LMFDB - Embedded newform 273.2.bd.b.127.4

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} - 4 x^{15} + 10 x^{14} - 8 x^{13} - 3 x^{12} + 32 x^{11} - 5 x^{10} - 44 x^{9} + 214 x^{8} - 132 x^{7} - 45 x^{6} + 864 x^{5} - 243 x^{4} - 1944 x^{3} + 7290 x^{2} - 8748 x + 6561 $ x^16 - 4x^15 + 10x^14 - 8x^13 - 3x^12 + 32x^11 - 5x^10 - 44x^9 + 214x^8 - 132x^7 - 45x^6 + 864x^5 - 243x^4 - 1944x^3 + 7290x^2 - 8748*x + 6561
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			127.4
Root			$-1.36010 + 1.07244i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.b.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654865 + 0.378087i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.714101 + 1.23686i) q^{4} +4.01537i q^{5} +(-0.654865 - 0.378087i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.59231i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.654865 + 0.378087i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.714101 + 1.23686i) q^{4} +4.01537i q^{5} +(-0.654865 - 0.378087i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.59231i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.51816 - 2.62953i) q^{10} +(-0.588269 + 0.339637i) q^{11} -1.42820 q^{12} +(-0.823013 - 3.51036i) q^{13} +0.756173 q^{14} +(-3.47741 + 2.00768i) q^{15} +(-0.448082 - 0.776101i) q^{16} +(1.48617 - 2.57413i) q^{17} -0.756173i q^{18} +(0.795577 + 0.459326i) q^{19} +(-4.96644 - 2.86738i) q^{20} -1.00000i q^{21} +(0.256825 - 0.444833i) q^{22} +(4.29961 + 7.44714i) q^{23} +(2.24501 - 1.29616i) q^{24} -11.1232 q^{25} +(1.86618 + 1.98764i) q^{26} -1.00000 q^{27} +(1.23686 - 0.714101i) q^{28} +(3.98933 + 6.90972i) q^{29} +(1.51816 - 2.62953i) q^{30} +3.29616i q^{31} +(5.07689 + 2.93114i) q^{32} +(-0.588269 - 0.339637i) q^{33} +2.24761i q^{34} +(2.00768 - 3.47741i) q^{35} +(-0.714101 - 1.23686i) q^{36} +(-4.70475 + 2.71629i) q^{37} -0.694661 q^{38} +(2.62856 - 2.46793i) q^{39} +10.4091 q^{40} +(-7.98678 + 4.61117i) q^{41} +(0.378087 + 0.654865i) q^{42} +(2.53067 - 4.38324i) q^{43} -0.970141i q^{44} +(-3.47741 - 2.00768i) q^{45} +(-5.63133 - 3.25125i) q^{46} -3.03541i q^{47} +(0.448082 - 0.776101i) q^{48} +(0.500000 + 0.866025i) q^{49} +(7.28419 - 4.20553i) q^{50} +2.97235 q^{51} +(4.92954 + 1.48880i) q^{52} +1.32745 q^{53} +(0.654865 - 0.378087i) q^{54} +(-1.36377 - 2.36212i) q^{55} +(-1.29616 + 2.24501i) q^{56} +0.918653i q^{57} +(-5.22495 - 3.01663i) q^{58} +(4.18507 + 2.41625i) q^{59} -5.73476i q^{60} +(2.23470 - 3.87061i) q^{61} +(-1.24623 - 2.15854i) q^{62} +(0.866025 - 0.500000i) q^{63} -2.64058 q^{64} +(14.0954 - 3.30470i) q^{65} +0.513649 q^{66} +(3.49940 - 2.02038i) q^{67} +(2.12256 + 3.67638i) q^{68} +(-4.29961 + 7.44714i) q^{69} +3.03631i q^{70} +(-2.08894 - 1.20605i) q^{71} +(2.24501 + 1.29616i) q^{72} +7.82146i q^{73} +(2.05398 - 3.55761i) q^{74} +(-5.56159 - 9.63296i) q^{75} +(-1.13624 + 0.656011i) q^{76} +0.679275 q^{77} +(-0.788259 + 2.60999i) q^{78} +16.1827 q^{79} +(3.11633 - 1.79921i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.48684 - 6.03939i) q^{82} +4.78597i q^{83} +(1.23686 + 0.714101i) q^{84} +(10.3361 + 5.96754i) q^{85} +3.82724i q^{86} +(-3.98933 + 6.90972i) q^{87} +(0.880447 + 1.52498i) q^{88} +(-3.91913 + 2.26271i) q^{89} +3.03631 q^{90} +(-1.04243 + 3.45157i) q^{91} -12.2814 q^{92} +(-2.85455 + 1.64808i) q^{93} +(1.14765 + 1.98779i) q^{94} +(-1.84436 + 3.19453i) q^{95} +5.86229i q^{96} +(-7.40406 - 4.27474i) q^{97} +(-0.654865 - 0.378087i) q^{98} -0.679275i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * 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 $

$2$	−0.654865	+	0.378087i	−0.463060	+	0.267348i	−0.713330	−	0.700828i	$-0.752814\pi$
$2$	−0.654865	+	0.378087i	−0.463060	+	0.267348i	0.250270	+	0.968176i	$0.419481\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.714101	+	1.23686i	−0.357050	+	0.618430i
$5$			4.01537i			1.79573i	0.440274	+	0.897864i	$0.354881\pi$
$5$			4.01537i			1.79573i	−0.440274	+	0.897864i	$0.645119\pi$
$6$	−0.654865	−	0.378087i	−0.267348	−	0.154353i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		−	2.59231i		−	0.916522i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.51816	−	2.62953i	−0.480084	−	0.831529i
$11$	−0.588269	+	0.339637i	−0.177370	+	0.102404i	−0.586056	−	0.810270i	$-0.699320\pi$
$11$	−0.588269	+	0.339637i	−0.177370	+	0.102404i	0.408687	+	0.912675i	$0.365987\pi$
$12$	−1.42820			−0.412286
$13$	−0.823013	−	3.51036i	−0.228263	−	0.973600i
$13$	−0.823013	−	3.51036i	−0.228263	−	0.973600i
$14$	0.756173			0.202096
$15$	−3.47741	+	2.00768i	−0.897864	+	0.518382i
$16$	−0.448082	−	0.776101i	−0.112020	−	0.194025i
$17$	1.48617	−	2.57413i	0.360450	−	0.624318i	−0.627585	−	0.778548i	$-0.715956\pi$
$17$	1.48617	−	2.57413i	0.360450	−	0.624318i	0.988035	+	0.154230i	$0.0492898\pi$
$18$		−	0.756173i		−	0.178232i
$19$	0.795577	+	0.459326i	0.182518	+	0.105377i	0.588475	−	0.808515i	$-0.299729\pi$
$19$	0.795577	+	0.459326i	0.182518	+	0.105377i	−0.405957	+	0.913892i	$0.633062\pi$
$20$	−4.96644	−	2.86738i	−1.11053	−	0.641165i
$21$		−	1.00000i		−	0.218218i
$22$	0.256825	−	0.444833i	0.0547552	−	0.0948388i
$23$	4.29961	+	7.44714i	0.896530	+	1.55284i	0.831899	+	0.554927i	$0.187254\pi$
$23$	4.29961	+	7.44714i	0.896530	+	1.55284i	0.0646308	+	0.997909i	$0.479413\pi$
$24$	2.24501	−	1.29616i	0.458261	−	0.264577i
$25$	−11.1232			−2.22464
$26$	1.86618	+	1.98764i	0.365989	+	0.389809i
$27$	−1.00000			−0.192450
$28$	1.23686	−	0.714101i	0.233744	−	0.134952i
$29$	3.98933	+	6.90972i	0.740800	+	1.28310i	0.952131	+	0.305689i	$0.0988867\pi$
$29$	3.98933	+	6.90972i	0.740800	+	1.28310i	−0.211331	+	0.977414i	$0.567780\pi$
$30$	1.51816	−	2.62953i	0.277176	−	0.480084i
$31$			3.29616i			0.592007i	0.955187	+	0.296004i	$0.0956540\pi$
$31$			3.29616i			0.592007i	−0.955187	+	0.296004i	$0.904346\pi$
$32$	5.07689	+	2.93114i	0.897475	+	0.518158i
$33$	−0.588269	−	0.339637i	−0.102404	−	0.0591233i
$34$			2.24761i			0.385462i
$35$	2.00768	−	3.47741i	0.339361	−	0.587790i
$36$	−0.714101	−	1.23686i	−0.119017	−	0.206143i
$37$	−4.70475	+	2.71629i	−0.773456	+	0.446555i	−0.834106	−	0.551604i	$-0.814016\pi$
$37$	−4.70475	+	2.71629i	−0.773456	+	0.446555i	0.0606502	+	0.998159i	$0.480683\pi$
$38$	−0.694661			−0.112689
$39$	2.62856	−	2.46793i	0.420906	−	0.395185i
$40$	10.4091			1.64582
$41$	−7.98678	+	4.61117i	−1.24733	+	0.720144i	−0.970575	−	0.240798i	$-0.922591\pi$
$41$	−7.98678	+	4.61117i	−1.24733	+	0.720144i	−0.276751	+	0.960942i	$0.589258\pi$
$42$	0.378087	+	0.654865i	0.0583400	+	0.101048i
$43$	2.53067	−	4.38324i	0.385923	−	0.668438i	−0.605974	−	0.795485i	$-0.707216\pi$
$43$	2.53067	−	4.38324i	0.385923	−	0.668438i	0.991897	+	0.127046i	$0.0405497\pi$
$44$		−	0.970141i		−	0.146254i
$45$	−3.47741	−	2.00768i	−0.518382	−	0.299288i
$46$	−5.63133	−	3.25125i	−0.830294	−	0.479370i
