LMFDB - Embedded newform 243.2.e.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 + 0.0126039i$ of defining polynomial
Character	$\chi$	$=$	243.109
Dual form			243.2.e.a.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28765 + 1.08047i) q^{2} +(0.143341 - 0.812925i) q^{4} +(-1.06142 + 0.386327i) q^{5} +(-0.678777 - 3.84954i) q^{7} +(-0.987144 - 1.70978i) q^{8} +O(q^{10})$	\(q+(-1.28765 + 1.08047i) q^{2} +(0.143341 - 0.812925i) q^{4} +(-1.06142 + 0.386327i) q^{5} +(-0.678777 - 3.84954i) q^{7} +(-0.987144 - 1.70978i) q^{8} +(0.949332 - 1.64429i) q^{10} +(-1.75765 - 0.639734i) q^{11} +(-0.561203 - 0.470905i) q^{13} +(5.03334 + 4.22347i) q^{14} +(4.66984 + 1.69968i) q^{16} +(0.944822 - 1.63648i) q^{17} +(-1.37143 - 2.37538i) q^{19} +(0.161910 + 0.918235i) q^{20} +(2.95446 - 1.07534i) q^{22} +(1.01197 - 5.73916i) q^{23} +(-2.85285 + 2.39382i) q^{25} +1.23143 q^{26} -3.22668 q^{28} +(4.07531 - 3.41959i) q^{29} +(0.232793 - 1.32023i) q^{31} +(-4.13914 + 1.50652i) q^{32} +(0.551563 + 3.12807i) q^{34} +(2.20765 + 3.82376i) q^{35} +(-1.69806 + 2.94112i) q^{37} +(4.33245 + 1.57688i) q^{38} +(1.70831 + 1.43345i) q^{40} +(-1.37607 - 1.15466i) q^{41} +(-4.72680 - 1.72041i) q^{43} +(-0.771999 + 1.33714i) q^{44} +(4.89793 + 8.48346i) q^{46} +(-0.296709 - 1.68272i) q^{47} +(-7.78035 + 2.83182i) q^{49} +(1.08703 - 6.16483i) q^{50} +(-0.463253 + 0.388716i) q^{52} -2.84494 q^{53} +2.11276 q^{55} +(-5.91183 + 4.96061i) q^{56} +(-1.55282 + 8.80649i) q^{58} +(-10.5810 + 3.85116i) q^{59} +(0.908335 + 5.15142i) q^{61} +(1.12672 + 1.95153i) q^{62} +(-1.26751 + 2.19540i) q^{64} +(0.777597 + 0.283022i) q^{65} +(-1.44708 - 1.21424i) q^{67} +(-1.19490 - 1.00264i) q^{68} +(-6.97415 - 2.53838i) q^{70} +(-6.09193 + 10.5515i) q^{71} +(-4.94384 - 8.56298i) q^{73} +(-0.991282 - 5.62184i) q^{74} +(-2.12759 + 0.774379i) q^{76} +(-1.26962 + 7.20039i) q^{77} +(9.46285 - 7.94028i) q^{79} -5.61331 q^{80} +3.01948 q^{82} +(8.94982 - 7.50979i) q^{83} +(-0.370641 + 2.10201i) q^{85} +(7.94533 - 2.89186i) q^{86} +(0.641252 + 3.63672i) q^{88} +(-2.86437 - 4.96123i) q^{89} +(-1.43183 + 2.48001i) q^{91} +(-4.52045 - 1.64531i) q^{92} +(2.20018 + 1.84617i) q^{94} +(2.37334 + 1.99147i) q^{95} +(0.322670 + 0.117442i) q^{97} +(6.95870 - 12.0528i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8	$ 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28} + 24 q^{29} + 12 q^{31} - 27 q^{32} - 12 q^{35} - 3 q^{37} + 30 q^{38} - 15 q^{40} - 6 q^{41} - 15 q^{43} - 3 q^{44} - 3 q^{46} - 12 q^{47} - 33 q^{49} - 21 q^{50} - 45 q^{52} + 18 q^{53} - 12 q^{55} - 30 q^{56} - 51 q^{58} + 3 q^{59} - 33 q^{61} + 12 q^{62} + 12 q^{64} - 21 q^{65} - 6 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} + 21 q^{74} + 6 q^{76} + 12 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 6 q^{83} + 36 q^{85} + 21 q^{86} + 42 q^{88} - 9 q^{89} + 6 q^{91} + 3 q^{92} + 48 q^{94} - 3 q^{95} + 39 q^{97} + 45 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 + 6 * q^11 + 3 * q^13 + 21 * q^14 + 9 * q^16 - 9 * q^17 - 3 * q^19 - 24 * q^20 + 12 * q^22 + 12 * q^23 + 12 * q^25 + 30 * q^26 - 12 * q^28 + 24 * q^29 + 12 * q^31 - 27 * q^32 - 12 * q^35 - 3 * q^37 + 30 * q^38 - 15 * q^40 - 6 * q^41 - 15 * q^43 - 3 * q^44 - 3 * q^46 - 12 * q^47 - 33 * q^49 - 21 * q^50 - 45 * q^52 + 18 * q^53 - 12 * q^55 - 30 * q^56 - 51 * q^58 + 3 * q^59 - 33 * q^61 + 12 * q^62 + 12 * q^64 - 21 * q^65 - 6 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 + 21 * q^74 + 6 * q^76 + 12 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 6 * q^83 + 36 * q^85 + 21 * q^86 + 42 * q^88 - 9 * q^89 + 6 * q^91 + 3 * q^92 + 48 * q^94 - 3 * q^95 + 39 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.28765	+	1.08047i	−0.910508	+	0.764007i	−0.972216	−	0.234087i	$-0.924790\pi$
$2$	−1.28765	+	1.08047i	−0.910508	+	0.764007i	0.0617072	+	0.998094i	$0.480346\pi$
$3$		0			0
$3$		0			0
$4$	0.143341	−	0.812925i	0.0716703	−	0.406463i
$5$	−1.06142	+	0.386327i	−0.474683	+	0.172771i	−0.568273	−	0.822840i	$-0.692388\pi$
$5$	−1.06142	+	0.386327i	−0.474683	+	0.172771i	0.0935894	+	0.995611i	$0.470166\pi$
$6$		0			0
$7$	−0.678777	−	3.84954i	−0.256554	−	1.45499i	−0.792053	−	0.610453i	$-0.790988\pi$
$7$	−0.678777	−	3.84954i	−0.256554	−	1.45499i	0.535499	−	0.844536i	$-0.320124\pi$
$8$	−0.987144	−	1.70978i	−0.349008	−	0.604500i
$9$		0			0
$10$	0.949332	−	1.64429i	0.300205	−	0.519971i
$11$	−1.75765	−	0.639734i	−0.529953	−	0.192887i	0.0631646	−	0.998003i	$-0.479881\pi$
$11$	−1.75765	−	0.639734i	−0.529953	−	0.192887i	−0.593117	+	0.805116i	$0.702103\pi$
$12$		0			0
$13$	−0.561203	−	0.470905i	−0.155650	−	0.130606i	0.561637	−	0.827384i	$-0.310172\pi$
$13$	−0.561203	−	0.470905i	−0.155650	−	0.130606i	−0.717287	+	0.696778i	$0.754616\pi$
$14$	5.03334	+	4.22347i	1.34522	+	1.12877i
$15$		0			0
$16$	4.66984	+	1.69968i	1.16746	+	0.424921i
$17$	0.944822	−	1.63648i	0.229153	−	0.396905i	−0.728404	−	0.685147i	$-0.759738\pi$
$17$	0.944822	−	1.63648i	0.229153	−	0.396905i	0.957557	+	0.288243i	$0.0930711\pi$
$18$		0			0
$19$	−1.37143	−	2.37538i	−0.314627	−	0.544950i	0.664731	−	0.747083i	$-0.268546\pi$
$19$	−1.37143	−	2.37538i	−0.314627	−	0.544950i	−0.979358	+	0.202133i	$0.935213\pi$
$20$	0.161910	+	0.918235i	0.0362041	+	0.205324i
$21$		0			0
$22$	2.95446	−	1.07534i	0.629893	−	0.229262i
$23$	1.01197	−	5.73916i	0.211010	−	1.19670i	−0.676687	−	0.736271i	$-0.736585\pi$
$23$	1.01197	−	5.73916i	0.211010	−	1.19670i	0.887697	−	0.460428i	$-0.152304\pi$
$24$		0			0
$25$	−2.85285	+	2.39382i	−0.570570	+	0.478765i
$26$	1.23143			0.241504
$27$		0			0
$28$	−3.22668			−0.609786
$29$	4.07531	−	3.41959i	0.756765	−	0.635002i	−0.180517	−	0.983572i	$-0.557777\pi$
$29$	4.07531	−	3.41959i	0.756765	−	0.635002i	0.937283	+	0.348570i	$0.113333\pi$
$30$		0			0
$31$	0.232793	−	1.32023i	0.0418108	−	0.237121i	−0.956740	−	0.290946i	$-0.906030\pi$
$31$	0.232793	−	1.32023i	0.0418108	−	0.237121i	0.998550	+	0.0538247i	$0.0171412\pi$
$32$	−4.13914	+	1.50652i	−0.731703	+	0.266318i
$33$		0			0
$34$	0.551563	+	3.12807i	0.0945923	+	0.536459i
$35$	2.20765	+	3.82376i	0.373161	+	0.646334i
$36$		0			0
$37$	−1.69806	+	2.94112i	−0.279159	+	0.483517i	−0.971176	−	0.238364i	$-0.923389\pi$
$37$	−1.69806	+	2.94112i	−0.279159	+	0.483517i	0.692017	+	0.721881i	$0.256722\pi$
$38$	4.33245	+	1.57688i	0.702817	+	0.255804i
