LMFDB - Embedded newform 729.2.g.a.703.8

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			703.8
Character	$\chi$	$=$	729.703
Dual form			729.2.g.a.28.8

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{27}\right)$

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	0.989535	−	0.144290i	$-0.0460898\pi$
$2$	1.76633	+	1.16173i	1.24898	+	0.821468i	0.259446	+	0.965758i	$0.416460\pi$
$3$		0			0
$3$		0			0
$4$	0.978129	+	2.26756i	0.489065	+	1.13378i
$5$	2.05186	+	2.17484i	0.917618	+	0.972618i	0.999712	−	0.0240065i	$-0.00764223\pi$
$5$	2.05186	+	2.17484i	0.917618	+	0.972618i	−0.0820939	+	0.996625i	$0.526161\pi$
$6$		0			0
$7$	3.48897	−	0.407803i	1.31871	−	0.154135i	0.572532	−	0.819883i	$-0.305961\pi$
$7$	3.48897	−	0.407803i	1.31871	−	0.154135i	0.746177	+	0.665748i	$0.231887\pi$
$8$	−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	−0.999958	−	0.00917522i	$-0.997079\pi$
$11$	−0.562324	−	1.87829i	−0.169547	−	0.566327i	0.830411	−	0.557152i	$-0.188106\pi$
$12$		0			0
$13$	−0.0969288	−	1.66420i	−0.0268832	−	0.461567i	−0.984708	−	0.174214i	$-0.944262\pi$
$13$	−0.0969288	−	1.66420i	−0.0268832	−	0.461567i	0.957825	−	0.287353i	$-0.0927754\pi$
$14$	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	−0.141833	−	0.989891i	$-0.545300\pi$
$17$	−3.65626	−	1.33077i	−0.886772	−	0.322759i	−0.744940	+	0.667132i	$0.767522\pi$
$18$		0			0
$19$	−0.0155726	+	0.00566795i	−0.00357259	+	0.00130032i	−0.343806	−	0.939041i	$-0.611716\pi$
$19$	−0.0155726	+	0.00566795i	−0.00357259	+	0.00130032i	0.340233	+	0.940341i	$0.389494\pi$
$20$	−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	−0.731103	−	0.682267i	$-0.760994\pi$
$23$	−7.67257	−	0.896795i	−1.59984	−	0.186995i	−0.868738	+	0.495272i	$0.835068\pi$
$24$		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	−0.788839	−	0.614600i	$-0.789317\pi$
$29$	−4.12997	+	2.07415i	−0.766916	+	0.385159i	0.0219232	+	0.999760i	$0.493021\pi$
$30$		0			0
$31$	−6.12985	+	8.23381i	−1.10095	+	1.47884i	−0.239571	+	0.970879i	$0.577007\pi$
$31$	−6.12985	+	8.23381i	−1.10095	+	1.47884i	−0.861382	+	0.507957i	$0.830401\pi$
$32$	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	−0.0690302	−	0.997615i	$-0.521990\pi$
$37$	5.48325	−	4.60100i	0.901441	−	0.756399i	0.970472	+	0.241215i	$0.0775460\pi$
$38$	−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	−0.862043	−	0.506835i	$-0.830815\pi$
$41$	−4.72613	+	3.10842i	−0.738097	+	0.485454i	0.123946	+	0.992289i	$0.460445\pi$
$42$		0			0
$43$	−4.44056	−	1.05243i	−0.677179	−	0.160494i	−0.122386	−	0.992483i	$-0.539054\pi$
$43$	−4.44056	−	1.05243i	−0.677179	−	0.160494i	−0.554793	+	0.831988i	$0.687203\pi$
$44$	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	0.909554	−	0.415586i	$-0.136423\pi$
$47$	1.71778	+	2.30738i	0.250564	+	0.336566i	−0.658990	+	0.752152i	$0.729016\pi$
$48$		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	0.946201	−	0.323580i	$-0.104887\pi$
$53$	1.40413	+	2.43202i	0.192872	+	0.334063i	−0.753329	+	0.657644i	$0.771553\pi$
$54$		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	0.814208	+	0.580573i	$0.197172\pi$
