LMFDB - Embedded newform 567.2.g.j.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(109,567)]

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([2, 4]))

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

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

chi := DirichletCharacter("567.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Embedding invariants

Embedding label			109.2
Root			$0.0512865 + 1.21608i$ of defining polynomial
Character	$\chi$	$=$	567.109
Dual form			567.2.g.j.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.768262 + 1.33067i) q^{2} +(-0.180452 - 0.312552i) q^{4} +3.15761 q^{5} +(-0.00900690 + 2.64574i) q^{7} -2.51851 q^{8} +O(q^{10})$	\(q+(-0.768262 + 1.33067i) q^{2} +(-0.180452 - 0.312552i) q^{4} +3.15761 q^{5} +(-0.00900690 + 2.64574i) q^{7} -2.51851 q^{8} +(-2.42587 + 4.20173i) q^{10} -5.74916 q^{11} +(0.180452 - 0.312552i) q^{13} +(-3.51368 - 2.04460i) q^{14} +(2.29578 - 3.97640i) q^{16} +(-1.38842 + 2.40481i) q^{17} +(3.61533 + 6.26193i) q^{19} +(-0.569796 - 0.986916i) q^{20} +(4.41686 - 7.65023i) q^{22} -0.824381 q^{23} +4.97047 q^{25} +(0.277269 + 0.480243i) q^{26} +(0.828555 - 0.474613i) q^{28} +(2.13910 + 3.70502i) q^{29} +(2.49099 + 4.31453i) q^{31} +(1.00901 + 1.74765i) q^{32} +(-2.13334 - 3.69505i) q^{34} +(-0.0284402 + 8.35419i) q^{35} +(-3.74542 - 6.48725i) q^{37} -11.1101 q^{38} -7.95246 q^{40} +(1.66569 - 2.88506i) q^{41} +(3.93487 + 6.81540i) q^{43} +(1.03745 + 1.79691i) q^{44} +(0.633340 - 1.09698i) q^{46} +(1.74075 - 3.01506i) q^{47} +(-6.99984 - 0.0476598i) q^{49} +(-3.81862 + 6.61405i) q^{50} -0.130252 q^{52} +(1.45772 - 2.52485i) q^{53} -18.1536 q^{55} +(0.0226840 - 6.66331i) q^{56} -6.57354 q^{58} +(-1.19939 - 2.07740i) q^{59} +(-1.60056 + 2.77226i) q^{61} -7.65494 q^{62} +6.08239 q^{64} +(0.569796 - 0.986916i) q^{65} +(-0.949637 - 1.64482i) q^{67} +1.00217 q^{68} +(-11.0948 - 6.45605i) q^{70} +1.60957 q^{71} +(7.70688 - 13.3487i) q^{73} +11.5098 q^{74} +(1.30478 - 2.25995i) q^{76} +(0.0517821 - 15.2108i) q^{77} +(-2.73641 + 4.73960i) q^{79} +(7.24916 - 12.5559i) q^{80} +(2.55937 + 4.43296i) q^{82} +(6.51742 + 11.2885i) q^{83} +(-4.38408 + 7.59346i) q^{85} -12.0921 q^{86} +14.4793 q^{88} +(7.13384 + 12.3562i) q^{89} +(0.825304 + 0.480243i) q^{91} +(0.148761 + 0.257662i) q^{92} +(2.67470 + 4.63271i) q^{94} +(11.4158 + 19.7727i) q^{95} +(-8.00266 - 13.8610i) q^{97} +(5.44113 - 9.27785i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 5 q^{4} + 4 q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) $ 8 * q - q^2 - 5 * q^4 + 4 * q^5 - 2 * q^7 - 6 * q^8	$ 8 q - q^{2} - 5 q^{4} + 4 q^{5} - 2 q^{7} - 6 q^{8} + 7 q^{10} + 10 q^{11} + 5 q^{13} + 7 q^{14} + q^{16} - 6 q^{17} + 8 q^{19} + 8 q^{20} + 7 q^{22} - 24 q^{23} + 16 q^{25} - q^{26} + 5 q^{28} + 10 q^{29} + 18 q^{31} + 10 q^{32} + 23 q^{35} - 40 q^{38} - 36 q^{40} + 5 q^{41} + 7 q^{43} - 13 q^{44} - 12 q^{46} + 21 q^{47} + 2 q^{49} - 38 q^{50} - 50 q^{52} + 12 q^{53} - 52 q^{55} - 33 q^{56} - 14 q^{58} - 6 q^{59} + 20 q^{61} + 36 q^{62} - 46 q^{64} - 8 q^{65} + 5 q^{67} + 102 q^{68} - 46 q^{70} - 18 q^{71} + 6 q^{73} - 5 q^{76} - 16 q^{77} + 10 q^{79} + 2 q^{80} + 35 q^{82} - 9 q^{83} + 9 q^{85} - 44 q^{86} + 36 q^{88} + 22 q^{89} + 13 q^{91} + 36 q^{92} + 15 q^{94} + 16 q^{95} + 9 q^{97} + 11 q^{98}+O(q^{100}) $ 8 * q - q^2 - 5 * q^4 + 4 * q^5 - 2 * q^7 - 6 * q^8 + 7 * q^10 + 10 * q^11 + 5 * q^13 + 7 * q^14 + q^16 - 6 * q^17 + 8 * q^19 + 8 * q^20 + 7 * q^22 - 24 * q^23 + 16 * q^25 - q^26 + 5 * q^28 + 10 * q^29 + 18 * q^31 + 10 * q^32 + 23 * q^35 - 40 * q^38 - 36 * q^40 + 5 * q^41 + 7 * q^43 - 13 * q^44 - 12 * q^46 + 21 * q^47 + 2 * q^49 - 38 * q^50 - 50 * q^52 + 12 * q^53 - 52 * q^55 - 33 * q^56 - 14 * q^58 - 6 * q^59 + 20 * q^61 + 36 * q^62 - 46 * q^64 - 8 * q^65 + 5 * q^67 + 102 * q^68 - 46 * q^70 - 18 * q^71 + 6 * q^73 - 5 * q^76 - 16 * q^77 + 10 * q^79 + 2 * q^80 + 35 * q^82 - 9 * q^83 + 9 * q^85 - 44 * q^86 + 36 * q^88 + 22 * q^89 + 13 * q^91 + 36 * q^92 + 15 * q^94 + 16 * q^95 + 9 * q^97 + 11 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−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
$5$	3.15761			1.41212			0.706062	−	0.708150i	$-0.250470\pi$
$5$	3.15761			1.41212			0.706062	+	0.708150i	$0.250470\pi$
$6$		0			0
$7$	−0.00900690	+	2.64574i	−0.00340429	+	0.999994i
$7$	−0.00900690	+	2.64574i	−0.00340429	+	0.999994i
$8$	−2.51851			−0.890428
$9$		0			0
$10$	−2.42587	+	4.20173i	−0.767127	+	1.32870i
$11$	−5.74916			−1.73344			−0.866719	−	0.498797i	$-0.833775\pi$
$11$	−5.74916			−1.73344			−0.866719	+	0.498797i	$0.833775\pi$
$12$		0			0
$13$	0.180452	−	0.312552i	0.0500484	−	0.0866863i	−0.839916	−	0.542717i	$-0.817396\pi$
$13$	0.180452	−	0.312552i	0.0500484	−	0.0866863i	0.889964	+	0.456030i	$0.150729\pi$
$14$	−3.51368	−	2.04460i	−0.939070	−	0.546443i
$15$		0			0
$16$	2.29578	−	3.97640i	0.573945	−	0.994101i
$17$	−1.38842	+	2.40481i	−0.336741	+	0.583253i	−0.983818	−	0.179172i	$-0.942658\pi$
$17$	−1.38842	+	2.40481i	−0.336741	+	0.583253i	0.647076	+	0.762425i	$0.275991\pi$
$18$		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
$23$	−0.824381			−0.171895			−0.0859476	−	0.996300i	$-0.527392\pi$
$23$	−0.824381			−0.171895			−0.0859476	+	0.996300i	$0.527392\pi$
$24$		0			0
$25$	4.97047			0.994095
