LMFDB - Embedded newform 276.2.c.a.47.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(47,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("276.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.c (of order $2$, degree $1$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.14
Character	$\chi$	$=$	276.47
Dual form			276.2.c.a.47.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456308 + 1.33857i) q^{2} +(0.784130 + 1.54439i) q^{3} +(-1.58357 + 1.22161i) q^{4} +1.42397i q^{5} +(-1.70948 + 1.75433i) q^{6} -1.12562i q^{7} +(-2.35780 - 1.56229i) q^{8} +(-1.77028 + 2.42200i) q^{9} +O(q^{10})$	\(q+(0.456308 + 1.33857i) q^{2} +(0.784130 + 1.54439i) q^{3} +(-1.58357 + 1.22161i) q^{4} +1.42397i q^{5} +(-1.70948 + 1.75433i) q^{6} -1.12562i q^{7} +(-2.35780 - 1.56229i) q^{8} +(-1.77028 + 2.42200i) q^{9} +(-1.90608 + 0.649767i) q^{10} -1.68304 q^{11} +(-3.12836 - 1.48775i) q^{12} +5.14341 q^{13} +(1.50673 - 0.513630i) q^{14} +(-2.19916 + 1.11657i) q^{15} +(1.01536 - 3.86898i) q^{16} +4.65065i q^{17} +(-4.04983 - 1.26447i) q^{18} -5.86444i q^{19} +(-1.73952 - 2.25494i) q^{20} +(1.73840 - 0.882634i) q^{21} +(-0.767985 - 2.25288i) q^{22} +1.00000 q^{23} +(0.563966 - 4.86641i) q^{24} +2.97232 q^{25} +(2.34698 + 6.88484i) q^{26} +(-5.12865 - 0.834839i) q^{27} +(1.37507 + 1.78250i) q^{28} +3.67220i q^{29} +(-2.49811 - 2.43424i) q^{30} +3.79271i q^{31} +(5.64224 - 0.406310i) q^{32} +(-1.31972 - 2.59927i) q^{33} +(-6.22524 + 2.12213i) q^{34} +1.60285 q^{35} +(-0.155376 - 5.99799i) q^{36} -2.52020 q^{37} +(7.85000 - 2.67599i) q^{38} +(4.03310 + 7.94343i) q^{39} +(2.22465 - 3.35743i) q^{40} -8.23771i q^{41} +(1.97472 + 1.92423i) q^{42} +3.72497i q^{43} +(2.66521 - 2.05601i) q^{44} +(-3.44885 - 2.52082i) q^{45} +(0.456308 + 1.33857i) q^{46} +7.62360 q^{47} +(6.77140 - 1.46567i) q^{48} +5.73298 q^{49} +(1.35629 + 3.97868i) q^{50} +(-7.18241 + 3.64671i) q^{51} +(-8.14493 + 6.28321i) q^{52} +2.23179i q^{53} +(-1.22275 - 7.24603i) q^{54} -2.39659i q^{55} +(-1.75855 + 2.65400i) q^{56} +(9.05699 - 4.59848i) q^{57} +(-4.91552 + 1.67565i) q^{58} -3.98448 q^{59} +(2.11850 - 4.45467i) q^{60} -7.14195 q^{61} +(-5.07682 + 1.73064i) q^{62} +(2.72626 + 1.99267i) q^{63} +(3.11848 + 7.36716i) q^{64} +7.32404i q^{65} +(2.87712 - 2.95262i) q^{66} -12.2990i q^{67} +(-5.68125 - 7.36460i) q^{68} +(0.784130 + 1.54439i) q^{69} +(0.731392 + 2.14553i) q^{70} -3.55458 q^{71} +(7.95786 - 2.94491i) q^{72} +13.8147 q^{73} +(-1.14999 - 3.37348i) q^{74} +(2.33069 + 4.59043i) q^{75} +(7.16403 + 9.28673i) q^{76} +1.89447i q^{77} +(-8.79254 + 9.02326i) q^{78} +5.27297i q^{79} +(5.50930 + 1.44584i) q^{80} +(-2.73221 - 8.57526i) q^{81} +(11.0268 - 3.75894i) q^{82} +12.9095 q^{83} +(-1.67464 + 3.52135i) q^{84} -6.62236 q^{85} +(-4.98615 + 1.69973i) q^{86} +(-5.67131 + 2.87948i) q^{87} +(3.96828 + 2.62940i) q^{88} -15.9010i q^{89} +(1.80057 - 5.76681i) q^{90} -5.78953i q^{91} +(-1.58357 + 1.22161i) q^{92} +(-5.85742 + 2.97398i) q^{93} +(3.47871 + 10.2048i) q^{94} +8.35076 q^{95} +(5.05175 + 8.39522i) q^{96} -11.9616 q^{97} +(2.61600 + 7.67402i) q^{98} +(2.97946 - 4.07633i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.456308	+	1.33857i	0.322659	+	0.946515i
$2$	0.456308	+	1.33857i	0.322659	+	0.946515i
$3$	0.784130	+	1.54439i	0.452718	+	0.891654i
$3$	0.784130	+	1.54439i	0.452718	+	0.891654i
$4$	−1.58357	+	1.22161i	−0.791783	+	0.610803i
$5$			1.42397i			0.636817i	0.947954	+	0.318408i	$0.103148\pi$
$5$			1.42397i			0.636817i	−0.947954	+	0.318408i	$0.896852\pi$
$6$	−1.70948	+	1.75433i	−0.697891	+	0.716204i
$7$		−	1.12562i		−	0.425445i	−0.977113	−	0.212723i	$-0.931767\pi$
$7$		−	1.12562i		−	0.425445i	0.977113	−	0.212723i	$-0.0682330\pi$
$8$	−2.35780	−	1.56229i	−0.833610	−	0.552354i
$9$	−1.77028	+	2.42200i	−0.590094	+	0.807335i
$10$	−1.90608	+	0.649767i	−0.602757	+	0.205474i
$11$	−1.68304			−0.507456			−0.253728	−	0.967276i	$-0.581657\pi$
$11$	−1.68304			−0.507456			−0.253728	+	0.967276i	$0.581657\pi$
$12$	−3.12836	−	1.48775i	−0.903079	−	0.429475i
$13$	5.14341			1.42652			0.713262	−	0.700897i	$-0.247217\pi$
$13$	5.14341			1.42652			0.713262	+	0.700897i	$0.247217\pi$
$14$	1.50673	−	0.513630i	0.402690	−	0.137273i
$15$	−2.19916	+	1.11657i	−0.567820	+	0.288298i
$16$	1.01536	−	3.86898i	0.253841	−	0.967246i
$17$			4.65065i			1.12795i	0.825793	+	0.563974i	$0.190728\pi$
$17$			4.65065i			1.12795i	−0.825793	+	0.563974i	$0.809272\pi$
$18$	−4.04983	−	1.26447i	−0.954554	−	0.298039i
$19$		−	5.86444i		−	1.34540i	−0.739918	−	0.672698i	$-0.765135\pi$
$19$		−	5.86444i		−	1.34540i	0.739918	−	0.672698i	$-0.234865\pi$
$20$	−1.73952	−	2.25494i	−0.388969	−	0.504221i
$21$	1.73840	−	0.882634i	0.379350	−	0.192606i
$22$	−0.767985	−	2.25288i	−0.163735	−	0.480315i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	0.563966	−	4.86641i	0.115119	−	0.993352i
$25$	2.97232			0.594465
$26$	2.34698	+	6.88484i	0.460280	+	1.35023i
$27$	−5.12865	−	0.834839i	−0.987009	−	0.160665i
$28$	1.37507	+	1.78250i	0.259863	+	0.336860i
$29$			3.67220i			0.681911i	0.940080	+	0.340955i	$0.110750\pi$
$29$			3.67220i			0.681911i	−0.940080	+	0.340955i	$0.889250\pi$
$30$	−2.49811	−	2.43424i	−0.456091	−	0.444429i
$31$			3.79271i			0.681191i	0.940210	+	0.340595i	$0.110629\pi$
$31$			3.79271i			0.681191i	−0.940210	+	0.340595i	$0.889371\pi$
$32$	5.64224	−	0.406310i	0.997417	−	0.0718262i
$33$	−1.31972	−	2.59927i	−0.229734	−	0.452475i
$34$	−6.22524	+	2.12213i	−1.06762	+	0.363942i
$35$	1.60285			0.270931
$36$	−0.155376	−	5.99799i	−0.0258960	−	0.999665i
$37$	−2.52020			−0.414319			−0.207159	−	0.978307i	$-0.566422\pi$