$59$	−1.42165	+	4.74864i	−0.185083	+	0.618221i	−0.999291	+	0.0376473i	$0.988014\pi$
$60$		0			0
$61$	3.71633	−	8.61543i	0.475828	−	1.10309i	−0.496196	−	0.868211i	$-0.665270\pi$
$61$	3.71633	−	8.61543i	0.475828	−	1.10309i	0.972024	−	0.234882i	$-0.0754705\pi$
$62$	−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	0.186916	−	0.982376i	$-0.440151\pi$
$67$	−4.00634	−	2.01206i	−0.489453	−	0.245812i	−0.676368	+	0.736564i	$0.736447\pi$
$68$	−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	0.955302	+	0.295631i	$0.0955300\pi$
$71$	1.33743	+	7.58494i	0.158724	+	0.900166i	−0.796578	+	0.604535i	$0.793359\pi$
$72$		0			0
$73$	−0.696188	+	3.94828i	−0.0814827	+	0.462111i	0.916578	+	0.399857i	$0.130940\pi$
$73$	−0.696188	+	3.94828i	−0.0814827	+	0.462111i	−0.998060	+	0.0622545i	$0.980171\pi$
$74$	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	0.105205	−	0.994451i	$-0.466450\pi$
$79$	−6.81054	−	4.47936i	−0.766245	−	0.503967i	−0.871451	+	0.490483i	$0.836820\pi$
$80$	8.49305			0.949552
$81$		0			0
$82$	−11.9590			−1.32065
$83$	4.30784	+	2.83331i	0.472846	+	0.310996i	0.763472	−	0.645841i	$-0.223493\pi$
$83$	4.30784	+	2.83331i	0.472846	+	0.310996i	−0.290626	+	0.956837i	$0.593863\pi$
$84$		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	0.908727	+	0.417390i	$0.137055\pi$
$89$	−0.829745	+	4.70572i	−0.0879528	+	0.498805i	−0.996680	+	0.0814153i	$0.974056\pi$
$90$		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	−0.181838	−	0.983329i	$-0.558205\pi$
$97$	7.98151	−	8.45991i	0.810400	−	0.858974i	0.992238	+	0.124355i	$0.0396861\pi$
$98$	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	−0.965222	−	0.261431i	$-0.915805\pi$
$101$	−1.13250	+	2.62543i	−0.112688	+	0.261240i	0.852534	+	0.522672i	$0.175065\pi$
$102$		0			0
$103$	0.820517	−	2.74072i	0.0808479	−	0.270051i	−0.908002	−	0.418966i	$-0.862393\pi$
$103$	0.820517	−	2.74072i	0.0808479	−	0.270051i	0.988850	+	0.148915i	$0.0475780\pi$
$104$	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	−0.178229	−	0.983989i	$-0.557037\pi$
$107$	7.89300	−	13.6711i	0.763045	−	1.32163i	0.941274	−	0.337644i	$-0.109630\pi$
$108$		0			0
$109$	0.145393	+	0.251828i	0.0139261	+	0.0241207i	0.872904	−	0.487891i	$-0.162234\pi$
$109$	0.145393	+	0.251828i	0.0139261	+	0.0241207i	−0.858978	+	0.512012i	$0.828900\pi$
$110$	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	−0.0799359	−	0.996800i	$-0.525472\pi$
$113$	3.14646	−	0.745724i	0.295994	−	0.0701518i	0.375930	+	0.926648i	$0.377323\pi$
$114$		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	0.968704	−	0.248220i	$-0.0798457\pi$
$127$	10.0576	+	8.43933i	0.892468	+	0.748870i	−0.0762356	+	0.997090i	$0.524290\pi$
$128$	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	−0.802115	−	0.597170i	$-0.796292\pi$
$131$	0.000192729	0	0.000258880i	1.68388e−5	0	2.26184e-5i	0.802132	+	0.597147i	$0.203699\pi$
$132$		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	−0.801181	−	0.598422i	$-0.795794\pi$
$137$	0.749748	−	12.8727i	0.0640553	−	1.09979i	0.865236	−	0.501365i	$-0.167168\pi$
$138$		0			0
$139$	−0.637020	−	0.0744569i	−0.0540313	−	0.00631535i	0.0890343	−	0.996029i	$-0.471622\pi$
