LMFDB - Embedded newform 273.2.bd.a.127.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(43,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("273.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bd (of order $6$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 $ x^16 + 22x^14 + 187x^12 + 774x^10 + 1619x^8 + 1618x^6 + 690x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.8
Root			$-2.45308i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.a.43.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.12443 - 1.22654i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.00879 - 3.47933i) q^{4} +0.0682999i q^{5} +(-2.12443 - 1.22654i) q^{6} +(0.866025 + 0.500000i) q^{7} -4.94928i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(2.12443 - 1.22654i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.00879 - 3.47933i) q^{4} +0.0682999i q^{5} +(-2.12443 - 1.22654i) q^{6} +(0.866025 + 0.500000i) q^{7} -4.94928i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0837724 + 0.145098i) q^{10} +(0.587365 - 0.339115i) q^{11} -4.01758 q^{12} +(-3.24851 + 1.56434i) q^{13} +2.45308 q^{14} +(0.0591494 - 0.0341499i) q^{15} +(-2.05290 - 3.55573i) q^{16} +(-0.467479 + 0.809698i) q^{17} +2.45308i q^{18} +(-1.79066 - 1.03384i) q^{19} +(0.237638 + 0.137200i) q^{20} -1.00000i q^{21} +(0.831875 - 1.44085i) q^{22} +(2.14974 + 3.72346i) q^{23} +(-4.28620 + 2.47464i) q^{24} +4.99534 q^{25} +(-4.98251 + 7.30775i) q^{26} +1.00000 q^{27} +(3.47933 - 2.00879i) q^{28} +(-4.00723 - 6.94072i) q^{29} +(0.0837724 - 0.145098i) q^{30} +10.0622i q^{31} +(-0.150064 - 0.0866393i) q^{32} +(-0.587365 - 0.339115i) q^{33} +2.29352i q^{34} +(-0.0341499 + 0.0591494i) q^{35} +(2.00879 + 3.47933i) q^{36} +(0.456821 - 0.263746i) q^{37} -5.07216 q^{38} +(2.97901 + 2.03113i) q^{39} +0.338035 q^{40} +(4.44943 - 2.56888i) q^{41} +(-1.22654 - 2.12443i) q^{42} +(-0.894286 + 1.54895i) q^{43} -2.72485i q^{44} +(-0.0591494 - 0.0341499i) q^{45} +(9.13393 + 5.27348i) q^{46} -4.22889i q^{47} +(-2.05290 + 3.55573i) q^{48} +(0.500000 + 0.866025i) q^{49} +(10.6122 - 6.12697i) q^{50} +0.934958 q^{51} +(-1.08274 + 14.4451i) q^{52} -3.21495 q^{53} +(2.12443 - 1.22654i) q^{54} +(0.0231615 + 0.0401169i) q^{55} +(2.47464 - 4.28620i) q^{56} +2.06767i q^{57} +(-17.0261 - 9.83004i) q^{58} +(-7.21179 - 4.16373i) q^{59} -0.274400i q^{60} +(-0.505267 + 0.875148i) q^{61} +(12.3416 + 21.3763i) q^{62} +(-0.866025 + 0.500000i) q^{63} +7.78654 q^{64} +(-0.106844 - 0.221873i) q^{65} -1.66375 q^{66} +(-6.32225 + 3.65015i) q^{67} +(1.87814 + 3.25303i) q^{68} +(2.14974 - 3.72346i) q^{69} +0.167545i q^{70} +(-8.58321 - 4.95552i) q^{71} +(4.28620 + 2.47464i) q^{72} +3.42254i q^{73} +(0.646989 - 1.12062i) q^{74} +(-2.49767 - 4.32609i) q^{75} +(-7.19411 + 4.15352i) q^{76} +0.678230 q^{77} +(8.81995 + 0.661105i) q^{78} -14.0484 q^{79} +(0.242856 - 0.140213i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.30166 - 10.9148i) q^{82} -7.03411i q^{83} +(-3.47933 - 2.00879i) q^{84} +(-0.0553023 - 0.0319288i) q^{85} +4.38750i q^{86} +(-4.00723 + 6.94072i) q^{87} +(-1.67838 - 2.90703i) q^{88} +(13.6436 - 7.87714i) q^{89} -0.167545 q^{90} +(-3.59547 - 0.269500i) q^{91} +17.2735 q^{92} +(8.71409 - 5.03108i) q^{93} +(-5.18689 - 8.98395i) q^{94} +(0.0706109 - 0.122302i) q^{95} +0.173279i q^{96} +(-14.4370 - 8.33523i) q^{97} +(2.12443 + 1.22654i) q^{98} +0.678230i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	2.12443	−	1.22654i	1.50220	−	0.867293i	0.502199	−	0.864752i	$-0.332524\pi$
$2$	2.12443	−	1.22654i	1.50220	−	0.867293i	0.999997	−	0.00254149i	$-0.000808981\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	2.00879	−	3.47933i	1.00440	−	1.73966i
$5$			0.0682999i			0.0305446i	0.999883	+	0.0152723i	$0.00486152\pi$
$5$			0.0682999i			0.0305446i	−0.999883	+	0.0152723i	$0.995138\pi$
$6$	−2.12443	−	1.22654i	−0.867293	−	0.500732i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		−	4.94928i		−	1.74984i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.0837724	+	0.145098i	0.0264912	+	0.0458840i
$11$	0.587365	−	0.339115i	0.177097	−	0.102247i	−0.408831	−	0.912610i	$-0.634063\pi$
$11$	0.587365	−	0.339115i	0.177097	−	0.102247i	0.585928	+	0.810363i	$0.300730\pi$
$12$	−4.01758			−1.15978
$13$	−3.24851	+	1.56434i	−0.900976	+	0.433869i
$13$	−3.24851	+	1.56434i	−0.900976	+	0.433869i
$14$	2.45308			0.655612
$15$	0.0591494	−	0.0341499i	0.0152723	−	0.00881748i
$16$	−2.05290	−	3.55573i	−0.513225	−	0.888932i
$17$	−0.467479	+	0.809698i	−0.113380	+	0.196381i	−0.917131	−	0.398586i	$-0.869501\pi$
$17$	−0.467479	+	0.809698i	−0.113380	+	0.196381i	0.803751	+	0.594966i	$0.202835\pi$
$18$			2.45308i			0.578196i
$19$	−1.79066	−	1.03384i	−0.410805	−	0.237178i	0.280331	−	0.959903i	$-0.409556\pi$
$19$	−1.79066	−	1.03384i	−0.410805	−	0.237178i	−0.691135	+	0.722725i	$0.742889\pi$
$20$	0.237638	+	0.137200i	0.0531374	+	0.0306789i
$21$		−	1.00000i		−	0.218218i
$22$	0.831875	−	1.44085i	0.177356	−	0.307190i
$23$	2.14974	+	3.72346i	0.448252	+	0.776395i	0.998272	−	0.0587563i	$-0.0187135\pi$
$23$	2.14974	+	3.72346i	0.448252	+	0.776395i	−0.550021	+	0.835151i	$0.685380\pi$
$24$	−4.28620	+	2.47464i	−0.874918	+	0.505134i
$25$	4.99534			0.999067
$26$	−4.98251	+	7.30775i	−0.977150	+	1.43317i
$27$	1.00000			0.192450
$28$	3.47933	−	2.00879i	0.657531	−	0.379626i
$29$	−4.00723	−	6.94072i	−0.744124	−	1.28886i	−0.950603	−	0.310409i	$-0.899534\pi$
$29$	−4.00723	−	6.94072i	−0.744124	−	1.28886i	0.206479	−	0.978451i	$-0.433799\pi$
$30$	0.0837724	−	0.145098i	0.0152947	−	0.0264912i
$31$			10.0622i			1.80722i	0.428358	+	0.903609i	$0.359092\pi$
$31$			10.0622i			1.80722i	−0.428358	+	0.903609i	$0.640908\pi$
$32$	−0.150064	−	0.0866393i	−0.0265278	−	0.0153158i
$33$	−0.587365	−	0.339115i	−0.102247	−	0.0590324i
$34$			2.29352i			0.393336i
$35$	−0.0341499	+	0.0591494i	−0.00577239	+	0.00999808i
$36$	2.00879	+	3.47933i	0.334799	+	0.579888i
$37$	0.456821	−	0.263746i	0.0751010	−	0.0433596i	−0.461979	−	0.886891i	$-0.652861\pi$
$37$	0.456821	−	0.263746i	0.0751010	−	0.0433596i	0.537080	+	0.843531i	$0.319527\pi$
$38$	−5.07216			−0.822812
$39$	2.97901	+	2.03113i	0.477024	+	0.325241i
$40$	0.338035			0.0534481
$41$	4.44943	−	2.56888i	0.694884	−	0.401191i	−0.110555	−	0.993870i	$-0.535263\pi$
$41$	4.44943	−	2.56888i	0.694884	−	0.401191i	0.805439	+	0.592679i	$0.201930\pi$
$42$	−1.22654	−	2.12443i	−0.189259	−	0.327806i
$43$	−0.894286	+	1.54895i	−0.136377	+	0.236212i	−0.926123	−	0.377222i	$-0.876879\pi$
$43$	−0.894286	+	1.54895i	−0.136377	+	0.236212i	0.789745	+	0.613435i	$0.210213\pi$
$44$		−	2.72485i		−	0.410786i
$45$	−0.0591494	−	0.0341499i	−0.00881748	−	0.00509077i
$46$	9.13393	+	5.27348i	1.34672	+	0.777532i
$47$		−	4.22889i		−	0.616846i	−0.951249	−	0.308423i	$-0.900199\pi$
$47$		−	4.22889i		−	0.616846i	0.951249	−	0.308423i	$-0.0998013\pi$
