 24 * q^38 + 32 * q^42 - 4 * q^49 + 8 * q^51 + 36 * q^52 - 4 * q^53 - 4 * q^54 - 144 * q^57 + 48 * q^59 - 52 * q^62 - 32 * q^63 - 28 * q^64 - 4 * q^65 - 24 * q^71 - 16 * q^74 - 44 * q^78 - 12 * q^80 + 4 * q^81 - 32 * q^82 - 8 * q^83 + 72 * q^86 - 24 * q^88 + 32 * q^91 + 56 * q^92 + 52 * q^93 - 20 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

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 $

$2$	2.35368	+	0.537213i	1.66431	+	0.379867i	0.948088	−	0.318009i	$-0.103014\pi$
$2$	2.35368	+	0.537213i	1.66431	+	0.379867i	0.716218	+	0.697876i	$0.245871\pi$
$3$	−1.04749	−	2.17513i	−0.604767	−	1.25581i	−0.948510	−	0.316749i	$-0.897409\pi$
$3$	−1.04749	−	2.17513i	−0.604767	−	1.25581i	0.343742	−	0.939064i	$-0.388305\pi$
$4$	3.44929	+	1.66109i	1.72465	+	0.830546i
$5$	−0.222521	+	0.974928i	−0.0995144	+	0.436001i	0.900485	+	0.434887i	$0.143212\pi$
$5$	−0.222521	+	0.974928i	−0.0995144	+	0.436001i	−0.999999	+	0.00111393i	$0.999645\pi$
$6$	−1.29695	−	5.68230i	−0.529476	−	2.31979i
$7$	2.54832	−	1.22721i	0.963176	−	0.463841i	0.114889	−	0.993378i	$-0.463349\pi$
$7$	2.54832	−	1.22721i	0.963176	−	0.463841i	0.848287	+	0.529537i	$0.177634\pi$
$8$	3.45117	+	2.75222i	1.22017	+	0.973056i
$9$	−1.76350	+	2.21135i	−0.587832	+	0.737118i
$10$	−1.04749	+	2.17513i	−0.331245	+	0.687837i
$11$	0.323845	−	0.258258i	0.0976430	−	0.0778677i	−0.573452	−	0.819240i	$-0.694396\pi$
$11$	0.323845	−	0.258258i	0.0976430	−	0.0778677i	0.671095	+	0.741372i	$0.265824\pi$
$12$		−	9.24264i		−	2.66812i
$13$	2.38699	+	2.99318i	0.662031	+	0.830160i	0.993563	−	0.113284i	$-0.0361369\pi$
$13$	2.38699	+	2.99318i	0.662031	+	0.830160i	−0.331532	+	0.943444i	$0.607566\pi$
$14$	6.65722	−	1.51947i	1.77922	−	0.406095i
$15$	2.35368	−	0.537213i	0.607719	−	0.138708i
$16$	1.87047	+	2.34549i	0.467617	+	0.586374i
$17$			0.828427i			0.200923i	0.994941	+	0.100462i	$0.0320319\pi$
$17$			0.828427i			0.200923i	−0.994941	+	0.100462i	$0.967968\pi$
$18$	−5.33868	+	4.25745i	−1.25834	+	1.00349i
$19$	2.60330	−	5.40581i	0.597239	−	1.24018i	−0.355012	−	0.934862i	$-0.615523\pi$
$19$	2.60330	−	5.40581i	0.597239	−	1.24018i	0.952251	−	0.305317i	$-0.0987624\pi$
$20$	−2.38699	+	2.99318i	−0.533746	+	0.669296i
$21$	−5.33868	−	4.25745i	−1.16500	−	0.929053i
$22$	0.900969	−	0.433884i	0.192087	−	0.0925043i
$23$	−0.813727	−	3.56517i	−0.169674	−	0.743389i	−0.986129	−	0.165981i	$-0.946921\pi$
$23$	−0.813727	−	3.56517i	−0.169674	−	0.743389i	0.816455	−	0.577409i	$-0.195936\pi$
$24$	2.37137	−	10.3897i	0.484055	−	2.12078i
$25$	3.60388	+	1.73553i	0.720775	+	0.347107i
$26$	4.01023	+	8.32733i	0.786471	+	1.63312i
$27$	−0.403828	−	0.0921712i	−0.0777168	−	0.0177384i
$28$	10.8284			2.04638
$29$		0			0
$29$		0			0
$30$	5.82843			1.06412
$31$	−9.81857	−	2.24102i	−1.76347	−	0.402500i	−0.786791	−	0.617220i	$-0.788259\pi$
$31$	−9.81857	−	2.24102i	−1.76347	−	0.402500i	−0.976676	+	0.214720i	$0.931116\pi$
$32$	−0.688047	−	1.42874i	−0.121631	−	0.252569i
$33$	−0.900969	−	0.433884i	−0.156839	−	0.0755295i
$34$	−0.445042	+	1.94986i	−0.0763241	+	0.334398i
$35$	0.629384	+	2.75751i	0.106385	+	0.466105i
$36$	−9.75608	+	4.69828i	−1.62601	+	0.783046i
$37$	3.12733	+	2.49396i	0.514129	+	0.410004i	0.845889	−	0.533360i	$-0.179071\pi$
$37$	3.12733	+	2.49396i	0.514129	+	0.410004i	−0.331759	+	0.943364i	$0.607642\pi$
$38$	9.03143	−	11.3250i	1.46509	−	1.83717i
$39$	4.01023	−	8.32733i	0.642151	−	1.33344i
$40$	−3.45117	+	2.75222i	−0.545678	+	0.435164i
$41$			4.48528i			0.700483i	0.936659	+	0.350242i	$0.113901\pi$
$41$			4.48528i			0.700483i	−0.936659	+	0.350242i	$0.886099\pi$
$42$	−10.2784	−	12.8887i	−1.58599	−	1.98877i
$43$	3.49588	−	0.797913i	0.533117	−	0.121681i	0.0525165	−	0.998620i	$-0.483276\pi$
$43$	3.49588	−	0.797913i	0.533117	−	0.121681i	0.480601	+	0.876940i	$0.340419\pi$
$44$	1.54603	−	0.352871i	0.233072	−	0.0531973i
$45$	−1.76350	−	2.21135i	−0.262886	−	0.329649i
$46$		−	8.82843i		−	1.30168i
$47$	−2.53520	+	2.02175i	−0.369797	+	0.294903i	−0.790702	−	0.612202i	$-0.790284\pi$
$47$	−2.53520	+	2.02175i	−0.369797	+	0.294903i	0.420905	+	0.907105i	$0.361713\pi$
$48$	3.14246	−	6.52539i	0.453576	−	0.941859i
$49$	0.623490	−	0.781831i	0.0890700	−	0.111690i
$50$	7.55003	+	6.02095i	1.06774	+	0.851491i
$51$	1.80194	−	0.867767i	0.252322	−	0.121512i
$52$	3.26146	+	14.2894i	0.452283	+	1.98158i
$53$	−2.11067	+	9.24747i	−0.289923	+	1.27024i	0.594706	+	0.803943i	$0.297268\pi$
$53$	−2.11067	+	9.24747i	−0.289923	+	1.27024i	−0.884630	+	0.466294i	$0.845589\pi$
$54$	−0.900969	−	0.433884i	−0.122606	−	0.0590441i
$55$	0.179721	+	0.373194i	0.0242335	+	0.0503214i
$56$	12.1722	+	2.77824i	1.62659	+	0.371257i
$57$	−14.4853			−1.91862
$58$		0			0
$59$	−3.65685			−0.476082			−0.238041	−	0.971255i	$-0.576505\pi$
$59$	−3.65685			−0.476082			−0.238041	+	0.971255i	$0.576505\pi$
$60$	9.01091	+	2.05668i	1.16330	+	0.265516i
$61$	2.09498	+	4.35026i	0.268234	+	0.556994i	0.990963	−	0.134138i	$-0.0428266\pi$
$61$	2.09498	+	4.35026i	0.268234	+	0.556994i	−0.722728	+	0.691132i	$0.757112\pi$
$62$	−21.9059	−	10.5493i	−2.78205	−	1.33977i
$63$	−1.78017	+	7.79942i	−0.224280	+	0.982635i
$64$	−2.18703	−	9.58201i	−0.273379	−	1.19775i
$65$	−3.44929	+	1.66109i	−0.427832	+	0.206033i
$66$	−1.88751	−	1.50524i	−0.232336	−	0.185282i
$67$	−3.52699	+	4.42271i	−0.430891	+	0.540320i	−0.949117	−	0.314924i	$-0.898021\pi$
$67$	−3.52699	+	4.42271i	−0.430891	+	0.540320i	0.518226	+	0.855243i	$0.326592\pi$
$68$	−1.37609	+	2.85749i	−0.166876	+	0.346521i
$69$	−6.90234	+	5.50443i	−0.830944	+	0.662656i
$70$			6.82843i			0.816153i
$71$	5.50443	+	6.90234i	0.653256	+	0.819157i	0.992590	−	0.121509i	$-0.0387732\pi$
$71$	5.50443	+	6.90234i	0.653256	+	0.819157i	−0.339334	+	0.940666i	$0.610202\pi$
$72$	−12.1722	+	2.77824i	−1.43451	+	0.327418i
$73$	−3.89971	+	0.890084i	−0.456427	+	0.104176i	−0.444552	−	0.895753i	$-0.646637\pi$
$73$	−3.89971	+	0.890084i	−0.456427	+	0.104176i	−0.0118748	+	0.999929i	$0.503780\pi$
$74$	6.02095	+	7.55003i	0.699921	+	0.877673i
$75$		−	9.65685i		−	1.11508i
$76$	17.9591	−	14.3219i	2.06005	−	1.64284i
$77$	0.508326	−	1.05555i	0.0579292	−	0.120291i
$78$	13.9124	−	17.4456i	1.57527	−	1.97532i
$79$	−1.88751	−	1.50524i	−0.212361	−	0.169352i	0.511532	−	0.859264i	$-0.329078\pi$
$79$	−1.88751	−	1.50524i	−0.212361	−	0.169352i	−0.723894	+	0.689911i	$0.757649\pi$
$80$	−2.70291	+	1.30165i	−0.302194	+	0.145529i
$81$	2.11067	+	9.24747i	0.234519	+	1.02750i
$82$	−2.40955	+	10.5569i	−0.266090	+	1.16582i
$83$	−6.89859	−	3.32218i	−0.757218	−	0.364657i	0.0151057	−	0.999886i	$-0.495192\pi$
$83$	−6.89859	−	3.32218i	−0.757218	−	0.364657i	−0.772324	+	0.635229i	$0.780906\pi$
$84$	−11.3426	−	23.5533i	−1.23758	−	2.56987i
$85$	−0.807657	−	0.184342i	−0.0876027	−	0.0199947i
$86$	8.65685			0.933493
$87$		0			0
$88$	1.82843			0.194911
$89$	12.1722	+	2.77824i	1.29026	+	0.294492i	0.811964	−	0.583708i	$-0.198399\pi$
$89$	12.1722	+	2.77824i	1.29026	+	0.294492i	0.478292	+	0.878201i	$0.341256\pi$
$90$	−2.96274	−	6.15220i	−0.312301	−	0.648499i
$91$	9.75608	+	4.69828i	1.02271	+	0.492513i
$92$	3.11529	−	13.6490i	0.324792	−	1.42301i
$93$	5.41031	+	23.7041i	0.561023	+	2.45800i
$94$	−7.05317	+	3.39663i	−0.727479	+	0.350335i
$95$	4.69099	+	3.74094i	0.481285	+	0.383812i
$96$	−2.38699	+	2.99318i	−0.243621	+	0.305491i
$97$	−1.94609	+	4.04110i	−0.197596	+	0.410311i	−0.976098	−	0.217330i	$-0.930265\pi$
$97$	−1.94609	+	4.04110i	−0.197596	+	0.410311i	0.778503	+	0.627641i	$0.215980\pi$
$98$	1.88751	−	1.50524i	0.190667	−	0.152052i
$99$			1.17157i			0.117748i
$100$	9.54794	+	11.9727i	0.954794	+	1.19727i
$101$	−2.28440	+	0.521399i	−0.227306	+	0.0518811i	−0.334657	−	0.942340i	$-0.608620\pi$
$101$	−2.28440	+	0.521399i	−0.227306	+	0.0518811i	0.107351	+	0.994221i	$0.465763\pi$
$102$	4.70737	−	1.07443i	0.466099	−	0.106384i
$103$	−3.01048	−	3.77502i	−0.296631	−	0.371963i	0.611073	−	0.791574i	$-0.290738\pi$
$103$	−3.01048	−	3.77502i	−0.296631	−	0.371963i	−0.907704	+	0.419611i	$0.862167\pi$
$104$			16.8995i			1.65713i
$105$	5.33868	−	4.25745i	0.521002	−	0.415485i
$106$	−9.93572	+	20.6317i	−0.965042	+	2.00393i
$107$	−9.24537	+	11.5933i	−0.893784	+	1.12077i	0.0982954	+	0.995157i	$0.468661\pi$
$107$	−9.24537	+	11.5933i	−0.893784	+	1.12077i	−0.992079	+	0.125612i	$0.959910\pi$
$108$	−1.23982	−	0.988722i	−0.119302	−	0.0951398i
$109$	11.4034	−	5.49160i	1.09225	−	0.526000i	0.201037	−	0.979584i	$-0.435569\pi$
$109$	11.4034	−	5.49160i	1.09225	−	0.526000i	0.891214	+	0.453583i	$0.149855\pi$
$110$	0.222521	+	0.974928i	0.0212165	+	0.0929557i
$111$	2.14885	−	9.41474i	0.203960	−	0.893607i
$112$	7.64497	+	3.68163i	0.722382	+	0.347881i
$113$	−5.77660	−	11.9952i	−0.543417	−	1.12842i	−0.974143	−	0.225934i	$-0.927457\pi$
$113$	−5.77660	−	11.9952i	−0.543417	−	1.12842i	0.430726	−	0.902483i	$-0.358258\pi$
$114$	−34.0938	−	7.78168i	−3.19317	−	0.728821i
$115$	3.65685			0.341003
$116$		0			0
$117$	−10.8284			−1.00109
$118$	−8.60708	−	1.96451i	−0.792346	−	0.180848i