$139$	−0.637020	−	0.0744569i	−0.0540313	−	0.00631535i	−0.143066	+	0.989713i	$0.545696\pi$
$140$	−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	0.877755	+	0.479110i	$0.159041\pi$
$149$	0.751391	+	12.9009i	0.0615563	+	1.05688i	−0.816199	+	0.577772i	$0.803922\pi$
$150$		0			0
$151$	4.81347	+	16.0781i	0.391714	+	1.30842i	0.895682	+	0.444695i	$0.146688\pi$
$151$	4.81347	+	16.0781i	0.391714	+	1.30842i	−0.503968	+	0.863722i	$0.668127\pi$
$152$	−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	0.918720	−	0.394910i	$-0.129224\pi$
$157$	5.90236	+	6.25613i	0.471059	+	0.499294i	−0.447660	+	0.894204i	$0.647743\pi$
$158$	−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	0.140565	−	0.990071i	$-0.455108\pi$
$167$	−11.0620	−	11.7251i	−0.856004	−	0.907312i	−0.996570	+	0.0827597i	$0.973627\pi$
$168$		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	0.932621	+	0.360858i	$0.117516\pi$
$173$	4.62618	+	15.4525i	0.351722	+	1.17483i	−0.580898	+	0.813976i	$0.697299\pi$
$174$		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	0.0478318	−	0.998855i	$-0.484769\pi$
$179$	−7.45990	−	2.71518i	−0.557579	−	0.202942i	−0.605411	+	0.795913i	$0.706991\pi$
$180$		0			0
$181$	13.0001	−	4.73166i	0.966292	−	0.351702i	0.189796	−	0.981824i	$-0.439217\pi$
$181$	13.0001	−	4.73166i	0.966292	−	0.351702i	0.776496	+	0.630122i	$0.216995\pi$
$182$	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	0.0813890	−	0.996682i	$-0.474064\pi$
$191$	12.8453	−	6.45115i	0.929453	−	0.466789i	0.848064	+	0.529893i	$0.177768\pi$
$192$		0			0
$193$	−2.49845	+	3.35600i	−0.179842	+	0.241570i	−0.882898	−	0.469564i	$-0.844411\pi$
$193$	−2.49845	+	3.35600i	−0.179842	+	0.241570i	0.703056	+	0.711135i	$0.251818\pi$
$194$	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	0.649218	−	0.760602i	$-0.275096\pi$
$197$	0.181162	+	0.152013i	0.0129073	+	0.0108305i	−0.636311	+	0.771432i	$0.719541\pi$
$198$		0			0
$199$	19.9860	−	16.7702i	1.41677	−	1.18881i	0.463726	−	0.885979i	$-0.346512\pi$
$199$	19.9860	−	16.7702i	1.41677	−	1.18881i	0.953044	−	0.302832i	$-0.0979322\pi$
$200$	−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	−0.605934	−	0.795515i	$-0.707200\pi$
$211$	−11.4811	+	2.72107i	−0.790390	+	0.187326i	−0.184456	+	0.982841i	$0.559052\pi$
$212$	−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	0.0837965	+	0.996483i	$0.473295\pi$
$223$	−10.4312	+	24.1822i	−0.698524	+	1.61936i	−0.782320	+	0.622877i	$0.785964\pi$
$224$	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	−0.750175	−	0.661239i	$-0.770031\pi$
$227$	−0.699631	+	0.741565i	−0.0464361	+	0.0492194i	0.703739	+	0.710458i	$0.251512\pi$
$228$		0			0
$229$	23.3073	+	11.7054i	1.54019	+	0.773512i	0.997780	−	0.0666015i	$-0.0212156\pi$
$229$	23.3073	+	11.7054i	1.54019	+	0.773512i	0.542410	+	0.840114i	$0.317512\pi$
$230$	−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	0.948567	−	0.316577i	$-0.102533\pi$
$233$	−0.779551	−	4.42105i	−0.0510701	−	0.289633i	−0.999637	+	0.0269441i	$0.991422\pi$
$234$		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	0.936634	−	0.350310i	$-0.113924\pi$
