LMFDB - Embedded newform 1323.2.h.g.802.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.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:	$10.5642081874$
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^{5} $
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.1
Root			$1.82904 - 1.05600i$ of defining polynomial
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.g.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46050 q^{2} +4.05408 q^{4} +(-1.82904 + 3.16799i) q^{5} -5.05408 q^{8} +O(q^{10})$	\(q-2.46050 q^{2} +4.05408 q^{4} +(-1.82904 + 3.16799i) q^{5} -5.05408 q^{8} +(4.50036 - 7.79485i) q^{10} +(0.203210 + 0.351971i) q^{11} +(0.243398 + 0.421578i) q^{13} +4.32743 q^{16} +(2.42792 - 4.20528i) q^{17} +(0.986757 + 1.70911i) q^{19} +(-7.41507 + 12.8433i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(2.32383 - 4.02499i) q^{23} +(-4.19076 - 7.25860i) q^{25} +(-0.598883 - 1.03729i) q^{26} +(3.82383 - 6.62307i) q^{29} +7.02720 q^{31} -0.539495 q^{32} +(-5.97391 + 10.3471i) q^{34} +(-1.16372 - 2.01561i) q^{37} +(-2.42792 - 4.20528i) q^{38} +(9.24411 - 16.0113i) q^{40} +(3.75700 + 6.50731i) q^{41} +(1.16372 - 2.01561i) q^{43} +(0.823832 + 1.42692i) q^{44} +(-5.71780 + 9.90352i) q^{46} +6.31623 q^{47} +(10.3114 + 17.8598i) q^{50} +(0.986757 + 1.70911i) q^{52} +(-1.78434 + 3.09056i) q^{53} -1.48672 q^{55} +(-9.40856 + 16.2961i) q^{58} -6.11839 q^{59} -8.02712 q^{61} -17.2905 q^{62} -7.32743 q^{64} -1.78074 q^{65} +3.60078 q^{67} +(9.84299 - 17.0486i) q^{68} -8.46050 q^{71} +(-0.986757 + 1.70911i) q^{73} +(2.86333 + 4.95943i) q^{74} +(4.00040 + 6.92889i) q^{76} +8.16225 q^{79} +(-7.91503 + 13.7092i) q^{80} +(-9.24411 - 16.0113i) q^{82} +(6.08600 - 10.5413i) q^{83} +(8.88151 + 15.3832i) q^{85} +(-2.86333 + 4.95943i) q^{86} +(-1.02704 - 1.77889i) q^{88} +(7.41507 + 12.8433i) q^{89} +(9.42101 - 16.3177i) q^{92} -15.5411 q^{94} -7.21926 q^{95} +(4.74375 - 8.21642i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 12 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} - 32 q^{32} + 6 q^{37} - 6 q^{43} - 14 q^{44} - 12 q^{46} + 56 q^{50} + 28 q^{53} - 18 q^{58} - 48 q^{64} + 12 q^{65} - 76 q^{71} + 36 q^{74} - 12 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} - 120 q^{95}+O(q^{100}) $ 12 * q - 4 * q^2 + 12 * q^4 - 24 * q^8 + 8 * q^11 + 12 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 - 32 * q^32 + 6 * q^37 - 6 * q^43 - 14 * q^44 - 12 * q^46 + 56 * q^50 + 28 * q^53 - 18 * q^58 - 48 * q^64 + 12 * q^65 - 76 * q^71 + 36 * q^74 - 12 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 - 120 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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	$-0.835830\pi$
$2$	−2.46050			−1.73984			−0.869920	+	0.493193i	$0.835830\pi$
$3$		0			0
$3$		0			0
$4$	4.05408			2.02704
$5$	−1.82904	+	3.16799i	−0.817970	+	1.41677i	0.0892047	+	0.996013i	$0.471567\pi$
$5$	−1.82904	+	3.16799i	−0.817970	+	1.41677i	−0.907175	+	0.420753i	$0.861766\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−5.05408			−1.78689
$9$		0			0
$10$	4.50036	−	7.79485i	1.42314	−	2.46495i
$11$	0.203210	+	0.351971i	0.0612702	+	0.106123i	0.895033	−	0.445999i	$-0.147152\pi$
$11$	0.203210	+	0.351971i	0.0612702	+	0.106123i	−0.833763	+	0.552122i	$0.813818\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	4.32743			1.08186
$17$	2.42792	−	4.20528i	0.588857	−	1.01993i	−0.405525	−	0.914084i	$-0.632911\pi$
$17$	2.42792	−	4.20528i	0.588857	−	1.01993i	0.994382	−	0.105847i	$-0.0337553\pi$
$18$		0			0
$19$	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	−0.515290	−	0.857016i	$-0.672316\pi$
$23$	2.32383	−	4.02499i	0.484552	−	0.839269i	0.999843	+	0.0177464i	$0.00564915\pi$
$24$		0			0
$25$	−4.19076	−	7.25860i	−0.838151	−	1.45172i
$26$	−0.598883	−	1.03729i	−0.117451	−	0.203430i
$27$		0			0
$28$		0			0
$29$	3.82383	−	6.62307i	0.710068	−	1.22987i	−0.254764	−	0.967003i	$-0.581998\pi$
$29$	3.82383	−	6.62307i	0.710068	−	1.22987i	0.964831	−	0.262870i	$-0.0846690\pi$
$30$		0			0
$31$	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			0
$34$	−5.97391	+	10.3471i	−1.02452	+	1.77452i
$35$		0			0
$36$		0			0
$37$	−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			0
$40$	9.24411	−	16.0113i	1.46162	−	2.53160i
$41$	3.75700	+	6.50731i	0.586744	+	1.01627i	0.994655	+	0.103249i	$0.0329240\pi$
$41$	3.75700	+	6.50731i	0.586744	+	1.01627i	−0.407911	+	0.913022i	$0.633743\pi$
$42$		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
$45$		0			0
$46$	−5.71780	+	9.90352i	−0.843044	+	1.46019i
$47$	6.31623			0.921317			0.460658	−	0.887578i	$-0.347613\pi$
$47$	6.31623			0.921317			0.460658	+	0.887578i	$0.347613\pi$
$48$		0			0
$49$		0			0
$50$	10.3114	+	17.8598i	1.45825	+	2.52576i
$51$		0			0
$52$	0.986757	+	1.70911i	0.136839	+	0.237011i
$53$	−1.78434	+	3.09056i	−0.245097	+	0.424521i	−0.962159	−	0.272489i	$-0.912153\pi$
