LMFDB - Embedded newform 729.2.g.a.28.8

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			28.8
Character	$\chi$	$=$	729.28
Dual form			729.2.g.a.703.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.76633 - 1.16173i) q^{2} +(0.978129 - 2.26756i) q^{4} +(2.05186 - 2.17484i) q^{5} +(3.48897 + 0.407803i) q^{7} +(-0.172370 - 0.977557i) q^{8} +O(q^{10})$	\(q+(1.76633 - 1.16173i) q^{2} +(0.978129 - 2.26756i) q^{4} +(2.05186 - 2.17484i) q^{5} +(3.48897 + 0.407803i) q^{7} +(-0.172370 - 0.977557i) q^{8} +(1.09767 - 6.22518i) q^{10} +(-0.562324 + 1.87829i) q^{11} +(-0.0969288 + 1.66420i) q^{13} +(6.63642 - 3.33294i) q^{14} +(1.94926 + 2.06610i) q^{16} +(-3.65626 + 1.33077i) q^{17} +(-0.0155726 - 0.00566795i) q^{19} +(-2.92460 - 6.77998i) q^{20} +(1.18882 + 3.97095i) q^{22} +(-7.67257 + 0.896795i) q^{23} +(-0.229093 - 3.93338i) q^{25} +(1.76215 + 3.05213i) q^{26} +(4.33738 - 7.51257i) q^{28} +(-4.12997 - 2.07415i) q^{29} +(-6.12985 - 8.23381i) q^{31} +(7.77505 + 1.84272i) q^{32} +(-4.91215 + 6.59816i) q^{34} +(8.04578 - 6.75121i) q^{35} +(5.48325 + 4.60100i) q^{37} +(-0.0340908 + 0.00807968i) q^{38} +(-2.47971 - 1.63093i) q^{40} +(-4.72613 - 3.10842i) q^{41} +(-4.44056 + 1.05243i) q^{43} +(3.70912 + 3.11232i) q^{44} +(-12.5104 + 10.4975i) q^{46} +(1.71778 - 2.30738i) q^{47} +(5.19533 + 1.23132i) q^{49} +(-4.97418 - 6.68148i) q^{50} +(3.67887 + 1.84760i) q^{52} +(1.40413 - 2.43202i) q^{53} +(2.93118 + 5.07695i) q^{55} +(-0.202743 - 3.48096i) q^{56} +(-9.70447 + 1.13429i) q^{58} +(-1.42165 - 4.74864i) q^{59} +(3.71633 + 8.61543i) q^{61} +(-20.3928 - 7.42236i) q^{62} +(10.5356 - 3.83466i) q^{64} +(3.42049 + 3.62551i) q^{65} +(-4.00634 + 2.01206i) q^{67} +(-0.558696 + 9.59244i) q^{68} +(6.36838 - 21.2719i) q^{70} +(1.33743 - 7.58494i) q^{71} +(-0.696188 - 3.94828i) q^{73} +(15.0303 + 1.75679i) q^{74} +(-0.0280844 + 0.0297677i) q^{76} +(-2.72791 + 6.32400i) q^{77} +(-6.81054 + 4.47936i) q^{79} +8.49305 q^{80} -11.9590 q^{82} +(4.30784 - 2.83331i) q^{83} +(-4.60790 + 10.6823i) q^{85} +(-6.62083 + 7.01767i) q^{86} +(1.93307 + 0.225943i) q^{88} +(-0.829745 - 4.70572i) q^{89} +(-1.01685 + 5.76683i) q^{91} +(-5.47123 + 18.2752i) q^{92} +(0.353607 - 6.07119i) q^{94} +(-0.0442795 + 0.0222380i) q^{95} +(7.98151 + 8.45991i) q^{97} +(10.6071 - 3.86067i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 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 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

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 $

$2$	1.76633	−	1.16173i	1.24898	−	0.821468i	0.259446	−	0.965758i	$-0.416460\pi$
$2$	1.76633	−	1.16173i	1.24898	−	0.821468i	0.989535	+	0.144290i	$0.0460898\pi$
$3$		0			0
$3$		0			0
$4$	0.978129	−	2.26756i	0.489065	−	1.13378i
$5$	2.05186	−	2.17484i	0.917618	−	0.972618i	−0.0820939	−	0.996625i	$-0.526161\pi$
$5$	2.05186	−	2.17484i	0.917618	−	0.972618i	0.999712	+	0.0240065i	$0.00764223\pi$
$6$		0			0
$7$	3.48897	+	0.407803i	1.31871	+	0.154135i	0.746177	−	0.665748i	$-0.231887\pi$
$7$	3.48897	+	0.407803i	1.31871	+	0.154135i	0.572532	+	0.819883i	$0.305961\pi$
$8$	−0.172370	−	0.977557i	−0.0609419	−	0.345618i
$9$		0			0
$10$	1.09767	−	6.22518i	0.347113	−	1.96858i
$11$	−0.562324	+	1.87829i	−0.169547	+	0.566327i	0.830411	+	0.557152i	$0.188106\pi$
$11$	−0.562324	+	1.87829i	−0.169547	+	0.566327i	−0.999958	+	0.00917522i	$0.997079\pi$
$12$		0			0
$13$	−0.0969288	+	1.66420i	−0.0268832	+	0.461567i	0.957825	+	0.287353i	$0.0927754\pi$
$13$	−0.0969288	+	1.66420i	−0.0268832	+	0.461567i	−0.984708	+	0.174214i	$0.944262\pi$
$14$	6.63642	−	3.33294i	1.77366	−	0.890765i
$15$		0			0
$16$	1.94926	+	2.06610i	0.487316	+	0.516525i
$17$	−3.65626	+	1.33077i	−0.886772	+	0.322759i	−0.744940	−	0.667132i	$-0.767522\pi$
$17$	−3.65626	+	1.33077i	−0.886772	+	0.322759i	−0.141833	+	0.989891i	$0.545300\pi$
$18$		0			0
$19$	−0.0155726	−	0.00566795i	−0.00357259	−	0.00130032i	0.340233	−	0.940341i	$-0.389494\pi$
$19$	−0.0155726	−	0.00566795i	−0.00357259	−	0.00130032i	−0.343806	+	0.939041i	$0.611716\pi$
$20$	−2.92460	−	6.77998i	−0.653960	−	1.51605i
$21$		0			0
$22$	1.18882	+	3.97095i	0.253458	+	0.846609i
$23$	−7.67257	+	0.896795i	−1.59984	+	0.186995i	−0.868738	−	0.495272i	$-0.835068\pi$
$23$	−7.67257	+	0.896795i	−1.59984	+	0.186995i	−0.731103	+	0.682267i	$0.760994\pi$
$24$		0			0
$25$	−0.229093	−	3.93338i	−0.0458186	−	0.786675i
$26$	1.76215	+	3.05213i	0.345586	+	0.598572i
$27$		0			0
$28$	4.33738	−	7.51257i	0.819689	−	1.41974i
$29$	−4.12997	−	2.07415i	−0.766916	−	0.385159i	0.0219232	−	0.999760i	$-0.493021\pi$
$29$	−4.12997	−	2.07415i	−0.766916	−	0.385159i	−0.788839	+	0.614600i	$0.789317\pi$
$30$		0			0
$31$	−6.12985	−	8.23381i	−1.10095	−	1.47884i	−0.861382	−	0.507957i	$-0.830401\pi$
$31$	−6.12985	−	8.23381i	−1.10095	−	1.47884i	−0.239571	−	0.970879i	$-0.577007\pi$
$32$	7.77505	+	1.84272i	1.37445	+	0.325750i
$33$		0			0
$34$	−4.91215	+	6.59816i	−0.842426	+	1.13157i
$35$	8.04578	−	6.75121i	1.35998	−	1.14116i
$36$		0			0
$37$	5.48325	+	4.60100i	0.901441	+	0.756399i	0.970472	−	0.241215i	$-0.0775460\pi$
$37$	5.48325	+	4.60100i	0.901441	+	0.756399i	−0.0690302	+	0.997615i	$0.521990\pi$
$38$	−0.0340908	+	0.00807968i	−0.00553026	+	0.00131070i
$39$		0			0
$40$	−2.47971	−	1.63093i	−0.392076	−	0.257873i
$41$	−4.72613	−	3.10842i	−0.738097	−	0.485454i	0.123946	−	0.992289i	$-0.460445\pi$
$41$	−4.72613	−	3.10842i	−0.738097	−	0.485454i	−0.862043	+	0.506835i	$0.830815\pi$
$42$		0			0
$43$	−4.44056	+	1.05243i	−0.677179	+	0.160494i	−0.554793	−	0.831988i	$-0.687203\pi$
$43$	−4.44056	+	1.05243i	−0.677179	+	0.160494i	−0.122386	+	0.992483i	$0.539054\pi$
$44$	3.70912	+	3.11232i	0.559170	+	0.469199i
$45$		0			0
$46$	−12.5104	+	10.4975i	−1.84456	+	1.54777i
$47$	1.71778	−	2.30738i	0.250564	−	0.336566i	−0.658990	−	0.752152i	$-0.729016\pi$
$47$	1.71778	−	2.30738i	0.250564	−	0.336566i	0.909554	+	0.415586i	$0.136423\pi$
$48$		0			0
$49$	5.19533	+	1.23132i	0.742190	+	0.175902i
$50$	−4.97418	−	6.68148i	−0.703455	−	0.944904i
$51$		0			0
$52$	3.67887	+	1.84760i	0.510167	+	0.256216i
$53$	1.40413	−	2.43202i	0.192872	−	0.334063i	−0.753329	−	0.657644i	$-0.771553\pi$
$53$	1.40413	−	2.43202i	0.192872	−	0.334063i	0.946201	+	0.323580i	$0.104887\pi$
$54$		0			0
$55$	2.93118	+	5.07695i	0.395240	+	0.684576i
$56$	−0.202743	−	3.48096i	−0.0270927	−	0.465163i
$57$		0			0
$58$	−9.70447	+	1.13429i	−1.27426	+	0.148940i
$59$	−1.42165	−	4.74864i	−0.185083	−	0.618221i	−0.999291	−	0.0376473i	$-0.988014\pi$
$59$	−1.42165	−	4.74864i	−0.185083	−	0.618221i	0.814208	−	0.580573i	$-0.197172\pi$
$60$		0			0
$61$	3.71633	+	8.61543i	0.475828	+	1.10309i	0.972024	+	0.234882i	$0.0754705\pi$
$61$	3.71633	+	8.61543i	0.475828	+	1.10309i	−0.496196	+	0.868211i	$0.665270\pi$
$62$	−20.3928	−	7.42236i	−2.58989	−	0.942641i
$63$		0			0
$64$	10.5356	−	3.83466i	1.31695	−	0.479332i
$65$	3.42049	+	3.62551i	0.424260	+	0.449689i
$66$		0			0
$67$	−4.00634	+	2.01206i	−0.489453	+	0.245812i	−0.676368	−	0.736564i	$-0.736447\pi$
$67$	−4.00634	+	2.01206i	−0.489453	+	0.245812i	0.186916	+	0.982376i	$0.440151\pi$
$68$	−0.558696	+	9.59244i	−0.0677518	+	1.16325i
$69$		0			0
$70$	6.36838	−	21.2719i	0.761167	−	2.54247i
$71$	1.33743	−	7.58494i	0.158724	−	0.900166i	−0.796578	−	0.604535i	$-0.793359\pi$
$71$	1.33743	−	7.58494i	0.158724	−	0.900166i	0.955302	−	0.295631i	$-0.0955300\pi$
$72$		0			0
$73$	−0.696188	−	3.94828i	−0.0814827	−	0.462111i	−0.998060	−	0.0622545i	$-0.980171\pi$
$73$	−0.696188	−	3.94828i	−0.0814827	−	0.462111i	0.916578	−	0.399857i	$-0.130940\pi$
$74$	15.0303	+	1.75679i	1.74724	+	0.204223i
$75$		0			0
$76$	−0.0280844	+	0.0297677i	−0.00322150	+	0.00341459i
$77$	−2.72791	+	6.32400i	−0.310874	+	0.720687i
$78$		0			0
$79$	−6.81054	+	4.47936i	−0.766245	+	0.503967i	−0.871451	−	0.490483i	$-0.836820\pi$
