LMFDB - Embedded newform 1323.2.g.g.361.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(361,1323)]

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, 4]))

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

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

chi := DirichletCharacter("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.g (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:	$\Z[a_1, \ldots, a_{5}]$
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			361.6
Root			$-1.82904 + 1.05600i$ of defining polynomial
Character	$\chi$	$=$	1323.361
Dual form			1323.2.g.g.667.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23025 - 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} +3.65808 q^{5} -5.05408 q^{8} +O(q^{10})$	\(q+(1.23025 - 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} +3.65808 q^{5} -5.05408 q^{8} +(4.50036 - 7.79485i) q^{10} -0.406421 q^{11} +(0.243398 - 0.421578i) q^{13} +(-2.16372 + 3.74766i) q^{16} +(2.42792 - 4.20528i) q^{17} +(0.986757 + 1.70911i) q^{19} +(-7.41507 - 12.8433i) q^{20} +(-0.500000 + 0.866025i) q^{22} -4.64766 q^{23} +8.38151 q^{25} +(-0.598883 - 1.03729i) q^{26} +(3.82383 + 6.62307i) q^{29} +(-3.51360 - 6.08573i) q^{31} +(0.269748 + 0.467216i) q^{32} +(-5.97391 - 10.3471i) q^{34} +(-1.16372 - 2.01561i) q^{37} +4.85584 q^{38} -18.4882 q^{40} +(3.75700 - 6.50731i) q^{41} +(1.16372 + 2.01561i) q^{43} +(0.823832 + 1.42692i) q^{44} +(-5.71780 + 9.90352i) q^{46} +(-3.15811 + 5.47002i) q^{47} +(10.3114 - 17.8598i) q^{50} -1.97351 q^{52} +(-1.78434 + 3.09056i) q^{53} -1.48672 q^{55} +18.8171 q^{58} +(3.05919 + 5.29868i) q^{59} +(4.01356 - 6.95169i) q^{61} -17.2905 q^{62} -7.32743 q^{64} +(0.890369 - 1.54216i) q^{65} +(-1.80039 - 3.11836i) q^{67} -19.6860 q^{68} -8.46050 q^{71} +(-0.986757 + 1.70911i) q^{73} -5.72665 q^{74} +(4.00040 - 6.92889i) q^{76} +(-4.08113 + 7.06872i) q^{79} +(-7.91503 + 13.7092i) q^{80} +(-9.24411 - 16.0113i) q^{82} +(6.08600 + 10.5413i) q^{83} +(8.88151 - 15.3832i) q^{85} +5.72665 q^{86} +2.05408 q^{88} +(7.41507 + 12.8433i) q^{89} +(9.42101 + 16.3177i) q^{92} +(7.77056 + 13.4590i) q^{94} +(3.60963 + 6.25206i) q^{95} +(4.74375 + 8.21642i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8	$ 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8} - 16 q^{11} - 6 q^{16} - 6 q^{22} - 8 q^{23} + 24 q^{25} + 22 q^{29} + 16 q^{32} + 6 q^{37} - 6 q^{43} - 14 q^{44} - 12 q^{46} + 56 q^{50} + 28 q^{53} + 36 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} - 72 q^{74} + 6 q^{79} + 30 q^{85} + 72 q^{86} - 12 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) $ 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 - 16 * q^11 - 6 * q^16 - 6 * q^22 - 8 * q^23 + 24 * q^25 + 22 * q^29 + 16 * q^32 + 6 * q^37 - 6 * q^43 - 14 * q^44 - 12 * q^46 + 56 * q^50 + 28 * q^53 + 36 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 - 72 * q^74 + 6 * q^79 + 30 * q^85 + 72 * q^86 - 12 * q^88 + 62 * q^92 + 60 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.23025	−	2.13086i	0.869920	−	1.50675i	0.00784213	−	0.999969i	$-0.497504\pi$
$2$	1.23025	−	2.13086i	0.869920	−	1.50675i	0.862078	−	0.506776i	$-0.169163\pi$
$3$		0			0
$3$		0			0
$4$	−2.02704	−	3.51094i	−1.01352	−	1.75547i
$5$	3.65808			1.63594			0.817970	−	0.575260i	$-0.195099\pi$
$5$	3.65808			1.63594			0.817970	+	0.575260i	$0.195099\pi$
$6$		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
$11$	−0.406421			−0.122540			−0.0612702	−	0.998121i	$-0.519515\pi$
$11$	−0.406421			−0.122540			−0.0612702	+	0.998121i	$0.519515\pi$
$12$		0			0
$13$	0.243398	−	0.421578i	0.0675065	−	0.116925i	−0.830297	−	0.557322i	$-0.811829\pi$
$13$	0.243398	−	0.421578i	0.0675065	−	0.116925i	0.897803	+	0.440397i	$0.145162\pi$
$14$		0			0
$15$		0			0
$16$	−2.16372	+	3.74766i	−0.540929	+	0.936916i
$17$	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
$23$	−4.64766			−0.969105			−0.484552	−	0.874762i	$-0.661018\pi$
$23$	−4.64766			−0.969105			−0.484552	+	0.874762i	$0.661018\pi$
$24$		0			0
$25$	8.38151			1.67630
$26$	−0.598883	−	1.03729i	−0.117451	−	0.203430i
$27$		0			0
$28$		0			0
$29$	3.82383	+	6.62307i	0.710068	+	1.22987i	0.964831	+	0.262870i	$0.0846690\pi$
$29$	3.82383	+	6.62307i	0.710068	+	1.22987i	−0.254764	+	0.967003i	$0.581998\pi$
$30$		0			0
$31$	−3.51360	−	6.08573i	−0.631061	−	1.09303i	−0.987335	−	0.158648i	$-0.949286\pi$
$31$	−3.51360	−	6.08573i	−0.631061	−	1.09303i	0.356274	−	0.934381i	$-0.384047\pi$
$32$	0.269748	+	0.467216i	0.0476851	+	0.0825930i
$33$		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	$0.894608\pi$
$38$	4.85584			0.787721
$39$		0			0
$40$	−18.4882			−2.92324
$41$	3.75700	−	6.50731i	0.586744	−	1.01627i	−0.407911	−	0.913022i	$-0.633743\pi$
$41$	3.75700	−	6.50731i	0.586744	−	1.01627i	0.994655	−	0.103249i	$-0.0329240\pi$
$42$		0			0
$43$	1.16372	+	2.01561i	0.177465	+	0.307378i	0.941012	−	0.338374i	$-0.109877\pi$
$43$	1.16372	+	2.01561i	0.177465	+	0.307378i	−0.763547	+	0.645753i	$0.776544\pi$
$44$	0.823832	+	1.42692i	0.124197	+	0.215116i
$45$		0			0
$46$	−5.71780	+	9.90352i	−0.843044	+	1.46019i
$47$	−3.15811	+	5.47002i	−0.460658	+	0.797884i	−0.998994	−	0.0448469i	$-0.985720\pi$
$47$	−3.15811	+	5.47002i	−0.460658	+	0.797884i	0.538335	+	0.842731i	$0.319053\pi$
$48$		0			0
$49$		0			0