$39$		0			0
$40$	1.70831	+	1.43345i	0.270108	+	0.226648i
$41$	−1.37607	−	1.15466i	−0.214906	−	0.180328i	0.528980	−	0.848635i	$-0.322575\pi$
$41$	−1.37607	−	1.15466i	−0.214906	−	0.180328i	−0.743886	+	0.668307i	$0.767019\pi$
$42$		0			0
$43$	−4.72680	−	1.72041i	−0.720830	−	0.262361i	−0.0445518	−	0.999007i	$-0.514186\pi$
$43$	−4.72680	−	1.72041i	−0.720830	−	0.262361i	−0.676278	+	0.736646i	$0.736408\pi$
$44$	−0.771999	+	1.33714i	−0.116383	+	0.201582i
$45$		0			0
$46$	4.89793	+	8.48346i	0.722160	+	1.25082i
$47$	−0.296709	−	1.68272i	−0.0432794	−	0.245450i	0.955491	−	0.295019i	$-0.0953261\pi$
$47$	−0.296709	−	1.68272i	−0.0432794	−	0.245450i	−0.998771	+	0.0495697i	$0.984215\pi$
$48$		0			0
$49$	−7.78035	+	2.83182i	−1.11148	+	0.404545i
$50$	1.08703	−	6.16483i	0.153729	−	0.871839i
$51$		0			0
$52$	−0.463253	+	0.388716i	−0.0642417	+	0.0539052i
$53$	−2.84494			−0.390783			−0.195391	−	0.980725i	$-0.562598\pi$
$53$	−2.84494			−0.390783			−0.195391	+	0.980725i	$0.562598\pi$
$54$		0			0
$55$	2.11276			0.284885
$56$	−5.91183	+	4.96061i	−0.790001	+	0.662890i
$57$		0			0
$58$	−1.55282	+	8.80649i	−0.203895	+	1.15635i
$59$	−10.5810	+	3.85116i	−1.37753	+	0.501379i	−0.921427	−	0.388550i	$-0.872976\pi$
$59$	−10.5810	+	3.85116i	−1.37753	+	0.501379i	−0.456099	+	0.889929i	$0.650754\pi$
$60$		0			0
$61$	0.908335	+	5.15142i	0.116300	+	0.659572i	0.986098	+	0.166164i	$0.0531381\pi$
$61$	0.908335	+	5.15142i	0.116300	+	0.659572i	−0.869798	+	0.493408i	$0.835751\pi$
$62$	1.12672	+	1.95153i	0.143093	+	0.247844i
$63$		0			0
$64$	−1.26751	+	2.19540i	−0.158439	+	0.274425i
$65$	0.777597	+	0.283022i	0.0964491	+	0.0351046i
$66$		0			0
$67$	−1.44708	−	1.21424i	−0.176789	−	0.148343i	0.550099	−	0.835099i	$-0.314590\pi$
$67$	−1.44708	−	1.21424i	−0.176789	−	0.148343i	−0.726888	+	0.686756i	$0.759034\pi$
$68$	−1.19490	−	1.00264i	−0.144903	−	0.121588i
$69$		0			0
$70$	−6.97415	−	2.53838i	−0.833570	−	0.303395i
$71$	−6.09193	+	10.5515i	−0.722980	+	1.25224i	0.236821	+	0.971553i	$0.423895\pi$
$71$	−6.09193	+	10.5515i	−0.722980	+	1.25224i	−0.959800	+	0.280684i	$0.909439\pi$
$72$		0			0
$73$	−4.94384	−	8.56298i	−0.578633	−	1.00222i	−0.995637	−	0.0933164i	$-0.970253\pi$
$73$	−4.94384	−	8.56298i	−0.578633	−	1.00222i	0.417004	−	0.908905i	$-0.363080\pi$
$74$	−0.991282	−	5.62184i	−0.115234	−	0.653526i
$75$		0			0
$76$	−2.12759	+	0.774379i	−0.244051	+	0.0888274i
$77$	−1.26962	+	7.20039i	−0.144687	+	0.820561i
$78$		0			0
$79$	9.46285	−	7.94028i	1.06465	−	0.893351i	0.0700965	−	0.997540i	$-0.477669\pi$
$79$	9.46285	−	7.94028i	1.06465	−	0.893351i	0.994557	+	0.104189i	$0.0332248\pi$
$80$	−5.61331			−0.627587
$81$		0			0
$82$	3.01948			0.333445
$83$	8.94982	−	7.50979i	0.982371	−	0.824307i	−0.00207468	−	0.999998i	$-0.500660\pi$
$83$	8.94982	−	7.50979i	0.982371	−	0.824307i	0.984445	+	0.175691i	$0.0562159\pi$
$84$		0			0
$85$	−0.370641	+	2.10201i	−0.0402016	+	0.227995i
$86$	7.94533	−	2.89186i	0.856767	−	0.311838i
$87$		0			0
$88$	0.641252	+	3.63672i	0.0683576	+	0.387675i
$89$	−2.86437	−	4.96123i	−0.303622	−	0.525889i	0.673331	−	0.739341i	$-0.264863\pi$
$89$	−2.86437	−	4.96123i	−0.303622	−	0.525889i	−0.976954	+	0.213452i	$0.931529\pi$
$90$		0			0
$91$	−1.43183	+	2.48001i	−0.150097	+	0.259976i
$92$	−4.52045	−	1.64531i	−0.471290	−	0.171535i
$93$		0			0
$94$	2.20018	+	1.84617i	0.226932	+	0.190418i
$95$	2.37334	+	1.99147i	0.243500	+	0.204320i
$96$		0			0
$97$	0.322670	+	0.117442i	0.0327622	+	0.0119245i	0.358349	−	0.933588i	$-0.383340\pi$
$97$	0.322670	+	0.117442i	0.0327622	+	0.0119245i	−0.325587	+	0.945512i	$0.605562\pi$
$98$	6.95870	−	12.0528i	0.702935	−	1.21752i
$99$		0			0
$100$	1.53707	+	2.66228i	0.153707	+	0.266228i
$101$	3.02187	+	17.1379i	0.300687	+	1.70528i	0.643141	+	0.765748i	$0.277631\pi$
$101$	3.02187	+	17.1379i	0.300687	+	1.70528i	−0.342454	+	0.939535i	$0.611258\pi$
$102$		0			0
$103$	14.8594	−	5.40837i	1.46414	−	0.532902i	0.517635	−	0.855602i	$-0.326813\pi$
$103$	14.8594	−	5.40837i	1.46414	−	0.532902i	0.946501	+	0.322700i	$0.104590\pi$
$104$	−0.251158	+	1.42439i	−0.0246280	+	0.139673i
$105$		0			0
$106$	3.66330	−	3.07387i	0.355811	−	0.298561i
$107$	16.5298			1.59800			0.798999	−	0.601332i	$-0.205363\pi$
$107$	16.5298			1.59800			0.798999	+	0.601332i	$0.205363\pi$
$108$		0			0
$109$	−4.71844			−0.451945			−0.225972	−	0.974134i	$-0.572556\pi$
$109$	−4.71844			−0.451945			−0.225972	+	0.974134i	$0.572556\pi$
$110$	−2.72051	+	2.28278i	−0.259390	+	0.217654i
$111$		0			0
$112$	3.37321	−	19.1304i	0.318738	−	1.80765i
$113$	18.7420	−	6.82153i	1.76310	−	0.641715i	0.763109	−	0.646270i	$-0.223672\pi$
$113$	18.7420	−	6.82153i	1.76310	−	0.641715i	0.999990	+	0.00455445i	$0.00144973\pi$
$114$		0			0
$115$	1.14306	+	6.48264i	0.106591	+	0.604509i
$116$	−2.19571	−	3.80308i	−0.203867	−	0.353108i
$117$		0			0
$118$	9.46357	−	16.3914i	0.871193	−	1.50895i
$119$	−6.94101	−	2.52632i	−0.636281	−	0.231588i
$120$		0			0
$121$	−5.74640	−	4.82180i	−0.522400	−	0.438346i
$122$	−6.73558	−	5.65182i	−0.609811	−	0.511692i
$123$		0			0
$124$	−1.03988	−	0.378486i	−0.0933842	−	0.0339891i
$125$	4.92714	−	8.53407i	0.440697	−	0.763310i
$126$		0			0
$127$	−0.534728	−	0.926176i	−0.0474495	−	0.0821849i	0.841325	−	0.540529i	$-0.181776\pi$
$127$	−0.534728	−	0.926176i	−0.0474495	−	0.0821849i	−0.888775	+	0.458344i	$0.848443\pi$
$128$	−2.26971	−	12.8721i	−0.200616	−	1.13775i
$129$		0			0
$130$	−1.30707	+	0.475736i	−0.114638	+	0.0417248i
$131$	−1.32672	+	7.52422i	−0.115916	+	0.657395i	0.870376	+	0.492388i	$0.163876\pi$
$131$	−1.32672	+	7.52422i	−0.115916	+	0.657395i	−0.986292	+	0.165007i	$0.947235\pi$
$132$		0			0
$133$	−8.21323	+	6.89172i	−0.712178	+	0.597588i
$134$	3.17529			0.274303
$135$		0			0
$136$	−3.73070			−0.319905
$137$	−11.9890	+	10.0599i	−1.02429	+	0.859479i	−0.990160	−	0.139938i	$-0.955310\pi$
$137$	−11.9890	+	10.0599i	−1.02429	+	0.859479i	−0.0341275	+	0.999417i	$0.510865\pi$
$138$		0			0
$139$	1.50326	−	8.52542i	0.127505	−	0.723116i	−0.852284	−	0.523080i	$-0.824783\pi$
$139$	1.50326	−	8.52542i	0.127505	−	0.723116i	0.979788	−	0.200036i	$-0.0641060\pi$
$140$	3.42488	−	1.24655i	0.289455	−	0.105353i
$141$		0			0
$142$	−3.55632	−	20.1689i	−0.298439	−	1.69253i
$143$	0.685146	+	1.18671i	0.0572948	+	0.0992375i
$144$		0			0
$145$	−3.00455	+	5.20403i	−0.249514	+	0.432172i
$146$	15.6180	+	5.68448i	1.29255	+	0.470451i
