LMFDB - Embedded newform 441.2.h.g.214.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			214.5
Root			$1.82904 - 1.05600i$ of defining polynomial
Character	$\chi$	$=$	441.214
Dual form			441.2.h.g.373.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.46050 q^{2} +(-1.25233 + 1.19652i) q^{3} +4.05408 q^{4} +(1.82904 - 3.16799i) q^{5} +(-3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(0.136673 - 2.99689i) q^{9} +O(q^{10})$	\(q+2.46050 q^{2} +(-1.25233 + 1.19652i) q^{3} +4.05408 q^{4} +(1.82904 - 3.16799i) q^{5} +(-3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(0.136673 - 2.99689i) q^{9} +(4.50036 - 7.79485i) q^{10} +(-0.203210 - 0.351971i) q^{11} +(-5.07706 + 4.85080i) q^{12} +(0.243398 + 0.421578i) q^{13} +(1.50000 + 6.15585i) q^{15} +4.32743 q^{16} +(-2.42792 + 4.20528i) q^{17} +(0.336285 - 7.37385i) q^{18} +(0.986757 + 1.70911i) q^{19} +(7.41507 - 12.8433i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.32383 + 4.02499i) q^{23} +(-6.32939 + 6.04732i) q^{24} +(-4.19076 - 7.25860i) q^{25} +(0.598883 + 1.03729i) q^{26} +(3.41468 + 3.91663i) q^{27} +(-3.82383 + 6.62307i) q^{29} +(3.69076 + 15.1465i) q^{30} +7.02720 q^{31} +0.539495 q^{32} +(0.675627 + 0.197639i) q^{33} +(-5.97391 + 10.3471i) q^{34} +(0.554084 - 12.1496i) q^{36} +(-1.16372 - 2.01561i) q^{37} +(2.42792 + 4.20528i) q^{38} +(-0.809243 - 0.236725i) q^{39} +(9.24411 - 16.0113i) q^{40} +(-3.75700 - 6.50731i) q^{41} +(1.16372 - 2.01561i) q^{43} +(-0.823832 - 1.42692i) q^{44} +(-9.24411 - 5.91439i) q^{45} +(-5.71780 + 9.90352i) q^{46} -6.31623 q^{47} +(-5.41938 + 5.17786i) q^{48} +(-10.3114 - 17.8598i) q^{50} +(-1.99115 - 8.17147i) q^{51} +(0.986757 + 1.70911i) q^{52} +(1.78434 - 3.09056i) q^{53} +(8.40183 + 9.63688i) q^{54} -1.48672 q^{55} +(-3.28074 - 0.959702i) q^{57} +(-9.40856 + 16.2961i) q^{58} +6.11839 q^{59} +(6.08113 + 24.9564i) q^{60} -8.02712 q^{61} +17.2905 q^{62} -7.32743 q^{64} +1.78074 q^{65} +(1.66238 + 0.486291i) q^{66} +3.60078 q^{67} +(-9.84299 + 17.0486i) q^{68} +(-1.90578 - 7.82115i) q^{69} +8.46050 q^{71} +(0.690757 - 15.1465i) q^{72} +(-0.986757 + 1.70911i) q^{73} +(-2.86333 - 4.95943i) q^{74} +(13.9333 + 4.07586i) q^{75} +(4.00040 + 6.92889i) q^{76} +(-1.99115 - 0.582462i) q^{78} +8.16225 q^{79} +(7.91503 - 13.7092i) q^{80} +(-8.96264 - 0.819187i) q^{81} +(-9.24411 - 16.0113i) q^{82} +(-6.08600 + 10.5413i) q^{83} +(8.88151 + 15.3832i) q^{85} +(2.86333 - 4.95943i) q^{86} +(-3.13594 - 12.8696i) q^{87} +(-1.02704 - 1.77889i) q^{88} +(-7.41507 - 12.8433i) q^{89} +(-22.7452 - 14.5524i) q^{90} +(-9.42101 + 16.3177i) q^{92} +(-8.80039 + 8.40819i) q^{93} -15.5411 q^{94} +7.21926 q^{95} +(-0.675627 + 0.645517i) q^{96} +(4.74375 - 8.21642i) q^{97} +(-1.08259 + 0.560893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8	$ 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 8 q^{11} + 18 q^{15} + 12 q^{16} + 24 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} + 6 q^{30} + 32 q^{32} - 30 q^{36} + 6 q^{37} - 48 q^{39} - 6 q^{43} + 14 q^{44} - 12 q^{46} - 56 q^{50} + 36 q^{51} - 28 q^{53} - 6 q^{57} - 18 q^{58} + 18 q^{60} - 48 q^{64} - 12 q^{65} + 76 q^{71} - 30 q^{72} - 36 q^{74} + 36 q^{78} - 12 q^{79} + 24 q^{81} + 30 q^{85} + 36 q^{86} + 6 q^{88} - 62 q^{92} - 84 q^{93} + 120 q^{95} - 48 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8 - 8 * q^11 + 18 * q^15 + 12 * q^16 + 24 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 + 6 * q^30 + 32 * q^32 - 30 * q^36 + 6 * q^37 - 48 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 + 36 * q^51 - 28 * q^53 - 6 * q^57 - 18 * q^58 + 18 * q^60 - 48 * q^64 - 12 * q^65 + 76 * q^71 - 30 * q^72 - 36 * q^74 + 36 * q^78 - 12 * q^79 + 24 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 - 84 * q^93 + 120 * q^95 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.46050			1.73984			0.869920	−	0.493193i	$-0.164170\pi$
$2$	2.46050			1.73984			0.869920	+	0.493193i	$0.164170\pi$
$3$	−1.25233	+	1.19652i	−0.723034	+	0.690812i
$3$	−1.25233	+	1.19652i	−0.723034	+	0.690812i
$4$	4.05408			2.02704
$5$	1.82904	−	3.16799i	0.817970	−	1.41677i	−0.0892047	−	0.996013i	$-0.528433\pi$
$5$	1.82904	−	3.16799i	0.817970	−	1.41677i	0.907175	−	0.420753i	$-0.138234\pi$
$6$	−3.08137	+	2.94405i	−1.25796	+	1.20190i
$7$		0			0
$7$		0			0
$8$	5.05408			1.78689
$9$	0.136673	−	2.99689i	0.0455577	−	0.998962i
$10$	4.50036	−	7.79485i	1.42314	−	2.46495i
$11$	−0.203210	−	0.351971i	−0.0612702	−	0.106123i	0.833763	−	0.552122i	$-0.186182\pi$
$11$	−0.203210	−	0.351971i	−0.0612702	−	0.106123i	−0.895033	+	0.445999i	$0.852848\pi$
$12$	−5.07706	+	4.85080i	−1.46562	+	1.40030i
$13$	0.243398	+	0.421578i	0.0675065	+	0.116925i	0.897803	−	0.440397i	$-0.145162\pi$
$13$	0.243398	+	0.421578i	0.0675065	+	0.116925i	−0.830297	+	0.557322i	$0.811829\pi$
$14$		0			0
$15$	1.50000	+	6.15585i	0.387298	+	1.58943i
$16$	4.32743			1.08186
$17$	−2.42792	+	4.20528i	−0.588857	+	1.01993i	0.405525	+	0.914084i	$0.367089\pi$
$17$	−2.42792	+	4.20528i	−0.588857	+	1.01993i	−0.994382	+	0.105847i	$0.966245\pi$
$18$	0.336285	−	7.37385i	0.0792631	−	1.73803i
$19$	0.986757	+	1.70911i	0.226378	+	0.392097i	0.956732	−	0.290971i	$-0.0939784\pi$
$19$	0.986757	+	1.70911i	0.226378	+	0.392097i	−0.730354	+	0.683069i	$0.760645\pi$
$20$	7.41507	−	12.8433i	1.65806	−	2.87185i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	−2.32383	+	4.02499i	−0.484552	+	0.839269i	−0.999843	−	0.0177464i	$-0.994351\pi$
$23$	−2.32383	+	4.02499i	−0.484552	+	0.839269i	0.515290	+	0.857016i	$0.327684\pi$
$24$	−6.32939	+	6.04732i	−1.29198	+	1.23440i
$25$	−4.19076	−	7.25860i	−0.838151	−	1.45172i
$26$	0.598883	+	1.03729i	0.117451	+	0.203430i
$27$	3.41468	+	3.91663i	0.657155	+	0.753756i
$28$		0			0
$29$	−3.82383	+	6.62307i	−0.710068	+	1.22987i	0.254764	+	0.967003i	$0.418002\pi$
$29$	−3.82383	+	6.62307i	−0.710068	+	1.22987i	−0.964831	+	0.262870i	$0.915331\pi$
$30$	3.69076	+	15.1465i	0.673837	+	2.76536i
$31$	7.02720			1.26212			0.631061	−	0.775733i	$-0.282620\pi$
$31$	7.02720			1.26212			0.631061	+	0.775733i	$0.282620\pi$
$32$	0.539495			0.0953702
$33$	0.675627	+	0.197639i	0.117612	+	0.0344045i
$34$	−5.97391	+	10.3471i	−1.02452	+	1.77452i
$35$		0			0
$36$	0.554084	−	12.1496i	0.0923474	−	2.02494i
$37$	−1.16372	−	2.01561i	−0.191314	−	0.331365i	0.754372	−	0.656447i	$-0.227941\pi$
$37$	−1.16372	−	2.01561i	−0.191314	−	0.331365i	−0.945686	+	0.325082i	$0.894608\pi$
$38$	2.42792	+	4.20528i	0.393861	+	0.682187i
$39$	−0.809243	−	0.236725i	−0.129583	−	0.0379063i
$40$	9.24411	−	16.0113i	1.46162	−	2.53160i
$41$	−3.75700	−	6.50731i	−0.586744	−	1.01627i	−0.994655	−	0.103249i	$-0.967076\pi$
$41$	−3.75700	−	6.50731i	−0.586744	−	1.01627i	0.407911	−	0.913022i	$-0.366257\pi$
$42$		0			0
$43$	1.16372	−	2.01561i	0.177465	−	0.307378i	−0.763547	−	0.645753i	$-0.776544\pi$
$43$	1.16372	−	2.01561i	0.177465	−	0.307378i	0.941012	+	0.338374i	$0.109877\pi$
$44$	−0.823832	−	1.42692i	−0.124197	−	0.215116i
$45$	−9.24411	−	5.91439i	−1.37803	−	0.881666i
$46$	−5.71780	+	9.90352i	−0.843044	+	1.46019i
$47$	−6.31623			−0.921317			−0.460658	−	0.887578i	$-0.652387\pi$
$47$	−6.31623			−0.921317			−0.460658	+	0.887578i	$0.652387\pi$
$48$	−5.41938	+	5.17786i	−0.782220	+	0.747360i
$49$		0			0
$50$	−10.3114	−	17.8598i	−1.45825	−	2.52576i
$51$	−1.99115	−	8.17147i	−0.278816	−	1.14423i
$52$	0.986757	+	1.70911i	0.136839	+	0.237011i
$53$	1.78434	−	3.09056i	0.245097	−	0.424521i	−0.717062	−	0.697010i	$-0.754513\pi$
$53$	1.78434	−	3.09056i	0.245097	−	0.424521i	0.962159	+	0.272489i	$0.0878467\pi$
$54$	8.40183	+	9.63688i	1.14334	+	1.31141i
$55$	−1.48672			−0.200469
$56$		0			0
$57$	−3.28074	−	0.959702i	−0.434544	−	0.127116i
$58$	−9.40856	+	16.2961i	−1.23540	+	2.13978i
$59$	6.11839			0.796546			0.398273	−	0.917267i	$-0.369610\pi$
$59$	6.11839			0.796546			0.398273	+	0.917267i	$0.369610\pi$
$60$	6.08113	+	24.9564i	0.785070	+	3.22185i
$61$	−8.02712			−1.02777			−0.513884	−	0.857860i	$-0.671794\pi$
$61$	−8.02712			−1.02777			−0.513884	+	0.857860i	$0.671794\pi$
$62$	17.2905			2.19589
$63$		0			0
$64$	−7.32743			−0.915929
$65$	1.78074			0.220873
$66$	1.66238	+	0.486291i	0.204625	+	0.0598583i
$67$	3.60078			0.439905			0.219952	−	0.975511i	$-0.429410\pi$
$67$	3.60078			0.439905			0.219952	+	0.975511i	$0.429410\pi$
$68$	−9.84299	+	17.0486i	−1.19364	+	2.06744i
$69$	−1.90578	−	7.82115i	−0.229429	−	0.941555i
$70$		0			0
