LMFDB - Embedded newform 567.2.e.c.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(163,567)]

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([0, 2]))

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

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

chi := DirichletCharacter("567.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, degree $2$, 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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.2
Root			$0.0512865 + 1.21608i$ of defining polynomial
Character	$\chi$	$=$	567.163
Dual form			567.2.e.c.487.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.768262 + 1.33067i) q^{2} +(-0.180452 - 0.312552i) q^{4} +(-1.57880 + 2.73457i) q^{5} +(-2.28677 + 1.33067i) q^{7} -2.51851 q^{8} +O(q^{10})$	\(q+(-0.768262 + 1.33067i) q^{2} +(-0.180452 - 0.312552i) q^{4} +(-1.57880 + 2.73457i) q^{5} +(-2.28677 + 1.33067i) q^{7} -2.51851 q^{8} +(-2.42587 - 4.20173i) q^{10} +(2.87458 + 4.97892i) q^{11} -0.360904 q^{13} +(-0.0138393 - 4.06523i) q^{14} +(2.29578 - 3.97640i) q^{16} +(-1.38842 - 2.40481i) q^{17} +(3.61533 - 6.26193i) q^{19} +1.13959 q^{20} -8.83372 q^{22} +(0.412190 - 0.713934i) q^{23} +(-2.48524 - 4.30456i) q^{25} +(0.277269 - 0.480243i) q^{26} +(0.828555 + 0.474613i) q^{28} -4.27819 q^{29} +(2.49099 + 4.31453i) q^{31} +(1.00901 + 1.74765i) q^{32} +4.26668 q^{34} +(-0.0284402 - 8.35419i) q^{35} +(-3.74542 + 6.48725i) q^{37} +(5.55503 + 9.62160i) q^{38} +(3.97623 - 6.88703i) q^{40} -3.33138 q^{41} -7.86975 q^{43} +(1.03745 - 1.79691i) q^{44} +(0.633340 + 1.09698i) q^{46} +(1.74075 - 3.01506i) q^{47} +(3.45864 - 6.08587i) q^{49} +7.63725 q^{50} +(0.0651258 + 0.112801i) q^{52} +(1.45772 + 2.52485i) q^{53} -18.1536 q^{55} +(5.75925 - 3.35130i) q^{56} +(3.28677 - 5.69285i) q^{58} +(-1.19939 - 2.07740i) q^{59} +(-1.60056 + 2.77226i) q^{61} -7.65494 q^{62} +6.08239 q^{64} +(0.569796 - 0.986916i) q^{65} +(-0.949637 - 1.64482i) q^{67} +(-0.501086 + 0.867907i) q^{68} +(11.1385 + 6.38036i) q^{70} +1.60957 q^{71} +(7.70688 + 13.3487i) q^{73} +(-5.75492 - 9.96781i) q^{74} -2.60957 q^{76} +(-13.1988 - 7.56054i) q^{77} +(-2.73641 + 4.73960i) q^{79} +(7.24916 + 12.5559i) q^{80} +(2.55937 - 4.43296i) q^{82} -13.0348 q^{83} +8.76817 q^{85} +(6.04603 - 10.4720i) q^{86} +(-7.23966 - 12.5395i) q^{88} +(7.13384 - 12.3562i) q^{89} +(0.825304 - 0.480243i) q^{91} -0.297522 q^{92} +(2.67470 + 4.63271i) q^{94} +(11.4158 + 19.7727i) q^{95} +16.0053 q^{97} +(5.44113 + 9.27785i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 5 q^{4} - 2 q^{5} + q^{7} - 6 q^{8}+O(q^{10}) $ 8 * q - q^2 - 5 * q^4 - 2 * q^5 + q^7 - 6 * q^8	$ 8 q - q^{2} - 5 q^{4} - 2 q^{5} + q^{7} - 6 q^{8} + 7 q^{10} - 5 q^{11} - 10 q^{13} - 23 q^{14} + q^{16} - 6 q^{17} + 8 q^{19} - 16 q^{20} - 14 q^{22} + 12 q^{23} - 8 q^{25} - q^{26} + 5 q^{28} - 20 q^{29} + 18 q^{31} + 10 q^{32} + 23 q^{35} + 20 q^{38} + 18 q^{40} - 10 q^{41} - 14 q^{43} - 13 q^{44} - 12 q^{46} + 21 q^{47} + 17 q^{49} + 76 q^{50} + 25 q^{52} + 12 q^{53} - 52 q^{55} + 39 q^{56} + 7 q^{58} - 6 q^{59} + 20 q^{61} + 36 q^{62} - 46 q^{64} - 8 q^{65} + 5 q^{67} - 51 q^{68} + 17 q^{70} - 18 q^{71} + 6 q^{73} + 10 q^{76} - 37 q^{77} + 10 q^{79} + 2 q^{80} + 35 q^{82} + 18 q^{83} - 18 q^{85} + 22 q^{86} - 18 q^{88} + 22 q^{89} + 13 q^{91} - 72 q^{92} + 15 q^{94} + 16 q^{95} - 18 q^{97} + 11 q^{98}+O(q^{100}) $ 8 * q - q^2 - 5 * q^4 - 2 * q^5 + q^7 - 6 * q^8 + 7 * q^10 - 5 * q^11 - 10 * q^13 - 23 * q^14 + q^16 - 6 * q^17 + 8 * q^19 - 16 * q^20 - 14 * q^22 + 12 * q^23 - 8 * q^25 - q^26 + 5 * q^28 - 20 * q^29 + 18 * q^31 + 10 * q^32 + 23 * q^35 + 20 * q^38 + 18 * q^40 - 10 * q^41 - 14 * q^43 - 13 * q^44 - 12 * q^46 + 21 * q^47 + 17 * q^49 + 76 * q^50 + 25 * q^52 + 12 * q^53 - 52 * q^55 + 39 * q^56 + 7 * q^58 - 6 * q^59 + 20 * q^61 + 36 * q^62 - 46 * q^64 - 8 * q^65 + 5 * q^67 - 51 * q^68 + 17 * q^70 - 18 * q^71 + 6 * q^73 + 10 * q^76 - 37 * q^77 + 10 * q^79 + 2 * q^80 + 35 * q^82 + 18 * q^83 - 18 * q^85 + 22 * q^86 - 18 * q^88 + 22 * q^89 + 13 * q^91 - 72 * q^92 + 15 * q^94 + 16 * q^95 - 18 * q^97 + 11 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.768262	+	1.33067i	−0.543243	+	0.940925i	0.455472	+	0.890250i	$0.349470\pi$
$2$	−0.768262	+	1.33067i	−0.543243	+	0.940925i	−0.998715	+	0.0506745i	$0.983863\pi$
$3$		0			0
$3$		0			0
$4$	−0.180452	−	0.312552i	−0.0902259	−	0.156276i
$5$	−1.57880	+	2.73457i	−0.706062	+	1.22294i	0.260245	+	0.965543i	$0.416197\pi$
$5$	−1.57880	+	2.73457i	−0.706062	+	1.22294i	−0.966307	+	0.257393i	$0.917137\pi$
$6$		0			0
$7$	−2.28677	+	1.33067i	−0.864318	+	0.502945i
$7$	−2.28677	+	1.33067i	−0.864318	+	0.502945i
$8$	−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	$0.167109\pi$
$11$	2.87458	+	4.97892i	0.866719	+	1.50120i	0.00138834	+	0.999999i	$0.499558\pi$
$12$		0			0
$13$	−0.360904			−0.100097			−0.0500484	−	0.998747i	$-0.515938\pi$
$13$	−0.360904			−0.100097			−0.0500484	+	0.998747i	$0.515938\pi$
$14$	−0.0138393	−	4.06523i	−0.00369871	−	1.08648i
$15$		0			0
$16$	2.29578	−	3.97640i	0.573945	−	0.994101i
$17$	−1.38842	−	2.40481i	−0.336741	−	0.583253i	0.647076	−	0.762425i	$-0.275991\pi$
$17$	−1.38842	−	2.40481i	−0.336741	−	0.583253i	−0.983818	+	0.179172i	$0.942658\pi$
$18$		0			0
$19$	3.61533	−	6.26193i	0.829413	−	1.43658i	−0.0690869	−	0.997611i	$-0.522009\pi$
$19$	3.61533	−	6.26193i	0.829413	−	1.43658i	0.898500	−	0.438974i	$-0.144658\pi$
$20$	1.13959			0.254820
$21$		0			0
$22$	−8.83372			−1.88336
$23$	0.412190	−	0.713934i	0.0859476	−	0.148866i	−0.819847	−	0.572583i	$-0.805942\pi$
$23$	0.412190	−	0.713934i	0.0859476	−	0.148866i	0.905795	+	0.423717i	$0.139275\pi$
$24$		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
$29$	−4.27819			−0.794440			−0.397220	−	0.917723i	$-0.630025\pi$
$29$	−4.27819			−0.794440			−0.397220	+	0.917723i	$0.630025\pi$
$30$		0			0
$31$	2.49099	+	4.31453i	0.447396	+	0.774912i	0.998216	−	0.0597122i	$-0.0190183\pi$
$31$	2.49099	+	4.31453i	0.447396	+	0.774912i	−0.550820	+	0.834624i	$0.685685\pi$
$32$	1.00901	+	1.74765i	0.178369	+	0.308944i
$33$		0			0
$34$	4.26668			0.731730
$35$	−0.0284402	−	8.35419i	−0.00480728	−	1.41212i
$36$		0			0
$37$	−3.74542	+	6.48725i	−0.615743	+	1.06650i	0.374511	+	0.927222i	$0.377811\pi$
$37$	−3.74542	+	6.48725i	−0.615743	+	1.06650i	−0.990254	+	0.139275i	$0.955523\pi$
$38$	5.55503	+	9.62160i	0.901145	+	1.56083i
$39$		0			0
$40$	3.97623	−	6.88703i	0.628697	−	1.08894i
$41$	−3.33138			−0.520274			−0.260137	−	0.965572i	$-0.583768\pi$
$41$	−3.33138			−0.520274			−0.260137	+	0.965572i	$0.583768\pi$
