LMFDB - Embedded newform 63.2.o.a.20.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(20,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.o (of order $6$, degree $2$, 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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			20.6
Root			$1.82904 + 1.05600i$ of defining polynomial
Character	$\chi$	$=$	63.20
Dual form			63.2.o.a.41.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02704 + 0.592963i) q^{2} +(0.410052 + 1.68281i) q^{3} +(-0.296790 - 0.514055i) q^{4} +(-1.41899 - 2.45776i) q^{5} +(-0.576705 + 1.97146i) q^{6} +(-0.387972 + 2.61715i) q^{7} -3.07579i q^{8} +(-2.66372 + 1.38008i) q^{9} +O(q^{10})$	\(q+(1.02704 + 0.592963i) q^{2} +(0.410052 + 1.68281i) q^{3} +(-0.296790 - 0.514055i) q^{4} +(-1.41899 - 2.45776i) q^{5} +(-0.576705 + 1.97146i) q^{6} +(-0.387972 + 2.61715i) q^{7} -3.07579i q^{8} +(-2.66372 + 1.38008i) q^{9} -3.36562i q^{10} +(0.136673 + 0.0789082i) q^{11} +(0.743359 - 0.710230i) q^{12} +(3.41468 - 1.97146i) q^{13} +(-1.95034 + 2.45787i) q^{14} +(3.55408 - 3.39569i) q^{15} +(1.23025 - 2.13086i) q^{16} -4.14487 q^{17} +(-3.55408 - 0.162084i) q^{18} +6.33597i q^{19} +(-0.842281 + 1.45887i) q^{20} +(-4.56326 + 0.420284i) q^{21} +(0.0935793 + 0.162084i) q^{22} +(0.472958 - 0.273062i) q^{23} +(5.17598 - 1.26123i) q^{24} +(-1.52704 + 2.64491i) q^{25} +4.67602 q^{26} +(-3.41468 - 3.91663i) q^{27} +(1.46050 - 0.577305i) q^{28} +(4.02704 + 2.32501i) q^{29} +(5.66372 - 1.38008i) q^{30} +(-0.112086 + 0.0647129i) q^{31} +(-2.80039 + 1.61680i) q^{32} +(-0.0767447 + 0.262352i) q^{33} +(-4.25696 - 2.45776i) q^{34} +(6.98284 - 2.76016i) q^{35} +(1.50000 + 0.959702i) q^{36} -2.46050 q^{37} +(-3.75700 + 6.50731i) q^{38} +(4.71780 + 4.93786i) q^{39} +(-7.55955 + 4.36451i) q^{40} +(1.99569 + 3.45664i) q^{41} +(-4.93588 - 2.27420i) q^{42} +(3.28434 - 5.68864i) q^{43} -0.0936766i q^{44} +(7.17167 + 4.58845i) q^{45} +0.647664 q^{46} +(4.33370 - 7.50619i) q^{47} +(4.09030 + 1.19652i) q^{48} +(-6.69896 - 2.03076i) q^{49} +(-3.13667 + 1.81096i) q^{50} +(-1.69961 - 6.97504i) q^{51} +(-2.02688 - 1.17022i) q^{52} +2.60234i q^{53} +(-1.18460 - 6.04732i) q^{54} -0.447879i q^{55} +(8.04981 + 1.19332i) q^{56} +(-10.6623 + 2.59808i) q^{57} +(2.75729 + 4.77577i) q^{58} +(-1.80686 - 3.12957i) q^{59} +(-2.80039 - 0.819187i) q^{60} +(2.91472 + 1.68281i) q^{61} -0.153489 q^{62} +(-2.57843 - 7.50678i) q^{63} -8.75583 q^{64} +(-9.69076 - 5.59496i) q^{65} +(-0.234385 + 0.223939i) q^{66} +(-0.663715 - 1.14959i) q^{67} +(1.23016 + 2.13069i) q^{68} +(0.653450 + 0.683930i) q^{69} +(8.80835 + 1.30577i) q^{70} +0.409310i q^{71} +(4.24484 + 8.19304i) q^{72} -15.0124i q^{73} +(-2.52704 - 1.45899i) q^{74} +(-5.07706 - 1.48517i) q^{75} +(3.25704 - 1.88045i) q^{76} +(-0.259540 + 0.327080i) q^{77} +(1.91741 + 7.86887i) q^{78} +(-2.16372 + 3.74766i) q^{79} -6.98284 q^{80} +(5.19076 - 7.35228i) q^{81} +4.73348i q^{82} +(-3.22585 + 5.58733i) q^{83} +(1.57038 + 2.22103i) q^{84} +(5.88151 + 10.1871i) q^{85} +(6.74630 - 3.89498i) q^{86} +(-2.26127 + 7.73013i) q^{87} +(0.242705 - 0.420378i) q^{88} -5.05368 q^{89} +(4.64483 + 8.96507i) q^{90} +(3.83482 + 9.70160i) q^{91} +(-0.280738 - 0.162084i) q^{92} +(-0.154861 - 0.162084i) q^{93} +(8.90179 - 5.13945i) q^{94} +(15.5723 - 8.99066i) q^{95} +(-3.86908 - 4.04955i) q^{96} +(2.18452 + 1.26123i) q^{97} +(-5.67594 - 6.05791i) q^{98} +(-0.472958 - 0.0215693i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9	$ 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9} - 12 q^{14} + 6 q^{15} + 2 q^{16} - 6 q^{18} - 24 q^{21} - 10 q^{22} + 24 q^{23} - 8 q^{28} + 30 q^{29} + 48 q^{30} - 12 q^{32} + 18 q^{36} - 4 q^{37} + 36 q^{42} - 10 q^{43} - 40 q^{46} + 6 q^{49} - 36 q^{50} - 42 q^{51} + 42 q^{56} - 18 q^{57} + 2 q^{58} - 12 q^{60} + 24 q^{63} + 16 q^{64} - 78 q^{65} + 12 q^{67} + 18 q^{70} - 24 q^{72} - 12 q^{74} - 24 q^{77} - 12 q^{78} - 6 q^{79} + 24 q^{81} - 60 q^{84} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 24 q^{91} + 30 q^{92} + 78 q^{93} + 72 q^{95} - 24 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9 - 12 * q^14 + 6 * q^15 + 2 * q^16 - 6 * q^18 - 24 * q^21 - 10 * q^22 + 24 * q^23 - 8 * q^28 + 30 * q^29 + 48 * q^30 - 12 * q^32 + 18 * q^36 - 4 * q^37 + 36 * q^42 - 10 * q^43 - 40 * q^46 + 6 * q^49 - 36 * q^50 - 42 * q^51 + 42 * q^56 - 18 * q^57 + 2 * q^58 - 12 * q^60 + 24 * q^63 + 16 * q^64 - 78 * q^65 + 12 * q^67 + 18 * q^70 - 24 * q^72 - 12 * q^74 - 24 * q^77 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 60 * q^84 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 24 * q^91 + 30 * q^92 + 78 * q^93 + 72 * q^95 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.02704	+	0.592963i	0.726228	+	0.419288i	0.817041	−	0.576580i	$-0.195613\pi$
$2$	1.02704	+	0.592963i	0.726228	+	0.419288i	−0.0908124	+	0.995868i	$0.528946\pi$
$3$	0.410052	+	1.68281i	0.236743	+	0.971572i
$3$	0.410052	+	1.68281i	0.236743	+	0.971572i
$4$	−0.296790	−	0.514055i	−0.148395	−	0.257027i
$5$	−1.41899	−	2.45776i	−0.634590	−	1.09914i	−0.986602	−	0.163146i	$-0.947836\pi$
$5$	−1.41899	−	2.45776i	−0.634590	−	1.09914i	0.352012	−	0.935995i	$-0.385498\pi$
$6$	−0.576705	+	1.97146i	−0.235439	+	0.804847i
$7$	−0.387972	+	2.61715i	−0.146640	+	0.989190i
$7$	−0.387972	+	2.61715i	−0.146640	+	0.989190i
$8$		−	3.07579i		−	1.08746i
$9$	−2.66372	+	1.38008i	−0.887905	+	0.460027i
$10$		−	3.36562i		−	1.06430i
$11$	0.136673	+	0.0789082i	0.0412085	+	0.0237917i	0.520463	−	0.853884i	$-0.325759\pi$
$11$	0.136673	+	0.0789082i	0.0412085	+	0.0237917i	−0.479254	+	0.877676i	$0.659093\pi$
$12$	0.743359	−	0.710230i	0.214589	−	0.205026i
$13$	3.41468	−	1.97146i	0.947061	−	0.546786i	0.0548943	−	0.998492i	$-0.482518\pi$
$13$	3.41468	−	1.97146i	0.947061	−	0.546786i	0.892167	+	0.451706i	$0.149184\pi$
$14$	−1.95034	+	2.45787i	−0.521249	+	0.656894i
$15$	3.55408	−	3.39569i	0.917661	−	0.876764i
$16$	1.23025	−	2.13086i	0.307563	−	0.532715i
$17$	−4.14487			−1.00528			−0.502640	−	0.864496i	$-0.667638\pi$
$17$	−4.14487			−1.00528			−0.502640	+	0.864496i	$0.667638\pi$
$18$	−3.55408	−	0.162084i	−0.837706	−	0.0382036i
$19$			6.33597i			1.45357i	0.686864	+	0.726786i	$0.258987\pi$
$19$			6.33597i			1.45357i	−0.686864	+	0.726786i	$0.741013\pi$
$20$	−0.842281	+	1.45887i	−0.188340	+	0.326214i
$21$	−4.56326	+	0.420284i	−0.995785	+	0.0917134i
$22$	0.0935793	+	0.162084i	0.0199512	+	0.0345565i
$23$	0.472958	−	0.273062i	0.0986185	−	0.0569374i	−0.449880	−	0.893089i	$-0.648533\pi$
$23$	0.472958	−	0.273062i	0.0986185	−	0.0569374i	0.548498	+	0.836152i	$0.315200\pi$
$24$	5.17598	−	1.26123i	1.05654	−	0.257448i
$25$	−1.52704	+	2.64491i	−0.305408	+	0.528983i
$26$	4.67602			0.917044
$27$	−3.41468	−	3.91663i	−0.657155	−	0.753756i
$28$	1.46050	−	0.577305i	0.276009	−	0.109100i
$29$	4.02704	+	2.32501i	0.747803	+	0.431744i	0.824900	−	0.565279i	$-0.191232\pi$
$29$	4.02704	+	2.32501i	0.747803	+	0.431744i	−0.0770966	+	0.997024i	$0.524565\pi$
$30$	5.66372	−	1.38008i	1.03405	−	0.251967i
$31$	−0.112086	+	0.0647129i	−0.0201313	+	0.0116228i	−0.510032	−	0.860156i	$-0.670366\pi$
$31$	−0.112086	+	0.0647129i	−0.0201313	+	0.0116228i	0.489901	+	0.871778i	$0.337033\pi$
$32$	−2.80039	+	1.61680i	−0.495043	+	0.285813i
$33$	−0.0767447	+	0.262352i	−0.0133595	+	0.0456696i
$34$	−4.25696	−	2.45776i	−0.730062	−	0.421502i
$35$	6.98284	−	2.76016i	1.18032	−	0.466552i
$36$	1.50000	+	0.959702i	0.250000	+	0.159950i
$37$	−2.46050			−0.404505			−0.202252	−	0.979333i	$-0.564826\pi$
$37$	−2.46050			−0.404505			−0.202252	+	0.979333i	$0.564826\pi$
$38$	−3.75700	+	6.50731i	−0.609465	+	1.05563i
$39$	4.71780	+	4.93786i	0.755453	+	0.790690i
$40$	−7.55955	+	4.36451i	−1.19527	+	0.690089i
$41$	1.99569	+	3.45664i	0.311675	+	0.539836i	0.978725	−	0.205176i	$-0.0657768\pi$
$41$	1.99569	+	3.45664i	0.311675	+	0.539836i	−0.667050	+	0.745013i	$0.732443\pi$
$42$	−4.93588	−	2.27420i	−0.761622	−	0.350916i
$43$	3.28434	−	5.68864i	0.500857	−	0.867509i	−0.499143	−	0.866520i	$-0.666352\pi$
$43$	3.28434	−	5.68864i	0.500857	−	0.867509i	1.00000		0.000989450i	$-0.000314952\pi$
$44$		−	0.0936766i		−	0.0141223i
$45$	7.17167	+	4.58845i	1.06909	+	0.684005i
$46$	0.647664			0.0954928
$47$	4.33370	−	7.50619i	0.632135	−	1.09489i	−0.354979	−	0.934874i	$-0.615512\pi$
$47$	4.33370	−	7.50619i	0.632135	−	1.09489i	0.987114	−	0.160016i	$-0.0511547\pi$
$48$	4.09030	+	1.19652i	0.590385	+	0.172703i
$49$	−6.69896	−	2.03076i	−0.956994	−	0.290109i
$50$	−3.13667	+	1.81096i	−0.443593	+	0.256108i
$51$	−1.69961	−	6.97504i	−0.237993	−	0.976701i
$52$	−2.02688	−	1.17022i	−0.281078	−	0.162280i
$53$			2.60234i			0.357459i	0.983898	+	0.178730i	$0.0571988\pi$
$53$			2.60234i			0.357459i	−0.983898	+	0.178730i	$0.942801\pi$
$54$	−1.18460	−	6.04732i	−0.161204	−	0.822936i
$55$		−	0.447879i		−	0.0603920i
$56$	8.04981	+	1.19332i	1.07570	+	0.159464i
$57$	−10.6623	+	2.59808i	−1.41225	+	0.344124i
$58$	2.75729	+	4.77577i	0.362051	+	0.627090i
$59$	−1.80686	−	3.12957i	−0.235233	−	0.407436i	0.724107	−	0.689687i	$-0.242252\pi$
$59$	−1.80686	−	3.12957i	−0.235233	−	0.407436i	−0.959340	+	0.282252i	$0.908919\pi$
$60$	−2.80039	−	0.819187i	−0.361529	−	0.105757i
$61$	2.91472	+	1.68281i	0.373191	+	0.215462i	0.674852	−	0.737953i	$-0.264208\pi$
$61$	2.91472	+	1.68281i	0.373191	+	0.215462i	−0.301660	+	0.953415i	$0.597541\pi$
$62$	−0.153489			−0.0194932
$63$	−2.57843	−	7.50678i	−0.324852	−	0.945765i