$48$	−2.05290	+	3.55573i	−0.296311	+	0.513225i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	10.6122	−	6.12697i	1.50079	−	0.866484i
$51$	0.934958			0.130920
$52$	−1.08274	+	14.4451i	−0.150149	+	2.00317i
$53$	−3.21495			−0.441608			−0.220804	−	0.975318i	$-0.570868\pi$
$53$	−3.21495			−0.441608			−0.220804	+	0.975318i	$0.570868\pi$
$54$	2.12443	−	1.22654i	0.289098	−	0.166911i
$55$	0.0231615	+	0.0401169i	0.00312310	+	0.00540937i
$56$	2.47464	−	4.28620i	0.330688	−	0.572768i
$57$			2.06767i			0.273870i
$58$	−17.0261	−	9.83004i	−2.23564	−	1.29075i
$59$	−7.21179	−	4.16373i	−0.938895	−	0.542071i	−0.0492814	−	0.998785i	$-0.515693\pi$
$59$	−7.21179	−	4.16373i	−0.938895	−	0.542071i	−0.889614	+	0.456714i	$0.849026\pi$
$60$		−	0.274400i		−	0.0354249i
$61$	−0.505267	+	0.875148i	−0.0646928	+	0.112051i	−0.896558	−	0.442927i	$-0.853940\pi$
$61$	−0.505267	+	0.875148i	−0.0646928	+	0.112051i	0.831865	+	0.554978i	$0.187273\pi$
$62$	12.3416	+	21.3763i	1.56739	+	2.71480i
$63$	−0.866025	+	0.500000i	−0.109109	+	0.0629941i
$64$	7.78654			0.973317
$65$	−0.106844	−	0.221873i	−0.0132524	−	0.0275200i
$66$	−1.66375			−0.204794
$67$	−6.32225	+	3.65015i	−0.772385	+	0.445937i	−0.833725	−	0.552180i	$-0.813796\pi$
$67$	−6.32225	+	3.65015i	−0.772385	+	0.445937i	0.0613395	+	0.998117i	$0.480463\pi$
$68$	1.87814	+	3.25303i	0.227757	+	0.394487i
$69$	2.14974	−	3.72346i	0.258798	−	0.448252i
$70$			0.167545i			0.0200254i
$71$	−8.58321	−	4.95552i	−1.01864	−	0.588112i	−0.104930	−	0.994480i	$-0.533462\pi$
$71$	−8.58321	−	4.95552i	−1.01864	−	0.588112i	−0.913710	+	0.406367i	$0.866795\pi$
$72$	4.28620	+	2.47464i	0.505134	+	0.291639i
$73$			3.42254i			0.400578i	0.979737	+	0.200289i	$0.0641880\pi$
$73$			3.42254i			0.400578i	−0.979737	+	0.200289i	$0.935812\pi$
$74$	0.646989	−	1.12062i	0.0752109	−	0.130269i
$75$	−2.49767	−	4.32609i	−0.288406	−	0.499534i
$76$	−7.19411	+	4.15352i	−0.825221	+	0.476441i
$77$	0.678230			0.0772915
$78$	8.81995	+	0.661105i	0.998663	+	0.0748554i
$79$	−14.0484			−1.58057			−0.790283	−	0.612742i	$-0.790066\pi$
$79$	−14.0484			−1.58057			−0.790283	+	0.612742i	$0.790066\pi$
$80$	0.242856	−	0.140213i	0.0271521	−	0.0156763i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.30166	−	10.9148i	0.695901	−	1.20534i
$83$		−	7.03411i		−	0.772094i	−0.922479	−	0.386047i	$-0.873840\pi$
$83$		−	7.03411i		−	0.772094i	0.922479	−	0.386047i	$-0.126160\pi$
$84$	−3.47933	−	2.00879i	−0.379626	−	0.219177i
$85$	−0.0553023	−	0.0319288i	−0.00599837	−	0.00346316i
$86$			4.38750i			0.473117i
$87$	−4.00723	+	6.94072i	−0.429620	+	0.744124i
$88$	−1.67838	−	2.90703i	−0.178916	−	0.309891i
$89$	13.6436	−	7.87714i	1.44622	−	0.834975i	0.447966	−	0.894051i	$-0.352149\pi$
$89$	13.6436	−	7.87714i	1.44622	−	0.834975i	0.998254	+	0.0590753i	$0.0188152\pi$
$90$	−0.167545			−0.0176608
$91$	−3.59547	−	0.269500i	−0.376907	−	0.0282513i
$92$	17.2735			1.80089
$93$	8.71409	−	5.03108i	0.903609	−	0.521699i
$94$	−5.18689	−	8.98395i	−0.534987	−	0.926624i
$95$	0.0706109	−	0.122302i	0.00724452	−	0.0125479i
$96$			0.173279i			0.0176852i
$97$	−14.4370	−	8.33523i	−1.46586	−	0.846314i	−0.466587	−	0.884475i	$-0.654517\pi$
$97$	−14.4370	−	8.33523i	−1.46586	−	0.846314i	−0.999272	+	0.0381612i	$0.987850\pi$
$98$	2.12443	+	1.22654i	0.214599	+	0.123899i
$99$			0.678230i			0.0681647i
$100$	10.0346	−	17.3804i	1.00346	−	1.73804i
$101$	−0.752145	−	1.30275i	−0.0748412	−	0.129629i	0.826176	−	0.563412i	$-0.190512\pi$
$101$	−0.752145	−	1.30275i	−0.0748412	−	0.129629i	−0.901017	+	0.433783i	$0.857178\pi$
$102$	1.98625	−	1.14676i	0.196668	−	0.113546i
$103$	2.21721			0.218468			0.109234	−	0.994016i	$-0.465160\pi$
$103$	2.21721			0.218468			0.109234	+	0.994016i	$0.465160\pi$
$104$	7.74235	+	16.0778i	0.759200	+	1.57656i
$105$	0.0682999			0.00666539
$106$	−6.82993	+	3.94326i	−0.663381	+	0.383003i
$107$	9.89298	+	17.1351i	0.956390	+	1.65652i	0.731154	+	0.682212i	$0.238982\pi$
$107$	9.89298	+	17.1351i	0.956390	+	1.65652i	0.225236	+	0.974304i	$0.427685\pi$
$108$	2.00879	−	3.47933i	0.193296	−	0.334799i
$109$			1.71086i			0.163870i	0.996638	+	0.0819352i	$0.0261101\pi$
$109$			1.71086i			0.163870i	−0.996638	+	0.0819352i	$0.973890\pi$
$110$	0.0984099	+	0.0568170i	0.00938302	+	0.00541729i
$111$	−0.456821	−	0.263746i	−0.0433596	−	0.0250337i
$112$		−	4.10580i		−	0.387962i
$113$	6.81962	−	11.8119i	0.641536	−	1.11117i	−0.343554	−	0.939133i	$-0.611631\pi$
$113$	6.81962	−	11.8119i	0.641536	−	1.11117i	0.985090	−	0.172040i	$-0.0550357\pi$
$114$	2.53608	+	4.39262i	0.237525	+	0.411406i
$115$	−0.254312	+	0.146827i	−0.0237147	+	0.0136917i
$116$	−32.1987			−2.98958
$117$	0.269500	−	3.59547i	0.0249153	−	0.332401i
$118$	−20.4279			−1.88054
$119$	−0.809698	+	0.467479i	−0.0742249	+	0.0428537i
$120$	−0.169018	−	0.292747i	−0.0154291	−	0.0267240i
$121$	−5.27000	+	9.12791i	−0.479091	+	0.829810i
$122$			2.47892i			0.224430i
$123$	−4.44943	−	2.56888i	−0.401191	−	0.231628i
$124$	35.0096	+	20.2128i	3.14395	+	1.81516i
$125$			0.682680i			0.0610608i
$126$	−1.22654	+	2.12443i	−0.109269	+	0.189259i
$127$	−4.00220	−	6.93201i	−0.355138	−	0.615116i	0.632004	−	0.774965i	$-0.282233\pi$
$127$	−4.00220	−	6.93201i	−0.355138	−	0.615116i	−0.987141	+	0.159849i	$0.948899\pi$
$128$	16.8421	−	9.72376i	1.48864	−	0.859467i
$129$	1.78857			0.157475
$130$	−0.499118	−	0.340305i	−0.0437756	−	0.0298467i
$131$	−10.2912			−0.899146			−0.449573	−	0.893244i	$-0.648424\pi$
$131$	−10.2912			−0.899146			−0.449573	+	0.893244i	$0.648424\pi$
$132$	−2.35979	+	1.36242i	−0.205393	+	0.118584i
$133$	−1.03384	−	1.79066i	−0.0896449	−	0.155270i
$134$	−8.95410	+	15.5090i	−0.773516	+	1.33977i
$135$			0.0682999i			0.00587832i
$136$	4.00742	+	2.31369i	0.343634	+	0.198397i
$137$	−3.13463	−	1.80978i	−0.267809	−	0.154620i	0.360082	−	0.932921i	$-0.382749\pi$
$137$	−3.13463	−	1.80978i	−0.267809	−	0.154620i	−0.627892	+	0.778301i	$0.716082\pi$
$138$		−	10.5470i		−	0.897816i
$139$	−0.609074	+	1.05495i	−0.0516610	+	0.0894794i	−0.890699	−	0.454593i	$-0.849785\pi$
$139$	−0.609074	+	1.05495i	−0.0516610	+	0.0894794i	0.839039	+	0.544072i	$0.183118\pi$
$140$	0.137200	+	0.237638i	0.0115955	+	0.0200841i
$141$	−3.66232	+	2.11444i	−0.308423	+	0.178068i
$142$	−24.3125			−2.04026
$143$	−1.37757	+	2.02046i	−0.115198	+	0.168959i
$144$	4.10580			0.342150
$145$	0.474051	−	0.273693i	0.0393678	−	0.0227290i
$146$	4.19787	+	7.27092i	0.347418	+	0.601746i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$		−	2.11924i		−	0.174201i
$149$	−14.3130	−	8.26363i	−1.17257	−	0.676983i	−0.218285	−	0.975885i	$-0.570046\pi$
$149$	−14.3130	−	8.26363i	−1.17257	−	0.676983i	−0.954284	+	0.298902i	$0.903380\pi$
$150$	−10.6122	−	6.12697i	−0.866484	−	0.500265i
$151$			20.3543i			1.65641i	0.560424	+	0.828206i	$0.310638\pi$
$151$			20.3543i			1.65641i	−0.560424	+	0.828206i	$0.689362\pi$
$152$	−5.11674	+	8.86246i	−0.415023	+	0.718841i