$42$		0			0
$43$	−7.86975			−1.20013			−0.600063	−	0.799953i	$-0.704858\pi$
$43$	−7.86975			−1.20013			−0.600063	+	0.799953i	$0.704858\pi$
$44$	1.03745	−	1.79691i	0.156401	−	0.270895i
$45$		0			0
$46$	0.633340	+	1.09698i	0.0933809	+	0.161740i
$47$	1.74075	−	3.01506i	0.253914	−	0.439792i	−0.710686	−	0.703509i	$-0.751615\pi$
$47$	1.74075	−	3.01506i	0.253914	−	0.439792i	0.964600	+	0.263718i	$0.0849487\pi$
$48$		0			0
$49$	3.45864	−	6.08587i	0.494092	−	0.869410i
$50$	7.63725			1.08007
$51$		0			0
$52$	0.0651258	+	0.112801i	0.00903132	+	0.0156427i
$53$	1.45772	+	2.52485i	0.200233	+	0.346814i	0.948604	−	0.316467i	$-0.102497\pi$
$53$	1.45772	+	2.52485i	0.200233	+	0.346814i	−0.748370	+	0.663281i	$0.769163\pi$
$54$		0			0
$55$	−18.1536			−2.44783
$56$	5.75925	−	3.35130i	0.769613	−	0.447836i
$57$		0			0
$58$	3.28677	−	5.69285i	0.431574	−	0.747508i
$59$	−1.19939	−	2.07740i	−0.156147	−	0.270455i	0.777329	−	0.629094i	$-0.216574\pi$
$59$	−1.19939	−	2.07740i	−0.156147	−	0.270455i	−0.933476	+	0.358639i	$0.883241\pi$
$60$		0			0
$61$	−1.60056	+	2.77226i	−0.204931	+	0.354951i	−0.950111	−	0.311913i	$-0.899030\pi$
$61$	−1.60056	+	2.77226i	−0.204931	+	0.354951i	0.745180	+	0.666864i	$0.232364\pi$
$62$	−7.65494			−0.972178
$63$		0			0
$64$	6.08239			0.760298
$65$	0.569796	−	0.986916i	0.0706745	−	0.122412i
$66$		0			0
$67$	−0.949637	−	1.64482i	−0.116017	−	0.200947i	0.802169	−	0.597097i	$-0.203679\pi$
$67$	−0.949637	−	1.64482i	−0.116017	−	0.200947i	−0.918186	+	0.396150i	$0.870346\pi$
$68$	−0.501086	+	0.867907i	−0.0607656	+	0.105249i
$69$		0			0
$70$	11.1385	+	6.38036i	1.33131	+	0.762599i
$71$	1.60957			0.191021			0.0955104	−	0.995428i	$-0.469552\pi$
$71$	1.60957			0.191021			0.0955104	+	0.995428i	$0.469552\pi$
$72$		0			0
$73$	7.70688	+	13.3487i	0.902022	+	1.56235i	0.824865	+	0.565330i	$0.191251\pi$
$73$	7.70688	+	13.3487i	0.902022	+	1.56235i	0.0771572	+	0.997019i	$0.475416\pi$
$74$	−5.75492	−	9.96781i	−0.668996	−	1.15873i
$75$		0			0
$76$	−2.60957			−0.299338
$77$	−13.1988	−	7.56054i	−1.50414	−	0.861603i
$78$		0			0
$79$	−2.73641	+	4.73960i	−0.307870	+	0.533247i	−0.977896	−	0.209091i	$-0.932950\pi$
$79$	−2.73641	+	4.73960i	−0.307870	+	0.533247i	0.670026	+	0.742337i	$0.266283\pi$
$80$	7.24916	+	12.5559i	0.810481	+	1.40379i
$81$		0			0
$82$	2.55937	−	4.43296i	0.282635	−	0.489538i
$83$	−13.0348			−1.43076			−0.715380	−	0.698735i	$-0.753746\pi$
$83$	−13.0348			−1.43076			−0.715380	+	0.698735i	$0.753746\pi$
$84$		0			0
$85$	8.76817			0.951041
$86$	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	−0.188598	−	0.982054i	$-0.560394\pi$
$89$	7.13384	−	12.3562i	0.756185	−	1.30975i	0.944783	−	0.327697i	$-0.106272\pi$
$90$		0			0
$91$	0.825304	−	0.480243i	0.0865154	−	0.0503432i
$92$	−0.297522			−0.0310188
$93$		0			0
$94$	2.67470	+	4.63271i	0.275874	+	0.477827i
$95$	11.4158	+	19.7727i	1.17123	+	2.02864i
$96$		0			0
$97$	16.0053			1.62509			0.812547	−	0.582896i	$-0.198080\pi$
$97$	16.0053			1.62509			0.812547	+	0.582896i	$0.198080\pi$
$98$	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	0.781462	−	0.623953i	$-0.214474\pi$
$101$	−1.50375	−	2.60456i	−0.149628	−	0.259164i	−0.931090	+	0.364789i	$0.881141\pi$
$102$		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	$0.325631\pi$
$104$	0.908940			0.0891289
$105$		0			0
$106$	−4.47964			−0.435101
$107$	−5.21214	+	9.02770i	−0.503877	+	0.872740i	0.496113	+	0.868258i	$0.334760\pi$
$107$	−5.21214	+	9.02770i	−0.503877	+	0.872740i	−0.999990	+	0.00448241i	$0.998573\pi$
$108$		0			0
$109$	2.33713	+	4.04803i	0.223857	+	0.387731i	0.955976	−	0.293445i	$-0.0948019\pi$
$109$	2.33713	+	4.04803i	0.223857	+	0.387731i	−0.732119	+	0.681177i	$0.761469\pi$
$110$	13.9467	−	24.1564i	1.32977	−	2.30322i
$111$		0			0
$112$	0.0413557	+	12.1480i	0.00390775	+	1.14788i
$113$	4.68664			0.440882			0.220441	−	0.975400i	$-0.429250\pi$
$113$	4.68664			0.440882			0.220441	+	0.975400i	$0.429250\pi$
$114$		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
$119$	6.37501	+	3.65173i	0.584396	+	0.334754i
$120$		0			0
$121$	−11.0264	+	19.0983i	−1.00240	+	1.73621i
$122$	−2.45930	−	4.25964i	−0.222655	−	0.385649i
$123$		0			0
$124$	0.899009	−	1.55713i	0.0807334	−	0.139834i
$125$	−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	$0.633211\pi$
$128$	−6.69088	+	11.5889i	−0.591396	+	1.02433i
$129$		0			0
$130$	0.875505	+	1.51642i	0.0767868	+	0.132999i
$131$	−4.60582	+	7.97752i	−0.402413	+	0.696999i	−0.994017	−	0.109230i	$-0.965162\pi$
$131$	−4.60582	+	7.97752i	−0.402413	+	0.696999i	0.591604	+	0.806229i	$0.298495\pi$
$132$		0			0
$133$	0.0651258	+	19.1304i	0.00564712	+	1.65882i
$134$	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	0.682647	−	0.730748i	$-0.260829\pi$
$137$	−3.41219	−	5.91009i	−0.291523	−	0.504933i	−0.974170	+	0.225815i	$0.927495\pi$
$138$		0			0
$139$	−5.68664			−0.482334			−0.241167	−	0.970484i	$-0.577530\pi$
$139$	−5.68664			−0.482334			−0.241167	+	0.970484i	$0.577530\pi$
$140$	−2.60599	+	1.51642i	−0.220246	+	0.128161i
$141$		0			0
$142$	−1.23657	+	2.14180i	−0.103771	+	0.179736i
$143$	−1.03745	−	1.79691i	−0.0867557	−	0.150265i
$144$		0			0
$145$	6.75442	−	11.6990i	0.560924	−	0.971549i
$146$	−23.6836			−1.96007
$147$		0			0
$148$	2.70347			0.222224
$149$	−10.7943	+	18.6962i	−0.884301	+	1.53165i	−0.0377873	+	0.999286i	$0.512031\pi$
$149$	−10.7943	+	18.6962i	−0.884301	+	1.53165i	−0.846513	+	0.532368i	$0.821302\pi$
$150$		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
$155$	−15.7311			−1.26356
$156$		0			0
$157$	−3.03560	−	5.25781i	−0.242267	−	0.419619i	0.719093	−	0.694914i	$-0.244558\pi$
$157$	−3.03560	−	5.25781i	−0.242267	−	0.419619i	−0.961360	+	0.275295i	$0.911224\pi$
$158$	−4.20456	−	7.28250i	−0.334496	−	0.579365i
$159$		0			0
$160$	−6.37209			−0.503758
$161$	0.00742511	+	2.18109i	0.000585181	+	0.171894i
$162$		0			0
$163$	1.92630	−	3.33644i	0.150879	−	0.261330i	−0.780672	−	0.624941i	$-0.785123\pi$
$163$	1.92630	−	3.33644i	0.150879	−	0.261330i	0.931551	+	0.363611i	$0.118456\pi$
$164$	0.601153	+	1.04123i	0.0469422	+	0.0813063i
$165$		0			0
$166$	10.0142	−	17.3451i	0.777251	−	1.34624i
$167$	−3.53837			−0.273807			−0.136904	−	0.990584i	$-0.543715\pi$
$167$	−3.53837			−0.273807			−0.136904	+	0.990584i	$0.543715\pi$
$168$		0			0
$169$	−12.8697			−0.989981
$170$	−6.73625	+	11.6675i	−0.516647	+	0.894858i
$171$		0			0
$172$	1.42011	+	2.45970i	0.108282	+	0.187551i
$173$	4.92679	−	8.53345i	0.374577	−	0.648786i	−0.615687	−	0.787991i	$-0.711121\pi$
$173$	4.92679	−	8.53345i	0.374577	−	0.648786i	0.990264	+	0.139205i	$0.0444546\pi$
$174$		0			0
