LMFDB - Embedded newform 729.2.g.b.55.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			55.4
Character	$\chi$	$=$	729.55
Dual form			729.2.g.b.676.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0800459 - 0.185567i) q^{2} +(1.34446 + 1.42504i) q^{4} +(0.0529885 + 0.909778i) q^{5} +(0.159621 + 0.0378310i) q^{7} +(0.751874 - 0.273660i) q^{8} +O(q^{10})$	\(q+(0.0800459 - 0.185567i) q^{2} +(1.34446 + 1.42504i) q^{4} +(0.0529885 + 0.909778i) q^{5} +(0.159621 + 0.0378310i) q^{7} +(0.751874 - 0.273660i) q^{8} +(0.173067 + 0.0629911i) q^{10} +(-0.626618 - 0.412133i) q^{11} +(3.50987 + 0.410245i) q^{13} +(0.0197972 - 0.0265923i) q^{14} +(-0.218428 + 3.75026i) q^{16} +(3.09332 - 2.59561i) q^{17} +(1.63194 + 1.36936i) q^{19} +(-1.22523 + 1.29867i) q^{20} +(-0.126637 + 0.0832903i) q^{22} +(-7.98355 + 1.89214i) q^{23} +(4.14130 - 0.484049i) q^{25} +(0.357079 - 0.618479i) q^{26} +(0.160693 + 0.278329i) q^{28} +(3.92999 + 5.27889i) q^{29} +(-1.60483 + 5.36050i) q^{31} +(2.10848 + 1.05892i) q^{32} +(-0.234052 - 0.781788i) q^{34} +(-0.0259597 + 0.147225i) q^{35} +(0.783915 + 4.44580i) q^{37} +(0.384740 - 0.193224i) q^{38} +(0.288810 + 0.669538i) q^{40} +(-4.33453 - 10.0486i) q^{41} +(-3.09218 + 1.55295i) q^{43} +(-0.255154 - 1.44705i) q^{44} +(-0.287932 + 1.63294i) q^{46} +(2.56133 + 8.55545i) q^{47} +(-6.23138 - 3.12952i) q^{49} +(0.241671 - 0.807237i) q^{50} +(4.13425 + 5.55326i) q^{52} +(-3.06986 - 5.31715i) q^{53} +(0.341746 - 0.591922i) q^{55} +(0.130368 - 0.0152378i) q^{56} +(1.29417 - 0.306724i) q^{58} +(-2.43628 + 1.60237i) q^{59} +(4.84595 - 5.13641i) q^{61} +(0.866274 + 0.726890i) q^{62} +(-5.39019 + 4.52290i) q^{64} +(-0.187249 + 3.21494i) q^{65} +(5.30383 - 7.12428i) q^{67} +(7.85768 + 0.918431i) q^{68} +(0.0252421 + 0.0166020i) q^{70} +(8.94644 + 3.25624i) q^{71} +(8.28233 - 3.01452i) q^{73} +(0.887745 + 0.210399i) q^{74} +(0.242679 + 4.16663i) q^{76} +(-0.0844303 - 0.0894909i) q^{77} +(-1.27718 + 2.96084i) q^{79} -3.42347 q^{80} -2.21165 q^{82} +(6.66541 - 15.4521i) q^{83} +(2.52534 + 2.67670i) q^{85} +(0.0406606 + 0.698115i) q^{86} +(-0.583922 - 0.138392i) q^{88} +(-10.7409 + 3.90935i) q^{89} +(0.544730 + 0.198266i) q^{91} +(-13.4299 - 8.83298i) q^{92} +(1.79264 + 0.209529i) q^{94} +(-1.15934 + 1.55727i) q^{95} +(0.263420 - 4.52275i) q^{97} +(-1.07953 + 0.905836i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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 $

$2$	0.0800459	−	0.185567i	0.0566010	−	0.131216i	−0.887569	−	0.460675i	$-0.847607\pi$
$2$	0.0800459	−	0.185567i	0.0566010	−	0.131216i	0.944170	+	0.329459i	$0.106866\pi$
$3$		0			0
$3$		0			0
$4$	1.34446	+	1.42504i	0.672228	+	0.712520i
$5$	0.0529885	+	0.909778i	0.0236972	+	0.406865i	0.989210	+	0.146508i	$0.0468033\pi$
$5$	0.0529885	+	0.909778i	0.0236972	+	0.406865i	−0.965512	+	0.260357i	$0.916160\pi$
$6$		0			0
$7$	0.159621	+	0.0378310i	0.0603312	+	0.0142988i	0.260671	−	0.965428i	$-0.416056\pi$
$7$	0.159621	+	0.0378310i	0.0603312	+	0.0142988i	−0.200339	+	0.979727i	$0.564204\pi$
$8$	0.751874	−	0.273660i	0.265828	−	0.0967534i
$9$		0			0
$10$	0.173067	+	0.0629911i	0.0547284	+	0.0199195i
$11$	−0.626618	−	0.412133i	−0.188932	−	0.124263i	0.451519	−	0.892262i	$-0.350882\pi$
$11$	−0.626618	−	0.412133i	−0.188932	−	0.124263i	−0.640451	+	0.767999i	$0.721253\pi$
$12$		0			0
$13$	3.50987	+	0.410245i	0.973463	+	0.113781i	0.587929	−	0.808912i	$-0.299943\pi$
$13$	3.50987	+	0.410245i	0.973463	+	0.113781i	0.385533	+	0.922694i	$0.374017\pi$
$14$	0.0197972	−	0.0265923i	0.00529104	−	0.00710710i
$15$		0			0
$16$	−0.218428	+	3.75026i	−0.0546069	+	0.937564i
$17$	3.09332	−	2.59561i	0.750241	−	0.629527i	−0.185326	−	0.982677i	$-0.559334\pi$
$17$	3.09332	−	2.59561i	0.750241	−	0.629527i	0.935567	+	0.353150i	$0.114890\pi$
$18$		0			0
$19$	1.63194	+	1.36936i	0.374394	+	0.314154i	0.810497	−	0.585743i	$-0.199197\pi$
$19$	1.63194	+	1.36936i	0.374394	+	0.314154i	−0.436103	+	0.899897i	$0.643642\pi$
$20$	−1.22523	+	1.29867i	−0.273969	+	0.290391i
$21$		0			0
$22$	−0.126637	+	0.0832903i	−0.0269990	+	0.0177575i
$23$	−7.98355	+	1.89214i	−1.66469	+	0.394538i	−0.951794	−	0.306737i	$-0.900763\pi$
$23$	−7.98355	+	1.89214i	−1.66469	+	0.394538i	−0.712891	+	0.701275i	$0.752615\pi$
$24$		0			0
$25$	4.14130	−	0.484049i	0.828261	−	0.0968098i
$26$	0.357079	−	0.618479i	0.0700289	−	0.121294i
$27$		0			0
$28$	0.160693	+	0.278329i	0.0303682	+	0.0525992i
$29$	3.92999	+	5.27889i	0.729780	+	0.980265i	0.999848	+	0.0174234i	$0.00554633\pi$
$29$	3.92999	+	5.27889i	0.729780	+	0.980265i	−0.270068	+	0.962841i	$0.587046\pi$
$30$		0			0
$31$	−1.60483	+	5.36050i	−0.288236	+	0.962774i	0.684140	+	0.729351i	$0.260178\pi$
$31$	−1.60483	+	5.36050i	−0.288236	+	0.962774i	−0.972375	+	0.233423i	$0.925007\pi$
$32$	2.10848	+	1.05892i	0.372730	+	0.187192i
$33$		0			0
$34$	−0.234052	−	0.781788i	−0.0401396	−	0.134075i
$35$	−0.0259597	+	0.147225i	−0.00438799	+	0.0248855i
$36$		0			0
$37$	0.783915	+	4.44580i	0.128875	+	0.730885i	0.978931	+	0.204193i	$0.0654569\pi$
$37$	0.783915	+	4.44580i	0.128875	+	0.730885i	−0.850056	+	0.526692i	$0.823432\pi$
$38$	0.384740	−	0.193224i	0.0624130	−	0.0313450i
$39$		0			0
$40$	0.288810	+	0.669538i	0.0456649	+	0.105863i
$41$	−4.33453	−	10.0486i	−0.676940	−	1.56932i	−0.815363	−	0.578950i	$-0.803463\pi$
$41$	−4.33453	−	10.0486i	−0.676940	−	1.56932i	0.138423	−	0.990373i	$-0.455797\pi$
$42$		0			0
$43$	−3.09218	+	1.55295i	−0.471553	+	0.236823i	−0.668673	−	0.743557i	$-0.733137\pi$
$43$	−3.09218	+	1.55295i	−0.471553	+	0.236823i	0.197120	+	0.980379i	$0.436841\pi$
$44$	−0.255154	−	1.44705i	−0.0384659	−	0.218151i
$45$		0			0
$46$	−0.287932	+	1.63294i	−0.0424533	+	0.240764i
$47$	2.56133	+	8.55545i	0.373609	+	1.24794i	0.913719	+	0.406346i	$0.133197\pi$
$47$	2.56133	+	8.55545i	0.373609	+	1.24794i	−0.540110	+	0.841594i	$0.681617\pi$
$48$		0			0
$49$	−6.23138	−	3.12952i	−0.890197	−	0.447074i
$50$	0.241671	−	0.807237i	0.0341774	−	0.114161i
$51$		0			0
$52$	4.13425	+	5.55326i	0.573317	+	0.770098i
$53$	−3.06986	−	5.31715i	−0.421677	−	0.730366i	0.574426	−	0.818556i	$-0.305225\pi$
$53$	−3.06986	−	5.31715i	−0.421677	−	0.730366i	−0.996104	+	0.0881898i	$0.971892\pi$
$54$		0			0
$55$	0.341746	−	0.591922i	0.0460810	−	0.0798147i