$119$	1.01665	+	2.11110i	0.0931964	+	0.193524i
$120$	9.60149	+	4.62384i	0.876492	+	0.422097i
$121$	−2.40955	+	10.5569i	−0.219050	+	0.959721i
$122$	2.59389	+	11.3646i	0.234840	+	1.02890i
$123$	9.75608	−	4.69828i	0.879676	−	0.423630i
$124$	−30.1446	−	24.0395i	−2.70706	−	2.15881i
$125$	−5.61141	+	7.03648i	−0.501900	+	0.629362i
$126$	−8.37990	+	17.4011i	−0.746541	+	1.55021i
$127$	3.39561	−	2.70791i	0.301311	−	0.240288i	−0.461149	−	0.887323i	$-0.652563\pi$
$127$	3.39561	−	2.70791i	0.301311	−	0.240288i	0.762460	+	0.647035i	$0.223991\pi$
$128$		−	20.5563i		−	1.81694i
$129$	−5.39746	−	6.76820i	−0.475220	−	0.595907i
$130$	−9.01091	+	2.05668i	−0.790309	+	0.180383i
$131$	−20.7793	+	4.74275i	−1.81550	+	0.414376i	−0.988920	−	0.148447i	$-0.952573\pi$
$131$	−20.7793	+	4.74275i	−1.81550	+	0.414376i	−0.826578	+	0.562822i	$0.809716\pi$
$132$	−2.38699	−	2.99318i	−0.207760	−	0.260523i
$133$		−	16.9706i		−	1.47153i
$134$	−10.6774	+	8.51491i	−0.922383	+	0.735576i
$135$	0.179721	−	0.373194i	0.0154679	−	0.0321194i
$136$	−2.28001	+	2.85904i	−0.195509	+	0.245161i
$137$	9.38198	+	7.48188i	0.801556	+	0.639220i	0.936118	−	0.351685i	$-0.114391\pi$
$137$	9.38198	+	7.48188i	0.801556	+	0.639220i	−0.134562	+	0.990905i	$0.542963\pi$
$138$	−19.2030	+	9.24767i	−1.63467	+	0.787214i
$139$	−3.11529	−	13.6490i	−0.264236	−	1.15769i	−0.916606	−	0.399792i	$-0.869082\pi$
$139$	−3.11529	−	13.6490i	−0.264236	−	1.15769i	0.652370	−	0.757900i	$-0.273775\pi$
$140$	−2.40955	+	10.5569i	−0.203644	+	0.892224i
$141$	7.05317	+	3.39663i	0.593984	+	0.286048i
$142$	9.24767	+	19.2030i	0.776047	+	1.61148i
$143$	1.54603	+	0.352871i	0.129285	+	0.0295085i
$144$	−8.48528			−0.707107
$145$		0			0
$146$	−9.65685			−0.799207
$147$	−2.35368	−	0.537213i	−0.194129	−	0.0443086i
$148$	6.64437	+	13.7972i	0.546164	+	1.13412i
$149$	−7.05317	−	3.39663i	−0.577818	−	0.278263i	0.122062	−	0.992522i	$-0.461049\pi$
$149$	−7.05317	−	3.39663i	−0.577818	−	0.278263i	−0.699881	+	0.714260i	$0.746763\pi$
$150$	5.18779	−	22.7292i	0.423581	−	1.85583i
$151$	−3.14692	−	13.7876i	−0.256093	−	1.12202i	−0.925389	−	0.379020i	$-0.876261\pi$
$151$	−3.14692	−	13.7876i	−0.256093	−	1.12202i	0.669296	−	0.742996i	$-0.266596\pi$
$152$	23.8624	−	11.4915i	1.93550	−	0.932086i
$153$	−1.83195	−	1.46093i	−0.148104	−	0.118109i
$154$	1.76350	−	2.21135i	0.142107	−	0.178196i
$155$	4.36967	−	9.07372i	0.350981	−	0.728819i
$156$	27.6649	−	22.0620i	2.21497	−	1.76638i
$157$		−	8.48528i		−	0.677199i	−0.940931	−	0.338600i	$-0.890047\pi$
$157$		−	8.48528i		−	0.677199i	0.940931	−	0.338600i	$-0.109953\pi$
$158$	−3.63396	−	4.55685i	−0.289103	−	0.362523i
$159$	22.3254	−	5.09562i	1.77052	−	0.404109i
$160$	1.54603	−	0.352871i	0.122224	−	0.0278969i
$161$	−6.44885	−	8.08660i	−0.508240	−	0.637313i
$162$			22.8995i			1.79915i
$163$	3.07176	−	2.44965i	0.240599	−	0.191871i	−0.495765	−	0.868457i	$-0.665112\pi$
$163$	3.07176	−	2.44965i	0.240599	−	0.191871i	0.736364	+	0.676585i	$0.236541\pi$
$164$	−7.45047	+	15.4711i	−0.581784	+	1.20809i
$165$	0.623490	−	0.781831i	0.0485386	−	0.0608655i
$166$	−14.4524	−	11.5254i	−1.12172	−	0.894543i
$167$	−2.85749	+	1.37609i	−0.221119	+	0.106485i	−0.541164	−	0.840917i	$-0.682016\pi$
$167$	−2.85749	+	1.37609i	−0.221119	+	0.106485i	0.320045	+	0.947402i	$0.396302\pi$
$168$	−6.70726	−	29.3864i	−0.517476	−	2.26721i
$169$	−0.368685	+	1.61531i	−0.0283604	+	0.124255i
$170$	−1.80194	−	0.867767i	−0.138202	−	0.0665547i
$171$	7.36325	+	15.2899i	0.563082	+	1.16925i
$172$	13.3837	+	3.05475i	1.02050	+	0.232923i
$173$	−12.3431			−0.938432			−0.469216	−	0.883083i	$-0.655463\pi$
$173$	−12.3431			−0.938432			−0.469216	+	0.883083i	$0.655463\pi$
$174$		0			0
$175$	11.3137			0.855236
$176$	1.21149	+	0.276514i	0.0913191	+	0.0208430i
$177$	3.83051	+	7.95414i	0.287919	+	0.597870i
$178$	27.1571	+	13.0782i	2.03551	+	0.980251i
$179$	−1.44311	+	6.32268i	−0.107863	+	0.472579i	0.891929	+	0.452176i	$0.149352\pi$
$179$	−1.44311	+	6.32268i	−0.107863	+	0.472579i	−0.999792	+	0.0204033i	$0.993505\pi$
$180$	−2.40955	−	10.5569i	−0.179597	−	0.786868i
$181$	−7.49039	+	3.60718i	−0.556756	+	0.268120i	−0.691032	−	0.722824i	$-0.742844\pi$
$181$	−7.49039	+	3.60718i	−0.556756	+	0.268120i	0.134275	+	0.990944i	$0.457129\pi$
$182$	20.4387	+	16.2994i	1.51502	+	1.20819i
$183$	7.26793	−	9.11370i	0.537261	−	0.673704i
$184$	7.00381	−	14.5436i	0.516328	−	1.07217i
$185$	−3.12733	+	2.49396i	−0.229926	+	0.183360i
$186$			58.6985i			4.30398i
$187$	0.213948	+	0.268282i	0.0156454	+	0.0196187i
$188$	−12.1030	+	2.76242i	−0.882699	+	0.201470i
$189$	−1.14220	+	0.260699i	−0.0830828	+	0.0189631i
$190$	9.03143	+	11.3250i	0.655208	+	0.821605i
$191$			25.3137i			1.83164i	0.401594	+	0.915818i	$0.368456\pi$
$191$			25.3137i			1.83164i	−0.401594	+	0.915818i	$0.631544\pi$
$192$	−18.5512	+	14.7941i	−1.33882	+	1.06767i
$193$	−2.24386	+	4.65943i	−0.161517	+	0.335393i	−0.965983	−	0.258605i	$-0.916737\pi$
$193$	−2.24386	+	4.65943i	−0.161517	+	0.335393i	0.804466	+	0.593998i	$0.202451\pi$
$194$	−6.75141	+	8.46601i	−0.484723	+	0.607824i
$195$	7.22619	+	5.76269i	0.517478	+	0.412675i
$196$	3.44929	−	1.66109i	0.246378	−	0.118649i
$197$	−0.445042	−	1.94986i	−0.0317079	−	0.138921i	0.956596	−	0.291416i	$-0.0941264\pi$
$197$	−0.445042	−	1.94986i	−0.0317079	−	0.138921i	−0.988304	+	0.152495i	$0.951269\pi$
$198$	−0.629384	+	2.75751i	−0.0447284	+	0.195968i
$199$	0.437223	+	0.210556i	0.0309939	+	0.0149259i	0.449317	−	0.893373i	$-0.351668\pi$
$199$	0.437223	+	0.210556i	0.0309939	+	0.0149259i	−0.418323	+	0.908299i	$0.637382\pi$
$200$	7.66102	+	15.9083i	0.541716	+	1.12488i
$201$	13.3144	+	3.03894i	0.939129	+	0.214350i
$202$	−5.65685			−0.398015
$203$		0			0
$204$	7.65685			0.536087
$205$	−4.37283	−	0.998069i	−0.305411	−	0.0697082i
$206$	−5.05772	−	10.5025i	−0.352388	−	0.731741i
$207$	9.31885	+	4.48772i	0.647705	+	0.311918i
$208$	−2.55572	+	11.1973i	−0.177207	+	0.776395i
$209$	−0.553027	−	2.42297i	−0.0382537	−	0.167600i
$210$	14.8527	−	7.15270i	1.02494	−	0.493583i
$211$	15.1556	+	12.0862i	1.04336	+	0.832049i	0.986074	−	0.166309i	$-0.0531849\pi$
$211$	15.1556	+	12.0862i	1.04336	+	0.832049i	0.0572828	+	0.998358i	$0.481756\pi$
$212$	−22.6412	+	28.3912i	−1.55501	+	1.94992i
$213$	9.24767	−	19.2030i	0.633640	−	1.31577i
$214$	−27.9888	+	22.3203i	−1.91327	+	1.52578i
$215$			3.58579i			0.244549i
$216$	−1.14001	−	1.42952i	−0.0775676	−	0.0972666i
$217$	−27.7711	+	6.33857i	−1.88522	+	0.430290i
$218$	29.7902	−	6.79943i	2.01765	−	0.460515i
$219$	6.02095	+	7.55003i	0.406858	+	0.510184i
$220$			1.58579i			0.106914i
$221$	−2.47964	+	1.97744i	−0.166798	+	0.133017i
$222$	10.1154	−	21.0049i	0.678904	−	1.40976i
$223$	−1.97744	+	2.47964i	−0.132419	+	0.166049i	−0.843620	−	0.536940i	$-0.819580\pi$
$223$	−1.97744	+	2.47964i	−0.132419	+	0.166049i	0.711201	+	0.702989i	$0.248152\pi$
$224$	−3.50673	−	2.79653i	−0.234304	−	0.186851i
$225$	−10.1933	+	4.90883i	−0.679553	+	0.327256i
$226$	−7.15230	−	31.3363i	−0.475764	−	2.08446i
$227$	1.81180	−	7.93800i	0.120253	−	0.526863i	−0.878536	−	0.477675i	$-0.841480\pi$
$227$	1.81180	−	7.93800i	0.120253	−	0.526863i	0.998790	−	0.0491879i	$-0.0156633\pi$
$228$	−49.9640	−	24.0614i	−3.30895	−	1.59350i
$229$	−1.52498	−	3.16665i	−0.100773	−	0.209258i	0.844486	−	0.535577i	$-0.179906\pi$
$229$	−1.52498	−	3.16665i	−0.100773	−	0.209258i	−0.945260	+	0.326319i	$0.894192\pi$
$230$	8.60708	+	1.96451i	0.567534	+	0.129536i
$231$	−2.82843			−0.186097
$232$		0			0
$233$	18.3137			1.19977			0.599885	−	0.800086i	$-0.295213\pi$
$233$	18.3137			1.19977			0.599885	+	0.800086i	$0.295213\pi$
$234$	−25.4867	−	5.81717i	−1.66612	−	0.380280i
$235$	−1.40693	−	2.92152i	−0.0917779	−	0.190579i
$236$	−12.6136	−	6.07437i	−0.821073	−	0.395408i
$237$	−1.29695	+	5.68230i	−0.0842458	+	0.369105i
$238$	1.25877	+	5.51503i	0.0815938	+	0.357486i
$239$	17.7102	−	8.52879i	1.14558	−	0.551682i	0.237876	−	0.971296i	$-0.423549\pi$
$239$	17.7102	−	8.52879i	1.14558	−	0.551682i	0.907703	+	0.419614i	$0.137835\pi$
$240$	5.66252	+	4.51571i	0.365514	+	0.291488i
$241$	11.4184	−	14.3182i	0.735524	−	0.922319i	−0.263580	−	0.964638i	$-0.584903\pi$
$241$	11.4184	−	14.3182i	0.735524	−	0.922319i	0.999104	+	0.0423191i	$0.0134746\pi$
$242$	−11.3426	+	23.5533i	−0.729133	+	1.51406i
$243$	16.9320	−	13.5028i	1.08619	−	0.866207i
$244$			18.4853i			1.18340i
$245$	0.623490	+	0.781831i	0.0398333	+	0.0499494i
$246$	25.4867	−	5.81717i	1.62497	−	0.370889i
$247$	22.3946	−	5.11143i	1.42494	−	0.325233i
$248$	−27.7178	−	34.7570i	−1.76008	−	2.20707i
$249$			18.4853i			1.17146i
$250$	−16.9876	+	13.5471i	−1.07439	+	0.856796i
$251$	8.70851	−	18.0834i	0.549676	−	1.14141i	−0.422326	−	0.906444i	$-0.638786\pi$
$251$	8.70851	−	18.0834i	0.549676	−	1.14141i	0.972002	−	0.234971i	$-0.0754994\pi$
$252$	−19.0959	+	23.9455i	−1.20293	+	1.50842i
$253$	−1.18425	−	0.944412i	−0.0744535	−	0.0593746i
$254$	9.44691	−	4.54939i	0.592752	−	0.285454i
$255$	0.445042	+	1.94986i	0.0278696	+	0.122105i