$79$	−6.81054	+	4.47936i	−0.766245	+	0.503967i	0.105205	+	0.994451i	$0.466450\pi$
$80$	8.49305			0.949552
$81$		0			0
$82$	−11.9590			−1.32065
$83$	4.30784	−	2.83331i	0.472846	−	0.310996i	−0.290626	−	0.956837i	$-0.593863\pi$
$83$	4.30784	−	2.83331i	0.472846	−	0.310996i	0.763472	+	0.645841i	$0.223493\pi$
$84$		0			0
$85$	−4.60790	+	10.6823i	−0.499797	+	1.15866i
$86$	−6.62083	+	7.01767i	−0.713943	+	0.756735i
$87$		0			0
$88$	1.93307	+	0.225943i	0.206066	+	0.0240856i
$89$	−0.829745	−	4.70572i	−0.0879528	−	0.498805i	−0.996680	−	0.0814153i	$-0.974056\pi$
$89$	−0.829745	−	4.70572i	−0.0879528	−	0.498805i	0.908727	−	0.417390i	$-0.137055\pi$
$90$		0			0
$91$	−1.01685	+	5.76683i	−0.106595	+	0.604528i
$92$	−5.47123	+	18.2752i	−0.570415	+	1.90532i
$93$		0			0
$94$	0.353607	−	6.07119i	0.0364717	−	0.626196i
$95$	−0.0442795	+	0.0222380i	−0.00454298	+	0.00228157i
$96$		0			0
$97$	7.98151	+	8.45991i	0.810400	+	0.858974i	0.992238	−	0.124355i	$-0.0396861\pi$
$97$	7.98151	+	8.45991i	0.810400	+	0.858974i	−0.181838	+	0.983329i	$0.558205\pi$
$98$	10.6071	−	3.86067i	1.07148	−	0.389986i
$99$		0			0
$100$	−9.14325	−	3.32787i	−0.914325	−	0.332787i
$101$	−1.13250	−	2.62543i	−0.112688	−	0.261240i	0.852534	−	0.522672i	$-0.175065\pi$
$101$	−1.13250	−	2.62543i	−0.112688	−	0.261240i	−0.965222	+	0.261431i	$0.915805\pi$
$102$		0			0
$103$	0.820517	+	2.74072i	0.0808479	+	0.270051i	0.988850	−	0.148915i	$-0.0475780\pi$
$103$	0.820517	+	2.74072i	0.0808479	+	0.270051i	−0.908002	+	0.418966i	$0.862393\pi$
$104$	1.64356	−	0.192105i	0.161164	−	0.0188374i
$105$		0			0
$106$	−0.345206	−	5.92695i	−0.0335293	−	0.575676i
$107$	7.89300	+	13.6711i	0.763045	+	1.32163i	0.941274	+	0.337644i	$0.109630\pi$
$107$	7.89300	+	13.6711i	0.763045	+	1.32163i	−0.178229	+	0.983989i	$0.557037\pi$
$108$		0			0
$109$	0.145393	−	0.251828i	0.0139261	−	0.0241207i	−0.858978	−	0.512012i	$-0.828900\pi$
$109$	0.145393	−	0.251828i	0.0139261	−	0.0241207i	0.872904	+	0.487891i	$0.162234\pi$
$110$	11.0755	+	5.56231i	1.05600	+	0.530346i
$111$		0			0
$112$	5.95837	+	8.00349i	0.563013	+	0.756258i
$113$	3.14646	+	0.745724i	0.295994	+	0.0701518i	0.375930	−	0.926648i	$-0.377323\pi$
$113$	3.14646	+	0.745724i	0.295994	+	0.0701518i	−0.0799359	+	0.996800i	$0.525472\pi$
$114$		0			0
$115$	−13.7926	+	18.5267i	−1.28617	+	1.72762i
$116$	−8.74289	+	7.33616i	−0.811757	+	0.681145i
$117$		0			0
$118$	−8.02774	−	6.73608i	−0.739014	−	0.620106i
$119$	−13.2993	+	3.15199i	−1.21914	+	0.288942i
$120$		0			0
$121$	5.97859	+	3.93218i	0.543508	+	0.357471i
$122$	16.5731	+	10.9003i	1.50046	+	0.986865i
$123$		0			0
$124$	−24.6664	+	5.84605i	−2.21511	+	0.524991i
$125$	2.42779	+	2.03716i	0.217149	+	0.182209i
$126$		0			0
$127$	10.0576	−	8.43933i	0.892468	−	0.748870i	−0.0762356	−	0.997090i	$-0.524290\pi$
$127$	10.0576	−	8.43933i	0.892468	−	0.748870i	0.968704	+	0.248220i	$0.0798457\pi$
$128$	4.61142	−	6.19421i	0.407596	−	0.547496i
$129$		0			0
$130$	10.2536	+	2.43014i	0.899297	+	0.213137i
$131$	0.000192729	0	0.000258880i	1.68388e−5	0	2.26184e-5i	0.802132	−	0.597147i	$-0.203699\pi$
$131$	0.000192729	0	0.000258880i	1.68388e−5	0	2.26184e-5i	−0.802115	+	0.597170i	$0.796292\pi$
$132$		0			0
$133$	−0.0520209	−	0.0261259i	−0.00451078	−	0.00226540i
$134$	−4.73903	+	8.20825i	−0.409390	+	0.709085i
$135$		0			0
$136$	1.93113	+	3.34481i	0.165593	+	0.286815i
$137$	0.749748	+	12.8727i	0.0640553	+	1.09979i	0.865236	+	0.501365i	$0.167168\pi$
$137$	0.749748	+	12.8727i	0.0640553	+	1.09979i	−0.801181	+	0.598422i	$0.795794\pi$
$138$		0			0
$139$	−0.637020	+	0.0744569i	−0.0540313	+	0.00631535i	−0.143066	−	0.989713i	$-0.545696\pi$
$139$	−0.637020	+	0.0744569i	−0.0540313	+	0.00631535i	0.0890343	+	0.996029i	$0.471622\pi$
$140$	−7.43895	−	24.8478i	−0.628706	−	2.10003i
$141$		0			0
$142$	−6.44932	−	14.9512i	−0.541215	−	1.25468i
$143$	−3.07136	−	1.11788i	−0.256840	−	0.0934820i
$144$		0			0
$145$	−12.9850	+	4.72617i	−1.07835	+	0.392487i
$146$	−5.81653	−	6.16517i	−0.481380	−	0.510233i
$147$		0			0
$148$	15.7964	−	7.93323i	1.29845	−	0.652108i
$149$	0.751391	−	12.9009i	0.0615563	−	1.05688i	−0.816199	−	0.577772i	$-0.803922\pi$
$149$	0.751391	−	12.9009i	0.0615563	−	1.05688i	0.877755	−	0.479110i	$-0.159041\pi$
$150$		0			0
$151$	4.81347	−	16.0781i	0.391714	−	1.30842i	−0.503968	−	0.863722i	$-0.668127\pi$
$151$	4.81347	−	16.0781i	0.391714	−	1.30842i	0.895682	−	0.444695i	$-0.146688\pi$
$152$	−0.00285650	+	0.0162000i	−0.000231693	+	0.00131400i
$153$		0			0
$154$	2.52841	+	14.3393i	0.203745	+	1.15550i
$155$	−30.4848	−	3.56316i	−2.44860	−	0.286200i
$156$		0			0
$157$	5.90236	−	6.25613i	0.471059	−	0.499294i	−0.447660	−	0.894204i	$-0.647743\pi$
$157$	5.90236	−	6.25613i	0.471059	−	0.499294i	0.918720	+	0.394910i	$0.129224\pi$
$158$	−6.82582	+	15.8240i	−0.543033	+	1.25889i
$159$		0			0
$160$	19.9609	−	13.1285i	1.57805	−	1.03790i
$161$	−27.1351			−2.13855
$162$		0			0
$163$	0.674482			0.0528295			0.0264148	−	0.999651i	$-0.491591\pi$
$163$	0.674482			0.0528295			0.0264148	+	0.999651i	$0.491591\pi$
$164$	−11.6713	+	7.67634i	−0.911376	+	0.599421i
$165$		0			0
$166$	4.31750	−	10.0091i	0.335103	−	0.776856i
$167$	−11.0620	+	11.7251i	−0.856004	+	0.907312i	−0.996570	−	0.0827597i	$-0.973627\pi$
$167$	−11.0620	+	11.7251i	−0.856004	+	0.907312i	0.140565	+	0.990071i	$0.455108\pi$
$168$		0			0
$169$	10.1519	+	1.18659i	0.780917	+	0.0912761i
$170$	4.27092	+	24.2216i	0.327565	+	1.85771i
$171$		0			0
$172$	−1.95699	+	11.0986i	−0.149219	+	0.846263i
$173$	4.62618	−	15.4525i	0.351722	−	1.17483i	−0.580898	−	0.813976i	$-0.697299\pi$
$173$	4.62618	−	15.4525i	0.351722	−	1.17483i	0.932621	−	0.360858i	$-0.117516\pi$
$174$		0			0
$175$	0.804742	−	13.8169i	0.0608327	−	1.04446i
$176$	−4.97686	+	2.49947i	−0.375145	+	0.188405i
$177$		0			0
$178$	−6.93238	−	7.34790i	−0.519604	−	0.550748i
$179$	−7.45990	+	2.71518i	−0.557579	+	0.202942i	−0.605411	−	0.795913i	$-0.706991\pi$
$179$	−7.45990	+	2.71518i	−0.557579	+	0.202942i	0.0478318	+	0.998855i	$0.484769\pi$
$180$		0			0
$181$	13.0001	+	4.73166i	0.966292	+	0.351702i	0.776496	−	0.630122i	$-0.216995\pi$
$181$	13.0001	+	4.73166i	0.966292	+	0.351702i	0.189796	+	0.981824i	$0.439217\pi$
$182$	4.90342	+	11.3674i	0.363466	+	0.842609i
$183$		0			0
$184$	2.19919	+	7.34579i	0.162126	+	0.541539i
$185$	21.2573	−	2.48462i	1.56287	−	0.182673i
$186$		0			0
$187$	−0.443573	−	7.61585i	−0.0324372	−	0.556926i
$188$	−3.55191	−	6.15209i	−0.259050	−	0.448687i
$189$		0			0
$190$	−0.0523775	+	0.0907205i	−0.00379986	+	0.00658155i
$191$	12.8453	+	6.45115i	0.929453	+	0.466789i	0.848064	−	0.529893i	$-0.177768\pi$
$191$	12.8453	+	6.45115i	0.929453	+	0.466789i	0.0813890	+	0.996682i	$0.474064\pi$
$192$		0			0
$193$	−2.49845	−	3.35600i	−0.179842	−	0.241570i	0.703056	−	0.711135i	$-0.251818\pi$
$193$	−2.49845	−	3.35600i	−0.179842	−	0.241570i	−0.882898	+	0.469564i	$0.844411\pi$
$194$	23.9261	+	5.67059i	1.71779	+	0.407125i
$195$		0			0
$196$	7.87378	−	10.5763i	0.562413	−	0.755452i
$197$	0.181162	−	0.152013i	0.0129073	−	0.0108305i	−0.636311	−	0.771432i	$-0.719541\pi$
$197$	0.181162	−	0.152013i	0.0129073	−	0.0108305i	0.649218	+	0.760602i	$0.275096\pi$
$198$		0			0
$199$	19.9860	+	16.7702i	1.41677	+	1.18881i	0.953044	+	0.302832i	$0.0979322\pi$
$199$	19.9860	+	16.7702i	1.41677	+	1.18881i	0.463726	+	0.885979i	$0.346512\pi$
$200$	−3.80561	+	0.901946i	−0.269097	+	0.0637772i
$201$		0			0
$202$	−5.05042	−	3.32171i	−0.355346	−	0.233715i
$203$	−13.5635	−	8.92086i	−0.951972	−	0.626122i
$204$		0			0
$205$	−16.4577	+	3.90054i	−1.14945	+	0.272425i
$206$	4.63328	+	3.88778i	0.322816	+	0.270874i
$207$		0			0
$208$	−3.62735	+	3.04371i	−0.251511	+	0.211043i
$209$	0.0194029	−	0.0260626i	0.00134213	−	0.00180279i
$210$		0			0
$211$	−11.4811	−	2.72107i	−0.790390	−	0.187326i	−0.184456	−	0.982841i	$-0.559052\pi$
