LMFDB - Embedded newform 63.2.o.a.41.5

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			41.5
Root			$-1.82904 + 1.05600i$ of defining polynomial
Character	$\chi$	$=$	63.41
Dual form			63.2.o.a.20.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02704 - 0.592963i) q^{2} +(-0.410052 + 1.68281i) q^{3} +(-0.296790 + 0.514055i) q^{4} +(1.41899 - 2.45776i) q^{5} +(0.576705 + 1.97146i) q^{6} +(-2.07253 - 1.64457i) q^{7} +3.07579i q^{8} +(-2.66372 - 1.38008i) q^{9} +O(q^{10})$	\(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} +(-2.07253 - 1.64457i) 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} +(-3.10375 - 0.460106i) 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} +(3.61735 - 2.81333i) 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} +(2.04697 - 5.03436i) 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} +(1.59079 + 6.81685i) 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} +(5.05835 - 6.37468i) 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} +(3.25100 + 7.24092i) 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} +(-5.53500 + 6.97537i) 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} +(-0.413030 - 0.0612283i) 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} +(0.372613 + 2.69448i) 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	−0.0908124	−	0.995868i	$-0.528946\pi$
$2$	1.02704	−	0.592963i	0.726228	−	0.419288i	0.817041	+	0.576580i	$0.195613\pi$
$3$	−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	−0.352012	−	0.935995i	$-0.614502\pi$
$5$	1.41899	−	2.45776i	0.634590	−	1.09914i	0.986602	−	0.163146i	$-0.0521643\pi$
$6$	0.576705	+	1.97146i	0.235439	+	0.804847i
$7$	−2.07253	−	1.64457i	−0.783344	−	0.621589i
$7$	−2.07253	−	1.64457i	−0.783344	−	0.621589i
$8$			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	−0.479254	−	0.877676i	$-0.659093\pi$
$11$	0.136673	−	0.0789082i	0.0412085	−	0.0237917i	0.520463	+	0.853884i	$0.325759\pi$
$12$	−0.743359	−	0.710230i	−0.214589	−	0.205026i
$13$	−3.41468	−	1.97146i	−0.947061	−	0.546786i	−0.0548943	−	0.998492i	$-0.517482\pi$
$13$	−3.41468	−	1.97146i	−0.947061	−	0.546786i	−0.892167	+	0.451706i	$0.850816\pi$
$14$	−3.10375	−	0.460106i	−0.829511	−	0.122968i
$15$	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	$-0.332362\pi$
$17$	4.14487			1.00528			0.502640	+	0.864496i	$0.332362\pi$
$18$	−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
$21$	3.61735	−	2.81333i	0.789370	−	0.613918i
$22$	0.0935793	−	0.162084i	0.0199512	−	0.0345565i
$23$	0.472958	+	0.273062i	0.0986185	+	0.0569374i	0.548498	−	0.836152i	$-0.315200\pi$
$23$	0.472958	+	0.273062i	0.0986185	+	0.0569374i	−0.449880	+	0.893089i	$0.648533\pi$
$24$	−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	−0.0770966	−	0.997024i	$-0.524565\pi$
$29$	4.02704	−	2.32501i	0.747803	−	0.431744i	0.824900	+	0.565279i	$0.191232\pi$
$30$	5.66372	+	1.38008i	1.03405	+	0.251967i
$31$	0.112086	+	0.0647129i	0.0201313	+	0.0116228i	0.510032	−	0.860156i	$-0.329634\pi$
$31$	0.112086	+	0.0647129i	0.0201313	+	0.0116228i	−0.489901	+	0.871778i	$0.662967\pi$
$32$	−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	$-0.934223\pi$
$41$	−1.99569	+	3.45664i	−0.311675	+	0.539836i	0.667050	+	0.745013i	$0.267557\pi$
$42$	2.04697	−	5.03436i	0.315854	−	0.776818i
$43$	3.28434	+	5.68864i	0.500857	+	0.867509i	1.00000		0.000989450i	$0.000314952\pi$
$43$	3.28434	+	5.68864i	0.500857	+	0.867509i	−0.499143	+	0.866520i	$0.666352\pi$
$44$			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	−0.987114	−	0.160016i	$-0.948845\pi$
$47$	−4.33370	−	7.50619i	−0.632135	−	1.09489i	0.354979	−	0.934874i	$-0.384488\pi$
$48$	−4.09030	+	1.19652i	−0.590385	+	0.172703i
$49$	1.59079	+	6.81685i	0.227255	+	0.973835i
$50$	−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	$-0.942801\pi$
$53$		−	2.60234i		−	0.357459i	0.983898	−	0.178730i	$-0.0571988\pi$
$54$	1.18460	−	6.04732i	0.161204	−	0.822936i
$55$		−	0.447879i		−	0.0603920i
$56$	5.05835	−	6.37468i	0.675951	−	0.851853i
$57$	−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	$-0.757748\pi$
$59$	1.80686	−	3.12957i	0.235233	−	0.407436i	0.959340	+	0.282252i	$0.0910813\pi$
$60$	−2.80039	+	0.819187i	−0.361529	+	0.105757i
$61$	−2.91472	+	1.68281i	−0.373191	+	0.215462i	−0.674852	−	0.737953i	$-0.735792\pi$
$61$	−2.91472	+	1.68281i	−0.373191	+	0.215462i	0.301660	+	0.953415i	$0.402459\pi$
$62$	0.153489			0.0194932
$63$	3.25100	+	7.24092i	0.409588	+	0.912271i
$64$	−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	−0.903717	−	0.428131i	$-0.859172\pi$
$67$	−0.663715	+	1.14959i	−0.0810857	+	0.140445i	0.822631	+	0.568576i	$0.192505\pi$
$68$	−1.23016	+	2.13069i	−0.149178	+	0.258384i
$69$	−0.653450	+	0.683930i	−0.0786661	+	0.0823355i
$70$	−5.53500	+	6.97537i	−0.661559	+	0.833716i
$71$		−	0.409310i		−	0.0485761i	−0.999705	−	0.0242881i	$-0.992268\pi$
$71$		−	0.409310i		−	0.0485761i	0.999705	−	0.0242881i	$-0.00773189\pi$
$72$	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
$77$	−0.413030	−	0.0612283i	−0.0470691	−	0.00697762i
$78$	1.91741	−	7.86887i	0.217104	−	0.890974i
$79$	−2.16372	−	3.74766i	−0.243437	−	0.421645i	0.718254	−	0.695781i	$-0.244942\pi$