$50$	10.3114	−	17.8598i	1.45825	−	2.52576i
$51$		0			0
$52$	−1.97351			−0.273677
$53$	−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
$58$	18.8171			2.47081
$59$	3.05919	+	5.29868i	0.398273	+	0.689829i	0.993513	−	0.113719i	$-0.0362763\pi$
$59$	3.05919	+	5.29868i	0.398273	+	0.689829i	−0.595240	+	0.803548i	$0.702943\pi$
$60$		0			0
$61$	4.01356	−	6.95169i	0.513884	−	0.890073i	−0.485987	−	0.873966i	$-0.661540\pi$
$61$	4.01356	−	6.95169i	0.513884	−	0.890073i	0.999870	−	0.0161063i	$-0.00512703\pi$
$62$	−17.2905			−2.19589
$63$		0			0
$64$	−7.32743			−0.915929
$65$	0.890369	−	1.54216i	0.110437	−	0.191282i
$66$		0			0
$67$	−1.80039	−	3.11836i	−0.219952	−	0.380969i	0.734841	−	0.678240i	$-0.237257\pi$
$67$	−1.80039	−	3.11836i	−0.219952	−	0.380969i	−0.954793	+	0.297271i	$0.903924\pi$
$68$	−19.6860			−2.38728
$69$		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	$0.203511\pi$
$74$	−5.72665			−0.665710
$75$		0			0
$76$	4.00040	−	6.92889i	0.458877	−	0.794798i
$77$		0			0
$78$		0			0
$79$	−4.08113	+	7.06872i	−0.459163	+	0.795293i	−0.998917	−	0.0465297i	$-0.985184\pi$
$79$	−4.08113	+	7.06872i	−0.459163	+	0.795293i	0.539754	+	0.841823i	$0.318517\pi$
$80$	−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	0.978456	+	0.206457i	$0.0661933\pi$
$83$	6.08600	+	10.5413i	0.668025	+	1.15705i	−0.310431	+	0.950596i	$0.600473\pi$
$84$		0			0
$85$	8.88151	−	15.3832i	0.963336	−	1.66855i
$86$	5.72665			0.617521
$87$		0			0
$88$	2.05408			0.218966
$89$	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
$94$	7.77056	+	13.4590i	0.801472	+	1.38819i
$95$	3.60963	+	6.25206i	0.370340	+	0.641448i
$96$		0			0
$97$	4.74375	+	8.21642i	0.481655	+	0.834251i	0.999778	−	0.0210547i	$-0.00670241\pi$
$97$	4.74375	+	8.21642i	0.481655	+	0.834251i	−0.518123	+	0.855306i	$0.673369\pi$
$98$		0			0
$99$		0			0
$100$	−16.9897	−	29.4270i	−1.69897	−	2.94270i
$101$	−8.71176			−0.866852			−0.433426	−	0.901189i	$-0.642696\pi$
$101$	−8.71176			−0.866852			−0.433426	+	0.901189i	$0.642696\pi$
$102$		0			0
$103$	8.02712			0.790936			0.395468	−	0.918480i	$-0.370582\pi$
$103$	8.02712			0.790936			0.395468	+	0.918480i	$0.370582\pi$
$104$	−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	$0.206417\pi$
$110$	−1.82904	+	3.16799i	−0.174392	+	0.302056i
$111$		0			0
$112$		0			0
$113$	−6.97509	+	12.0812i	−0.656162	+	1.13651i	0.325440	+	0.945563i	$0.394488\pi$
$113$	−6.97509	+	12.0812i	−0.656162	+	1.13651i	−0.981601	+	0.190942i	$0.938846\pi$
$114$		0			0
$115$	−17.0015			−1.58540
$116$	15.5021	−	26.8505i	1.43934	−	2.49301i
$117$		0			0
$118$	15.0543			1.38586
$119$		0			0
$120$		0			0
$121$	−10.8348			−0.984984
$122$	−9.87538	−	17.1047i	−0.894075	−	1.54858i
$123$		0			0
$124$	−14.2444	+	24.6721i	−1.27919	+	2.21562i
$125$	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	$0.742233\pi$
$128$	−9.55408	+	16.5482i	−0.844470	+	1.46266i
$129$		0			0
$130$	−2.19076	−	3.79450i	−0.192142	−	0.332800i
$131$	8.51392			0.743864			0.371932	−	0.928260i	$-0.378695\pi$
$131$	8.51392			0.743864			0.371932	+	0.928260i	$0.378695\pi$
$132$		0			0
$133$		0			0
$134$	−8.85973			−0.765364
$135$		0			0
$136$	−12.2709	+	21.2538i	−1.05222	+	1.82250i
$137$	−0.377242			−0.0322300			−0.0161150	−	0.999870i	$-0.505130\pi$
$137$	−0.377242			−0.0322300			−0.0161150	+	0.999870i	$0.505130\pi$
$138$		0			0
$139$	9.50067	−	16.4556i	0.805837	−	1.39575i	−0.109888	−	0.993944i	$-0.535049\pi$
$139$	9.50067	−	16.4556i	0.805837	−	1.39575i	0.915725	−	0.401806i	$-0.131617\pi$
$140$		0			0
$141$		0			0
$142$	−10.4086	+	18.0281i	−0.873467	+	1.51289i
$143$	−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
$149$	9.70175			0.794798			0.397399	−	0.917646i	$-0.369913\pi$
$149$	9.70175			0.794798			0.397399	+	0.917646i	$0.369913\pi$
$150$		0			0
$151$	−12.8348			−1.04448			−0.522242	−	0.852798i	$-0.674904\pi$
$151$	−12.8348			−1.04448			−0.522242	+	0.852798i	$0.674904\pi$
$152$	−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
$157$	−10.4743	−	18.1420i	−0.835937	−	1.44789i	−0.893265	−	0.449531i	$-0.851591\pi$
$157$	−10.4743	−	18.1420i	−0.835937	−	1.44789i	0.0573276	−	0.998355i	$-0.481742\pi$
$158$	10.0416	+	17.3926i	0.798869	+	1.38368i
$159$		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	$0.689322\pi$
$164$	−30.4624			−2.37871
$165$		0			0
$166$	29.9492			2.32451
$167$	1.73012	−	2.99665i	0.133880	−	0.231888i	−0.791289	−	0.611443i	$-0.790590\pi$
$167$	1.73012	−	2.99665i	0.133880	−	0.231888i	0.925169	+	0.379555i	$0.123923\pi$
$168$		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
$173$	−3.02680	+	5.24258i	−0.230124	+	0.398586i	−0.957844	−	0.287288i	$-0.907246\pi$
$173$	−3.02680	+	5.24258i	−0.230124	+	0.398586i	0.727721	+	0.685874i	$0.240580\pi$
$174$		0			0
$175$		0			0
$176$	0.879379	−	1.52313i	0.0662857	−	0.114810i
$177$		0			0
$178$	36.4896			2.73501
$179$	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
$184$	23.4897			1.73168
$185$	−4.25696	−	7.37327i	−0.312978	−	0.542093i
$186$		0			0
$187$	−0.986757	+	1.70911i	−0.0721588	+	0.124983i
$188$	25.6065			1.86755
$189$		0			0
$190$	17.7630			1.28867
$191$	4.57014	−	7.91571i	0.330683	−	0.572760i	−0.651963	−	0.758251i	$-0.726054\pi$
$191$	4.57014	−	7.91571i	0.330683	−	0.572760i	0.982646	+	0.185491i	$0.0593874\pi$
$192$		0			0