$71$	8.46050			1.00408			0.502039	−	0.864845i	$-0.332584\pi$
$71$	8.46050			1.00408			0.502039	+	0.864845i	$0.332584\pi$
$72$	0.690757	−	15.1465i	0.0814065	−	1.78503i
$73$	−0.986757	+	1.70911i	−0.115491	+	0.200037i	−0.917976	−	0.396636i	$-0.870178\pi$
$73$	−0.986757	+	1.70911i	−0.115491	+	0.200037i	0.802485	+	0.596673i	$0.203511\pi$
$74$	−2.86333	−	4.95943i	−0.332855	−	0.576522i
$75$	13.9333	+	4.07586i	1.60888	+	0.470639i
$76$	4.00040	+	6.92889i	0.458877	+	0.794798i
$77$		0			0
$78$	−1.99115	−	0.582462i	−0.225453	−	0.0659509i
$79$	8.16225			0.918325			0.459163	−	0.888352i	$-0.348150\pi$
$79$	8.16225			0.918325			0.459163	+	0.888352i	$0.348150\pi$
$80$	7.91503	−	13.7092i	0.884928	−	1.53274i
$81$	−8.96264	−	0.819187i	−0.995849	−	0.0910208i
$82$	−9.24411	−	16.0113i	−1.02084	−	1.76815i
$83$	−6.08600	+	10.5413i	−0.668025	+	1.15705i	0.310431	+	0.950596i	$0.399527\pi$
$83$	−6.08600	+	10.5413i	−0.668025	+	1.15705i	−0.978456	+	0.206457i	$0.933807\pi$
$84$		0			0
$85$	8.88151	+	15.3832i	0.963336	+	1.66855i
$86$	2.86333	−	4.95943i	0.308760	−	0.534789i
$87$	−3.13594	−	12.8696i	−0.336208	−	1.37976i
$88$	−1.02704	−	1.77889i	−0.109483	−	0.189630i
$89$	−7.41507	−	12.8433i	−0.785996	−	1.36139i	−0.928402	−	0.371577i	$-0.878817\pi$
$89$	−7.41507	−	12.8433i	−0.785996	−	1.36139i	0.142406	−	0.989808i	$-0.454516\pi$
$90$	−22.7452	−	14.5524i	−2.39755	−	1.53396i
$91$		0			0
$92$	−9.42101	+	16.3177i	−0.982208	+	1.70123i
$93$	−8.80039	+	8.40819i	−0.912558	+	0.871889i
$94$	−15.5411			−1.60294
$95$	7.21926			0.740681
$96$	−0.675627	+	0.645517i	−0.0689559	+	0.0658829i
$97$	4.74375	−	8.21642i	0.481655	−	0.834251i	−0.518123	−	0.855306i	$-0.673369\pi$
$97$	4.74375	−	8.21642i	0.481655	−	0.834251i	0.999778	+	0.0210547i	$0.00670241\pi$
$98$		0			0
$99$	−1.08259	+	0.560893i	−0.108804	+	0.0563719i
$100$	−16.9897	−	29.4270i	−1.69897	−	2.94270i
$101$	−4.35588	−	7.54461i	−0.433426	−	0.750716i	0.563739	−	0.825953i	$-0.309362\pi$
$101$	−4.35588	−	7.54461i	−0.433426	−	0.750716i	−0.997166	+	0.0752364i	$0.976029\pi$
$102$	−4.89922	−	20.1059i	−0.485095	−	1.99078i
$103$	−4.01356	+	6.95169i	−0.395468	+	0.684970i	−0.993161	−	0.116755i	$-0.962751\pi$
$103$	−4.01356	+	6.95169i	−0.395468	+	0.684970i	0.597693	+	0.801725i	$0.296084\pi$
$104$	1.23016	+	2.13069i	0.120627	+	0.208931i
$105$		0			0
$106$	4.39037	−	7.60434i	0.426430	−	0.738599i
$107$	−6.42101	−	11.1215i	−0.620742	−	1.07516i	−0.989348	−	0.145571i	$-0.953498\pi$
$107$	−6.42101	−	11.1215i	−0.620742	−	1.07516i	0.368605	−	0.929586i	$-0.379835\pi$
$108$	13.8434	+	15.8783i	1.33208	+	1.52789i
$109$	−1.30039	+	2.25234i	−0.124555	+	0.215735i	−0.921559	−	0.388239i	$-0.873084\pi$
$109$	−1.30039	+	2.25234i	−0.124555	+	0.215735i	0.797004	+	0.603974i	$0.206417\pi$
$110$	−3.65808			−0.348784
$111$	3.86908	+	1.13181i	0.367237	+	0.107427i
$112$		0			0
$113$	6.97509	+	12.0812i	0.656162	+	1.13651i	0.981601	+	0.190942i	$0.0611544\pi$
$113$	6.97509	+	12.0812i	0.656162	+	1.13651i	−0.325440	+	0.945563i	$0.605512\pi$
$114$	−8.07227	−	2.36135i	−0.756038	−	0.221161i
$115$	8.50075	+	14.7237i	0.792699	+	1.37300i
$116$	−15.5021	+	26.8505i	−1.43934	+	2.49301i
$117$	1.29669	−	0.671818i	0.119879	−	0.0621096i
$118$	15.0543			1.38586
$119$		0			0
$120$	7.58113	+	31.1122i	0.692059	+	2.84014i
$121$	5.41741	−	9.38323i	0.492492	−	0.853021i
$122$	−19.7508			−1.78815
$123$	12.4911	+	3.65399i	1.12629	+	0.329469i
$124$	28.4889			2.55837
$125$	−12.3698			−1.10639
$126$		0			0
$127$	−15.5438			−1.37929			−0.689643	−	0.724149i	$-0.742233\pi$
$127$	−15.5438			−1.37929			−0.689643	+	0.724149i	$0.742233\pi$
$128$	−19.1082			−1.68894
$129$	0.954367	+	3.91663i	0.0840273	+	0.344840i
$130$	4.38151			0.384284
$131$	4.25696	−	7.37327i	0.371932	−	0.644205i	−0.617931	−	0.786233i	$-0.712029\pi$
$131$	4.25696	−	7.37327i	0.371932	−	0.644205i	0.989863	+	0.142027i	$0.0453621\pi$
$132$	2.73905	+	0.801244i	0.238404	+	0.0697393i
$133$		0			0
$134$	8.85973			0.765364
$135$	18.6534	−	3.65399i	1.60543	−	0.314485i
$136$	−12.2709	+	21.2538i	−1.05222	+	1.82250i
$137$	−0.188621	−	0.326702i	−0.0161150	−	0.0279120i	0.857855	−	0.513891i	$-0.171796\pi$
$137$	−0.188621	−	0.326702i	−0.0161150	−	0.0279120i	−0.873970	+	0.485979i	$0.838463\pi$
$138$	−4.68919	−	19.2440i	−0.399170	−	1.63816i
$139$	9.50067	+	16.4556i	0.805837	+	1.39575i	0.915725	+	0.401806i	$0.131617\pi$
$139$	9.50067	+	16.4556i	0.805837	+	1.39575i	−0.109888	+	0.993944i	$0.535049\pi$
$140$		0			0
$141$	7.91002	−	7.55750i	0.666144	−	0.636457i
$142$	20.8171			1.74693
$143$	0.0989221	−	0.171338i	0.00827228	−	0.0143280i
$144$	0.591443	−	12.9688i	0.0492869	−	1.08073i
$145$	13.9879	+	24.2277i	1.16163	+	2.01200i
$146$	−2.42792	+	4.20528i	−0.200936	+	0.348032i
$147$		0			0
$148$	−4.71780	−	8.17147i	−0.387801	−	0.671691i
$149$	4.85087	−	8.40196i	0.397399	−	0.688315i	−0.596005	−	0.802981i	$-0.703246\pi$
$149$	4.85087	−	8.40196i	0.397399	−	0.688315i	0.993404	+	0.114665i	$0.0365795\pi$
$150$	34.2829	+	10.0287i	2.79919	+	0.818837i
$151$	6.41741	+	11.1153i	0.522242	+	0.904549i	0.999665	+	0.0258756i	$0.00823738\pi$
$151$	6.41741	+	11.1153i	0.522242	+	0.904549i	−0.477424	+	0.878673i	$0.658429\pi$
$152$	4.98715	+	8.63800i	0.404511	+	0.700634i
$153$	12.2709	+	7.85095i	0.992045	+	0.634711i
$154$		0			0
$155$	12.8530	−	22.2621i	1.03238	−	1.78813i
$156$	−3.28074	−	0.959702i	−0.262669	−	0.0768377i
$157$	20.9485			1.67187			0.835937	−	0.548825i	$-0.184925\pi$
$157$	20.9485			1.67187			0.835937	+	0.548825i	$0.184925\pi$
$158$	20.0833			1.59774
$159$	1.46334	+	6.00541i	0.116050	+	0.476260i
$160$	0.986757	−	1.70911i	0.0780100	−	0.135117i
$161$		0			0
$162$	−22.0526	−	2.01561i	−1.73262	−	0.158362i
$163$	5.58113	+	9.66679i	0.437148	+	0.757162i	0.997468	−	0.0711140i	$-0.0226554\pi$
$163$	5.58113	+	9.66679i	0.437148	+	0.757162i	−0.560321	+	0.828276i	$0.689322\pi$
$164$	−15.2312	−	26.3812i	−1.18936	−	2.06002i
$165$	1.86186	−	1.77889i	0.144946	−	0.138486i
$166$	−14.9746	+	25.9368i	−1.16226	+	2.01309i
$167$	−1.73012	−	2.99665i	−0.133880	−	0.231888i	0.791289	−	0.611443i	$-0.209410\pi$
$167$	−1.73012	−	2.99665i	−0.133880	−	0.231888i	−0.925169	+	0.379555i	$0.876077\pi$
$168$		0			0
$169$	6.38151	−	11.0531i	0.490886	−	0.850239i
$170$	21.8530	+	37.8505i	1.67605	+	2.90300i
$171$	5.25688	−	2.72361i	0.402004	−	0.208279i
$172$	4.71780	−	8.17147i	0.359729	−	0.623069i
$173$	−6.05361			−0.460247			−0.230124	−	0.973161i	$-0.573913\pi$
$173$	−6.05361			−0.460247			−0.230124	+	0.973161i	$0.573913\pi$
$174$	−7.71599	−	31.6657i	−0.584948	−	2.40057i
$175$		0			0
$176$	−0.879379	−	1.52313i	−0.0662857	−	0.114810i
$177$	−7.66225	+	7.32078i	−0.575930	+	0.550263i
$178$	−18.2448	−	31.6010i	−1.36751	−	2.36859i
$179$	−4.56654	+	7.90947i	−0.341319	+	0.591182i	−0.984678	−	0.174383i	$-0.944207\pi$
$179$	−4.56654	+	7.90947i	−0.341319	+	0.591182i	0.643359	+	0.765565i	$0.277540\pi$
$180$	−37.4764	−	23.9775i	−2.79333	−	1.78717i
$181$	11.9478			0.888074			0.444037	−	0.896008i	$-0.353546\pi$
$181$	11.9478			0.888074			0.444037	+	0.896008i	$0.353546\pi$
$182$		0			0
$183$	10.0526	−	9.60462i	0.743111	−	0.709994i
$184$	−11.7448	+	20.3427i	−0.865841	+	1.49968i
$185$	−8.51392			−0.625956
$186$	−21.6534	+	20.6884i	−1.58770	+	1.51695i
$187$	1.97351			0.144318
$188$	−25.6065			−1.86755
$189$		0			0
$190$	17.7630			1.28867
$191$	9.14027			0.661367			0.330683	−	0.943742i	$-0.392721\pi$
$191$	9.14027			0.661367			0.330683	+	0.943742i	$0.392721\pi$
$192$	9.17638	−	8.76743i	0.662248	−	0.632735i
$193$	16.9430			1.21958			0.609792	−	0.792562i	$-0.291253\pi$
$193$	16.9430			1.21958			0.609792	+	0.792562i	$0.291253\pi$
$194$	11.6720	−	20.2165i	0.838003	−	1.45146i
$195$	−2.23008	+	2.13069i	−0.159699	+	0.152582i
$196$		0			0
$197$	−21.3173			−1.51880			−0.759398	−	0.650627i	$-0.774506\pi$
$197$	−21.3173			−1.51880			−0.759398	+	0.650627i	$0.774506\pi$
$198$	−2.66372	+	1.38008i	−0.189302	+	0.0980780i
$199$	−4.98715	+	8.63800i	−0.353530	+	0.612332i	−0.986865	−	0.161546i	$-0.948352\pi$
$199$	−4.98715	+	8.63800i	−0.353530	+	0.612332i	0.633335	+	0.773877i	$0.281685\pi$
$200$	−21.1804	−	36.6856i	−1.49768	−	2.59406i
$201$	−4.50937	+	4.30841i	−0.318066	+	0.303892i
$202$	−10.7177	−	18.5635i	−0.754092	−	1.30613i
$203$		0			0
$204$	−8.07227	−	33.1278i	−0.565172	−	2.31941i
$205$	−27.4868			−1.91976
$206$	−9.87538	+	17.1047i	−0.688051	+	1.19174i
$207$	11.7448	+	7.51437i	0.816323	+	0.522284i
$208$	1.05329	+	1.82435i	0.0730324	+	0.126496i
