LMFDB - Embedded newform 798.2.bu.a.53.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(53,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 12, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bu (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,-81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.4
Character	$\chi$	$=$	798.53
Dual form			798.2.bu.a.527.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 + 0.984808i) q^{2} +(-1.60498 - 0.651180i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.122408 + 0.336313i) q^{5} +(0.362585 - 1.69367i) q^{6} +(-2.54737 + 0.714792i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.15193 + 2.09026i) q^{9} +(-0.352459 - 0.0621481i) q^{10} -4.13664i q^{11} +(1.73091 + 0.0629732i) q^{12} +(0.464568 + 0.0819158i) q^{13} +(-1.14628 - 2.38454i) q^{14} +(0.415462 - 0.460066i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.75354 - 2.08979i) q^{17} +(-1.68483 + 2.48221i) q^{18} +(3.58887 + 2.47387i) q^{19} -0.357897i q^{20} +(4.55393 + 0.511566i) q^{21} +(4.07380 - 0.718321i) q^{22} +(1.60312 + 0.282674i) q^{23} +(0.238552 + 1.71554i) q^{24} +(3.73210 + 3.13160i) q^{25} +0.471734i q^{26} +(-2.09267 - 4.75613i) q^{27} +(2.14927 - 1.54294i) q^{28} +(-0.141207 + 0.0513951i) q^{29} +(0.525221 + 0.329261i) q^{30} +(-0.771575 + 0.445469i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-2.69370 + 6.63924i) q^{33} +(1.75354 - 2.08979i) q^{34} +(0.0714238 - 0.944208i) q^{35} +(-2.73706 - 1.22820i) q^{36} +(8.04416 - 4.64430i) q^{37} +(-1.81308 + 3.96393i) q^{38} +(-0.692281 - 0.433991i) q^{39} +(0.352459 - 0.0621481i) q^{40} +(1.78310 + 10.1124i) q^{41} +(0.286988 + 4.57358i) q^{42} +(3.95923 - 3.32219i) q^{43} +(1.41482 + 3.88717i) q^{44} +(-0.966395 + 0.467857i) q^{45} +1.62785i q^{46} +(7.29024 - 8.68817i) q^{47} +(-1.64806 + 0.532829i) q^{48} +(5.97814 - 3.64167i) q^{49} +(-2.43596 + 4.21920i) q^{50} +(1.45357 + 4.49595i) q^{51} +(-0.464568 + 0.0819158i) q^{52} +(11.6079 - 4.22494i) q^{53} +(4.32048 - 2.88677i) q^{54} +(1.39121 + 0.506358i) q^{55} +(1.89271 + 1.84869i) q^{56} +(-4.14913 - 6.30751i) q^{57} +(-0.0751346 - 0.130137i) q^{58} +(3.59807 - 3.01914i) q^{59} +(-0.233055 + 0.574417i) q^{60} +(-1.59361 + 9.03782i) q^{61} +(-0.572684 - 0.682499i) q^{62} +(-6.97585 - 3.78648i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0844161 + 0.146213i) q^{65} +(-7.00613 - 1.49989i) q^{66} +(1.59956 + 0.282046i) q^{67} +(2.36254 + 1.36401i) q^{68} +(-2.38891 - 1.49761i) q^{69} +(0.942266 - 0.0936213i) q^{70} +(-2.88214 + 2.41840i) q^{71} +(0.734257 - 2.90876i) q^{72} +(-0.136857 - 0.0498120i) q^{73} +(5.97059 + 7.11548i) q^{74} +(-3.95071 - 7.45643i) q^{75} +(-4.21855 - 1.09721i) q^{76} +(2.95684 + 10.5375i) q^{77} +(0.307184 - 0.757125i) q^{78} +(-2.38818 - 2.84612i) q^{79} +(0.122408 + 0.336313i) q^{80} +(0.261597 + 8.99620i) q^{81} +(-9.64917 + 3.51201i) q^{82} +(-3.58230 - 2.06824i) q^{83} +(-4.45426 + 1.07682i) q^{84} +(0.917471 - 0.333932i) q^{85} +(3.95923 + 3.32219i) q^{86} +(0.260102 + 0.00946293i) q^{87} +(-3.58244 + 2.06832i) q^{88} +(-8.53780 + 3.10751i) q^{89} +(-0.628562 - 0.870471i) q^{90} +(-1.24198 + 0.123400i) q^{91} +(-1.60312 + 0.282674i) q^{92} +(1.52844 - 0.212535i) q^{93} +(9.82211 + 5.67080i) q^{94} +(-1.27130 + 0.904161i) q^{95} +(-0.810916 - 1.53049i) q^{96} +(5.26058 - 14.4533i) q^{97} +(4.62444 + 5.25495i) q^{98} +(8.64668 - 8.90176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) $ 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	−1.60498	−	0.651180i	−0.926636	−	0.375959i
$3$	−1.60498	−	0.651180i	−0.926636	−	0.375959i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.122408	+	0.336313i	−0.0547424	+	0.150404i	−0.964050	−	0.265721i	$-0.914390\pi$
$5$	−0.122408	+	0.336313i	−0.0547424	+	0.150404i	0.909307	+	0.416125i	$0.136612\pi$
$6$	0.362585	−	1.69367i	0.148025	−	0.691440i
$7$	−2.54737	+	0.714792i	−0.962814	+	0.270166i
$7$	−2.54737	+	0.714792i	−0.962814	+	0.270166i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.15193	+	2.09026i	0.717310	+	0.696755i
$10$	−0.352459	−	0.0621481i	−0.111457	−	0.0196530i
$11$		−	4.13664i		−	1.24725i	−0.781726	−	0.623623i	$-0.785660\pi$
$11$		−	4.13664i		−	1.24725i	0.781726	−	0.623623i	$-0.214340\pi$
$12$	1.73091	+	0.0629732i	0.499669	+	0.0181788i
$13$	0.464568	+	0.0819158i	0.128848	+	0.0227194i	0.237700	−	0.971339i	$-0.423606\pi$
$13$	0.464568	+	0.0819158i	0.128848	+	0.0227194i	−0.108852	+	0.994058i	$0.534718\pi$
$14$	−1.14628	−	2.38454i	−0.306356	−	0.637296i
$15$	0.415462	−	0.460066i	0.107272	−	0.118789i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−1.75354	−	2.08979i	−0.425297	−	0.506849i	0.510262	−	0.860019i	$-0.329548\pi$
$17$	−1.75354	−	2.08979i	−0.425297	−	0.506849i	−0.935559	+	0.353170i	$0.885104\pi$
$18$	−1.68483	+	2.48221i	−0.397118	+	0.585062i
$19$	3.58887	+	2.47387i	0.823343	+	0.567544i
$19$	3.58887	+	2.47387i	0.823343	+	0.567544i
$20$		−	0.357897i		−	0.0800281i
$21$	4.55393	+	0.511566i	0.993750	+	0.111633i
$22$	4.07380	−	0.718321i	0.868537	−	0.153146i
$23$	1.60312	+	0.282674i	0.334274	+	0.0589415i	0.338266	−	0.941051i	$-0.390160\pi$
$23$	1.60312	+	0.282674i	0.334274	+	0.0589415i	−0.00399208	+	0.999992i	$0.501271\pi$
$24$	0.238552	+	1.71554i	0.0486942	+	0.350184i
$25$	3.73210	+	3.13160i	0.746420	+	0.626321i
$26$			0.471734i			0.0925147i
$27$	−2.09267	−	4.75613i	−0.402734	−	0.915317i
$28$	2.14927	−	1.54294i	0.406173	−	0.291587i
$29$	−0.141207	+	0.0513951i	−0.0262214	+	0.00954382i	−0.355098	−	0.934829i	$-0.615552\pi$
$29$	−0.141207	+	0.0513951i	−0.0262214	+	0.00954382i	0.328876	+	0.944373i	$0.393330\pi$
$30$	0.525221	+	0.329261i	0.0958918	+	0.0601146i
$31$	−0.771575	+	0.445469i	−0.138579	+	0.0800086i	−0.567687	−	0.823245i	$-0.692161\pi$
$31$	−0.771575	+	0.445469i	−0.138579	+	0.0800086i	0.429108	+	0.903253i	$0.358828\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−2.69370	+	6.63924i	−0.468913	+	1.15574i
$34$	1.75354	−	2.08979i	0.300730	−	0.358396i
$35$	0.0714238	−	0.944208i	0.0120728	−	0.159600i
$36$	−2.73706	−	1.22820i	−0.456177	−	0.204700i
$37$	8.04416	−	4.64430i	1.32245	−	0.763518i	0.338332	−	0.941027i	$-0.390137\pi$
$37$	8.04416	−	4.64430i	1.32245	−	0.763518i	0.984119	+	0.177509i	$0.0568039\pi$
$38$	−1.81308	+	3.96393i	−0.294121	+	0.643034i
$39$	−0.692281	−	0.433991i	−0.110854	−	0.0694941i
$40$	0.352459	−	0.0621481i	0.0557287	−	0.00982648i
$41$	1.78310	+	10.1124i	0.278473	+	1.57930i	0.727710	+	0.685885i	$0.240585\pi$
$41$	1.78310	+	10.1124i	0.278473	+	1.57930i	−0.449238	+	0.893412i	$0.648304\pi$
$42$	0.286988	+	4.57358i	0.0442833	+	0.705719i
$43$	3.95923	−	3.32219i	0.603777	−	0.506629i	−0.288880	−	0.957365i	$-0.593283\pi$
$43$	3.95923	−	3.32219i	0.603777	−	0.506629i	0.892657	+	0.450736i	$0.148838\pi$
$44$	1.41482	+	3.88717i	0.213291	+	0.586014i
$45$	−0.966395	+	0.467857i	−0.144062	+	0.0697439i
$46$			1.62785i			0.240014i
$47$	7.29024	−	8.68817i	1.06339	−	1.26730i	0.101216	−	0.994864i	$-0.467727\pi$
$47$	7.29024	−	8.68817i	1.06339	−	1.26730i	0.962174	−	0.272435i	$-0.0878289\pi$
$48$	−1.64806	+	0.532829i	−0.237877	+	0.0769073i
$49$	5.97814	−	3.64167i	0.854021	−	0.520239i
$50$	−2.43596	+	4.21920i	−0.344496	+	0.596685i
$51$	1.45357	+	4.49595i	0.203541	+	0.629559i
$52$	−0.464568	+	0.0819158i	−0.0644240	+	0.0113597i
$53$	11.6079	−	4.22494i	1.59447	−	0.580340i	0.616186	−	0.787601i	$-0.288677\pi$
$53$	11.6079	−	4.22494i	1.59447	−	0.580340i	0.978286	+	0.207260i	$0.0664547\pi$
$54$	4.32048	−	2.88677i	0.587943	−	0.392839i
$55$	1.39121	+	0.506358i	0.187590	+	0.0682773i
$56$	1.89271	+	1.84869i	0.252924	+	0.247041i
$57$	−4.14913	−	6.30751i	−0.549566	−	0.835450i
$58$	−0.0751346	−	0.130137i	−0.00986565	−	0.0170878i
$59$	3.59807	−	3.01914i	0.468429	−	0.393058i	−0.377792	−	0.925890i	$-0.623317\pi$
$59$	3.59807	−	3.01914i	0.468429	−	0.393058i	0.846221	+	0.532832i	$0.178872\pi$
$60$	−0.233055	+	0.574417i	−0.0300873	+	0.0741569i
$61$	−1.59361	+	9.03782i	−0.204041	+	1.15717i	0.694901	+	0.719106i	$0.255448\pi$
$61$	−1.59361	+	9.03782i	−0.204041	+	1.15717i	−0.898942	+	0.438069i	$0.855663\pi$
$62$	−0.572684	−	0.682499i	−0.0727310	−	0.0866774i
$63$	−6.97585	−	3.78648i	−0.878875	−	0.477052i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.0844161	+	0.146213i	−0.0104705	+	0.0181355i
$66$	−7.00613	−	1.49989i	−0.862395	−	0.184623i
$67$	1.59956	+	0.282046i	0.195418	+	0.0344574i	0.270500	−	0.962720i	$-0.412811\pi$
$67$	1.59956	+	0.282046i	0.195418	+	0.0344574i	−0.0750826	+	0.997177i	$0.523922\pi$
$68$	2.36254	+	1.36401i	0.286500	+	0.165411i
$69$	−2.38891	−	1.49761i	−0.287591	−	0.180291i
$70$	0.942266	−	0.0936213i	0.112622	−	0.0111899i
$71$	−2.88214	+	2.41840i	−0.342047	+	0.287012i	−0.797587	−	0.603204i	$-0.793891\pi$
$71$	−2.88214	+	2.41840i	−0.342047	+	0.287012i	0.455540	+	0.890215i	$0.349446\pi$
$72$	0.734257	−	2.90876i	0.0865330	−	0.342800i
$73$	−0.136857	−	0.0498120i	−0.0160179	−	0.00583005i	0.333999	−	0.942574i	$-0.391602\pi$
$73$	−0.136857	−	0.0498120i	−0.0160179	−	0.00583005i	−0.350017	+	0.936743i	$0.613824\pi$
$74$	5.97059	+	7.11548i	0.694067	+	0.827157i
$75$	−3.95071	−	7.45643i	−0.456189	−	0.860995i
$76$	−4.21855	−	1.09721i	−0.483900	−	0.125859i
$77$	2.95684	+	10.5375i	0.336963	+	1.20086i
$78$	0.307184	−	0.757125i	0.0347818	−	0.0857275i