$211$	−11.4811	−	2.72107i	−0.790390	−	0.187326i	−0.605934	+	0.795515i	$0.707200\pi$
$212$	−4.14133	−	5.56277i	−0.284427	−	0.382052i
$213$		0			0
$214$	29.8237	+	14.9780i	2.03871	+	1.02388i
$215$	−6.82251	+	11.8169i	−0.465292	+	0.805909i
$216$		0			0
$217$	−18.0291	−	31.2273i	−1.22390	−	2.11985i
$218$	−0.0357450	−	0.613717i	−0.00242095	−	0.0415662i
$219$		0			0
$220$	14.3794	−	1.68071i	0.969456	−	0.113313i
$221$	−1.86027	−	6.21374i	−0.125135	−	0.417982i
$222$		0			0
$223$	−10.4312	−	24.1822i	−0.698524	−	1.61936i	−0.782320	−	0.622877i	$-0.785964\pi$
$223$	−10.4312	−	24.1822i	−0.698524	−	1.61936i	0.0837965	−	0.996483i	$-0.473295\pi$
$224$	26.3755	+	9.59989i	1.76229	+	0.641420i
$225$		0			0
$226$	6.42400	−	2.33814i	0.427318	−	0.155531i
$227$	−0.699631	−	0.741565i	−0.0464361	−	0.0492194i	0.703739	−	0.710458i	$-0.251512\pi$
$227$	−0.699631	−	0.741565i	−0.0464361	−	0.0492194i	−0.750175	+	0.661239i	$0.770031\pi$
$228$		0			0
$229$	23.3073	−	11.7054i	1.54019	−	0.773512i	0.542410	−	0.840114i	$-0.317512\pi$
$229$	23.3073	−	11.7054i	1.54019	−	0.773512i	0.997780	+	0.0666015i	$0.0212156\pi$
$230$	−2.83922	+	48.7475i	−0.187213	+	3.21432i
$231$		0			0
$232$	−1.31572	+	4.39480i	−0.0863810	+	0.288533i
$233$	−0.779551	+	4.42105i	−0.0510701	+	0.289633i	−0.999637	−	0.0269441i	$-0.991422\pi$
$233$	−0.779551	+	4.42105i	−0.0510701	+	0.289633i	0.948567	+	0.316577i	$0.102533\pi$
$234$		0			0
$235$	−1.49355	−	8.47032i	−0.0974282	−	0.552543i
$236$	−12.1584	−	1.42111i	−0.791443	−	0.0925065i
$237$		0			0
$238$	−19.8291	+	21.0176i	−1.28533	+	1.36237i
$239$	0.604016	−	1.40027i	0.0390706	−	0.0905757i	−0.897563	−	0.440886i	$-0.854664\pi$
$239$	0.604016	−	1.40027i	0.0390706	−	0.0905757i	0.936634	+	0.350310i	$0.113924\pi$
$240$		0			0
$241$	−0.703622	+	0.462779i	−0.0453243	+	0.0298102i	−0.571969	−	0.820275i	$-0.693820\pi$
$241$	−0.703622	+	0.462779i	−0.0453243	+	0.0298102i	0.526645	+	0.850086i	$0.323450\pi$
$242$	15.1283			0.972482
$243$		0			0
$244$	23.1711			1.48337
$245$	13.3380	−	8.77253i	0.852132	−	0.560456i
$246$		0			0
$247$	0.0109420	−	0.0253665i	0.000696225	−	0.00161403i
$248$	−6.99242	+	7.41153i	−0.444019	+	0.470633i
$249$		0			0
$250$	6.65491	+	0.777848i	0.420894	+	0.0491954i
$251$	−2.59126	−	14.6958i	−0.163559	−	0.927590i	−0.950538	−	0.310609i	$-0.899467\pi$
$251$	−2.59126	−	14.6958i	−0.163559	−	0.927590i	0.786978	−	0.616980i	$-0.211644\pi$
$252$		0			0
$253$	2.63003	−	14.9156i	0.165348	−	0.937737i
$254$	7.96078	−	26.5908i	0.499503	−	1.66846i
$255$		0			0
$256$	−0.354552	+	6.08743i	−0.0221595	+	0.380464i
$257$	8.24289	−	4.13974i	0.514178	−	0.258230i	−0.172737	−	0.984968i	$-0.555261\pi$
$257$	8.24289	−	4.13974i	0.514178	−	0.258230i	0.686914	+	0.726738i	$0.258965\pi$
$258$		0			0
$259$	17.2546	+	18.2888i	1.07215	+	1.13641i
$260$	11.5667	−	4.20995i	0.717339	−	0.261090i
$261$		0			0
$262$	0.000641171	0	0.000233367i	3.96117e−5	0	1.44175e-5i
$263$	−0.0942800	−	0.218566i	−0.00581355	−	0.0134773i	0.915285	−	0.402808i	$-0.131966\pi$
$263$	−0.0942800	−	0.218566i	−0.00581355	−	0.0134773i	−0.921098	+	0.389330i	$0.872706\pi$
$264$		0			0
$265$	−2.40819	−	8.04390i	−0.147934	−	0.494133i
$266$	−0.122237	+	0.0142875i	−0.00749483	+	0.000876020i
$267$		0			0
$268$	0.643745	+	11.0527i	0.0393230	+	0.675150i
$269$	−7.21026	−	12.4885i	−0.439617	−	0.761439i	0.558043	−	0.829812i	$-0.311553\pi$
$269$	−7.21026	−	12.4885i	−0.439617	−	0.761439i	−0.997660	+	0.0683731i	$0.978219\pi$
$270$		0			0
$271$	−8.33200	+	14.4314i	−0.506133	+	0.876648i	0.493842	+	0.869552i	$0.335592\pi$
$271$	−8.33200	+	14.4314i	−0.506133	+	0.876648i	−0.999975	+	0.00709598i	$0.997741\pi$
$272$	−9.87651	−	4.96017i	−0.598851	−	0.300755i
$273$		0			0
$274$	16.2789	+	21.8663i	0.983444	+	1.32099i
$275$	7.51686	+	1.78153i	0.453284	+	0.107430i
$276$		0			0
$277$	14.8198	−	19.9065i	0.890436	−	1.19606i	−0.0893469	−	0.996001i	$-0.528478\pi$
$277$	14.8198	−	19.9065i	0.890436	−	1.19606i	0.979783	−	0.200063i	$-0.0641146\pi$
$278$	−1.03869	+	0.871561i	−0.0622962	+	0.0522727i
$279$		0			0
$280$	−7.98654	−	6.70150i	−0.477287	−	0.400491i
$281$	18.8042	−	4.45667i	1.12176	−	0.265862i	0.372432	−	0.928059i	$-0.378524\pi$
$281$	18.8042	−	4.45667i	1.12176	−	0.265862i	0.749330	+	0.662197i	$0.230376\pi$
$282$		0			0
$283$	−0.932620	−	0.613394i	−0.0554385	−	0.0364625i	0.521487	−	0.853259i	$-0.325377\pi$
$283$	−0.932620	−	0.613394i	−0.0554385	−	0.0364625i	−0.576926	+	0.816797i	$0.695748\pi$
$284$	−15.8911	−	10.4517i	−0.942964	−	0.620197i
$285$		0			0
$286$	−6.72369	+	1.59354i	−0.397580	+	0.0942283i
$287$	−15.2217	−	12.7725i	−0.898510	−	0.753939i
$288$		0			0
$289$	−1.42549	+	1.19613i	−0.0838523	+	0.0703605i
$290$	−17.4453	+	23.4331i	−1.02442	+	1.37604i
$291$		0			0
$292$	−9.63392	−	2.28328i	−0.563783	−	0.133619i
$293$	4.79976	+	6.44720i	0.280405	+	0.376650i	0.919905	−	0.392142i	$-0.128266\pi$
$293$	4.79976	+	6.44720i	0.280405	+	0.376650i	−0.639500	+	0.768792i	$0.720858\pi$
$294$		0			0
$295$	−13.2446	−	6.65167i	−0.771128	−	0.387275i
$296$	3.55259	−	6.15326i	0.206490	−	0.357651i
$297$		0			0
$298$	−13.6602	−	23.6601i	−0.791311	−	1.37059i
$299$	−0.748755	−	12.8556i	−0.0433016	−	0.743461i
$300$		0			0
$301$	−15.9222	+	1.86104i	−0.917739	+	0.107268i
$302$	−10.1763	−	33.9911i	−0.585579	−	1.95597i
$303$		0			0
$304$	−0.0186445	−	0.0432228i	−0.00106933	−	0.00247900i
$305$	26.3626	+	9.59519i	1.50952	+	0.549419i
$306$		0			0
$307$	−15.7796	+	5.74331i	−0.900590	+	0.327788i	−0.750489	−	0.660883i	$-0.770182\pi$
$307$	−15.7796	+	5.74331i	−0.900590	+	0.327788i	−0.150101	+	0.988671i	$0.547960\pi$
$308$	11.6718	+	12.3714i	0.665062	+	0.704925i
$309$		0			0
$310$	−57.9855	+	29.1214i	−3.29336	+	1.65399i
$311$	−0.299735	+	5.14625i	−0.0169964	+	0.291817i	0.979090	+	0.203429i	$0.0652086\pi$
$311$	−0.299735	+	5.14625i	−0.0169964	+	0.291817i	−0.996086	+	0.0883881i	$0.971828\pi$
$312$		0			0
$313$	−8.01329	+	26.7663i	−0.452938	+	1.51292i	0.361334	+	0.932436i	$0.382321\pi$
$313$	−8.01329	+	26.7663i	−0.452938	+	1.51292i	−0.814273	+	0.580483i	$0.802864\pi$
$314$	3.15754	−	17.9073i	0.178191	−	1.01057i
$315$		0			0
$316$	3.49563	+	19.8247i	0.196644	+	1.11523i
$317$	−9.13214	−	1.06739i	−0.512912	−	0.0599508i	−0.144300	−	0.989534i	$-0.546093\pi$
$317$	−9.13214	−	1.06739i	−0.512912	−	0.0599508i	−0.368612	+	0.929583i	$0.620167\pi$
$318$		0			0
$319$	6.21824	−	6.59095i	0.348155	−	0.369022i
$320$	13.2778	−	30.7815i	0.742254	−	1.72074i
$321$		0			0
$322$	−47.9295	+	31.5237i	−2.67100	+	1.75675i
$323$	0.0644800			0.00358776
$324$		0			0
$325$	6.56814			0.364335
$326$	1.19136	−	0.783567i	0.0659831	−	0.0433978i
$327$		0			0
$328$	−2.22402	+	5.15586i	−0.122801	+	0.284685i
$329$	6.93426	−	7.34988i	0.382298	−	0.405212i
$330$		0			0
$331$	−16.8364	−	1.96789i	−0.925411	−	0.108165i	−0.359979	−	0.932960i	$-0.617216\pi$
$331$	−16.8364	−	1.96789i	−0.925411	−	0.108165i	−0.565431	+	0.824795i	$0.691290\pi$
$332$	−2.21107	−	12.5396i	−0.121348	−	0.688201i
$333$		0			0
$334$	−5.91777	+	33.5613i	−0.323806	+	1.83640i
$335$	−3.84453	+	12.8416i	−0.210049	+	0.701613i
$336$		0			0
$337$	−0.758539	+	13.0236i	−0.0413203	+	0.709442i	0.912502	+	0.409071i	$0.134147\pi$
$337$	−0.758539	+	13.0236i	−0.0413203	+	0.709442i	−0.953823	+	0.300370i	$0.902890\pi$
$338$	19.3101	−	9.69790i	1.05033	−	0.527496i
$339$		0			0
$340$	19.7157	+	20.8974i	1.06923	+	1.13332i
$341$	18.9125	−	6.88358i	1.02417	−	0.372767i
$342$		0			0
$343$	−5.48195	−	1.99527i	−0.295997	−	0.107734i
$344$	1.79423	+	4.15949i	0.0967383	+	0.224265i
$345$		0			0
$346$	−9.78033	−	32.6686i	−0.525794	−	1.75627i
$347$	−14.2961	+	1.67098i	−0.767457	+	0.0897029i	−0.490808	−	0.871268i	$-0.663298\pi$
$347$	−14.2961	+	1.67098i	−0.767457	+	0.0897029i	−0.276650	+	0.960971i	$0.589224\pi$
$348$		0			0