$209$	0.401038	−	0.694619i	0.0277404	−	0.0480478i
$210$		0			0
$211$	−2.44592	−	4.23645i	−0.168384	−	0.291649i	0.769468	−	0.638685i	$-0.220521\pi$
$211$	−2.44592	−	4.23645i	−0.168384	−	0.291649i	−0.937852	+	0.347036i	$0.887188\pi$
$212$	7.23385	−	12.5294i	0.496823	−	0.860523i
$213$	−10.5954	+	10.1232i	−0.725982	+	0.693629i
$214$	−15.7989	−	27.3645i	−1.07999	−	1.87060i
$215$	−4.25696	−	7.37327i	−0.290322	−	0.502853i
$216$	17.2581	+	19.7950i	1.17426	+	1.34688i
$217$		0			0
$218$	−3.19961	+	5.54189i	−0.216705	+	0.375344i
$219$	−0.809243	−	3.32105i	−0.0546836	−	0.224416i
$220$	−6.02728			−0.406359
$221$	−2.36381			−0.159007
$222$	9.51990	+	2.78482i	0.638934	+	0.186905i
$223$	11.7044	−	20.2727i	0.783786	−	1.35756i	−0.145936	−	0.989294i	$-0.546619\pi$
$223$	11.7044	−	20.2727i	0.783786	−	1.35756i	0.929722	−	0.368263i	$-0.120047\pi$
$224$		0			0
$225$	−22.3260	+	11.5672i	−1.48840	+	0.771144i
$226$	17.1623	+	29.7259i	1.14162	+	1.97734i
$227$	3.05919	+	5.29868i	0.203046	+	0.351686i	0.949508	−	0.313742i	$-0.101583\pi$
$227$	3.05919	+	5.29868i	0.203046	+	0.351686i	−0.746463	+	0.665427i	$0.768249\pi$
$228$	−13.3004	−	3.89071i	−0.880840	−	0.257669i
$229$	−0.730195	+	1.26473i	−0.0482526	+	0.0835760i	−0.889143	−	0.457630i	$-0.848699\pi$
$229$	−0.730195	+	1.26473i	−0.0482526	+	0.0835760i	0.840890	+	0.541206i	$0.182032\pi$
$230$	20.9161	+	36.2278i	1.37917	+	2.38879i
$231$		0			0
$232$	−19.3260	+	33.4736i	−1.26881	+	2.19765i
$233$	6.62422	+	11.4735i	0.433967	+	0.751653i	0.997211	−	0.0746378i	$-0.0237801\pi$
$233$	6.62422	+	11.4735i	0.433967	+	0.751653i	−0.563244	+	0.826291i	$0.690447\pi$
$234$	3.19050	−	1.65301i	0.208570	−	0.108061i
$235$	−11.5526	+	20.0097i	−0.753610	+	1.30529i
$236$	24.8045			1.61463
$237$	−10.2219	+	9.76631i	−0.663981	+	0.634390i
$238$		0			0
$239$	−9.69436	−	16.7911i	−0.627076	−	1.08613i	−0.988136	−	0.153584i	$-0.950918\pi$
$239$	−9.69436	−	16.7911i	−0.627076	−	1.08613i	0.361060	−	0.932543i	$-0.382415\pi$
$240$	6.49115	+	26.6390i	0.419002	+	1.71954i
$241$	2.52684	+	4.37662i	0.162768	+	0.281923i	0.935860	−	0.352371i	$-0.114624\pi$
$241$	2.52684	+	4.37662i	0.162768	+	0.281923i	−0.773092	+	0.634294i	$0.781291\pi$
$242$	13.3296	−	23.0875i	0.856857	−	1.48412i
$243$	12.2044	−	9.69810i	0.782911	−	0.622133i
$244$	−32.5426			−2.08333
$245$		0			0
$246$	30.7345	+	8.99066i	1.95956	+	0.573223i
$247$	−0.480350	+	0.831990i	−0.0305639	+	0.0529383i
$248$	35.5161			2.25527
$249$	−4.99115	−	20.4832i	−0.316301	−	1.29807i
$250$	−30.4360			−1.92494
$251$	−15.0928			−0.952647			−0.476324	−	0.879270i	$-0.658031\pi$
$251$	−15.0928			−0.952647			−0.476324	+	0.879270i	$0.658031\pi$
$252$		0			0
$253$	1.88891			0.118755
$254$	−38.2455			−2.39974
$255$	−29.5290	−	8.63800i	−1.84918	−	0.540933i
$256$	−32.3609			−2.02256
$257$	3.85592	−	6.67865i	0.240526	−	0.416603i	−0.720338	−	0.693623i	$-0.756014\pi$
$257$	3.85592	−	6.67865i	0.240526	−	0.416603i	0.960864	+	0.277020i	$0.0893469\pi$
$258$	2.34822	+	9.63688i	0.146194	+	0.599966i
$259$		0			0
$260$	7.21926			0.447720
$261$	19.3260	+	12.3648i	1.19625	+	0.765361i
$262$	10.4743	−	18.1420i	0.647102	−	1.12081i
$263$	−2.10603	−	3.64776i	−0.129864	−	0.224930i	0.793760	−	0.608231i	$-0.208121\pi$
$263$	−2.10603	−	3.64776i	−0.129864	−	0.224930i	−0.923624	+	0.383301i	$0.874787\pi$
$264$	3.41468	+	0.998883i	0.210159	+	0.0614770i
$265$	−6.52724	−	11.3055i	−0.400965	−	0.694492i
$266$		0			0
$267$	24.6534	+	7.21177i	1.50876	+	0.441353i
$268$	14.5979			0.891706
$269$	10.3753	−	17.9706i	0.632596	−	1.09569i	−0.354423	−	0.935085i	$-0.615323\pi$
$269$	10.3753	−	17.9706i	0.632596	−	1.09569i	0.987019	−	0.160603i	$-0.0513439\pi$
$270$	45.8968	−	8.99066i	2.79319	−	0.547154i
$271$	−14.2444	−	24.6721i	−0.865287	−	1.49872i	−0.866762	−	0.498723i	$-0.833803\pi$
$271$	−14.2444	−	24.6721i	−0.865287	−	1.49872i	0.00147433	−	0.999999i	$-0.499531\pi$
$272$	−10.5067	+	18.1981i	−0.637060	+	1.10342i
$273$		0			0
$274$	−0.464103	−	0.803851i	−0.0280375	−	0.0485624i
$275$	−1.70321	+	2.95005i	−0.102707	+	0.177895i
$276$	−7.72620	−	31.7076i	−0.465063	−	1.90857i
$277$	−8.58113	−	14.8629i	−0.515590	−	0.893028i	−0.999836	−	0.0180962i	$-0.994239\pi$
$277$	−8.58113	−	14.8629i	−0.515590	−	0.893028i	0.484246	−	0.874932i	$-0.339094\pi$
$278$	23.3765	+	40.4892i	1.40203	+	2.42838i
$279$	0.960429	−	21.0597i	0.0574994	−	1.26081i
$280$		0			0
$281$	−4.72140	+	8.17770i	−0.281655	+	0.487841i	−0.971793	−	0.235837i	$-0.924217\pi$
$281$	−4.72140	+	8.17770i	−0.281655	+	0.487841i	0.690138	+	0.723678i	$0.257550\pi$
$282$	19.4626	−	18.5953i	1.15898	−	1.10733i
$283$	−16.8684			−1.00272			−0.501362	−	0.865237i	$-0.667168\pi$
$283$	−16.8684			−1.00272			−0.501362	+	0.865237i	$0.667168\pi$
$284$	34.2996			2.03531
$285$	−9.04092	+	8.63800i	−0.535538	+	0.511671i
$286$	0.243398	−	0.421578i	0.0143924	−	0.0249284i
$287$		0			0
$288$	0.0737345	−	1.61680i	0.00434485	−	0.0952711i
$289$	−3.28959	−	5.69774i	−0.193505	−	0.335161i
$290$	34.4172	+	59.6124i	2.02105	+	3.50056i
$291$	3.89037	+	15.9657i	0.228057	+	0.935926i
$292$	−4.00040	+	6.92889i	−0.234105	+	0.405483i
$293$	−1.86143	−	3.22409i	−0.108746	−	0.188353i	0.806517	−	0.591211i	$-0.201350\pi$
$293$	−1.86143	−	3.22409i	−0.108746	−	0.188353i	−0.915262	+	0.402858i	$0.868017\pi$
$294$		0			0
$295$	11.1908	−	19.3830i	0.651551	−	1.12852i
$296$	−5.88151	−	10.1871i	−0.341856	−	0.592112i
$297$	0.684641	−	1.99777i	0.0397269	−	0.115922i
$298$	11.9356	−	20.6731i	0.691411	−	1.19756i
$299$	−2.26247			−0.130842
$300$	56.4868	+	16.5239i	3.26126	+	0.954006i
$301$		0			0
$302$	15.7901	+	27.3492i	0.908617	+	1.57377i
$303$	14.4823	+	4.23645i	0.831986	+	0.243378i
$304$	4.27012	+	7.39607i	0.244908	+	0.424194i
$305$	−14.6819	+	25.4298i	−0.840683	+	1.45611i
$306$	30.1926	+	19.3173i	1.72600	+	1.10430i
$307$	−30.5691			−1.74467			−0.872335	−	0.488908i	$-0.837395\pi$
$307$	−30.5691			−1.74467			−0.872335	+	0.488908i	$0.837395\pi$
$308$		0			0
$309$	−3.29153	−	13.5081i	−0.187249	−	0.768451i
$310$	31.6249	−	54.7759i	1.79617	−	3.11106i
$311$	10.4348			0.591702			0.295851	−	0.955234i	$-0.404397\pi$
$311$	10.4348			0.591702			0.295851	+	0.955234i	$0.404397\pi$
$312$	−4.08998	−	1.19643i	−0.231550	−	0.0677343i
$313$	0.619860			0.0350366			0.0175183	−	0.999847i	$-0.494423\pi$
$313$	0.619860			0.0350366			0.0175183	+	0.999847i	$0.494423\pi$
$314$	51.5440			2.90879
$315$		0			0
$316$	33.0905			1.86148
$317$	10.2484			0.575610			0.287805	−	0.957689i	$-0.407075\pi$
$317$	10.2484			0.575610			0.287805	+	0.957689i	$0.407075\pi$
$318$	3.60056	+	14.7763i	0.201909	+	0.828616i
$319$	3.10817			0.174024
$320$	−13.4021	+	23.2132i	−0.749203	+	1.29766i
$321$	21.3484	+	6.24496i	1.19155	+	0.348560i
$322$		0			0
$323$	−9.58307			−0.533216
$324$	−36.3353	−	3.32105i	−2.01863	−	0.184503i
$325$	2.04005	−	3.53346i	0.113161	−	0.196001i
$326$	13.7324	+	23.7852i	0.760567	+	1.31734i
$327$	−1.06645	−	4.37662i	−0.0589750	−	0.242028i
$328$	−18.9882	−	32.8885i	−1.04845	−	1.81596i
$329$		0			0
$330$	4.58113	−	4.37697i	0.252183	−	0.240944i
$331$	−20.3638			−1.11930			−0.559648	−	0.828730i	$-0.689064\pi$
$331$	−20.3638			−1.11930			−0.559648	+	0.828730i	$0.689064\pi$
$332$	−24.6731	+	42.7351i	−1.35411	+	2.34539i
$333$	−6.19961	+	3.21204i	−0.339737	+	0.176019i
$334$	−4.25696	−	7.37327i	−0.232930	−	0.403447i
$335$	6.58596	−	11.4072i	0.359829	−	0.623242i
$336$		0			0
$337$	2.85594	+	4.94662i	0.155573	+	0.269460i	0.933267	−	0.359182i	$-0.116944\pi$
$337$	2.85594	+	4.94662i	0.155573	+	0.269460i	−0.777695	+	0.628642i	$0.783611\pi$
$338$	15.7017	−	27.1962i	0.854062	−	1.47928i
$339$	−23.1906	−	6.78385i	−1.25954	−	0.368448i
$340$	36.0064	+	62.3649i	1.95272	+	3.38221i
$341$	−1.42800	−	2.47337i	−0.0773305	−	0.133940i
$342$	12.9346	−	6.70145i	0.699422	−	0.362373i
$343$		0			0
$344$	5.88151	−	10.1871i	0.317110	−	0.549251i
$345$	−28.2630	−	8.26768i	−1.52163	−	0.445117i
$346$	−14.8949			−0.800756
$347$	8.88132			0.476774			0.238387	−	0.971170i	$-0.423381\pi$
$347$	8.88132			0.476774			0.238387	+	0.971170i	$0.423381\pi$
$348$	−12.7134	−	52.1744i	−0.681507	−	2.79684i
$349$	−10.4874	+	18.1648i	−0.561379	+	0.972337i	0.435997	+	0.899948i	$0.356396\pi$
$349$	−10.4874	+	18.1648i	−0.561379	+	0.972337i	−0.997376	+	0.0723893i	$0.976938\pi$
$350$		0			0
$351$	−0.820039	+	2.39285i	−0.0437704	+	0.127721i
$352$	−0.109631	−	0.189886i	−0.00584335	−	0.0101210i
