LMFDB - Embedded newform 729.2.g.d.28.1

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			28.1
Character	$\chi$	$=$	729.28
Dual form			729.2.g.d.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76633 + 1.16173i) q^{2} +(0.978129 - 2.26756i) q^{4} +(-2.05186 + 2.17484i) q^{5} +(3.48897 + 0.407803i) q^{7} +(0.172370 + 0.977557i) q^{8} +O(q^{10})$	\(q+(-1.76633 + 1.16173i) q^{2} +(0.978129 - 2.26756i) q^{4} +(-2.05186 + 2.17484i) q^{5} +(3.48897 + 0.407803i) q^{7} +(0.172370 + 0.977557i) q^{8} +(1.09767 - 6.22518i) q^{10} +(0.562324 - 1.87829i) q^{11} +(-0.0969288 + 1.66420i) q^{13} +(-6.63642 + 3.33294i) q^{14} +(1.94926 + 2.06610i) q^{16} +(3.65626 - 1.33077i) q^{17} +(-0.0155726 - 0.00566795i) q^{19} +(2.92460 + 6.77998i) q^{20} +(1.18882 + 3.97095i) q^{22} +(7.67257 - 0.896795i) q^{23} +(-0.229093 - 3.93338i) q^{25} +(-1.76215 - 3.05213i) q^{26} +(4.33738 - 7.51257i) q^{28} +(4.12997 + 2.07415i) q^{29} +(-6.12985 - 8.23381i) q^{31} +(-7.77505 - 1.84272i) q^{32} +(-4.91215 + 6.59816i) q^{34} +(-8.04578 + 6.75121i) q^{35} +(5.48325 + 4.60100i) q^{37} +(0.0340908 - 0.00807968i) q^{38} +(-2.47971 - 1.63093i) q^{40} +(4.72613 + 3.10842i) q^{41} +(-4.44056 + 1.05243i) q^{43} +(-3.70912 - 3.11232i) q^{44} +(-12.5104 + 10.4975i) q^{46} +(-1.71778 + 2.30738i) q^{47} +(5.19533 + 1.23132i) q^{49} +(4.97418 + 6.68148i) q^{50} +(3.67887 + 1.84760i) q^{52} +(-1.40413 + 2.43202i) q^{53} +(2.93118 + 5.07695i) q^{55} +(0.202743 + 3.48096i) q^{56} +(-9.70447 + 1.13429i) q^{58} +(1.42165 + 4.74864i) q^{59} +(3.71633 + 8.61543i) q^{61} +(20.3928 + 7.42236i) q^{62} +(10.5356 - 3.83466i) q^{64} +(-3.42049 - 3.62551i) q^{65} +(-4.00634 + 2.01206i) q^{67} +(0.558696 - 9.59244i) q^{68} +(6.36838 - 21.2719i) q^{70} +(-1.33743 + 7.58494i) q^{71} +(-0.696188 - 3.94828i) q^{73} +(-15.0303 - 1.75679i) q^{74} +(-0.0280844 + 0.0297677i) q^{76} +(2.72791 - 6.32400i) q^{77} +(-6.81054 + 4.47936i) q^{79} -8.49305 q^{80} -11.9590 q^{82} +(-4.30784 + 2.83331i) q^{83} +(-4.60790 + 10.6823i) q^{85} +(6.62083 - 7.01767i) q^{86} +(1.93307 + 0.225943i) q^{88} +(0.829745 + 4.70572i) q^{89} +(-1.01685 + 5.76683i) q^{91} +(5.47123 - 18.2752i) q^{92} +(0.353607 - 6.07119i) q^{94} +(0.0442795 - 0.0222380i) q^{95} +(7.98151 + 8.45991i) q^{97} +(-10.6071 + 3.86067i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.989535	−	0.144290i	$-0.953910\pi$
$2$	−1.76633	+	1.16173i	−1.24898	+	0.821468i	−0.259446	+	0.965758i	$0.583540\pi$
$3$		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	$-0.992358\pi$
$5$	−2.05186	+	2.17484i	−0.917618	+	0.972618i	0.0820939	+	0.996625i	$0.473839\pi$
$6$		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	$-0.811894\pi$
$11$	0.562324	−	1.87829i	0.169547	−	0.566327i	0.999958	−	0.00917522i	$-0.00292060\pi$
$12$		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	0.141833	−	0.989891i	$-0.454700\pi$
$17$	3.65626	−	1.33077i	0.886772	−	0.322759i	0.744940	+	0.667132i	$0.232478\pi$
$18$		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	0.731103	−	0.682267i	$-0.239006\pi$
$23$	7.67257	−	0.896795i	1.59984	−	0.186995i	0.868738	+	0.495272i	$0.164932\pi$
$24$		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	$-0.210683\pi$
$29$	4.12997	+	2.07415i	0.766916	+	0.385159i	−0.0219232	+	0.999760i	$0.506979\pi$
$30$		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	0.862043	−	0.506835i	$-0.169185\pi$
$41$	4.72613	+	3.10842i	0.738097	+	0.485454i	−0.123946	+	0.992289i	$0.539555\pi$
$42$		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	−0.909554	−	0.415586i	$-0.863577\pi$