$79$	−2.38818	−	2.84612i	−0.268691	−	0.320213i	0.614781	−	0.788698i	$-0.289245\pi$
$79$	−2.38818	−	2.84612i	−0.268691	−	0.320213i	−0.883472	+	0.468485i	$0.844800\pi$
$80$	0.122408	+	0.336313i	0.0136856	+	0.0376009i
$81$	0.261597	+	8.99620i	0.0290663	+	0.999577i
$82$	−9.64917	+	3.51201i	−1.06557	+	0.387837i
$83$	−3.58230	−	2.06824i	−0.393208	−	0.227019i	0.290341	−	0.956923i	$-0.406231\pi$
$83$	−3.58230	−	2.06824i	−0.393208	−	0.227019i	−0.683549	+	0.729904i	$0.739565\pi$
$84$	−4.45426	+	1.07682i	−0.486000	+	0.117491i
$85$	0.917471	−	0.333932i	0.0995137	−	0.0362200i
$86$	3.95923	+	3.32219i	0.426935	+	0.358241i
$87$	0.260102	+	0.00946293i	0.0278858	+	0.00101453i
$88$	−3.58244	+	2.06832i	−0.381889	+	0.220484i
$89$	−8.53780	+	3.10751i	−0.905005	+	0.329395i	−0.752257	−	0.658870i	$-0.771035\pi$
$89$	−8.53780	+	3.10751i	−0.905005	+	0.329395i	−0.152749	+	0.988265i	$0.548812\pi$
$90$	−0.628562	−	0.870471i	−0.0662562	−	0.0917557i
$91$	−1.24198	+	0.123400i	−0.130195	+	0.0129358i
$92$	−1.60312	+	0.282674i	−0.167137	+	0.0294708i
$93$	1.52844	−	0.212535i	0.158492	−	0.0220389i
$94$	9.82211	+	5.67080i	1.01307	+	0.584898i
$95$	−1.27130	+	0.904161i	−0.130433	+	0.0927650i
$96$	−0.810916	−	1.53049i	−0.0827638	−	0.156205i
$97$	5.26058	−	14.4533i	0.534131	−	1.46751i	−0.319981	−	0.947424i	$-0.603676\pi$
$97$	5.26058	−	14.4533i	0.534131	−	1.46751i	0.854112	−	0.520089i	$-0.174101\pi$
$98$	4.62444	+	5.25495i	0.467139	+	0.530830i
$99$	8.64668	−	8.90176i	0.869024	−	0.894661i
$100$	−4.57810	−	1.66629i	−0.457810	−	0.166629i
$101$	−5.27493	+	6.28642i	−0.524876	+	0.625522i	−0.961726	−	0.274012i	$-0.911649\pi$
$101$	−5.27493	+	6.28642i	−0.524876	+	0.625522i	0.436851	+	0.899534i	$0.356094\pi$
$102$	−4.17523	+	2.21220i	−0.413410	+	0.219041i
$103$	−13.4072	−	7.74064i	−1.32105	−	0.762708i	−0.337152	−	0.941450i	$-0.609464\pi$
$103$	−13.4072	−	7.74064i	−1.32105	−	0.762708i	−0.983896	+	0.178742i	$0.942797\pi$
$104$	−0.161343	−	0.443285i	−0.0158210	−	0.0434677i
$105$	−0.729483	+	1.46893i	−0.0711903	+	0.143352i
$106$	6.17645	+	10.6979i	0.599910	+	1.03907i
$107$	4.14215			0.400436			0.200218	−	0.979751i	$-0.435835\pi$
$107$	4.14215			0.400436			0.200218	+	0.979751i	$0.435835\pi$
$108$	3.59316	+	3.75356i	0.345752	+	0.361187i
$109$	2.34045	−	0.412685i	0.224175	−	0.0395281i	−0.0604324	−	0.998172i	$-0.519248\pi$
$109$	2.34045	−	0.412685i	0.224175	−	0.0395281i	0.284607	+	0.958644i	$0.408137\pi$
$110$	−0.257085	+	1.45800i	−0.0245120	+	0.139015i
$111$	−15.9350	+	2.21581i	−1.51248	+	0.210316i
$112$	−1.49194	+	2.18498i	−0.140975	+	0.206461i
$113$	12.2857			1.15574			0.577870	−	0.816129i	$-0.303884\pi$
$113$	12.2857			1.15574			0.577870	+	0.816129i	$0.303884\pi$
$114$	5.49120	−	5.18138i	0.514298	−	0.485281i
$115$	−0.291301	+	0.504549i	−0.0271640	+	0.0470494i
$116$	0.115113	−	0.0965911i	0.0106880	−	0.00896826i
$117$	0.828491	+	1.14735i	0.0765940	+	0.106072i
$118$	3.59807	+	3.01914i	0.331229	+	0.277934i
$119$	5.96068	+	4.07004i	0.546415	+	0.373100i
$120$	−0.606160	−	0.129768i	−0.0553346	−	0.0118461i
$121$	−6.11183			−0.555620
$122$	−9.17724			−0.830869
$123$	3.72318	−	17.3914i	0.335708	−	1.56813i
$124$	0.572684	−	0.682499i	0.0514286	−	0.0612902i
$125$	−3.05977	+	1.76656i	−0.273675	+	0.158006i
$126$	2.51761	−	7.52739i	0.224287	−	0.670593i
$127$	−7.71873	−	1.36102i	−0.684926	−	0.120771i	−0.179653	−	0.983730i	$-0.557497\pi$
$127$	−7.71873	−	1.36102i	−0.684926	−	0.120771i	−0.505274	+	0.862959i	$0.668608\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−8.51784	+	2.75388i	−0.749954	+	0.242466i
$130$	−0.158650	−	0.0577440i	−0.0139146	−	0.00506448i
$131$	−16.6656	+	2.93860i	−1.45608	+	0.256746i	−0.844976	−	0.534804i	$-0.820386\pi$
$131$	−16.6656	+	2.93860i	−1.45608	+	0.256746i	−0.611104	+	0.791550i	$0.709274\pi$
$132$	0.260498	−	7.16014i	0.0226734	−	0.623210i
$133$	−10.9105	−	3.73655i	−0.946057	−	0.324000i
$134$			1.62424i			0.140313i
$135$	1.85571	−	0.121604i	0.159714	−	0.0104660i
$136$	−0.933041	+	2.56351i	−0.0800076	+	0.219819i
$137$	−6.11448	−	16.7994i	−0.522395	−	1.43527i	−0.867846	−	0.496832i	$-0.834496\pi$
$137$	−6.11448	−	16.7994i	−0.522395	−	1.43527i	0.345451	−	0.938437i	$-0.387726\pi$
$138$	1.06003	−	2.61267i	0.0902353	−	0.222405i
$139$	2.93901	−	16.6679i	0.249283	−	1.41376i	−0.561047	−	0.827784i	$-0.689601\pi$
$139$	2.93901	−	16.6679i	0.249283	−	1.41376i	0.810331	−	0.585973i	$-0.199288\pi$
$140$	0.255822	+	0.911693i	0.0216209	+	0.0770522i
$141$	−17.3583	+	9.19709i	−1.46183	+	0.774534i
$142$	−2.88214	−	2.41840i	−0.241864	−	0.202948i
$143$	0.338857	−	1.92175i	0.0283366	−	0.160705i
$144$	2.99207	+	0.218001i	0.249339	+	0.0181668i
$145$		−	0.0537808i		−	0.00446625i
$146$	0.0252902	−	0.143428i	0.00209303	−	0.0118702i
$147$	−11.9662	+	1.95197i	−0.986955	+	0.160996i
$148$	−5.97059	+	7.11548i	−0.490780	+	0.584889i
$149$	4.96092	+	5.91220i	0.406415	+	0.484346i	0.929965	−	0.367649i	$-0.119837\pi$
$149$	4.96092	+	5.91220i	0.406415	+	0.484346i	−0.523550	+	0.851995i	$0.675393\pi$
$150$	6.65712	−	5.18549i	0.543552	−	0.423393i
$151$	18.9939	+	10.9661i	1.54570	+	0.892410i	0.998462	+	0.0554327i	$0.0176538\pi$
$151$	18.9939	+	10.9661i	1.54570	+	0.892410i	0.547237	+	0.836977i	$0.315680\pi$
$152$	0.347999	−	4.34499i	0.0282265	−	0.352425i
$153$	0.594714	−	8.16245i	0.0480798	−	0.659895i
$154$	−9.86401	+	4.74175i	−0.794864	+	0.382101i
$155$	−0.0553701	−	0.314020i	−0.00444744	−	0.0252227i
$156$	0.798964	+	0.171044i	0.0639684	+	0.0136945i
$157$	1.24114	+	7.03884i	0.0990536	+	0.561761i	0.993430	+	0.114445i	$0.0365089\pi$
$157$	1.24114	+	7.03884i	0.0990536	+	0.561761i	−0.894376	+	0.447316i	$0.852380\pi$
$158$	2.38818	−	2.84612i	0.189993	−	0.226425i
$159$	−21.3817	−	0.777902i	−1.69568	−	0.0616917i
$160$	−0.309948	+	0.178948i	−0.0245035	+	0.0141471i
$161$	−4.28579	+	0.425826i	−0.337768	+	0.0335598i
$162$	−8.81410	+	1.81980i	−0.692501	+	0.142977i
$163$	6.88177	−	11.9196i	0.539022	−	0.933613i	−0.459935	−	0.887953i	$-0.652127\pi$
$163$	6.88177	−	11.9196i	0.539022	−	0.933613i	0.998957	−	0.0456608i	$-0.0145393\pi$
$164$	−5.13422	−	8.89273i	−0.400915	−	0.694405i
$165$	−1.90313	−	1.71862i	−0.148158	−	0.133794i
$166$	1.41476	−	3.88702i	0.109807	−	0.301691i
$167$	9.35649	+	7.85102i	0.724027	+	0.607531i	0.928496	−	0.371342i	$-0.121102\pi$
$167$	9.35649	+	7.85102i	0.724027	+	0.607531i	−0.204469	+	0.978873i	$0.565547\pi$
$168$	−1.83394	−	4.19960i	−0.141491	−	0.324006i
$169$	−12.0069	−	4.37015i	−0.923607	−	0.336165i
$170$	0.488176	+	0.845546i	0.0374414	+	0.0648504i
$171$	2.55195	+	12.8253i	0.195153	+	0.980773i
$172$	−2.58421	+	4.47598i	−0.197044	+	0.341290i
$173$	2.06698	+	11.7224i	0.157150	+	0.891240i	0.956794	+	0.290766i	$0.0939101\pi$
$173$	2.06698	+	11.7224i	0.157150	+	0.891240i	−0.799645	+	0.600474i	$0.794979\pi$
$174$	0.0358470	+	0.257793i	0.00271756	+	0.0195433i
$175$	−11.7455	−	5.30966i	−0.887874	−	0.401373i
$176$	−2.65898	−	3.16885i	−0.200428	−	0.238861i
$177$	−7.74084	+	2.50267i	−0.581837	+	0.188112i
$178$	−4.54287	−	7.86848i	−0.340502	−	0.589768i
$179$	17.9115			1.33877			0.669385	−	0.742916i	$-0.266558\pi$
$179$	17.9115			1.33877			0.669385	+	0.742916i	$0.266558\pi$
$180$	0.748098	−	0.770168i	0.0557599	−	0.0574049i
$181$	−2.98840	−	8.21056i	−0.222126	−	0.610286i	0.777706	−	0.628628i	$-0.216383\pi$
$181$	−2.98840	−	8.21056i	−0.222126	−	0.610286i	−0.999832	+	0.0183425i	$0.994161\pi$
$182$	−0.337192	−	1.20168i	−0.0249943	−	0.0890745i
$183$	8.44297	−	13.4678i	0.624122	−	0.995569i
$184$	−0.556758	−	1.52968i	−0.0410448	−	0.112770i
$185$	0.577268	+	3.27385i	0.0424416	+	0.240698i
$186$	0.474718	+	1.46832i	0.0348080	+	0.107662i
$187$	−8.64472	+	7.25379i	−0.632165	+	0.530449i
$188$	−3.87905	+	10.6576i	−0.282909	+	0.777286i
$189$	8.73043	+	10.6198i	0.635046	+	0.772475i
$190$	−1.11118	−	1.09498i	−0.0806137	−	0.0794382i
$191$	11.4642	−	6.61887i	0.829522	−	0.478925i	−0.0241670	−	0.999708i	$-0.507693\pi$
$191$	11.4642	−	6.61887i	0.829522	−	0.478925i	0.853689	+	0.520783i	$0.174360\pi$
$192$	1.36643	−	1.06436i	0.0986135	−	0.0768139i
$193$	−0.431678	+	1.18603i	−0.0310729	+	0.0853720i	−0.954259	−	0.298981i	$-0.903353\pi$
$193$	−0.431678	+	1.18603i	−0.0310729	+	0.0853720i	0.923186	+	0.384353i	$0.125575\pi$
$194$	15.1472	+	2.67087i	1.08751	+	0.191757i
$195$	0.230697	−	0.179699i	0.0165206	−	0.0128685i
$196$	−4.37209	+	5.46670i	−0.312292	+	0.390479i
$197$	−11.9020	−	6.87160i	−0.847980	−	0.489581i	0.0119889	−	0.999928i	$-0.496184\pi$
$197$	−11.9020	−	6.87160i	−0.847980	−	0.489581i	−0.859969	+	0.510347i	$0.829517\pi$
$198$	10.2680	+	6.96954i	0.729715	+	0.495304i
$199$	1.09606	−	6.21607i	0.0776977	−	0.440645i	−0.920997	−	0.389569i	$-0.872624\pi$
$199$	1.09606	−	6.21607i	0.0776977	−	0.440645i	0.998695	−	0.0510760i	$-0.0162651\pi$
$200$	0.845998	−	4.79789i	0.0598211	−	0.339262i
$201$	−2.38360	−	1.49428i	−0.168126	−	0.105398i
$202$	−7.10690	−	4.10317i	−0.500040	−	0.288698i
$203$	0.322969	−	0.231856i	0.0226679	−	0.0162731i
$204$	−2.90362	−	3.72766i	−0.203294	−	0.260988i
$205$	−3.61921	−	0.638164i	−0.252776	−	0.0445713i
$206$	5.29491	−	14.5476i	0.368914	−	1.01358i
$207$	2.85894	+	3.95924i	0.198710	+	0.275186i
$208$	0.408534	−	0.235867i	0.0283267	−	0.0163545i
$209$	10.2335	−	14.8459i	0.707867	−	1.02691i
$210$	−1.57328	−	0.463324i	−0.108567	−	0.0319724i
$211$	−7.00396	+	19.2432i	−0.482172	+	1.32476i	0.425455	+	0.904980i	$0.360114\pi$