$79$	−2.16372	−	3.74766i	−0.243437	−	0.421645i	−0.961691	+	0.274136i	$0.911608\pi$
$80$	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	$-0.0514598\pi$
$83$	3.22585	+	5.58733i	0.354083	+	0.613289i	−0.632878	+	0.774252i	$0.718126\pi$
$84$	0.372613	+	2.69448i	0.0406554	+	0.293992i
$85$	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	$-0.413689\pi$
$89$	5.05368			0.535689			0.267845	+	0.963462i	$0.413689\pi$
$90$	−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	$-0.707541\pi$
$97$	−2.18452	+	1.26123i	−0.221805	+	0.128059i	0.384981	+	0.922925i	$0.374208\pi$
$98$	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	$-0.119116\pi$
$101$	1.49573	+	2.59068i	0.148831	+	0.257782i	−0.781965	+	0.623323i	$0.785782\pi$
$102$	2.39037	+	8.17147i	0.236682	+	0.809096i
$103$	−11.4286	−	6.59832i	−1.12610	−	0.650152i	−0.183146	−	0.983086i	$-0.558628\pi$
$103$	−11.4286	−	6.59832i	−1.12610	−	0.650152i	−0.942950	+	0.332934i	$0.891962\pi$
$104$	6.06382	−	10.5028i	0.594606	−	1.02989i
$105$	−1.78151	−	12.8826i	−0.173857	−	1.25722i
$106$	−1.54309	−	2.67272i	−0.149879	−	0.259597i
$107$		−	19.5555i		−	1.89051i	−0.326339	−	0.945253i	$-0.605815\pi$
$107$		−	19.5555i		−	1.89051i	0.326339	−	0.945253i	$-0.394185\pi$
$108$	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
$112$	0.954606	−	6.43951i	0.0902018	−	0.608477i
$113$	−8.72665	−	5.03834i	−0.820935	−	0.473967i	0.0298041	−	0.999556i	$-0.490512\pi$
$113$	−8.72665	−	5.03834i	−0.820935	−	0.473967i	−0.850739	+	0.525589i	$0.823845\pi$
$114$	−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
$119$	−8.59038	−	6.81653i	−0.787479	−	0.624870i
$120$	−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
$126$	7.63252	+	5.50901i	0.679959	+	0.490782i
$127$	−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	$-0.977936\pi$
$131$	−5.02249	+	8.69921i	−0.438817	+	0.760054i	0.558781	+	0.829315i	$0.311269\pi$
$132$	−0.157640	−	0.0384123i	−0.0137208	−	0.00334336i
$133$	10.4199	−	13.1315i	0.903524	−	1.13865i
$134$			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	−0.767066	−	0.641569i	$-0.778284\pi$
$137$	−6.96410	+	4.02073i	−0.594984	+	0.343514i	0.172082	+	0.985083i	$0.444951\pi$
$138$	−0.265576	+	1.08990i	−0.0226073	+	0.0927781i
$139$	16.3702	+	9.45136i	1.38850	+	0.801654i	0.993147	−	0.116873i	$-0.0372872\pi$
$139$	16.3702	+	9.45136i	1.38850	+	0.801654i	0.395358	+	0.918527i	$0.370621\pi$
$140$	0.653562	−	4.40875i	0.0552361	−	0.372607i
$141$	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
$147$	−12.1238	−	0.118263i	−0.999952	−	0.00975413i
$148$	0.730252	−	1.26483i	0.0600264	−	0.103969i
$149$	16.8063	+	9.70313i	1.37683	+	0.794912i	0.991776	−	0.127984i	$-0.0408505\pi$
$149$	16.8063	+	9.70313i	1.37683	+	0.794912i	0.385051	+	0.922895i	$0.374184\pi$
$150$	4.33370	−	4.53585i	0.353845	−	0.370350i
$151$	0.893968	+	1.54840i	0.0727501	+	0.126007i	0.900106	−	0.435672i	$-0.143489\pi$
$151$	0.893968	+	1.54840i	0.0727501	+	0.126007i	−0.827356	+	0.561678i	$0.810156\pi$
$152$	−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	$-0.277272\pi$
$157$	3.80255	+	2.19540i	0.303477	+	0.175212i	−0.340527	+	0.940235i	$0.610605\pi$
$158$	−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	$-0.966573\pi$
$167$	−5.25273	+	9.09799i	−0.406468	+	0.704024i	0.588023	+	0.808844i	$0.299907\pi$
$168$	8.65321	+	11.1262i	0.667610	+	0.858406i
$169$	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	0.978603	+	0.205757i	$0.0659656\pi$
$173$	8.77949	+	15.2065i	0.667492	+	1.15613i	−0.311111	+	0.950374i	$0.600701\pi$
$174$	6.90610	+	6.59832i	0.523550	+	0.500218i
$175$	−1.18490	+	7.99300i	−0.0895699	+	0.604214i
$176$	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	$-0.761855\pi$
$179$		−	18.2033i		−	1.36058i	0.732945	−	0.680288i	$-0.238145\pi$
$180$	−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	$0.921096\pi$
$182$	9.69121	+	7.69004i	0.718360	+	0.570024i
$183$	−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
$189$	−13.5182	+	2.50167i	−0.983304	+	0.181970i
$190$	21.3245			1.54704
$191$	−12.3063	+	7.10506i	−0.890454	+	0.514104i	−0.874091	−	0.485762i	$-0.838542\pi$
$191$	−12.3063	+	7.10506i	−0.890454	+	0.514104i	−0.0163630	+	0.999866i	$0.505209\pi$
$192$	3.59034	−	14.7344i	0.259111	−	1.06337i
$193$	5.00214	−	8.66395i	0.360062	−	0.623645i	−0.627909	−	0.778287i	$-0.716089\pi$
$193$	5.00214	−	8.66395i	0.360062	−	0.623645i	0.987971	+	0.154642i	$0.0494223\pi$
$194$	−1.49573	+	2.59068i	−0.107387	+	0.186000i
$195$	−5.44156	−	18.6020i	−0.389678	−	1.33211i
$196$	−3.97636	−	1.20542i	−0.284026	−	0.0861013i
$197$			20.1017i			1.43218i	0.698006	+	0.716092i	$0.254071\pi$
$197$			20.1017i			1.43218i	−0.698006	+	0.716092i	$0.745929\pi$
$198$	−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
$203$	−12.1698	−	1.80408i	−0.854154	−	0.126622i
$204$	−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
$210$	−9.46860	−	12.1746i	−0.653396	−	0.840129i
$211$	−4.50720	+	7.80669i	−0.310288	+	0.537435i	−0.978425	−	0.206604i	$-0.933759\pi$
$211$	−4.50720	+	7.80669i	−0.310288	+	0.537435i	0.668136	+	0.744039i	$0.267092\pi$