$193$	−8.47150	−	14.6731i	−0.609792	−	1.05619i	−0.991274	−	0.131814i	$-0.957920\pi$
$193$	−8.47150	−	14.6731i	−0.609792	−	1.05619i	0.381483	−	0.924376i	$-0.375414\pi$
$194$	23.3441			1.67601
$195$		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	$0.281685\pi$
$200$	−42.3609			−2.99537
$201$		0			0
$202$	−10.7177	+	18.5635i	−0.754092	+	1.30613i
$203$		0			0
$204$		0			0
$205$	13.7434	−	23.8042i	0.959879	−	1.66256i
$206$	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	−0.937852	−	0.347036i	$-0.887188\pi$
$211$	−2.44592	+	4.23645i	−0.168384	+	0.291649i	0.769468	+	0.638685i	$0.220521\pi$
$212$	14.4677			0.993646
$213$		0			0
$214$	31.5979			2.15998
$215$	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
$220$	3.01364	+	5.21978i	0.203179	+	0.351917i
$221$	−1.18190	−	2.04712i	−0.0795034	−	0.137704i
$222$		0			0
$223$	11.7044	+	20.2727i	0.783786	+	1.35756i	0.929722	+	0.368263i	$0.120047\pi$
$223$	11.7044	+	20.2727i	0.783786	+	1.35756i	−0.145936	+	0.989294i	$0.546619\pi$
$224$		0			0
$225$		0			0
$226$	17.1623	+	29.7259i	1.14162	+	1.97734i
$227$	6.11839			0.406092			0.203046	−	0.979169i	$-0.434916\pi$
$227$	6.11839			0.406092			0.203046	+	0.979169i	$0.434916\pi$
$228$		0			0
$229$	1.46039			0.0965052			0.0482526	−	0.998835i	$-0.484635\pi$
$229$	1.46039			0.0965052			0.0482526	+	0.998835i	$0.484635\pi$
$230$	−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
$236$	12.4022	−	21.4813i	0.807316	−	1.39831i
$237$		0			0
$238$		0			0
$239$	9.69436	−	16.7911i	0.627076	−	1.08613i	−0.361060	−	0.932543i	$-0.617585\pi$
$239$	9.69436	−	16.7911i	0.627076	−	1.08613i	0.988136	−	0.153584i	$-0.0490817\pi$
$240$		0			0
$241$	−5.05368			−0.325536			−0.162768	−	0.986664i	$-0.552042\pi$
$241$	−5.05368			−0.325536			−0.162768	+	0.986664i	$0.552042\pi$
$242$	−13.3296	+	23.0875i	−0.856857	+	1.48412i
$243$		0			0
$244$	−32.5426			−2.08333
$245$		0			0
$246$		0			0
$247$	0.960699			0.0611278
$248$	17.7580	+	30.7578i	1.12764	+	1.95312i
$249$		0			0
$250$	15.2180	−	26.3584i	0.962472	−	1.66705i
$251$	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
$254$	−19.1228	+	33.1216i	−1.19987	+	2.07823i
$255$		0			0
$256$	16.1804	+	28.0253i	1.01128	+	1.75158i
$257$	7.71184			0.481051			0.240526	−	0.970643i	$-0.422680\pi$
$257$	7.71184			0.481051			0.240526	+	0.970643i	$0.422680\pi$
$258$		0			0
$259$		0			0
$260$	−7.21926			−0.447720
$261$		0			0
$262$	10.4743	−	18.1420i	0.647102	−	1.12081i
$263$	−4.21206			−0.259727			−0.129864	−	0.991532i	$-0.541454\pi$
$263$	−4.21206			−0.259727			−0.129864	+	0.991532i	$0.541454\pi$
$264$		0			0
$265$	−6.52724	+	11.3055i	−0.400965	+	0.694492i
$266$		0			0
$267$		0			0
$268$	−7.29893	+	12.6421i	−0.445853	+	0.772240i
$269$	−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
$275$	−3.40642			−0.205415
$276$		0			0
$277$	17.1623			1.03118			0.515590	−	0.856835i	$-0.327573\pi$
$277$	17.1623			1.03118			0.515590	+	0.856835i	$0.327573\pi$
$278$	−23.3765	−	40.4892i	−1.40203	−	2.42838i
$279$		0			0
$280$		0			0
$281$	4.72140	+	8.17770i	0.281655	+	0.487841i	0.971793	−	0.235837i	$-0.0757833\pi$
$281$	4.72140	+	8.17770i	0.281655	+	0.487841i	−0.690138	+	0.723678i	$0.742450\pi$
$282$		0			0
$283$	8.43422	+	14.6085i	0.501362	+	0.868385i	0.999999	+	0.00157378i	$0.000500949\pi$
$283$	8.43422	+	14.6085i	0.501362	+	0.868385i	−0.498636	+	0.866811i	$0.666166\pi$
$284$	17.1498	+	29.7043i	1.01765	+	1.76263i
$285$		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
$290$	68.8344			4.04210
$291$		0			0
$292$	8.00079			0.468211
$293$	1.86143	−	3.22409i	0.108746	−	0.188353i	−0.806517	−	0.591211i	$-0.798650\pi$
$293$	1.86143	−	3.22409i	0.108746	−	0.188353i	0.915262	+	0.402858i	$0.131983\pi$
$294$		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
$299$	−1.13123	+	1.95935i	−0.0654209	+	0.113312i
$300$		0			0
$301$		0			0
$302$	−15.7901	+	27.3492i	−0.908617	+	1.57377i
$303$		0			0
$304$	−8.54024			−0.489817
$305$	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
$310$	−63.2498			−3.59235
$311$	5.21739	+	9.03678i	0.295851	+	0.512429i	0.975182	−	0.221403i	$-0.0710635\pi$
$311$	5.21739	+	9.03678i	0.295851	+	0.512429i	−0.679332	+	0.733831i	$0.737730\pi$
$312$		0			0
$313$	−0.309930	+	0.536815i	−0.0175183	+	0.0303426i	−0.874652	−	0.484752i	$-0.838910\pi$
$313$	−0.309930	+	0.536815i	−0.0175183	+	0.0303426i	0.857133	+	0.515095i	$0.172243\pi$
$314$	−51.5440			−2.90879
$315$		0			0
$316$	33.0905			1.86148
$317$	5.12422	−	8.87541i	0.287805	−	0.498493i	−0.685481	−	0.728091i	$-0.740408\pi$
$317$	5.12422	−	8.87541i	0.287805	−	0.498493i	0.973285	+	0.229598i	$0.0737412\pi$
$318$		0			0
$319$	−1.55408	−	2.69175i	−0.0870120	−	0.150709i
$320$	−26.8043			−1.49841
$321$		0			0
$322$		0			0
$323$	9.58307			0.533216
$324$		0			0
$325$	2.04005	−	3.53346i	0.113161	−	0.196001i
$326$	27.4648			1.52113
$327$		0			0
$328$	−18.9882	+	32.8885i	−1.04845	+	1.81596i
$329$		0			0
$330$		0			0
$331$	10.1819	−	17.6356i	0.559648	−	0.969339i	−0.437878	−	0.899035i	$-0.644270\pi$
$331$	10.1819	−	17.6356i	0.559648	−	0.969339i	0.997526	−	0.0703042i	$-0.0223970\pi$
$332$	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	−0.777695	−	0.628642i	$-0.783611\pi$
$337$	2.85594	−	4.94662i	0.155573	−	0.269460i	0.933267	+	0.359182i	$0.116944\pi$
$338$	31.4035			1.70812
$339$		0			0
$340$	−72.0128			−3.90544