$56$	0.130368	−	0.0152378i	0.0174212	−	0.00203624i
$57$		0			0
$58$	1.29417	−	0.306724i	0.169933	−	0.0402748i
$59$	−2.43628	+	1.60237i	−0.317177	+	0.208611i	−0.698107	−	0.715993i	$-0.745974\pi$
$59$	−2.43628	+	1.60237i	−0.317177	+	0.208611i	0.380930	+	0.924604i	$0.375604\pi$
$60$		0			0
$61$	4.84595	−	5.13641i	0.620461	−	0.657650i	−0.338573	−	0.940940i	$-0.609944\pi$
$61$	4.84595	−	5.13641i	0.620461	−	0.657650i	0.959034	+	0.283290i	$0.0914258\pi$
$62$	0.866274	+	0.726890i	0.110017	+	0.0923151i
$63$		0			0
$64$	−5.39019	+	4.52290i	−0.673774	+	0.565363i
$65$	−0.187249	+	3.21494i	−0.0232254	+	0.398764i
$66$		0			0
$67$	5.30383	−	7.12428i	0.647966	−	0.870370i	−0.349824	−	0.936816i	$-0.613759\pi$
$67$	5.30383	−	7.12428i	0.647966	−	0.870370i	0.997790	+	0.0664457i	$0.0211659\pi$
$68$	7.85768	+	0.918431i	0.952883	+	0.111376i
$69$		0			0
$70$	0.0252421	+	0.0166020i	0.00301701	+	0.00198432i
$71$	8.94644	+	3.25624i	1.06175	+	0.386444i	0.813084	−	0.582146i	$-0.197787\pi$
$71$	8.94644	+	3.25624i	1.06175	+	0.386444i	0.248663	+	0.968590i	$0.420009\pi$
$72$		0			0
$73$	8.28233	−	3.01452i	0.969373	−	0.352823i	0.191673	−	0.981459i	$-0.438609\pi$
$73$	8.28233	−	3.01452i	0.969373	−	0.352823i	0.777700	+	0.628636i	$0.216386\pi$
$74$	0.887745	+	0.210399i	0.103198	+	0.0244584i
$75$		0			0
$76$	0.242679	+	4.16663i	0.0278372	+	0.477946i
$77$	−0.0844303	−	0.0894909i	−0.00962173	−	0.0101984i
$78$		0			0
$79$	−1.27718	+	2.96084i	−0.143694	+	0.333121i	−0.974830	−	0.222948i	$-0.928432\pi$
$79$	−1.27718	+	2.96084i	−0.143694	+	0.333121i	0.831136	+	0.556069i	$0.187691\pi$
$80$	−3.42347			−0.382756
$81$		0			0
$82$	−2.21165			−0.244236
$83$	6.66541	−	15.4521i	0.731623	−	1.69609i	0.0137642	−	0.999905i	$-0.495619\pi$
$83$	6.66541	−	15.4521i	0.731623	−	1.69609i	0.717859	−	0.696188i	$-0.245122\pi$
$84$		0			0
$85$	2.52534	+	2.67670i	0.273911	+	0.290329i
$86$	0.0406606	+	0.698115i	0.00438454	+	0.0752797i
$87$		0			0
$88$	−0.583922	−	0.138392i	−0.0622463	−	0.0147527i
$89$	−10.7409	+	3.90935i	−1.13853	+	0.414390i	−0.841382	−	0.540442i	$-0.818257\pi$
$89$	−10.7409	+	3.90935i	−1.13853	+	0.414390i	−0.297146	+	0.954832i	$0.596035\pi$
$90$		0			0
$91$	0.544730	+	0.198266i	0.0571033	+	0.0207839i
$92$	−13.4299	−	8.83298i	−1.40016	−	0.920902i
$93$		0			0
$94$	1.79264	+	0.209529i	0.184896	+	0.0216113i
$95$	−1.15934	+	1.55727i	−0.118946	+	0.159772i
$96$		0			0
$97$	0.263420	−	4.52275i	0.0267463	−	0.459216i	−0.958172	−	0.286194i	$-0.907610\pi$
$97$	0.263420	−	4.52275i	0.0267463	−	0.459216i	0.984918	−	0.173022i	$-0.0553531\pi$
$98$	−1.07953	+	0.905836i	−0.109049	+	0.0915032i
$99$		0			0
$100$	6.25759	+	5.25074i	0.625759	+	0.525074i
$101$	1.57950	−	1.67417i	0.157166	−	0.166586i	−0.644006	−	0.765020i	$-0.722729\pi$
$101$	1.57950	−	1.67417i	0.157166	−	0.166586i	0.801172	+	0.598435i	$0.204210\pi$
$102$		0			0
$103$	−2.17433	+	1.43008i	−0.214243	+	0.140910i	−0.652095	−	0.758137i	$-0.726110\pi$
$103$	−2.17433	+	1.43008i	−0.214243	+	0.140910i	0.437852	+	0.899047i	$0.355739\pi$
$104$	2.75125	−	0.652058i	0.269782	−	0.0639395i
$105$		0			0
$106$	−1.23242	+	0.144049i	−0.119703	+	0.0139913i
$107$	5.97720	−	10.3528i	0.577837	−	1.00084i	−0.417890	−	0.908498i	$-0.637230\pi$
$107$	5.97720	−	10.3528i	0.577837	−	1.00084i	0.995727	−	0.0923460i	$-0.0294366\pi$
$108$		0			0
$109$	−9.06553	−	15.7020i	−0.868320	−	1.50397i	−0.863712	−	0.503985i	$-0.831867\pi$
$109$	−9.06553	−	15.7020i	−0.868320	−	1.50397i	−0.00460743	−	0.999989i	$-0.501467\pi$
$110$	−0.0824859	−	0.110798i	−0.00786472	−	0.0105642i
$111$		0			0
$112$	−0.176742	+	0.590358i	−0.0167005	+	0.0557836i
$113$	10.6343	+	5.34075i	1.00039	+	0.502416i	0.872104	−	0.489321i	$-0.162756\pi$
$113$	10.6343	+	5.34075i	1.00039	+	0.502416i	0.128288	+	0.991737i	$0.459052\pi$
$114$		0			0
$115$	−2.14446	−	7.16299i	−0.199972	−	0.667953i
$116$	−2.23893	+	12.6976i	−0.207880	+	1.17894i
$117$		0			0
$118$	0.102333	+	0.580358i	0.00942050	+	0.0534263i
$119$	0.591955	−	0.297291i	0.0542644	−	0.0272526i
$120$		0			0
$121$	−4.13408	−	9.58388i	−0.375826	−	0.871262i
$122$	−0.565251	−	1.31040i	−0.0511754	−	0.118638i
$123$		0			0
$124$	−9.79654	+	4.92001i	−0.879756	+	0.441830i
$125$	1.45106	+	8.22939i	0.129787	+	0.736059i
$126$		0			0
$127$	2.53378	−	14.3698i	0.224837	−	1.27511i	−0.638160	−	0.769903i	$-0.720304\pi$
$127$	2.53378	−	14.3698i	0.224837	−	1.27511i	0.862997	−	0.505209i	$-0.168585\pi$
$128$	1.76124	+	5.88294i	0.155673	+	0.519983i
$129$		0			0
$130$	0.581599	+	0.292090i	0.0510096	+	0.0256180i
$131$	−1.91215	+	6.38704i	−0.167066	+	0.558038i	0.832923	+	0.553388i	$0.186665\pi$
$131$	−1.91215	+	6.38704i	−0.167066	+	0.558038i	−0.999989	+	0.00465022i	$0.998520\pi$
$132$		0			0
$133$	0.208689	+	0.280318i	0.0180956	+	0.0243066i
$134$	−0.897484	−	1.55449i	−0.0775308	−	0.134287i
$135$		0			0
$136$	1.61548	−	2.79809i	0.138526	−	0.239934i
$137$	−14.5286	+	1.69815i	−1.24126	+	0.145082i	−0.711268	−	0.702921i	$-0.751879\pi$
$137$	−14.5286	+	1.69815i	−1.24126	+	0.145082i	−0.529991	+	0.848003i	$0.677805\pi$
$138$		0			0
$139$	−3.22602	+	0.764581i	−0.273628	+	0.0648509i	−0.365139	−	0.930953i	$-0.618978\pi$
$139$	−3.22602	+	0.764581i	−0.273628	+	0.0648509i	0.0915111	+	0.995804i	$0.470830\pi$
$140$	−0.244703	+	0.160943i	−0.0206811	+	0.0136022i
$141$		0			0
$142$	1.32038	−	1.39952i	0.110804	−	0.117445i
$143$	−2.03027	−	1.70360i	−0.169780	−	0.142462i
$144$		0			0
$145$	−4.59437	+	3.85513i	−0.381542	+	0.320151i
$146$	0.103570	−	1.77823i	0.00857152	−	0.147167i
$147$		0			0
$148$	−5.28150	+	7.09429i	−0.434137	+	0.583147i
$149$	4.86894	+	0.569097i	0.398879	+	0.0466223i	0.313168	−	0.949698i	$-0.398610\pi$
$149$	4.86894	+	0.569097i	0.398879	+	0.0466223i	0.0857110	+	0.996320i	$0.472684\pi$
$150$		0			0
$151$	−13.4990	−	8.87841i	−1.09853	−	0.722515i	−0.135196	−	0.990819i	$-0.543166\pi$
$151$	−13.4990	−	8.87841i	−1.09853	−	0.722515i	−0.963334	+	0.268304i	$0.913537\pi$
$152$	1.60176	+	0.582992i	0.129920	+	0.0472869i
$153$		0			0
$154$	−0.0233649	+	0.00850413i	−0.00188280	+	0.000685282i
$155$	−4.96190	−	1.17599i	−0.398549	−	0.0944580i
$156$		0			0
$157$	−0.718876	−	12.3426i	−0.0573726	−	0.985049i	−0.897040	−	0.441949i	$-0.854287\pi$
$157$	−0.718876	−	12.3426i	−0.0573726	−	0.985049i	0.839668	−	0.543100i	$-0.182750\pi$