$64$	−8.75583			−1.09448
$65$	−9.69076	−	5.59496i	−1.20199	−	0.693970i
$66$	−0.234385	+	0.223939i	−0.0288508	+	0.0275650i
$67$	−0.663715	−	1.14959i	−0.0810857	−	0.140445i	0.822631	−	0.568576i	$-0.192505\pi$
$67$	−0.663715	−	1.14959i	−0.0810857	−	0.140445i	−0.903717	+	0.428131i	$0.859172\pi$
$68$	1.23016	+	2.13069i	0.149178	+	0.258384i
$69$	0.653450	+	0.683930i	0.0786661	+	0.0823355i
$70$	8.80835	+	1.30577i	1.05280	+	0.156069i
$71$			0.409310i			0.0485761i	0.999705	+	0.0242881i	$0.00773189\pi$
$71$			0.409310i			0.0485761i	−0.999705	+	0.0242881i	$0.992268\pi$
$72$	4.24484	+	8.19304i	0.500259	+	0.965559i
$73$		−	15.0124i		−	1.75707i	−0.477681	−	0.878533i	$-0.658522\pi$
$73$		−	15.0124i		−	1.75707i	0.477681	−	0.878533i	$-0.341478\pi$
$74$	−2.52704	−	1.45899i	−0.293763	−	0.169604i
$75$	−5.07706	−	1.48517i	−0.586249	−	0.171493i
$76$	3.25704	−	1.88045i	0.373608	−	0.215703i
$77$	−0.259540	+	0.327080i	−0.0295773	+	0.0372742i
$78$	1.91741	+	7.86887i	0.217104	+	0.890974i
$79$	−2.16372	+	3.74766i	−0.243437	+	0.421645i	−0.961691	−	0.274136i	$-0.911608\pi$
$79$	−2.16372	+	3.74766i	−0.243437	+	0.421645i	0.718254	+	0.695781i	$0.244942\pi$
$80$	−6.98284			−0.780706
$81$	5.19076	−	7.35228i	0.576751	−	0.816920i
$82$			4.73348i			0.522726i
$83$	−3.22585	+	5.58733i	−0.354083	+	0.613289i	−0.986961	−	0.160963i	$-0.948540\pi$
$83$	−3.22585	+	5.58733i	−0.354083	+	0.613289i	0.632878	+	0.774252i	$0.281874\pi$
$84$	1.57038	+	2.22103i	0.171342	+	0.242334i
$85$	5.88151	+	10.1871i	0.637940	+	1.10494i
$86$	6.74630	−	3.89498i	0.727473	−	0.420007i
$87$	−2.26127	+	7.73013i	−0.242433	+	0.828757i
$88$	0.242705	−	0.420378i	0.0258725	−	0.0448125i
$89$	−5.05368			−0.535689			−0.267845	−	0.963462i	$-0.586311\pi$
$89$	−5.05368			−0.535689			−0.267845	+	0.963462i	$0.586311\pi$
$90$	4.64483	+	8.96507i	0.489608	+	0.945001i
$91$	3.83482	+	9.70160i	0.401999	+	1.01700i
$92$	−0.280738	−	0.162084i	−0.0292690	−	0.0168984i
$93$	−0.154861	−	0.162084i	−0.0160583	−	0.0168073i
$94$	8.90179	−	5.13945i	0.918150	−	0.530094i
$95$	15.5723	−	8.99066i	1.59768	−	0.922422i
$96$	−3.86908	−	4.04955i	−0.394887	−	0.413306i
$97$	2.18452	+	1.26123i	0.221805	+	0.128059i	0.606786	−	0.794866i	$-0.292459\pi$
$97$	2.18452	+	1.26123i	0.221805	+	0.128059i	−0.384981	+	0.922925i	$0.625792\pi$
$98$	−5.67594	−	6.05791i	−0.573357	−	0.611941i
$99$	−0.472958	−	0.0215693i	−0.0475341	−	0.00216779i
$100$	1.81284			0.181284
$101$	−1.49573	+	2.59068i	−0.148831	+	0.257782i	−0.930796	−	0.365540i	$-0.880884\pi$
$101$	−1.49573	+	2.59068i	−0.148831	+	0.257782i	0.781965	+	0.623323i	$0.214218\pi$
$102$	2.39037	−	8.17147i	0.236682	−	0.809096i
$103$	11.4286	−	6.59832i	1.12610	−	0.650152i	0.183146	−	0.983086i	$-0.441372\pi$
$103$	11.4286	−	6.59832i	1.12610	−	0.650152i	0.942950	+	0.332934i	$0.108038\pi$
$104$	−6.06382	−	10.5028i	−0.594606	−	1.02989i
$105$	7.50816	+	10.6190i	0.732721	+	1.03631i
$106$	−1.54309	+	2.67272i	−0.149879	+	0.259597i
$107$			19.5555i			1.89051i	0.326339	+	0.945253i	$0.394185\pi$
$107$			19.5555i			1.89051i	−0.326339	+	0.945253i	$0.605815\pi$
$108$	−0.999921	+	2.91775i	−0.0962174	+	0.280760i
$109$	13.2484			1.26897			0.634485	−	0.772935i	$-0.281212\pi$
$109$	13.2484			1.26897			0.634485	+	0.772935i	$0.281212\pi$
$110$	0.265576	−	0.459990i	0.0253216	−	0.0438584i
$111$	−1.00893	−	4.14057i	−0.0957638	−	0.393005i
$112$	5.09948	+	4.04647i	0.481855	+	0.382355i
$113$	−8.72665	+	5.03834i	−0.820935	+	0.473967i	−0.850739	−	0.525589i	$-0.823845\pi$
$113$	−8.72665	+	5.03834i	−0.820935	+	0.473967i	0.0298041	+	0.999556i	$0.490512\pi$
$114$	−12.4911	−	3.65399i	−1.16990	−	0.342227i
$115$	−1.34224	−	0.774943i	−0.125165	−	0.0722638i
$116$		−	2.76016i		−	0.256274i
$117$	−6.37495	+	9.96395i	−0.589364	+	0.921167i
$118$		−	4.28561i		−	0.394522i
$119$	1.60809	−	10.8478i	0.147414	−	0.994412i
$120$	−10.4445	−	10.9316i	−0.953444	−	0.997917i
$121$	−5.48755	−	9.50471i	−0.498868	−	0.864065i
$122$	1.99569	+	3.45664i	0.180681	+	0.312949i
$123$	−4.99854	+	4.77577i	−0.450703	+	0.430617i
$124$	0.0665320	+	0.0384123i	0.00597475	+	0.00344952i
$125$	−5.52245			−0.493943
$126$	1.80308	−	9.23869i	0.160631	−	0.823048i
$127$	−12.4897			−1.10828			−0.554140	−	0.832423i	$-0.686953\pi$
$127$	−12.4897			−1.10828			−0.554140	+	0.832423i	$0.686953\pi$
$128$	−3.39183	−	1.95827i	−0.299798	−	0.173089i
$129$	10.9197	+	3.19429i	0.961422	+	0.281241i
$130$	−6.63521	−	11.4925i	−0.581946	−	1.00796i
$131$	5.02249	+	8.69921i	0.438817	+	0.760054i	0.997599	−	0.0692612i	$-0.0220642\pi$
$131$	5.02249	+	8.69921i	0.438817	+	0.760054i	−0.558781	+	0.829315i	$0.688731\pi$
$132$	0.157640	−	0.0384123i	0.0137208	−	0.00334336i
$133$	−16.5822	−	2.45818i	−1.43786	−	0.213151i
$134$		−	1.57423i		−	0.135993i
$135$	−4.78074	+	13.9501i	−0.411460	+	1.20063i
$136$			12.7488i			1.09320i
$137$	−6.96410	−	4.02073i	−0.594984	−	0.343514i	0.172082	−	0.985083i	$-0.444951\pi$
$137$	−6.96410	−	4.02073i	−0.594984	−	0.343514i	−0.767066	+	0.641569i	$0.778284\pi$
$138$	0.265576	+	1.08990i	0.0226073	+	0.0927781i
$139$	−16.3702	+	9.45136i	−1.38850	+	0.801654i	−0.993147	−	0.116873i	$-0.962713\pi$
$139$	−16.3702	+	9.45136i	−1.38850	+	0.801654i	−0.395358	+	0.918527i	$0.629379\pi$
$140$	−3.49131	−	2.77038i	−0.295070	−	0.234140i
$141$	14.4086	+	4.21488i	1.21342	+	0.354957i
$142$	−0.242705	+	0.420378i	−0.0203674	+	0.0352774i
$143$	0.622259			0.0520359
$144$	−0.336285	+	7.37385i	−0.0280237	+	0.614488i
$145$		−	13.1966i		−	1.09592i
$146$	8.90179	−	15.4184i	0.736717	−	1.27603i
$147$	0.670471	−	12.1058i	0.0552995	−	0.998470i
$148$	0.730252	+	1.26483i	0.0600264	+	0.103969i
$149$	16.8063	−	9.70313i	1.37683	−	0.794912i	0.385051	−	0.922895i	$-0.374184\pi$
$149$	16.8063	−	9.70313i	1.37683	−	0.794912i	0.991776	+	0.127984i	$0.0408505\pi$
$150$	−4.33370	−	4.53585i	−0.353845	−	0.370350i
$151$	0.893968	−	1.54840i	0.0727501	−	0.126007i	−0.827356	−	0.561678i	$-0.810156\pi$
$151$	0.893968	−	1.54840i	0.0727501	−	0.126007i	0.900106	+	0.435672i	$0.143489\pi$
$152$	19.4881			1.58070
$153$	11.0408	−	5.72026i	0.892592	−	0.462455i
$154$	−0.460505	+	0.182027i	−0.0371085	+	0.0146682i
$155$	0.318097	+	0.183653i	0.0255502	+	0.0147514i
$156$	1.13814	−	3.89071i	0.0911238	−	0.311506i
$157$	−3.80255	+	2.19540i	−0.303477	+	0.175212i	−0.644004	−	0.765022i	$-0.722728\pi$
$157$	−3.80255	+	2.19540i	−0.303477	+	0.175212i	0.340527	+	0.940235i	$0.389395\pi$
$158$	−4.44445	+	2.56601i	−0.353582	+	0.204140i
$159$	−4.37926	+	1.06710i	−0.347298	+	0.0846262i
$160$	7.94742	+	4.58845i	0.628299	+	0.362749i
$161$	0.531151	+	1.34374i	0.0418606	+	0.105902i
$162$	9.69076	−	4.47318i	0.761378	−	0.351446i
$163$	5.43560			0.425749			0.212874	−	0.977080i	$-0.431717\pi$
$163$	5.43560			0.425749			0.212874	+	0.977080i	$0.431717\pi$
$164$	1.18460	−	2.05179i	0.0925018	−	0.160218i
$165$	0.753696	−	0.183653i	0.0586751	−	0.0142974i
$166$	−6.62616	+	3.82562i	−0.514290	+	0.296925i
$167$	5.25273	+	9.09799i	0.406468	+	0.704024i	0.994491	−	0.104821i	$-0.0334268\pi$
$167$	5.25273	+	9.09799i	0.406468	+	0.704024i	−0.588023	+	0.808844i	$0.700093\pi$
$168$	1.29271	+	14.0357i	0.0997344	+	1.08287i
$169$	1.27335	−	2.20550i	0.0979497	−	0.169654i
$170$			13.9501i			1.06992i
$171$	−8.74415	−	16.8772i	−0.668682	−	1.29063i
$172$	−3.89903			−0.297298
$173$	−8.77949	+	15.2065i	−0.667492	+	1.15613i	0.311111	+	0.950374i	$0.399299\pi$
$173$	−8.77949	+	15.2065i	−0.667492	+	1.15613i	−0.978603	+	0.205757i	$0.934034\pi$
$174$	−6.90610	+	6.59832i	−0.523550	+	0.500218i
$175$	−6.32969	−	5.02265i	−0.478480	−	0.379677i
$176$	0.336285	−	0.194154i	0.0253484	−	0.0146349i
$177$	4.52558	−	4.32389i	0.340163	−	0.325004i
$178$	−5.19035	−	2.99665i	−0.389033	−	0.224608i
$179$			18.2033i			1.36058i	0.732945	+	0.680288i	$0.238145\pi$
$179$			18.2033i			1.36058i	−0.732945	+	0.680288i	$0.761855\pi$
$180$	0.230234	−	5.04844i	0.0171606	−	0.376288i
$181$			6.60182i			0.490710i	0.969433	+	0.245355i	$0.0789045\pi$
$181$			6.60182i			0.490710i	−0.969433	+	0.245355i	$0.921096\pi$
$182$	−1.81416	+	12.2379i	−0.134475	+	0.907130i
$183$	−1.63667	+	5.59496i	−0.120986	+	0.413591i
$184$	−0.839883	−	1.45472i	−0.0619170	−	0.107243i
$185$	3.49142	+	6.04732i	0.256694	+	0.444608i
$186$	−0.0629386	−	0.258294i	−0.00461488	−	0.0189390i
$187$	−0.566492	−	0.327065i	−0.0414260	−	0.0239173i
$188$	−5.14479			−0.375223
$189$	11.5752	−	7.41718i	0.841972	−	0.539521i
$190$	21.3245			1.54704
$191$	−12.3063	−	7.10506i	−0.890454	−	0.514104i	−0.0163630	−	0.999866i	$-0.505209\pi$
$191$	−12.3063	−	7.10506i	−0.890454	−	0.514104i	−0.874091	+	0.485762i	$0.838542\pi$
$192$	−3.59034	−	14.7344i	−0.259111	−	1.06337i
$193$	5.00214	+	8.66395i	0.360062	+	0.623645i	0.987971	−	0.154642i	$-0.0494223\pi$
$193$	5.00214	+	8.66395i	0.360062	+	0.623645i	−0.627909	+	0.778287i	$0.716089\pi$
$194$	1.49573	+	2.59068i	0.107387	+	0.186000i
$195$	5.44156	−	18.6020i	0.389678	−	1.33211i
$196$	0.944259	+	4.04634i	0.0674470	+	0.289024i
$197$		−	20.1017i		−	1.43218i	−0.698006	−	0.716092i	$-0.745929\pi$
$197$		−	20.1017i		−	1.43218i	0.698006	−	0.716092i	$-0.254071\pi$
$198$	−0.472958	−	0.302599i	−0.0336117	−	0.0215048i
$199$			12.9378i			0.917136i	0.888659	+	0.458568i	$0.151637\pi$
$199$			12.9378i			0.917136i	−0.888659	+	0.458568i	$0.848363\pi$
$200$	8.13521	+	4.69687i	0.575246	+	0.332119i
$201$	1.66238	−	1.58830i	0.117256	−	0.112030i
$202$	−3.07236	+	1.77383i	−0.216170	+	0.124806i
$203$	−7.64729	+	9.63734i	−0.536735	+	0.676408i
