LMFDB - Embedded newform 567.2.h.j.298.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(298,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("567.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.h (of order $3$, degree $2$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			298.2
Root			$0.0512865 + 1.21608i$ of defining polynomial
Character	$\chi$	$=$	567.298
Dual form			567.2.h.j.352.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.53652 q^{2} +0.360904 q^{4} +(1.57880 - 2.73457i) q^{5} +(2.29578 - 1.31507i) q^{7} +2.51851 q^{8} +O(q^{10})$	\(q-1.53652 q^{2} +0.360904 q^{4} +(1.57880 - 2.73457i) q^{5} +(2.29578 - 1.31507i) q^{7} +2.51851 q^{8} +(-2.42587 + 4.20173i) q^{10} +(-2.87458 - 4.97892i) q^{11} +(0.180452 + 0.312552i) q^{13} +(-3.52752 + 2.02063i) q^{14} -4.59156 q^{16} +(1.38842 - 2.40481i) q^{17} +(3.61533 + 6.26193i) q^{19} +(0.569796 - 0.986916i) q^{20} +(4.41686 + 7.65023i) q^{22} +(-0.412190 + 0.713934i) q^{23} +(-2.48524 - 4.30456i) q^{25} +(-0.277269 - 0.480243i) q^{26} +(0.828555 - 0.474613i) q^{28} +(-2.13910 + 3.70502i) q^{29} -4.98199 q^{31} +2.01801 q^{32} +(-2.13334 + 3.69505i) q^{34} +(0.0284402 - 8.35419i) q^{35} +(-3.74542 - 6.48725i) q^{37} +(-5.55503 - 9.62160i) q^{38} +(3.97623 - 6.88703i) q^{40} +(-1.66569 - 2.88506i) q^{41} +(3.93487 - 6.81540i) q^{43} +(-1.03745 - 1.79691i) q^{44} +(0.633340 - 1.09698i) q^{46} +3.48149 q^{47} +(3.54119 - 6.03821i) q^{49} +(3.81862 + 6.61405i) q^{50} +(0.0651258 + 0.112801i) q^{52} +(-1.45772 + 2.52485i) q^{53} -18.1536 q^{55} +(5.78194 - 3.31201i) q^{56} +(3.28677 - 5.69285i) q^{58} -2.39878 q^{59} +3.20113 q^{61} +7.65494 q^{62} +6.08239 q^{64} +1.13959 q^{65} +1.89927 q^{67} +(0.501086 - 0.867907i) q^{68} +(-0.0436991 + 12.8364i) q^{70} -1.60957 q^{71} +(7.70688 - 13.3487i) q^{73} +(5.75492 + 9.96781i) q^{74} +(1.30478 + 2.25995i) q^{76} +(-13.1470 - 7.65023i) q^{77} +5.47282 q^{79} +(-7.24916 + 12.5559i) q^{80} +(2.55937 + 4.43296i) q^{82} +(-6.51742 + 11.2885i) q^{83} +(-4.38408 - 7.59346i) q^{85} +(-6.04603 + 10.4720i) q^{86} +(-7.23966 - 12.5395i) q^{88} +(-7.13384 - 12.3562i) q^{89} +(0.825304 + 0.480243i) q^{91} +(-0.148761 + 0.257662i) q^{92} -5.34939 q^{94} +22.8315 q^{95} +(-8.00266 + 13.8610i) q^{97} +(-5.44113 + 9.27785i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8	$ 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8} + 7 q^{10} + 5 q^{11} + 5 q^{13} - 16 q^{14} - 2 q^{16} + 6 q^{17} + 8 q^{19} - 8 q^{20} + 7 q^{22} - 12 q^{23} - 8 q^{25} + q^{26} + 5 q^{28} - 10 q^{29} - 36 q^{31} + 20 q^{32} - 23 q^{35} - 20 q^{38} + 18 q^{40} - 5 q^{41} + 7 q^{43} + 13 q^{44} - 12 q^{46} + 42 q^{47} - 19 q^{49} + 38 q^{50} + 25 q^{52} - 12 q^{53} - 52 q^{55} + 6 q^{56} + 7 q^{58} - 12 q^{59} - 40 q^{61} - 36 q^{62} - 46 q^{64} - 16 q^{65} - 10 q^{67} + 51 q^{68} + 29 q^{70} + 18 q^{71} + 6 q^{73} - 5 q^{76} - 53 q^{77} - 20 q^{79} - 2 q^{80} + 35 q^{82} + 9 q^{83} + 9 q^{85} - 22 q^{86} - 18 q^{88} - 22 q^{89} + 13 q^{91} - 36 q^{92} - 30 q^{94} + 32 q^{95} + 9 q^{97} - 11 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8 + 7 * q^10 + 5 * q^11 + 5 * q^13 - 16 * q^14 - 2 * q^16 + 6 * q^17 + 8 * q^19 - 8 * q^20 + 7 * q^22 - 12 * q^23 - 8 * q^25 + q^26 + 5 * q^28 - 10 * q^29 - 36 * q^31 + 20 * q^32 - 23 * q^35 - 20 * q^38 + 18 * q^40 - 5 * q^41 + 7 * q^43 + 13 * q^44 - 12 * q^46 + 42 * q^47 - 19 * q^49 + 38 * q^50 + 25 * q^52 - 12 * q^53 - 52 * q^55 + 6 * q^56 + 7 * q^58 - 12 * q^59 - 40 * q^61 - 36 * q^62 - 46 * q^64 - 16 * q^65 - 10 * q^67 + 51 * q^68 + 29 * q^70 + 18 * q^71 + 6 * q^73 - 5 * q^76 - 53 * q^77 - 20 * q^79 - 2 * q^80 + 35 * q^82 + 9 * q^83 + 9 * q^85 - 22 * q^86 - 18 * q^88 - 22 * q^89 + 13 * q^91 - 36 * q^92 - 30 * q^94 + 32 * q^95 + 9 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.53652			−1.08649			−0.543243	−	0.839576i	$-0.682804\pi$
$2$	−1.53652			−1.08649			−0.543243	+	0.839576i	$0.682804\pi$
$3$		0			0
$3$		0			0
$4$	0.360904			0.180452
$5$	1.57880	−	2.73457i	0.706062	−	1.22294i	−0.260245	−	0.965543i	$-0.583803\pi$
$5$	1.57880	−	2.73457i	0.706062	−	1.22294i	0.966307	−	0.257393i	$-0.0828634\pi$
$6$		0			0
$7$	2.29578	−	1.31507i	0.867723	−	0.497049i
$7$	2.29578	−	1.31507i	0.867723	−	0.497049i
$8$	2.51851			0.890428
$9$		0			0
$10$	−2.42587	+	4.20173i	−0.767127	+	1.32870i
$11$	−2.87458	−	4.97892i	−0.866719	−	1.50120i	−0.865330	−	0.501202i	$-0.832891\pi$
$11$	−2.87458	−	4.97892i	−0.866719	−	1.50120i	−0.00138834	−	0.999999i	$-0.500442\pi$
$12$		0			0
$13$	0.180452	+	0.312552i	0.0500484	+	0.0866863i	0.889964	−	0.456030i	$-0.150729\pi$
$13$	0.180452	+	0.312552i	0.0500484	+	0.0866863i	−0.839916	+	0.542717i	$0.817396\pi$
$14$	−3.52752	+	2.02063i	−0.942768	+	0.540037i
$15$		0			0
$16$	−4.59156			−1.14789
$17$	1.38842	−	2.40481i	0.336741	−	0.583253i	−0.647076	−	0.762425i	$-0.724009\pi$
$17$	1.38842	−	2.40481i	0.336741	−	0.583253i	0.983818	+	0.179172i	$0.0573419\pi$
$18$		0			0
$19$	3.61533	+	6.26193i	0.829413	+	1.43658i	0.898500	+	0.438974i	$0.144658\pi$
$19$	3.61533	+	6.26193i	0.829413	+	1.43658i	−0.0690869	+	0.997611i	$0.522009\pi$
$20$	0.569796	−	0.986916i	0.127410	−	0.220681i
$21$		0			0
$22$	4.41686	+	7.65023i	0.941678	+	1.63103i
$23$	−0.412190	+	0.713934i	−0.0859476	+	0.148866i	−0.905795	−	0.423717i	$-0.860725\pi$
$23$	−0.412190	+	0.713934i	−0.0859476	+	0.148866i	0.819847	+	0.572583i	$0.194058\pi$
$24$		0			0
$25$	−2.48524	−	4.30456i	−0.497047	−	0.860911i
$26$	−0.277269	−	0.480243i	−0.0543768	−	0.0941834i
$27$		0			0
$28$	0.828555	−	0.474613i	0.156582	−	0.0896934i
$29$	−2.13910	+	3.70502i	−0.397220	+	0.688006i	−0.993382	−	0.114859i	$-0.963358\pi$
$29$	−2.13910	+	3.70502i	−0.397220	+	0.688006i	0.596162	+	0.802864i	$0.296692\pi$
$30$		0			0
$31$	−4.98199			−0.894791			−0.447396	−	0.894336i	$-0.647648\pi$
$31$	−4.98199			−0.894791			−0.447396	+	0.894336i	$0.647648\pi$
$32$	2.01801			0.356738
$33$		0			0
$34$	−2.13334	+	3.69505i	−0.365865	+	0.633696i
$35$	0.0284402	−	8.35419i	0.00480728	−	1.41212i
$36$		0			0
$37$	−3.74542	−	6.48725i	−0.615743	−	1.06650i	−0.990254	−	0.139275i	$-0.955523\pi$
$37$	−3.74542	−	6.48725i	−0.615743	−	1.06650i	0.374511	−	0.927222i	$-0.377811\pi$
$38$	−5.55503	−	9.62160i	−0.901145	−	1.56083i
$39$		0			0
$40$	3.97623	−	6.88703i	0.628697	−	1.08894i
$41$	−1.66569	−	2.88506i	−0.260137	−	0.450570i	0.706141	−	0.708071i	$-0.250434\pi$
$41$	−1.66569	−	2.88506i	−0.260137	−	0.450570i	−0.966278	+	0.257501i	$0.917101\pi$
$42$		0			0
$43$	3.93487	−	6.81540i	0.600063	−	1.03934i	−0.392748	−	0.919646i	$-0.628476\pi$
$43$	3.93487	−	6.81540i	0.600063	−	1.03934i	0.992811	−	0.119693i	$-0.0381910\pi$
$44$	−1.03745	−	1.79691i	−0.156401	−	0.270895i
$45$		0			0
$46$	0.633340	−	1.09698i	0.0933809	−	0.161740i
$47$	3.48149			0.507828			0.253914	−	0.967227i	$-0.418282\pi$
$47$	3.48149			0.507828			0.253914	+	0.967227i	$0.418282\pi$
$48$		0			0
$49$	3.54119	−	6.03821i	0.505885	−	0.862601i
$50$	3.81862	+	6.61405i	0.540035	+	0.935368i
$51$		0			0
$52$	0.0651258	+	0.112801i	0.00903132	+	0.0156427i
$53$	−1.45772	+	2.52485i	−0.200233	+	0.346814i	−0.948604	−	0.316467i	$-0.897503\pi$
$53$	−1.45772	+	2.52485i	−0.200233	+	0.346814i	0.748370	+	0.663281i	$0.230837\pi$
$54$		0			0
$55$	−18.1536			−2.44783
$56$	5.78194	−	3.31201i	0.772644	−	0.442586i
$57$		0			0
$58$	3.28677	−	5.69285i	0.431574	−	0.747508i
$59$	−2.39878			−0.312294			−0.156147	−	0.987734i	$-0.549907\pi$
$59$	−2.39878			−0.312294			−0.156147	+	0.987734i	$0.549907\pi$