$256$	6.66908	−	29.2191i	0.416817	−	1.82620i
$257$	16.3720	+	7.88435i	1.02126	+	0.491812i	0.868100	−	0.496389i	$-0.165341\pi$
$257$	16.3720	+	7.88435i	1.02126	+	0.491812i	0.153159	+	0.988202i	$0.451055\pi$
$258$	−9.06795	−	18.8298i	−0.564546	−	1.17229i
$259$	11.0301	+	2.51754i	0.685374	+	0.156432i
$260$	−14.6569			−0.908980
$261$		0			0
$262$	−51.4558			−3.17895
$263$	−2.68823	−	0.613570i	−0.165763	−	0.0378344i	0.138834	−	0.990316i	$-0.455665\pi$
$263$	−2.68823	−	0.613570i	−0.165763	−	0.0378344i	−0.304597	+	0.952481i	$0.598522\pi$
$264$	−1.91526	−	3.97707i	−0.117876	−	0.244772i
$265$	−8.54594	−	4.11551i	−0.524973	−	0.252814i
$266$	9.11681	−	39.9433i	0.558987	−	2.44908i
$267$	−6.70726	−	29.3864i	−0.410477	−	1.79842i
$268$	−19.5122	+	9.39656i	−1.19189	+	0.573986i
$269$	−24.5932	−	19.6124i	−1.49947	−	1.19579i	−0.926546	−	0.376182i	$-0.877237\pi$
$269$	−24.5932	−	19.6124i	−1.49947	−	1.19579i	−0.572926	−	0.819607i	$-0.694192\pi$
$270$	0.623490	−	0.781831i	0.0379444	−	0.0475807i
$271$	−7.18353	+	14.9168i	−0.436368	+	0.906128i	0.560583	+	0.828099i	$0.310577\pi$
$271$	−7.18353	+	14.9168i	−0.436368	+	0.906128i	−0.996951	+	0.0780298i	$0.975137\pi$
$272$	−1.94307	+	1.54955i	−0.117816	+	0.0939551i
$273$		−	26.1421i		−	1.58219i
$274$	18.0629	+	22.6501i	1.09122	+	1.36834i
$275$	1.61531	−	0.368685i	0.0974071	−	0.0222325i
$276$	−32.9516	+	7.52098i	−1.98345	+	0.452710i
$277$	−10.7949	−	13.5364i	−0.648604	−	0.813324i	0.343445	−	0.939173i	$-0.388406\pi$
$277$	−10.7949	−	13.5364i	−0.648604	−	0.813324i	−0.992049	+	0.125849i	$0.959835\pi$
$278$		−	33.7990i		−	2.02713i
$279$	22.2707	−	17.7603i	1.33331	−	1.06328i
$280$	−5.41716	+	11.2488i	−0.323737	+	0.672247i
$281$	19.9333	−	24.9956i	1.18912	−	1.49111i	0.359175	−	0.933270i	$-0.383058\pi$
$281$	19.9333	−	24.9956i	1.18912	−	1.49111i	0.829947	−	0.557842i	$-0.188370\pi$
$282$	14.7762	+	11.7836i	0.879911	+	0.701706i
$283$	10.5025	−	5.05772i	0.624307	−	0.300650i	−0.0948571	−	0.995491i	$-0.530239\pi$
$283$	10.5025	−	5.05772i	0.624307	−	0.300650i	0.719164	+	0.694841i	$0.244525\pi$
$284$	7.52098	+	32.9516i	0.446288	+	1.95532i
$285$	3.22328	−	14.1221i	0.190931	−	0.836521i
$286$	3.44929	+	1.66109i	0.203961	+	0.0982224i
$287$	5.50438	+	11.4300i	0.324913	+	0.674689i
$288$	4.37283	+	0.998069i	0.257671	+	0.0588118i
$289$	16.3137			0.959630
$290$		0			0
$291$	10.8284			0.634774
$292$	−14.9298	−	3.40762i	−0.873698	−	0.199416i
$293$	−3.32218	−	6.89859i	−0.194084	−	0.403020i	0.781103	−	0.624402i	$-0.214657\pi$
$293$	−3.32218	−	6.89859i	−0.194084	−	0.403020i	−0.975187	+	0.221382i	$0.928943\pi$
$294$	−5.25123	−	2.52886i	−0.306258	−	0.147486i
$295$	0.813727	−	3.56517i	0.0473770	−	0.207572i
$296$	3.92902	+	17.2142i	0.228370	+	1.00055i
$297$	−0.154582	+	0.0744427i	−0.00896975	+	0.00431960i
$298$	−14.7762	−	11.7836i	−0.855963	−	0.682608i
$299$	8.72886	−	10.9456i	0.504803	−	0.633003i
$300$	16.0409	−	33.3093i	0.926123	−	1.92311i
$301$	7.92944	−	6.32352i	0.457045	−	0.364482i
$302$		−	34.1421i		−	1.96466i
$303$	3.52699	+	4.42271i	0.202620	+	0.254078i
$304$	17.5487	−	4.00538i	1.00649	−	0.229724i
$305$	−4.70737	+	1.07443i	−0.269543	+	0.0615215i
$306$	−3.52699	−	4.42271i	−0.201625	−	0.252829i
$307$			2.89949i			0.165483i	0.996571	+	0.0827415i	$0.0263676\pi$
$307$			2.89949i			0.165483i	−0.996571	+	0.0827415i	$0.973632\pi$
$308$	3.50673	−	2.79653i	0.199815	−	0.159347i
$309$	−5.05772	+	10.5025i	−0.287724	+	0.597464i
$310$	15.1593	−	19.0092i	0.860993	−	1.07965i
$311$	2.10023	+	1.67488i	0.119093	+	0.0949735i	0.681225	−	0.732074i	$-0.261447\pi$
$311$	2.10023	+	1.67488i	0.119093	+	0.0949735i	−0.562132	+	0.827047i	$0.690019\pi$
$312$	36.7586	−	17.7020i	2.08105	−	1.00218i
$313$	−2.18703	−	9.58201i	−0.123618	−	0.541607i	−0.998372	−	0.0570392i	$-0.981834\pi$
$313$	−2.18703	−	9.58201i	−0.123618	−	0.541607i	0.874754	−	0.484568i	$-0.161023\pi$
$314$	4.55840	−	19.9717i	0.257246	−	1.12707i
$315$	−7.20775	−	3.47107i	−0.406111	−	0.195573i
$316$	−4.01023	−	8.32733i	−0.225593	−	0.468449i
$317$	−30.6672	−	6.99958i	−1.72244	−	0.393136i	−0.756929	−	0.653497i	$-0.773301\pi$
$317$	−30.6672	−	6.99958i	−1.72244	−	0.393136i	−0.965511	+	0.260361i	$0.916158\pi$
$318$	55.2843			3.10019
$319$		0			0
$320$	9.82843			0.549426
$321$	34.9014	+	7.96602i	1.94801	+	0.444620i
$322$	−10.8343	−	22.4977i	−0.603773	−	1.25375i
$323$	4.47832	+	2.15665i	0.249181	+	0.119999i
$324$	−8.08056	+	35.4032i	−0.448920	+	1.96685i
$325$	3.40762	+	14.9298i	0.189021	+	0.828154i
$326$	8.54594	−	4.11551i	0.473316	−	0.227937i
$327$	−23.8899	−	19.0516i	−1.32112	−	1.05355i
$328$	−12.3445	+	15.4795i	−0.681609	+	0.854711i
$329$	−3.97940	+	8.26330i	−0.219391	+	0.455571i
$330$	1.88751	−	1.50524i	0.103904	−	0.0828606i
$331$			2.41421i			0.132697i	0.997797	+	0.0663486i	$0.0211349\pi$
$331$			2.41421i			0.132697i	−0.997797	+	0.0663486i	$0.978865\pi$
$332$	−18.2768	−	22.9184i	−1.00307	−	1.25781i
$333$	−11.0301	+	2.51754i	−0.604443	+	0.137960i
$334$	−7.46488	+	1.70381i	−0.408460	+	0.0932284i
$335$	−3.52699	−	4.42271i	−0.192700	−	0.241638i
$336$		−	20.4853i		−	1.11756i
$337$	17.0431	−	13.5914i	0.928399	−	0.740373i	−0.0374991	−	0.999297i	$-0.511939\pi$
$337$	17.0431	−	13.5914i	0.928399	−	0.740373i	0.965898	+	0.258923i	$0.0833677\pi$
$338$	−1.73553	+	3.60388i	−0.0944007	+	0.196025i
$339$	−20.0403	+	25.1297i	−1.08844	+	1.36486i
$340$	−2.47964	−	1.97744i	−0.134477	−	0.107242i
$341$	−3.75846	+	1.80998i	−0.203532	+	0.0980158i
$342$	9.11681	+	39.9433i	0.492981	+	2.15989i
$343$	−3.77631	+	16.5451i	−0.203901	+	0.893350i
$344$	14.2609	+	6.86770i	0.768897	+	0.370281i
$345$	−3.83051	−	7.95414i	−0.206228	−	0.428236i
$346$	−29.0519	−	6.63090i	−1.56184	−	0.356479i
$347$	−2.48528			−0.133417			−0.0667084	−	0.997773i	$-0.521250\pi$
$347$	−2.48528			−0.133417			−0.0667084	+	0.997773i	$0.521250\pi$
$348$		0			0
$349$	−5.14214			−0.275252			−0.137626	−	0.990484i	$-0.543947\pi$
$349$	−5.14214			−0.275252			−0.137626	+	0.990484i	$0.543947\pi$
$350$	26.6289	+	6.07787i	1.42337	+	0.324876i
$351$	−0.688047	−	1.42874i	−0.0367252	−	0.0762607i
$352$	−0.591805	−	0.284998i	−0.0315433	−	0.0151905i
$353$	6.00151	−	26.2944i	0.319428	−	1.39951i	−0.519130	−	0.854695i	$-0.673744\pi$
$353$	6.00151	−	26.2944i	0.319428	−	1.39951i	0.838558	−	0.544812i	$-0.183399\pi$
$354$	4.74275	+	20.7793i	0.252074	+	1.10441i
$355$	−7.95414	+	3.83051i	−0.422162	+	0.203302i
$356$	37.3708	+	29.8022i	1.98065	+	1.57951i
$357$	3.52699	−	4.42271i	0.186668	−	0.234074i
$358$	−6.79325	+	14.1063i	−0.359035	+	0.745543i
$359$	−3.07176	+	2.44965i	−0.162121	+	0.129288i	−0.701190	−	0.712974i	$-0.747348\pi$
$359$	−3.07176	+	2.44965i	−0.162121	+	0.129288i	0.539069	+	0.842262i	$0.318776\pi$
$360$		−	12.4853i		−	0.658032i
$361$	−10.5993	−	13.2911i	−0.557859	−	0.699533i
$362$	−19.5678	+	4.46623i	−1.02846	+	0.234740i
$363$	25.4867	−	5.81717i	1.33770	−	0.305322i
$364$	25.8473	+	32.4115i	1.35477	+	1.69882i
$365$		−	4.00000i		−	0.209370i
$366$	22.0024	−	17.5463i	1.15008	−	0.917162i
$367$	7.80991	−	16.2174i	0.407674	−	0.846543i	−0.591516	−	0.806293i	$-0.701470\pi$
$367$	7.80991	−	16.2174i	0.407674	−	0.846543i	0.999190	−	0.0402500i	$-0.0128154\pi$
$368$	6.84003	−	8.57713i	0.356561	−	0.447114i
$369$	−9.91854	−	7.90977i	−0.516339	−	0.411766i
$370$	−8.70053	+	4.18995i	−0.452319	+	0.217825i
$371$	5.96989	+	26.1558i	0.309941	+	1.35794i
$372$	−20.7130	+	90.7495i	−1.07392	+	4.70514i
$373$	23.7078	+	11.4171i	1.22755	+	0.591155i	0.931403	−	0.363989i	$-0.118586\pi$
$373$	23.7078	+	11.4171i	1.22755	+	0.591155i	0.296142	+	0.955144i	$0.404300\pi$
$374$	0.359441	+	0.746387i	0.0185863	+	0.0385948i
$375$	21.1832	+	4.83492i	1.09389	+	0.249674i
$376$	−14.3137			−0.738173
$377$		0			0
$378$	−2.82843			−0.145479
$379$	6.79580	+	1.55110i	0.349077	+	0.0796745i	0.393464	−	0.919340i	$-0.371277\pi$
$379$	6.79580	+	1.55110i	0.349077	+	0.0796745i	−0.0443876	+	0.999014i	$0.514134\pi$
$380$	9.96655	+	20.6958i	0.511273	+	1.06167i
$381$	−9.44691	−	4.54939i	−0.483980	−	0.233072i
$382$	−13.5989	+	59.5805i	−0.695778	+	3.04840i
$383$	−0.782098	−	3.42660i	−0.0399634	−	0.175091i	0.951008	−	0.309167i	$-0.100050\pi$
$383$	−0.782098	−	3.42660i	−0.0399634	−	0.175091i	−0.990971	+	0.134077i	$0.957193\pi$
$384$	−44.7128	+	21.5325i	−2.28174	+	1.09883i
$385$	0.915973	+	0.730464i	0.0466823	+	0.0372279i
$386$	−7.78445	+	9.76139i	−0.396218	+	0.496841i
$387$	−4.40051	+	9.13775i	−0.223690	+	0.464498i
$388$	−13.4253	+	10.7063i	−0.681565	+	0.543530i
$389$		−	3.02944i		−	0.153599i	−0.997047	−	0.0767993i	$-0.975530\pi$
$389$		−	3.02944i		−	0.153599i	0.997047	−	0.0767993i	$-0.0244701\pi$
$390$	13.9124	+	17.4456i	0.704480	+	0.883390i
$391$	2.95348	−	0.674113i	0.149364	−	0.0340914i
$392$	4.30354	−	0.982255i	0.217362	−	0.0496114i
$393$	32.0822	+	40.2298i	1.61833	+	2.02932i
$394$		−	4.82843i		−	0.243253i
$395$	1.88751	−	1.50524i	0.0949708	−	0.0757367i
$396$	−1.94609	+	4.04110i	−0.0977947	+	0.203073i