$239$	0.604016	+	1.40027i	0.0390706	+	0.0905757i	−0.897563	+	0.440886i	$0.854664\pi$
$240$		0			0
$241$	−0.703622	−	0.462779i	−0.0453243	−	0.0298102i	0.526645	−	0.850086i	$-0.323450\pi$
$241$	−0.703622	−	0.462779i	−0.0453243	−	0.0298102i	−0.571969	+	0.820275i	$0.693820\pi$
$242$	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	0.786978	+	0.616980i	$0.211644\pi$
$251$	−2.59126	+	14.6958i	−0.163559	+	0.927590i	−0.950538	+	0.310609i	$0.899467\pi$
$252$		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	0.686914	−	0.726738i	$-0.258965\pi$
$257$	8.24289	+	4.13974i	0.514178	+	0.258230i	−0.172737	+	0.984968i	$0.555261\pi$
$258$		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	−0.921098	−	0.389330i	$-0.872706\pi$
$263$	−0.0942800	+	0.218566i	−0.00581355	+	0.0134773i	0.915285	+	0.402808i	$0.131966\pi$
$264$		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	−0.997660	−	0.0683731i	$-0.978219\pi$
$269$	−7.21026	+	12.4885i	−0.439617	+	0.761439i	0.558043	+	0.829812i	$0.311553\pi$
$270$		0			0
$271$	−8.33200	−	14.4314i	−0.506133	−	0.876648i	−0.999975	−	0.00709598i	$-0.997741\pi$
$271$	−8.33200	−	14.4314i	−0.506133	−	0.876648i	0.493842	−	0.869552i	$-0.335592\pi$
$272$	−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	0.979783	+	0.200063i	$0.0641146\pi$
$277$	14.8198	+	19.9065i	0.890436	+	1.19606i	−0.0893469	+	0.996001i	$0.528478\pi$
$278$	−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	0.749330	−	0.662197i	$-0.230376\pi$
$281$	18.8042	+	4.45667i	1.12176	+	0.265862i	0.372432	+	0.928059i	$0.378524\pi$
$282$		0			0
$283$	−0.932620	+	0.613394i	−0.0554385	+	0.0364625i	−0.576926	−	0.816797i	$-0.695748\pi$
$283$	−0.932620	+	0.613394i	−0.0554385	+	0.0364625i	0.521487	+	0.853259i	$0.325377\pi$
$284$	−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	−0.639500	−	0.768792i	$-0.720858\pi$
$293$	4.79976	−	6.44720i	0.280405	−	0.376650i	0.919905	+	0.392142i	$0.128266\pi$
$294$		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	−0.150101	−	0.988671i	$-0.547960\pi$
$307$	−15.7796	−	5.74331i	−0.900590	−	0.327788i	−0.750489	+	0.660883i	$0.770182\pi$
$308$	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	−0.996086	−	0.0883881i	$-0.971828\pi$
$311$	−0.299735	−	5.14625i	−0.0169964	−	0.291817i	0.979090	−	0.203429i	$-0.0652086\pi$
$312$		0			0
$313$	−8.01329	−	26.7663i	−0.452938	−	1.51292i	−0.814273	−	0.580483i	$-0.802864\pi$
$313$	−8.01329	−	26.7663i	−0.452938	−	1.51292i	0.361334	−	0.932436i	$-0.382321\pi$
$314$	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	−0.368612	−	0.929583i	$-0.620167\pi$
$317$	−9.13214	+	1.06739i	−0.512912	+	0.0599508i	−0.144300	+	0.989534i	$0.546093\pi$
$318$		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	−0.565431	−	0.824795i	$-0.691290\pi$
$331$	−16.8364	+	1.96789i	−0.925411	+	0.108165i	−0.359979	+	0.932960i	$0.617216\pi$
$332$	−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	−0.953823	−	0.300370i	$-0.902890\pi$
$337$	−0.758539	−	13.0236i	−0.0413203	−	0.709442i	0.912502	−	0.409071i	$-0.134147\pi$