$147$		0			0
$148$	2.14751	+	1.80197i	0.176524	+	0.148121i
$149$	1.88740	+	1.58371i	0.154622	+	0.129743i	0.716817	−	0.697262i	$-0.245598\pi$
$149$	1.88740	+	1.58371i	0.154622	+	0.129743i	−0.562195	+	0.827005i	$0.690043\pi$
$150$		0			0
$151$	9.87937	+	3.59580i	0.803972	+	0.292622i	0.711131	−	0.703059i	$-0.248183\pi$
$151$	9.87937	+	3.59580i	0.803972	+	0.292622i	0.0928406	+	0.995681i	$0.470405\pi$
$152$	−2.70760	+	4.68969i	−0.219615	+	0.380384i
$153$		0			0
$154$	−6.14497	−	10.6434i	−0.495176	−	0.857669i
$155$	0.262950	+	1.49126i	0.0211206	+	0.119781i
$156$		0			0
$157$	−0.338241	+	0.123110i	−0.0269946	+	0.00982522i	−0.355482	−	0.934683i	$-0.615683\pi$
$157$	−0.338241	+	0.123110i	−0.0269946	+	0.00982522i	0.328488	+	0.944508i	$0.393461\pi$
$158$	−3.60565	+	20.4486i	−0.286850	+	1.62681i
$159$		0			0
$160$	3.81137	−	3.19812i	0.301315	−	0.252834i
$161$	−22.7800			−1.79532
$162$		0			0
$163$	14.6186			1.14502			0.572508	−	0.819899i	$-0.305971\pi$
$163$	14.6186			1.14502			0.572508	+	0.819899i	$0.305971\pi$
$164$	−1.13590	+	0.953132i	−0.0886988	+	0.0744271i
$165$		0			0
$166$	−3.41017	+	19.3400i	−0.264680	+	1.50108i
$167$	2.04463	−	0.744184i	0.158218	−	0.0575867i	−0.261697	−	0.965150i	$-0.584282\pi$
$167$	2.04463	−	0.744184i	0.158218	−	0.0575867i	0.419915	+	0.907563i	$0.362060\pi$
$168$		0			0
$169$	−2.16423	−	12.2740i	−0.166479	−	0.944150i
$170$	−1.79390	−	3.10712i	−0.137586	−	0.238306i
$171$		0			0
$172$	−2.07611	+	3.59593i	−0.158302	+	0.274187i
$173$	−16.5076	−	6.00828i	−1.25505	−	0.456801i	−0.372945	−	0.927854i	$-0.621652\pi$
$173$	−16.5076	−	6.00828i	−1.25505	−	0.456801i	−0.882105	+	0.471053i	$0.843874\pi$
$174$		0			0
$175$	11.1516	+	9.35728i	0.842979	+	0.707344i
$176$	−7.12061	−	5.97490i	−0.536736	−	0.450375i
$177$		0			0
$178$	9.04877	+	3.29348i	0.678234	+	0.246857i
$179$	0.502236	−	0.869898i	0.0375388	−	0.0650192i	−0.846646	−	0.532157i	$-0.821382\pi$
$179$	0.502236	−	0.869898i	0.0375388	−	0.0650192i	0.884184	+	0.467138i	$0.154715\pi$
$180$		0			0
$181$	10.5866	+	18.3366i	0.786898	+	1.36295i	0.927859	+	0.372932i	$0.121647\pi$
$181$	10.5866	+	18.3366i	0.786898	+	1.36295i	−0.140961	+	0.990015i	$0.545019\pi$
$182$	−0.835869	−	4.74045i	−0.0619587	−	0.351385i
$183$		0			0
$184$	−10.8117	+	3.93513i	−0.797049	+	0.290102i
$185$	0.666125	−	3.77778i	0.0489745	−	0.277748i
$186$		0			0
$187$	−2.70758	+	2.27193i	−0.197998	+	0.166140i
$188$	−1.41045			−0.102868
$189$		0			0
$190$	−5.20776			−0.377811
$191$	7.52898	−	6.31756i	0.544778	−	0.457123i	−0.328390	−	0.944542i	$-0.606506\pi$
$191$	7.52898	−	6.31756i	0.544778	−	0.457123i	0.873168	+	0.487419i	$0.162062\pi$
$192$		0			0
$193$	−1.93723	+	10.9866i	−0.139445	+	0.790833i	0.832215	+	0.554452i	$0.187072\pi$
$193$	−1.93723	+	10.9866i	−0.139445	+	0.790833i	−0.971661	+	0.236380i	$0.924039\pi$
$194$	−0.542380	+	0.197410i	−0.0389406	+	0.0141732i
$195$		0			0
$196$	1.18681	+	6.73076i	0.0847724	+	0.480768i
$197$	4.54497	+	7.87212i	0.323816	+	0.560865i	0.981272	−	0.192628i	$-0.0617009\pi$
$197$	4.54497	+	7.87212i	0.323816	+	0.560865i	−0.657456	+	0.753493i	$0.728368\pi$
$198$		0			0
$199$	7.34694	−	12.7253i	0.520811	−	0.902071i	−0.478896	−	0.877872i	$-0.658963\pi$
$199$	7.34694	−	12.7253i	0.520811	−	0.902071i	0.999707	−	0.0241994i	$-0.00770367\pi$
$200$	6.90910	+	2.51471i	0.488547	+	0.177817i
$201$		0			0
$202$	−22.4081	−	18.8026i	−1.57663	−	1.32295i
$203$	−15.9301	−	13.3669i	−1.11807	−	0.938173i
$204$		0			0
$205$	1.90667	+	0.693971i	0.133168	+	0.0484691i
$206$	−13.2901	+	23.0192i	−0.925968	+	1.60382i
$207$		0			0
$208$	−1.82034	−	3.15292i	−0.126218	−	0.218615i
$209$	0.890883	+	5.05245i	0.0616237	+	0.349485i
$210$		0			0
$211$	−7.38439	+	2.68770i	−0.508362	+	0.185029i	−0.583451	−	0.812148i	$-0.698298\pi$
$211$	−7.38439	+	2.68770i	−0.508362	+	0.185029i	0.0750892	+	0.997177i	$0.476076\pi$
$212$	−0.407796	+	2.31273i	−0.0280075	+	0.158839i
$213$		0			0
$214$	−21.2847	+	17.8600i	−1.45499	+	1.22088i
$215$	5.68178			0.387494
$216$		0			0
$217$	−5.24030			−0.355735
$218$	6.07572	−	5.09813i	0.411499	−	0.345289i
$219$		0			0
$220$	0.302845	−	1.71752i	0.0204178	−	0.115795i
$221$	−1.30086	+	0.473475i	−0.0875055	+	0.0318494i
$222$		0			0
$223$	−1.51784	−	8.60809i	−0.101642	−	0.576440i	−0.992509	−	0.122175i	$-0.961013\pi$
$223$	−1.51784	−	8.60809i	−0.101642	−	0.576440i	0.890867	−	0.454265i	$-0.150098\pi$
$224$	8.60897	+	14.9112i	0.575211	+	0.996295i
$225$		0			0
$226$	−16.7627	+	29.0339i	−1.11504	+	1.93131i
$227$	3.82306	+	1.39148i	0.253745	+	0.0923558i	0.465761	−	0.884910i	$-0.345781\pi$
$227$	3.82306	+	1.39148i	0.253745	+	0.0923558i	−0.212016	+	0.977266i	$0.568003\pi$
$228$		0			0
$229$	12.3761	+	10.3848i	0.817837	+	0.686247i	0.952464	−	0.304650i	$-0.0985394\pi$
$229$	12.3761	+	10.3848i	0.817837	+	0.686247i	−0.134628	+	0.990896i	$0.542984\pi$
$230$	−8.47616	−	7.11235i	−0.558902	−	0.468974i
$231$		0			0
$232$	−9.86968	−	3.59227i	−0.647976	−	0.235844i
$233$	8.60658	−	14.9070i	0.563836	−	0.976592i	−0.433321	−	0.901240i	$-0.642658\pi$
$233$	8.60658	−	14.9070i	0.563836	−	0.976592i	0.997157	−	0.0753527i	$-0.0240083\pi$
$234$		0			0
$235$	0.965013	+	1.67145i	0.0629505	+	0.109034i
$236$	1.61402	+	9.15357i	0.105064	+	0.595847i
$237$		0			0
$238$	11.6672	−	4.24652i	0.756274	−	0.275261i
$239$	0.266626	−	1.51211i	0.0172466	−	0.0978104i	−0.974969	−	0.222339i	$-0.928631\pi$
$239$	0.266626	−	1.51211i	0.0172466	−	0.0978104i	0.992216	+	0.124529i	$0.0397419\pi$
$240$		0			0
$241$	−4.22985	+	3.54926i	−0.272468	+	0.228628i	−0.768775	−	0.639519i	$-0.779134\pi$
$241$	−4.22985	+	3.54926i	−0.272468	+	0.228628i	0.496307	+	0.868147i	$0.334689\pi$
$242$	12.6092			0.810549
$243$		0			0
$244$	4.31792			0.276427
$245$	7.16425	−	6.01152i	0.457707	−	0.384062i
$246$		0			0
$247$	−0.348931	+	1.97888i	−0.0222019	+	0.125913i
$248$	−2.48712	+	0.905236i	−0.157932	+	0.0574826i
$249$		0			0
$250$	2.87634	+	16.3125i	0.181916	+	1.03170i
$251$	−10.7204	−	18.5683i	−0.676668	−	1.17202i	−0.975978	−	0.217868i	$-0.930090\pi$
$251$	−10.7204	−	18.5683i	−0.676668	−	1.17202i	0.299310	−	0.954156i	$-0.403244\pi$
$252$		0			0
$253$	−5.45023	+	9.44007i	−0.342653	+	0.593492i
$254$	1.68925	+	0.614837i	0.105993	+	0.0385783i
$255$		0			0
$256$	12.9467	+	10.8635i	0.809167	+	0.678971i
$257$	11.3271	+	9.50456i	0.706565	+	0.592878i	0.923633	−	0.383278i	$-0.125205\pi$