$53$	−1.78434	+	3.09056i	−0.245097	+	0.424521i	0.717062	+	0.697010i	$0.245487\pi$
$54$		0			0
$55$	−1.48672			−0.200469
$56$		0			0
$57$		0			0
$58$	−9.40856	+	16.2961i	−1.23540	+	2.13978i
$59$	−6.11839			−0.796546			−0.398273	−	0.917267i	$-0.630390\pi$
$59$	−6.11839			−0.796546			−0.398273	+	0.917267i	$0.630390\pi$
$60$		0			0
$61$	−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
$66$		0			0
$67$	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
$69$		0			0
$70$		0			0
$71$	−8.46050			−1.00408			−0.502039	−	0.864845i	$-0.667416\pi$
$71$	−8.46050			−1.00408			−0.502039	+	0.864845i	$0.667416\pi$
$72$		0			0
$73$	−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
$75$		0			0
$76$	4.00040	+	6.92889i	0.458877	+	0.794798i
$77$		0			0
$78$		0			0
$79$	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
$81$		0			0
$82$	−9.24411	−	16.0113i	−1.02084	−	1.76815i
$83$	6.08600	−	10.5413i	0.668025	−	1.15705i	−0.310431	−	0.950596i	$-0.600473\pi$
$83$	6.08600	−	10.5413i	0.668025	−	1.15705i	0.978456	−	0.206457i	$-0.0661933\pi$
$84$		0			0
$85$	8.88151	+	15.3832i	0.963336	+	1.66855i
$86$	−2.86333	+	4.95943i	−0.308760	+	0.534789i
$87$		0			0
$88$	−1.02704	−	1.77889i	−0.109483	−	0.189630i
$89$	7.41507	+	12.8433i	0.785996	+	1.36139i	0.928402	+	0.371577i	$0.121183\pi$
$89$	7.41507	+	12.8433i	0.785996	+	1.36139i	−0.142406	+	0.989808i	$0.545484\pi$
$90$		0			0
$91$		0			0
$92$	9.42101	−	16.3177i	0.982208	−	1.70123i
$93$		0			0
$94$	−15.5411			−1.60294
$95$	−7.21926			−0.740681
$96$		0			0
$97$	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
$99$		0			0
$100$	−16.9897	−	29.4270i	−1.69897	−	2.94270i
$101$	4.35588	+	7.54461i	0.433426	+	0.750716i	0.997166	−	0.0752364i	$-0.0239711\pi$
$101$	4.35588	+	7.54461i	0.433426	+	0.750716i	−0.563739	+	0.825953i	$0.690638\pi$
$102$		0			0
$103$	−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	$0.0465021\pi$
$107$	6.42101	+	11.1215i	0.620742	+	1.07516i	−0.368605	+	0.929586i	$0.620165\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$		0			0
$113$	−6.97509	−	12.0812i	−0.656162	−	1.13651i	−0.981601	−	0.190942i	$-0.938846\pi$
$113$	−6.97509	−	12.0812i	−0.656162	−	1.13651i	0.325440	−	0.945563i	$-0.394488\pi$
$114$		0			0
$115$	8.50075	+	14.7237i	0.792699	+	1.37300i
$116$	15.5021	−	26.8505i	1.43934	−	2.49301i
$117$		0			0
$118$	15.0543			1.38586
$119$		0			0
$120$		0			0
$121$	5.41741	−	9.38323i	0.492492	−	0.853021i
$122$	19.7508			1.78815
$123$		0			0
$124$	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			0
$130$	4.38151			0.384284
$131$	−4.25696	+	7.37327i	−0.371932	+	0.644205i	−0.989863	−	0.142027i	$-0.954638\pi$
$131$	−4.25696	+	7.37327i	−0.371932	+	0.644205i	0.617931	+	0.786233i	$0.287971\pi$
$132$		0			0
$133$		0			0
$134$	−8.85973			−0.765364
$135$		0			0
$136$	−12.2709	+	21.2538i	−1.05222	+	1.82250i
$137$	0.188621	+	0.326702i	0.0161150	+	0.0279120i	0.873970	−	0.485979i	$-0.161537\pi$
$137$	0.188621	+	0.326702i	0.0161150	+	0.0279120i	−0.857855	+	0.513891i	$0.828204\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	20.8171			1.74693
$143$	−0.0989221	+	0.171338i	−0.00827228	+	0.0143280i
$144$		0			0
$145$	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	−0.993404	−	0.114665i	$-0.963420\pi$
$149$	−4.85087	+	8.40196i	−0.397399	+	0.688315i	0.596005	+	0.802981i	$0.296754\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$		0			0
$155$	−12.8530	+	22.2621i	−1.03238	+	1.78813i
$156$		0			0
$157$	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
$159$		0			0
$160$	0.986757	−	1.70911i	0.0780100	−	0.135117i
$161$		0			0
$162$		0			0
$163$	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
$165$		0			0
$166$	−14.9746	+	25.9368i	−1.16226	+	2.01309i
$167$	1.73012	+	2.99665i	0.133880	+	0.231888i	0.925169	−	0.379555i	$-0.123923\pi$
$167$	1.73012	+	2.99665i	0.133880	+	0.231888i	−0.791289	+	0.611443i	$0.790590\pi$
$168$		0			0
$169$	6.38151	−	11.0531i	0.490886	−	0.850239i
$170$	−21.8530	−	37.8505i	−1.67605	−	2.90300i
$171$		0			0
$172$	4.71780	−	8.17147i	0.359729	−	0.623069i
$173$	6.05361			0.460247			0.230124	−	0.973161i	$-0.426087\pi$
$173$	6.05361			0.460247			0.230124	+	0.973161i	$0.426087\pi$
$174$		0			0
$175$		0			0
$176$	0.879379	+	1.52313i	0.0662857	+	0.114810i
$177$		0			0
$178$	−18.2448	−	31.6010i	−1.36751	−	2.36859i
$179$	4.56654	−	7.90947i	0.341319	−	0.591182i	−0.643359	−	0.765565i	$-0.722460\pi$
$179$	4.56654	−	7.90947i	0.341319	−	0.591182i	0.984678	+	0.174383i	$0.0557930\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	−11.7448	+	20.3427i	−0.865841	+	1.49968i
$185$	8.51392			0.625956
$186$		0			0
$187$	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	$-0.607279\pi$
$191$	−9.14027			−0.661367			−0.330683	+	0.943742i	$0.607279\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$		0			0
$197$	21.3173			1.51880			0.759398	−	0.650627i	$-0.225494\pi$
$197$	21.3173			1.51880			0.759398	+	0.650627i	$0.225494\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	−10.7177	−	18.5635i	−0.754092	−	1.30613i