$211$	−7.00396	+	19.2432i	−0.482172	+	1.32476i	−0.907627	+	0.419778i	$0.862108\pi$
$212$	−9.46287	+	7.94029i	−0.649913	+	0.545342i
$213$	6.20059	−	2.00470i	0.424858	−	0.137360i
$214$	0.719276	+	4.07922i	0.0491687	+	0.278850i
$215$	0.632654	+	1.73820i	0.0431466	+	0.118544i
$216$	−3.07259	+	4.19037i	−0.209063	+	0.285118i
$217$	1.64707	−	1.68629i	0.111810	−	0.114473i
$218$	0.812831	+	2.23323i	0.0550519	+	0.151254i
$219$	0.187217	+	0.169066i	0.0126509	+	0.0114244i
$220$	−1.48049			−0.0998147
$221$	−0.643453	−	1.11449i	−0.0432833	−	0.0749689i
$222$	−4.94923	−	15.3081i	−0.332171	−	1.02741i
$223$	3.51154	+	4.18490i	0.235150	+	0.280241i	0.870696	−	0.491822i	$-0.163669\pi$
$223$	3.51154	+	4.18490i	0.235150	+	0.280241i	−0.635545	+	0.772064i	$0.719225\pi$
$224$	−2.41085	−	1.08985i	−0.161082	−	0.0728188i
$225$	1.48534	+	14.5401i	0.0990225	+	0.969337i
$226$	2.13339	+	12.0990i	0.141911	+	0.804815i
$227$	1.66728	−	2.88781i	0.110661	−	0.191670i	−0.805376	−	0.592764i	$-0.798037\pi$
$227$	1.66728	−	2.88781i	0.110661	−	0.191670i	0.916037	+	0.401094i	$0.131370\pi$
$228$	6.05620	+	4.50804i	0.401082	+	0.298552i
$229$	0.135619	+	0.234898i	0.00896192	+	0.0155225i	0.870472	−	0.492219i	$-0.163814\pi$
$229$	0.135619	+	0.234898i	0.00896192	+	0.0155225i	−0.861510	+	0.507741i	$0.830481\pi$
$230$	−0.547468	−	0.199262i	−0.0360989	−	0.0131389i
$231$	2.11617	−	18.8380i	0.139233	−	1.23945i
$232$	0.115113	+	0.0965911i	0.00755753	+	0.00634152i
$233$	1.59734	−	4.38866i	0.104645	−	0.287511i	−0.876309	−	0.481750i	$-0.840001\pi$
$233$	1.59734	−	4.38866i	0.104645	−	0.287511i	0.980954	+	0.194239i	$0.0622237\pi$
$234$	−0.986049	+	1.01514i	−0.0644601	+	0.0663617i
$235$	2.02956	+	3.51530i	0.132394	+	0.229313i
$236$	−2.34847	+	4.06768i	−0.152873	+	0.264783i
$237$	1.97964	+	6.12310i	0.128592	+	0.397738i
$238$	−2.97315	+	6.57688i	−0.192721	+	0.426316i
$239$	−18.7202	+	10.8081i	−1.21091	+	0.699119i	−0.962957	−	0.269654i	$-0.913091\pi$
$239$	−18.7202	+	10.8081i	−1.21091	+	0.699119i	−0.247952	+	0.968772i	$0.579757\pi$
$240$	0.0225379	−	0.619485i	0.00145482	−	0.0399876i
$241$	14.3138	−	17.0585i	0.922031	−	1.09883i	−0.0728063	−	0.997346i	$-0.523195\pi$
$241$	14.3138	−	17.0585i	0.922031	−	1.09883i	0.994837	−	0.101487i	$-0.0323601\pi$
$242$	−1.06131	−	6.01897i	−0.0682234	−	0.386914i
$243$	5.43829	−	14.6091i	0.348866	−	0.937173i
$244$	−1.59361	−	9.03782i	−0.102021	−	0.578587i
$245$	0.492970	+	2.45630i	0.0314947	+	0.156927i
$246$	17.7737	+	0.646637i	1.13321	+	0.0412280i
$247$	1.46462	+	1.44326i	0.0931918	+	0.0918327i
$248$	0.771575	+	0.445469i	0.0489951	+	0.0282873i
$249$	4.40272	+	5.65221i	0.279011	+	0.358194i
$250$	−2.27105	−	2.70653i	−0.143634	−	0.171176i
$251$	8.89978	−	10.6063i	0.561749	−	0.669467i	−0.408166	−	0.912908i	$-0.633832\pi$
$251$	8.89978	−	10.6063i	0.561749	−	0.669467i	0.969916	+	0.243441i	$0.0782762\pi$
$252$	7.85021	+	1.17225i	0.494517	+	0.0738447i
$253$	1.16932	−	6.63154i	0.0735145	−	0.416922i
$254$		−	7.83780i		−	0.491787i
$255$	−1.68997	−	0.0614841i	−0.105830	−	0.00385028i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	10.9548	+	9.19214i	0.683340	+	0.573390i	0.916980	−	0.398933i	$-0.130619\pi$
$257$	10.9548	+	9.19214i	0.683340	+	0.573390i	−0.233640	+	0.972323i	$0.575064\pi$
$258$	−4.19115	−	7.91023i	−0.260930	−	0.492469i
$259$	−17.1717	+	17.5806i	−1.06700	+	1.09241i
$260$	0.0293174	−	0.166267i	0.00181819	−	0.0103115i
$261$	−0.411296	−	0.184561i	−0.0254586	−	0.0114240i
$262$	−5.78790	−	15.9021i	−0.357578	−	0.982437i
$263$	−4.02533	+	11.0595i	−0.248212	+	0.681958i	0.751540	+	0.659688i	$0.229312\pi$
$263$	−4.02533	+	11.0595i	−0.248212	+	0.681958i	−0.999752	+	0.0222699i	$0.992911\pi$
$264$	7.09660	−	0.986805i	0.436765	−	0.0607337i
$265$			4.42106i			0.271584i
$266$	1.78520	−	11.3936i	0.109458	−	0.698584i
$267$	15.7266	+	0.572158i	0.962450	+	0.0350155i
$268$	−1.59956	+	0.282046i	−0.0977088	+	0.0172287i
$269$	7.15736	+	2.60507i	0.436392	+	0.158834i	0.550868	−	0.834592i	$-0.314297\pi$
$269$	7.15736	+	2.60507i	0.436392	+	0.158834i	−0.114476	+	0.993426i	$0.536519\pi$
$270$	0.441996	+	1.80640i	0.0268990	+	0.109934i
$271$	−3.25083	−	1.18321i	−0.197474	−	0.0718747i	0.241390	−	0.970428i	$-0.422397\pi$
$271$	−3.25083	−	1.18321i	−0.197474	−	0.0718747i	−0.438864	+	0.898554i	$0.644619\pi$
$272$	−2.68658	−	0.473717i	−0.162898	−	0.0287233i
$273$	2.07370	+	0.610696i	0.125506	+	0.0369610i
$274$	15.4824	−	8.93877i	0.935326	−	0.540011i
$275$	12.9543	−	15.4384i	0.781175	−	0.930969i
$276$	2.75705	+	0.590235i	0.165955	+	0.0355280i
$277$	21.9489			1.31878			0.659389	−	0.751802i	$-0.270815\pi$
$277$	21.9489			1.31878			0.659389	+	0.751802i	$0.270815\pi$
$278$	16.9251			1.01510
$279$	−2.59152	−	0.654178i	−0.155150	−	0.0391646i
$280$	−0.853420	+	0.410249i	−0.0510016	+	0.0245171i
$281$	3.58360	+	3.00699i	0.213779	+	0.179382i	0.743389	−	0.668859i	$-0.233217\pi$
$281$	3.58360	+	3.00699i	0.213779	+	0.179382i	−0.529610	+	0.848241i	$0.677662\pi$
$282$	−12.0716	−	15.4975i	−0.718853	−	0.922862i
$283$	−11.9821	+	10.0542i	−0.712263	+	0.597659i	−0.925233	−	0.379399i	$-0.876131\pi$
$283$	−11.9821	+	10.0542i	−0.712263	+	0.597659i	0.212970	+	0.977059i	$0.431686\pi$
$284$	1.88118	−	3.25830i	0.111628	−	0.193345i
$285$	2.62918	−	0.623317i	0.155739	−	0.0369221i
$286$	1.95140			0.115389
$287$	−11.7705	−	24.4855i	−0.694790	−	1.44534i
$288$	0.304878	+	2.98447i	0.0179651	+	0.175861i
$289$	1.65970	−	9.41265i	0.0976297	−	0.553685i
$290$	0.0529638	−	0.00933894i	0.00311014	−	0.000548401i
$291$	−17.8549	+	19.7717i	−1.04667	+	1.15904i
$292$	0.145640			0.00852296
$293$	13.5836	+	23.5276i	0.793565	+	1.37449i	0.923747	+	0.383004i	$0.125110\pi$
$293$	13.5836	+	23.5276i	0.793565	+	1.37449i	−0.130182	+	0.991490i	$0.541556\pi$
$294$	−4.00022	−	11.4454i	−0.233298	−	0.667512i
$295$	0.574943	+	1.57964i	0.0334745	+	0.0919704i
$296$	−8.04416	−	4.64430i	−0.467557	−	0.269944i
$297$	−19.6744	+	8.65662i	−1.14162	+	0.502308i
$298$	−4.96092	+	5.91220i	−0.287379	+	0.342484i
$299$	0.721603	+	0.262642i	0.0417314	+	0.0151890i
$300$	6.26271	+	5.65553i	0.361577	+	0.326522i
$301$	−7.71094	+	11.2929i	−0.444451	+	0.650910i
$302$	−7.50127	+	20.6096i	−0.431649	+	1.18595i
$303$	12.5598	−	6.65466i	0.721539	−	0.382300i
$304$	4.33940	−	0.411786i	0.248882	−	0.0236176i
$305$	−2.84446	−	1.64225i	−0.162874	−	0.0940351i
$306$	8.14172	−	0.831716i	0.465431	−	0.0475460i
$307$	14.8249	−	2.61403i	0.846103	−	0.149191i	0.266242	−	0.963906i	$-0.414218\pi$
$307$	14.8249	−	2.61403i	0.846103	−	0.149191i	0.579861	+	0.814715i	$0.303107\pi$
$308$	−6.38257	−	8.89075i	−0.363681	−	0.506598i
$309$	16.4777	+	21.1541i	0.937385	+	1.20341i
$310$	0.299634	−	0.109058i	0.0170181	−	0.00619407i
$311$	−11.7204	+	6.76680i	−0.664606	+	0.383710i	−0.794030	−	0.607879i	$-0.792021\pi$
$311$	−11.7204	+	6.76680i	−0.664606	+	0.383710i	0.129424	+	0.991589i	$0.458687\pi$
$312$	−0.0297066	+	0.816528i	−0.00168181	+	0.0462268i
$313$	−8.32688	−	6.98708i	−0.470663	−	0.394933i	0.376373	−	0.926468i	$-0.377171\pi$
$313$	−8.32688	−	6.98708i	−0.470663	−	0.394933i	−0.847036	+	0.531535i	$0.821615\pi$
$314$	−6.71639	+	2.44456i	−0.379028	+	0.137955i
$315$	2.12734	−	1.88257i	0.119862	−	0.106071i
$316$	3.21758	+	1.85767i	0.181003	+	0.104502i
$317$	−18.2484	+	6.64187i	−1.02493	+	0.373044i	−0.799149	−	0.601133i	$-0.794716\pi$
$317$	−18.2484	+	6.64187i	−1.02493	+	0.373044i	−0.225782	+	0.974178i	$0.572494\pi$
$318$	−2.94681	−	21.1920i	−0.165249	−	1.18839i
$319$	0.212603	+	0.584122i	0.0119035	+	0.0327046i
$320$	−0.230051	−	0.274165i	−0.0128603	−	0.0153263i
$321$	−6.64807	−	2.69728i	−0.371059	−	0.150548i
$322$	−1.16358	−	4.14674i	−0.0648436	−	0.231089i
$323$	−1.12337	−	11.8380i	−0.0625057	−	0.658685i
$324$	−3.32270	−	8.36419i	−0.184595	−	0.464677i
$325$	1.47729	+	1.76056i	0.0819450	+	0.0976583i
$326$	12.9335	+	4.70741i	0.716320	+	0.260719i
$327$	−4.02512	−	0.861705i	−0.222589	−	0.0476524i
$328$	7.86608	−	6.60042i	0.434332	−	0.364447i
$329$	−12.3607	+	27.3429i	−0.681466	+	1.50747i
$330$	1.36204	−	2.17265i	0.0749776	−	0.119601i
$331$	15.1161	+	8.72727i	0.830855	+	0.479694i	0.854145	−	0.520034i	$-0.174081\pi$
$331$	15.1161	+	8.72727i	0.830855	+	0.479694i	−0.0232904	+	0.999729i	$0.507414\pi$
$332$	4.07364	+	0.718292i	0.223570	+	0.0394214i
$333$	27.0183	+	6.82021i	1.48059	+	0.373745i
$334$	−6.10701	+	10.5777i	−0.334161	+	0.578784i
$335$	−0.290654	+	0.503428i	−0.0158801	+	0.0275052i
$336$	3.81734	−	2.53533i	0.208253	−	0.138314i
$337$	−23.2611	−	27.7215i	−1.26711	−	1.51009i	−0.762914	−	0.646500i	$-0.776232\pi$
$337$	−23.2611	−	27.7215i	−1.26711	−	1.51009i	−0.504199	−	0.863587i	$-0.668212\pi$
$338$	2.21878	−	12.5833i	0.120686	−	0.684444i
$339$	−19.7183	−	8.00019i	−1.07095	−	0.434511i
$340$	−0.747929	+	0.627587i	−0.0405622	+	0.0340357i
$341$	1.84275	+	3.19173i	0.0997904	+	0.172842i
$342$	−12.1873	+	4.74027i	−0.659013	+	0.256324i
$343$	−12.6255	+	13.5498i	−0.681712	+	0.731621i
$344$	−4.85672	−	1.76770i	−0.261857	−	0.0953080i
$345$	0.796085	−	0.620102i	0.0428598	−	0.0333852i
$346$	−11.1854	+	4.07116i	−0.601331	+	0.218867i
$347$	−9.75678	+	1.72038i	−0.523771	+	0.0923550i	−0.429281	−	0.903171i	$-0.641233\pi$
$347$	−9.75678	+	1.72038i	−0.523771	+	0.0923550i	−0.0944900	+	0.995526i	$0.530122\pi$
$348$	−0.247652	+	0.0800678i	−0.0132755	+	0.00429208i
$349$	16.0504	−	27.8002i	0.859161	−	1.48811i	−0.0135697	−	0.999908i	$-0.504319\pi$