$175$	11.4111	+	6.53651i	0.862598	+	0.494114i
$176$	26.3976			1.98979
$177$		0			0
$178$	10.9613	+	18.9855i	0.821585	+	1.42303i
$179$	9.94855	+	17.2314i	0.743590	+	1.28794i	0.950851	+	0.309649i	$0.100212\pi$
$179$	9.94855	+	17.2314i	0.743590	+	1.28794i	−0.207261	+	0.978286i	$0.566455\pi$
$180$		0			0
$181$	12.0930			0.898869			0.449434	−	0.893313i	$-0.351626\pi$
$181$	12.0930			0.898869			0.449434	+	0.893313i	$0.351626\pi$
$182$	0.00499466	+	1.46716i	0.000370229	+	0.108753i
$183$		0			0
$184$	−1.03811	+	1.79805i	−0.0765301	+	0.132554i
$185$	−11.8265	−	20.4842i	−0.869505	−	1.50603i
$186$		0			0
$187$	7.98225	−	13.8257i	0.583720	−	1.01103i
$188$	−1.25648			−0.0916385
$189$		0			0
$190$	−35.0812			−2.54506
$191$	−4.85982	+	8.41745i	−0.351644	+	0.609065i	−0.986538	−	0.163534i	$-0.947711\pi$
$191$	−4.85982	+	8.41745i	−0.351644	+	0.609065i	0.634894	+	0.772600i	$0.281044\pi$
$192$		0			0
$193$	1.15093	+	1.99346i	0.0828454	+	0.143492i	0.904471	−	0.426535i	$-0.140266\pi$
$193$	1.15093	+	1.99346i	0.0828454	+	0.143492i	−0.821626	+	0.570027i	$0.806933\pi$
$194$	−12.2963	+	21.2978i	−0.882821	+	1.52909i
$195$		0			0
$196$	−2.52627	+	0.0172006i	−0.180448	+	0.00122861i
$197$	5.06470			0.360845			0.180422	−	0.983589i	$-0.442254\pi$
$197$	5.06470			0.360845			0.180422	+	0.983589i	$0.442254\pi$
$198$		0			0
$199$	4.97666	+	8.61982i	0.352786	+	0.611043i	0.986736	−	0.162330i	$-0.0519011\pi$
$199$	4.97666	+	8.61982i	0.352786	+	0.611043i	−0.633951	+	0.773374i	$0.718568\pi$
$200$	6.25909	+	10.8411i	0.442585	+	0.766579i
$201$		0			0
$202$	4.62108			0.325138
$203$	9.78325	−	5.69285i	0.686649	−	0.399560i
$204$		0			0
$205$	5.25959	−	9.10987i	0.367346	−	0.636261i
$206$	−7.46798	−	12.9349i	−0.520319	−	0.901219i
$207$		0			0
$208$	−0.828555	+	1.43510i	−0.0574500	+	0.0995062i
$209$	41.5702			2.87547
$210$		0			0
$211$	−23.3007			−1.60408			−0.802042	−	0.597267i	$-0.796253\pi$
$211$	−23.3007			−1.60408			−0.802042	+	0.597267i	$0.796253\pi$
$212$	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
$218$	−7.18212			−0.486435
$219$		0			0
$220$	3.27585	+	5.67394i	0.220858	+	0.382537i
$221$	0.501086	+	0.867907i	0.0337067	+	0.0583817i
$222$		0			0
$223$	−11.8754			−0.795235			−0.397618	−	0.917551i	$-0.630163\pi$
$223$	−11.8754			−0.795235			−0.397618	+	0.917551i	$0.630163\pi$
$224$	−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	0.750004	−	0.661434i	$-0.230052\pi$
$227$	−2.98040	−	5.16221i	−0.197816	−	0.342628i	−0.947820	+	0.318806i	$0.896718\pi$
$228$		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	$-0.120030\pi$
$230$	−3.99968			−0.263731
$231$		0			0
$232$	10.7747			0.707392
$233$	6.92961	−	12.0024i	0.453974	−	0.786306i	−0.544654	−	0.838661i	$-0.683339\pi$
$233$	6.92961	−	12.0024i	0.453974	−	0.786306i	0.998629	+	0.0523544i	$0.0166725\pi$
$234$		0			0
$235$	5.49659	+	9.52037i	0.358558	+	0.621040i
$236$	−0.432864	+	0.749743i	−0.0281771	+	0.0488041i
$237$		0			0
$238$	−9.75692	+	5.67754i	−0.632447	+	0.368020i
$239$	22.3426			1.44522			0.722610	−	0.691256i	$-0.242942\pi$
$239$	22.3426			1.44522			0.722610	+	0.691256i	$0.242942\pi$
$240$		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
$245$	11.1817	+	19.0663i	0.714372	+	1.21810i
$246$		0			0
$247$	−1.30478	+	2.25995i	−0.0830215	+	0.143797i
$248$	−6.27359	−	10.8662i	−0.398373	−	0.690003i
$249$		0			0
$250$	0.0716270	−	0.124062i	0.00453009	−	0.00784635i
$251$	−6.51950			−0.411507			−0.205754	−	0.978604i	$-0.565965\pi$
$251$	−6.51950			−0.411507			−0.205754	+	0.978604i	$0.565965\pi$
$252$		0			0
$253$	4.73950			0.297970
$254$	7.03686	−	12.1882i	0.441532	−	0.764755i
$255$		0			0
$256$	−4.19830	−	7.27167i	−0.262394	−	0.454480i
$257$	−2.76501	+	4.78914i	−0.172477	+	0.298738i	−0.939285	−	0.343138i	$-0.888510\pi$
$257$	−2.76501	+	4.78914i	−0.172477	+	0.298738i	0.766808	+	0.641876i	$0.221844\pi$
$258$		0			0
$259$	−0.0674692	−	19.8188i	−0.00419233	−	1.23148i
$260$	−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	0.700288	−	0.713861i	$-0.253055\pi$
$263$	−4.34749	−	7.53008i	−0.268078	−	0.464325i	−0.968365	+	0.249536i	$0.919722\pi$
$264$		0			0
$265$	−9.20581			−0.565509
$266$	−25.5062	−	14.6105i	−1.56389	−	0.895827i
$267$		0			0
$268$	−0.342728	+	0.593622i	−0.0209354	+	0.0362612i
$269$	1.88951	+	3.27272i	0.115205	+	0.199541i	0.917862	−	0.396900i	$-0.129914\pi$
$269$	1.88951	+	3.27272i	0.115205	+	0.199541i	−0.802657	+	0.596442i	$0.796581\pi$
$270$		0			0
$271$	−3.30995	+	5.73300i	−0.201065	+	0.348255i	−0.948872	−	0.315661i	$-0.897774\pi$
$271$	−3.30995	+	5.73300i	−0.201065	+	0.348255i	0.747807	+	0.663916i	$0.231107\pi$
$272$	−12.7500			−0.773083
$273$		0			0
$274$	10.4858			0.633472
$275$	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
$281$	7.42442			0.442904			0.221452	−	0.975171i	$-0.428920\pi$
$281$	7.42442			0.442904			0.221452	+	0.975171i	$0.428920\pi$
$282$		0			0
$283$	−7.71013	−	13.3543i	−0.458320	−	0.793833i	0.540553	−	0.841310i	$-0.318215\pi$
$283$	−7.71013	−	13.3543i	−0.458320	−	0.793833i	−0.998872	+	0.0474771i	$0.984882\pi$
$284$	−0.290450	−	0.503074i	−0.0172350	−	0.0298520i
$285$		0			0
$286$	3.18812			0.188518
$287$	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
$293$	30.5797			1.78649			0.893243	−	0.449574i	$-0.148424\pi$
$293$	30.5797			1.78649			0.893243	+	0.449574i	$0.148424\pi$
$294$		0			0
$295$	7.57440			0.440999
$296$	9.43286	−	16.3382i	0.548274	−	0.949639i
$297$		0			0
$298$	−16.5856	−	28.7272i	−0.960780	−	1.66412i
$299$	−0.148761	+	0.257662i	−0.00860307	+	0.0149010i
$300$		0			0
$301$	17.9963	−	10.4720i	1.03729	−	0.603597i
$302$	−8.53620			−0.491203
$303$		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	$0.806730\pi$
$308$	0.0186884	+	5.48962i	0.00106487	+	0.312800i
$309$		0			0
$310$	12.0856	−	20.9329i	0.686418	−	1.18891i
$311$	1.28628	+	2.22789i	0.0729380	+	0.126332i	0.900188	−	0.435502i	$-0.143429\pi$
$311$	1.28628	+	2.22789i	0.0729380	+	0.126332i	−0.827250	+	0.561834i	$0.810096\pi$
$312$		0			0
$313$	9.25724	−	16.0340i	0.523250	−	0.906296i	−0.476383	−	0.879238i	$-0.658053\pi$
$313$	9.25724	−	16.0340i	0.523250	−	0.906296i	0.999634	−	0.0270587i	$-0.00861409\pi$
$314$	9.32854			0.526440
$315$		0			0
$316$	1.97516			0.111111
$317$	−7.75909	+	13.4391i	−0.435794	+	0.754817i	−0.997360	−	0.0726145i	$-0.976866\pi$
$317$	−7.75909	+	13.4391i	−0.435794	+	0.754817i	0.561566	+	0.827432i	$0.310199\pi$
$318$		0			0
$319$	−12.2980	−	21.3008i	−0.688556	−	1.19261i
$320$	−9.60289	+	16.6327i	−0.536818	+	0.929796i
$321$		0			0
$322$	−2.90802	−	1.66577i	−0.162057	−	0.0928297i