$47$	−1.71778	+	2.30738i	−0.250564	+	0.336566i	0.658990	+	0.752152i	$0.270984\pi$
$48$		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	$-0.895113\pi$
$53$	−1.40413	+	2.43202i	−0.192872	+	0.334063i	0.753329	+	0.657644i	$0.228447\pi$
$54$		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	$0.0119863\pi$
$59$	1.42165	+	4.74864i	0.185083	+	0.618221i	−0.814208	+	0.580573i	$0.802828\pi$
$60$		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	$0.206641\pi$
$71$	−1.33743	+	7.58494i	−0.158724	+	0.900166i	−0.955302	+	0.295631i	$0.904470\pi$
$72$		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	−0.763472	−	0.645841i	$-0.776507\pi$
$83$	−4.30784	+	2.83331i	−0.472846	+	0.310996i	0.290626	+	0.956837i	$0.406137\pi$
$84$		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	$0.0259440\pi$
$89$	0.829745	+	4.70572i	0.0879528	+	0.498805i	−0.908727	+	0.417390i	$0.862945\pi$
$90$		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	0.965222	−	0.261431i	$-0.0841945\pi$
$101$	1.13250	+	2.62543i	0.112688	+	0.261240i	−0.852534	+	0.522672i	$0.824935\pi$
$102$		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	$-0.890370\pi$
$107$	−7.89300	−	13.6711i	−0.763045	−	1.32163i	0.178229	−	0.983989i	$-0.442963\pi$
$108$		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	0.0799359	−	0.996800i	$-0.474528\pi$
$113$	−3.14646	−	0.745724i	−0.295994	−	0.0701518i	−0.375930	+	0.926648i	$0.622677\pi$
$114$		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	0.802115	−	0.597170i	$-0.203708\pi$
$131$	−0.000192729	0	0.000258880i	−1.68388e−5	0	2.26184e-5i	−0.802132	+	0.597147i	$0.796301\pi$
$132$		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	$-0.832832\pi$
$137$	−0.749748	−	12.8727i	−0.0640553	−	1.09979i	0.801181	−	0.598422i	$-0.204206\pi$
$138$		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	$0.196078\pi$
$149$	−0.751391	+	12.9009i	−0.0615563	+	1.05688i	−0.877755	+	0.479110i	$0.840959\pi$
$150$		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	−0.140565	−	0.990071i	$-0.544892\pi$
$167$	11.0620	−	11.7251i	0.856004	−	0.907312i	0.996570	+	0.0827597i	$0.0263734\pi$
$168$		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	$0.302701\pi$
$173$	−4.62618	+	15.4525i	−0.351722	+	1.17483i	−0.932621	+	0.360858i	$0.882484\pi$
$174$		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	$-0.515231\pi$
$179$	7.45990	−	2.71518i	0.557579	−	0.202942i	0.605411	+	0.795913i	$0.293009\pi$
$180$		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	−0.0813890	−	0.996682i	$-0.525936\pi$
$191$	−12.8453	−	6.45115i	−0.929453	−	0.466789i	−0.848064	+	0.529893i	$0.822232\pi$
$192$		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	−0.649218	−	0.760602i	$-0.724904\pi$
$197$	−0.181162	+	0.152013i	−0.0129073	+	0.0108305i	0.636311	+	0.771432i	$0.280459\pi$
$198$		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	0.750175	−	0.661239i	$-0.229969\pi$
$227$	0.699631	+	0.741565i	0.0464361	+	0.0492194i	−0.703739	+	0.710458i	$0.748488\pi$
$228$		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	−0.948567	−	0.316577i	$-0.897467\pi$
$233$	0.779551	−	4.42105i	0.0510701	−	0.289633i	0.999637	+	0.0269441i	$0.00857761\pi$
$234$		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	$-0.886076\pi$
$239$	−0.604016	+	1.40027i	−0.0390706	+	0.0905757i	0.897563	+	0.440886i	$0.145336\pi$
$240$		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	$0.100533\pi$
$251$	2.59126	+	14.6958i	0.163559	+	0.927590i	−0.786978	+	0.616980i	$0.788356\pi$
$252$		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	$-0.741035\pi$