$26$	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	$-0.0366416\pi$
$29$	2.13910	+	3.70502i	0.397220	+	0.688006i	−0.596162	+	0.802864i	$0.703308\pi$
$30$		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
$34$	−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	$-0.377811\pi$
$38$	−11.1101			−1.80229
$39$		0			0
$40$	−7.95246			−1.25739
$41$	1.66569	−	2.88506i	0.260137	−	0.450570i	−0.706141	−	0.708071i	$-0.749566\pi$
$41$	1.66569	−	2.88506i	0.260137	−	0.450570i	0.966278	+	0.257501i	$0.0828990\pi$
$42$		0			0
$43$	3.93487	+	6.81540i	0.600063	+	1.03934i	0.992811	+	0.119693i	$0.0381910\pi$
$43$	3.93487	+	6.81540i	0.600063	+	1.03934i	−0.392748	+	0.919646i	$0.628476\pi$
$44$	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
$49$	−6.99984	−	0.0476598i	−0.999977	−	0.00680854i
$50$	−3.81862	+	6.61405i	−0.540035	+	0.935368i
$51$		0			0
$52$	−0.130252			−0.0180626
$53$	1.45772	−	2.52485i	0.200233	−	0.346814i	−0.748370	−	0.663281i	$-0.769163\pi$
$53$	1.45772	−	2.52485i	0.200233	−	0.346814i	0.948604	+	0.316467i	$0.102497\pi$
$54$		0			0
$55$	−18.1536			−2.44783
$56$	0.0226840	−	6.66331i	0.00303127	−	0.890422i
$57$		0			0
$58$	−6.57354			−0.863148
$59$	−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	$0.870346\pi$
$68$	1.00217			0.121531
$69$		0			0
$70$	−11.0948	−	6.45605i	−1.32608	−	0.771645i
$71$	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	0.0771572	−	0.997019i	$-0.475416\pi$
$73$	7.70688	−	13.3487i	0.902022	−	1.56235i	0.824865	−	0.565330i	$-0.191251\pi$
$74$	11.5098			1.33799
$75$		0			0
$76$	1.30478	−	2.25995i	0.149669	−	0.259234i
$77$	0.0517821	−	15.2108i	0.00590112	−	1.73343i
$78$		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
$83$	6.51742	+	11.2885i	0.715380	+	1.23907i	0.962813	+	0.270170i	$0.0870798\pi$
$83$	6.51742	+	11.2885i	0.715380	+	1.23907i	−0.247433	+	0.968905i	$0.579587\pi$
$84$		0			0
$85$	−4.38408	+	7.59346i	−0.475521	+	0.823626i
$86$	−12.0921			−1.30392
$87$		0			0
$88$	14.4793			1.54350
$89$	7.13384	+	12.3562i	0.756185	+	1.30975i	0.944783	+	0.327697i	$0.106272\pi$
$89$	7.13384	+	12.3562i	0.756185	+	1.30975i	−0.188598	+	0.982054i	$0.560394\pi$
$90$		0			0
$91$	0.825304	+	0.480243i	0.0865154	+	0.0503432i
$92$	0.148761	+	0.257662i	0.0155094	+	0.0268631i
$93$		0			0
$94$	2.67470	+	4.63271i	0.275874	+	0.477827i
$95$	11.4158	+	19.7727i	1.17123	+	2.02864i
$96$		0			0
$97$	−8.00266	−	13.8610i	−0.812547	−	1.40737i	−0.911076	−	0.412239i	$-0.864747\pi$
$97$	−8.00266	−	13.8610i	−0.812547	−	1.40737i	0.0985289	−	0.995134i	$-0.468586\pi$
$98$	5.44113	−	9.27785i	0.549637	−	0.937204i
$99$		0			0
$100$	−0.896931	−	1.55353i	−0.0896931	−	0.155353i
$101$	3.00749			0.299257			0.149628	−	0.988742i	$-0.452192\pi$
$101$	3.00749			0.299257			0.149628	+	0.988742i	$0.452192\pi$
$102$		0			0
$103$	9.72063			0.957802			0.478901	−	0.877869i	$-0.341035\pi$
$103$	9.72063			0.957802			0.478901	+	0.877869i	$0.341035\pi$
$104$	−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	$-0.998573\pi$
$107$	−5.21214	−	9.02770i	−0.503877	−	0.872740i	0.496113	−	0.868258i	$-0.334760\pi$
$108$		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	$0.0948019\pi$
$110$	13.9467	−	24.1564i	1.32977	−	2.30322i
$111$		0			0
$112$	10.4998	+	6.10984i	0.992141	+	0.577325i
$113$	−2.34332	+	4.05875i	−0.220441	+	0.381815i	−0.954942	−	0.296793i	$-0.904083\pi$
$113$	−2.34332	+	4.05875i	−0.220441	+	0.381815i	0.734501	+	0.678608i	$0.237416\pi$
$114$		0			0
$115$	−2.60307			−0.242737
$116$	0.772008	−	1.33716i	0.0716791	−	0.124152i
$117$		0			0
$118$	3.68578			0.339304
$119$	−6.35000	−	3.69505i	−0.582103	−	0.338725i
$120$		0			0
$121$	22.0529			2.00481
$122$	−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
$131$	9.21165			0.804825			0.402413	−	0.915458i	$-0.368172\pi$
$131$	9.21165			0.804825			0.402413	+	0.915458i	$0.368172\pi$
$132$		0			0
$133$	−16.6000	+	9.50880i	−1.43940	+	0.824517i
$134$	2.91828			0.252101
$135$		0			0
$136$	3.49675	−	6.05655i	0.299844	−	0.519345i
$137$	6.82438			0.583046			0.291523	−	0.956564i	$-0.405838\pi$
$137$	6.82438			0.583046			0.291523	+	0.956564i	$0.405838\pi$
$138$		0			0
$139$	2.84332	−	4.92477i	0.241167	−	0.417714i	−0.719880	−	0.694099i	$-0.755803\pi$
$139$	2.84332	−	4.92477i	0.241167	−	0.417714i	0.961047	+	0.276385i	$0.0891365\pi$
$140$	2.61625	−	1.49864i	0.221113	−	0.126658i
$141$		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
$146$	11.8418	+	20.5106i	0.980035	+	1.69747i
$147$		0			0
$148$	−1.35173	+	2.34127i	−0.111112	+	0.192451i
$149$	21.5885			1.76860			0.884301	−	0.466918i	$-0.154636\pi$
$149$	21.5885			1.76860			0.884301	+	0.466918i	$0.154636\pi$
$150$		0			0
$151$	−5.55553			−0.452102			−0.226051	−	0.974115i	$-0.572582\pi$
$151$	−5.55553			−0.452102			−0.226051	+	0.974115i	$0.572582\pi$
$152$	−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
$157$	−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
$160$	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	$0.785123\pi$
$164$	−1.20231			−0.0938844
$165$		0			0
$166$	−20.0283			−1.55450
$167$	1.76919	−	3.06432i	0.136904	−	0.237124i	−0.789419	−	0.613854i	$-0.789618\pi$
$167$	1.76919	−	3.06432i	0.136904	−	0.237124i	0.926323	+	0.376730i	$0.122952\pi$
$168$		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
$173$	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