$158$	0.447203	+	0.474007i	0.0355775	+	0.0377100i
$159$		0			0
$160$	−0.851656	+	1.97436i	−0.0673293	+	0.156087i
$161$	−1.34593			−0.106074
$162$		0			0
$163$	−12.1435			−0.951151			−0.475576	−	0.879675i	$-0.657760\pi$
$163$	−12.1435			−0.951151			−0.475576	+	0.879675i	$0.657760\pi$
$164$	8.49203	−	19.6867i	0.663116	−	1.53728i
$165$		0			0
$166$	−2.33388	−	2.47376i	−0.181144	−	0.192001i
$167$	0.147754	+	2.53683i	0.0114335	+	0.196306i	0.999188	+	0.0402900i	$0.0128282\pi$
$167$	0.147754	+	2.53683i	0.0114335	+	0.196306i	−0.987754	+	0.156016i	$0.950135\pi$
$168$		0			0
$169$	−0.498703	−	0.118195i	−0.0383618	−	0.00909191i
$170$	0.698851	−	0.254361i	0.0535994	−	0.0195086i
$171$		0			0
$172$	−6.37031	−	2.31860i	−0.485732	−	0.176792i
$173$	−8.13490	−	5.35041i	−0.618485	−	0.406784i	0.201240	−	0.979542i	$-0.435503\pi$
$173$	−8.13490	−	5.35041i	−0.618485	−	0.406784i	−0.819724	+	0.572758i	$0.805873\pi$
$174$		0			0
$175$	0.679353	+	0.0794050i	0.0513543	+	0.00600245i
$176$	1.68248	−	2.25996i	0.126821	−	0.170351i
$177$		0			0
$178$	−0.134314	+	2.30608i	−0.0100672	+	0.172848i
$179$	2.85196	−	2.39308i	0.213165	−	0.178867i	−0.529953	−	0.848027i	$-0.677790\pi$
$179$	2.85196	−	2.39308i	0.213165	−	0.178867i	0.743118	+	0.669160i	$0.233346\pi$
$180$		0			0
$181$	−5.59668	−	4.69618i	−0.415998	−	0.349064i	0.410640	−	0.911798i	$-0.365305\pi$
$181$	−5.59668	−	4.69618i	−0.415998	−	0.349064i	−0.826638	+	0.562734i	$0.809750\pi$
$182$	0.0803951	−	0.0852138i	0.00595928	−	0.00631647i
$183$		0			0
$184$	−5.48482	+	3.60743i	−0.404347	+	0.265943i
$185$	−4.00315	+	0.948764i	−0.294318	+	0.0697545i
$186$		0			0
$187$	−3.00807	+	0.351593i	−0.219972	+	0.0257110i
$188$	−8.74825	+	15.1524i	−0.638032	+	1.10510i
$189$		0			0
$190$	0.196177	+	0.339789i	0.0142322	+	0.0246509i
$191$	12.4068	+	16.6652i	0.897724	+	1.20585i	0.977900	+	0.209072i	$0.0670442\pi$
$191$	12.4068	+	16.6652i	0.897724	+	1.20585i	−0.0801764	+	0.996781i	$0.525548\pi$
$192$		0			0
$193$	1.00178	−	3.34618i	0.0721097	−	0.240863i	−0.914335	−	0.404960i	$-0.867286\pi$
$193$	1.00178	−	3.34618i	0.0721097	−	0.240863i	0.986444	+	0.164096i	$0.0524708\pi$
$194$	−0.818189	−	0.410910i	−0.0587426	−	0.0295016i
$195$		0			0
$196$	−3.91813	−	13.0875i	−0.279866	−	0.934819i
$197$	0.205736	−	1.16678i	0.0146580	−	0.0831299i	−0.976601	−	0.215058i	$-0.931006\pi$
$197$	0.205736	−	1.16678i	0.0146580	−	0.0831299i	0.991259	+	0.131928i	$0.0421169\pi$
$198$		0			0
$199$	−0.191285	−	1.08483i	−0.0135599	−	0.0769018i	0.977277	−	0.211967i	$-0.0679868\pi$
$199$	−0.191285	−	1.08483i	−0.0135599	−	0.0769018i	−0.990837	+	0.135065i	$0.956876\pi$
$200$	2.98128	−	1.49725i	0.210808	−	0.105872i
$201$		0			0
$202$	−0.184239	−	0.427113i	−0.0129630	−	0.0300516i
$203$	0.427605	+	0.991299i	0.0300120	+	0.0695755i
$204$		0			0
$205$	8.91228	−	4.47592i	0.622461	−	0.312612i
$206$	0.0913296	+	0.517956i	0.00636324	+	0.0360877i
$207$		0			0
$208$	−2.30518	+	13.0733i	−0.159835	+	0.906470i
$209$	−0.458245	−	1.53065i	−0.0316975	−	0.105877i
$210$		0			0
$211$	−13.3899	−	6.72464i	−0.921795	−	0.462943i	−0.0763959	−	0.997078i	$-0.524341\pi$
$211$	−13.3899	−	6.72464i	−0.921795	−	0.462943i	−0.845400	+	0.534134i	$0.820638\pi$
$212$	3.44986	−	11.5233i	0.236937	−	0.791426i
$213$		0			0
$214$	−1.44269	−	1.93787i	−0.0986205	−	0.132470i
$215$	−1.57669	−	2.73091i	−0.107529	−	0.186246i
$216$		0			0
$217$	−0.458958	+	0.794939i	−0.0311561	+	0.0539640i
$218$	−3.63943	+	0.425388i	−0.246493	+	0.0288109i
$219$		0			0
$220$	1.30297	−	0.308810i	0.0878465	−	0.0208200i
$221$	11.9220	−	7.84122i	0.801960	−	0.527457i
$222$		0			0
$223$	−3.50053	+	3.71034i	−0.234413	+	0.248463i	−0.833892	−	0.551927i	$-0.813893\pi$
$223$	−3.50053	+	3.71034i	−0.234413	+	0.248463i	0.599480	+	0.800390i	$0.295374\pi$
$224$	0.296499	+	0.248792i	0.0198107	+	0.0166231i
$225$		0			0
$226$	1.84230	−	1.54588i	0.122548	−	0.102830i
$227$	−0.974692	+	16.7348i	−0.0646926	+	1.11073i	0.797226	+	0.603681i	$0.206300\pi$
$227$	−0.974692	+	16.7348i	−0.0646926	+	1.11073i	−0.861918	+	0.507047i	$0.830737\pi$
$228$		0			0
$229$	9.62801	−	12.9327i	0.636237	−	0.854614i	−0.360712	−	0.932677i	$-0.617466\pi$
$229$	9.62801	−	12.9327i	0.636237	−	0.854614i	0.996948	+	0.0780631i	$0.0248736\pi$
$230$	−1.50087	−	0.175427i	−0.0989646	−	0.0115673i
$231$		0			0
$232$	4.39947	+	2.89358i	0.288840	+	0.189973i
$233$	−9.85526	−	3.58702i	−0.645639	−	0.234993i	−0.00161517	−	0.999999i	$-0.500514\pi$
$233$	−9.85526	−	3.58702i	−0.645639	−	0.234993i	−0.644024	+	0.765005i	$0.722736\pi$
$234$		0			0
$235$	−7.64784	+	2.78358i	−0.498890	+	0.181581i
$236$	−5.55892	−	1.31749i	−0.361855	−	0.0857611i
$237$		0			0
$238$	−0.00778390	−	0.133644i	−0.000504556	−	0.00866289i
$239$	0.0373051	+	0.0395411i	0.00241307	+	0.00255770i	0.728579	−	0.684962i	$-0.240181\pi$
$239$	0.0373051	+	0.0395411i	0.00241307	+	0.00255770i	−0.726166	+	0.687519i	$0.758700\pi$
$240$		0			0
$241$	4.71185	−	10.9233i	0.303517	−	0.703631i	−0.696385	−	0.717669i	$-0.745209\pi$
$241$	4.71185	−	10.9233i	0.303517	−	0.703631i	0.999901	+	0.0140375i	$0.00446842\pi$
$242$	−2.10937			−0.135596
$243$		0			0
$244$	13.8348			0.885680
$245$	2.51697	−	5.83500i	0.160804	−	0.372784i
$246$		0			0
$247$	5.16613	+	5.47578i	0.328713	+	0.348416i
$248$	0.260325	+	4.46960i	0.0165306	+	0.283820i
$249$		0			0
$250$	1.64326	+	0.389459i	0.103929	+	0.0246316i
$251$	−4.18194	+	1.52210i	−0.263961	+	0.0960741i	−0.470611	−	0.882341i	$-0.655966\pi$
$251$	−4.18194	+	1.52210i	−0.263961	+	0.0960741i	0.206649	+	0.978415i	$0.433744\pi$
$252$		0			0
$253$	5.78245	+	2.10464i	0.363540	+	0.132318i
$254$	−2.46374	−	1.62043i	−0.154589	−	0.101675i
$255$		0			0
$256$	−12.7450	−	1.48967i	−0.796560	−	0.0931045i
$257$	9.24063	−	12.4123i	0.576415	−	0.774259i	−0.414311	−	0.910135i	$-0.635977\pi$
$257$	9.24063	−	12.4123i	0.576415	−	0.774259i	0.990726	+	0.135876i	$0.0433849\pi$
$258$		0			0
$259$	−0.0430594	+	0.739301i	−0.00267558	+	0.0459380i
$260$	−4.83316	+	4.05550i	−0.299740	+	0.251512i
$261$		0			0
$262$	1.03217	+	0.866090i	0.0637674	+	0.0535072i
$263$	9.83748	−	10.4271i	0.606605	−	0.642964i	−0.349171	−	0.937059i	$-0.613537\pi$
$263$	9.83748	−	10.4271i	0.606605	−	0.642964i	0.955776	+	0.294095i	$0.0950183\pi$
$264$		0			0