$212$	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	$-0.690740\pi$
$223$	−1.95429	+	1.12831i	−0.130869	+	0.0755571i	0.433136	+	0.901328i	$0.357407\pi$
$224$	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	−0.989733	−	0.142929i	$-0.954348\pi$
$227$	−9.32085	−	16.1442i	−0.618647	−	1.07153i	0.371086	−	0.928598i	$-0.378985\pi$
$228$	4.50000	−	4.70990i	0.298020	−	0.311921i
$229$	−12.3891	−	7.15283i	−0.818692	−	0.472672i	0.0312731	−	0.999511i	$-0.490044\pi$
$229$	−12.3891	−	7.15283i	−0.818692	−	0.472672i	−0.849965	+	0.526839i	$0.823377\pi$
$230$	0.919025	−	1.59180i	0.0605987	−	0.104960i
$231$	0.272399	−	0.669944i	0.0179226	−	0.0440791i
$232$	7.15126	+	12.3863i	0.469503	+	0.813204i
$233$			17.0679i			1.11815i	0.829116	+	0.559077i	$0.188844\pi$
$233$			17.0679i			1.11815i	−0.829116	+	0.559077i	$0.811156\pi$
$234$	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
$238$	−12.8646	−	1.90708i	−0.833890	−	0.123618i
$239$	1.93560	+	1.11752i	0.125203	+	0.0722863i	0.561294	−	0.827617i	$-0.310304\pi$
$239$	1.93560	+	1.11752i	0.125203	+	0.0722863i	−0.436090	+	0.899903i	$0.643637\pi$
$240$	−2.86333	+	11.7508i	−0.184827	+	0.758512i
$241$	−3.91464	+	2.26012i	−0.252164	+	0.145587i	−0.620755	−	0.784005i	$-0.713174\pi$
$241$	−3.91464	+	2.26012i	−0.252164	+	0.145587i	0.368591	+	0.929592i	$0.379840\pi$
$242$			13.0157i			0.836678i
$243$	−14.5010	+	5.72026i	−0.930239	+	0.366955i
$244$		−	1.99777i		−	0.127894i
$245$	19.0114	+	5.76324i	1.21460	+	0.368200i
$246$	−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	$-0.732937\pi$
$251$	−21.1727			−1.33641			−0.668205	+	0.743978i	$0.732937\pi$
$252$	−4.68710	−	0.477839i	−0.295259	−	0.0301010i
$253$	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	0.300440	−	0.953801i	$-0.402866\pi$
$257$	15.6502	−	27.1070i	0.976236	−	1.69089i	0.675796	−	0.737089i	$-0.263800\pi$
$258$	−9.32085	+	9.75562i	−0.580291	+	0.607358i
$259$	5.09948	+	4.04647i	0.316866	+	0.251435i
$260$		−	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	−0.667564	−	0.744552i	$-0.732663\pi$
$263$	−5.78220	+	3.33836i	−0.356546	+	0.205852i	0.311019	+	0.950404i	$0.399330\pi$
$264$	−0.806939	+	0.236051i	−0.0496637	+	0.0145279i
$265$	−6.39593	−	3.69269i	−0.392899	−	0.226840i
$266$	2.91522	−	19.6653i	0.178743	−	1.20575i
$267$	−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	$-0.605345\pi$
$269$	−10.6589			−0.649887			−0.324944	+	0.945733i	$0.605345\pi$
$270$	−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
$273$	−17.8984	+	2.47513i	−1.08326	+	0.149802i
$274$	−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	0.920998	+	0.389568i	$0.127376\pi$
$277$	13.2793	+	23.0004i	0.797874	+	1.38196i	−0.123124	+	0.992391i	$0.539291\pi$
$278$	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	0.285862	−	0.958271i	$-0.407720\pi$
$281$	21.0993	−	12.1817i	1.25868	−	0.726699i	0.972818	+	0.231572i	$0.0743869\pi$
$282$	12.2989	−	12.8726i	0.732390	−	0.766552i
$283$	7.49302	+	4.32610i	0.445414	+	0.257160i	0.705891	−	0.708320i	$-0.250547\pi$
$283$	7.49302	+	4.32610i	0.445414	+	0.257160i	−0.260478	+	0.965480i	$0.583880\pi$
$284$	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	$-0.750578\pi$
$293$	4.40023	−	7.62143i	0.257064	−	0.445249i	0.965454	+	0.260573i	$0.0839114\pi$
$294$	−12.5218	+	7.06749i	−0.730284	+	0.412185i
$295$	−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
$301$	2.54846	−	17.1912i	0.146891	−	0.990885i
$302$	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	$-0.103309\pi$
$308$	0.154058	−	0.194148i	0.00877825	−	0.0110626i
$309$	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	$-0.679338\pi$
$311$	8.20279	−	14.2076i	0.465137	−	0.805641i	0.999208	+	0.0397985i	$0.0126716\pi$
$312$	15.1878	+	14.5110i	0.859842	+	0.821522i
$313$	−7.10514	+	4.10216i	−0.401606	+	0.231868i	−0.687177	−	0.726490i	$-0.741150\pi$
$313$	−7.10514	+	4.10216i	−0.401606	+	0.231868i	0.285570	+	0.958358i	$0.407817\pi$
$314$	5.20717			0.293858
$315$	22.4095	+	2.28460i	1.26264	+	0.128723i
$316$	2.56867			0.144499
$317$	19.8427	−	11.4562i	1.11448	−	0.643443i	0.174491	−	0.984659i	$-0.444172\pi$
$317$	19.8427	−	11.4562i	1.11448	−	0.643443i	0.939985	+	0.341215i	$0.110839\pi$
$318$	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
$322$	−1.34230	−	1.06513i	−0.0748037	−	0.0593572i
$323$			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
$329$	−3.36271	+	22.6839i	−0.185392	+	1.25060i
$330$	0.882977	−	0.258294i	0.0486063	−	0.0142186i
$331$	−9.63161	−	16.6824i	−0.529401	−	0.916950i	−0.999412	−	0.0342892i	$-0.989083\pi$
$331$	−9.63161	−	16.6824i	−0.529401	−	0.916950i	0.470011	−	0.882661i	$-0.344250\pi$
$332$	−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
$336$	10.4451	+	4.24696i	0.569824	+	0.231690i
$337$	−2.26829	+	3.92878i	−0.123561	+	0.214015i	−0.921170	−	0.389161i	$-0.872765\pi$
$337$	−2.26829	+	3.92878i	−0.123561	+	0.214015i	0.797608	+	0.603176i	$0.206098\pi$
$338$	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	0.689070	−	0.724695i	$-0.258019\pi$
$347$	7.56294	+	4.36646i	0.406000	+	0.234404i	−0.283070	+	0.959099i	$0.591353\pi$
$348$	−4.64483	−	1.13181i	−0.248989	−	0.0606713i