$60$		0			0
$61$	3.20113			0.409862			0.204931	−	0.978776i	$-0.434303\pi$
$61$	3.20113			0.409862			0.204931	+	0.978776i	$0.434303\pi$
$62$	7.65494			0.972178
$63$		0			0
$64$	6.08239			0.760298
$65$	1.13959			0.141349
$66$		0			0
$67$	1.89927			0.232033			0.116017	−	0.993247i	$-0.462987\pi$
$67$	1.89927			0.232033			0.116017	+	0.993247i	$0.462987\pi$
$68$	0.501086	−	0.867907i	0.0607656	−	0.105249i
$69$		0			0
$70$	−0.0436991	+	12.8364i	−0.00522304	+	1.53424i
$71$	−1.60957			−0.191021			−0.0955104	−	0.995428i	$-0.530448\pi$
$71$	−1.60957			−0.191021			−0.0955104	+	0.995428i	$0.530448\pi$
$72$		0			0
$73$	7.70688	−	13.3487i	0.902022	−	1.56235i	0.0771572	−	0.997019i	$-0.475416\pi$
$73$	7.70688	−	13.3487i	0.902022	−	1.56235i	0.824865	−	0.565330i	$-0.191251\pi$
$74$	5.75492	+	9.96781i	0.668996	+	1.15873i
$75$		0			0
$76$	1.30478	+	2.25995i	0.149669	+	0.259234i
$77$	−13.1470	−	7.65023i	−1.49824	−	0.871824i
$78$		0			0
$79$	5.47282			0.615740			0.307870	−	0.951428i	$-0.400384\pi$
$79$	5.47282			0.615740			0.307870	+	0.951428i	$0.400384\pi$
$80$	−7.24916	+	12.5559i	−0.810481	+	1.40379i
$81$		0			0
$82$	2.55937	+	4.43296i	0.282635	+	0.489538i
$83$	−6.51742	+	11.2885i	−0.715380	+	1.23907i	0.247433	+	0.968905i	$0.420413\pi$
$83$	−6.51742	+	11.2885i	−0.715380	+	1.23907i	−0.962813	+	0.270170i	$0.912920\pi$
$84$		0			0
$85$	−4.38408	−	7.59346i	−0.475521	−	0.823626i
$86$	−6.04603	+	10.4720i	−0.651960	+	1.12923i
$87$		0			0
$88$	−7.23966	−	12.5395i	−0.771750	−	1.33671i
$89$	−7.13384	−	12.3562i	−0.756185	−	1.30975i	−0.944783	−	0.327697i	$-0.893728\pi$
$89$	−7.13384	−	12.3562i	−0.756185	−	1.30975i	0.188598	−	0.982054i	$-0.439606\pi$
$90$		0			0
$91$	0.825304	+	0.480243i	0.0865154	+	0.0503432i
$92$	−0.148761	+	0.257662i	−0.0155094	+	0.0268631i
$93$		0			0
$94$	−5.34939			−0.551748
$95$	22.8315			2.34247
$96$		0			0
$97$	−8.00266	+	13.8610i	−0.812547	+	1.40737i	0.0985289	+	0.995134i	$0.468586\pi$
$97$	−8.00266	+	13.8610i	−0.812547	+	1.40737i	−0.911076	+	0.412239i	$0.864747\pi$
$98$	−5.44113	+	9.27785i	−0.549637	+	0.937204i
$99$		0			0
$100$	−0.896931	−	1.55353i	−0.0896931	−	0.155353i
$101$	1.50375	+	2.60456i	0.149628	+	0.259164i	0.931090	−	0.364789i	$-0.118859\pi$
$101$	1.50375	+	2.60456i	0.149628	+	0.259164i	−0.781462	+	0.623953i	$0.785526\pi$
$102$		0			0
$103$	−4.86031	+	8.41831i	−0.478901	+	0.829481i	−0.999707	−	0.0241941i	$-0.992298\pi$
$103$	−4.86031	+	8.41831i	−0.478901	+	0.829481i	0.520806	+	0.853675i	$0.325631\pi$
$104$	0.454470	+	0.787165i	0.0445644	+	0.0771879i
$105$		0			0
$106$	2.23982	−	3.87948i	0.217551	−	0.376809i
$107$	5.21214	+	9.02770i	0.503877	+	0.872740i	0.999990	+	0.00448241i	$0.00142680\pi$
$107$	5.21214	+	9.02770i	0.503877	+	0.872740i	−0.496113	+	0.868258i	$0.665240\pi$
$108$		0			0
$109$	2.33713	−	4.04803i	0.223857	−	0.387731i	−0.732119	−	0.681177i	$-0.761469\pi$
$109$	2.33713	−	4.04803i	0.223857	−	0.387731i	0.955976	+	0.293445i	$0.0948019\pi$
$110$	27.8934			2.65953
$111$		0			0
$112$	−10.5412	+	6.03821i	−0.996049	+	0.570557i
$113$	2.34332	+	4.05875i	0.220441	+	0.381815i	0.954942	−	0.296793i	$-0.0959171\pi$
$113$	2.34332	+	4.05875i	0.220441	+	0.381815i	−0.734501	+	0.678608i	$0.762584\pi$
$114$		0			0
$115$	1.30153	+	2.25432i	0.121369	+	0.210217i
$116$	−0.772008	+	1.33716i	−0.0716791	+	0.124152i
$117$		0			0
$118$	3.68578			0.339304
$119$	0.0250107	−	7.34679i	0.00229273	−	0.673479i
$120$		0			0
$121$	−11.0264	+	19.0983i	−1.00240	+	1.73621i
$122$	−4.91860			−0.445310
$123$		0			0
$124$	−1.79802			−0.161467
$125$	0.0932326			0.00833898
$126$		0			0
$127$	−9.15945			−0.812770			−0.406385	−	0.913702i	$-0.633211\pi$
$127$	−9.15945			−0.812770			−0.406385	+	0.913702i	$0.633211\pi$
$128$	−13.3818			−1.18279
$129$		0			0
$130$	−1.75101			−0.153574
$131$	4.60582	−	7.97752i	0.402413	−	0.696999i	−0.591604	−	0.806229i	$-0.701505\pi$
$131$	4.60582	−	7.97752i	0.402413	−	0.696999i	0.994017	+	0.109230i	$0.0348384\pi$
$132$		0			0
$133$	16.5348	+	9.62160i	1.43375	+	0.834298i
$134$	−2.91828			−0.252101
$135$		0			0
$136$	3.49675	−	6.05655i	0.299844	−	0.519345i
$137$	3.41219	+	5.91009i	0.291523	+	0.504933i	0.974170	−	0.225815i	$-0.0725046\pi$
$137$	3.41219	+	5.91009i	0.291523	+	0.504933i	−0.682647	+	0.730748i	$0.739171\pi$
$138$		0			0
$139$	2.84332	+	4.92477i	0.241167	+	0.417714i	0.961047	−	0.276385i	$-0.0891365\pi$
$139$	2.84332	+	4.92477i	0.241167	+	0.417714i	−0.719880	+	0.694099i	$0.755803\pi$
$140$	0.0102642	−	3.01506i	0.000867483	−	0.254819i
$141$		0			0
$142$	2.47314			0.207541
$143$	1.03745	−	1.79691i	0.0867557	−	0.150265i
$144$		0			0
$145$	6.75442	+	11.6990i	0.560924	+	0.971549i
$146$	−11.8418	+	20.5106i	−0.980035	+	1.69747i
$147$		0			0
$148$	−1.35173	−	2.34127i	−0.111112	−	0.192451i
$149$	10.7943	−	18.6962i	0.884301	−	1.53165i	0.0377873	−	0.999286i	$-0.487969\pi$
$149$	10.7943	−	18.6962i	0.884301	−	1.53165i	0.846513	−	0.532368i	$-0.178698\pi$
$150$		0			0
$151$	2.77776	+	4.81123i	0.226051	+	0.391532i	0.956634	−	0.291292i	$-0.0940850\pi$
$151$	2.77776	+	4.81123i	0.226051	+	0.391532i	−0.730583	+	0.682824i	$0.760752\pi$
$152$	9.10523	+	15.7707i	0.738532	+	1.27917i
$153$		0			0
$154$	20.2007	+	11.7548i	1.62782	+	0.947225i
$155$	−7.86557	+	13.6236i	−0.631778	+	1.09427i
$156$		0			0
$157$	6.07120			0.484534			0.242267	−	0.970210i	$-0.422109\pi$
$157$	6.07120			0.484534			0.242267	+	0.970210i	$0.422109\pi$
$158$	−8.40911			−0.668993
$159$		0			0
$160$	3.18605	−	5.51839i	0.251879	−	0.436267i
$161$	−0.00742511	+	2.18109i	−0.000585181	+	0.171894i
$162$		0			0
$163$	1.92630	+	3.33644i	0.150879	+	0.261330i	0.931551	−	0.363611i	$-0.118456\pi$
$163$	1.92630	+	3.33644i	0.150879	+	0.261330i	−0.780672	+	0.624941i	$0.785123\pi$
$164$	−0.601153	−	1.04123i	−0.0469422	−	0.0813063i
$165$		0			0
$166$	10.0142	−	17.3451i	0.777251	−	1.34624i
$167$	−1.76919	−	3.06432i	−0.136904	−	0.237124i	0.789419	−	0.613854i	$-0.210382\pi$
$167$	−1.76919	−	3.06432i	−0.136904	−	0.237124i	−0.926323	+	0.376730i	$0.877048\pi$
$168$		0			0
$169$	6.43487	−	11.1455i	0.494990	−	0.857348i
$170$	6.73625	+	11.6675i	0.516647	+	0.894858i
$171$		0			0
$172$	1.42011	−	2.45970i	0.108282	−	0.187551i
$173$	9.85358			0.749154			0.374577	−	0.927196i	$-0.377788\pi$
$173$	9.85358			0.749154			0.374577	+	0.927196i	$0.377788\pi$
$174$		0			0
$175$	−11.3663	−	6.61405i	−0.859214	−	0.499975i
$176$	13.1988	+	22.8610i	0.994897	+	1.72321i
$177$		0			0
$178$	10.9613	+	18.9855i	0.821585	+	1.42303i
$179$	−9.94855	+	17.2314i	−0.743590	+	1.28794i	0.207261	+	0.978286i	$0.433545\pi$
$179$	−9.94855	+	17.2314i	−0.743590	+	1.28794i	−0.950851	+	0.309649i	$0.899788\pi$
$180$		0			0
$181$	12.0930			0.898869			0.449434	−	0.893313i	$-0.351626\pi$
$181$	12.0930			0.898869			0.449434	+	0.893313i	$0.351626\pi$
$182$	−1.26810	−	0.737905i	−0.0939978	−	0.0546971i
$183$		0			0
$184$	−1.03811	+	1.79805i	−0.0765301	+	0.132554i
$185$	−23.6531			−1.73901
$186$		0			0
$187$	−15.9645			−1.16744
$188$	1.25648			0.0916385
$189$		0			0
$190$	−35.0812			−2.54506
$191$	−9.71964			−0.703288			−0.351644	−	0.936134i	$-0.614377\pi$
$191$	−9.71964			−0.703288			−0.351644	+	0.936134i	$0.614377\pi$
$192$		0			0
$193$	−2.30185			−0.165691			−0.0828454	−	0.996562i	$-0.526401\pi$
$193$	−2.30185			−0.165691			−0.0828454	+	0.996562i	$0.526401\pi$
$194$	12.2963	−	21.2978i	0.882821	−	1.52909i
$195$		0			0
$196$	1.27803	−	2.17921i	0.0912879	−	0.155658i
$197$	−5.06470			−0.360845			−0.180422	−	0.983589i	$-0.557746\pi$