$37$	−2.52020			−0.414319			−0.207159	+	0.978307i	$0.566422\pi$
$38$	7.85000	−	2.67599i	1.27344	−	0.434103i
$39$	4.03310	+	7.94343i	0.645813	+	1.27197i
$40$	2.22465	−	3.35743i	0.351748	−	0.530856i
$41$		−	8.23771i		−	1.28651i	−0.765650	−	0.643257i	$-0.777583\pi$
$41$		−	8.23771i		−	1.28651i	0.765650	−	0.643257i	$-0.222417\pi$
$42$	1.97472	+	1.92423i	0.304705	+	0.296914i
$43$			3.72497i			0.568052i	0.958817	+	0.284026i	$0.0916703\pi$
$43$			3.72497i			0.568052i	−0.958817	+	0.284026i	$0.908330\pi$
$44$	2.66521	−	2.05601i	0.401795	−	0.309955i
$45$	−3.44885	−	2.52082i	−0.514124	−	0.375781i
$46$	0.456308	+	1.33857i	0.0672790	+	0.197362i
$47$	7.62360			1.11202			0.556008	−	0.831177i	$-0.312332\pi$
$47$	7.62360			1.11202			0.556008	+	0.831177i	$0.312332\pi$
$48$	6.77140	−	1.46567i	0.977367	−	0.211551i
$49$	5.73298			0.818996
$50$	1.35629	+	3.97868i	0.191809	+	0.562670i
$51$	−7.18241	+	3.64671i	−1.00574	+	0.510642i
$52$	−8.14493	+	6.28321i	−1.12950	+	0.871325i
$53$			2.23179i			0.306560i	0.988183	+	0.153280i	$0.0489837\pi$
$53$			2.23179i			0.306560i	−0.988183	+	0.153280i	$0.951016\pi$
$54$	−1.22275	−	7.24603i	−0.166395	−	0.986059i
$55$		−	2.39659i		−	0.323156i
$56$	−1.75855	+	2.65400i	−0.234996	+	0.354655i
$57$	9.05699	−	4.59848i	1.19963	−	0.609084i
$58$	−4.91552	+	1.67565i	−0.645439	+	0.220024i
$59$	−3.98448			−0.518735			−0.259367	−	0.965779i	$-0.583514\pi$
$59$	−3.98448			−0.518735			−0.259367	+	0.965779i	$0.583514\pi$
$60$	2.11850	−	4.45467i	0.273497	−	0.575095i
$61$	−7.14195			−0.914433			−0.457217	−	0.889355i	$-0.651154\pi$
$61$	−7.14195			−0.914433			−0.457217	+	0.889355i	$0.651154\pi$
$62$	−5.07682	+	1.73064i	−0.644757	+	0.219792i
$63$	2.72626	+	1.99267i	0.343477	+	0.251052i
$64$	3.11848	+	7.36716i	0.389810	+	0.920895i
$65$			7.32404i			0.908435i
$66$	2.87712	−	2.95262i	0.354149	−	0.363442i
$67$		−	12.2990i		−	1.50257i	−0.659981	−	0.751283i	$-0.729435\pi$
$67$		−	12.2990i		−	1.50257i	0.659981	−	0.751283i	$-0.270565\pi$
$68$	−5.68125	−	7.36460i	−0.688953	−	0.893090i
$69$	0.784130	+	1.54439i	0.0943981	+	0.185923i
$70$	0.731392	+	2.14553i	0.0874180	+	0.256440i
$71$	−3.55458			−0.421851			−0.210925	−	0.977502i	$-0.567648\pi$
$71$	−3.55458			−0.421851			−0.210925	+	0.977502i	$0.567648\pi$
$72$	7.95786	−	2.94491i	0.937842	−	0.347061i
$73$	13.8147			1.61689			0.808447	−	0.588570i	$-0.200309\pi$
$73$	13.8147			1.61689			0.808447	+	0.588570i	$0.200309\pi$
$74$	−1.14999	−	3.37348i	−0.133683	−	0.392159i
$75$	2.33069	+	4.59043i	0.269125	+	0.530057i
$76$	7.16403	+	9.28673i	0.821771	+	1.06526i
$77$			1.89447i			0.215895i
$78$	−8.79254	+	9.02326i	−0.995559	+	1.02168i
$79$			5.27297i			0.593255i	0.954993	+	0.296628i	$0.0958620\pi$
$79$			5.27297i			0.593255i	−0.954993	+	0.296628i	$0.904138\pi$
$80$	5.50930	+	1.44584i	0.615958	+	0.161650i
$81$	−2.73221	−	8.57526i	−0.303579	−	0.952806i
$82$	11.0268	−	3.75894i	1.21771	−	0.415105i
$83$	12.9095			1.41700			0.708502	−	0.705709i	$-0.249371\pi$
$83$	12.9095			1.41700			0.708502	+	0.705709i	$0.249371\pi$
$84$	−1.67464	+	3.52135i	−0.182718	+	0.384210i
$85$	−6.62236			−0.718296
$86$	−4.98615	+	1.69973i	−0.537670	+	0.183287i
$87$	−5.67131	+	2.87948i	−0.608028	+	0.308713i
$88$	3.96828	+	2.62940i	0.423020	+	0.280295i
$89$		−	15.9010i		−	1.68550i	−0.538303	−	0.842751i	$-0.680935\pi$
$89$		−	15.9010i		−	1.68550i	0.538303	−	0.842751i	$-0.319065\pi$
$90$	1.80057	−	5.76681i	0.189796	−	0.607876i
$91$		−	5.78953i		−	0.606908i
$92$	−1.58357	+	1.22161i	−0.165098	+	0.127361i
$93$	−5.85742	+	2.97398i	−0.607386	+	0.308387i
$94$	3.47871	+	10.2048i	0.358802	+	1.05254i
$95$	8.35076			0.856770
$96$	5.05175	+	8.39522i	0.515592	+	0.856834i
$97$	−11.9616			−1.21451			−0.607256	−	0.794506i	$-0.707730\pi$
$97$	−11.9616			−1.21451			−0.607256	+	0.794506i	$0.707730\pi$
$98$	2.61600	+	7.67402i	0.264256	+	0.775193i
$99$	2.97946	−	4.07633i	0.299447	−	0.409687i
$100$	−4.70687	+	3.63101i	−0.470687	+	0.363101i
$101$			1.11023i			0.110472i	0.998473	+	0.0552362i	$0.0175912\pi$
$101$			1.11023i			0.110472i	−0.998473	+	0.0552362i	$0.982409\pi$
$102$	−8.15879	−	7.95017i	−0.807840	−	0.787184i
$103$		−	16.6642i		−	1.64197i	−0.570949	−	0.820985i	$-0.693425\pi$
$103$		−	16.6642i		−	1.64197i	0.570949	−	0.820985i	$-0.306575\pi$
$104$	−12.1271	−	8.03551i	−1.18916	−	0.787947i
$105$	1.25684	+	2.47542i	0.122655	+	0.241576i
$106$	−2.98742	+	1.01838i	−0.290164	+	0.0989143i
$107$	−5.17617			−0.500400			−0.250200	−	0.968194i	$-0.580496\pi$
$107$	−5.17617			−0.500400			−0.250200	+	0.968194i	$0.580496\pi$
$108$	9.14140	−	4.94316i	0.879631	−	0.475656i
$109$	−1.88125			−0.180191			−0.0900953	−	0.995933i	$-0.528717\pi$
$109$	−1.88125			−0.180191			−0.0900953	+	0.995933i	$0.528717\pi$
$110$	3.20802	−	1.09358i	0.305873	−	0.104269i
$111$	−1.97617	−	3.89218i	−0.187569	−	0.369429i
$112$	−4.35501	−	1.14291i	−0.411510	−	0.107995i
$113$		−	10.8879i		−	1.02425i	−0.858911	−	0.512124i	$-0.828859\pi$
$113$		−	10.8879i		−	1.02425i	0.858911	−	0.512124i	$-0.171141\pi$
$114$	10.2882	+	10.0251i	0.963577	+	0.938939i
$115$			1.42397i			0.132785i
$116$	−4.48598	−	5.81517i	−0.416513	−	0.539925i
$117$	−9.10528	+	12.4574i	−0.841783	+	1.15168i
$118$	−1.81815	−	5.33352i	−0.167374	−	0.490990i
$119$	5.23487			0.479880
$120$	6.92960	+	0.803069i	0.632583	+	0.0733098i
$121$	−8.16737			−0.742488
$122$	−3.25893	−	9.56004i	−0.295050	−	0.865525i
$123$	12.7222	−	6.45944i	1.14713	−	0.582428i
$124$	−4.63319	−	6.00600i	−0.416073	−	0.539355i
$125$			11.3523i			1.01538i
$126$	−1.42332	+	4.55858i	−0.126799	+	0.406110i
$127$			8.80731i			0.781523i	0.920492	+	0.390761i	$0.127788\pi$