$397$	12.0603	−	15.1231i	0.605287	−	0.759006i	−0.380905	−	0.924614i	$-0.624387\pi$
$397$	12.0603	−	15.1231i	0.605287	−	0.759006i	0.986192	+	0.165609i	$0.0529589\pi$
$398$	0.915973	+	0.730464i	0.0459136	+	0.0366148i
$399$	−36.9132	+	17.7765i	−1.84797	+	0.889936i
$400$	2.67025	+	11.6991i	0.133513	+	0.584957i
$401$	4.15154	−	18.1891i	0.207318	−	0.908320i	−0.759025	−	0.651062i	$-0.774324\pi$
$401$	4.15154	−	18.1891i	0.207318	−	0.908320i	0.966343	−	0.257258i	$-0.0828190\pi$
$402$	29.7055	+	14.3054i	1.48157	+	0.713488i
$403$	−16.7290	−	34.7381i	−0.833329	−	1.73043i
$404$	−8.74565	−	1.99614i	−0.435112	−	0.0993116i
$405$	−9.48528			−0.471327
$406$		0			0
$407$	1.65685			0.0821272
$408$	8.60708	+	1.96451i	0.426114	+	0.0972577i
$409$	8.23102	+	17.0919i	0.406998	+	0.845139i	0.999225	+	0.0393683i	$0.0125346\pi$
$409$	8.23102	+	17.0919i	0.406998	+	0.845139i	−0.592227	+	0.805771i	$0.701751\pi$
$410$	−9.75608	−	4.69828i	−0.481818	−	0.232031i
$411$	6.44656	−	28.2442i	0.317985	−	1.39318i
$412$	−4.11336	−	18.0218i	−0.202651	−	0.887871i
$413$	−9.31885	+	4.48772i	−0.458551	+	0.220826i
$414$	19.5228	+	15.5689i	0.959492	+	0.765169i
$415$	4.77397	−	5.98637i	0.234345	−	0.293859i
$416$	2.63414	−	5.46984i	0.129149	−	0.268181i
$417$	−26.4251	+	21.0733i	−1.29404	+	1.03197i
$418$		−	6.00000i		−	0.293470i
$419$	5.93233	+	7.43891i	0.289813	+	0.363414i	0.905330	−	0.424710i	$-0.139624\pi$
$419$	5.93233	+	7.43891i	0.289813	+	0.363414i	−0.615516	+	0.788124i	$0.711052\pi$
$420$	25.4867	−	5.81717i	1.24362	−	0.283849i
$421$	−36.1822	+	8.25835i	−1.76341	+	0.402487i	−0.976662	−	0.214783i	$-0.931096\pi$
$421$	−36.1822	+	8.25835i	−1.76341	+	0.402487i	−0.786751	+	0.617270i	$0.788238\pi$
$422$	29.1787	+	36.5889i	1.42040	+	1.78112i
$423$		−	9.17157i		−	0.445937i
$424$	−32.7353	+	26.1056i	−1.58977	+	1.26780i
$425$	−1.43776	+	2.98555i	−0.0697418	+	0.144820i
$426$	32.0822	−	40.2298i	1.55439	−	1.94914i
$427$	10.6774	+	8.51491i	0.516714	+	0.412065i
$428$	−51.1476	+	24.6314i	−2.47231	+	1.19060i
$429$	−0.851905	−	3.73244i	−0.0411304	−	0.180204i
$430$	−1.92633	+	8.43981i	−0.0928959	+	0.407004i
$431$	−17.7102	−	8.52879i	−0.853071	−	0.410817i	−0.0443544	−	0.999016i	$-0.514123\pi$
$431$	−17.7102	−	8.52879i	−0.853071	−	0.410817i	−0.808717	+	0.588199i	$0.799837\pi$
$432$	−0.539162	−	1.11958i	−0.0259404	−	0.0538658i
$433$	29.8595	+	6.81524i	1.43496	+	0.327520i	0.868138	−	0.496323i	$-0.165317\pi$
$433$	29.8595	+	6.81524i	1.43496	+	0.327520i	0.566819	+	0.823842i	$0.308174\pi$
$434$	−68.7696			−3.30104
$435$		0			0
$436$	48.4558			2.32061
$437$	−21.3910	−	4.88236i	−1.02327	−	0.233555i
$438$	10.1154	+	21.0049i	0.483334	+	1.00365i
$439$	−0.309164	−	0.148885i	−0.0147556	−	0.00710591i	0.426491	−	0.904492i	$-0.359749\pi$
$439$	−0.309164	−	0.148885i	−0.0147556	−	0.00710591i	−0.441247	+	0.897386i	$0.645464\pi$
$440$	−0.406863	+	1.78258i	−0.0193964	+	0.0849814i
$441$	0.629384	+	2.75751i	0.0299707	+	0.131310i
$442$	−6.89859	+	3.32218i	−0.328132	+	0.158020i
$443$	19.0322	+	15.1777i	0.904249	+	0.721114i	0.960787	−	0.277286i	$-0.0894349\pi$
$443$	19.0322	+	15.1777i	0.904249	+	0.721114i	−0.0565385	+	0.998400i	$0.518006\pi$
$444$	23.0508	−	28.9047i	1.09394	−	1.37176i
$445$	−5.41716	+	11.2488i	−0.256798	+	0.533247i
$446$	−5.98637	+	4.77397i	−0.283463	+	0.226054i
$447$			18.8995i			0.893915i
$448$	−17.3324	−	21.7341i	−0.818878	−	1.02684i
$449$	−34.0938	+	7.78168i	−1.60898	+	0.367240i	−0.930187	−	0.367085i	$-0.880356\pi$
$449$	−34.0938	+	7.78168i	−1.60898	+	0.367240i	−0.678798	+	0.734325i	$0.737499\pi$
$450$	−26.6289	+	6.07787i	−1.25530	+	0.286514i
$451$	1.15836	+	1.45254i	0.0545450	+	0.0683973i
$452$		−	50.9706i		−	2.39745i
$453$	−26.6934	+	21.2873i	−1.25417	+	1.00016i
$454$	8.52879	−	17.7102i	0.400276	−	0.831182i
$455$	−6.75141	+	8.46601i	−0.316511	+	0.396892i
$456$	−49.9912	−	39.8666i	−2.34105	−	1.86693i
$457$	0.927491	−	0.446656i	0.0433862	−	0.0208937i	−0.412065	−	0.911155i	$-0.635192\pi$
$457$	0.927491	−	0.446656i	0.0433862	−	0.0208937i	0.455451	+	0.890261i	$0.349478\pi$
$458$	−1.88815	−	8.27254i	−0.0882276	−	0.386550i
$459$	0.0763571	−	0.334542i	0.00356404	−	0.0156151i
$460$	12.6136	+	6.07437i	0.588110	+	0.283219i
$461$	6.07437	+	12.6136i	0.282912	+	0.587472i	0.993198	−	0.116441i	$-0.0371486\pi$
$461$	6.07437	+	12.6136i	0.282912	+	0.587472i	−0.710286	+	0.703913i	$0.751434\pi$
$462$	−6.65722	−	1.51947i	−0.309722	−	0.0706920i
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$		0			0
$465$	−24.3137			−1.12752
$466$	43.1047	+	9.83836i	1.99679	+	0.455753i
$467$	16.6418	+	34.5570i	0.770089	+	1.59911i	0.800328	+	0.599563i	$0.204659\pi$
$467$	16.6418	+	34.5570i	0.770089	+	1.59911i	−0.0302389	+	0.999543i	$0.509627\pi$
$468$	−37.3504	−	17.9870i	−1.72652	−	0.831450i
$469$	−3.56033	+	15.5988i	−0.164401	+	0.720288i
$470$	−1.74199	−	7.63215i	−0.0803520	−	0.352045i
$471$	−18.4566	+	8.88823i	−0.850435	+	0.409548i
$472$	−12.6204	−	10.0645i	−0.580902	−	0.463254i
$473$	0.926058	−	1.16124i	0.0425802	−	0.0533939i
$474$	−6.10521	+	12.6776i	−0.280421	+	0.582301i
$475$	18.7640	−	14.9638i	0.860949	−	0.686584i
$476$			8.97056i			0.411165i
$477$	−16.7273	−	20.9753i	−0.765888	−	0.960393i
$478$	46.2660	−	10.5599i	2.11616	−	0.482999i
$479$	−6.72651	+	1.53528i	−0.307342	+	0.0701488i	−0.373410	−	0.927666i	$-0.621812\pi$
$479$	−6.72651	+	1.53528i	−0.307342	+	0.0701488i	0.0660682	+	0.997815i	$0.478954\pi$
$480$	−2.38699	−	2.99318i	−0.108950	−	0.136620i
$481$			15.3137i			0.698245i
$482$	34.5673	−	27.5665i	1.57450	−	1.25562i
$483$	−10.8343	+	22.4977i	−0.492979	+	1.02368i
$484$	−25.8473	+	32.4115i	−1.17488	+	1.47325i
$485$	−3.50673	−	2.79653i	−0.159233	−	0.126984i
$486$	47.1065	−	22.6853i	2.13679	−	1.02903i
$487$	2.56227	+	11.2260i	0.116107	+	0.508700i	0.999218	+	0.0395351i	$0.0125877\pi$
$487$	2.56227	+	11.2260i	0.116107	+	0.508700i	−0.883111	+	0.469164i	$0.844555\pi$
$488$	−4.74275	+	20.7793i	−0.214694	+	0.940636i
$489$	−8.54594	−	4.11551i	−0.386461	−	0.186110i
$490$	1.04749	+	2.17513i	0.0473207	+	0.0982624i
$491$	−20.7100	−	4.72693i	−0.934631	−	0.213323i	−0.272024	−	0.962290i	$-0.587693\pi$
$491$	−20.7100	−	4.72693i	−0.934631	−	0.213323i	−0.662607	+	0.748967i	$0.730550\pi$
$492$	41.4558			1.86897
$493$		0			0
$494$	55.4558			2.49508
$495$	−1.14220	−	0.260699i	−0.0513380	−	0.0117176i
$496$	−13.1090	−	27.2212i	−0.588612	−	1.22227i
$497$	22.4977	+	10.8343i	1.00916	+	0.485986i
$498$	−9.93053	+	43.5085i	−0.444998	+	1.94966i
$499$	4.22135	+	18.4949i	0.188973	+	0.827947i	0.977159	+	0.212509i	$0.0681636\pi$
$499$	4.22135	+	18.4949i	0.188973	+	0.827947i	−0.788186	+	0.615438i	$0.788979\pi$
$500$	−31.0436	+	14.9498i	−1.38831	+	0.668577i
$501$	5.98637	+	4.77397i	0.267451	+	0.213285i
$502$	30.2117	−	37.8843i	1.34842	−	1.69086i
$503$	−0.118050	+	0.245134i	−0.00526360	+	0.0109300i	−0.903584	−	0.428411i	$-0.859074\pi$
$503$	−0.118050	+	0.245134i	−0.00526360	+	0.0109300i	0.898320	+	0.439341i	$0.144788\pi$
$504$	−27.6094	+	22.0177i	−1.22982	+	0.980748i
$505$		−	2.34315i		−	0.104269i
$506$	−2.28001	−	2.85904i	−0.101359	−	0.127100i
$507$	3.89971	−	0.890084i	0.173192	−	0.0395300i
$508$	16.2105	−	3.69995i	0.719226	−	0.164159i
$509$	−6.55582	−	8.22074i	−0.290582	−	0.364378i	0.615017	−	0.788514i	$-0.289149\pi$
$509$	−6.55582	−	8.22074i	−0.290582	−	0.364378i	−0.905598	+	0.424136i	$0.860578\pi$
$510$			4.82843i			0.213806i
$511$	−8.84541	+	7.05398i	−0.391298	+	0.312050i
$512$	13.5557	−	28.1486i	0.599082	−	1.24401i
$513$	−1.54955	+	1.94307i	−0.0684142	+	0.0857887i
$514$	34.2990	+	27.3525i	1.51286	+	1.20647i
$515$	4.35026	−	2.09498i	0.191695	−	0.0923157i
$516$	−7.37482	−	32.3112i	−0.324658	−	1.42242i
$517$	−0.298878	+	1.30947i	−0.0131446	+	0.0575904i
$518$	24.6088	+	11.8510i	1.08125	+	0.520702i
$519$	12.9293	+	26.8480i	0.567533	+	1.17849i
$520$	−16.4758	−	3.76049i	−0.722511	−	0.164908i
$521$	29.1421			1.27674			0.638370	−	0.769730i	$-0.279609\pi$
$521$	29.1421			1.27674			0.638370	+	0.769730i	$0.279609\pi$
$522$		0			0
$523$	4.68629			0.204917			0.102459	−	0.994737i	$-0.467329\pi$
$523$	4.68629			0.204917			0.102459	+	0.994737i	$0.467329\pi$
$524$	−79.5521	−	18.1573i	−3.47525	−	0.793204i
$525$	−11.8510	−	24.6088i	−0.517219	−	1.07402i
$526$	−5.99762	−	2.88830i	−0.261509	−	0.125936i
$527$	1.85652	−	8.13397i	0.0808715	−	0.354321i
$528$	−0.667563	−	2.92478i	−0.0290519	−	0.127285i
$529$	8.67400	−	4.17718i	0.377131	−	0.181617i
$530$	−17.9035	−	14.2776i	−0.777680	−	0.620179i
$531$	6.44885	−	8.08660i	0.279856	−	0.350928i
$532$	28.1897	−	58.5365i	1.22218	−	2.53788i
$533$	−13.4253	+	10.7063i	−0.581513	+	0.463741i
$534$		−	72.7696i		−	3.14905i
$535$	−9.24537	−	11.5933i	−0.399712	−	0.501223i
$536$	−24.3445	+	5.55647i	−1.05152	+	0.240003i
$537$	15.2643	−	3.48398i	0.658703	−	0.150345i
$538$	−47.3485	−	59.3732i	−2.04134	−	2.55976i
$539$		−	0.414214i		−	0.0178414i
$540$	1.23982	−	0.988722i	0.0533533	−	0.0425478i
$541$	−4.48772	+	9.31885i	−0.192942	+	0.400649i	−0.974887	−	0.222699i	$-0.928513\pi$