$341$	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
$346$	7.44746	+	12.8994i	0.400378	+	0.693475i
$347$	4.44066	+	7.69145i	0.238387	+	0.412899i	0.960252	−	0.279136i	$-0.0900480\pi$
$347$	4.44066	+	7.69145i	0.238387	+	0.412899i	−0.721865	+	0.692034i	$0.756715\pi$
$348$		0			0
$349$	−10.4874	−	18.1648i	−0.561379	−	0.972337i	−0.997376	−	0.0723893i	$-0.976938\pi$
$349$	−10.4874	−	18.1648i	−0.561379	−	0.972337i	0.435997	−	0.899948i	$-0.356396\pi$
$350$		0			0
$351$		0			0
$352$	−0.109631	−	0.189886i	−0.00584335	−	0.0101210i
$353$	14.7654			0.785881			0.392941	−	0.919564i	$-0.371458\pi$
$353$	14.7654			0.785881			0.392941	+	0.919564i	$0.371458\pi$
$354$		0			0
$355$	−30.9492			−1.64261
$356$	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
$362$	14.6988	−	25.4591i	0.772554	−	1.33810i
$363$		0			0
$364$		0			0
$365$	−3.60963	+	6.25206i	−0.188937	+	0.327248i
$366$		0			0
$367$	−10.9742			−0.572850			−0.286425	−	0.958103i	$-0.592467\pi$
$367$	−10.9742			−0.572850			−0.286425	+	0.958103i	$0.592467\pi$
$368$	10.0562	−	17.4179i	0.524217	−	0.907970i
$369$		0			0
$370$	−20.9485			−1.08906
$371$		0			0
$372$		0			0
$373$	−0.543767			−0.0281552			−0.0140776	−	0.999901i	$-0.504481\pi$
$373$	−0.543767			−0.0281552			−0.0140776	+	0.999901i	$0.504481\pi$
$374$	2.42792	+	4.20528i	0.125545	+	0.217450i
$375$		0			0
$376$	15.9614	−	27.6459i	0.823145	−	1.42573i
$377$	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	$0.698037\pi$
$380$	14.6337	−	25.3464i	0.750695	−	1.30024i
$381$		0			0
$382$	−11.2448	−	19.4766i	−0.575336	−	0.996511i
$383$	−35.7139			−1.82489			−0.912447	−	0.409194i	$-0.865810\pi$
$383$	−35.7139			−1.82489			−0.912447	+	0.409194i	$0.865810\pi$
$384$		0			0
$385$		0			0
$386$	−41.6883			−2.12188
$387$		0			0
$388$	19.2316	−	33.3101i	0.976336	−	1.69106i
$389$	−38.6591			−1.96010			−0.980048	−	0.198761i	$-0.936308\pi$
$389$	−38.6591			−1.96010			−0.980048	+	0.198761i	$0.936308\pi$
$390$		0			0
$391$	−11.2842	+	19.5447i	−0.570664	+	0.988420i
$392$		0			0
$393$		0			0
$394$	26.2257	−	45.4242i	1.32123	−	2.28844i
$395$	−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
$401$	−32.3566			−1.61581			−0.807906	−	0.589311i	$-0.799399\pi$
$401$	−32.3566			−1.61581			−0.807906	+	0.589311i	$0.799399\pi$
$402$		0			0
$403$	−3.42082			−0.170403
$404$	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
$409$	−9.48751	−	16.4328i	−0.469127	−	0.812552i	0.530250	−	0.847841i	$-0.322098\pi$
$409$	−9.48751	−	16.4328i	−0.469127	−	0.812552i	−0.999377	+	0.0352893i	$0.988765\pi$
$410$	−33.8157	−	58.5704i	−1.67004	−	2.89259i
$411$		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
$416$	0.262624			0.0128762
$417$		0			0
$418$	−1.97351			−0.0965277
$419$	−8.64523	+	14.9740i	−0.422347	+	0.731526i	−0.996169	−	0.0874539i	$-0.972127\pi$
$419$	−8.64523	+	14.9740i	−0.422347	+	0.731526i	0.573822	+	0.818980i	$0.305460\pi$
$420$		0			0
$421$	−9.30039	−	16.1087i	−0.453273	−	0.785092i	0.545314	−	0.838232i	$-0.316410\pi$
$421$	−9.30039	−	16.1087i	−0.453273	−	0.785092i	−0.998587	+	0.0531397i	$0.983077\pi$
$422$	6.01819	+	10.4238i	0.292961	+	0.507423i
$423$		0			0
$424$	9.01819	−	15.6200i	0.437962	−	0.758572i
$425$	20.3496	−	35.2466i	0.987103	−	1.70971i
$426$		0			0
$427$		0			0
$428$	26.0313	−	45.0876i	1.25827	−	2.17939i
$429$		0			0
$430$	20.9485			1.01023
$431$	−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
$436$	10.5438			0.504955
$437$	−4.58611	−	7.94338i	−0.219384	−	0.379984i
$438$		0			0
$439$	−6.23047	+	10.7915i	−0.297364	+	0.515050i	−0.975532	−	0.219857i	$-0.929441\pi$
$439$	−6.23047	+	10.7915i	−0.297364	+	0.515050i	0.678168	+	0.734907i	$0.262774\pi$
$440$	7.51399			0.358216
$441$		0			0
$442$	−5.81616			−0.276646
$443$	−4.11537	+	7.12802i	−0.195527	+	0.338663i	−0.947073	−	0.321018i	$-0.895975\pi$
$443$	−4.11537	+	7.12802i	−0.195527	+	0.338663i	0.751546	+	0.659680i	$0.229308\pi$
$444$		0			0
$445$	27.1249	+	46.9817i	1.28584	+	2.22715i
$446$	57.5976			2.72732
$447$		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
$452$	56.5552			2.66013
$453$		0			0
$454$	7.52716	−	13.0374i	0.353267	−	0.611876i
$455$		0			0
$456$		0			0
$457$	−2.53443	+	4.38977i	−0.118556	+	0.205345i	−0.919196	−	0.393801i	$-0.871160\pi$
$457$	−2.53443	+	4.38977i	−0.118556	+	0.205345i	0.800640	+	0.599146i	$0.204493\pi$
$458$	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	0.761158	−	0.648567i	$-0.224631\pi$
$461$	−3.88831	−	6.73475i	−0.181097	−	0.313669i	−0.942254	+	0.334898i	$0.891298\pi$
$462$		0			0
$463$	4.58998	−	7.95008i	0.213314	−	0.369472i	−0.739435	−	0.673228i	$-0.764907\pi$
$463$	4.58998	−	7.95008i	0.213314	−	0.369472i	0.952750	+	0.303756i	$0.0982408\pi$
$464$	−33.0947			−1.53638
$465$		0			0
$466$	−32.5979			−1.51007
$467$	−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
$472$	−15.4614	−	26.7800i	−0.711669	−	1.23265i
$473$	−0.472958	−	0.819187i	−0.0217466	−	0.0376663i
$474$		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
$479$	−8.71176			−0.398050			−0.199025	−	0.979994i	$-0.563778\pi$
$479$	−8.71176			−0.398050			−0.199025	+	0.979994i	$0.563778\pi$
$480$		0			0
$481$	−1.13298			−0.0516597
$482$	−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	$0.0326653\pi$
$488$	−20.2849	+	35.1344i	−0.918253	+	1.59046i
$489$		0			0