$47$		−	3.03541i		−	0.442760i	−0.975188	−	0.221380i	$-0.928944\pi$
$47$		−	3.03541i		−	0.442760i	0.975188	−	0.221380i	$-0.0710562\pi$
$48$	0.448082	−	0.776101i	0.0646751	−	0.112020i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	7.28419	−	4.20553i	1.03014	−	0.594751i
$51$	2.97235			0.416212
$52$	4.92954	+	1.48880i	0.683604	+	0.206460i
$53$	1.32745			0.182339			0.0911695	−	0.995835i	$-0.470940\pi$
$53$	1.32745			0.182339			0.0911695	+	0.995835i	$0.470940\pi$
$54$	0.654865	−	0.378087i	0.0891159	−	0.0514511i
$55$	−1.36377	−	2.36212i	−0.183891	−	0.318508i
$56$	−1.29616	+	2.24501i	−0.173206	+	0.300002i
$57$			0.918653i			0.121679i
$58$	−5.22495	−	3.01663i	−0.686069	−	0.396102i
$59$	4.18507	+	2.41625i	0.544850	+	0.314569i	0.747042	−	0.664777i	$-0.231473\pi$
$59$	4.18507	+	2.41625i	0.544850	+	0.314569i	−0.202193	+	0.979346i	$0.564807\pi$
$60$		−	5.73476i		−	0.740354i
$61$	2.23470	−	3.87061i	0.286124	−	0.495581i	−0.686757	−	0.726887i	$-0.740966\pi$
$61$	2.23470	−	3.87061i	0.286124	−	0.495581i	0.972881	+	0.231306i	$0.0742998\pi$
$62$	−1.24623	−	2.15854i	−0.158272	−	0.274135i
$63$	0.866025	−	0.500000i	0.109109	−	0.0629941i
$64$	−2.64058			−0.330072
$65$	14.0954	−	3.30470i	1.74832	−	0.409898i
$66$	0.513649			0.0632259
$67$	3.49940	−	2.02038i	0.427520	−	0.246829i	−0.270769	−	0.962644i	$-0.587278\pi$
$67$	3.49940	−	2.02038i	0.427520	−	0.246829i	0.698290	+	0.715815i	$0.253945\pi$
$68$	2.12256	+	3.67638i	0.257398	+	0.445826i
$69$	−4.29961	+	7.44714i	−0.517612	+	0.896530i
$70$			3.03631i			0.362909i
$71$	−2.08894	−	1.20605i	−0.247912	−	0.143132i	0.370896	−	0.928674i	$-0.379051\pi$
$71$	−2.08894	−	1.20605i	−0.247912	−	0.143132i	−0.618808	+	0.785543i	$0.712384\pi$
$72$	2.24501	+	1.29616i	0.264577	+	0.152754i
$73$			7.82146i			0.915433i	0.889098	+	0.457716i	$0.151332\pi$
$73$			7.82146i			0.915433i	−0.889098	+	0.457716i	$0.848668\pi$
$74$	2.05398	−	3.55761i	0.238771	−	0.413563i
$75$	−5.56159	−	9.63296i	−0.642197	−	1.11232i
$76$	−1.13624	+	0.656011i	−0.130336	+	0.0752496i
$77$	0.679275			0.0774105
$78$	−0.788259	+	2.60999i	−0.0892527	+	0.295523i
$79$	16.1827			1.82069			0.910346	−	0.413848i	$-0.135815\pi$
$79$	16.1827			1.82069			0.910346	+	0.413848i	$0.135815\pi$
$80$	3.11633	−	1.79921i	0.348416	−	0.201158i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.48684	−	6.03939i	0.385058	−	0.666939i
$83$			4.78597i			0.525328i	0.964887	+	0.262664i	$0.0846011\pi$
$83$			4.78597i			0.525328i	−0.964887	+	0.262664i	$0.915399\pi$
$84$	1.23686	+	0.714101i	0.134952	+	0.0779148i
$85$	10.3361	+	5.96754i	1.12110	+	0.647270i
$86$			3.82724i			0.412702i
$87$	−3.98933	+	6.90972i	−0.427701	+	0.740800i
$88$	0.880447	+	1.52498i	0.0938559	+	0.162563i
$89$	−3.91913	+	2.26271i	−0.415426	+	0.239847i	−0.693119	−	0.720824i	$-0.743764\pi$
$89$	−3.91913	+	2.26271i	−0.415426	+	0.239847i	0.277692	+	0.960670i	$0.410430\pi$
$90$	3.03631			0.320056
$91$	−1.04243	+	3.45157i	−0.109276	+	0.361823i
$92$	−12.2814			−1.28043
$93$	−2.85455	+	1.64808i	−0.296004	+	0.170898i
$94$	1.14765	+	1.98779i	0.118371	+	0.205025i
$95$	−1.84436	+	3.19453i	−0.189228	+	0.327752i
$96$			5.86229i			0.598317i
$97$	−7.40406	−	4.27474i	−0.751768	−	0.434034i	0.0745642	−	0.997216i	$-0.476243\pi$
$97$	−7.40406	−	4.27474i	−0.751768	−	0.434034i	−0.826332	+	0.563183i	$0.809577\pi$
$98$	−0.654865	−	0.378087i	−0.0661514	−	0.0381925i
$99$		−	0.679275i		−	0.0682697i
$100$	7.94307	−	13.7578i	0.794307	−	1.37578i
$101$	−6.72418	−	11.6466i	−0.669080	−	1.15888i	−0.978162	−	0.207846i	$-0.933355\pi$
$101$	−6.72418	−	11.6466i	−0.669080	−	1.15888i	0.309081	−	0.951036i	$-0.399979\pi$
$102$	−1.94649	+	1.12381i	−0.192731	+	0.111273i
$103$	12.9919			1.28013			0.640066	−	0.768320i	$-0.278907\pi$
$103$	12.9919			1.28013			0.640066	+	0.768320i	$0.278907\pi$
$104$	−9.09997	+	2.13351i	−0.892325	+	0.209208i
$105$	4.01537			0.391860
$106$	−0.869299	+	0.501890i	−0.0844338	+	0.0487479i
$107$	3.02164	+	5.23363i	0.292113	+	0.505954i	0.974309	−	0.225215i	$-0.0723085\pi$
$107$	3.02164	+	5.23363i	0.292113	+	0.505954i	−0.682197	+	0.731169i	$0.738975\pi$
$108$	0.714101	−	1.23686i	0.0687144	−	0.119017i
$109$		−	18.1361i		−	1.73712i	−0.495582	−	0.868561i	$-0.665045\pi$
$109$		−	18.1361i		−	1.73712i	0.495582	−	0.868561i	$-0.334955\pi$
$110$	1.78617	+	1.03125i	0.170305	+	0.0983254i
$111$	−4.70475	−	2.71629i	−0.446555	−	0.257819i
$112$			0.896164i			0.0846795i
$113$	10.2874	−	17.8183i	0.967756	−	1.67620i	0.265736	−	0.964046i	$-0.414385\pi$
$113$	10.2874	−	17.8183i	0.967756	−	1.67620i	0.702020	−	0.712157i	$-0.252282\pi$
$114$	−0.347330	−	0.601594i	−0.0325305	−	0.0563444i
$115$	−29.9030	+	17.2645i	−2.78847	+	1.60992i
$116$	−11.3951			−1.05801
$117$	3.45157	+	1.04243i	0.319098	+	0.0963728i
$118$	−3.65421			−0.336397
$119$	−2.57413	+	1.48617i	−0.235970	+	0.136237i
$120$	5.20455	+	9.01454i	0.475108	+	0.822912i
$121$	−5.26929	+	9.12668i	−0.479027	+	0.829698i
$122$			3.37964i			0.305978i
$123$	−7.98678	−	4.61117i	−0.720144	−	0.415775i
$124$	−4.07688	−	2.35379i	−0.366115	−	0.211376i
$125$		−	24.5868i		−	2.19911i
$126$	−0.378087	+	0.654865i	−0.0336826	+	0.0583400i
$127$	9.88317	+	17.1182i	0.876989	+	1.51899i	0.854628	+	0.519240i	$0.173785\pi$
$127$	9.88317	+	17.1182i	0.876989	+	1.51899i	0.0223611	+	0.999750i	$0.492882\pi$
$128$	−8.42455	+	4.86392i	−0.744632	+	0.429914i
$129$	5.06133			0.445625
$130$	−7.98113	+	7.49342i	−0.699991	+	0.657216i
$131$	−7.92094			−0.692056			−0.346028	−	0.938224i	$-0.612470\pi$
$131$	−7.92094			−0.692056			−0.346028	+	0.938224i	$0.612470\pi$
$132$	0.840167	−	0.485071i	0.0731271	−	0.0422200i
$133$	−0.459326	−	0.795577i	−0.0398286	−	0.0689852i
$134$	−1.52776	+	2.64616i	−0.131978	+	0.228593i
$135$		−	4.01537i		−	0.345588i
$136$	−6.67295	−	3.85263i	−0.572201	−	0.330360i
$137$	8.44751	+	4.87717i	0.721719	+	0.416685i	0.815385	−	0.578919i	$-0.196525\pi$
$137$	8.44751	+	4.87717i	0.721719	+	0.416685i	−0.0936658	+	0.995604i	$0.529859\pi$
$138$		−	6.50250i		−	0.553529i
$139$	6.11671	−	10.5944i	0.518812	−	0.898609i	−0.480949	−	0.876749i	$-0.659708\pi$
$139$	6.11671	−	10.5944i	0.518812	−	0.898609i	0.999761	−	0.0218607i	$-0.00695903\pi$
$140$	2.86738	+	4.96644i	0.242338	+	0.419741i
$141$	2.62874	−	1.51771i	0.221380	−	0.127814i
$142$	1.82397			0.153064
$143$	1.67640	+	1.78551i	0.140188	+	0.149312i
$144$	0.896164			0.0746803
$145$	−27.7451	+	16.0186i	−2.30410	+	1.33027i
$146$	−2.95719	−	5.12200i	−0.244739	−	0.423900i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$		−	7.75881i		−	0.637771i
$149$	−5.18348	−	2.99268i	−0.424647	−	0.245170i	0.272416	−	0.962179i	$-0.412177\pi$
$149$	−5.18348	−	2.99268i	−0.424647	−	0.245170i	−0.697064	+	0.717009i	$0.745511\pi$
$150$	7.28419	+	4.20553i	0.594751	+	0.343380i
$151$			13.1858i			1.07304i	0.843887	+	0.536521i	$0.180262\pi$