$203$		0			0
$204$		0			0
$205$	−27.4868			−1.91976
$206$	9.87538	−	17.1047i	0.688051	−	1.19174i
$207$		0			0
$208$	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
$213$		0			0
$214$	−15.7989	−	27.3645i	−1.07999	−	1.87060i
$215$	4.25696	+	7.37327i	0.290322	+	0.502853i
$216$		0			0
$217$		0			0
$218$	3.19961	−	5.54189i	0.216705	−	0.375344i
$219$		0			0
$220$	−6.02728			−0.406359
$221$	2.36381			0.159007
$222$		0			0
$223$	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
$225$		0			0
$226$	17.1623	+	29.7259i	1.14162	+	1.97734i
$227$	−3.05919	−	5.29868i	−0.203046	−	0.351686i	0.746463	−	0.665427i	$-0.231751\pi$
$227$	−3.05919	−	5.29868i	−0.203046	−	0.351686i	−0.949508	+	0.313742i	$0.898417\pi$
$228$		0			0
$229$	−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	0.563244	−	0.826291i	$-0.309553\pi$
$233$	−6.62422	−	11.4735i	−0.433967	−	0.751653i	−0.997211	+	0.0746378i	$0.976220\pi$
$234$		0			0
$235$	−11.5526	+	20.0097i	−0.753610	+	1.30529i
$236$	−24.8045			−1.61463
$237$		0			0
$238$		0			0
$239$	9.69436	+	16.7911i	0.627076	+	1.08613i	0.988136	+	0.153584i	$0.0490817\pi$
$239$	9.69436	+	16.7911i	0.627076	+	1.08613i	−0.361060	+	0.932543i	$0.617585\pi$
$240$		0			0
$241$	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
$243$		0			0
$244$	−32.5426			−2.08333
$245$		0			0
$246$		0			0
$247$	−0.480350	+	0.831990i	−0.0305639	+	0.0529383i
$248$	−35.5161			−2.25527
$249$		0			0
$250$	−30.4360			−1.92494
$251$	15.0928			0.952647			0.476324	−	0.879270i	$-0.341969\pi$
$251$	15.0928			0.952647			0.476324	+	0.879270i	$0.341969\pi$
$252$		0			0
$253$	1.88891			0.118755
$254$	38.2455			2.39974
$255$		0			0
$256$	−32.3609			−2.02256
$257$	−3.85592	+	6.67865i	−0.240526	+	0.416603i	−0.960864	−	0.277020i	$-0.910653\pi$
$257$	−3.85592	+	6.67865i	−0.240526	+	0.416603i	0.720338	+	0.693623i	$0.243986\pi$
$258$		0			0
$259$		0			0
$260$	−7.21926			−0.447720
$261$		0			0
$262$	10.4743	−	18.1420i	0.647102	−	1.12081i
$263$	2.10603	+	3.64776i	0.129864	+	0.224930i	0.923624	−	0.383301i	$-0.125213\pi$
$263$	2.10603	+	3.64776i	0.129864	+	0.224930i	−0.793760	+	0.608231i	$0.791879\pi$
$264$		0			0
$265$	−6.52724	−	11.3055i	−0.400965	−	0.694492i
$266$		0			0
$267$		0			0
$268$	14.5979			0.891706
$269$	−10.3753	+	17.9706i	−0.632596	+	1.09569i	0.354423	+	0.935085i	$0.384677\pi$
$269$	−10.3753	+	17.9706i	−0.632596	+	1.09569i	−0.987019	+	0.160603i	$0.948656\pi$
$270$		0			0
$271$	−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
$276$		0			0
$277$	−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			0
$280$		0			0
$281$	4.72140	−	8.17770i	0.281655	−	0.487841i	−0.690138	−	0.723678i	$-0.742450\pi$
$281$	4.72140	−	8.17770i	0.281655	−	0.487841i	0.971793	+	0.235837i	$0.0757833\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	0.243398	−	0.421578i	0.0143924	−	0.0249284i
$287$		0			0
$288$		0			0
$289$	−3.28959	−	5.69774i	−0.193505	−	0.335161i
$290$	−34.4172	−	59.6124i	−2.02105	−	3.50056i
$291$		0			0
$292$	−4.00040	+	6.92889i	−0.234105	+	0.405483i
$293$	1.86143	+	3.22409i	0.108746	+	0.188353i	0.915262	−	0.402858i	$-0.131983\pi$
$293$	1.86143	+	3.22409i	0.108746	+	0.188353i	−0.806517	+	0.591211i	$0.798650\pi$
$294$		0			0
$295$	11.1908	−	19.3830i	0.651551	−	1.12852i
$296$	5.88151	+	10.1871i	0.341856	+	0.592112i
$297$		0			0
$298$	11.9356	−	20.6731i	0.691411	−	1.19756i
$299$	2.26247			0.130842
$300$		0			0
$301$		0			0
$302$	−15.7901	−	27.3492i	−0.908617	−	1.57377i
$303$		0			0
$304$	4.27012	+	7.39607i	0.244908	+	0.424194i
$305$	14.6819	−	25.4298i	0.840683	−	1.45611i
$306$		0			0
$307$	−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
$309$		0			0
$310$	31.6249	−	54.7759i	1.79617	−	3.11106i
$311$	−10.4348			−0.591702			−0.295851	−	0.955234i	$-0.595603\pi$
$311$	−10.4348			−0.591702			−0.295851	+	0.955234i	$0.595603\pi$
$312$		0			0
$313$	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	$-0.592925\pi$
$317$	−10.2484			−0.575610			−0.287805	+	0.957689i	$0.592925\pi$
$318$		0			0
$319$	3.10817			0.174024
$320$	13.4021	−	23.2132i	0.749203	−	1.29766i
$321$		0			0
$322$		0			0
$323$	9.58307			0.533216
$324$		0			0
$325$	2.04005	−	3.53346i	0.113161	−	0.196001i
$326$	−13.7324	−	23.7852i	−0.760567	−	1.31734i
$327$		0			0
$328$	−18.9882	−	32.8885i	−1.04845	−	1.81596i
$329$		0			0
$330$		0			0
$331$	−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
$333$		0			0
$334$	−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
$339$		0			0
$340$	36.0064	+	62.3649i	1.95272	+	3.38221i
$341$	1.42800	+	2.47337i	0.0773305	+	0.133940i
$342$		0			0
$343$		0			0
$344$	−5.88151	+	10.1871i	−0.317110	+	0.549251i
$345$		0			0
$346$	−14.8949			−0.800756
$347$	−8.88132			−0.476774			−0.238387	−	0.971170i	$-0.576619\pi$
$347$	−8.88132			−0.476774			−0.238387	+	0.971170i	$0.576619\pi$
$348$		0			0
$349$	−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			0