$153$	−0.467479	−	0.809698i	−0.0377935	−	0.0654602i
$154$	1.44085	−	0.831875i	0.116107	−	0.0670344i
$155$	−0.687245			−0.0552008
$156$	13.0512	−	6.28486i	1.04493	−	0.503191i
$157$	15.1583			1.20976			0.604881	−	0.796316i	$-0.293221\pi$
$157$	15.1583			1.20976			0.604881	+	0.796316i	$0.293221\pi$
$158$	−29.8447	+	17.2309i	−2.37432	+	1.37081i
$159$	1.60748	+	2.78423i	0.127481	+	0.220804i
$160$	0.00591746	−	0.0102493i	0.000467816	−	0.000810281i
$161$			4.29948i			0.338846i
$162$	−2.12443	−	1.22654i	−0.166911	−	0.0963659i
$163$	14.5849	+	8.42058i	1.14238	+	0.659551i	0.947018	−	0.321182i	$-0.104080\pi$
$163$	14.5849	+	8.42058i	1.14238	+	0.659551i	0.195357	+	0.980732i	$0.437413\pi$
$164$		−	20.6414i		−	1.61182i
$165$	0.0231615	−	0.0401169i	0.00180312	−	0.00312310i
$166$	−8.62761	−	14.9435i	−0.669632	−	1.15984i
$167$	1.43006	−	0.825643i	0.110661	−	0.0638902i	−0.443648	−	0.896201i	$-0.646316\pi$
$167$	1.43006	−	0.825643i	0.110661	−	0.0638902i	0.554309	+	0.832311i	$0.312983\pi$
$168$	−4.94928			−0.381845
$169$	8.10569	−	10.1636i	0.623515	−	0.781812i
$170$	−0.156647			−0.0120143
$171$	1.79066	−	1.03384i	0.136935	−	0.0790594i
$172$	3.59287	+	6.22303i	0.273954	+	0.474502i
$173$	12.3893	−	21.4589i	0.941943	−	1.63149i	0.180185	−	0.983633i	$-0.442330\pi$
$173$	12.3893	−	21.4589i	0.941943	−	1.63149i	0.761759	−	0.647861i	$-0.224336\pi$
$174$			19.6601i			1.49043i
$175$	4.32609	+	2.49767i	0.327021	+	0.188806i
$176$	−2.41160	−	1.39234i	−0.181781	−	0.104952i
$177$			8.32746i			0.625930i
$178$	19.3232	−	33.4688i	1.44834	−	2.50859i
$179$	−3.15142	−	5.45842i	−0.235548	−	0.407982i	0.723884	−	0.689922i	$-0.242355\pi$
$179$	−3.15142	−	5.45842i	−0.235548	−	0.407982i	−0.959432	+	0.281940i	$0.909022\pi$
$180$	−0.237638	+	0.137200i	−0.0177125	+	0.0102263i
$181$	18.9468			1.40830			0.704152	−	0.710049i	$-0.251327\pi$
$181$	18.9468			1.40830			0.704152	+	0.710049i	$0.251327\pi$
$182$	−7.96885	+	3.83744i	−0.590691	+	0.284450i
$183$	1.01053			0.0747008
$184$	18.4284	−	10.6397i	1.35856	−	0.784367i
$185$	0.0180138	+	0.0312008i	0.00132440	+	0.00229393i
$186$	12.3416	−	21.3763i	0.904932	−	1.56739i
$187$			0.634117i			0.0463712i
$188$	−14.7137	−	8.49495i	−1.07311	−	0.619558i
$189$	0.866025	+	0.500000i	0.0629941	+	0.0363696i
$190$		−	0.346428i		−	0.0251325i
$191$	4.39705	−	7.61592i	0.318159	−	0.551068i	−0.661945	−	0.749553i	$-0.730269\pi$
$191$	4.39705	−	7.61592i	0.318159	−	0.551068i	0.980104	+	0.198484i	$0.0636019\pi$
$192$	−3.89327	−	6.74334i	−0.280972	−	0.486659i
$193$	5.36850	−	3.09951i	0.386433	−	0.223107i	−0.294180	−	0.955750i	$-0.595047\pi$
$193$	5.36850	−	3.09951i	0.386433	−	0.223107i	0.680614	+	0.732643i	$0.261713\pi$
$194$	−40.8939			−2.93601
$195$	−0.138726	+	0.203466i	−0.00993436	+	0.0145705i
$196$	4.01758			0.286970
$197$	−13.1145	+	7.57168i	−0.934372	+	0.539460i	−0.888192	−	0.459473i	$-0.848038\pi$
$197$	−13.1145	+	7.57168i	−0.934372	+	0.539460i	−0.0461801	+	0.998933i	$0.514705\pi$
$198$	0.831875	+	1.44085i	0.0591188	+	0.102397i
$199$	7.51860	−	13.0226i	0.532979	−	0.923147i	−0.466279	−	0.884638i	$-0.654406\pi$
$199$	7.51860	−	13.0226i	0.532979	−	0.923147i	0.999258	−	0.0385094i	$-0.0122610\pi$
$200$		−	24.7233i		−	1.74820i
$201$	6.32225	+	3.65015i	0.445937	+	0.257462i
$202$	−3.19575	−	1.84507i	−0.224852	−	0.129819i
$203$		−	8.01446i		−	0.562505i
$204$	1.87814	−	3.25303i	0.131496	−	0.227757i
$205$	0.175454	+	0.303895i	0.0122542	+	0.0212250i
$206$	4.71030	−	2.71949i	0.328182	−	0.189476i
$207$	−4.29948			−0.298834
$208$	12.2312	+	8.33940i	0.848084	+	0.578234i
$209$	−1.40236			−0.0970031
$210$	0.145098	−	0.0837724i	0.0100127	−	0.00578084i
$211$	−12.7371	−	22.0613i	−0.876856	−	1.51876i	−0.854772	−	0.519004i	$-0.826303\pi$
$211$	−12.7371	−	22.0613i	−0.876856	−	1.51876i	−0.0220844	−	0.999756i	$-0.507030\pi$
$212$	−6.45817	+	11.1859i	−0.443549	+	0.768249i
$213$			9.91104i			0.679093i
$214$	42.0338	+	24.2682i	2.87337	+	1.65894i
$215$	−0.105793	−	0.0610796i	−0.00721502	−	0.00416560i
$216$		−	4.94928i		−	0.336756i
$217$	−5.03108	+	8.71409i	−0.341532	+	0.591551i
$218$	2.09843	+	3.63459i	0.142124	+	0.246166i
$219$	2.96400	−	1.71127i	0.200289	−	0.115637i
$220$	0.186107			0.0125473
$221$	0.251972	−	3.36161i	0.0169494	−	0.226126i
$222$	−1.29398			−0.0868461
$223$	−6.06784	+	3.50327i	−0.406333	+	0.234596i	−0.689213	−	0.724559i	$-0.742043\pi$
$223$	−6.06784	+	3.50327i	−0.406333	+	0.234596i	0.282880	+	0.959155i	$0.408710\pi$
$224$	−0.0866393	−	0.150064i	−0.00578883	−	0.0100266i
$225$	−2.49767	+	4.32609i	−0.166511	+	0.288406i
$226$		−	33.4581i		−	2.22560i
$227$	24.0383	+	13.8785i	1.59548	+	0.921151i	0.992343	+	0.123513i	$0.0394160\pi$
$227$	24.0383	+	13.8785i	1.59548	+	0.921151i	0.603137	+	0.797638i	$0.293917\pi$
$228$	7.19411	+	4.15352i	0.476441	+	0.275074i
$229$		−	3.61011i		−	0.238563i	−0.992860	−	0.119281i	$-0.961941\pi$
$229$		−	3.61011i		−	0.238563i	0.992860	−	0.119281i	$-0.0380591\pi$
$230$	−0.360178	+	0.623846i	−0.0237494	+	0.0411352i
$231$	−0.339115	−	0.587365i	−0.0223121	−	0.0386458i
$232$	−34.3516	+	19.8329i	−2.25529	+	1.30209i
$233$	15.6176			1.02315			0.511573	−	0.859240i	$-0.329063\pi$
$233$	15.6176			1.02315			0.511573	+	0.859240i	$0.329063\pi$
$234$	−3.83744	−	7.96885i	−0.250861	−	0.520940i
$235$	0.288832			0.0188413
$236$	−28.9740	+	16.7281i	−1.88604	+	1.08891i
$237$	7.02419	+	12.1662i	0.456270	+	0.790283i
$238$	−1.14676	+	1.98625i	−0.0743335	+	0.128749i
$239$			27.9831i			1.81008i	0.425332	+	0.905038i	$0.360157\pi$
$239$			27.9831i			1.81008i	−0.425332	+	0.905038i	$0.639843\pi$
$240$	−0.242856	−	0.140213i	−0.0156763	−	0.00905070i
$241$	22.4935	+	12.9866i	1.44893	+	0.836541i	0.998418	−	0.0562280i	$-0.0179074\pi$
$241$	22.4935	+	12.9866i	1.44893	+	0.836541i	0.450514	+	0.892769i	$0.351241\pi$
$242$			25.8554i			1.66205i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.02995	+	3.51598i	0.129954	+	0.225087i
$245$	−0.0591494	+	0.0341499i	−0.00377892	+	0.00218176i
$246$	−12.6033			−0.803558
$247$	7.43424	+	0.557238i	0.473029	+	0.0354562i
$248$	49.8005			3.16233
$249$	−6.09172	+	3.51706i	−0.386047	+	0.222884i
$250$	0.837333	+	1.45030i	0.0529576	+	0.0917253i
$251$	−3.19262	+	5.52979i	−0.201517	+	0.349037i	−0.949017	−	0.315224i	$-0.897920\pi$
$251$	−3.19262	+	5.52979i	−0.201517	+	0.349037i	0.747501	+	0.664261i	$0.231254\pi$
$252$			4.01758i			0.253084i
$253$	2.52536	+	1.45802i	0.158768	+	0.0916649i
$254$	−17.0047	−	9.81769i	−1.06697	−	0.616017i
$255$			0.0638575i			0.00399891i
$256$	16.0666	−	27.8282i	1.00416	−	1.73926i
$257$	−6.90893	−	11.9666i	−0.430967	−	0.746457i	0.565990	−	0.824412i	$-0.308494\pi$
$257$	−6.90893	−	11.9666i	−0.430967	−	0.746457i	−0.996957	+	0.0779556i	$0.975161\pi$
$258$	3.79969	−	2.19375i	0.236558	−	0.136577i
$259$	0.527492			0.0327767
$260$	−0.986597	−	0.0739510i	−0.0611861	−	0.00458625i