$204$	−3.08113	+	2.94381i	−0.215722	+	0.206108i
$205$	5.66372	−	9.80984i	0.395571	−	0.685149i
$206$	15.6502			1.09040
$207$	−0.882977	+	1.38008i	−0.0613712	+	0.0959222i
$208$		−	9.70160i		−	0.672685i
$209$	−0.499960	+	0.865957i	−0.0345830	+	0.0598995i
$210$	1.41452	+	15.3582i	0.0976109	+	1.05982i
$211$	−4.50720	−	7.80669i	−0.310288	−	0.537435i	0.668136	−	0.744039i	$-0.267092\pi$
$211$	−4.50720	−	7.80669i	−0.310288	−	0.537435i	−0.978425	+	0.206604i	$0.933759\pi$
$212$	1.33775	−	0.772349i	0.0918769	−	0.0530451i
$213$	−0.688791	+	0.167838i	−0.0471952	+	0.0115001i
$214$	−11.5957	+	20.0844i	−0.792667	+	1.37294i
$215$	−18.6417			−1.27135
$216$	−12.0467	+	10.5028i	−0.819677	+	0.714628i
$217$	−0.125877	−	0.318453i	−0.00854510	−	0.0216180i
$218$	13.6067	+	7.85584i	0.921562	+	0.532064i
$219$	25.2630	−	6.15585i	1.70712	−	0.415974i
$220$	−0.230234	+	0.132926i	−0.0155224	+	0.00896185i
$221$	−14.1534	+	8.17147i	−0.952061	+	0.549672i
$222$	1.41899	−	4.85080i	0.0952361	−	0.325564i
$223$	1.95429	+	1.12831i	0.130869	+	0.0755571i	0.564005	−	0.825771i	$-0.309260\pi$
$223$	1.95429	+	1.12831i	0.130869	+	0.0755571i	−0.433136	+	0.901328i	$0.642593\pi$
$224$	−3.14495	−	7.95631i	−0.210131	−	0.531604i
$225$	0.417411	−	9.15274i	0.0278274	−	0.610183i
$226$	−11.9502			−0.794915
$227$	9.32085	−	16.1442i	0.618647	−	1.07153i	−0.371086	−	0.928598i	$-0.621015\pi$
$227$	9.32085	−	16.1442i	0.618647	−	1.07153i	0.989733	−	0.142929i	$-0.0456522\pi$
$228$	4.50000	+	4.70990i	0.298020	+	0.311921i
$229$	12.3891	−	7.15283i	0.818692	−	0.472672i	−0.0312731	−	0.999511i	$-0.509956\pi$
$229$	12.3891	−	7.15283i	0.818692	−	0.472672i	0.849965	+	0.526839i	$0.176623\pi$
$230$	−0.919025	−	1.59180i	−0.0605987	−	0.104960i
$231$	−0.656839	−	0.302638i	−0.0432168	−	0.0199121i
$232$	7.15126	−	12.3863i	0.469503	−	0.813204i
$233$		−	17.0679i		−	1.11815i	−0.829116	−	0.559077i	$-0.811156\pi$
$233$		−	17.0679i		−	1.11815i	0.829116	−	0.559077i	$-0.188844\pi$
$234$	−12.4556	+	6.45329i	−0.814248	+	0.421865i
$235$	−24.5979			−1.60459
$236$	−1.07251	+	1.85765i	−0.0698148	+	0.120923i
$237$	−7.19385	−	2.10439i	−0.467291	−	0.136695i
$238$	8.08390	−	10.1876i	0.524001	−	0.660361i
$239$	1.93560	−	1.11752i	0.125203	−	0.0722863i	−0.436090	−	0.899903i	$-0.643637\pi$
$239$	1.93560	−	1.11752i	0.125203	−	0.0722863i	0.561294	+	0.827617i	$0.310304\pi$
$240$	−2.86333	−	11.7508i	−0.184827	−	0.758512i
$241$	3.91464	+	2.26012i	0.252164	+	0.145587i	0.620755	−	0.784005i	$-0.286826\pi$
$241$	3.91464	+	2.26012i	0.252164	+	0.145587i	−0.368591	+	0.929592i	$0.620160\pi$
$242$		−	13.0157i		−	0.836678i
$243$	14.5010	+	5.72026i	0.930239	+	0.366955i
$244$		−	1.99777i		−	0.127894i
$245$	4.51461	+	19.3460i	0.288428	+	1.23597i
$246$	−7.96557	+	1.94097i	−0.507866	+	0.123752i
$247$	12.4911	+	21.6353i	0.794793	+	1.37662i
$248$	0.199044	+	0.344754i	0.0126393	+	0.0218919i
$249$	−10.7252	−	3.13740i	−0.679681	−	0.198825i
$250$	−5.67179	−	3.27461i	−0.358716	−	0.207105i
$251$	21.1727			1.33641			0.668205	−	0.743978i	$-0.267063\pi$
$251$	21.1727			1.33641			0.668205	+	0.743978i	$0.267063\pi$
$252$	−3.09364	+	3.55339i	−0.194881	+	0.223842i
$253$	0.0861875			0.00541856
$254$	−12.8274	−	7.40592i	−0.804865	−	0.464689i
$255$	−14.7312	+	14.0747i	−0.922505	+	0.881393i
$256$	6.43346	+	11.1431i	0.402091	+	0.696443i
$257$	−15.6502	−	27.1070i	−0.976236	−	1.69089i	−0.675796	−	0.737089i	$-0.736200\pi$
$257$	−15.6502	−	27.1070i	−0.976236	−	1.69089i	−0.300440	−	0.953801i	$-0.597134\pi$
$258$	9.32085	+	9.75562i	0.580291	+	0.607358i
$259$	0.954606	−	6.43951i	0.0593163	−	0.400132i
$260$			6.64211i			0.411926i
$261$	−13.9356	−	0.635534i	−0.862592	−	0.0393385i
$262$			11.9126i			0.735964i
$263$	−5.78220	−	3.33836i	−0.356546	−	0.205852i	0.311019	−	0.950404i	$-0.399330\pi$
$263$	−5.78220	−	3.33836i	−0.356546	−	0.205852i	−0.667564	+	0.744552i	$0.732663\pi$
$264$	0.806939	+	0.236051i	0.0496637	+	0.0145279i
$265$	6.39593	−	3.69269i	0.392899	−	0.226840i
$266$	−15.5730	−	12.3573i	−0.954842	−	0.757673i
$267$	−2.07227	−	8.50440i	−0.126821	−	0.520461i
$268$	−0.393968	+	0.682372i	−0.0240654	+	0.0416825i
$269$	10.6589			0.649887			0.324944	−	0.945733i	$-0.394655\pi$
$269$	10.6589			0.649887			0.324944	+	0.945733i	$0.394655\pi$
$270$	−13.1819	+	11.4925i	−0.802225	+	0.699413i
$271$		−	7.44498i		−	0.452250i	−0.974098	−	0.226125i	$-0.927394\pi$
$271$		−	7.44498i		−	0.452250i	0.974098	−	0.226125i	$-0.0726058\pi$
$272$	−5.09924	+	8.83214i	−0.309187	+	0.535527i
$273$	−14.7535	+	10.4314i	−0.892922	+	0.631340i
$274$	−4.76829	−	8.25891i	−0.288063	−	0.498939i
$275$	−0.417411	+	0.240992i	−0.0251708	+	0.0145324i
$276$	0.157640	−	0.538892i	0.00948882	−	0.0324375i
$277$	13.2793	−	23.0004i	0.797874	−	1.38196i	−0.123124	−	0.992391i	$-0.539291\pi$
$277$	13.2793	−	23.0004i	0.797874	−	1.38196i	0.920998	−	0.389568i	$-0.127376\pi$
$278$	−22.4172			−1.34450
$279$	0.209256	−	0.327065i	0.0125278	−	0.0195808i
$280$	−8.48968	−	21.4778i	−0.507356	−	1.28354i
$281$	21.0993	+	12.1817i	1.25868	+	0.726699i	0.972818	−	0.231572i	$-0.0743869\pi$
$281$	21.0993	+	12.1817i	1.25868	+	0.726699i	0.285862	+	0.958271i	$0.407720\pi$
$282$	12.2989	+	12.8726i	0.732390	+	0.766552i
$283$	−7.49302	+	4.32610i	−0.445414	+	0.257160i	−0.705891	−	0.708320i	$-0.749453\pi$
$283$	−7.49302	+	4.32610i	−0.445414	+	0.257160i	0.260478	+	0.965480i	$0.416120\pi$
$284$	0.210408	−	0.121479i	0.0124854	−	0.00720844i
$285$	21.5150	+	22.5186i	1.27444	+	1.33389i
$286$	0.639086	+	0.368977i	0.0377900	+	0.0218181i
$287$	−9.82082	+	3.88195i	−0.579704	+	0.229144i
$288$	5.22812	−	8.17147i	0.308070	−	0.481508i
$289$	0.179961			0.0105860
$290$	7.82512	−	13.5535i	0.459507	−	0.795890i
$291$	−1.22665	+	4.19331i	−0.0719077	+	0.245816i
$292$	−7.71719	+	4.45552i	−0.451614	+	0.260740i
$293$	−4.40023	−	7.62143i	−0.257064	−	0.445249i	0.708390	−	0.705821i	$-0.249422\pi$
$293$	−4.40023	−	7.62143i	−0.257064	−	0.445249i	−0.965454	+	0.260573i	$0.916089\pi$
$294$	7.86690	−	12.0356i	0.458807	−	0.701931i
$295$	−5.12782	+	8.88164i	−0.298553	+	0.517109i
$296$			7.56800i			0.439881i
$297$	−0.157640	−	0.804744i	−0.00914721	−	0.0466960i
$298$	23.0144			1.33319
$299$	1.07667	−	1.86484i	0.0622652	−	0.107846i
$300$	0.743359	+	3.05067i	0.0429178	+	0.176131i
$301$	13.6138	+	10.8026i	0.784686	+	0.622654i
$302$	1.83628	−	1.06018i	0.105666	−	0.0610065i
$303$	−4.97296	−	1.45472i	−0.285689	−	0.0835715i
$304$	13.5011	+	7.79485i	0.774339	+	0.447065i
$305$		−	9.55155i		−	0.546920i
$306$	14.7312	+	0.671818i	0.842128	+	0.0384053i
$307$		−	11.1747i		−	0.637771i	−0.947793	−	0.318886i	$-0.896691\pi$
$307$		−	11.1747i		−	0.637771i	0.947793	−	0.318886i	$-0.103309\pi$
$308$	0.245166	+	0.0363439i	0.0139696	+	0.00207088i
$309$	15.7901	+	16.5266i	0.898266	+	0.940165i
$310$	0.217799	+	0.377240i	0.0123702	+	0.0214258i
$311$	−8.20279	−	14.2076i	−0.465137	−	0.805641i	0.534070	−	0.845440i	$-0.320662\pi$
$311$	−8.20279	−	14.2076i	−0.465137	−	0.805641i	−0.999208	+	0.0397985i	$0.987328\pi$
$312$	15.1878	−	14.5110i	0.859842	−	0.821522i
$313$	7.10514	+	4.10216i	0.401606	+	0.231868i	0.687177	−	0.726490i	$-0.258850\pi$
$313$	7.10514	+	4.10216i	0.401606	+	0.231868i	−0.285570	+	0.958358i	$0.592183\pi$
$314$	−5.20717			−0.293858
$315$	−14.7911	+	16.9892i	−0.833382	+	0.957231i
$316$	2.56867			0.144499
$317$	19.8427	+	11.4562i	1.11448	+	0.643443i	0.939985	−	0.341215i	$-0.110839\pi$
$317$	19.8427	+	11.4562i	1.11448	+	0.643443i	0.174491	+	0.984659i	$0.444172\pi$
$318$	−5.13043	−	1.50079i	−0.287700	−	0.0841599i
$319$	0.366926	+	0.635534i	0.0205439	+	0.0355831i
$320$	12.4244	+	21.5197i	0.694545	+	1.20299i
$321$	−32.9083	+	8.01878i	−1.83676	+	0.447565i
$322$	−0.251275	+	1.69503i	−0.0140030	+	0.0944605i
$323$		−	26.2618i		−	1.46125i
$324$	−5.32004	−	0.486253i	−0.295558	−	0.0270140i
$325$			12.0420i			0.667972i
$326$	5.58259	+	3.22311i	0.309191	+	0.178512i
$327$	5.43255	+	22.2946i	0.300420	+	1.23290i
$328$	10.6319	−	6.13833i	0.587049	−	0.338933i
$329$	17.9635	+	14.2541i	0.990359	+	0.785856i
$330$	0.882977	+	0.258294i	0.0486063	+	0.0142186i
$331$	−9.63161	+	16.6824i	−0.529401	+	0.916950i	0.470011	+	0.882661i	$0.344250\pi$
$331$	−9.63161	+	16.6824i	−0.529401	+	0.916950i	−0.999412	+	0.0342892i	$0.989083\pi$
$332$	3.82959			0.210176
$333$	6.55408	−	3.39569i	0.359162	−	0.186083i
$334$			12.4587i			0.681709i
$335$	−1.88361	+	3.26250i	−0.102912	+	0.178249i
$336$	−4.71840	+	10.2407i	−0.257410	+	0.558677i
$337$	−2.26829	−	3.92878i	−0.123561	−	0.214015i	0.797608	−	0.603176i	$-0.206098\pi$
$337$	−2.26829	−	3.92878i	−0.123561	−	0.214015i	−0.921170	+	0.389161i	$0.872765\pi$
$338$	2.61556	−	1.51009i	0.142268	−	0.0821383i
$339$	−12.0570	−	12.6193i	−0.654844	−	0.685389i
$340$	3.49115	−	6.04684i	0.189334	−	0.327936i
$341$	−0.0204255			−0.00110610
$342$	1.02696	−	22.5186i	0.0555317	−	1.21767i
$343$	7.91381	−	16.7443i	0.427306	−	0.904107i
$344$	−17.4971	−	10.1019i	−0.943379	−	0.544660i
$345$	0.753696	−	2.57651i	0.0405776	−	0.138714i
$346$	−18.0338	+	10.4118i	−0.969504	+	0.559743i
$347$	7.56294	−	4.36646i	0.406000	−	0.234404i	−0.283070	−	0.959099i	$-0.591353\pi$
$347$	7.56294	−	4.36646i	0.406000	−	0.234404i	0.689070	+	0.724695i	$0.258019\pi$
$348$	4.64483	−	1.13181i	0.248989	−	0.0606713i
$349$	−7.82927	−	4.52023i	−0.419091	−	0.241963i	0.275597	−	0.961273i	$-0.411124\pi$
$349$	−7.82927	−	4.52023i	−0.419091	−	0.241963i	−0.694689	+	0.719311i	$0.744458\pi$
$350$	−3.52261	−	8.91175i	−0.188292	−	0.476353i