$349$	−0.472908	−	8.11951i	−0.0253142	−	0.434627i	−0.987026	−	0.160563i	$-0.948669\pi$
$349$	−0.472908	−	8.11951i	−0.0253142	−	0.434627i	0.961711	−	0.274064i	$-0.0883681\pi$
$350$	−14.6301	−	25.3400i	−0.782010	−	1.35448i
$351$		0			0
$352$	−7.83327	+	13.5676i	−0.417515	+	0.723157i
$353$	24.2226	+	12.1651i	1.28924	+	0.647481i	0.955446	−	0.295165i	$-0.0953745\pi$
$353$	24.2226	+	12.1651i	1.28924	+	0.647481i	0.333795	+	0.942646i	$0.391671\pi$
$354$		0			0
$355$	−13.7518	−	18.4719i	−0.729871	−	0.980386i
$356$	−11.4821	−	2.72131i	−0.608550	−	0.144229i
$357$		0			0
$358$	−10.0223	+	13.4623i	−0.529695	+	0.711504i
$359$	−19.0992	+	16.0261i	−1.00802	+	0.845828i	−0.988075	−	0.153974i	$-0.950793\pi$
$359$	−19.0992	+	16.0261i	−1.00802	+	0.845828i	−0.0199431	+	0.999801i	$0.506349\pi$
$360$		0			0
$361$	−14.5546	−	12.2128i	−0.766033	−	0.642778i
$362$	28.4594	−	6.74500i	1.49579	−	0.354509i
$363$		0			0
$364$	12.0820	+	7.94647i	0.633270	+	0.416508i
$365$	−10.0154	−	6.58720i	−0.524228	−	0.344790i
$366$		0			0
$367$	12.7392	−	3.01925i	0.664982	−	0.157604i	0.115756	−	0.993278i	$-0.463071\pi$
$367$	12.7392	−	3.01925i	0.664982	−	0.157604i	0.549226	+	0.835674i	$0.314923\pi$
$368$	−16.8087	−	14.1042i	−0.876216	−	0.735232i
$369$		0			0
$370$	34.6608	−	29.0839i	1.80193	−	1.51200i
$371$	5.89074	−	7.91264i	0.305832	−	0.410804i
$372$		0			0
$373$	−27.9998	−	6.63609i	−1.44978	−	0.343604i	−0.571045	−	0.820919i	$-0.693462\pi$
$373$	−27.9998	−	6.63609i	−1.44978	−	0.343604i	−0.878732	+	0.477315i	$0.841610\pi$
$374$	−9.63106	−	12.9368i	−0.498010	−	0.668944i
$375$		0			0
$376$	−2.55169	−	1.28151i	−0.131593	−	0.0660887i
$377$	3.85211	−	6.67206i	0.198394	−	0.343628i
$378$		0			0
$379$	10.4915	+	18.1718i	0.538912	+	0.933422i	0.998963	+	0.0455300i	$0.0144977\pi$
$379$	10.4915	+	18.1718i	0.538912	+	0.933422i	−0.460051	+	0.887892i	$0.652169\pi$
$380$	0.00711490	+	0.122158i	0.000364987	+	0.00626658i
$381$		0			0
$382$	30.1835	−	3.52794i	1.54432	−	0.180505i
$383$	7.02527	+	23.4660i	0.358974	+	1.19906i	0.926688	+	0.375832i	$0.122643\pi$
$383$	7.02527	+	23.4660i	0.358974	+	1.19906i	−0.567714	+	0.823226i	$0.692172\pi$
$384$		0			0
$385$	8.15642	+	18.9087i	0.415690	+	0.963677i
$386$	−8.31185	−	3.02526i	−0.423062	−	0.153982i
$387$		0			0
$388$	26.9903	−	9.82366i	1.37022	−	0.498721i
$389$	−10.8199	−	11.4684i	−0.548589	−	0.581470i	0.392448	−	0.919774i	$-0.371628\pi$
$389$	−10.8199	−	11.4684i	−0.548589	−	0.581470i	−0.941037	+	0.338304i	$0.890147\pi$
$390$		0			0
$391$	26.8595	−	13.4893i	1.35834	−	0.682184i
$392$	0.308164	−	5.29097i	0.0155646	−	0.267234i
$393$		0			0
$394$	0.143393	−	0.478966i	0.00722403	−	0.0241300i
$395$	−4.23235	+	24.0028i	−0.212953	+	1.20771i
$396$		0			0
$397$	−4.48471	−	25.4340i	−0.225081	−	1.27650i	−0.862530	−	0.506005i	$-0.831122\pi$
$397$	−4.48471	−	25.4340i	−0.225081	−	1.27650i	0.637449	−	0.770492i	$-0.279989\pi$
$398$	54.7843	+	6.40337i	2.74609	+	0.320972i
$399$		0			0
$400$	7.68019	−	8.14052i	0.384009	−	0.407026i
$401$	−6.48724	+	15.0391i	−0.323957	+	0.751017i	0.675944	+	0.736953i	$0.263736\pi$
$401$	−6.48724	+	15.0391i	−0.323957	+	0.751017i	−0.999901	+	0.0140640i	$0.995523\pi$
$402$		0			0
$403$	14.2969	−	9.40321i	0.712179	−	0.468407i
$404$	−7.06106			−0.351301
$405$		0			0
$406$	−34.3212			−1.70333
$407$	−11.7254	+	7.71191i	−0.581206	+	0.382265i
$408$		0			0
$409$	−10.0430	+	23.2823i	−0.496596	+	1.15124i	0.467093	+	0.884208i	$0.345301\pi$
$409$	−10.0430	+	23.2823i	−0.496596	+	1.15124i	−0.963688	+	0.267030i	$0.913958\pi$
$410$	−24.5382	+	26.0090i	−1.21186	+	1.28449i
$411$		0			0
$412$	7.01731	+	0.820206i	0.345718	+	0.0404086i
$413$	−3.02359	−	17.1476i	−0.148781	−	0.843781i
$414$		0			0
$415$	2.67707	−	15.1824i	0.131412	−	0.745275i
$416$	−3.82029	+	12.7606i	−0.187305	+	0.625642i
$417$		0			0
$418$	0.00399410	−	0.0685760i	0.000195358	−	0.00335416i
$419$	5.68329	−	2.85426i	0.277647	−	0.139440i	−0.304527	−	0.952504i	$-0.598498\pi$
$419$	5.68329	−	2.85426i	0.277647	−	0.139440i	0.582174	+	0.813064i	$0.302202\pi$
$420$		0			0
$421$	−18.0240	−	19.1043i	−0.878434	−	0.931086i	0.119658	−	0.992815i	$-0.461820\pi$
$421$	−18.0240	−	19.1043i	−0.878434	−	0.931086i	−0.998093	+	0.0617290i	$0.980339\pi$
$422$	−23.4405	+	8.53163i	−1.14106	+	0.415313i
$423$		0			0
$424$	−2.61946	−	0.953407i	−0.127212	−	0.0463015i
$425$	6.07204	+	14.0766i	0.294537	+	0.682814i
$426$		0			0
$427$	9.45280	+	31.5746i	0.457453	+	1.52800i
$428$	38.7203	−	4.52576i	1.87162	−	0.218761i
$429$		0			0
$430$	1.67732	+	28.7985i	0.0808876	+	1.38879i
$431$	−6.16440	−	10.6771i	−0.296929	−	0.514296i	0.678503	−	0.734598i	$-0.262629\pi$
$431$	−6.16440	−	10.6771i	−0.296929	−	0.514296i	−0.975432	+	0.220302i	$0.929296\pi$
$432$		0			0
$433$	3.37556	−	5.84664i	0.162219	−	0.280972i	−0.773445	−	0.633863i	$-0.781468\pi$
$433$	3.37556	−	5.84664i	0.162219	−	0.280972i	0.935664	+	0.352891i	$0.114802\pi$
$434$	−68.1230	−	34.2127i	−3.27001	−	1.64226i
$435$		0			0
$436$	−0.428821	−	0.576007i	−0.0205368	−	0.0275857i
$437$	0.124564	+	0.0295223i	0.00595873	+	0.00141224i
$438$		0			0
$439$	−2.66717	+	3.58263i	−0.127297	+	0.170989i	−0.861202	−	0.508262i	$-0.830288\pi$
$439$	−2.66717	+	3.58263i	−0.127297	+	0.170989i	0.733905	+	0.679252i	$0.237695\pi$
$440$	4.45776	−	3.74051i	0.212516	−	0.178322i
$441$		0			0
$442$	−10.5045	−	8.81436i	−0.499650	−	0.419256i
$443$	−27.4508	+	6.50597i	−1.30423	+	0.309108i	−0.823277	−	0.567639i	$-0.807857\pi$
$443$	−27.4508	+	6.50597i	−1.30423	+	0.309108i	−0.480952	+	0.876747i	$0.659709\pi$
$444$		0			0
$445$	−11.9367	−	7.85090i	−0.565854	−	0.372168i
$446$	−46.5181	−	30.5954i	−2.20269	−	1.44873i
$447$		0			0
$448$	38.3224	−	9.08256i	1.81056	−	0.429111i
$449$	20.0933	+	16.8603i	0.948260	+	0.795685i	0.979004	−	0.203842i	$-0.0653430\pi$
$449$	20.0933	+	16.8603i	0.948260	+	0.795685i	−0.0307434	+	0.999527i	$0.509787\pi$
$450$		0			0
$451$	8.49615	−	7.12912i	0.400068	−	0.335697i
$452$	4.76862	−	6.40536i	0.224297	−	0.301283i
$453$		0			0
$454$	−2.09728	−	0.497063i	−0.0984300	−	0.0233283i
$455$	10.4555	+	14.0442i	0.490162	+	0.658402i
$456$		0			0
$457$	−21.5678	−	10.8317i	−1.00890	−	0.506687i	−0.133992	−	0.990982i	$-0.542780\pi$
$457$	−21.5678	−	10.8317i	−1.00890	−	0.506687i	−0.874905	+	0.484295i	$0.839076\pi$
$458$	27.5698	−	47.7523i	1.28825	−	2.23132i
$459$		0			0
$460$	28.5194	+	49.3971i	1.32972	+	2.30315i
$461$	−1.09933	−	18.8747i	−0.0512007	−	0.879082i	−0.921939	−	0.387335i	$-0.873396\pi$
$461$	−1.09933	−	18.8747i	−0.0512007	−	0.879082i	0.870738	−	0.491747i	$-0.163641\pi$
$462$		0			0
$463$	−1.68749	+	0.197239i	−0.0784242	+	0.00916647i	−0.155215	−	0.987881i	$-0.549607\pi$
$463$	−1.68749	+	0.197239i	−0.0784242	+	0.00916647i	0.0767903	+	0.997047i	$0.475533\pi$
$464$	−3.76500	−	12.5760i	−0.174786	−	0.583825i
$465$		0			0
$466$	3.75913	+	8.71465i	0.174138	+	0.403698i
$467$	1.44533	+	0.526058i	0.0668820	+	0.0243431i	0.375245	−	0.926926i	$-0.377559\pi$
$467$	1.44533	+	0.526058i	0.0668820	+	0.0243431i	−0.308362	+	0.951269i	$0.599781\pi$
$468$		0			0
$469$	−14.7986	+	5.38623i	−0.683334	+	0.248713i
$470$	−12.4783	−	13.2262i	−0.575582	−	0.610081i
$471$		0			0
$472$	−4.39702	+	2.20827i	−0.202389	+	0.101644i
$473$	0.520258	−	8.93248i	0.0239215	−	0.410716i
$474$		0			0
$475$	−0.0187266	+	0.0625512i	−0.000859236	+	0.00287005i
$476$	−5.86110	+	33.2399i	−0.268643	+	1.52355i
$477$		0			0
$478$	−0.559844	−	3.17503i	−0.0256067	−	0.145223i
$479$	15.7830	+	1.84476i	0.721142	+	0.0842895i	0.468744	−	0.883334i	$-0.344707\pi$
$479$	15.7830	+	1.84476i	0.721142	+	0.0842895i	0.252398	+	0.967623i	$0.418781\pi$
$480$		0			0
$481$	−8.18848	+	8.67928i	−0.373362	+	0.395741i
$482$	−0.705200	+	1.63484i	−0.0321210	+	0.0744648i
$483$		0			0
$484$	14.7643	−	9.71062i	0.671104	−	0.441392i
$485$	34.7759			1.57909