$197$	−5.06470			−0.360845			−0.180422	+	0.983589i	$0.557746\pi$
$198$		0			0
$199$	4.97666	−	8.61982i	0.352786	−	0.611043i	−0.633951	−	0.773374i	$-0.718568\pi$
$199$	4.97666	−	8.61982i	0.352786	−	0.611043i	0.986736	+	0.162330i	$0.0519011\pi$
$200$	−6.25909	−	10.8411i	−0.442585	−	0.766579i
$201$		0			0
$202$	−2.31054	−	4.00197i	−0.162569	−	0.281578i
$203$	−0.0385333	+	11.3190i	−0.00270450	+	0.794436i
$204$		0			0
$205$	−10.5192			−0.734691
$206$	7.46798	−	12.9349i	0.520319	−	0.901219i
$207$		0			0
$208$	−0.828555	−	1.43510i	−0.0574500	−	0.0995062i
$209$	20.7851	−	36.0008i	1.43774	−	2.49023i
$210$		0			0
$211$	11.6503	+	20.1790i	0.802042	+	1.38918i	0.918270	+	0.395955i	$0.129586\pi$
$211$	11.6503	+	20.1790i	0.802042	+	1.38918i	−0.116228	+	0.993223i	$0.537080\pi$
$212$	−0.526097	+	0.911226i	−0.0361325	+	0.0625833i
$213$		0			0
$214$	−8.00858	−	13.8713i	−0.547455	−	0.948220i
$215$	−12.4248	−	21.5204i	−0.847363	−	1.46768i
$216$		0			0
$217$	−11.4375	+	6.55165i	−0.776430	+	0.444755i
$218$	−3.59106	+	6.21990i	−0.243217	+	0.421265i
$219$		0			0
$220$	−6.55170			−0.441715
$221$	1.00217			0.0674134
$222$		0			0
$223$	5.93770	−	10.2844i	0.397618	−	0.688694i	−0.595814	−	0.803123i	$-0.703170\pi$
$223$	5.93770	−	10.2844i	0.397618	−	0.688694i	0.993431	+	0.114429i	$0.0365037\pi$
$224$	4.63291	−	2.65382i	0.309549	−	0.177316i
$225$		0			0
$226$	−3.60056	−	6.23636i	−0.239506	−	0.414836i
$227$	2.98040	+	5.16221i	0.197816	+	0.342628i	0.947820	−	0.318806i	$-0.103282\pi$
$227$	2.98040	+	5.16221i	0.197816	+	0.342628i	−0.750004	+	0.661434i	$0.769948\pi$
$228$		0			0
$229$	11.8603	−	20.5427i	0.783752	−	1.35750i	−0.145990	−	0.989286i	$-0.546637\pi$
$229$	11.8603	−	20.5427i	0.783752	−	1.35750i	0.929742	−	0.368212i	$-0.120030\pi$
$230$	−1.99984	−	3.46382i	−0.131865	−	0.228398i
$231$		0			0
$232$	−5.38733	+	9.33114i	−0.353696	+	0.612619i
$233$	−6.92961	−	12.0024i	−0.453974	−	0.786306i	0.544654	−	0.838661i	$-0.316661\pi$
$233$	−6.92961	−	12.0024i	−0.453974	−	0.786306i	−0.998629	+	0.0523544i	$0.983327\pi$
$234$		0			0
$235$	5.49659	−	9.52037i	0.358558	−	0.621040i
$236$	−0.865728			−0.0563541
$237$		0			0
$238$	−0.0384296	+	11.2885i	−0.00249102	+	0.731725i
$239$	11.1713	+	19.3492i	0.722610	+	1.25160i	0.959950	+	0.280171i	$0.0903911\pi$
$239$	11.1713	+	19.3492i	0.722610	+	1.25160i	−0.237340	+	0.971427i	$0.576276\pi$
$240$		0			0
$241$	−4.86031	−	8.41831i	−0.313080	−	0.542271i	0.665947	−	0.745999i	$-0.268028\pi$
$241$	−4.86031	−	8.41831i	−0.313080	−	0.542271i	−0.979028	+	0.203728i	$0.934694\pi$
$242$	16.9424	−	29.3450i	1.08910	−	1.88637i
$243$		0			0
$244$	1.15530			0.0739604
$245$	−10.9210	−	19.2168i	−0.697719	−	1.22771i
$246$		0			0
$247$	−1.30478	+	2.25995i	−0.0830215	+	0.143797i
$248$	−12.5472			−0.796747
$249$		0			0
$250$	−0.143254			−0.00906018
$251$	6.51950			0.411507			0.205754	−	0.978604i	$-0.434035\pi$
$251$	6.51950			0.411507			0.205754	+	0.978604i	$0.434035\pi$
$252$		0			0
$253$	4.73950			0.297970
$254$	14.0737			0.883063
$255$		0			0
$256$	8.39661			0.524788
$257$	2.76501	−	4.78914i	0.172477	−	0.298738i	−0.766808	−	0.641876i	$-0.778156\pi$
$257$	2.76501	−	4.78914i	0.172477	−	0.298738i	0.939285	+	0.343138i	$0.111490\pi$
$258$		0			0
$259$	−17.1298	−	9.96781i	−1.06439	−	0.619370i
$260$	0.411283			0.0255067
$261$		0			0
$262$	−7.07696	+	12.2576i	−0.437216	+	0.757280i
$263$	4.34749	+	7.53008i	0.268078	+	0.464325i	0.968365	−	0.249536i	$-0.0802782\pi$
$263$	4.34749	+	7.53008i	0.268078	+	0.464325i	−0.700288	+	0.713861i	$0.746945\pi$
$264$		0			0
$265$	4.60291	+	7.97247i	0.282754	+	0.489745i
$266$	−25.4062	−	14.7838i	−1.55775	−	0.906454i
$267$		0			0
$268$	0.685455			0.0418709
$269$	−1.88951	+	3.27272i	−0.115205	+	0.199541i	−0.917862	−	0.396900i	$-0.870086\pi$
$269$	−1.88951	+	3.27272i	−0.115205	+	0.199541i	0.802657	+	0.596442i	$0.203419\pi$
$270$		0			0
$271$	−3.30995	−	5.73300i	−0.201065	−	0.348255i	0.747807	−	0.663916i	$-0.231107\pi$
$271$	−3.30995	−	5.73300i	−0.201065	−	0.348255i	−0.948872	+	0.315661i	$0.897774\pi$
$272$	−6.37501	+	11.0418i	−0.386542	+	0.669510i
$273$		0			0
$274$	−5.24291	−	9.08099i	−0.316736	−	0.548602i
$275$	−14.2880	+	24.7476i	−0.861601	+	1.49234i
$276$		0			0
$277$	12.6329	+	21.8808i	0.759038	+	1.31469i	0.943342	+	0.331823i	$0.107664\pi$
$277$	12.6329	+	21.8808i	0.759038	+	1.31469i	−0.184303	+	0.982869i	$0.559003\pi$
$278$	−4.36882	−	7.56703i	−0.262025	−	0.453840i
$279$		0			0
$280$	0.0716270	−	21.0401i	0.00428053	−	1.25739i
$281$	3.71221	−	6.42974i	0.221452	−	0.383566i	−0.733797	−	0.679369i	$-0.762254\pi$
$281$	3.71221	−	6.42974i	0.221452	−	0.383566i	0.955249	+	0.295803i	$0.0955871\pi$
$282$		0			0
$283$	15.4203			0.916640			0.458320	−	0.888787i	$-0.348451\pi$
$283$	15.4203			0.916640			0.458320	+	0.888787i	$0.348451\pi$
$284$	−0.580900			−0.0344701
$285$		0			0
$286$	−1.59406	+	2.76100i	−0.0942588	+	0.163261i
$287$	−7.61810	−	4.43296i	−0.449682	−	0.261669i
$288$		0			0
$289$	4.64458	+	8.04465i	0.273211	+	0.473215i
$290$	−10.3783	−	17.9758i	−0.609436	−	1.05557i
$291$		0			0
$292$	2.78144	−	4.81760i	0.162772	−	0.281929i
$293$	15.2899	+	26.4828i	0.893243	+	1.54714i	0.835964	+	0.548784i	$0.184909\pi$
$293$	15.2899	+	26.4828i	0.893243	+	1.54714i	0.0572791	+	0.998358i	$0.481758\pi$
$294$		0			0
$295$	−3.78720	+	6.55962i	−0.220499	+	0.381916i
$296$	−9.43286	−	16.3382i	−0.548274	−	0.949639i
$297$		0			0
$298$	−16.5856	+	28.7272i	−0.960780	+	1.66412i
$299$	−0.297522			−0.0172061
$300$		0			0
$301$	0.0708821	−	20.8213i	0.00408557	−	1.20012i
$302$	−4.26810	−	7.39256i	−0.245602	−	0.425394i
$303$		0			0
$304$	−16.6000	−	28.7520i	−0.952074	−	1.64904i
$305$	5.05395	−	8.75369i	0.289388	−	0.501235i
$306$		0			0
$307$	−28.7794			−1.64252			−0.821262	−	0.570551i	$-0.806730\pi$
$307$	−28.7794			−1.64252			−0.821262	+	0.570551i	$0.806730\pi$
$308$	−4.74481	−	2.76100i	−0.270361	−	0.157322i
$309$		0			0
$310$	12.0856	−	20.9329i	0.686418	−	1.18891i
$311$	2.57255			0.145876			0.0729380	−	0.997336i	$-0.476762\pi$
$311$	2.57255			0.145876			0.0729380	+	0.997336i	$0.476762\pi$
$312$		0			0
$313$	−18.5145			−1.04650			−0.523250	−	0.852179i	$-0.675281\pi$
$313$	−18.5145			−1.04650			−0.523250	+	0.852179i	$0.675281\pi$
$314$	−9.32854			−0.526440
$315$		0			0
$316$	1.97516			0.111111
$317$	−15.5182			−0.871588			−0.435794	−	0.900046i	$-0.643532\pi$
$317$	−15.5182			−0.871588			−0.435794	+	0.900046i	$0.643532\pi$
$318$		0			0
$319$	24.5960			1.37711
$320$	9.60289	−	16.6327i	0.536818	−	0.929796i
$321$		0			0
$322$	0.0114089	−	3.35130i	0.000635791	−	0.186761i
$323$	20.0784			1.11719
$324$		0			0
$325$	0.896931	−	1.55353i	0.0497528	−	0.0861744i
$326$	−2.95980	−	5.12652i	−0.163928	−	0.283932i
$327$		0			0
$328$	−4.19505	−	7.26604i	−0.231633	−	0.401200i
$329$	7.99273	−	4.57840i	0.440653	−	0.252415i
$330$		0			0
$331$	31.5904			1.73636			0.868182	−	0.496246i	$-0.165289\pi$
$331$	31.5904			1.73636			0.868182	+	0.496246i	$0.165289\pi$
$332$	−2.35216	+	4.07407i	−0.129092	+	0.223593i
$333$		0			0
$334$	2.71839	+	4.70840i	0.148744	+	0.257632i
$335$	2.99858	−	5.19369i	0.163830	−	0.283762i
$336$		0			0
$337$	5.70406	+	9.87972i	0.310720	+	0.538183i	0.978518	−	0.206159i	$-0.0660965\pi$
$337$	5.70406	+	9.87972i	0.310720	+	0.538183i	−0.667798	+	0.744342i	$0.732763\pi$
$338$	−9.88733	+	17.1254i	−0.537800	+	0.931497i
$339$		0			0
$340$	−1.58223	−	2.74051i	−0.0858086	−	0.148625i
$341$	14.3211	+	24.8049i	0.775532	+	1.34326i
$342$		0			0