$175$	−0.0447686	+	13.1506i	−0.00338419	+	0.994089i
$176$	−13.1988	+	22.8610i	−0.994897	+	1.72321i
$177$		0			0
$178$	−21.9226			−1.64317
$179$	9.94855	−	17.2314i	0.743590	−	1.28794i	−0.207261	−	0.978286i	$-0.566455\pi$
$179$	9.94855	−	17.2314i	0.743590	−	1.28794i	0.950851	−	0.309649i	$-0.100212\pi$
$180$		0			0
$181$	12.0930			0.898869			0.449434	−	0.893313i	$-0.351626\pi$
$181$	12.0930			0.898869			0.449434	+	0.893313i	$0.351626\pi$
$182$	−1.27309	+	0.729254i	−0.0943680	+	0.0540559i
$183$		0			0
$184$	2.07621			0.153060
$185$	−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	$0.806933\pi$
$194$	24.5925			1.76564
$195$		0			0
$196$	1.24824	+	2.19641i	0.0891598	+	0.156887i
$197$	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	−0.633951	−	0.773374i	$-0.718568\pi$
$199$	4.97666	−	8.61982i	0.352786	−	0.611043i	0.986736	+	0.162330i	$0.0519011\pi$
$200$	−12.5182			−0.885169
$201$		0			0
$202$	−2.31054	+	4.00197i	−0.162569	+	0.281578i
$203$	−9.82178	+	5.62611i	−0.689354	+	0.394876i
$204$		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
$209$	−20.7851	−	36.0008i	−1.43774	−	2.49023i
$210$		0			0
$211$	11.6503	−	20.1790i	0.802042	−	1.38918i	−0.116228	−	0.993223i	$-0.537080\pi$
$211$	11.6503	−	20.1790i	0.802042	−	1.38918i	0.918270	−	0.395955i	$-0.129586\pi$
$212$	−1.05219			−0.0722650
$213$		0			0
$214$	16.0172			1.09491
$215$	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
$220$	3.27585	+	5.67394i	0.220858	+	0.382537i
$221$	0.501086	+	0.867907i	0.0337067	+	0.0583817i
$222$		0			0
$223$	5.93770	+	10.2844i	0.397618	+	0.688694i	0.993431	−	0.114429i	$-0.0365037\pi$
$223$	5.93770	+	10.2844i	0.397618	+	0.688694i	−0.595814	+	0.803123i	$0.703170\pi$
$224$	−4.63291	+	2.65382i	−0.309549	+	0.177316i
$225$		0			0
$226$	−3.60056	−	6.23636i	−0.239506	−	0.414836i
$227$	5.96081			0.395633			0.197816	−	0.980239i	$-0.436615\pi$
$227$	5.96081			0.395633			0.197816	+	0.980239i	$0.436615\pi$
$228$		0			0
$229$	−23.7206			−1.56750			−0.783752	−	0.621074i	$-0.786696\pi$
$229$	−23.7206			−1.56750			−0.783752	+	0.621074i	$0.786696\pi$
$230$	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	0.998629	−	0.0523544i	$-0.0166725\pi$
$233$	6.92961	+	12.0024i	0.453974	+	0.786306i	−0.544654	+	0.838661i	$0.683339\pi$
$234$		0			0
$235$	5.49659	−	9.52037i	0.358558	−	0.621040i
$236$	−0.432864	+	0.749743i	−0.0281771	+	0.0488041i
$237$		0			0
$238$	9.79535	−	5.61097i	0.634938	−	0.363705i
$239$	−11.1713	+	19.3492i	−0.722610	+	1.25160i	0.237340	+	0.971427i	$0.423724\pi$
$239$	−11.1713	+	19.3492i	−0.722610	+	1.25160i	−0.959950	+	0.280171i	$0.909609\pi$
$240$		0			0
$241$	9.72063			0.626161			0.313080	−	0.949727i	$-0.398639\pi$
$241$	9.72063			0.626161			0.313080	+	0.949727i	$0.398639\pi$
$242$	−16.9424	+	29.3450i	−1.08910	+	1.88637i
$243$		0			0
$244$	1.15530			0.0739604
$245$	−22.1027	−	0.150491i	−1.41209	−	0.00961450i
$246$		0			0
$247$	2.60957			0.166043
$248$	−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
$257$	5.53002			0.344953			0.172477	−	0.985014i	$-0.444823\pi$
$257$	5.53002			0.344953			0.172477	+	0.985014i	$0.444823\pi$
$258$		0			0
$259$	17.1973	−	9.85095i	1.06859	−	0.612108i
$260$	−0.411283			−0.0255067
$261$		0			0
$262$	−7.07696	+	12.2576i	−0.437216	+	0.757280i
$263$	8.69499			0.536156			0.268078	−	0.963397i	$-0.413612\pi$
$263$	8.69499			0.536156			0.268078	+	0.963397i	$0.413612\pi$
$264$		0			0
$265$	4.60291	−	7.97247i	0.282754	−	0.489745i
$266$	0.100067	−	29.3943i	0.00613552	−	1.80228i
$267$		0			0
$268$	−0.342728	+	0.593622i	−0.0209354	+	0.0362612i
$269$	1.88951	−	3.27272i	0.115205	−	0.199541i	−0.802657	−	0.596442i	$-0.796581\pi$
$269$	1.88951	−	3.27272i	0.115205	−	0.199541i	0.917862	+	0.396900i	$0.129914\pi$
$270$		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
$275$	−28.5761			−1.72320
$276$		0			0
$277$	−25.2658			−1.51808			−0.759038	−	0.651046i	$-0.774330\pi$
$277$	−25.2658			−1.51808			−0.759038	+	0.651046i	$0.774330\pi$
$278$	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	$-0.237746\pi$
$281$	−3.71221	−	6.42974i	−0.221452	−	0.383566i	−0.955249	+	0.295803i	$0.904413\pi$
$282$		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
$286$	−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
$290$	−20.7567			−1.21887
$291$		0			0
$292$	−5.56289			−0.325543
$293$	−15.2899	+	26.4828i	−0.893243	+	1.54714i	−0.0572791	+	0.998358i	$0.518242\pi$
$293$	−15.2899	+	26.4828i	−0.893243	+	1.54714i	−0.835964	+	0.548784i	$0.815091\pi$
$294$		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
$299$	−0.148761	+	0.257662i	−0.00860307	+	0.0149010i
$300$		0			0
$301$	−18.0672	+	10.3493i	−1.04138	+	0.596521i
$302$	4.26810	−	7.39256i	0.245602	−	0.425394i
$303$		0			0
$304$	33.1999			1.90415
$305$	−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	$0.806730\pi$
$308$	−4.76350	+	2.72863i	−0.271425	+	0.155478i
$309$		0			0
$310$	−24.1713			−1.37284
$311$	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
$320$	19.2058			1.07364
$321$		0			0
$322$	2.89661	+	1.68553i	0.161422	+	0.0939309i
$323$	−20.0784			−1.11719
$324$		0			0
$325$	0.896931	−	1.55353i	0.0497528	−	0.0861744i
$326$	−5.91960			−0.327856
$327$		0			0
$328$	−4.19505	+	7.26604i	−0.231633	+	0.401200i
$329$	7.96137	+	4.63271i	0.438925	+	0.255409i
$330$		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