$257$	11.3271	+	9.50456i	0.706565	+	0.592878i	−0.217068	+	0.976156i	$0.569649\pi$
$258$		0			0
$259$	12.4746	+	4.54037i	0.775131	+	0.282125i
$260$	0.341537	−	0.591560i	0.0211812	−	0.0366870i
$261$		0			0
$262$	−6.42133	−	11.1221i	−0.396711	−	0.687124i
$263$	−0.486694	−	2.76018i	−0.0300108	−	0.170200i	0.966119	−	0.258099i	$-0.0830959\pi$
$263$	−0.486694	−	2.76018i	−0.0300108	−	0.170200i	−0.996129	+	0.0878987i	$0.971985\pi$
$264$		0			0
$265$	3.01969	−	1.09908i	0.185498	−	0.0675158i
$266$	3.12950	−	17.7483i	0.191882	−	1.08822i
$267$		0			0
$268$	−1.19451	+	1.00232i	−0.0729666	+	0.0612262i
$269$	0.356528			0.0217379			0.0108689	−	0.999941i	$-0.496540\pi$
$269$	0.356528			0.0217379			0.0108689	+	0.999941i	$0.496540\pi$
$270$		0			0
$271$	−12.1467			−0.737857			−0.368928	−	0.929458i	$-0.620275\pi$
$271$	−12.1467			−0.737857			−0.368928	+	0.929458i	$0.620275\pi$
$272$	7.19366	−	6.03620i	0.436180	−	0.365998i
$273$		0			0
$274$	4.56818	−	25.9075i	0.275974	−	1.56513i
$275$	6.54573	−	2.38245i	0.394722	−	0.143667i
$276$		0			0
$277$	4.33946	+	24.6103i	0.260733	+	1.47869i	0.780916	+	0.624636i	$0.214752\pi$
$277$	4.33946	+	24.6103i	0.260733	+	1.47869i	−0.520183	+	0.854055i	$0.674136\pi$
$278$	7.27577	+	12.6020i	0.436372	+	0.755818i
$279$		0			0
$280$	4.35854	−	7.54921i	0.260473	−	0.451152i
$281$	6.88125	+	2.50457i	0.410501	+	0.149410i	0.539012	−	0.842298i	$-0.318798\pi$
$281$	6.88125	+	2.50457i	0.410501	+	0.149410i	−0.128511	+	0.991708i	$0.541020\pi$
$282$		0			0
$283$	−11.0219	−	9.24848i	−0.655185	−	0.549765i	0.253454	−	0.967347i	$-0.418433\pi$
$283$	−11.0219	−	9.24848i	−0.655185	−	0.549765i	−0.908639	+	0.417582i	$0.862878\pi$
$284$	7.70439	+	6.46475i	0.457171	+	0.383612i
$285$		0			0
$286$	−2.16443	−	0.787789i	−0.127986	−	0.0465829i
$287$	−3.51086	+	6.08099i	−0.207240	+	0.358950i
$288$		0			0
$289$	6.71462	+	11.6301i	0.394978	+	0.684122i
$290$	−1.75398	−	9.94732i	−0.102997	−	0.584127i
$291$		0			0
$292$	−7.66971	+	2.79155i	−0.448836	+	0.163363i
$293$	2.50323	−	14.1965i	0.146240	−	0.829369i	−0.820123	−	0.572187i	$-0.806095\pi$
$293$	2.50323	−	14.1965i	0.146240	−	0.829369i	0.966363	−	0.257182i	$-0.0827938\pi$
$294$		0			0
$295$	9.74310	−	8.17543i	0.567265	−	0.475992i
$296$	6.70491			0.389715
$297$		0			0
$298$	−4.14147			−0.239909
$299$	−3.27052	+	2.74429i	−0.189139	+	0.158707i
$300$		0			0
$301$	−3.41435	+	19.3638i	−0.196800	+	1.11611i
$302$	−16.6064	+	6.04422i	−0.955589	+	0.347806i
$303$		0			0
$304$	−2.36695	−	13.4236i	−0.135754	−	0.769899i
$305$	−2.95426	−	5.11693i	−0.169161	−	0.292995i
$306$		0			0
$307$	15.2163	−	26.3554i	0.868440	−	1.50418i	0.00484869	−	0.999988i	$-0.498457\pi$
$307$	15.2163	−	26.3554i	0.868440	−	1.50418i	0.863591	−	0.504193i	$-0.168210\pi$
$308$	5.67139	+	2.06422i	0.323157	+	0.117620i
$309$		0			0
$310$	−1.94985	−	1.63612i	−0.110744	−	0.0929254i
$311$	10.7213	+	8.99620i	0.607947	+	0.510128i	0.893989	−	0.448089i	$-0.147895\pi$
$311$	10.7213	+	8.99620i	0.607947	+	0.510128i	−0.286042	+	0.958217i	$0.592340\pi$
$312$		0			0
$313$	−20.7555	−	7.55439i	−1.17317	−	0.426999i	−0.319386	−	0.947625i	$-0.603477\pi$
$313$	−20.7555	−	7.55439i	−1.17317	−	0.426999i	−0.853785	+	0.520625i	$0.825699\pi$
$314$	0.302521	−	0.523982i	0.0170722	−	0.0295700i
$315$		0			0
$316$	−5.09844	−	8.83075i	−0.286810	−	0.496769i
$317$	−3.01952	−	17.1245i	−0.169593	−	0.961810i	−0.944201	−	0.329369i	$-0.893164\pi$
$317$	−3.01952	−	17.1245i	−0.169593	−	0.961810i	0.774608	−	0.632441i	$-0.217947\pi$
$318$		0			0
$319$	−9.35060	+	3.40334i	−0.523533	+	0.190551i
$320$	0.497229	−	2.81993i	0.0277959	−	0.157639i
$321$		0			0
$322$	29.3328	−	24.6131i	1.63465	−	1.37164i
$323$	−5.18302			−0.288391
$324$		0			0
$325$	2.72829			0.151338
$326$	−18.8237	+	15.7949i	−1.04255	+	0.874800i
$327$		0			0
$328$	−0.615840	+	3.49260i	−0.0340041	+	0.192847i
$329$	−6.27629	+	2.28438i	−0.346023	+	0.125942i
$330$		0			0
$331$	0.150058	+	0.851019i	0.00824791	+	0.0467762i	0.988654	−	0.150211i	$-0.0479953\pi$
$331$	0.150058	+	0.851019i	0.00824791	+	0.0467762i	−0.980406	+	0.196987i	$0.936884\pi$
$332$	−4.82203	−	8.35199i	−0.264643	−	0.458375i
$333$		0			0
$334$	−1.82870	+	3.16741i	−0.100062	+	0.173313i
$335$	2.00506	+	0.729782i	0.109548	+	0.0398723i
$336$		0			0
$337$	0.320612	+	0.269025i	0.0174648	+	0.0146547i	0.651478	−	0.758667i	$-0.274149\pi$
$337$	0.320612	+	0.269025i	0.0174648	+	0.0146547i	−0.634013	+	0.773322i	$0.718594\pi$
$338$	16.0484	+	13.4662i	0.872918	+	0.732466i
$339$		0			0
$340$	1.65565	+	0.602606i	0.0897901	+	0.0326809i
$341$	−1.25377	+	2.17159i	−0.0678953	+	0.117598i
$342$		0			0
$343$	2.50108	+	4.33199i	0.135046	+	0.233906i
$344$	1.72450	+	9.78010i	0.0929786	+	0.527308i
$345$		0			0
$346$	27.7478	−	10.0994i	1.49173	−	0.542946i
$347$	−4.06506	+	23.0541i	−0.218224	+	1.23761i	0.657000	+	0.753891i	$0.271825\pi$
$347$	−4.06506	+	23.0541i	−0.218224	+	1.23761i	−0.875224	+	0.483718i	$0.839286\pi$
$348$		0			0
$349$	16.2221	−	13.6119i	0.868347	−	0.728630i	−0.0954022	−	0.995439i	$-0.530414\pi$
$349$	16.2221	−	13.6119i	0.868347	−	0.728630i	0.963749	+	0.266809i	$0.0859693\pi$
$350$	−24.4696			−1.30796
$351$		0			0
$352$	8.23894			0.439137
$353$	−18.0361	+	15.1341i	−0.959965	+	0.805506i	−0.980947	−	0.194274i	$-0.937765\pi$
$353$	−18.0361	+	15.1341i	−0.959965	+	0.805506i	0.0209824	+	0.999780i	$0.493321\pi$
$354$		0			0
$355$	2.38978	−	13.5531i	0.126837	−	0.719326i
$356$	−4.44369	+	1.61737i	−0.235515	+	0.0857204i
$357$		0			0
$358$	0.293192	+	1.66278i	0.0154957	+	0.0878805i
$359$	−5.23047	−	9.05943i	−0.276053	−	0.478139i	0.694347	−	0.719640i	$-0.255693\pi$
$359$	−5.23047	−	9.05943i	−0.276053	−	0.478139i	−0.970400	+	0.241502i	$0.922360\pi$
$360$		0			0
$361$	5.73837	−	9.93915i	0.302019	−	0.523113i
$362$	−33.4440	−	12.1726i	−1.75778	−	0.639779i
$363$		0			0
$364$	1.81082	+	1.51946i	0.0949129	+	0.0796414i
$365$	8.55562	+	7.17902i	0.447822	+	0.375767i
$366$		0			0
$367$	−19.9762	−	7.27076i	−1.04275	−	0.379530i	−0.236829	−	0.971551i	$-0.576108\pi$
$367$	−19.9762	−	7.27076i	−1.04275	−	0.379530i	−0.805923	+	0.592021i	$0.798330\pi$
$368$	14.4805	−	25.0809i	0.754848	−	1.30743i
$369$		0			0
$370$	3.22404	+	5.58420i	0.167610	+	0.290309i
$371$	1.93108	+	10.9517i	0.100257	+	0.568585i
$372$		0			0
$373$	−2.17077	+	0.790096i	−0.112398	+	0.0409096i	−0.397607	−	0.917556i	$-0.630159\pi$