$323$	−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
$328$	8.39011			0.463266
$329$	0.0313574	+	9.21110i	0.00172879	+	0.507825i
$330$		0			0
$331$	−15.7952	+	27.3581i	−0.868182	+	1.50374i	−0.00432948	+	0.999991i	$0.501378\pi$
$331$	−15.7952	+	27.3581i	−0.868182	+	1.50374i	−0.863853	+	0.503745i	$0.831955\pi$
$332$	2.35216	+	4.07407i	0.129092	+	0.223593i
$333$		0			0
$334$	2.71839	−	4.70840i	0.148744	−	0.257632i
$335$	5.99716			0.327660
$336$		0			0
$337$	−11.4081			−0.621440			−0.310720	−	0.950502i	$-0.600570\pi$
$337$	−11.4081			−0.621440			−0.310720	+	0.950502i	$0.600570\pi$
$338$	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
$344$	19.8200			1.06862
$345$		0			0
$346$	7.57013	+	13.1118i	0.406973	+	0.704897i
$347$	2.04070	+	3.53459i	0.109550	+	0.189747i	0.915588	−	0.402117i	$-0.131726\pi$
$347$	2.04070	+	3.53459i	0.109550	+	0.189747i	−0.806038	+	0.591864i	$0.798392\pi$
$348$		0			0
$349$	−24.2779			−1.29956			−0.649782	−	0.760120i	$-0.725140\pi$
$349$	−24.2779			−1.29956			−0.649782	+	0.760120i	$0.725140\pi$
$350$	−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	$0.194908\pi$
$353$	17.0395	+	29.5133i	0.906922	+	1.57083i	0.0886057	+	0.996067i	$0.471759\pi$
$354$		0			0
$355$	−2.54119	+	4.40148i	−0.134873	+	0.233606i
$356$	−5.14926			−0.272910
$357$		0			0
$358$	−30.5724			−1.61580
$359$	−2.74465	+	4.75388i	−0.144857	+	0.250900i	−0.929320	−	0.369276i	$-0.879606\pi$
$359$	−2.74465	+	4.75388i	−0.144857	+	0.250900i	0.784462	+	0.620176i	$0.212939\pi$
$360$		0			0
$361$	−16.6412	−	28.8233i	−0.875851	−	1.51702i
$362$	−9.29062	+	16.0918i	−0.488304	+	0.845768i
$363$		0			0
$364$	−0.299029	−	0.171290i	−0.0156734	−	0.00897802i
$365$	−48.6706			−2.54754
$366$		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
$371$	−6.69321	−	3.83400i	−0.347494	−	0.199051i
$372$		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	$0.240876\pi$
$374$	12.2649	+	21.2435i	0.634204	+	1.09847i
$375$		0			0
$376$	−4.38408	+	7.59346i	−0.226092	+	0.391603i
$377$	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	$0.223784\pi$
$380$	4.12000	−	7.13604i	0.211351	−	0.366071i
$381$		0			0
$382$	−7.46722	−	12.9336i	−0.382056	−	0.661741i
$383$	8.85505	−	15.3374i	0.452472	−	0.783705i	−0.546067	−	0.837742i	$-0.683876\pi$
$383$	8.85505	−	15.3374i	0.452472	−	0.783705i	0.998539	+	0.0540370i	$0.0172089\pi$
$384$		0			0
$385$	41.5131	−	24.1564i	2.11570	−	1.23112i
$386$	−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	$-0.984855\pi$
$389$	−10.6628	−	18.4685i	−0.540624	−	0.936388i	0.458244	−	0.888826i	$-0.348478\pi$
$390$		0			0
$391$	−2.28917			−0.115768
$392$	−8.71063	+	15.3273i	−0.439953	+	0.774146i
$393$		0			0
$394$	−3.89101	+	6.73943i	−0.196026	+	0.339528i
$395$	−8.64050	−	14.9658i	−0.434751	−	0.753010i
$396$		0			0
$397$	1.11783	−	1.93614i	0.0561024	−	0.0971722i	−0.836610	−	0.547799i	$-0.815466\pi$
$397$	1.11783	−	1.93614i	0.0561024	−	0.0971722i	0.892713	+	0.450626i	$0.148799\pi$
$398$	−15.2935			−0.766594
$399$		0			0
$400$	−22.8222			−1.14111
$401$	−4.36851	+	7.56648i	−0.218153	+	0.377852i	−0.954243	−	0.299031i	$-0.903336\pi$
$401$	−4.36851	+	7.56648i	−0.218153	+	0.377852i	0.736090	+	0.676883i	$0.236670\pi$
$402$		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
$407$	−43.0660			−2.13470
$408$		0			0
$409$	14.3460	+	24.8480i	0.709363	+	1.22865i	0.965094	+	0.261905i	$0.0843506\pi$
$409$	14.3460	+	24.8480i	0.709363	+	1.22865i	−0.255731	+	0.966748i	$0.582316\pi$
$410$	8.08148	+	13.9975i	0.399116	+	0.691289i
$411$		0			0
$412$	3.50821			0.172837
$413$	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
$419$	8.64442			0.422307			0.211154	−	0.977453i	$-0.432278\pi$
$419$	8.64442			0.422307			0.211154	+	0.977453i	$0.432278\pi$
$420$		0			0
$421$	18.4669			0.900024			0.450012	−	0.893022i	$-0.351420\pi$
$421$	18.4669			0.900024			0.450012	+	0.893022i	$0.351420\pi$
$422$	17.9010	−	31.0055i	0.871408	−	1.50932i
$423$		0			0
$424$	−3.67128	−	6.35885i	−0.178293	−	0.308813i
$425$	−6.90111	+	11.9531i	−0.334753	+	0.579809i
$426$		0			0
$427$	−0.0288322	−	8.46933i	−0.00139529	−	0.409860i
$428$	3.76216			0.181851
$429$		0			0
$430$	19.0910	+	33.0665i	0.920648	+	1.59461i
$431$	2.90368	+	5.02932i	0.139865	+	0.242254i	0.927445	−	0.373958i	$-0.122000\pi$
$431$	2.90368	+	5.02932i	0.139865	+	0.242254i	−0.787580	+	0.616212i	$0.788666\pi$
$432$		0			0
$433$	3.63877			0.174868			0.0874341	−	0.996170i	$-0.472133\pi$
$433$	3.63877			0.174868			0.0874341	+	0.996170i	$0.472133\pi$
$434$	17.5051	−	10.1862i	0.840271	−	0.488952i
$435$		0			0
$436$	0.843480	−	1.46095i	0.0403954	−	0.0699669i
$437$	−2.98040	−	5.16221i	−0.142572	−	0.246942i
$438$		0			0
$439$	9.33095	−	16.1617i	0.445342	−	0.771355i	−0.552734	−	0.833358i	$-0.686415\pi$
$439$	9.33095	−	16.1617i	0.445342	−	0.771355i	0.998076	+	0.0620029i	$0.0197488\pi$
$440$	45.7200			2.17961
$441$		0			0
$442$	−1.53986			−0.0732437
$443$	13.0455	−	22.5955i	0.619812	−	1.07355i	−0.369708	−	0.929148i	$-0.620542\pi$
$443$	13.0455	−	22.5955i	0.619812	−	1.07355i	0.989520	−	0.144398i	$-0.0461244\pi$
$444$		0			0
$445$	22.5258	+	39.0159i	1.06783	+	1.84953i
$446$	9.12341	−	15.8022i	0.432006	−	0.748256i
$447$		0			0
$448$	−13.9090	+	8.09364i	−0.657140	+	0.382388i
$449$	−5.63824			−0.266085			−0.133042	−	0.991110i	$-0.542475\pi$
$449$	−5.63824			−0.266085			−0.133042	+	0.991110i	$0.542475\pi$
$450$		0			0
$451$	−9.57631	−	16.5867i	−0.450931	−	0.781035i
$452$	−0.845712	−	1.46482i	−0.0397790	−	0.0688992i
$453$		0			0
$454$	9.15892			0.429849
$455$	0.0102642	+	3.01506i	0.000481193	+	0.141348i
$456$		0			0
$457$	9.99616	−	17.3139i	0.467601	−	0.809908i	−0.531714	−	0.846924i	$-0.678452\pi$
$457$	9.99616	−	17.3139i	0.467601	−	0.809908i	0.999315	+	0.0370159i	$0.0117852\pi$
$458$	18.2236	+	31.5643i	0.851535	+	1.47490i
$459$		0			0
$460$	0.469729	−	0.813594i	0.0219012	−	0.0379340i
$461$	37.4495			1.74420			0.872098	−	0.489332i	$-0.162759\pi$
$461$	37.4495			1.74420			0.872098	+	0.489332i	$0.162759\pi$
$462$		0			0
$463$	2.45513			0.114099			0.0570497	−	0.998371i	$-0.481831\pi$
$463$	2.45513			0.114099			0.0570497	+	0.998371i	$0.481831\pi$
$464$	−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	0.162862	+	0.986649i	$0.447928\pi$
$467$	−16.7054	+	28.9345i	−0.773032	+	1.33893i	−0.935894	+	0.352282i	$0.885406\pi$
$468$		0			0
$469$	4.36031	+	2.49768i	0.201341	+	0.115332i
$470$	−16.8913			−0.779136
$471$		0			0
$472$	3.02067	+	5.23196i	0.139038	+	0.240821i
$473$	−22.6222	−	39.1828i	−1.04017	−	1.80163i
$474$		0			0
$475$	−35.9398			−1.64903
$476$	−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	$-0.875396\pi$