$261$	8.01446			0.496083
$262$	−21.8629	+	12.6225i	−1.35069	+	0.779823i
$263$	5.66821	+	9.81762i	0.349517	+	0.605380i	0.986164	−	0.165775i	$-0.0530125\pi$
$263$	5.66821	+	9.81762i	0.349517	+	0.605380i	−0.636647	+	0.771155i	$0.719679\pi$
$264$	−1.67838	+	2.90703i	−0.103297	+	0.178916i
$265$		−	0.219581i		−	0.0134887i
$266$	−4.39262	−	2.53608i	−0.269329	−	0.155497i
$267$	−13.6436	−	7.87714i	−0.834975	−	0.482073i
$268$			29.3296i			1.79159i
$269$	−10.5001	+	18.1867i	−0.640202	+	1.10886i	0.345185	+	0.938535i	$0.387816\pi$
$269$	−10.5001	+	18.1867i	−0.640202	+	1.10886i	−0.985387	+	0.170328i	$0.945517\pi$
$270$	0.0837724	+	0.145098i	0.00509823	+	0.00883039i
$271$	−25.3269	+	14.6225i	−1.53850	+	0.888253i	−0.539573	+	0.841939i	$0.681414\pi$
$271$	−25.3269	+	14.6225i	−1.53850	+	0.888253i	−0.998927	+	0.0463142i	$0.985252\pi$
$272$	3.83875			0.232759
$273$	1.56434	+	3.24851i	0.0946781	+	0.196609i
$274$	−8.87904			−0.536403
$275$	2.93408	−	1.69399i	0.176932	−	0.102152i
$276$	−8.63676	−	14.9593i	−0.519872	−	0.900444i
$277$	8.25178	−	14.2925i	0.495801	−	0.858753i	−0.504187	−	0.863595i	$-0.668208\pi$
$277$	8.25178	−	14.2925i	0.495801	−	0.858753i	0.999988	+	0.00484129i	$0.00154104\pi$
$278$			2.98821i			0.179221i
$279$	−8.71409	−	5.03108i	−0.521699	−	0.301203i
$280$	0.292747	+	0.169018i	0.0174950	+	0.0101007i
$281$		−	1.12161i		−	0.0669094i	−0.999440	−	0.0334547i	$-0.989349\pi$
$281$		−	1.12161i		−	0.0669094i	0.999440	−	0.0334547i	$-0.0106509\pi$
$282$	−5.18689	+	8.98395i	−0.308875	+	0.534987i
$283$	5.47060	+	9.47536i	0.325194	+	0.563252i	0.981552	−	0.191198i	$-0.0612372\pi$
$283$	5.47060	+	9.47536i	0.325194	+	0.563252i	−0.656358	+	0.754450i	$0.727904\pi$
$284$	−34.4838	+	19.9092i	−2.04624	+	1.18139i
$285$	−0.141222			−0.00836525
$286$	−0.448382	+	5.98196i	−0.0265134	+	0.353721i
$287$	5.13776			0.303272
$288$	0.150064	−	0.0866393i	0.00884259	−	0.00510527i
$289$	8.06293	+	13.9654i	0.474290	+	0.821494i
$290$	0.671390	−	1.16288i	0.0394254	−	0.0682868i
$291$			16.6705i			0.977239i
$292$	11.9081	+	6.87516i	0.696870	+	0.402338i
$293$	−13.4669	−	7.77514i	−0.786747	−	0.454229i	0.0520690	−	0.998643i	$-0.483418\pi$
$293$	−13.4669	−	7.77514i	−0.786747	−	0.454229i	−0.838816	+	0.544415i	$0.816752\pi$
$294$		−	2.45308i		−	0.143066i
$295$	0.284382	−	0.492564i	0.0165574	−	0.0286782i
$296$	−1.30535	−	2.26094i	−0.0758721	−	0.131414i
$297$	0.587365	−	0.339115i	0.0340824	−	0.0196775i
$298$	−40.5426			−2.34857
$299$	−12.8082	−	8.73279i	−0.740718	−	0.505030i
$300$	−20.0692			−1.15869
$301$	−1.54895	+	0.894286i	−0.0892799	+	0.0515458i
$302$	24.9653	+	43.2413i	1.43659	+	2.48825i
$303$	−0.752145	+	1.30275i	−0.0432096	+	0.0748412i
$304$			8.48945i			0.486903i
$305$	−0.0597725	−	0.0345097i	−0.00342256	−	0.00197602i
$306$	−1.98625	−	1.14676i	−0.113546	−	0.0655560i
$307$		−	0.119003i		−	0.00679184i	−0.999994	−	0.00339592i	$-0.998919\pi$
$307$		−	0.119003i		−	0.00679184i	0.999994	−	0.00339592i	$-0.00108096\pi$
$308$	1.36242	−	2.35979i	0.0776313	−	0.134461i
$309$	−1.10860	−	1.92016i	−0.0630663	−	0.109234i
$310$	−1.46000	+	0.842932i	−0.0829224	+	0.0478753i
$311$	31.4738			1.78472			0.892358	−	0.451327i	$-0.149049\pi$
$311$	31.4738			1.78472			0.892358	+	0.451327i	$0.149049\pi$
$312$	10.0526	−	14.7440i	0.569118	−	0.834714i
$313$	14.1243			0.798355			0.399178	−	0.916874i	$-0.369296\pi$
$313$	14.1243			0.798355			0.399178	+	0.916874i	$0.369296\pi$
$314$	32.2026	−	18.5922i	1.81730	−	1.04922i
$315$	−0.0341499	−	0.0591494i	−0.00192413	−	0.00333269i
$316$	−28.2202	+	48.8789i	−1.58751	+	2.74965i
$317$			18.6470i			1.04732i	0.851927	+	0.523661i	$0.175434\pi$
$317$			18.6470i			1.04732i	−0.851927	+	0.523661i	$0.824566\pi$
$318$	6.82993	+	3.94326i	0.383003	+	0.221127i
$319$	−4.70741	−	2.71783i	−0.263564	−	0.152169i
$320$			0.531820i			0.0297296i
$321$	9.89298	−	17.1351i	0.552172	−	0.956390i
$322$	5.27348	+	9.13393i	0.293879	+	0.509014i
$323$	1.67419	−	0.966593i	0.0931544	−	0.0537827i
$324$	−4.01758			−0.223199
$325$	−16.2274	+	7.81439i	−0.900135	+	0.433465i
$326$	41.3126			2.28810
$327$	1.48165	−	0.855429i	0.0819352	−	0.0473053i
$328$	−12.7141	−	22.0215i	−0.702019	−	1.21593i
$329$	2.11444	−	3.66232i	0.116573	−	0.201910i
$330$		−	0.113634i		−	0.00625535i
$331$	−19.1255	−	11.0421i	−1.05123	−	0.606930i	−0.128240	−	0.991743i	$-0.540933\pi$
$331$	−19.1255	−	11.0421i	−1.05123	−	0.606930i	−0.922995	+	0.384813i	$0.874266\pi$
$332$	−24.4740	−	14.1301i	−1.34318	−	0.775488i
$333$			0.527492i			0.0289064i
$334$	2.02537	−	3.50804i	0.110823	−	0.191951i
$335$	−0.249305	−	0.431809i	−0.0136210	−	0.0235922i
$336$	−3.55573	+	2.05290i	−0.193981	+	0.111995i
$337$	32.5355			1.77232			0.886161	−	0.463377i	$-0.153362\pi$
$337$	32.5355			1.77232			0.886161	+	0.463377i	$0.153362\pi$
$338$	4.75396	−	31.5337i	0.258581	−	1.71520i
$339$	−13.6392			−0.740782
$340$	−0.222181	+	0.128276i	−0.0120495	+	0.00695677i
$341$	3.41223	+	5.91016i	0.184783	+	0.320053i
$342$	2.53608	−	4.39262i	0.137135	−	0.237525i
$343$			1.00000i			0.0539949i
$344$	7.66618	+	4.42607i	0.413333	+	0.238638i
$345$	0.254312	+	0.146827i	0.0136917	+	0.00790490i
$346$		−	60.7839i		−	3.26776i
$347$	−2.20612	+	3.82111i	−0.118431	+	0.205128i	−0.919146	−	0.393917i	$-0.871120\pi$
$347$	−2.20612	+	3.82111i	−0.118431	+	0.205128i	0.800715	+	0.599045i	$0.204453\pi$
$348$	16.0994	+	27.8849i	0.863017	+	1.49479i
$349$	−6.16974	+	3.56210i	−0.330259	+	0.190675i	−0.655956	−	0.754799i	$-0.727734\pi$
$349$	−6.16974	+	3.56210i	−0.330259	+	0.190675i	0.325697	+	0.945474i	$0.394401\pi$
$350$	12.2539			0.655000
$351$	−3.24851	+	1.56434i	−0.173393	+	0.0834982i
$352$	−0.117523			−0.00626399
$353$	2.88961	−	1.66832i	0.153799	−	0.0887957i	−0.421126	−	0.907002i	$-0.638365\pi$
$353$	2.88961	−	1.66832i	0.153799	−	0.0887957i	0.574924	+	0.818207i	$0.305032\pi$
$354$	10.2139	+	17.6911i	0.542865	+	0.940270i
$355$	0.338462	−	0.586233i	0.0179637	−	0.0311140i
$356$		−	63.2941i		−	3.35458i
$357$	0.809698	+	0.467479i	0.0428537	+	0.0247416i
$358$	−13.3899	−	7.73068i	−0.707680	−	0.408579i
$359$			24.5869i			1.29765i	0.760940	+	0.648823i	$0.224738\pi$
$359$			24.5869i			1.29765i	−0.760940	+	0.648823i	$0.775262\pi$
$360$	−0.169018	+	0.292747i	−0.00890801	+	0.0154291i
$361$	−7.36237	−	12.7520i	−0.387493	−	0.671158i
$362$	40.2511	−	23.2390i	2.11555	−	1.22141i
$363$	10.5400			0.553207
$364$	−8.16022	+	11.9684i	−0.427712	+	0.627316i
$365$	−0.233759			−0.0122355
$366$	2.14680	−	1.23946i	0.112215	−	0.0647875i
$367$	7.53829	+	13.0567i	0.393495	+	0.681554i	0.992908	−	0.118886i	$-0.0379324\pi$
$367$	7.53829	+	13.0567i	0.393495	+	0.681554i	−0.599412	+	0.800440i	$0.704599\pi$
$368$	8.82640	−	15.2878i	0.460108	−	0.796931i
$369$			5.13776i			0.267461i
$370$	0.0765380	+	0.0441893i	0.00397902	+	0.00229729i
$371$	−2.78423	−	1.60748i	−0.144550	−	0.0834560i
$372$		−	40.4256i		−	2.09597i