$127$			8.80731i			0.781523i	−0.920492	+	0.390761i	$0.872212\pi$
$128$	−8.43851	+	7.53601i	−0.745866	+	0.666096i
$129$	−5.75280	+	2.92086i	−0.506506	+	0.257167i
$130$	−9.80377	+	3.34202i	−0.859848	+	0.293114i
$131$	−18.3393			−1.60231			−0.801155	−	0.598457i	$-0.795781\pi$
$131$	−18.3393			−1.60231			−0.801155	+	0.598457i	$0.795781\pi$
$132$	5.26515	+	2.50394i	0.458273	+	0.217940i
$133$	−6.60114			−0.572392
$134$	16.4632	−	5.61215i	1.42220	−	0.484816i
$135$	1.18878	−	7.30302i	0.102314	−	0.628544i
$136$	7.26567	−	10.9653i	0.623026	−	0.940268i
$137$			5.76597i			0.492620i	0.969191	+	0.246310i	$0.0792181\pi$
$137$			5.76597i			0.492620i	−0.969191	+	0.246310i	$0.920782\pi$
$138$	−1.70948	+	1.75433i	−0.145520	+	0.149339i
$139$		−	2.41616i		−	0.204936i	−0.994736	−	0.102468i	$-0.967326\pi$
$139$		−	2.41616i		−	0.204936i	0.994736	−	0.102468i	$-0.0326739\pi$
$140$	−2.53821	+	1.95805i	−0.214518	+	0.165485i
$141$	5.97789	+	11.7738i	0.503429	+	0.991534i
$142$	−1.62198	−	4.75807i	−0.136114	−	0.399288i
$143$	−8.65657			−0.723899
$144$	7.57322	+	9.30840i	0.631102	+	0.775700i
$145$	−5.22909			−0.434252
$146$	6.30378	+	18.4921i	0.521704	+	1.53041i
$147$	4.49540	+	8.85395i	0.370774	+	0.730261i
$148$	3.99091	−	3.07869i	0.328050	−	0.253067i
$149$		−	17.0925i		−	1.40027i	−0.714008	−	0.700137i	$-0.753122\pi$
$149$		−	17.0925i		−	1.40027i	0.714008	−	0.700137i	$-0.246878\pi$
$150$	−5.08112	+	5.21445i	−0.414872	+	0.425758i
$151$			6.22274i			0.506399i	0.967414	+	0.253200i	$0.0814829\pi$
$151$			6.22274i			0.506399i	−0.967414	+	0.253200i	$0.918517\pi$
$152$	−9.16198	+	13.8272i	−0.743135	+	1.12153i
$153$	−11.2639	−	8.23295i	−0.910631	−	0.665595i
$154$	−2.53589	+	0.864461i	−0.204348	+	0.0696603i
$155$	−5.40068			−0.433793
$156$	−16.0904	−	7.65209i	−1.28826	−	0.612657i
$157$	−12.6190			−1.00711			−0.503553	−	0.863964i	$-0.667974\pi$
$157$	−12.6190			−1.00711			−0.503553	+	0.863964i	$0.667974\pi$
$158$	−7.05826	+	2.40610i	−0.561525	+	0.191419i
$159$	−3.44676	+	1.75001i	−0.273346	+	0.138785i
$160$	0.578572	+	8.03436i	0.0457401	+	0.635172i
$161$		−	1.12562i		−	0.0887114i
$162$	10.2319	−	7.57023i	0.803894	−	0.594773i
$163$		−	14.7432i		−	1.15478i	−0.816469	−	0.577390i	$-0.804071\pi$
$163$		−	14.7432i		−	1.15478i	0.816469	−	0.577390i	$-0.195929\pi$
$164$	10.0632	+	13.0450i	0.785806	+	1.01864i
$165$	3.70127	−	1.87924i	0.288144	−	0.146299i
$166$	5.89072	+	17.2804i	0.457209	+	1.34122i
$167$	−21.1334			−1.63535			−0.817674	−	0.575681i	$-0.804737\pi$
$167$	−21.1334			−1.63535			−0.817674	+	0.575681i	$0.804737\pi$
$168$	−5.47774	−	0.634813i	−0.422617	−	0.0489769i
$169$	13.4547			1.03497
$170$	−3.02184	−	8.86452i	−0.231764	−	0.679878i
$171$	14.2037	+	10.3817i	1.08618	+	0.793909i
$172$	−4.55044	−	5.89873i	−0.346968	−	0.449774i
$173$		−	1.66069i		−	0.126260i	−0.998005	−	0.0631299i	$-0.979892\pi$
$173$		−	1.66069i		−	0.126260i	0.998005	−	0.0631299i	$-0.0201083\pi$
$174$	−6.44227	−	6.27754i	−0.488387	−	0.475899i
$175$		−	3.34571i		−	0.252912i
$176$	−1.70890	+	6.51166i	−0.128813	+	0.490835i
$177$	−3.12435	−	6.15358i	−0.234840	−	0.462532i
$178$	21.2847	−	7.25575i	1.59535	−	0.543842i
$179$	−0.693693			−0.0518491			−0.0259245	−	0.999664i	$-0.508253\pi$
$179$	−0.693693			−0.0518491			−0.0259245	+	0.999664i	$0.508253\pi$
$180$	8.54093	−	0.221250i	0.636603	−	0.0164910i
$181$	8.70102			0.646742			0.323371	−	0.946272i	$-0.395184\pi$
$181$	8.70102			0.646742			0.323371	+	0.946272i	$0.395184\pi$
$182$	7.74973	−	2.64181i	0.574448	−	0.195824i
$183$	−5.60022	−	11.0300i	−0.413980	−	0.815358i
$184$	−2.35780	−	1.56229i	−0.173820	−	0.115174i
$185$		−	3.58868i		−	0.263845i
$186$	−6.65368	−	6.48355i	−0.487871	−	0.475397i
$187$		−	7.82723i		−	0.572384i
$188$	−12.0725	+	9.31303i	−0.880476	+	0.679223i
$189$	−0.939713	+	5.77292i	−0.0683541	+	0.419918i
$190$	3.81052	+	11.1781i	0.276444	+	0.810946i
$191$	11.9566			0.865150			0.432575	−	0.901598i	$-0.357605\pi$
$191$	11.9566			0.865150			0.432575	+	0.901598i	$0.357605\pi$
$192$	−8.93248	+	10.5930i	−0.644646	+	0.764481i
$193$	−11.3568			−0.817480			−0.408740	−	0.912651i	$-0.634032\pi$
$193$	−11.3568			−0.817480			−0.408740	+	0.912651i	$0.634032\pi$
$194$	−5.45815	−	16.0114i	−0.391873	−	1.14955i
$195$	−11.3112	+	5.74299i	−0.810009	+	0.411264i
$196$	−9.07854	+	7.00343i	−0.648467	+	0.500245i
$197$		−	4.63430i		−	0.330180i	−0.986278	−	0.165090i	$-0.947208\pi$
$197$		−	4.63430i		−	0.330180i	0.986278	−	0.165090i	$-0.0527915\pi$
$198$	6.81603	+	2.12816i	0.484394	+	0.151242i
$199$			18.1750i			1.28839i	0.764861	+	0.644196i	$0.222808\pi$
$199$			18.1750i			1.28839i	−0.764861	+	0.644196i	$0.777192\pi$
$200$	−7.00816	−	4.64364i	−0.495551	−	0.328355i
$201$	18.9945	−	9.64403i	1.33977	−	0.680238i
$202$	−1.48613	+	0.506608i	−0.104564	+	0.0356448i
$203$	4.13351			0.290116
$204$	6.91898	−	14.5489i	0.484426	−	1.01863i
$205$	11.7302			0.819274
$206$	22.3063	−	7.60400i	1.55415	−	0.529796i
$207$	−1.77028	+	2.42200i	−0.123043	+	0.168341i
$208$	5.22242	−	19.8998i	0.362110	−	1.37980i
$209$			9.87010i			0.682729i
$210$	−2.74003	+	2.81193i	−0.189080	+	0.194041i
$211$			12.9459i			0.891231i	0.895225	+	0.445615i	$0.147015\pi$
$211$			12.9459i			0.891231i	−0.895225	+	0.445615i	$0.852985\pi$
$212$	−2.72637	−	3.53419i	−0.187248	−	0.242729i
$213$	−2.78725	−	5.48965i	−0.190979	−	0.376145i
$214$	−2.36193	−	6.92870i	−0.161458	−	0.473636i
$215$	−5.30423			−0.361745
$216$	10.7881	+	9.98084i	0.734036	+	0.679110i
$217$	4.26916			0.289809
$218$	−0.858427	−	2.51819i	−0.0581400	−	0.170553i
$219$	10.8325	+	21.3353i	0.731996	+	1.44171i
$220$	2.92769	+	3.79516i	0.197385	+	0.255870i