$351$	−19.3815	−	6.64211i	−1.03451	−	0.354529i
$352$	−0.510317			−0.0272000
$353$	−0.607896	+	1.05291i	−0.0323550	+	0.0560406i	−0.881750	−	0.471718i	$-0.843634\pi$
$353$	−0.607896	+	1.05291i	−0.0323550	+	0.0560406i	0.849394	+	0.527758i	$0.176967\pi$
$354$	7.21187	−	1.75732i	0.383307	−	0.0934005i
$355$	1.00598	−	0.580805i	0.0533920	−	0.0308259i
$356$	1.49988	+	2.59787i	0.0794936	+	0.137687i
$357$	18.9141	−	1.74202i	1.00104	−	0.0921975i
$358$	−10.7939	+	18.6955i	−0.570473	+	0.988089i
$359$			17.3069i			0.913424i	0.889615	+	0.456712i	$0.150973\pi$
$359$			17.3069i			0.913424i	−0.889615	+	0.456712i	$0.849027\pi$
$360$	14.1131	−	22.0586i	0.743826	−	1.16259i
$361$	−21.1445			−1.11287
$362$	−3.91464	+	6.78035i	−0.205749	+	0.356367i
$363$	13.7445	−	13.1319i	0.721397	−	0.689248i
$364$	3.84902	−	4.85064i	0.201743	−	0.254243i
$365$	−36.8968	+	21.3024i	−1.93127	+	1.11502i
$366$	−4.99854	+	4.77577i	−0.261278	+	0.249634i
$367$	24.4297	+	14.1045i	1.27522	+	0.736250i	0.975966	−	0.217923i	$-0.0699282\pi$
$367$	24.4297	+	14.1045i	1.27522	+	0.736250i	0.299256	+	0.954173i	$0.403262\pi$
$368$		−	1.34374i		−	0.0700474i
$369$	−10.0864	−	6.45329i	−0.525077	−	0.335945i
$370$			8.28114i			0.430516i
$371$	−6.81073	−	1.00964i	−0.353595	−	0.0524177i
$372$	−0.0373591	+	0.127712i	−0.00193698	+	0.00662155i
$373$	−14.1264	−	24.4676i	−0.731435	−	1.26688i	−0.956270	−	0.292486i	$-0.905518\pi$
$373$	−14.1264	−	24.4676i	−0.731435	−	1.26688i	0.224835	−	0.974397i	$-0.427816\pi$
$374$	−0.387874	−	0.671818i	−0.0200565	−	0.0347389i
$375$	−2.26449	−	9.29325i	−0.116938	−	0.479902i
$376$	−23.0875	−	13.3296i	−1.19065	−	0.687420i
$377$	18.3347			0.944287
$378$	16.2863	−	0.754090i	0.837679	−	0.0387862i
$379$	14.6447			0.752250			0.376125	−	0.926569i	$-0.377256\pi$
$379$	14.6447			0.752250			0.376125	+	0.926569i	$0.377256\pi$
$380$	−9.24338	−	5.33667i	−0.474175	−	0.273765i
$381$	−5.12142	−	21.0178i	−0.262378	−	1.07677i
$382$	−8.42607	−	14.5944i	−0.431115	−	0.746714i
$383$	−12.3932	−	21.4657i	−0.633264	−	1.09684i	−0.986880	−	0.161454i	$-0.948382\pi$
$383$	−12.3932	−	21.4657i	−0.633264	−	1.09684i	0.353617	−	0.935390i	$-0.384952\pi$
$384$	1.90458	−	6.51081i	0.0971928	−	0.332253i
$385$	1.17217	+	0.173764i	0.0597391	+	0.00885585i
$386$			11.8643i			0.603878i
$387$	−0.897761	+	19.6856i	−0.0456357	+	1.00067i
$388$		−	1.49729i		−	0.0760131i
$389$	4.43706	+	2.56174i	0.224968	+	0.129885i	0.608248	−	0.793747i	$-0.291872\pi$
$389$	4.43706	+	2.56174i	0.224968	+	0.129885i	−0.383281	+	0.923632i	$0.625206\pi$
$390$	16.6190	−	15.8783i	0.841535	−	0.804031i
$391$	−1.96035	+	1.13181i	−0.0991391	+	0.0572380i
$392$	−6.24620	+	20.6046i	−0.315481	+	1.04069i
$393$	−12.5797	+	12.0190i	−0.634560	+	0.606280i
$394$	11.9195	−	20.6453i	0.600498	−	1.04009i
$395$	12.2811			0.617930
$396$	0.129281	+	0.249528i	0.00649663	+	0.0125392i
$397$			1.92094i			0.0964093i	0.998837	+	0.0482046i	$0.0153500\pi$
$397$			1.92094i			0.0964093i	−0.998837	+	0.0482046i	$0.984650\pi$
$398$	−7.67163	+	13.2877i	−0.384544	+	0.666050i
$399$	−2.66290	−	28.9127i	−0.133312	−	1.44745i
$400$	3.75729	+	6.50783i	0.187865	+	0.325391i
$401$	−12.4612	+	7.19446i	−0.622282	+	0.359274i	−0.777757	−	0.628565i	$-0.783642\pi$
$401$	−12.4612	+	7.19446i	−0.622282	+	0.359274i	0.155475	+	0.987840i	$0.450309\pi$
$402$	2.64914	−	0.645517i	0.132127	−	0.0321955i
$403$	−0.255158	+	0.441947i	−0.0127103	+	0.0220150i
$404$	1.77567			0.0883429
$405$	−25.4357	−	2.32483i	−1.26391	−	0.115522i
$406$	−13.5687	+	5.36339i	−0.673402	+	0.266181i
$407$	−0.336285	−	0.194154i	−0.0166690	−	0.00962386i
$408$	−21.4538	+	5.22765i	−1.06212	+	0.258807i
$409$	−8.42281	+	4.86291i	−0.416481	+	0.240455i	−0.693571	−	0.720389i	$-0.743963\pi$
$409$	−8.42281	+	4.86291i	−0.416481	+	0.240455i	0.277090	+	0.960844i	$0.410630\pi$
$410$	11.6337	−	6.71675i	0.574550	−	0.331717i
$411$	3.91049	−	13.3680i	0.192890	−	0.659394i
$412$	−6.78380	−	3.91663i	−0.334214	−	0.192958i
$413$	8.89158	−	3.51464i	0.437526	−	0.172944i
$414$	−1.72519	+	0.893828i	−0.0847885	+	0.0439292i
$415$	18.3097			0.898789
$416$	−6.37495	+	11.0417i	−0.312558	+	0.541366i
$417$	−22.6175	−	23.6725i	−1.10758	−	1.15925i
$418$	−1.02696	+	0.592916i	−0.0502303	+	0.0290005i
$419$	14.9512	+	25.8963i	0.730416	+	1.26512i	0.956706	+	0.291058i	$0.0940072\pi$
$419$	14.9512	+	25.8963i	0.730416	+	1.26512i	−0.226289	+	0.974060i	$0.572660\pi$
$420$	3.23041	−	7.01122i	0.157628	−	0.342112i
$421$	−12.5452	+	21.7290i	−0.611417	+	1.05901i	0.379585	+	0.925157i	$0.376067\pi$
$421$	−12.5452	+	21.7290i	−0.611417	+	1.05901i	−0.991002	+	0.133848i	$0.957266\pi$
$422$		−	10.6904i		−	0.520401i
$423$	−1.18460	+	25.9752i	−0.0575973	+	1.26296i
$424$	8.00427			0.388722
$425$	6.32939	−	10.9628i	0.307021	−	0.531775i
$426$	−0.806939	−	0.236051i	−0.0390963	−	0.0114367i
$427$	−5.53500	+	6.97537i	−0.267857	+	0.337562i
$428$	10.0526	−	5.80388i	0.485912	−	0.280541i
$429$	0.255158	+	1.04715i	0.0123192	+	0.0505567i
$430$	−19.1458	−	11.0538i	−0.923293	−	0.533064i
$431$			6.39061i			0.307825i	0.988084	+	0.153913i	$0.0491874\pi$
$431$			6.39061i			0.307825i	−0.988084	+	0.153913i	$0.950813\pi$
$432$	−12.5467	+	2.45776i	−0.603653	+	0.118249i
$433$			33.1771i			1.59439i	0.603721	+	0.797196i	$0.293684\pi$
$433$			33.1771i			1.59439i	−0.603721	+	0.797196i	$0.706316\pi$
$434$	0.0595496	−	0.401705i	0.00285847	−	0.0192825i
$435$	22.2075	−	5.41131i	1.06477	−	0.259452i
$436$	−3.93200	−	6.81042i	−0.188309	−	0.326160i
$437$	1.73012	+	2.99665i	0.0827627	+	0.143349i
$438$	29.5964	+	8.65772i	1.41417	+	0.413682i
$439$	−7.32931	−	4.23158i	−0.349809	−	0.201962i	0.314792	−	0.949161i	$-0.398065\pi$
$439$	−7.32931	−	4.23158i	−0.349809	−	0.201962i	−0.664601	+	0.747198i	$0.731399\pi$
$440$	−1.37758			−0.0656737
$441$	20.6467	−	3.83573i	0.983177	−	0.182654i
$442$	−19.3815			−0.921885
$443$	16.1082	+	9.30006i	0.765322	+	0.441859i	0.831203	−	0.555969i	$-0.187652\pi$
$443$	16.1082	+	9.30006i	0.765322	+	0.441859i	−0.0658812	+	0.997827i	$0.520986\pi$
$444$	−1.82904	+	1.74753i	−0.0868023	+	0.0829339i
$445$	7.17111	+	12.4207i	0.339943	+	0.588799i
$446$	1.33809	+	2.31764i	0.0633604	+	0.109743i
$447$	23.2200	+	24.3031i	1.09827	+	1.14950i
$448$	3.39702	−	22.9153i	0.160494	−	1.08265i
$449$			20.3100i			0.958489i	0.877681	+	0.479245i	$0.159089\pi$
$449$			20.3100i			0.958489i	−0.877681	+	0.479245i	$0.840911\pi$
$450$	5.85594	−	9.15274i	0.276051	−	0.431464i
$451$			0.629906i			0.0296611i
$452$	5.17996	+	2.99065i	0.243645	+	0.140668i
$453$	2.97224	+	0.869457i	0.139648	+	0.0408506i
$454$	19.1458	−	11.0538i	0.898558	−	0.518783i
$455$	18.4026	−	23.1915i	0.862727	−	1.08723i
$456$	7.99115	+	32.7949i	0.374220	+	1.53576i
$457$	−5.67830	+	9.83511i	−0.265620	+	0.460067i	−0.967726	−	0.252005i	$-0.918910\pi$
$457$	−5.67830	+	9.83511i	−0.265620	+	0.460067i	0.702106	+	0.712072i	$0.252243\pi$
$458$	16.9654			0.792743
$459$	14.1534	+	16.2339i	0.660624	+	0.757735i
$460$			0.919981i			0.0428943i
$461$	19.4984	−	33.7721i	0.908129	−	1.57293i	0.0914676	−	0.995808i	$-0.470844\pi$
$461$	19.4984	−	33.7721i	0.908129	−	1.57293i	0.816661	−	0.577117i	$-0.195822\pi$
$462$	−0.495148	−	0.700303i	−0.0230364	−	0.0325810i
$463$	−5.03443	−	8.71990i	−0.233970	−	0.405248i	0.725003	−	0.688746i	$-0.241838\pi$
$463$	−5.03443	−	8.71990i	−0.233970	−	0.405248i	−0.958973	+	0.283498i	$0.908505\pi$
$464$	9.90856	−	5.72071i	0.459993	−	0.265577i
$465$	−0.178618	+	0.610605i	−0.00828321	+	0.0283161i
$466$	10.1206	−	17.5294i	0.468829	−	0.812035i
$467$	−3.59330			−0.166278			−0.0831389	−	0.996538i	$-0.526495\pi$
$467$	−3.59330			−0.166278			−0.0831389	+	0.996538i	$0.526495\pi$
$468$	7.01403	+	0.319875i	0.324224	+	0.0147862i
$469$	3.26615	−	1.29103i	0.150817	−	0.0596145i
$470$	−25.2630	−	14.5856i	−1.16530	−	0.672784i
$471$	−5.25370	−	5.49875i	−0.242078	−	0.253369i
$472$	−9.62592	+	5.55753i	−0.443069	+	0.255806i
$473$	0.897761	−	0.518322i	0.0412791	−	0.0238325i
$474$	−6.14056	−	6.42699i	−0.282045	−	0.295201i
$475$	−16.7581	−	9.67530i	−0.768915	−	0.443933i
$476$	−6.05361	+	2.39285i	−0.277467	+	0.109676i
$477$	−3.59144	−	6.93190i	−0.164441	−	0.317390i
$478$	2.65059			0.121235
$479$	−0.811090	+	1.40485i	−0.0370597	+	0.0641892i	−0.883960	−	0.467562i	$-0.845132\pi$
$479$	−0.811090	+	1.40485i	−0.0370597	+	0.0641892i	0.846901	+	0.531751i	$0.178466\pi$
$480$	−4.46264	+	15.2555i	−0.203691	+	0.696316i
$481$	−8.40183	+	4.85080i	−0.383090	+	0.221177i
$482$	2.68033	+	4.64247i	0.122086	+	0.211459i
$483$	−2.04347	+	1.44483i	−0.0929810	+	0.0657421i
$484$	−3.25729	+	5.64180i	−0.148059	+	0.256445i
$485$		−	7.15869i		−	0.325060i
$486$	11.5012	+	14.4735i	0.521706	+	0.656531i
$487$	7.99573			0.362321			0.181161	−	0.983454i	$-0.442015\pi$
$487$	7.99573			0.362321			0.181161	+	0.983454i	$0.442015\pi$
$488$	5.17598	−	8.96507i	0.234306	−	0.405829i
$489$	2.22888	+	9.14709i	0.100793	+	0.413646i
$490$	−6.83478	+	22.5462i	−0.308764	+	1.01853i
$491$	9.30632	−	5.37300i	0.419988	−	0.242480i	−0.275084	−	0.961420i	$-0.588706\pi$
$491$	9.30632	−	5.37300i	0.419988	−	0.242480i	0.695072	+	0.718940i	$0.255372\pi$
$492$	3.93852	+	1.15212i	0.177562	+	0.0519417i
$493$	−16.6916	−	9.63688i	−0.751751	−	0.434023i
$494$			29.6272i			1.33299i
$495$	0.618109	+	1.19302i	0.0277819	+	0.0536223i
$496$			0.318453i			0.0142990i
$497$	−1.07122	−	0.158801i	−0.0480510	−	0.00712318i
$498$	−9.15486	−	9.58188i	−0.410239	−	0.429374i
$499$	−8.46050	−	14.6540i	−0.378744	−	0.656004i	0.612136	−	0.790753i	$-0.290311\pi$