$373$	−2.17077	+	0.790096i	−0.112398	+	0.0409096i	0.285209	+	0.958465i	$0.407937\pi$
$374$	1.03167	−	5.85092i	0.0533466	−	0.302544i
$375$		0			0
$376$	−2.58419	+	2.16839i	−0.133270	+	0.111826i
$377$	−3.89737			−0.200725
$378$		0			0
$379$	12.5539			0.644850			0.322425	−	0.946595i	$-0.395502\pi$
$379$	12.5539			0.644850			0.322425	+	0.946595i	$0.395502\pi$
$380$	1.95911	−	1.64389i	0.100500	−	0.0843298i
$381$		0			0
$382$	−2.86878	+	16.2697i	−0.146780	+	0.832428i
$383$	−18.4692	+	6.72225i	−0.943733	+	0.343491i	−0.767639	−	0.640883i	$-0.778569\pi$
$383$	−18.4692	+	6.72225i	−0.943733	+	0.343491i	−0.176094	+	0.984373i	$0.556346\pi$
$384$		0			0
$385$	−1.43410	−	8.13316i	−0.0730883	−	0.414504i
$386$	−9.37620	−	16.2401i	−0.477236	−	0.826597i
$387$		0			0
$388$	0.141724	−	0.245472i	0.00719492	−	0.0124620i
$389$	−17.7062	−	6.44454i	−0.897742	−	0.326751i	−0.148394	−	0.988928i	$-0.547411\pi$
$389$	−17.7062	−	6.44454i	−0.897742	−	0.326751i	−0.749348	+	0.662177i	$0.769633\pi$
$390$		0			0
$391$	−8.43589	−	7.07855i	−0.426621	−	0.357978i
$392$	12.5221	+	10.5073i	0.632463	+	0.530699i
$393$		0			0
$394$	−14.3579	−	5.22586i	−0.723342	−	0.263275i
$395$	−6.97656	+	12.0838i	−0.351029	+	0.608000i
$396$		0			0
$397$	−10.0589	−	17.4225i	−0.504841	−	0.874410i	−0.999984	−	0.00559897i	$-0.998218\pi$
$397$	−10.0589	−	17.4225i	−0.504841	−	0.874410i	0.495143	−	0.868811i	$-0.335116\pi$
$398$	4.28896	+	24.3239i	0.214986	+	1.21925i
$399$		0			0
$400$	−17.3911	+	6.32984i	−0.869554	+	0.316492i
$401$	5.34935	−	30.3377i	0.267134	−	1.51499i	−0.495755	−	0.868462i	$-0.665109\pi$
$401$	5.34935	−	30.3377i	0.267134	−	1.51499i	0.762889	−	0.646529i	$-0.223780\pi$
$402$		0			0
$403$	−0.752349	+	0.631295i	−0.0374772	+	0.0314471i
$404$	14.3650			0.714684
$405$		0			0
$406$	34.9549			1.73478
$407$	4.86613	−	4.08317i	0.241205	−	0.202395i
$408$		0			0
$409$	6.89245	−	39.0891i	0.340810	−	1.93283i	−0.0190394	−	0.999819i	$-0.506061\pi$
$409$	6.89245	−	39.0891i	0.340810	−	1.93283i	0.359849	−	0.933010i	$-0.382828\pi$
$410$	−3.20495	+	1.16650i	−0.158281	+	0.0576096i
$411$		0			0
$412$	−2.26665	−	12.8548i	−0.111670	−	0.633310i
$413$	22.0073	+	38.1178i	1.08291	+	1.87565i
$414$		0			0
$415$	−6.59832	+	11.4286i	−0.323899	+	0.561010i
$416$	3.03232	+	1.10368i	0.148672	+	0.0541122i
$417$		0			0
$418$	−6.60617	−	5.54323i	−0.323118	−	0.271128i
$419$	−11.8286	−	9.92537i	−0.577865	−	0.484886i	0.306380	−	0.951909i	$-0.400882\pi$
$419$	−11.8286	−	9.92537i	−0.577865	−	0.484886i	−0.884245	+	0.467023i	$0.845326\pi$
$420$		0			0
$421$	17.0025	+	6.18839i	0.828649	+	0.301604i	0.721304	−	0.692618i	$-0.243543\pi$
$421$	17.0025	+	6.18839i	0.828649	+	0.301604i	0.107345	+	0.994222i	$0.465765\pi$
$422$	6.60456	−	11.4394i	0.321505	−	0.556863i
$423$		0			0
$424$	2.80837	+	4.86424i	0.136386	+	0.236228i
$425$	1.22201	+	6.93037i	0.0592762	+	0.336172i
$426$		0			0
$427$	19.2140	−	6.99334i	0.929833	−	0.338431i
$428$	2.36939	−	13.4375i	0.114529	−	0.649526i
$429$		0			0
$430$	−7.31616	+	6.13899i	−0.352817	+	0.296048i
$431$	28.9683			1.39535			0.697677	−	0.716412i	$-0.254217\pi$
$431$	28.9683			1.39535			0.697677	+	0.716412i	$0.254217\pi$
$432$		0			0
$433$	−37.5902			−1.80647			−0.903235	−	0.429146i	$-0.858815\pi$
$433$	−37.5902			−1.80647			−0.903235	+	0.429146i	$0.858815\pi$
$434$	6.74770	−	5.66199i	0.323900	−	0.271784i
$435$		0			0
$436$	−0.676344	+	3.83574i	−0.0323910	+	0.183699i
$437$	−15.0206	+	5.46704i	−0.718531	+	0.261524i
$438$		0			0
$439$	1.78224	+	10.1076i	0.0850619	+	0.482410i	0.997343	+	0.0728458i	$0.0232081\pi$
$439$	1.78224	+	10.1076i	0.0850619	+	0.482410i	−0.912281	+	0.409564i	$0.865681\pi$
$440$	−2.08560	−	3.61237i	−0.0994272	−	0.172213i
$441$		0			0
$442$	1.16348	−	2.01521i	0.0553413	−	0.0958540i
$443$	20.5873	+	7.49315i	0.978130	+	0.356010i	0.781113	−	0.624390i	$-0.214652\pi$
$443$	20.5873	+	7.49315i	0.978130	+	0.356010i	0.197017	+	0.980400i	$0.436875\pi$
$444$		0			0
$445$	4.95696	+	4.15939i	0.234983	+	0.197174i
$446$	11.2552	+	9.44426i	0.532951	+	0.447199i
$447$		0			0
$448$	9.31164	+	3.38916i	0.439933	+	0.160123i
$449$	4.98565	−	8.63540i	0.235287	−	0.407530i	−0.724069	−	0.689728i	$-0.757730\pi$
$449$	4.98565	−	8.63540i	0.235287	−	0.407530i	0.959356	+	0.282198i	$0.0910635\pi$
$450$		0			0
$451$	1.67998	+	2.90981i	0.0791072	+	0.137018i
$452$	−2.85890	−	16.2136i	−0.134471	−	0.762625i
$453$		0			0
$454$	−6.42623	+	2.33896i	−0.301598	+	0.109773i
$455$	0.561689	−	3.18550i	0.0263324	−	0.149338i
$456$		0			0
$457$	−5.83580	+	4.89682i	−0.272987	+	0.229064i	−0.768995	−	0.639254i	$-0.779243\pi$
$457$	−5.83580	+	4.89682i	−0.272987	+	0.229064i	0.496008	+	0.868318i	$0.334799\pi$
$458$	−27.1566			−1.26894
$459$		0			0
$460$	5.43375			0.253350
$461$	17.4662	−	14.6559i	0.813483	−	0.682593i	−0.137953	−	0.990439i	$-0.544052\pi$
$461$	17.4662	−	14.6559i	0.813483	−	0.682593i	0.951436	+	0.307845i	$0.0996080\pi$
$462$		0			0
$463$	−1.52736	+	8.66211i	−0.0709826	+	0.402562i	0.928527	+	0.371264i	$0.121075\pi$
$463$	−1.52736	+	8.66211i	−0.0709826	+	0.402562i	−0.999510	+	0.0312986i	$0.990036\pi$
$464$	24.8432	−	9.04220i	1.15332	−	0.419774i
$465$		0			0
$466$	5.02430	+	28.4942i	0.232746	+	1.31997i
$467$	−5.49878	−	9.52416i	−0.254453	−	0.440726i	0.710294	−	0.703905i	$-0.248562\pi$
$467$	−5.49878	−	9.52416i	−0.254453	−	0.440726i	−0.964747	+	0.263180i	$0.915229\pi$
$468$		0			0
$469$	−3.69203	+	6.39479i	−0.170482	+	0.295284i
$470$	−3.04856	−	1.10958i	−0.140619	−	0.0511813i
$471$		0			0
$472$	17.0296	+	14.2895i	0.783852	+	0.657730i
$473$	7.20747	+	6.04778i	0.331400	+	0.278077i
$474$		0			0
$475$	9.59873	+	3.49365i	0.440420	+	0.160300i
$476$	−3.04864	+	5.28040i	−0.139734	+	0.242027i
$477$		0			0
$478$	1.29047	+	2.23516i	0.0590247	+	0.102234i
$479$	−4.46146	−	25.3022i	−0.203849	−	1.15609i	−0.899240	−	0.437455i	$-0.855880\pi$
$479$	−4.46146	−	25.3022i	−0.203849	−	1.15609i	0.695391	−	0.718632i	$-0.255231\pi$
$480$		0			0
$481$	2.33794	−	0.850941i	0.106601	−	0.0387996i
$482$	1.61171	−	9.14044i	0.0734112	−	0.416336i
$483$		0			0
$484$	−4.74346	+	3.98023i	−0.215612	+	0.180920i
$485$	−0.387861			−0.0176119
$486$		0			0
$487$	−30.3800			−1.37665			−0.688325	−	0.725402i	$-0.741654\pi$
$487$	−30.3800			−1.37665			−0.688325	+	0.725402i	$0.741654\pi$
$488$	7.91117	−	6.63826i	0.358122	−	0.300500i
$489$		0			0
$490$	−2.72981	+	15.4815i	−0.123320	+	0.699383i