$221$			23.9202i			1.60905i
$222$	4.30823	−	4.42128i	0.289149	−	0.296737i
$223$			1.17720i			0.0788314i	0.999223	+	0.0394157i	$0.0125497\pi$
$223$			1.17720i			0.0788314i	−0.999223	+	0.0394157i	$0.987450\pi$
$224$	−0.457352	−	6.35103i	−0.0305581	−	0.424346i
$225$	−5.26185	+	7.19898i	−0.350790	+	0.479932i
$226$	14.5743	−	4.96824i	0.969467	−	0.330483i
$227$	−23.4475			−1.55626			−0.778132	−	0.628101i	$-0.783832\pi$
$227$	−23.4475			−1.55626			−0.778132	+	0.628101i	$0.783832\pi$
$228$	−8.72480	+	18.3461i	−0.577814	+	1.21500i
$229$	27.6644			1.82811			0.914057	−	0.405586i	$-0.132933\pi$
$229$	27.6644			1.82811			0.914057	+	0.405586i	$0.132933\pi$
$230$	−1.90608	+	0.649767i	−0.125683	+	0.0428444i
$231$	−2.92580	+	1.48551i	−0.192503	+	0.0977393i
$232$	5.73706	−	8.65833i	0.376656	−	0.568447i
$233$		−	13.5634i		−	0.888566i	−0.895887	−	0.444283i	$-0.853459\pi$
$233$		−	13.5634i		−	0.888566i	0.895887	−	0.444283i	$-0.146541\pi$
$234$	−20.8299	−	6.50371i	−1.36169	−	0.425161i
$235$			10.8557i			0.708151i
$236$	6.30968	−	4.86746i	0.410725	−	0.316844i
$237$	−8.14352	+	4.13469i	−0.528978	+	0.268577i
$238$	2.38871	+	7.00727i	0.154837	+	0.454214i
$239$	29.8334			1.92976			0.964882	−	0.262683i	$-0.0846075\pi$
$239$	29.8334			1.92976			0.964882	+	0.262683i	$0.0846075\pi$
$240$	2.08706	+	9.64223i	0.134719	+	0.622403i
$241$	19.2786			1.24184			0.620922	−	0.783873i	$-0.286759\pi$
$241$	19.2786			1.24184			0.620922	+	0.783873i	$0.286759\pi$
$242$	−3.72684	−	10.9326i	−0.239570	−	0.702777i
$243$	11.1011	−	10.9437i	0.712138	−	0.702039i
$244$	11.3098	−	8.72465i	0.724033	−	0.558538i
$245$			8.16356i			0.521551i
$246$	14.4517	+	14.0822i	0.921407	+	0.897847i
$247$		−	30.1632i		−	1.91924i
$248$	5.92532	−	8.94246i	0.376258	−	0.567847i
$249$	10.1227	+	19.9373i	0.641503	+	1.26348i
$250$	−15.1959	+	5.18015i	−0.961074	+	0.327622i
$251$	−12.7274			−0.803345			−0.401673	−	0.915783i	$-0.631571\pi$
$251$	−12.7274			−0.803345			−0.401673	+	0.915783i	$0.631571\pi$
$252$	−6.75147	+	0.174894i	−0.425302	+	0.0110173i
$253$	−1.68304			−0.105812
$254$	−11.7893	+	4.01885i	−0.739723	+	0.252165i
$255$	−5.19279	−	10.2275i	−0.325185	−	0.640471i
$256$	−13.9381	−	7.85684i	−0.871130	−	0.491052i
$257$		−	15.8466i		−	0.988484i	−0.869324	−	0.494242i	$-0.835446\pi$
$257$		−	15.8466i		−	0.988484i	0.869324	−	0.494242i	$-0.164554\pi$
$258$	−6.53484	−	6.36775i	−0.406841	−	0.396439i
$259$			2.83679i			0.176270i
$260$	−8.94708	−	11.5981i	−0.554874	−	0.719283i
$261$	−8.89409	−	6.50083i	−0.550530	−	0.402391i
$262$	−8.36836	−	24.5485i	−0.516999	−	1.51661i
$263$	24.4640			1.50852			0.754258	−	0.656578i	$-0.227997\pi$
$263$	24.4640			1.50852			0.754258	+	0.656578i	$0.227997\pi$
$264$	−0.949179	+	8.19037i	−0.0584179	+	0.504082i
$265$	−3.17799			−0.195223
$266$	−3.01216	−	8.83613i	−0.184687	−	0.541778i
$267$	24.5573	−	12.4684i	1.50288	−	0.763056i
$268$	15.0246	+	19.4763i	0.917771	+	1.18971i
$269$		−	2.06964i		−	0.126188i	−0.998008	−	0.0630941i	$-0.979903\pi$
$269$		−	2.06964i		−	0.126188i	0.998008	−	0.0630941i	$-0.0200968\pi$
$270$	10.3181	−	1.74115i	0.627939	−	0.105963i
$271$			23.7171i			1.44071i	0.693604	+	0.720357i	$0.256022\pi$
$271$			23.7171i			1.44071i	−0.693604	+	0.720357i	$0.743978\pi$
$272$	17.9933	+	4.72209i	1.09100	+	0.286319i
$273$	8.94130	−	4.53975i	0.541152	−	0.274758i
$274$	−7.71818	+	2.63106i	−0.466272	+	0.158948i
$275$	−5.00254			−0.301665
$276$	−3.12836	−	1.48775i	−0.188305	−	0.0895518i
$277$	−13.0359			−0.783250			−0.391625	−	0.920125i	$-0.628087\pi$
$277$	−13.0359			−0.783250			−0.391625	+	0.920125i	$0.628087\pi$
$278$	3.23421	−	1.10251i	0.193975	−	0.0661244i
$279$	−9.18596	−	6.71416i	−0.549949	−	0.401966i
$280$	−3.77920	−	2.50412i	−0.225850	−	0.149650i
$281$		−	14.5979i		−	0.870838i	−0.900228	−	0.435419i	$-0.856600\pi$
$281$		−	14.5979i		−	0.870838i	0.900228	−	0.435419i	$-0.143400\pi$
$282$	−13.0324	+	13.3743i	−0.776067	+	0.796431i
$283$			22.7921i			1.35485i	0.735593	+	0.677424i	$0.236904\pi$
$283$			22.7921i			1.35485i	−0.735593	+	0.677424i	$0.763096\pi$
$284$	5.62891	−	4.34229i	0.334014	−	0.257668i
$285$	6.54808	+	12.8968i	0.387875	+	0.763942i
$286$	−3.95006	−	11.5875i	−0.233572	−	0.685181i
$287$	−9.27255			−0.547341
$288$	−9.00427	+	14.3848i	−0.530582	+	0.847634i
$289$	−4.62851			−0.272265
$290$	−2.38607	−	6.99952i	−0.140115	−	0.411026i
$291$	−9.37941	−	18.4733i	−0.549831	−	1.08292i
$292$	−21.8766	+	16.8762i	−1.28023	+	0.987602i
$293$			27.1247i			1.58464i	0.610106	+	0.792320i	$0.291127\pi$
$293$			27.1247i			1.58464i	−0.610106	+	0.792320i	$0.708873\pi$
$294$	−9.80039	+	10.0576i	−0.571570	+	0.586568i
$295$		−	5.67375i		−	0.330339i
$296$	5.94214	+	3.93730i	0.345380	+	0.228851i
$297$	8.63173	+	1.40507i	0.500864	+	0.0815304i
$298$	22.8796	−	7.79946i	1.32538	−	0.451811i
$299$	5.14341			0.297451
$300$	−9.29848	−	4.42206i	−0.536848	−	0.255308i
$301$	4.19291			0.241675
$302$	−8.32960	+	2.83949i	−0.479315	+	0.163394i
$303$	−1.71463	+	0.870567i	−0.0985031	+	0.0500127i
$304$	−22.6894	−	5.95453i	−1.30133	−	0.341516i
$305$		−	10.1699i		−	0.582326i
$306$	5.88062	−	18.8343i	0.336173	−	1.07669i
$307$			18.0198i			1.02844i	0.857658	+	0.514221i	$0.171919\pi$
$307$			18.0198i			1.02844i	−0.857658	+	0.514221i	$0.828081\pi$
$308$	−2.31429	−	3.00002i	−0.131869	−	0.170942i
$309$	25.7360	−	13.0669i	1.46407	−	0.743349i
$310$	−2.46438	−	7.22922i	−0.139967	−	0.410592i
$311$	15.4078			0.873697			0.436848	−	0.899535i	$-0.356095\pi$
$311$	15.4078			0.873697			0.436848	+	0.899535i	$0.356095\pi$
$312$	2.90071	−	25.0299i	0.164220	−	1.41704i
$313$	−1.19493			−0.0675416			−0.0337708	−	0.999430i	$-0.510752\pi$