$349$	7.82927	−	4.52023i	0.419091	−	0.241963i	−0.275597	−	0.961273i	$-0.588876\pi$
$349$	7.82927	−	4.52023i	0.419091	−	0.241963i	0.694689	+	0.719311i	$0.255542\pi$
$350$	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	$-0.156366\pi$
$353$	0.607896	+	1.05291i	0.0323550	+	0.0560406i	−0.849394	+	0.527758i	$0.823033\pi$
$354$	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
$357$	14.9934	−	11.6609i	0.793537	−	0.617159i
$358$	−10.7939	−	18.6955i	−0.570473	−	0.988089i
$359$		−	17.3069i		−	0.913424i	−0.889615	−	0.456712i	$-0.849027\pi$
$359$		−	17.3069i		−	0.913424i	0.889615	−	0.456712i	$-0.150973\pi$
$360$	−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
$364$	−6.12529	−	0.908025i	−0.321052	−	0.0475934i
$365$	−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	$-0.930072\pi$
$367$	−24.4297	+	14.1045i	−1.27522	+	0.736250i	−0.299256	+	0.954173i	$0.596738\pi$
$368$			1.34374i			0.0700474i
$369$	10.0864	−	6.45329i	0.525077	−	0.335945i
$370$			8.28114i			0.430516i
$371$	−4.27973	+	5.39344i	−0.222193	+	0.280014i
$372$	−0.0373591	−	0.127712i	−0.00193698	−	0.00662155i
$373$	−14.1264	+	24.4676i	−0.731435	+	1.26688i	0.224835	+	0.974397i	$0.427816\pi$
$373$	−14.1264	+	24.4676i	−0.731435	+	1.26688i	−0.956270	+	0.292486i	$0.905518\pi$
$374$	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
$378$	−12.4004	+	10.5851i	−0.637806	+	0.544439i
$379$	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	−0.353617	−	0.935390i	$-0.615048\pi$
$383$	12.3932	−	21.4657i	0.633264	−	1.09684i	0.986880	−	0.161454i	$-0.0516184\pi$
$384$	−1.90458	−	6.51081i	−0.0971928	−	0.332253i
$385$	−0.736567	+	0.928244i	−0.0375390	+	0.0473077i
$386$		−	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	−0.383281	−	0.923632i	$-0.625206\pi$
$389$	4.43706	−	2.56174i	0.224968	−	0.129885i	0.608248	+	0.793747i	$0.291872\pi$
$390$	−16.6190	−	15.8783i	−0.841535	−	0.804031i
$391$	1.96035	+	1.13181i	0.0991391	+	0.0572380i
$392$	−20.9672	+	4.89293i	−1.05900	+	0.247130i
$393$	−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
$399$	17.8252	+	22.9194i	0.892374	+	1.14741i
$400$	3.75729	−	6.50783i	0.187865	−	0.325391i
$401$	−12.4612	−	7.19446i	−0.622282	−	0.359274i	0.155475	−	0.987840i	$-0.450309\pi$
$401$	−12.4612	−	7.19446i	−0.622282	−	0.359274i	−0.777757	+	0.628565i	$0.783642\pi$
$402$	−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	$-0.256037\pi$
$409$	8.42281	+	4.86291i	0.416481	+	0.240455i	−0.277090	+	0.960844i	$0.589370\pi$
$410$	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	0.226289	+	0.974060i	$0.427340\pi$
$419$	−14.9512	+	25.8963i	−0.730416	+	1.26512i	−0.956706	+	0.291058i	$0.905993\pi$
$420$	7.15111	+	2.90764i	0.348938	+	0.141878i
$421$	−12.5452	−	21.7290i	−0.611417	−	1.05901i	−0.991002	−	0.133848i	$-0.957266\pi$
$421$	−12.5452	−	21.7290i	−0.611417	−	1.05901i	0.379585	−	0.925157i	$-0.376067\pi$
$422$			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
$427$	8.80835	+	1.30577i	0.426266	+	0.0631905i
$428$	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	$-0.950813\pi$
$431$		−	6.39061i		−	0.307825i	0.988084	−	0.153913i	$-0.0491874\pi$
$432$	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	$0.706316\pi$
$434$	−0.318112	−	0.252424i	−0.0152699	−	0.0121167i
$435$	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	$-0.601935\pi$
$439$	7.32931	−	4.23158i	0.349809	−	0.201962i	0.664601	+	0.747198i	$0.268601\pi$
$440$	1.37758			0.0656737
$441$	5.17039	−	20.3536i	0.246209	−	0.969217i
$442$	−19.3815			−0.921885
$443$	16.1082	−	9.30006i	0.765322	−	0.441859i	−0.0658812	−	0.997827i	$-0.520986\pi$
$443$	16.1082	−	9.30006i	0.765322	−	0.441859i	0.831203	+	0.555969i	$0.187652\pi$
$444$	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
$448$	18.1468	+	14.3996i	0.857353	+	0.680316i
$449$		−	20.3100i		−	0.958489i	−0.877681	−	0.479245i	$-0.840911\pi$
$449$		−	20.3100i		−	0.958489i	0.877681	−	0.479245i	$-0.159089\pi$
$450$	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
$455$	29.2857	+	4.34137i	1.37294	+	0.203527i
$456$	7.99115	−	32.7949i	0.374220	−	1.53576i
$457$	−5.67830	−	9.83511i	−0.265620	−	0.460067i	0.702106	−	0.712072i	$-0.252243\pi$
$457$	−5.67830	−	9.83511i	−0.265620	−	0.460067i	−0.967726	+	0.252005i	$0.918910\pi$
$458$	−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	−0.816661	−	0.577117i	$-0.804178\pi$
$461$	−19.4984	−	33.7721i	−0.908129	−	1.57293i	−0.0914676	−	0.995808i	$-0.529156\pi$
$462$	−0.117487	−	0.849584i	−0.00546598	−	0.0395262i
$463$	−5.03443	+	8.71990i	−0.233970	+	0.405248i	−0.958973	−	0.283498i	$-0.908505\pi$
$463$	−5.03443	+	8.71990i	−0.233970	+	0.405248i	0.725003	+	0.688746i	$0.241838\pi$
$464$	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	$-0.473505\pi$
$467$	3.59330			0.166278			0.0831389	+	0.996538i	$0.473505\pi$
$468$	−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	$-0.154868\pi$
$479$	0.811090	+	1.40485i	0.0370597	+	0.0641892i	−0.846901	+	0.531751i	$0.821534\pi$
$480$	−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
$483$	2.47907	−	0.342824i	0.112801	−	0.0155990i
$484$	−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
$490$	22.9429	−	5.35399i	1.03646	−	0.241869i