$373$	12.6236	−	21.8646i	0.653623	−	1.13211i	−0.328614	−	0.944464i	$-0.606581\pi$
$373$	12.6236	−	21.8646i	0.653623	−	1.13211i	0.982237	−	0.187644i	$-0.0600852\pi$
$374$	0.777769	+	1.34714i	0.0402175	+	0.0696587i
$375$	0.591218	−	0.341340i	0.0305304	−	0.0176267i
$376$	−20.9299			−1.07938
$377$	23.8752	+	16.2784i	1.22963	+	0.838379i
$378$	2.45308			0.126173
$379$	20.8220	−	12.0216i	1.06955	−	0.617508i	0.141495	−	0.989939i	$-0.454809\pi$
$379$	20.8220	−	12.0216i	1.06955	−	0.617508i	0.928060	+	0.372431i	$0.121476\pi$
$380$	−0.283685	−	0.491357i	−0.0145527	−	0.0252061i
$381$	−4.00220	+	6.93201i	−0.205039	+	0.355138i
$382$		−	21.5726i		−	1.10375i
$383$	3.93109	+	2.26962i	0.200869	+	0.115972i	0.597061	−	0.802196i	$-0.296335\pi$
$383$	3.93109	+	2.26962i	0.200869	+	0.115972i	−0.396192	+	0.918168i	$0.629668\pi$
$384$	−16.8421	−	9.72376i	−0.859467	−	0.496214i
$385$			0.0463231i			0.00236084i
$386$	7.60333	−	13.1693i	0.386999	−	0.670302i
$387$	−0.894286	−	1.54895i	−0.0454591	−	0.0787375i
$388$	−58.0020	+	33.4875i	−2.94460	+	1.70007i
$389$	−19.7847			−1.00313			−0.501563	−	0.865121i	$-0.667242\pi$
$389$	−19.7847			−1.00313			−0.501563	+	0.865121i	$0.667242\pi$
$390$	−0.0451534	+	0.602401i	−0.00228643	+	0.0305038i
$391$	−4.01983			−0.203292
$392$	4.28620	−	2.47464i	0.216486	−	0.124988i
$393$	5.14560	+	8.91244i	0.259561	+	0.449573i
$394$	−18.5739	+	32.1709i	−0.935740	+	1.62075i
$395$		−	0.959502i		−	0.0482778i
$396$	2.35979	+	1.36242i	0.118584	+	0.0684643i
$397$	9.05725	+	5.22920i	0.454570	+	0.262446i	0.709758	−	0.704445i	$-0.248804\pi$
$397$	9.05725	+	5.22920i	0.454570	+	0.262446i	−0.255188	+	0.966891i	$0.582137\pi$
$398$		−	36.8874i		−	1.84900i
$399$	−1.03384	+	1.79066i	−0.0517565	+	0.0896449i
$400$	−10.2549	−	17.7621i	−0.512746	−	0.888103i
$401$	−19.4194	+	11.2118i	−0.969759	+	0.559891i	−0.899163	−	0.437614i	$-0.855824\pi$
$401$	−19.4194	+	11.2118i	−0.969759	+	0.559891i	−0.0705965	+	0.997505i	$0.522490\pi$
$402$	17.9082			0.893180
$403$	−15.7406	−	32.6871i	−0.784097	−	1.62826i
$404$	−6.04361			−0.300681
$405$	0.0591494	−	0.0341499i	0.00293916	−	0.00169692i
$406$	−9.83004	−	17.0261i	−0.487857	−	0.844992i
$407$	0.178880	−	0.309830i	0.00886678	−	0.0153577i
$408$		−	4.62737i		−	0.229089i
$409$	−21.1661	−	12.2203i	−1.04660	−	0.604253i	−0.124902	−	0.992169i	$-0.539862\pi$
$409$	−21.1661	−	12.2203i	−1.04660	−	0.604253i	−0.921695	+	0.387916i	$0.873195\pi$
$410$	0.745479	+	0.430402i	0.0368166	+	0.0212561i
$411$			3.61956i			0.178539i
$412$	4.45391	−	7.71440i	0.219428	−	0.380061i
$413$	−4.16373	−	7.21179i	−0.204884	−	0.354869i
$414$	−9.13393	+	5.27348i	−0.448908	+	0.259177i
$415$	0.480429			0.0235833
$416$	0.623017	+	0.0466987i	0.0305459	+	0.00228959i
$417$	1.21815			0.0596529
$418$	−2.97921	+	1.72005i	−0.145718	+	0.0841302i
$419$	−13.8981	−	24.0722i	−0.678965	−	1.17600i	−0.975293	−	0.220916i	$-0.929095\pi$
$419$	−13.8981	−	24.0722i	−0.678965	−	1.17600i	0.296328	−	0.955086i	$-0.404238\pi$
$420$	0.137200	−	0.237638i	0.00669468	−	0.0115955i
$421$		−	15.8324i		−	0.771626i	−0.922577	−	0.385813i	$-0.873921\pi$
$421$		−	15.8324i		−	0.771626i	0.922577	−	0.385813i	$-0.126079\pi$
$422$	−54.1179	−	31.2450i	−2.63442	−	1.52098i
$423$	3.66232	+	2.11444i	0.178068	+	0.102808i
$424$			15.9117i			0.772741i
$425$	−2.33522	+	4.04471i	−0.113275	+	0.196197i
$426$	12.1563	+	21.0553i	0.588973	+	1.02013i
$427$	−0.875148	+	0.505267i	−0.0423514	+	0.0244516i
$428$	79.4917			3.84238
$429$	2.43855	+	0.182783i	0.117734	+	0.00882487i
$430$	−0.299666			−0.0144512
$431$	15.7701	−	9.10489i	0.759621	−	0.438567i	−0.0695388	−	0.997579i	$-0.522153\pi$
$431$	15.7701	−	9.10489i	0.759621	−	0.438567i	0.829160	+	0.559012i	$0.188819\pi$
$432$	−2.05290	−	3.55573i	−0.0987702	−	0.171075i
$433$	−4.70224	+	8.14452i	−0.225975	+	0.391401i	−0.956612	−	0.291366i	$-0.905890\pi$
$433$	−4.70224	+	8.14452i	−0.225975	+	0.391401i	0.730636	+	0.682767i	$0.239224\pi$
$434$			24.6833i			1.18483i
$435$	−0.474051	−	0.273693i	−0.0227290	−	0.0131226i
$436$	5.95264	+	3.43676i	0.285080	+	0.164591i
$437$		−	8.88991i		−	0.425262i
$438$	4.19787	−	7.27092i	0.200582	−	0.347418i
$439$	−9.61695	−	16.6570i	−0.458992	−	0.794998i	0.539916	−	0.841719i	$-0.318456\pi$
$439$	−9.61695	−	16.6570i	−0.458992	−	0.794998i	−0.998908	+	0.0467214i	$0.985123\pi$
$440$	0.198550	−	0.114633i	0.00946550	−	0.00546491i
$441$	−1.00000			−0.0476190
$442$	−3.58785	−	7.45055i	−0.170656	−	0.354386i
$443$	−5.40445			−0.256773			−0.128387	−	0.991724i	$-0.540980\pi$
$443$	−5.40445			−0.256773			−0.128387	+	0.991724i	$0.540980\pi$
$444$	−1.83532	+	1.05962i	−0.0871003	+	0.0502874i
$445$	0.538008	+	0.931857i	0.0255040	+	0.0441742i
$446$	−8.59378	+	14.8849i	−0.406927	+	0.704819i
$447$			16.5273i			0.781713i
$448$	6.74334	+	3.89327i	0.318593	+	0.183940i
$449$	−11.7376	−	6.77669i	−0.553930	−	0.319812i	0.196775	−	0.980449i	$-0.436953\pi$
$449$	−11.7376	−	6.77669i	−0.553930	−	0.319812i	−0.750706	+	0.660637i	$0.770286\pi$
$450$			12.2539i			0.577656i
$451$	1.74229	−	3.01774i	0.0820413	−	0.142100i
$452$	−27.3984	−	47.4554i	−1.28871	−	2.23211i
$453$	17.6274	−	10.1772i	0.828206	−	0.478165i
$454$	68.0902			3.19563
$455$	0.0184068	−	0.245570i	0.000862926	−	0.0115125i
$456$	10.2335			0.479227
$457$	−25.8274	+	14.9114i	−1.20815	+	0.697528i	−0.962356	−	0.271793i	$-0.912383\pi$
$457$	−25.8274	+	14.9114i	−1.20815	+	0.697528i	−0.245798	+	0.969321i	$0.579050\pi$
$458$	−4.42794	−	7.66942i	−0.206904	−	0.358368i
$459$	−0.467479	+	0.809698i	−0.0218201	+	0.0377935i
$460$			1.17978i			0.0550075i
$461$	−1.92953	−	1.11402i	−0.0898673	−	0.0518849i	0.454393	−	0.890801i	$-0.349856\pi$
$461$	−1.92953	−	1.11402i	−0.0898673	−	0.0518849i	−0.544260	+	0.838916i	$0.683190\pi$
$462$	−1.44085	−	0.831875i	−0.0670344	−	0.0387023i
$463$		−	21.6086i		−	1.00424i	−0.864799	−	0.502118i	$-0.832554\pi$
$463$		−	21.6086i		−	1.00424i	0.864799	−	0.502118i	$-0.167446\pi$
$464$	−16.4529	+	28.4972i	−0.763806	+	1.32295i
$465$	0.343622	+	0.595171i	0.0159351	+	0.0276004i
$466$	33.1785	−	19.1556i	1.53696	−	0.887367i
$467$	24.0068			1.11090			0.555452	−	0.831549i	$-0.312545\pi$
$467$	24.0068			1.11090			0.555452	+	0.831549i	$0.312545\pi$
$468$	−11.9684	−	8.16022i	−0.553241	−	0.377206i
$469$	−7.30030			−0.337097
$470$	0.613603	−	0.354264i	0.0283034	−	0.0163410i
$471$	−7.57914	−	13.1274i	−0.349228	−	0.604881i
$472$	−20.6075	+	35.6932i	−0.948536	+	1.64291i
$473$			1.21306i			0.0557767i
$474$	29.8447	+	17.2309i	1.37081	+	0.791440i
$475$	−8.94493	−	5.16436i	−0.410421	−	0.236957i
$476$			3.75627i			0.172168i
$477$	1.60748	−	2.78423i	0.0736013	−	0.127481i
$478$	34.3223	+	59.4480i	1.56987	+	2.71909i
$479$	−26.5801	+	15.3461i	−1.21448	+	0.701179i	−0.963732	−	0.266874i	$-0.914009\pi$
$479$	−26.5801	+	15.3461i	−1.21448	+	0.701179i	−0.250746	+	0.968053i	$0.580676\pi$
$480$	−0.0118349			−0.000540187