$486$		0			0
$487$	39.0750			1.77066			0.885330	−	0.464964i	$-0.153933\pi$
$487$	39.0750			1.77066			0.885330	+	0.464964i	$0.153933\pi$
$488$	7.78149	−	5.11797i	0.352251	−	0.231679i
$489$		0			0
$490$	13.3679	−	30.9903i	0.603900	−	1.40000i
$491$	−26.4780	+	28.0650i	−1.19494	+	1.26656i	−0.239655	+	0.970858i	$0.577034\pi$
$491$	−26.4780	+	28.0650i	−1.19494	+	1.26656i	−0.955281	+	0.295700i	$0.904447\pi$
$492$		0			0
$493$	17.8604	+	2.08758i	0.804393	+	0.0940201i
$494$	−0.0101418	−	0.0575172i	−0.000456303	−	0.00258782i
$495$		0			0
$496$	5.06319	−	28.7147i	0.227344	−	1.28933i
$497$	7.75941	−	25.9182i	0.348057	−	1.16259i
$498$		0			0
$499$	−0.309871	+	5.32027i	−0.0138717	+	0.238168i	0.984244	+	0.176814i	$0.0565790\pi$
$499$	−0.309871	+	5.32027i	−0.0138717	+	0.238168i	−0.998116	+	0.0613544i	$0.980458\pi$
$500$	6.99408	−	3.51256i	0.312785	−	0.157086i
$501$		0			0
$502$	−21.6496	−	22.9472i	−0.966267	−	1.02418i
$503$	−21.2859	+	7.74742i	−0.949090	+	0.345440i	−0.769749	−	0.638347i	$-0.779619\pi$
$503$	−21.2859	+	7.74742i	−0.949090	+	0.345440i	−0.179341	+	0.983787i	$0.557396\pi$
$504$		0			0
$505$	−8.03363	−	2.92400i	−0.357492	−	0.130116i
$506$	−12.6825	−	29.4012i	−0.563804	−	1.30704i
$507$		0			0
$508$	−9.29904	−	31.0610i	−0.412578	−	1.37811i
$509$	31.0714	−	3.63172i	1.37721	−	0.160973i	0.604945	−	0.796268i	$-0.293195\pi$
$509$	31.0714	−	3.63172i	1.37721	−	0.160973i	0.772270	+	0.635294i	$0.219121\pi$
$510$		0			0
$511$	−0.818864	−	14.0594i	−0.0362244	−	0.621949i
$512$	14.1680	+	24.5396i	0.626141	+	1.08451i
$513$		0			0
$514$	9.75038	−	16.8881i	0.430071	−	0.744904i
$515$	7.64420	+	3.83906i	0.336844	+	0.169169i
$516$		0			0
$517$	3.36799	+	4.52400i	0.148124	+	0.198965i
$518$	51.7240	+	12.2588i	2.27262	+	0.538622i
$519$		0			0
$520$	2.95455	−	3.96865i	0.129566	−	0.174037i
$521$	22.0317	−	18.4868i	0.965226	−	0.809921i	−0.0165695	−	0.999863i	$-0.505274\pi$
$521$	22.0317	−	18.4868i	0.965226	−	0.809921i	0.981795	+	0.189942i	$0.0608300\pi$
$522$		0			0
$523$	−5.64380	−	4.73571i	−0.246786	−	0.207078i	0.511001	−	0.859580i	$-0.329275\pi$
$523$	−5.64380	−	4.73571i	−0.246786	−	0.207078i	−0.757787	+	0.652502i	$0.773719\pi$
$524$	0.000775539	0	0.000183806i	3.38796e−5	0	8.02961e-6i
$525$		0			0
$526$	−0.420443	−	0.276530i	−0.0183322	−	0.0120573i
$527$	33.3696	+	21.9475i	1.45360	+	0.956049i
$528$		0			0
$529$	35.6840	−	8.45727i	1.55148	−	0.367707i
$530$	−13.5985	−	11.4105i	−0.590680	−	0.495640i
$531$		0			0
$532$	−0.110125	+	0.0924059i	−0.00477453	+	0.00400630i
$533$	5.63115	−	7.56394i	0.243912	−	0.327631i
$534$		0			0
$535$	45.9277	+	10.8851i	1.98563	+	0.470602i
$536$	2.65748	+	3.56961i	0.114785	+	0.154184i
$537$		0			0
$538$	−27.2440	−	13.6824i	−1.17457	−	0.589892i
$539$	−5.23423	+	9.06595i	−0.225454	+	0.390498i
$540$		0			0
$541$	12.6202	+	21.8588i	0.542583	+	0.939782i	0.998755	+	0.0498899i	$0.0158870\pi$
$541$	12.6202	+	21.8588i	0.542583	+	0.939782i	−0.456171	+	0.889892i	$0.650780\pi$
$542$	2.04843	+	35.1702i	0.0879876	+	1.51069i
$543$		0			0
$544$	−30.8798	+	3.60933i	−1.32396	+	0.154749i
$545$	−0.249360	−	0.832920i	−0.0106814	−	0.0356784i
$546$		0			0
$547$	7.17326	+	16.6295i	0.306706	+	0.711025i	0.999953	−	0.00967491i	$-0.00307967\pi$
$547$	7.17326	+	16.6295i	0.306706	+	0.711025i	−0.693247	+	0.720700i	$0.743820\pi$
$548$	29.9229	+	10.8910i	1.27824	+	0.465242i
$549$		0			0
$550$	15.3469	−	5.58581i	0.654393	−	0.238180i
$551$	0.0525580	+	0.0557082i	0.00223905	+	0.00237325i
$552$		0			0
$553$	−25.5885	+	12.8510i	−1.08813	+	0.546481i
$554$	3.05067	−	52.3779i	0.129610	−	2.22533i
$555$		0			0
$556$	−0.454252	+	1.51731i	−0.0192646	+	0.0643482i
$557$	−1.58101	+	8.96634i	−0.0669894	+	0.379916i	0.932819	+	0.360345i	$0.117341\pi$
$557$	−1.58101	+	8.96634i	−0.0669894	+	0.379916i	−0.999808	+	0.0195708i	$0.993770\pi$
$558$		0			0
$559$	−1.32104	−	7.49200i	−0.0558741	−	0.316878i
$560$	29.6320	+	3.46349i	1.25218	+	0.146359i
$561$		0			0
$562$	28.0368	−	29.7173i	1.18266	−	1.25355i
$563$	7.00644	−	16.2428i	0.295286	−	0.684550i	−0.704395	−	0.709808i	$-0.748781\pi$
$563$	7.00644	−	16.2428i	0.295286	−	0.684550i	0.999681	+	0.0252581i	$0.00804074\pi$
$564$		0			0
$565$	8.07791	−	5.31292i	0.339840	−	0.223516i
$566$	−2.35991			−0.0991944
$567$		0			0
$568$	−7.64524			−0.320787
$569$	−34.9033	+	22.9563i	−1.46322	+	0.962377i	−0.466249	+	0.884654i	$0.654395\pi$
$569$	−34.9033	+	22.9563i	−1.46322	+	0.962377i	−0.996975	+	0.0777237i	$0.975235\pi$
$570$		0			0
$571$	7.80567	−	18.0956i	0.326657	−	0.757276i	−0.673184	−	0.739475i	$-0.735074\pi$
$571$	7.80567	−	18.0956i	0.326657	−	0.757276i	0.999842	−	0.0178017i	$-0.00566675\pi$
$572$	−5.53905	+	5.87105i	−0.231599	+	0.245481i
$573$		0			0
$574$	−41.7248	−	4.87693i	−1.74156	−	0.203559i
$575$	5.28516	+	29.9737i	0.220407	+	1.24999i
$576$		0			0
$577$	−1.35567	+	7.68841i	−0.0564374	+	0.320073i	−0.999936	−	0.0113037i	$-0.996402\pi$
$577$	−1.35567	+	7.68841i	−0.0564374	+	0.320073i	0.943499	+	0.331376i	$0.107513\pi$
$578$	−1.12830	+	3.76879i	−0.0469311	+	0.156761i
$579$		0			0
$580$	−1.98418	+	34.0671i	−0.0823888	+	1.41456i
$581$	16.1854	−	8.12859i	0.671482	−	0.337231i
$582$		0			0
$583$	3.77847	+	4.00494i	0.156488	+	0.165868i
$584$	−3.73967	+	1.36113i	−0.154748	+	0.0563238i
$585$		0			0
$586$	15.9679	+	5.81183i	0.659626	+	0.240084i
$587$	−8.30634	−	19.2563i	−0.342839	−	0.794791i	−0.999186	−	0.0403319i	$-0.987158\pi$
$587$	−8.30634	−	19.2563i	−0.342839	−	0.794791i	0.656347	−	0.754459i	$-0.272101\pi$
$588$		0			0
$589$	0.0487886	+	0.162965i	0.00201030	+	0.00671486i
$590$	−31.1217	+	3.63760i	−1.28126	+	0.149758i
$591$		0			0
$592$	1.18220	+	20.2975i	0.0485879	+	0.834222i
$593$	11.8196	+	20.4722i	0.485373	+	0.840691i	0.999859	−	0.0168078i	$-0.00535033\pi$
$593$	11.8196	+	20.4722i	0.485373	+	0.840691i	−0.514485	+	0.857499i	$0.672017\pi$
$594$		0			0
$595$	−20.4331	+	35.3912i	−0.837677	+	1.45090i
$596$	−28.5186	−	14.3226i	−1.16817	−	0.586675i
$597$		0			0
$598$	−16.2573	−	21.8374i	−0.664812	−	0.892997i
$599$	1.55457	+	0.368441i	0.0635182	+	0.0150541i	0.262252	−	0.964999i	$-0.415535\pi$
$599$	1.55457	+	0.368441i	0.0635182	+	0.0150541i	−0.198734	+	0.980053i	$0.563683\pi$
$600$		0			0
$601$	18.9415	−	25.4429i	0.772641	−	1.03784i	−0.225337	−	0.974281i	$-0.572348\pi$
$601$	18.9415	−	25.4429i	0.772641	−	1.03784i	0.997978	−	0.0635563i	$-0.0202443\pi$
$602$	−25.9617	+	21.7845i	−1.05812	+	0.887869i
$603$		0			0
$604$	−31.7498	−	26.6413i	−1.29188	−	1.08402i
$605$	20.8191	−	4.93421i	0.846415	−	0.200604i
$606$		0			0
$607$	−8.88733	−	5.84529i	−0.360726	−	0.237253i	0.356189	−	0.934414i	$-0.384076\pi$
$607$	−8.88733	−	5.84529i	−0.360726	−	0.237253i	−0.716915	+	0.697161i	$0.754446\pi$
$608$	−0.110633	−	0.0727644i	−0.00448676	−	0.00295099i
$609$		0			0
$610$	57.7119	−	13.6780i	2.33669	−	0.553805i
$611$	3.67345	+	3.08239i	0.148612	+	0.124700i
$612$		0			0
$613$	−34.7629	+	29.1695i	−1.40406	+	1.17815i	−0.444796	+	0.895632i	$0.646724\pi$
$613$	−34.7629	+	29.1695i	−1.40406	+	1.17815i	−0.959263	+	0.282513i	$0.908832\pi$
$614$	−21.1998	+	28.4762i	−0.855553	+	1.14921i
$615$		0			0
$616$	6.65228	+	1.57662i	0.268028	+	0.0635238i
$617$	−13.7903	−	18.5236i	−0.555178	−	0.745733i	0.432603	−	0.901585i	$-0.357595\pi$
$617$	−13.7903	−	18.5236i	−0.555178	−	0.745733i	−0.987781	+	0.155851i	$0.950188\pi$
$618$		0			0
$619$	1.75718	+	0.882490i	0.0706271	+	0.0354703i	0.483762	−	0.875200i	$-0.339270\pi$
$619$	1.75718	+	0.882490i	0.0706271	+	0.0354703i	−0.413135	+	0.910670i	$0.635566\pi$
$620$	−37.8977	+	65.6408i	−1.52201	+	2.63620i
$621$		0			0
$622$	5.44913	+	9.43817i	0.218490	+	0.378436i
$623$	−0.975956	−	16.7565i	−0.0391008	−	0.671335i
$624$		0			0
$625$	28.9790	−	3.38716i	1.15916	−	0.135486i
$626$	16.9411	+	56.5872i	0.677103	+	2.26168i
$627$		0			0