$349$	16.0504	−	27.8002i	0.859161	−	1.48811i	0.872731	−	0.488202i	$-0.162347\pi$
$350$	3.18942	−	12.4890i	0.170482	−	0.667567i
$351$	−0.582584	−	2.38097i	−0.0310960	−	0.127087i
$352$	2.65898	−	3.16885i	0.141724	−	0.168900i
$353$			17.7916i			0.946953i	0.880806	+	0.473476i	$0.157001\pi$
$353$			17.7916i			0.946953i	−0.880806	+	0.473476i	$0.842999\pi$
$354$	−3.80883	−	7.18865i	−0.202437	−	0.382073i
$355$	−0.460543	−	1.26533i	−0.0244431	−	0.0671568i
$356$	6.96008	−	5.84020i	0.368884	−	0.309530i
$357$	−6.91645	−	10.4138i	−0.366058	−	0.551158i
$358$	3.11030	+	17.6394i	0.164385	+	0.932271i
$359$	−0.923865	+	0.162902i	−0.0487597	+	0.00859765i	−0.197975	−	0.980207i	$-0.563436\pi$
$359$	−0.923865	+	0.162902i	−0.0487597	+	0.00859765i	0.149215	+	0.988805i	$0.452325\pi$
$360$	0.888373	+	0.602995i	0.0468214	+	0.0317806i
$361$	6.75995	+	17.7568i	0.355787	+	0.934567i
$362$	7.56689	−	4.36875i	0.397707	−	0.229616i
$363$	9.80936	+	3.97990i	0.514858	+	0.208891i
$364$	1.12487	−	0.540739i	0.0589593	−	0.0283424i
$365$	0.0335048	−	0.0399295i	0.00175372	−	0.00209000i
$366$	14.7293	+	5.97604i	0.769913	+	0.312373i
$367$	6.13529	+	5.14812i	0.320259	+	0.268730i	0.788717	−	0.614756i	$-0.210746\pi$
$367$	6.13529	+	5.14812i	0.320259	+	0.268730i	−0.468458	+	0.883486i	$0.655190\pi$
$368$	1.40976	−	0.813926i	0.0734889	−	0.0424288i
$369$	−17.3006	+	25.4884i	−0.900631	+	1.32687i
$370$	−3.12387	+	1.13700i	−0.162402	+	0.0591096i
$371$	−26.5497	+	19.0597i	−1.37839	+	0.989532i
$372$	−1.36358	+	0.722477i	−0.0706982	+	0.0374587i
$373$			29.7883i			1.54238i	0.636606	+	0.771189i	$0.280338\pi$
$373$			29.7883i			1.54238i	−0.636606	+	0.771189i	$0.719662\pi$
$374$	−8.64472	−	7.25379i	−0.447008	−	0.375084i
$375$	6.06123	−	0.842834i	0.313001	−	0.0435238i
$376$	−11.1693	−	1.96945i	−0.576012	−	0.101566i
$377$	−0.0698102	+	0.0123094i	−0.00359541	+	0.000633967i
$378$	−8.94241	+	10.4419i	−0.459948	+	0.537073i
$379$			20.1744i			1.03629i	0.855293	+	0.518144i	$0.173377\pi$
$379$			20.1744i			1.03629i	−0.855293	+	0.518144i	$0.826623\pi$
$380$	0.885389	−	1.28444i	0.0454195	−	0.0658906i
$381$	11.5021	+	7.21069i	0.589273	+	0.369415i
$382$	8.50906	+	10.1407i	0.435361	+	0.518843i
$383$	−21.9217	+	18.3945i	−1.12015	+	0.939915i	−0.998612	−	0.0526717i	$-0.983226\pi$
$383$	−21.9217	+	18.3945i	−1.12015	+	0.939915i	−0.121536	+	0.992587i	$0.538782\pi$
$384$	1.28547	+	1.16085i	0.0655990	+	0.0592391i
$385$	−3.90585	−	0.295455i	−0.199061	−	0.0150578i
$386$	−1.24297	−	0.219169i	−0.0632654	−	0.0111554i
$387$	15.4642	+	1.12672i	0.786092	+	0.0572745i
$388$			15.3809i			0.780848i
$389$	−1.65104	−	0.291122i	−0.0837108	−	0.0147605i	0.131636	−	0.991298i	$-0.457977\pi$
$389$	−1.65104	−	0.291122i	−0.0837108	−	0.0147605i	−0.215347	+	0.976538i	$0.569088\pi$
$390$	0.217029	+	0.195988i	0.0109897	+	0.00992424i
$391$	−2.22041	−	3.84587i	−0.112291	−	0.194494i
$392$	−6.14285	−	3.35639i	−0.310261	−	0.169523i
$393$	28.6615	+	6.13592i	1.44578	+	0.309516i
$394$	4.70045	−	12.9144i	0.236805	−	0.650617i
$395$	1.24952	−	0.454787i	0.0628701	−	0.0228828i
$396$	−5.08064	+	11.3223i	−0.255312	+	0.568965i
$397$	3.76145	+	21.3323i	0.188782	+	1.07064i	0.920999	+	0.389564i	$0.127374\pi$
$397$	3.76145	+	21.3323i	0.188782	+	1.07064i	−0.732217	+	0.681071i	$0.761514\pi$
$398$	6.31196			0.316390
$399$	15.0779	+	13.1018i	0.754840	+	0.655909i
$400$	4.87191			0.243596
$401$	3.18251	+	18.0489i	0.158927	+	0.901320i	0.955107	+	0.296261i	$0.0957397\pi$
$401$	3.18251	+	18.0489i	0.158927	+	0.901320i	−0.796180	+	0.605060i	$0.793149\pi$
$402$	1.05767	−	2.60687i	0.0527518	−	0.130019i
$403$	−0.394940	+	0.143746i	−0.0196734	+	0.00716052i
$404$	2.80673	−	7.71144i	0.139640	−	0.383658i
$405$	−3.05756	−	1.01323i	−0.151931	−	0.0503476i
$406$	0.284416	+	0.277801i	0.0141153	+	0.0137870i
$407$	−19.2118	−	33.2758i	−0.952294	−	1.64942i
$408$	3.16682	−	3.50681i	0.156781	−	0.173613i
$409$	−5.58912	−	0.985513i	−0.276364	−	0.0487305i	0.0337481	−	0.999430i	$-0.489256\pi$
$409$	−5.58912	−	0.985513i	−0.276364	−	0.0487305i	−0.310112	+	0.950700i	$0.600367\pi$
$410$		−	3.67504i		−	0.181497i
$411$	−1.12581	+	30.9443i	−0.0555319	+	1.52637i
$412$	15.2461	+	2.68829i	0.751120	+	0.132443i
$413$	−7.00754	+	10.2627i	−0.344819	+	0.504996i
$414$	−3.40264	+	3.50302i	−0.167231	+	0.172164i
$415$	1.13408	−	0.951603i	0.0556696	−	0.0467124i
$416$	0.303225	+	0.361370i	0.0148668	+	0.0177176i
$417$	−15.5709	+	24.8379i	−0.762510	+	1.21632i
$418$	16.3974	+	7.50009i	0.802021	+	0.366841i
$419$		−	27.3117i		−	1.33426i	−0.744940	−	0.667131i	$-0.767522\pi$
$419$		−	27.3117i		−	1.33426i	0.744940	−	0.667131i	$-0.232478\pi$
$420$	0.183088	−	1.62984i	0.00893376	−	0.0795279i
$421$	34.7533	−	6.12794i	1.69377	−	0.298658i	0.758260	−	0.651952i	$-0.226050\pi$
$421$	34.7533	−	6.12794i	1.69377	−	0.298658i	0.935512	+	0.353295i	$0.114939\pi$
$422$	−20.1671	−	3.55600i	−0.981719	−	0.173103i
$423$	33.8486	−	3.45780i	1.64578	−	0.168124i
$424$	−9.46287	−	7.94029i	−0.459558	−	0.385615i
$425$		−	13.2907i		−	0.644694i
$426$	3.05096	+	5.75828i	0.147820	+	0.278990i
$427$	−2.40065	−	24.1617i	−0.116176	−	1.16927i
$428$	−3.89234	+	1.41670i	−0.188144	+	0.0684787i
$429$	−1.79526	+	2.86372i	−0.0866762	+	0.138262i
$430$	−1.60194	+	0.924878i	−0.0772522	+	0.0446016i
$431$	−15.6396	−	13.1232i	−0.753332	−	0.632120i	0.183050	−	0.983104i	$-0.441403\pi$
$431$	−15.6396	−	13.1232i	−0.753332	−	0.632120i	−0.936382	+	0.350983i	$0.885847\pi$
$432$	−4.66026	−	2.29826i	−0.224217	−	0.110575i
$433$	12.8146	−	15.2718i	0.615829	−	0.733917i	−0.364518	−	0.931196i	$-0.618766\pi$
$433$	12.8146	−	15.2718i	0.615829	−	0.733917i	0.980347	+	0.197280i	$0.0632107\pi$
$434$	1.94668	+	1.32922i	0.0934437	+	0.0638047i
$435$	−0.0350210	+	0.0863172i	−0.00167913	+	0.00413859i
$436$	−2.05816	+	1.18828i	−0.0985680	+	0.0569083i
$437$	5.05410	+	4.98039i	0.241770	+	0.238244i
$438$	−0.133988	+	0.213730i	−0.00640218	+	0.0102124i
$439$	39.8735	−	7.03078i	1.90306	−	0.335561i	0.906770	−	0.421626i	$-0.138540\pi$
$439$	39.8735	−	7.03078i	1.90306	−	0.335561i	0.996290	+	0.0860650i	$0.0274293\pi$
$440$	−0.257085	−	1.45800i	−0.0122560	−	0.0695074i
$441$	20.4766	+	4.65927i	0.975076	+	0.221870i
$442$	0.985827	−	0.827207i	0.0468910	−	0.0393462i
$443$	0.730451	+	2.00690i	0.0347048	+	0.0953506i	0.955835	−	0.293904i	$-0.0949547\pi$
$443$	0.730451	+	2.00690i	0.0347048	+	0.0953506i	−0.921130	+	0.389255i	$0.872733\pi$
$444$	14.2161	−	7.53227i	0.674668	−	0.357466i
$445$		−	3.25176i		−	0.154148i
$446$	−3.51154	+	4.18490i	−0.166276	+	0.198161i
$447$	−4.11228	−	12.7194i	−0.194504	−	0.601608i
$448$	0.654655	−	2.56348i	0.0309295	−	0.121113i
$449$	7.33594	−	12.7062i	0.346205	−	0.599644i	−0.639367	−	0.768901i	$-0.720804\pi$
$449$	7.33594	−	12.7062i	0.346205	−	0.599644i	0.985572	+	0.169258i	$0.0541370\pi$
$450$	−14.0612	+	3.98763i	−0.662853	+	0.187979i
$451$	41.8315	−	7.37603i	1.96977	−	0.347324i
$452$	−11.5448	+	4.20195i	−0.543020	+	0.197643i
$453$	−23.3439	−	29.9688i	−1.09679	−	1.40806i
$454$	3.13345	+	1.14048i	0.147060	+	0.0535256i
$455$	0.110527	−	0.432798i	0.00518157	−	0.0202899i
$456$	−3.38790	+	6.74701i	−0.158653	+	0.315958i
$457$	4.18824	+	7.25424i	0.195917	+	0.339339i	0.947201	−	0.320641i	$-0.103898\pi$
$457$	4.18824	+	7.25424i	0.195917	+	0.339339i	−0.751283	+	0.659980i	$0.770565\pi$
$458$	−0.207780	+	0.174348i	−0.00970891	+	0.00814674i
$459$	−6.26973	+	12.7133i	−0.292646	+	0.593407i
$460$	0.101168	−	0.573752i	0.00471698	−	0.0267513i
$461$	0.251694	+	0.299957i	0.0117226	+	0.0139704i	0.771874	−	0.635776i	$-0.219320\pi$
$461$	0.251694	+	0.299957i	0.0117226	+	0.0139704i	−0.760151	+	0.649746i	$0.774875\pi$
$462$	18.9193	−	1.18717i	0.880204	−	0.0552321i
$463$	−6.23711	+	10.8030i	−0.289863	+	0.502057i	−0.973777	−	0.227505i	$-0.926943\pi$
$463$	−6.23711	+	10.8030i	−0.289863	+	0.502057i	0.683914	+	0.729563i	$0.260276\pi$
$464$	−0.0751346	+	0.130137i	−0.00348803	+	0.00604145i
$465$	−0.115615	+	0.540051i	−0.00536153	+	0.0250443i
$466$	4.59936	+	0.810992i	0.213061	+	0.0375685i
$467$	−12.6097	−	7.28020i	−0.583506	−	0.336887i	0.179019	−	0.983846i	$-0.442708\pi$
$467$	−12.6097	−	7.28020i	−0.583506	−	0.336887i	−0.762526	+	0.646958i	$0.776041\pi$
$468$	−1.17094	−	0.794792i	−0.0541268	−	0.0367393i
$469$	−4.27627	+	0.424880i	−0.197460	+	0.0196191i
$470$	−3.10946	+	2.60915i	−0.143429	+	0.120351i
$471$	2.59155	−	12.1054i	0.119412	−	0.557788i
$472$	−4.41369	−	1.60645i	−0.203156	−	0.0739429i
$473$	−13.7427	−	16.3779i	−0.631891	−	0.753058i
$474$	−5.68632	+	3.01283i	−0.261181	+	0.138384i
$475$	5.64684	+	20.4716i	0.259095	+	0.939303i
$476$	−6.99325	−	1.78592i	−0.320535	−	0.0818574i
$477$	33.8107	+	15.1719i	1.54808	+	0.694672i
$478$	−13.8946	−	16.5590i	−0.635526	−	0.757391i
$479$	4.86885	+	13.3770i	0.222463	+	0.611213i	0.999841	−	0.0178210i	$-0.00567289\pi$
$479$	4.86885	+	13.3770i	0.222463	+	0.611213i	−0.777378	+	0.629034i	$0.783451\pi$
$480$	0.613988	−	0.0853770i	0.0280246	−	0.00389691i
$481$	4.11750	−	1.49865i	0.187742	−	0.0683324i
$482$	19.2849	+	11.1341i	0.878402	+	0.507146i
$483$	7.15590	+	2.10738i	0.325605	+	0.0958890i
$484$	5.74324	−	2.09037i	0.261056	−	0.0950167i
$485$	4.21690	+	3.53840i	0.191480	+	0.160671i
$486$	15.3315	+	2.81883i	0.695450	+	0.127865i
$487$	−27.8945	+	16.1049i	−1.26402	+	0.729782i	−0.973850	−	0.227193i	$-0.927045\pi$
$487$	−27.8945	+	16.1049i	−1.26402	+	0.729782i	−0.290170	+	0.956975i	$0.593712\pi$