$541$	−4.48772	+	9.31885i	−0.192942	+	0.400649i	0.781945	+	0.623347i	$0.214228\pi$
$542$	−24.9212	+	31.2502i	−1.07046	+	1.34231i
$543$	15.6922	+	12.5141i	0.673416	+	0.537032i
$544$	1.18361	−	0.569997i	0.0507469	−	0.0244384i
$545$	2.81642	+	12.3395i	0.120642	+	0.528567i
$546$	14.0439	−	61.5303i	0.601023	−	2.63326i
$547$	−32.2538	−	15.5326i	−1.37907	−	0.664126i	−0.410270	−	0.911964i	$-0.634566\pi$
$547$	−32.2538	−	15.5326i	−1.37907	−	0.664126i	−0.968802	+	0.247838i	$0.920280\pi$
$548$	19.9331	+	41.3915i	0.851500	+	1.76816i
$549$	−13.3144	−	3.03894i	−0.568247	−	0.129699i
$550$	4.00000			0.170561
$551$		0			0
$552$	−38.9706			−1.65870
$553$	−6.65722	−	1.51947i	−0.283094	−	0.0646144i
$554$	−18.1359	−	37.6596i	−0.770521	−	1.60000i
$555$	8.70053	+	4.18995i	0.369317	+	0.177854i
$556$	11.9267	−	52.2542i	0.505804	−	2.21607i
$557$	−3.85266	−	16.8796i	−0.163243	−	0.715212i	−0.988596	−	0.150595i	$-0.951881\pi$
$557$	−3.85266	−	16.8796i	−0.163243	−	0.715212i	0.825353	−	0.564617i	$-0.190976\pi$
$558$	61.9592	−	29.8380i	2.62294	−	1.26314i
$559$	10.7329	+	8.55922i	0.453954	+	0.362016i
$560$	−5.29049	+	6.63406i	−0.223564	+	0.280340i
$561$	0.359441	−	0.746387i	0.0151756	−	0.0315125i
$562$	60.3447	−	48.1233i	2.54549	−	2.02996i
$563$			0.757359i			0.0319189i	0.999873	+	0.0159594i	$0.00508026\pi$
$563$			0.757359i			0.0319189i	−0.999873	+	0.0159594i	$0.994920\pi$
$564$	18.6863	+	23.4319i	0.786837	+	0.986662i
$565$	12.9799	−	2.96258i	0.546069	−	0.124637i
$566$	27.4366	−	6.26221i	1.15324	−	0.263221i
$567$	16.7273	+	20.9753i	0.702479	+	0.880880i
$568$			38.9706i			1.63517i
$569$	−31.0050	+	24.7256i	−1.29980	+	1.03655i	−0.303302	+	0.952895i	$0.598089\pi$
$569$	−31.0050	+	24.7256i	−1.29980	+	1.03655i	−0.996494	+	0.0836584i	$0.973340\pi$
$570$	15.1732	−	31.5074i	0.635534	−	1.31970i
$571$	9.12005	−	11.4362i	0.381662	−	0.478589i	−0.553480	−	0.832863i	$-0.686700\pi$
$571$	9.12005	−	11.4362i	0.381662	−	0.478589i	0.935142	+	0.354274i	$0.115272\pi$
$572$	4.74655	+	3.78525i	0.198463	+	0.158269i
$573$	55.0606	−	26.5158i	2.30019	−	1.10771i
$574$	6.81524	+	29.8595i	0.284463	+	1.24631i
$575$	3.25491	−	14.2607i	0.135739	−	0.594711i
$576$	25.0460	+	12.0615i	1.04358	+	0.502564i
$577$	−12.9293	−	26.8480i	−0.538254	−	1.11770i	−0.975833	−	0.218516i	$-0.929879\pi$
$577$	−12.9293	−	26.8480i	−0.538254	−	1.11770i	0.437580	−	0.899180i	$-0.355836\pi$
$578$	38.3973	+	8.76394i	1.59712	+	0.364532i
$579$	12.4853			0.518871
$580$		0			0
$581$	−21.6569			−0.898478
$582$	25.4867	+	5.81717i	1.05646	+	0.241130i
$583$	1.70470	+	3.53985i	0.0706015	+	0.146605i
$584$	−15.9083	−	7.66102i	−0.658289	−	0.317015i
$585$	2.40955	−	10.5569i	0.0996227	−	0.436476i
$586$	−4.11336	−	18.0218i	−0.169921	−	0.744474i
$587$	−6.89859	+	3.32218i	−0.284735	+	0.137121i	−0.570800	−	0.821089i	$-0.693367\pi$
$587$	−6.89859	+	3.32218i	−0.284735	+	0.137121i	0.286065	+	0.958210i	$0.407653\pi$
$588$	−7.22619	−	5.76269i	−0.298003	−	0.237649i
$589$	−37.6752	+	47.2433i	−1.55238	+	1.94662i
$590$	3.83051	−	7.95414i	0.157700	−	0.327467i
$591$	−3.77502	+	3.01048i	−0.155283	+	0.123834i
$592$			12.0000i			0.493197i
$593$	12.1489	+	15.2342i	0.498894	+	0.625594i	0.965980	−	0.258619i	$-0.0832672\pi$
$593$	12.1489	+	15.2342i	0.498894	+	0.625594i	−0.467085	+	0.884212i	$0.654696\pi$
$594$	−0.403828	+	0.0921712i	−0.0165693	+	0.00378183i
$595$	−2.28440	+	0.521399i	−0.0936512	+	0.0213753i
$596$	−18.6863	−	23.4319i	−0.765422	−	0.959809i
$597$		−	1.17157i		−	0.0479493i
$598$	26.4251	−	21.0733i	1.08060	−	0.861752i
$599$	4.28246	−	8.89261i	0.174976	−	0.363342i	−0.794974	−	0.606643i	$-0.792516\pi$
$599$	4.28246	−	8.89261i	0.174976	−	0.363342i	0.969951	+	0.243300i	$0.0782301\pi$
$600$	26.5778	−	33.3275i	1.08503	−	1.36059i
$601$	−13.4253	−	10.7063i	−0.547628	−	0.436719i	0.310188	−	0.950675i	$-0.399608\pi$
$601$	−13.4253	−	10.7063i	−0.547628	−	0.436719i	−0.857816	+	0.513956i	$0.828179\pi$
$602$	22.0605	−	10.6238i	0.899118	−	0.432992i
$603$	−3.56033	−	15.5988i	−0.144988	−	0.635234i
$604$	12.0478	−	52.7847i	0.490216	−	2.14778i
$605$	−9.75608	−	4.69828i	−0.396641	−	0.191012i
$606$	5.92549	+	12.3044i	0.240706	+	0.499832i
$607$	−7.53417	−	1.71962i	−0.305802	−	0.0697974i	0.0668661	−	0.997762i	$-0.478700\pi$
$607$	−7.53417	−	1.71962i	−0.305802	−	0.0697974i	−0.372668	+	0.927965i	$0.621557\pi$
$608$	−9.51472			−0.385873
$609$		0			0
$610$	−11.6569			−0.471972
$611$	−12.1030	−	2.76242i	−0.489633	−	0.111756i
$612$	−3.89218	−	8.08220i	−0.157332	−	0.326703i
$613$	−8.10872	−	3.90495i	−0.327508	−	0.157720i	0.262903	−	0.964822i	$-0.415320\pi$
$613$	−8.10872	−	3.90495i	−0.327508	−	0.157720i	−0.590411	+	0.807103i	$0.701034\pi$
$614$	−1.55765	+	6.82450i	−0.0628615	+	0.275414i
$615$	2.40955	+	10.5569i	0.0971625	+	0.425697i
$616$	4.65943	−	2.24386i	0.187734	−	0.0904078i
$617$	−0.536564	−	0.427896i	−0.0216013	−	0.0172264i	0.612630	−	0.790370i	$-0.290112\pi$
$617$	−0.536564	−	0.427896i	−0.0216013	−	0.0172264i	−0.634231	+	0.773144i	$0.718683\pi$
$618$	−17.5463	+	22.0024i	−0.705817	+	0.885067i
$619$	−14.5723	+	30.2597i	−0.585711	+	1.21624i	0.371925	+	0.928263i	$0.378698\pi$
$619$	−14.5723	+	30.2597i	−0.585711	+	1.21624i	−0.957637	+	0.287979i	$0.907017\pi$
$620$	30.1446	−	24.0395i	1.21063	−	0.965449i
$621$			1.51472i			0.0607836i
$622$	4.04351	+	5.07040i	0.162130	+	0.203304i
$623$	34.4283	−	7.85804i	1.37934	−	0.314826i
$624$	27.0327	−	6.17004i	1.08218	−	0.246999i
$625$	6.85839	+	8.60015i	0.274336	+	0.344006i
$626$		−	23.7279i		−	0.948358i
$627$	−4.69099	+	3.74094i	−0.187340	+	0.149399i
$628$	14.0948	−	29.2682i	0.562445	−	1.16793i
$629$	−2.06606	+	2.59076i	−0.0823793	+	0.103300i
$630$	−15.1001	−	12.0419i	−0.601601	−	0.479761i
$631$	−33.1813	+	15.9793i	−1.32093	+	0.636124i	−0.955576	−	0.294746i	$-0.904765\pi$
$631$	−33.1813	+	15.9793i	−1.32093	+	0.636124i	−0.365350	+	0.930870i	$0.619051\pi$
$632$	−2.37137	−	10.3897i	−0.0943282	−	0.413279i
$633$	10.4138	−	45.6256i	0.413910	−	1.81346i
$634$	−68.4206	−	32.9496i	−2.71733	−	1.30860i
$635$	1.88442	+	3.91304i	0.0747809	+	0.155284i
$636$	85.4710	+	19.5082i	3.38915	+	0.773550i
$637$	3.82843			0.151688
$638$		0			0
$639$	−24.9706			−0.987820
$640$	20.0410	+	4.57422i	0.792188	+	0.180812i
$641$	−7.72269	−	16.0363i	−0.305028	−	0.633397i	0.690959	−	0.722894i	$-0.257188\pi$
$641$	−7.72269	−	16.0363i	−0.305028	−	0.633397i	−0.995987	+	0.0894967i	$0.971474\pi$
$642$	77.8675	+	37.4990i	3.07319	+	1.47997i
$643$	7.22866	−	31.6708i	0.285070	−	1.24897i	−0.606130	−	0.795365i	$-0.707279\pi$
$643$	7.22866	−	31.6708i	0.285070	−	1.24897i	0.891201	−	0.453609i	$-0.149864\pi$
$644$	−8.81138	−	38.6052i	−0.347217	−	1.52126i
$645$	7.79956	−	3.75607i	0.307107	−	0.147895i
$646$	9.38198	+	7.48188i	0.369129	+	0.294371i
$647$	−24.7256	+	31.0050i	−0.972065	+	1.21893i	0.00367336	+	0.999993i	$0.498831\pi$
$647$	−24.7256	+	31.0050i	−0.972065	+	1.21893i	−0.975739	+	0.218938i	$0.929741\pi$
$648$	−18.1667	+	37.7236i	−0.713657	+	1.48192i
$649$	−1.18425	+	0.944412i	−0.0464861	+	0.0370714i
$650$			36.9706i			1.45010i
$651$	42.8771	+	53.7662i	1.68049	+	2.10726i
$652$	14.6645	−	3.34708i	0.574306	−	0.131082i
$653$	29.3864	−	6.70726i	1.14998	−	0.262475i	0.395289	−	0.918557i	$-0.370644\pi$
$653$	29.3864	−	6.70726i	1.14998	−	0.262475i	0.754690	+	0.656082i	$0.227787\pi$
$654$	−45.9946	−	57.6754i	−1.79853	−	2.25528i
$655$		−	21.3137i		−	0.832796i
$656$	−10.5202	+	8.38958i	−0.410745	+	0.327558i
$657$	4.90883	−	10.1933i	0.191512	−	0.397678i
$658$	−13.8054	+	17.3114i	−0.538190	+	0.674869i
$659$	11.2695	+	8.98712i	0.438997	+	0.350088i	0.817912	−	0.575343i	$-0.195131\pi$
$659$	11.2695	+	8.98712i	0.438997	+	0.350088i	−0.378915	+	0.925431i	$0.623703\pi$
$660$	3.44929	−	1.66109i	0.134264	−	0.0646579i
$661$	−7.41300	−	32.4785i	−0.288332	−	1.26327i	−0.886813	−	0.462129i	$-0.847086\pi$
$661$	−7.41300	−	32.4785i	−0.288332	−	1.26327i	0.598481	−	0.801137i	$-0.295771\pi$
$662$	−1.29695	+	5.68230i	−0.0504073	+	0.220849i
$663$	6.89859	+	3.32218i	0.267919	+	0.129023i
$664$	−14.6648	−	30.4518i	−0.569106	−	1.18176i
$665$	16.5451	+	3.77631i	0.641591	+	0.146439i
$666$	−27.3137			−1.05838
$667$		0			0
$668$	−12.1421			−0.469793
$669$	7.46488	+	1.70381i	0.288609	+	0.0658731i
$670$	−5.92549	−	12.3044i	−0.228922	−	0.475360i
$671$	1.80194	+	0.867767i	0.0695630	+	0.0334998i
$672$	−2.40955	+	10.5569i	−0.0929505	+	0.407243i
$673$	−4.81255	−	21.0852i	−0.185510	−	0.812774i	−0.978946	−	0.204120i	$-0.934567\pi$
$673$	−4.81255	−	21.0852i	−0.185510	−	0.812774i	0.793436	−	0.608654i	$-0.208290\pi$
$674$	47.4157	−	22.8342i	1.82638	−	0.879540i
$675$	−1.29538	−	1.03303i	−0.0498592	−	0.0397614i
$676$	−3.95489	+	4.95927i	−0.152111	+	0.190741i
$677$	9.54544	−	19.8213i	0.366861	−	0.761795i	−0.633063	−	0.774100i	$-0.718203\pi$
$677$	9.54544	−	19.8213i	0.366861	−	0.761795i	0.999924	+	0.0123051i	$0.00391695\pi$
$678$	−60.6685	+	48.3815i	−2.32996	+	1.85808i