$628$	−8.41288	−	19.5033i	−0.335711	−	0.778264i
$629$	−26.1710	−	9.52548i	−1.04351	−	0.379806i
$630$		0			0
$631$	−45.7709	+	16.6593i	−1.82211	+	0.663195i	−0.827265	+	0.561812i	$0.810104\pi$
$631$	−45.7709	+	16.6593i	−1.82211	+	0.663195i	−0.994848	+	0.101382i	$0.967673\pi$
$632$	5.55276	+	5.88558i	0.220877	+	0.234116i
$633$		0			0
$634$	−17.3704	+	8.72372i	−0.689865	+	0.346463i
$635$	2.28256	−	39.1900i	0.0905805	−	1.55521i
$636$		0			0
$637$	−2.55274	+	8.52673i	−0.101143	+	0.337841i
$638$	3.32653	−	18.8657i	0.131699	−	0.746899i
$639$		0			0
$640$	−4.00945	−	22.7387i	−0.158487	−	0.898827i
$641$	−24.5011	−	2.86377i	−0.967737	−	0.113112i	−0.382483	−	0.923962i	$-0.624931\pi$
$641$	−24.5011	−	2.86377i	−0.967737	−	0.113112i	−0.585254	+	0.810850i	$0.699005\pi$
$642$		0			0
$643$	7.26830	−	7.70395i	0.286634	−	0.303814i	−0.568018	−	0.823016i	$-0.692289\pi$
$643$	7.26830	−	7.70395i	0.286634	−	0.303814i	0.854651	+	0.519202i	$0.173771\pi$
$644$	−26.5416	+	61.5305i	−1.04589	+	2.42464i
$645$		0			0
$646$	0.113893	−	0.0749084i	0.00448105	−	0.00294723i
$647$	12.2785			0.482716			0.241358	−	0.970436i	$-0.422407\pi$
$647$	12.2785			0.482716			0.241358	+	0.970436i	$0.422407\pi$
$648$		0			0
$649$	9.71877			0.381495
$650$	11.6015	−	7.63041i	0.455048	−	0.299289i
$651$		0			0
$652$	0.659731	−	1.52943i	0.0258371	−	0.0598970i
$653$	−1.96487	+	2.08264i	−0.0768914	+	0.0815001i	−0.764677	−	0.644414i	$-0.777101\pi$
$653$	−1.96487	+	2.08264i	−0.0768914	+	0.0815001i	0.687786	+	0.725914i	$0.258583\pi$
$654$		0			0
$655$	0.000958475	0	0.000112030i	3.74507e−5	0	4.37736e-6i
$656$	−2.79016	−	15.8238i	−0.108938	−	0.617815i
$657$		0			0
$658$	3.70957	−	21.0380i	0.144614	−	0.820148i
$659$	−13.3973	+	44.7501i	−0.521885	+	1.74322i	0.136603	+	0.990626i	$0.456381\pi$
$659$	−13.3973	+	44.7501i	−0.521885	+	1.74322i	−0.658488	+	0.752591i	$0.728804\pi$
$660$		0			0
$661$	−1.38632	+	23.8022i	−0.0539215	+	0.925797i	0.857542	+	0.514415i	$0.171991\pi$
$661$	−1.38632	+	23.8022i	−0.0539215	+	0.925797i	−0.911463	+	0.411382i	$0.865046\pi$
$662$	−32.0247	+	16.0834i	−1.24467	+	0.625099i
$663$		0			0
$664$	−3.51226	−	3.72278i	−0.136302	−	0.144472i
$665$	−0.163559	+	0.0595306i	−0.00634254	+	0.00230850i
$666$		0			0
$667$	33.5475	+	12.2103i	1.29897	+	0.472785i
$668$	15.7672	+	36.5524i	0.610050	+	1.41425i
$669$		0			0
$670$	8.12781	+	27.1488i	0.314005	+	1.04885i
$671$	−18.2721	+	2.13570i	−0.705386	+	0.0824479i
$672$		0			0
$673$	−0.262422	−	4.50561i	−0.0101156	−	0.173679i	−0.999582	−	0.0289148i	$-0.990795\pi$
$673$	−0.262422	−	4.50561i	−0.0101156	−	0.173679i	0.989466	−	0.144764i	$-0.0462422\pi$
$674$	13.7901	+	23.8852i	0.531175	+	0.920023i
$675$		0			0
$676$	12.6206	−	21.8594i	0.485406	−	0.840748i
$677$	−11.2705	−	5.66027i	−0.433162	−	0.217542i	0.218838	−	0.975761i	$-0.429773\pi$
$677$	−11.2705	−	5.66027i	−0.433162	−	0.217542i	−0.652000	+	0.758219i	$0.726070\pi$
$678$		0			0
$679$	24.3973	+	32.7713i	0.936283	+	1.25765i
$680$	11.2368	+	2.66318i	0.430913	+	0.102128i
$681$		0			0
$682$	25.4087	−	34.1299i	0.972951	−	1.30690i
$683$	13.8210	−	11.5972i	0.528845	−	0.443754i	−0.338857	−	0.940838i	$-0.610040\pi$
$683$	13.8210	−	11.5972i	0.528845	−	0.443754i	0.867702	+	0.497084i	$0.165596\pi$
$684$		0			0
$685$	29.5344	+	24.7823i	1.12845	+	0.946883i
$686$	−12.0009	+	2.84426i	−0.458195	+	0.108594i
$687$		0			0
$688$	−10.8303	−	7.12317i	−0.412899	−	0.271568i
$689$	3.91127	+	2.57248i	0.149008	+	0.0980038i
$690$		0			0
$691$	−32.3764	+	7.67336i	−1.23166	+	0.291908i	−0.794382	−	0.607419i	$-0.792205\pi$
$691$	−32.3764	+	7.67336i	−1.23166	+	0.291908i	−0.437276	+	0.899327i	$0.644057\pi$
$692$	−30.5145	−	25.6047i	−1.15999	−	0.973345i
$693$		0			0
$694$	−23.3104	+	19.5598i	−0.884852	+	0.742479i
$695$	−1.14514	+	1.53819i	−0.0434377	+	0.0583469i
$696$		0			0
$697$	21.4165	+	5.07581i	0.811209	+	0.192260i
$698$	−10.2680	−	13.7923i	−0.388649	−	0.522047i
$699$		0			0
$700$	−30.5434	−	15.3395i	−1.15443	−	0.579778i
$701$	9.13385	−	15.8203i	0.344981	−	0.597524i	−0.640370	−	0.768067i	$-0.721219\pi$
$701$	9.13385	−	15.8203i	0.344981	−	0.597524i	0.985350	+	0.170543i	$0.0545522\pi$
$702$		0			0
$703$	−0.0593101	−	0.102728i	−0.00223692	−	0.00387446i
$704$	1.27817	+	21.9453i	0.0481729	+	0.827096i
$705$		0			0
$706$	56.9176	−	6.65272i	2.14212	−	0.250378i
$707$	−2.88061	−	9.62191i	−0.108337	−	0.361869i
$708$		0			0
$709$	0.783606	+	1.81660i	0.0294290	+	0.0682240i	0.932297	−	0.361694i	$-0.117802\pi$
$709$	0.783606	+	1.81660i	0.0294290	+	0.0682240i	−0.902868	+	0.429918i	$0.858542\pi$
$710$	−45.7496	−	16.6515i	−1.71695	−	0.624919i
$711$		0			0
$712$	−4.45709	+	1.62225i	−0.167036	+	0.0607963i
$713$	54.4157	+	57.6773i	2.03788	+	2.16003i
$714$		0			0
$715$	−8.73320	+	4.38598i	−0.326603	+	0.164026i
$716$	−1.13991	+	19.5716i	−0.0426006	+	0.731423i
$717$		0			0
$718$	−15.1174	+	50.4955i	−0.564175	+	1.88448i
$719$	−2.42853	+	13.7729i	−0.0905690	+	0.513642i	0.905446	+	0.424461i	$0.139536\pi$
$719$	−2.42853	+	13.7729i	−0.0905690	+	0.513642i	−0.996015	+	0.0891816i	$0.971575\pi$
$720$		0			0
$721$	1.74509	+	9.89690i	0.0649906	+	0.368580i
$722$	−39.8962	−	4.66320i	−1.48478	−	0.173546i
$723$		0			0
$724$	23.4451	−	24.8504i	0.871332	−	0.923558i
$725$	−7.21226	+	16.7199i	−0.267856	+	0.620961i
$726$		0			0
$727$	−31.2308	+	20.5408i	−1.15829	+	0.761817i	−0.975210	−	0.221281i	$-0.928976\pi$
$727$	−31.2308	+	20.5408i	−1.15829	+	0.761817i	−0.183077	+	0.983099i	$0.558606\pi$
$728$	5.81268			0.215432
$729$		0			0
$730$	−25.3429			−0.937984
$731$	14.8353	−	9.75731i	0.548702	−	0.360887i
$732$		0			0
$733$	10.5389	−	24.4320i	0.389265	−	0.902417i	−0.605075	−	0.796168i	$-0.706857\pi$
$733$	10.5389	−	24.4320i	0.389265	−	0.902417i	0.994340	−	0.106248i	$-0.0338838\pi$
$734$	18.9941	−	20.1325i	0.701084	−	0.743105i
$735$		0			0
$736$	−61.3071	−	7.16578i	−2.25981	−	0.264134i
$737$	−1.52638	−	8.65652i	−0.0562249	−	0.318867i
$738$		0			0
$739$	7.56956	−	42.9291i	0.278451	−	1.57917i	−0.449332	−	0.893365i	$-0.648338\pi$
$739$	7.56956	−	42.9291i	0.278451	−	1.57917i	0.727782	−	0.685808i	$-0.240551\pi$
$740$	15.1583	−	50.6324i	0.557232	−	1.86128i
$741$		0			0
$742$	1.21261	−	20.8198i	0.0445164	−	0.764317i
$743$	−45.4564	+	22.8291i	−1.66763	+	0.837517i	−0.672380	+	0.740206i	$0.734728\pi$
$743$	−45.4564	+	22.8291i	−1.66763	+	0.837517i	−0.995254	+	0.0973110i	$0.968976\pi$
$744$		0			0
$745$	−26.5156	−	28.1049i	−0.971457	−	1.02968i
$746$	−57.1662	+	20.8068i	−2.09300	+	0.761791i
$747$		0			0
$748$	−17.7033	−	6.44346i	−0.647295	−	0.235596i
$749$	21.9634	+	50.9168i	0.802524	+	1.86046i
$750$		0			0
$751$	−3.63443	−	12.1398i	−0.132622	−	0.442989i	0.865721	−	0.500527i	$-0.166860\pi$
$751$	−3.63443	−	12.1398i	−0.132622	−	0.442989i	−0.998343	+	0.0575375i	$0.981675\pi$
$752$	8.11570	−	0.948589i	0.295949	−	0.0345915i
$753$		0			0
$754$	−0.947046	−	16.2602i	−0.0344894	−	0.592160i
$755$	−25.0908	−	43.4585i	−0.913146	−	1.58162i
$756$		0			0
$757$	7.49384	−	12.9797i	0.272368	−	0.471756i	−0.697100	−	0.716974i	$-0.745526\pi$
$757$	7.49384	−	12.9797i	0.272368	−	0.471756i	0.969468	+	0.245219i	$0.0788598\pi$
$758$	39.6421	+	19.9090i	1.43987	+	0.723128i
$759$		0			0
$760$	0.0293714	+	0.0394526i	0.00106541	+	0.00143110i
$761$	−10.2662	−	2.43313i	−0.372149	−	0.0882010i	0.0402853	−	0.999188i	$-0.487173\pi$
$761$	−10.2662	−	2.43313i	−0.372149	−	0.0882010i	−0.412435	+	0.910987i	$0.635321\pi$
$762$		0			0
$763$	0.609968	−	0.819329i	0.0220823	−	0.0296617i
$764$	27.1927	−	22.8174i	0.983798	−	0.825505i
$765$		0			0
$766$	39.6701	+	33.2872i	1.43334	+	1.20271i
$767$	8.04050	−	1.90563i	0.290326	−	0.0688085i
$768$		0			0
$769$	32.8627	+	21.6141i	1.18506	+	0.779426i	0.979936	−	0.199310i	$-0.0638701\pi$
$769$	32.8627	+	21.6141i	1.18506	+	0.779426i	0.205123	+	0.978736i	$0.434240\pi$