$488$	8.62379	−	3.13880i	0.390381	−	0.142087i
$489$	−18.8069	+	14.6494i	−0.850478	+	0.662470i
$490$	−2.33338	+	0.912012i	−0.105411	+	0.0412005i
$491$	20.9837	−	3.69998i	0.946979	−	0.166978i	0.321229	−	0.947002i	$-0.395904\pi$
$491$	20.9837	−	3.69998i	0.946979	−	0.166978i	0.625750	+	0.780024i	$0.284793\pi$
$492$	2.44956	+	17.6160i	0.110435	+	0.794189i
$493$	0.355017	+	0.204969i	0.0159892	+	0.00923135i
$494$	−1.16701	+	1.69299i	−0.0525062	+	0.0761713i
$495$	1.93536	+	3.99763i	0.0869878	+	0.179680i
$496$	−0.304719	+	0.837208i	−0.0136823	+	0.0375918i
$497$	5.61321	−	8.22068i	0.251787	−	0.368748i
$498$	−4.80181	+	5.31733i	−0.215174	+	0.238275i
$499$	19.7503	+	7.18851i	0.884143	+	0.321802i	0.743880	−	0.668313i	$-0.232983\pi$
$499$	19.7503	+	7.18851i	0.884143	+	0.321802i	0.140262	+	0.990114i	$0.455205\pi$
$500$	2.27105	−	2.70653i	0.101564	−	0.121040i
$501$	−9.90455	−	18.6935i	−0.442503	−	0.835164i
$502$	11.9906	+	6.92280i	0.535169	+	0.308980i
$503$	−7.87755	−	21.6434i	−0.351243	−	0.965032i	−0.981972	−	0.189028i	$-0.939466\pi$
$503$	−7.87755	−	21.6434i	−0.351243	−	0.965032i	0.630729	−	0.776003i	$-0.282756\pi$
$504$	0.208736	+	7.93451i	0.00929786	+	0.353431i
$505$	−1.46851	−	2.54354i	−0.0653479	−	0.113186i
$506$	6.73385			0.299356
$507$	16.4251	+	14.8327i	0.729463	+	0.658741i
$508$	7.71873	−	1.36102i	0.342463	−	0.0603855i
$509$	−6.26705	+	35.5422i	−0.277782	+	1.57538i	0.452201	+	0.891916i	$0.350639\pi$
$509$	−6.26705	+	35.5422i	−0.277782	+	1.57538i	−0.729983	+	0.683465i	$0.760472\pi$
$510$	−0.232911	−	1.67498i	−0.0103135	−	0.0741692i
$511$	0.384231	+	0.0290648i	0.0169974	+	0.00128575i
$512$	1.00000			0.0441942
$513$	4.25573	−	22.2461i	0.187895	−	0.982189i
$514$	−7.15022	+	12.3845i	−0.315383	+	0.546259i
$515$	4.24442	−	3.56149i	0.187031	−	0.156938i
$516$	7.06227	−	5.50107i	0.310899	−	0.242171i
$517$	−35.9399	−	30.1571i	−1.58063	−	1.32631i
$518$	−20.2954	−	13.8580i	−0.891727	−	0.608885i
$519$	4.31595	−	20.1603i	0.189449	−	0.884937i
$520$	0.168832			0.00740378
$521$	−9.38772			−0.411283			−0.205642	−	0.978627i	$-0.565928\pi$
$521$	−9.38772			−0.411283			−0.205642	+	0.978627i	$0.565928\pi$
$522$	0.110336	−	0.437096i	0.00482928	−	0.0191312i
$523$	8.94312	−	10.6580i	0.391055	−	0.466042i	−0.534216	−	0.845348i	$-0.679393\pi$
$523$	8.94312	−	10.6580i	0.391055	−	0.466042i	0.925271	+	0.379307i	$0.123837\pi$
$524$	14.6555	−	8.46135i	0.640228	−	0.369636i
$525$	15.3937	+	16.1703i	0.671837	+	0.705731i
$526$	−11.5905	−	2.04371i	−0.505369	−	0.0891101i
$527$	2.28393	+	0.831282i	0.0994895	+	0.0362112i
$528$	2.20412	+	6.81743i	0.0959222	+	0.296690i
$529$	−19.1228	−	6.96014i	−0.831428	−	0.302615i
$530$	−4.35390	+	0.767709i	−0.189121	+	0.0333472i
$531$	14.0536	+	1.02394i	0.609874	+	0.0444353i
$532$	11.5305	−	0.220386i	0.499909	−	0.00955494i
$533$			4.84398i			0.209816i
$534$	2.16742	+	15.5870i	0.0937935	+	0.674515i
$535$	−0.507031	+	1.39306i	−0.0219209	+	0.0602271i
$536$	−0.555522	−	1.52628i	−0.0239949	−	0.0659254i
$537$	−28.7476	−	11.6636i	−1.24055	−	0.503322i
$538$	−1.32263	+	7.50099i	−0.0570225	+	0.323391i
$539$	−15.0643	−	24.7295i	−0.648866	−	1.06517i
$540$	−1.70220	+	0.748959i	−0.0732511	+	0.0322300i
$541$	−29.3241	−	24.6058i	−1.26074	−	1.05789i	−0.995603	−	0.0936761i	$-0.970138\pi$
$541$	−29.3241	−	24.6058i	−1.26074	−	1.05789i	−0.265138	−	0.964211i	$-0.585417\pi$
$542$	0.600730	−	3.40691i	0.0258036	−	0.146339i
$543$	−0.550228	+	15.1238i	−0.0236125	+	0.649023i
$544$		−	2.72803i		−	0.116963i
$545$	−0.147699	+	0.837640i	−0.00632671	+	0.0358806i
$546$	−0.241323	+	2.14825i	−0.0103277	+	0.0919365i
$547$	4.97691	−	5.93125i	0.212797	−	0.253602i	−0.649078	−	0.760721i	$-0.724845\pi$
$547$	4.97691	−	5.93125i	0.212797	−	0.253602i	0.861876	+	0.507120i	$0.169290\pi$
$548$	11.4915	+	13.6950i	0.490891	+	0.585021i
$549$	−22.3208	+	16.1177i	−0.952627	+	0.687886i
$550$	17.4533	+	10.0767i	0.744212	+	0.429671i
$551$	−0.633917	−	0.164877i	−0.0270058	−	0.00702399i
$552$	−0.102511	+	2.81766i	−0.00436316	+	0.119928i
$553$	8.11795	+	5.54306i	0.345210	+	0.235715i
$554$	3.81138	+	21.6154i	0.161930	+	0.918350i
$555$	1.20536	−	5.63038i	0.0511648	−	0.238996i
$556$	2.93901	+	16.6679i	0.124642	+	0.706878i
$557$	10.0801	−	12.0130i	0.427108	−	0.509008i	−0.508977	−	0.860780i	$-0.669976\pi$
$557$	10.0801	−	12.0130i	0.427108	−	0.509008i	0.936086	+	0.351772i	$0.114421\pi$
$558$	0.194226	−	2.66575i	0.00822224	−	0.112850i
$559$	2.11147	−	1.21906i	0.0893057	−	0.0515607i
$560$	−0.552211	−	0.769215i	−0.0233352	−	0.0325053i
$561$	18.5981	−	6.01292i	0.785214	−	0.253866i
$562$	−2.33903	+	4.05131i	−0.0986658	+	0.170894i
$563$	14.8500	+	25.7210i	0.625855	+	1.08401i	0.988375	+	0.152036i	$0.0485830\pi$
$563$	14.8500	+	25.7210i	0.625855	+	1.08401i	−0.362520	+	0.931976i	$0.618084\pi$
$564$	13.1658	−	14.5793i	0.554382	−	0.613900i
$565$	−1.50386	+	4.13183i	−0.0632680	+	0.173827i
$566$	−11.9821	−	10.0542i	−0.503646	−	0.422609i
$567$	−7.09680	−	22.7296i	−0.298037	−	0.954554i
$568$	3.53547	+	1.28680i	0.148345	+	0.0539931i
$569$	−15.4047	−	26.6817i	−0.645798	−	1.11855i	−0.984117	−	0.177523i	$-0.943191\pi$
$569$	−15.4047	−	26.6817i	−0.645798	−	1.11855i	0.338319	−	0.941032i	$-0.390142\pi$
$570$	1.07040	+	2.48100i	0.0448341	+	0.103918i
$571$	0.717775	−	1.24322i	0.0300379	−	0.0520272i	−0.850616	−	0.525788i	$-0.823771\pi$
$571$	0.717775	−	1.24322i	0.0300379	−	0.0520272i	0.880654	+	0.473761i	$0.157104\pi$
$572$	0.338857	+	1.92175i	0.0141683	+	0.0803525i
$573$	−22.7099	+	3.15789i	−0.948721	+	0.131923i
$574$	22.0696	−	15.8435i	0.921168	−	0.661296i
$575$	5.09779	+	6.07531i	0.212592	+	0.253358i
$576$	−2.88619	+	0.818493i	−0.120258	+	0.0341039i
$577$	−19.9441	−	34.5442i	−0.830283	−	1.43809i	−0.897814	−	0.440375i	$-0.854845\pi$
$577$	−19.9441	−	34.5442i	−0.830283	−	1.43809i	0.0675307	−	0.997717i	$-0.478488\pi$
$578$	9.55786			0.397554
$579$	1.46515	−	1.62245i	0.0608896	−	0.0674267i
$580$	0.0183941	+	0.0505374i	0.000763774	+	0.00209845i
$581$	10.6038	+	2.70797i	0.439919	+	0.112345i
$582$	−22.5718	−	14.1503i	−0.935632	−	0.586548i
$583$	−17.4771	−	48.0179i	−0.723827	−	1.98870i
$584$	0.0252902	+	0.143428i	0.00104652	+	0.00593509i
$585$	−0.487281	+	0.138188i	−0.0201466	+	0.00571337i
$586$	−20.8113	+	17.4628i	−0.859709	+	0.721381i
$587$	4.14049	−	11.3759i	0.170896	−	0.469534i	−0.824446	−	0.565941i	$-0.808513\pi$
$587$	4.14049	−	11.3759i	0.170896	−	0.469534i	0.995342	+	0.0964072i	$0.0307351\pi$
$588$	10.5769	−	5.92693i	0.436185	−	0.244423i
$589$	−3.87111	−	0.310046i	−0.159507	−	0.0127752i
$590$	−1.45581	+	0.840511i	−0.0599346	+	0.0346033i
$591$	14.6278	+	18.7791i	0.601706	+	0.772470i
$592$	3.17689	−	8.72842i	0.130569	−	0.358736i
$593$	21.7873	+	3.84168i	0.894696	+	0.157759i	0.602047	−	0.798461i	$-0.294352\pi$
$593$	21.7873	+	3.84168i	0.894696	+	0.157759i	0.292649	+	0.956220i	$0.405463\pi$
$594$	−11.9415	−	17.8723i	−0.489967	−	0.733309i
$595$	−2.09844	+	1.50645i	−0.0860277	+	0.0617584i
$596$	−6.68383	−	3.85891i	−0.273780	−	0.158067i
$597$	−5.80694	+	9.26294i	−0.237662	+	0.379107i
$598$	−0.133347	+	0.756248i	−0.00545296	+	0.0309253i
$599$	7.03885	−	39.9193i	0.287600	−	1.63106i	−0.408250	−	0.912870i	$-0.633861\pi$
$599$	7.03885	−	39.9193i	0.287600	−	1.63106i	0.695849	−	0.718188i	$-0.255028\pi$
$600$	−4.48210	+	7.14963i	−0.182981	+	0.291883i
$601$	35.7458	+	20.6378i	1.45810	+	0.841834i	0.998918	−	0.0465082i	$-0.0148094\pi$
$601$	35.7458	+	20.6378i	1.45810	+	0.841834i	0.459182	+	0.888342i	$0.348143\pi$
$602$	−12.4603	−	5.63281i	−0.507843	−	0.229576i
$603$	2.85259	+	3.95045i	0.116167	+	0.160875i
$604$	−21.5990	−	3.80849i	−0.878852	−	0.154965i
$605$	0.748135	−	2.05548i	0.0304160	−	0.0835673i
$606$	8.73454	+	11.2134i	0.354816	+	0.455513i
$607$	−1.44885	+	0.836493i	−0.0588070	+	0.0339522i	−0.529115	−	0.848550i	$-0.677476\pi$
$607$	−1.44885	+	0.836493i	−0.0588070	+	0.0339522i	0.470308	+	0.882502i	$0.344143\pi$
$608$	1.15906	+	4.20197i	0.0470061	+	0.170413i
$609$	−0.669338	+	0.161813i	−0.0271230	+	0.00655700i
$610$	1.12337	−	3.08642i	0.0454838	−	0.124966i
$611$	4.09851	−	3.43906i	0.165808	−	0.139129i
$612$	2.23287	+	7.87360i	0.0902586	+	0.318271i
$613$	2.23138	+	12.6548i	0.0901247	+	0.511122i	0.996133	+	0.0878618i	$0.0280034\pi$
$613$	2.23138	+	12.6548i	0.0901247	+	0.511122i	−0.906008	+	0.423261i	$0.860885\pi$
$614$	5.14864	+	14.1458i	0.207782	+	0.570877i
$615$	5.39320	+	3.38100i	0.217475	+	0.136335i
$616$	7.64736	−	7.82947i	0.308121	−	0.315458i
$617$	−13.7660	−	37.8218i	−0.554199	−	1.52265i	−0.827924	−	0.560840i	$-0.810478\pi$
$617$	−13.7660	−	37.8218i	−0.554199	−	1.52265i	0.273726	−	0.961808i	$-0.411744\pi$
$618$	−17.9714	+	19.9007i	−0.722914	+	0.800525i
$619$	3.05526			0.122801			0.0614006	−	0.998113i	$-0.480443\pi$
$619$	3.05526			0.122801			0.0614006	+	0.998113i	$0.480443\pi$
$620$	0.159432	+	0.276144i	0.00640294	+	0.0110902i
$621$	−2.01037	−	8.21619i	−0.0806733	−	0.329704i
$622$	−8.69924	−	10.3673i	−0.348808	−	0.415693i
$623$	19.5277	−	14.0187i	0.782360	−	0.561648i
$624$	−0.809282	+	0.112533i	−0.0323972	+	0.00450494i
$625$	4.01041	+	22.7442i	0.160417	+	0.909768i
$626$	5.43498	−	9.41367i	0.217226	−	0.376246i
$627$	−26.0919	+	17.1635i	−1.04201	+	0.685443i
$628$	−3.57371	−	6.18985i	−0.142607	−	0.247002i
$629$	−23.8114	−	8.66664i	−0.949423	−	0.345562i
$630$	2.22338	+	1.76812i	0.0885817	+	0.0704435i