$499$	−8.46050	−	14.6540i	−0.378744	−	0.656004i	−0.990880	+	0.134749i	$0.956977\pi$
$500$	1.63901	+	2.83884i	0.0732986	+	0.126957i
$501$	−13.1563	+	12.5700i	−0.587781	+	0.561586i
$502$	21.7453	+	12.5546i	0.970538	+	0.560341i
$503$	−33.9226			−1.51253			−0.756267	−	0.654263i	$-0.772979\pi$
$503$	−33.9226			−1.51253			−0.756267	+	0.654263i	$0.772979\pi$
$504$	−23.0893	+	7.93072i	−1.02848	+	0.353262i
$505$	8.48968			0.377786
$506$	0.0885182	+	0.0511060i	0.00393511	+	0.00227194i
$507$	4.23358	+	1.23843i	0.188020	+	0.0550008i
$508$	3.70681	+	6.42038i	0.164463	+	0.284858i
$509$	5.06805	+	8.77812i	0.224637	+	0.389083i	0.956211	−	0.292680i	$-0.0945469\pi$
$509$	5.06805	+	8.77812i	0.224637	+	0.389083i	−0.731573	+	0.681763i	$0.761214\pi$
$510$	−23.4754	+	5.72026i	−1.03951	+	0.253297i
$511$	39.2897	+	5.82438i	1.73807	+	0.257655i
$512$			23.0923i			1.02055i
$513$	24.8157	−	21.6353i	1.09564	−	0.955222i
$514$		−	37.1201i		−	1.63730i
$515$	−32.4341	−	18.7259i	−1.42922	−	0.825160i
$516$	−1.59880	−	6.56133i	−0.0703834	−	0.288847i
$517$	1.18460	−	0.683930i	0.0520987	−	0.0300792i
$518$	4.79881	−	6.04760i	0.210848	−	0.265716i
$519$	−29.1898	−	8.53878i	−1.28129	−	0.374811i
$520$	−17.2089	+	29.8068i	−0.754662	+	1.30711i
$521$	−31.6986			−1.38874			−0.694370	−	0.719618i	$-0.744317\pi$
$521$	−31.6986			−1.38874			−0.694370	+	0.719618i	$0.744317\pi$
$522$	−13.9356	−	8.91601i	−0.609945	−	0.390243i
$523$			8.09911i			0.354149i	0.984197	+	0.177075i	$0.0566634\pi$
$523$			8.09911i			0.354149i	−0.984197	+	0.177075i	$0.943337\pi$
$524$	2.98125	−	5.16367i	0.130236	−	0.225576i
$525$	5.85668	−	12.7112i	0.255606	−	0.554764i
$526$	−3.95904	−	6.85726i	−0.172622	−	0.298991i
$527$	0.464582	−	0.268227i	0.0202375	−	0.0116841i
$528$	0.464619	+	0.486291i	0.0202200	+	0.0211631i
$529$	−11.3509	+	19.6603i	−0.493516	+	0.854795i
$530$	8.75851			0.380446
$531$	9.13202	+	5.84268i	0.396296	+	0.253551i
$532$	3.65779	+	9.25372i	0.158585	+	0.401200i
$533$	13.6293	+	7.86887i	0.590350	+	0.340839i
$534$	2.91449	−	9.96316i	0.126122	−	0.431148i
$535$	48.0628	−	27.7490i	2.07793	−	1.19970i
$536$	−3.53590	+	2.04145i	−0.152727	+	0.0881772i
$537$	−30.6327	+	7.46428i	−1.32190	+	0.322107i
$538$	10.9472	+	6.32036i	0.471967	+	0.272490i
$539$	−0.755323	−	0.806153i	−0.0325341	−	0.0347235i
$540$	8.58998	−	1.68268i	0.369654	−	0.0724110i
$541$	1.21634			0.0522944			0.0261472	−	0.999658i	$-0.491676\pi$
$541$	1.21634			0.0522944			0.0261472	+	0.999658i	$0.491676\pi$
$542$	4.41460	−	7.64631i	0.189623	−	0.328437i
$543$	−11.1096	+	2.70709i	−0.476760	+	0.116172i
$544$	11.6073	−	6.70145i	0.497657	−	0.287322i
$545$	−18.7994	−	32.5614i	−0.805276	−	1.39478i
$546$	−21.3379	+	1.96526i	−0.913179	+	0.0841052i
$547$	13.1278	−	22.7380i	0.561305	−	0.972209i	−0.436078	−	0.899909i	$-0.643633\pi$
$547$	13.1278	−	22.7380i	0.561305	−	0.972209i	0.997383	−	0.0722999i	$-0.0230339\pi$
$548$			4.77324i			0.203903i
$549$	−10.0864	−	0.459990i	−0.430477	−	0.0196319i
$550$	−0.571598			−0.0243730
$551$	−14.7312	+	25.5152i	−0.627571	+	1.08699i
$552$	2.10363	−	2.00988i	0.0895363	−	0.0855460i
$553$	−8.96874	−	7.11676i	−0.381390	−	0.302635i
$554$	27.2768	−	15.7482i	1.15888	−	0.669079i
$555$	−8.74484	+	8.35512i	−0.371198	+	0.354655i
$556$	9.71703	+	5.61013i	0.412094	+	0.237923i
$557$		−	27.2172i		−	1.15323i	−0.817016	−	0.576615i	$-0.804373\pi$
$557$		−	27.2172i		−	1.15323i	0.817016	−	0.576615i	$-0.195627\pi$
$558$	0.408852	−	0.211828i	0.0173081	−	0.00896739i
$559$		−	25.8998i		−	1.09545i
$560$	2.70915	−	18.2752i	0.114482	−	0.772266i
$561$	0.318097	−	1.08741i	0.0134301	−	0.0459106i
$562$	14.4466	+	25.0222i	0.609393	+	1.05550i
$563$	4.68017	+	8.10630i	0.197246	+	0.341640i	0.947634	−	0.319357i	$-0.103467\pi$
$563$	4.68017	+	8.10630i	0.197246	+	0.341640i	−0.750389	+	0.660997i	$0.770134\pi$
$564$	−2.10963	−	8.65772i	−0.0888315	−	0.364556i
$565$	24.7660	+	14.2987i	1.04191	+	0.601549i
$566$	−10.2609			−0.431296
$567$	17.2282	+	16.4375i	0.723515	+	0.690309i
$568$	1.25895			0.0528244
$569$	−30.2424	−	17.4605i	−1.26783	−	0.731980i	−0.293251	−	0.956036i	$-0.594737\pi$
$569$	−30.2424	−	17.4605i	−1.26783	−	0.731980i	−0.974576	+	0.224055i	$0.928070\pi$
$570$	8.74415	+	35.8851i	0.366252	+	1.50306i
$571$	0.735987	+	1.27477i	0.0308001	+	0.0533473i	0.881015	−	0.473089i	$-0.156861\pi$
$571$	0.735987	+	1.27477i	0.0308001	+	0.0533473i	−0.850214	+	0.526436i	$0.823528\pi$
$572$	−0.184680	−	0.319875i	−0.00772186	−	0.0133747i
$573$	6.91025	−	23.6227i	0.288680	−	0.986851i
$574$	−12.3882	−	1.83646i	−0.517075	−	0.0766523i
$575$			1.66791i			0.0695567i
$576$	23.3230	−	12.0838i	0.971793	−	0.503490i
$577$		−	18.6196i		−	0.775146i	−0.921839	−	0.387573i	$-0.873314\pi$
$577$		−	18.6196i		−	0.775146i	0.921839	−	0.387573i	$-0.126686\pi$
$578$	0.184828	+	0.106710i	0.00768783	+	0.00443857i
$579$	−12.5287	+	11.9703i	−0.520674	+	0.497470i
$580$	−6.78380	+	3.91663i	−0.281682	+	0.162629i
$581$	−13.3713	−	10.6103i	−0.554737	−	0.440187i
$582$	−3.74630	+	3.57935i	−0.155289	+	0.148369i
$583$	−0.205346	+	0.355670i	−0.00850458	+	0.0147304i
$584$	−46.1750			−1.91073
$585$	33.5349	+	1.52936i	1.38650	+	0.0632313i
$586$		−	10.4367i		−	0.431136i
$587$	−9.28551	+	16.0830i	−0.383254	+	0.663816i	−0.991525	−	0.129914i	$-0.958530\pi$
$587$	−9.28551	+	16.0830i	−0.383254	+	0.663816i	0.608271	+	0.793729i	$0.291863\pi$
$588$	−6.42204	+	3.24822i	−0.264840	+	0.133954i
$589$	−0.410019	−	0.710174i	−0.0168945	−	0.0292622i
$590$	−10.5330	+	6.08121i	−0.433636	+	0.250360i
$591$	33.8273	−	8.24272i	1.39147	−	0.339060i
$592$	−3.02704	+	5.24299i	−0.124411	+	0.215486i
$593$	30.9228			1.26985			0.634924	−	0.772574i	$-0.281031\pi$
$593$	30.9228			1.26985			0.634924	+	0.772574i	$0.281031\pi$
$594$	0.315280	−	0.919981i	0.0129361	−	0.0377473i
$595$	−28.9430	+	11.4405i	−1.18655	+	0.469015i
$596$	−9.97588	−	5.75958i	−0.408628	−	0.235922i
$597$	−21.7719	+	5.30517i	−0.891064	+	0.217126i
$598$	2.21156	−	1.27685i	0.0904375	−	0.0522141i
$599$	11.8741	−	6.85553i	0.485164	−	0.280109i	−0.237402	−	0.971411i	$-0.576296\pi$
$599$	11.8741	−	6.85553i	0.485164	−	0.280109i	0.722566	+	0.691302i	$0.242963\pi$
$600$	−4.56809	+	15.6160i	−0.186491	+	0.637520i
$601$	17.1065	+	9.87644i	0.697788	+	0.402868i	0.806523	−	0.591203i	$-0.201347\pi$
$601$	17.1065	+	9.87644i	0.697788	+	0.402868i	−0.108735	+	0.994071i	$0.534680\pi$
$602$	7.57638	+	19.1672i	0.308790	+	0.781198i
$603$	3.35447	+	2.14620i	0.136605	+	0.0873999i
$604$	−1.06128			−0.0431829
$605$	−15.5735	+	26.9741i	−0.633153	+	1.09665i
$606$	−4.24484	−	4.44284i	−0.172435	−	0.180478i
$607$	15.5219	−	8.96157i	0.630014	−	0.363739i	−0.150744	−	0.988573i	$-0.548167\pi$
$607$	15.5219	−	8.96157i	0.630014	−	0.363739i	0.780757	+	0.624834i	$0.214833\pi$
$608$	−10.2440	−	17.7432i	−0.415450	−	0.719581i
$609$	−19.3536	−	8.91715i	−0.784248	−	0.361341i
$610$	5.66372	−	9.80984i	0.229317	−	0.397189i
$611$		−	34.1750i		−	1.38257i
$612$	−6.21731	−	3.97784i	−0.251320	−	0.160795i
$613$	−41.4327			−1.67345			−0.836725	−	0.547623i	$-0.815533\pi$
$613$	−41.4327			−1.67345			−0.836725	+	0.547623i	$0.815533\pi$
$614$	6.62616	−	11.4768i	0.267410	−	0.463168i
$615$	18.8305	+	5.50843i	0.759321	+	0.222121i
$616$	1.00603	+	0.798292i	0.0405341	+	0.0321641i
$617$	19.9686	−	11.5289i	0.803904	−	0.464134i	−0.0409302	−	0.999162i	$-0.513032\pi$
$617$	19.9686	−	11.5289i	0.803904	−	0.464134i	0.844835	+	0.535028i	$0.179699\pi$
$618$	6.41741	+	26.3364i	0.258146	+	1.05941i
$619$	−1.67850	−	0.969082i	−0.0674646	−	0.0389507i	0.465888	−	0.884844i	$-0.345735\pi$
$619$	−1.67850	−	0.969082i	−0.0674646	−	0.0389507i	−0.533353	+	0.845893i	$0.679068\pi$
$620$		−	0.218026i		−	0.00875613i
$621$	−2.68448	−	0.919981i	−0.107725	−	0.0369176i
$622$		−	19.4558i		−	0.780106i
$623$	1.96069	−	13.2263i	0.0785532	−	0.529899i
$624$	16.3260	−	3.97816i	0.653562	−	0.159254i
$625$	15.4715	+	26.7974i	0.618860	+	1.07190i
$626$	4.86485	+	8.42617i	0.194439	+	0.336778i
$627$	−1.66225	−	0.486253i	−0.0663840	−	0.0194191i
$628$	2.25712	+	1.30315i	0.0900687	+	0.0520012i
$629$	10.1985			0.406640
$630$	−25.2650	+	8.67803i	−1.00658	+	0.345741i
$631$	23.5831			0.938827			0.469414	−	0.882978i	$-0.344465\pi$
$631$	23.5831			0.938827			0.469414	+	0.882978i	$0.344465\pi$
$632$	11.5270	+	6.65514i	0.458521	+	0.264727i
$633$	11.2890	−	10.7859i	0.448698	−	0.428702i
$634$	13.5862	+	23.5320i	0.539576	+	0.934574i
$635$	17.7227	+	30.6966i	0.703303	+	1.21816i
$636$	1.84826	+	1.93447i	0.0732884	+	0.0767069i
$637$	−26.8783	+	6.27236i	−1.06496	+	0.248520i
$638$			0.870293i			0.0344552i
$639$	−0.564880	−	1.09028i	−0.0223463	−	0.0431310i
$640$			11.1151i			0.439361i
$641$	21.5093	+	12.4184i	0.849568	+	0.490498i	0.860505	−	0.509442i	$-0.170148\pi$
$641$	21.5093	+	12.4184i	0.849568	+	0.490498i	−0.0109373	+	0.999940i	$0.503482\pi$
$642$	−38.5531	−	11.2778i	−1.52157	−	0.445099i
$643$	−37.9247	+	21.8959i	−1.49561	+	0.863489i	−0.999987	−	0.00505169i	$-0.998392\pi$
$643$	−37.9247	+	21.8959i	−1.49561	+	0.863489i	−0.495619	+	0.868540i	$0.665059\pi$
$644$	0.533117	−	0.671850i	0.0210078	−	0.0264746i
$645$	−7.64406	−	31.3705i	−0.300985	−	1.23521i
$646$	15.5723	−	26.9720i	0.612683	−	1.06120i
$647$	−29.3713			−1.15471			−0.577353	−	0.816494i	$-0.695914\pi$
$647$	−29.3713			−1.15471			−0.577353	+	0.816494i	$0.695914\pi$
$648$	−22.6141	−	15.9657i	−0.888366	−	0.627192i
$649$		−	0.570305i		−	0.0223864i
$650$	−7.14048	+	12.3677i	−0.280073	+	0.485100i