$490$		0			0
$491$	1.02344	−	1.77266i	0.0461874	−	0.0799989i	−0.842007	−	0.539466i	$-0.818626\pi$
$491$	1.02344	−	1.77266i	0.0461874	−	0.0799989i	0.888195	+	0.459467i	$0.151960\pi$
$492$		0			0
$493$	37.1358			1.67251
$494$	1.18190	−	2.04712i	0.0531763	−	0.0921041i
$495$		0			0
$496$	30.4097			1.36544
$497$		0			0
$498$		0			0
$499$	−39.0875			−1.74980			−0.874899	−	0.484305i	$-0.839072\pi$
$499$	−39.0875			−1.74980			−0.874899	+	0.484305i	$0.839072\pi$
$500$	−25.0742	−	43.4297i	−1.12135	−	1.94224i
$501$		0			0
$502$	18.5679	−	32.1606i	0.828727	−	1.43540i
$503$	−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
$506$	2.32383	−	4.02499i	0.103307	−	0.178933i
$507$		0			0
$508$	31.5079	+	54.5732i	1.39794	+	2.42130i
$509$	29.5272			1.30877			0.654386	−	0.756161i	$-0.272927\pi$
$509$	29.5272			1.30877			0.654386	+	0.756161i	$0.272927\pi$
$510$		0			0
$511$		0			0
$512$	41.4078			1.82998
$513$		0			0
$514$	9.48751	−	16.4328i	0.418476	−	0.724822i
$515$	29.3638			1.29392
$516$		0			0
$517$	1.28352	−	2.22313i	0.0564493	−	0.0977730i
$518$		0			0
$519$		0			0
$520$	−4.50000	+	7.79423i	−0.197338	+	0.341800i
$521$	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
$527$	−34.1230			−1.48642
$528$		0			0
$529$	−1.39922			−0.0608358
$530$	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
$535$	23.4885	+	40.6833i	1.01550	+	1.75889i
$536$	9.09931	+	15.7605i	0.393031	+	0.680749i
$537$		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	$0.571561\pi$
$542$	−70.0970			−3.01092
$543$		0			0
$544$	2.61970			0.112319
$545$	−4.75692	+	8.23922i	−0.203764	+	0.352930i
$546$		0			0
$547$	2.97150	+	5.14678i	0.127052	+	0.220060i	0.922533	−	0.385918i	$-0.126115\pi$
$547$	2.97150	+	5.14678i	0.127052	+	0.220060i	−0.795481	+	0.605978i	$0.792782\pi$
$548$	0.764686	+	1.32448i	0.0326658	+	0.0565788i
$549$		0			0
$550$	−4.19076	+	7.25860i	−0.178694	+	0.309508i
$551$	−7.54638	+	13.0707i	−0.321487	+	0.556831i
$552$		0			0
$553$		0			0
$554$	21.1139	−	36.5704i	0.897044	−	1.55373i
$555$		0			0
$556$	−77.0331			−3.26693
$557$	−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
$562$	23.2340			0.980069
$563$	9.81060	+	16.9925i	0.413468	+	0.716147i	0.995266	−	0.0971860i	$-0.0309842\pi$
$563$	9.81060	+	16.9925i	0.413468	+	0.716147i	−0.581799	+	0.813333i	$0.697651\pi$
$564$		0			0
$565$	−25.5154	+	44.1940i	−1.07344	+	1.85926i
$566$	41.5049			1.74458
$567$		0			0
$568$	42.7601			1.79417
$569$	−0.687159	+	1.19019i	−0.0288072	+	0.0498955i	−0.880070	−	0.474845i	$-0.842504\pi$
$569$	−0.687159	+	1.19019i	−0.0288072	+	0.0498955i	0.851262	+	0.524740i	$0.175838\pi$
$570$		0			0
$571$	−8.69076	−	15.0528i	−0.363697	−	0.629941i	0.624869	−	0.780729i	$-0.285152\pi$
$571$	−8.69076	−	15.0528i	−0.363697	−	0.629941i	−0.988566	+	0.150788i	$0.951819\pi$
$572$	0.802077			0.0335365
$573$		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	$0.976255\pi$
$578$	−16.1881			−0.673337
$579$		0			0
$580$	56.7080	−	98.2211i	2.35467	−	4.07841i
$581$		0			0
$582$		0			0
$583$	0.725191	−	1.25607i	0.0300344	−	0.0520210i
$584$	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	0.778016	−	0.628245i	$-0.216226\pi$
$587$	−3.75700	−	6.50731i	−0.155068	−	0.268585i	−0.933084	+	0.359659i	$0.882893\pi$
$588$		0			0
$589$	6.93414	−	12.0103i	0.285716	−	0.494875i
$590$	55.0698			2.26719
$591$		0			0
$592$	10.0718			0.413948
$593$	−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
$598$	2.78340	+	4.82100i	0.113822	+	0.197145i
$599$	−5.74105	−	9.94379i	−0.234573	−	0.406292i	0.724576	−	0.689195i	$-0.242036\pi$
$599$	−5.74105	−	9.94379i	−0.234573	−	0.406292i	−0.959148	+	0.282903i	$0.908702\pi$
$600$		0			0
$601$	−0.190030	−	0.329142i	−0.00775150	−	0.0134260i	0.862124	−	0.506698i	$-0.169134\pi$
$601$	−0.190030	−	0.329142i	−0.00775150	−	0.0134260i	−0.869875	+	0.493272i	$0.835801\pi$
$602$		0			0
$603$		0			0
$604$	26.0167	+	45.0623i	1.05861	+	1.83356i
$605$	−39.6346			−1.61138
$606$		0			0
$607$	18.5409			0.752551			0.376275	−	0.926508i	$-0.377205\pi$
$607$	18.5409			0.752551			0.376275	+	0.926508i	$0.377205\pi$
$608$	−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	$0.213924\pi$
$614$	−37.6077	+	65.1385i	−1.51772	+	2.62877i
$615$		0			0
$616$		0			0
$617$	−12.7427	+	22.0710i	−0.513002	+	0.888546i	0.486884	+	0.873466i	$0.338133\pi$
$617$	−12.7427	+	22.0710i	−0.513002	+	0.888546i	−0.999886	+	0.0150791i	$0.995200\pi$
$618$		0			0
$619$	−32.8963			−1.32222			−0.661108	−	0.750291i	$-0.729913\pi$
$619$	−32.8963			−1.32222			−0.661108	+	0.750291i	$0.729913\pi$
$620$	−52.1072	+	90.2523i	−2.09267	+	3.62462i
$621$		0			0
$622$	25.6748			1.02947
$623$		0			0
$624$		0			0
$625$	3.34221			0.133689
$626$	0.762585	+	1.32084i	0.0304790	+	0.0527912i
$627$		0			0
$628$	−42.4636	+	73.5490i	−1.69448	+	2.93493i
$629$	−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	$0.297343\pi$
$632$	20.6264	−	35.7259i	0.820472	−	1.42110i
$633$		0			0
$634$	−12.6082	−	21.8380i	−0.500734	−	0.867297i
$635$	−56.8603			−2.25643
$636$		0			0
$637$		0			0
$638$	−7.64766			−0.302774
$639$		0			0
$640$	−34.9496	+	60.5344i	−1.38150	+	2.39283i
$641$	−11.4605			−0.452663			−0.226331	−	0.974050i	$-0.572673\pi$
$641$	−11.4605			−0.452663			−0.226331	+	0.974050i	$0.572673\pi$
$642$		0			0
$643$	−8.69078	+	15.0529i	−0.342731	+	0.593627i	−0.984939	−	0.172903i	$-0.944685\pi$