$353$	7.38268	+	12.7872i	0.392941	+	0.680593i	0.992836	−	0.119485i	$-0.0381245\pi$
$353$	7.38268	+	12.7872i	0.392941	+	0.680593i	−0.599895	+	0.800078i	$0.704791\pi$
$354$	−18.8530	+	18.0128i	−1.00203	+	0.957370i
$355$	15.4746	−	26.8028i	0.821306	−	1.42254i
$356$	−30.0613	−	52.0677i	−1.59325	−	2.75959i
$357$		0			0
$358$	−11.2360	+	19.4613i	−0.593840	+	1.02856i
$359$	−3.60603	−	6.24583i	−0.190319	−	0.329642i	0.755037	−	0.655682i	$-0.227619\pi$
$359$	−3.60603	−	6.24583i	−0.190319	−	0.329642i	−0.945356	+	0.326040i	$0.894286\pi$
$360$	−46.7205	−	29.8918i	−2.46239	−	1.57544i
$361$	7.55262	−	13.0815i	0.397506	−	0.688501i
$362$	29.3977			1.54511
$363$	4.44284	+	18.2330i	0.233188	+	0.956983i
$364$		0			0
$365$	3.60963	+	6.25206i	0.188937	+	0.327248i
$366$	24.7345	−	23.6322i	1.29289	−	1.23528i
$367$	5.48711	+	9.50396i	0.286425	+	0.496103i	0.972954	−	0.231000i	$-0.0741998\pi$
$367$	5.48711	+	9.50396i	0.286425	+	0.496103i	−0.686529	+	0.727103i	$0.740866\pi$
$368$	−10.0562	+	17.4179i	−0.524217	+	0.907970i
$369$	−20.0151	+	10.3699i	−1.04195	+	0.539836i
$370$	−20.9485			−1.08906
$371$		0			0
$372$	−35.6775	+	34.0875i	−1.84979	+	1.76736i
$373$	0.271884	−	0.470916i	0.0140776	−	0.0243831i	−0.858901	−	0.512142i	$-0.828852\pi$
$373$	0.271884	−	0.470916i	0.0140776	−	0.0243831i	0.872978	+	0.487759i	$0.162185\pi$
$374$	4.85584			0.251090
$375$	15.4911	−	14.8008i	0.799959	−	0.764309i
$376$	−31.9228			−1.64629
$377$	−3.72286			−0.191737
$378$		0			0
$379$	−22.6912			−1.16557			−0.582785	−	0.812626i	$-0.698037\pi$
$379$	−22.6912			−1.16557			−0.582785	+	0.812626i	$0.698037\pi$
$380$	29.2675			1.50139
$381$	19.4660	−	18.5985i	0.997272	−	0.952827i
$382$	22.4897			1.15067
$383$	−17.8569	+	30.9291i	−0.912447	+	1.58041i	−0.101851	+	0.994800i	$0.532477\pi$
$383$	−17.8569	+	30.9291i	−0.912447	+	1.58041i	−0.810596	+	0.585606i	$0.800857\pi$
$384$	23.9298	−	22.8633i	1.22116	−	1.16674i
$385$		0			0
$386$	41.6883			2.12188
$387$	−5.88151	−	3.76300i	−0.298974	−	0.191284i
$388$	19.2316	−	33.3101i	0.976336	−	1.69106i
$389$	−19.3296	−	33.4798i	−0.980048	−	1.69749i	−0.662156	−	0.749366i	$-0.730359\pi$
$389$	−19.3296	−	33.4798i	−0.980048	−	1.69749i	−0.317892	−	0.948127i	$-0.602975\pi$
$390$	−5.48711	+	5.24258i	−0.277851	+	0.265468i
$391$	−11.2842	−	19.5447i	−0.570664	−	0.988420i
$392$		0			0
$393$	3.49115	+	14.3273i	0.176105	+	0.722718i
$394$	−52.4513			−2.64246
$395$	14.9291	−	25.8579i	0.751163	−	1.30105i
$396$	−4.38891	+	2.27391i	−0.220551	+	0.114268i
$397$	5.97391	+	10.3471i	0.299822	+	0.519307i	0.976095	−	0.217344i	$-0.0697394\pi$
$397$	5.97391	+	10.3471i	0.299822	+	0.519307i	−0.676273	+	0.736651i	$0.736406\pi$
$398$	−12.2709	+	21.2538i	−0.615085	+	1.06536i
$399$		0			0
$400$	−18.1352	−	31.4111i	−0.906761	−	1.57056i
$401$	−16.1783	+	28.0216i	−0.807906	+	1.39933i	0.106406	+	0.994323i	$0.466066\pi$
$401$	−16.1783	+	28.0216i	−0.807906	+	1.39933i	−0.914312	+	0.405011i	$0.867268\pi$
$402$	−11.0953	+	10.6009i	−0.553385	+	0.528723i
$403$	1.71041	+	2.96251i	0.0852015	+	0.147573i
$404$	−17.6591	−	30.5865i	−0.878573	−	1.52173i
$405$	−18.9882	+	26.8952i	−0.943530	+	1.33643i
$406$		0			0
$407$	−0.472958	+	0.819187i	−0.0234437	+	0.0406056i
$408$	−10.0634	−	41.2993i	−0.498213	−	2.04462i
$409$	18.9750			0.938254			0.469127	−	0.883131i	$-0.344569\pi$
$409$	18.9750			0.938254			0.469127	+	0.883131i	$0.344569\pi$
$410$	−67.6313			−3.34007
$411$	0.627122	+	0.183450i	0.0309336	+	0.00904890i
$412$	−16.2713	+	28.1827i	−0.801630	+	1.38846i
$413$		0			0
$414$	28.8982	+	18.4891i	1.42027	+	0.908691i
$415$	22.2630	+	38.5607i	1.09285	+	1.89287i
$416$	0.131312	+	0.227439i	0.00643811	+	0.0111511i
$417$	−31.5875	−	9.24018i	−1.54685	−	0.452494i
$418$	0.986757	−	1.70911i	0.0482639	−	0.0835955i
$419$	8.64523	+	14.9740i	0.422347	+	0.731526i	0.996169	−	0.0874539i	$-0.0278730\pi$
$419$	8.64523	+	14.9740i	0.422347	+	0.731526i	−0.573822	+	0.818980i	$0.694540\pi$
$420$		0			0
$421$	−9.30039	+	16.1087i	−0.453273	+	0.785092i	−0.998587	−	0.0531397i	$-0.983077\pi$
$421$	−9.30039	+	16.1087i	−0.453273	+	0.785092i	0.545314	+	0.838232i	$0.316410\pi$
$422$	−6.01819	−	10.4238i	−0.292961	−	0.507423i
$423$	−0.863259	+	18.9290i	−0.0419731	+	0.920360i
$424$	9.01819	−	15.6200i	0.437962	−	0.758572i
$425$	40.6993			1.97421
$426$	−26.0699	+	24.9081i	−1.26309	+	1.20680i
$427$		0			0
$428$	−26.0313	−	45.0876i	−1.25827	−	2.17939i
$429$	0.0811263	+	0.332935i	0.00391682	+	0.0160742i
$430$	−10.4743	−	18.1420i	−0.505114	−	0.874883i
$431$	7.93920	−	13.7511i	0.382418	−	0.662367i	−0.608990	−	0.793178i	$-0.708425\pi$
$431$	7.93920	−	13.7511i	0.382418	−	0.662367i	0.991407	+	0.130811i	$0.0417582\pi$
$432$	14.7768	+	16.9489i	0.710948	+	0.815456i
$433$	40.4367			1.94326			0.971631	−	0.236501i	$-0.0760007\pi$
$433$	40.4367			1.94326			0.971631	+	0.236501i	$0.0760007\pi$
$434$		0			0
$435$	−46.5064	−	13.6043i	−2.22981	−	0.652278i
$436$	−5.27188	+	9.13117i	−0.252477	+	0.437304i
$437$	−9.17223			−0.438767
$438$	−1.99115	−	8.17147i	−0.0951406	−	0.390448i
$439$	12.4609			0.594728			0.297364	−	0.954764i	$-0.403892\pi$
$439$	12.4609			0.594728			0.297364	+	0.954764i	$0.403892\pi$
$440$	−7.51399			−0.358216
$441$		0			0
$442$	−5.81616			−0.276646
$443$	−8.23073			−0.391054			−0.195527	−	0.980698i	$-0.562642\pi$
$443$	−8.23073			−0.391054			−0.195527	+	0.980698i	$0.562642\pi$
$444$	15.6856	+	4.58845i	0.744405	+	0.217758i
$445$	−54.2498			−2.57169
$446$	28.7988	−	49.8810i	1.36366	−	2.36193i
$447$	3.97822	+	16.3262i	0.188163	+	0.772204i
$448$		0			0
$449$	5.64474			0.266392			0.133196	−	0.991090i	$-0.457476\pi$
$449$	5.64474			0.266392			0.133196	+	0.991090i	$0.457476\pi$
$450$	−54.9332	+	28.4611i	−2.58957	+	1.34167i
$451$	−1.52692	+	2.64471i	−0.0718999	+	0.124534i
$452$	28.2776	+	48.9783i	1.33007	+	2.30374i
$453$	−21.3364	−	6.24146i	−1.00247	−	0.293249i
$454$	7.52716	+	13.0374i	0.353267	+	0.611876i
$455$		0			0
$456$	−16.5811	−	4.85041i	−0.776482	−	0.227141i
$457$	5.06887			0.237112			0.118556	−	0.992947i	$-0.462174\pi$
$457$	5.06887			0.237112			0.118556	+	0.992947i	$0.462174\pi$
$458$	−1.79665	+	3.11188i	−0.0839518	+	0.145409i
$459$	−24.7611	+	4.85041i	−1.15575	+	0.226398i
$460$	34.4628	+	59.6913i	1.60683	+	2.78312i
$461$	3.88831	−	6.73475i	0.181097	−	0.313669i	−0.761158	−	0.648567i	$-0.775369\pi$
$461$	3.88831	−	6.73475i	0.181097	−	0.313669i	0.942254	+	0.334898i	$0.108702\pi$
$462$		0			0
$463$	4.58998	+	7.95008i	0.213314	+	0.369472i	0.952750	−	0.303756i	$-0.0982408\pi$
$463$	4.58998	+	7.95008i	0.213314	+	0.369472i	−0.739435	+	0.673228i	$0.764907\pi$
$464$	−16.5474	+	28.6609i	−0.768192	+	1.33055i
$465$	10.5408	+	43.2584i	0.488818	+	2.00606i
$466$	16.2989	+	28.2306i	0.755033	+	1.30776i
$467$	6.88272	+	11.9212i	0.318494	+	0.551648i	0.980174	−	0.198138i	$-0.0634895\pi$
$467$	6.88272	+	11.9212i	0.318494	+	0.551648i	−0.661680	+	0.749787i	$0.730156\pi$
$468$	5.25688	−	2.72361i	0.242999	−	0.125899i
$469$		0			0
$470$	−28.4253	+	49.2340i	−1.31116	+	2.27100i
$471$	−26.2345	+	25.0654i	−1.20882	+	1.15495i
$472$	30.9228			1.42334
$473$	−0.945916			−0.0434933
$474$	−25.1509	+	24.0301i	−1.15522	+	1.10374i
$475$	8.27052	−	14.3250i	0.379477	−	0.657274i
$476$		0			0
$477$	−9.01819	−	5.76985i	−0.412914	−	0.264183i
$478$	−23.8530	−	41.3146i	−1.09101	−	1.88969i
$479$	−4.35588	−	7.54461i	−0.199025	−	0.344722i	0.749187	−	0.662358i	$-0.230444\pi$
$479$	−4.35588	−	7.54461i	−0.199025	−	0.344722i	−0.948213	+	0.317636i	$0.897111\pi$
$480$	0.809243	+	3.32105i	0.0369367	+	0.151585i
$481$	0.566492	−	0.981194i	0.0258298	−	0.0447386i
$482$	6.21731	+	10.7687i	0.283191	+	0.490501i
$483$		0			0
$484$	21.9626	−	38.0404i	0.998302	−	1.72911i
$485$	−17.3530	−	30.0563i	−0.787960	−	1.36479i
$486$	30.0289	−	23.8622i	1.36214	−	1.08241i
$487$	9.01819	−	15.6200i	0.408653	−	0.707808i	−0.586086	−	0.810249i	$-0.699332\pi$
$487$	9.01819	−	15.6200i	0.408653	−	0.707808i	0.994739	+	0.102441i	$0.0326653\pi$
$488$	−40.5697			−1.83651
$489$	−18.5560	−	5.42810i	−0.839129	−	0.245467i
$490$		0			0
$491$	−1.02344	−	1.77266i	−0.0461874	−	0.0799989i	0.842007	−	0.539466i	$-0.181374\pi$
$491$	−1.02344	−	1.77266i	−0.0461874	−	0.0799989i	−0.888195	+	0.459467i	$0.848040\pi$
$492$	50.6402	+	14.8136i	2.28303	+	0.667848i
$493$	−18.5679	−	32.1606i	−0.836257	−	1.44844i
$494$	−1.18190	+	2.04712i	−0.0531763	+	0.0921041i
$495$	−0.203194	+	4.45552i	−0.00913290	+	0.200261i
$496$	30.4097			1.36544
$497$		0			0