$491$	9.30632	+	5.37300i	0.419988	+	0.242480i	0.695072	−	0.718940i	$-0.255372\pi$
$491$	9.30632	+	5.37300i	0.419988	+	0.242480i	−0.275084	+	0.961420i	$0.588706\pi$
$492$	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
$497$	−0.673138	+	0.848308i	−0.0301944	+	0.0380518i
$498$	−9.15486	+	9.58188i	−0.410239	+	0.429374i
$499$	−8.46050	+	14.6540i	−0.378744	+	0.656004i	−0.990880	−	0.134749i	$-0.956977\pi$
$499$	−8.46050	+	14.6540i	−0.378744	+	0.656004i	0.612136	+	0.790753i	$0.290311\pi$
$500$	−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	$-0.227021\pi$
$503$	33.9226			1.51253			0.756267	+	0.654263i	$0.227021\pi$
$504$	−22.2716	+	9.99941i	−0.992055	+	0.445409i
$505$	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	$-0.905453\pi$
$509$	−5.06805	+	8.77812i	−0.224637	+	0.389083i	0.731573	+	0.681763i	$0.238786\pi$
$510$	23.4754	+	5.72026i	1.03951	+	0.253297i
$511$	−24.6889	+	31.1137i	−1.09217	+	1.37639i
$512$		−	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
$518$	7.63679	+	1.13209i	0.335541	+	0.0497413i
$519$	−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	$-0.255683\pi$
$521$	31.6986			1.38874			0.694370	+	0.719618i	$0.255683\pi$
$522$	−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
$525$	−12.9648	−	5.27150i	−0.565832	−	0.230067i
$526$	−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
$546$	−16.9148	+	13.1552i	−0.723886	+	0.562990i
$547$	13.1278	+	22.7380i	0.561305	+	0.972209i	0.997383	+	0.0722999i	$0.0230339\pi$
$547$	13.1278	+	22.7380i	0.561305	+	0.972209i	−0.436078	+	0.899909i	$0.643633\pi$
$548$		−	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
$553$	−1.67892	+	11.3255i	−0.0713950	+	0.481611i
$554$	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	$0.195627\pi$
$557$			27.2172i			1.15323i	−0.817016	+	0.576615i	$0.804373\pi$
$558$	−0.408852	−	0.211828i	−0.0173081	−	0.00896739i
$559$		−	25.8998i		−	1.09545i
$560$	−14.4722	−	11.4838i	−0.611561	−	0.485278i
$561$	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	$-0.896533\pi$
$563$	−4.68017	+	8.10630i	−0.197246	+	0.341640i	0.750389	+	0.660997i	$0.229866\pi$
$564$	−2.10963	+	8.65772i	−0.0888315	+	0.364556i
$565$	−24.7660	+	14.2987i	−1.04191	+	0.601549i
$566$	10.2609			0.431296
$567$	1.33331	−	23.7744i	0.0559940	−	0.998431i
$568$	1.25895			0.0528244
$569$	−30.2424	+	17.4605i	−1.26783	+	0.731980i	−0.974576	−	0.224055i	$-0.928070\pi$
$569$	−30.2424	+	17.4605i	−1.26783	+	0.731980i	−0.293251	+	0.956036i	$0.594737\pi$
$570$	−8.74415	+	35.8851i	−0.366252	+	1.50306i
$571$	0.735987	−	1.27477i	0.0308001	−	0.0533473i	−0.850214	−	0.526436i	$-0.823528\pi$
$571$	0.735987	−	1.27477i	0.0308001	−	0.0533473i	0.881015	+	0.473089i	$0.156861\pi$
$572$	0.184680	−	0.319875i	0.00772186	−	0.0133747i
$573$	−6.91025	−	23.6227i	−0.288680	−	0.986851i
$574$	7.78454	−	9.81030i	0.324920	−	0.409474i
$575$		−	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
$581$	2.50307	−	16.8851i	0.103845	−	0.700510i
$582$	−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	$-0.0414700\pi$
$587$	9.28551	+	16.0830i	0.383254	+	0.663816i	−0.608271	+	0.793729i	$0.708137\pi$
$588$	3.65901	−	6.19719i	0.150895	−	0.255568i
$589$	−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	$-0.718969\pi$
$593$	−30.9228			−1.26985			−0.634924	+	0.772574i	$0.718969\pi$
$594$	−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	0.722566	−	0.691302i	$-0.242963\pi$
$599$	11.8741	+	6.85553i	0.485164	+	0.280109i	−0.237402	+	0.971411i	$0.576296\pi$
$600$	4.56809	+	15.6160i	0.186491	+	0.637520i
$601$	−17.1065	+	9.87644i	−0.697788	+	0.402868i	−0.806523	−	0.591203i	$-0.798653\pi$
$601$	−17.1065	+	9.87644i	−0.697788	+	0.402868i	0.108735	+	0.994071i	$0.465320\pi$
$602$	−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	$-0.451833\pi$
$607$	−15.5219	−	8.96157i	−0.630014	−	0.363739i	−0.780757	+	0.624834i	$0.785167\pi$
$608$	10.2440	−	17.7432i	0.415450	−	0.719581i
$609$	8.02618	−	19.7398i	0.325237	−	0.799896i
$610$	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
$616$	0.188326	−	1.27039i	0.00758786	−	0.0511856i
$617$	19.9686	+	11.5289i	0.803904	+	0.464134i	0.844835	−	0.535028i	$-0.179699\pi$
$617$	19.9686	+	11.5289i	0.803904	+	0.464134i	−0.0409302	+	0.999162i	$0.513032\pi$
$618$	6.41741	−	26.3364i	0.258146	−	1.05941i
$619$	1.67850	−	0.969082i	0.0674646	−	0.0389507i	−0.465888	−	0.884844i	$-0.654265\pi$
$619$	1.67850	−	0.969082i	0.0674646	−	0.0389507i	0.533353	+	0.845893i	$0.320932\pi$
$620$			0.218026i			0.00875613i
$621$	2.68448	−	0.919981i	0.107725	−	0.0369176i
$622$		−	19.4558i		−	0.780106i
$623$	−10.4739	−	8.31113i	−0.419629	−	0.332978i
$624$	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
$630$	24.3702	−	10.9417i	0.970933	−	0.435926i
$631$	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
$637$	8.00715	−	26.4135i	0.317255	−	1.04654i
$638$		−	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	−0.0109373	−	0.999940i	$-0.503482\pi$
$641$	21.5093	−	12.4184i	0.849568	−	0.490498i	0.860505	+	0.509442i	$0.170148\pi$
$642$	38.5531	−	11.2778i	1.52157	−	0.445099i
$643$	37.9247	+	21.8959i	1.49561	+	0.863489i	0.999987	−	0.00505169i	$-0.00160801\pi$