$491$	8.18310	−	2.97840i	0.369298	−	0.134414i	−0.150703	−	0.988579i	$-0.548154\pi$
$491$	8.18310	−	2.97840i	0.369298	−	0.134414i	0.520001	+	0.854166i	$0.325932\pi$
$492$		0			0
$493$	−1.74565	−	9.90006i	−0.0786200	−	0.445876i
$494$	−1.68882	−	2.92512i	−0.0759837	−	0.131608i
$495$		0			0
$496$	3.33108	−	5.76961i	0.149570	−	0.259063i
$497$	44.7536	+	16.2890i	2.00747	+	0.730661i
$498$		0			0
$499$	8.91329	+	7.47914i	0.399014	+	0.334812i	0.820112	−	0.572203i	$-0.193911\pi$
$499$	8.91329	+	7.47914i	0.399014	+	0.334812i	−0.421099	+	0.907015i	$0.638355\pi$
$500$	−6.23130	−	5.22868i	−0.278672	−	0.233834i
$501$		0			0
$502$	33.8667	+	12.3265i	1.51155	+	0.550158i
$503$	−18.8996	+	32.7350i	−0.842689	+	1.45958i	0.0449234	+	0.998990i	$0.485696\pi$
$503$	−18.8996	+	32.7350i	−0.842689	+	1.45958i	−0.887613	+	0.460590i	$0.847638\pi$
$504$		0			0
$505$	−9.82831	−	17.0231i	−0.437354	−	0.757519i
$506$	−3.18170	−	18.0443i	−0.141444	−	0.802169i
$507$		0			0
$508$	−0.829560	+	0.301935i	−0.0368058	+	0.0133962i
$509$	−4.09352	+	23.2155i	−0.181442	+	1.02901i	0.749000	+	0.662570i	$0.230534\pi$
$509$	−4.09352	+	23.2155i	−0.181442	+	1.02901i	−0.930442	+	0.366439i	$0.880577\pi$
$510$		0			0
$511$	−29.6078	+	24.8439i	−1.30977	+	1.09903i
$512$	−2.26711			−0.100193
$513$		0			0
$514$	−24.8548			−1.09630
$515$	−13.6827	+	11.4811i	−0.602931	+	0.505919i
$516$		0			0
$517$	−0.554981	+	3.14745i	−0.0244080	+	0.138425i
$518$	−20.9686	+	7.63196i	−0.921309	+	0.335329i
$519$		0			0
$520$	−0.283694	−	1.60891i	−0.0124408	−	0.0705553i
$521$	3.93474	+	6.81517i	0.172384	+	0.298578i	0.939253	−	0.343226i	$-0.111520\pi$
$521$	3.93474	+	6.81517i	0.172384	+	0.298578i	−0.766869	+	0.641804i	$0.778186\pi$
$522$		0			0
$523$	−16.6467	+	28.8330i	−0.727911	+	1.26078i	0.229854	+	0.973225i	$0.426175\pi$
$523$	−16.6467	+	28.8330i	−0.727911	+	1.26078i	−0.957765	+	0.287554i	$0.907158\pi$
$524$	5.92646	+	2.15705i	0.258898	+	0.0942313i
$525$		0			0
$526$	3.60898	+	3.02829i	0.157359	+	0.132040i
$527$	−1.94059	−	1.62835i	−0.0845333	−	0.0709319i
$528$		0			0
$529$	−10.3010	−	3.74925i	−0.447869	−	0.163011i
$530$	−2.70080	+	4.67792i	−0.117315	+	0.203196i
$531$		0			0
$532$	4.42516	+	7.66461i	0.191855	+	0.332303i
$533$	0.228519	+	1.29600i	0.00989826	+	0.0561358i
$534$		0			0
$535$	−17.5452	+	6.38591i	−0.758543	+	0.276087i
$536$	−0.647619	+	3.67283i	−0.0279729	+	0.158642i
$537$		0			0
$538$	−0.459084	+	0.385217i	−0.0197925	+	0.0166079i
$539$	15.4868			0.667062
$540$		0			0
$541$	22.4283			0.964266			0.482133	−	0.876098i	$-0.339862\pi$
$541$	22.4283			0.964266			0.482133	+	0.876098i	$0.339862\pi$
$542$	15.6407	−	13.1241i	0.671825	−	0.563728i
$543$		0			0
$544$	−1.44535	+	8.19701i	−0.0619690	+	0.351444i
$545$	5.00827	−	1.82286i	0.214531	−	0.0780827i
$546$		0			0
$547$	−3.62771	−	20.5738i	−0.155110	−	0.879671i	−0.958685	−	0.284468i	$-0.908183\pi$
$547$	−3.62771	−	20.5738i	−0.155110	−	0.879671i	0.803576	−	0.595202i	$-0.202928\pi$
$548$	6.45948	+	11.1881i	0.275935	+	0.477934i
$549$		0			0
$550$	−5.85447	+	10.1402i	−0.249635	+	0.432381i
$551$	−13.7118	−	4.99070i	−0.584143	−	0.212611i
$552$		0			0
$553$	−36.9896	−	31.0379i	−1.57296	−	1.31987i
$554$	−32.1784	−	27.0009i	−1.36713	−	1.14716i
$555$		0			0
$556$	−6.71505	−	2.44408i	−0.284781	−	0.103652i
$557$	4.28920	−	7.42911i	0.181739	−	0.314782i	−0.760734	−	0.649064i	$-0.775161\pi$
$557$	4.28920	−	7.42911i	0.181739	−	0.314782i	0.942473	+	0.334283i	$0.108494\pi$
$558$		0			0
$559$	1.84254	+	3.19137i	0.0779311	+	0.134981i
$560$	3.81019	+	21.6087i	0.161010	+	0.913132i
$561$		0			0
$562$	−11.5668	+	4.20996i	−0.487915	+	0.177586i
$563$	2.72886	−	15.4761i	0.115008	−	0.652241i	−0.871739	−	0.489971i	$-0.837007\pi$
$563$	2.72886	−	15.4761i	0.115008	−	0.652241i	0.986746	−	0.162270i	$-0.0518816\pi$
$564$		0			0
$565$	−17.2579	+	14.4811i	−0.726044	+	0.609223i
$566$	24.1851			1.01658
$567$		0			0
$568$	24.0545			1.00930
$569$	−9.70792	+	8.14591i	−0.406977	+	0.341494i	−0.823183	−	0.567776i	$-0.807804\pi$
$569$	−9.70792	+	8.14591i	−0.406977	+	0.341494i	0.416206	+	0.909270i	$0.363360\pi$
$570$		0			0
$571$	−4.57089	+	25.9228i	−0.191286	+	1.08483i	0.726324	+	0.687352i	$0.241227\pi$
$571$	−4.57089	+	25.9228i	−0.191286	+	1.08483i	−0.917610	+	0.397483i	$0.869884\pi$
$572$	1.06291	−	0.386869i	0.0444427	−	0.0161758i
$573$		0			0
$574$	−2.04955	−	11.6236i	−0.0855467	−	0.485159i
$575$	10.8516	+	18.7954i	0.452541	+	0.783824i
$576$		0			0
$577$	11.0577	−	19.1525i	0.460338	−	0.797329i	−0.538640	−	0.842536i	$-0.681062\pi$
$577$	11.0577	−	19.1525i	0.460338	−	0.797329i	0.998978	+	0.0452074i	$0.0143949\pi$
$578$	−21.2120	−	7.72055i	−0.882305	−	0.321133i
$579$		0			0
$580$	3.79982	+	3.18842i	0.157779	+	0.132392i
$581$	−34.9842	−	29.3552i	−1.45139	−	1.21786i
$582$		0			0
$583$	5.00042	+	1.82001i	0.207096	+	0.0753769i
$584$	−9.76057	+	16.9058i	−0.403895	+	0.699567i
$585$		0			0
$586$	12.1156	+	20.9848i	0.500491	+	0.866876i
$587$	−2.48371	−	14.0858i	−0.102514	−	0.581385i	−0.992184	−	0.124781i	$-0.960177\pi$
$587$	−2.48371	−	14.0858i	−0.102514	−	0.581385i	0.889670	−	0.456603i	$-0.150934\pi$
$588$		0			0
$589$	−3.45532	+	1.25763i	−0.142374	+	0.0518199i
$590$	−3.71243	+	21.0543i	−0.152838	+	0.866790i
$591$		0			0
$592$	−12.9286	+	10.8484i	−0.531363	+	0.445866i
$593$	−47.7300			−1.96004			−0.980018	−	0.198908i	$-0.936260\pi$
$593$	−47.7300			−1.96004			−0.980018	+	0.198908i	$0.936260\pi$
$594$		0			0
$595$	8.34334			0.342044
$596$	1.55798	−	1.30730i	0.0638174	−	0.0535492i
$597$		0			0
$598$	1.24617	−	7.06739i	0.0509598	−	0.289007i
$599$	−0.469442	+	0.170863i	−0.0191809	+	0.00698127i	−0.351593	−	0.936153i	$-0.614360\pi$
$599$	−0.469442	+	0.170863i	−0.0191809	+	0.00698127i	0.332412	+	0.943134i	$0.392138\pi$
$600$		0			0
$601$	−2.93936	−	16.6699i	−0.119899	−	0.679980i	−0.984208	−	0.177019i	$-0.943355\pi$
$601$	−2.93936	−	16.6699i	−0.119899	−	0.679980i	0.864309	−	0.502962i	$-0.167756\pi$
$602$	−16.5254	−	28.6229i	−0.673527	−	1.16658i
$603$		0			0
$604$	4.33923	−	7.51577i	0.176561	−	0.305812i
$605$	7.96216	+	2.89799i	0.323708	+	0.117820i
$606$		0			0
$607$	0.532119	+	0.446501i	0.0215981	+	0.0181229i	0.653523	−	0.756907i	$-0.273290\pi$
$607$	0.532119	+	0.446501i	0.0215981	+	0.0181229i	−0.631925	+	0.775030i	$0.717735\pi$
$608$	9.25510	+	7.76595i	0.375344	+	0.314951i
$609$		0			0