$631$	5.51363	+	4.62648i	0.219494	+	0.184177i	0.745904	−	0.666054i	$-0.232018\pi$
$631$	5.51363	+	4.62648i	0.219494	+	0.184177i	−0.526410	+	0.850231i	$0.676462\pi$
$632$	−1.27072	+	3.49128i	−0.0505466	+	0.138876i
$633$	23.7720	−	26.3242i	0.944853	−	1.04629i
$634$	−9.70976	−	16.8178i	−0.385624	−	0.667920i
$635$	1.40256	−	2.42931i	0.0556589	−	0.0964041i
$636$	20.3583	−	6.58199i	0.807259	−	0.260993i
$637$	3.07556	−	1.20210i	0.121858	−	0.0476289i
$638$	−0.538330	+	0.310805i	−0.0213127	+	0.0123049i
$639$	−11.2573	−	0.820201i	−0.445330	−	0.0324467i
$640$	0.230051	−	0.274165i	0.00909358	−	0.0108373i
$641$	−1.95998	−	11.1156i	−0.0774146	−	0.439040i	−0.998737	−	0.0502408i	$-0.984001\pi$
$641$	−1.95998	−	11.1156i	−0.0774146	−	0.439040i	0.921323	−	0.388799i	$-0.127110\pi$
$642$	1.50188	−	7.01545i	0.0592745	−	0.276878i
$643$	2.03853	+	11.5611i	0.0803919	+	0.455925i	0.998256	+	0.0590308i	$0.0188010\pi$
$643$	2.03853	+	11.5611i	0.0803919	+	0.455925i	−0.917864	+	0.396895i	$0.870088\pi$
$644$	3.88168	−	1.86597i	0.152960	−	0.0735296i
$645$	0.116485	−	3.20175i	0.00458660	−	0.126069i
$646$	11.4631	−	3.16195i	0.451010	−	0.124405i
$647$	−0.770395	−	0.444788i	−0.0302874	−	0.0174864i	0.484780	−	0.874636i	$-0.338900\pi$
$647$	−0.770395	−	0.444788i	−0.0302874	−	0.0174864i	−0.515067	+	0.857150i	$0.672233\pi$
$648$	7.66014	−	4.72465i	0.300919	−	0.185602i
$649$	−12.4891	−	14.8839i	−0.490240	−	0.584246i
$650$	−1.47729	+	1.76056i	−0.0579439	+	0.0690548i
$651$	−3.74159	+	1.63393i	−0.146644	+	0.0640386i
$652$	−2.39001	+	13.5544i	−0.0936002	+	0.530833i
$653$			26.4027i			1.03322i	0.856222	+	0.516608i	$0.172806\pi$
$653$			26.4027i			1.03322i	−0.856222	+	0.516608i	$0.827194\pi$
$654$	0.149660	−	4.11360i	0.00585215	−	0.160854i
$655$	1.05171	−	5.96456i	0.0410938	−	0.233055i
$656$	7.86608	+	6.60042i	0.307119	+	0.257703i
$657$	−0.190387	−	0.393260i	−0.00742770	−	0.0153425i
$658$	−29.0739	−	7.42483i	−1.13342	−	0.289450i
$659$	−8.15982	+	46.2766i	−0.317862	+	1.80268i	0.237844	+	0.971303i	$0.423559\pi$
$659$	−8.15982	+	46.2766i	−0.317862	+	1.80268i	−0.555706	+	0.831379i	$0.687552\pi$
$660$	2.37616	+	0.964066i	0.0924919	+	0.0375262i
$661$	−4.27319	−	11.7405i	−0.166208	−	0.456652i	0.828428	−	0.560096i	$-0.189236\pi$
$661$	−4.27319	−	11.7405i	−0.166208	−	0.456652i	−0.994635	+	0.103444i	$0.967014\pi$
$662$	−5.96981	+	16.4019i	−0.232023	+	0.637478i
$663$	0.306994	+	2.20774i	0.0119227	+	0.0857417i
$664$			4.13648i			0.160527i
$665$	2.59218	−	3.21194i	0.100520	−	0.124554i
$666$	−2.02493	+	27.7921i	−0.0784643	+	1.07692i
$667$	−0.240900	+	0.0424771i	−0.00932767	+	0.00164472i
$668$	−11.4774	−	4.17744i	−0.444075	−	0.161630i
$669$	−2.91084	−	9.00333i	−0.112540	−	0.348089i
$670$	−0.546252	−	0.198819i	−0.0211035	−	0.00768106i
$671$	37.3863	+	6.59220i	1.44328	+	0.254489i
$672$	3.15969	+	3.31909i	0.121888	+	0.128037i
$673$	−1.66159	+	0.959319i	−0.0640496	+	0.0369790i	−0.531683	−	0.846944i	$-0.678440\pi$
$673$	−1.66159	+	0.959319i	−0.0640496	+	0.0369790i	0.467633	+	0.883923i	$0.345107\pi$
$674$	23.2611	−	27.7215i	0.895985	−	1.06779i
$675$	7.08426	−	24.3037i	0.272673	−	0.935452i
$676$	12.7775			0.491441
$677$	−5.44424			−0.209239			−0.104620	−	0.994512i	$-0.533363\pi$
$677$	−5.44424			−0.209239			−0.104620	+	0.994512i	$0.533363\pi$
$678$	4.45460	−	20.8079i	0.171078	−	0.799124i
$679$	−3.06950	+	40.5781i	−0.117796	+	1.55725i
$680$	−0.747929	−	0.627587i	−0.0286818	−	0.0240669i
$681$	−4.55643	+	3.54918i	−0.174603	+	0.136005i
$682$	−2.82325	+	2.36899i	−0.108108	+	0.0907134i
$683$	−11.7513	+	20.3539i	−0.449652	+	0.778821i	−0.998363	−	0.0571916i	$-0.981785\pi$
$683$	−11.7513	+	20.3539i	−0.449652	+	0.778821i	0.548711	+	0.836012i	$0.315119\pi$
$684$	−6.78455	−	11.1790i	−0.259414	−	0.427439i
$685$	6.39831			0.244467
$686$	−15.5363	−	10.0808i	−0.593181	−	0.384886i
$687$	−0.0647042	−	0.465319i	−0.00246862	−	0.0177530i
$688$	0.897485	−	5.08989i	0.0342163	−	0.194050i
$689$	5.73876	−	1.01190i	0.218629	−	0.0385503i
$690$	0.748920	+	0.676312i	0.0285109	+	0.0257467i
$691$	−45.3916			−1.72678			−0.863389	−	0.504539i	$-0.831663\pi$
$691$	−45.3916			−1.72678			−0.863389	+	0.504539i	$0.831663\pi$
$692$	−5.95163	−	10.3085i	−0.226247	−	0.391871i
$693$	−15.6633	+	28.8566i	−0.595001	+	1.09617i
$694$	−3.38849	−	9.30981i	−0.128625	−	0.353396i
$695$	5.24589	+	3.02871i	0.198988	+	0.114886i
$696$	−0.121856	−	0.229986i	−0.00461893	−	0.00871760i
$697$	18.0061	−	21.4589i	0.682032	−	0.812814i
$698$	30.1650	+	10.9792i	1.14176	+	0.415567i
$699$	−5.42151	+	6.00356i	−0.205060	+	0.227075i
$700$	12.8531	+	0.972264i	0.485803	+	0.0367481i
$701$	2.91974	−	8.02191i	0.110277	−	0.302983i	−0.872263	−	0.489038i	$-0.837348\pi$
$701$	2.91974	−	8.02191i	0.110277	−	0.302983i	0.982539	+	0.186055i	$0.0595702\pi$
$702$	2.24363	−	0.987183i	0.0846803	−	0.0372588i
$703$	40.3588	+	3.23242i	1.52216	+	0.121913i
$704$	3.58244	+	2.06832i	0.135018	+	0.0779528i
$705$	−0.968311	−	6.96360i	−0.0364687	−	0.262264i
$706$	−17.5213	+	3.08948i	−0.659424	+	0.116274i
$707$	8.94370	−	19.7843i	0.336362	−	0.744065i
$708$	6.41804	−	4.99926i	0.241205	−	0.187884i
$709$	−28.7683	+	10.4708i	−1.08041	+	0.393239i	−0.820062	−	0.572275i	$-0.806061\pi$
$709$	−28.7683	+	10.4708i	−1.08041	+	0.393239i	−0.260353	+	0.965514i	$0.583839\pi$
$710$	1.16614	−	0.673269i	0.0437643	−	0.0252673i
$711$	0.809951	−	11.1166i	0.0303755	−	0.416904i
$712$	6.96008	+	5.84020i	0.260840	+	0.218871i
$713$	−1.36285	+	0.496037i	−0.0510392	+	0.0185767i
$714$	9.05458	−	8.61972i	0.338859	−	0.322585i
$715$	0.604831	+	0.349199i	0.0226194	+	0.0130593i
$716$	−16.8313	+	6.12610i	−0.629016	+	0.228943i
$717$	37.0836	−	5.15660i	1.38491	−	0.192577i
$718$	−0.320855	−	0.881542i	−0.0119742	−	0.0328988i
$719$	6.55553	+	7.81258i	0.244480	+	0.291360i	0.874305	−	0.485377i	$-0.161318\pi$
$719$	6.55553	+	7.81258i	0.244480	+	0.291360i	−0.629825	+	0.776737i	$0.716873\pi$
$720$	−0.439569	+	0.979586i	−0.0163818	+	0.0365070i
$721$	39.6859	+	10.1349i	1.47798	+	0.377443i
$722$	−16.3132	+	9.74068i	−0.607113	+	0.362511i
$723$	−34.0815	+	18.0577i	−1.26750	+	0.671573i
$724$	5.61635	+	6.69331i	0.208730	+	0.248755i
$725$	−0.687947	−	0.250392i	−0.0255497	−	0.00929933i
$726$	−2.21606	+	10.3514i	−0.0822456	+	0.384178i
$727$	−35.1903	+	29.5281i	−1.30513	+	1.09514i	−0.315901	+	0.948792i	$0.602307\pi$
$727$	−35.1903	+	29.5281i	−1.30513	+	1.09514i	−0.989233	+	0.146346i	$0.953249\pi$
$728$	0.727856	+	1.01388i	0.0269761	+	0.0375770i
$729$	−18.2415	+	19.9060i	−0.675611	+	0.737259i
$730$	0.0451409	+	0.0260621i	0.00167074	+	0.000964602i
$731$	−13.8854	−	2.44837i	−0.513569	−	0.0905561i
$732$	−3.32753	+	15.5433i	−0.122989	+	0.574495i
$733$	10.6842	−	18.5056i	0.394631	−	0.683521i	−0.598423	−	0.801180i	$-0.704206\pi$
$733$	10.6842	−	18.5056i	0.394631	−	0.683521i	0.993054	+	0.117659i	$0.0375390\pi$
$734$	−4.00452	+	6.93604i	−0.147810	+	0.256014i
$735$	0.808283	−	4.26332i	0.0298140	−	0.157255i
$736$	1.04636	+	1.24701i	0.0385695	+	0.0459653i
$737$	1.16672	−	6.61682i	0.0429768	−	0.243734i
$738$	−28.1054	−	12.6117i	−1.03457	−	0.464244i
$739$	−6.68673	+	5.61083i	−0.245975	+	0.206398i	−0.757437	−	0.652908i	$-0.773549\pi$
$739$	−6.68673	+	5.61083i	−0.245975	+	0.206398i	0.511462	+	0.859306i	$0.329104\pi$
$740$	−1.66218	−	2.87898i	−0.0611029	−	0.105833i
$741$	−1.41087	−	3.27015i	−0.0518295	−	0.120132i
$742$	−23.3805	−	22.8367i	−0.858324	−	0.838360i
$743$	−3.44640	−	1.25439i	−0.126436	−	0.0460190i	0.278027	−	0.960573i	$-0.410319\pi$
$743$	−3.44640	−	1.25439i	−0.126436	−	0.0460190i	−0.404463	+	0.914554i	$0.632542\pi$
$744$	−0.948283	−	1.21740i	−0.0347658	−	0.0446322i
$745$	−2.59560	+	0.944722i	−0.0950955	+	0.0346119i
$746$	−29.3357	+	5.17268i	−1.07406	+	0.189385i
$747$	−3.38568	−	11.9386i	−0.123876	−	0.436812i
$748$	5.64244	−	9.77300i	0.206308	−	0.357336i
$749$	−10.5516	+	2.96077i	−0.385546	+	0.108184i
$750$	1.88255	+	5.82279i	0.0687410	+	0.212618i
$751$	4.05919	−	4.83755i	0.148122	−	0.176525i	−0.686882	−	0.726769i	$-0.741021\pi$
$751$	4.05919	−	4.83755i	0.148122	−	0.176525i	0.835004	+	0.550244i	$0.185465\pi$
$752$		−	11.3416i		−	0.413585i
$753$	−21.1906	+	11.2276i	−0.772229	+	0.409157i
$754$	−0.0242448	−	0.0666121i	−0.000882945	−	0.00242587i
$755$	−6.01305	+	5.04554i	−0.218837	+	0.183626i
$756$	−11.8361	−	6.99334i	−0.430475	−	0.254345i
$757$	−2.46204	−	13.9629i	−0.0894842	−	0.507490i	−0.996299	−	0.0859601i	$-0.972604\pi$
$757$	−2.46204	−	13.9629i	−0.0894842	−	0.507490i	0.906814	−	0.421530i	$-0.138507\pi$
$758$	−19.8679	+	3.50325i	−0.721634	+	0.127244i
$759$	−6.19507	+	9.88207i	−0.224867	+	0.358696i
$760$	1.41868	+	0.648897i	0.0514608	+	0.0235380i
$761$	6.16726	−	3.56067i	0.223563	−	0.129074i	−0.384036	−	0.923318i	$-0.625466\pi$
$761$	6.16726	−	3.56067i	0.223563	−	0.129074i	0.607599	+	0.794244i	$0.292133\pi$
$762$	−5.10382	+	12.5795i	−0.184892	+	0.455708i
$763$	−5.66701	+	2.72420i	−0.205159	+	0.0986226i
$764$	−8.50906	+	10.1407i	−0.307847	+	0.366878i
$765$	2.67234	+	1.19916i	0.0966186	+	0.0433557i
$766$	−21.9217	−	18.3945i	−0.792064	−	0.664621i
$767$	1.91886	−	1.10786i	0.0692861	−	0.0400024i
$768$	−0.919989	+	1.46752i	−0.0331973	+	0.0529546i
$769$	−5.08698	+	1.85151i	−0.183441	+	0.0667672i	−0.432108	−	0.901822i	$-0.642230\pi$
$769$	−5.08698	+	1.85151i	−0.183441	+	0.0667672i	0.248666	+	0.968589i	$0.420008\pi$
$770$	−0.387278	−	3.89782i	−0.0139565	−	0.140468i