$352$	−0.109631	−	0.189886i	−0.00584335	−	0.0101210i
$353$	−7.38268	−	12.7872i	−0.392941	−	0.680593i	0.599895	−	0.800078i	$-0.295209\pi$
$353$	−7.38268	−	12.7872i	−0.392941	−	0.680593i	−0.992836	+	0.119485i	$0.961876\pi$
$354$		0			0
$355$	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	0.945356	−	0.326040i	$-0.105714\pi$
$359$	3.60603	+	6.24583i	0.190319	+	0.329642i	−0.755037	+	0.655682i	$0.772381\pi$
$360$		0			0
$361$	7.55262	−	13.0815i	0.397506	−	0.688501i
$362$	−29.3977			−1.54511
$363$		0			0
$364$		0			0
$365$	−3.60963	−	6.25206i	−0.188937	−	0.327248i
$366$		0			0
$367$	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
$369$		0			0
$370$	−20.9485			−1.08906
$371$		0			0
$372$		0			0
$373$	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
$375$		0			0
$376$	−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
$381$		0			0
$382$	22.4897			1.15067
$383$	17.8569	−	30.9291i	0.912447	−	1.58041i	0.101851	−	0.994800i	$-0.467523\pi$
$383$	17.8569	−	30.9291i	0.912447	−	1.58041i	0.810596	−	0.585606i	$-0.199143\pi$
$384$		0			0
$385$		0			0
$386$	−41.6883			−2.12188
$387$		0			0
$388$	19.2316	−	33.3101i	0.976336	−	1.69106i
$389$	19.3296	+	33.4798i	0.980048	+	1.69749i	0.662156	+	0.749366i	$0.269641\pi$
$389$	19.3296	+	33.4798i	0.980048	+	1.69749i	0.317892	+	0.948127i	$0.397025\pi$
$390$		0			0
$391$	−11.2842	−	19.5447i	−0.570664	−	0.988420i
$392$		0			0
$393$		0			0
$394$	−52.4513			−2.64246
$395$	−14.9291	+	25.8579i	−0.751163	+	1.30105i
$396$		0			0
$397$	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	$-0.533934\pi$
$401$	16.1783	−	28.0216i	0.807906	−	1.39933i	0.914312	−	0.405011i	$-0.132732\pi$
$402$		0			0
$403$	1.71041	+	2.96251i	0.0852015	+	0.147573i
$404$	17.6591	+	30.5865i	0.878573	+	1.52173i
$405$		0			0
$406$		0			0
$407$	0.472958	−	0.819187i	0.0234437	−	0.0406056i
$408$		0			0
$409$	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			0
$412$	−16.2713	+	28.1827i	−0.801630	+	1.38846i
$413$		0			0
$414$		0			0
$415$	22.2630	+	38.5607i	1.09285	+	1.89287i
$416$	−0.131312	−	0.227439i	−0.00643811	−	0.0111511i
$417$		0			0
$418$	0.986757	−	1.70911i	0.0482639	−	0.0835955i
$419$	−8.64523	−	14.9740i	−0.422347	−	0.731526i	0.573822	−	0.818980i	$-0.305460\pi$
$419$	−8.64523	−	14.9740i	−0.422347	−	0.731526i	−0.996169	+	0.0874539i	$0.972127\pi$
$420$		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			0
$424$	9.01819	−	15.6200i	0.437962	−	0.758572i
$425$	−40.6993			−1.97421
$426$		0			0
$427$		0			0
$428$	26.0313	+	45.0876i	1.25827	+	2.17939i
$429$		0			0
$430$	−10.4743	−	18.1420i	−0.505114	−	0.874883i
$431$	−7.93920	+	13.7511i	−0.382418	+	0.662367i	−0.991407	−	0.130811i	$-0.958242\pi$
$431$	−7.93920	+	13.7511i	−0.382418	+	0.662367i	0.608990	+	0.793178i	$0.291575\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	−5.27188	+	9.13117i	−0.252477	+	0.437304i
$437$	9.17223			0.438767
$438$		0			0
$439$	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	$-0.437358\pi$
$443$	8.23073			0.391054			0.195527	+	0.980698i	$0.437358\pi$
$444$		0			0
$445$	−54.2498			−2.57169
$446$	−28.7988	+	49.8810i	−1.36366	+	2.36193i
$447$		0			0
$448$		0			0
$449$	−5.64474			−0.266392			−0.133196	−	0.991090i	$-0.542524\pi$
$449$	−5.64474			−0.266392			−0.133196	+	0.991090i	$0.542524\pi$
$450$		0			0
$451$	−1.52692	+	2.64471i	−0.0718999	+	0.124534i
$452$	−28.2776	−	48.9783i	−1.33007	−	2.30374i
$453$		0			0
$454$	7.52716	+	13.0374i	0.353267	+	0.611876i
$455$		0			0
$456$		0			0
$457$	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
$459$		0			0
$460$	34.4628	+	59.6913i	1.60683	+	2.78312i
$461$	−3.88831	+	6.73475i	−0.181097	+	0.313669i	−0.942254	−	0.334898i	$-0.891298\pi$
$461$	−3.88831	+	6.73475i	−0.181097	+	0.313669i	0.761158	+	0.648567i	$0.224631\pi$
$462$		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
$465$		0			0
$466$	16.2989	+	28.2306i	0.755033	+	1.30776i
$467$	−6.88272	−	11.9212i	−0.318494	−	0.551648i	0.661680	−	0.749787i	$-0.269844\pi$
$467$	−6.88272	−	11.9212i	−0.318494	−	0.551648i	−0.980174	+	0.198138i	$0.936511\pi$
$468$		0			0
$469$		0			0
$470$	28.4253	−	49.2340i	1.31116	−	2.27100i
$471$		0			0
$472$	30.9228			1.42334
$473$	0.945916			0.0434933
$474$		0			0
$475$	8.27052	−	14.3250i	0.379477	−	0.657274i
$476$		0			0
$477$		0			0
$478$	−23.8530	−	41.3146i	−1.09101	−	1.88969i
$479$	4.35588	+	7.54461i	0.199025	+	0.344722i	0.948213	−	0.317636i	$-0.102889\pi$
$479$	4.35588	+	7.54461i	0.199025	+	0.344722i	−0.749187	+	0.662358i	$0.769556\pi$
$480$		0			0
$481$	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
$486$		0			0
$487$	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
$489$		0			0
$490$		0			0
$491$	1.02344	+	1.77266i	0.0461874	+	0.0799989i	0.888195	−	0.459467i	$-0.151960\pi$
$491$	1.02344	+	1.77266i	0.0461874	+	0.0799989i	−0.842007	+	0.539466i	$0.818626\pi$
$492$		0			0
$493$	−18.5679	−	32.1606i	−0.836257	−	1.44844i