$343$	0.189142	−	18.5193i	0.0102127	−	0.999948i
$344$	9.91002	−	17.1647i	0.534312	−	0.925456i
$345$		0			0
$346$	−15.1403			−0.813945
$347$	4.08140			0.219101			0.109550	−	0.993981i	$-0.465059\pi$
$347$	4.08140			0.219101			0.109550	+	0.993981i	$0.465059\pi$
$348$		0			0
$349$	12.1389	−	21.0253i	0.649782	−	1.12546i	−0.333392	−	0.942788i	$-0.608193\pi$
$349$	12.1389	−	21.0253i	0.649782	−	1.12546i	0.983175	−	0.182668i	$-0.0584733\pi$
$350$	17.4646	+	10.1626i	0.933524	+	0.543216i
$351$		0			0
$352$	−5.80094	−	10.0475i	−0.309191	−	0.535535i
$353$	−17.0395	−	29.5133i	−0.906922	−	1.57083i	−0.818316	−	0.574768i	$-0.805092\pi$
$353$	−17.0395	−	29.5133i	−0.906922	−	1.57083i	−0.0886057	−	0.996067i	$-0.528241\pi$
$354$		0			0
$355$	−2.54119	+	4.40148i	−0.134873	+	0.233606i
$356$	−2.57463	−	4.45939i	−0.136455	−	0.236347i
$357$		0			0
$358$	15.2862	−	26.4764i	0.807900	−	1.39932i
$359$	2.74465	+	4.75388i	0.144857	+	0.250900i	0.929320	−	0.369276i	$-0.120394\pi$
$359$	2.74465	+	4.75388i	0.144857	+	0.250900i	−0.784462	+	0.620176i	$0.787061\pi$
$360$		0			0
$361$	−16.6412	+	28.8233i	−0.875851	+	1.51702i
$362$	−18.5812			−0.976608
$363$		0			0
$364$	0.297855	+	0.173322i	0.0156119	+	0.00908452i
$365$	−24.3353	−	42.1500i	−1.27377	−	2.20623i
$366$		0			0
$367$	6.81955	+	11.8118i	0.355978	+	0.616571i	0.987285	−	0.158962i	$-0.0508146\pi$
$367$	6.81955	+	11.8118i	0.355978	+	0.616571i	−0.631307	+	0.775533i	$0.717481\pi$
$368$	1.89259	−	3.27807i	0.0986583	−	0.170881i
$369$		0			0
$370$	36.3435			1.88941
$371$	−0.0262591	+	7.71349i	−0.00136330	+	0.400464i
$372$		0			0
$373$	−4.46189	+	7.72823i	−0.231028	+	0.400153i	−0.958111	−	0.286397i	$-0.907542\pi$
$373$	−4.46189	+	7.72823i	−0.231028	+	0.400153i	0.727083	+	0.686550i	$0.240876\pi$
$374$	24.5298			1.26841
$375$		0			0
$376$	8.76817			0.452184
$377$	−1.54402			−0.0795209
$378$		0			0
$379$	29.7035			1.52576			0.762882	−	0.646537i	$-0.223784\pi$
$379$	29.7035			1.52576			0.762882	+	0.646537i	$0.223784\pi$
$380$	8.23999			0.422703
$381$		0			0
$382$	14.9344			0.764113
$383$	−8.85505	+	15.3374i	−0.452472	+	0.783705i	−0.998539	−	0.0540370i	$-0.982791\pi$
$383$	−8.85505	+	15.3374i	−0.452472	+	0.783705i	0.546067	+	0.837742i	$0.316124\pi$
$384$		0			0
$385$	−41.6766	+	23.8732i	−2.12404	+	1.21669i
$386$	3.53685			0.180021
$387$		0			0
$388$	−2.88819	+	5.00249i	−0.146626	+	0.253963i
$389$	10.6628	+	18.4685i	0.540624	+	0.936388i	0.998868	+	0.0475619i	$0.0151451\pi$
$389$	10.6628	+	18.4685i	0.540624	+	0.936388i	−0.458244	+	0.888826i	$0.651522\pi$
$390$		0			0
$391$	1.14459	+	1.98248i	0.0578842	+	0.100258i
$392$	8.91853	−	15.2073i	0.450454	−	0.768084i
$393$		0			0
$394$	7.78203			0.392053
$395$	8.64050	−	14.9658i	0.434751	−	0.753010i
$396$		0			0
$397$	1.11783	+	1.93614i	0.0561024	+	0.0971722i	0.892713	−	0.450626i	$-0.148799\pi$
$397$	1.11783	+	1.93614i	0.0561024	+	0.0971722i	−0.836610	+	0.547799i	$0.815466\pi$
$398$	−7.64675	+	13.2446i	−0.383297	+	0.663890i
$399$		0			0
$400$	11.4111	+	19.7646i	0.570555	+	0.988231i
$401$	4.36851	−	7.56648i	0.218153	−	0.377852i	−0.736090	−	0.676883i	$-0.763330\pi$
$401$	4.36851	−	7.56648i	0.218153	−	0.377852i	0.954243	+	0.299031i	$0.0966635\pi$
$402$		0			0
$403$	−0.899009	−	1.55713i	−0.0447828	−	0.0775661i
$404$	0.542708	+	0.939997i	0.0270007	+	0.0467666i
$405$		0			0
$406$	0.0592072	−	17.3919i	0.00293841	−	0.863143i
$407$	−21.5330	+	37.2962i	−1.06735	+	1.84871i
$408$		0			0
$409$	−28.6920			−1.41873			−0.709363	−	0.704843i	$-0.751017\pi$
$409$	−28.6920			−1.41873			−0.709363	+	0.704843i	$0.751017\pi$
$410$	16.1630			0.798232
$411$		0			0
$412$	−1.75411	+	3.03820i	−0.0864186	+	0.149681i
$413$	−5.50706	+	3.15456i	−0.270985	+	0.155226i
$414$		0			0
$415$	20.5795	+	35.6447i	1.01021	+	1.74973i
$416$	0.364154	+	0.630734i	0.0178541	+	0.0309243i
$417$		0			0
$418$	−31.9368	+	55.3161i	−1.56208	+	2.70560i
$419$	4.32221	+	7.48628i	0.211154	+	0.365729i	0.952076	−	0.305862i	$-0.0989446\pi$
$419$	4.32221	+	7.48628i	0.211154	+	0.365729i	−0.740922	+	0.671591i	$0.765611\pi$
$420$		0			0
$421$	−9.23347	+	15.9928i	−0.450012	+	0.779444i	−0.998386	−	0.0567894i	$-0.981914\pi$
$421$	−9.23347	+	15.9928i	−0.450012	+	0.779444i	0.548374	+	0.836233i	$0.315247\pi$
$422$	−17.9010	−	31.0055i	−0.871408	−	1.50932i
$423$		0			0
$424$	−3.67128	+	6.35885i	−0.178293	+	0.308813i
$425$	−13.8022			−0.669506
$426$		0			0
$427$	7.34907	−	4.20970i	0.355647	−	0.203722i
$428$	1.88108	+	3.25813i	0.0909255	+	0.157488i
$429$		0			0
$430$	19.0910	+	33.0665i	0.920648	+	1.59461i
$431$	−2.90368	+	5.02932i	−0.139865	+	0.242254i	−0.927445	−	0.373958i	$-0.878000\pi$
$431$	−2.90368	+	5.02932i	−0.139865	+	0.242254i	0.787580	+	0.616212i	$0.211334\pi$
$432$		0			0
$433$	3.63877			0.174868			0.0874341	−	0.996170i	$-0.472133\pi$
$433$	3.63877			0.174868			0.0874341	+	0.996170i	$0.472133\pi$
$434$	17.5740	−	10.0668i	0.843581	−	0.483220i
$435$		0			0
$436$	0.843480	−	1.46095i	0.0403954	−	0.0699669i
$437$	−5.96081			−0.285144
$438$		0			0
$439$	−18.6619			−0.890684			−0.445342	−	0.895361i	$-0.646918\pi$
$439$	−18.6619			−0.890684			−0.445342	+	0.895361i	$0.646918\pi$
$440$	−45.7200			−2.17961
$441$		0			0
$442$	−1.53986			−0.0732437
$443$	26.0911			1.23962			0.619812	−	0.784750i	$-0.287209\pi$
$443$	26.0911			1.23962			0.619812	+	0.784750i	$0.287209\pi$
$444$		0			0
$445$	−45.0517			−2.13565
$446$	−9.12341	+	15.8022i	−0.432006	+	0.748256i
$447$		0			0
$448$	13.9638	−	7.99875i	0.659728	−	0.377905i
$449$	5.63824			0.266085			0.133042	−	0.991110i	$-0.457525\pi$
$449$	5.63824			0.266085			0.133042	+	0.991110i	$0.457525\pi$
$450$		0			0
$451$	−9.57631	+	16.5867i	−0.450931	+	0.781035i
$452$	0.845712	+	1.46482i	0.0397790	+	0.0688992i
$453$		0			0
$454$	−4.57946	−	7.93186i	−0.214925	−	0.372261i
$455$	2.61625	−	1.49864i	0.122652	−	0.0702574i
$456$		0			0
$457$	−19.9923			−0.935201			−0.467601	−	0.883940i	$-0.654881\pi$
$457$	−19.9923			−0.935201			−0.467601	+	0.883940i	$0.654881\pi$
$458$	−18.2236	+	31.5643i	−0.851535	+	1.47490i
$459$		0			0
$460$	0.469729	+	0.813594i	0.0219012	+	0.0379340i
$461$	18.7247	−	32.4322i	0.872098	−	1.51052i	0.0122753	−	0.999925i	$-0.496093\pi$
$461$	18.7247	−	32.4322i	0.872098	−	1.51052i	0.859823	−	0.510593i	$-0.170574\pi$
$462$		0			0
$463$	−1.22756	−	2.12620i	−0.0570497	−	0.0988130i	0.836090	−	0.548592i	$-0.184836\pi$
$463$	−1.22756	−	2.12620i	−0.0570497	−	0.0988130i	−0.893140	+	0.449779i	$0.851503\pi$
$464$	9.82178	−	17.0118i	0.455965	−	0.789754i
$465$		0			0
$466$	10.6475	+	18.4420i	0.493236	+	0.854311i
$467$	16.7054	+	28.9345i	0.773032	+	1.33893i	0.935894	+	0.352282i	$0.114594\pi$
$467$	16.7054	+	28.9345i	0.773032	+	1.33893i	−0.162862	+	0.986649i	$0.552072\pi$
$468$		0			0
$469$	4.36031	−	2.49768i	0.201341	−	0.115332i
$470$	−8.44563	+	14.6283i	−0.389568	+	0.674752i
$471$		0			0
$472$	−6.04135			−0.278076
$473$	−45.2445			−2.08034
$474$		0			0
$475$	17.9699	−	31.1248i	0.824515	−	1.42810i
$476$	0.00902647	−	2.65148i	0.000413727	−	0.121531i
$477$		0			0
$478$	−17.1649	−	29.7305i	−0.785106	−	1.35984i
$479$	17.3468	+	30.0455i	0.792595	+	1.37281i	0.924355	+	0.381533i	$0.124604\pi$
$479$	17.3468	+	30.0455i	0.792595	+	1.37281i	−0.131760	+	0.991282i	$0.542063\pi$
$480$		0			0
$481$	1.35173	−	2.34127i	0.0616338	−	0.106753i
$482$	7.46798	+	12.9349i	0.340157	+	0.589170i
$483$		0			0
$484$	−3.97948	+	6.89266i	−0.180885	+	0.313303i
$485$	25.2692	+	43.7676i	1.14742	+	1.98739i
$486$		0			0