$770$	36.3737	+	23.9234i	1.31082	+	0.862139i
$771$		0			0
$772$	−10.0537	+	2.38278i	−0.361842	+	0.0857581i
$773$	37.1233	+	31.1502i	1.33523	+	1.12039i	0.982824	+	0.184547i	$0.0590818\pi$
$773$	37.1233	+	31.1502i	1.33523	+	1.12039i	0.352409	+	0.935846i	$0.385363\pi$
$774$		0			0
$775$	−30.9824	+	25.9973i	−1.11292	+	0.933851i
$776$	6.89427	−	9.26061i	0.247490	−	0.332437i
$777$		0			0
$778$	−32.4346	−	7.68714i	−1.16284	−	0.275597i
$779$	0.0559795	+	0.0751936i	0.00200568	+	0.00269409i
$780$		0			0
$781$	13.4947	+	6.77728i	0.482877	+	0.242510i
$782$	31.7716	−	55.0300i	1.13615	−	1.96787i
$783$		0			0
$784$	7.58305	+	13.1342i	0.270823	+	0.469079i
$785$	−1.49530	−	25.6734i	−0.0533697	−	0.916322i
$786$		0			0
$787$	−19.0016	+	2.22097i	−0.677335	+	0.0791691i	−0.447803	−	0.894132i	$-0.647794\pi$
$787$	−19.0016	+	2.22097i	−0.677335	+	0.0791691i	−0.229532	+	0.973301i	$0.573719\pi$
$788$	−0.167498	−	0.559484i	−0.00596688	−	0.0199308i
$789$		0			0
$790$	20.4091	+	47.3137i	0.726124	+	1.68335i
$791$	10.6738	+	3.88495i	0.379517	+	0.138133i
$792$		0			0
$793$	−14.6980	+	5.34965i	−0.521943	+	0.189972i
$794$	−37.4690	−	39.7148i	−1.32972	−	1.40942i
$795$		0			0
$796$	57.5764	−	28.9160i	2.04074	−	1.02490i
$797$	−3.09296	+	53.1041i	−0.109558	+	1.88104i	0.279941	+	0.960017i	$0.409685\pi$
$797$	−3.09296	+	53.1041i	−0.109558	+	1.88104i	−0.389500	+	0.921027i	$0.627352\pi$
$798$		0			0
$799$	−3.21006	+	10.7224i	−0.113564	+	0.379330i
$800$	5.46690	−	31.0044i	0.193284	−	1.09617i
$801$		0			0
$802$	6.01282	+	34.1004i	0.212320	+	1.20413i
$803$	7.80751	+	0.912567i	0.275521	+	0.0322038i
$804$		0			0
$805$	−55.6773	+	59.0145i	−1.96237	+	2.07999i
$806$	14.3290	−	33.2183i	0.504716	−	1.17006i
$807$		0			0
$808$	−2.37130	+	1.55963i	−0.0834221	+	0.0548676i
$809$	−52.4325			−1.84343			−0.921715	−	0.387868i	$-0.873211\pi$
$809$	−52.4325			−1.84343			−0.921715	+	0.387868i	$0.873211\pi$
$810$		0			0
$811$	−16.1664			−0.567679			−0.283839	−	0.958872i	$-0.591608\pi$
$811$	−16.1664			−0.567679			−0.283839	+	0.958872i	$0.591608\pi$
$812$	−33.4954	+	22.0303i	−1.17546	+	0.773112i
$813$		0			0
$814$	−11.7517	+	27.2435i	−0.411897	+	0.954884i
$815$	1.38394	−	1.46689i	0.0484773	−	0.0513830i
$816$		0			0
$817$	0.0751160	+	0.00877980i	0.00262797	+	0.000307166i
$818$	9.30857	+	52.7915i	0.325466	+	1.84581i
$819$		0			0
$820$	−7.25303	+	41.1340i	−0.253287	+	1.43646i
$821$	−16.1644	+	53.9928i	−0.564141	+	1.88436i	−0.108753	+	0.994069i	$0.534686\pi$
$821$	−16.1644	+	53.9928i	−0.564141	+	1.88436i	−0.455388	+	0.890293i	$0.650500\pi$
$822$		0			0
$823$	2.31684	−	39.7787i	0.0807601	−	1.38660i	−0.677921	−	0.735135i	$-0.737119\pi$
$823$	2.31684	−	39.7787i	0.0807601	−	1.38660i	0.758681	−	0.651462i	$-0.225844\pi$
$824$	2.53777	−	1.27452i	0.0884075	−	0.0443999i
$825$		0			0
$826$	−25.2616	−	26.7757i	−0.878964	−	0.931647i
$827$	25.1842	−	9.16629i	0.875739	−	0.318743i	0.135250	−	0.990811i	$-0.456816\pi$
$827$	25.1842	−	9.16629i	0.875739	−	0.318743i	0.740489	+	0.672068i	$0.234594\pi$
$828$		0			0
$829$	−49.7705	−	18.1150i	−1.72860	−	0.629159i	−0.730071	−	0.683371i	$-0.760513\pi$
$829$	−49.7705	−	18.1150i	−1.72860	−	0.629159i	−0.998529	+	0.0542117i	$0.982735\pi$
$830$	−12.9093	−	29.9271i	−0.448088	−	1.03878i
$831$		0			0
$832$	5.36044	+	17.9051i	0.185840	+	0.620749i
$833$	−20.6340	+	2.41177i	−0.714927	+	0.0835630i
$834$		0			0
$835$	2.80245	+	48.1162i	0.0969828	+	1.66513i
$836$	−0.0401200	−	0.0694898i	−0.00138758	−	0.00240336i
$837$		0			0
$838$	6.72267	−	11.6440i	0.232231	−	0.402235i
$839$	32.6997	+	16.4224i	1.12892	+	0.566965i	0.912395	−	0.409312i	$-0.134231\pi$
$839$	32.6997	+	16.4224i	1.12892	+	0.566965i	0.216526	+	0.976277i	$0.430527\pi$
$840$		0			0
$841$	−4.56306	−	6.12925i	−0.157347	−	0.211354i
$842$	−54.0302	−	12.8054i	−1.86201	−	0.441303i
$843$		0			0
$844$	−17.4002	+	23.3725i	−0.598938	+	0.804513i
$845$	23.4109	−	19.6441i	0.805360	−	0.675778i
$846$		0			0
$847$	19.2556	+	16.1574i	0.661630	+	0.555173i
$848$	7.76180	−	1.83958i	0.266541	−	0.0631715i
$849$		0			0
$850$	27.0784	+	17.8097i	0.928781	+	0.610869i
$851$	−46.1968	−	30.3841i	−1.58361	−	1.04155i
$852$		0			0
$853$	53.3561	−	12.6456i	1.82688	−	0.432978i	0.833965	−	0.551817i	$-0.186065\pi$
$853$	53.3561	−	12.6456i	1.82688	−	0.432978i	0.992914	+	0.118839i	$0.0379172\pi$
$854$	53.3779	+	44.7893i	1.82655	+	1.53266i
$855$		0			0
$856$	12.0037	−	10.0723i	0.410279	−	0.344265i
$857$	25.8992	−	34.7886i	0.884698	−	1.18836i	−0.0964961	−	0.995333i	$-0.530764\pi$
$857$	25.8992	−	34.7886i	0.884698	−	1.18836i	0.981194	−	0.193023i	$-0.0618291\pi$
$858$		0			0
$859$	−10.9882	−	2.60425i	−0.374912	−	0.0888557i	0.0388400	−	0.999245i	$-0.487634\pi$
$859$	−10.9882	−	2.60425i	−0.374912	−	0.0888557i	−0.413752	+	0.910390i	$0.635782\pi$
$860$	20.1223	+	27.0289i	0.686165	+	0.921680i
$861$		0			0
$862$	−23.2922	−	11.6978i	−0.793336	−	0.398428i
$863$	−5.77243	+	9.99814i	−0.196496	+	0.340341i	−0.947390	−	0.320082i	$-0.896290\pi$
$863$	−5.77243	+	9.99814i	−0.196496	+	0.340341i	0.750894	+	0.660423i	$0.229623\pi$
$864$		0			0
$865$	−24.1145	−	41.7676i	−0.819919	−	1.42014i
$866$	−0.829885	−	14.2486i	−0.0282006	−	0.484186i
$867$		0			0
$868$	−88.4446	+	10.3377i	−3.00201	+	0.350884i
$869$	−4.58383	−	15.3110i	−0.155496	−	0.519392i
$870$		0			0
$871$	−2.96015	−	6.86240i	−0.100301	−	0.232523i
$872$	−0.271237	−	0.0987223i	−0.00918525	−	0.00334316i
$873$		0			0
$874$	0.254318	−	0.0925644i	0.00860245	−	0.00313104i
$875$	7.63976	+	8.09767i	0.258271	+	0.273751i
$876$		0			0
$877$	−30.2634	+	15.1988i	−1.02192	+	0.513228i	−0.879159	−	0.476528i	$-0.841895\pi$
$877$	−30.2634	+	15.1988i	−1.02192	+	0.513228i	−0.142763	+	0.989757i	$0.545599\pi$
$878$	−0.549038	+	9.42662i	−0.0185291	+	0.318133i
$879$		0			0
$880$	−4.77585	+	15.9524i	−0.160994	+	0.537757i
$881$	4.38212	−	24.8523i	0.147637	−	0.837294i	−0.817574	−	0.575824i	$-0.804682\pi$
$881$	4.38212	−	24.8523i	0.147637	−	0.837294i	0.965212	−	0.261470i	$-0.0842074\pi$
$882$		0			0
$883$	−1.13935	−	6.46156i	−0.0383421	−	0.217449i	0.959617	−	0.281311i	$-0.0907693\pi$
$883$	−1.13935	−	6.46156i	−0.0383421	−	0.217449i	−0.997959	+	0.0638623i	$0.979658\pi$
$884$	−15.9096	−	1.85957i	−0.535098	−	0.0625440i
$885$		0			0
$886$	−40.9290	+	43.3822i	−1.37504	+	1.45745i
$887$	18.9027	−	43.8215i	0.634692	−	1.47138i	−0.232091	−	0.972694i	$-0.574557\pi$
$887$	18.9027	−	43.8215i	0.634692	−	1.47138i	0.866783	−	0.498686i	$-0.166184\pi$
$888$		0			0
$889$	38.5323	−	25.3431i	1.29233	−	0.849980i
$890$	−30.2047			−1.01247
$891$		0			0
$892$	−65.0376			−2.17762
$893$	−0.0398284	+	0.0261955i	−0.00133281	+	0.000876601i
$894$		0			0
$895$	−9.40155	+	21.7952i	−0.314259	+	0.728535i
$896$	18.6151	−	19.7309i	0.621888	−	0.659163i
$897$		0			0
$898$	55.0784	+	6.43774i	1.83799	+	0.214830i
$899$	8.23792	+	46.7196i	0.274750	+	1.55819i
$900$		0			0
$901$	−1.89739	+	10.7606i	−0.0632113	+	0.358489i
$902$	6.72486	−	22.4626i	0.223913	−	0.747922i
$903$		0			0
$904$	0.186634	−	3.20438i	0.00620735	−	0.106576i
$905$	36.9650	−	18.5645i	1.22876	−	0.617106i
$906$		0			0
$907$	−13.8077	−	14.6353i	−0.458477	−	0.485957i	0.456352	−	0.889799i	$-0.349156\pi$
$907$	−13.8077	−	14.6353i	−0.458477	−	0.485957i	−0.914829	+	0.403842i	$0.867674\pi$
$908$	−2.36587	+	0.861107i	−0.0785142	+	0.0285768i
$909$		0			0
$910$	34.7834	+	12.6601i	1.15306	+	0.419679i
$911$	17.3046	+	40.1165i	0.573326	+	1.32912i	0.920288	+	0.391241i	$0.127954\pi$
$911$	17.3046	+	40.1165i	0.573326	+	1.32912i	−0.346962	+	0.937879i	$0.612787\pi$
$912$		0			0
$913$	2.89938	+	9.68462i	0.0959556	+	0.320514i
$914$	−50.6793	+	5.92355i	−1.67632	+	0.195934i
$915$		0			0
$916$	−3.74505	−	64.3000i	−0.123740	−	2.12453i
$917$	0.000566855	0	0.000981821i	1.87192e−5	0	3.24226e-5i
$918$		0			0