$481$	−1.07140	+	1.57141i	−0.0488518	+	0.0716499i
$482$	63.7143			2.90211
$483$	3.72346	−	2.14974i	0.169423	−	0.0978165i
$484$	21.1727	+	36.6721i	0.962394	+	1.66692i
$485$	0.569295	−	0.986048i	0.0258504	−	0.0447741i
$486$			2.45308i			0.111274i
$487$	15.4765	+	8.93535i	0.701306	+	0.404899i	0.807834	−	0.589411i	$-0.200640\pi$
$487$	15.4765	+	8.93535i	0.701306	+	0.404899i	−0.106528	+	0.994310i	$0.533973\pi$
$488$	4.33135	+	2.50071i	0.196071	+	0.113202i
$489$		−	16.8412i		−	0.761583i
$490$	−0.0837724	+	0.145098i	−0.00378445	+	0.00655486i
$491$	−6.78481	−	11.7516i	−0.306194	−	0.530344i	0.671332	−	0.741156i	$-0.265722\pi$
$491$	−6.78481	−	11.7516i	−0.306194	−	0.530344i	−0.977526	+	0.210813i	$0.932389\pi$
$492$	−17.8759	+	10.3207i	−0.805910	+	0.465292i
$493$	7.49318			0.337476
$494$	16.4770	−	7.93457i	0.741334	−	0.356993i
$495$	−0.0463231			−0.00208207
$496$	35.7783	−	20.6566i	1.60649	−	0.927510i
$497$	−4.95552	−	8.58321i	−0.222286	−	0.385010i
$498$	−8.62761	+	14.9435i	−0.386612	+	0.669632i
$499$			10.4240i			0.466644i	0.972399	+	0.233322i	$0.0749597\pi$
$499$			10.4240i			0.466644i	−0.972399	+	0.233322i	$0.925040\pi$
$500$	2.37527	+	1.37136i	0.106225	+	0.0613292i
$501$	−1.43006	−	0.825643i	−0.0638902	−	0.0368870i
$502$			15.6635i			0.699096i
$503$	−2.52407	+	4.37181i	−0.112543	+	0.194929i	−0.916795	−	0.399359i	$-0.869233\pi$
$503$	−2.52407	+	4.37181i	−0.112543	+	0.194929i	0.804252	+	0.594288i	$0.202566\pi$
$504$	2.47464	+	4.28620i	0.110229	+	0.190923i
$505$	0.0889779	−	0.0513714i	0.00395946	−	0.00228600i
$506$	7.15326			0.318001
$507$	−12.8547	−	1.93796i	−0.570899	−	0.0860678i
$508$	−32.1583			−1.42679
$509$	−7.78769	+	4.49623i	−0.345183	+	0.199292i	−0.662562	−	0.749007i	$-0.730531\pi$
$509$	−7.78769	+	4.49623i	−0.345183	+	0.199292i	0.317378	+	0.948299i	$0.397197\pi$
$510$	0.0783237	+	0.135661i	0.00346823	+	0.00600715i
$511$	−1.71127	+	2.96400i	−0.0757020	+	0.131120i
$512$		−	39.9301i		−	1.76468i
$513$	−1.79066	−	1.03384i	−0.0790594	−	0.0456450i
$514$	−29.3550	−	16.9481i	−1.29479	−	0.747549i
$515$			0.151435i			0.00667303i
$516$	3.59287	−	6.22303i	0.158167	−	0.273954i
$517$	−1.43408	−	2.48390i	−0.0630707	−	0.109242i
$518$	1.12062	−	0.646989i	0.0492371	−	0.0284271i
$519$	−24.7787			−1.08766
$520$	−1.09811	+	0.528802i	−0.0481554	+	0.0231895i
$521$	−9.21666			−0.403789			−0.201895	−	0.979407i	$-0.564710\pi$
$521$	−9.21666			−0.403789			−0.201895	+	0.979407i	$0.564710\pi$
$522$	17.0261	−	9.83004i	0.745213	−	0.430249i
$523$	−9.33282	−	16.1649i	−0.408096	−	0.706842i	0.586581	−	0.809891i	$-0.300474\pi$
$523$	−9.33282	−	16.1649i	−0.408096	−	0.706842i	−0.994676	+	0.103048i	$0.967140\pi$
$524$	−20.6729	+	35.8064i	−0.903098	+	1.56421i
$525$		−	4.99534i		−	0.218014i
$526$	24.0834	+	13.9045i	1.05008	+	0.606267i
$527$	−8.14731	−	4.70385i	−0.354902	−	0.204903i
$528$			2.78468i			0.121188i
$529$	2.25724	−	3.90965i	0.0981407	−	0.169985i
$530$	−0.269324	−	0.466483i	−0.0116987	−	0.0202627i
$531$	7.21179	−	4.16373i	0.312965	−	0.180690i
$532$	−8.30704			−0.360156
$533$	−10.4354	+	15.3055i	−0.452009	+	0.662953i
$534$	−38.6465			−1.67240
$535$	−1.17033	+	0.675689i	−0.0505977	+	0.0292126i
$536$	18.0656	+	31.2906i	0.780316	+	1.35155i
$537$	−3.15142	+	5.45842i	−0.135994	+	0.235548i
$538$			51.5151i			2.22097i
$539$	0.587365	+	0.339115i	0.0252996	+	0.0146067i
$540$	0.237638	+	0.137200i	0.0102263	+	0.00590416i
$541$		−	16.3383i		−	0.702437i	−0.936293	−	0.351219i	$-0.885767\pi$
$541$		−	16.3383i		−	0.702437i	0.936293	−	0.351219i	$-0.114233\pi$
$542$	−35.8701	+	62.1288i	−1.54075	+	2.66866i
$543$	−9.47339	−	16.4084i	−0.406542	−	0.704152i
$544$	0.140303	−	0.0810042i	0.00601546	−	0.00347302i
$545$	−0.116851			−0.00500536
$546$	7.30775	+	4.98251i	0.312743	+	0.213232i
$547$	5.07719			0.217085			0.108542	−	0.994092i	$-0.465382\pi$
$547$	5.07719			0.217085			0.108542	+	0.994092i	$0.465382\pi$
$548$	−12.5936	+	7.27093i	−0.537973	+	0.310599i
$549$	−0.505267	−	0.875148i	−0.0215643	−	0.0373504i
$550$	4.15550	−	7.19753i	0.177191	−	0.306904i
$551$			16.5713i			0.705960i
$552$	−18.4284	−	10.6397i	−0.784367	−	0.452854i
$553$	−12.1662	−	7.02419i	−0.517362	−	0.298699i
$554$		−	40.4845i		−	1.72002i
$555$	0.0180138	−	0.0312008i	0.000764644	−	0.00132440i
$556$	2.44700	+	4.23833i	0.103776	+	0.179745i
$557$	−1.11171	+	0.641845i	−0.0471046	+	0.0271959i	−0.523367	−	0.852107i	$-0.675324\pi$
$557$	−1.11171	+	0.641845i	−0.0471046	+	0.0271959i	0.476263	+	0.879303i	$0.341991\pi$
$558$	−24.6833			−1.04493
$559$	0.482021	−	6.43075i	0.0203873	−	0.271992i
$560$	0.280426			0.0118502
$561$	0.549162	−	0.317059i	0.0231856	−	0.0133862i
$562$	−1.37569	−	2.38277i	−0.0580301	−	0.100511i
$563$	8.48990	−	14.7049i	0.357807	−	0.619739i	−0.629788	−	0.776767i	$-0.716858\pi$
$563$	8.48990	−	14.7049i	0.357807	−	0.619739i	0.987594	+	0.157028i	$0.0501914\pi$
$564$			16.9899i			0.715404i
$565$	0.806753	+	0.465779i	0.0339404	+	0.0195955i
$566$	23.2438	+	13.4198i	0.977009	+	0.564076i
$567$		−	1.00000i		−	0.0419961i
$568$	−24.5263	+	42.4807i	−1.02910	+	1.78245i
$569$	−17.9814	−	31.1447i	−0.753820	−	1.30566i	−0.945959	−	0.324287i	$-0.894876\pi$
$569$	−17.9814	−	31.1447i	−0.753820	−	1.30566i	0.192138	−	0.981368i	$-0.438458\pi$
$570$	−0.300015	+	0.173214i	−0.0125663	+	0.00725513i
$571$	20.6811			0.865475			0.432738	−	0.901520i	$-0.357548\pi$
$571$	20.6811			0.865475			0.432738	+	0.901520i	$0.357548\pi$
$572$	4.26258	+	8.85170i	0.178228	+	0.370108i
$573$	−8.79410			−0.367379
$574$	10.9148	−	6.30166i	0.455574	−	0.263026i
$575$	10.7387	+	18.5999i	0.447834	+	0.775670i
$576$	−3.89327	+	6.74334i	−0.162220	+	0.280972i
$577$		−	3.67781i		−	0.153109i	−0.997065	−	0.0765546i	$-0.975608\pi$
$577$		−	3.67781i		−	0.153109i	0.997065	−	0.0765546i	$-0.0243920\pi$
$578$	34.2582	+	19.7790i	1.42495	+	0.822697i
$579$	−5.36850	−	3.09951i	−0.223107	−	0.128811i
$580$		−	2.19917i		−	0.0913156i
$581$	3.51706	−	6.09172i	0.145912	−	0.252727i
$582$	20.4469	+	35.4151i	0.847553	+	1.46800i
$583$	−1.88835	+	1.09024i	−0.0782074	+	0.0451531i
$584$	16.9391			0.700945
$585$	0.245570	+	0.0184068i	0.0101531	+	0.000761030i
$586$	−38.1460			−1.57580
$587$	10.4298	−	6.02163i	0.430482	−	0.248539i	−0.269070	−	0.963121i	$-0.586716\pi$
$587$	10.4298	−	6.02163i	0.430482	−	0.248539i	0.699552	+	0.714582i	$0.253383\pi$
$588$	−2.00879	−	3.47933i	−0.0828411	−	0.143485i
$589$	10.4026	−	18.0179i	0.428633	−	0.742414i
$590$		−	1.39522i		−	0.0574404i
$591$	13.1145	+	7.57168i	0.539460	+	0.311457i
$592$	−1.87562	−	1.08289i	−0.0770874	−	0.0445064i
$593$			24.4737i			1.00501i	0.864573	+	0.502507i	$0.167589\pi$
$593$			24.4737i			1.00501i	−0.864573	+	0.502507i	$0.832411\pi$
$594$	0.831875	−	1.44085i	0.0341323	−	0.0591188i
$595$	−0.0319288	−	0.0553023i	−0.00130895	−	0.00226717i
$596$	−57.5038	+	33.1998i	−2.35545	+	1.35992i
$597$	−15.0372			−0.615431