$494$	1.18190	−	2.04712i	0.0531763	−	0.0921041i
$495$		0			0
$496$	30.4097			1.36544
$497$		0			0
$498$		0			0
$499$	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
$501$		0			0
$502$	−37.1358			−1.65745
$503$	−5.11846			−0.228221			−0.114111	−	0.993468i	$-0.536402\pi$
$503$	−5.11846			−0.228221			−0.114111	+	0.993468i	$0.536402\pi$
$504$		0			0
$505$	−31.8683			−1.41812
$506$	−4.64766			−0.206614
$507$		0			0
$508$	−63.0157			−2.79587
$509$	−14.7636	+	25.5713i	−0.654386	+	1.13343i	0.327662	+	0.944795i	$0.393739\pi$
$509$	−14.7636	+	25.5713i	−0.654386	+	1.13343i	−0.982047	+	0.188634i	$0.939594\pi$
$510$		0			0
$511$		0			0
$512$	41.4078			1.82998
$513$		0			0
$514$	9.48751	−	16.4328i	0.418476	−	0.724822i
$515$	−14.6819	−	25.4298i	−0.646962	−	1.12057i
$516$		0			0
$517$	1.28352	+	2.22313i	0.0564493	+	0.0977730i
$518$		0			0
$519$		0			0
$520$	9.00000			0.394676
$521$	0.532351	−	0.922058i	0.0233227	−	0.0403961i	−0.854128	−	0.520062i	$-0.825909\pi$
$521$	0.532351	−	0.922058i	0.0233227	−	0.0403961i	0.877451	+	0.479666i	$0.159242\pi$
$522$		0			0
$523$	−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
$528$		0			0
$529$	0.699612	+	1.21176i	0.0304179	+	0.0526853i
$530$	16.0603	+	27.8173i	0.697615	+	1.20830i
$531$		0			0
$532$		0			0
$533$	−1.82889	+	3.16774i	−0.0792181	+	0.137210i
$534$		0			0
$535$	−46.9771			−2.03100
$536$	−18.1986			−0.786061
$537$		0			0
$538$	25.5286	−	44.2168i	1.10062	−	1.90632i
$539$		0			0
$540$		0			0
$541$	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
$543$		0			0
$544$	−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
$549$		0			0
$550$	−4.19076	+	7.25860i	−0.178694	+	0.309508i
$551$	15.0928			0.642974
$552$		0			0
$553$		0			0
$554$	21.1139	+	36.5704i	0.897044	+	1.55373i
$555$		0			0
$556$	38.5165	+	66.7126i	1.63346	+	2.82924i
$557$	−15.0402	+	26.0503i	−0.637272	+	1.10379i	0.348756	+	0.937213i	$0.386604\pi$
$557$	−15.0402	+	26.0503i	−0.637272	+	1.10379i	−0.986029	+	0.166575i	$0.946729\pi$
$558$		0			0
$559$	1.13298			0.0479202
$560$		0			0
$561$		0			0
$562$	−11.6170	+	20.1213i	−0.490035	+	0.848765i
$563$	−19.6212			−0.826935			−0.413468	−	0.910519i	$-0.635683\pi$
$563$	−19.6212			−0.826935			−0.413468	+	0.910519i	$0.635683\pi$
$564$		0			0
$565$	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	$-0.490829\pi$
$569$	1.37432			0.0576144			0.0288072	+	0.999585i	$0.490829\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$		0			0
$575$	−38.9545			−1.62451
$576$		0			0
$577$	−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
$579$		0			0
$580$	56.7080	+	98.2211i	2.35467	+	4.07841i
$581$		0			0
$582$		0			0
$583$	−1.45038			−0.0600687
$584$	4.98715	−	8.63800i	0.206370	−	0.357443i
$585$		0			0
$586$	−4.58005	−	7.93288i	−0.189200	−	0.327704i
$587$	−3.75700	+	6.50731i	−0.155068	+	0.268585i	−0.933084	−	0.359659i	$-0.882893\pi$
$587$	−3.75700	+	6.50731i	−0.155068	+	0.268585i	0.778016	+	0.628245i	$0.216226\pi$
$588$		0			0
$589$	6.93414	+	12.0103i	0.285716	+	0.494875i
$590$	−27.5349	+	47.6919i	−1.13359	+	1.96344i
$591$		0			0
$592$	−5.03590	−	8.72243i	−0.206974	−	0.358490i
$593$	−17.7904	−	30.8139i	−0.730565	−	1.26538i	−0.956642	−	0.291266i	$-0.905924\pi$
$593$	−17.7904	−	30.8139i	−0.730565	−	1.26538i	0.226077	−	0.974109i	$-0.427410\pi$
$594$		0			0
$595$		0			0
$596$	−19.6659	+	34.0623i	−0.805545	+	1.39524i
$597$		0			0
$598$	−5.56681			−0.227644
$599$	11.4821			0.469146			0.234573	−	0.972099i	$-0.424631\pi$
$599$	11.4821			0.469146			0.234573	+	0.972099i	$0.424631\pi$
$600$		0			0
$601$	−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			0
$604$	26.0167	+	45.0623i	1.05861	+	1.83356i
$605$	19.8173	+	34.3246i	0.805688	+	1.39549i
$606$		0			0
$607$	−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
$612$		0			0
$613$	−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
$615$		0			0
$616$		0			0
$617$	−12.7427	−	22.0710i	−0.513002	−	0.888546i	−0.999886	−	0.0150791i	$-0.995200\pi$
$617$	−12.7427	−	22.0710i	−0.513002	−	0.888546i	0.486884	−	0.873466i	$-0.338133\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$	25.6748			1.02947
$623$		0			0
$624$		0			0
$625$	−1.67111	+	2.89444i	−0.0668443	+	0.115778i
$626$	−1.52517			−0.0609580
$627$		0			0
$628$	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
$633$		0			0
$634$	25.2163			1.00147
$635$	28.4301	−	49.2424i	1.12822	−	1.95413i
$636$		0			0
$637$		0			0
$638$	−7.64766			−0.302774
$639$		0			0
$640$	−34.9496	+	60.5344i	−1.38150	+	2.39283i
$641$	5.73025	+	9.92509i	0.226331	+	0.392017i	0.956718	−	0.291016i	$-0.0939934\pi$
$641$	5.73025	+	9.92509i	0.226331	+	0.392017i	−0.730387	+	0.683034i	$0.760660\pi$
$642$		0			0
$643$	−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
$645$		0			0
$646$	−23.5792			−0.927711
$647$	−12.6720	+	21.9485i	−0.498186	+	0.862883i	−0.999998	−	0.00209358i	$-0.999334\pi$
$647$	−12.6720	+	21.9485i	−0.498186	+	0.862883i	0.501812	+	0.864977i	$0.332667\pi$