$771$	−11.5965	−	21.8867i	−0.417636	−	0.788232i
$772$		−	1.26214i		−	0.0454255i
$773$	24.3503	+	20.4324i	0.875821	+	0.734901i	0.965315	−	0.261086i	$-0.0840807\pi$
$773$	24.3503	+	20.4324i	0.875821	+	0.734901i	−0.0894945	+	0.995987i	$0.528525\pi$
$774$	1.57573	+	15.4250i	0.0566386	+	0.554439i
$775$	−4.27463	−	0.753732i	−0.153549	−	0.0270749i
$776$	−15.1472	+	2.67087i	−0.543754	+	0.0958786i
$777$	39.0084	−	17.0347i	1.39942	−	0.611116i
$778$		−	1.67651i		−	0.0601056i
$779$	−18.6175	+	40.7033i	−0.667043	+	1.45835i
$780$	−0.155324	+	0.247765i	−0.00556148	+	0.00887140i
$781$	10.0041	+	11.9224i	0.357974	+	0.426616i
$782$	3.40187	−	2.85451i	0.121651	−	0.102077i
$783$	0.539940	+	0.564045i	0.0192959	+	0.0201573i
$784$	2.23870	−	6.63236i	0.0799536	−	0.236870i
$785$	−2.51918	−	0.444199i	−0.0899133	−	0.0158541i
$786$	−1.06568	+	29.2916i	−0.0380114	+	1.04480i
$787$		−	12.7934i		−	0.456035i	−0.973657	−	0.228018i	$-0.926776\pi$
$787$		−	12.7934i		−	0.456035i	0.973657	−	0.228018i	$-0.0732244\pi$
$788$	13.5344	+	2.38648i	0.482144	+	0.0850149i
$789$	13.6623	−	15.1291i	0.486391	−	0.538609i
$790$	0.664855	+	1.15156i	0.0236545	+	0.0409707i
$791$	−31.2961	+	8.78171i	−1.11276	+	0.312242i
$792$	−12.0325	−	3.03736i	−0.427556	−	0.107928i
$793$	−1.48068	+	4.06814i	−0.0525805	+	0.144464i
$794$	−20.3550	+	7.40861i	−0.722372	+	0.262922i
$795$	2.87891	−	7.09572i	0.102104	−	0.251659i
$796$	1.09606	+	6.21607i	0.0388488	+	0.220323i
$797$	−28.7818			−1.01950			−0.509752	−	0.860321i	$-0.670263\pi$
$797$	−28.7818			−1.01950			−0.509752	+	0.860321i	$0.670263\pi$
$798$	−10.2845	+	17.1239i	−0.364066	+	0.606181i
$799$	−30.9402			−1.09459
$800$	0.845998	+	4.79789i	0.0299106	+	0.169631i
$801$	−24.8683	−	11.1591i	−0.878676	−	0.394288i
$802$	−17.2221	+	6.26833i	−0.608133	+	0.221342i
$803$	−0.206054	+	0.566130i	−0.00727150	+	0.0199783i
$804$	2.75093	+	0.588924i	0.0970178	+	0.0207698i
$805$	0.381404	−	1.49349i	0.0134427	−	0.0526386i
$806$	−0.210143	−	0.363979i	−0.00740198	−	0.0128206i
$807$	−9.79106	−	8.84181i	−0.344662	−	0.311246i
$808$	8.08167	+	1.42502i	0.284312	+	0.0501319i
$809$		−	37.0075i		−	1.30111i	−0.759457	−	0.650557i	$-0.774535\pi$
$809$		−	37.0075i		−	1.30111i	0.759457	−	0.650557i	$-0.225465\pi$
$810$	0.466894	−	3.18705i	0.0164050	−	0.111982i
$811$	−11.8074	−	2.08196i	−0.414613	−	0.0731075i	−0.0375494	−	0.999295i	$-0.511955\pi$
$811$	−11.8074	−	2.08196i	−0.414613	−	0.0731075i	−0.377064	+	0.926187i	$0.623066\pi$
$812$	−0.224192	+	0.328335i	−0.00786759	+	0.0115223i
$813$	4.44705	+	4.01590i	0.155965	+	0.140844i
$814$	29.4342	−	24.6982i	1.03167	−	0.865672i
$815$	3.16632	+	3.77348i	0.110911	+	0.132179i
$816$	4.00344	+	2.50976i	0.140149	+	0.0878591i
$817$	22.4278	−	2.12828i	0.784650	−	0.0744591i
$818$		−	5.67535i		−	0.198434i
$819$	−2.93058	−	2.33051i	−0.102403	−	0.0814346i
$820$	3.61921	−	0.638164i	0.126388	−	0.0222856i
$821$	−37.8055	−	6.66613i	−1.31942	−	0.232650i	−0.530784	−	0.847507i	$-0.678102\pi$
$821$	−37.8055	−	6.66613i	−1.31942	−	0.232650i	−0.788638	+	0.614858i	$0.789213\pi$
$822$	−30.6697	+	4.26472i	−1.06973	+	0.148749i
$823$	−25.2352	−	21.1748i	−0.879643	−	0.738108i	0.0864630	−	0.996255i	$-0.472444\pi$
$823$	−25.2352	−	21.1748i	−0.879643	−	0.738108i	−0.966106	+	0.258147i	$0.916888\pi$
$824$			15.4813i			0.539316i
$825$	−30.8446	+	16.3427i	−1.07387	+	0.568979i
$826$	−11.3237	−	5.11898i	−0.394000	−	0.178112i
$827$	−3.99427	+	1.45380i	−0.138894	+	0.0505535i	−0.410532	−	0.911846i	$-0.634657\pi$
$827$	−3.99427	+	1.45380i	−0.138894	+	0.0505535i	0.271638	+	0.962400i	$0.412435\pi$
$828$	−4.04067	−	2.74265i	−0.140423	−	0.0953138i
$829$	−22.9841	+	13.2699i	−0.798272	+	0.460882i	−0.842866	−	0.538123i	$-0.819134\pi$
$829$	−22.9841	+	13.2699i	−0.798272	+	0.460882i	0.0445948	+	0.999005i	$0.485800\pi$
$830$	1.13408	+	0.951603i	0.0393644	+	0.0330306i
$831$	−35.2275	−	14.2927i	−1.22203	−	0.495807i
$832$	−0.303225	+	0.361370i	−0.0105124	+	0.0125282i
$833$	−18.0933	−	6.10724i	−0.626895	−	0.211603i
$834$	−27.1644	−	11.0213i	−0.940627	−	0.381636i
$835$	−3.78571	+	2.18568i	−0.131010	+	0.0756385i
$836$	−4.53877	+	17.4506i	−0.156977	+	0.603542i
$837$	3.73336	+	2.73749i	0.129044	+	0.0946215i
$838$	26.8967	−	4.74262i	0.929133	−	0.163831i
$839$	−3.70144	−	20.9919i	−0.127788	−	0.724720i	−0.979613	−	0.200894i	$-0.935615\pi$
$839$	−3.70144	−	20.9919i	−0.127788	−	0.724720i	0.851825	−	0.523826i	$-0.175496\pi$
$840$	1.63687	−	0.102712i	0.0564773	−	0.00354390i
$841$	−22.1980	+	18.6263i	−0.765448	+	0.642287i
$842$	12.0697	+	33.1612i	0.415949	+	1.14281i
$843$	−3.79351	−	7.15973i	−0.130655	−	0.246594i
$844$		−	20.4782i		−	0.704889i
$845$	2.93948	−	3.50313i	0.101121	−	0.120511i
$846$	9.28302	+	32.7340i	0.319157	+	1.12542i
$847$	15.5691	−	4.36869i	0.534959	−	0.150110i
$848$	6.17645	−	10.6979i	0.212100	−	0.367368i
$849$	25.7781	−	8.33426i	0.884704	−	0.286031i
$850$	13.0888	−	2.30791i	0.448942	−	0.0791606i
$851$	14.2086	−	5.17150i	0.487064	−	0.177277i
$852$	−5.14101	+	4.00453i	−0.176128	+	0.137193i
$853$	−18.2280	−	6.63444i	−0.624114	−	0.227159i	0.0105532	−	0.999944i	$-0.496641\pi$
$853$	−18.2280	−	6.63444i	−0.624114	−	0.227159i	−0.634668	+	0.772785i	$0.718863\pi$
$854$	23.3778	−	6.55982i	0.799972	−	0.224473i
$855$	−4.62568	−	0.711660i	−0.158195	−	0.0243382i
$856$	−2.07107	−	3.58720i	−0.0707878	−	0.122608i
$857$	12.8358	−	10.7705i	0.438462	−	0.367913i	−0.396672	−	0.917961i	$-0.629835\pi$
$857$	12.8358	−	10.7705i	0.438462	−	0.367913i	0.835133	+	0.550047i	$0.185390\pi$
$858$	−3.13196	−	1.27071i	−0.106923	−	0.0433814i
$859$	−0.0805546	+	0.456848i	−0.00274849	+	0.0155875i	−0.986151	−	0.165849i	$-0.946964\pi$
$859$	−0.0805546	+	0.456848i	−0.00274849	+	0.0155875i	0.983403	+	0.181436i	$0.0580747\pi$
$860$	−1.18900	−	1.41700i	−0.0405446	−	0.0483192i
$861$	2.94692	+	46.9635i	0.100431	+	1.60051i
$862$	10.2080	−	17.6808i	0.347686	−	0.602210i
$863$	13.3548	−	23.1312i	0.454603	−	0.787396i	−0.544062	−	0.839045i	$-0.683114\pi$
$863$	13.3548	−	23.1312i	0.454603	−	0.787396i	0.998665	+	0.0516493i	$0.0164478\pi$
$864$	1.45410	−	4.98855i	0.0494696	−	0.169714i
$865$	−4.19542	−	0.739765i	−0.142648	−	0.0251528i
$866$	17.2650	+	9.96797i	0.586690	+	0.338725i
$867$	−8.79312	+	14.0264i	−0.298630	+	0.476360i
$868$	−0.970992	+	2.14792i	−0.0329576	+	0.0729053i
$869$	−11.7734	+	9.87904i	−0.399385	+	0.335124i
$870$	−0.0910872	−	0.0195001i	−0.00308814	−	0.000661116i
$871$	0.720001	+	0.262059i	0.0243963	+	0.00887952i
$872$	−1.52762	−	1.82055i	−0.0517318	−	0.0616516i
$873$	41.5317	−	20.1065i	1.40563	−	0.680503i
$874$	−4.02709	+	5.84215i	−0.136218	+	0.197614i
$875$	6.53164	−	6.68718i	0.220810	−	0.226068i
$876$	−0.233750	−	0.0948382i	−0.00789769	−	0.00320428i
$877$	−16.5222	−	19.6904i	−0.557915	−	0.664897i	0.411189	−	0.911550i	$-0.365114\pi$
$877$	−16.5222	−	19.6904i	−0.557915	−	0.664897i	−0.969104	+	0.246653i	$0.920669\pi$
$878$	13.8479	+	38.0469i	0.467345	+	1.28402i
$879$	−6.48081	−	46.6067i	−0.218592	−	1.57200i
$880$	1.39121	−	0.506358i	0.0468976	−	0.0170693i
$881$	−29.3877	−	16.9670i	−0.990096	−	0.571632i	−0.0847930	−	0.996399i	$-0.527023\pi$
$881$	−29.3877	−	16.9670i	−0.990096	−	0.571632i	−0.905303	+	0.424766i	$0.860356\pi$
$882$	−1.03276	+	20.9746i	−0.0347749	+	0.706251i
$883$	−24.4402	+	8.89552i	−0.822479	+	0.299358i	−0.718768	−	0.695250i	$-0.755294\pi$
$883$	−24.4402	+	8.89552i	−0.822479	+	0.299358i	−0.103711	+	0.994607i	$0.533072\pi$
$884$	0.985827	+	0.827207i	0.0331569	+	0.0278220i
$885$	0.105859	−	2.90969i	0.00355842	−	0.0978081i
$886$	−1.84957	+	1.06785i	−0.0621374	+	0.0358750i
$887$	−4.67101	+	1.70011i	−0.156837	+	0.0570841i	−0.419246	−	0.907873i	$-0.637705\pi$
$887$	−4.67101	+	1.70011i	−0.156837	+	0.0570841i	0.262408	+	0.964957i	$0.415483\pi$
$888$	9.88645	+	12.6922i	0.331768	+	0.425923i
$889$	20.6353	−	2.05027i	0.692085	−	0.0687639i
$890$	3.20235	−	0.564661i	0.107343	−	0.0189275i
$891$	37.2141	−	1.08213i	1.24672	−	0.0362528i
$892$	−4.73109	−	2.73150i	−0.158409	−	0.0914573i
$893$	47.6571	−	13.1456i	1.59478	−	0.439900i
$894$	11.8121	−	6.25851i	0.395055	−	0.209316i
$895$	−2.19251	+	6.02387i	−0.0732875	+	0.201356i
$896$	2.63821	+	0.199565i	0.0881365	+	0.00666701i
$897$	−0.987132	−	0.891429i	−0.0329594	−	0.0297640i
$898$	13.7871	+	5.01808i	0.460080	+	0.167455i
$899$	0.0860568	−	0.102558i	0.00287015	−	0.00342052i
$900$	−6.36875	−	13.1552i	−0.212292	−	0.438506i
$901$	−29.1843	−	16.8495i	−0.972269	−	0.561340i
$902$	14.5279	+	39.9152i	0.483728	+	1.32903i
$903$	19.7296	−	13.1036i	0.656560	−	0.436061i
$904$	−6.14284	−	10.6397i	−0.204308	−	0.353871i
$905$	3.12712			0.103949
$906$	25.4599	−	28.1933i	0.845850	−	0.936659i
$907$	−38.2689	+	6.74784i	−1.27070	+	0.224058i	−0.768026	−	0.640418i	$-0.778761\pi$
$907$	−38.2689	+	6.74784i	−1.27070	+	0.224058i	−0.502673	+	0.864477i	$0.667650\pi$
$908$	−0.579039	+	3.28389i	−0.0192161	+	0.108980i
$909$	−24.4916	+	2.50193i	−0.812334	+	0.0829838i
$910$	0.445415	+	0.0336930i	0.0147654	+	0.00111691i
$911$	−19.0321			−0.630561			−0.315281	−	0.948998i	$-0.602099\pi$
$911$	−19.0321			−0.630561			−0.315281	+	0.948998i	$0.602099\pi$
$912$	−7.23281	−	2.16482i	−0.239502	−	0.0716845i
$913$	−8.55557	+	14.8187i	−0.283148	+	0.490427i
$914$	−6.41675	+	5.38429i	−0.212247	+	0.178097i
$915$	3.49591	+	4.48804i	0.115571	+	0.148370i
$916$	−0.207780	−	0.174348i	−0.00686523	−	0.00576061i