$338$	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	−0.276650	−	0.960971i	$-0.589224\pi$
$347$	−14.2961	−	1.67098i	−0.767457	−	0.0897029i	−0.490808	+	0.871268i	$0.663298\pi$
$348$		0			0
$349$	−0.472908	+	8.11951i	−0.0253142	+	0.434627i	0.961711	+	0.274064i	$0.0883681\pi$
$349$	−0.472908	+	8.11951i	−0.0253142	+	0.434627i	−0.987026	+	0.160563i	$0.948669\pi$
$350$	−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	0.333795	−	0.942646i	$-0.391671\pi$
$353$	24.2226	−	12.1651i	1.28924	−	0.647481i	0.955446	+	0.295165i	$0.0953745\pi$
$354$		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	−0.0199431	−	0.999801i	$-0.506349\pi$
$359$	−19.0992	−	16.0261i	−1.00802	−	0.845828i	−0.988075	+	0.153974i	$0.950793\pi$
$360$		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	0.549226	−	0.835674i	$-0.314923\pi$
$367$	12.7392	+	3.01925i	0.664982	+	0.157604i	0.115756	+	0.993278i	$0.463071\pi$
$368$	−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	−0.878732	−	0.477315i	$-0.841610\pi$
$373$	−27.9998	+	6.63609i	−1.44978	+	0.343604i	−0.571045	+	0.820919i	$0.693462\pi$
$374$	−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	−0.460051	−	0.887892i	$-0.652169\pi$
$379$	10.4915	−	18.1718i	0.538912	−	0.933422i	0.998963	−	0.0455300i	$-0.0144977\pi$
$380$	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	−0.567714	−	0.823226i	$-0.692172\pi$
$383$	7.02527	−	23.4660i	0.358974	−	1.19906i	0.926688	−	0.375832i	$-0.122643\pi$
$384$		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	−0.941037	−	0.338304i	$-0.890147\pi$
$389$	−10.8199	+	11.4684i	−0.548589	+	0.581470i	0.392448	+	0.919774i	$0.371628\pi$
$390$		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	0.637449	+	0.770492i	$0.279989\pi$
$397$	−4.48471	+	25.4340i	−0.225081	+	1.27650i	−0.862530	+	0.506005i	$0.831122\pi$
$398$	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	−0.999901	−	0.0140640i	$-0.995523\pi$
$401$	−6.48724	−	15.0391i	−0.323957	−	0.751017i	0.675944	−	0.736953i	$-0.263736\pi$
$402$		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	−0.963688	−	0.267030i	$-0.913958\pi$
$409$	−10.0430	−	23.2823i	−0.496596	−	1.15124i	0.467093	−	0.884208i	$-0.345301\pi$
$410$	−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	0.582174	−	0.813064i	$-0.302202\pi$
$419$	5.68329	+	2.85426i	0.277647	+	0.139440i	−0.304527	+	0.952504i	$0.598498\pi$
$420$		0			0
$421$	−18.0240	+	19.1043i	−0.878434	+	0.931086i	−0.998093	−	0.0617290i	$-0.980339\pi$
$421$	−18.0240	+	19.1043i	−0.878434	+	0.931086i	0.119658	+	0.992815i	$0.461820\pi$
$422$	−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	−0.975432	−	0.220302i	$-0.929296\pi$
$431$	−6.16440	+	10.6771i	−0.296929	+	0.514296i	0.678503	+	0.734598i	$0.262629\pi$
$432$		0			0
$433$	3.37556	+	5.84664i	0.162219	+	0.280972i	0.935664	−	0.352891i	$-0.114802\pi$
$433$	3.37556	+	5.84664i	0.162219	+	0.280972i	−0.773445	+	0.633863i	$0.781468\pi$
$434$	−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	0.733905	−	0.679252i	$-0.237695\pi$
$439$	−2.66717	−	3.58263i	−0.127297	−	0.170989i	−0.861202	+	0.508262i	$0.830288\pi$