$151$			13.1858i			1.07304i	−0.843887	+	0.536521i	$0.819738\pi$
$152$	1.19072	−	2.06238i	0.0965800	−	0.167282i
$153$	1.48617	+	2.57413i	0.120150	+	0.208106i
$154$	−0.444833	+	0.256825i	−0.0358457	+	0.0206955i
$155$	−13.2353			−1.06308
$156$	1.17543	+	5.01351i	0.0941097	+	0.401402i
$157$	11.0004			0.877928			0.438964	−	0.898505i	$-0.355346\pi$
$157$	11.0004			0.877928			0.438964	+	0.898505i	$0.355346\pi$
$158$	−10.5975	+	6.11845i	−0.843089	+	0.486758i
$159$	0.663724	+	1.14960i	0.0526367	+	0.0911695i
$160$	−11.7696	+	20.3856i	−0.930470	+	1.61162i
$161$		−	8.59922i		−	0.677713i
$162$	0.654865	+	0.378087i	0.0514511	+	0.0297053i
$163$	6.01786	+	3.47441i	0.471355	+	0.272137i	0.716807	−	0.697272i	$-0.245603\pi$
$163$	6.01786	+	3.47441i	0.471355	+	0.272137i	−0.245452	+	0.969409i	$0.578936\pi$
$164$		−	13.1714i		−	1.02851i
$165$	1.36377	−	2.36212i	0.106169	−	0.183891i
$166$	−1.80951	−	3.13416i	−0.140445	−	0.243258i
$167$	−2.24914	+	1.29854i	−0.174043	+	0.100484i	−0.584491	−	0.811400i	$-0.698706\pi$
$167$	−2.24914	+	1.29854i	−0.174043	+	0.100484i	0.410448	+	0.911884i	$0.365372\pi$
$168$	−2.59231			−0.200001
$169$	−11.6453	+	5.77815i	−0.895792	+	0.444473i
$170$	−9.02498			−0.692185
$171$	−0.795577	+	0.459326i	−0.0608393	+	0.0351256i
$172$	3.61430	+	6.26015i	0.275588	+	0.477332i
$173$	−1.87648	+	3.25016i	−0.142666	+	0.247105i	−0.928500	−	0.371333i	$-0.878901\pi$
$173$	−1.87648	+	3.25016i	−0.142666	+	0.247105i	0.785834	+	0.618438i	$0.212234\pi$
$174$		−	6.03325i		−	0.457380i
$175$	9.63296	+	5.56159i	0.728183	+	0.420417i
$176$	0.527185	+	0.304371i	0.0397381	+	0.0229428i
$177$			4.83250i			0.363233i
$178$	1.71100	−	2.96354i	0.128245	−	0.222127i
$179$	9.60443	+	16.6354i	0.717869	+	1.24339i	0.961842	+	0.273604i	$0.0882157\pi$
$179$	9.60443	+	16.6354i	0.717869	+	1.24339i	−0.243973	+	0.969782i	$0.578451\pi$
$180$	4.96644	−	2.86738i	0.370177	−	0.213722i
$181$	−5.21963			−0.387972			−0.193986	−	0.981004i	$-0.562142\pi$
$181$	−5.21963			−0.387972			−0.193986	+	0.981004i	$0.562142\pi$
$182$	−0.622341	−	2.65444i	−0.0461310	−	0.196760i
$183$	4.46940			0.330387
$184$	19.3053	−	11.1459i	1.42321	−	0.821689i
$185$	−10.9069	−	18.8913i	−0.801891	−	1.38892i
$186$	1.24623	−	2.15854i	0.0913782	−	0.158272i
$187$			2.01904i			0.147647i
$188$	3.75438	+	2.16759i	0.273816	+	0.158088i
$189$	0.866025	+	0.500000i	0.0629941	+	0.0363696i
$190$		−	2.78932i		−	0.202358i
$191$	−0.293802	+	0.508881i	−0.0212588	+	0.0368213i	−0.876459	−	0.481476i	$-0.840101\pi$
$191$	−0.293802	+	0.508881i	−0.0212588	+	0.0368213i	0.855200	+	0.518298i	$0.173434\pi$
$192$	−1.32029	−	2.28681i	−0.0952836	−	0.165036i
$193$	12.9473	−	7.47511i	0.931965	−	0.538070i	0.0445322	−	0.999008i	$-0.485820\pi$
$193$	12.9473	−	7.47511i	0.931965	−	0.538070i	0.887432	+	0.460938i	$0.152487\pi$
$194$	6.46488			0.464151
$195$	9.90966	+	10.5546i	0.709645	+	0.755832i
$196$	−1.42820			−0.102014
$197$	18.2117	−	10.5145i	1.29753	−	0.749130i	0.317554	−	0.948240i	$-0.397138\pi$
$197$	18.2117	−	10.5145i	1.29753	−	0.749130i	0.979977	+	0.199110i	$0.0638050\pi$
$198$	0.256825	+	0.444833i	0.0182517	+	0.0316129i
$199$	13.0893	−	22.6714i	0.927879	−	1.60713i	0.141014	−	0.990008i	$-0.454964\pi$
$199$	13.0893	−	22.6714i	0.927879	−	1.60713i	0.786865	−	0.617125i	$-0.211703\pi$
$200$			28.8348i			2.03893i
$201$	3.49940	+	2.02038i	0.246829	+	0.142507i
$202$	8.80686	+	5.08464i	0.619648	+	0.357754i
$203$		−	7.97866i		−	0.559992i
$204$	−2.12256	+	3.67638i	−0.148609	+	0.257398i
$205$	−18.5155	−	32.0699i	−1.29318	−	2.23986i
$206$	−8.50795	+	4.91207i	−0.592777	+	0.342240i
$207$	−8.59922			−0.597687
$208$	−2.35562	+	2.21167i	−0.163333	+	0.153352i
$209$	−0.624017			−0.0431642
$210$	−2.62953	+	1.51816i	−0.181455	+	0.104763i
$211$	−6.09641	−	10.5593i	−0.419694	−	0.726931i	0.576215	−	0.817298i	$-0.304529\pi$
$211$	−6.09641	−	10.5593i	−0.419694	−	0.726931i	−0.995909	+	0.0903672i	$0.971196\pi$
$212$	−0.947932	+	1.64187i	−0.0651042	+	0.112764i
$213$		−	2.41210i		−	0.165274i
$214$	−3.95753	−	2.28488i	−0.270531	−	0.156191i
$215$	17.6003	+	10.1616i	1.20033	+	0.693012i
$216$			2.59231i			0.176385i
$217$	1.64808	−	2.85455i	0.111879	−	0.193780i
$218$	6.85701	+	11.8767i	0.464416	+	0.804391i
$219$	−6.77358	+	3.91073i	−0.457716	+	0.264263i
$220$	3.89547			0.262633
$221$	−10.2593	−	3.09847i	−0.690113	−	0.208425i
$222$	4.10797			0.275709
$223$	6.51239	−	3.75993i	0.436102	−	0.251784i	−0.265841	−	0.964017i	$-0.585650\pi$
$223$	6.51239	−	3.75993i	0.436102	−	0.251784i	0.701943	+	0.712233i	$0.252316\pi$
$224$	−2.93114	−	5.07689i	−0.195845	−	0.339214i
$225$	5.56159	−	9.63296i	0.370773	−	0.642197i
$226$			15.5581i			1.03491i
$227$	−21.4873	−	12.4057i	−1.42616	−	0.823394i	−0.429346	−	0.903140i	$-0.641256\pi$
$227$	−21.4873	−	12.4057i	−1.42616	−	0.823394i	−0.996815	+	0.0797459i	$0.974589\pi$
$228$	−1.13624	−	0.656011i	−0.0752496	−	0.0434454i
$229$		−	8.08968i		−	0.534581i	−0.963616	−	0.267290i	$-0.913872\pi$
$229$		−	8.08968i		−	0.534581i	0.963616	−	0.267290i	$-0.0861283\pi$
$230$	13.0550	−	22.6119i	0.860819	−	1.49098i
$231$	0.339637	+	0.588269i	0.0223465	+	0.0387053i
$232$	17.9122	−	10.3416i	1.17599	−	0.678959i
$233$	2.29275			0.150203			0.0751014	−	0.997176i	$-0.476072\pi$
$233$	2.29275			0.150203			0.0751014	+	0.997176i	$0.476072\pi$
$234$	−2.65444	+	0.622341i	−0.173526	+	0.0406837i
$235$	12.1883			0.795077
$236$	−5.97712	+	3.45089i	−0.389078	+	0.224634i
$237$	8.09133	+	14.0146i	0.525589	+	0.910346i
$238$	1.12381	−	1.94649i	0.0728455	−	0.126172i
$239$		0	0.000676538i		0	4.37616e-5i	−1.00000		2.18808e-5i	$-0.999993\pi$
$239$		0	0.000676538i		0	4.37616e-5i	1.00000		2.18808e-5i	$-6.96487e-6\pi$
$240$	3.11633	+	1.79921i	0.201158	+	0.116139i
$241$	16.2376	+	9.37476i	1.04595	+	0.603881i	0.921514	−	0.388346i	$-0.126953\pi$
$241$	16.2376	+	9.37476i	1.04595	+	0.603881i	0.124439	+	0.992227i	$0.460287\pi$
$242$		−	7.96900i		−	0.512267i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	3.19160	+	5.52801i	0.204321	+	0.353895i
$245$	−3.47741	+	2.00768i	−0.222164	+	0.128266i
$246$	6.97369			0.444626
$247$	0.957632	−	3.17079i	0.0609327	−	0.201753i
$248$	8.54467			0.542587
$249$	−4.14477	+	2.39298i	−0.262664	+	0.151649i
$250$	9.29596	+	16.1011i	0.587928	+	1.01832i
$251$	3.21408	−	5.56696i	0.202871	−	0.351383i	−0.746581	−	0.665294i	$-0.768306\pi$
$251$	3.21408	−	5.56696i	0.202871	−	0.351383i	0.949452	+	0.313911i	$0.101639\pi$
$252$			1.42820i			0.0899683i
$253$	−5.05865	−	2.92061i	−0.318035	−	0.183617i
$254$	−12.9443	−	7.47339i	−0.812197	−	0.468922i
$255$			11.9351i			0.747403i
$256$	6.31854	−	10.9440i	0.394909	−	0.684002i
$257$	−1.05501	−	1.82733i	−0.0658096	−	0.113986i	0.831243	−	0.555909i	$-0.187630\pi$
$257$	−1.05501	−	1.82733i	−0.0658096	−	0.113986i	−0.897053	+	0.441923i	$0.854296\pi$
$258$	−3.31449	+	1.91362i	−0.206351	+	0.119137i