$313$	−1.19493			−0.0675416			−0.0337708	+	0.999430i	$0.510752\pi$
$314$	−5.75815	−	16.8915i	−0.324951	−	0.953241i
$315$	−2.83749	+	3.88210i	−0.159874	+	0.218732i
$316$	−6.44148	−	8.35009i	−0.362362	−	0.469729i
$317$			4.92932i			0.276858i	0.990372	+	0.138429i	$0.0442053\pi$
$317$			4.92932i			0.276858i	−0.990372	+	0.138429i	$0.955795\pi$
$318$	−3.91531	−	3.81520i	−0.219560	−	0.213946i
$319$		−	6.18047i		−	0.346040i
$320$	−10.4906	+	4.44060i	−0.586441	+	0.248237i
$321$	−4.05879	−	7.99403i	−0.226540	−	0.446183i
$322$	1.50673	−	0.513630i	0.0839667	−	0.0286235i
$323$	27.2734			1.51754
$324$	14.8022	+	10.2418i	0.822345	+	0.568989i
$325$	15.2879			0.848019
$326$	19.7349	−	6.72746i	1.09302	−	0.372600i
$327$	−1.47514	−	2.90538i	−0.0815755	−	0.160668i
$328$	−12.8697	+	19.4229i	−0.710612	+	1.07245i
$329$		−	8.58129i		−	0.473102i
$330$	4.20442	+	4.09692i	0.231446	+	0.225528i
$331$			12.5469i			0.689639i	0.938669	+	0.344819i	$0.112060\pi$
$331$			12.5469i			0.689639i	−0.938669	+	0.344819i	$0.887940\pi$
$332$	−20.4431	+	15.7703i	−1.12196	+	0.865510i
$333$	4.46147	−	6.10394i	0.244487	−	0.334494i
$334$	−9.64332	−	28.2886i	−0.527659	−	1.54788i
$335$	17.5134			0.956859
$336$	−1.64979	−	7.62203i	−0.0900035	−	0.415816i
$337$	21.1109			1.14998			0.574991	−	0.818160i	$-0.305006\pi$
$337$	21.1109			1.14998			0.574991	+	0.818160i	$0.305006\pi$
$338$	6.13947	+	18.0101i	0.333943	+	0.979618i
$339$	16.8152	−	8.53754i	0.913275	−	0.463695i
$340$	10.4869	−	8.08991i	0.568734	−	0.438737i
$341$		−	6.38328i		−	0.345674i
$342$	−7.41543	+	23.7500i	−0.400981	+	1.28425i
$343$		−	14.3325i		−	0.773883i
$344$	5.81949	−	8.78274i	0.313766	−	0.473534i
$345$	−2.19916	+	1.11657i	−0.118399	+	0.0601143i
$346$	2.22296	−	0.757786i	0.119507	−	0.0407388i
$347$	1.73613			0.0932006			0.0466003	−	0.998914i	$-0.485161\pi$
$347$	1.73613			0.0932006			0.0466003	+	0.998914i	$0.485161\pi$
$348$	5.46330	−	11.4880i	0.292864	−	0.615819i
$349$	−14.9792			−0.801820			−0.400910	−	0.916117i	$-0.631306\pi$
$349$	−14.9792			−0.801820			−0.400910	+	0.916117i	$0.631306\pi$
$350$	4.47849	−	1.52668i	0.239385	−	0.0816042i
$351$	−26.3787	−	4.29392i	−1.40799	−	0.229192i
$352$	−9.49613	+	0.683837i	−0.506145	+	0.0364487i
$353$		−	0.688688i		−	0.0366551i	−0.999832	−	0.0183276i	$-0.994166\pi$
$353$		−	0.688688i		−	0.0366551i	0.999832	−	0.0183276i	$-0.00583417\pi$
$354$	6.81137	−	6.99010i	0.362020	−	0.371520i
$355$		−	5.06159i		−	0.268642i
$356$	19.4247	+	25.1803i	1.02951	+	1.33455i
$357$	4.10482	+	8.08468i	0.217250	+	0.427887i
$358$	−0.316538	−	0.928561i	−0.0167295	−	0.0490759i
$359$	−29.0421			−1.53278			−0.766392	−	0.642373i	$-0.777950\pi$
$359$	−29.0421			−1.53278			−0.766392	+	0.642373i	$0.777950\pi$
$360$	4.19345	+	11.3317i	0.221014	+	0.597234i
$361$	−15.3917			−0.810088
$362$	3.97035	+	11.6470i	0.208677	+	0.612151i
$363$	−6.40428	−	12.6136i	−0.336137	−	0.662043i
$364$	7.07252	+	9.16811i	0.370701	+	0.480539i
$365$			19.6717i			1.02966i
$366$	12.2090	−	12.5294i	0.638175	−	0.654921i
$367$			12.6525i			0.660457i	0.943901	+	0.330229i	$0.107126\pi$
$367$			12.6525i			0.660457i	−0.943901	+	0.330229i	$0.892874\pi$
$368$	1.01536	−	3.86898i	0.0529294	−	0.201685i
$369$	19.9518	+	14.5831i	1.03865	+	0.759164i
$370$	4.80372	−	1.63754i	0.249733	−	0.0851318i
$371$	2.51215			0.130425
$372$	5.64259	−	11.8649i	0.292555	−	0.615169i
$373$	−22.3439			−1.15693			−0.578463	−	0.815709i	$-0.696347\pi$
$373$	−22.3439			−1.15693			−0.578463	+	0.815709i	$0.696347\pi$
$374$	10.4773	−	3.57163i	0.541770	−	0.184684i
$375$	−17.5324	+	8.90168i	−0.905369	+	0.459681i
$376$	−17.9750	−	11.9103i	−0.926988	−	0.614227i
$377$			18.8876i			0.972762i
$378$	−8.15629	+	1.37635i	−0.419514	+	0.0707920i
$379$			3.26510i			0.167717i	0.996478	+	0.0838585i	$0.0267244\pi$
$379$			3.26510i			0.167717i	−0.996478	+	0.0838585i	$0.973276\pi$
$380$	−13.2240	+	10.2013i	−0.678376	+	0.523317i
$381$	−13.6019	+	6.90608i	−0.696848	+	0.353809i
$382$	5.45589	+	16.0048i	0.279148	+	0.818877i
$383$	−37.8875			−1.93596			−0.967979	−	0.251030i	$-0.919231\pi$
$383$	−37.8875			−1.93596			−0.967979	+	0.251030i	$0.919231\pi$
$384$	−18.2554	−	7.12314i	−0.931594	−	0.363501i
$385$	−2.69766			−0.137485
$386$	−5.18219	−	15.2019i	−0.263767	−	0.773757i
$387$	−9.02189	−	6.59424i	−0.458608	−	0.335204i
$388$	18.9419	−	14.6123i	0.961630	−	0.741827i
$389$		−	0.929471i		−	0.0471261i	−0.999722	−	0.0235630i	$-0.992499\pi$
$389$		−	0.929471i		−	0.0471261i	0.999722	−	0.0235630i	$-0.00750104\pi$
$390$	−12.8488	−	12.5203i	−0.650624	−	0.633989i
$391$			4.65065i			0.235193i
$392$	−13.5172	−	8.95659i	−0.682723	−	0.452376i
$393$	−14.3804	−	28.3230i	−0.725394	−	1.42871i
$394$	6.20336	−	2.11467i	0.312521	−	0.106536i
$395$	−7.50852			−0.377795
$396$	0.261504	+	10.0949i	0.0131411	+	0.507286i
$397$	−12.6204			−0.633398			−0.316699	−	0.948526i	$-0.602575\pi$
$397$	−12.6204			−0.633398			−0.316699	+	0.948526i	$0.602575\pi$
$398$	−24.3286	+	8.29340i	−1.21948	+	0.415710i
$399$	−5.17615	−	10.1947i	−0.259132	−	0.510375i
$400$	3.01798	−	11.4999i	0.150899	−	0.574994i
$401$			11.5308i			0.575823i	0.957657	+	0.287911i	$0.0929609\pi$
$401$			11.5308i			0.575823i	−0.957657	+	0.287911i	$0.907039\pi$
$402$	21.5766	+	21.0249i	1.07614	+	1.04863i
$403$			19.5074i			0.971735i
$404$	−1.35627	−	1.75813i	−0.0674768	−	0.0874701i
$405$	12.2109	−	3.89057i	0.606763	−	0.193324i
$406$	1.88615	+	5.53301i	0.0936082	+	0.274599i
$407$	4.24160			0.210249
$408$	22.6319	+	2.62281i	1.12045	+	0.129848i
$409$	23.2167			1.14799			0.573996	−	0.818858i	$-0.305393\pi$
$409$	23.2167			1.14799			0.573996	+	0.818858i	$0.305393\pi$