$679$			12.6863i			0.486855i
$680$	−2.28001	−	2.85904i	−0.0874344	−	0.109639i
$681$	−19.1640	+	4.37406i	−0.734367	+	0.167614i
$682$	−9.81857	+	2.24102i	−0.375972	+	0.0858132i
$683$	13.0749	+	16.3954i	0.500298	+	0.627354i	0.966297	−	0.257431i	$-0.0828761\pi$
$683$	13.0749	+	16.3954i	0.500298	+	0.627354i	−0.465998	+	0.884786i	$0.654305\pi$
$684$			64.9706i			2.48421i
$685$	−9.38198	+	7.48188i	−0.358467	+	0.285868i
$686$	−17.7765	+	36.9132i	−0.678708	+	1.40935i
$687$	−5.29049	+	6.63406i	−0.201845	+	0.253105i
$688$	8.41044	+	6.70710i	0.320645	+	0.255706i
$689$	−32.7175	+	15.7559i	−1.24644	+	0.600253i
$690$	−4.74275	−	20.7793i	−0.180553	−	0.791056i
$691$	−10.6810	+	46.7965i	−0.406325	+	1.78022i	0.194562	+	0.980890i	$0.437671\pi$
$691$	−10.6810	+	46.7965i	−0.406325	+	1.78022i	−0.600887	+	0.799334i	$0.705186\pi$
$692$	−42.5751	−	20.5031i	−1.61846	−	0.779411i
$693$	1.43776	+	2.98555i	0.0546161	+	0.113412i
$694$	−5.84957	−	1.33513i	−0.222047	−	0.0506807i
$695$	14.0000			0.531050
$696$		0			0
$697$	−3.71573			−0.140743
$698$	−12.1030	−	2.76242i	−0.458104	−	0.104559i
$699$	−19.1834	−	39.8347i	−0.725582	−	1.50669i
$700$	39.0243	+	18.7931i	1.47498	+	0.710313i
$701$	−8.92592	+	39.1070i	−0.337127	+	1.47705i	0.467883	+	0.883790i	$0.345017\pi$
$701$	−8.92592	+	39.1070i	−0.337127	+	1.47705i	−0.805011	+	0.593260i	$0.797840\pi$
$702$	−0.851905	−	3.73244i	−0.0321531	−	0.140872i
$703$	21.6233	−	10.4132i	0.815536	−	0.392742i
$704$	−3.18289	−	2.53827i	−0.119960	−	0.0956646i
$705$	−4.88094	+	6.12051i	−0.183827	+	0.230512i
$706$	28.2513	−	58.6645i	1.06325	−	2.20787i
$707$	−5.18152	+	4.13213i	−0.194871	+	0.155405i
$708$			33.7990i			1.27024i
$709$	−18.1698	−	22.7842i	−0.682382	−	0.855680i	0.313189	−	0.949691i	$-0.398603\pi$
$709$	−18.1698	−	22.7842i	−0.682382	−	0.855680i	−0.995571	+	0.0940107i	$0.970031\pi$
$710$	−20.7793	+	4.74275i	−0.779834	+	0.177992i
$711$	6.65722	−	1.51947i	0.249665	−	0.0569845i
$712$	34.3622	+	43.0888i	1.28778	+	1.61482i
$713$			36.8284i			1.37924i
$714$	10.6774	−	8.51491i	0.399590	−	0.318662i
$715$	−0.688047	+	1.42874i	−0.0257315	+	0.0534320i
$716$	−15.4803	+	19.4116i	−0.578525	+	0.725447i
$717$	−37.1025	−	29.5882i	−1.38562	−	1.10499i
$718$	−8.54594	+	4.11551i	−0.318932	+	0.153589i
$719$	4.48205	+	19.6371i	0.167152	+	0.732341i	0.987127	+	0.159941i	$0.0511305\pi$
$719$	4.48205	+	19.6371i	0.167152	+	0.732341i	−0.819974	+	0.572400i	$0.806012\pi$
$720$	1.88815	−	8.27254i	0.0703673	−	0.308299i
$721$	−12.3044	−	5.92549i	−0.458240	−	0.220677i
$722$	−17.8073	−	36.9772i	−0.662719	−	1.37615i
$723$	−43.1047	−	9.83836i	−1.60308	−	0.365893i
$724$	−31.8284			−1.18289
$725$		0			0
$726$	63.1127			2.34233
$727$	−1.28077	−	0.292328i	−0.0475012	−	0.0108418i	0.198704	−	0.980059i	$-0.436327\pi$
$727$	−1.28077	−	0.292328i	−0.0475012	−	0.0108418i	−0.246205	+	0.969218i	$0.579184\pi$
$728$	20.7392	+	43.0654i	0.768646	+	1.59611i
$729$	−21.4687	−	10.3388i	−0.795136	−	0.382917i
$730$	2.14885	−	9.41474i	0.0795326	−	0.348455i
$731$	0.661012	+	2.89608i	0.0244484	+	0.107116i
$732$	40.2079	−	19.3631i	1.48613	−	0.715681i
$733$	32.2543	+	25.7220i	1.19134	+	0.950063i	0.999508	−	0.0313650i	$-0.00998544\pi$
$733$	32.2543	+	25.7220i	1.19134	+	0.950063i	0.191833	+	0.981428i	$0.438557\pi$
$734$	27.0943	−	33.9751i	1.00007	−	1.25405i
$735$	1.04749	−	2.17513i	0.0386372	−	0.0802309i
$736$	−4.53383	+	3.61561i	−0.167119	+	0.133273i
$737$			2.34315i			0.0863109i
$738$	−19.0959	−	23.9455i	−0.702929	−	0.881445i
$739$	3.96900	−	0.905898i	0.146002	−	0.0333240i	−0.148895	−	0.988853i	$-0.547572\pi$
$739$	3.96900	−	0.905898i	0.146002	−	0.0333240i	0.294897	+	0.955529i	$0.404715\pi$
$740$	−14.9298	+	3.40762i	−0.548829	+	0.125267i
$741$	−34.5762	−	43.3571i	−1.27019	−	1.59276i
$742$			64.7696i			2.37777i
$743$	18.4957	−	14.7498i	0.678540	−	0.541118i	−0.222457	−	0.974943i	$-0.571408\pi$
$743$	18.4957	−	14.7498i	0.678540	−	0.541118i	0.900997	+	0.433825i	$0.142836\pi$
$744$	−46.5670	+	96.6973i	−1.70723	+	3.54509i
$745$	4.88094	−	6.12051i	0.178824	−	0.224238i
$746$	49.6673	+	39.6084i	1.81845	+	1.45017i
$747$	19.5122	−	9.39656i	0.713912	−	0.343802i
$748$	0.292328	+	1.28077i	0.0106886	+	0.0468296i
$749$	−9.33278	+	40.8896i	−0.341012	+	1.49407i
$750$	47.2611	+	22.7597i	1.72573	+	0.831068i
$751$	10.9832	+	22.8069i	0.400783	+	0.832234i	0.999511	+	0.0312816i	$0.00995888\pi$
$751$	10.9832	+	22.8069i	0.400783	+	0.832234i	−0.598728	+	0.800953i	$0.704327\pi$
$752$	−9.48402	−	2.16467i	−0.345847	−	0.0789373i
$753$	−48.4558			−1.76583
$754$		0			0
$755$	14.1421			0.514685
$756$	−4.37283	−	0.998069i	−0.159038	−	0.0362994i
$757$	−11.0704	−	22.9880i	−0.402361	−	0.835512i	−0.999444	−	0.0333324i	$-0.989388\pi$
$757$	−11.0704	−	22.9880i	−0.402361	−	0.835512i	0.597083	−	0.802179i	$-0.296326\pi$
$758$	15.1619	+	7.30158i	0.550705	+	0.265205i
$759$	−0.813727	+	3.56517i	−0.0295364	+	0.129407i
$760$	5.89353	+	25.8212i	0.213781	+	0.936635i
$761$	−41.0824	+	19.7842i	−1.48923	+	0.717177i	−0.988890	−	0.148649i	$-0.952508\pi$
$761$	−41.0824	+	19.7842i	−1.48923	+	0.717177i	−0.500344	+	0.865826i	$0.666793\pi$
$762$	−19.7911	−	15.7828i	−0.716954	−	0.571752i
$763$	22.3203	−	27.9888i	0.808049	−	1.01326i
$764$	−42.0484	+	87.3144i	−1.52126	+	3.15892i
$765$	1.83195	−	1.46093i	0.0662341	−	0.0528199i
$766$		−	8.48528i		−	0.306586i
$767$	−8.72886	−	10.9456i	−0.315181	−	0.395224i
$768$	−70.5412	+	16.1006i	−2.54544	+	0.580980i
$769$	47.8813	−	10.9286i	1.72665	−	0.394096i	0.759941	−	0.649992i	$-0.225228\pi$
$769$	47.8813	−	10.9286i	1.72665	−	0.394096i	0.966704	+	0.255896i	$0.0823706\pi$
$770$	1.76350	+	2.21135i	0.0635520	+	0.0796916i
$771$		−	43.8701i		−	1.57994i
$772$	−15.4795	+	12.3445i	−0.557118	+	0.444287i
$773$	−8.46712	+	17.5822i	−0.304541	+	0.632386i	−0.995933	−	0.0900935i	$-0.971283\pi$
$773$	−8.46712	+	17.5822i	−0.304541	+	0.632386i	0.691392	+	0.722480i	$0.256998\pi$
$774$	−15.2663	+	19.1434i	−0.548737	+	0.688094i
$775$	−31.4955	−	25.1168i	−1.13135	−	0.902223i
$776$	−17.8383	+	8.59046i	−0.640357	+	0.308380i
$777$	−6.07787	−	26.6289i	−0.218042	−	0.955306i
$778$	1.62745	−	7.13034i	0.0583470	−	0.255635i
$779$	24.2466	+	11.6765i	0.868724	+	0.418356i
$780$	15.3529	+	31.8806i	0.549721	+	1.14151i
$781$	3.56517	+	0.813727i	0.127572	+	0.0291174i
$782$	7.31371			0.261538
$783$		0			0
$784$	3.00000			0.107143
$785$	8.27254	+	1.88815i	0.295260	+	0.0673911i
$786$	53.8994	+	111.923i	1.92253	+	3.99217i
$787$	−48.7273	−	23.4658i	−1.73694	−	0.836467i	−0.983952	−	0.178435i	$-0.942896\pi$
$787$	−48.7273	−	23.4658i	−1.73694	−	0.836467i	−0.752990	−	0.658032i	$-0.771389\pi$
$788$	1.70381	−	7.46488i	0.0606957	−	0.265925i
$789$	1.48129	+	6.48995i	0.0527353	+	0.231048i
$790$	5.25123	−	2.52886i	0.186830	−	0.0899728i
$791$	−29.4413	−	23.4787i	−1.04681	−	0.834805i
$792$	−3.22442	+	4.04330i	−0.114575	+	0.143672i
$793$	−8.02046	+	16.6547i	−0.284815	+	0.591424i
$794$	36.5103	−	29.1160i	1.29570	−	1.03329i
$795$			22.8995i			0.812161i
$796$	1.15836	+	1.45254i	0.0410570	+	0.0514838i
$797$	50.4429	−	11.5133i	1.78678	−	0.407821i	0.804304	−	0.594218i	$-0.202538\pi$
$797$	50.4429	−	11.5133i	1.78678	−	0.407821i	0.982474	+	0.186397i	$0.0596812\pi$
$798$	−96.4318	+	22.0099i	−3.41365	+	0.779143i
$799$	−1.67488	−	2.10023i	−0.0592528	−	0.0743007i
$800$		−	6.34315i		−	0.224264i
$801$	−27.6094	+	22.0177i	−0.975529	+	0.777958i
$802$	19.5428	−	40.5811i	0.690081	−	1.43297i
$803$	−1.03303	+	1.29538i	−0.0364549	+	0.0457130i
$804$	40.8775	+	32.5987i	1.44164	+	1.14967i
$805$	9.31885	−	4.48772i	0.328446	−	0.158171i
$806$	−20.7130	−	90.7495i	−0.729583	−	3.19651i
$807$	−16.8985	+	74.0371i	−0.594855	+	2.60623i
$808$	−9.31885	−	4.48772i	−0.327836	−	0.157878i
$809$	15.7432	+	32.6910i	0.553500	+	1.14935i	0.970646	+	0.240515i	$0.0773162\pi$
$809$	15.7432	+	32.6910i	0.553500	+	1.14935i	−0.417146	+	0.908840i	$0.636970\pi$
$810$	−22.3254	−	5.09562i	−0.784433	−	0.179042i
$811$	−10.8284			−0.380238			−0.190119	−	0.981761i	$-0.560887\pi$
$811$	−10.8284			−0.380238			−0.190119	+	0.981761i	$0.560887\pi$
$812$		0			0
$813$	39.9706			1.40183
$814$	3.89971	+	0.890084i	0.136685	+	0.0311974i
$815$	1.70470	+	3.53985i	0.0597130	+	0.123995i
$816$	5.40581	+	2.60330i	0.189241	+	0.0911338i
$817$	4.78748	−	20.9753i	0.167493	−	0.733833i
$818$	10.1912	+	44.6507i	0.356328	+	1.56118i
$819$	−27.5943	+	13.2887i	−0.964225	+	0.464346i
$820$	−13.4253	−	10.7063i	−0.468831	−	0.373880i
$821$	0.926058	−	1.16124i	0.0323196	−	0.0405275i	−0.765409	−	0.643544i	$-0.777463\pi$
$821$	0.926058	−	1.16124i	0.0323196	−	0.0405275i	0.797729	+	0.603017i	$0.206035\pi$
$822$	30.3463	−	63.0148i	1.05845	−	2.19789i
$823$	42.4412	−	33.8457i	1.47941	−	1.17979i	0.537798	−	0.843074i	$-0.319256\pi$
$823$	42.4412	−	33.8457i	1.47941	−	1.17979i	0.941607	−	0.336713i	$-0.109315\pi$
$824$		−	21.3137i		−	0.742498i
$825$	−2.49396	−	3.12733i	−0.0868285	−	0.108880i
$826$	−24.3445	+	5.55647i	−0.847053	+	0.193334i