$487$	−0.479909	+	0.831226i	−0.0217467	+	0.0376665i	−0.876694	−	0.481049i	$-0.840256\pi$
$487$	−0.479909	+	0.831226i	−0.0217467	+	0.0376665i	0.854947	+	0.518715i	$0.173589\pi$
$488$	8.06207			0.364953
$489$		0			0
$490$	16.7804	+	29.5270i	0.758062	+	1.33389i
$491$	7.88691	+	13.6605i	0.355931	+	0.616491i	0.987277	−	0.159011i	$-0.0508305\pi$
$491$	7.88691	+	13.6605i	0.355931	+	0.616491i	−0.631346	+	0.775501i	$0.717497\pi$
$492$		0			0
$493$	5.93993	+	10.2883i	0.267521	+	0.463360i
$494$	2.00483	−	3.47247i	0.0902017	−	0.156234i
$495$		0			0
$496$	22.8751			1.02712
$497$	−3.69522	+	2.11669i	−0.165753	+	0.0949467i
$498$		0			0
$499$	9.56437	−	16.5660i	0.428160	−	0.741595i	−0.568550	−	0.822649i	$-0.692495\pi$
$499$	9.56437	−	16.5660i	0.428160	−	0.741595i	0.996710	+	0.0810539i	$0.0258286\pi$
$500$	0.0336480			0.00150478
$501$		0			0
$502$	−10.0174			−0.447097
$503$	33.3898			1.48878			0.744388	−	0.667747i	$-0.232741\pi$
$503$	33.3898			1.48878			0.744388	+	0.667747i	$0.232741\pi$
$504$		0			0
$505$	9.49648			0.422588
$506$	−7.28235			−0.323740
$507$		0			0
$508$	−3.30568			−0.146666
$509$	16.7588	−	29.0271i	0.742822	−	1.28660i	−0.208384	−	0.978047i	$-0.566820\pi$
$509$	16.7588	−	29.0271i	0.742822	−	1.28660i	0.951206	−	0.308558i	$-0.0998463\pi$
$510$		0			0
$511$	0.138830	−	40.7808i	0.00614149	−	1.80403i
$512$	13.8619			0.612617
$513$		0			0
$514$	−4.24850	+	7.35862i	−0.187393	+	0.324575i
$515$	15.3470	+	26.5817i	0.676268	+	1.17133i
$516$		0			0
$517$	−10.0078	−	17.3341i	−0.440144	−	0.762351i
$518$	26.3204	+	15.3158i	1.15645	+	0.672936i
$519$		0			0
$520$	2.87007			0.125861
$521$	−13.3622	+	23.1439i	−0.585407	+	1.01395i	0.409418	+	0.912347i	$0.365732\pi$
$521$	−13.3622	+	23.1439i	−0.585407	+	1.01395i	−0.994825	+	0.101607i	$0.967601\pi$
$522$		0			0
$523$	−8.53219	−	14.7782i	−0.373086	−	0.646205i	0.616952	−	0.787001i	$-0.288367\pi$
$523$	−8.53219	−	14.7782i	−0.373086	−	0.646205i	−0.990039	+	0.140796i	$0.955034\pi$
$524$	1.66226	−	2.87912i	0.0726161	−	0.125775i
$525$		0			0
$526$	−6.68002	−	11.5701i	−0.291263	−	0.504482i
$527$	−6.91709	+	11.9808i	−0.301313	+	0.521890i
$528$		0			0
$529$	11.1602	+	19.3300i	0.485226	+	0.840436i
$530$	−7.07247	−	12.2499i	−0.307209	−	0.532101i
$531$		0			0
$532$	5.96749	+	3.47247i	0.258723	+	0.150551i
$533$	0.601153	−	1.04123i	0.0260388	−	0.0451006i
$534$		0			0
$535$	32.9158			1.42307
$536$	4.78334			0.206609
$537$		0			0
$538$	2.90327	−	5.02861i	0.125169	−	0.216799i
$539$	−40.2432	−	0.274004i	−1.73340	−	0.0118022i
$540$		0			0
$541$	−6.17128	−	10.6890i	−0.265324	−	0.459555i	0.702324	−	0.711857i	$-0.252146\pi$
$541$	−6.17128	−	10.6890i	−0.265324	−	0.459555i	−0.967648	+	0.252302i	$0.918812\pi$
$542$	5.08582	+	8.80889i	0.218455	+	0.378374i
$543$		0			0
$544$	2.80185	−	4.85295i	0.120128	−	0.208068i
$545$	−7.37975	−	12.7821i	−0.316114	−	0.547525i
$546$		0			0
$547$	−11.7212	+	20.3017i	−0.501163	+	0.868040i	0.498836	+	0.866696i	$0.333761\pi$
$547$	−11.7212	+	20.3017i	−0.501163	+	0.868040i	−0.999999	+	0.00134350i	$0.999572\pi$
$548$	1.23147	+	2.13297i	0.0526059	+	0.0911161i
$549$		0			0
$550$	21.9539	−	38.0252i	0.936117	−	1.62140i
$551$	−30.9341			−1.31784
$552$		0			0
$553$	12.5644	−	7.19713i	0.534291	−	0.306053i
$554$	−19.4108	−	33.6204i	−0.824684	−	1.42840i
$555$		0			0
$556$	1.02616	+	1.77737i	0.0435191	+	0.0753772i
$557$	−12.2557	+	21.2275i	−0.519292	+	0.899440i	0.480457	+	0.877018i	$0.340471\pi$
$557$	−12.2557	+	21.2275i	−0.519292	+	0.899440i	−0.999749	+	0.0224216i	$0.992862\pi$
$558$		0			0
$559$	2.84022			0.120129
$560$	−0.130585	+	38.3587i	−0.00551822	+	1.62095i
$561$		0			0
$562$	−5.70390	+	9.87944i	−0.240604	+	0.416739i
$563$	13.3714			0.563538			0.281769	−	0.959482i	$-0.409079\pi$
$563$	13.3714			0.563538			0.281769	+	0.959482i	$0.409079\pi$
$564$		0			0
$565$	14.7985			0.622580
$566$	−23.6936			−0.995916
$567$		0			0
$568$	−4.05372			−0.170090
$569$	14.2488			0.597341			0.298670	−	0.954356i	$-0.403457\pi$
$569$	14.2488			0.597341			0.298670	+	0.954356i	$0.403457\pi$
$570$		0			0
$571$	−29.3237			−1.22716			−0.613579	−	0.789633i	$-0.710271\pi$
$571$	−29.3237			−1.22716			−0.613579	+	0.789633i	$0.710271\pi$
$572$	0.374419	−	0.648512i	0.0156552	−	0.0271157i
$573$		0			0
$574$	11.7054	+	6.81134i	0.488573	+	0.284300i
$575$	4.09756			0.170880
$576$		0			0
$577$	9.05004	−	15.6751i	0.376758	−	0.652564i	−0.613830	−	0.789438i	$-0.710372\pi$
$577$	9.05004	−	15.6751i	0.376758	−	0.652564i	0.990588	+	0.136874i	$0.0437055\pi$
$578$	−7.13650	−	12.3608i	−0.296839	−	0.514141i
$579$		0			0
$580$	2.43770	+	4.22221i	0.101220	+	0.175318i
$581$	−0.117404	+	34.4868i	−0.00487072	+	1.43075i
$582$		0			0
$583$	16.7613			0.694184
$584$	19.4099	−	33.6189i	0.803186	−	1.39116i
$585$		0			0
$586$	−23.4932	−	40.6915i	−0.970496	−	1.68095i
$587$	3.26402	−	5.65345i	0.134721	−	0.233343i	−0.790770	−	0.612113i	$-0.790320\pi$
$587$	3.26402	−	5.65345i	0.134721	−	0.233343i	0.925491	+	0.378770i	$0.123653\pi$
$588$		0			0
$589$	−18.0115	−	31.1968i	−0.742151	−	1.28544i
$590$	5.81912	−	10.0790i	0.239569	−	0.414946i
$591$		0			0
$592$	17.1973	+	29.7866i	0.706804	+	1.22422i
$593$	−12.7202	−	22.0321i	−0.522357	−	0.904749i	−0.999662	−	0.0260111i	$-0.991719\pi$
$593$	−12.7202	−	22.0321i	−0.522357	−	0.904749i	0.477305	−	0.878738i	$-0.341614\pi$
$594$		0			0
$595$	−20.0508	−	11.6675i	−0.822002	−	0.478322i
$596$	3.89569	−	6.74753i	0.159574	−	0.276390i
$597$		0			0
$598$	0.457150			0.0186942
$599$	−6.17931			−0.252480			−0.126240	−	0.992000i	$-0.540291\pi$
$599$	−6.17931			−0.252480			−0.126240	+	0.992000i	$0.540291\pi$
$600$		0			0
$601$	6.46722	−	11.2016i	0.263804	−	0.456921i	−0.703446	−	0.710749i	$-0.748356\pi$
$601$	6.46722	−	11.2016i	0.263804	−	0.456921i	0.967249	+	0.253828i	$0.0816896\pi$
$602$	−0.108912	+	31.9924i	−0.00443892	+	1.30391i
$603$		0			0
$604$	1.00251	+	1.73639i	0.0407914	+	0.0706527i
$605$	34.8171	+	60.3050i	1.41552	+	2.45175i
$606$		0			0
$607$	11.5378	−	19.9840i	0.468304	−	0.811126i	−0.531040	−	0.847347i	$-0.678199\pi$
$607$	11.5378	−	19.9840i	0.468304	−	0.811126i	0.999344	+	0.0362205i	$0.0115319\pi$
$608$	7.29578	+	12.6367i	0.295883	+	0.512484i
$609$		0			0
$610$	−7.76551	+	13.4503i	−0.314416	+	0.544585i
$611$	0.628242	+	1.08815i	0.0254159	+	0.0440217i
$612$		0			0
$613$	8.81363	−	15.2657i	0.355979	−	0.616574i	−0.631306	−	0.775534i	$-0.717481\pi$
$613$	8.81363	−	15.2657i	0.355979	−	0.616574i	0.987285	+	0.158960i	$0.0508141\pi$
$614$	44.2201			1.78458
$615$		0			0
$616$	−33.1109	−	19.2672i	−1.33408	−	0.776296i
$617$	10.8220	+	18.7443i	0.435679	+	0.754618i	0.997351	−	0.0727418i	$-0.0231749\pi$
$617$	10.8220	+	18.7443i	0.435679	+	0.754618i	−0.561672	+	0.827360i	$0.689842\pi$
$618$		0			0
$619$	4.78970	+	8.29601i	0.192514	+	0.333445i	0.946083	−	0.323925i	$-0.105002\pi$
$619$	4.78970	+	8.29601i	0.192514	+	0.333445i	−0.753568	+	0.657370i	$0.771669\pi$
$620$	−2.83872	+	4.91680i	−0.114006	+	0.197463i
$621$		0			0
$622$	−3.95278			−0.158492
$623$	−32.6269	−	18.9855i	−1.30717	−	0.760639i
$624$		0			0
$625$	12.5734	−	21.7777i	0.502935	−	0.871109i
$626$	28.4479			1.13701
$627$		0			0
$628$	2.19112			0.0874352
$629$	−20.8008			−0.829384
$630$		0			0
$631$	−31.1742			−1.24103			−0.620514	−	0.784196i	$-0.713076\pi$
$631$	−31.1742			−1.24103			−0.620514	+	0.784196i	$0.713076\pi$
$632$	13.7833			0.548272
$633$		0			0
$634$	23.8441			0.946968
$635$	−14.4610	+	25.0471i	−0.573866	+	0.993965i
$636$		0			0
$637$	2.52627	+	0.0172006i	0.100094	+	0.000681512i
$638$	−37.7924			−1.49621