$410$	5.35259	+	15.7018i	0.264346	+	0.775455i
$411$	−8.90490	+	4.52127i	−0.439246	+	0.223018i
$412$	20.3570	+	26.3888i	1.00292	+	1.30008i
$413$			4.48501i			0.220693i
$414$	−4.04983	−	1.26447i	−0.199038	−	0.0621455i
$415$			18.3827i			0.902372i
$416$	29.0204	−	2.08982i	1.42284	−	0.102462i
$417$	3.73149	−	1.89458i	0.182732	−	0.0927781i
$418$	−13.2119	+	4.50381i	−0.646213	+	0.220288i
$419$	−29.3409			−1.43339			−0.716697	−	0.697384i	$-0.754347\pi$
$419$	−29.3409			−1.43339			−0.716697	+	0.697384i	$0.754347\pi$
$420$	−5.01427	−	2.38463i	−0.244672	−	0.116358i
$421$	−25.5900			−1.24718			−0.623591	−	0.781751i	$-0.714327\pi$
$421$	−25.5900			−1.24718			−0.623591	+	0.781751i	$0.714327\pi$
$422$	−17.3290	+	5.90731i	−0.843564	+	0.287563i
$423$	−13.4959	+	18.4644i	−0.656194	+	0.897770i
$424$	3.48671	−	5.26213i	0.169330	−	0.255552i
$425$			13.8232i			0.670525i
$426$	6.07647	−	6.23592i	0.294406	−	0.302131i
$427$			8.03914i			0.389041i
$428$	8.19681	−	6.32324i	0.396208	−	0.305645i
$429$	−6.78787	−	13.3691i	−0.327722	−	0.645467i
$430$	−2.42036	−	7.10010i	−0.116720	−	0.342397i
$431$	18.0908			0.871401			0.435700	−	0.900092i	$-0.356501\pi$
$431$	18.0908			0.871401			0.435700	+	0.900092i	$0.356501\pi$
$432$	−8.43742	+	18.9950i	−0.405945	+	0.913897i
$433$	−2.87373			−0.138103			−0.0690514	−	0.997613i	$-0.521997\pi$
$433$	−2.87373			−0.138103			−0.0690514	+	0.997613i	$0.521997\pi$
$434$	1.94805	+	5.71459i	0.0935094	+	0.274309i
$435$	−4.10028	−	8.07575i	−0.196593	−	0.387202i
$436$	2.97908	−	2.29814i	0.142672	−	0.110061i
$437$		−	5.86444i		−	0.280534i
$438$	−23.6160	+	24.2357i	−1.12842	+	1.15803i
$439$			27.8221i			1.32788i	0.747787	+	0.663939i	$0.231116\pi$
$439$			27.8221i			1.32788i	−0.747787	+	0.663939i	$0.768884\pi$
$440$	−3.74418	+	5.65069i	−0.178497	+	0.269386i
$441$	−10.1490	+	13.8853i	−0.483285	+	0.661204i
$442$	−32.0189	+	10.9150i	−1.52299	+	0.519172i
$443$	−3.54917			−0.168626			−0.0843131	−	0.996439i	$-0.526870\pi$
$443$	−3.54917			−0.168626			−0.0843131	+	0.996439i	$0.526870\pi$
$444$	7.88409	+	3.74942i	0.374162	+	0.177940i
$445$	22.6425			1.07336
$446$	−1.57578	+	0.537168i	−0.0746152	+	0.0254356i
$447$	26.3975	−	13.4028i	1.24856	−	0.633929i
$448$	8.29264	−	3.51023i	0.391790	−	0.165843i
$449$			12.1412i			0.572980i	0.958083	+	0.286490i	$0.0924885\pi$
$449$			12.1412i			0.572980i	−0.958083	+	0.286490i	$0.907511\pi$
$450$	−12.0374	−	3.75843i	−0.567448	−	0.177174i
$451$			13.8644i			0.652850i
$452$	13.3007	+	17.2417i	0.625614	+	0.810983i
$453$	−9.61033	+	4.87943i	−0.451533	+	0.229256i
$454$	−10.6993	−	31.3862i	−0.502142	−	1.47303i
$455$	8.24409			0.386489
$456$	−28.5388	−	3.30735i	−1.33645	−	0.154881i
$457$	−28.7263			−1.34376			−0.671879	−	0.740660i	$-0.734513\pi$
$457$	−28.7263			−1.34376			−0.671879	+	0.740660i	$0.734513\pi$
$458$	12.6235	+	37.0308i	0.589856	+	1.73034i
$459$	3.88254	−	23.8515i	0.181222	−	1.11329i
$460$	−1.73952	−	2.25494i	−0.0811057	−	0.105137i
$461$			22.0190i			1.02553i	0.858530	+	0.512763i	$0.171378\pi$
$461$			22.0190i			1.02553i	−0.858530	+	0.512763i	$0.828622\pi$
$462$	−3.32353	−	3.23855i	−0.154625	−	0.150671i
$463$		−	25.7220i		−	1.19540i	−0.801719	−	0.597701i	$-0.796081\pi$
$463$		−	25.7220i		−	1.19540i	0.801719	−	0.597701i	$-0.203919\pi$
$464$	14.2077	+	3.72861i	0.659575	+	0.173097i
$465$	−4.23484	−	8.34076i	−0.196386	−	0.386794i
$466$	18.1556	−	6.18907i	0.841041	−	0.286703i
$467$	18.8463			0.872105			0.436052	−	0.899921i	$-0.356376\pi$
$467$	18.8463			0.872105			0.436052	+	0.899921i	$0.356376\pi$
$468$	−0.799161	−	30.8501i	−0.0369412	−	1.42605i
$469$	−13.8441			−0.639259
$470$	−14.5312	+	4.95356i	−0.670275	+	0.228491i
$471$	−9.89493	−	19.4887i	−0.455934	−	0.897990i
$472$	9.39461	+	6.22492i	0.432422	+	0.286525i
$473$		−	6.26928i		−	0.288262i
$474$	−9.25055	−	9.01402i	−0.424892	−	0.414028i
$475$		−	17.4310i		−	0.799790i
$476$	−8.28976	+	6.39494i	−0.379961	+	0.293112i
$477$	−5.40541	−	3.95090i	−0.247497	−	0.180899i
$478$	13.6132	+	39.9343i	0.622655	+	1.82655i
$479$	0.112079			0.00512102			0.00256051	−	0.999997i	$-0.499185\pi$
$479$	0.112079			0.00512102			0.00256051	+	0.999997i	$0.499185\pi$
$480$	−11.9545	+	7.19352i	−0.545646	+	0.328338i
$481$	−12.9624			−0.591036
$482$	8.79698	+	25.8058i	0.400691	+	1.17542i
$483$	1.73840	−	0.882634i	0.0790999	−	0.0401612i
$484$	12.9336	−	9.97730i	0.587890	−	0.453514i
$485$		−	17.0328i		−	0.773421i
$486$	19.7145	+	9.86600i	0.894269	+	0.447531i
$487$		−	27.4672i		−	1.24466i	−0.782756	−	0.622329i	$-0.786187\pi$
$487$		−	27.4672i		−	1.24466i	0.782756	−	0.622329i	$-0.213813\pi$
$488$	16.8393	+	11.1578i	0.762280	+	0.505091i
$489$	22.7693	−	11.5606i	1.02966	−	0.522789i
$490$	−10.9275	+	3.72510i	−0.493656	+	0.168283i
$491$	11.2094			0.505875			0.252938	−	0.967483i	$-0.418603\pi$
$491$	11.2094			0.505875			0.252938	+	0.967483i	$0.418603\pi$
$492$	−12.2556	+	25.7705i	−0.552526	+	1.16182i
$493$	−17.0781			−0.769159
$494$	40.3757	−	13.7637i	1.81659	−	0.619259i
$495$	5.80456	+	4.24264i	0.260895	+	0.190693i
$496$	14.6739	+	3.85097i	0.658879	+	0.172914i
$497$			4.00111i			0.179474i
$498$	−22.0685	+	22.6476i	−0.988915	+	1.01486i
$499$			0.0293070i			0.00131196i	1.00000		0.000655980i	$0.000208805\pi$
$499$			0.0293070i			0.00131196i	−1.00000		0.000655980i	$0.999791\pi$
$500$	−13.8680	−	17.9771i	−0.620198	−	0.803962i
$501$	−16.5713	−	32.6382i	−0.740351	−	1.45817i
$502$	−5.80761	−	17.0366i	−0.259206	−	0.760379i
$503$	34.0242			1.51706			0.758532	−	0.651636i	$-0.225917\pi$
$503$	34.0242			1.51706			0.758532	+	0.651636i	$0.225917\pi$