$651$	0.484280	−	0.342410i	0.0189804	−	0.0134201i
$652$	−1.61323	−	2.79420i	−0.0631789	−	0.109429i
$653$	−28.0816	+	16.2129i	−1.09892	+	0.634461i	−0.935937	−	0.352168i	$-0.885444\pi$
$653$	−28.0816	+	16.2129i	−1.09892	+	0.634461i	−0.162981	+	0.986629i	$0.552111\pi$
$654$	−7.64044	+	26.1188i	−0.298765	+	1.02133i
$655$	14.2537	−	24.6881i	0.556938	−	0.964645i
$656$	9.82082			0.383438
$657$	20.7183	+	39.9887i	0.808298	+	1.56011i
$658$	9.99707	+	25.2913i	0.389727	+	0.985957i
$659$	−0.203016	−	0.117211i	−0.00790837	−	0.00456590i	0.496041	−	0.868299i	$-0.334787\pi$
$659$	−0.203016	−	0.117211i	−0.00790837	−	0.00456590i	−0.503949	+	0.863733i	$0.668120\pi$
$660$	−0.318097	−	0.332935i	−0.0123819	−	0.0129595i
$661$	3.05138	−	1.76171i	0.118685	−	0.0685227i	−0.439482	−	0.898251i	$-0.644838\pi$
$661$	3.05138	−	1.76171i	0.118685	−	0.0685227i	0.558167	+	0.829728i	$0.311505\pi$
$662$	−19.7841	+	11.4224i	−0.768933	+	0.443943i
$663$	−19.5547	−	20.4668i	−0.759441	−	0.794864i
$664$	17.1855	+	9.92204i	0.666926	+	0.385050i
$665$	17.4883	+	44.2431i	0.678167	+	1.71567i
$666$	8.74484	+	0.398809i	0.338856	+	0.0154535i
$667$	2.53950			0.0983296
$668$	3.11791	−	5.40038i	0.120636	−	0.208947i
$669$	−1.09737	+	3.75136i	−0.0424269	+	0.145036i
$670$	−3.86908	+	2.23382i	−0.149476	+	0.0862999i
$671$	0.265576	+	0.459990i	0.0102524	+	0.0177577i
$672$	12.0994	−	8.55486i	0.466744	−	0.330011i
$673$	9.16585	−	15.8757i	0.353318	−	0.611964i	−0.633511	−	0.773734i	$-0.718387\pi$
$673$	9.16585	−	15.8757i	0.353318	−	0.611964i	0.986829	+	0.161770i	$0.0517202\pi$
$674$		−	5.38004i		−	0.207231i
$675$	15.5735	−	3.05067i	0.599424	−	0.117420i
$676$	−1.51166			−0.0581409
$677$	16.9260	−	29.3166i	0.650517	−	1.12673i	−0.332480	−	0.943110i	$-0.607885\pi$
$677$	16.9260	−	29.3166i	0.650517	−	1.12673i	0.982998	−	0.183619i	$-0.0587812\pi$
$678$	−4.90019	−	20.1099i	−0.188191	−	0.772317i
$679$	−4.14837	+	5.22790i	−0.159200	+	0.200628i
$680$	31.3334	−	18.0903i	1.20158	−	0.693732i
$681$	30.9897	+	9.06530i	1.18753	+	0.347383i
$682$	−0.0209779	−	0.0121116i	−0.000803285	−	0.000463777i
$683$			28.0284i			1.07248i	0.844066	+	0.536239i	$0.180156\pi$
$683$			28.0284i			1.07248i	−0.844066	+	0.536239i	$0.819844\pi$
$684$	−6.08065	+	9.50396i	−0.232499	+	0.363393i
$685$			22.8214i			0.871962i
$686$	18.0566	−	12.5045i	0.689403	−	0.477424i
$687$	17.1170	+	17.9154i	0.653055	+	0.683517i
$688$	−8.08113	−	13.9969i	−0.308090	−	0.533628i
$689$	5.13043	+	8.88616i	0.195454	+	0.338536i
$690$	2.30185	−	2.19927i	0.0876300	−	0.0837247i
$691$	−42.7393	−	24.6756i	−1.62588	−	0.938703i	−0.985304	−	0.170809i	$-0.945362\pi$
$691$	−42.7393	−	24.6756i	−1.62588	−	0.938703i	−0.640577	−	0.767894i	$-0.721305\pi$
$692$	10.4226			0.396210
$693$	0.239944	−	1.22943i	0.00911473	−	0.0467023i
$694$	10.3566			0.393131
$695$	46.4583	+	26.8227i	1.76226	+	1.01744i
$696$	23.7763	+	6.95519i	0.901238	+	0.263636i
$697$	−8.27188	−	14.3273i	−0.313320	−	0.542686i
$698$	−5.36066	−	9.28494i	−0.202904	−	0.351440i
$699$	28.7220	−	6.99871i	1.08637	−	0.264716i
$700$	−0.703331	+	4.74448i	−0.0265834	+	0.179324i
$701$		−	26.3889i		−	0.996696i	−0.866977	−	0.498348i	$-0.833940\pi$
$701$		−	26.3889i		−	0.996696i	0.866977	−	0.498348i	$-0.166060\pi$
$702$	−15.9671	−	18.3142i	−0.602640	−	0.691227i
$703$		−	15.5897i		−	0.587976i
$704$	−1.19669	−	0.690907i	−0.0451018	−	0.0260396i
$705$	−10.0864	−	41.3936i	−0.379875	−	1.55897i
$706$	−1.24867	+	0.720920i	−0.0469943	+	0.0271322i
$707$	−6.19990	−	4.91966i	−0.233171	−	0.185023i
$708$	−3.56586	−	1.04311i	−0.134013	−	0.0392024i
$709$	5.35661	−	9.27792i	0.201172	−	0.348440i	−0.747735	−	0.663998i	$-0.768858\pi$
$709$	5.35661	−	9.27792i	0.201172	−	0.348440i	0.948906	+	0.315558i	$0.102192\pi$
$710$	1.37758			0.0516998
$711$	0.591443	−	12.9688i	0.0221809	−	0.486368i
$712$			15.5441i			0.582539i
$713$	−0.0353413	+	0.0612130i	−0.00132354	+	0.00229244i
$714$	20.4586	+	9.42625i	0.765643	+	0.352769i
$715$	−0.882977	−	1.52936i	−0.0330215	−	0.0571949i
$716$	9.35748	−	5.40254i	0.349705	−	0.201902i
$717$	2.67427	+	2.79901i	0.0998724	+	0.104531i
$718$	−10.2624	+	17.7749i	−0.382988	+	0.663354i
$719$	17.5794			0.655601			0.327801	−	0.944747i	$-0.393693\pi$
$719$	17.5794			0.655601			0.327801	+	0.944747i	$0.393693\pi$
$720$	18.6003	−	9.63688i	0.693192	−	0.359145i
$721$	12.8348	+	32.4704i	0.477994	+	1.20926i
$722$	−21.7163	−	12.5379i	−0.808198	−	0.466614i
$723$	−2.19815	+	7.51437i	−0.0817500	+	0.279462i
$724$	3.39370	−	1.95935i	0.126126	−	0.0728188i
$725$	−12.2989	+	7.10079i	−0.456771	+	0.263717i
$726$	21.9029	−	5.33709i	0.812893	−	0.198078i
$727$	−43.4695	−	25.0971i	−1.61220	−	0.930802i	−0.988860	−	0.148847i	$-0.952444\pi$
$727$	−43.4695	−	25.0971i	−1.61220	−	0.930802i	−0.623336	−	0.781954i	$-0.714223\pi$
$728$	29.8401	−	11.7951i	1.10595	−	0.437156i
$729$	−3.67996	+	26.7480i	−0.136295	+	0.990668i
$730$	−50.5261			−1.87005
$731$	−13.6132	+	23.5787i	−0.503501	+	0.872089i
$732$	3.36186	−	0.819187i	0.124258	−	0.0302780i
$733$	−34.5617	+	19.9542i	−1.27656	+	0.737025i	−0.976215	−	0.216804i	$-0.930437\pi$
$733$	−34.5617	+	19.9542i	−1.27656	+	0.737025i	−0.300350	+	0.953829i	$0.597103\pi$
$734$	16.7269	+	28.9719i	0.617402	+	1.06937i
$735$	−30.7045	+	15.5301i	−1.13255	+	0.572837i
$736$	−0.882977	+	1.52936i	−0.0325470	+	0.0563730i
$737$		−	0.209490i		−	0.00771668i
$738$	−6.53259	−	12.6087i	−0.240468	−	0.464131i
$739$	30.3432			1.11619			0.558096	−	0.829777i	$-0.311532\pi$
$739$	30.3432			1.11619			0.558096	+	0.829777i	$0.311532\pi$
$740$	2.07244	−	3.58956i	0.0761843	−	0.131955i
$741$	−31.2861	+	29.8918i	−1.14932	+	1.09810i
$742$	−6.39623	−	5.07545i	−0.234813	−	0.186326i
$743$	−39.5861	+	22.8550i	−1.45227	+	0.838470i	−0.998610	−	0.0527041i	$-0.983216\pi$
$743$	−39.5861	+	22.8550i	−1.45227	+	0.838470i	−0.453662	+	0.891174i	$0.649883\pi$
$744$	−0.498537	+	0.476320i	−0.0182773	+	0.0174627i
$745$	−47.6959	−	27.5372i	−1.74744	−	1.00889i
$746$		−	33.5056i		−	1.22673i
$747$	0.881773	−	19.3350i	0.0322624	−	0.707430i
$748$			0.388278i			0.0141968i
$749$	−51.1798	−	7.58700i	−1.87007	−	0.277223i
$750$	3.18483	−	10.8873i	0.116293	−	0.397549i
$751$	−6.07753	−	10.5266i	−0.221772	−	0.384121i	0.733574	−	0.679610i	$-0.237851\pi$
$751$	−6.07753	−	10.5266i	−0.221772	−	0.384121i	−0.955346	+	0.295489i	$0.904517\pi$
$752$	−10.6631	−	18.4690i	−0.388843	−	0.673496i
$753$	8.68190	+	35.6297i	0.316386	+	1.29842i
$754$	18.8305	+	10.8718i	0.685768	+	0.395928i
$755$	−5.07411			−0.184666
$756$	−7.24824	−	3.74895i	−0.263616	−	0.136348i
$757$	−9.71614			−0.353139			−0.176570	−	0.984288i	$-0.556500\pi$
$757$	−9.71614			−0.353139			−0.176570	+	0.984288i	$0.556500\pi$
$758$	15.0408	+	8.68379i	0.546305	+	0.315409i
$759$	0.0353413	+	0.145037i	0.00128281	+	0.00526452i
$760$	−27.6534	−	47.8971i	−1.00309	−	1.73741i
$761$	19.4175	+	33.6320i	0.703882	+	1.21916i	0.967093	+	0.254422i	$0.0818851\pi$
$761$	19.4175	+	33.6320i	0.703882	+	1.21916i	−0.263211	+	0.964738i	$0.584782\pi$
$762$	7.20287	−	24.6230i	0.260932	−	0.891996i
$763$	−5.14002	+	34.6732i	−0.186081	+	1.25525i
$764$			8.43483i			0.305161i
$765$	−29.7257	−	19.0185i	−1.07473	−	0.687616i
$766$		−	29.3949i		−	1.06208i
$767$	−12.3397	−	7.12432i	−0.445560	−	0.257244i
$768$	−16.1137	+	15.3956i	−0.581452	+	0.555539i
$769$	9.42879	−	5.44371i	0.340011	−	0.196305i	−0.320266	−	0.947328i	$-0.603772\pi$
$769$	9.42879	−	5.44371i	0.340011	−	0.196305i	0.660277	+	0.751022i	$0.270439\pi$
$770$	1.10083	+	0.873514i	0.0396711	+	0.0314793i
$771$	39.1986	−	37.4517i	1.41170	−	1.34879i
$772$	2.96916	−	5.14274i	0.106863	−	0.185091i
$773$	37.3337			1.34280			0.671400	−	0.741096i	$-0.265693\pi$
$773$	37.3337			1.34280			0.671400	+	0.741096i	$0.265693\pi$
$774$	−12.5948	+	19.6856i	−0.452712	+	0.707583i
$775$		−	0.395277i		−	0.0141988i
$776$	3.87930	−	6.71914i	0.139259	−	0.241203i
$777$	11.2279	−	1.03411i	0.402800	−	0.0370985i
$778$	3.03803	+	5.26203i	0.108919	+	0.188653i
$779$	−21.9012	+	12.6446i	−0.784691	+	0.453041i
$780$	−11.1774	+	2.72361i	−0.400216	+	0.0975208i
$781$	−0.0322979	+	0.0559416i	−0.00115571	+	0.00200175i
$782$	−2.68448			−0.0959969
$783$	−4.64483	−	23.7116i	−0.165993	−	0.847383i
$784$	−12.5687	+	11.7762i	−0.448881	+	0.420578i
$785$	10.7915	+	6.23049i	0.385166	+	0.222376i
$786$	−20.0467	+	4.88479i	−0.715042	+	0.174235i
$787$	15.4554	−	8.92315i	0.550924	−	0.318076i	−0.198571	−	0.980087i	$-0.563630\pi$
$787$	15.4554	−	8.92315i	0.550924	−	0.318076i	0.749495	+	0.662011i	$0.230297\pi$
$788$	−10.3334	+	5.96597i	−0.368111	+	0.212529i
$789$	3.24682	−	11.0993i	0.115590	−	0.395144i
$790$	12.6132	+	7.28225i	0.448759	+	0.259091i
$791$	−9.80039	−	24.7937i	−0.348462	−	0.881562i
$792$	−0.0663426	+	1.45472i	−0.00235738	+	0.0516913i
$793$	13.2704			0.471246
$794$	−1.13905	+	1.97289i	−0.0404233	+	0.0700151i
$795$	8.83676	+	9.24895i	0.313408	+	0.328026i
$796$	6.65074	−	3.83980i	0.235729	−	0.136098i
$797$	−5.74854	−	9.95676i	−0.203624	−	0.352687i	0.746070	−	0.665868i	$-0.231939\pi$
$797$	−5.74854	−	9.95676i	−0.203624	−	0.352687i	−0.949693	+	0.313181i	$0.898605\pi$
$798$	14.4092	−	31.2736i	0.510082	−	1.10707i
$799$	−17.9626	+	31.1122i	−0.635473	+	1.10067i
$800$		−	9.87572i		−	0.349159i
$801$	13.4616	−	6.97449i	0.475641	−	0.246431i
$802$	−17.0642			−0.602558
$803$	1.18460	−	2.05179i	0.0418037	−	0.0724061i
$804$	−1.30985	−	0.383166i	−0.0461949	−	0.0135132i
$805$	2.54890	−	3.21219i	0.0898367	−	0.113215i