$259$	5.43258			0.337564
$260$	−5.97809	+	19.7939i	−0.370745	+	1.22757i
$261$	−7.97866			−0.493867
$262$	5.18715	−	2.99480i	0.320463	−	0.185020i
$263$	8.76380	+	15.1793i	0.540399	+	0.935999i	0.998881	+	0.0472950i	$0.0150601\pi$
$263$	8.76380	+	15.1793i	0.540399	+	0.935999i	−0.458482	+	0.888704i	$0.651607\pi$
$264$	−0.880447	+	1.52498i	−0.0541878	+	0.0938559i
$265$			5.33019i			0.327431i
$266$	0.601594	+	0.347330i	0.0368861	+	0.0212962i
$267$	−3.91913	−	2.26271i	−0.239847	−	0.138475i
$268$			5.77103i			0.352522i
$269$	−13.5213	+	23.4196i	−0.824408	+	1.42792i	0.0779621	+	0.996956i	$0.475159\pi$
$269$	−13.5213	+	23.4196i	−0.824408	+	1.42792i	−0.902371	+	0.430961i	$0.858175\pi$
$270$	1.51816	+	2.62953i	0.0923921	+	0.160028i
$271$	−14.1092	+	8.14598i	−0.857076	+	0.494833i	−0.863032	−	0.505149i	$-0.831437\pi$
$271$	−14.1092	+	8.14598i	−0.857076	+	0.494833i	0.00595628	+	0.999982i	$0.498104\pi$
$272$	−2.66371			−0.161511
$273$	−3.51036	+	0.823013i	−0.212457	+	0.0498110i
$274$	−7.37597			−0.445599
$275$	6.54342	−	3.77785i	0.394583	−	0.227813i
$276$	−6.14071	−	10.6360i	−0.369627	−	0.640213i
$277$	14.0359	−	24.3110i	0.843338	−	1.46070i	−0.0437194	−	0.999044i	$-0.513921\pi$
$277$	14.0359	−	24.3110i	0.843338	−	1.46070i	0.887057	−	0.461660i	$-0.152746\pi$
$278$			9.25058i			0.554813i
$279$	−2.85455	−	1.64808i	−0.170898	−	0.0986678i
$280$	−9.01454	−	5.20455i	−0.538722	−	0.311031i
$281$		−	8.95674i		−	0.534314i	−0.963653	−	0.267157i	$-0.913916\pi$
$281$		−	8.95674i		−	0.534314i	0.963653	−	0.267157i	$-0.0860843\pi$
$282$	−1.14765	+	1.98779i	−0.0683415	+	0.118371i
$283$	−2.51977	−	4.36437i	−0.149785	−	0.259435i	0.781363	−	0.624077i	$-0.214525\pi$
$283$	−2.51977	−	4.36437i	−0.149785	−	0.259435i	−0.931148	+	0.364642i	$0.881191\pi$
$284$	2.98343	−	1.72248i	0.177034	−	0.102211i
$285$	−3.68873			−0.218501
$286$	−1.77290	−	0.535444i	−0.104834	−	0.0316615i
$287$	9.22234			0.544378
$288$	−5.07689	+	2.93114i	−0.299158	+	0.172719i
$289$	4.08257	+	7.07122i	0.240151	+	0.415954i
$290$	12.1129	−	20.9801i	0.711292	−	1.23199i
$291$		−	8.54947i		−	0.501179i
$292$	−9.67404	−	5.58531i	−0.566131	−	0.326856i
$293$	4.26570	+	2.46280i	0.249205	+	0.143879i	0.619400	−	0.785075i	$-0.287376\pi$
$293$	4.26570	+	2.46280i	0.249205	+	0.143879i	−0.370195	+	0.928954i	$0.620709\pi$
$294$		−	0.756173i		−	0.0441009i
$295$	−9.70214	+	16.8046i	−0.564880	+	0.978401i
$296$	7.04147	+	12.1962i	0.409277	+	0.708889i
$297$	0.588269	−	0.339637i	0.0341348	−	0.0197078i
$298$	4.52598			0.262183
$299$	22.6035	−	21.2223i	1.30720	−	1.22732i
$300$	15.8861			0.917187
$301$	−4.38324	+	2.53067i	−0.252646	+	0.145865i
$302$	−4.98536	−	8.63491i	−0.286876	−	0.496883i
$303$	6.72418	−	11.6466i	0.386294	−	0.669080i
$304$		−	0.823263i		−	0.0472174i
$305$	15.5419	+	8.97313i	0.889928	+	0.513800i
$306$	−1.94649	−	1.12381i	−0.111273	−	0.0642437i
$307$		−	11.2027i		−	0.639371i	−0.947524	−	0.319685i	$-0.896423\pi$
$307$		−	11.2027i		−	0.639371i	0.947524	−	0.319685i	$-0.103577\pi$
$308$	−0.485071	+	0.840167i	−0.0276395	+	0.0478729i
$309$	6.49596	+	11.2513i	0.369542	+	0.640066i
$310$	8.66733	−	5.00408i	0.492271	−	0.284213i
$311$	−9.44321			−0.535475			−0.267738	−	0.963492i	$-0.586276\pi$
$311$	−9.44321			−0.535475			−0.267738	+	0.963492i	$0.586276\pi$
$312$	−6.39766	−	6.81405i	−0.362196	−	0.385769i
$313$	−28.0752			−1.58690			−0.793451	−	0.608634i	$-0.791718\pi$
$313$	−28.0752			−1.58690			−0.793451	+	0.608634i	$0.791718\pi$
$314$	−7.20378	+	4.15911i	−0.406533	+	0.234712i
$315$	2.00768	+	3.47741i	0.113120	+	0.195930i
$316$	−11.5561	+	20.0157i	−0.650079	+	1.12597i
$317$		−	8.48965i		−	0.476826i	−0.971164	−	0.238413i	$-0.923373\pi$
$317$		−	8.48965i		−	0.476826i	0.971164	−	0.238413i	$-0.0766272\pi$
$318$	−0.869299	−	0.501890i	−0.0487479	−	0.0281446i
$319$	−4.69360	−	2.70985i	−0.262791	−	0.151722i
$320$		−	10.6029i		−	0.592719i
$321$	−3.02164	+	5.23363i	−0.168651	+	0.292113i
$322$	3.25125	+	5.63133i	0.181185	+	0.313822i
$323$	2.36473	−	1.36528i	0.131577	−	0.0759661i
$324$	1.42820			0.0793445
$325$	9.15453	+	39.0464i	0.507802	+	2.16591i
$326$	−5.25452			−0.291021
$327$	15.7063	−	9.06805i	0.868561	−	0.501464i
$328$	11.9536	+	20.7043i	0.660028	+	1.14320i
$329$	−1.51771	+	2.62874i	−0.0836738	+	0.144927i
$330$			2.06249i			0.113536i
$331$	−27.3718	−	15.8031i	−1.50449	−	0.868617i	−0.999986	−	0.00520645i	$-0.998343\pi$
$331$	−27.3718	−	15.8031i	−1.50449	−	0.868617i	−0.504502	−	0.863410i	$-0.668324\pi$
$332$	−5.91957	−	3.41766i	−0.324879	−	0.187569i
$333$		−	5.43258i		−	0.297703i
$334$	0.981921	−	1.70074i	0.0537283	−	0.0930602i
$335$	8.11258	+	14.0514i	0.443237	+	0.767710i
$336$	−0.776101	+	0.448082i	−0.0423398	+	0.0244449i
$337$	3.80886			0.207482			0.103741	−	0.994604i	$-0.466919\pi$
$337$	3.80886			0.207482			0.103741	+	0.994604i	$0.466919\pi$
$338$	5.44146	−	8.18684i	0.295976	−	0.445306i
$339$	20.5748			1.11747
$340$	−14.7620	+	8.52285i	−0.800582	+	0.462216i
$341$	−1.11950	−	1.93903i	−0.0606242	−	0.105004i
$342$	0.347330	−	0.601594i	0.0187815	−	0.0325305i
$343$		−	1.00000i		−	0.0539949i
$344$	−11.3627	−	6.56028i	−0.612638	−	0.353707i
$345$	−29.9030	−	17.2645i	−1.60992	−	0.929490i
$346$		−	2.83789i		−	0.152566i
$347$	8.01119	−	13.8758i	0.430063	−	0.744891i	−0.566815	−	0.823845i	$-0.691825\pi$
$347$	8.01119	−	13.8758i	0.430063	−	0.744891i	0.996878	+	0.0789539i	$0.0251580\pi$
$348$	−5.69757	−	9.86848i	−0.305422	−	0.529006i
$349$	10.6548	−	6.15153i	0.570336	−	0.329284i	−0.186947	−	0.982370i	$-0.559859\pi$
$349$	10.6548	−	6.15153i	0.570336	−	0.329284i	0.757284	+	0.653086i	$0.226526\pi$
$350$	−8.41105			−0.449590
$351$	0.823013	+	3.51036i	0.0439292	+	0.187369i
$352$	−3.98210			−0.212247
$353$	27.8491	−	16.0787i	1.48226	−	0.855782i	0.482460	−	0.875918i	$-0.339743\pi$
$353$	27.8491	−	16.0787i	1.48226	−	0.855782i	0.999797	+	0.0201363i	$0.00641000\pi$
$354$	−1.82710	−	3.16464i	−0.0971095	−	0.168199i
$355$	4.84274	−	8.38786i	0.257026	−	0.445182i
$356$		−	6.46321i		−	0.342549i
$357$	−2.57413	−	1.48617i	−0.136237	−	0.0786567i
$358$	−12.5792	−	7.26262i	−0.664833	−	0.383841i
$359$			26.7993i			1.41441i	0.707006	+	0.707207i	$0.250045\pi$
$359$			26.7993i			1.41441i	−0.707006	+	0.707207i	$0.749955\pi$
$360$	−5.20455	+	9.01454i	−0.274304	+	0.475108i
$361$	−9.07804	−	15.7236i	−0.477792	−	0.827559i
$362$	3.41815	−	1.97347i	0.179654	−	0.103723i
$363$	−10.5386			−0.553132
$364$	−3.52471	−	3.75411i	−0.184745	−	0.196769i
$365$	−31.4060			−1.64387
$366$	−2.92685	+	1.68982i	−0.152989	+	0.0883283i
$367$	−2.75619	−	4.77386i	−0.143872	−	0.249193i	0.785080	−	0.619395i	$-0.212622\pi$
$367$	−2.75619	−	4.77386i	−0.143872	−	0.249193i	−0.928951	+	0.370201i	$0.879289\pi$
$368$	3.85315	−	6.67386i	0.200860	−	0.347899i
$369$		−	9.22234i		−	0.480096i
$370$	14.2851	+	8.24750i	0.742647	+	0.428767i