$498$	−12.2807	−	50.3990i	−0.550313	−	2.25843i
$499$	19.5438	−	33.8508i	0.874899	−	1.51537i	0.0180291	−	0.999837i	$-0.494261\pi$
$499$	19.5438	−	33.8508i	0.874899	−	1.51537i	0.856870	−	0.515532i	$-0.172406\pi$
$500$	−50.1484			−2.24270
$501$	5.75223	+	1.68268i	0.256991	+	0.0751766i
$502$	−37.1358			−1.65745
$503$	5.11846			0.228221			0.114111	−	0.993468i	$-0.463598\pi$
$503$	5.11846			0.228221			0.114111	+	0.993468i	$0.463598\pi$
$504$		0			0
$505$	−31.8683			−1.41812
$506$	4.64766			0.206614
$507$	5.23350	+	21.4778i	0.232428	+	0.953862i
$508$	−63.0157			−2.79587
$509$	14.7636	−	25.5713i	0.654386	−	1.13343i	−0.327662	−	0.944795i	$-0.606261\pi$
$509$	14.7636	−	25.5713i	0.654386	−	1.13343i	0.982047	−	0.188634i	$-0.0604060\pi$
$510$	−72.6562	−	21.2538i	−3.21727	−	0.941136i
$511$		0			0
$512$	−41.4078			−1.82998
$513$	−3.32451	+	9.70083i	−0.146780	+	0.428302i
$514$	9.48751	−	16.4328i	0.418476	−	0.724822i
$515$	14.6819	+	25.4298i	0.646962	+	1.12057i
$516$	3.86908	+	15.8783i	0.170327	+	0.699005i
$517$	1.28352	+	2.22313i	0.0564493	+	0.0977730i
$518$		0			0
$519$	7.58113	−	7.24327i	0.332775	−	0.317944i
$520$	9.00000			0.394676
$521$	−0.532351	+	0.922058i	−0.0233227	+	0.0403961i	−0.877451	−	0.479666i	$-0.840758\pi$
$521$	−0.532351	+	0.922058i	−0.0233227	+	0.0403961i	0.854128	+	0.520062i	$0.174091\pi$
$522$	47.5516	+	30.4236i	2.08128	+	1.33160i
$523$	−6.69094	−	11.5890i	−0.292574	−	0.506754i	0.681843	−	0.731498i	$-0.261179\pi$
$523$	−6.69094	−	11.5890i	−0.292574	−	0.506754i	−0.974418	+	0.224745i	$0.927845\pi$
$524$	17.2581	−	29.8918i	0.753922	−	1.30583i
$525$		0			0
$526$	−5.18190	−	8.97532i	−0.225942	−	0.391343i
$527$	−17.0615	+	29.5513i	−0.743210	+	1.28728i
$528$	2.92373	+	0.855268i	0.127239	+	0.0372208i
$529$	0.699612	+	1.21176i	0.0304179	+	0.0526853i
$530$	−16.0603	−	27.8173i	−0.697615	−	1.20830i
$531$	0.836219	−	18.3361i	0.0362888	−	0.795719i
$532$		0			0
$533$	1.82889	−	3.16774i	0.0792181	−	0.137210i
$534$	60.6598	+	17.7446i	2.62501	+	0.767883i
$535$	−46.9771			−2.03100
$536$	18.1986			0.786061
$537$	−3.74503	−	15.3693i	−0.161610	−	0.663232i
$538$	25.5286	−	44.2168i	1.10062	−	1.90632i
$539$		0			0
$540$	75.6224	−	14.8136i	3.25427	−	0.637475i
$541$	17.0438	+	29.5207i	0.732769	+	1.26919i	0.955695	+	0.294358i	$0.0951056\pi$
$541$	17.0438	+	29.5207i	0.732769	+	1.26919i	−0.222927	+	0.974835i	$0.571561\pi$
$542$	−35.0485	−	60.7058i	−1.50546	−	2.60754i
$543$	−14.9626	+	14.2958i	−0.642108	+	0.613492i
$544$	−1.30985	+	2.26873i	−0.0561594	+	0.0972709i
$545$	4.75692	+	8.23922i	0.203764	+	0.352930i
$546$		0			0
$547$	2.97150	−	5.14678i	0.127052	−	0.220060i	−0.795481	−	0.605978i	$-0.792782\pi$
$547$	2.97150	−	5.14678i	0.127052	−	0.220060i	0.922533	+	0.385918i	$0.126115\pi$
$548$	−0.764686	−	1.32448i	−0.0326658	−	0.0565788i
$549$	−1.09709	+	24.0564i	−0.0468227	+	1.02670i
$550$	−4.19076	+	7.25860i	−0.178694	+	0.309508i
$551$	−15.0928			−0.642974
$552$	−9.63198	−	39.5287i	−0.409964	−	1.68245i
$553$		0			0
$554$	−21.1139	−	36.5704i	−0.897044	−	1.55373i
$555$	10.6623	−	10.1871i	0.452587	−	0.432418i
$556$	38.5165	+	66.7126i	1.63346	+	2.82924i
$557$	15.0402	−	26.0503i	0.637272	−	1.10379i	−0.348756	−	0.937213i	$-0.613396\pi$
$557$	15.0402	−	26.0503i	0.637272	−	1.10379i	0.986029	−	0.166575i	$-0.0532707\pi$
$558$	2.36314	−	51.8175i	0.100040	−	2.19361i
$559$	1.13298			0.0479202
$560$		0			0
$561$	−2.47150	+	2.36135i	−0.104347	+	0.0996963i
$562$	−11.6170	+	20.1213i	−0.490035	+	0.848765i
$563$	19.6212			0.826935			0.413468	−	0.910519i	$-0.364317\pi$
$563$	19.6212			0.826935			0.413468	+	0.910519i	$0.364317\pi$
$564$	32.0679	−	30.6388i	1.35030	−	1.29012i
$565$	51.0308			2.14688
$566$	−41.5049			−1.74458
$567$		0			0
$568$	42.7601			1.79417
$569$	−1.37432			−0.0576144			−0.0288072	−	0.999585i	$-0.509171\pi$
$569$	−1.37432			−0.0576144			−0.0288072	+	0.999585i	$0.509171\pi$
$570$	−22.2452	+	21.2538i	−0.931750	+	0.890226i
$571$	17.3815			0.727394			0.363697	−	0.931517i	$-0.381514\pi$
$571$	17.3815			0.727394			0.363697	+	0.931517i	$0.381514\pi$
$572$	0.401038	−	0.694619i	0.0167683	−	0.0290435i
$573$	−11.4467	+	10.9365i	−0.478191	+	0.456880i
$574$		0			0
$575$	38.9545			1.62451
$576$	−1.00146	+	21.9595i	−0.0417276	+	0.914978i
$577$	−13.5274	+	23.4301i	−0.563153	+	0.975409i	0.434066	+	0.900881i	$0.357078\pi$
$577$	−13.5274	+	23.4301i	−0.563153	+	0.975409i	−0.997219	+	0.0745283i	$0.976255\pi$
$578$	−8.09406	−	14.0193i	−0.336668	−	0.583127i
$579$	−21.2183	+	20.2727i	−0.881801	+	0.842503i
$580$	56.7080	+	98.2211i	2.35467	+	4.07841i
$581$		0			0
$582$	9.57227	+	39.2837i	0.396783	+	1.62836i
$583$	−1.45038			−0.0600687
$584$	−4.98715	+	8.63800i	−0.206370	+	0.357443i
$585$	0.243379	−	5.33667i	0.0100625	−	0.220644i
$586$	−4.58005	−	7.93288i	−0.189200	−	0.327704i
$587$	3.75700	−	6.50731i	0.155068	−	0.268585i	−0.778016	−	0.628245i	$-0.783774\pi$
$587$	3.75700	−	6.50731i	0.155068	−	0.268585i	0.933084	+	0.359659i	$0.117107\pi$
$588$		0			0
$589$	6.93414	+	12.0103i	0.285716	+	0.494875i
$590$	27.5349	−	47.6919i	1.13359	−	1.96344i
$591$	26.6964	−	25.5066i	1.09814	−	1.04920i
$592$	−5.03590	−	8.72243i	−0.206974	−	0.358490i
$593$	17.7904	+	30.8139i	0.730565	+	1.26538i	0.956642	+	0.291266i	$0.0940765\pi$
$593$	17.7904	+	30.8139i	0.730565	+	1.26538i	−0.226077	+	0.974109i	$0.572590\pi$
$594$	1.68456	−	4.91551i	0.0691184	−	0.201686i
$595$		0			0
$596$	19.6659	−	34.0623i	0.805545	−	1.39524i
$597$	−4.08998	−	16.7849i	−0.167392	−	0.686960i
$598$	−5.56681			−0.227644
$599$	−11.4821			−0.469146			−0.234573	−	0.972099i	$-0.575369\pi$
$599$	−11.4821			−0.469146			−0.234573	+	0.972099i	$0.575369\pi$
$600$	70.4201	+	20.5997i	2.87489	+	0.840980i
$601$	−0.190030	+	0.329142i	−0.00775150	+	0.0134260i	−0.869875	−	0.493272i	$-0.835801\pi$
$601$	−0.190030	+	0.329142i	−0.00775150	+	0.0134260i	0.862124	+	0.506698i	$0.169134\pi$
$602$		0			0
$603$	0.492129	−	10.7911i	0.0200411	−	0.439448i
$604$	26.0167	+	45.0623i	1.05861	+	1.83356i
$605$	−19.8173	−	34.3246i	−0.805688	−	1.39549i
$606$	35.6337	+	10.4238i	1.44752	+	0.423438i
$607$	−9.27044	+	16.0569i	−0.376275	+	0.651728i	−0.990517	−	0.137390i	$-0.956129\pi$
$607$	−9.27044	+	16.0569i	−0.376275	+	0.651728i	0.614242	+	0.789118i	$0.289462\pi$
$608$	0.532351	+	0.922058i	0.0215897	+	0.0373944i
$609$		0			0
$610$	−36.1249	+	62.5702i	−1.46265	+	2.53339i
$611$	−1.53736	−	2.66278i	−0.0621949	−	0.107725i
$612$	49.7473	+	31.8284i	2.01092	+	1.28659i
$613$	−3.66225	+	6.34321i	−0.147917	+	0.256200i	−0.930457	−	0.366400i	$-0.880590\pi$
$613$	−3.66225	+	6.34321i	−0.147917	+	0.256200i	0.782540	+	0.622600i	$0.213924\pi$
$614$	−75.2154			−3.03545
$615$	34.4226	−	32.8885i	1.38805	−	1.32619i
$616$		0			0
$617$	12.7427	+	22.0710i	0.513002	+	0.888546i	0.999886	+	0.0150791i	$0.00480000\pi$
$617$	12.7427	+	22.0710i	0.513002	+	0.888546i	−0.486884	+	0.873466i	$0.661867\pi$
$618$	−8.09884	−	33.2368i	−0.325783	−	1.33698i
$619$	16.4482	+	28.4891i	0.661108	+	1.14507i	0.980325	+	0.197391i	$0.0632468\pi$
$619$	16.4482	+	28.4891i	0.661108	+	1.14507i	−0.319217	+	0.947682i	$0.603420\pi$
$620$	52.1072	−	90.2523i	2.09267	−	3.62462i
$621$	−23.6995	+	4.64247i	−0.951030	+	0.186296i
$622$	25.6748			1.02947
$623$		0			0
$624$	−3.50194	−	1.02441i	−0.140190	−	0.0410092i
$625$	−1.67111	+	2.89444i	−0.0668443	+	0.115778i
$626$	1.52517			0.0609580
$627$	0.328893	+	1.34974i	0.0131347	+	0.0539036i
$628$	84.9271			3.38896
$629$	11.3016			0.450626
$630$		0			0
$631$	29.8683			1.18904			0.594519	−	0.804082i	$-0.297343\pi$
$631$	29.8683			1.18904			0.594519	+	0.804082i	$0.297343\pi$
$632$	41.2527			1.64094
$633$	8.13210	+	2.37885i	0.323222	+	0.0945509i
$634$	25.2163			1.00147
$635$	−28.4301	+	49.2424i	−1.12822	+	1.95413i
$636$	5.93251	+	24.3464i	0.235239	+	0.965399i
$637$		0			0
$638$	7.64766			0.302774
$639$	1.15632	−	25.3552i	0.0457434	−	1.00303i
$640$	−34.9496	+	60.5344i	−1.38150	+	2.39283i
$641$	−5.73025	−	9.92509i	−0.226331	−	0.392017i	0.730387	−	0.683034i	$-0.239340\pi$
$641$	−5.73025	−	9.92509i	−0.226331	−	0.392017i	−0.956718	+	0.291016i	$0.906007\pi$
$642$	52.5278	+	15.3658i	2.07311	+	0.606438i
$643$	−8.69078	−	15.0529i	−0.342731	−	0.593627i	0.642208	−	0.766531i	$-0.278019\pi$
$643$	−8.69078	−	15.0529i	−0.342731	−	0.593627i	−0.984939	+	0.172903i	$0.944685\pi$
$644$		0			0
$645$	14.1534	+	4.14024i	0.557290	+	0.163022i
$646$	−23.5792			−0.927711