$643$	−8.69078	+	15.0529i	−0.342731	+	0.593627i	0.642208	+	0.766531i	$0.278019\pi$
$644$		0			0
$645$		0			0
$646$	11.7896	−	20.4202i	0.463855	−	0.803421i
$647$	−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
$653$	−14.0833			−0.551121			−0.275560	−	0.961284i	$-0.588863\pi$
$653$	−14.0833			−0.551121			−0.275560	+	0.961284i	$0.588863\pi$
$654$		0			0
$655$	31.1445			1.21692
$656$	16.2581	+	28.1599i	0.634774	+	1.09946i
$657$		0			0
$658$		0			0
$659$	19.0854	+	33.0569i	0.743462	+	1.28771i	0.950910	+	0.309467i	$0.100151\pi$
$659$	19.0854	+	33.0569i	0.743462	+	1.28771i	−0.207449	+	0.978246i	$0.566516\pi$
$660$		0			0
$661$	−0.176866	−	0.306341i	−0.00687930	−	0.0119153i	0.862565	−	0.505946i	$-0.168856\pi$
$661$	−0.176866	−	0.306341i	−0.00687930	−	0.0119153i	−0.869445	+	0.494031i	$0.835523\pi$
$662$	−25.0526	−	43.3924i	−0.973698	−	1.68649i
$663$		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
$668$	−14.0281			−0.542762
$669$		0			0
$670$	−32.4096			−1.25209
$671$	−1.63119	+	2.82531i	−0.0629715	+	0.109070i
$672$		0			0
$673$	10.5555	+	18.2827i	0.406886	+	0.704748i	0.994539	−	0.104365i	$-0.0332811\pi$
$673$	10.5555	+	18.2827i	0.406886	+	0.704748i	−0.587653	+	0.809113i	$0.699948\pi$
$674$	−7.02704	−	12.1712i	−0.270672	−	0.468817i
$675$		0			0
$676$	25.8712	−	44.8102i	0.995046	−	1.72347i
$677$	−10.5732	+	18.3133i	−0.406361	+	0.703837i	−0.994479	−	0.104938i	$-0.966536\pi$
$677$	−10.5732	+	18.3133i	−0.406361	+	0.703837i	0.588118	+	0.808775i	$0.299869\pi$
$678$		0			0
$679$		0			0
$680$	−44.8879	+	77.7482i	−1.72137	+	2.98151i
$681$		0			0
$682$	7.02720			0.269085
$683$	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
$688$	−10.0718			−0.383984
$689$	0.868609	+	1.50447i	0.0330914	+	0.0573159i
$690$		0			0
$691$	17.3246	−	30.0071i	0.659059	−	1.14152i	−0.321801	−	0.946807i	$-0.604288\pi$
$691$	17.3246	−	30.0071i	0.659059	−	1.14152i	0.980860	−	0.194716i	$-0.0623785\pi$
$692$	24.5418			0.932940
$693$		0			0
$694$	21.8525			0.829511
$695$	34.7542	−	60.1960i	1.31830	−	2.28336i
$696$		0			0
$697$	−18.2434	−	31.5985i	−0.691017	−	1.19688i
$698$	−51.6087			−1.95342
$699$		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
$704$	2.97802			0.112238
$705$		0			0
$706$	18.1651	−	31.4629i	0.683654	−	1.18412i
$707$		0			0
$708$		0			0
$709$	−2.05408	+	3.55778i	−0.0771428	+	0.133615i	−0.902016	−	0.431702i	$-0.857913\pi$
$709$	−2.05408	+	3.55778i	−0.0771428	+	0.133615i	0.824873	+	0.565318i	$0.191246\pi$
$710$	−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
$716$	−37.0263			−1.38374
$717$		0			0
$718$	17.7453			0.662249
$719$	−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
$724$	−24.2187	−	41.9481i	−0.900082	−	1.55899i
$725$	32.0495	+	55.5114i	1.19029	+	2.06164i
$726$		0			0
$727$	−20.5151	−	35.5332i	−0.760863	−	1.31785i	−0.942406	−	0.334470i	$-0.891443\pi$
$727$	−20.5151	−	35.5332i	−0.760863	−	1.31785i	0.181543	−	0.983383i	$-0.441891\pi$
$728$		0			0
$729$		0			0
$730$	8.88151	+	15.3832i	0.328720	+	0.569359i
$731$	11.3016			0.418006
$732$		0			0
$733$	−30.5428			−1.12812			−0.564062	−	0.825733i	$-0.690762\pi$
$733$	−30.5428			−1.12812			−0.564062	+	0.825733i	$0.690762\pi$
$734$	−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	$0.311021\pi$
$740$	−17.2581	+	29.8918i	−0.634419	+	1.09885i
$741$		0			0
$742$		0			0
$743$	5.26089	−	9.11213i	0.193003	−	0.334292i	−0.753241	−	0.657745i	$-0.771510\pi$
$743$	5.26089	−	9.11213i	0.193003	−	0.334292i	0.946244	+	0.323453i	$0.104844\pi$
$744$		0			0
$745$	35.4897			1.30024
$746$	−0.668971	+	1.15869i	−0.0244928	+	0.0424227i
$747$		0			0
$748$	8.00079			0.292538
$749$		0			0
$750$		0			0
$751$	−10.2704			−0.374773			−0.187386	−	0.982286i	$-0.560002\pi$
$751$	−10.2704			−0.374773			−0.187386	+	0.982286i	$0.560002\pi$
$752$	−13.6665	−	23.6711i	−0.498367	−	0.863197i
$753$		0			0
$754$	4.58005	−	7.93288i	0.166796	−	0.288899i
$755$	−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	$0.453329\pi$
$758$	−27.9159	+	48.3518i	−1.01395	+	1.75622i
$759$		0			0
$760$	−18.2434	−	31.5985i	−0.661757	−	1.14620i
$761$	27.6604			1.00269			0.501345	−	0.865247i	$-0.332839\pi$
$761$	27.6604			1.00269			0.501345	+	0.865247i	$0.332839\pi$
$762$		0			0
$763$		0			0
$764$	−37.0554			−1.34062
$765$		0			0
$766$	−43.9371	+	76.1013i	−1.58751	+	2.74965i
$767$	2.97841			0.107544
$768$		0			0
$769$	−16.9613	+	29.3778i	−0.611640	+	1.05939i	0.379324	+	0.925264i	$0.376157\pi$
$769$	−16.9613	+	29.3778i	−0.611640	+	1.05939i	−0.990964	+	0.134128i	$0.957177\pi$
$770$		0			0
$771$		0			0
$772$	−34.3442	+	59.4858i	−1.23607	+	2.14094i
$773$	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
$779$	14.8290			0.531303
$780$		0			0
$781$	3.43852			0.123040
$782$	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
$787$	23.0017	+	39.8402i	0.819923	+	1.42015i	0.905738	+	0.423838i	$0.139317\pi$
$787$	23.0017	+	39.8402i	0.819923	+	1.42015i	−0.0858145	+	0.996311i	$0.527349\pi$
$788$	−43.2111	−	74.8438i	−1.53933	−	2.66620i
$789$		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
$794$	29.3977			1.04328
$795$		0			0
$796$	40.4367			1.43324
$797$	18.4558	−	31.9664i	0.653739	−	1.13231i	−0.328469	−	0.944515i	$-0.606533\pi$
$797$	18.4558	−	31.9664i	0.653739	−	1.13231i	0.982208	−	0.187795i	$-0.0601339\pi$