$371$	−1.14960	−	0.663724i	−0.0596844	−	0.0344588i
$372$		−	4.70758i		−	0.244076i
$373$	−8.72847	+	15.1181i	−0.451943	+	0.782788i	−0.998507	−	0.0546294i	$-0.982602\pi$
$373$	−8.72847	+	15.1181i	−0.451943	+	0.782788i	0.546564	+	0.837417i	$0.315936\pi$
$374$	−0.763372	−	1.32220i	−0.0394730	−	0.0683693i
$375$	21.2928	−	12.2934i	1.09956	−	0.634829i
$376$	−7.86874			−0.405800
$377$	20.9724	−	19.6908i	1.08013	−	1.01413i
$378$	−0.756173			−0.0388934
$379$	−6.26298	+	3.61593i	−0.321708	+	0.185738i	−0.652153	−	0.758087i	$-0.726134\pi$
$379$	−6.26298	+	3.61593i	−0.321708	+	0.185738i	0.330446	+	0.943825i	$0.392801\pi$
$380$	−2.63412	−	4.56244i	−0.135128	−	0.234048i
$381$	−9.88317	+	17.1182i	−0.506330	+	0.876989i
$382$		−	0.444331i		−	0.0227340i
$383$	14.2141	+	8.20650i	0.726305	+	0.419333i	0.817069	−	0.576540i	$-0.195597\pi$
$383$	14.2141	+	8.20650i	0.726305	+	0.419333i	−0.0907636	+	0.995872i	$0.528931\pi$
$384$	−8.42455	−	4.86392i	−0.429914	−	0.248211i
$385$			2.72754i			0.139008i
$386$	−5.65248	+	9.79038i	−0.287704	+	0.498317i
$387$	2.53067	+	4.38324i	0.128641	+	0.222813i
$388$	10.5745	−	6.10518i	0.536838	−	0.309944i
$389$	−20.7408			−1.05160			−0.525800	−	0.850608i	$-0.676234\pi$
$389$	−20.7408			−1.05160			−0.525800	+	0.850608i	$0.676234\pi$
$390$	−10.4801	−	3.16515i	−0.530678	−	0.160274i
$391$	25.5599			1.29262
$392$	2.24501	−	1.29616i	0.113390	−	0.0654658i
$393$	−3.96047	−	6.85974i	−0.199779	−	0.346028i
$394$	−7.95082	+	13.7712i	−0.400556	+	0.693784i
$395$			64.9794i			3.26947i
$396$	0.840167	+	0.485071i	0.0422200	+	0.0243757i
$397$	−5.71573	−	3.29998i	−0.286864	−	0.165621i	0.349663	−	0.936876i	$-0.386296\pi$
$397$	−5.71573	−	3.29998i	−0.286864	−	0.165621i	−0.636527	+	0.771255i	$0.719630\pi$
$398$			19.7956i			0.992265i
$399$	0.459326	−	0.795577i	0.0229951	−	0.0398286i
$400$	4.98410	+	8.63271i	0.249205	+	0.431636i
$401$	−31.0468	+	17.9249i	−1.55040	+	0.895126i	−0.552296	+	0.833648i	$0.686248\pi$
$401$	−31.0468	+	17.9249i	−1.55040	+	0.895126i	−0.998108	+	0.0614779i	$0.980419\pi$
$402$	−3.05552			−0.152395
$403$	11.5707	−	2.71278i	0.576378	−	0.135133i
$404$	19.2070			0.955582
$405$	3.47741	−	2.00768i	0.172794	−	0.0997626i
$406$	3.01663	+	5.22495i	0.149713	+	0.259310i
$407$	1.84511	−	3.19582i	0.0914585	−	0.158411i
$408$		−	7.70526i		−	0.381467i
$409$	−13.3711	−	7.71982i	−0.661159	−	0.381721i	0.131559	−	0.991308i	$-0.458002\pi$
$409$	−13.3711	−	7.71982i	−0.661159	−	0.381721i	−0.792719	+	0.609588i	$0.791335\pi$
$410$	24.2504	+	14.0010i	1.19764	+	0.691458i
$411$			9.75434i			0.481146i
$412$	−9.27754	+	16.0692i	−0.457071	+	0.791671i
$413$	−2.41625	−	4.18507i	−0.118896	−	0.205934i
$414$	5.63133	−	3.25125i	0.276765	−	0.159790i
$415$	−19.2174			−0.943346
$416$	6.11103	−	20.2341i	0.299618	−	0.992058i
$417$	12.2334			0.599073
$418$	0.408647	−	0.235933i	0.0199876	−	0.0115398i
$419$	5.63285	+	9.75638i	0.275183	+	0.476630i	0.970181	−	0.242381i	$-0.0779284\pi$
$419$	5.63285	+	9.75638i	0.275183	+	0.476630i	−0.694999	+	0.719011i	$0.744595\pi$
$420$	−2.86738	+	4.96644i	−0.139914	+	0.242338i
$421$		−	1.85065i		−	0.0901953i	−0.998983	−	0.0450976i	$-0.985640\pi$
$421$		−	1.85065i		−	0.0901953i	0.998983	−	0.0450976i	$-0.0143599\pi$
$422$	7.98465	+	4.60994i	0.388687	+	0.224408i
$423$	2.62874	+	1.51771i	0.127814	+	0.0737934i
$424$		−	3.44116i		−	0.167118i
$425$	−16.5310	+	28.6325i	−0.801871	+	1.38888i
$426$	0.911983	+	1.57960i	0.0441857	+	0.0765319i
$427$	−3.87061	+	2.23470i	−0.187312	+	0.108145i
$428$	−8.63101			−0.417196
$429$	−0.708097	+	2.34456i	−0.0341872	+	0.113197i
$430$	−15.3678			−0.741101
$431$	12.3913	−	7.15413i	0.596869	−	0.344602i	−0.170940	−	0.985281i	$-0.554680\pi$
$431$	12.3913	−	7.15413i	0.596869	−	0.344602i	0.767809	+	0.640679i	$0.221347\pi$
$432$	0.448082	+	0.776101i	0.0215584	+	0.0373402i
$433$	−12.6865	+	21.9737i	−0.609674	+	1.05599i	0.381620	+	0.924319i	$0.375366\pi$
$433$	−12.6865	+	21.9737i	−0.609674	+	1.05599i	−0.991294	+	0.131667i	$0.957967\pi$
$434$			2.49247i			0.119642i
$435$	−27.7451	−	16.0186i	−1.33027	−	0.768035i
$436$	22.4318	+	12.9510i	1.07429	+	0.620240i
$437$			7.89969i			0.377893i
$438$	2.95719	−	5.12200i	0.141300	−	0.244739i
$439$	−14.3262	−	24.8138i	−0.683754	−	1.18430i	−0.973827	−	0.227292i	$-0.927013\pi$
$439$	−14.3262	−	24.8138i	−0.683754	−	1.18430i	0.290073	−	0.957004i	$-0.406320\pi$
$440$	−6.12335	+	3.53532i	−0.291919	+	0.168540i
$441$	−1.00000			−0.0476190
$442$	7.88993	−	1.84981i	0.375286	−	0.0879867i
$443$	0.854762			0.0406110			0.0203055	−	0.999794i	$-0.493536\pi$
$443$	0.854762			0.0406110			0.0203055	+	0.999794i	$0.493536\pi$
$444$	6.71933	−	3.87941i	0.318885	−	0.184109i
$445$	−9.08561	−	15.7367i	−0.430699	−	0.745993i
$446$	−2.84316	+	4.92450i	−0.134628	+	0.233182i
$447$		−	5.98537i		−	0.283098i
$448$	2.28681	+	1.32029i	0.108041	+	0.0623777i
$449$	3.76317	+	2.17267i	0.177595	+	0.102534i	0.586162	−	0.810194i	$-0.300638\pi$
$449$	3.76317	+	2.17267i	0.177595	+	0.102534i	−0.408567	+	0.912728i	$0.633971\pi$
$450$			8.41105i			0.396501i
$451$	3.13225	−	5.42522i	0.147492	−	0.255464i
$452$	14.6925	+	25.4481i	0.691076	+	1.19698i
$453$	−11.4192	+	6.59289i	−0.536521	+	0.309761i
$454$	18.7617			0.880530
$455$	−13.8593	−	4.18574i	−0.649735	−	0.196231i
$456$	2.38144			0.111521
$457$	−25.9117	+	14.9602i	−1.21210	+	0.699806i	−0.963216	−	0.268727i	$-0.913397\pi$
$457$	−25.9117	+	14.9602i	−1.21210	+	0.699806i	−0.248884	+	0.968533i	$0.580064\pi$
$458$	3.05860	+	5.29765i	0.142919	+	0.247543i
$459$	−1.48617	+	2.57413i	−0.0693687	+	0.120150i
$460$		−	49.3144i		−	2.29930i
$461$	−18.6533	−	10.7695i	−0.868773	−	0.501586i	−0.00183267	−	0.999998i	$-0.500583\pi$
$461$	−18.6533	−	10.7695i	−0.868773	−	0.501586i	−0.866940	+	0.498412i	$0.833917\pi$
$462$	−0.444833	−	0.256825i	−0.0206955	−	0.0119486i
$463$		−	15.6213i		−	0.725984i	−0.931792	−	0.362992i	$-0.881755\pi$
$463$		−	15.6213i		−	0.725984i	0.931792	−	0.362992i	$-0.118245\pi$
$464$	3.57509	−	6.19224i	0.165970	−	0.287468i
$465$	−6.61764	−	11.4621i	−0.306886	−	0.531542i
$466$	−1.50144	+	0.866857i	−0.0695528	+	0.0401564i
$467$	−39.7675			−1.84022			−0.920109	−	0.391662i	$-0.871900\pi$
$467$	−39.7675			−1.84022			−0.920109	+	0.391662i	$0.871900\pi$
$468$	−3.75411	+	3.52471i	−0.173534	+	0.162930i
$469$	−4.04076			−0.186585
$470$	−7.98169	+	4.60823i	−0.368168	+	0.212562i
$471$	5.50020	+	9.52663i	0.253436	+	0.438964i
$472$	6.26368	−	10.8490i	0.288309	−	0.499366i
$473$			3.43803i			0.158081i
$474$	−10.5975	−	6.11845i	−0.486758	−	0.281030i
$475$	−8.84934	−	5.10917i	−0.406036	−	0.234425i
$476$		−	4.24511i		−	0.194574i
$477$	−0.663724	+	1.14960i	−0.0303898	+	0.0526367i
$478$	0.000255790	0	0.000443041i	1.16996e−5	0	2.02642e-5i
$479$	30.2828	−	17.4838i	1.38366	−	0.798855i	0.391067	−	0.920362i	$-0.372106\pi$
$479$	30.2828	−	17.4838i	1.38366	−	0.798855i	0.992591	+	0.121507i	$0.0387727\pi$