$335$	−2.99858	−	5.19369i	−0.163830	−	0.283762i
$336$		0			0
$337$	5.70406	−	9.87972i	0.310720	−	0.538183i	−0.667798	−	0.744342i	$-0.732763\pi$
$337$	5.70406	−	9.87972i	0.310720	−	0.538183i	0.978518	+	0.206159i	$0.0660965\pi$
$338$	−19.7747			−1.07560
$339$		0			0
$340$	3.16446			0.171617
$341$	−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
$346$	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
$349$	12.1389	+	21.0253i	0.649782	+	1.12546i	0.983175	+	0.182668i	$0.0584733\pi$
$349$	12.1389	+	21.0253i	0.649782	+	1.12546i	−0.333392	+	0.942788i	$0.608193\pi$
$350$	−17.4646	−	10.1626i	−0.933524	−	0.543216i
$351$		0			0
$352$	−5.80094	−	10.0475i	−0.309191	−	0.535535i
$353$	−34.0790			−1.81384			−0.906922	−	0.421299i	$-0.861574\pi$
$353$	−34.0790			−1.81384			−0.906922	+	0.421299i	$0.861574\pi$
$354$		0			0
$355$	5.08239			0.269745
$356$	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	0.784462	−	0.620176i	$-0.212939\pi$
$359$	−2.74465	−	4.75388i	−0.144857	−	0.250900i	−0.929320	+	0.369276i	$0.879606\pi$
$360$		0			0
$361$	−16.6412	+	28.8233i	−0.875851	+	1.51702i
$362$	−9.29062	+	16.0918i	−0.488304	+	0.845768i
$363$		0			0
$364$	0.00117316	−	0.344611i	6.14904e−5	−	0.0180625i
$365$	24.3353	−	42.1500i	1.27377	−	2.20623i
$366$		0			0
$367$	−13.6391			−0.711955			−0.355978	−	0.934495i	$-0.615852\pi$
$367$	−13.6391			−0.711955			−0.355978	+	0.934495i	$0.615852\pi$
$368$	−1.89259	+	3.27807i	−0.0986583	+	0.170881i
$369$		0			0
$370$	36.3435			1.88941
$371$	6.66695	+	3.87948i	0.346131	+	0.201413i
$372$		0			0
$373$	8.92379			0.462056			0.231028	−	0.972947i	$-0.425791\pi$
$373$	8.92379			0.462056			0.231028	+	0.972947i	$0.425791\pi$
$374$	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
$383$	−17.7101			−0.904944			−0.452472	−	0.891779i	$-0.649458\pi$
$383$	−17.7101			−0.904944			−0.452472	+	0.891779i	$0.649458\pi$
$384$		0			0
$385$	0.163508	−	48.0296i	0.00833312	−	2.44781i
$386$	−3.53685			−0.180021
$387$		0			0
$388$	−2.88819	+	5.00249i	−0.146626	+	0.253963i
$389$	21.3255			1.08125			0.540624	−	0.841264i	$-0.318188\pi$
$389$	21.3255			1.08125			0.540624	+	0.841264i	$0.318188\pi$
$390$		0			0
$391$	1.14459	−	1.98248i	0.0578842	−	0.100258i
$392$	17.6292	+	0.120032i	0.890407	+	0.00606251i
$393$		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	0.892713	−	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
$401$	8.73702			0.436306			0.218153	−	0.975915i	$-0.429997\pi$
$401$	8.73702			0.436306			0.218153	+	0.975915i	$0.429997\pi$
$402$		0			0
$403$	1.79802			0.0895656
$404$	−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
$409$	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
$412$	−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
$416$	0.728309			0.0357083
$417$		0			0
$418$	63.8736			3.12416
$419$	−4.32221	+	7.48628i	−0.211154	+	0.365729i	−0.952076	−	0.305862i	$-0.901055\pi$
$419$	−4.32221	+	7.48628i	−0.211154	+	0.365729i	0.740922	+	0.671591i	$0.234389\pi$
$420$		0			0
$421$	−9.23347	−	15.9928i	−0.450012	−	0.779444i	0.548374	−	0.836233i	$-0.315247\pi$
$421$	−9.23347	−	15.9928i	−0.450012	−	0.779444i	−0.998386	+	0.0567894i	$0.981914\pi$
$422$	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
$427$	−7.32024	−	4.25964i	−0.354251	−	0.206138i
$428$	−1.88108	+	3.25813i	−0.0909255	+	0.157488i
$429$		0			0
$430$	−38.1819			−1.84130
$431$	2.90368	−	5.02932i	0.139865	−	0.242254i	−0.787580	−	0.616212i	$-0.788666\pi$
$431$	2.90368	−	5.02932i	0.139865	−	0.242254i	0.927445	+	0.373958i	$0.122000\pi$
$432$		0			0
$433$	3.63877			0.174868			0.0874341	−	0.996170i	$-0.472133\pi$
$433$	3.63877			0.174868			0.0874341	+	0.996170i	$0.472133\pi$
$434$	0.0689473	−	20.2529i	0.00330958	−	0.972172i
$435$		0			0
$436$	−1.68696			−0.0807908
$437$	−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
$446$	−18.2468			−0.864012
$447$		0			0
$448$	−0.0547835	+	16.0924i	−0.00258828	+	0.760294i
$449$	−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
$452$	1.69142			0.0795579
$453$		0			0
$454$	−4.57946	+	7.93186i	−0.214925	+	0.372261i
$455$	2.60599	+	1.51642i	0.122170	+	0.0710908i
$456$		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
$461$	−18.7247	−	32.4322i	−0.872098	−	1.51052i	−0.859823	−	0.510593i	$-0.829426\pi$
$461$	−18.7247	−	32.4322i	−0.872098	−	1.51052i	−0.0122753	−	0.999925i	$-0.503907\pi$
$462$		0			0
$463$	−1.22756	+	2.12620i	−0.0570497	+	0.0988130i	−0.893140	−	0.449779i	$-0.851503\pi$
$463$	−1.22756	+	2.12620i	−0.0570497	+	0.0988130i	0.836090	+	0.548592i	$0.184836\pi$
$464$	19.6436			0.911929
$465$		0			0
$466$	−21.2950			−0.986473
$467$	−16.7054	−	28.9345i	−0.773032	−	1.33893i	−0.935894	−	0.352282i	$-0.885406\pi$
$467$	−16.7054	−	28.9345i	−0.773032	−	1.33893i	0.162862	−	0.986649i	$-0.447928\pi$
$468$		0			0
$469$	4.36031	−	2.49768i	0.201341	−	0.115332i
$470$	8.44563	+	14.6283i	0.389568	+	0.674752i
$471$		0			0
$472$	3.02067	+	5.23196i	0.139038	+	0.240821i
$473$	−22.6222	−	39.1828i	−1.04017	−	1.80163i
$474$		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
$479$	34.6936			1.58519			0.792595	−	0.609748i	$-0.208729\pi$
$479$	34.6936			1.58519			0.792595	+	0.609748i	$0.208729\pi$
$480$		0			0
$481$	−2.70347			−0.123268
$482$	−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	$0.173589\pi$