$265$	4.67476	−	3.07463i	0.287168	−	0.188873i
$266$	0.0687225	−	0.0162875i	0.00421365	−	0.000998653i
$267$		0			0
$268$	17.2832	−	2.02011i	1.05574	−	0.123398i
$269$	0.910225	−	1.57656i	0.0554974	−	0.0961243i	−0.836942	−	0.547292i	$-0.815659\pi$
$269$	0.910225	−	1.57656i	0.0554974	−	0.0961243i	0.892439	+	0.451167i	$0.148992\pi$
$270$		0			0
$271$	6.79318	+	11.7661i	0.412656	+	0.714742i	0.995179	−	0.0980726i	$-0.0312677\pi$
$271$	6.79318	+	11.7661i	0.412656	+	0.714742i	−0.582523	+	0.812814i	$0.697934\pi$
$272$	9.05852	+	12.1677i	0.549254	+	0.737776i
$273$		0			0
$274$	−0.847832	+	2.83196i	−0.0512194	+	0.171085i
$275$	−2.79451	−	1.40346i	−0.168515	−	0.0846315i
$276$		0			0
$277$	6.27704	+	20.9668i	0.377150	+	1.25977i	0.910371	+	0.413794i	$0.135797\pi$
$277$	6.27704	+	20.9668i	0.377150	+	1.25977i	−0.533220	+	0.845977i	$0.679018\pi$
$278$	−0.116349	+	0.659846i	−0.00697813	+	0.0395749i
$279$		0			0
$280$	0.0207711	+	0.117799i	0.00124131	+	0.00703981i
$281$	22.5755	−	11.3379i	1.34674	−	0.676360i	0.378321	−	0.925675i	$-0.376502\pi$
$281$	22.5755	−	11.3379i	1.34674	−	0.676360i	0.968422	+	0.249315i	$0.0802054\pi$
$282$		0			0
$283$	8.86520	+	20.5519i	0.526982	+	1.22168i	0.949053	+	0.315118i	$0.102044\pi$
$283$	8.86520	+	20.5519i	0.526982	+	1.22168i	−0.422071	+	0.906563i	$0.638697\pi$
$284$	7.38782	+	17.1269i	0.438387	+	1.01629i
$285$		0			0
$286$	−0.478648	+	0.240386i	−0.0283030	+	0.0142143i
$287$	−0.311737	−	1.76795i	−0.0184012	−	0.104359i
$288$		0			0
$289$	−0.120543	+	0.683633i	−0.00709076	+	0.0402137i
$290$	0.347626	+	1.16115i	0.0204133	+	0.0681852i
$291$		0			0
$292$	15.4310	+	7.74975i	0.903033	+	0.453520i
$293$	−3.75533	+	12.5437i	−0.219389	+	0.732809i	0.775456	+	0.631401i	$0.217520\pi$
$293$	−3.75533	+	12.5437i	−0.219389	+	0.732809i	−0.994845	+	0.101408i	$0.967665\pi$
$294$		0			0
$295$	−1.58690	−	2.13157i	−0.0923926	−	0.124105i
$296$	1.80604	+	3.12816i	0.104974	+	0.181820i
$297$		0			0
$298$	0.495345	−	0.857962i	0.0286945	−	0.0497004i
$299$	−28.7975	+	3.36594i	−1.66540	+	0.194657i
$300$		0			0
$301$	−0.552328	+	0.130904i	−0.0318357	+	0.00754519i
$302$	−2.72808	+	1.79429i	−0.156983	+	0.103250i
$303$		0			0
$304$	−5.49193	+	5.82110i	−0.314984	+	0.333863i
$305$	4.92977	+	4.13657i	0.282278	+	0.236859i
$306$		0			0
$307$	11.2563	−	9.44513i	0.642429	−	0.539062i	−0.262334	−	0.964977i	$-0.584492\pi$
$307$	11.2563	−	9.44513i	0.642429	−	0.539062i	0.904763	+	0.425915i	$0.140048\pi$
$308$	0.0140153	−	0.240633i	0.000798595	−	0.0137113i
$309$		0			0
$310$	−0.615406	+	0.826633i	−0.0349527	+	0.0469496i
$311$	−33.1562	−	3.87540i	−1.88011	−	0.219754i	−0.902578	−	0.430525i	$-0.858328\pi$
$311$	−33.1562	−	3.87540i	−1.88011	−	0.219754i	−0.977535	+	0.210772i	$0.932402\pi$
$312$		0			0
$313$	19.0991	+	12.5617i	1.07954	+	0.710027i	0.959207	−	0.282706i	$-0.0912321\pi$
$313$	19.0991	+	12.5617i	1.07954	+	0.710027i	0.120337	+	0.992733i	$0.461602\pi$
$314$	−2.34793	−	0.854577i	−0.132501	−	0.0482266i
$315$		0			0
$316$	−5.93643	+	2.16069i	−0.333950	+	0.121548i
$317$	−18.2788	−	4.33215i	−1.02664	−	0.243318i	−0.317404	−	0.948290i	$-0.602811\pi$
$317$	−18.2788	−	4.33215i	−1.02664	−	0.243318i	−0.709235	+	0.704972i	$0.750959\pi$
$318$		0			0
$319$	−0.286996	−	4.92752i	−0.0160687	−	0.275888i
$320$	−4.40046	−	4.66421i	−0.245993	−	0.260737i
$321$		0			0
$322$	−0.107736	+	0.249760i	−0.00600389	+	0.0139186i
$323$	8.60246			0.478654
$324$		0			0
$325$	14.7340			0.817296
$326$	−0.972037	+	2.25343i	−0.0538361	+	0.124806i
$327$		0			0
$328$	−6.00891	−	6.36907i	−0.331787	−	0.351673i
$329$	0.0851827	+	1.46253i	0.00469628	+	0.0806320i
$330$		0			0
$331$	−5.75969	−	1.36507i	−0.316581	−	0.0750312i	0.0692533	−	0.997599i	$-0.477938\pi$
$331$	−5.75969	−	1.36507i	−0.316581	−	0.0750312i	−0.385835	+	0.922568i	$0.626086\pi$
$332$	30.9813	−	11.2763i	1.70032	−	0.618865i
$333$		0			0
$334$	0.482581	+	0.175645i	0.0264056	+	0.00961087i
$335$	6.76256	+	4.44780i	0.369478	+	0.243009i
$336$		0			0
$337$	12.0532	+	1.40882i	0.656579	+	0.0767431i	0.437858	−	0.899044i	$-0.355737\pi$
$337$	12.0532	+	1.40882i	0.656579	+	0.0767431i	0.218721	+	0.975787i	$0.429811\pi$
$338$	−0.0618523	+	0.0830821i	−0.00336432	+	0.00451907i
$339$		0			0
$340$	−0.419201	+	7.19740i	−0.0227344	+	0.390334i
$341$	3.21485	−	2.69758i	0.174094	−	0.146082i
$342$		0			0
$343$	−1.75592	−	1.47339i	−0.0948108	−	0.0795557i
$344$	−1.89995	+	2.01383i	−0.102438	+	0.108578i
$345$		0			0
$346$	−1.64403	+	1.08129i	−0.0883834	+	0.0581307i
$347$	2.37343	−	0.562512i	0.127412	−	0.0301972i	−0.166415	−	0.986056i	$-0.553219\pi$
$347$	2.37343	−	0.562512i	0.127412	−	0.0301972i	0.293827	+	0.955859i	$0.405071\pi$
$348$		0			0
$349$	−22.8259	+	2.66797i	−1.22184	+	0.142813i	−0.702456	−	0.711727i	$-0.747913\pi$
$349$	−22.8259	+	2.66797i	−1.22184	+	0.142813i	−0.519386	+	0.854540i	$0.673839\pi$
$350$	0.0691144	−	0.119710i	0.00369432	−	0.00639875i
$351$		0			0
$352$	−0.884797	−	1.53251i	−0.0471598	−	0.0816833i
$353$	13.8275	+	18.5736i	0.735965	+	0.988573i	0.999712	+	0.0239812i	$0.00763418\pi$
$353$	13.8275	+	18.5736i	0.735965	+	0.988573i	−0.263747	+	0.964592i	$0.584958\pi$
$354$		0			0
$355$	−2.48839	+	8.31181i	−0.132070	+	0.441145i
$356$	−20.0116	−	10.0502i	−1.06061	−	0.532659i
$357$		0			0
$358$	−0.215789	−	0.720786i	−0.0114048	−	0.0380947i
$359$	5.43706	−	30.8351i	0.286957	−	1.62741i	−0.411254	−	0.911521i	$-0.634909\pi$
$359$	5.43706	−	30.8351i	0.286957	−	1.62741i	0.698211	−	0.715892i	$-0.253980\pi$
$360$		0			0
$361$	−2.51123	−	14.2419i	−0.132170	−	0.749574i
$362$	−1.31945	+	0.662652i	−0.0693487	+	0.0348282i
$363$		0			0
$364$	0.449829	+	1.04282i	0.0235775	+	0.0546587i
$365$	3.18141	+	7.37534i	0.166523	+	0.386043i
$366$		0			0
$367$	6.85833	−	3.44438i	0.358002	−	0.179795i	−0.260702	−	0.965419i	$-0.583954\pi$
$367$	6.85833	−	3.44438i	0.358002	−	0.179795i	0.618704	+	0.785624i	$0.287658\pi$
$368$	−5.35217	−	30.3537i	−0.279001	−	1.58229i
$369$		0			0
$370$	−0.144376	+	0.818799i	−0.00750577	+	0.0425673i
$371$	−0.288862	−	0.964867i	−0.0149970	−	0.0500934i
$372$		0			0
$373$	23.1933	+	11.6481i	1.20090	+	0.603116i	0.932842	−	0.360286i	$-0.117321\pi$
$373$	23.1933	+	11.6481i	1.20090	+	0.603116i	0.268061	+	0.963402i	$0.413617\pi$
$374$	−0.175540	+	0.586343i	−0.00907693	+	0.0303191i