$480$	−23.5392			−1.07441
$481$	13.4072	+	14.2798i	0.611317	+	0.651104i
$482$	−14.1779			−0.645785
$483$	7.44714	−	4.29961i	0.338857	−	0.195639i
$484$	−7.52561	−	13.0347i	−0.342073	−	0.592488i
$485$	17.1646	−	29.7300i	0.779406	−	1.34997i
$486$			0.756173i			0.0343007i
$487$	21.7770	+	12.5730i	0.986810	+	0.569735i	0.904319	−	0.426857i	$-0.140379\pi$
$487$	21.7770	+	12.5730i	0.986810	+	0.569735i	0.0824906	+	0.996592i	$0.473713\pi$
$488$	−10.0338	−	5.79304i	−0.454211	−	0.262239i
$489$			6.94883i			0.314237i
$490$	1.51816	−	2.62953i	0.0685834	−	0.118790i
$491$	−1.21391	−	2.10255i	−0.0547830	−	0.0948870i	0.837333	−	0.546693i	$-0.184113\pi$
$491$	−1.21391	−	2.10255i	−0.0547830	−	0.0948870i	−0.892116	+	0.451806i	$0.850780\pi$
$492$	11.4067	−	6.58568i	0.514255	−	0.296905i
$493$	23.7154			1.06809
$494$	0.571715	+	2.43851i	0.0257227	+	0.109714i
$495$	2.72754			0.122594
$496$	2.55815	−	1.47695i	0.114864	−	0.0663169i
$497$	1.20605	+	2.08894i	0.0540987	+	0.0937018i
$498$	1.80951	−	3.13416i	0.0810861	−	0.140445i
$499$			1.45843i			0.0652881i	0.999467	+	0.0326440i	$0.0103928\pi$
$499$			1.45843i			0.0652881i	−0.999467	+	0.0326440i	$0.989607\pi$
$500$	30.4104	+	17.5575i	1.36000	+	0.785194i
$501$	−2.24914	−	1.29854i	−0.100484	−	0.0580144i
$502$			4.86081i			0.216949i
$503$	6.20452	−	10.7466i	0.276646	−	0.479165i	−0.693903	−	0.720068i	$-0.744110\pi$
$503$	6.20452	−	10.7466i	0.276646	−	0.479165i	0.970549	+	0.240903i	$0.0774437\pi$
$504$	−1.29616	−	2.24501i	−0.0577354	−	0.100001i
$505$	46.7654	−	27.0000i	2.08103	−	1.20149i
$506$	4.41698			0.196359
$507$	−10.8267	−	7.19605i	−0.480830	−	0.319588i
$508$	−28.2303			−1.25252
$509$	3.07231	−	1.77380i	0.136178	−	0.0786224i	−0.430363	−	0.902656i	$-0.641615\pi$
$509$	3.07231	−	1.77380i	0.136178	−	0.0786224i	0.566541	+	0.824033i	$0.308281\pi$
$510$	−4.51249	−	7.81587i	−0.199817	−	0.346092i
$511$	3.91073	−	6.77358i	0.173001	−	0.299646i
$512$		−	9.89985i		−	0.437516i
$513$	−0.795577	−	0.459326i	−0.0351256	−	0.0202798i
$514$	1.38178	+	0.797769i	0.0609476	+	0.0351881i
$515$			52.1673i			2.29877i
$516$	−3.61430	+	6.26015i	−0.159111	+	0.275588i
$517$	1.03094	+	1.78564i	0.0453407	+	0.0785323i
$518$	−3.55761	+	2.05398i	−0.156312	+	0.0902469i
$519$	−3.75296			−0.164737
$520$	−8.56683	−	36.5397i	−0.375680	−	1.60237i
$521$	−27.9069			−1.22262			−0.611312	−	0.791390i	$-0.709358\pi$
$521$	−27.9069			−1.22262			−0.611312	+	0.791390i	$0.709358\pi$
$522$	5.22495	−	3.01663i	0.228690	−	0.132034i
$523$	5.70451	+	9.88050i	0.249441	+	0.432044i	0.963371	−	0.268173i	$-0.0864199\pi$
$523$	5.70451	+	9.88050i	0.249441	+	0.432044i	−0.713930	+	0.700217i	$0.753087\pi$
$524$	5.65635	−	9.79709i	0.247099	−	0.427988i
$525$			11.1232i			0.485456i
$526$	−11.4782	−	6.62695i	−0.500474	−	0.288949i
$527$	8.48473	+	4.89866i	0.369601	+	0.213389i
$528$			0.608741i			0.0264921i
$529$	−25.4732	+	44.1210i	−1.10753	+	1.91830i
$530$	−2.01527	−	3.49056i	−0.0875379	−	0.151620i
$531$	−4.18507	+	2.41625i	−0.181617	+	0.104856i
$532$	1.31202			0.0568833
$533$	22.7601	+	24.2414i	0.985850	+	1.05001i
$534$	3.42200			0.148084
$535$	−21.0149	+	12.1330i	−0.908555	+	0.524555i
$536$	−5.23747	−	9.07156i	−0.226224	−	0.391832i
$537$	−9.60443	+	16.6354i	−0.414462	+	0.717869i
$538$		−	20.4489i		−	0.881615i
$539$	−0.588269	−	0.339637i	−0.0253385	−	0.0146292i
$540$	4.96644	+	2.86738i	0.213722	+	0.123392i
$541$			0.700149i			0.0301018i	0.999887	+	0.0150509i	$0.00479102\pi$
$541$			0.700149i			0.0301018i	−0.999887	+	0.0150509i	$0.995209\pi$
$542$	6.15977	−	10.6690i	0.264585	−	0.458274i
$543$	−2.60981	−	4.52033i	−0.111998	−	0.193986i
$544$	15.0903	−	8.71238i	0.646990	−	0.373540i
$545$	72.8231			3.11940
$546$	1.98764	−	1.86618i	0.0850633	−	0.0798653i
$547$	−21.4832			−0.918557			−0.459278	−	0.888292i	$-0.651892\pi$
$547$	−21.4832			−0.918557			−0.459278	+	0.888292i	$0.651892\pi$
$548$	−12.0647	+	6.96559i	−0.515380	+	0.297555i
$549$	2.23470	+	3.87061i	0.0953746	+	0.165194i
$550$	−2.85671	+	4.94796i	−0.121810	+	0.210982i
$551$			7.32962i			0.312252i
$552$	19.3053	+	11.1459i	0.821689	+	0.474403i
$553$	−14.0146	−	8.09133i	−0.595961	−	0.344078i
$554$			21.2272i			0.901857i
$555$	10.9069	−	18.8913i	0.462972	−	0.801891i
$556$	8.73589	+	15.1310i	0.370484	+	0.641698i
$557$	13.5574	−	7.82737i	0.574446	−	0.331656i	−0.184477	−	0.982837i	$-0.559059\pi$
$557$	13.5574	−	7.82737i	0.574446	−	0.331656i	0.758923	+	0.651180i	$0.225726\pi$
$558$	2.49247			0.105514
$559$	−17.4695	−	5.27609i	−0.738883	−	0.223155i
$560$	−3.59843			−0.152061
$561$	−1.74854	+	1.00952i	−0.0738234	+	0.0426220i
$562$	3.38642	+	5.86546i	0.142848	+	0.247419i
$563$	−10.7469	+	18.6141i	−0.452927	+	0.784493i	−0.998566	−	0.0535274i	$-0.982954\pi$
$563$	−10.7469	+	18.6141i	−0.452927	+	0.784493i	0.545639	+	0.838020i	$0.316287\pi$
$564$			4.33518i			0.182544i
$565$	71.5470	+	41.3077i	3.01000	+	1.73783i
$566$	3.30022	+	1.90538i	0.138719	+	0.0800892i
$567$			1.00000i			0.0419961i
$568$	−3.12646	+	5.41519i	−0.131183	+	0.227216i
$569$	3.05340	+	5.28864i	0.128005	+	0.221711i	0.922904	−	0.385031i	$-0.125809\pi$
$569$	3.05340	+	5.28864i	0.128005	+	0.221711i	−0.794899	+	0.606742i	$0.792476\pi$
$570$	2.41562	−	1.39466i	0.101179	−	0.0584158i
$571$	4.49229			0.187996			0.0939982	−	0.995572i	$-0.470035\pi$
$571$	4.49229			0.187996			0.0939982	+	0.995572i	$0.470035\pi$
$572$	−3.40555	+	0.798439i	−0.142393	+	0.0333844i
$573$	−0.587605			−0.0245475
$574$	−6.03939	+	3.48684i	−0.252079	+	0.145538i
$575$	−47.8253	−	82.8359i	−1.99445	−	3.45450i
$576$	1.32029	−	2.28681i	0.0550120	−	0.0952836i
$577$		−	8.80521i		−	0.366566i	−0.983060	−	0.183283i	$-0.941328\pi$
$577$		−	8.80521i		−	0.366566i	0.983060	−	0.183283i	$-0.0586724\pi$
$578$	−5.34707	−	3.08713i	−0.222409	−	0.128408i
$579$	12.9473	+	7.47511i	0.538070	+	0.310655i
$580$		−	45.7557i		−	1.89990i
$581$	2.39298	−	4.14477i	0.0992777	−	0.171954i
$582$	3.23244	+	5.59875i	0.133989	+	0.232076i
$583$	−0.780896	+	0.450851i	−0.0323414	+	0.0186723i
$584$	20.2757			0.839014
$585$	−4.18574	+	13.8593i	−0.173059	+	0.573013i
$586$	−3.72461			−0.153862
$587$	21.1492	−	12.2105i	0.872920	−	0.503981i	0.00460255	−	0.999989i	$-0.498535\pi$
$587$	21.1492	−	12.2105i	0.872920	−	0.503981i	0.868318	+	0.496009i	$0.165202\pi$
$588$	−0.714101	−	1.23686i	−0.0294490	−	0.0510072i
$589$	−1.51401	+	2.62234i	−0.0623837	+	0.108052i
$590$		−	14.6730i		−	0.604078i
$591$	18.2117	+	10.5145i	0.749130	+	0.432511i
$592$	4.21623	+	2.43424i	0.173286	+	0.100047i
$593$		−	16.0560i		−	0.659340i	−0.944096	−	0.329670i	$-0.893063\pi$
$593$		−	16.0560i		−	0.659340i	0.944096	−	0.329670i	$-0.106937\pi$
$594$	−0.256825	+	0.444833i	−0.0105376	+	0.0182517i
$595$	−5.96754	−	10.3361i	−0.244645	−	0.423738i
$596$	7.40306	−	4.27416i	0.303241	−	0.175076i
$597$	26.1787			1.07142