$610$	9.33276	+	3.39685i	0.377872	+	0.137534i
$611$	−0.625887	+	1.08407i	−0.0253207	+	0.0438567i
$612$		0			0
$613$	16.3317	+	28.2873i	0.659630	+	1.14251i	0.980711	+	0.195461i	$0.0626204\pi$
$613$	16.3317	+	28.2873i	0.659630	+	1.14251i	−0.321081	+	0.947052i	$0.604046\pi$
$614$	8.88288	+	50.3773i	0.358484	+	2.03306i
$615$		0			0
$616$	13.5644	−	4.93704i	0.546526	−	0.198919i
$617$	−3.97384	+	22.5368i	−0.159981	+	0.907296i	0.794109	+	0.607775i	$0.207938\pi$
$617$	−3.97384	+	22.5368i	−0.159981	+	0.907296i	−0.954090	+	0.299521i	$0.903173\pi$
$618$		0			0
$619$	6.50045	−	5.45453i	0.261275	−	0.219236i	−0.502734	−	0.864441i	$-0.667673\pi$
$619$	6.50045	−	5.45453i	0.261275	−	0.219236i	0.764009	+	0.645205i	$0.223228\pi$
$620$	1.24998			0.0502002
$621$		0			0
$622$	−23.5254			−0.943282
$623$	−17.1542	+	14.3941i	−0.687267	+	0.576686i
$624$		0			0
$625$	1.30059	−	7.37601i	0.0520236	−	0.295040i
$626$	34.8882	−	12.6983i	1.39441	−	0.507525i
$627$		0			0
$628$	0.0515953	+	0.292611i	0.00205887	+	0.0116765i
$629$	3.20872	+	5.55767i	0.127940	+	0.221599i
$630$		0			0
$631$	−0.795865	+	1.37848i	−0.0316829	+	0.0548763i	−0.881432	−	0.472311i	$-0.843420\pi$
$631$	−0.795865	+	1.37848i	−0.0316829	+	0.0548763i	0.849749	+	0.527187i	$0.176753\pi$
$632$	−22.9174	−	8.34124i	−0.911604	−	0.331797i
$633$		0			0
$634$	22.3906	+	18.7880i	0.889246	+	0.746166i
$635$	0.925380	+	0.776486i	0.0367226	+	0.0308139i
$636$		0			0
$637$	5.69987	+	2.07458i	0.225837	+	0.0821980i
$638$	8.36313	−	14.4854i	0.331099	−	0.573481i
$639$		0			0
$640$	7.38198	+	12.7860i	0.291798	+	0.505409i
$641$	−3.76377	−	21.3454i	−0.148660	−	0.843092i	−0.964355	−	0.264610i	$-0.914757\pi$
$641$	−3.76377	−	21.3454i	−0.148660	−	0.843092i	0.815696	−	0.578481i	$-0.196354\pi$
$642$		0			0
$643$	6.48582	−	2.36064i	0.255776	−	0.0930947i	−0.210950	−	0.977497i	$-0.567656\pi$
$643$	6.48582	−	2.36064i	0.255776	−	0.0930947i	0.466726	+	0.884402i	$0.345434\pi$
$644$	−3.26530	+	18.5185i	−0.128671	+	0.729729i
$645$		0			0
$646$	6.67393	−	5.60010i	0.262582	−	0.220333i
$647$	6.18972			0.243343			0.121671	−	0.992570i	$-0.461175\pi$
$647$	6.18972			0.243343			0.121671	+	0.992570i	$0.461175\pi$
$648$		0			0
$649$	21.0614			0.826733
$650$	−3.51309	+	2.94783i	−0.137795	+	0.115624i
$651$		0			0
$652$	2.09544	−	11.8838i	0.0820636	−	0.465406i
$653$	−25.5732	+	9.30790i	−1.00076	+	0.364246i	−0.789877	−	0.613265i	$-0.789856\pi$
$653$	−25.5732	+	9.30790i	−1.00076	+	0.364246i	−0.210881	+	0.977512i	$0.567633\pi$
$654$		0			0
$655$	−1.49859	−	8.49894i	−0.0585549	−	0.332081i
$656$	−4.46347	−	7.73096i	−0.174269	−	0.301843i
$657$		0			0
$658$	5.61348	−	9.72283i	0.218836	−	0.379035i
$659$	4.96345	+	1.80655i	0.193349	+	0.0703732i	0.436880	−	0.899520i	$-0.356084\pi$
$659$	4.96345	+	1.80655i	0.193349	+	0.0703732i	−0.243531	+	0.969893i	$0.578306\pi$
$660$		0			0
$661$	8.93594	+	7.49814i	0.347568	+	0.291644i	0.799813	−	0.600250i	$-0.204932\pi$
$661$	8.93594	+	7.49814i	0.347568	+	0.291644i	−0.452245	+	0.891894i	$0.649377\pi$
$662$	−1.11272	−	0.933685i	−0.0432472	−	0.0362887i
$663$		0			0
$664$	−21.6749	−	7.88902i	−0.841149	−	0.306153i
$665$	6.05527	−	10.4880i	0.234813	−	0.406708i
$666$		0			0
$667$	−15.5015	−	26.8494i	−0.600220	−	1.03961i
$668$	−0.311887	−	1.76880i	−0.0120673	−	0.0684370i
$669$		0			0
$670$	−3.37033	+	1.22670i	−0.130207	+	0.0473915i
$671$	1.69900	−	9.63551i	0.0655892	−	0.371975i
$672$		0			0
$673$	37.6146	−	31.5624i	1.44994	−	1.21664i	0.517312	−	0.855797i	$-0.326933\pi$
$673$	37.6146	−	31.5624i	1.44994	−	1.21664i	0.932626	−	0.360845i	$-0.117512\pi$
$674$	−0.703510			−0.0270982
$675$		0			0
$676$	−10.2880			−0.395693
$677$	17.3272	−	14.5392i	0.665938	−	0.558789i	−0.245922	−	0.969290i	$-0.579091\pi$
$677$	17.3272	−	14.5392i	0.665938	−	0.558789i	0.911860	+	0.410501i	$0.134646\pi$
$678$		0			0
$679$	0.233077	−	1.32185i	0.00894469	−	0.0507279i
$680$	3.95986	−	1.44127i	0.151854	−	0.0552702i
$681$		0			0
$682$	−0.731918	−	4.15091i	−0.0280266	−	0.158947i
$683$	−8.56931	−	14.8425i	−0.327896	−	0.567932i	0.654198	−	0.756323i	$-0.273006\pi$
$683$	−8.56931	−	14.8425i	−0.327896	−	0.567932i	−0.982094	+	0.188391i	$0.939673\pi$
$684$		0			0
$685$	8.83897	−	15.3095i	0.337720	−	0.584947i
$686$	−7.90111	−	2.87577i	−0.301666	−	0.109797i
$687$		0			0
$688$	−19.1492	−	16.0681i	−0.730057	−	0.612591i
$689$	1.59659	+	1.33970i	0.0608252	+	0.0510384i
$690$		0			0
$691$	−17.1549	−	6.24389i	−0.652605	−	0.237529i	−0.00556457	−	0.999985i	$-0.501771\pi$
$691$	−17.1549	−	6.24389i	−0.652605	−	0.237529i	−0.647040	+	0.762456i	$0.723993\pi$
$692$	−7.25049	+	12.5582i	−0.275622	+	0.477392i
$693$		0			0
$694$	−19.6749	−	34.0779i	−0.746848	−	1.29358i
$695$	1.69800	+	9.62983i	0.0644088	+	0.365280i
$696$		0			0
$697$	−3.18972	+	1.16096i	−0.120819	+	0.0439746i
$698$	−6.18112	+	35.0549i	−0.233959	+	1.32685i
$699$		0			0
$700$	9.20524	−	7.72411i	0.347925	−	0.291944i
$701$	2.92075			0.110315			0.0551575	−	0.998478i	$-0.482434\pi$
$701$	2.92075			0.110315			0.0551575	+	0.998478i	$0.482434\pi$
$702$		0			0
$703$	9.31505			0.351324
$704$	3.63232	−	3.04788i	0.136898	−	0.114871i
$705$		0			0
$706$	6.87233	−	38.9749i	0.258644	−	1.46684i
$707$	63.9217	−	23.2656i	2.40402	−	0.874993i
$708$		0			0
$709$	5.21419	+	29.5711i	0.195823	+	1.11057i	0.911242	+	0.411872i	$0.135125\pi$
$709$	5.21419	+	29.5711i	0.195823	+	1.11057i	−0.715419	+	0.698696i	$0.753764\pi$
$710$	11.5665	+	20.0338i	0.434084	+	0.751856i
$711$		0			0
$712$	−5.65509	+	9.79490i	−0.211933	+	0.367079i
$713$	−7.34146	−	2.67207i	−0.274940	−	0.100070i
$714$		0			0
$715$	−1.18569	−	0.994910i	−0.0443422	−	0.0372075i
$716$	−0.635171	−	0.532971i	−0.0237374	−	0.0199181i
$717$		0			0
$718$	16.5235	+	6.01405i	0.616650	+	0.224442i
$719$	20.0285	−	34.6903i	0.746936	−	1.29373i	−0.202349	−	0.979314i	$-0.564857\pi$
$719$	20.0285	−	34.6903i	0.746936	−	1.29373i	0.949285	−	0.314418i	$-0.101809\pi$
$720$		0			0
$721$	−30.9059	−	53.5306i	−1.15100	−	1.99358i
$722$	3.34992	+	18.9983i	0.124671	+	0.707044i
$723$		0			0
$724$	16.4238	−	5.97776i	0.610384	−	0.222162i
$725$	−3.44034	+	19.5111i	−0.127771	+	0.724626i
$726$		0			0
$727$	−1.17877	+	0.989109i	−0.0437183	+	0.0366840i	−0.664385	−	0.747390i	$-0.731306\pi$
$727$	−1.17877	+	0.989109i	−0.0437183	+	0.0366840i	0.620667	+	0.784075i	$0.286862\pi$
$728$	5.65371			0.209540
$729$		0			0