$375$		0			0
$376$	4.26708	+	5.73169i	0.220058	+	0.295589i
$377$	11.6281	+	20.1405i	0.598878	+	1.03729i
$378$		0			0
$379$	−13.2851	+	23.0104i	−0.682408	+	1.18197i	0.291835	+	0.956469i	$0.405734\pi$
$379$	−13.2851	+	23.0104i	−0.682408	+	1.18197i	−0.974244	+	0.225497i	$0.927599\pi$
$380$	−3.77785	+	0.441567i	−0.193800	+	0.0226519i
$381$		0			0
$382$	4.08563	−	0.968313i	0.209039	−	0.0495432i
$383$	−2.25216	+	1.48127i	−0.115080	+	0.0756892i	−0.605744	−	0.795659i	$-0.707125\pi$
$383$	−2.25216	+	1.48127i	−0.115080	+	0.0756892i	0.490664	+	0.871349i	$0.336754\pi$
$384$		0			0
$385$	0.0769430	−	0.0815548i	0.00392138	−	0.00415642i
$386$	−0.540753	−	0.453746i	−0.0275236	−	0.0230951i
$387$		0			0
$388$	6.79926	−	5.70525i	0.345180	−	0.289640i
$389$	−1.37770	+	23.6542i	−0.0698522	+	1.19932i	0.763215	+	0.646144i	$0.223620\pi$
$389$	−1.37770	+	23.6542i	−0.0698522	+	1.19932i	−0.833067	+	0.553172i	$0.813417\pi$
$390$		0			0
$391$	−19.7845	+	26.5751i	−1.00054	+	1.34396i
$392$	−5.54164	−	0.647725i	−0.279895	−	0.0327150i
$393$		0			0
$394$	−0.200049	−	0.131574i	−0.0100783	−	0.00662861i
$395$	−2.76138	−	1.00506i	−0.138940	−	0.0505702i
$396$		0			0
$397$	−0.102939	+	0.0374669i	−0.00516638	+	0.00188041i	−0.344602	−	0.938749i	$-0.611986\pi$
$397$	−0.102939	+	0.0374669i	−0.00516638	+	0.00188041i	0.339436	+	0.940629i	$0.389764\pi$
$398$	−0.216621	−	0.0513402i	−0.0108582	−	0.00257345i
$399$		0			0
$400$	0.910733	+	15.6367i	0.0455367	+	0.781834i
$401$	−5.79656	−	6.14400i	−0.289467	−	0.306817i	0.566279	−	0.824214i	$-0.308383\pi$
$401$	−5.79656	−	6.14400i	−0.289467	−	0.306817i	−0.855745	+	0.517397i	$0.826901\pi$
$402$		0			0
$403$	−7.83185	+	18.1563i	−0.390132	+	0.904429i
$404$	4.50932			0.224347
$405$		0			0
$406$	0.218181			0.0108281
$407$	1.34105	−	3.10890i	0.0664732	−	0.154102i
$408$		0			0
$409$	3.46931	+	3.67725i	0.171546	+	0.181828i	0.807443	−	0.589946i	$-0.200851\pi$
$409$	3.46931	+	3.67725i	0.171546	+	0.181828i	−0.635896	+	0.771774i	$0.719369\pi$
$410$	−0.117192	−	2.01211i	−0.00578770	−	0.0993709i
$411$		0			0
$412$	−4.96120	−	1.17583i	−0.244421	−	0.0579288i
$413$	−0.449503	+	0.163606i	−0.0221186	+	0.00805050i
$414$		0			0
$415$	14.4112	+	5.24525i	0.707418	+	0.257479i
$416$	6.96608	+	4.58166i	0.341540	+	0.224634i
$417$		0			0
$418$	−0.320719	−	0.0374866i	−0.0156869	−	0.00183353i
$419$	−7.62869	+	10.2471i	−0.372686	+	0.500604i	−0.948413	−	0.317038i	$-0.897312\pi$
$419$	−7.62869	+	10.2471i	−0.372686	+	0.500604i	0.575727	+	0.817642i	$0.304719\pi$
$420$		0			0
$421$	1.05866	−	18.1765i	0.0515960	−	0.885870i	−0.868868	−	0.495043i	$-0.835152\pi$
$421$	1.05866	−	18.1765i	0.0515960	−	0.885870i	0.920464	−	0.390826i	$-0.127811\pi$
$422$	−2.31968	+	1.94644i	−0.112920	+	0.0947512i
$423$		0			0
$424$	−3.76324	−	3.15773i	−0.182759	−	0.153353i
$425$	11.5540	−	12.2465i	0.560451	−	0.594043i
$426$		0			0
$427$	0.967834	−	0.636554i	0.0468368	−	0.0308050i
$428$	22.7892	−	5.40115i	1.10156	−	0.261074i
$429$		0			0
$430$	−0.632975	+	0.0739842i	−0.0305248	+	0.00356783i
$431$	11.5675	−	20.0355i	0.557188	−	0.965077i	−0.440542	−	0.897732i	$-0.645214\pi$
$431$	11.5675	−	20.0355i	0.557188	−	0.965077i	0.997730	−	0.0673455i	$-0.0214530\pi$
$432$		0			0
$433$	16.7531	+	29.0173i	0.805104	+	1.39448i	0.916221	+	0.400674i	$0.131224\pi$
$433$	16.7531	+	29.0173i	0.805104	+	1.39448i	−0.111116	+	0.993807i	$0.535443\pi$
$434$	0.110777	+	0.148799i	0.00531746	+	0.00714259i
$435$		0			0
$436$	10.1877	−	34.0293i	0.487903	−	1.62971i
$437$	−15.6197	−	7.84452i	−0.747193	−	0.375254i
$438$		0			0
$439$	9.07834	+	30.3238i	0.433286	+	1.44727i	0.844411	+	0.535696i	$0.179951\pi$
$439$	9.07834	+	30.3238i	0.433286	+	1.44727i	−0.411125	+	0.911579i	$0.634864\pi$
$440$	0.0949649	−	0.538573i	0.00452727	−	0.0256755i
$441$		0			0
$442$	−0.500767	−	2.83999i	−0.0238191	−	0.135085i
$443$	20.2054	−	10.1475i	0.959988	−	0.482124i	0.101431	−	0.994843i	$-0.467658\pi$
$443$	20.2054	−	10.1475i	0.959988	−	0.482124i	0.858557	+	0.512718i	$0.171362\pi$
$444$		0			0
$445$	−4.12578	−	9.56464i	−0.195581	−	0.453407i
$446$	0.408316	+	0.946582i	0.0193343	+	0.0448219i
$447$		0			0
$448$	−1.03150	+	0.518037i	−0.0487336	+	0.0244749i
$449$	3.12921	+	17.7466i	0.147677	+	0.837515i	0.965179	+	0.261590i	$0.0842469\pi$
$449$	3.12921	+	17.7466i	0.147677	+	0.837515i	−0.817503	+	0.575925i	$0.804642\pi$
$450$		0			0
$451$	−1.42525	+	8.08302i	−0.0671126	+	0.380615i
$452$	6.68657	+	22.3347i	0.314510	+	1.05054i
$453$		0			0
$454$	3.02742	+	1.52042i	0.142084	+	0.0713571i
$455$	−0.151513	+	0.506089i	−0.00710305	+	0.0237258i
$456$		0			0
$457$	−14.0687	−	18.8975i	−0.658104	−	0.883987i	0.340309	−	0.940314i	$-0.389468\pi$
$457$	−14.0687	−	18.8975i	−0.658104	−	0.883987i	−0.998412	+	0.0563271i	$0.982061\pi$
$458$	−1.62920	−	2.82185i	−0.0761274	−	0.131856i
$459$		0			0
$460$	7.32442	−	12.6863i	0.341503	−	0.591500i
$461$	−39.9000	+	4.66364i	−1.85833	+	0.217207i	−0.970186	−	0.242363i	$-0.922077\pi$
$461$	−39.9000	+	4.66364i	−1.85833	+	0.217207i	−0.888141	+	0.459570i	$0.848003\pi$
$462$		0			0
$463$	−10.6863	+	2.53271i	−0.496636	+	0.117705i	−0.471298	−	0.881974i	$-0.656214\pi$
$463$	−10.6863	+	2.53271i	−0.496636	+	0.117705i	−0.0253382	+	0.999679i	$0.508066\pi$
$464$	−20.6556	+	13.5854i	−0.958912	+	0.630686i
$465$		0			0
$466$	−1.45451	+	1.54169i	−0.0673787	+	0.0714173i
$467$	1.29116	+	1.08341i	0.0597479	+	0.0501344i	0.672173	−	0.740395i	$-0.265361\pi$
$467$	1.29116	+	1.08341i	0.0597479	+	0.0501344i	−0.612425	+	0.790529i	$0.709806\pi$
$468$		0			0
$469$	1.11612	−	0.936540i	0.0515378	−	0.0432454i
$470$	−0.0956358	+	1.64200i	−0.00441135	+	0.0757400i
$471$		0			0
$472$	−1.39328	+	1.87149i	−0.0641307	+	0.0861425i
$473$	2.57764	+	0.301283i	0.118520	+	0.0138530i
$474$		0			0
$475$	7.42121	+	4.88101i	0.340509	+	0.223956i
$476$	1.21951	+	0.443865i	0.0558961	+	0.0203445i
$477$		0			0
$478$	0.0103237	−	0.00375751i	0.000472194	−	0.000171864i
$479$	19.3534	+	4.58684i	0.884280	+	0.209578i	0.647573	−	0.762003i	$-0.275784\pi$
$479$	19.3534	+	4.58684i	0.884280	+	0.209578i	0.236706	+	0.971581i	$0.423932\pi$
$480$		0			0
$481$	0.927571	+	15.9258i	0.0422936	+	0.726153i
$482$	−1.64984	−	1.74873i	−0.0751483	−	0.0796525i
$483$		0			0
$484$	8.09932	−	18.7763i	0.368151	−	0.853469i