$257$	−8.24289	+	4.13974i	−0.514178	+	0.258230i	0.172737	+	0.984968i	$0.444739\pi$
$258$		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	$-0.127294\pi$
$263$	0.0942800	+	0.218566i	0.00581355	+	0.0134773i	−0.915285	+	0.402808i	$0.868034\pi$
$264$		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	$-0.0217808\pi$
$269$	7.21026	+	12.4885i	0.439617	+	0.761439i	−0.558043	+	0.829812i	$0.688447\pi$
$270$		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	−0.749330	−	0.662197i	$-0.769624\pi$
$281$	−18.8042	+	4.45667i	−1.12176	+	0.265862i	−0.372432	+	0.928059i	$0.621476\pi$
$282$		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	0.639500	−	0.768792i	$-0.279142\pi$
$293$	−4.79976	−	6.44720i	−0.280405	−	0.376650i	−0.919905	+	0.392142i	$0.871734\pi$
$294$		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	$-0.934791\pi$
$311$	0.299735	−	5.14625i	0.0169964	−	0.291817i	0.996086	−	0.0883881i	$-0.0281716\pi$
$312$		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	0.368612	−	0.929583i	$-0.379833\pi$
$317$	9.13214	+	1.06739i	0.512912	+	0.0599508i	0.144300	+	0.989534i	$0.453907\pi$
$318$		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	0.276650	−	0.960971i	$-0.410776\pi$
$347$	14.2961	−	1.67098i	0.767457	−	0.0897029i	0.490808	+	0.871268i	$0.336702\pi$
$348$		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	−0.333795	−	0.942646i	$-0.608329\pi$
$353$	−24.2226	−	12.1651i	−1.28924	−	0.647481i	−0.955446	+	0.295165i	$0.904626\pi$
$354$		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	$-0.493651\pi$
$359$	19.0992	−	16.0261i	1.00802	−	0.845828i	0.988075	+	0.153974i	$0.0492071\pi$
$360$		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	$-0.877357\pi$
$383$	−7.02527	−	23.4660i	−0.358974	−	1.19906i	0.567714	−	0.823226i	$-0.307828\pi$
$384$		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	$-0.109853\pi$
$389$	10.8199	+	11.4684i	0.548589	+	0.581470i	−0.392448	+	0.919774i	$0.628372\pi$
$390$		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	$-0.736264\pi$
$401$	6.48724	−	15.0391i	0.323957	−	0.751017i	0.999901	−	0.0140640i	$-0.00447687\pi$
$402$		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	−0.582174	−	0.813064i	$-0.697798\pi$
$419$	−5.68329	+	2.85426i	−0.277647	+	0.139440i	0.304527	+	0.952504i	$0.401502\pi$
$420$		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	0.975432	−	0.220302i	$-0.0707042\pi$
$431$	6.16440	+	10.6771i	0.296929	+	0.514296i	−0.678503	+	0.734598i	$0.737371\pi$
$432$		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	0.480952	−	0.876747i	$-0.340291\pi$
$443$	27.4508	−	6.50597i	1.30423	−	0.309108i	0.823277	+	0.567639i	$0.192143\pi$
$444$		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	$-0.490213\pi$
$449$	−20.0933	−	16.8603i	−0.948260	−	0.795685i	−0.979004	+	0.203842i	$0.934657\pi$
$450$		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	$0.126604\pi$
$461$	1.09933	+	18.8747i	0.0512007	+	0.879082i	−0.870738	+	0.491747i	$0.836359\pi$
$462$		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	0.308362	−	0.951269i	$-0.400219\pi$
$467$	−1.44533	−	0.526058i	−0.0668820	−	0.0243431i	−0.375245	+	0.926926i	$0.622441\pi$
$468$		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	$-0.581219\pi$
$479$	−15.7830	−	1.84476i	−0.721142	−	0.0842895i	−0.468744	+	0.883334i	$0.655293\pi$
$480$		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	$-0.422966\pi$
$491$	26.4780	−	28.0650i	1.19494	−	1.26656i	0.955281	−	0.295700i	$-0.0955528\pi$