$643$	37.9247	+	21.8959i	1.49561	+	0.863489i	0.495619	+	0.868540i	$0.334941\pi$
$644$	0.848397	+	0.125768i	0.0334315	+	0.00495596i
$645$	−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	$-0.304086\pi$
$647$	29.3713			1.15471			0.577353	+	0.816494i	$0.304086\pi$
$648$	−22.6141	+	15.9657i	−0.888366	+	0.627192i
$649$		−	0.570305i		−	0.0223864i
$650$	7.14048	+	12.3677i	0.280073	+	0.485100i
$651$	0.587513	−	0.0812456i	0.0230264	−	0.00318427i
$652$	−1.61323	+	2.79420i	−0.0631789	+	0.109429i
$653$	−28.0816	−	16.2129i	−1.09892	−	0.634461i	−0.162981	−	0.986629i	$-0.552111\pi$
$653$	−28.0816	−	16.2129i	−1.09892	−	0.634461i	−0.935937	+	0.352168i	$0.885444\pi$
$654$	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	−0.503949	−	0.863733i	$-0.668120\pi$
$659$	−0.203016	+	0.117211i	−0.00790837	+	0.00456590i	0.496041	+	0.868299i	$0.334787\pi$
$660$	−0.318097	+	0.332935i	−0.0123819	+	0.0129595i
$661$	−3.05138	−	1.76171i	−0.118685	−	0.0685227i	0.439482	−	0.898251i	$-0.355162\pi$
$661$	−3.05138	−	1.76171i	−0.118685	−	0.0685227i	−0.558167	+	0.829728i	$0.688495\pi$
$662$	−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
$672$	−14.6786	+	2.02986i	−0.566238	+	0.0783036i
$673$	9.16585	+	15.8757i	0.353318	+	0.611964i	0.986829	−	0.161770i	$-0.0517202\pi$
$673$	9.16585	+	15.8757i	0.353318	+	0.611964i	−0.633511	+	0.773734i	$0.718387\pi$
$674$			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	−0.982998	−	0.183619i	$-0.941219\pi$
$677$	−16.9260	−	29.3166i	−0.650517	−	1.12673i	0.332480	−	0.943110i	$-0.392115\pi$
$678$	4.90019	−	20.1099i	0.188191	−	0.772317i
$679$	6.60168	+	0.978646i	0.253349	+	0.0375570i
$680$	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	$-0.819844\pi$
$683$		−	28.0284i		−	1.07248i	0.844066	−	0.536239i	$-0.180156\pi$
$684$	6.08065	+	9.50396i	0.232499	+	0.363393i
$685$			22.8214i			0.871962i
$686$	−1.80093	−	21.8897i	−0.0687599	−	0.835753i
$687$	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	0.640577	−	0.767894i	$-0.278695\pi$
$691$	42.7393	−	24.6756i	1.62588	−	0.938703i	0.985304	−	0.170809i	$-0.0546381\pi$
$692$	−10.4226			−0.396210
$693$	1.01569	+	0.733109i	0.0385830	+	0.0278485i
$694$	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
$700$	−3.75717	−	2.98134i	−0.142008	−	0.112684i
$701$			26.3889i			0.996696i	0.866977	+	0.498348i	$0.166060\pi$
$701$			26.3889i			0.996696i	−0.866977	+	0.498348i	$0.833940\pi$
$702$	−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
$707$	1.16060	−	7.82911i	0.0436489	−	0.294444i
$708$	−3.56586	+	1.04311i	−0.134013	+	0.0392024i
$709$	5.35661	+	9.27792i	0.201172	+	0.348440i	0.948906	−	0.315558i	$-0.102192\pi$
$709$	5.35661	+	9.27792i	0.201172	+	0.348440i	−0.747735	+	0.663998i	$0.768858\pi$
$710$	−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
$714$	8.48442	−	20.8668i	0.317522	−	0.780919i
$715$	−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	$-0.606307\pi$
$719$	−17.5794			−0.655601			−0.327801	+	0.944747i	$0.606307\pi$
$720$	−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	0.623336	−	0.781954i	$-0.285777\pi$
$727$	43.4695	−	25.0971i	1.61220	−	0.930802i	0.988860	−	0.148847i	$-0.0475563\pi$
$728$	−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	$-0.0695633\pi$
$733$	34.5617	+	19.9542i	1.27656	+	0.737025i	0.300350	+	0.953829i	$0.402897\pi$
$734$	−16.7269	+	28.9719i	−0.617402	+	1.06937i
$735$	−17.4941	+	29.6295i	−0.645281	+	1.09290i
$736$	−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
$742$	−1.19735	+	8.07702i	−0.0439562	+	0.296517i
$743$	−39.5861	−	22.8550i	−1.45227	−	0.838470i	−0.453662	−	0.891174i	$-0.649883\pi$
$743$	−39.5861	−	22.8550i	−1.45227	−	0.838470i	−0.998610	+	0.0527041i	$0.983216\pi$
$744$	−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
$749$	−32.1604	+	40.5295i	−1.17512	+	1.48092i
$750$	3.18483	+	10.8873i	0.116293	+	0.397549i
$751$	−6.07753	+	10.5266i	−0.221772	+	0.384121i	−0.955346	−	0.295489i	$-0.904517\pi$
$751$	−6.07753	+	10.5266i	−0.221772	+	0.384121i	0.733574	+	0.679610i	$0.237851\pi$
$752$	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
$756$	2.72606	−	7.69156i	0.0991460	−	0.279739i
$757$	−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	0.263211	+	0.964738i	$0.415218\pi$
$761$	−19.4175	+	33.6320i	−0.703882	+	1.21916i	−0.967093	+	0.254422i	$0.918115\pi$
$762$	−7.20287	−	24.6230i	−0.260932	−	0.891996i
$763$	−27.4578	−	21.7880i	−0.994040	−	0.788777i
$764$		−	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	$-0.396228\pi$
$769$	−9.42879	−	5.44371i	−0.340011	−	0.196305i	−0.660277	+	0.751022i	$0.729561\pi$
$770$	−0.206072	+	1.39010i	−0.00742630	+	0.0500958i
$771$	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	$-0.734307\pi$
$773$	−37.3337			−1.34280			−0.671400	+	0.741096i	$0.734307\pi$
$774$	−12.5948	−	19.6856i	−0.452712	−	0.707583i
$775$		−	0.395277i		−	0.0141988i
$776$	−3.87930	−	6.71914i	−0.139259	−	0.241203i
$777$	−8.90050	+	6.92220i	−0.319304	+	0.248333i
$778$	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	$-0.436370\pi$
$787$	−15.4554	−	8.92315i	−0.550924	−	0.318076i	−0.749495	+	0.662011i	$0.769703\pi$