$827$	−32.0746	+	7.32083i	−1.11534	+	0.254570i	−0.740194	−	0.672394i	$-0.765266\pi$
$827$	−32.0746	+	7.32083i	−1.11534	+	0.254570i	−0.375151	+	0.926964i	$0.622409\pi$
$828$	24.6889	+	30.9589i	0.858000	+	1.07590i
$829$		−	29.7990i		−	1.03496i	−0.855695	−	0.517481i	$-0.826870\pi$
$829$		−	29.7990i		−	1.03496i	0.855695	−	0.517481i	$-0.173130\pi$
$830$	14.4524	−	11.5254i	0.501649	−	0.400052i
$831$	−18.1359	+	37.6596i	−0.629127	+	1.30640i
$832$	23.4603	−	29.4183i	0.813340	−	1.01990i
$833$	0.647690	+	0.516516i	0.0224411	+	0.0178962i
$834$	−73.5172	+	35.4040i	−2.54569	+	1.22594i
$835$	−0.705741	−	3.09205i	−0.0244232	−	0.107005i
$836$	2.11722	−	9.27616i	0.0732257	−	0.320823i
$837$	3.75846	+	1.80998i	0.129911	+	0.0625620i
$838$	9.96655	+	20.6958i	0.344289	+	0.714923i
$839$	−7.73014	−	1.76435i	−0.266874	−	0.0609122i	0.0869898	−	0.996209i	$-0.472275\pi$
$839$	−7.73014	−	1.76435i	−0.266874	−	0.0609122i	−0.353864	+	0.935297i	$0.615132\pi$
$840$	30.1421			1.04000
$841$		0			0
$842$	−89.5980			−3.08775
$843$	−75.2486	−	17.1750i	−2.59170	−	0.591539i
$844$	32.1999	+	66.8638i	1.10837	+	2.30155i
$845$	−1.49277	−	0.718882i	−0.0513530	−	0.0247303i
$846$	4.92709	−	21.5870i	0.169397	−	0.742176i
$847$	6.81524	+	29.8595i	0.234174	+	1.02599i
$848$	−25.6378	+	12.3465i	−0.880407	+	0.423982i
$849$	−22.0024	−	17.5463i	−0.755121	−	0.602189i
$850$	−4.98792	+	6.25465i	−0.171084	+	0.214533i
$851$	6.34660	−	13.1788i	0.217559	−	0.451765i
$852$	63.7959	−	50.8755i	2.18561	−	1.74297i
$853$			22.9706i			0.786497i	0.919432	+	0.393249i	$0.128649\pi$
$853$			22.9706i			0.786497i	−0.919432	+	0.393249i	$0.871351\pi$
$854$	20.5568	+	25.7774i	0.703440	+	0.882085i
$855$	−16.5451	+	3.77631i	−0.565830	+	0.129147i
$856$	−63.8147	+	14.5653i	−2.18114	+	0.497832i
$857$	−3.84791	−	4.82513i	−0.131442	−	0.164823i	0.711755	−	0.702428i	$-0.247901\pi$
$857$	−3.84791	−	4.82513i	−0.131442	−	0.164823i	−0.843197	+	0.537605i	$0.819329\pi$
$858$		−	9.24264i		−	0.315539i
$859$	15.4239	−	12.3002i	0.526257	−	0.419676i	−0.323989	−	0.946061i	$-0.605024\pi$
$859$	15.4239	−	12.3002i	0.526257	−	0.419676i	0.850247	+	0.526385i	$0.176453\pi$
$860$	−5.95632	+	12.3684i	−0.203109	+	0.421760i
$861$	19.0959	−	23.9455i	0.650786	−	0.816060i
$862$	−37.1025	−	29.5882i	−1.26372	−	1.00778i
$863$	15.4180	−	7.42492i	0.524835	−	0.252747i	−0.152654	−	0.988280i	$-0.548782\pi$
$863$	15.4180	−	7.42492i	0.524835	−	0.252747i	0.677490	+	0.735532i	$0.263068\pi$
$864$	0.146164	+	0.640386i	0.00497259	+	0.0217864i
$865$	2.74661	−	12.0337i	0.0933875	−	0.409157i
$866$	66.6187	+	32.0819i	2.26379	+	1.09019i
$867$	−17.0884	−	35.4845i	−0.580353	−	1.20512i
$868$	−106.320	−	24.2668i	−3.60872	−	0.823667i
$869$	−1.00000			−0.0339227
$870$		0			0
$871$	−21.6569			−0.733815
$872$	54.4693	+	12.4323i	1.84456	+	0.421009i
$873$	−5.50438	−	11.4300i	−0.186295	−	0.386845i
$874$	−47.7248	−	22.9831i	−1.61432	−	0.777414i
$875$	−5.66446	+	24.8176i	−0.191494	+	0.838988i
$876$	8.22672	+	36.0436i	0.277955	+	1.21780i
$877$	33.4639	−	16.1154i	1.13000	−	0.544177i	0.227029	−	0.973888i	$-0.427099\pi$
$877$	33.4639	−	16.1154i	1.13000	−	0.544177i	0.902967	+	0.429711i	$0.141384\pi$
$878$	−0.647690	−	0.516516i	−0.0218585	−	0.0174316i
$879$	−11.5254	+	14.4524i	−0.388742	+	0.487467i
$880$	−0.539162	+	1.11958i	−0.0181751	+	0.0377411i
$881$	−10.9456	+	8.72886i	−0.368768	+	0.294083i	−0.790287	−	0.612737i	$-0.790069\pi$
$881$	−10.9456	+	8.72886i	−0.368768	+	0.294083i	0.421519	+	0.906820i	$0.361497\pi$
$882$			6.82843i			0.229925i
$883$	−23.9585	−	30.0430i	−0.806267	−	1.01103i	−0.999553	−	0.0298842i	$-0.990486\pi$
$883$	−23.9585	−	30.0430i	−0.806267	−	1.01103i	0.193287	−	0.981142i	$-0.438085\pi$
$884$	−11.8377	+	2.70188i	−0.398145	+	0.0908740i
$885$	−8.60708	+	1.96451i	−0.289324	+	0.0660363i
$886$	36.6422	+	45.9479i	1.23102	+	1.54365i
$887$			17.1005i			0.574179i	0.957904	+	0.287089i	$0.0926877\pi$
$887$			17.1005i			0.574179i	−0.957904	+	0.287089i	$0.907312\pi$
$888$	33.3275	−	26.5778i	1.11840	−	0.891891i
$889$	5.32995	−	11.0677i	0.178761	−	0.371200i
$890$	−18.7933	+	23.5661i	−0.629953	+	0.789936i
$891$	3.07176	+	2.44965i	0.102908	+	0.0820663i
$892$	−10.9397	+	5.26828i	−0.366288	+	0.176395i
$893$	4.32933	+	18.9680i	0.144876	+	0.634741i
$894$	−10.1531	+	44.4834i	−0.339569	+	1.48775i
$895$	−5.84304	−	2.81386i	−0.195311	−	0.0940569i
$896$	−25.2269	−	52.3843i	−0.842772	−	1.75004i
$897$	−32.9516	−	7.52098i	−1.10022	−	0.251118i
$898$	−84.4264			−2.81735
$899$		0			0
$900$	−43.3137			−1.44379
$901$	−7.66085	−	1.74854i	−0.255220	−	0.0582523i
$902$	1.94609	+	4.04110i	0.0647977	+	0.134554i
$903$	−22.0605	−	10.6238i	−0.734127	−	0.353537i
$904$	13.0775	−	57.2961i	0.434950	−	1.90564i
$905$	−1.84997	−	8.10527i	−0.0614952	−	0.269428i
$906$	−74.2636	+	35.7635i	−2.46724	+	1.18816i
$907$	−17.4225	−	13.8940i	−0.578506	−	0.461343i	0.289997	−	0.957028i	$-0.406346\pi$
$907$	−17.4225	−	13.8940i	−0.578506	−	0.461343i	−0.868503	+	0.495684i	$0.834917\pi$
$908$	19.4352	−	24.3709i	0.644978	−	0.808777i
$909$	2.87553	−	5.97110i	0.0953753	−	0.198049i
$910$	−20.4387	+	16.2994i	−0.677538	+	0.540318i
$911$			15.4437i			0.511671i	0.966720	+	0.255835i	$0.0823505\pi$
$911$			15.4437i			0.511671i	−0.966720	+	0.255835i	$0.917649\pi$
$912$	−27.0943	−	33.9751i	−0.897181	−	1.12503i
$913$	−3.09205	+	0.705741i	−0.102332	+	0.0233566i
$914$	2.42297	−	0.553027i	0.0801447	−	0.0182925i
$915$	7.26793	+	9.11370i	0.240270	+	0.301289i
$916$		−	13.4558i		−	0.444594i
$917$	−47.1321	+	37.5866i	−1.55644	+	1.24122i
$918$	0.359441	−	0.746387i	0.0118633	−	0.0246344i
$919$	5.07654	−	6.36578i	0.167460	−	0.209988i	−0.691020	−	0.722836i	$-0.742838\pi$
$919$	5.07654	−	6.36578i	0.167460	−	0.209988i	0.858479	+	0.512848i	$0.171410\pi$
$920$	12.6204	+	10.0645i	0.416083	+	0.331815i
$921$	6.30678	−	3.03719i	0.207816	−	0.100079i
$922$	7.52098	+	32.9516i	0.247690	+	1.08520i
$923$	−7.52098	+	32.9516i	−0.247556	+	1.08461i
$924$	−9.75608	−	4.69828i	−0.320951	−	0.154562i
$925$	6.94214	+	14.4155i	0.228256	+	0.473979i
$926$	61.1958	+	13.9675i	2.01102	+	0.459002i
$927$	13.6569			0.448550
$928$		0			0
$929$	18.6863			0.613077			0.306539	−	0.951858i	$-0.400829\pi$
$929$	18.6863			0.613077			0.306539	+	0.951858i	$0.400829\pi$
$930$	−57.2268	−	13.0616i	−1.87654	−	0.428308i
$931$	−2.60330	−	5.40581i	−0.0853198	−	0.177168i
$932$	63.1694	+	30.4208i	2.06918	+	0.996465i
$933$	1.44311	−	6.32268i	0.0472453	−	0.206995i
$934$	20.6050	+	90.2764i	0.674216	+	2.95393i
$935$	−0.309164	+	0.148885i	−0.0101107	+	0.00486907i
$936$	−37.3708	−	29.8022i	−1.22150	−	0.974115i
$937$	10.3670	−	12.9998i	0.338676	−	0.424686i	−0.583105	−	0.812397i	$-0.698163\pi$
$937$	10.3670	−	12.9998i	0.338676	−	0.424686i	0.921781	+	0.387710i	$0.126734\pi$
$938$	−16.7598	+	34.8021i	−0.547227	+	1.13633i
$939$	−18.5512	+	14.7941i	−0.605397	+	0.482788i
$940$		−	12.4142i		−	0.404907i
$941$	35.2883	+	44.2501i	1.15036	+	1.44251i	0.876928	+	0.480621i	$0.159589\pi$
$941$	35.2883	+	44.2501i	1.15036	+	1.44251i	0.273436	+	0.961890i	$0.411840\pi$
$942$	−48.2159	+	11.0050i	−1.57096	+	0.358561i
$943$	15.9908	−	3.64979i	0.520732	−	0.118854i
$944$	−6.84003	−	8.57713i	−0.222624	−	0.279162i
$945$		−	1.17157i		−	0.0381113i
$946$	2.80348	−	2.23570i	0.0911490	−	0.0726889i
$947$	1.13470	−	2.35624i	0.0368729	−	0.0765674i	−0.881719	−	0.471776i	$-0.843613\pi$
$947$	1.13470	−	2.35624i	0.0368729	−	0.0765674i	0.918592	+	0.395208i	$0.129328\pi$
$948$	−13.9124	+	17.4456i	−0.451853	+	0.566605i
$949$	−11.9727	−	9.54794i	−0.388652	−	0.309939i
$950$	52.2032	−	25.1397i	1.69369	−	0.815640i
$951$	16.8985	+	74.0371i	0.547971	+	2.40082i
$952$	−2.30157	+	10.0838i	−0.0745942	+	0.326819i
$953$	32.0992	+	15.4582i	1.03979	+	0.500739i	0.874256	−	0.485465i	$-0.161350\pi$
$953$	32.0992	+	15.4582i	1.03979	+	0.500739i	0.165538	+	0.986203i	$0.447064\pi$
$954$	−28.1025	−	58.3554i	−0.909851	−	1.88932i
$955$	−24.6790	−	5.63283i	−0.798595	−	0.182274i
$956$	75.2548			2.43392
$957$		0			0
$958$	−16.6569			−0.538159
$959$	33.0902	+	7.55261i	1.06854	+	0.243887i
$960$	−10.2952	−	21.3781i	−0.332275	−	0.689976i
$961$	63.4520	+	30.5569i	2.04684	+	0.985706i
$962$	−8.22672	+	36.0436i	−0.265240	+	1.16209i
$963$	−9.33278	−	40.8896i	−0.300745	−	1.31765i
$964$	63.1694	−	30.4208i	2.03455	−	0.979787i
$965$	−4.04330	−	3.22442i	−0.130158	−	0.103798i
$966$	−37.5866	+	47.1321i	−1.20933	+	1.51645i
$967$	15.2912	−	31.7525i	0.491732	−	1.02109i	−0.496487	−	0.868044i	$-0.665377\pi$
$967$	15.2912	−	31.7525i	0.491732	−	1.02109i	0.988219	−	0.153048i	$-0.0489089\pi$
$968$	−37.3708	+	29.8022i	−1.20114	+	0.957878i
$969$		−	12.0000i		−	0.385496i
$970$	−6.75141	−	8.46601i	−0.216775	−	0.271827i
$971$	−15.2643	+	3.48398i	−0.489855	+	0.111806i	−0.460312	−	0.887757i	$-0.652262\pi$
$971$	−15.2643	+	3.48398i	−0.489855	+	0.111806i	−0.0295431	+	0.999564i	$0.509405\pi$
$972$	80.8329	−	18.4496i	2.59272	−	0.591771i
$973$	−24.6889	−	30.9589i	−0.791491	−	0.992498i