$479$	−17.3468	−	30.0455i	−0.792595	−	1.37281i	0.131760	−	0.991282i	$-0.457937\pi$
$480$		0			0
$481$	1.35173	−	2.34127i	0.0616338	−	0.106753i
$482$	14.9360			0.680315
$483$		0			0
$484$	7.95896			0.361771
$485$	−25.2692	+	43.7676i	−1.14742	+	1.98739i
$486$		0			0
$487$	−0.479909	−	0.831226i	−0.0217467	−	0.0376665i	0.854947	−	0.518715i	$-0.173589\pi$
$487$	−0.479909	−	0.831226i	−0.0217467	−	0.0376665i	−0.876694	+	0.481049i	$0.840256\pi$
$488$	4.03103	−	6.98195i	0.182476	−	0.316058i
$489$		0			0
$490$	−33.9614	+	0.231233i	−1.53422	+	0.0104460i
$491$	15.7738			0.711862			0.355931	−	0.934512i	$-0.384164\pi$
$491$	15.7738			0.711862			0.355931	+	0.934512i	$0.384164\pi$
$492$		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
$497$	−3.68072	+	2.14180i	−0.165103	+	0.0960730i
$498$		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	$0.0258286\pi$
$500$	0.0168240	+	0.0291400i	0.000752392	+	0.00130318i
$501$		0			0
$502$	5.00868	−	8.67529i	0.223548	−	0.387197i
$503$	−33.3898			−1.48878			−0.744388	−	0.667747i	$-0.767259\pi$
$503$	−33.3898			−1.48878			−0.744388	+	0.667747i	$0.767259\pi$
$504$		0			0
$505$	9.49648			0.422588
$506$	−3.64117	+	6.30670i	−0.161870	+	0.280367i
$507$		0			0
$508$	1.65284	+	2.86280i	0.0733330	+	0.127016i
$509$	−16.7588	+	29.0271i	−0.742822	+	1.28660i	0.208384	+	0.978047i	$0.433180\pi$
$509$	−16.7588	+	29.0271i	−0.742822	+	1.28660i	−0.951206	+	0.308558i	$0.900154\pi$
$510$		0			0
$511$	−35.3866	−	20.2701i	−1.56541	−	0.896698i
$512$	−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
$517$	20.0157			0.880287
$518$	26.4240	+	15.1362i	1.16101	+	0.665047i
$519$		0			0
$520$	−1.43504	+	2.48556i	−0.0629305	+	0.108999i
$521$	13.3622	+	23.1439i	0.585407	+	1.01395i	0.994825	+	0.101607i	$0.0323986\pi$
$521$	13.3622	+	23.1439i	0.585407	+	1.01395i	−0.409418	+	0.912347i	$0.634268\pi$
$522$		0			0
$523$	−8.53219	+	14.7782i	−0.373086	+	0.646205i	−0.990039	−	0.140796i	$-0.955034\pi$
$523$	−8.53219	+	14.7782i	−0.373086	+	0.646205i	0.616952	+	0.787001i	$0.288367\pi$
$524$	3.32452			0.145232
$525$		0			0
$526$	13.3600			0.582526
$527$	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
$533$	1.20231			0.0520777
$534$		0			0
$535$	−16.4579	−	28.5059i	−0.711537	−	1.23242i
$536$	2.39167	+	4.14250i	0.103304	+	0.178929i
$537$		0			0
$538$	−5.80654			−0.250338
$539$	40.2432	−	0.274004i	1.73340	−	0.0118022i
$540$		0			0
$541$	−6.17128	+	10.6890i	−0.265324	+	0.459555i	−0.967648	−	0.252302i	$-0.918812\pi$
$541$	−6.17128	+	10.6890i	−0.265324	+	0.459555i	0.702324	+	0.711857i	$0.252146\pi$
$542$	−5.08582	−	8.80889i	−0.218455	−	0.378374i
$543$		0			0
$544$	2.80185	−	4.85295i	0.120128	−	0.208068i
$545$	−14.7595			−0.632227
$546$		0			0
$547$	23.4424			1.00233			0.501163	−	0.865353i	$-0.332906\pi$
$547$	23.4424			1.00233			0.501163	+	0.865353i	$0.332906\pi$
$548$	−1.23147	+	2.13297i	−0.0526059	+	0.0911161i
$549$		0			0
$550$	21.9539	+	38.0252i	0.936117	+	1.62140i
$551$	−15.4671	+	26.7897i	−0.658919	+	1.14128i
$552$		0			0
$553$	−0.0492931	−	14.4796i	−0.00209616	−	0.615736i
$554$	−38.8215			−1.64937
$555$		0			0
$556$	1.02616	+	1.77737i	0.0435191	+	0.0753772i
$557$	12.2557	+	21.2275i	0.519292	+	0.899440i	0.999749	+	0.0224216i	$0.00713761\pi$
$557$	12.2557	+	21.2275i	0.519292	+	0.899440i	−0.480457	+	0.877018i	$0.659529\pi$
$558$		0			0
$559$	2.84022			0.120129
$560$	−33.2849	−	19.0663i	−1.40655	−	0.805697i
$561$		0			0
$562$	−5.70390	+	9.87944i	−0.240604	+	0.416739i
$563$	6.68571	+	11.5800i	0.281769	+	0.488039i	0.971821	−	0.235722i	$-0.0757454\pi$
$563$	6.68571	+	11.5800i	0.281769	+	0.488039i	−0.690051	+	0.723760i	$0.742412\pi$
$564$		0			0
$565$	−7.39927	+	12.8159i	−0.311290	+	0.539170i
$566$	23.6936			0.995916
$567$		0			0
$568$	−4.05372			−0.170090
$569$	7.12440	−	12.3398i	0.298670	−	0.517312i	−0.677162	−	0.735834i	$-0.736790\pi$
$569$	7.12440	−	12.3398i	0.298670	−	0.517312i	0.975832	+	0.218522i	$0.0701235\pi$
$570$		0			0
$571$	14.6618	+	25.3951i	0.613579	+	1.06275i	0.990632	+	0.136559i	$0.0436042\pi$
$571$	14.6618	+	25.3951i	0.613579	+	1.06275i	−0.377053	+	0.926192i	$0.623062\pi$
$572$	−0.374419	+	0.648512i	−0.0156552	+	0.0271157i
$573$		0			0
$574$	0.0461040	+	13.5428i	0.00192434	+	0.565267i
$575$	−4.09756			−0.170880
$576$		0			0
$577$	9.05004	+	15.6751i	0.376758	+	0.652564i	0.990588	−	0.136874i	$-0.0437055\pi$
$577$	9.05004	+	15.6751i	0.376758	+	0.652564i	−0.613830	+	0.789438i	$0.710372\pi$
$578$	7.13650	+	12.3608i	0.296839	+	0.514141i
$579$		0			0
$580$	−4.87539			−0.202440
$581$	29.8077	−	17.3451i	1.23663	−	0.719594i
$582$		0			0
$583$	−8.38067	+	14.5157i	−0.347092	+	0.601181i
$584$	−19.4099	−	33.6189i	−0.803186	−	1.39116i
$585$		0			0
$586$	−23.4932	+	40.6915i	−0.970496	+	1.68095i
$587$	6.52804			0.269441			0.134721	−	0.990884i	$-0.456986\pi$
$587$	6.52804			0.269441			0.134721	+	0.990884i	$0.456986\pi$
$588$		0			0
$589$	36.0230			1.48430
$590$	−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	−0.477305	−	0.878738i	$-0.658386\pi$
$593$	12.7202	−	22.0321i	0.522357	−	0.904749i	0.999662	−	0.0260111i	$-0.00828051\pi$
$594$		0			0
$595$	−20.0508	+	11.6675i	−0.822002	+	0.478322i
$596$	7.79138			0.319147
$597$		0			0
$598$	−0.228575	−	0.395903i	−0.00934712	−	0.0161897i
$599$	−3.08966	−	5.35144i	−0.126240	−	0.218654i	0.795977	−	0.605327i	$-0.206958\pi$
$599$	−3.08966	−	5.35144i	−0.126240	−	0.218654i	−0.922217	+	0.386673i	$0.873624\pi$
$600$		0			0
$601$	−12.9344			−0.527607			−0.263804	−	0.964576i	$-0.584977\pi$
$601$	−12.9344			−0.527607			−0.263804	+	0.964576i	$0.584977\pi$
$602$	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	$0.0115319\pi$
$608$	14.5916			0.591766
$609$		0			0
$610$	15.5310			0.628832
$611$	−0.628242	+	1.08815i	−0.0254159	+	0.0440217i
$612$		0			0
$613$	8.81363	+	15.2657i	0.355979	+	0.616574i	0.987285	−	0.158960i	$-0.0508141\pi$
$613$	8.81363	+	15.2657i	0.355979	+	0.616574i	−0.631306	+	0.775534i	$0.717481\pi$
$614$	22.1101	−	38.2958i	0.892290	−	1.54549i
$615$		0			0
$616$	33.2413	+	19.0413i	1.33933	+	0.767195i
$617$	21.6441			0.871358			0.435679	−	0.900102i	$-0.356508\pi$
$617$	21.6441			0.871358			0.435679	+	0.900102i	$0.356508\pi$
$618$		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
$623$	0.128508	+	37.7485i	0.00514854	+	1.51236i
$624$		0			0
$625$	12.5734	−	21.7777i	0.502935	−	0.871109i
$626$	14.2240	+	24.6366i	0.568504	+	0.984678i
$627$		0			0
$628$	−1.09556	+	1.89756i	−0.0437176	+	0.0757211i
$629$	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	$0.713076\pi$