$788$	−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	$-0.768061\pi$
$797$	5.74854	−	9.95676i	0.203624	−	0.352687i	0.949693	+	0.313181i	$0.101395\pi$
$798$	31.8975	+	12.9695i	1.12916	+	0.459117i
$799$	−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
$805$	−4.05629	−	0.601312i	−0.142965	−	0.0211935i
$806$	−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	$-0.925491\pi$
$809$		−	13.1945i		−	0.463893i	0.972729	−	0.231946i	$-0.0745094\pi$
$810$	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	$-0.304819\pi$
$812$	4.53927	−	5.72052i	0.159297	−	0.200751i
$813$	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
$819$	3.17411	−	31.1347i	0.110912	−	1.08793i
$820$	−6.72373			−0.234803
$821$	34.3623	−	19.8391i	1.19925	−	0.692390i	0.238865	−	0.971053i	$-0.423225\pi$
$821$	34.3623	−	19.8391i	1.19925	−	0.692390i	0.960389	+	0.278663i	$0.0898913\pi$
$822$	−11.9430	−	11.4107i	−0.416558	−	0.397994i
$823$	19.6156	−	33.9751i	0.683755	−	1.18430i	−0.290071	−	0.957005i	$-0.593679\pi$
$823$	19.6156	−	33.9751i	0.683755	−	1.18430i	0.973826	−	0.227294i	$-0.0729878\pi$
$824$	20.2951	−	35.1521i	0.707013	−	1.22458i
$825$	0.576705	−	0.603605i	0.0200783	−	0.0210148i
$826$	−7.04797	+	8.88206i	−0.245230	+	0.309046i
$827$		−	21.0827i		−	0.733118i	−0.930395	−	0.366559i	$-0.880536\pi$
$827$		−	21.0827i		−	0.733118i	0.930395	−	0.366559i	$-0.119464\pi$
$828$	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
$833$	6.59361	+	28.2550i	0.228455	+	0.978976i
$834$	−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	$-0.0730379\pi$
$839$	8.39768	+	14.5452i	0.289920	+	0.502156i	−0.683870	+	0.729604i	$0.739705\pi$
$840$	39.6243	−	5.47954i	1.36717	−	0.189062i
$841$	−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	$-0.914282\pi$
$853$	−35.5011	+	20.4966i	−1.21554	+	0.701790i	−0.251576	+	0.967838i	$0.580949\pi$
$854$	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	0.963739	+	0.266848i	$0.0859822\pi$
$857$	20.8718	+	36.1510i	0.712967	+	1.23489i	−0.250772	+	0.968046i	$0.580684\pi$
$858$	−0.358860	−	1.22676i	−0.0122513	−	0.0418810i
$859$	24.0479	+	13.8841i	0.820505	+	0.473719i	0.850590	−	0.525829i	$-0.176245\pi$
$859$	24.0479	+	13.8841i	0.820505	+	0.473719i	−0.0300858	+	0.999547i	$0.509578\pi$
$860$	−5.53267	+	9.58286i	−0.188662	+	0.326773i
$861$	2.50555	+	18.1184i	0.0853888	+	0.617473i
$862$	−3.78940	−	6.56343i	−0.129067	−	0.223551i
$863$			45.6090i			1.55255i	0.630396	+	0.776274i	$0.282893\pi$
$863$			45.6090i			1.55255i	−0.630396	+	0.776274i	$0.717107\pi$
$864$	−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
$868$	0.201061	+	0.0298057i	0.00682447	+	0.00101167i
$869$	−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
$875$	−11.4455	−	9.08206i	−0.386927	−	0.307030i
$876$	−10.6623	+	11.1596i	−0.360244	+	0.377048i
$877$	−8.84368	+	15.3177i	−0.298630	+	0.517242i	−0.975823	−	0.218564i	$-0.929863\pi$
$877$	−8.84368	+	15.3177i	−0.298630	+	0.517242i	0.677193	+	0.735805i	$0.263196\pi$
$878$	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	$-0.562695\pi$
$881$	−11.6169			−0.391384			−0.195692	+	0.980665i	$0.562695\pi$
$882$	−6.75870	−	23.9698i	−0.227577	−	0.807105i
$883$	−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	$-0.698109\pi$
$887$	12.2751	−	21.2610i	0.412156	−	0.713876i	0.995125	+	0.0986188i	$0.0314424\pi$
$888$	12.7355	+	3.10327i	0.427376	+	0.104139i
$889$	25.8853	+	20.5401i	0.868165	+	0.688894i
$890$		−	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
$896$	10.2502	+	1.51951i	0.342435	+	0.0507633i
$897$	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
$903$	27.8846	+	11.3379i	0.927941	+	0.377300i
$904$	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	−0.990796	−	0.135366i	$-0.956779\pi$
$907$	−18.4502	−	31.9567i	−0.612628	−	1.06110i	0.378167	−	0.925737i	$-0.376554\pi$
$908$	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	−0.946996	−	0.321245i	$-0.895899\pi$
$911$	−34.4774	+	19.9056i	−1.14229	+	0.659500i	−0.195292	+	0.980745i	$0.562565\pi$
$912$	−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
$924$	0.263543	+	0.338861i	0.00866992	+	0.0111477i
$925$	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	−0.947365	−	0.320156i	$-0.896265\pi$
$929$	−22.8885	−	39.6440i	−0.750946	−	1.30068i	0.196419	−	0.980520i	$-0.437069\pi$
$930$	0.545515	+	0.521203i	0.0178881	+	0.0170909i
$931$	−43.1913	+	10.0792i	−1.41554	+	0.330332i
$932$	−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	$-0.128226\pi$
$938$	2.58894	−	3.26265i	0.0845318	−	0.106529i
$939$	−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	$-0.816275\pi$
$941$	1.64316	−	2.84603i	0.0535654	−	0.0927780i	0.891565	+	0.452893i	$0.149608\pi$
$942$	−2.13521	+	8.76270i	−0.0695689	+	0.285504i
$943$	−1.88776	+	1.08990i	−0.0614738	+	0.0354919i
$944$	8.89158			0.289396
$945$	−13.0336	+	36.7743i	−0.423984	+	1.19627i
$946$	1.22938			0.0399707
$947$	−25.9420	+	14.9776i	−0.843002	+	0.486707i	−0.858284	−	0.513176i	$-0.828469\pi$
$947$	−25.9420	+	14.9776i	−0.843002	+	0.486707i	0.0152815	+	0.999883i	$0.495136\pi$
$948$	−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
$952$	20.9662	−	26.4222i	0.679519	−	0.856350i