$485$	4.12866			0.187473
$486$		0			0
$487$	−16.9386			−0.767563			−0.383782	−	0.923424i	$-0.625378\pi$
$487$	−16.9386			−0.767563			−0.383782	+	0.923424i	$0.625378\pi$
$488$	2.23792	−	5.18808i	0.101306	−	0.234853i
$489$		0			0
$490$	−0.881312	−	0.934136i	−0.0398136	−	0.0422000i
$491$	−1.99994	−	34.3376i	−0.0902558	−	1.54963i	−0.674635	−	0.738152i	$-0.735699\pi$
$491$	−1.99994	−	34.3376i	−0.0902558	−	1.54963i	0.584379	−	0.811481i	$-0.301338\pi$
$492$		0			0
$493$	25.8586	+	6.12861i	1.16461	+	0.276019i
$494$	1.42965	−	0.520352i	0.0643232	−	0.0234117i
$495$		0			0
$496$	−19.7527	−	7.18940i	−0.886923	−	0.322814i
$497$	1.30486	+	0.858218i	0.0585308	+	0.0384963i
$498$		0			0
$499$	−17.4742	−	2.04244i	−0.782251	−	0.0914320i	−0.284413	−	0.958702i	$-0.591799\pi$
$499$	−17.4742	−	2.04244i	−0.782251	−	0.0914320i	−0.497838	+	0.867270i	$0.665873\pi$
$500$	−9.77631	+	13.1319i	−0.437210	+	0.587275i
$501$		0			0
$502$	−0.0522949	+	0.897869i	−0.00233404	+	0.0400738i
$503$	−17.6438	+	14.8049i	−0.786697	+	0.660117i	−0.944925	−	0.327286i	$-0.893866\pi$
$503$	−17.6438	+	14.8049i	−0.786697	+	0.660117i	0.158229	+	0.987402i	$0.449422\pi$
$504$		0			0
$505$	1.60682	+	1.34828i	0.0715023	+	0.0599976i
$506$	0.853414	−	0.904566i	0.0379389	−	0.0402129i
$507$		0			0
$508$	23.8841	−	15.7088i	1.05968	−	0.696965i
$509$	31.1626	−	7.38567i	1.38126	−	0.327364i	0.528173	−	0.849137i	$-0.322877\pi$
$509$	31.1626	−	7.38567i	1.38126	−	0.327364i	0.853085	+	0.521773i	$0.174729\pi$
$510$		0			0
$511$	1.43608	−	0.167854i	0.0635284	−	0.00742541i
$512$	−7.43754	+	12.8822i	−0.328696	+	0.569318i
$513$		0			0
$514$	−1.56365	−	2.70831i	−0.0689695	−	0.119459i
$515$	−1.41627	−	1.90238i	−0.0624082	−	0.0838287i
$516$		0			0
$517$	1.92101	−	6.41661i	0.0844858	−	0.282202i
$518$	0.133743	+	0.0671685i	0.00587635	+	0.00295121i
$519$		0			0
$520$	0.739012	+	2.46847i	0.0324078	+	0.108250i
$521$	−0.436835	+	2.47742i	−0.0191381	+	0.108538i	−0.992880	−	0.119116i	$-0.961994\pi$
$521$	−0.436835	+	2.47742i	−0.0191381	+	0.108538i	0.973742	+	0.227653i	$0.0731052\pi$
$522$		0			0
$523$	4.83329	+	27.4110i	0.211345	+	1.19860i	0.887137	+	0.461506i	$0.152691\pi$
$523$	4.83329	+	27.4110i	0.211345	+	1.19860i	−0.675792	+	0.737092i	$0.736198\pi$
$524$	−11.6726	+	5.86220i	−0.509920	+	0.256091i
$525$		0			0
$526$	−1.14748	−	2.66016i	−0.0500326	−	0.115989i
$527$	8.94950	+	20.7473i	0.389846	+	0.903765i
$528$		0			0
$529$	39.6034	−	19.8896i	1.72188	−	0.864763i
$530$	−0.196357	−	1.11359i	−0.00852919	−	0.0483714i
$531$		0			0
$532$	−0.118891	+	0.674265i	−0.00515458	+	0.0292331i
$533$	−11.0913	−	37.0474i	−0.480416	−	1.60470i
$534$		0			0
$535$	9.73548	+	4.88934i	0.420901	+	0.211385i
$536$	2.03819	−	6.80801i	0.0880362	−	0.294061i
$537$		0			0
$538$	−0.219698	−	0.295105i	−0.00947184	−	0.0127229i
$539$	2.61492	+	4.52917i	0.112633	+	0.195085i
$540$		0			0
$541$	3.23851	−	5.60926i	0.139234	−	0.241161i	−0.787973	−	0.615710i	$-0.788869\pi$
$541$	3.23851	−	5.60926i	0.139234	−	0.241161i	0.927207	+	0.374549i	$0.122203\pi$
$542$	2.72718	−	0.318761i	0.117142	−	0.0136920i
$543$		0			0
$544$	9.27075	−	2.19721i	0.397480	−	0.0942046i
$545$	13.8049	−	9.07964i	0.591338	−	0.388929i
$546$		0			0
$547$	−10.5678	+	11.2012i	−0.451847	+	0.478930i	−0.912749	−	0.408521i	$-0.866045\pi$
$547$	−10.5678	+	11.2012i	−0.451847	+	0.478930i	0.460902	+	0.887451i	$0.347526\pi$
$548$	−21.9529	−	18.4207i	−0.937783	−	0.786893i
$549$		0			0
$550$	−0.484125	+	0.406229i	−0.0206431	+	0.0173217i
$551$	−0.815199	+	13.9964i	−0.0347286	+	0.596268i
$552$		0			0
$553$	−0.315877	+	0.424297i	−0.0134325	+	0.0180429i
$554$	4.39320	+	0.513491i	0.186649	+	0.0218161i
$555$		0			0
$556$	−5.42680	−	3.56926i	−0.230148	−	0.151370i
$557$	−21.2492	−	7.73409i	−0.900359	−	0.327704i	−0.149963	−	0.988692i	$-0.547915\pi$
$557$	−21.2492	−	7.73409i	−0.900359	−	0.327704i	−0.750397	+	0.660988i	$0.770138\pi$
$558$		0			0
$559$	−11.4902	+	4.18210i	−0.485985	+	0.176884i
$560$	−0.546460	−	0.129513i	−0.0230921	−	0.00547294i
$561$		0			0
$562$	−0.296857	−	5.09683i	−0.0125221	−	0.214997i
$563$	16.2816	+	17.2575i	0.686189	+	0.727318i	0.973035	−	0.230659i	$-0.0740882\pi$
$563$	16.2816	+	17.2575i	0.686189	+	0.727318i	−0.286846	+	0.957977i	$0.592607\pi$
$564$		0			0
$565$	−4.29540	+	9.95785i	−0.180709	+	0.418930i
$566$	4.52338			0.190132
$567$		0			0
$568$	7.61770			0.319632
$569$	0.250584	−	0.580919i	0.0105050	−	0.0243534i	−0.912883	−	0.408222i	$-0.866149\pi$
$569$	0.250584	−	0.580919i	0.0105050	−	0.0243534i	0.923388	+	0.383868i	$0.125408\pi$
$570$		0			0
$571$	−27.5133	−	29.1624i	−1.15140	−	1.22041i	−0.971581	−	0.236708i	$-0.923932\pi$
$571$	−27.5133	−	29.1624i	−1.15140	−	1.22041i	−0.179815	−	0.983700i	$-0.557550\pi$
$572$	−0.301912	−	5.18363i	−0.0126236	−	0.216739i
$573$		0			0
$574$	−0.353026	−	0.0836688i	−0.0147350	−	0.00349227i
$575$	−32.1464	+	11.7003i	−1.34060	+	0.487938i
$576$		0			0
$577$	15.7332	+	5.72640i	0.654980	+	0.238393i	0.648068	−	0.761583i	$-0.275577\pi$
$577$	15.7332	+	5.72640i	0.654980	+	0.238393i	0.00691246	+	0.999976i	$0.497800\pi$
$578$	0.117211	+	0.0770909i	0.00487533	+	0.00320656i
$579$		0			0
$580$	−11.6706	−	1.36410i	−0.484597	−	0.0566413i
$581$	1.64851	−	2.21434i	0.0683918	−	0.0918661i
$582$		0			0
$583$	−0.267745	+	4.59701i	−0.0110889	+	0.190389i
$584$	5.40231	−	4.53308i	0.223549	−	0.187580i
$585$		0			0
$586$	2.02710	+	1.70094i	0.0837386	+	0.0702650i
$587$	11.3031	−	11.9806i	0.466531	−	0.494494i	−0.450797	−	0.892626i	$-0.648860\pi$
$587$	11.3031	−	11.9806i	0.466531	−	0.494494i	0.917328	+	0.398133i	$0.130342\pi$
$588$		0			0
$589$	−9.95946	+	6.55044i	−0.410372	+	0.269906i
$590$	−0.522574	+	0.123852i	−0.0215140	+	0.00509892i
$591$		0			0
$592$	−16.8441	+	1.96880i	−0.692289	+	0.0809170i
$593$	−20.1750	+	34.9441i	−0.828487	+	1.43498i	0.0707373	+	0.997495i	$0.477465\pi$
$593$	−20.1750	+	34.9441i	−0.828487	+	1.43498i	−0.899225	+	0.437487i	$0.855869\pi$
$594$		0			0
$595$	0.301836	+	0.522795i	0.0123741	+	0.0214325i
$596$	5.73508	+	7.70355i	0.234918	+	0.315550i
$597$		0			0
$598$	−1.68051	+	5.61330i	−0.0687212	+	0.229545i
$599$	−5.03341	−	2.52787i	−0.205660	−	0.103286i	0.342988	−	0.939340i	$-0.388561\pi$
$599$	−5.03341	−	2.52787i	−0.205660	−	0.103286i	−0.548648	+	0.836054i	$0.684857\pi$