$639$		0			0
$640$	−21.1272	+	36.5933i	−0.835124	+	1.44648i
$641$	−4.12607	−	7.14656i	−0.162970	−	0.282272i	0.772963	−	0.634452i	$-0.218774\pi$
$641$	−4.12607	−	7.14656i	−0.162970	−	0.282272i	−0.935933	+	0.352179i	$0.885441\pi$
$642$		0			0
$643$	−12.2159	−	21.1585i	−0.481748	−	0.834411i	0.518033	−	0.855361i	$-0.326664\pi$
$643$	−12.2159	−	21.1585i	−0.481748	−	0.834411i	−0.999781	+	0.0209493i	$0.993331\pi$
$644$	−0.00267975	+	0.787165i	−0.000105597	+	0.0310186i
$645$		0			0
$646$	−30.8509			−1.21381
$647$	19.3432	−	33.5034i	0.760461	−	1.31716i	−0.182153	−	0.983270i	$-0.558307\pi$
$647$	19.3432	−	33.5034i	0.760461	−	1.31716i	0.942613	−	0.333886i	$-0.108360\pi$
$648$		0			0
$649$	6.89548	+	11.9433i	0.270671	+	0.468817i
$650$	−1.37816	+	2.38704i	−0.0540557	+	0.0936273i
$651$		0			0
$652$	0.695207	+	1.20413i	0.0272264	+	0.0471575i
$653$	3.82715	−	6.62882i	0.149768	−	0.259406i	−0.781374	−	0.624064i	$-0.785481\pi$
$653$	3.82715	−	6.62882i	0.149768	−	0.259406i	0.931142	+	0.364658i	$0.118814\pi$
$654$		0			0
$655$	−14.5434	−	25.1899i	−0.568257	−	0.984249i
$656$	7.64810	+	13.2469i	0.298608	+	0.517205i
$657$		0			0
$658$	−12.2810	+	7.03481i	−0.478764	+	0.274246i
$659$	19.2572	−	33.3545i	0.750156	−	1.29931i	−0.197591	−	0.980285i	$-0.563312\pi$
$659$	19.2572	−	33.3545i	0.750156	−	1.29931i	0.947747	−	0.319023i	$-0.103355\pi$
$660$		0			0
$661$	32.2132			1.25295			0.626474	−	0.779443i	$-0.284498\pi$
$661$	32.2132			1.25295			0.626474	+	0.779443i	$0.284498\pi$
$662$	−48.5393			−1.88654
$663$		0			0
$664$	−16.4142	+	28.4302i	−0.636994	+	1.10331i
$665$	52.4162	−	30.0250i	2.03261	−	1.16432i
$666$		0			0
$667$	−1.76343	−	3.05435i	−0.0682803	−	0.118265i
$668$	−0.638506	−	1.10592i	−0.0247045	−	0.0427895i
$669$		0			0
$670$	−4.60739	+	7.98023i	−0.177999	+	0.308303i
$671$	−9.20190	−	15.9382i	−0.355235	−	0.615285i
$672$		0			0
$673$	−0.630680	+	1.09237i	−0.0243109	+	0.0421077i	−0.877925	−	0.478798i	$-0.841073\pi$
$673$	−0.630680	+	1.09237i	−0.0243109	+	0.0421077i	0.853614	+	0.520906i	$0.174406\pi$
$674$	−8.76442	−	15.1804i	−0.337593	−	0.584728i
$675$		0			0
$676$	2.32237	−	4.02246i	0.0893219	−	0.154710i
$677$	−14.8318			−0.570031			−0.285016	−	0.958523i	$-0.591999\pi$
$677$	−14.8318			−0.570031			−0.285016	+	0.958523i	$0.591999\pi$
$678$		0			0
$679$	−0.144158	+	42.3459i	−0.00553229	+	1.62508i
$680$	−11.0414	−	19.1242i	−0.423417	−	0.733379i
$681$		0			0
$682$	−22.0047	−	38.1133i	−0.842605	−	1.45943i
$683$	−2.76560	+	4.79016i	−0.105823	+	0.183290i	−0.914074	−	0.405547i	$-0.867081\pi$
$683$	−2.76560	+	4.79016i	−0.105823	+	0.183290i	0.808251	+	0.588838i	$0.200414\pi$
$684$		0			0
$685$	21.5487			0.823334
$686$	−0.290621	+	28.4553i	−0.0110960	+	1.08643i
$687$		0			0
$688$	−18.0672	+	31.2933i	−0.688805	+	1.19305i
$689$	−1.05219			−0.0400854
$690$		0			0
$691$	8.63792			0.328602			0.164301	−	0.986410i	$-0.447463\pi$
$691$	8.63792			0.328602			0.164301	+	0.986410i	$0.447463\pi$
$692$	3.55620			0.135186
$693$		0			0
$694$	−6.27116			−0.238050
$695$	17.9562			0.681116
$696$		0			0
$697$	−9.25070			−0.350395
$698$	−18.6518	+	32.3058i	−0.705979	+	1.22279i
$699$		0			0
$700$	−4.10215	−	2.38704i	−0.155047	−	0.0902215i
$701$	−26.5897			−1.00428			−0.502140	−	0.864786i	$-0.667454\pi$
$701$	−26.5897			−1.00428			−0.502140	+	0.864786i	$0.667454\pi$
$702$		0			0
$703$	27.0818	−	46.9070i	1.02141	−	1.76913i
$704$	−17.4843	−	30.2837i	−0.658965	−	1.14136i
$705$		0			0
$706$	26.1816	+	45.3479i	0.985358	+	1.70669i
$707$	6.87745	+	4.00197i	0.258653	+	0.150510i
$708$		0			0
$709$	10.1261			0.380294			0.190147	−	0.981756i	$-0.439104\pi$
$709$	10.1261			0.380294			0.190147	+	0.981756i	$0.439104\pi$
$710$	3.90460	−	6.76297i	0.146537	−	0.253810i
$711$		0			0
$712$	−17.9666	−	31.1191i	−0.673328	−	1.16624i
$713$	2.05353	−	3.55681i	0.0769052	−	0.133204i
$714$		0			0
$715$	−3.27585	−	5.67394i	−0.122510	−	0.212193i
$716$	−3.59047	+	6.21888i	−0.134182	+	0.232410i
$717$		0			0
$718$	−4.21722	−	7.30445i	−0.157385	−	0.272600i
$719$	16.1938	+	28.0485i	0.603927	+	1.04603i	0.992220	+	0.124496i	$0.0397315\pi$
$719$	16.1938	+	28.0485i	0.603927	+	1.04603i	−0.388293	+	0.921536i	$0.626935\pi$
$720$		0			0
$721$	−0.0875527	+	25.7182i	−0.00326063	+	0.957796i
$722$	25.5695	−	44.2877i	0.951600	−	1.64822i
$723$		0			0
$724$	4.36443			0.162203
$725$	21.2646			0.789749
$726$		0			0
$727$	−12.6174	+	21.8540i	−0.467953	+	0.810519i	−0.999329	−	0.0366171i	$-0.988342\pi$
$727$	−12.6174	+	21.8540i	−0.467953	+	0.810519i	0.531376	+	0.847136i	$0.321675\pi$
$728$	2.07854	+	1.20950i	0.0770357	+	0.0448269i
$729$		0			0
$730$	37.3917	+	64.7644i	1.38393	+	2.39704i
$731$	−10.9265	−	18.9253i	−0.404132	−	0.699977i
$732$		0			0
$733$	−1.42336	+	2.46533i	−0.0525731	+	0.0910592i	−0.891114	−	0.453779i	$-0.850076\pi$
$733$	−1.42336	+	2.46533i	−0.0525731	+	0.0910592i	0.838541	+	0.544838i	$0.183409\pi$
$734$	−10.4784	−	18.1491i	−0.386765	−	0.669896i
$735$		0			0
$736$	−0.831806	+	1.44073i	−0.0306608	+	0.0531060i
$737$	−5.45962	−	9.45634i	−0.201108	−	0.348329i
$738$		0			0
$739$	−12.2708	+	21.2537i	−0.451390	+	0.781830i	−0.998473	−	0.0552485i	$-0.982405\pi$
$739$	−12.2708	+	21.2537i	−0.451390	+	0.781830i	0.547083	+	0.837078i	$0.315738\pi$
$740$	−8.53649			−0.313808
$741$		0			0
$742$	0.0403477	−	11.8520i	0.00148121	−	0.435099i
$743$	2.29535	+	3.97566i	0.0842082	+	0.145853i	0.905054	−	0.425298i	$-0.139831\pi$
$743$	2.29535	+	3.97566i	0.0842082	+	0.145853i	−0.820845	+	0.571151i	$0.806497\pi$
$744$		0			0
$745$	−34.0840	−	59.0353i	−1.24874	−	2.16288i
$746$	6.85581	−	11.8746i	0.251009	−	0.434760i
$747$		0			0
$748$	−5.76165			−0.210667
$749$	23.8380	+	13.8713i	0.871020	+	0.506845i
$750$		0			0
$751$	−15.7178	+	27.2240i	−0.573551	+	0.993419i	0.422647	+	0.906295i	$0.361101\pi$
$751$	−15.7178	+	27.2240i	−0.573551	+	0.993419i	−0.996197	+	0.0871246i	$0.972232\pi$
$752$	−15.9855			−0.582930
$753$		0			0
$754$	2.37242			0.0863983
$755$	17.5422			0.638425
$756$		0			0
$757$	29.5432			1.07376			0.536882	−	0.843657i	$-0.319602\pi$
$757$	29.5432			1.07376			0.536882	+	0.843657i	$0.319602\pi$
$758$	−45.6401			−1.65772
$759$		0			0
$760$	57.5015			2.08580
$761$	−23.2437	+	40.2592i	−0.842582	+	1.45940i	0.0451218	+	0.998981i	$0.485632\pi$
$761$	−23.2437	+	40.2592i	−0.842582	+	1.45940i	−0.887704	+	0.460414i	$0.847701\pi$
$762$		0			0
$763$	0.0421007	−	12.3669i	0.00152415	−	0.447711i
$764$	−3.50785			−0.126910
$765$		0			0
$766$	13.6060	−	23.5663i	0.491605	−	0.851484i
$767$	−0.432864	−	0.749743i	−0.0156298	−	0.0270716i
$768$		0			0
$769$	−7.08532	−	12.2721i	−0.255503	−	0.442545i	0.709529	−	0.704676i	$-0.248908\pi$
$769$	−7.08532	−	12.2721i	−0.255503	−	0.442545i	−0.965032	+	0.262132i	$0.915574\pi$
$770$	64.0371	−	36.6817i	2.30774	−	1.32192i
$771$		0			0
$772$	−0.830747			−0.0298992
$773$	−17.0042	+	29.4522i	−0.611600	+	1.05932i	0.379371	+	0.925245i	$0.376140\pi$
$773$	−17.0042	+	29.4522i	−0.611600	+	1.05932i	−0.990971	+	0.134078i	$0.957193\pi$
$774$		0			0
$775$	12.3814	+	21.4452i	0.444754	+	0.770336i
$776$	−20.1548	+	34.9091i	−0.723514	+	1.25316i
$777$		0			0
$778$	−16.3836	−	28.3772i	−0.587380	−	1.01737i
$779$	12.0440	−	20.8608i	0.431522	−	0.747417i
$780$		0			0
$781$	4.62684	+	8.01392i	0.165561	+	0.286761i
$782$	−1.75868	−	3.04613i	−0.0628904	−	0.108929i
$783$		0			0
$784$	−16.2596	+	27.7248i	−0.580700	+	0.990170i
$785$	9.58523	−	16.6021i	0.342111	−	0.592554i
$786$		0			0
$787$	−29.1059			−1.03751			−0.518757	−	0.854921i	$-0.673605\pi$