$798$		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
$803$	0.401038	−	0.694619i	0.0141523	−	0.0245126i
$804$		0			0
$805$		0			0
$806$	−4.20847	+	7.28928i	−0.148237	+	0.256754i
$807$		0			0
$808$	44.0300			1.54897
$809$	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
$814$	2.32743			0.0815764
$815$	20.4162	+	35.3619i	0.715148	+	1.23867i
$816$		0			0
$817$	−2.29661	+	3.97784i	−0.0803481	+	0.139167i
$818$	−46.6881			−1.63241
$819$		0			0
$820$	−111.434			−3.89143
$821$	−19.6321	+	34.0038i	−0.685165	+	1.18674i	0.288220	+	0.957564i	$0.406936\pi$
$821$	−19.6321	+	34.0038i	−0.685165	+	1.18674i	−0.973385	+	0.229176i	$0.926397\pi$
$822$		0			0
$823$	−11.3815	−	19.7134i	−0.396735	−	0.687165i	0.596586	−	0.802549i	$-0.296523\pi$
$823$	−11.3815	−	19.7134i	−0.396735	−	0.687165i	−0.993321	+	0.115384i	$0.963190\pi$
$824$	−40.5697			−1.41331
$825$		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	$-0.0342172\pi$
$830$	109.557			3.80276
$831$		0			0
$832$	−1.78348	+	3.08908i	−0.0618312	+	0.107095i
$833$		0			0
$834$		0			0
$835$	6.32889	−	10.9620i	0.219020	−	0.379354i
$836$	−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	0.981474	+	0.191595i	$0.0613659\pi$
$839$	19.0206	+	32.9446i	0.656663	+	1.13737i	−0.324811	+	0.945779i	$0.605301\pi$
$840$		0			0
$841$	−14.7434	+	25.5363i	−0.508392	+	0.880561i
$842$	−45.7673			−1.57725
$843$		0			0
$844$	19.8319			0.682642
$845$	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
$850$	−50.0704	−	86.7245i	−1.71740	−	2.97463i
$851$	5.40856	+	9.36790i	0.185403	+	0.321127i
$852$		0			0
$853$	−4.90746	−	8.49996i	−0.168028	−	0.291033i	0.769698	−	0.638408i	$-0.220407\pi$
$853$	−4.90746	−	8.49996i	−0.168028	−	0.291033i	−0.937726	+	0.347374i	$0.887073\pi$
$854$		0			0
$855$		0			0
$856$	−32.4523	−	56.2091i	−1.10920	−	1.92119i
$857$	−26.7360			−0.913285			−0.456642	−	0.889650i	$-0.650948\pi$
$857$	−26.7360			−0.913285			−0.456642	+	0.889650i	$0.650948\pi$
$858$		0			0
$859$	−18.4882			−0.630810			−0.315405	−	0.948957i	$-0.602140\pi$
$859$	−18.4882			−0.630810			−0.315405	+	0.948957i	$0.602140\pi$
$860$	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
$866$	49.7473	−	86.1649i	1.69048	−	2.92800i
$867$		0			0
$868$		0			0
$869$	1.65865	−	2.87287i	0.0562660	−	0.0974555i
$870$		0			0
$871$	−1.75285			−0.0593929
$872$	6.57227	−	11.3835i	0.222565	−	0.385494i
$873$		0			0
$874$	−22.5683			−0.763385
$875$		0			0
$876$		0			0
$877$	22.6883			0.766130			0.383065	−	0.923721i	$-0.374869\pi$
$877$	22.6883			0.766130			0.383065	+	0.923721i	$0.374869\pi$
$878$	15.3301	+	26.5525i	0.517366	+	0.896104i
$879$		0			0
$880$	3.21683	−	5.57172i	0.108439	−	0.187823i
$881$	−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	$0.333817\pi$
$884$	−4.79153	+	8.29918i	−0.161157	+	0.279132i
$885$		0			0
$886$	10.1259	+	17.5385i	0.340185	+	0.589219i
$887$	18.7650			0.630069			0.315034	−	0.949080i	$-0.397984\pi$
$887$	18.7650			0.630069			0.315034	+	0.949080i	$0.397984\pi$
$888$		0			0
$889$		0			0
$890$	133.482			4.47432
$891$		0			0
$892$	47.4507	−	82.1870i	1.58877	−	2.75183i
$893$	−12.4652			−0.417131
$894$		0			0
$895$	16.7047	−	28.9335i	0.558378	−	0.967139i
$896$		0			0
$897$		0			0
$898$	−6.94445	+	12.0281i	−0.231739	+	0.401384i
$899$	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
$905$	43.7060			1.45284
$906$		0			0
$907$	−31.1082			−1.03293			−0.516465	−	0.856308i	$-0.672752\pi$
$907$	−31.1082			−1.03293			−0.516465	+	0.856308i	$0.672752\pi$
$908$	−12.4022	−	21.4813i	−0.411582	−	0.712881i
$909$		0			0
$910$		0			0
$911$	8.73764	+	15.1340i	0.289491	+	0.501413i	0.973688	−	0.227884i	$-0.0731806\pi$
$911$	8.73764	+	15.1340i	0.289491	+	0.501413i	−0.684197	+	0.729297i	$0.739847\pi$
$912$		0			0
$913$	−2.47347	−	4.28418i	−0.0818600	−	0.141786i
$914$	6.23599	+	10.8010i	0.206268	+	0.357267i
$915$		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	$-0.411706\pi$
$920$	85.9270			2.83293
$921$		0			0
$922$	−19.1344			−0.630158
$923$	−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
$929$	24.2056	−	41.9253i	0.794159	−	1.37552i	−0.129213	−	0.991617i	$-0.541245\pi$
$929$	24.2056	−	41.9253i	0.794159	−	1.37552i	0.923372	−	0.383907i	$-0.125422\pi$
$930$		0			0
$931$		0			0
$932$	−26.8551	+	46.5145i	−0.879670	+	1.52363i
$933$		0			0
$934$	−33.8699			−1.10826
$935$	−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
$940$	93.6706			3.05520
$941$	−24.9753	−	43.2584i	−0.814170	−	1.41018i	−0.909922	−	0.414779i	$-0.863859\pi$
$941$	−24.9753	−	43.2584i	−0.814170	−	1.41018i	0.0957523	−	0.995405i	$-0.469474\pi$
$942$		0			0
$943$	−17.4613	+	30.2438i	−0.568617	+	0.984873i
$944$	−26.4769			−0.861749
$945$		0			0
$946$	−2.32743			−0.0756713
$947$	8.85613	−	15.3393i	0.287786	−	0.498459i	−0.685495	−	0.728077i	$-0.740414\pi$
$947$	8.85613	−	15.3393i	0.287786	−	0.498459i	0.973281	+	0.229618i	$0.0737476\pi$
$948$		0			0
$949$	0.480350	+	0.831990i	0.0155928	+	0.0270075i
$950$	40.6993			1.32046
$951$		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
$956$	−78.6035			−2.54222
$957$		0			0
$958$	−10.7177	+	18.5635i	−0.346272	+	0.599761i
$959$		0			0
$960$		0			0
$961$	−9.19076	+	15.9189i	−0.296476	+	0.513512i
$962$	−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	−0.501346	−	0.865247i	$-0.667162\pi$