$648$		0			0
$649$	−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	−0.694716	−	0.719284i	$-0.744470\pi$
$653$	7.04163	−	12.1965i	0.275560	−	0.477284i	0.970276	+	0.242000i	$0.0778033\pi$
$654$		0			0
$655$	−15.5723	−	26.9720i	−0.608459	−	1.05388i
$656$	16.2581	+	28.1599i	0.634774	+	1.09946i
$657$		0			0
$658$		0			0
$659$	19.0854	−	33.0569i	0.743462	−	1.28771i	−0.207449	−	0.978246i	$-0.566516\pi$
$659$	19.0854	−	33.0569i	0.743462	−	1.28771i	0.950910	−	0.309467i	$-0.100151\pi$
$660$		0			0
$661$	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
$663$		0			0
$664$	−30.7591	+	53.2764i	−1.19369	+	2.06752i
$665$		0			0
$666$		0			0
$667$	−17.7719	−	30.7818i	−0.688130	−	1.19188i
$668$	7.01403	+	12.1487i	0.271381	+	0.470046i
$669$		0			0
$670$	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
$675$		0			0
$676$	25.8712	−	44.8102i	0.995046	−	1.72347i
$677$	21.1464			0.812721			0.406361	−	0.913713i	$-0.366798\pi$
$677$	21.1464			0.812721			0.406361	+	0.913713i	$0.366798\pi$
$678$		0			0
$679$		0			0
$680$	−44.8879	−	77.7482i	−1.72137	−	2.98151i
$681$		0			0
$682$	−3.51360	−	6.08573i	−0.134543	−	0.233035i
$683$	17.3858	−	30.1131i	0.665249	−	1.15224i	−0.313969	−	0.949433i	$-0.601659\pi$
$683$	17.3858	−	30.1131i	0.665249	−	1.15224i	0.979218	−	0.202811i	$-0.0650078\pi$
$684$		0			0
$685$	−1.37998			−0.0527264
$686$		0			0
$687$		0			0
$688$	5.03590	−	8.72243i	0.191992	−	0.332539i
$689$	−1.73722			−0.0661827
$690$		0			0
$691$	−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
$696$		0			0
$697$	36.4868			1.38203
$698$	25.8044	−	44.6945i	0.976710	−	1.69171i
$699$		0			0
$700$		0			0
$701$	48.6050			1.83579			0.917894	−	0.396826i	$-0.129889\pi$
$701$	48.6050			1.83579			0.917894	+	0.396826i	$0.129889\pi$
$702$		0			0
$703$	2.29661	−	3.97784i	0.0866182	−	0.150027i
$704$	−1.48901	−	2.57904i	−0.0561192	−	0.0972012i
$705$		0			0
$706$	18.1651	+	31.4629i	0.683654	+	1.18412i
$707$		0			0
$708$		0			0
$709$	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
$711$		0			0
$712$	−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
$717$		0			0
$718$	−8.87266	−	15.3679i	−0.331125	−	0.573525i
$719$	−24.1408	−	41.8131i	−0.900299	−	1.55936i	−0.827106	−	0.562047i	$-0.810014\pi$
$719$	−24.1408	−	41.8131i	−0.900299	−	1.55936i	−0.0731939	−	0.997318i	$-0.523319\pi$
$720$		0			0
$721$		0			0
$722$	−18.5833	+	32.1872i	−0.691597	+	1.19788i
$723$		0			0
$724$	48.4375			1.80016
$725$	−64.0990			−2.38058
$726$		0			0
$727$	−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
$729$		0			0
$730$	8.88151	+	15.3832i	0.328720	+	0.569359i
$731$	−5.65082	−	9.78750i	−0.209003	−	0.362004i
$732$		0			0
$733$	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
$738$		0			0
$739$	−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			0
$742$		0			0
$743$	5.26089	+	9.11213i	0.193003	+	0.334292i	0.946244	−	0.323453i	$-0.104844\pi$
$743$	5.26089	+	9.11213i	0.193003	+	0.334292i	−0.753241	+	0.657745i	$0.771510\pi$
$744$		0			0
$745$	−17.7449	−	30.7350i	−0.650121	−	1.12604i
$746$	−0.668971	+	1.15869i	−0.0244928	+	0.0424227i
$747$		0			0
$748$	8.00079			0.292538
$749$		0			0
$750$		0			0
$751$	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
$753$		0			0
$754$	−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
$759$		0			0
$760$	36.4868			1.32351
$761$	−13.8302	+	23.9547i	−0.501345	+	0.868355i	0.498654	+	0.866801i	$0.333828\pi$
$761$	−13.8302	+	23.9547i	−0.501345	+	0.868355i	−0.999999	+	0.00155404i	$0.999505\pi$
$762$		0			0
$763$		0			0
$764$	−37.0554			−1.34062
$765$		0			0
$766$	−43.9371	+	76.1013i	−1.58751	+	2.74965i
$767$	−1.48920	−	2.57938i	−0.0537720	−	0.0931359i
$768$		0			0
$769$	−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
$771$		0			0
$772$	68.6883			2.47215
$773$	14.2978	−	24.7645i	0.514256	−	0.890717i	−0.485607	−	0.874177i	$-0.661401\pi$
$773$	14.2978	−	24.7645i	0.514256	−	0.890717i	0.999863	−	0.0165403i	$-0.00526518\pi$
$774$		0			0
$775$	−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
$780$		0			0
$781$	−1.71926	−	2.97785i	−0.0615200	−	0.106556i
$782$	27.7647	+	48.0899i	0.992864	+	1.71969i
$783$		0			0
$784$		0			0
$785$	−38.3157	+	66.3647i	−1.36754	+	2.36866i
$786$		0			0
$787$	−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
$789$		0			0
$790$	36.7330	−	63.6235i	1.30690	−	2.26362i
$791$		0			0
$792$		0			0
$793$	−1.95379	−	3.38406i	−0.0693810	−	0.120171i
$794$	−14.6988	−	25.4591i	−0.521642	−	0.903511i
$795$		0			0
$796$	−20.2183	+	35.0192i	−0.716620	+	1.24122i
$797$	18.4558	+	31.9664i	0.653739	+	1.13231i	0.982208	+	0.187795i	$0.0601339\pi$
$797$	18.4558	+	31.9664i	0.653739	+	1.13231i	−0.328469	+	0.944515i	$0.606533\pi$
$798$		0			0
$799$	15.3353	−	26.5615i	0.542524	−	0.939679i
$800$	2.26089	+	3.91598i	0.0799346	+	0.138451i
$801$		0			0
$802$	−39.8068	+	68.9474i	−1.40563	+	2.43462i
$803$	−0.802077			−0.0283047