$787$	−29.1059			−1.03751			−0.518757	+	0.854921i	$0.673605\pi$
$788$	−1.82787			−0.0651151
$789$		0			0
$790$	−13.2763	+	22.9953i	−0.472351	+	0.818135i
$791$	10.7173	+	6.23636i	0.381062	+	0.221739i
$792$		0			0
$793$	0.577649	+	1.00052i	0.0205129	+	0.0355294i
$794$	−1.71757	−	2.97493i	−0.0609544	−	0.105576i
$795$		0			0
$796$	1.79609	−	3.11093i	0.0636609	−	0.110264i
$797$	−9.25192	−	16.0248i	−0.327720	−	0.567627i	0.654339	−	0.756201i	$-0.272947\pi$
$797$	−9.25192	−	16.0248i	−0.327720	−	0.567627i	−0.982059	+	0.188574i	$0.939613\pi$
$798$		0			0
$799$	4.83377	−	8.37234i	0.171007	−	0.296192i
$800$	−5.01524	−	8.68665i	−0.177316	−	0.307120i
$801$		0			0
$802$	−6.71231	+	11.6261i	−0.237020	+	0.410531i
$803$	−88.6162			−3.12720
$804$		0			0
$805$	5.95262	+	3.46382i	0.209802	+	0.122084i
$806$	1.38135	+	2.39257i	0.0486559	+	0.0842745i
$807$		0			0
$808$	3.78720	+	6.55962i	0.133233	+	0.230767i
$809$	20.5407	−	35.5775i	0.722172	−	1.25084i	−0.237956	−	0.971276i	$-0.576477\pi$
$809$	20.5407	−	35.5775i	0.722172	−	1.25084i	0.960128	−	0.279562i	$-0.0901892\pi$
$810$		0			0
$811$	−43.1361			−1.51471			−0.757357	−	0.653001i	$-0.773510\pi$
$811$	−43.1361			−1.51471			−0.757357	+	0.653001i	$0.773510\pi$
$812$	−0.0139068	+	4.08506i	−0.000488033	+	0.143357i
$813$		0			0
$814$	33.0860	−	57.3066i	1.15966	−	2.00859i
$815$	12.1650			0.426120
$816$		0			0
$817$	56.9034			1.99080
$818$	44.0859			1.54143
$819$		0			0
$820$	−3.79641			−0.132576
$821$	−13.1748			−0.459802			−0.229901	−	0.973214i	$-0.573840\pi$
$821$	−13.1748			−0.459802			−0.229901	+	0.973214i	$0.573840\pi$
$822$		0			0
$823$	−11.9817			−0.417654			−0.208827	−	0.977953i	$-0.566965\pi$
$823$	−11.9817			−0.417654			−0.208827	+	0.977953i	$0.566965\pi$
$824$	−12.2407	+	21.2016i	−0.426427	+	0.738592i
$825$		0			0
$826$	8.46173	−	4.84705i	0.294421	−	0.168650i
$827$	−29.9879			−1.04278			−0.521391	−	0.853318i	$-0.674587\pi$
$827$	−29.9879			−1.04278			−0.521391	+	0.853318i	$0.674587\pi$
$828$		0			0
$829$	−13.4619	+	23.3167i	−0.467551	+	0.809822i	−0.999313	−	0.0370721i	$-0.988197\pi$
$829$	−13.4619	+	23.3167i	−0.467551	+	0.809822i	0.531762	+	0.846894i	$0.321530\pi$
$830$	−31.6208	−	54.7688i	−1.09757	−	1.90105i
$831$		0			0
$832$	1.09758	+	1.90106i	0.0380517	+	0.0659074i
$833$	−9.60410	−	16.8995i	−0.332762	−	0.585532i
$834$		0			0
$835$	−11.1728			−0.386650
$836$	7.50142	−	12.9928i	0.259442	−	0.449367i
$837$		0			0
$838$	−6.64117	−	11.5029i	−0.229416	−	0.397359i
$839$	−5.61191	+	9.72012i	−0.193745	+	0.335576i	−0.946488	−	0.322738i	$-0.895397\pi$
$839$	−5.61191	+	9.72012i	−0.193745	+	0.335576i	0.752744	+	0.658314i	$0.228730\pi$
$840$		0			0
$841$	5.34853	+	9.26393i	0.184432	+	0.319446i
$842$	14.1874	−	24.5734i	0.488932	−	0.846855i
$843$		0			0
$844$	4.20465	+	7.28267i	0.144730	+	0.250680i
$845$	−20.3188	−	35.1932i	−0.698988	−	1.21068i
$846$		0			0
$847$	−0.198628	+	58.3460i	−0.00682494	+	2.00479i
$848$	6.69321	−	11.5930i	0.229846	−	0.398104i
$849$		0			0
$850$	21.2074			0.727408
$851$	6.17529			0.211686
$852$		0			0
$853$	6.09672	−	10.5598i	0.208748	−	0.361562i	−0.742573	−	0.669766i	$-0.766395\pi$
$853$	6.09672	−	10.5598i	0.208748	−	0.361562i	0.951320	+	0.308204i	$0.0997279\pi$
$854$	−11.2920	+	6.46830i	−0.386405	+	0.221341i
$855$		0			0
$856$	13.1268	+	22.7363i	0.448666	+	0.777112i
$857$	−18.7191	−	32.4225i	−0.639433	−	1.10753i	−0.985557	−	0.169341i	$-0.945836\pi$
$857$	−18.7191	−	32.4225i	−0.639433	−	1.10753i	0.346125	−	0.938188i	$-0.387497\pi$
$858$		0			0
$859$	−0.378867	+	0.656216i	−0.0129268	+	0.0223898i	−0.872416	−	0.488763i	$-0.837448\pi$
$859$	−0.378867	+	0.656216i	−0.0129268	+	0.0223898i	0.859490	+	0.511153i	$0.170781\pi$
$860$	−4.48415	−	7.76678i	−0.152908	−	0.264845i
$861$		0			0
$862$	4.46157	−	7.72767i	0.151962	−	0.263205i
$863$	11.7796	+	20.4029i	0.400983	+	0.694522i	0.993845	−	0.110782i	$-0.0353354\pi$
$863$	11.7796	+	20.4029i	0.400983	+	0.694522i	−0.592862	+	0.805304i	$0.702002\pi$
$864$		0			0
$865$	15.5569	−	26.9453i	0.528949	−	0.916167i
$866$	−5.59106			−0.189992
$867$		0			0
$868$	−4.12785	+	2.36452i	−0.140108	+	0.0802569i
$869$	−15.7321	−	27.2487i	−0.533673	−	0.924349i
$870$		0			0
$871$	0.342728	+	0.593622i	0.0116129	+	0.0201141i
$872$	5.88609	−	10.1950i	0.199328	−	0.345247i
$873$		0			0
$874$	9.15892			0.309805
$875$	0.214041	−	0.122607i	0.00723592	−	0.00414488i
$876$		0			0
$877$	−18.3370	+	31.7606i	−0.619196	+	1.07248i	0.370437	+	0.928857i	$0.379208\pi$
$877$	−18.3370	+	31.7606i	−0.619196	+	1.07248i	−0.989633	+	0.143621i	$0.954125\pi$
$878$	28.6744			0.967716
$879$		0			0
$880$	83.3532			2.80984
$881$	39.4357			1.32862			0.664311	−	0.747456i	$-0.268725\pi$
$881$	39.4357			1.32862			0.664311	+	0.747456i	$0.268725\pi$
$882$		0			0
$883$	−8.76912			−0.295105			−0.147552	−	0.989054i	$-0.547139\pi$
$883$	−8.76912			−0.295105			−0.147552	+	0.989054i	$0.547139\pi$
$884$	0.361688			0.0121649
$885$		0			0
$886$	−40.0895			−1.34683
$887$	3.91300	−	6.77752i	0.131386	−	0.227567i	−0.792825	−	0.609449i	$-0.791391\pi$
$887$	3.91300	−	6.77752i	0.131386	−	0.227567i	0.924211	+	0.381882i	$0.124724\pi$
$888$		0			0
$889$	−21.0281	+	12.0453i	−0.705259	+	0.403986i
$890$	69.2230			2.32036
$891$		0			0
$892$	2.14294	−	3.71168i	0.0717508	−	0.124276i
$893$	12.5867	+	21.8008i	0.421199	+	0.729537i
$894$		0			0
$895$	31.4136	+	54.4100i	1.05004	+	1.81872i
$896$	−30.7215	+	17.5979i	−1.02633	+	0.587905i
$897$		0			0
$898$	−8.66329			−0.289098
$899$	10.6569	−	18.4584i	0.355429	−	0.615621i
$900$		0			0
$901$	4.04786	+	7.01109i	0.134854	+	0.233573i
$902$	14.7142	−	25.4858i	0.489930	−	0.848584i
$903$		0			0
$904$	5.90167	+	10.2220i	0.196287	+	0.339978i
$905$	19.0925	−	33.0692i	0.634657	−	1.09926i
$906$		0			0
$907$	−25.9666	−	44.9755i	−0.862208	−	1.49339i	−0.869793	−	0.493416i	$-0.835748\pi$
$907$	−25.9666	−	44.9755i	−0.862208	−	1.49339i	0.00758572	−	0.999971i	$-0.497585\pi$
$908$	1.07564	+	1.86306i	0.0356963	+	0.0618279i
$909$		0			0
$910$	−4.01993	+	2.30270i	−0.133259	+	0.0763336i
$911$	18.0762	−	31.3089i	0.598891	−	1.03731i	−0.394094	−	0.919070i	$-0.628941\pi$
$911$	18.0762	−	31.3089i	0.598891	−	1.03731i	0.992985	−	0.118240i	$-0.0377252\pi$
$912$		0			0
$913$	74.9394			2.48013
$914$	30.7187			1.01608
$915$		0			0
$916$	4.28043	−	7.41393i	0.141429	−	0.244963i
$917$	0.0829684	−	24.3716i	0.00273986	−	0.804821i
$918$		0			0
$919$	5.58842	+	9.67942i	0.184345	+	0.319295i	0.943356	−	0.331783i	$-0.107650\pi$
$919$	5.58842	+	9.67942i	0.184345	+	0.319295i	−0.759011	+	0.651078i	$0.774317\pi$
$920$	3.27793	+	5.67754i	0.108070	+	0.187183i
$921$		0			0
$922$	−28.7710	+	49.8328i	−0.947522	+	1.64116i
$923$	−0.290450	−	0.503074i	−0.00956028	−	0.0165589i
$924$		0			0
$925$	−18.6165	+	32.2447i	−0.612106	+	1.06020i
$926$	1.88618	+	3.26696i	0.0619837	+	0.107359i
$927$		0			0
$928$	−4.31673	+	7.47679i	−0.141703	+	0.245438i
$929$	−32.8384			−1.07739			−0.538696	−	0.842500i	$-0.681083\pi$
$929$	−32.8384			−1.07739			−0.538696	+	0.842500i	$0.681083\pi$
$930$		0			0
$931$	50.6134	+	0.344611i	1.65879	+	0.0112942i
$932$	−2.50092	−	4.33173i	−0.0819205	−	0.141890i
$933$		0			0
$934$	−25.6682	−	44.4586i	−0.839889	−	1.45473i
$935$	−25.2048	+	43.6560i	−0.824285	+	1.42770i
$936$		0			0
$937$	−25.9566			−0.847965			−0.423983	−	0.905670i	$-0.639368\pi$
$937$	−25.9566			−0.847965			−0.423983	+	0.905670i	$0.639368\pi$
$938$	−6.69972	+	3.83774i	−0.218754	+	0.125307i
$939$		0			0
$940$	1.98374	−	3.43594i	0.0647024	−	0.112068i