$632$	6.89167	−	11.9367i	0.274136	−	0.474817i
$633$		0			0
$634$	−11.9220	−	20.6496i	−0.473484	−	0.820099i
$635$	14.4610	−	25.0471i	0.573866	−	0.993965i
$636$		0			0
$637$	−1.24824	+	2.19641i	−0.0494570	+	0.0870250i
$638$	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	0.935933	−	0.352179i	$-0.114559\pi$
$641$	4.12607	+	7.14656i	0.162970	+	0.282272i	−0.772963	+	0.634452i	$0.781226\pi$
$642$		0			0
$643$	24.4318			0.963495			0.481748	−	0.876310i	$-0.340002\pi$
$643$	24.4318			0.963495			0.481748	+	0.876310i	$0.340002\pi$
$644$	0.680365	−	0.395903i	0.0268101	−	0.0156008i
$645$		0			0
$646$	15.4254	−	26.7176i	0.606906	−	1.05119i
$647$	−19.3432	−	33.5034i	−0.760461	−	1.31716i	−0.942613	−	0.333886i	$-0.891640\pi$
$647$	−19.3432	−	33.5034i	−0.760461	−	1.31716i	0.182153	−	0.983270i	$-0.441693\pi$
$648$		0			0
$649$	6.89548	−	11.9433i	0.270671	−	0.468817i
$650$	−2.75631			−0.108111
$651$		0			0
$652$	−1.39041			−0.0544528
$653$	−3.82715	+	6.62882i	−0.149768	+	0.259406i	−0.931142	−	0.364658i	$-0.881186\pi$
$653$	−3.82715	+	6.62882i	−0.149768	+	0.259406i	0.781374	+	0.624064i	$0.214519\pi$
$654$		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
$659$	38.5145			1.50031			0.750156	−	0.661261i	$-0.229978\pi$
$659$	38.5145			1.50031			0.750156	+	0.661261i	$0.229978\pi$
$660$		0			0
$661$	−16.1066	−	27.8974i	−0.626474	−	1.08508i	−0.988254	−	0.152821i	$-0.951164\pi$
$661$	−16.1066	−	27.8974i	−0.626474	−	1.08508i	0.361780	−	0.932263i	$-0.382169\pi$
$662$	−24.2697	−	42.0363i	−0.943268	−	1.63379i
$663$		0			0
$664$	32.8284			1.27399
$665$	−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
$671$	−18.4038			−0.710470
$672$		0			0
$673$	1.26136			0.0486218			0.0243109	−	0.999704i	$-0.492261\pi$
$673$	1.26136			0.0486218			0.0243109	+	0.999704i	$0.492261\pi$
$674$	8.76442	−	15.1804i	0.337593	−	0.584728i
$675$		0			0
$676$	2.32237	+	4.02246i	0.0893219	+	0.154710i
$677$	−7.41589	+	12.8447i	−0.285016	+	0.493662i	−0.972613	−	0.232431i	$-0.925332\pi$
$677$	−7.41589	+	12.8447i	−0.285016	+	0.493662i	0.687597	+	0.726092i	$0.258665\pi$
$678$		0			0
$679$	−36.6005	+	21.2978i	−1.40460	+	0.817333i
$680$	−22.0827			−0.846833
$681$		0			0
$682$	−22.0047	−	38.1133i	−0.842605	−	1.45943i
$683$	2.76560	+	4.79016i	0.105823	+	0.183290i	0.914074	−	0.405547i	$-0.132919\pi$
$683$	2.76560	+	4.79016i	0.105823	+	0.183290i	−0.808251	+	0.588838i	$0.799586\pi$
$684$		0			0
$685$	21.5487			0.823334
$686$	−24.7883	−	13.9760i	−0.946423	−	0.533605i
$687$		0			0
$688$	−18.0672	+	31.2933i	−0.688805	+	1.19305i
$689$	−0.526097	−	0.911226i	−0.0200427	−	0.0347150i
$690$		0			0
$691$	−4.31896	+	7.48065i	−0.164301	+	0.284577i	−0.936407	−	0.350916i	$-0.885870\pi$
$691$	−4.31896	+	7.48065i	−0.164301	+	0.284577i	0.772106	+	0.635494i	$0.219203\pi$
$692$	−3.55620			−0.135186
$693$		0			0
$694$	−6.27116			−0.238050
$695$	8.97808	−	15.5505i	0.340558	−	0.589864i
$696$		0			0
$697$	4.62535	+	8.01134i	0.175198	+	0.303451i
$698$	18.6518	−	32.3058i	0.705979	−	1.22279i
$699$		0			0
$700$	−0.0161571	−	4.74609i	−0.000610683	−	0.179385i
$701$	26.5897			1.00428			0.502140	−	0.864786i	$-0.332546\pi$
$701$	26.5897			1.00428			0.502140	+	0.864786i	$0.332546\pi$
$702$		0			0
$703$	27.0818	+	46.9070i	1.02141	+	1.76913i
$704$	17.4843	+	30.2837i	0.658965	+	1.14136i
$705$		0			0
$706$	−52.3632			−1.97072
$707$	6.90454	+	3.95506i	0.259672	+	0.148745i
$708$		0			0
$709$	−5.06305	+	8.76946i	−0.190147	+	0.329344i	−0.945299	−	0.326206i	$-0.894230\pi$
$709$	−5.06305	+	8.76946i	−0.190147	+	0.329344i	0.755152	+	0.655550i	$0.227563\pi$
$710$	−3.90460	−	6.76297i	−0.146537	−	0.253810i
$711$		0			0
$712$	−17.9666	+	31.1191i	−0.673328	+	1.16624i
$713$	4.10705			0.153810
$714$		0			0
$715$	6.55170			0.245020
$716$	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	0.388293	+	0.921536i	$0.373065\pi$
$719$	−16.1938	+	28.0485i	−0.603927	+	1.04603i	−0.992220	+	0.124496i	$0.960269\pi$
$720$		0			0
$721$	−0.0875527	−	25.7182i	−0.00326063	−	0.957796i
$722$	51.1391			1.90320
$723$		0			0
$724$	−2.18221	−	3.77970i	−0.0811013	−	0.140472i
$725$	10.6323	+	18.4157i	0.394874	+	0.683943i
$726$		0			0
$727$	25.2348			0.935907			0.467953	−	0.883753i	$-0.344992\pi$
$727$	25.2348			0.935907			0.467953	+	0.883753i	$0.344992\pi$
$728$	−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	$0.183409\pi$
$734$	−20.9568			−0.773529
$735$		0			0
$736$	1.66361			0.0613215
$737$	5.45962	−	9.45634i	0.201108	−	0.348329i
$738$		0			0
$739$	−12.2708	−	21.2537i	−0.451390	−	0.781830i	0.547083	−	0.837078i	$-0.315738\pi$
$739$	−12.2708	−	21.2537i	−0.451390	−	0.781830i	−0.998473	+	0.0552485i	$0.982405\pi$
$740$	−4.26824	+	7.39282i	−0.156904	+	0.271765i
$741$		0			0
$742$	10.2439	−	5.96092i	0.376066	−	0.218832i
$743$	4.59070			0.168416			0.0842082	−	0.996448i	$-0.473164\pi$
$743$	4.59070			0.168416			0.0842082	+	0.996448i	$0.473164\pi$
$744$		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
$749$	−0.0938905	−	27.5799i	−0.00343068	−	1.00775i
$750$		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	$0.972232\pi$
$752$	−7.99273	−	13.8438i	−0.291465	−	0.504832i
$753$		0			0
$754$	−1.18621	+	2.05457i	−0.0431992	+	0.0748231i
$755$	−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	$0.319602\pi$
$758$	−22.8200	+	39.5255i	−0.828861	+	1.43563i
$759$		0			0
$760$	−28.7507	−	49.7977i	−1.04290	−	1.80635i
$761$	23.2437	−	40.2592i	0.842582	−	1.45940i	−0.0451218	−	0.998981i	$-0.514368\pi$
$761$	23.2437	−	40.2592i	0.842582	−	1.45940i	0.887704	−	0.460414i	$-0.152299\pi$
$762$		0			0
$763$	−10.7311	−	6.14698i	−0.388491	−	0.222536i
$764$	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
$769$	14.1706			0.511006			0.255503	−	0.966808i	$-0.417759\pi$
$769$	14.1706			0.511006			0.255503	+	0.966808i	$0.417759\pi$
$770$	0.251233	+	73.7986i	0.00905382	+	2.65952i
$771$		0			0
$772$	0.415373	−	0.719448i	0.0149496	−	0.0258935i
$773$	17.0042	+	29.4522i	0.611600	+	1.05932i	0.990971	+	0.134078i	$0.0428072\pi$
$773$	17.0042	+	29.4522i	0.611600	+	1.05932i	−0.379371	+	0.925245i	$0.623860\pi$
$774$		0			0
$775$	12.3814	−	21.4452i	0.444754	−	0.770336i
$776$	−40.3096			−1.44703
$777$		0			0
$778$	32.7672			1.17476
$779$	−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
$785$	19.1705			0.684223
$786$		0			0
$787$	14.5530	+	25.2065i	0.518757	+	0.898514i	0.999762	+	0.0217964i	$0.00693855\pi$
$787$	14.5530	+	25.2065i	0.518757	+	0.898514i	−0.481005	+	0.876718i	$0.659728\pi$
$788$	−0.913934	−	1.58298i	−0.0325576	−	0.0563914i
$789$		0			0
$790$	26.5527			0.944701
$791$	−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