$600$		0			0
$601$	−4.90209	−	16.3741i	−0.199960	−	0.667914i	−0.997876	−	0.0651446i	$-0.979249\pi$
$601$	−4.90209	−	16.3741i	−0.199960	−	0.667914i	0.797916	−	0.602769i	$-0.205936\pi$
$602$	−0.0199201	+	0.112972i	−0.000811882	+	0.00460441i
$603$		0			0
$604$	−5.49667	−	31.1732i	−0.223656	−	1.26842i
$605$	8.50014	−	4.26893i	0.345580	−	0.173557i
$606$		0			0
$607$	7.17870	+	16.6421i	0.291374	+	0.675482i	0.999533	−	0.0305719i	$-0.00973286\pi$
$607$	7.17870	+	16.6421i	0.291374	+	0.675482i	−0.708158	+	0.706054i	$0.750474\pi$
$608$	1.99088	+	4.61537i	0.0807408	+	0.187178i
$609$		0			0
$610$	1.16222	−	0.583689i	0.0470569	−	0.0236329i
$611$	5.48012	+	31.0793i	0.221702	+	1.25733i
$612$		0			0
$613$	3.85172	−	21.8442i	0.155570	−	0.882279i	−0.802694	−	0.596392i	$-0.796601\pi$
$613$	3.85172	−	21.8442i	0.155570	−	0.882279i	0.958263	−	0.285887i	$-0.0922883\pi$
$614$	−0.851690	−	2.84484i	−0.0343714	−	0.114808i
$615$		0			0
$616$	−0.0879710	−	0.0441807i	−0.00354445	−	0.00178009i
$617$	2.87922	−	9.61726i	0.115913	−	0.387176i	−0.880269	−	0.474474i	$-0.842638\pi$
$617$	2.87922	−	9.61726i	0.115913	−	0.387176i	0.996182	+	0.0872982i	$0.0278233\pi$
$618$		0			0
$619$	−11.9054	−	15.9918i	−0.478520	−	0.642764i	0.495665	−	0.868514i	$-0.334924\pi$
$619$	−11.9054	−	15.9918i	−0.478520	−	0.642764i	−0.974185	+	0.225750i	$0.927517\pi$
$620$	−4.99522	−	8.65197i	−0.200613	−	0.347472i
$621$		0			0
$622$	−3.37316	+	5.84249i	−0.135252	+	0.234263i
$623$	−1.86236	+	0.217679i	−0.0746141	+	0.00872113i
$624$		0			0
$625$	12.8755	−	3.05155i	0.515021	−	0.122062i
$626$	3.85984	−	2.53866i	0.154270	−	0.101465i
$627$		0			0
$628$	16.6222	−	17.6185i	0.663299	−	0.703056i
$629$	13.9644	+	11.7176i	0.556799	+	0.467210i
$630$		0			0
$631$	1.55588	−	1.30554i	0.0619385	−	0.0519726i	−0.611293	−	0.791404i	$-0.709350\pi$
$631$	1.55588	−	1.30554i	0.0619385	−	0.0519726i	0.673231	+	0.739432i	$0.264906\pi$
$632$	−0.150017	+	2.57570i	−0.00596736	+	0.102456i
$633$		0			0
$634$	−2.26705	+	3.04518i	−0.0900360	+	0.120939i
$635$	13.2076	+	1.54374i	0.524127	+	0.0612616i
$636$		0			0
$637$	−20.5875	−	13.5406i	−0.815705	−	0.536498i
$638$	−0.937360	−	0.341171i	−0.0371105	−	0.0135071i
$639$		0			0
$640$	−5.25884	+	1.91406i	−0.207874	+	0.0756599i
$641$	−26.0313	−	6.16954i	−1.02818	−	0.243682i	−0.318286	−	0.947995i	$-0.603107\pi$
$641$	−26.0313	−	6.16954i	−1.02818	−	0.243682i	−0.709890	+	0.704312i	$0.751255\pi$
$642$		0			0
$643$	0.509005	+	8.73928i	0.0200732	+	0.344643i	0.993360	+	0.115050i	$0.0367027\pi$
$643$	0.509005	+	8.73928i	0.0200732	+	0.344643i	−0.973287	+	0.229594i	$0.926260\pi$
$644$	−1.80954	−	1.91800i	−0.0713058	−	0.0755798i
$645$		0			0
$646$	0.688592	−	1.59634i	0.0270923	−	0.0628070i
$647$	−1.73387			−0.0681653			−0.0340827	−	0.999419i	$-0.510851\pi$
$647$	−1.73387			−0.0681653			−0.0340827	+	0.999419i	$0.510851\pi$
$648$		0			0
$649$	2.18701			0.0858477
$650$	1.17940	−	2.73415i	0.0462598	−	0.107242i
$651$		0			0
$652$	−16.3264	−	17.3049i	−0.639390	−	0.677714i
$653$	1.50395	+	25.8218i	0.0588540	+	1.01048i	0.890444	+	0.455094i	$0.150394\pi$
$653$	1.50395	+	25.8218i	0.0588540	+	1.01048i	−0.831590	+	0.555391i	$0.812569\pi$
$654$		0			0
$655$	−5.91211	−	1.40120i	−0.231005	−	0.0547493i
$656$	38.6315	−	14.0607i	1.50831	−	0.548979i
$657$		0			0
$658$	0.278217	+	0.101263i	0.0108460	+	0.00394763i
$659$	−6.50297	−	4.27707i	−0.253320	−	0.166611i	0.416498	−	0.909137i	$-0.363257\pi$
$659$	−6.50297	−	4.27707i	−0.253320	−	0.166611i	−0.669818	+	0.742526i	$0.733628\pi$
$660$		0			0
$661$	−7.77288	−	0.908519i	−0.302330	−	0.0353373i	−0.0364244	−	0.999336i	$-0.511597\pi$
$661$	−7.77288	−	0.908519i	−0.302330	−	0.0353373i	−0.265905	+	0.963999i	$0.585671\pi$
$662$	−0.714353	+	0.959543i	−0.0277641	+	0.0372937i
$663$		0			0
$664$	0.782915	−	13.4421i	0.0303830	−	0.521656i
$665$	−0.243969	+	0.204714i	−0.00946070	+	0.00793847i
$666$		0			0
$667$	−41.3636	−	34.7082i	−1.60161	−	1.34391i
$668$	−3.41644	+	3.62122i	−0.132186	+	0.140109i
$669$		0			0
$670$	1.36668	−	0.898881i	0.0527995	−	0.0347268i
$671$	−5.15345	+	1.22139i	−0.198947	+	0.0471512i
$672$		0			0
$673$	−6.28264	+	0.734335i	−0.242178	+	0.0283066i	−0.236316	−	0.971676i	$-0.575940\pi$
$673$	−6.28264	+	0.734335i	−0.242178	+	0.0283066i	−0.00586206	+	0.999983i	$0.501866\pi$
$674$	1.22624	−	2.12391i	0.0472330	−	0.0818099i
$675$		0			0
$676$	−0.502052	−	0.869580i	−0.0193097	−	0.0334454i
$677$	−14.7295	−	19.7852i	−0.566102	−	0.760407i	0.423240	−	0.906018i	$-0.360893\pi$
$677$	−14.7295	−	19.7852i	−0.566102	−	0.760407i	−0.989342	+	0.145610i	$0.953485\pi$
$678$		0			0
$679$	0.213148	−	0.711963i	0.00817986	−	0.0273226i
$680$	2.63124	+	1.32146i	0.100903	+	0.0506756i
$681$		0			0
$682$	−0.243247	−	0.812503i	−0.00931442	−	0.0311123i
$683$	3.77494	−	21.4087i	0.144444	−	0.819183i	−0.823368	−	0.567508i	$-0.807908\pi$
$683$	3.77494	−	21.4087i	0.144444	−	0.819183i	0.967812	−	0.251675i	$-0.0809813\pi$
$684$		0			0
$685$	−2.31478	−	13.1278i	−0.0884433	−	0.501587i
$686$	−0.413968	+	0.207902i	−0.0158054	+	0.00793775i
$687$		0			0
$688$	−5.14855	−	11.9357i	−0.196287	−	0.455043i
$689$	−8.59346	−	19.9219i	−0.327385	−	0.758963i
$690$		0			0
$691$	−43.4188	+	21.8058i	−1.65173	+	0.829530i	−0.654428	+	0.756125i	$0.727090\pi$
$691$	−43.4188	+	21.8058i	−1.65173	+	0.829530i	−0.997302	+	0.0734052i	$0.976613\pi$
$692$	−3.31247	−	18.7859i	−0.125921	−	0.714134i
$693$		0			0
$694$	0.0855992	−	0.485457i	0.00324930	−	0.0184277i
$695$	−0.866541	−	2.89445i	−0.0328698	−	0.109793i
$696$		0			0
$697$	−39.4902	−	19.8327i	−1.49580	−	0.751219i
$698$	−1.33203	+	4.44930i	−0.0504182	+	0.168409i
$699$		0			0
$700$	0.800205	+	1.07486i	0.0302449	+	0.0406259i
$701$	12.9938	+	22.5060i	0.490770	+	0.850039i	0.999944	−	0.0106253i	$-0.00338221\pi$
$701$	12.9938	+	22.5060i	0.490770	+	0.850039i	−0.509174	+	0.860664i	$0.670049\pi$
$702$		0			0
$703$	−4.80861	+	8.32876i	−0.181360	+	0.314125i
$704$	5.24163	−	0.612659i	0.197551	−	0.0230904i
$705$		0			0
$706$	4.55349	−	1.07920i	0.171373	−	0.0406161i
$707$	0.315457	−	0.207479i	0.0118640	−	0.00780306i
$708$		0			0
$709$	−24.8863	+	26.3779i	−0.934624	+	0.990643i	−0.999974	−	0.00721930i	$-0.997702\pi$