$941$	−29.4679			−0.960627			−0.480314	−	0.877097i	$-0.659477\pi$
$941$	−29.4679			−0.960627			−0.480314	+	0.877097i	$0.659477\pi$
$942$		0			0
$943$	2.74632			0.0894326
$944$	11.0141			0.358479
$945$		0			0
$946$	69.5192			2.26026
$947$	11.5227			0.374439			0.187219	−	0.982318i	$-0.440052\pi$
$947$	11.5227			0.374439			0.187219	+	0.982318i	$0.440052\pi$
$948$		0			0
$949$	5.56289			0.180579
$950$	−27.6111	+	47.8239i	−0.895824	+	1.55161i
$951$		0			0
$952$	0.0629898	−	18.5030i	0.00204151	−	0.599684i
$953$	−29.2912			−0.948835			−0.474417	−	0.880300i	$-0.657341\pi$
$953$	−29.2912			−0.948835			−0.474417	+	0.880300i	$0.657341\pi$
$954$		0			0
$955$	−15.3454	+	26.5790i	−0.496565	+	0.860076i
$956$	4.03176	+	6.98321i	0.130396	+	0.225853i
$957$		0			0
$958$	−26.6537	−	46.1656i	−0.861144	−	1.49154i
$959$	15.6058	+	9.08099i	0.503937	+	0.293240i
$960$		0			0
$961$	−6.17981			−0.199349
$962$	−2.07697	+	3.59742i	−0.0669643	+	0.115985i
$963$		0			0
$964$	−1.75411	−	3.03820i	−0.0564959	−	0.0978538i
$965$	−3.63417	+	6.29457i	−0.116988	+	0.202629i
$966$		0			0
$967$	−21.0402	−	36.4427i	−0.676606	−	1.17192i	−0.975997	−	0.217786i	$-0.930117\pi$
$967$	−21.0402	−	36.4427i	−0.676606	−	1.17192i	0.299390	−	0.954131i	$-0.403217\pi$
$968$	−27.7702	+	48.0993i	−0.892567	+	1.54597i
$969$		0			0
$970$	−38.8268	−	67.2500i	−1.24665	−	2.15927i
$971$	−17.5774	−	30.4450i	−0.564087	−	0.977027i	−0.997134	−	0.0756560i	$-0.975895\pi$
$971$	−17.5774	−	30.4450i	−0.564087	−	0.977027i	0.433047	−	0.901371i	$-0.357438\pi$
$972$		0			0
$973$	13.0040	+	7.56703i	0.416890	+	0.242588i
$974$	0.737391	−	1.27720i	0.0236275	−	0.0409241i
$975$		0			0
$976$	−14.6981			−0.470476
$977$	4.43025			0.141736			0.0708682	−	0.997486i	$-0.477423\pi$
$977$	4.43025			0.141736			0.0708682	+	0.997486i	$0.477423\pi$
$978$		0			0
$979$	−41.0136	+	71.0376i	−1.31080	+	2.27037i
$980$	−3.94144	−	6.93540i	−0.125905	−	0.221543i
$981$		0			0
$982$	−12.1184	−	20.9897i	−0.386714	−	0.669809i
$983$	11.0801	+	19.1912i	0.353399	+	0.612105i	0.986843	−	0.161684i	$-0.0516925\pi$
$983$	11.0801	+	19.1912i	0.353399	+	0.612105i	−0.633444	+	0.773789i	$0.718359\pi$
$984$		0			0
$985$	−7.99616	+	13.8498i	−0.254779	+	0.441290i
$986$	−9.12684	−	15.8081i	−0.290658	−	0.503434i
$987$		0			0
$988$	−0.470902	+	0.815626i	−0.0149814	+	0.0259485i
$989$	3.24383	+	5.61848i	0.103148	+	0.178657i
$990$		0			0
$991$	18.3602	−	31.8007i	0.583229	−	1.01018i	−0.411864	−	0.911245i	$-0.635122\pi$
$991$	18.3602	−	31.8007i	0.583229	−	1.01018i	0.995094	−	0.0989378i	$-0.0315445\pi$
$992$	−10.0537			−0.319206
$993$		0			0
$994$	5.67778	−	3.25235i	0.180088	−	0.103158i
$995$	−15.7143	−	27.2180i	−0.498178	−	0.862869i
$996$		0			0
$997$	19.9515	+	34.5571i	0.631872	+	1.09443i	0.987169	+	0.159681i	$0.0510464\pi$
$997$	19.9515	+	34.5571i	0.631872	+	1.09443i	−0.355297	+	0.934753i	$0.615620\pi$
$998$	−14.6959	+	25.4540i	−0.465190	+	0.805733i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.h.j.298.2		8
3.2	odd	2		567.2.h.k.298.3		8
7.2	even	3		567.2.g.k.541.3		8
9.2	odd	6		567.2.e.c.487.2	yes	8
9.4	even	3		567.2.g.k.109.3		8
9.5	odd	6		567.2.g.j.109.2		8
9.7	even	3		567.2.e.d.487.3	yes	8
21.2	odd	6		567.2.g.j.541.2		8
63.2	odd	6		567.2.e.c.163.2	✓	8
63.11	odd	6		3969.2.a.x.1.3		4
63.16	even	3		567.2.e.d.163.3	yes	8
63.23	odd	6		567.2.h.k.352.3		8
63.25	even	3		3969.2.a.s.1.2		4
63.38	even	6		3969.2.a.w.1.3		4
63.52	odd	6		3969.2.a.t.1.2		4
63.58	even	3	inner	567.2.h.j.352.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.2	✓	8	63.2	odd	6
567.2.e.c.487.2	yes	8	9.2	odd	6
567.2.e.d.163.3	yes	8	63.16	even	3
567.2.e.d.487.3	yes	8	9.7	even	3
567.2.g.j.109.2		8	9.5	odd	6
567.2.g.j.541.2		8	21.2	odd	6
567.2.g.k.109.3		8	9.4	even	3
567.2.g.k.541.3		8	7.2	even	3
567.2.h.j.298.2		8	1.1	even	1	trivial
567.2.h.j.352.2		8	63.58	even	3	inner
567.2.h.k.298.3		8	3.2	odd	2
567.2.h.k.352.3		8	63.23	odd	6
3969.2.a.s.1.2		4	63.25	even	3
3969.2.a.t.1.2		4	63.52	odd	6
3969.2.a.w.1.3		4	63.38	even	6
3969.2.a.x.1.3		4	63.11	odd	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.53652 q^{2} +0.360904 q^{4} +(1.57880 - 2.73457i) q^{5} +(2.29578 - 1.31507i) q^{7} +2.51851 q^{8} +O(q^{10})\)	\(q-1.53652 q^{2} +0.360904 q^{4} +(1.57880 - 2.73457i) q^{5} +(2.29578 - 1.31507i) q^{7} +2.51851 q^{8} +(-2.42587 + 4.20173i) q^{10} +(-2.87458 - 4.97892i) q^{11} +(0.180452 + 0.312552i) q^{13} +(-3.52752 + 2.02063i) q^{14} -4.59156 q^{16} +(1.38842 - 2.40481i) q^{17} +(3.61533 + 6.26193i) q^{19} +(0.569796 - 0.986916i) q^{20} +(4.41686 + 7.65023i) q^{22} +(-0.412190 + 0.713934i) q^{23} +(-2.48524 - 4.30456i) q^{25} +(-0.277269 - 0.480243i) q^{26} +(0.828555 - 0.474613i) q^{28} +(-2.13910 + 3.70502i) q^{29} -4.98199 q^{31} +2.01801 q^{32} +(-2.13334 + 3.69505i) q^{34} +(0.0284402 - 8.35419i) q^{35} +(-3.74542 - 6.48725i) q^{37} +(-5.55503 - 9.62160i) q^{38} +(3.97623 - 6.88703i) q^{40} +(-1.66569 - 2.88506i) q^{41} +(3.93487 - 6.81540i) q^{43} +(-1.03745 - 1.79691i) q^{44} +(0.633340 - 1.09698i) q^{46} +3.48149 q^{47} +(3.54119 - 6.03821i) q^{49} +(3.81862 + 6.61405i) q^{50} +(0.0651258 + 0.112801i) q^{52} +(-1.45772 + 2.52485i) q^{53} -18.1536 q^{55} +(5.78194 - 3.31201i) q^{56} +(3.28677 - 5.69285i) q^{58} -2.39878 q^{59} +3.20113 q^{61} +7.65494 q^{62} +6.08239 q^{64} +1.13959 q^{65} +1.89927 q^{67} +(0.501086 - 0.867907i) q^{68} +(-0.0436991 + 12.8364i) q^{70} -1.60957 q^{71} +(7.70688 - 13.3487i) q^{73} +(5.75492 + 9.96781i) q^{74} +(1.30478 + 2.25995i) q^{76} +(-13.1470 - 7.65023i) q^{77} +5.47282 q^{79} +(-7.24916 + 12.5559i) q^{80} +(2.55937 + 4.43296i) q^{82} +(-6.51742 + 11.2885i) q^{83} +(-4.38408 - 7.59346i) q^{85} +(-6.04603 + 10.4720i) q^{86} +(-7.23966 - 12.5395i) q^{88} +(-7.13384 - 12.3562i) q^{89} +(0.825304 + 0.480243i) q^{91} +(-0.148761 + 0.257662i) q^{92} -5.34939 q^{94} +22.8315 q^{95} +(-8.00266 + 13.8610i) q^{97} +(-5.44113 + 9.27785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8	\( 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8} + 7 q^{10} + 5 q^{11} + 5 q^{13} - 16 q^{14} - 2 q^{16} + 6 q^{17} + 8 q^{19} - 8 q^{20} + 7 q^{22} - 12 q^{23} - 8 q^{25} + q^{26} + 5 q^{28} - 10 q^{29} - 36 q^{31} + 20 q^{32} - 23 q^{35} - 20 q^{38} + 18 q^{40} - 5 q^{41} + 7 q^{43} + 13 q^{44} - 12 q^{46} + 42 q^{47} - 19 q^{49} + 38 q^{50} + 25 q^{52} - 12 q^{53} - 52 q^{55} + 6 q^{56} + 7 q^{58} - 12 q^{59} - 40 q^{61} - 36 q^{62} - 46 q^{64} - 16 q^{65} - 10 q^{67} + 51 q^{68} + 29 q^{70} + 18 q^{71} + 6 q^{73} - 5 q^{76} - 53 q^{77} - 20 q^{79} - 2 q^{80} + 35 q^{82} + 9 q^{83} + 9 q^{85} - 22 q^{86} - 18 q^{88} - 22 q^{89} + 13 q^{91} - 36 q^{92} - 30 q^{94} + 32 q^{95} + 9 q^{97} - 11 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8 + 7 * q^10 + 5 * q^11 + 5 * q^13 - 16 * q^14 - 2 * q^16 + 6 * q^17 + 8 * q^19 - 8 * q^20 + 7 * q^22 - 12 * q^23 - 8 * q^25 + q^26 + 5 * q^28 - 10 * q^29 - 36 * q^31 + 20 * q^32 - 23 * q^35 - 20 * q^38 + 18 * q^40 - 5 * q^41 + 7 * q^43 + 13 * q^44 - 12 * q^46 + 42 * q^47 - 19 * q^49 + 38 * q^50 + 25 * q^52 - 12 * q^53 - 52 * q^55 + 6 * q^56 + 7 * q^58 - 12 * q^59 - 40 * q^61 - 36 * q^62 - 46 * q^64 - 16 * q^65 - 10 * q^67 + 51 * q^68 + 29 * q^70 + 18 * q^71 + 6 * q^73 - 5 * q^76 - 53 * q^77 - 20 * q^79 - 2 * q^80 + 35 * q^82 + 9 * q^83 + 9 * q^85 - 22 * q^86 - 18 * q^88 - 22 * q^89 + 13 * q^91 - 36 * q^92 - 30 * q^94 + 32 * q^95 + 9 * q^97 - 11 * q^98

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