$967$	15.5064	−	26.8579i	0.498652	−	0.863691i	0.999999	+	0.00155529i	$0.000495066\pi$
$968$	54.7601			1.76006
$969$		0			0
$970$	85.3943			2.74185
$971$	−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
$976$	17.3684	+	30.0830i	0.555949	+	0.962932i
$977$	−23.9399	−	41.4651i	−0.765904	−	1.32659i	−0.939767	−	0.341815i	$-0.888958\pi$
$977$	−23.9399	−	41.4651i	−0.765904	−	1.32659i	0.173863	−	0.984770i	$-0.444375\pi$
$978$		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
$983$	44.4257			1.41696			0.708479	−	0.705732i	$-0.249382\pi$
$983$	44.4257			1.41696			0.708479	+	0.705732i	$0.249382\pi$
$984$		0			0
$985$	77.9803			2.48466
$986$	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	$-0.0631929\pi$
$992$	1.89557	−	3.28322i	0.0601844	−	0.104242i
$993$		0			0
$994$		0			0
$995$	−18.2434	+	31.5985i	−0.578354	+	1.00174i
$996$		0			0
$997$	13.0281			0.412606			0.206303	−	0.978488i	$-0.433857\pi$
$997$	13.0281			0.412606			0.206303	+	0.978488i	$0.433857\pi$
$998$	−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.g.g.361.6		12
3.2	odd	2		441.2.g.g.67.1		12
7.2	even	3		1323.2.h.g.226.1		12
7.3	odd	6		1323.2.f.g.442.6		12
7.4	even	3		1323.2.f.g.442.5		12
7.5	odd	6		1323.2.h.g.226.2		12
7.6	odd	2	inner	1323.2.g.g.361.5		12
9.2	odd	6		441.2.h.g.214.5		12
9.7	even	3		1323.2.h.g.802.1		12
21.2	odd	6		441.2.h.g.373.5		12
21.5	even	6		441.2.h.g.373.6		12
21.11	odd	6		441.2.f.g.148.2	yes	12
21.17	even	6		441.2.f.g.148.1	✓	12
21.20	even	2		441.2.g.g.67.2		12
63.2	odd	6		441.2.g.g.79.1		12
63.4	even	3		3969.2.a.bd.1.2		6
63.11	odd	6		441.2.f.g.295.2	yes	12
63.16	even	3	inner	1323.2.g.g.667.6		12
63.20	even	6		441.2.h.g.214.6		12
63.25	even	3		1323.2.f.g.883.5		12
63.31	odd	6		3969.2.a.bd.1.1		6
63.32	odd	6		3969.2.a.be.1.5		6
63.34	odd	6		1323.2.h.g.802.2		12
63.38	even	6		441.2.f.g.295.1	yes	12
63.47	even	6		441.2.g.g.79.2		12
63.52	odd	6		1323.2.f.g.883.6		12
63.59	even	6		3969.2.a.be.1.6		6
63.61	odd	6	inner	1323.2.g.g.667.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.1	✓	12	21.17	even	6
441.2.f.g.148.2	yes	12	21.11	odd	6
441.2.f.g.295.1	yes	12	63.38	even	6
441.2.f.g.295.2	yes	12	63.11	odd	6
441.2.g.g.67.1		12	3.2	odd	2
441.2.g.g.67.2		12	21.20	even	2
441.2.g.g.79.1		12	63.2	odd	6
441.2.g.g.79.2		12	63.47	even	6
441.2.h.g.214.5		12	9.2	odd	6
441.2.h.g.214.6		12	63.20	even	6
441.2.h.g.373.5		12	21.2	odd	6
441.2.h.g.373.6		12	21.5	even	6
1323.2.f.g.442.5		12	7.4	even	3
1323.2.f.g.442.6		12	7.3	odd	6
1323.2.f.g.883.5		12	63.25	even	3
1323.2.f.g.883.6		12	63.52	odd	6
1323.2.g.g.361.5		12	7.6	odd	2	inner
1323.2.g.g.361.6		12	1.1	even	1	trivial
1323.2.g.g.667.5		12	63.61	odd	6	inner
1323.2.g.g.667.6		12	63.16	even	3	inner
1323.2.h.g.226.1		12	7.2	even	3
1323.2.h.g.226.2		12	7.5	odd	6
1323.2.h.g.802.1		12	9.7	even	3
1323.2.h.g.802.2		12	63.34	odd	6
3969.2.a.bd.1.1		6	63.31	odd	6
3969.2.a.bd.1.2		6	63.4	even	3
3969.2.a.be.1.5		6	63.32	odd	6
3969.2.a.be.1.6		6	63.59	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.23025 - 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} +3.65808 q^{5} -5.05408 q^{8} +O(q^{10})\)	\(q+(1.23025 - 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} +3.65808 q^{5} -5.05408 q^{8} +(4.50036 - 7.79485i) q^{10} -0.406421 q^{11} +(0.243398 - 0.421578i) q^{13} +(-2.16372 + 3.74766i) q^{16} +(2.42792 - 4.20528i) q^{17} +(0.986757 + 1.70911i) q^{19} +(-7.41507 - 12.8433i) q^{20} +(-0.500000 + 0.866025i) q^{22} -4.64766 q^{23} +8.38151 q^{25} +(-0.598883 - 1.03729i) q^{26} +(3.82383 + 6.62307i) q^{29} +(-3.51360 - 6.08573i) q^{31} +(0.269748 + 0.467216i) q^{32} +(-5.97391 - 10.3471i) q^{34} +(-1.16372 - 2.01561i) q^{37} +4.85584 q^{38} -18.4882 q^{40} +(3.75700 - 6.50731i) q^{41} +(1.16372 + 2.01561i) q^{43} +(0.823832 + 1.42692i) q^{44} +(-5.71780 + 9.90352i) q^{46} +(-3.15811 + 5.47002i) q^{47} +(10.3114 - 17.8598i) q^{50} -1.97351 q^{52} +(-1.78434 + 3.09056i) q^{53} -1.48672 q^{55} +18.8171 q^{58} +(3.05919 + 5.29868i) q^{59} +(4.01356 - 6.95169i) q^{61} -17.2905 q^{62} -7.32743 q^{64} +(0.890369 - 1.54216i) q^{65} +(-1.80039 - 3.11836i) q^{67} -19.6860 q^{68} -8.46050 q^{71} +(-0.986757 + 1.70911i) q^{73} -5.72665 q^{74} +(4.00040 - 6.92889i) q^{76} +(-4.08113 + 7.06872i) q^{79} +(-7.91503 + 13.7092i) q^{80} +(-9.24411 - 16.0113i) q^{82} +(6.08600 + 10.5413i) q^{83} +(8.88151 - 15.3832i) q^{85} +5.72665 q^{86} +2.05408 q^{88} +(7.41507 + 12.8433i) q^{89} +(9.42101 + 16.3177i) q^{92} +(7.77056 + 13.4590i) q^{94} +(3.60963 + 6.25206i) q^{95} +(4.74375 + 8.21642i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8} - 16 q^{11} - 6 q^{16} - 6 q^{22} - 8 q^{23} + 24 q^{25} + 22 q^{29} + 16 q^{32} + 6 q^{37} - 6 q^{43} - 14 q^{44} - 12 q^{46} + 56 q^{50} + 28 q^{53} + 36 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} - 72 q^{74} + 6 q^{79} + 30 q^{85} + 72 q^{86} - 12 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 - 16 * q^11 - 6 * q^16 - 6 * q^22 - 8 * q^23 + 24 * q^25 + 22 * q^29 + 16 * q^32 + 6 * q^37 - 6 * q^43 - 14 * q^44 - 12 * q^46 + 56 * q^50 + 28 * q^53 + 36 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 - 72 * q^74 + 6 * q^79 + 30 * q^85 + 72 * q^86 - 12 * q^88 + 62 * q^92 + 60 * q^95

Introduction

L-functions

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