$504$	−3.31486	−	8.95754i	−0.147656	−	0.399000i
$505$	−1.58093			−0.0703506
$506$	−0.767985	−	2.25288i	−0.0341411	−	0.100153i
$507$	10.5502	+	20.7792i	0.468551	+	0.922838i
$508$	−10.7591	−	13.9470i	−0.477356	−	0.618796i
$509$			3.40402i			0.150880i	0.997150	+	0.0754402i	$0.0240362\pi$
$509$			3.40402i			0.150880i	−0.997150	+	0.0754402i	$0.975964\pi$
$510$	11.3208	−	11.6178i	0.501292	−	0.514446i
$511$		−	15.5502i		−	0.687899i
$512$	4.15691	−	22.2423i	0.183711	−	0.982980i
$513$	−4.89587	+	30.0767i	−0.216158	+	1.32792i
$514$	21.2119	−	7.23093i	0.935615	−	0.318943i
$515$	23.7292			1.04563
$516$	5.54181	−	11.6530i	0.243965	−	0.512996i
$517$	−12.8308			−0.564300
$518$	−3.79726	+	1.29445i	−0.166842	+	0.0568750i
$519$	2.56475	−	1.30220i	0.112580	−	0.0571601i
$520$	11.4423	−	17.2686i	0.501778	−	0.757280i
$521$		−	18.1993i		−	0.797324i	−0.917098	−	0.398662i	$-0.869475\pi$
$521$		−	18.1993i		−	0.797324i	0.917098	−	0.398662i	$-0.130525\pi$
$522$	4.64340	−	14.8718i	0.203236	−	0.650920i
$523$		−	3.70416i		−	0.161972i	−0.996715	−	0.0809859i	$-0.974193\pi$
$523$		−	3.70416i		−	0.161972i	0.996715	−	0.0809859i	$-0.0258069\pi$
$524$	29.0415	−	22.4034i	1.26868	−	0.978695i
$525$	5.16708	−	2.62347i	0.225510	−	0.114498i
$526$	11.1631	+	32.7469i	0.486735	+	1.42783i
$527$	−17.6385			−0.768347
$528$	−11.3965	+	2.46678i	−0.495971	+	0.107353i
$529$	1.00000			0.0434783
$530$	−1.45014	−	4.25398i	−0.0629902	−	0.184781i
$531$	7.05364	−	9.65042i	0.306102	−	0.418792i
$532$	10.4533	−	8.06399i	0.453210	−	0.349618i
$533$		−	42.3699i		−	1.83525i
$534$	27.8957	+	27.1824i	1.20716	+	1.17630i
$535$		−	7.37069i		−	0.318663i
$536$	−19.2147	+	28.9987i	−0.829948	+	1.25255i
$537$	−0.543946	−	1.07133i	−0.0234730	−	0.0462314i
$538$	2.77037	−	0.944394i	0.119439	−	0.0407157i
$539$	−9.64883			−0.415605
$540$	7.03889	+	13.0170i	0.302906	+	0.560164i
$541$	−33.2070			−1.42768			−0.713840	−	0.700309i	$-0.753046\pi$
$541$	−33.2070			−1.42768			−0.713840	+	0.700309i	$0.753046\pi$
$542$	−31.7472	+	10.8223i	−1.36366	+	0.464858i
$543$	6.82273	+	13.4378i	0.292791	+	0.576670i
$544$	1.88961	+	26.2401i	0.0810162	+	1.12503i
$545$		−	2.67883i		−	0.114748i
$546$	10.1568	+	9.89708i	0.434670	+	0.423556i
$547$		−	3.26242i		−	0.139491i	−0.997565	−	0.0697456i	$-0.977781\pi$
$547$		−	3.26242i		−	0.139491i	0.997565	−	0.0697456i	$-0.0222188\pi$
$548$	−7.04374	−	9.13079i	−0.300893	−	0.390048i
$549$	12.6433	−	17.2978i	0.539601	−	0.738254i
$550$	−2.28270	−	6.69628i	−0.0973347	−	0.285530i
$551$	21.5354			0.917439
$552$	0.563966	−	4.86641i	0.0240040	−	0.207128i
$553$	5.93537			0.252398
$554$	−5.94837	−	17.4495i	−0.252722	−	0.741358i
$555$	5.54232	−	2.81399i	0.235258	−	0.119447i
$556$	2.95159	+	3.82615i	0.125175	+	0.162265i
$557$		−	9.81979i		−	0.416078i	−0.978121	−	0.208039i	$-0.933292\pi$
$557$		−	9.81979i		−	0.416078i	0.978121	−	0.208039i	$-0.0667081\pi$
$558$	4.79578	−	15.3598i	0.203022	−	0.650233i
$559$			19.1590i			0.810341i
$560$	1.62747	−	6.20139i	0.0687731	−	0.262056i
$561$	12.0883	−	6.13756i	0.510368	−	0.259128i
$562$	19.5404	−	6.66115i	0.824262	−	0.280983i
$563$	−40.6115			−1.71157			−0.855786	−	0.517329i	$-0.826926\pi$
$563$	−40.6115			−1.71157			−0.855786	+	0.517329i	$0.826926\pi$
$564$	−23.8493	−	11.3420i	−1.00424	−	0.477584i
$565$	15.5040			0.652258
$566$	−30.5089	+	10.4002i	−1.28239	+	0.437153i
$567$	−9.65250	+	3.07543i	−0.405367	+	0.129156i
$568$	8.38100	+	5.55329i	0.351659	+	0.233011i
$569$		−	9.32103i		−	0.390758i	−0.980728	−	0.195379i	$-0.937406\pi$
$569$		−	9.32103i		−	0.390758i	0.980728	−	0.195379i	$-0.0625937\pi$
$570$	−14.2754	+	14.6500i	−0.597932	+	0.613622i
$571$		−	45.0437i		−	1.88502i	−0.334178	−	0.942510i	$-0.608459\pi$
$571$		−	45.0437i		−	1.88502i	0.334178	−	0.942510i	$-0.391541\pi$
$572$	13.7082	−	10.5749i	0.573171	−	0.442159i
$573$	9.37553	+	18.4657i	0.391668	+	0.771414i
$574$	−4.23114	−	12.4120i	−0.176604	−	0.518067i
$575$	2.97232			0.123954
$576$	−23.3639	−	5.48898i	−0.973495	−	0.228708i
$577$	18.7099			0.778902			0.389451	−	0.921047i	$-0.372665\pi$
$577$	18.7099			0.778902			0.389451	+	0.921047i	$0.372665\pi$
$578$	−2.11203	−	6.19561i	−0.0878487	−	0.257703i
$579$	−8.90520	−	17.5393i	−0.370087	−	0.728909i
$580$	8.28060	−	6.38788i	0.343833	−	0.265242i
$581$		−	14.5312i		−	0.602858i
$582$	20.4480	−	20.9846i	0.847597	−	0.869838i
$583$		−	3.75620i		−	0.155566i
$584$	−32.5725	−	21.5827i	−1.34786	−	0.893098i
$585$	−17.7388	−	12.9656i	−0.733411	−	0.536062i
$586$	−36.3084	+	12.3772i	−1.49989	+	0.511297i
$587$	−4.79917			−0.198083			−0.0990415	−	0.995083i	$-0.531578\pi$
$587$	−4.79917			−0.198083			−0.0990415	+	0.995083i	$0.531578\pi$
$588$	−17.9348	−	8.52921i	−0.739618	−	0.351739i
$589$	22.2421			0.916470
$590$	7.59475	−	2.58898i	0.312671	−	0.106587i
$591$	7.15717	−	3.63389i	0.294407	−	0.149478i
$592$	−2.55892	+	9.75062i	−0.105171	+	0.400748i
$593$			37.6994i			1.54813i	0.633106	+	0.774065i	$0.281780\pi$
$593$			37.6994i			1.54813i	−0.633106	+	0.774065i	$0.718220\pi$
$594$	2.05794	+	12.1954i	0.0844382	+	0.500382i
$595$			7.45427i			0.305595i
$596$	20.8803	+	27.0672i	0.855291	+	1.10871i
$597$	−28.0693	+	14.2516i	−1.14880	+	0.583277i
$598$	2.34698	+	6.88484i	0.0959751	+	0.281542i
$599$	40.4030			1.65082			0.825411	−	0.564532i	$-0.190943\pi$
$599$	40.4030			1.65082			0.825411	+	0.564532i	$0.190943\pi$
$600$	1.67629	−	14.4645i	0.0684343	−	0.590512i
$601$	−8.44230			−0.344369			−0.172184	−	0.985065i	$-0.555082\pi$
$601$	−8.44230			−0.344369			−0.172184	+	0.985065i	$0.555082\pi$
$602$	1.91326	+	5.61252i	0.0779785	+	0.228749i
$603$	29.7883	+	21.7727i	1.21307	+	0.886654i