$953$			16.0580i			0.520169i	0.965586	+	0.260084i	$0.0837504\pi$
$953$			16.0580i			0.520169i	−0.965586	+	0.260084i	$0.916250\pi$
$954$	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
$959$	21.0457	+	3.11986i	0.679601	+	0.100745i
$960$	−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
$966$	2.34282	−	1.82209i	0.0753791	−	0.0586248i
$967$	25.0275	−	43.3489i	0.804831	−	1.39401i	−0.111574	−	0.993756i	$-0.535589\pi$
$967$	25.0275	−	43.3489i	0.804831	−	1.39401i	0.916405	−	0.400252i	$-0.131077\pi$
$968$	−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	$-0.505322\pi$
$971$	−1.04188			−0.0334354			−0.0167177	+	0.999860i	$0.505322\pi$
$972$	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	0.798910	−	0.601450i	$-0.205410\pi$
$977$	21.1765	+	12.2262i	0.677495	+	0.391152i	−0.121416	+	0.992602i	$0.538743\pi$
$978$	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	−0.833092	−	0.553135i	$-0.813431\pi$
$983$	−28.0788	−	48.6339i	−0.895575	−	1.55118i	−0.0624829	−	0.998046i	$-0.519902\pi$
$984$	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
$987$	−36.7939	−	14.9604i	−1.17116	−	0.476194i
$988$	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
$994$	−0.188326	+	1.27039i	−0.00597333	+	0.0402944i
$995$	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	$-0.850232\pi$
$997$	−29.8197	+	17.2164i	−0.944399	+	0.545249i	−0.0530623	+	0.998591i	$0.516898\pi$
$998$			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.41.5	yes	12
3.2	odd	2		189.2.o.a.125.1		12
4.3	odd	2		1008.2.cc.a.545.4		12
7.2	even	3		441.2.s.c.374.1		12
7.3	odd	6		441.2.i.c.68.5		12
7.4	even	3		441.2.i.c.68.6		12
7.5	odd	6		441.2.s.c.374.2		12
7.6	odd	2	inner	63.2.o.a.41.6	yes	12
9.2	odd	6	inner	63.2.o.a.20.6	yes	12
9.4	even	3		567.2.c.c.566.9		12
9.5	odd	6		567.2.c.c.566.4		12
9.7	even	3		189.2.o.a.62.2		12
12.11	even	2		3024.2.cc.a.881.1		12
21.2	odd	6		1323.2.s.c.962.6		12
21.5	even	6		1323.2.s.c.962.5		12
21.11	odd	6		1323.2.i.c.1097.1		12
21.17	even	6		1323.2.i.c.1097.2		12
21.20	even	2		189.2.o.a.125.2		12
28.27	even	2		1008.2.cc.a.545.3		12
36.7	odd	6		3024.2.cc.a.2897.6		12
36.11	even	6		1008.2.cc.a.209.3		12
63.2	odd	6		441.2.i.c.227.1		12
63.11	odd	6		441.2.s.c.362.2		12
63.13	odd	6		567.2.c.c.566.10		12
63.16	even	3		1323.2.i.c.521.6		12
63.20	even	6	inner	63.2.o.a.20.5	✓	12
63.25	even	3		1323.2.s.c.656.5		12
63.34	odd	6		189.2.o.a.62.1		12
63.38	even	6		441.2.s.c.362.1		12
63.41	even	6		567.2.c.c.566.3		12
63.47	even	6		441.2.i.c.227.2		12
63.52	odd	6		1323.2.s.c.656.6		12
63.61	odd	6		1323.2.i.c.521.5		12
84.83	odd	2		3024.2.cc.a.881.6		12
252.83	odd	6		1008.2.cc.a.209.4		12
252.223	even	6		3024.2.cc.a.2897.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.5	✓	12	63.20	even	6	inner
63.2.o.a.20.6	yes	12	9.2	odd	6	inner
63.2.o.a.41.5	yes	12	1.1	even	1	trivial
63.2.o.a.41.6	yes	12	7.6	odd	2	inner
189.2.o.a.62.1		12	63.34	odd	6
189.2.o.a.62.2		12	9.7	even	3
189.2.o.a.125.1		12	3.2	odd	2
189.2.o.a.125.2		12	21.20	even	2
441.2.i.c.68.5		12	7.3	odd	6
441.2.i.c.68.6		12	7.4	even	3
441.2.i.c.227.1		12	63.2	odd	6
441.2.i.c.227.2		12	63.47	even	6
441.2.s.c.362.1		12	63.38	even	6
441.2.s.c.362.2		12	63.11	odd	6
441.2.s.c.374.1		12	7.2	even	3
441.2.s.c.374.2		12	7.5	odd	6
567.2.c.c.566.3		12	63.41	even	6
567.2.c.c.566.4		12	9.5	odd	6
567.2.c.c.566.9		12	9.4	even	3
567.2.c.c.566.10		12	63.13	odd	6
1008.2.cc.a.209.3		12	36.11	even	6
1008.2.cc.a.209.4		12	252.83	odd	6
1008.2.cc.a.545.3		12	28.27	even	2
1008.2.cc.a.545.4		12	4.3	odd	2
1323.2.i.c.521.5		12	63.61	odd	6
1323.2.i.c.521.6		12	63.16	even	3
1323.2.i.c.1097.1		12	21.11	odd	6
1323.2.i.c.1097.2		12	21.17	even	6
1323.2.s.c.656.5		12	63.25	even	3
1323.2.s.c.656.6		12	63.52	odd	6
1323.2.s.c.962.5		12	21.5	even	6
1323.2.s.c.962.6		12	21.2	odd	6
3024.2.cc.a.881.1		12	12.11	even	2
3024.2.cc.a.881.6		12	84.83	odd	2
3024.2.cc.a.2897.1		12	252.223	even	6
3024.2.cc.a.2897.6		12	36.7	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.02704 - 0.592963i) q^{2} +(-0.410052 + 1.68281i) q^{3} +(-0.296790 + 0.514055i) q^{4} +(1.41899 - 2.45776i) q^{5} +(0.576705 + 1.97146i) q^{6} +(-2.07253 - 1.64457i) q^{7} +3.07579i q^{8} +(-2.66372 - 1.38008i) q^{9} +O(q^{10})\)	\(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} +(-2.07253 - 1.64457i) 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} +(-3.10375 - 0.460106i) 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} +(3.61735 - 2.81333i) 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} +(2.04697 - 5.03436i) 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} +(1.59079 + 6.81685i) 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} +(5.05835 - 6.37468i) 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} +(3.25100 + 7.24092i) 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} +(-5.53500 + 6.97537i) 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} +(-0.413030 - 0.0612283i) 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} +(0.372613 + 2.69448i) 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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