$647$	12.6720	−	21.9485i	0.498186	−	0.862883i	−0.501812	−	0.864977i	$-0.667333\pi$
$647$	12.6720	−	21.9485i	0.498186	−	0.862883i	0.999998	+	0.00209358i	$0.000666408\pi$
$648$	−45.2979	−	4.14024i	−1.77947	−	0.162644i
$649$	−1.24332	−	2.15349i	−0.0488045	−	0.0845320i
$650$	5.01954	−	8.69410i	0.196883	−	0.341011i
$651$		0			0
$652$	22.6264	+	39.1900i	0.886116	+	1.53480i
$653$	−7.04163	+	12.1965i	−0.275560	+	0.477284i	−0.970276	−	0.242000i	$-0.922197\pi$
$653$	−7.04163	+	12.1965i	−0.275560	+	0.477284i	0.694716	+	0.719284i	$0.255530\pi$
$654$	−2.62401	−	10.7687i	−0.102607	−	0.421089i
$655$	−15.5723	−	26.9720i	−0.608459	−	1.05388i
$656$	−16.2581	−	28.1599i	−0.634774	−	1.09946i
$657$	4.98715	+	3.19079i	0.194567	+	0.124484i
$658$		0			0
$659$	−19.0854	+	33.0569i	−0.743462	+	1.28771i	0.207449	+	0.978246i	$0.433484\pi$
$659$	−19.0854	+	33.0569i	−0.743462	+	1.28771i	−0.950910	+	0.309467i	$0.899849\pi$
$660$	7.54815	−	7.21177i	0.293812	−	0.280718i
$661$	0.353732			0.0137586			0.00687930	−	0.999976i	$-0.497810\pi$
$661$	0.353732			0.0137586			0.00687930	+	0.999976i	$0.497810\pi$
$662$	−50.1052			−1.94740
$663$	2.96027	−	2.82834i	0.114967	−	0.109844i
$664$	−30.7591	+	53.2764i	−1.19369	+	2.06752i
$665$		0			0
$666$	−15.2542	+	7.90324i	−0.591087	+	0.306244i
$667$	−17.7719	−	30.7818i	−0.688130	−	1.19188i
$668$	−7.01403	−	12.1487i	−0.271381	−	0.470046i
$669$	9.59884	+	39.3927i	0.371112	+	1.52301i
$670$	16.2048	−	28.0675i	0.626045	−	1.08434i
$671$	1.63119	+	2.82531i	0.0629715	+	0.109070i
$672$		0			0
$673$	10.5555	−	18.2827i	0.406886	−	0.704748i	−0.587653	−	0.809113i	$-0.699948\pi$
$673$	10.5555	−	18.2827i	0.406886	−	0.704748i	0.994539	+	0.104365i	$0.0332811\pi$
$674$	7.02704	+	12.1712i	0.270672	+	0.468817i
$675$	14.1192	−	41.1994i	0.543447	−	1.58577i
$676$	25.8712	−	44.8102i	0.995046	−	1.72347i
$677$	−21.1464			−0.812721			−0.406361	−	0.913713i	$-0.633202\pi$
$677$	−21.1464			−0.812721			−0.406361	+	0.913713i	$0.633202\pi$
$678$	−57.0605	−	16.6917i	−2.19140	−	0.641041i
$679$		0			0
$680$	44.8879	+	77.7482i	1.72137	+	2.98151i
$681$	−10.1711	−	2.97532i	−0.389758	−	0.114014i
$682$	−3.51360	−	6.08573i	−0.134543	−	0.233035i
$683$	−17.3858	+	30.1131i	−0.665249	+	1.15224i	0.313969	+	0.949433i	$0.398341\pi$
$683$	−17.3858	+	30.1131i	−0.665249	+	1.15224i	−0.979218	+	0.202811i	$0.934992\pi$
$684$	21.3118	−	11.0417i	0.814878	−	0.422191i
$685$	−1.37998			−0.0527264
$686$		0			0
$687$	−0.598835	−	2.45756i	−0.0228470	−	0.0937618i
$688$	5.03590	−	8.72243i	0.191992	−	0.332539i
$689$	1.73722			0.0661827
$690$	−69.5413	−	20.3427i	−2.64739	−	0.774432i
$691$	−34.6492			−1.31812			−0.659059	−	0.752091i	$-0.729045\pi$
$691$	−34.6492			−1.31812			−0.659059	+	0.752091i	$0.729045\pi$
$692$	−24.5418			−0.932940
$693$		0			0
$694$	21.8525			0.829511
$695$	69.5083			2.63660
$696$	−15.8493	−	65.0440i	−0.600766	−	2.46548i
$697$	36.4868			1.38203
$698$	−25.8044	+	44.6945i	−0.976710	+	1.69171i
$699$	−22.0240	−	6.44260i	−0.833024	−	0.243681i
$700$		0			0
$701$	−48.6050			−1.83579			−0.917894	−	0.396826i	$-0.870111\pi$
$701$	−48.6050			−1.83579			−0.917894	+	0.396826i	$0.870111\pi$
$702$	−2.01771	+	5.88763i	−0.0761535	+	0.222214i
$703$	2.29661	−	3.97784i	0.0866182	−	0.150027i
$704$	1.48901	+	2.57904i	0.0561192	+	0.0972012i
$705$	−9.47434	−	38.8818i	−0.356824	−	1.46437i
$706$	18.1651	+	31.4629i	0.683654	+	1.18412i
$707$		0			0
$708$	−31.0634	+	29.6791i	−1.16743	+	1.11541i
$709$	4.10817			0.154286			0.0771428	−	0.997020i	$-0.475420\pi$
$709$	4.10817			0.154286			0.0771428	+	0.997020i	$0.475420\pi$
$710$	38.0753	−	65.9483i	1.42894	−	2.47500i
$711$	1.11556	−	24.4613i	0.0418368	−	0.917372i
$712$	−37.4764	−	64.9110i	−1.40449	−	2.43264i
$713$	−16.3300	+	28.2844i	−0.611564	+	1.05926i
$714$		0			0
$715$	−0.361864	−	0.626767i	−0.0135330	−	0.0234398i
$716$	−18.5131	+	32.0657i	−0.691868	+	1.19835i
$717$	32.2315	+	9.42856i	1.20371	+	0.352116i
$718$	−8.87266	−	15.3679i	−0.331125	−	0.573525i
$719$	24.1408	+	41.8131i	0.900299	+	1.55936i	0.827106	+	0.562047i	$0.189986\pi$
$719$	24.1408	+	41.8131i	0.900299	+	1.55936i	0.0731939	+	0.997318i	$0.476681\pi$
$720$	−40.0032	−	25.5941i	−1.49083	−	0.953837i
$721$		0			0
$722$	18.5833	−	32.1872i	0.691597	−	1.19788i
$723$	−8.40116	−	2.45756i	−0.312443	−	0.0913977i
$724$	48.4375			1.80016
$725$	64.0990			2.38058
$726$	10.9316	+	44.8623i	0.405711	+	1.66500i
$727$	−20.5151	+	35.5332i	−0.760863	+	1.31785i	0.181543	+	0.983383i	$0.441891\pi$
$727$	−20.5151	+	35.5332i	−0.760863	+	1.31785i	−0.942406	+	0.334470i	$0.891443\pi$
$728$		0			0
$729$	−3.67996	+	26.7480i	−0.136295	+	0.990668i
$730$	8.88151	+	15.3832i	0.328720	+	0.569359i
$731$	5.65082	+	9.78750i	0.209003	+	0.362004i
$732$	40.7542	−	38.9379i	1.50632	−	1.43919i
$733$	15.2714	−	26.4508i	0.564062	−	0.976983i	−0.433075	−	0.901358i	$-0.642571\pi$
$733$	15.2714	−	26.4508i	0.564062	−	0.976983i	0.997136	−	0.0756253i	$-0.0240953\pi$
$734$	13.5011	+	23.3845i	0.498334	+	0.863139i
$735$		0			0
$736$	−1.25370	+	2.17147i	−0.0462118	+	0.0800413i
$737$	−0.731715	−	1.26737i	−0.0269531	−	0.0466841i
$738$	−49.2474	+	25.5152i	−1.81282	+	0.939228i
$739$	−11.9100	+	20.6288i	−0.438117	+	0.758841i	−0.997544	−	0.0700384i	$-0.977688\pi$
$739$	−11.9100	+	20.6288i	−0.438117	+	0.758841i	0.559427	+	0.828880i	$0.311021\pi$
$740$	−34.5161			−1.26884
$741$	−0.393936	−	1.61668i	−0.0144716	−	0.0593901i
$742$		0			0
$743$	−5.26089	−	9.11213i	−0.193003	−	0.334292i	0.753241	−	0.657745i	$-0.228490\pi$
$743$	−5.26089	−	9.11213i	−0.193003	−	0.334292i	−0.946244	+	0.323453i	$0.895156\pi$
$744$	−44.4779	+	42.4957i	−1.63064	+	1.55797i
$745$	−17.7449	−	30.7350i	−0.650121	−	1.12604i
$746$	0.668971	−	1.15869i	0.0244928	−	0.0424227i
$747$	30.7591	+	19.6797i	1.12542	+	0.720044i
$748$	8.00079			0.292538
$749$		0			0
$750$	38.1160	−	36.4174i	1.39180	−	1.32977i
$751$	5.13521	−	8.89445i	0.187386	−	0.324563i	−0.756992	−	0.653425i	$-0.773332\pi$
$751$	5.13521	−	8.89445i	0.187386	−	0.324563i	0.944378	+	0.328862i	$0.106665\pi$
$752$	−27.3330			−0.996734
$753$	18.9012	−	18.0588i	0.688797	−	0.658100i
$754$	−9.16010			−0.333591
$755$	46.9507			1.70871
$756$		0			0
$757$	8.03930			0.292193			0.146097	−	0.989270i	$-0.453329\pi$
$757$	8.03930			0.292193			0.146097	+	0.989270i	$0.453329\pi$
$758$	−55.8319			−2.02791
$759$	−2.36554	+	2.26012i	−0.0858636	+	0.0820371i
$760$	36.4868			1.32351
$761$	13.8302	−	23.9547i	0.501345	−	0.868355i	−0.498654	−	0.866801i	$-0.666172\pi$
$761$	13.8302	−	23.9547i	0.501345	−	0.868355i	0.999999	−	0.00155404i	$-0.000494668\pi$
$762$	47.8961	−	45.7616i	1.73509	−	1.65777i
$763$		0			0
$764$	37.0554			1.34062
$765$	47.3157	−	24.5144i	1.71070	−	0.886320i
$766$	−43.9371	+	76.1013i	−1.58751	+	2.74965i
$767$	1.48920	+	2.57938i	0.0537720	+	0.0931359i
$768$	40.5266	−	38.7205i	1.46238	−	1.39721i
$769$	−16.9613	−	29.3778i	−0.611640	−	1.05939i	−0.990964	−	0.134128i	$-0.957177\pi$
$769$	−16.9613	−	29.3778i	−0.611640	−	1.05939i	0.379324	−	0.925264i	$-0.376157\pi$
$770$		0			0
$771$	3.16225	+	12.9776i	0.113886	+	0.467376i
$772$	68.6883			2.47215
$773$	−14.2978	+	24.7645i	−0.514256	+	0.890717i	0.485607	+	0.874177i	$0.338599\pi$
$773$	−14.2978	+	24.7645i	−0.514256	+	0.890717i	−0.999863	+	0.0165403i	$0.994735\pi$
$774$	−14.4715	−	9.25888i	−0.520167	−	0.332804i
$775$	−29.4493	−	51.0077i	−1.05785	−	1.83225i
$776$	23.9753	−	41.5265i	0.860664	−	1.49071i
$777$		0			0
$778$	−47.5605	−	82.3772i	−1.70513	−	2.95337i
$779$	7.41449	−	12.8423i	0.265652	−	0.460122i
$780$	−9.04092	+	8.63800i	−0.323717	+	0.309290i
$781$	−1.71926	−	2.97785i	−0.0615200	−	0.106556i
$782$	−27.7647	−	48.0899i	−0.992864	−	1.71969i
$783$	−38.9973	+	7.63912i	−1.39365	+	0.273000i
$784$		0			0
$785$	38.3157	−	66.3647i	1.36754	−	2.36866i
$786$	8.58998	+	35.2524i	0.306394	+	1.25741i
$787$	−46.0035			−1.63985			−0.819923	−	0.572473i	$-0.805984\pi$
$787$	−46.0035			−1.63985			−0.819923	+	0.572473i	$0.805984\pi$
$788$	−86.4222			−3.07866
$789$	7.00207	+	2.04829i	0.249280	+	0.0729210i
$790$	36.7330	−	63.6235i	1.30690	−	2.26362i
$791$		0			0
$792$	−5.47150	+	2.83480i	−0.194421	+	0.100730i
$793$	−1.95379	−	3.38406i	−0.0693810	−	0.120171i
$794$	14.6988	+	25.4591i	0.521642	+	0.903511i
$795$	21.7016	+	6.34827i	0.769675	+	0.225150i
$796$	−20.2183	+	35.0192i	−0.716620	+	1.24122i
$797$	−18.4558	−	31.9664i	−0.653739	−	1.13231i	−0.982208	−	0.187795i	$-0.939866\pi$
$797$	−18.4558	−	31.9664i	−0.653739	−	1.13231i	0.328469	−	0.944515i	$-0.393467\pi$