$804$		0			0
$805$		0			0
$806$	−4.20847	−	7.28928i	−0.148237	−	0.256754i
$807$		0			0
$808$	−22.0150	−	38.1311i	−0.774484	−	1.34145i
$809$	23.8444	−	41.2996i	0.838323	−	1.45202i	−0.0529735	−	0.998596i	$-0.516870\pi$
$809$	23.8444	−	41.2996i	0.838323	−	1.45202i	0.891296	−	0.453422i	$-0.149797\pi$
$810$		0			0
$811$	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
$813$		0			0
$814$	−1.16372	+	2.01561i	−0.0407882	+	0.0706472i
$815$	−40.8324			−1.43030
$816$		0			0
$817$	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	$-0.259730\pi$
$821$	39.2642			1.37033			0.685165	+	0.728388i	$0.259730\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$		0			0
$827$	28.9286			1.00595			0.502973	−	0.864302i	$-0.332240\pi$
$827$	28.9286			1.00595			0.502973	+	0.864302i	$0.332240\pi$
$828$		0			0
$829$	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
$831$		0			0
$832$	−1.78348	−	3.08908i	−0.0618312	−	0.107095i
$833$		0			0
$834$		0			0
$835$	−12.6578			−0.438041
$836$	−1.62584	+	2.81604i	−0.0562310	+	0.0973949i
$837$		0			0
$838$	21.2716	+	36.8435i	0.734816	+	1.27274i
$839$	19.0206	−	32.9446i	0.656663	−	1.13737i	−0.324811	−	0.945779i	$-0.605301\pi$
$839$	19.0206	−	32.9446i	0.656663	−	1.13737i	0.981474	−	0.191595i	$-0.0613659\pi$
$840$		0			0
$841$	−14.7434	−	25.5363i	−0.508392	−	0.880561i
$842$	22.8837	−	39.6356i	0.788623	−	1.36593i
$843$		0			0
$844$	−9.91595	−	17.1749i	−0.341321	−	0.591185i
$845$	23.3441	+	40.4331i	0.803060	+	1.39094i
$846$		0			0
$847$		0			0
$848$	−7.72159	+	13.3742i	−0.265161	+	0.459272i
$849$		0			0
$850$	100.141			3.43480
$851$	−10.8171			−0.370806
$852$		0			0
$853$	−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			0
$856$	−32.4523	−	56.2091i	−1.10920	−	1.92119i
$857$	13.3680	+	23.1541i	0.456642	+	0.790928i	0.998781	−	0.0493613i	$-0.0157186\pi$
$857$	13.3680	+	23.1541i	0.456642	+	0.790928i	−0.542139	+	0.840289i	$0.682385\pi$
$858$		0			0
$859$	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	0.777615	−	0.628741i	$-0.216429\pi$
$863$	−4.57393	−	7.92228i	−0.155698	−	0.269677i	−0.933313	+	0.359064i	$0.883096\pi$
$864$		0			0
$865$	−11.0723	+	19.1777i	−0.376469	+	0.652063i
$866$	−99.4946			−3.38097
$867$		0			0
$868$		0			0
$869$	1.65865	+	2.87287i	0.0562660	+	0.0974555i
$870$		0			0
$871$	0.876423	+	1.51801i	0.0296964	+	0.0514358i
$872$	6.57227	−	11.3835i	0.222565	−	0.385494i
$873$		0			0
$874$	−22.5683			−0.763385
$875$		0			0
$876$		0			0
$877$	−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
$879$		0			0
$880$	−6.43367			−0.216879
$881$	−15.3696			−0.517815			−0.258907	−	0.965902i	$-0.583362\pi$
$881$	−15.3696			−0.517815			−0.258907	+	0.965902i	$0.583362\pi$
$882$		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
$885$		0			0
$886$	−20.2518			−0.680371
$887$	−9.38252	+	16.2510i	−0.315034	+	0.545655i	−0.979445	−	0.201712i	$-0.935349\pi$
$887$	−9.38252	+	16.2510i	−0.315034	+	0.545655i	0.664410	+	0.747368i	$0.268683\pi$
$888$		0			0
$889$		0			0
$890$	133.482			4.47432
$891$		0			0
$892$	47.4507	−	82.1870i	1.58877	−	2.75183i
$893$	6.23258	+	10.7952i	0.208565	+	0.361246i
$894$		0			0
$895$	16.7047	+	28.9335i	0.558378	+	0.967139i
$896$		0			0
$897$		0			0
$898$	13.8889			0.463479
$899$	26.8708	−	46.5416i	0.896192	−	1.55225i
$900$		0			0
$901$	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
$906$		0			0
$907$	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
$909$		0			0
$910$		0			0
$911$	8.73764	−	15.1340i	0.289491	−	0.501413i	−0.684197	−	0.729297i	$-0.739847\pi$
$911$	8.73764	−	15.1340i	0.289491	−	0.501413i	0.973688	+	0.227884i	$0.0731806\pi$
$912$		0			0
$913$	4.94695			0.163720
$914$	−12.4720			−0.412536
$915$		0			0
$916$	−2.96027	+	5.12734i	−0.0978101	+	0.169412i
$917$		0			0
$918$		0			0
$919$	−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
$921$		0			0
$922$	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
$927$		0			0
$928$	−2.06294	+	3.57311i	−0.0677193	+	0.117293i
$929$	−48.4111			−1.58832			−0.794159	−	0.607710i	$-0.792088\pi$
$929$	−48.4111			−1.58832			−0.794159	+	0.607710i	$0.792088\pi$
$930$		0			0
$931$		0			0
$932$	−26.8551	−	46.5145i	−0.879670	−	1.52363i
$933$		0			0
$934$	16.9350	+	29.3322i	0.554129	+	0.959780i
$935$	−3.60963	+	6.25206i	−0.118048	+	0.204464i
$936$		0			0
$937$	−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			0
$940$	−46.8353	+	81.1211i	−1.52760	+	2.64588i
$941$	49.9505			1.62834			0.814170	−	0.580627i	$-0.197192\pi$
$941$	49.9505			1.62834			0.814170	+	0.580627i	$0.197192\pi$
$942$		0			0
$943$	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	$-0.592919\pi$
$947$	−17.7123			−0.575571			−0.287786	+	0.957695i	$0.592919\pi$
$948$		0			0
$949$	−0.960699			−0.0311856
$950$	−20.3496	+	35.2466i	−0.660230	+	1.14355i
$951$		0			0
$952$		0			0
$953$	−38.0229			−1.23168			−0.615842	−	0.787870i	$-0.711184\pi$
$953$	−38.0229			−1.23168			−0.615842	+	0.787870i	$0.711184\pi$