$919$	6.27118	−	10.8620i	0.206867	−	0.358304i	−0.743859	−	0.668337i	$-0.767007\pi$
$919$	6.27118	−	10.8620i	0.206867	−	0.358304i	0.950726	+	0.310032i	$0.100340\pi$
$920$	20.4883	+	10.2896i	0.675480	+	0.339239i
$921$		0			0
$922$	−23.8691	−	32.0617i	−0.786086	−	1.05590i
$923$	12.4932	+	2.96095i	0.411220	+	0.0974609i
$924$		0			0
$925$	16.8413	−	22.6218i	0.553738	−	0.743799i
$926$	−2.75151	+	2.30879i	−0.0904204	+	0.0758717i
$927$		0			0
$928$	−28.2886	−	23.7370i	−0.928620	−	0.779204i
$929$	−30.7885	+	7.29700i	−1.01014	+	0.239407i	−0.702185	−	0.711995i	$-0.747792\pi$
$929$	−30.7885	+	7.29700i	−1.01014	+	0.239407i	−0.307952	+	0.951402i	$0.599644\pi$
$930$		0			0
$931$	−0.0739255	−	0.0486216i	−0.00242281	−	0.00159351i
$932$	9.26249	+	6.09204i	0.303403	+	0.199551i
$933$		0			0
$934$	3.16407	−	0.749898i	0.103531	−	0.0245374i
$935$	−17.4734	−	14.6619i	−0.571441	−	0.479496i
$936$		0			0
$937$	27.0749	−	22.7185i	0.884498	−	0.742182i	−0.0826013	−	0.996583i	$-0.526323\pi$
$937$	27.0749	−	22.7185i	0.884498	−	0.742182i	0.967099	+	0.254401i	$0.0818783\pi$
$938$	−19.8817	+	26.7058i	−0.649161	+	0.871975i
$939$		0			0
$940$	−20.6678	−	4.89837i	−0.674110	−	0.159767i
$941$	16.6510	+	22.3662i	0.542807	+	0.729116i	0.985896	−	0.167362i	$-0.0535248\pi$
$941$	16.6510	+	22.3662i	0.542807	+	0.729116i	−0.443089	+	0.896478i	$0.646117\pi$
$942$		0			0
$943$	39.0492	+	19.6112i	1.27162	+	0.638630i
$944$	7.04000	−	12.1936i	0.229132	−	0.396869i
$945$		0			0
$946$	−9.45819	−	16.3821i	−0.307512	−	0.532627i
$947$	1.02636	+	17.6220i	0.0333524	+	0.572638i	0.973045	+	0.230617i	$0.0740744\pi$
$947$	1.02636	+	17.6220i	0.0333524	+	0.572638i	−0.939692	+	0.342021i	$0.888889\pi$
$948$		0			0
$949$	6.63822	−	0.775897i	0.215486	−	0.0251867i
$950$	0.0395904	+	0.132241i	0.00128448	+	0.00429047i
$951$		0			0
$952$	5.37364	+	12.4575i	0.174161	+	0.403750i
$953$	−1.09020	−	0.396799i	−0.0353149	−	0.0128536i	0.324302	−	0.945953i	$-0.394870\pi$
$953$	−1.09020	−	0.396799i	−0.0353149	−	0.0128536i	−0.359617	+	0.933100i	$0.617093\pi$
$954$		0			0
$955$	40.3869	−	14.6996i	1.30689	−	0.475669i
$956$	−2.58438	−	2.73928i	−0.0835849	−	0.0885948i
$957$		0			0
$958$	30.0210	−	15.0771i	0.969934	−	0.487119i
$959$	−2.63366	+	45.2182i	−0.0850453	+	1.46017i
$960$		0			0
$961$	−21.3297	+	71.2463i	−0.688056	+	2.29827i
$962$	−4.38053	+	24.8432i	−0.141234	+	0.800978i
$963$		0			0
$964$	0.361146	+	2.04816i	0.0116317	+	0.0659668i
$965$	−12.4252	−	1.45230i	−0.399982	−	0.0467512i
$966$		0			0
$967$	25.7487	−	27.2920i	0.828022	−	0.877652i	−0.166079	−	0.986113i	$-0.553111\pi$
$967$	25.7487	−	27.2920i	0.828022	−	0.877652i	0.994101	+	0.108460i	$0.0345921\pi$
$968$	2.81340	−	6.52220i	0.0904261	−	0.209631i
$969$		0			0
$970$	61.4255	−	40.4002i	1.97225	−	1.29717i
$971$	13.1664			0.422531			0.211265	−	0.977429i	$-0.432242\pi$
$971$	13.1664			0.422531			0.211265	+	0.977429i	$0.432242\pi$
$972$		0			0
$973$	−2.25291			−0.0722250
$974$	69.0193	−	45.3947i	2.21152	−	1.45454i
$975$		0			0
$976$	−10.5562	+	24.4721i	−0.337896	+	0.783332i
$977$	18.3951	−	19.4977i	0.588512	−	0.623786i	−0.362855	−	0.931845i	$-0.618198\pi$
$977$	18.3951	−	19.4977i	0.588512	−	0.623786i	0.951367	+	0.308060i	$0.0996796\pi$
$978$		0			0
$979$	9.30531	+	1.08763i	0.297399	+	0.0347610i
$980$	−6.84595	−	38.8253i	−0.218686	−	1.24023i
$981$		0			0
$982$	−14.1648	+	80.3323i	−0.452016	+	2.56351i
$983$	3.46932	−	11.5883i	0.110654	−	0.369611i	−0.884668	−	0.466221i	$-0.845615\pi$
$983$	3.46932	−	11.5883i	0.110654	−	0.369611i	0.995322	+	0.0966108i	$0.0308002\pi$
$984$		0			0
$985$	0.0411144	−	0.705907i	0.00131001	−	0.0224921i
$986$	33.9725	−	17.0617i	1.08191	−	0.543354i
$987$		0			0
$988$	−0.0468173	−	0.0496234i	−0.00148946	−	0.00157873i
$989$	33.1267	−	12.0571i	1.05337	−	0.383394i
$990$		0			0
$991$	23.4272	+	8.52680i	0.744189	+	0.270863i	0.686159	−	0.727452i	$-0.259296\pi$
$991$	23.4272	+	8.52680i	0.744189	+	0.270863i	0.0580307	+	0.998315i	$0.481518\pi$
$992$	−32.4872	−	75.3139i	−1.03147	−	2.39122i
$993$		0			0
$994$	−16.4044	−	54.7944i	−0.520315	−	1.73797i
$995$	77.4810	−	9.05623i	2.45631	−	0.287102i
$996$		0			0
$997$	1.94655	+	33.4210i	0.0616479	+	1.05845i	0.877310	+	0.479925i	$0.159336\pi$
$997$	1.94655	+	33.4210i	0.0616479	+	1.05845i	−0.815662	+	0.578529i	$0.803627\pi$
$998$	5.63339	+	9.75732i	0.178322	+	0.308863i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.28.8		144
3.2	odd	2		729.2.g.d.28.1		144
9.2	odd	6		729.2.g.c.271.8		144
9.4	even	3		243.2.g.a.91.8		144
9.5	odd	6		81.2.g.a.40.1	✓	144
9.7	even	3		729.2.g.b.271.1		144
81.2	odd	54		729.2.g.c.460.8		144
81.25	even	27		243.2.g.a.235.8		144
81.29	odd	54		729.2.g.d.703.1		144
81.32	odd	54		6561.2.a.c.1.62		72
81.49	even	27		6561.2.a.d.1.11		72
81.52	even	27	inner	729.2.g.a.703.8		144
81.56	odd	54		81.2.g.a.79.1	yes	144
81.79	even	27		729.2.g.b.460.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.40.1	✓	144	9.5	odd	6
81.2.g.a.79.1	yes	144	81.56	odd	54
243.2.g.a.91.8		144	9.4	even	3
243.2.g.a.235.8		144	81.25	even	27
729.2.g.a.28.8		144	1.1	even	1	trivial
729.2.g.a.703.8		144	81.52	even	27	inner
729.2.g.b.271.1		144	9.7	even	3
729.2.g.b.460.1		144	81.79	even	27
729.2.g.c.271.8		144	9.2	odd	6
729.2.g.c.460.8		144	81.2	odd	54
729.2.g.d.28.1		144	3.2	odd	2
729.2.g.d.703.1		144	81.29	odd	54
6561.2.a.c.1.62		72	81.32	odd	54
6561.2.a.d.1.11		72	81.49	even	27

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)

\(f(q)\)	\(=\)	\(q+(1.76633 - 1.16173i) q^{2} +(0.978129 - 2.26756i) q^{4} +(2.05186 - 2.17484i) q^{5} +(3.48897 + 0.407803i) q^{7} +(-0.172370 - 0.977557i) q^{8} +O(q^{10})\)	\(q+(1.76633 - 1.16173i) q^{2} +(0.978129 - 2.26756i) q^{4} +(2.05186 - 2.17484i) q^{5} +(3.48897 + 0.407803i) q^{7} +(-0.172370 - 0.977557i) q^{8} +(1.09767 - 6.22518i) q^{10} +(-0.562324 + 1.87829i) q^{11} +(-0.0969288 + 1.66420i) q^{13} +(6.63642 - 3.33294i) q^{14} +(1.94926 + 2.06610i) q^{16} +(-3.65626 + 1.33077i) q^{17} +(-0.0155726 - 0.00566795i) q^{19} +(-2.92460 - 6.77998i) q^{20} +(1.18882 + 3.97095i) q^{22} +(-7.67257 + 0.896795i) q^{23} +(-0.229093 - 3.93338i) q^{25} +(1.76215 + 3.05213i) q^{26} +(4.33738 - 7.51257i) q^{28} +(-4.12997 - 2.07415i) q^{29} +(-6.12985 - 8.23381i) q^{31} +(7.77505 + 1.84272i) q^{32} +(-4.91215 + 6.59816i) q^{34} +(8.04578 - 6.75121i) q^{35} +(5.48325 + 4.60100i) q^{37} +(-0.0340908 + 0.00807968i) q^{38} +(-2.47971 - 1.63093i) q^{40} +(-4.72613 - 3.10842i) q^{41} +(-4.44056 + 1.05243i) q^{43} +(3.70912 + 3.11232i) q^{44} +(-12.5104 + 10.4975i) q^{46} +(1.71778 - 2.30738i) q^{47} +(5.19533 + 1.23132i) q^{49} +(-4.97418 - 6.68148i) q^{50} +(3.67887 + 1.84760i) q^{52} +(1.40413 - 2.43202i) q^{53} +(2.93118 + 5.07695i) q^{55} +(-0.202743 - 3.48096i) q^{56} +(-9.70447 + 1.13429i) q^{58} +(-1.42165 - 4.74864i) q^{59} +(3.71633 + 8.61543i) q^{61} +(-20.3928 - 7.42236i) q^{62} +(10.5356 - 3.83466i) q^{64} +(3.42049 + 3.62551i) q^{65} +(-4.00634 + 2.01206i) q^{67} +(-0.558696 + 9.59244i) q^{68} +(6.36838 - 21.2719i) q^{70} +(1.33743 - 7.58494i) q^{71} +(-0.696188 - 3.94828i) q^{73} +(15.0303 + 1.75679i) q^{74} +(-0.0280844 + 0.0297677i) q^{76} +(-2.72791 + 6.32400i) q^{77} +(-6.81054 + 4.47936i) q^{79} +8.49305 q^{80} -11.9590 q^{82} +(4.30784 - 2.83331i) q^{83} +(-4.60790 + 10.6823i) q^{85} +(-6.62083 + 7.01767i) q^{86} +(1.93307 + 0.225943i) q^{88} +(-0.829745 - 4.70572i) q^{89} +(-1.01685 + 5.76683i) q^{91} +(-5.47123 + 18.2752i) q^{92} +(0.353607 - 6.07119i) q^{94} +(-0.0442795 + 0.0222380i) q^{95} +(7.98151 + 8.45991i) q^{97} +(10.6071 - 3.86067i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) 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 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

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