$806$	−0.524117	+	0.302599i	−0.0184612	+	0.0106586i
$807$	4.37072	+	17.9370i	0.153857	+	0.631413i
$808$	7.96840	+	4.60056i	0.280327	+	0.161847i
$809$			13.1945i			0.463893i	0.972729	+	0.231946i	$0.0745094\pi$
$809$			13.1945i			0.463893i	−0.972729	+	0.231946i	$0.925491\pi$
$810$	−24.7450	−	17.4701i	−0.869451	−	0.613838i
$811$		−	46.5800i		−	1.63565i	−0.575469	−	0.817823i	$-0.695181\pi$
$811$		−	46.5800i		−	1.63565i	0.575469	−	0.817823i	$-0.304819\pi$
$812$	7.22376	+	1.07086i	0.253504	+	0.0375800i
$813$	12.5285	−	3.05283i	0.439394	−	0.107067i
$814$	−0.230252	−	0.398809i	−0.00807034	−	0.0139782i
$815$	−7.71304	−	13.3594i	−0.270176	−	0.467958i
$816$	−16.9538	−	4.95943i	−0.593501	−	0.173615i
$817$	36.0431	+	20.8095i	1.26099	+	0.728031i
$818$	−11.5341			−0.403280
$819$	−23.6039	−	20.5499i	−0.824785	−	0.718073i
$820$	−6.72373			−0.234803
$821$	34.3623	+	19.8391i	1.19925	+	0.692390i	0.960389	−	0.278663i	$-0.0898913\pi$
$821$	34.3623	+	19.8391i	1.19925	+	0.692390i	0.238865	+	0.971053i	$0.423225\pi$
$822$	11.9430	−	11.4107i	0.416558	−	0.397994i
$823$	19.6156	+	33.9751i	0.683755	+	1.18430i	0.973826	+	0.227294i	$0.0729878\pi$
$823$	19.6156	+	33.9751i	0.683755	+	1.18430i	−0.290071	+	0.957005i	$0.593679\pi$
$824$	−20.2951	−	35.1521i	−0.707013	−	1.22458i
$825$	−0.576705	−	0.603605i	−0.0200783	−	0.0210148i
$826$	11.2161	+	1.66269i	0.390257	+	0.0578525i
$827$			21.0827i			0.733118i	0.930395	+	0.366559i	$0.119464\pi$
$827$			21.0827i			0.733118i	−0.930395	+	0.366559i	$0.880536\pi$
$828$	0.971495	+	0.0443051i	0.0337618	+	0.00153971i
$829$			13.3261i			0.462834i	0.972855	+	0.231417i	$0.0743361\pi$
$829$			13.3261i			0.462834i	−0.972855	+	0.231417i	$0.925664\pi$
$830$	18.8049	+	10.8570i	0.652726	+	0.376852i
$831$	44.1505	+	12.9152i	1.53156	+	0.448023i
$832$	−29.8983	+	17.2618i	−1.03654	+	0.598446i
$833$	27.7663	+	8.41724i	0.962046	+	0.291640i
$834$	−9.19222	−	37.7240i	−0.318301	−	1.30627i
$835$	14.9071	−	25.8198i	0.515881	−	0.893533i
$836$	0.593532			0.0205277
$837$	0.636194	+	0.218026i	0.0219901	+	0.00753607i
$838$			35.4621i			1.22502i
$839$	−8.39768	+	14.5452i	−0.289920	+	0.502156i	−0.973790	−	0.227447i	$-0.926962\pi$
$839$	−8.39768	+	14.5452i	−0.289920	+	0.502156i	0.683870	+	0.729604i	$0.260295\pi$
$840$	32.6619	−	23.0935i	1.12694	−	0.796803i
$841$	−3.68862	−	6.38888i	−0.127194	−	0.220306i
$842$	−25.7690	+	14.8777i	−0.888057	+	0.512720i
$843$	−11.8477	+	40.5013i	−0.408056	+	1.39494i
$844$	−2.67538	+	4.63389i	−0.0920903	+	0.159505i
$845$	−7.22744			−0.248632
$846$	−16.6190	+	25.9752i	−0.571372	+	0.893046i
$847$	27.0043	−	10.6742i	0.927878	−	0.366769i
$848$	5.54523	+	3.20154i	0.190424	+	0.109941i
$849$	−10.3525	−	10.8354i	−0.355298	−	0.371871i
$850$	13.0011	−	7.50619i	0.445934	−	0.257460i
$851$	−1.16372	+	0.671871i	−0.0398916	+	0.0230315i
$852$	0.290704	+	0.304264i	0.00995936	+	0.0104239i
$853$	35.5011	+	20.4966i	1.21554	+	0.701790i	0.963960	−	0.266048i	$-0.0857179\pi$
$853$	35.5011	+	20.4966i	1.21554	+	0.701790i	0.251576	+	0.967838i	$0.419051\pi$
$854$	−9.82082	+	3.88195i	−0.336061	+	0.132837i
$855$	−29.0723	+	45.4395i	−0.994251	+	1.55400i
$856$	60.1488			2.05584
$857$	−20.8718	+	36.1510i	−0.712967	+	1.23489i	0.250772	+	0.968046i	$0.419316\pi$
$857$	−20.8718	+	36.1510i	−0.712967	+	1.23489i	−0.963739	+	0.266848i	$0.914018\pi$
$858$	−0.358860	+	1.22676i	−0.0122513	+	0.0418810i
$859$	−24.0479	+	13.8841i	−0.820505	+	0.473719i	−0.850590	−	0.525829i	$-0.823755\pi$
$859$	−24.0479	+	13.8841i	−0.820505	+	0.473719i	0.0300858	+	0.999547i	$0.490422\pi$
$860$	5.53267	+	9.58286i	0.188662	+	0.326773i
$861$	−10.5596	−	14.9348i	−0.359871	−	0.508976i
$862$	−3.78940	+	6.56343i	−0.129067	+	0.223551i
$863$		−	45.6090i		−	1.55255i	−0.630396	−	0.776274i	$-0.717107\pi$
$863$		−	45.6090i		−	1.55255i	0.630396	−	0.776274i	$-0.282893\pi$
$864$	15.8948	+	5.44721i	0.540754	+	0.185318i
$865$	49.8319			1.69434
$866$	−19.6728	+	34.0743i	−0.668510	+	1.15789i
$867$	0.0737935	+	0.302841i	0.00250616	+	0.0102850i
$868$	−0.126343	+	0.159221i	−0.00428837	+	0.00540432i
$869$	−0.591443	+	0.341470i	−0.0200633	+	0.0115836i
$870$	26.0167	+	7.61058i	0.882050	+	0.258023i
$871$	−4.53275	−	2.61698i	−0.153586	−	0.0886731i
$872$		−	40.7495i		−	1.37995i
$873$	−7.55955	−	0.344754i	−0.255852	−	0.0116681i
$874$			4.10358i			0.138806i
$875$	2.14256	−	14.4531i	0.0724316	−	0.488604i
$876$	−10.6623	−	11.1596i	−0.360244	−	0.377048i
$877$	−8.84368	−	15.3177i	−0.298630	−	0.517242i	0.677193	−	0.735805i	$-0.263196\pi$
$877$	−8.84368	−	15.3177i	−0.298630	−	0.517242i	−0.975823	+	0.218564i	$0.929863\pi$
$878$	−5.01834	−	8.69203i	−0.169361	−	0.293342i
$879$	11.0211	−	10.5299i	0.371733	−	0.355166i
$880$	−0.954367	−	0.551004i	−0.0321717	−	0.0185743i
$881$	11.6169			0.391384			0.195692	−	0.980665i	$-0.437305\pi$
$881$	11.6169			0.391384			0.195692	+	0.980665i	$0.437305\pi$
$882$	23.4795	+	8.30329i	0.790596	+	0.279586i
$883$	−35.5480			−1.19629			−0.598143	−	0.801389i	$-0.704095\pi$
$883$	−35.5480			−1.19629			−0.598143	+	0.801389i	$0.704095\pi$
$884$	8.40116	+	4.85041i	0.282562	+	0.163137i
$885$	−17.0488	−	4.98722i	−0.573089	−	0.167644i
$886$	11.0292	+	19.1031i	0.370532	+	0.641781i
$887$	−12.2751	−	21.2610i	−0.412156	−	0.713876i	0.582969	−	0.812494i	$-0.301891\pi$
$887$	−12.2751	−	21.2610i	−0.412156	−	0.713876i	−0.995125	+	0.0986188i	$0.968558\pi$
$888$	−12.7355	+	3.10327i	−0.427376	+	0.104139i
$889$	4.84564	−	32.6874i	0.162518	−	1.09630i
$890$			17.0088i			0.570136i
$891$	1.28959	−	0.595265i	0.0432030	−	0.0199421i
$892$		−	1.33948i		−	0.0448492i
$893$	47.5590	+	27.4582i	1.59150	+	0.918854i
$894$	9.43709	+	38.7289i	0.315624	+	1.29529i
$895$	44.7392	−	25.8302i	1.49547	−	0.863408i
$896$	6.44104	−	8.11718i	0.215180	−	0.271176i
$897$	3.57966	+	1.04715i	0.119521	+	0.0349632i
$898$	−12.0431	+	20.8593i	−0.401883	+	0.696082i
$899$	−0.601834			−0.0200723
$900$	−4.82889	+	2.50187i	−0.160963	+	0.0833955i
$901$		−	10.7864i		−	0.359346i
$902$	−0.373511	+	0.646940i	−0.0124366	+	0.0215407i
$903$	−12.5964	+	27.3391i	−0.419184	+	0.909788i
$904$	15.4969	+	26.8414i	0.515419	+	0.892731i
$905$	16.2257	−	9.36790i	0.539360	−	0.311399i
$906$	2.53705	+	2.65539i	0.0842880	+	0.0882196i
$907$	−18.4502	+	31.9567i	−0.612628	+	1.06110i	0.378167	+	0.925737i	$0.376554\pi$
$907$	−18.4502	+	31.9567i	−0.612628	+	1.06110i	−0.990796	+	0.135366i	$0.956779\pi$
$908$	−11.0653			−0.367216
$909$	0.408852	−	8.96507i	0.0135608	−	0.297352i
$910$	32.6519	−	12.9066i	1.08240	−	0.427849i
$911$	−34.4774	−	19.9056i	−1.14229	−	0.659500i	−0.195292	−	0.980745i	$-0.562565\pi$
$911$	−34.4774	−	19.9056i	−1.14229	−	0.659500i	−0.946996	+	0.321245i	$0.895899\pi$
$912$	−7.58113	+	25.9161i	−0.251036	+	0.858166i
$913$	−0.881773	+	0.509092i	−0.0291824	+	0.0168485i
$914$	−11.6637	+	6.73405i	−0.385801	+	0.222743i
$915$	16.0735	−	3.91663i	0.531372	−	0.129480i
$916$	−7.35389	−	4.24577i	−0.242979	−	0.140284i
$917$	−24.7157	+	9.76957i	−0.816186	+	0.322620i
$918$	4.91002	+	25.0654i	0.162055	+	0.827280i
$919$	−56.8725			−1.87605			−0.938026	−	0.346565i	$-0.887348\pi$
$919$	−56.8725			−1.87605			−0.938026	+	0.346565i	$0.887348\pi$
$920$	−2.38357	+	4.12846i	−0.0785838	+	0.136111i
$921$	18.8049	−	4.58219i	0.619641	−	0.150988i
$922$	40.0513	−	23.1236i	1.31902	−	0.761535i
$923$	0.806939	+	1.39766i	0.0265607	+	0.0460045i
$924$	0.0393707	+	0.427471i	0.00129520	+	0.0140628i
$925$	3.75729	−	6.50783i	0.123539	−	0.213976i
$926$		−	11.9409i		−	0.392403i
$927$	−21.3364	+	33.3485i	−0.700779	+	1.09531i
$928$	−15.0364			−0.493593
$929$	22.8885	−	39.6440i	0.750946	−	1.30068i	−0.196419	−	0.980520i	$-0.562931\pi$
$929$	22.8885	−	39.6440i	0.750946	−	1.30068i	0.947365	−	0.320156i	$-0.103735\pi$
$930$	−0.545515	+	0.521203i	−0.0178881	+	0.0170909i
$931$	12.8668	−	42.4444i	0.421694	−	1.39106i
$932$	−8.77383	+	5.06557i	−0.287396	+	0.165928i
$933$	20.5452	−	19.6296i	0.672621	−	0.642645i
$934$	−3.69047	−	2.13069i	−0.120756	−	0.0697183i
$935$			1.85640i			0.0607108i
$936$	30.6470	+	19.6080i	1.00173	+	0.640908i
$937$		−	24.0003i		−	0.784054i	−0.919954	−	0.392027i	$-0.871774\pi$
$937$		−	24.0003i		−	0.784054i	0.919954	−	0.392027i	$-0.128226\pi$
$938$	4.12001	+	0.610758i	0.134523	+	0.0199420i
$939$	−3.98968	+	13.6387i	−0.130198	+	0.445083i
$940$	7.30039	+	12.6446i	0.238112	+	0.412423i
$941$	−1.64316	−	2.84603i	−0.0535654	−	0.0927780i	0.837999	−	0.545671i	$-0.183725\pi$
$941$	−1.64316	−	2.84603i	−0.0535654	−	0.0927780i	−0.891565	+	0.452893i	$0.850392\pi$
$942$	−2.13521	−	8.76270i	−0.0695689	−	0.285504i
$943$	1.88776	+	1.08990i	0.0614738	+	0.0354919i
$944$	−8.89158			−0.289396
$945$	−34.6547	−	17.9241i	−1.12732	−	0.583073i
$946$	1.22938			0.0399707
$947$	−25.9420	−	14.9776i	−0.843002	−	0.486707i	0.0152815	−	0.999883i	$-0.495136\pi$
$947$	−25.9420	−	14.9776i	−0.843002	−	0.486707i	−0.858284	+	0.513176i	$0.828469\pi$
$948$	1.05329	+	4.32260i	0.0342092	+	0.140391i
$949$	−29.5964	−	51.2624i	−0.960739	−	1.66405i
$950$	−11.4742	−	19.8739i	−0.372272	−	0.644794i
$951$	−11.1421	+	38.0892i	−0.361307	+	1.23513i
$952$	−33.3654	−	4.94616i	−1.08138	−	0.160306i
$953$		−	16.0580i		−	0.520169i	−0.965586	−	0.260084i	$-0.916250\pi$
$953$		−	16.0580i		−	0.520169i	0.965586	−	0.260084i	$-0.0837504\pi$
$954$	0.421799	−	9.24895i	0.0136562	−	0.299446i
$955$			40.3279i			1.30498i
$956$	−1.14893	−	0.663336i	−0.0371591	−	0.0214538i
$957$	−0.919025	+	0.878068i	−0.0297079	+	0.0283839i
$958$	−1.66605	+	0.961893i	−0.0538275	+	0.0310773i