$488$	4.03103	−	6.98195i	0.182476	−	0.316058i
$489$		0			0
$490$	17.1809	−	29.2958i	0.776155	−	1.32345i
$491$	−7.88691	+	13.6605i	−0.355931	+	0.616491i	−0.987277	−	0.159011i	$-0.949170\pi$
$491$	−7.88691	+	13.6605i	−0.355931	+	0.616491i	0.631346	+	0.775501i	$0.282503\pi$
$492$		0			0
$493$	−11.8799			−0.535042
$494$	−2.00483	+	3.47247i	−0.0902017	+	0.156234i
$495$		0			0
$496$	22.8751			1.02712
$497$	−0.0144972	+	4.25850i	−0.000650290	+	0.191020i
$498$		0			0
$499$	−19.1287			−0.856320			−0.428160	−	0.903703i	$-0.640838\pi$
$499$	−19.1287			−0.856320			−0.428160	+	0.903703i	$0.640838\pi$
$500$	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
$509$	33.5176			1.48564			0.742822	−	0.669489i	$-0.233487\pi$
$509$	33.5176			1.48564			0.742822	+	0.669489i	$0.233487\pi$
$510$		0			0
$511$	35.2478	+	20.5106i	1.55927	+	0.907336i
$512$	−13.8619			−0.612617
$513$		0			0
$514$	−4.24850	+	7.35862i	−0.187393	+	0.324575i
$515$	30.6939			1.35254
$516$		0			0
$517$	−10.0078	+	17.3341i	−0.440144	+	0.762351i
$518$	−0.103668	+	30.4520i	−0.00455491	+	1.33798i
$519$		0			0
$520$	−1.43504	+	2.48556i	−0.0629305	+	0.108999i
$521$	13.3622	−	23.1439i	0.585407	−	1.01395i	−0.409418	−	0.912347i	$-0.634268\pi$
$521$	13.3622	−	23.1439i	0.585407	−	1.01395i	0.994825	−	0.101607i	$-0.0323986\pi$
$522$		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
$527$	−13.8342			−0.602626
$528$		0			0
$529$	−22.3204			−0.970452
$530$	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
$535$	−16.4579	−	28.5059i	−0.711537	−	1.23242i
$536$	2.39167	+	4.14250i	0.103304	+	0.178929i
$537$		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	$0.918812\pi$
$542$	10.1716			0.436909
$543$		0			0
$544$	−5.60370			−0.240257
$545$	7.37975	−	12.7821i	0.316114	−	0.547525i
$546$		0			0
$547$	−11.7212	−	20.3017i	−0.501163	−	0.868040i	−0.999999	−	0.00134350i	$-0.999572\pi$
$547$	−11.7212	−	20.3017i	−0.501163	−	0.868040i	0.498836	−	0.866696i	$-0.333761\pi$
$548$	−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
$553$	−12.5151	−	7.28250i	−0.532195	−	0.309684i
$554$	19.4108	−	33.6204i	0.824684	−	1.42840i
$555$		0			0
$556$	−2.05233			−0.0870381
$557$	12.2557	−	21.2275i	0.519292	−	0.899440i	−0.480457	−	0.877018i	$-0.659529\pi$
$557$	12.2557	−	21.2275i	0.519292	−	0.899440i	0.999749	−	0.0224216i	$-0.00713761\pi$
$558$		0			0
$559$	2.84022			0.120129
$560$	33.1543	+	19.2925i	1.40103	+	0.815255i
$561$		0			0
$562$	11.4078			0.481209
$563$	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	$0.623062\pi$
$572$	0.748837			0.0313105
$573$		0			0
$574$	−11.7515	+	6.73149i	−0.490498	+	0.280967i
$575$	−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	$0.0437055\pi$
$578$	−14.2730			−0.593679
$579$		0			0
$580$	2.43770	−	4.22221i	0.101220	−	0.175318i
$581$	−29.9251	+	17.1417i	−1.24150	+	0.711158i
$582$		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
$587$	−3.26402	−	5.65345i	−0.134721	−	0.233343i	0.790770	−	0.612113i	$-0.209680\pi$
$587$	−3.26402	−	5.65345i	−0.134721	−	0.233343i	−0.925491	+	0.378770i	$0.876347\pi$
$588$		0			0
$589$	−18.0115	+	31.1968i	−0.742151	+	1.28544i
$590$	11.6382			0.479139
$591$		0			0
$592$	−34.3946			−1.41361
$593$	12.7202	+	22.0321i	0.522357	+	0.904749i	0.999662	+	0.0260111i	$0.00828051\pi$
$593$	12.7202	+	22.0321i	0.522357	+	0.904749i	−0.477305	+	0.878738i	$0.658386\pi$
$594$		0			0
$595$	−20.0508	−	11.6675i	−0.822002	−	0.478322i
$596$	−3.89569	−	6.74753i	−0.159574	−	0.276390i
$597$		0			0
$598$	−0.228575	−	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
$601$	6.46722	+	11.2016i	0.263804	+	0.456921i	0.967249	−	0.253828i	$-0.0816896\pi$
$601$	6.46722	+	11.2016i	0.263804	+	0.456921i	−0.703446	+	0.710749i	$0.748356\pi$
$602$	0.108912	−	31.9924i	0.00443892	−	1.30391i
$603$		0			0
$604$	1.00251	+	1.73639i	0.0407914	+	0.0706527i
$605$	69.6342			2.83103
$606$		0			0
$607$	−23.0756			−0.936608			−0.468304	−	0.883567i	$-0.655135\pi$
$607$	−23.0756			−0.936608			−0.468304	+	0.883567i	$0.655135\pi$
$608$	−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	$0.0508141\pi$
$614$	22.1101	−	38.2958i	0.892290	−	1.54549i
$615$		0			0
$616$	−0.130414	+	38.3085i	−0.00525452	+	1.54349i
$617$	−10.8220	+	18.7443i	−0.435679	+	0.754618i	−0.997351	−	0.0727418i	$-0.976825\pi$
$617$	−10.8220	+	18.7443i	−0.435679	+	0.754618i	0.561672	+	0.827360i	$0.310158\pi$
$618$		0			0
$619$	−9.57941			−0.385029			−0.192514	−	0.981294i	$-0.561664\pi$
$619$	−9.57941			−0.385029			−0.192514	+	0.981294i	$0.561664\pi$
$620$	2.83872	−	4.91680i	0.114006	−	0.197463i
$621$		0			0
$622$	−3.95278			−0.158492
$623$	−32.7554	+	18.7630i	−1.31232	+	0.751722i
$624$		0			0
$625$	−25.1468			−1.00587
$626$	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
$635$	−28.9219			−1.14773
$636$		0			0
$637$	−1.27803	+	2.17921i	−0.0506374	+	0.0863435i
$638$	37.7924			1.49621
$639$		0			0
$640$	−21.1272	+	36.5933i	−0.835124	+	1.44648i
$641$	−8.25214			−0.325940			−0.162970	−	0.986631i	$-0.552107\pi$
$641$	−8.25214			−0.325940			−0.162970	+	0.986631i	$0.552107\pi$
$642$		0			0
$643$	−12.2159	+	21.1585i	−0.481748	+	0.834411i	−0.999781	−	0.0209493i	$-0.993331\pi$
$643$	−12.2159	+	21.1585i	−0.481748	+	0.834411i	0.518033	+	0.855361i	$0.326664\pi$
$644$	−0.683045	+	0.391262i	−0.0269157	+	0.0154179i
$645$		0			0
$646$	15.4254	−	26.7176i	0.606906	−	1.05119i