$954$		0			0
$955$	16.7179	−	28.9563i	0.540979	−	0.937002i
$956$	39.3017	+	68.0726i	1.27111	+	2.20163i
$957$		0			0
$958$	−10.7177	−	18.5635i	−0.346272	−	0.599761i
$959$		0			0
$960$		0			0
$961$	18.3815			0.592952
$962$	−1.39386	+	2.41423i	−0.0449398	+	0.0778380i
$963$		0			0
$964$	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
$969$		0			0
$970$	−42.6972	−	73.9537i	−1.37092	−	2.37451i
$971$	−7.28376	−	12.6158i	−0.233747	−	0.404862i	0.725161	−	0.688580i	$-0.241765\pi$
$971$	−7.28376	−	12.6158i	−0.233747	−	0.404862i	−0.958908	+	0.283718i	$0.908432\pi$
$972$		0			0
$973$		0			0
$974$	−22.1893	+	38.4330i	−0.710991	+	1.23147i
$975$		0			0
$976$	−34.7368			−1.11190
$977$	47.8797			1.53181			0.765904	−	0.642955i	$-0.222292\pi$
$977$	47.8797			1.53181			0.765904	+	0.642955i	$0.222292\pi$
$978$		0			0
$979$	−3.01364	+	5.21978i	−0.0963163	+	0.166825i
$980$		0			0
$981$		0			0
$982$	−2.51819	−	4.36163i	−0.0803586	−	0.139185i
$983$	−22.2128	−	38.4737i	−0.708479	−	1.22712i	−0.965421	−	0.260695i	$-0.916048\pi$
$983$	−22.2128	−	38.4737i	−0.708479	−	1.22712i	0.256942	−	0.966427i	$-0.417285\pi$
$984$		0			0
$985$	−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			0
$991$	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
$993$		0			0
$994$		0			0
$995$	−18.2434	−	31.5985i	−0.578354	−	1.00174i
$996$		0			0
$997$	−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
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.1	✓	12	63.59	even	6
441.2.f.g.148.2	yes	12	63.32	odd	6
441.2.f.g.295.1	yes	12	21.17	even	6
441.2.f.g.295.2	yes	12	21.11	odd	6
441.2.g.g.67.1		12	9.5	odd	6
441.2.g.g.67.2		12	63.41	even	6
441.2.g.g.79.1		12	21.2	odd	6
441.2.g.g.79.2		12	21.5	even	6
441.2.h.g.214.5		12	3.2	odd	2
441.2.h.g.214.6		12	21.20	even	2
441.2.h.g.373.5		12	63.23	odd	6
441.2.h.g.373.6		12	63.5	even	6
1323.2.f.g.442.5		12	63.4	even	3
1323.2.f.g.442.6		12	63.31	odd	6
1323.2.f.g.883.5		12	7.4	even	3
1323.2.f.g.883.6		12	7.3	odd	6
1323.2.g.g.361.5		12	63.13	odd	6
1323.2.g.g.361.6		12	9.4	even	3
1323.2.g.g.667.5		12	7.5	odd	6
1323.2.g.g.667.6		12	7.2	even	3
1323.2.h.g.226.1		12	63.58	even	3	inner
1323.2.h.g.226.2		12	63.40	odd	6	inner
1323.2.h.g.802.1		12	1.1	even	1	trivial
1323.2.h.g.802.2		12	7.6	odd	2	inner
3969.2.a.bd.1.1		6	63.52	odd	6
3969.2.a.bd.1.2		6	63.25	even	3
3969.2.a.be.1.5		6	63.11	odd	6
3969.2.a.be.1.6		6	63.38	even	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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.46050 q^{2} +4.05408 q^{4} +(-1.82904 + 3.16799i) q^{5} -5.05408 q^{8} +O(q^{10})\)	\(q-2.46050 q^{2} +4.05408 q^{4} +(-1.82904 + 3.16799i) q^{5} -5.05408 q^{8} +(4.50036 - 7.79485i) q^{10} +(0.203210 + 0.351971i) q^{11} +(0.243398 + 0.421578i) q^{13} +4.32743 q^{16} +(2.42792 - 4.20528i) q^{17} +(0.986757 + 1.70911i) q^{19} +(-7.41507 + 12.8433i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(2.32383 - 4.02499i) q^{23} +(-4.19076 - 7.25860i) q^{25} +(-0.598883 - 1.03729i) q^{26} +(3.82383 - 6.62307i) q^{29} +7.02720 q^{31} -0.539495 q^{32} +(-5.97391 + 10.3471i) q^{34} +(-1.16372 - 2.01561i) q^{37} +(-2.42792 - 4.20528i) q^{38} +(9.24411 - 16.0113i) q^{40} +(3.75700 + 6.50731i) q^{41} +(1.16372 - 2.01561i) q^{43} +(0.823832 + 1.42692i) q^{44} +(-5.71780 + 9.90352i) q^{46} +6.31623 q^{47} +(10.3114 + 17.8598i) q^{50} +(0.986757 + 1.70911i) q^{52} +(-1.78434 + 3.09056i) q^{53} -1.48672 q^{55} +(-9.40856 + 16.2961i) q^{58} -6.11839 q^{59} -8.02712 q^{61} -17.2905 q^{62} -7.32743 q^{64} -1.78074 q^{65} +3.60078 q^{67} +(9.84299 - 17.0486i) q^{68} -8.46050 q^{71} +(-0.986757 + 1.70911i) q^{73} +(2.86333 + 4.95943i) q^{74} +(4.00040 + 6.92889i) q^{76} +8.16225 q^{79} +(-7.91503 + 13.7092i) q^{80} +(-9.24411 - 16.0113i) q^{82} +(6.08600 - 10.5413i) q^{83} +(8.88151 + 15.3832i) q^{85} +(-2.86333 + 4.95943i) q^{86} +(-1.02704 - 1.77889i) q^{88} +(7.41507 + 12.8433i) q^{89} +(9.42101 - 16.3177i) q^{92} -15.5411 q^{94} -7.21926 q^{95} +(4.74375 - 8.21642i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 + 12 * q^4 - 24 * q^8	\( 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8} + 8 q^{11} + 12 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} - 32 q^{32} + 6 q^{37} - 6 q^{43} - 14 q^{44} - 12 q^{46} + 56 q^{50} + 28 q^{53} - 18 q^{58} - 48 q^{64} + 12 q^{65} - 76 q^{71} + 36 q^{74} - 12 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} - 120 q^{95}+O(q^{100}) \) 12 * q - 4 * q^2 + 12 * q^4 - 24 * q^8 + 8 * q^11 + 12 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 - 32 * q^32 + 6 * q^37 - 6 * q^43 - 14 * q^44 - 12 * q^46 + 56 * q^50 + 28 * q^53 - 18 * q^58 - 48 * q^64 + 12 * q^65 - 76 * q^71 + 36 * q^74 - 12 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 - 120 * q^95

Introduction

L-functions

Modular forms

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Database

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