$440$	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	−0.480952	−	0.876747i	$-0.659709\pi$
$443$	−27.4508	−	6.50597i	−1.30423	−	0.309108i	−0.823277	+	0.567639i	$0.807857\pi$
$444$		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	−0.0307434	−	0.999527i	$-0.509787\pi$
$449$	20.0933	−	16.8603i	0.948260	−	0.795685i	0.979004	+	0.203842i	$0.0653430\pi$
$450$		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	−0.874905	−	0.484295i	$-0.839076\pi$
$457$	−21.5678	+	10.8317i	−1.00890	+	0.506687i	−0.133992	+	0.990982i	$0.542780\pi$
$458$	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	0.870738	+	0.491747i	$0.163641\pi$
$461$	−1.09933	+	18.8747i	−0.0512007	+	0.879082i	−0.921939	+	0.387335i	$0.873396\pi$
$462$		0			0
$463$	−1.68749	−	0.197239i	−0.0784242	−	0.00916647i	0.0767903	−	0.997047i	$-0.475533\pi$
$463$	−1.68749	−	0.197239i	−0.0784242	−	0.00916647i	−0.155215	+	0.987881i	$0.549607\pi$
$464$	−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	−0.308362	−	0.951269i	$-0.599781\pi$
$467$	1.44533	−	0.526058i	0.0668820	−	0.0243431i	0.375245	+	0.926926i	$0.377559\pi$
$468$		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	0.252398	−	0.967623i	$-0.418781\pi$
$479$	15.7830	−	1.84476i	0.721142	−	0.0842895i	0.468744	+	0.883334i	$0.344707\pi$
$480$		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	−0.955281	−	0.295700i	$-0.904447\pi$
$491$	−26.4780	−	28.0650i	−1.19494	−	1.26656i	−0.239655	−	0.970858i	$-0.577034\pi$
$492$		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	−0.998116	−	0.0613544i	$-0.980458\pi$
$499$	−0.309871	−	5.32027i	−0.0138717	−	0.238168i	0.984244	−	0.176814i	$-0.0565790\pi$
$500$	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	−0.179341	−	0.983787i	$-0.557396\pi$
$503$	−21.2859	−	7.74742i	−0.949090	−	0.345440i	−0.769749	+	0.638347i	$0.779619\pi$
$504$		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	0.772270	−	0.635294i	$-0.219121\pi$
$509$	31.0714	+	3.63172i	1.37721	+	0.160973i	0.604945	+	0.796268i	$0.293195\pi$
$510$		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	0.981795	−	0.189942i	$-0.0608300\pi$
$521$	22.0317	+	18.4868i	0.965226	+	0.809921i	−0.0165695	+	0.999863i	$0.505274\pi$
$522$		0			0
$523$	−5.64380	+	4.73571i	−0.246786	+	0.207078i	−0.757787	−	0.652502i	$-0.773719\pi$
$523$	−5.64380	+	4.73571i	−0.246786	+	0.207078i	0.511001	+	0.859580i	$0.329275\pi$
$524$	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	−0.456171	−	0.889892i	$-0.650780\pi$
$541$	12.6202	−	21.8588i	0.542583	−	0.939782i	0.998755	−	0.0498899i	$-0.0158870\pi$
$542$	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	−0.693247	−	0.720700i	$-0.743820\pi$
$547$	7.17326	−	16.6295i	0.306706	−	0.711025i	0.999953	+	0.00967491i	$0.00307967\pi$
$548$	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	−0.999808	−	0.0195708i	$-0.993770\pi$
$557$	−1.58101	−	8.96634i	−0.0669894	−	0.379916i	0.932819	−	0.360345i	$-0.117341\pi$
$558$		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	0.999681	−	0.0252581i	$-0.00804074\pi$
$563$	7.00644	+	16.2428i	0.295286	+	0.684550i	−0.704395	+	0.709808i	$0.748781\pi$