$647$	−19.3432	+	33.5034i	−0.760461	+	1.31716i	0.182153	+	0.983270i	$0.441693\pi$
$647$	−19.3432	+	33.5034i	−0.760461	+	1.31716i	−0.942613	+	0.333886i	$0.891640\pi$
$648$		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
$653$	7.65430			0.299536			0.149768	−	0.988721i	$-0.452147\pi$
$653$	7.65430			0.299536			0.149768	+	0.988721i	$0.452147\pi$
$654$		0			0
$655$	29.0867			1.13651
$656$	−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	−0.947747	−	0.319023i	$-0.896645\pi$
$659$	−19.2572	−	33.3545i	−0.750156	−	1.29931i	0.197591	−	0.980285i	$-0.436688\pi$
$660$		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
$664$	−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
$668$	−1.27701			−0.0494091
$669$		0			0
$670$	9.21478			0.355998
$671$	9.20190	−	15.9382i	0.355235	−	0.615285i
$672$		0			0
$673$	−0.630680	−	1.09237i	−0.0243109	−	0.0421077i	0.853614	−	0.520906i	$-0.174406\pi$
$673$	−0.630680	−	1.09237i	−0.0243109	−	0.0421077i	−0.877925	+	0.478798i	$0.841073\pi$
$674$	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
$679$	36.7447	−	21.0481i	1.41013	−	0.807751i
$680$	11.0414	−	19.1242i	0.423417	−	0.733379i
$681$		0			0
$682$	44.0095			1.68521
$683$	2.76560	−	4.79016i	0.105823	−	0.183290i	−0.808251	−	0.588838i	$-0.799586\pi$
$683$	2.76560	−	4.79016i	0.105823	−	0.183290i	0.914074	+	0.405547i	$0.132919\pi$
$684$		0			0
$685$	21.5487			0.823334
$686$	24.4977	+	14.4793i	0.935327	+	0.552824i
$687$		0			0
$688$	36.1344			1.37761
$689$	−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
$698$	−37.3035			−1.41196
$699$		0			0
$700$	4.11831	−	2.35905i	0.155658	−	0.0891638i
$701$	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
$704$	−34.9686			−1.31793
$705$		0			0
$706$	26.1816	−	45.3479i	0.985358	−	1.70669i
$707$	−0.0270882	+	7.95703i	−0.00101876	+	0.299255i
$708$		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
$713$	−2.05353	−	3.55681i	−0.0769052	−	0.133204i
$714$		0			0
$715$	−3.27585	+	5.67394i	−0.122510	+	0.212193i
$716$	−7.18094			−0.268364
$717$		0			0
$718$	8.43445			0.314771
$719$	−16.1938	−	28.0485i	−0.603927	−	1.04603i	−0.992220	−	0.124496i	$-0.960269\pi$
$719$	−16.1938	−	28.0485i	−0.603927	−	1.04603i	0.388293	−	0.921536i	$-0.373065\pi$
$720$		0			0
$721$	−0.0875527	+	25.7182i	−0.00326063	+	0.957796i
$722$	−25.5695	−	44.2877i	−0.951600	−	1.64822i
$723$		0			0
$724$	−2.18221	−	3.77970i	−0.0811013	−	0.140472i
$725$	10.6323	+	18.4157i	0.394874	+	0.683943i
$726$		0			0
$727$	−12.6174	−	21.8540i	−0.467953	−	0.810519i	0.531376	−	0.847136i	$-0.321675\pi$
$727$	−12.6174	−	21.8540i	−0.467953	−	0.810519i	−0.999329	+	0.0366171i	$0.988342\pi$
$728$	−2.07854	−	1.20950i	−0.0770357	−	0.0448269i
$729$		0			0
$730$	37.3917	+	64.7644i	1.38393	+	2.39704i
$731$	−21.8530			−0.808264
$732$		0			0
$733$	2.84672			0.105146			0.0525731	−	0.998617i	$-0.483258\pi$
$733$	2.84672			0.105146			0.0525731	+	0.998617i	$0.483258\pi$
$734$	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	$0.315738\pi$
$740$	−4.26824	+	7.39282i	−0.156904	+	0.271765i
$741$		0			0
$742$	−10.2843	+	5.89103i	−0.377547	+	0.216267i
$743$	−2.29535	+	3.97566i	−0.0842082	+	0.145853i	−0.905054	−	0.425298i	$-0.860169\pi$
$743$	−2.29535	+	3.97566i	−0.0842082	+	0.145853i	0.820845	+	0.571151i	$0.193503\pi$
$744$		0			0
$745$	68.1681			2.49748
$746$	−6.85581	+	11.8746i	−0.251009	+	0.434760i
$747$		0			0
$748$	−5.76165			−0.210667
$749$	23.9318	−	13.7086i	0.874451	−	0.500903i
$750$		0			0
$751$	31.4356			1.14710			0.573551	−	0.819170i	$-0.305566\pi$
$751$	31.4356			1.14710			0.573551	+	0.819170i	$0.305566\pi$
$752$	−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
$761$	−46.4873			−1.68516			−0.842582	−	0.538567i	$-0.818966\pi$
$761$	−46.4873			−1.68516			−0.842582	+	0.538567i	$0.818966\pi$
$762$		0			0
$763$	10.6890	+	6.21990i	0.386967	+	0.225175i
$764$	3.50785			0.126910
$765$		0			0
$766$	13.6060	−	23.5663i	0.491605	−	0.851484i
$767$	−0.865728			−0.0312596
$768$		0			0
$769$	−7.08532	+	12.2721i	−0.255503	+	0.442545i	−0.965032	−	0.262132i	$-0.915574\pi$
$769$	−7.08532	+	12.2721i	−0.255503	+	0.442545i	0.709529	+	0.704676i	$0.248908\pi$
$770$	63.7858	+	37.1169i	2.29868	+	1.33760i
$771$		0			0
$772$	0.415373	−	0.719448i	0.0149496	−	0.0258935i
$773$	17.0042	−	29.4522i	0.611600	−	1.05932i	−0.379371	−	0.925245i	$-0.623860\pi$
$773$	17.0042	−	29.4522i	0.611600	−	1.05932i	0.990971	−	0.134078i	$-0.0428072\pi$
$774$		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
$779$	24.0880			0.863043
$780$		0			0
$781$	−9.25368			−0.331123
$782$	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
$787$	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
$790$	−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
$794$	−3.43515			−0.121909
$795$		0			0
$796$	−3.59219			−0.127322
$797$	9.25192	−	16.0248i	0.327720	−	0.567627i	−0.654339	−	0.756201i	$-0.727053\pi$
$797$	9.25192	−	16.0248i	0.327720	−	0.567627i	0.982059	+	0.188574i	$0.0603865\pi$
$798$		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
$803$	−44.3081	+	76.7439i	−1.56360	+	2.70823i
$804$		0			0
$805$	0.0234456	−	6.88703i	0.000826348	−	0.242736i
$806$	−1.38135	+	2.39257i	−0.0486559	+	0.0842745i
$807$		0			0
$808$	−7.57440			−0.266466
$809$	−20.5407	+	35.5775i	−0.722172	+	1.25084i	0.237956	+	0.971276i	$0.423523\pi$