$797$	−18.5038			−0.655439			−0.327720	−	0.944775i	$-0.606280\pi$
$797$	−18.5038			−0.655439			−0.327720	+	0.944775i	$0.606280\pi$
$798$		0			0
$799$	−9.66754			−0.342013
$800$	5.01524	−	8.68665i	0.177316	−	0.307120i
$801$		0			0
$802$	−6.71231	−	11.6261i	−0.237020	−	0.410531i
$803$	−44.3081	+	76.7439i	−1.56360	+	2.70823i
$804$		0			0
$805$	−5.97607	−	3.42321i	−0.210629	−	0.120652i
$806$	2.76270			0.0973118
$807$		0			0
$808$	3.78720	+	6.55962i	0.133233	+	0.230767i
$809$	−20.5407	−	35.5775i	−0.722172	−	1.25084i	−0.960128	−	0.279562i	$-0.909811\pi$
$809$	−20.5407	−	35.5775i	−0.722172	−	1.25084i	0.237956	−	0.971276i	$-0.423523\pi$
$810$		0			0
$811$	−43.1361			−1.51471			−0.757357	−	0.653001i	$-0.773510\pi$
$811$	−43.1361			−1.51471			−0.757357	+	0.653001i	$0.773510\pi$
$812$	−3.54472	−	2.03049i	−0.124395	−	0.0712561i
$813$		0			0
$814$	33.0860	−	57.3066i	1.15966	−	2.00859i
$815$	6.08248	+	10.5352i	0.213060	+	0.369031i
$816$		0			0
$817$	−28.4517	+	49.2798i	−0.995399	+	1.72408i
$818$	−44.0859			−1.54143
$819$		0			0
$820$	−3.79641			−0.132576
$821$	−6.58738	+	11.4097i	−0.229901	+	0.398201i	−0.957779	−	0.287507i	$-0.907174\pi$
$821$	−6.58738	+	11.4097i	−0.229901	+	0.398201i	0.727877	+	0.685707i	$0.240507\pi$
$822$		0			0
$823$	5.99083	+	10.3764i	0.208827	+	0.361699i	0.951345	−	0.308127i	$-0.0997020\pi$
$823$	5.99083	+	10.3764i	0.208827	+	0.361699i	−0.742518	+	0.669826i	$0.766369\pi$
$824$	12.2407	−	21.2016i	0.426427	−	0.738592i
$825$		0			0
$826$	−8.42854	+	4.90455i	−0.293266	+	0.170651i
$827$	29.9879			1.04278			0.521391	−	0.853318i	$-0.325413\pi$
$827$	29.9879			1.04278			0.521391	+	0.853318i	$0.325413\pi$
$828$		0			0
$829$	−13.4619	−	23.3167i	−0.467551	−	0.809822i	0.531762	−	0.846894i	$-0.321530\pi$
$829$	−13.4619	−	23.3167i	−0.467551	−	0.809822i	−0.999313	+	0.0370721i	$0.988197\pi$
$830$	31.6208	+	54.7688i	1.09757	+	1.90105i
$831$		0			0
$832$	−2.19516			−0.0761034
$833$	−19.4374	+	0.132344i	−0.673467	+	0.00458543i
$834$		0			0
$835$	5.58639	−	9.67591i	0.193325	−	0.334849i
$836$	−7.50142	−	12.9928i	−0.259442	−	0.449367i
$837$		0			0
$838$	−6.64117	+	11.5029i	−0.229416	+	0.397359i
$839$	−11.2238			−0.387490			−0.193745	−	0.981052i	$-0.562063\pi$
$839$	−11.2238			−0.387490			−0.193745	+	0.981052i	$0.562063\pi$
$840$		0			0
$841$	−10.6971			−0.368864
$842$	−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
$848$	13.3864			0.459691
$849$		0			0
$850$	−10.6037	−	18.3662i	−0.363704	−	0.629954i
$851$	3.08765	+	5.34796i	0.105843	+	0.183326i
$852$		0			0
$853$	−12.1934			−0.417496			−0.208748	−	0.977970i	$-0.566939\pi$
$853$	−12.1934			−0.417496			−0.208748	+	0.977970i	$0.566939\pi$
$854$	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	$0.0541641\pi$
$857$	18.7191	+	32.4225i	0.639433	+	1.10753i	−0.346125	+	0.938188i	$0.612503\pi$
$858$		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	$0.170781\pi$
$860$	−8.96830			−0.305817
$861$		0			0
$862$	−8.92314			−0.303923
$863$	−11.7796	+	20.4029i	−0.400983	+	0.694522i	−0.993845	−	0.110782i	$-0.964665\pi$
$863$	−11.7796	+	20.4029i	−0.400983	+	0.694522i	0.592862	+	0.805304i	$0.297998\pi$
$864$		0			0
$865$	15.5569	+	26.9453i	0.528949	+	0.916167i
$866$	−2.79553	+	4.84200i	−0.0949959	+	0.164538i
$867$		0			0
$868$	0.0161946	+	4.75708i	0.000549679	+	0.161466i
$869$	−31.4641			−1.06735
$870$		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
$875$	0.213202	−	0.124062i	0.00720753	−	0.00419405i
$876$		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	$0.954125\pi$
$878$	14.3372	+	24.8328i	0.483858	+	0.838066i
$879$		0			0
$880$	−41.6766	+	72.1860i	−1.40492	+	2.43339i
$881$	−39.4357			−1.32862			−0.664311	−	0.747456i	$-0.731275\pi$
$881$	−39.4357			−1.32862			−0.664311	+	0.747456i	$0.731275\pi$
$882$		0			0
$883$	−8.76912			−0.295105			−0.147552	−	0.989054i	$-0.547139\pi$
$883$	−8.76912			−0.295105			−0.147552	+	0.989054i	$0.547139\pi$
$884$	0.180844	−	0.313231i	0.00608244	−	0.0105351i
$885$		0			0
$886$	20.0448	+	34.7185i	0.673417	+	1.16639i
$887$	−3.91300	+	6.77752i	−0.131386	+	0.227567i	−0.924211	−	0.381882i	$-0.875276\pi$
$887$	−3.91300	+	6.77752i	−0.131386	+	0.227567i	0.792825	+	0.609449i	$0.208609\pi$
$888$		0			0
$889$	20.9456	−	12.1882i	0.702492	−	0.408779i
$890$	−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
$895$	−62.8272			−2.10008
$896$	−0.120528	−	35.4046i	−0.00402656	−	1.18278i
$897$		0			0
$898$	4.33164	−	7.50263i	0.144549	−	0.250366i
$899$	−10.6569	−	18.4584i	−0.355429	−	0.615621i
$900$		0			0
$901$	4.04786	−	7.01109i	0.134854	−	0.233573i
$902$	29.4285			0.979860
$903$		0			0
$904$	−11.8033			−0.392573
$905$	−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
$911$	36.1524			1.19778			0.598891	−	0.800830i	$-0.295608\pi$
$911$	36.1524			1.19778			0.598891	+	0.800830i	$0.295608\pi$
$912$		0			0
$913$	−37.4697	−	64.8995i	−1.24007	−	2.14786i
$914$	15.3593	+	26.6031i	0.508042	+	0.879954i
$915$		0			0
$916$	−8.56086			−0.282859
$917$	−0.0829684	−	24.3716i	−0.00273986	−	0.804821i
$918$		0			0
$919$	5.58842	−	9.67942i	0.184345	−	0.319295i	−0.759011	−	0.651078i	$-0.774317\pi$
$919$	5.58842	−	9.67942i	0.184345	−	0.319295i	0.943356	+	0.331783i	$0.107650\pi$
$920$	−3.27793	−	5.67754i	−0.108070	−	0.187183i
$921$		0			0
$922$	−28.7710	+	49.8328i	−0.947522	+	1.64116i
$923$	−0.580900			−0.0191206
$924$		0			0
$925$	37.2330			1.22421
$926$	−1.88618	+	3.26696i	−0.0619837	+	0.107359i
$927$		0			0
$928$	−4.31673	−	7.47679i	−0.141703	−	0.245438i
$929$	−16.4192	+	28.4389i	−0.538696	+	0.933049i	0.460279	+	0.887775i	$0.347750\pi$
$929$	−16.4192	+	28.4389i	−0.538696	+	0.933049i	−0.998975	+	0.0452744i	$0.985584\pi$
$930$		0			0
$931$	−25.6051	−	43.6602i	−0.839175	−	1.43090i
$932$	−5.00185			−0.163841
$933$		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	$0.639368\pi$
$938$	−6.67344	+	3.88326i	−0.217895	+	0.126793i
$939$		0			0
$940$	1.98374	−	3.43594i	0.0647024	−	0.112068i
$941$	−14.7340	−	25.5200i	−0.480314	−	0.831928i	0.519431	−	0.854512i	$-0.326144\pi$
$941$	−14.7340	−	25.5200i	−0.480314	−	0.831928i	−0.999745	+	0.0225845i	$0.992811\pi$
$942$		0			0
$943$	−1.37316	+	2.37839i	−0.0447163	+	0.0774509i
$944$	−11.0141			−0.358479
$945$		0			0
$946$	69.5192			2.26026
$947$	5.76137	−	9.97898i	0.187219	−	0.324273i	−0.757103	−	0.653296i	$-0.773386\pi$
$947$	5.76137	−	9.97898i	0.187219	−	0.324273i	0.944322	+	0.329022i	$0.106719\pi$
$948$		0			0
$949$	−2.78144	−	4.81760i	−0.0902895	−	0.156386i
$950$	27.6111	−	47.8239i	0.895824	−	1.55161i
$951$		0			0
$952$	−16.0555	−	9.19692i	−0.520362	−	0.298074i