$730$	−18.7734			−0.694834
$731$	−7.28140	+	6.10982i	−0.269312	+	0.225980i
$732$		0			0
$733$	−0.262538	+	1.48893i	−0.00969705	+	0.0549947i	−0.989272	−	0.146083i	$-0.953333\pi$
$733$	−0.262538	+	1.48893i	−0.00969705	+	0.0549947i	0.979575	+	0.201078i	$0.0644444\pi$
$734$	33.5783	−	12.2215i	1.23940	−	0.451104i
$735$		0			0
$736$	4.45750	+	25.2797i	0.164306	+	0.931824i
$737$	1.76667	+	3.05997i	0.0650762	+	0.112715i
$738$		0			0
$739$	−10.6779	+	18.4946i	−0.392792	+	0.680336i	−0.992817	−	0.119646i	$-0.961824\pi$
$739$	−10.6779	+	18.4946i	−0.392792	+	0.680336i	0.600024	+	0.799982i	$0.295157\pi$
$740$	−2.97557	−	1.08302i	−0.109384	−	0.0398126i
$741$		0			0
$742$	−14.3196	−	12.0155i	−0.525687	−	0.441104i
$743$	15.5727	+	13.0671i	0.571308	+	0.479384i	0.882080	−	0.471101i	$-0.156143\pi$
$743$	15.5727	+	13.0671i	0.571308	+	0.479384i	−0.310772	+	0.950485i	$0.600588\pi$
$744$		0			0
$745$	−2.61516	−	0.951841i	−0.0958121	−	0.0348728i
$746$	1.94153	−	3.36282i	0.0710843	−	0.123122i
$747$		0			0
$748$	1.45880	+	2.52672i	0.0533391	+	0.0923860i
$749$	−11.2201	−	63.6322i	−0.409972	−	2.32507i
$750$		0			0
$751$	−4.00606	+	1.45808i	−0.146183	+	0.0532063i	−0.414075	−	0.910243i	$-0.635895\pi$
$751$	−4.00606	+	1.45808i	−0.146183	+	0.0532063i	0.267892	+	0.963449i	$0.413673\pi$
$752$	1.47451	−	8.36233i	0.0537697	−	0.304943i
$753$		0			0
$754$	5.01847	−	4.21099i	0.182762	−	0.153355i
$755$	−11.8754			−0.432189
$756$		0			0
$757$	54.3419			1.97509			0.987546	−	0.157332i	$-0.0502892\pi$
$757$	54.3419			1.97509			0.987546	+	0.157332i	$0.0502892\pi$
$758$	−16.1651	+	13.5641i	−0.587141	+	0.492670i
$759$		0			0
$760$	1.06215	−	6.02377i	0.0385283	−	0.218505i
$761$	17.0659	−	6.21147i	0.618637	−	0.225165i	−0.0136411	−	0.999907i	$-0.504342\pi$
$761$	17.0659	−	6.21147i	0.618637	−	0.225165i	0.632278	+	0.774741i	$0.282120\pi$
$762$		0			0
$763$	3.20277	+	18.1638i	0.115948	+	0.657574i
$764$	−4.05650	−	7.02606i	−0.146759	−	0.254194i
$765$		0			0
$766$	16.5188	−	28.6113i	0.596847	−	1.03377i
$767$	7.75161	+	2.82135i	0.279894	+	0.101873i
$768$		0			0
$769$	19.0398	+	15.9763i	0.686594	+	0.576121i	0.917925	−	0.396755i	$-0.129864\pi$
$769$	19.0398	+	15.9763i	0.686594	+	0.576121i	−0.231331	+	0.972875i	$0.574308\pi$
$770$	10.6342	+	8.92319i	0.383232	+	0.321570i
$771$		0			0
$772$	8.65360	+	3.14965i	0.311450	+	0.113358i
$773$	19.2416	−	33.3274i	0.692071	−	1.19870i	−0.279087	−	0.960266i	$-0.590032\pi$
$773$	19.2416	−	33.3274i	0.692071	−	1.19870i	0.971158	−	0.238437i	$-0.0766350\pi$
$774$		0			0
$775$	2.49629	+	4.32369i	0.0896692	+	0.155312i
$776$	−0.117721	−	0.667629i	−0.00422594	−	0.0239665i
$777$		0			0
$778$	29.7626	−	10.8327i	1.06704	−	0.388372i
$779$	−0.855579	+	4.85223i	−0.0306543	+	0.173849i

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28765 + 1.08047i) q^{2} +(0.143341 - 0.812925i) q^{4} +(-1.06142 + 0.386327i) q^{5} +(-0.678777 - 3.84954i) q^{7} +(-0.987144 - 1.70978i) q^{8} +O(q^{10})\)	\(q+(-1.28765 + 1.08047i) q^{2} +(0.143341 - 0.812925i) q^{4} +(-1.06142 + 0.386327i) q^{5} +(-0.678777 - 3.84954i) q^{7} +(-0.987144 - 1.70978i) q^{8} +(0.949332 - 1.64429i) q^{10} +(-1.75765 - 0.639734i) q^{11} +(-0.561203 - 0.470905i) q^{13} +(5.03334 + 4.22347i) q^{14} +(4.66984 + 1.69968i) q^{16} +(0.944822 - 1.63648i) q^{17} +(-1.37143 - 2.37538i) q^{19} +(0.161910 + 0.918235i) q^{20} +(2.95446 - 1.07534i) q^{22} +(1.01197 - 5.73916i) q^{23} +(-2.85285 + 2.39382i) q^{25} +1.23143 q^{26} -3.22668 q^{28} +(4.07531 - 3.41959i) q^{29} +(0.232793 - 1.32023i) q^{31} +(-4.13914 + 1.50652i) q^{32} +(0.551563 + 3.12807i) q^{34} +(2.20765 + 3.82376i) q^{35} +(-1.69806 + 2.94112i) q^{37} +(4.33245 + 1.57688i) q^{38} +(1.70831 + 1.43345i) q^{40} +(-1.37607 - 1.15466i) q^{41} +(-4.72680 - 1.72041i) q^{43} +(-0.771999 + 1.33714i) q^{44} +(4.89793 + 8.48346i) q^{46} +(-0.296709 - 1.68272i) q^{47} +(-7.78035 + 2.83182i) q^{49} +(1.08703 - 6.16483i) q^{50} +(-0.463253 + 0.388716i) q^{52} -2.84494 q^{53} +2.11276 q^{55} +(-5.91183 + 4.96061i) q^{56} +(-1.55282 + 8.80649i) q^{58} +(-10.5810 + 3.85116i) q^{59} +(0.908335 + 5.15142i) q^{61} +(1.12672 + 1.95153i) q^{62} +(-1.26751 + 2.19540i) q^{64} +(0.777597 + 0.283022i) q^{65} +(-1.44708 - 1.21424i) q^{67} +(-1.19490 - 1.00264i) q^{68} +(-6.97415 - 2.53838i) q^{70} +(-6.09193 + 10.5515i) q^{71} +(-4.94384 - 8.56298i) q^{73} +(-0.991282 - 5.62184i) q^{74} +(-2.12759 + 0.774379i) q^{76} +(-1.26962 + 7.20039i) q^{77} +(9.46285 - 7.94028i) q^{79} -5.61331 q^{80} +3.01948 q^{82} +(8.94982 - 7.50979i) q^{83} +(-0.370641 + 2.10201i) q^{85} +(7.94533 - 2.89186i) q^{86} +(0.641252 + 3.63672i) q^{88} +(-2.86437 - 4.96123i) q^{89} +(-1.43183 + 2.48001i) q^{91} +(-4.52045 - 1.64531i) q^{92} +(2.20018 + 1.84617i) q^{94} +(2.37334 + 1.99147i) q^{95} +(0.322670 + 0.117442i) q^{97} +(6.95870 - 12.0528i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8	\( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28} + 24 q^{29} + 12 q^{31} - 27 q^{32} - 12 q^{35} - 3 q^{37} + 30 q^{38} - 15 q^{40} - 6 q^{41} - 15 q^{43} - 3 q^{44} - 3 q^{46} - 12 q^{47} - 33 q^{49} - 21 q^{50} - 45 q^{52} + 18 q^{53} - 12 q^{55} - 30 q^{56} - 51 q^{58} + 3 q^{59} - 33 q^{61} + 12 q^{62} + 12 q^{64} - 21 q^{65} - 6 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} + 21 q^{74} + 6 q^{76} + 12 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 6 q^{83} + 36 q^{85} + 21 q^{86} + 42 q^{88} - 9 q^{89} + 6 q^{91} + 3 q^{92} + 48 q^{94} - 3 q^{95} + 39 q^{97} + 45 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 + 6 * q^11 + 3 * q^13 + 21 * q^14 + 9 * q^16 - 9 * q^17 - 3 * q^19 - 24 * q^20 + 12 * q^22 + 12 * q^23 + 12 * q^25 + 30 * q^26 - 12 * q^28 + 24 * q^29 + 12 * q^31 - 27 * q^32 - 12 * q^35 - 3 * q^37 + 30 * q^38 - 15 * q^40 - 6 * q^41 - 15 * q^43 - 3 * q^44 - 3 * q^46 - 12 * q^47 - 33 * q^49 - 21 * q^50 - 45 * q^52 + 18 * q^53 - 12 * q^55 - 30 * q^56 - 51 * q^58 + 3 * q^59 - 33 * q^61 + 12 * q^62 + 12 * q^64 - 21 * q^65 - 6 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 + 21 * q^74 + 6 * q^76 + 12 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 6 * q^83 + 36 * q^85 + 21 * q^86 + 42 * q^88 - 9 * q^89 + 6 * q^91 + 3 * q^92 + 48 * q^94 - 3 * q^95 + 39 * q^97 + 45 * q^98

Introduction

L-functions

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