$809$	−20.5407	+	35.5775i	−0.722172	+	1.25084i	−0.960128	+	0.279562i	$0.909811\pi$
$810$		0			0
$811$	−43.1361			−1.51471			−0.757357	−	0.653001i	$-0.773510\pi$
$811$	−43.1361			−1.51471			−0.757357	+	0.653001i	$0.773510\pi$
$812$	3.53081	+	2.05457i	0.123907	+	0.0721014i
$813$		0			0
$814$	−66.1719			−2.31932
$815$	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	$0.766369\pi$
$824$	−24.4815			−0.852853
$825$		0			0
$826$	−0.0331975	+	9.75160i	−0.00115509	+	0.339302i
$827$	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	−0.999313	−	0.0370721i	$-0.988197\pi$
$829$	−13.4619	+	23.3167i	−0.467551	+	0.809822i	0.531762	+	0.846894i	$0.321530\pi$
$830$	−63.2416			−2.19515
$831$		0			0
$832$	1.09758	−	1.90106i	0.0380517	−	0.0659074i
$833$	9.83333	−	16.7671i	0.340705	−	0.580947i
$834$		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
$839$	5.61191	+	9.72012i	0.193745	+	0.335576i	0.946488	−	0.322738i	$-0.104603\pi$
$839$	5.61191	+	9.72012i	0.193745	+	0.335576i	−0.752744	+	0.658314i	$0.771270\pi$
$840$		0			0
$841$	5.34853	−	9.26393i	0.184432	−	0.319446i
$842$	28.3749			0.977864
$843$		0			0
$844$	−8.40930			−0.289460
$845$	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
$850$	−10.6037	−	18.3662i	−0.363704	−	0.629954i
$851$	3.08765	+	5.34796i	0.105843	+	0.183326i
$852$		0			0
$853$	6.09672	+	10.5598i	0.208748	+	0.361562i	0.951320	−	0.308204i	$-0.0997279\pi$
$853$	6.09672	+	10.5598i	0.208748	+	0.361562i	−0.742573	+	0.669766i	$0.766395\pi$
$854$	11.2920	−	6.46830i	0.386405	−	0.221341i
$855$		0			0
$856$	13.1268	+	22.7363i	0.448666	+	0.777112i
$857$	−37.4382			−1.27887			−0.639433	−	0.768847i	$-0.720831\pi$
$857$	−37.4382			−1.27887			−0.639433	+	0.768847i	$0.720831\pi$
$858$		0			0
$859$	0.757734			0.0258535			0.0129268	−	0.999916i	$-0.495885\pi$
$859$	0.757734			0.0258535			0.0129268	+	0.999916i	$0.495885\pi$
$860$	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	0.592862	−	0.805304i	$-0.297998\pi$
$863$	−11.7796	−	20.4029i	−0.400983	−	0.694522i	−0.993845	+	0.110782i	$0.964665\pi$
$864$		0			0
$865$	15.5569	−	26.9453i	0.528949	−	0.916167i
$866$	−2.79553	+	4.84200i	−0.0949959	+	0.164538i
$867$		0			0
$868$	4.11166	+	2.39257i	0.139559	+	0.0812089i
$869$	15.7321	−	27.2487i	0.533673	−	0.924349i
$870$		0			0
$871$	−0.685455			−0.0232258
$872$	−5.88609	+	10.1950i	−0.199328	+	0.345247i
$873$		0			0
$874$	9.15892			0.309805
$875$	0.000839737	−	0.246669i	2.83883e−5	−	0.00833893i
$876$		0			0
$877$	36.6739			1.23839			0.619196	−	0.785237i	$-0.287459\pi$
$877$	36.6739			1.23839			0.619196	+	0.785237i	$0.287459\pi$
$878$	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
$887$	7.82601			0.262772			0.131386	−	0.991331i	$-0.458057\pi$
$887$	7.82601			0.262772			0.131386	+	0.991331i	$0.458057\pi$
$888$		0			0
$889$	0.0824983	−	24.2335i	0.00276690	−	0.812765i
$890$	−69.2230			−2.32036
$891$		0			0
$892$	2.14294	−	3.71168i	0.0717508	−	0.124276i
$893$	25.1734			0.842397
$894$		0			0
$895$	31.4136	−	54.4100i	1.05004	−	1.81872i
$896$	−30.6010	−	17.8067i	−1.02231	−	0.594879i
$897$		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
$902$	−14.7142	−	25.4858i	−0.489930	−	0.848584i
$903$		0			0
$904$	5.90167	−	10.2220i	0.196287	−	0.339978i
$905$	38.1851			1.26931
$906$		0			0
$907$	51.9332			1.72442			0.862208	−	0.506555i	$-0.169081\pi$
$907$	51.9332			1.72442			0.862208	+	0.506555i	$0.169081\pi$
$908$	−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	−0.992985	−	0.118240i	$-0.962275\pi$
$911$	−18.0762	−	31.3089i	−0.598891	−	1.03731i	0.394094	−	0.919070i	$-0.371059\pi$
$912$		0			0
$913$	−37.4697	−	64.8995i	−1.24007	−	2.14786i
$914$	15.3593	+	26.6031i	0.508042	+	0.879954i
$915$		0			0
$916$	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	$0.774317\pi$
$920$	6.55585			0.216140
$921$		0			0
$922$	57.5420			1.89504
$923$	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
$929$	−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
$931$	−25.0083	−	44.0048i	−0.819612	−	1.44220i
$932$	2.50092	−	4.33173i	0.0819205	−	0.141890i
$933$		0			0
$934$	51.3364			1.67978
$935$	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	$0.639368\pi$
$938$	−0.0262847	+	7.72100i	−0.000858225	+	0.252100i
$939$		0			0
$940$	−3.96748			−0.129405
$941$	−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
$950$	−55.2223			−1.79165
$951$		0			0
$952$	15.9925	+	9.30603i	0.518321	+	0.301610i
$953$	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
$956$	8.06352			0.260793
$957$		0			0
$958$	−26.6537	+	46.1656i	−0.861144	+	1.49154i
$959$	−0.0614665	+	18.0555i	−0.00198486	+	0.583043i
$960$		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
$965$	3.63417	+	6.29457i	0.116988	+	0.202629i
$966$		0			0
$967$	−21.0402	+	36.4427i	−0.676606	+	1.17192i	0.299390	+	0.954131i	$0.403217\pi$
$967$	−21.0402	+	36.4427i	−0.676606	+	1.17192i	−0.975997	+	0.217786i	$0.930117\pi$
$968$	−55.5403			−1.78513
$969$		0			0
$970$	77.6536			2.49331
$971$	17.5774	+	30.4450i	0.564087	+	0.977027i	0.997134	+	0.0756560i	$0.0241051\pi$
$971$	17.5774	+	30.4450i	0.564087	+	0.977027i	−0.433047	+	0.901371i	$0.642562\pi$
$972$		0			0
$973$	13.0040	+	7.56703i	0.416890	+	0.242588i
$974$	−0.737391	−	1.27720i	−0.0236275	−	0.0409241i
$975$		0			0
$976$	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