$959$	13.2247	−	16.6662i	0.427049	−	0.538179i
$960$	−31.1190	+	29.7321i	−1.00436	+	0.959600i
$961$	−15.4916	+	26.8323i	−0.499730	+	0.865557i
$962$	−11.5054			−0.370948
$963$	−26.9882	−	52.0904i	−0.869683	−	1.67859i
$964$		−	2.68312i		−	0.0864174i
$965$	14.1959	−	24.5881i	0.456983	−	0.791518i
$966$	−2.95546	+	0.272202i	−0.0950903	+	0.00875797i
$967$	25.0275	+	43.3489i	0.804831	+	1.39401i	0.916405	+	0.400252i	$0.131077\pi$
$967$	25.0275	+	43.3489i	0.804831	+	1.39401i	−0.111574	+	0.993756i	$0.535589\pi$
$968$	−29.2345	+	16.8786i	−0.939633	+	0.542497i
$969$	44.1937	−	10.7687i	1.41971	−	0.345940i
$970$	4.24484	−	7.35228i	0.136294	−	0.236068i
$971$	1.04188			0.0334354			0.0167177	−	0.999860i	$-0.494678\pi$
$971$	1.04188			0.0334354			0.0167177	+	0.999860i	$0.494678\pi$
$972$	−1.36322	−	9.15202i	−0.0437253	−	0.293551i
$973$	−18.3844	−	46.5102i	−0.589378	−	1.49105i
$974$	8.21195	+	4.74117i	0.263128	+	0.151917i
$975$	−20.2645	+	4.93786i	−0.648983	+	0.158138i
$976$	7.17167	−	4.14057i	0.229560	−	0.132536i
$977$	21.1765	−	12.2262i	0.677495	−	0.391152i	−0.121416	−	0.992602i	$-0.538743\pi$
$977$	21.1765	−	12.2262i	0.677495	−	0.391152i	0.798910	+	0.601450i	$0.205410\pi$
$978$	−3.13474	+	10.7161i	−0.100238	+	0.342663i
$979$	−0.690703	−	0.398777i	−0.0220750	−	0.0127450i
$980$	8.60502	−	8.06246i	0.274877	−	0.257546i
$981$	−35.2901	+	18.2839i	−1.12673	+	0.583760i
$982$	12.7440			0.406677
$983$	28.0788	−	48.6339i	0.895575	−	1.55118i	0.0624829	−	0.998046i	$-0.480098\pi$
$983$	28.0788	−	48.6339i	0.895575	−	1.55118i	0.833092	−	0.553135i	$-0.186569\pi$
$984$	14.6893	+	15.3745i	0.468278	+	0.490120i
$985$	−49.4050	+	28.5240i	−1.57417	+	0.908850i
$986$	−11.4286	−	19.7950i	−0.363962	−	0.630400i
$987$	−16.6211	+	36.0741i	−0.529055	+	1.14825i
$988$	7.41449	−	12.8423i	0.235886	−	0.408567i
$989$		−	3.58731i		−	0.114070i
$990$	−0.0725941	+	1.59180i	−0.00230719	+	0.0505907i
$991$	18.2278			0.579025			0.289513	−	0.957174i	$-0.406507\pi$
$991$	18.2278			0.579025			0.289513	+	0.957174i	$0.406507\pi$
$992$	0.209256	−	0.362443i	0.00664390	−	0.0115076i
$993$	−32.0229	−	9.36753i	−1.01622	−	0.297270i
$994$	−1.00603	−	0.798292i	−0.0319093	−	0.0253203i
$995$	31.7979	−	18.3586i	1.00806	−	0.582005i
$996$	1.57033	+	6.44448i	0.0497578	+	0.204201i
$997$	29.8197	+	17.2164i	0.944399	+	0.545249i	0.891337	−	0.453342i	$-0.149768\pi$
$997$	29.8197	+	17.2164i	0.944399	+	0.545249i	0.0530623	+	0.998591i	$0.483102\pi$
$998$		−	20.0671i		−	0.635212i
$999$	8.40183	+	9.63688i	0.265822	+	0.304898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.o.a.20.6	yes	12
3.2	odd	2		189.2.o.a.62.2		12
4.3	odd	2		1008.2.cc.a.209.3		12
7.2	even	3		441.2.i.c.227.1		12
7.3	odd	6		441.2.s.c.362.1		12
7.4	even	3		441.2.s.c.362.2		12
7.5	odd	6		441.2.i.c.227.2		12
7.6	odd	2	inner	63.2.o.a.20.5	✓	12
9.2	odd	6		567.2.c.c.566.9		12
9.4	even	3		189.2.o.a.125.1		12
9.5	odd	6	inner	63.2.o.a.41.5	yes	12
9.7	even	3		567.2.c.c.566.4		12
12.11	even	2		3024.2.cc.a.2897.6		12
21.2	odd	6		1323.2.i.c.521.6		12
21.5	even	6		1323.2.i.c.521.5		12
21.11	odd	6		1323.2.s.c.656.5		12
21.17	even	6		1323.2.s.c.656.6		12
21.20	even	2		189.2.o.a.62.1		12
28.27	even	2		1008.2.cc.a.209.4		12
36.23	even	6		1008.2.cc.a.545.4		12
36.31	odd	6		3024.2.cc.a.881.1		12
63.4	even	3		1323.2.i.c.1097.1		12
63.5	even	6		441.2.s.c.374.2		12
63.13	odd	6		189.2.o.a.125.2		12
63.20	even	6		567.2.c.c.566.10		12
63.23	odd	6		441.2.s.c.374.1		12
63.31	odd	6		1323.2.i.c.1097.2		12
63.32	odd	6		441.2.i.c.68.6		12
63.34	odd	6		567.2.c.c.566.3		12
63.40	odd	6		1323.2.s.c.962.5		12
63.41	even	6	inner	63.2.o.a.41.6	yes	12
63.58	even	3		1323.2.s.c.962.6		12
63.59	even	6		441.2.i.c.68.5		12
84.83	odd	2		3024.2.cc.a.2897.1		12
252.139	even	6		3024.2.cc.a.881.6		12
252.167	odd	6		1008.2.cc.a.545.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.5	✓	12	7.6	odd	2	inner
63.2.o.a.20.6	yes	12	1.1	even	1	trivial
63.2.o.a.41.5	yes	12	9.5	odd	6	inner
63.2.o.a.41.6	yes	12	63.41	even	6	inner
189.2.o.a.62.1		12	21.20	even	2
189.2.o.a.62.2		12	3.2	odd	2
189.2.o.a.125.1		12	9.4	even	3
189.2.o.a.125.2		12	63.13	odd	6
441.2.i.c.68.5		12	63.59	even	6
441.2.i.c.68.6		12	63.32	odd	6
441.2.i.c.227.1		12	7.2	even	3
441.2.i.c.227.2		12	7.5	odd	6
441.2.s.c.362.1		12	7.3	odd	6
441.2.s.c.362.2		12	7.4	even	3
441.2.s.c.374.1		12	63.23	odd	6
441.2.s.c.374.2		12	63.5	even	6
567.2.c.c.566.3		12	63.34	odd	6
567.2.c.c.566.4		12	9.7	even	3
567.2.c.c.566.9		12	9.2	odd	6
567.2.c.c.566.10		12	63.20	even	6
1008.2.cc.a.209.3		12	4.3	odd	2
1008.2.cc.a.209.4		12	28.27	even	2
1008.2.cc.a.545.3		12	252.167	odd	6
1008.2.cc.a.545.4		12	36.23	even	6
1323.2.i.c.521.5		12	21.5	even	6
1323.2.i.c.521.6		12	21.2	odd	6
1323.2.i.c.1097.1		12	63.4	even	3
1323.2.i.c.1097.2		12	63.31	odd	6
1323.2.s.c.656.5		12	21.11	odd	6
1323.2.s.c.656.6		12	21.17	even	6
1323.2.s.c.962.5		12	63.40	odd	6
1323.2.s.c.962.6		12	63.58	even	3
3024.2.cc.a.881.1		12	36.31	odd	6
3024.2.cc.a.881.6		12	252.139	even	6
3024.2.cc.a.2897.1		12	84.83	odd	2
3024.2.cc.a.2897.6		12	12.11	even	2

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02704 + 0.592963i) q^{2} +(0.410052 + 1.68281i) q^{3} +(-0.296790 - 0.514055i) q^{4} +(-1.41899 - 2.45776i) q^{5} +(-0.576705 + 1.97146i) q^{6} +(-0.387972 + 2.61715i) q^{7} -3.07579i q^{8} +(-2.66372 + 1.38008i) q^{9} +O(q^{10})\)	\(q+(1.02704 + 0.592963i) q^{2} +(0.410052 + 1.68281i) q^{3} +(-0.296790 - 0.514055i) q^{4} +(-1.41899 - 2.45776i) q^{5} +(-0.576705 + 1.97146i) q^{6} +(-0.387972 + 2.61715i) q^{7} -3.07579i q^{8} +(-2.66372 + 1.38008i) q^{9} -3.36562i q^{10} +(0.136673 + 0.0789082i) q^{11} +(0.743359 - 0.710230i) q^{12} +(3.41468 - 1.97146i) q^{13} +(-1.95034 + 2.45787i) q^{14} +(3.55408 - 3.39569i) q^{15} +(1.23025 - 2.13086i) q^{16} -4.14487 q^{17} +(-3.55408 - 0.162084i) q^{18} +6.33597i q^{19} +(-0.842281 + 1.45887i) q^{20} +(-4.56326 + 0.420284i) q^{21} +(0.0935793 + 0.162084i) q^{22} +(0.472958 - 0.273062i) q^{23} +(5.17598 - 1.26123i) q^{24} +(-1.52704 + 2.64491i) q^{25} +4.67602 q^{26} +(-3.41468 - 3.91663i) q^{27} +(1.46050 - 0.577305i) q^{28} +(4.02704 + 2.32501i) q^{29} +(5.66372 - 1.38008i) q^{30} +(-0.112086 + 0.0647129i) q^{31} +(-2.80039 + 1.61680i) q^{32} +(-0.0767447 + 0.262352i) q^{33} +(-4.25696 - 2.45776i) q^{34} +(6.98284 - 2.76016i) q^{35} +(1.50000 + 0.959702i) q^{36} -2.46050 q^{37} +(-3.75700 + 6.50731i) q^{38} +(4.71780 + 4.93786i) q^{39} +(-7.55955 + 4.36451i) q^{40} +(1.99569 + 3.45664i) q^{41} +(-4.93588 - 2.27420i) q^{42} +(3.28434 - 5.68864i) q^{43} -0.0936766i q^{44} +(7.17167 + 4.58845i) q^{45} +0.647664 q^{46} +(4.33370 - 7.50619i) q^{47} +(4.09030 + 1.19652i) q^{48} +(-6.69896 - 2.03076i) q^{49} +(-3.13667 + 1.81096i) q^{50} +(-1.69961 - 6.97504i) q^{51} +(-2.02688 - 1.17022i) q^{52} +2.60234i q^{53} +(-1.18460 - 6.04732i) q^{54} -0.447879i q^{55} +(8.04981 + 1.19332i) q^{56} +(-10.6623 + 2.59808i) q^{57} +(2.75729 + 4.77577i) q^{58} +(-1.80686 - 3.12957i) q^{59} +(-2.80039 - 0.819187i) q^{60} +(2.91472 + 1.68281i) q^{61} -0.153489 q^{62} +(-2.57843 - 7.50678i) q^{63} -8.75583 q^{64} +(-9.69076 - 5.59496i) q^{65} +(-0.234385 + 0.223939i) q^{66} +(-0.663715 - 1.14959i) q^{67} +(1.23016 + 2.13069i) q^{68} +(0.653450 + 0.683930i) q^{69} +(8.80835 + 1.30577i) q^{70} +0.409310i q^{71} +(4.24484 + 8.19304i) q^{72} -15.0124i q^{73} +(-2.52704 - 1.45899i) q^{74} +(-5.07706 - 1.48517i) q^{75} +(3.25704 - 1.88045i) q^{76} +(-0.259540 + 0.327080i) q^{77} +(1.91741 + 7.86887i) q^{78} +(-2.16372 + 3.74766i) q^{79} -6.98284 q^{80} +(5.19076 - 7.35228i) q^{81} +4.73348i q^{82} +(-3.22585 + 5.58733i) q^{83} +(1.57038 + 2.22103i) q^{84} +(5.88151 + 10.1871i) q^{85} +(6.74630 - 3.89498i) q^{86} +(-2.26127 + 7.73013i) q^{87} +(0.242705 - 0.420378i) q^{88} -5.05368 q^{89} +(4.64483 + 8.96507i) q^{90} +(3.83482 + 9.70160i) q^{91} +(-0.280738 - 0.162084i) q^{92} +(-0.154861 - 0.162084i) q^{93} +(8.90179 - 5.13945i) q^{94} +(15.5723 - 8.99066i) q^{95} +(-3.86908 - 4.04955i) q^{96} +(2.18452 + 1.26123i) q^{97} +(-5.67594 - 6.05791i) q^{98} +(-0.472958 - 0.0215693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9	\( 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9} - 12 q^{14} + 6 q^{15} + 2 q^{16} - 6 q^{18} - 24 q^{21} - 10 q^{22} + 24 q^{23} - 8 q^{28} + 30 q^{29} + 48 q^{30} - 12 q^{32} + 18 q^{36} - 4 q^{37} + 36 q^{42} - 10 q^{43} - 40 q^{46} + 6 q^{49} - 36 q^{50} - 42 q^{51} + 42 q^{56} - 18 q^{57} + 2 q^{58} - 12 q^{60} + 24 q^{63} + 16 q^{64} - 78 q^{65} + 12 q^{67} + 18 q^{70} - 24 q^{72} - 12 q^{74} - 24 q^{77} - 12 q^{78} - 6 q^{79} + 24 q^{81} - 60 q^{84} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 24 q^{91} + 30 q^{92} + 78 q^{93} + 72 q^{95} - 24 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9 - 12 * q^14 + 6 * q^15 + 2 * q^16 - 6 * q^18 - 24 * q^21 - 10 * q^22 + 24 * q^23 - 8 * q^28 + 30 * q^29 + 48 * q^30 - 12 * q^32 + 18 * q^36 - 4 * q^37 + 36 * q^42 - 10 * q^43 - 40 * q^46 + 6 * q^49 - 36 * q^50 - 42 * q^51 + 42 * q^56 - 18 * q^57 + 2 * q^58 - 12 * q^60 + 24 * q^63 + 16 * q^64 - 78 * q^65 + 12 * q^67 + 18 * q^70 - 24 * q^72 - 12 * q^74 - 24 * q^77 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 60 * q^84 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 24 * q^91 + 30 * q^92 + 78 * q^93 + 72 * q^95 - 24 * q^99

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