$492$		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	0.179341	−	0.983787i	$-0.442604\pi$
$503$	21.2859	−	7.74742i	0.949090	−	0.345440i	0.769749	+	0.638347i	$0.220381\pi$
$504$		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	$-0.780879\pi$
$509$	−31.0714	+	3.63172i	−1.37721	+	0.160973i	−0.604945	+	0.796268i	$0.706805\pi$
$510$		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	$-0.939170\pi$
$521$	−22.0317	+	18.4868i	−0.965226	+	0.809921i	0.0165695	+	0.999863i	$0.494726\pi$
$522$		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	$-0.882659\pi$
$557$	1.58101	−	8.96634i	0.0669894	−	0.379916i	0.999808	−	0.0195708i	$-0.00622998\pi$
$558$		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	$-0.991959\pi$
$563$	−7.00644	+	16.2428i	−0.295286	+	0.684550i	0.704395	+	0.709808i	$0.251219\pi$
$564$		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	$-0.345605\pi$
$569$	34.9033	−	22.9563i	1.46322	−	0.962377i	0.996975	−	0.0777237i	$-0.0247652\pi$
$570$		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	$0.0128415\pi$
$587$	8.30634	+	19.2563i	0.342839	+	0.794791i	−0.656347	+	0.754459i	$0.727899\pi$
$588$		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	$-0.327983\pi$
$593$	−11.8196	−	20.4722i	−0.485373	−	0.840691i	−0.999859	+	0.0168078i	$0.994650\pi$
$594$		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	$-0.436317\pi$
$599$	−1.55457	−	0.368441i	−0.0635182	−	0.0150541i	−0.262252	+	0.964999i	$0.584465\pi$
$600$		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	0.987781	−	0.155851i	$-0.0498121\pi$
$617$	13.7903	+	18.5236i	0.555178	+	0.745733i	−0.432603	+	0.901585i	$0.642405\pi$
$618$		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	0.585254	−	0.810850i	$-0.300995\pi$
$641$	24.5011	+	2.86377i	0.967737	+	0.113112i	0.382483	+	0.923962i	$0.375069\pi$
$642$		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	$-0.577593\pi$
$647$	−12.2785			−0.482716			−0.241358	+	0.970436i	$0.577593\pi$
$648$		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	$-0.741417\pi$
$653$	1.96487	−	2.08264i	0.0768914	−	0.0815001i	0.764677	+	0.644414i	$0.222899\pi$
$654$		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	$-0.543619\pi$
$659$	13.3973	−	44.7501i	0.521885	−	1.74322i	0.658488	−	0.752591i	$-0.271196\pi$
$660$		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	0.652000	−	0.758219i	$-0.273930\pi$
$677$	11.2705	+	5.66027i	0.433162	+	0.217542i	−0.218838	+	0.975761i	$0.570227\pi$
$678$		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	$-0.834404\pi$
$683$	−13.8210	+	11.5972i	−0.528845	+	0.443754i	0.338857	+	0.940838i	$0.389960\pi$
$684$		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	−0.985350	−	0.170543i	$-0.945448\pi$
$701$	−9.13385	+	15.8203i	−0.344981	+	0.597524i	0.640370	+	0.768067i	$0.278781\pi$
$702$		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	$-0.860464\pi$
$719$	2.42853	−	13.7729i	0.0905690	−	0.513642i	0.996015	−	0.0891816i	$-0.0284252\pi$
$720$		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	$-0.265272\pi$
$743$	45.4564	−	22.8291i	1.66763	−	0.837517i	0.995254	−	0.0973110i	$-0.0310242\pi$
$744$		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	0.412435	−	0.910987i	$-0.364679\pi$
$761$	10.2662	+	2.43313i	0.372149	+	0.0882010i	−0.0402853	+	0.999188i	$0.512827\pi$
$762$		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	$-0.940918\pi$
$773$	−37.1233	−	31.1502i	−1.33523	−	1.12039i	−0.352409	−	0.935846i	$-0.614637\pi$
$774$		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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