$979$	−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
$983$	22.1601			0.706798			0.353399	−	0.935473i	$-0.385026\pi$
$983$	22.1601			0.706798			0.353399	+	0.935473i	$0.385026\pi$
$984$		0			0
$985$	15.9923			0.509558
$986$	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	$-0.0315445\pi$
$992$	−5.02686	+	8.70677i	−0.159603	+	0.276440i
$993$		0			0
$994$	−5.65551	−	3.29093i	−0.179382	−	0.104382i
$995$	15.7143	−	27.2180i	0.498178	−	0.862869i
$996$		0			0
$997$	−39.9031			−1.26374			−0.631872	−	0.775073i	$-0.717713\pi$
$997$	−39.9031			−1.26374			−0.631872	+	0.775073i	$0.717713\pi$
$998$	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.g.j.109.2		8
3.2	odd	2		567.2.g.k.109.3		8
7.2	even	3		567.2.h.k.352.3		8
9.2	odd	6		567.2.h.j.298.2		8
9.4	even	3		567.2.e.c.487.2	yes	8
9.5	odd	6		567.2.e.d.487.3	yes	8
9.7	even	3		567.2.h.k.298.3		8
21.2	odd	6		567.2.h.j.352.2		8
63.2	odd	6		567.2.g.k.541.3		8
63.4	even	3		3969.2.a.x.1.3		4
63.16	even	3	inner	567.2.g.j.541.2		8
63.23	odd	6		567.2.e.d.163.3	yes	8
63.31	odd	6		3969.2.a.w.1.3		4
63.32	odd	6		3969.2.a.s.1.2		4
63.58	even	3		567.2.e.c.163.2	✓	8
63.59	even	6		3969.2.a.t.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.2	✓	8	63.58	even	3
567.2.e.c.487.2	yes	8	9.4	even	3
567.2.e.d.163.3	yes	8	63.23	odd	6
567.2.e.d.487.3	yes	8	9.5	odd	6
567.2.g.j.109.2		8	1.1	even	1	trivial
567.2.g.j.541.2		8	63.16	even	3	inner
567.2.g.k.109.3		8	3.2	odd	2
567.2.g.k.541.3		8	63.2	odd	6
567.2.h.j.298.2		8	9.2	odd	6
567.2.h.j.352.2		8	21.2	odd	6
567.2.h.k.298.3		8	9.7	even	3
567.2.h.k.352.3		8	7.2	even	3
3969.2.a.s.1.2		4	63.32	odd	6
3969.2.a.t.1.2		4	63.59	even	6
3969.2.a.w.1.3		4	63.31	odd	6
3969.2.a.x.1.3		4	63.4	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.768262 + 1.33067i) q^{2} +(-0.180452 - 0.312552i) q^{4} +3.15761 q^{5} +(-0.00900690 + 2.64574i) q^{7} -2.51851 q^{8} +O(q^{10})\)	\(q+(-0.768262 + 1.33067i) q^{2} +(-0.180452 - 0.312552i) q^{4} +3.15761 q^{5} +(-0.00900690 + 2.64574i) q^{7} -2.51851 q^{8} +(-2.42587 + 4.20173i) q^{10} -5.74916 q^{11} +(0.180452 - 0.312552i) q^{13} +(-3.51368 - 2.04460i) q^{14} +(2.29578 - 3.97640i) q^{16} +(-1.38842 + 2.40481i) q^{17} +(3.61533 + 6.26193i) q^{19} +(-0.569796 - 0.986916i) q^{20} +(4.41686 - 7.65023i) q^{22} -0.824381 q^{23} +4.97047 q^{25} +(0.277269 + 0.480243i) q^{26} +(0.828555 - 0.474613i) q^{28} +(2.13910 + 3.70502i) q^{29} +(2.49099 + 4.31453i) q^{31} +(1.00901 + 1.74765i) q^{32} +(-2.13334 - 3.69505i) q^{34} +(-0.0284402 + 8.35419i) q^{35} +(-3.74542 - 6.48725i) q^{37} -11.1101 q^{38} -7.95246 q^{40} +(1.66569 - 2.88506i) q^{41} +(3.93487 + 6.81540i) q^{43} +(1.03745 + 1.79691i) q^{44} +(0.633340 - 1.09698i) q^{46} +(1.74075 - 3.01506i) q^{47} +(-6.99984 - 0.0476598i) q^{49} +(-3.81862 + 6.61405i) q^{50} -0.130252 q^{52} +(1.45772 - 2.52485i) q^{53} -18.1536 q^{55} +(0.0226840 - 6.66331i) q^{56} -6.57354 q^{58} +(-1.19939 - 2.07740i) q^{59} +(-1.60056 + 2.77226i) q^{61} -7.65494 q^{62} +6.08239 q^{64} +(0.569796 - 0.986916i) q^{65} +(-0.949637 - 1.64482i) q^{67} +1.00217 q^{68} +(-11.0948 - 6.45605i) q^{70} +1.60957 q^{71} +(7.70688 - 13.3487i) q^{73} +11.5098 q^{74} +(1.30478 - 2.25995i) q^{76} +(0.0517821 - 15.2108i) q^{77} +(-2.73641 + 4.73960i) q^{79} +(7.24916 - 12.5559i) q^{80} +(2.55937 + 4.43296i) q^{82} +(6.51742 + 11.2885i) q^{83} +(-4.38408 + 7.59346i) q^{85} -12.0921 q^{86} +14.4793 q^{88} +(7.13384 + 12.3562i) q^{89} +(0.825304 + 0.480243i) q^{91} +(0.148761 + 0.257662i) q^{92} +(2.67470 + 4.63271i) q^{94} +(11.4158 + 19.7727i) q^{95} +(-8.00266 - 13.8610i) q^{97} +(5.44113 - 9.27785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 5 q^{4} + 4 q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) \) 8 * q - q^2 - 5 * q^4 + 4 * q^5 - 2 * q^7 - 6 * q^8	\( 8 q - q^{2} - 5 q^{4} + 4 q^{5} - 2 q^{7} - 6 q^{8} + 7 q^{10} + 10 q^{11} + 5 q^{13} + 7 q^{14} + q^{16} - 6 q^{17} + 8 q^{19} + 8 q^{20} + 7 q^{22} - 24 q^{23} + 16 q^{25} - q^{26} + 5 q^{28} + 10 q^{29} + 18 q^{31} + 10 q^{32} + 23 q^{35} - 40 q^{38} - 36 q^{40} + 5 q^{41} + 7 q^{43} - 13 q^{44} - 12 q^{46} + 21 q^{47} + 2 q^{49} - 38 q^{50} - 50 q^{52} + 12 q^{53} - 52 q^{55} - 33 q^{56} - 14 q^{58} - 6 q^{59} + 20 q^{61} + 36 q^{62} - 46 q^{64} - 8 q^{65} + 5 q^{67} + 102 q^{68} - 46 q^{70} - 18 q^{71} + 6 q^{73} - 5 q^{76} - 16 q^{77} + 10 q^{79} + 2 q^{80} + 35 q^{82} - 9 q^{83} + 9 q^{85} - 44 q^{86} + 36 q^{88} + 22 q^{89} + 13 q^{91} + 36 q^{92} + 15 q^{94} + 16 q^{95} + 9 q^{97} + 11 q^{98}+O(q^{100}) \) 8 * q - q^2 - 5 * q^4 + 4 * q^5 - 2 * q^7 - 6 * q^8 + 7 * q^10 + 10 * q^11 + 5 * q^13 + 7 * q^14 + q^16 - 6 * q^17 + 8 * q^19 + 8 * q^20 + 7 * q^22 - 24 * q^23 + 16 * q^25 - q^26 + 5 * q^28 + 10 * q^29 + 18 * q^31 + 10 * q^32 + 23 * q^35 - 40 * q^38 - 36 * q^40 + 5 * q^41 + 7 * q^43 - 13 * q^44 - 12 * q^46 + 21 * q^47 + 2 * q^49 - 38 * q^50 - 50 * q^52 + 12 * q^53 - 52 * q^55 - 33 * q^56 - 14 * q^58 - 6 * q^59 + 20 * q^61 + 36 * q^62 - 46 * q^64 - 8 * q^65 + 5 * q^67 + 102 * q^68 - 46 * q^70 - 18 * q^71 + 6 * q^73 - 5 * q^76 - 16 * q^77 + 10 * q^79 + 2 * q^80 + 35 * q^82 - 9 * q^83 + 9 * q^85 - 44 * q^86 + 36 * q^88 + 22 * q^89 + 13 * q^91 + 36 * q^92 + 15 * q^94 + 16 * q^95 + 9 * q^97 + 11 * q^98

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