$598$	−6.77840	+	22.4438i	−0.277190	+	0.917796i
$599$	−11.3129			−0.462231			−0.231116	−	0.972926i	$-0.574238\pi$
$599$	−11.3129			−0.462231			−0.231116	+	0.972926i	$0.574238\pi$
$600$	−24.9717	+	14.4174i	−1.01946	+	0.588588i
$601$	−0.782082	−	1.35460i	−0.0319018	−	0.0552555i	0.849634	−	0.527373i	$-0.176823\pi$
$601$	−0.782082	−	1.35460i	−0.0319018	−	0.0552555i	−0.881535	+	0.472118i	$0.843490\pi$
$602$	1.91362	−	3.31449i	0.0779934	−	0.135089i
$603$			4.04076i			0.164553i
$604$	−16.3089	−	9.41597i	−0.663601	−	0.383130i
$605$	−36.6470	−	21.1582i	−1.48991	−	0.860201i
$606$			10.1693i			0.413099i
$607$	19.1956	−	33.2478i	0.779126	−	1.34949i	−0.153320	−	0.988177i	$-0.548997\pi$
$607$	19.1956	−	33.2478i	0.779126	−	1.34949i	0.932446	−	0.361309i	$-0.117670\pi$
$608$	2.69270	+	4.66390i	0.109203	+	0.189146i
$609$	6.90972	−	3.98933i	0.279996	−	0.161656i
$610$	−13.5705			−0.549453
$611$	−10.6554	+	2.49819i	−0.431071	+	0.101066i
$612$	−4.24511			−0.171599
$613$	3.73402	−	2.15584i	0.150816	−	0.0870734i	−0.422693	−	0.906273i	$-0.638915\pi$
$613$	3.73402	−	2.15584i	0.150816	−	0.0870734i	0.573509	+	0.819199i	$0.305582\pi$
$614$	4.23558	+	7.33625i	0.170934	+	0.296067i
$615$	18.5155	−	32.0699i	0.746619	−	1.29318i
$616$		−	1.76089i		−	0.0709484i
$617$	18.8708	+	10.8950i	0.759708	+	0.438618i	0.829191	−	0.558966i	$-0.188802\pi$
$617$	18.8708	+	10.8950i	0.759708	+	0.438618i	−0.0694830	+	0.997583i	$0.522135\pi$
$618$	−8.50795	−	4.91207i	−0.342240	−	0.197592i
$619$			19.3477i			0.777648i	0.921312	+	0.388824i	$0.127119\pi$
$619$			19.3477i			0.777648i	−0.921312	+	0.388824i	$0.872881\pi$
$620$	9.45132	−	16.3702i	0.379574	−	0.657442i
$621$	−4.29961	−	7.44714i	−0.172537	−	0.298843i
$622$	6.18403	−	3.57035i	0.247957	−	0.143158i
$623$	4.52542			0.181307
$624$	−3.09317	−	0.934189i	−0.123826	−	0.0373975i
$625$	43.1093			1.72437
$626$	18.3855	−	10.6148i	0.734831	−	0.424255i
$627$	−0.312009	−	0.540415i	−0.0124604	−	0.0215821i
$628$	−7.85540	+	13.6059i	−0.313464	+	0.542936i
$629$			16.1475i			0.643843i
$630$	−2.62953	−	1.51816i	−0.104763	−	0.0604848i
$631$	36.5830	+	21.1212i	1.45635	+	0.840821i	0.998829	−	0.0483799i	$-0.0154058\pi$
$631$	36.5830	+	21.1212i	1.45635	+	0.840821i	0.457516	+	0.889201i	$0.348739\pi$
$632$		−	41.9506i		−	1.66870i
$633$	6.09641	−	10.5593i	0.242310	−	0.419694i
$634$	3.20982	+	5.55958i	0.127478	+	0.220799i
$635$	−68.7357	+	39.6846i	−2.72769	+	1.57483i
$636$	−1.89586			−0.0751759
$637$	2.62856	−	2.46793i	0.104147	−	0.0977830i
$638$	4.09823			0.162251
$639$	2.08894	−	1.20605i	0.0826372	−	0.0477106i
$640$	−19.5304	−	33.8277i	−0.772008	−	1.33716i
$641$	−6.83984	+	11.8469i	−0.270157	+	0.467926i	−0.968902	−	0.247445i	$-0.920409\pi$
$641$	−6.83984	+	11.8469i	−0.270157	+	0.467926i	0.698745	+	0.715371i	$0.253742\pi$
$642$		−	4.56976i		−	0.180354i
$643$	22.9620	+	13.2571i	0.905534	+	0.522810i	0.878991	−	0.476838i	$-0.158217\pi$
$643$	22.9620	+	13.2571i	0.905534	+	0.522810i	0.0265421	+	0.999648i	$0.491550\pi$
$644$	10.6360	+	6.14071i	0.419118	+	0.241978i
$645$			20.3231i			0.800222i
$646$	−1.03239	+	1.78815i	−0.0406187	+	0.0703537i
$647$	−0.109255	−	0.189236i	−0.00429526	−	0.00743962i	0.863870	−	0.503715i	$-0.168034\pi$
$647$	−0.109255	−	0.189236i	−0.00429526	−	0.00743962i	−0.868165	+	0.496276i	$0.834701\pi$
$648$	−2.24501	+	1.29616i	−0.0881923	+	0.0509179i
$649$	−3.28260			−0.128853
$650$	−20.7579	−	22.1089i	−0.814192	−	0.867184i
$651$	3.29616			0.129187
$652$	−8.59472	+	4.96217i	−0.336595	+	0.194333i
$653$	3.05244	+	5.28699i	0.119451	+	0.206896i	0.919550	−	0.392972i	$-0.128553\pi$
$653$	3.05244	+	5.28699i	0.119451	+	0.206896i	−0.800099	+	0.599868i	$0.795220\pi$
$654$	−6.85701	+	11.8767i	−0.268130	+	0.464416i
$655$		−	31.8055i		−	1.24274i
$656$	7.15747	+	4.13237i	0.279452	+	0.161342i
$657$	−6.77358	−	3.91073i	−0.264263	−	0.152572i
$658$		−	2.29530i		−	0.0894800i
$659$	3.30655	−	5.72711i	0.128805	−	0.223097i	−0.794409	−	0.607383i	$-0.792219\pi$
$659$	3.30655	−	5.72711i	0.128805	−	0.223097i	0.923214	+	0.384287i	$0.125553\pi$
$660$	1.94774	+	3.37358i	0.0758156	+	0.131316i
$661$	12.3587	−	7.13528i	0.480697	−	0.277530i	−0.240010	−	0.970770i	$-0.577151\pi$
$661$	12.3587	−	7.13528i	0.480697	−	0.277530i	0.720707	+	0.693240i	$0.243817\pi$
$662$	23.8998			0.928891
$663$	−2.44628	−	10.4340i	−0.0950057	−	0.405224i
$664$	12.4067			0.481475
$665$	3.19453	−	1.84436i	0.123879	−	0.0715214i
$666$	2.05398	+	3.55761i	0.0795903	+	0.137854i
$667$	−34.3051	+	59.4182i	−1.32830	+	2.30068i
$668$		−	3.70915i		−	0.143511i
$669$	6.51239	+	3.75993i	0.251784	+	0.145367i
$670$	−10.6253	−	6.13452i	−0.410491	−	0.236997i
$671$			3.03595i			0.117201i
$672$	2.93114	−	5.07689i	0.113071	−	0.195845i
$673$	−13.3425	−	23.1099i	−0.514316	−	0.890822i	−0.999862	−	0.0166109i	$-0.994712\pi$
$673$	−13.3425	−	23.1099i	−0.514316	−	0.890822i	0.485546	−	0.874211i	$-0.338621\pi$
$674$	−2.49429	+	1.44008i	−0.0960765	+	0.0554698i
$675$	11.1232			0.428132
$676$	1.16916	−	18.5298i	0.0449676	−	0.712684i
$677$	−2.49411			−0.0958565			−0.0479282	−	0.998851i	$-0.515262\pi$
$677$	−2.49411			−0.0958565			−0.0479282	+	0.998851i	$0.515262\pi$
$678$	−13.4737	+	7.77905i	−0.517455	+	0.298753i
$679$	4.27474	+	7.40406i	0.164049	+	0.284142i
$680$	15.4697	−	26.7944i	0.593237	−	1.02752i
$681$		−	24.8114i		−	0.950774i
$682$	1.46624	+	0.846534i	0.0561452	+	0.0324155i
$683$	1.68368	+	0.972074i	0.0644243	+	0.0371954i	0.531866	−	0.846828i	$-0.321491\pi$
$683$	1.68368	+	0.972074i	0.0644243	+	0.0371954i	−0.467442	+	0.884024i	$0.654824\pi$
$684$		−	1.31202i		−	0.0501664i
$685$	−19.5836	+	33.9199i	−0.748252	+	1.29601i
$686$	0.378087	+	0.654865i	0.0144354	+	0.0250029i
$687$	7.00587	−	4.04484i	0.267290	−	0.154320i
$688$	−4.53578			−0.172925
$689$	−1.09251	−	4.65982i	−0.0416212	−	0.177525i
$690$	26.1099			0.993988
$691$	28.7188	−	16.5808i	1.09251	−	0.630763i	0.158269	−	0.987396i	$-0.449409\pi$
$691$	28.7188	−	16.5808i	1.09251	−	0.630763i	0.934245	+	0.356633i	$0.116075\pi$
$692$	−2.67999	−	4.64188i	−0.101878	−	0.176458i
$693$	−0.339637	+	0.588269i	−0.0129018	+	0.0223465i
$694$			12.1157i			0.459905i
$695$	42.5406	+	24.5608i	1.61366	+	0.931646i
$696$	17.9122	+	10.3416i	0.678959	+	0.391997i
$697$			27.4120i			1.03830i
$698$	−4.65162	+	8.05685i	−0.176066	+	0.304956i
$699$	1.14637	+	1.98558i	0.0433598	+	0.0751014i
$700$	−13.7578	+	7.94307i	−0.519996	+	0.300220i
$701$	11.6757			0.440986			0.220493	−	0.975389i	$-0.429233\pi$
$701$	11.6757			0.440986			0.220493	+	0.975389i	$0.429233\pi$
$702$	−1.86618	−	1.98764i	−0.0704346	−	0.0750188i
$703$	−4.99065			−0.188226
$704$	1.55337	−	0.896838i	0.0585448	−	0.0338009i
$705$	6.09415	+	10.5554i	0.229519	+	0.397538i
$706$	−12.1583	+	21.0587i	−0.457582	+	0.792556i
$707$			13.4484i			0.505777i
$708$	−5.97712	−	3.45089i	−0.224634	−	0.129693i