$974$			27.7990i			0.890737i
$975$	28.9047	−	23.0508i	0.925693	−	0.738215i
$976$	−6.28493	+	13.0508i	−0.201176	+	0.417746i
$977$	22.5526	−	28.2801i	0.721522	−	0.904760i	−0.276901	−	0.960898i	$-0.589307\pi$
$977$	22.5526	−	28.2801i	0.721522	−	0.904760i	0.998423	+	0.0561387i	$0.0178789\pi$
$978$	−17.9035	−	14.2776i	−0.572492	−	0.456547i
$979$	4.65943	−	2.24386i	0.148916	−	0.0717141i
$980$	0.851905	+	3.73244i	0.0272131	+	0.119228i
$981$	−7.96602	+	34.9014i	−0.254336	+	1.11432i
$982$	−46.2055	−	22.2514i	−1.47448	−	0.710071i
$983$	−9.48906	−	19.7042i	−0.302654	−	0.628468i	0.693067	−	0.720873i	$-0.256259\pi$
$983$	−9.48906	−	19.7042i	−0.302654	−	0.628468i	−0.995721	+	0.0924051i	$0.970545\pi$
$984$	46.6006	+	10.6363i	1.48557	+	0.339072i
$985$	2.00000			0.0637253
$986$		0			0
$987$	22.1421			0.704792
$988$	85.7363	+	19.5687i	2.72763	+	0.622565i
$989$	−5.68939	−	11.8141i	−0.180912	−	0.375668i
$990$	−2.54832	−	1.22721i	−0.0809911	−	0.0390032i
$991$	−2.85459	+	12.5068i	−0.0906792	+	0.397291i	−0.999816	−	0.0192072i	$-0.993886\pi$
$991$	−2.85459	+	12.5068i	−0.0906792	+	0.397291i	0.909136	+	0.416499i	$0.136743\pi$
$992$	3.55378	+	15.5701i	0.112833	+	0.494353i
$993$	5.25123	−	2.52886i	0.166643	−	0.0802509i
$994$	47.1321	+	37.5866i	1.49494	+	1.19218i
$995$	−0.302568	+	0.379408i	−0.00959205	+	0.0120281i
$996$	−30.7058	+	63.7612i	−0.972949	+	2.02035i
$997$	−22.1135	+	17.6350i	−0.700343	+	0.558505i	−0.907628	−	0.419776i	$-0.862109\pi$
$997$	−22.1135	+	17.6350i	−0.700343	+	0.558505i	0.207285	+	0.978281i	$0.433537\pi$
$998$			45.7990i			1.44974i
$999$	−1.03303	−	1.29538i	−0.0326837	−	0.0409840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.k.236.4		24
29.2	odd	28		841.2.d.j.190.2		12
29.3	odd	28		841.2.d.j.645.2		12
29.4	even	14	inner	841.2.e.k.267.4		24
29.5	even	14	inner	841.2.e.k.651.4		24
29.6	even	14		841.2.b.a.840.4		4
29.7	even	7	inner	841.2.e.k.196.1		24
29.8	odd	28		841.2.d.f.778.2		12
29.9	even	14	inner	841.2.e.k.63.1		24
29.10	odd	28		841.2.d.f.574.2		12
29.11	odd	28		841.2.d.j.571.2		12
29.12	odd	4		841.2.d.f.605.1		12
29.13	even	14	inner	841.2.e.k.270.1		24
29.14	odd	28		29.2.a.a.1.1	✓	2
29.15	odd	28		841.2.a.d.1.2		2
29.16	even	7	inner	841.2.e.k.270.4		24
29.17	odd	4		841.2.d.j.605.2		12
29.18	odd	28		841.2.d.f.571.1		12
29.19	odd	28		841.2.d.j.574.1		12
29.20	even	7	inner	841.2.e.k.63.4		24
29.21	odd	28		841.2.d.j.778.1		12
29.22	even	14	inner	841.2.e.k.196.4		24
29.23	even	7		841.2.b.a.840.1		4
29.24	even	7	inner	841.2.e.k.651.1		24
29.25	even	7	inner	841.2.e.k.267.1		24
29.26	odd	28		841.2.d.f.645.1		12
29.27	odd	28		841.2.d.f.190.1		12
29.28	even	2	inner	841.2.e.k.236.1		24
87.14	even	28		261.2.a.d.1.2		2
87.44	even	28		7569.2.a.c.1.1		2
116.43	even	28		464.2.a.h.1.1		2
145.14	odd	28		725.2.a.b.1.2		2
145.43	even	28		725.2.b.b.349.4		4
145.72	even	28		725.2.b.b.349.1		4
203.188	even	28		1421.2.a.j.1.1		2
232.43	even	28		1856.2.a.w.1.2		2
232.101	odd	28		1856.2.a.r.1.1		2
319.43	even	28		3509.2.a.j.1.2		2
348.275	odd	28		4176.2.a.bq.1.2		2
377.246	odd	28		4901.2.a.g.1.2		2
435.14	even	28		6525.2.a.o.1.1		2
493.101	odd	28		8381.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.1	✓	2	29.14	odd	28
261.2.a.d.1.2		2	87.14	even	28
464.2.a.h.1.1		2	116.43	even	28
725.2.a.b.1.2		2	145.14	odd	28
725.2.b.b.349.1		4	145.72	even	28
725.2.b.b.349.4		4	145.43	even	28
841.2.a.d.1.2		2	29.15	odd	28
841.2.b.a.840.1		4	29.23	even	7
841.2.b.a.840.4		4	29.6	even	14
841.2.d.f.190.1		12	29.27	odd	28
841.2.d.f.571.1		12	29.18	odd	28
841.2.d.f.574.2		12	29.10	odd	28
841.2.d.f.605.1		12	29.12	odd	4
841.2.d.f.645.1		12	29.26	odd	28
841.2.d.f.778.2		12	29.8	odd	28
841.2.d.j.190.2		12	29.2	odd	28
841.2.d.j.571.2		12	29.11	odd	28
841.2.d.j.574.1		12	29.19	odd	28
841.2.d.j.605.2		12	29.17	odd	4
841.2.d.j.645.2		12	29.3	odd	28
841.2.d.j.778.1		12	29.21	odd	28
841.2.e.k.63.1		24	29.9	even	14	inner
841.2.e.k.63.4		24	29.20	even	7	inner
841.2.e.k.196.1		24	29.7	even	7	inner
841.2.e.k.196.4		24	29.22	even	14	inner
841.2.e.k.236.1		24	29.28	even	2	inner
841.2.e.k.236.4		24	1.1	even	1	trivial
841.2.e.k.267.1		24	29.25	even	7	inner
841.2.e.k.267.4		24	29.4	even	14	inner
841.2.e.k.270.1		24	29.13	even	14	inner
841.2.e.k.270.4		24	29.16	even	7	inner
841.2.e.k.651.1		24	29.24	even	7	inner
841.2.e.k.651.4		24	29.5	even	14	inner
1421.2.a.j.1.1		2	203.188	even	28
1856.2.a.r.1.1		2	232.101	odd	28
1856.2.a.w.1.2		2	232.43	even	28
3509.2.a.j.1.2		2	319.43	even	28
4176.2.a.bq.1.2		2	348.275	odd	28
4901.2.a.g.1.2		2	377.246	odd	28
6525.2.a.o.1.1		2	435.14	even	28
7569.2.a.c.1.1		2	87.44	even	28
8381.2.a.e.1.1		2	493.101	odd	28

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.35368 + 0.537213i) q^{2} +(-1.04749 - 2.17513i) q^{3} +(3.44929 + 1.66109i) q^{4} +(-0.222521 + 0.974928i) q^{5} +(-1.29695 - 5.68230i) q^{6} +(2.54832 - 1.22721i) q^{7} +(3.45117 + 2.75222i) q^{8} +(-1.76350 + 2.21135i) q^{9} +O(q^{10})\)	\(q+(2.35368 + 0.537213i) q^{2} +(-1.04749 - 2.17513i) q^{3} +(3.44929 + 1.66109i) q^{4} +(-0.222521 + 0.974928i) q^{5} +(-1.29695 - 5.68230i) q^{6} +(2.54832 - 1.22721i) q^{7} +(3.45117 + 2.75222i) q^{8} +(-1.76350 + 2.21135i) q^{9} +(-1.04749 + 2.17513i) q^{10} +(0.323845 - 0.258258i) q^{11} -9.24264i q^{12} +(2.38699 + 2.99318i) q^{13} +(6.65722 - 1.51947i) q^{14} +(2.35368 - 0.537213i) q^{15} +(1.87047 + 2.34549i) q^{16} +0.828427i q^{17} +(-5.33868 + 4.25745i) q^{18} +(2.60330 - 5.40581i) q^{19} +(-2.38699 + 2.99318i) q^{20} +(-5.33868 - 4.25745i) q^{21} +(0.900969 - 0.433884i) q^{22} +(-0.813727 - 3.56517i) q^{23} +(2.37137 - 10.3897i) q^{24} +(3.60388 + 1.73553i) q^{25} +(4.01023 + 8.32733i) q^{26} +(-0.403828 - 0.0921712i) q^{27} +10.8284 q^{28} +5.82843 q^{30} +(-9.81857 - 2.24102i) q^{31} +(-0.688047 - 1.42874i) q^{32} +(-0.900969 - 0.433884i) q^{33} +(-0.445042 + 1.94986i) q^{34} +(0.629384 + 2.75751i) q^{35} +(-9.75608 + 4.69828i) q^{36} +(3.12733 + 2.49396i) q^{37} +(9.03143 - 11.3250i) q^{38} +(4.01023 - 8.32733i) q^{39} +(-3.45117 + 2.75222i) q^{40} +4.48528i q^{41} +(-10.2784 - 12.8887i) q^{42} +(3.49588 - 0.797913i) q^{43} +(1.54603 - 0.352871i) q^{44} +(-1.76350 - 2.21135i) q^{45} -8.82843i q^{46} +(-2.53520 + 2.02175i) q^{47} +(3.14246 - 6.52539i) q^{48} +(0.623490 - 0.781831i) q^{49} +(7.55003 + 6.02095i) q^{50} +(1.80194 - 0.867767i) q^{51} +(3.26146 + 14.2894i) q^{52} +(-2.11067 + 9.24747i) q^{53} +(-0.900969 - 0.433884i) q^{54} +(0.179721 + 0.373194i) q^{55} +(12.1722 + 2.77824i) q^{56} -14.4853 q^{57} -3.65685 q^{59} +(9.01091 + 2.05668i) q^{60} +(2.09498 + 4.35026i) q^{61} +(-21.9059 - 10.5493i) q^{62} +(-1.78017 + 7.79942i) q^{63} +(-2.18703 - 9.58201i) q^{64} +(-3.44929 + 1.66109i) q^{65} +(-1.88751 - 1.50524i) q^{66} +(-3.52699 + 4.42271i) q^{67} +(-1.37609 + 2.85749i) q^{68} +(-6.90234 + 5.50443i) q^{69} +6.82843i q^{70} +(5.50443 + 6.90234i) q^{71} +(-12.1722 + 2.77824i) q^{72} +(-3.89971 + 0.890084i) q^{73} +(6.02095 + 7.55003i) q^{74} -9.65685i q^{75} +(17.9591 - 14.3219i) q^{76} +(0.508326 - 1.05555i) q^{77} +(13.9124 - 17.4456i) q^{78} +(-1.88751 - 1.50524i) q^{79} +(-2.70291 + 1.30165i) q^{80} +(2.11067 + 9.24747i) q^{81} +(-2.40955 + 10.5569i) q^{82} +(-6.89859 - 3.32218i) q^{83} +(-11.3426 - 23.5533i) q^{84} +(-0.807657 - 0.184342i) q^{85} +8.65685 q^{86} +1.82843 q^{88} +(12.1722 + 2.77824i) q^{89} +(-2.96274 - 6.15220i) q^{90} +(9.75608 + 4.69828i) q^{91} +(3.11529 - 13.6490i) q^{92} +(5.41031 + 23.7041i) q^{93} +(-7.05317 + 3.39663i) q^{94} +(4.69099 + 3.74094i) q^{95} +(-2.38699 + 2.99318i) q^{96} +(-1.94609 + 4.04110i) q^{97} +(1.88751 - 1.50524i) q^{98} +1.17157i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6}+O(q^{10}) \) 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6	\( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6} - 4 q^{13} - 12 q^{16} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{24} + 16 q^{25} + 192 q^{28} + 72 q^{30} - 4 q^{33} - 8 q^{34} - 32 q^{36} - 24 q^{38} + 32 q^{42} - 4 q^{49} + 8 q^{51} + 36 q^{52} - 4 q^{53} - 4 q^{54} - 144 q^{57} + 48 q^{59} - 52 q^{62} - 32 q^{63} - 28 q^{64} - 4 q^{65} - 24 q^{71} - 16 q^{74} - 44 q^{78} - 12 q^{80} + 4 q^{81} - 32 q^{82} - 8 q^{83} + 72 q^{86} - 24 q^{88} + 32 q^{91} + 56 q^{92} + 52 q^{93} - 20 q^{94} + 4 q^{96}+O(q^{100}) \) 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6 - 4 * q^13 - 12 * q^16 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 20 * q^24 + 16 * q^25 + 192 * q^28 + 72 * q^30 - 4 * q^33 - 8 * q^34 - 32 * q^36 - 24 * q^38 + 32 * q^42 - 4 * q^49 + 8 * q^51 + 36 * q^52 - 4 * q^53 - 4 * q^54 - 144 * q^57 + 48 * q^59 - 52 * q^62 - 32 * q^63 - 28 * q^64 - 4 * q^65 - 24 * q^71 - 16 * q^74 - 44 * q^78 - 12 * q^80 + 4 * q^81 - 32 * q^82 - 8 * q^83 + 72 * q^86 - 24 * q^88 + 32 * q^91 + 56 * q^92 + 52 * q^93 - 20 * q^94 + 4 * q^96

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