$598$	−37.9212	−	2.84241i	−1.55071	−	0.116235i
$599$	−21.8012			−0.890773			−0.445387	−	0.895338i	$-0.646934\pi$
$599$	−21.8012			−0.890773			−0.445387	+	0.895338i	$0.646934\pi$
$600$	−21.4110	+	12.3617i	−0.874101	+	0.504663i
$601$	−3.29106	−	5.70029i	−0.134245	−	0.232520i	0.791064	−	0.611734i	$-0.209528\pi$
$601$	−3.29106	−	5.70029i	−0.134245	−	0.232520i	−0.925309	+	0.379214i	$0.876194\pi$
$602$	−2.19375	+	3.79969i	−0.0894106	+	0.154864i
$603$		−	7.30030i		−	0.297291i
$604$	70.8194	+	40.8876i	2.88160	+	1.66369i
$605$	−0.623435	−	0.359940i	−0.0253462	−	0.0146337i
$606$			3.69014i			0.149902i
$607$	−22.8466	+	39.5715i	−0.927317	+	1.60616i	−0.139524	+	0.990219i	$0.544557\pi$
$607$	−22.8466	+	39.5715i	−0.927317	+	1.60616i	−0.787792	+	0.615941i	$0.788776\pi$
$608$	0.179142	+	0.310282i	0.00726515	+	0.0125836i
$609$	−6.94072	+	4.00723i	−0.281252	+	0.162381i
$610$	−0.169310			−0.00685515
$611$	6.61541	+	13.7376i	0.267631	+	0.555764i
$612$	−3.75627			−0.151838
$613$	−36.3690	+	20.9977i	−1.46893	+	0.848088i	−0.999393	−	0.0348243i	$-0.988913\pi$
$613$	−36.3690	+	20.9977i	−1.46893	+	0.848088i	−0.469538	+	0.882912i	$0.655580\pi$
$614$	−0.145961	−	0.252812i	−0.00589052	−	0.0102027i
$615$	0.175454	−	0.303895i	0.00707499	−	0.0122542i
$616$		−	3.35675i		−	0.135247i
$617$	−21.1634	−	12.2187i	−0.852006	−	0.491906i	0.00932137	−	0.999957i	$-0.497033\pi$
$617$	−21.1634	−	12.2187i	−0.852006	−	0.491906i	−0.861327	+	0.508051i	$0.830366\pi$
$618$	−4.71030	−	2.71949i	−0.189476	−	0.109394i
$619$		−	24.1245i		−	0.969644i	−0.874613	−	0.484822i	$-0.838884\pi$
$619$		−	24.1245i		−	0.969644i	0.874613	−	0.484822i	$-0.161116\pi$
$620$	−1.38053	+	2.39115i	−0.0554434	+	0.0960309i
$621$	2.14974	+	3.72346i	0.0862661	+	0.149417i
$622$	66.8638	−	38.6038i	2.68099	−	1.54787i
$623$	15.7543			0.631182
$624$	1.10652	−	14.7623i	0.0442961	−	0.590964i
$625$	24.9300			0.997202
$626$	30.0061	−	17.3240i	1.19929	−	0.692408i
$627$	0.701179	+	1.21448i	0.0280024	+	0.0485016i
$628$	30.4498	−	52.7406i	1.21508	−	2.10458i
$629$			0.493183i			0.0196645i
$630$	−0.145098	−	0.0837724i	−0.00578084	−	0.00333757i
$631$	20.4155	+	11.7869i	0.812727	+	0.469228i	0.847902	−	0.530153i	$-0.177866\pi$
$631$	20.4155	+	11.7869i	0.812727	+	0.469228i	−0.0351753	+	0.999381i	$0.511199\pi$
$632$			69.5294i			2.76573i
$633$	−12.7371	+	22.0613i	−0.506253	+	0.876856i
$634$	22.8713	+	39.6142i	0.908335	+	1.57328i
$635$	0.473455	−	0.273350i	0.0187885	−	0.0108475i
$636$	12.9163			0.512166
$637$	−2.97901	−	2.03113i	−0.118033	−	0.0804762i
$638$	−13.3341			−0.527901
$639$	8.58321	−	4.95552i	0.339547	−	0.196037i
$640$	0.664132	+	1.15031i	0.0262521	+	0.0454700i
$641$	18.4479	−	31.9527i	0.728648	−	1.26205i	−0.228807	−	0.973472i	$-0.573482\pi$
$641$	18.4479	−	31.9527i	0.728648	−	1.26205i	0.957455	−	0.288583i	$-0.0931842\pi$
$642$		−	48.5365i		−	1.91558i
$643$	−21.8045	−	12.5888i	−0.859886	−	0.496455i	0.00408823	−	0.999992i	$-0.498699\pi$
$643$	−21.8045	−	12.5888i	−0.859886	−	0.496455i	−0.863974	+	0.503536i	$0.832032\pi$
$644$	14.9593	+	8.63676i	0.589479	+	0.340336i
$645$			0.122159i			0.00481002i
$646$	2.37113	−	4.10691i	0.0932907	−	0.161584i
$647$	2.50086	+	4.33161i	0.0983189	+	0.170293i	0.910989	−	0.412431i	$-0.135320\pi$
$647$	2.50086	+	4.33161i	0.0983189	+	0.170293i	−0.812670	+	0.582724i	$0.801987\pi$
$648$	−4.28620	+	2.47464i	−0.168378	+	0.0972131i
$649$	−5.64794			−0.221701
$650$	−24.8893	+	36.5046i	−0.976239	+	1.43183i
$651$	10.0622			0.394367
$652$	58.5959	−	33.8304i	2.29479	−	1.32490i
$653$	13.9272	+	24.1227i	0.545015	+	0.943993i	0.998606	+	0.0527834i	$0.0168093\pi$
$653$	13.9272	+	24.1227i	0.545015	+	0.943993i	−0.453591	+	0.891210i	$0.649857\pi$
$654$	2.09843	−	3.63459i	0.0820552	−	0.142124i
$655$		−	0.702887i		−	0.0274641i
$656$	−18.2685	−	10.5473i	−0.713264	−	0.411803i
$657$	−2.96400	−	1.71127i	−0.115637	−	0.0667629i
$658$		−	10.3738i		−	0.404412i
$659$	−2.39968	+	4.15637i	−0.0934783	+	0.161909i	−0.908973	−	0.416856i	$-0.863132\pi$
$659$	−2.39968	+	4.15637i	−0.0934783	+	0.161909i	0.815494	+	0.578765i	$0.196465\pi$
$660$	−0.0930533	−	0.161173i	−0.00362210	−	0.00627366i
$661$	2.64475	−	1.52695i	0.102869	−	0.0593914i	−0.447683	−	0.894192i	$-0.647751\pi$
$661$	2.64475	−	1.52695i	0.102869	−	0.0593914i	0.550552	+	0.834801i	$0.314417\pi$
$662$	−54.1744			−2.10555
$663$	−3.03723	+	1.46259i	−0.117956	+	0.0568023i
$664$	−34.8138			−1.35104
$665$	0.122302	−	0.0706109i	0.00474265	−	0.00273817i
$666$	0.646989	+	1.12062i	0.0250703	+	0.0434230i
$667$	17.2290	−	29.8415i	0.667110	−	1.15547i
$668$		−	6.63418i		−	0.256684i
$669$	6.06784	+	3.50327i	0.234596	+	0.135444i
$670$	−1.05926	−	0.611564i	−0.0409228	−	0.0236268i
$671$			0.685375i			0.0264586i
$672$	−0.0866393	+	0.150064i	−0.00334218	+	0.00578883i
$673$	6.39498	+	11.0764i	0.246508	+	0.426965i	0.962555	−	0.271088i	$-0.0873834\pi$
$673$	6.39498	+	11.0764i	0.246508	+	0.426965i	−0.716046	+	0.698053i	$0.754050\pi$
$674$	69.1193	−	39.9061i	2.66238	−	1.53712i
$675$	4.99534			0.192271
$676$	−19.0797	−	48.6188i	−0.733834	−	1.86995i
$677$	21.6803			0.833240			0.416620	−	0.909081i	$-0.363215\pi$
$677$	21.6803			0.833240			0.416620	+	0.909081i	$0.363215\pi$
$678$	−28.9756	+	16.7290i	−1.11280	+	0.642475i
$679$	−8.33523	−	14.4370i	−0.319877	−	0.554043i
$680$	−0.158024	+	0.273706i	−0.00605996	+	0.0104962i
$681$		−	27.7571i		−	1.06365i
$682$	14.4981	+	8.37047i	0.555160	+	0.320522i
$683$	29.4162	+	16.9835i	1.12558	+	0.649854i	0.942820	−	0.333303i	$-0.108163\pi$
$683$	29.4162	+	16.9835i	1.12558	+	0.649854i	0.182761	+	0.983157i	$0.441497\pi$
$684$		−	8.30704i		−	0.317628i
$685$	0.123608	−	0.214095i	0.00472280	−	0.00818014i
$686$	1.22654	+	2.12443i	0.0468294	+	0.0811110i
$687$	−3.12645	+	1.80506i	−0.119281	+	0.0688672i
$688$	7.34352			0.279969
$689$	10.4438	−	5.02927i	0.397878	−	0.191600i
$690$	0.720355			0.0274235
$691$	−37.4270	+	21.6085i	−1.42379	+	0.822026i	−0.996620	−	0.0821452i	$-0.973823\pi$
$691$	−37.4270	+	21.6085i	−1.42379	+	0.822026i	−0.427170	+	0.904171i	$0.640490\pi$
$692$	−49.7752	−	86.2131i	−1.89217	−	3.27733i
$693$	−0.339115	+	0.587365i	−0.0128819	+	0.0223121i
$694$			10.8235i			0.410856i
$695$	−0.0720527	−	0.0415997i	−0.00273312	−	0.00157796i
$696$	34.3516	+	19.8329i	1.30209	+	0.751764i
$697$			4.80359i			0.181949i
$698$	−8.73811	+	15.1349i	−0.330742	+	0.572863i
$699$	−7.80882	−	13.5253i	−0.295357	−	0.511573i
$700$	17.3804	−	10.0346i	0.656918	−	0.379272i
$701$	0.456718			0.0172500			0.00862500	−	0.999963i	$-0.497255\pi$
$701$	0.456718			0.0172500			0.00862500	+	0.999963i	$0.497255\pi$
$702$	−4.98251	+	7.30775i	−0.188053	+	0.275813i
$703$	−1.09068			−0.0411358
$704$	4.57354	−	2.64053i	0.172372	−	0.0995188i
$705$	−0.144416	−	0.250136i	−0.00543903	−	0.00942067i
$706$	4.09251	−	7.08844i	0.154024	−	0.266777i
$707$		−	1.50429i		−	0.0565746i