$798$		0			0
$799$	15.3353	−	26.5615i	0.542524	−	0.939679i
$800$	−2.26089	−	3.91598i	−0.0799346	−	0.138451i
$801$	−39.5033	+	20.4668i	−1.39578	+	0.723158i
$802$	−39.8068	+	68.9474i	−1.40563	+	2.43462i
$803$	0.802077			0.0283047
$804$	−18.2814	+	17.4666i	−0.644734	+	0.616001i
$805$		0			0
$806$	4.20847	+	7.28928i	0.148237	+	0.256754i
$807$	8.50885	+	34.9195i	0.299526	+	1.22923i
$808$	−22.0150	−	38.1311i	−0.774484	−	1.34145i
$809$	−23.8444	+	41.2996i	−0.838323	+	1.45202i	0.0529735	+	0.998596i	$0.483130\pi$
$809$	−23.8444	+	41.2996i	−0.838323	+	1.45202i	−0.891296	+	0.453422i	$0.850203\pi$
$810$	−46.7205	+	66.1758i	−1.64159	+	2.32518i
$811$	6.02728			0.211646			0.105823	−	0.994385i	$-0.466252\pi$
$811$	6.02728			0.211646			0.105823	+	0.994385i	$0.466252\pi$
$812$		0			0
$813$	47.3594	+	13.8539i	1.66097	+	0.485877i
$814$	−1.16372	+	2.01561i	−0.0407882	+	0.0706472i
$815$	40.8324			1.43030
$816$	−8.61654	−	35.3615i	−0.301639	−	1.23790i
$817$	4.59322			0.160696
$818$	46.6881			1.63241
$819$		0			0
$820$	−111.434			−3.89143
$821$	−39.2642			−1.37033			−0.685165	−	0.728388i	$-0.740270\pi$
$821$	−39.2642			−1.37033			−0.685165	+	0.728388i	$0.740270\pi$
$822$	1.54304	+	0.451379i	0.0538196	+	0.0157436i
$823$	22.7630			0.793469			0.396735	−	0.917933i	$-0.370143\pi$
$823$	22.7630			0.793469			0.396735	+	0.917933i	$0.370143\pi$
$824$	−20.2849	+	35.1344i	−0.706657	+	1.22397i
$825$	−1.39681	−	5.73237i	−0.0486306	−	0.199575i
$826$		0			0
$827$	−28.9286			−1.00595			−0.502973	−	0.864302i	$-0.667760\pi$
$827$	−28.9286			−1.00595			−0.502973	+	0.864302i	$0.667760\pi$
$828$	47.6146	+	30.4639i	1.65472	+	1.05869i
$829$	16.9883	−	29.4247i	0.590029	−	1.02196i	−0.404198	−	0.914671i	$-0.632449\pi$
$829$	16.9883	−	29.4247i	0.590029	−	1.02196i	0.994228	−	0.107290i	$-0.0342172\pi$
$830$	54.7783	+	94.8788i	1.90138	+	3.29329i
$831$	28.5303	+	8.34585i	0.989704	+	0.289514i
$832$	−1.78348	−	3.08908i	−0.0618312	−	0.107095i
$833$		0			0
$834$	−77.7213	−	22.7355i	−2.69127	−	0.787267i
$835$	−12.6578			−0.438041
$836$	1.62584	−	2.81604i	0.0562310	−	0.0973949i
$837$	23.9956	+	27.5229i	0.829410	+	0.951332i
$838$	21.2716	+	36.8435i	0.734816	+	1.27274i
$839$	−19.0206	+	32.9446i	−0.656663	+	1.13737i	0.324811	+	0.945779i	$0.394699\pi$
$839$	−19.0206	+	32.9446i	−0.656663	+	1.13737i	−0.981474	+	0.191595i	$0.938634\pi$
$840$		0			0
$841$	−14.7434	−	25.5363i	−0.508392	−	0.880561i
$842$	−22.8837	+	39.6356i	−0.788623	+	1.36593i
$843$	−3.87203	−	15.8905i	−0.133360	−	0.547296i
$844$	−9.91595	−	17.1749i	−0.341321	−	0.591185i
$845$	−23.3441	−	40.4331i	−0.803060	−	1.39094i
$846$	−2.12405	+	46.5749i	−0.0730264	+	1.60128i
$847$		0			0
$848$	7.72159	−	13.3742i	0.265161	−	0.459272i
$849$	21.1249	−	20.1834i	0.725004	−	0.692694i
$850$	100.141			3.43480
$851$	10.8171			0.370806
$852$	−42.9545	+	41.0402i	−1.47160	+	1.40601i
$853$	−4.90746	+	8.49996i	−0.168028	+	0.291033i	−0.937726	−	0.347374i	$-0.887073\pi$
$853$	−4.90746	+	8.49996i	−0.168028	+	0.291033i	0.769698	+	0.638408i	$0.220407\pi$
$854$		0			0
$855$	0.986679	−	21.6353i	0.0337437	−	0.739912i
$856$	−32.4523	−	56.2091i	−1.10920	−	1.92119i
$857$	−13.3680	−	23.1541i	−0.456642	−	0.790928i	0.542139	−	0.840289i	$-0.317615\pi$
$857$	−13.3680	−	23.1541i	−0.456642	−	0.790928i	−0.998781	+	0.0493613i	$0.984281\pi$
$858$	0.199612	+	0.819187i	0.00681463	+	0.0279666i
$859$	9.24411	−	16.0113i	0.315405	−	0.546297i	−0.664119	−	0.747627i	$-0.731193\pi$
$859$	9.24411	−	16.0113i	0.315405	−	0.546297i	0.979523	+	0.201330i	$0.0645263\pi$
$860$	−17.2581	−	29.8918i	−0.588495	−	1.01930i
$861$		0			0
$862$	19.5344	−	33.8346i	0.665345	−	1.15241i
$863$	4.57393	+	7.92228i	0.155698	+	0.269677i	0.933313	−	0.359064i	$-0.116904\pi$
$863$	4.57393	+	7.92228i	0.155698	+	0.269677i	−0.777615	+	0.628741i	$0.783571\pi$
$864$	1.84220	+	2.11300i	0.0626730	+	0.0718858i
$865$	−11.0723	+	19.1777i	−0.376469	+	0.652063i
$866$	99.4946			3.38097
$867$	10.9371	+	3.19940i	0.371444	+	0.108657i
$868$		0			0
$869$	−1.65865	−	2.87287i	−0.0562660	−	0.0974555i
$870$	−114.429	−	33.4736i	−3.87951	−	1.13486i
$871$	0.876423	+	1.51801i	0.0296964	+	0.0514358i
$872$	−6.57227	+	11.3835i	−0.222565	+	0.385494i
$873$	−23.9753	−	15.3395i	−0.811442	−	0.519162i
$874$	−22.5683			−0.763385
$875$		0			0
$876$	−3.28074	−	13.4638i	−0.110846	−	0.454901i
$877$	−11.3442	+	19.6487i	−0.383065	+	0.663488i	−0.991499	−	0.130117i	$-0.958465\pi$
$877$	−11.3442	+	19.6487i	−0.383065	+	0.663488i	0.608434	+	0.793605i	$0.291798\pi$
$878$	30.6602			1.03473
$879$	6.18882	+	1.81039i	0.208744	+	0.0610630i
$880$	−6.43367			−0.216879
$881$	15.3696			0.517815			0.258907	−	0.965902i	$-0.416638\pi$
$881$	15.3696			0.517815			0.258907	+	0.965902i	$0.416638\pi$
$882$		0			0
$883$	29.6372			0.997370			0.498685	−	0.866783i	$-0.333817\pi$
$883$	29.6372			0.997370			0.498685	+	0.866783i	$0.333817\pi$
$884$	−9.58307			−0.322313
$885$	9.17758	+	37.6639i	0.308501	+	1.26606i
$886$	−20.2518			−0.680371
$887$	9.38252	−	16.2510i	0.315034	−	0.545655i	−0.664410	−	0.747368i	$-0.731317\pi$
$887$	9.38252	−	16.2510i	0.315034	−	0.545655i	0.979445	+	0.201712i	$0.0646506\pi$
$888$	19.5547	+	5.72026i	0.656212	+	0.191959i
$889$		0			0
$890$	−133.482			−4.47432
$891$	1.53297	+	3.32105i	0.0513565	+	0.111259i
$892$	47.4507	−	82.1870i	1.58877	−	2.75183i
$893$	−6.23258	−	10.7952i	−0.208565	−	0.361246i
$894$	9.78843	+	40.1707i	0.327374	+	1.34351i
$895$	16.7047	+	28.9335i	0.558378	+	0.967139i
$896$		0			0
$897$	2.83336	−	2.70709i	0.0946031	−	0.0903871i
$898$	13.8889			0.463479
$899$	−26.8708	+	46.5416i	−0.896192	+	1.55225i
$900$	−90.5114	+	46.8943i	−3.01705	+	1.56314i
$901$	8.66445	+	15.0073i	0.288655	+	0.499965i
$902$	−3.75700	+	6.50731i	−0.125094	+	0.216670i
$903$		0			0
$904$	35.2527	+	61.0595i	1.17249	+	2.03081i
$905$	21.8530	−	37.8505i	0.726419	−	1.25819i
$906$	−52.4983	−	15.3571i	−1.74414	−	0.510207i
$907$	15.5541	+	26.9405i	0.516465	+	0.894543i	0.999817	+	0.0191175i	$0.00608567\pi$
$907$	15.5541	+	26.9405i	0.516465	+	0.894543i	−0.483352	+	0.875426i	$0.660581\pi$
$908$	12.4022	+	21.4813i	0.411582	+	0.712881i
$909$	−23.2056	+	12.0229i	−0.769683	+	0.398775i
$910$		0			0
$911$	−8.73764	+	15.1340i	−0.289491	+	0.501413i	−0.973688	−	0.227884i	$-0.926819\pi$
$911$	−8.73764	+	15.1340i	−0.289491	+	0.501413i	0.684197	+	0.729297i	$0.260153\pi$
$912$	−14.1972	−	4.15304i	−0.470115	−	0.137521i
$913$	4.94695			0.163720
$914$	12.4720			0.412536
$915$	−12.0407	−	49.4138i	−0.398053	−	1.63357i
$916$	−2.96027	+	5.12734i	−0.0978101	+	0.169412i
$917$		0			0
$918$	−60.9248	+	11.9345i	−2.01082	+	0.393896i
$919$	−21.0993	−	36.5451i	−0.696002	−	1.20551i	−0.969842	−	0.243736i	$-0.921627\pi$
$919$	−21.0993	−	36.5451i	−0.696002	−	1.20551i	0.273840	−	0.961775i	$-0.411706\pi$
$920$	42.9635	+	74.4150i	1.41647	+	2.45339i
$921$	38.2827	−	36.5766i	1.26146	−	1.20524i
$922$	9.56720	−	16.5709i	0.315079	−	0.545733i
$923$	2.05927	+	3.56676i	0.0677818	+	0.117401i
$924$		0			0
$925$	−9.75370	+	16.8939i	−0.320700	+	0.555468i
$926$	11.2937	+	19.5612i	0.371133	+	0.642821i
$927$	20.2849	+	12.9783i	0.666242	+	0.426263i
$928$	−2.06294	+	3.57311i	−0.0677193	+	0.117293i
$929$	48.4111			1.58832			0.794159	−	0.607710i	$-0.207912\pi$
$929$	48.4111			1.58832			0.794159	+	0.607710i	$0.207912\pi$
$930$	25.9357	+	106.438i	0.850465	+	3.49022i
$931$		0			0
$932$	26.8551	+	46.5145i	0.879670	+	1.52363i
$933$	−13.0678	+	12.4854i	−0.427821	+	0.408755i
$934$	16.9350	+	29.3322i	0.554129	+	0.959780i
$935$	3.60963	−	6.25206i	0.118048	−	0.204464i
$936$	6.55357	−	3.39543i	0.214210	−	0.110983i
$937$	−22.6750			−0.740762			−0.370381	−	0.928880i	$-0.620773\pi$
$937$	−22.6750			−0.740762			−0.370381	+	0.928880i	$0.620773\pi$
$938$		0			0
$939$	−0.776271	+	0.741676i	−0.0253327	+	0.0242037i
$940$	−46.8353	+	81.1211i	−1.52760	+	2.64588i
$941$	−49.9505			−1.62834			−0.814170	−	0.580627i	$-0.802808\pi$
$941$	−49.9505			−1.62834			−0.814170	+	0.580627i	$0.802808\pi$
$942$	−64.5502	+	61.6735i	−2.10316	+	2.00943i
$943$	34.9225			1.13723
$944$	26.4769			0.861749
$945$		0			0
$946$	−2.32743			−0.0756713
$947$	17.7123			0.575571			0.287786	−	0.957695i	$-0.407081\pi$
$947$	17.7123			0.575571			0.287786	+	0.957695i	$0.407081\pi$
$948$	−41.4403	+	39.5934i	−1.34592	+	1.28594i
$949$	−0.960699			−0.0311856
$950$	20.3496	−	35.2466i	0.660230	−	1.14355i
$951$	−12.8345	+	12.2625i	−0.416186	+	0.397638i