$709$	32.6205	+	18.8335i	1.22509	+	0.707305i	0.965998	−	0.258548i	$-0.0832440\pi$
$709$	32.6205	+	18.8335i	1.22509	+	0.707305i	0.259090	+	0.965853i	$0.416577\pi$
$710$			7.32390i			0.274861i
$711$	−8.09133	+	14.0146i	−0.303449	+	0.525589i
$712$	5.86565	+	10.1596i	0.219825	+	0.380747i
$713$	−24.5469	+	14.1722i	−0.919290	+	0.530752i
$714$	2.24761			0.0841147
$715$	−7.16949	+	6.73138i	−0.268124	+	0.251739i
$716$	−27.4341			−1.02526
$717$	0.000585899	0	0.000338269i	2.18808e−5	0	1.26329e-5i
$718$	−10.1325	−	17.5500i	−0.378140	−	0.654958i
$719$	−5.69782	+	9.86891i	−0.212493	+	0.368048i	−0.952494	−	0.304557i	$-0.901492\pi$
$719$	−5.69782	+	9.86891i	−0.212493	+	0.368048i	0.740001	+	0.672605i	$0.234825\pi$
$720$			3.59843i			0.134106i
$721$	−11.2513	−	6.49596i	−0.419021	−	0.241922i
$722$	11.8898	+	6.86457i	0.442492	+	0.255473i
$723$			18.7495i			0.697302i
$724$	3.72734	−	6.45594i	0.138525	−	0.239933i
$725$	−44.3740	−	76.8581i	−1.64801	−	2.85444i
$726$	6.90136	−	3.98450i	0.256133	−	0.147879i
$727$	4.63125			0.171764			0.0858818	−	0.996305i	$-0.472629\pi$
$727$	4.63125			0.171764			0.0858818	+	0.996305i	$0.472629\pi$
$728$	8.94756	+	2.70231i	0.331619	+	0.100154i
$729$	1.00000			0.0370370
$730$	20.5667	−	11.8742i	0.761209	−	0.439484i
$731$	−7.52202	−	13.0285i	−0.278212	−	0.481877i
$732$	−3.19160	+	5.52801i	−0.117965	+	0.204321i
$733$		−	6.56888i		−	0.242627i	−0.992614	−	0.121314i	$-0.961289\pi$
$733$		−	6.56888i		−	0.242627i	0.992614	−	0.121314i	$-0.0387106\pi$
$734$	3.60986	+	2.08416i	0.133243	+	0.0769276i
$735$	−3.47741	−	2.00768i	−0.128266	−	0.0740545i
$736$			50.4111i			1.85818i
$737$	−1.37239	+	2.37706i	−0.0505528	+	0.0875600i
$738$	3.48684	+	6.03939i	0.128353	+	0.222313i
$739$	−31.3633	+	18.1076i	−1.15372	+	0.666100i	−0.949791	−	0.312886i	$-0.898704\pi$
$739$	−31.3633	+	18.1076i	−1.15372	+	0.666100i	−0.203929	+	0.978986i	$0.565371\pi$
$740$	31.1545			1.14526
$741$	3.22480	−	0.756064i	0.118466	−	0.0277747i
$742$	1.00378			0.0368499
$743$	5.06325	−	2.92327i	0.185753	−	0.107244i	−0.404240	−	0.914653i	$-0.632464\pi$
$743$	5.06325	−	2.92327i	0.185753	−	0.107244i	0.589993	+	0.807409i	$0.299131\pi$
$744$	4.27234	+	7.39990i	0.156631	+	0.271294i
$745$	12.0167	−	20.8136i	0.440259	−	0.762551i
$746$		−	13.2005i		−	0.483304i
$747$	−4.14477	−	2.39298i	−0.151649	−	0.0875547i
$748$	−2.49727	−	1.44180i	−0.0913092	−	0.0527174i
$749$		−	6.04327i		−	0.220816i
$750$	−9.29596	+	16.1011i	−0.339440	+	0.587928i
$751$	−12.2662	−	21.2456i	−0.447598	−	0.775263i	0.550631	−	0.834749i	$-0.314387\pi$
$751$	−12.2662	−	21.2456i	−0.447598	−	0.775263i	−0.998229	+	0.0594857i	$0.981054\pi$
$752$	−2.35579	+	1.36011i	−0.0859067	+	0.0495982i
$753$	6.42817			0.234255
$754$	−6.28925	+	20.8242i	−0.229041	+	0.758372i
$755$	−52.9457			−1.92689
$756$	−1.23686	+	0.714101i	−0.0449841	+	0.0259716i
$757$	−0.439385	−	0.761037i	−0.0159697	−	0.0276604i	0.857930	−	0.513766i	$-0.171750\pi$
$757$	−0.439385	−	0.761037i	−0.0159697	−	0.0276604i	−0.873900	+	0.486106i	$0.838417\pi$
$758$	2.73427	−	4.73590i	0.0993132	−	0.172016i
$759$		−	5.84123i		−	0.212023i
$760$	8.28124	+	4.78117i	0.300392	+	0.173431i
$761$	28.1441	+	16.2490i	1.02022	+	0.589026i	0.914168	−	0.405335i	$-0.132845\pi$
$761$	28.1441	+	16.2490i	1.02022	+	0.589026i	0.106054	+	0.994360i	$0.466178\pi$
$762$		−	14.9468i		−	0.541465i
$763$	−9.06805	+	15.7063i	−0.328285	+	0.568607i
$764$	−0.419609	−	0.726784i	−0.0151809	−	0.0262941i
$765$	−10.3361	+	5.96754i	−0.373702	+	0.215757i
$766$	−12.4111			−0.448430
$767$	5.03755	−	16.6797i	0.181895	−	0.602270i
$768$	12.6371			0.456001
$769$	24.9246	−	14.3902i	0.898803	−	0.518924i	0.0219913	−	0.999758i	$-0.492999\pi$
$769$	24.9246	−	14.3902i	0.898803	−	0.518924i	0.876812	+	0.480834i	$0.159666\pi$

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)

\(f(q)\)	\(=\)	\(q+(-0.654865 + 0.378087i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.714101 + 1.23686i) q^{4} +4.01537i q^{5} +(-0.654865 - 0.378087i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.59231i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.654865 + 0.378087i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.714101 + 1.23686i) q^{4} +4.01537i q^{5} +(-0.654865 - 0.378087i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.59231i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.51816 - 2.62953i) q^{10} +(-0.588269 + 0.339637i) q^{11} -1.42820 q^{12} +(-0.823013 - 3.51036i) q^{13} +0.756173 q^{14} +(-3.47741 + 2.00768i) q^{15} +(-0.448082 - 0.776101i) q^{16} +(1.48617 - 2.57413i) q^{17} -0.756173i q^{18} +(0.795577 + 0.459326i) q^{19} +(-4.96644 - 2.86738i) q^{20} -1.00000i q^{21} +(0.256825 - 0.444833i) q^{22} +(4.29961 + 7.44714i) q^{23} +(2.24501 - 1.29616i) q^{24} -11.1232 q^{25} +(1.86618 + 1.98764i) q^{26} -1.00000 q^{27} +(1.23686 - 0.714101i) q^{28} +(3.98933 + 6.90972i) q^{29} +(1.51816 - 2.62953i) q^{30} +3.29616i q^{31} +(5.07689 + 2.93114i) q^{32} +(-0.588269 - 0.339637i) q^{33} +2.24761i q^{34} +(2.00768 - 3.47741i) q^{35} +(-0.714101 - 1.23686i) q^{36} +(-4.70475 + 2.71629i) q^{37} -0.694661 q^{38} +(2.62856 - 2.46793i) q^{39} +10.4091 q^{40} +(-7.98678 + 4.61117i) q^{41} +(0.378087 + 0.654865i) q^{42} +(2.53067 - 4.38324i) q^{43} -0.970141i q^{44} +(-3.47741 - 2.00768i) q^{45} +(-5.63133 - 3.25125i) q^{46} -3.03541i q^{47} +(0.448082 - 0.776101i) q^{48} +(0.500000 + 0.866025i) q^{49} +(7.28419 - 4.20553i) q^{50} +2.97235 q^{51} +(4.92954 + 1.48880i) q^{52} +1.32745 q^{53} +(0.654865 - 0.378087i) q^{54} +(-1.36377 - 2.36212i) q^{55} +(-1.29616 + 2.24501i) q^{56} +0.918653i q^{57} +(-5.22495 - 3.01663i) q^{58} +(4.18507 + 2.41625i) q^{59} -5.73476i q^{60} +(2.23470 - 3.87061i) q^{61} +(-1.24623 - 2.15854i) q^{62} +(0.866025 - 0.500000i) q^{63} -2.64058 q^{64} +(14.0954 - 3.30470i) q^{65} +0.513649 q^{66} +(3.49940 - 2.02038i) q^{67} +(2.12256 + 3.67638i) q^{68} +(-4.29961 + 7.44714i) q^{69} +3.03631i q^{70} +(-2.08894 - 1.20605i) q^{71} +(2.24501 + 1.29616i) q^{72} +7.82146i q^{73} +(2.05398 - 3.55761i) q^{74} +(-5.56159 - 9.63296i) q^{75} +(-1.13624 + 0.656011i) q^{76} +0.679275 q^{77} +(-0.788259 + 2.60999i) q^{78} +16.1827 q^{79} +(3.11633 - 1.79921i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.48684 - 6.03939i) q^{82} +4.78597i q^{83} +(1.23686 + 0.714101i) q^{84} +(10.3361 + 5.96754i) q^{85} +3.82724i q^{86} +(-3.98933 + 6.90972i) q^{87} +(0.880447 + 1.52498i) q^{88} +(-3.91913 + 2.26271i) q^{89} +3.03631 q^{90} +(-1.04243 + 3.45157i) q^{91} -12.2814 q^{92} +(-2.85455 + 1.64808i) q^{93} +(1.14765 + 1.98779i) q^{94} +(-1.84436 + 3.19453i) q^{95} +5.86229i q^{96} +(-7.40406 - 4.27474i) q^{97} +(-0.654865 - 0.378087i) q^{98} -0.679275i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

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