$708$	28.9740	+	16.7281i	1.08891	+	0.628681i
$709$	12.8902	+	7.44219i	0.484103	+	0.279497i	0.722125	−	0.691763i	$-0.243166\pi$
$709$	12.8902	+	7.44219i	0.484103	+	0.279497i	−0.238022	+	0.971260i	$0.576499\pi$
$710$		−	1.66054i		−	0.0623191i
$711$	7.02419	−	12.1662i	0.263428	−	0.456270i
$712$	−38.9862	−	67.5261i	−1.46107	−	2.53065i
$713$	−37.4660	+	21.6310i	−1.40311	+	0.810089i
$714$	2.29352			0.0858330
$715$	−0.137997	−	0.0940880i	−0.00516080	−	0.00351869i
$716$	−25.3222			−0.946335
$717$	24.2341	−	13.9915i	0.905038	−	0.522524i
$718$	30.1567	+	52.2330i	1.12544	+	1.94932i
$719$	4.98743	−	8.63849i	0.186000	−	0.322161i	−0.757913	−	0.652355i	$-0.773781\pi$
$719$	4.98743	−	8.63849i	0.186000	−	0.322161i	0.943913	+	0.330194i	$0.107114\pi$
$720$			0.280426i			0.0104509i
$721$	1.92016	+	1.10860i	0.0715105	+	0.0412866i
$722$	−31.2816	−	18.0604i	−1.16418	−	0.672140i
$723$		−	25.9732i		−	0.965955i
$724$	38.0601	−	65.9221i	1.41449	−	2.44998i
$725$	−20.0175	−	34.6712i	−0.743430	−	1.28766i
$726$	22.3915	−	12.9277i	0.831025	−	0.479793i
$727$	−10.4392			−0.387169			−0.193585	−	0.981084i	$-0.562011\pi$
$727$	−10.4392			−0.387169			−0.193585	+	0.981084i	$0.562011\pi$
$728$	−1.33383	+	17.7950i	−0.0494352	+	0.659526i
$729$	1.00000			0.0370370
$730$	−0.496603	+	0.286714i	−0.0183801	+	0.0106118i
$731$	−0.836120	−	1.44820i	−0.0309250	−	0.0535637i
$732$	2.02995	−	3.51598i	0.0750291	−	0.129954i
$733$			22.7887i			0.841718i	0.907126	+	0.420859i	$0.138271\pi$
$733$			22.7887i			0.841718i	−0.907126	+	0.420859i	$0.861729\pi$
$734$	32.0291	+	18.4920i	1.18221	+	0.682552i
$735$	0.0591494	+	0.0341499i	0.00218176	+	0.00125964i
$736$		−	0.745008i		−	0.0274614i
$737$	−2.47564	+	4.28794i	−0.0911915	+	0.157948i
$738$	6.30166	+	10.9148i	0.231967	+	0.401779i
$739$	36.6152	−	21.1398i	1.34691	−	0.777640i	0.359101	−	0.933299i	$-0.383084\pi$
$739$	36.6152	−	21.1398i	1.34691	−	0.777640i	0.987811	+	0.155659i	$0.0497502\pi$
$740$	0.144744			0.00532089
$741$	−3.23454	−	6.71686i	−0.118824	−	0.246750i
$742$	−7.88652			−0.289523
$743$	−6.04660	+	3.49101i	−0.221828	+	0.128073i	−0.606797	−	0.794857i	$-0.707546\pi$
$743$	−6.04660	+	3.49101i	−0.221828	+	0.128073i	0.384968	+	0.922930i	$0.374212\pi$
$744$	−24.9002	−	43.1285i	−0.912887	−	1.58117i
$745$	0.564405	−	0.977578i	0.0206782	−	0.0358157i
$746$		−	61.9331i		−	2.26753i
$747$	6.09172	+	3.51706i	0.222884	+	0.128682i
$748$	2.20630	+	1.27381i	0.0806704	+	0.0465751i
$749$			19.7860i			0.722963i
$750$	0.837333	−	1.45030i	0.0305751	−	0.0529576i
$751$	17.7765	+	30.7898i	0.648673	+	1.12353i	0.983440	+	0.181234i	$0.0580091\pi$
$751$	17.7765	+	30.7898i	0.648673	+	1.12353i	−0.334767	+	0.942301i	$0.608658\pi$
$752$	−15.0368	+	8.68148i	−0.548334	+	0.316581i
$753$	6.38525			0.232691
$754$	70.6871	+	5.29840i	2.57427	+	0.192956i
$755$	−1.39020			−0.0505945
$756$	3.47933	−	2.00879i	0.126542	−	0.0730590i
$757$	6.55855	+	11.3597i	0.238374	+	0.412877i	0.960248	−	0.279148i	$-0.0900521\pi$
$757$	6.55855	+	11.3597i	0.238374	+	0.412877i	−0.721874	+	0.692025i	$0.756719\pi$
$758$	29.4899	−	51.0780i	1.07112	−	1.85524i
$759$		−	2.91604i		−	0.105845i
$760$	−0.605305	−	0.349473i	−0.0219567	−	0.0126767i
$761$	−2.84572	−	1.64298i	−0.103157	−	0.0595578i	0.447534	−	0.894267i	$-0.352302\pi$
$761$	−2.84572	−	1.64298i	−0.103157	−	0.0595578i	−0.550691	+	0.834709i	$0.685636\pi$
$762$			19.6354i			0.711315i
$763$	−0.855429	+	1.48165i	−0.0309686	+	0.0536392i
$764$	−17.6655	−	30.5976i	−0.639116	−	1.10698i
$765$	0.0553023	−	0.0319288i	0.00199946	−	0.00115439i
$766$	11.1351			0.402327
$767$	29.9411	+	2.24425i	1.08111	+	0.0810353i
$768$	−32.1332			−1.15951
$769$	1.11552	−	0.644047i	0.0402267	−	0.0232249i	−0.479752	−	0.877404i	$-0.659273\pi$
$769$	1.11552	−	0.644047i	0.0402267	−	0.0232249i	0.519978	+	0.854179i	$0.325940\pi$

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.12443 - 1.22654i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.00879 - 3.47933i) q^{4} +0.0682999i q^{5} +(-2.12443 - 1.22654i) q^{6} +(0.866025 + 0.500000i) q^{7} -4.94928i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(2.12443 - 1.22654i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.00879 - 3.47933i) q^{4} +0.0682999i q^{5} +(-2.12443 - 1.22654i) q^{6} +(0.866025 + 0.500000i) q^{7} -4.94928i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0837724 + 0.145098i) q^{10} +(0.587365 - 0.339115i) q^{11} -4.01758 q^{12} +(-3.24851 + 1.56434i) q^{13} +2.45308 q^{14} +(0.0591494 - 0.0341499i) q^{15} +(-2.05290 - 3.55573i) q^{16} +(-0.467479 + 0.809698i) q^{17} +2.45308i q^{18} +(-1.79066 - 1.03384i) q^{19} +(0.237638 + 0.137200i) q^{20} -1.00000i q^{21} +(0.831875 - 1.44085i) q^{22} +(2.14974 + 3.72346i) q^{23} +(-4.28620 + 2.47464i) q^{24} +4.99534 q^{25} +(-4.98251 + 7.30775i) q^{26} +1.00000 q^{27} +(3.47933 - 2.00879i) q^{28} +(-4.00723 - 6.94072i) q^{29} +(0.0837724 - 0.145098i) q^{30} +10.0622i q^{31} +(-0.150064 - 0.0866393i) q^{32} +(-0.587365 - 0.339115i) q^{33} +2.29352i q^{34} +(-0.0341499 + 0.0591494i) q^{35} +(2.00879 + 3.47933i) q^{36} +(0.456821 - 0.263746i) q^{37} -5.07216 q^{38} +(2.97901 + 2.03113i) q^{39} +0.338035 q^{40} +(4.44943 - 2.56888i) q^{41} +(-1.22654 - 2.12443i) q^{42} +(-0.894286 + 1.54895i) q^{43} -2.72485i q^{44} +(-0.0591494 - 0.0341499i) q^{45} +(9.13393 + 5.27348i) q^{46} -4.22889i q^{47} +(-2.05290 + 3.55573i) q^{48} +(0.500000 + 0.866025i) q^{49} +(10.6122 - 6.12697i) q^{50} +0.934958 q^{51} +(-1.08274 + 14.4451i) q^{52} -3.21495 q^{53} +(2.12443 - 1.22654i) q^{54} +(0.0231615 + 0.0401169i) q^{55} +(2.47464 - 4.28620i) q^{56} +2.06767i q^{57} +(-17.0261 - 9.83004i) q^{58} +(-7.21179 - 4.16373i) q^{59} -0.274400i q^{60} +(-0.505267 + 0.875148i) q^{61} +(12.3416 + 21.3763i) q^{62} +(-0.866025 + 0.500000i) q^{63} +7.78654 q^{64} +(-0.106844 - 0.221873i) q^{65} -1.66375 q^{66} +(-6.32225 + 3.65015i) q^{67} +(1.87814 + 3.25303i) q^{68} +(2.14974 - 3.72346i) q^{69} +0.167545i q^{70} +(-8.58321 - 4.95552i) q^{71} +(4.28620 + 2.47464i) q^{72} +3.42254i q^{73} +(0.646989 - 1.12062i) q^{74} +(-2.49767 - 4.32609i) q^{75} +(-7.19411 + 4.15352i) q^{76} +0.678230 q^{77} +(8.81995 + 0.661105i) q^{78} -14.0484 q^{79} +(0.242856 - 0.140213i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.30166 - 10.9148i) q^{82} -7.03411i q^{83} +(-3.47933 - 2.00879i) q^{84} +(-0.0553023 - 0.0319288i) q^{85} +4.38750i q^{86} +(-4.00723 + 6.94072i) q^{87} +(-1.67838 - 2.90703i) q^{88} +(13.6436 - 7.87714i) q^{89} -0.167545 q^{90} +(-3.59547 - 0.269500i) q^{91} +17.2735 q^{92} +(8.71409 - 5.03108i) q^{93} +(-5.18689 - 8.98395i) q^{94} +(0.0706109 - 0.122302i) q^{95} +0.173279i q^{96} +(-14.4370 - 8.33523i) q^{97} +(2.12443 + 1.22654i) q^{98} +0.678230i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

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