$564$		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	−0.996975	−	0.0777237i	$-0.975235\pi$
$569$	−34.9033	−	22.9563i	−1.46322	−	0.962377i	−0.466249	−	0.884654i	$-0.654395\pi$
$570$		0			0
$571$	7.80567	+	18.0956i	0.326657	+	0.757276i	0.999842	+	0.0178017i	$0.00566675\pi$
$571$	7.80567	+	18.0956i	0.326657	+	0.757276i	−0.673184	+	0.739475i	$0.735074\pi$
$572$	−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	0.943499	−	0.331376i	$-0.107513\pi$
$577$	−1.35567	−	7.68841i	−0.0564374	−	0.320073i	−0.999936	+	0.0113037i	$0.996402\pi$
$578$	−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	0.656347	+	0.754459i	$0.272101\pi$
$587$	−8.30634	+	19.2563i	−0.342839	+	0.794791i	−0.999186	+	0.0403319i	$0.987158\pi$
$588$		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	−0.514485	−	0.857499i	$-0.672017\pi$
$593$	11.8196	−	20.4722i	0.485373	−	0.840691i	0.999859	+	0.0168078i	$0.00535033\pi$
$594$		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	−0.198734	−	0.980053i	$-0.563683\pi$
$599$	1.55457	−	0.368441i	0.0635182	−	0.0150541i	0.262252	+	0.964999i	$0.415535\pi$
$600$		0			0
$601$	18.9415	+	25.4429i	0.772641	+	1.03784i	0.997978	+	0.0635563i	$0.0202443\pi$
$601$	18.9415	+	25.4429i	0.772641	+	1.03784i	−0.225337	+	0.974281i	$0.572348\pi$
$602$	−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	−0.716915	−	0.697161i	$-0.754446\pi$
$607$	−8.88733	+	5.84529i	−0.360726	+	0.237253i	0.356189	+	0.934414i	$0.384076\pi$
$608$	−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	−0.959263	−	0.282513i	$-0.908832\pi$
$613$	−34.7629	−	29.1695i	−1.40406	−	1.17815i	−0.444796	−	0.895632i	$-0.646724\pi$
$614$	−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	−0.987781	−	0.155851i	$-0.950188\pi$
$617$	−13.7903	+	18.5236i	−0.555178	+	0.745733i	0.432603	+	0.901585i	$0.357595\pi$
$618$		0			0
$619$	1.75718	−	0.882490i	0.0706271	−	0.0354703i	−0.413135	−	0.910670i	$-0.635566\pi$
$619$	1.75718	−	0.882490i	0.0706271	−	0.0354703i	0.483762	+	0.875200i	$0.339270\pi$
$620$	−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	−0.994848	−	0.101382i	$-0.967673\pi$
$631$	−45.7709	−	16.6593i	−1.82211	−	0.663195i	−0.827265	−	0.561812i	$-0.810104\pi$
$632$	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	−0.585254	−	0.810850i	$-0.699005\pi$
$641$	−24.5011	+	2.86377i	−0.967737	+	0.113112i	−0.382483	+	0.923962i	$0.624931\pi$
$642$		0			0
$643$	7.26830	+	7.70395i	0.286634	+	0.303814i	0.854651	−	0.519202i	$-0.173771\pi$
$643$	7.26830	+	7.70395i	0.286634	+	0.303814i	−0.568018	+	0.823016i	$0.692289\pi$
$644$	−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	0.687786	−	0.725914i	$-0.258583\pi$
$653$	−1.96487	−	2.08264i	−0.0768914	−	0.0815001i	−0.764677	+	0.644414i	$0.777101\pi$
$654$		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	−0.658488	−	0.752591i	$-0.728804\pi$
$659$	−13.3973	−	44.7501i	−0.521885	−	1.74322i	0.136603	−	0.990626i	$-0.456381\pi$
$660$		0			0
$661$	−1.38632	−	23.8022i	−0.0539215	−	0.925797i	−0.911463	−	0.411382i	$-0.865046\pi$
$661$	−1.38632	−	23.8022i	−0.0539215	−	0.925797i	0.857542	−	0.514415i	$-0.171991\pi$