$952$		0			0
$953$	38.0229			1.23168			0.615842	−	0.787870i	$-0.288816\pi$
$953$	38.0229			1.23168			0.615842	+	0.787870i	$0.288816\pi$
$954$	−22.1893	−	14.1967i	−0.718405	−	0.459636i
$955$	16.7179	−	28.9563i	0.540979	−	0.937002i
$956$	−39.3017	−	68.0726i	−1.27111	−	2.20163i
$957$	−3.89246	+	3.71899i	−0.125825	+	0.120218i
$958$	−10.7177	−	18.5635i	−0.346272	−	0.599761i
$959$		0			0
$960$	−10.9911	−	45.1066i	−0.354738	−	1.45581i
$961$	18.3815			0.592952
$962$	1.39386	−	2.41423i	0.0449398	−	0.0778380i
$963$	−34.2075	+	17.7230i	−1.10232	+	0.571116i
$964$	10.2440	+	17.7432i	0.329938	+	0.571469i
$965$	30.9894	−	53.6752i	0.997583	−	1.72786i
$966$		0			0
$967$	15.5064	+	26.8579i	0.498652	+	0.863691i	0.999999	−	0.00155529i	$-0.000495066\pi$
$967$	15.5064	+	26.8579i	0.498652	+	0.863691i	−0.501346	+	0.865247i	$0.667162\pi$
$968$	27.3801	−	47.4236i	0.880028	−	1.52425i
$969$	12.0012	−	11.4663i	0.385534	−	0.368352i
$970$	−42.6972	−	73.9537i	−1.37092	−	2.37451i
$971$	7.28376	+	12.6158i	0.233747	+	0.404862i	0.958908	−	0.283718i	$-0.0915679\pi$
$971$	7.28376	+	12.6158i	0.233747	+	0.404862i	−0.725161	+	0.688580i	$0.758235\pi$
$972$	49.4776	−	39.3169i	1.58699	−	1.26109i
$973$		0			0
$974$	22.1893	−	38.4330i	0.710991	−	1.23147i
$975$	1.67305	+	6.86603i	0.0535804	+	0.219889i
$976$	−34.7368			−1.11190
$977$	−47.8797			−1.53181			−0.765904	−	0.642955i	$-0.777708\pi$
$977$	−47.8797			−1.53181			−0.765904	+	0.642955i	$0.777708\pi$
$978$	−45.6570	−	13.3559i	−1.45995	−	0.427074i
$979$	−3.01364	+	5.21978i	−0.0963163	+	0.166825i
$980$		0			0
$981$	6.57227	+	4.20495i	0.209836	+	0.134254i
$982$	−2.51819	−	4.36163i	−0.0803586	−	0.139185i
$983$	22.2128	+	38.4737i	0.708479	+	1.22712i	0.965421	+	0.260695i	$0.0839517\pi$
$983$	22.2128	+	38.4737i	0.708479	+	1.22712i	−0.256942	+	0.966427i	$0.582715\pi$
$984$	63.1313	+	18.4676i	2.01255	+	0.588724i
$985$	−38.9902	+	67.5329i	−1.24233	+	2.15178i
$986$	−45.6864	−	79.1313i	−1.45495	−	2.52005i
$987$		0			0
$988$	−1.94738	+	3.37296i	−0.0619544	+	0.107308i
$989$	5.40856	+	9.36790i	0.171982	+	0.297882i
$990$	−0.499960	+	10.9628i	−0.0158898	+	0.348422i
$991$	20.8078	−	36.0401i	0.660981	−	1.14485i	−0.319377	−	0.947628i	$-0.603474\pi$
$991$	20.8078	−	36.0401i	0.660981	−	1.14485i	0.980358	−	0.197225i	$-0.0631929\pi$
$992$	3.79114			0.120369
$993$	25.5023	−	24.3657i	0.809290	−	0.773223i
$994$		0			0
$995$	18.2434	+	31.5985i	0.578354	+	1.00174i
$996$	−20.2345	−	83.0405i	−0.641155	−	2.63124i
$997$	−6.51407	−	11.2827i	−0.206303	−	0.357327i	0.744244	−	0.667908i	$-0.232810\pi$
$997$	−6.51407	−	11.2827i	−0.206303	−	0.357327i	−0.950547	+	0.310581i	$0.899477\pi$
$998$	48.0875	−	83.2901i	1.52218	−	2.63650i
$999$	3.92070	−	11.4405i	0.124045	−	0.361962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.g.214.5		12
3.2	odd	2		1323.2.h.g.802.1		12
7.2	even	3		441.2.g.g.79.1		12
7.3	odd	6		441.2.f.g.295.1	yes	12
7.4	even	3		441.2.f.g.295.2	yes	12
7.5	odd	6		441.2.g.g.79.2		12
7.6	odd	2	inner	441.2.h.g.214.6		12
9.4	even	3		441.2.g.g.67.1		12
9.5	odd	6		1323.2.g.g.361.6		12
21.2	odd	6		1323.2.g.g.667.6		12
21.5	even	6		1323.2.g.g.667.5		12
21.11	odd	6		1323.2.f.g.883.5		12
21.17	even	6		1323.2.f.g.883.6		12
21.20	even	2		1323.2.h.g.802.2		12
63.4	even	3		441.2.f.g.148.2	yes	12
63.5	even	6		1323.2.h.g.226.2		12
63.11	odd	6		3969.2.a.bd.1.2		6
63.13	odd	6		441.2.g.g.67.2		12
63.23	odd	6		1323.2.h.g.226.1		12
63.25	even	3		3969.2.a.be.1.5		6
63.31	odd	6		441.2.f.g.148.1	✓	12
63.32	odd	6		1323.2.f.g.442.5		12
63.38	even	6		3969.2.a.bd.1.1		6
63.40	odd	6	inner	441.2.h.g.373.6		12
63.41	even	6		1323.2.g.g.361.5		12
63.52	odd	6		3969.2.a.be.1.6		6
63.58	even	3	inner	441.2.h.g.373.5		12
63.59	even	6		1323.2.f.g.442.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.1	✓	12	63.31	odd	6
441.2.f.g.148.2	yes	12	63.4	even	3
441.2.f.g.295.1	yes	12	7.3	odd	6
441.2.f.g.295.2	yes	12	7.4	even	3
441.2.g.g.67.1		12	9.4	even	3
441.2.g.g.67.2		12	63.13	odd	6
441.2.g.g.79.1		12	7.2	even	3
441.2.g.g.79.2		12	7.5	odd	6
441.2.h.g.214.5		12	1.1	even	1	trivial
441.2.h.g.214.6		12	7.6	odd	2	inner
441.2.h.g.373.5		12	63.58	even	3	inner
441.2.h.g.373.6		12	63.40	odd	6	inner
1323.2.f.g.442.5		12	63.32	odd	6
1323.2.f.g.442.6		12	63.59	even	6
1323.2.f.g.883.5		12	21.11	odd	6
1323.2.f.g.883.6		12	21.17	even	6
1323.2.g.g.361.5		12	63.41	even	6
1323.2.g.g.361.6		12	9.5	odd	6
1323.2.g.g.667.5		12	21.5	even	6
1323.2.g.g.667.6		12	21.2	odd	6
1323.2.h.g.226.1		12	63.23	odd	6
1323.2.h.g.226.2		12	63.5	even	6
1323.2.h.g.802.1		12	3.2	odd	2
1323.2.h.g.802.2		12	21.20	even	2
3969.2.a.bd.1.1		6	63.38	even	6
3969.2.a.bd.1.2		6	63.11	odd	6
3969.2.a.be.1.5		6	63.25	even	3
3969.2.a.be.1.6		6	63.52	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.46050 q^{2} +(-1.25233 + 1.19652i) q^{3} +4.05408 q^{4} +(1.82904 - 3.16799i) q^{5} +(-3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(0.136673 - 2.99689i) q^{9} +O(q^{10})\)	\(q+2.46050 q^{2} +(-1.25233 + 1.19652i) q^{3} +4.05408 q^{4} +(1.82904 - 3.16799i) q^{5} +(-3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(0.136673 - 2.99689i) q^{9} +(4.50036 - 7.79485i) q^{10} +(-0.203210 - 0.351971i) q^{11} +(-5.07706 + 4.85080i) q^{12} +(0.243398 + 0.421578i) q^{13} +(1.50000 + 6.15585i) q^{15} +4.32743 q^{16} +(-2.42792 + 4.20528i) q^{17} +(0.336285 - 7.37385i) q^{18} +(0.986757 + 1.70911i) q^{19} +(7.41507 - 12.8433i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.32383 + 4.02499i) q^{23} +(-6.32939 + 6.04732i) q^{24} +(-4.19076 - 7.25860i) q^{25} +(0.598883 + 1.03729i) q^{26} +(3.41468 + 3.91663i) q^{27} +(-3.82383 + 6.62307i) q^{29} +(3.69076 + 15.1465i) q^{30} +7.02720 q^{31} +0.539495 q^{32} +(0.675627 + 0.197639i) q^{33} +(-5.97391 + 10.3471i) q^{34} +(0.554084 - 12.1496i) q^{36} +(-1.16372 - 2.01561i) q^{37} +(2.42792 + 4.20528i) q^{38} +(-0.809243 - 0.236725i) q^{39} +(9.24411 - 16.0113i) q^{40} +(-3.75700 - 6.50731i) q^{41} +(1.16372 - 2.01561i) q^{43} +(-0.823832 - 1.42692i) q^{44} +(-9.24411 - 5.91439i) q^{45} +(-5.71780 + 9.90352i) q^{46} -6.31623 q^{47} +(-5.41938 + 5.17786i) q^{48} +(-10.3114 - 17.8598i) q^{50} +(-1.99115 - 8.17147i) q^{51} +(0.986757 + 1.70911i) q^{52} +(1.78434 - 3.09056i) q^{53} +(8.40183 + 9.63688i) q^{54} -1.48672 q^{55} +(-3.28074 - 0.959702i) q^{57} +(-9.40856 + 16.2961i) q^{58} +6.11839 q^{59} +(6.08113 + 24.9564i) q^{60} -8.02712 q^{61} +17.2905 q^{62} -7.32743 q^{64} +1.78074 q^{65} +(1.66238 + 0.486291i) q^{66} +3.60078 q^{67} +(-9.84299 + 17.0486i) q^{68} +(-1.90578 - 7.82115i) q^{69} +8.46050 q^{71} +(0.690757 - 15.1465i) q^{72} +(-0.986757 + 1.70911i) q^{73} +(-2.86333 - 4.95943i) q^{74} +(13.9333 + 4.07586i) q^{75} +(4.00040 + 6.92889i) q^{76} +(-1.99115 - 0.582462i) q^{78} +8.16225 q^{79} +(7.91503 - 13.7092i) q^{80} +(-8.96264 - 0.819187i) q^{81} +(-9.24411 - 16.0113i) q^{82} +(-6.08600 + 10.5413i) q^{83} +(8.88151 + 15.3832i) q^{85} +(2.86333 - 4.95943i) q^{86} +(-3.13594 - 12.8696i) q^{87} +(-1.02704 - 1.77889i) q^{88} +(-7.41507 - 12.8433i) q^{89} +(-22.7452 - 14.5524i) q^{90} +(-9.42101 + 16.3177i) q^{92} +(-8.80039 + 8.40819i) q^{93} -15.5411 q^{94} +7.21926 q^{95} +(-0.675627 + 0.645517i) q^{96} +(4.74375 - 8.21642i) q^{97} +(-1.08259 + 0.560893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8	\( 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 8 q^{11} + 18 q^{15} + 12 q^{16} + 24 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} + 6 q^{30} + 32 q^{32} - 30 q^{36} + 6 q^{37} - 48 q^{39} - 6 q^{43} + 14 q^{44} - 12 q^{46} - 56 q^{50} + 36 q^{51} - 28 q^{53} - 6 q^{57} - 18 q^{58} + 18 q^{60} - 48 q^{64} - 12 q^{65} + 76 q^{71} - 30 q^{72} - 36 q^{74} + 36 q^{78} - 12 q^{79} + 24 q^{81} + 30 q^{85} + 36 q^{86} + 6 q^{88} - 62 q^{92} - 84 q^{93} + 120 q^{95} - 48 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8 - 8 * q^11 + 18 * q^15 + 12 * q^16 + 24 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 + 6 * q^30 + 32 * q^32 - 30 * q^36 + 6 * q^37 - 48 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 + 36 * q^51 - 28 * q^53 - 6 * q^57 - 18 * q^58 + 18 * q^60 - 48 * q^64 - 12 * q^65 + 76 * q^71 - 30 * q^72 - 36 * q^74 + 36 * q^78 - 12 * q^79 + 24 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 - 84 * q^93 + 120 * q^95 - 48 * q^99

Introduction

L-functions

Modular forms

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