$917$	40.3529	−	19.3981i	1.33257	−	0.640583i
$918$	−13.6089	−	3.96684i	−0.449161	−	0.130925i
$919$	5.61876			0.185346			0.0926729	−	0.995697i	$-0.470459\pi$
$919$	5.61876			0.185346			0.0926729	+	0.995697i	$0.470459\pi$
$920$	0.582603			0.0192078
$921$	−25.4959	−	5.45822i	−0.840119	−	0.179854i
$922$	−0.251694	+	0.299957i	−0.00828911	+	0.00987857i
$923$	−1.53705	+	0.887419i	−0.0505928	+	0.0292097i
$924$	4.45443	+	18.4257i	0.146540	+	0.606161i
$925$	44.5657	+	7.85814i	1.46531	+	0.258374i
$926$	−11.7219	−	4.26643i	−0.385207	−	0.140204i
$927$	−12.6713	−	44.6818i	−0.416181	−	1.46754i
$928$	−0.141207	−	0.0513951i	−0.00463534	−	0.00168713i
$929$	−34.6025	+	6.10136i	−1.13527	+	0.200179i	−0.709537	−	0.704669i	$-0.751096\pi$
$929$	−34.6025	+	6.10136i	−1.13527	+	0.200179i	−0.425735	+	0.904848i	$0.639985\pi$
$930$	−0.551923	−	0.0200799i	−0.0180983	−	0.000658445i
$931$	30.4638	+	1.71965i	0.998411	+	0.0563594i
$932$			4.67031i			0.152981i
$933$	23.2175	−	3.22847i	0.760107	−	0.105695i
$934$	4.97995	−	13.6823i	0.162949	−	0.447699i
$935$	−1.38136	−	3.79525i	−0.0451753	−	0.124118i
$936$	0.579385	−	1.29117i	0.0189378	−	0.0422031i
$937$	0.232954	−	1.32115i	0.00761026	−	0.0431599i	−0.980766	−	0.195186i	$-0.937469\pi$
$937$	0.232954	−	1.32115i	0.00761026	−	0.0431599i	0.988376	+	0.152027i	$0.0485799\pi$
$938$	−1.16099	−	4.13753i	−0.0379077	−	0.135095i
$939$	8.81463	+	16.6364i	0.287655	+	0.542909i
$940$	−3.10946	−	2.60915i	−0.101420	−	0.0851011i
$941$	4.58760	−	26.0175i	0.149551	−	0.848148i	−0.814048	−	0.580798i	$-0.802741\pi$
$941$	4.58760	−	26.0175i	0.149551	−	0.848148i	0.963599	−	0.267350i	$-0.0861481\pi$
$942$	12.3715	+	0.450097i	0.403086	+	0.0146649i
$943$			16.7155i			0.544332i
$944$	0.815616	−	4.62559i	0.0265460	−	0.150550i
$945$	−4.64024	+	1.63621i	−0.150947	+	0.0532260i
$946$	13.7427	−	16.3779i	0.446814	−	0.532493i
$947$	26.6708	+	31.7851i	0.866685	+	1.03288i	0.999131	+	0.0416852i	$0.0132726\pi$
$947$	26.6708	+	31.7851i	0.866685	+	1.03288i	−0.132445	+	0.991190i	$0.542283\pi$
$948$	−3.95448	−	5.07676i	−0.128436	−	0.164885i
$949$	−0.0594991	−	0.0343518i	−0.00193142	−	0.00111511i
$950$	−19.1801	+	9.11591i	−0.622283	+	0.295759i
$951$	33.6134	+	1.22291i	1.08999	+	0.0396556i
$952$	0.544420	−	7.19713i	0.0176448	−	0.233260i
$953$	−5.17555	−	29.3520i	−0.167653	−	0.950805i	−0.946287	−	0.323328i	$-0.895198\pi$
$953$	−5.17555	−	29.3520i	−0.167653	−	0.950805i	0.778634	−	0.627478i	$-0.215913\pi$
$954$	−9.07020	+	35.9316i	−0.293659	+	1.16333i
$955$	0.822700	+	4.66577i	0.0266220	+	0.150981i
$956$	13.8946	−	16.5590i	0.449385	−	0.535556i
$957$	0.0391448	−	1.07595i	0.00126537	−	0.0347805i
$958$	−12.3284	+	7.11778i	−0.398311	+	0.229965i
$959$	27.5839	+	38.4236i	0.890730	+	1.24076i
$960$	0.190698	+	0.589834i	0.00615474	+	0.0190368i
$961$	−15.1031	+	26.1594i	−0.487197	+	0.843850i
$962$	2.19088	+	3.79471i	0.0706367	+	0.122346i
$963$	8.91360	+	8.65818i	0.287237	+	0.279006i
$964$	−7.61619	+	20.9253i	−0.245301	+	0.673959i
$965$	−0.346035	−	0.290358i	−0.0111393	−	0.00934695i
$966$	−0.832753	+	7.41313i	−0.0267934	+	0.238514i
$967$	0.972958	+	0.354128i	0.0312882	+	0.0113880i	0.357617	−	0.933868i	$-0.383589\pi$
$967$	0.972958	+	0.354128i	0.0312882	+	0.0113880i	−0.326329	+	0.945256i	$0.605812\pi$
$968$	3.05591	+	5.29300i	0.0982207	+	0.170123i
$969$	−5.90570	+	19.7313i	−0.189719	+	0.633861i
$970$	−2.75239	+	4.76728i	−0.0883739	+	0.153068i
$971$	−4.34277	−	24.6291i	−0.139366	−	0.790384i	−0.971719	−	0.236139i	$-0.924118\pi$
$971$	−4.34277	−	24.6291i	−0.139366	−	0.790384i	0.832353	−	0.554245i	$-0.186993\pi$
$972$	−0.113720	+	15.5880i	−0.00364757	+	0.499987i
$973$	4.42739	+	44.5601i	0.141936	+	1.42853i
$974$	−20.7040	−	24.6741i	−0.663400	−	0.790610i
$975$	−1.22457	−	3.78764i	−0.0392177	−	0.121302i
$976$	4.58862	+	7.94773i	0.146878	+	0.254401i
$977$	9.97508			0.319131			0.159566	−	0.987187i	$-0.448991\pi$
$977$	9.97508			0.319131			0.159566	+	0.987187i	$0.448991\pi$
$978$	−17.6927	−	15.9773i	−0.565749	−	0.510899i
$979$	12.8546	+	35.3179i	0.410836	+	1.12876i
$980$	−1.30334	−	2.13956i	−0.0416338	−	0.0683456i
$981$	5.89911	+	4.00410i	0.188344	+	0.127841i
$982$	7.28755	+	20.0224i	0.232555	+	0.638939i
$983$	0.505551	+	2.86712i	0.0161246	+	0.0914470i	0.991808	−	0.127737i	$-0.0407715\pi$
$983$	0.505551	+	2.86712i	0.0161246	+	0.0914470i	−0.975683	+	0.219184i	$0.929660\pi$
$984$	−16.9230	+	5.47132i	−0.539485	+	0.174419i
$985$	3.76790	−	3.16164i	0.120055	−	0.100738i
$986$	−0.140207	+	0.385216i	−0.00446511	+	0.0122678i
$987$	37.6438	−	35.8359i	1.19822	−	1.14067i
$988$	−1.86992	−	0.855295i	−0.0594901	−	0.0272105i
$989$	7.28623	−	4.20671i	0.231689	−	0.133765i
$990$	−3.60083	+	2.60014i	−0.114442	+	0.0826377i
$991$	0.606218	−	1.66557i	0.0192572	−	0.0529086i	−0.929692	−	0.368339i	$-0.879927\pi$
$991$	0.606218	−	1.66557i	0.0192572	−	0.0529086i	0.948949	+	0.315430i	$0.102149\pi$
$992$	−0.877403	−	0.154710i	−0.0278576	−	0.00491204i
$993$	−18.5780	−	23.8504i	−0.589555	−	0.756870i
$994$	9.07052	+	4.10042i	0.287699	+	0.130058i
$995$	1.95638	+	1.12951i	0.0620213	+	0.0358080i
$996$	−6.07037	−	3.80552i	−0.192347	−	0.120582i
$997$	5.36840	−	30.4457i	0.170019	−	0.964225i	−0.773719	−	0.633529i	$-0.781606\pi$
$997$	5.36840	−	30.4457i	0.170019	−	0.964225i	0.943737	−	0.330696i	$-0.107283\pi$
$998$	−3.64970	+	20.6985i	−0.115529	+	0.655199i
$999$	−38.9226	−	28.5401i	−1.23146	−	0.902968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bu.a.53.4	✓	162
3.2	odd	2		798.2.bu.b.53.24	yes	162
7.2	even	3		798.2.cc.a.737.22	yes	162
19.14	odd	18		798.2.cc.b.641.6	yes	162
21.2	odd	6		798.2.cc.b.737.6	yes	162
57.14	even	18		798.2.cc.a.641.22	yes	162
133.128	odd	18		798.2.bu.b.527.24	yes	162
399.128	even	18	inner	798.2.bu.a.527.4	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.53.4	✓	162	1.1	even	1	trivial
798.2.bu.a.527.4	yes	162	399.128	even	18	inner
798.2.bu.b.53.24	yes	162	3.2	odd	2
798.2.bu.b.527.24	yes	162	133.128	odd	18
798.2.cc.a.641.22	yes	162	57.14	even	18
798.2.cc.a.737.22	yes	162	7.2	even	3
798.2.cc.b.641.6	yes	162	19.14	odd	18
798.2.cc.b.737.6	yes	162	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bu (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-1.60498 - 0.651180i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.122408 + 0.336313i) q^{5} +(0.362585 - 1.69367i) q^{6} +(-2.54737 + 0.714792i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.15193 + 2.09026i) q^{9} +(-0.352459 - 0.0621481i) q^{10} -4.13664i q^{11} +(1.73091 + 0.0629732i) q^{12} +(0.464568 + 0.0819158i) q^{13} +(-1.14628 - 2.38454i) q^{14} +(0.415462 - 0.460066i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.75354 - 2.08979i) q^{17} +(-1.68483 + 2.48221i) q^{18} +(3.58887 + 2.47387i) q^{19} -0.357897i q^{20} +(4.55393 + 0.511566i) q^{21} +(4.07380 - 0.718321i) q^{22} +(1.60312 + 0.282674i) q^{23} +(0.238552 + 1.71554i) q^{24} +(3.73210 + 3.13160i) q^{25} +0.471734i q^{26} +(-2.09267 - 4.75613i) q^{27} +(2.14927 - 1.54294i) q^{28} +(-0.141207 + 0.0513951i) q^{29} +(0.525221 + 0.329261i) q^{30} +(-0.771575 + 0.445469i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-2.69370 + 6.63924i) q^{33} +(1.75354 - 2.08979i) q^{34} +(0.0714238 - 0.944208i) q^{35} +(-2.73706 - 1.22820i) q^{36} +(8.04416 - 4.64430i) q^{37} +(-1.81308 + 3.96393i) q^{38} +(-0.692281 - 0.433991i) q^{39} +(0.352459 - 0.0621481i) q^{40} +(1.78310 + 10.1124i) q^{41} +(0.286988 + 4.57358i) q^{42} +(3.95923 - 3.32219i) q^{43} +(1.41482 + 3.88717i) q^{44} +(-0.966395 + 0.467857i) q^{45} +1.62785i q^{46} +(7.29024 - 8.68817i) q^{47} +(-1.64806 + 0.532829i) q^{48} +(5.97814 - 3.64167i) q^{49} +(-2.43596 + 4.21920i) q^{50} +(1.45357 + 4.49595i) q^{51} +(-0.464568 + 0.0819158i) q^{52} +(11.6079 - 4.22494i) q^{53} +(4.32048 - 2.88677i) q^{54} +(1.39121 + 0.506358i) q^{55} +(1.89271 + 1.84869i) q^{56} +(-4.14913 - 6.30751i) q^{57} +(-0.0751346 - 0.130137i) q^{58} +(3.59807 - 3.01914i) q^{59} +(-0.233055 + 0.574417i) q^{60} +(-1.59361 + 9.03782i) q^{61} +(-0.572684 - 0.682499i) q^{62} +(-6.97585 - 3.78648i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0844161 + 0.146213i) q^{65} +(-7.00613 - 1.49989i) q^{66} +(1.59956 + 0.282046i) q^{67} +(2.36254 + 1.36401i) q^{68} +(-2.38891 - 1.49761i) q^{69} +(0.942266 - 0.0936213i) q^{70} +(-2.88214 + 2.41840i) q^{71} +(0.734257 - 2.90876i) q^{72} +(-0.136857 - 0.0498120i) q^{73} +(5.97059 + 7.11548i) q^{74} +(-3.95071 - 7.45643i) q^{75} +(-4.21855 - 1.09721i) q^{76} +(2.95684 + 10.5375i) q^{77} +(0.307184 - 0.757125i) q^{78} +(-2.38818 - 2.84612i) q^{79} +(0.122408 + 0.336313i) q^{80} +(0.261597 + 8.99620i) q^{81} +(-9.64917 + 3.51201i) q^{82} +(-3.58230 - 2.06824i) q^{83} +(-4.45426 + 1.07682i) q^{84} +(0.917471 - 0.333932i) q^{85} +(3.95923 + 3.32219i) q^{86} +(0.260102 + 0.00946293i) q^{87} +(-3.58244 + 2.06832i) q^{88} +(-8.53780 + 3.10751i) q^{89} +(-0.628562 - 0.870471i) q^{90} +(-1.24198 + 0.123400i) q^{91} +(-1.60312 + 0.282674i) q^{92} +(1.52844 - 0.212535i) q^{93} +(9.82211 + 5.67080i) q^{94} +(-1.27130 + 0.904161i) q^{95} +(-0.810916 - 1.53049i) q^{96} +(5.26058 - 14.4533i) q^{97} +(4.62444 + 5.25495i) q^{98} +(8.64668 - 8.90176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) \) 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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