$662$	−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	0.989466	+	0.144764i	$0.0462422\pi$
$673$	−0.262422	+	4.50561i	−0.0101156	+	0.173679i	−0.999582	+	0.0289148i	$0.990795\pi$
$674$	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	−0.652000	−	0.758219i	$-0.726070\pi$
$677$	−11.2705	+	5.66027i	−0.433162	+	0.217542i	0.218838	+	0.975761i	$0.429773\pi$
$678$		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	0.867702	−	0.497084i	$-0.165596\pi$
$683$	13.8210	+	11.5972i	0.528845	+	0.443754i	−0.338857	+	0.940838i	$0.610040\pi$
$684$		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	−0.437276	−	0.899327i	$-0.644057\pi$
$691$	−32.3764	−	7.67336i	−1.23166	−	0.291908i	−0.794382	+	0.607419i	$0.792205\pi$
$692$	−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	0.985350	−	0.170543i	$-0.0545522\pi$
$701$	9.13385	+	15.8203i	0.344981	+	0.597524i	−0.640370	+	0.768067i	$0.721219\pi$
$702$		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	−0.902868	−	0.429918i	$-0.858542\pi$
$709$	0.783606	−	1.81660i	0.0294290	−	0.0682240i	0.932297	+	0.361694i	$0.117802\pi$
$710$	−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	−0.996015	−	0.0891816i	$-0.971575\pi$
$719$	−2.42853	−	13.7729i	−0.0905690	−	0.513642i	0.905446	−	0.424461i	$-0.139536\pi$
$720$		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	−0.183077	−	0.983099i	$-0.558606\pi$
$727$	−31.2308	−	20.5408i	−1.15829	−	0.761817i	−0.975210	+	0.221281i	$0.928976\pi$
$728$	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	0.994340	+	0.106248i	$0.0338838\pi$
$733$	10.5389	+	24.4320i	0.389265	+	0.902417i	−0.605075	+	0.796168i	$0.706857\pi$
$734$	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	0.727782	+	0.685808i	$0.240551\pi$
$739$	7.56956	+	42.9291i	0.278451	+	1.57917i	−0.449332	+	0.893365i	$0.648338\pi$
$740$	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	−0.995254	−	0.0973110i	$-0.968976\pi$
$743$	−45.4564	−	22.8291i	−1.66763	−	0.837517i	−0.672380	−	0.740206i	$-0.734728\pi$
$744$		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	−0.998343	−	0.0575375i	$-0.981675\pi$
$751$	−3.63443	+	12.1398i	−0.132622	+	0.442989i	0.865721	+	0.500527i	$0.166860\pi$
$752$	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	0.969468	−	0.245219i	$-0.0788598\pi$
$757$	7.49384	+	12.9797i	0.272368	+	0.471756i	−0.697100	+	0.716974i	$0.745526\pi$
$758$	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	−0.412435	−	0.910987i	$-0.635321\pi$
$761$	−10.2662	+	2.43313i	−0.372149	+	0.0882010i	0.0402853	+	0.999188i	$0.487173\pi$
$762$		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	0.205123	−	0.978736i	$-0.434240\pi$
$769$	32.8627	−	21.6141i	1.18506	−	0.779426i	0.979936	+	0.199310i	$0.0638701\pi$
$770$	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	0.352409	−	0.935846i	$-0.385363\pi$
$773$	37.1233	−	31.1502i	1.33523	−	1.12039i	0.982824	−	0.184547i	$-0.0590818\pi$
$774$		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

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

L-functions

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