$709$	−24.8863	+	26.3779i	−0.934624	+	0.990643i	0.0653504	+	0.997862i	$0.479183\pi$
$710$	1.34322	+	1.12709i	0.0504100	+	0.0422990i
$711$		0			0
$712$	−7.00594	+	5.87868i	−0.262559	+	0.220313i
$713$	2.66943	−	45.8324i	0.0999710	−	1.71644i
$714$		0			0
$715$	1.44232	−	1.93737i	0.0539396	−	0.0724534i
$716$	7.24456	+	0.846768i	0.270742	+	0.0316452i
$717$		0			0
$718$	−5.28677	−	3.47716i	−0.197301	−	0.129767i
$719$	−0.547249	−	0.199183i	−0.0204090	−	0.00742825i	0.331795	−	0.943351i	$-0.392346\pi$
$719$	−0.547249	−	0.199183i	−0.0204090	−	0.00742825i	−0.352204	+	0.935923i	$0.614568\pi$
$720$		0			0
$721$	−0.401170	+	0.146014i	−0.0149404	+	0.00543785i
$722$	−2.84385	−	0.674004i	−0.105837	−	0.0250838i
$723$		0			0
$724$	−0.832257	−	14.2893i	−0.0309306	−	0.531057i
$725$	18.8305	+	19.9592i	0.699347	+	0.741265i
$726$		0			0
$727$	7.92165	−	18.3644i	0.293798	−	0.681100i	−0.705830	−	0.708381i	$-0.749426\pi$
$727$	7.92165	−	18.3644i	0.293798	−	0.681100i	0.999628	+	0.0272815i	$0.00868504\pi$
$728$	0.463826			0.0171905
$729$		0			0
$730$	1.62328			0.0600803
$731$	−5.53426	+	12.8299i	−0.204692	+	0.474530i
$732$		0			0
$733$	29.4243	+	31.1879i	1.08681	+	1.15195i	0.987617	+	0.156883i	$0.0501447\pi$
$733$	29.4243	+	31.1879i	1.08681	+	1.15195i	0.0991931	+	0.995068i	$0.468374\pi$
$734$	−0.0901836	−	1.54839i	−0.00332874	−	0.0571522i
$735$		0			0
$736$	−18.8368	−	4.46440i	−0.694333	−	0.164560i
$737$	−6.25963	+	2.27832i	−0.230577	+	0.0839230i
$738$		0			0
$739$	−30.4321	−	11.0764i	−1.11946	−	0.407452i	−0.285008	−	0.958525i	$-0.591996\pi$
$739$	−30.4321	−	11.0764i	−1.11946	−	0.407452i	−0.834457	+	0.551074i	$0.814218\pi$
$740$	−6.73408	−	4.42908i	−0.247550	−	0.162816i
$741$		0			0
$742$	−0.202170	−	0.0236303i	−0.00742189	−	0.000867495i
$743$	−7.48588	+	10.0553i	−0.274630	+	0.368893i	−0.917944	−	0.396710i	$-0.870152\pi$
$743$	−7.48588	+	10.0553i	−0.274630	+	0.368893i	0.643313	+	0.765603i	$0.277559\pi$
$744$		0			0
$745$	−0.259754	+	4.45981i	−0.00951666	+	0.163395i
$746$	4.01804	−	3.37153i	0.147111	−	0.123441i
$747$		0			0
$748$	−4.54525	−	3.81392i	−0.166191	−	0.139451i
$749$	1.34575	−	1.42641i	0.0491725	−	0.0521198i
$750$		0			0
$751$	20.4708	−	13.4639i	0.746991	−	0.491304i	−0.118048	−	0.993008i	$-0.537664\pi$
$751$	20.4708	−	13.4639i	0.746991	−	0.491304i	0.865039	+	0.501704i	$0.167293\pi$
$752$	−32.6446	+	7.73691i	−1.19043	+	0.282136i
$753$		0			0
$754$	4.66819	−	0.545634i	0.170006	−	0.0198708i
$755$	7.36209	−	12.7515i	0.267934	−	0.464075i
$756$		0			0
$757$	−10.7313	−	18.5872i	−0.390037	−	0.675564i	0.602417	−	0.798182i	$-0.294205\pi$
$757$	−10.7313	−	18.5872i	−0.390037	−	0.675564i	−0.992454	+	0.122617i	$0.960871\pi$
$758$	3.20657	+	4.30717i	0.116468	+	0.156443i
$759$		0			0
$760$	−0.445518	+	1.48813i	−0.0161606	+	0.0539803i
$761$	31.8202	+	15.9807i	1.15348	+	0.579301i	0.919558	−	0.392954i	$-0.128547\pi$
$761$	31.8202	+	15.9807i	1.15348	+	0.579301i	0.233925	+	0.972255i	$0.424843\pi$
$762$		0			0
$763$	−0.853032	−	2.84933i	−0.0308818	−	0.103153i
$764$	−7.06821	+	40.0858i	−0.255719	+	1.45025i
$765$		0			0
$766$	0.0945988	+	0.536496i	0.00341799	+	0.0193844i
$767$	−9.20840	+	4.62463i	−0.332496	+	0.166986i
$768$		0			0
$769$	−6.57150	−	15.2344i	−0.236974	−	0.549368i	0.757680	−	0.652626i	$-0.226333\pi$
$769$	−6.57150	−	15.2344i	−0.236974	−	0.549368i	−0.994655	+	0.103258i	$0.967073\pi$
$770$	−0.00897493	−	0.0208062i	−0.000323434	−	0.000749805i
$771$		0			0
$772$	6.11529	−	3.07121i	0.220094	−	0.110535i
$773$	−1.97712	−	11.2128i	−0.0711121	−	0.403297i	−0.999498	−	0.0316795i	$-0.989914\pi$
$773$	−1.97712	−	11.2128i	−0.0711121	−	0.403297i	0.928386	−	0.371617i	$-0.121197\pi$
$774$		0			0
$775$	−4.05134	+	22.9763i	−0.145528	+	0.825332i
$776$	−1.03964	−	3.47263i	−0.0373208	−	0.124660i
$777$		0			0
$778$	4.27917	+	2.14908i	0.153416	+	0.0770482i
$779$	6.68643	−	22.3342i	0.239566	−	0.800207i
$780$		0			0
$781$	−4.26400	−	5.72754i	−0.152578	−	0.204948i
$782$	3.34781	+	5.79858i	0.119718	+

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0800459 - 0.185567i) q^{2} +(1.34446 + 1.42504i) q^{4} +(0.0529885 + 0.909778i) q^{5} +(0.159621 + 0.0378310i) q^{7} +(0.751874 - 0.273660i) q^{8} +O(q^{10})\)	\(q+(0.0800459 - 0.185567i) q^{2} +(1.34446 + 1.42504i) q^{4} +(0.0529885 + 0.909778i) q^{5} +(0.159621 + 0.0378310i) q^{7} +(0.751874 - 0.273660i) q^{8} +(0.173067 + 0.0629911i) q^{10} +(-0.626618 - 0.412133i) q^{11} +(3.50987 + 0.410245i) q^{13} +(0.0197972 - 0.0265923i) q^{14} +(-0.218428 + 3.75026i) q^{16} +(3.09332 - 2.59561i) q^{17} +(1.63194 + 1.36936i) q^{19} +(-1.22523 + 1.29867i) q^{20} +(-0.126637 + 0.0832903i) q^{22} +(-7.98355 + 1.89214i) q^{23} +(4.14130 - 0.484049i) q^{25} +(0.357079 - 0.618479i) q^{26} +(0.160693 + 0.278329i) q^{28} +(3.92999 + 5.27889i) q^{29} +(-1.60483 + 5.36050i) q^{31} +(2.10848 + 1.05892i) q^{32} +(-0.234052 - 0.781788i) q^{34} +(-0.0259597 + 0.147225i) q^{35} +(0.783915 + 4.44580i) q^{37} +(0.384740 - 0.193224i) q^{38} +(0.288810 + 0.669538i) q^{40} +(-4.33453 - 10.0486i) q^{41} +(-3.09218 + 1.55295i) q^{43} +(-0.255154 - 1.44705i) q^{44} +(-0.287932 + 1.63294i) q^{46} +(2.56133 + 8.55545i) q^{47} +(-6.23138 - 3.12952i) q^{49} +(0.241671 - 0.807237i) q^{50} +(4.13425 + 5.55326i) q^{52} +(-3.06986 - 5.31715i) q^{53} +(0.341746 - 0.591922i) q^{55} +(0.130368 - 0.0152378i) q^{56} +(1.29417 - 0.306724i) q^{58} +(-2.43628 + 1.60237i) q^{59} +(4.84595 - 5.13641i) q^{61} +(0.866274 + 0.726890i) q^{62} +(-5.39019 + 4.52290i) q^{64} +(-0.187249 + 3.21494i) q^{65} +(5.30383 - 7.12428i) q^{67} +(7.85768 + 0.918431i) q^{68} +(0.0252421 + 0.0166020i) q^{70} +(8.94644 + 3.25624i) q^{71} +(8.28233 - 3.01452i) q^{73} +(0.887745 + 0.210399i) q^{74} +(0.242679 + 4.16663i) q^{76} +(-0.0844303 - 0.0894909i) q^{77} +(-1.27718 + 2.96084i) q^{79} -3.42347 q^{80} -2.21165 q^{82} +(6.66541 - 15.4521i) q^{83} +(2.52534 + 2.67670i) q^{85} +(0.0406606 + 0.698115i) q^{86} +(-0.583922 - 0.138392i) q^{88} +(-10.7409 + 3.90935i) q^{89} +(0.544730 + 0.198266i) q^{91} +(-13.4299 - 8.83298i) q^{92} +(1.79264 + 0.209529i) q^{94} +(-1.15934 + 1.55727i) q^{95} +(0.263420 - 4.52275i) q^{97} +(-1.07953 + 0.905836i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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