$953$	29.2912			0.948835			0.474417	−	0.880300i	$-0.342659\pi$
$953$	29.2912			0.948835			0.474417	+	0.880300i	$0.342659\pi$
$954$		0			0
$955$	−15.3454	−	26.5790i	−0.496565	−	0.860076i
$956$	−4.03176	−	6.98321i	−0.130396	−	0.225853i
$957$		0			0
$958$	53.3075			1.72229
$959$	15.6673	+	8.97452i	0.505922	+	0.289802i
$960$		0			0
$961$	3.08991	−	5.35188i	0.0996744	−	0.172641i
$962$	2.07697	+	3.59742i	0.0669643	+	0.115985i
$963$		0			0
$964$	−1.75411	+	3.03820i	−0.0564959	+	0.0978538i
$965$	−7.26834			−0.233976
$966$		0			0
$967$	42.0803			1.35321			0.676606	−	0.736345i	$-0.263450\pi$
$967$	42.0803			1.35321			0.676606	+	0.736345i	$0.263450\pi$
$968$	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	−0.433047	−	0.901371i	$-0.642562\pi$
$971$	17.5774	−	30.4450i	0.564087	−	0.977027i	0.997134	−	0.0756560i	$-0.0241051\pi$
$972$		0			0
$973$	13.0040	−	7.56703i	0.416890	−	0.242588i
$974$	1.47478			0.0472551
$975$		0			0
$976$	7.34907	+	12.7290i	0.235238	+	0.407444i
$977$	2.21513	+	3.83671i	0.0708682	+	0.122747i	0.899282	−	0.437369i	$-0.144090\pi$
$977$	2.21513	+	3.83671i	0.0708682	+	0.122747i	−0.828414	+	0.560117i	$0.810756\pi$
$978$		0			0
$979$	82.0271			2.62160
$980$	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	0.633444	−	0.773789i	$-0.281641\pi$
$983$	−11.0801	−	19.1912i	−0.353399	−	0.612105i	−0.986843	+	0.161684i	$0.948308\pi$
$984$		0			0
$985$	−7.99616	+	13.8498i	−0.254779	+	0.441290i
$986$	−18.2537			−0.581316
$987$		0			0
$988$	0.941804			0.0299628
$989$	−3.24383	+	5.61848i	−0.103148	+	0.178657i
$990$		0			0
$991$	18.3602	+	31.8007i	0.583229	+	1.01018i	0.995094	+	0.0989378i	$0.0315445\pi$
$991$	18.3602	+	31.8007i	0.583229	+	1.01018i	−0.411864	+	0.911245i	$0.635122\pi$
$992$	−5.02686	+	8.70677i	−0.159603	+	0.276440i
$993$		0			0
$994$	−0.0222753	−	6.54328i	−0.000706531	−	0.207540i
$995$	−31.4286			−0.996355
$996$		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.e.c.163.2	✓	8
3.2	odd	2		567.2.e.d.163.3	yes	8
7.2	even	3		3969.2.a.x.1.3		4
7.4	even	3	inner	567.2.e.c.487.2	yes	8
7.5	odd	6		3969.2.a.w.1.3		4
9.2	odd	6		567.2.h.j.352.2		8
9.4	even	3		567.2.g.j.541.2		8
9.5	odd	6		567.2.g.k.541.3		8
9.7	even	3		567.2.h.k.352.3		8
21.2	odd	6		3969.2.a.s.1.2		4
21.5	even	6		3969.2.a.t.1.2		4
21.11	odd	6		567.2.e.d.487.3	yes	8
63.4	even	3		567.2.h.k.298.3		8
63.11	odd	6		567.2.g.k.109.3		8
63.25	even	3		567.2.g.j.109.2		8
63.32	odd	6		567.2.h.j.298.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.2	✓	8	1.1	even	1	trivial
567.2.e.c.487.2	yes	8	7.4	even	3	inner
567.2.e.d.163.3	yes	8	3.2	odd	2
567.2.e.d.487.3	yes	8	21.11	odd	6
567.2.g.j.109.2		8	63.25	even	3
567.2.g.j.541.2		8	9.4	even	3
567.2.g.k.109.3		8	63.11	odd	6
567.2.g.k.541.3		8	9.5	odd	6
567.2.h.j.298.2		8	63.32	odd	6
567.2.h.j.352.2		8	9.2	odd	6
567.2.h.k.298.3		8	63.4	even	3
567.2.h.k.352.3		8	9.7	even	3
3969.2.a.s.1.2		4	21.2	odd	6
3969.2.a.t.1.2		4	21.5	even	6
3969.2.a.w.1.3		4	7.5	odd	6
3969.2.a.x.1.3		4	7.2	even	3

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.768262 + 1.33067i) q^{2} +(-0.180452 - 0.312552i) q^{4} +(-1.57880 + 2.73457i) q^{5} +(-2.28677 + 1.33067i) q^{7} -2.51851 q^{8} +O(q^{10})\)	\(q+(-0.768262 + 1.33067i) q^{2} +(-0.180452 - 0.312552i) q^{4} +(-1.57880 + 2.73457i) q^{5} +(-2.28677 + 1.33067i) q^{7} -2.51851 q^{8} +(-2.42587 - 4.20173i) q^{10} +(2.87458 + 4.97892i) q^{11} -0.360904 q^{13} +(-0.0138393 - 4.06523i) q^{14} +(2.29578 - 3.97640i) q^{16} +(-1.38842 - 2.40481i) q^{17} +(3.61533 - 6.26193i) q^{19} +1.13959 q^{20} -8.83372 q^{22} +(0.412190 - 0.713934i) q^{23} +(-2.48524 - 4.30456i) q^{25} +(0.277269 - 0.480243i) q^{26} +(0.828555 + 0.474613i) q^{28} -4.27819 q^{29} +(2.49099 + 4.31453i) q^{31} +(1.00901 + 1.74765i) q^{32} +4.26668 q^{34} +(-0.0284402 - 8.35419i) q^{35} +(-3.74542 + 6.48725i) q^{37} +(5.55503 + 9.62160i) q^{38} +(3.97623 - 6.88703i) q^{40} -3.33138 q^{41} -7.86975 q^{43} +(1.03745 - 1.79691i) q^{44} +(0.633340 + 1.09698i) q^{46} +(1.74075 - 3.01506i) q^{47} +(3.45864 - 6.08587i) q^{49} +7.63725 q^{50} +(0.0651258 + 0.112801i) q^{52} +(1.45772 + 2.52485i) q^{53} -18.1536 q^{55} +(5.75925 - 3.35130i) q^{56} +(3.28677 - 5.69285i) q^{58} +(-1.19939 - 2.07740i) q^{59} +(-1.60056 + 2.77226i) q^{61} -7.65494 q^{62} +6.08239 q^{64} +(0.569796 - 0.986916i) q^{65} +(-0.949637 - 1.64482i) q^{67} +(-0.501086 + 0.867907i) q^{68} +(11.1385 + 6.38036i) q^{70} +1.60957 q^{71} +(7.70688 + 13.3487i) q^{73} +(-5.75492 - 9.96781i) q^{74} -2.60957 q^{76} +(-13.1988 - 7.56054i) q^{77} +(-2.73641 + 4.73960i) q^{79} +(7.24916 + 12.5559i) q^{80} +(2.55937 - 4.43296i) q^{82} -13.0348 q^{83} +8.76817 q^{85} +(6.04603 - 10.4720i) q^{86} +(-7.23966 - 12.5395i) q^{88} +(7.13384 - 12.3562i) q^{89} +(0.825304 - 0.480243i) q^{91} -0.297522 q^{92} +(2.67470 + 4.63271i) q^{94} +(11.4158 + 19.7727i) q^{95} +16.0053 q^{97} +(5.44113 + 9.27785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 5 q^{4} - 2 q^{5} + q^{7} - 6 q^{8}+O(q^{10}) \) 8 * q - q^2 - 5 * q^4 - 2 * q^5 + q^7 - 6 * q^8	\( 8 q - q^{2} - 5 q^{4} - 2 q^{5} + q^{7} - 6 q^{8} + 7 q^{10} - 5 q^{11} - 10 q^{13} - 23 q^{14} + q^{16} - 6 q^{17} + 8 q^{19} - 16 q^{20} - 14 q^{22} + 12 q^{23} - 8 q^{25} - q^{26} + 5 q^{28} - 20 q^{29} + 18 q^{31} + 10 q^{32} + 23 q^{35} + 20 q^{38} + 18 q^{40} - 10 q^{41} - 14 q^{43} - 13 q^{44} - 12 q^{46} + 21 q^{47} + 17 q^{49} + 76 q^{50} + 25 q^{52} + 12 q^{53} - 52 q^{55} + 39 q^{56} + 7 q^{58} - 6 q^{59} + 20 q^{61} + 36 q^{62} - 46 q^{64} - 8 q^{65} + 5 q^{67} - 51 q^{68} + 17 q^{70} - 18 q^{71} + 6 q^{73} + 10 q^{76} - 37 q^{77} + 10 q^{79} + 2 q^{80} + 35 q^{82} + 18 q^{83} - 18 q^{85} + 22 q^{86} - 18 q^{88} + 22 q^{89} + 13 q^{91} - 72 q^{92} + 15 q^{94} + 16 q^{95} - 18 q^{97} + 11 q^{98}+O(q^{100}) \) 8 * q - q^2 - 5 * q^4 - 2 * q^5 + q^7 - 6 * q^8 + 7 * q^10 - 5 * q^11 - 10 * q^13 - 23 * q^14 + q^16 - 6 * q^17 + 8 * q^19 - 16 * q^20 - 14 * q^22 + 12 * q^23 - 8 * q^25 - q^26 + 5 * q^28 - 20 * q^29 + 18 * q^31 + 10 * q^32 + 23 * q^35 + 20 * q^38 + 18 * q^40 - 10 * q^41 - 14 * q^43 - 13 * q^44 - 12 * q^46 + 21 * q^47 + 17 * q^49 + 76 * q^50 + 25 * q^52 + 12 * q^53 - 52 * q^55 + 39 * q^56 + 7 * q^58 - 6 * q^59 + 20 * q^61 + 36 * q^62 - 46 * q^64 - 8 * q^65 + 5 * q^67 - 51 * q^68 + 17 * q^70 - 18 * q^71 + 6 * q^73 + 10 * q^76 - 37 * q^77 + 10 * q^79 + 2 * q^80 + 35 * q^82 + 18 * q^83 - 18 * q^85 + 22 * q^86 - 18 * q^88 + 22 * q^89 + 13 * q^91 - 72 * q^92 + 15 * q^94 + 16 * q^95 - 18 * q^97 + 11 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more