$604$	−7.60173	−	9.85412i	−0.309310	−	0.400958i
$605$		−	11.6301i		−	0.472829i
$606$	−1.94772	−	1.89792i	−0.0791207	−	0.0770976i
$607$		−	29.3385i		−	1.19081i	−0.803425	−	0.595406i	$-0.796991\pi$
$607$		−	29.3385i		−	1.19081i	0.803425	−	0.595406i	$-0.203009\pi$
$608$	−2.38278	−	33.0886i	−0.0966347	−	1.34192i
$609$	3.24121	+	6.38375i	0.131340	+	0.258683i
$610$	13.6132	−	4.64060i	0.551181	−	0.187893i
$611$	39.2113			1.58632
$612$	27.8945	−	0.722598i	1.12757	−	0.0292093i
$613$	22.9467			0.926809			0.463404	−	0.886147i	$-0.346628\pi$
$613$	22.9467			0.926809			0.463404	+	0.886147i	$0.346628\pi$
$614$	−24.1208	+	8.22256i	−0.973436	+	0.331835i
$615$	9.19801	+	18.1160i	0.370900	+	0.730509i
$616$	2.95972	−	4.46678i	0.119250	−	0.179972i
$617$		−	45.6198i		−	1.83658i	−0.395905	−	0.918292i	$-0.629569\pi$
$617$		−	45.6198i		−	1.83658i	0.395905	−	0.918292i	$-0.370431\pi$
$618$	29.2345	+	28.4870i	1.17599	+	1.14592i
$619$			29.6236i			1.19067i	0.803476	+	0.595337i	$0.202981\pi$
$619$			29.6236i			1.19067i	−0.803476	+	0.595337i	$0.797019\pi$
$620$	8.55234	−	6.59750i	0.343470	−	0.264962i
$621$	−5.12865	−	0.834839i	−0.205806	−	0.0335009i
$622$	7.03071	+	20.6245i	0.281906	+	0.826967i
$623$	−17.8985			−0.717089
$624$	34.8281	−	7.53854i	1.39424	−	0.301783i
$625$	−1.30368			−0.0521472
$626$	−0.545258	−	1.59951i	−0.0217929	−	0.0639292i
$627$	−15.2433	+	7.73944i	−0.608758	+	0.309083i
$628$	19.9830	−	15.4154i	0.797409	−	0.615143i
$629$		−	11.7206i		−	0.467330i
$630$	−6.49125	−	2.02676i	−0.258618	−	0.0807480i
$631$			21.9242i			0.872788i	0.899756	+	0.436394i	$0.143745\pi$
$631$			21.9242i			0.872788i	−0.899756	+	0.436394i	$0.856255\pi$
$632$	8.23792	−	12.4326i	0.327687	−	0.494543i
$633$	−19.9935	+	10.1512i	−0.794669	+	0.403476i
$634$	−6.59827	+	2.24929i	−0.262051	+	0.0893307i
$635$	−12.5413			−0.497687
$636$	3.32034	−	6.98184i	0.131660	−	0.276848i
$637$	29.4870			1.16832
$638$	8.27302	−	2.82020i	0.327532	−	0.111653i
$639$	6.29260	−	8.60920i	0.248931	−	0.340575i
$640$	−10.7310	−	12.0161i	−0.424181	−	0.474980i
$641$			31.3286i			1.23741i	0.785625	+	0.618704i	$0.212342\pi$
$641$			31.3286i			1.23741i	−0.785625	+	0.618704i	$0.787658\pi$
$642$	8.84855	−	9.08074i	0.349224	−	0.358388i
$643$		−	14.2291i		−	0.561141i	−0.959833	−	0.280570i	$-0.909476\pi$
$643$		−	14.2291i		−	0.561141i	0.959833	−	0.280570i	$-0.0905236\pi$
$644$	1.37507	+	1.78250i	0.0541852	+	0.0702402i
$645$	−4.15920	−	8.19179i	−0.163768	−	0.322552i
$646$	12.4451	+	36.5076i	0.489646	+	1.43637i
$647$	−22.6877			−0.891944			−0.445972	−	0.895047i	$-0.647142\pi$
$647$	−22.6877			−0.891944			−0.445972	+	0.895047i	$0.647142\pi$
$648$	−6.95505	+	24.4873i	−0.273220	+	0.961951i
$649$	6.70604			0.263235
$650$	6.97598	+	20.4640i	0.273620	+	0.802663i
$651$	3.34757	+	6.59324i	0.131202	+	0.258410i
$652$	18.0104	+	23.3469i	0.705342	+	0.914335i
$653$		−	47.5253i		−	1.85981i	−0.367799	−	0.929905i	$-0.619889\pi$
$653$		−	47.5253i		−	1.85981i	0.367799	−	0.929905i	$-0.380111\pi$
$654$	3.21595	−	3.30033i	0.125753	−	0.129053i
$655$		−	26.1145i		−	1.02038i
$656$	−31.8716	−	8.36426i	−1.24438	−	0.326570i
$657$	−24.4560	+	33.4594i	−0.954119	+	1.30537i
$658$	11.4867	−	3.91571i	0.447798	−	0.152650i
$659$	−19.0539			−0.742236			−0.371118	−	0.928586i	$-0.621025\pi$
$659$	−19.0539			−0.742236			−0.371118	+	0.928586i	$0.621025\pi$
$660$	−3.56552	+	7.49739i	−0.138788	+	0.291836i
$661$	8.25746			0.321178			0.160589	−	0.987021i	$-0.448661\pi$
$661$	8.25746			0.321178			0.160589	+	0.987021i	$0.448661\pi$
$662$	−16.7949	+	5.72524i	−0.652754	+	0.222518i
$663$	−36.9421	+	18.7565i	−1.43471	+	0.728443i
$664$	−30.4381	−	20.1685i	−1.18123	−	0.782688i
$665$		−	9.39980i		−	0.364509i
$666$	10.2064	+	3.18673i	0.395489	+	0.123483i
$667$			3.67220i			0.142188i
$668$	33.4661	−	25.8166i	1.29484	−	0.998875i
$669$	−1.81806	+	0.923081i	−0.0702904	+	0.0356884i
$670$	7.99150	+	23.4430i	0.308739	+	0.905681i
$671$	12.0202			0.464035
$672$	9.44985	−	5.68636i	0.364536	−	0.219356i
$673$	−30.1539			−1.16235			−0.581174	−	0.813779i	$-0.697407\pi$
$673$	−30.1539			−1.16235			−0.581174	+	0.813779i	$0.697407\pi$
$674$	9.63305	+	28.2585i	0.371051	+	1.08848i
$675$	−15.2440	−	2.48141i	−0.586742	−	0.0955096i
$676$	−21.3063	+	16.4363i	−0.819474	+	0.632164i
$677$			49.3523i			1.89676i	0.317133	+	0.948381i	$0.397280\pi$
$677$			49.3523i			1.89676i	−0.317133	+	0.948381i	$0.602720\pi$
$678$	19.1010	+	18.6126i	0.733571	+	0.714814i
$679$			13.4642i			0.516708i
$680$	15.6142	+	10.3461i	0.598778	+	0.396754i
$681$	−18.3859	−	36.2120i	−0.704548	−	1.38765i
$682$	8.54451	−	2.91274i	0.327186	−	0.111535i
$683$	−5.73685			−0.219514			−0.109757	−	0.993958i	$-0.535007\pi$
$683$	−5.73685			−0.219514			−0.109757	+	0.993958i	$0.535007\pi$
$684$	−35.1749	+	0.911192i	−1.34494	+	0.0348403i
$685$	−8.21054			−0.313708
$686$	19.1851	−	6.54004i	0.732492	−	0.249700i
$687$	21.6925	+	42.7246i	0.827619	+	1.63004i
$688$	14.4118	+	3.78219i	0.549446	+	0.144195i
$689$			11.4790i			0.437316i
$690$	−2.49811	−	2.43424i	−0.0951014	−	0.0926698i
$691$			6.45669i			0.245624i	0.992430	+	0.122812i	$0.0391912\pi$
$691$			6.45669i			0.245624i	−0.992430	+	0.122812i	$0.960809\pi$
$692$	2.02871	+	2.62981i	0.0771199	+	0.0999704i
$693$	−4.58841	−	3.35374i	−0.174299	−	0.127398i
$694$	0.792212	+	2.32395i	0.0300720	+	0.0882158i
$695$	3.44053			0.130507
$696$	17.8704	+	2.07100i	0.677377	+	0.0785010i
$697$	38.3107			1.45112
$698$	−6.83514	−	20.0508i	−0.258714	−	0.758935i
$699$	20.9471	−	10.6354i	0.792293	−	0.402269i
$700$	4.08714	+	5.29816i	0.154479	+	0.200251i
$701$		−	7.50410i		−	0.283426i	−0.989908	−	0.141713i	$-0.954739\pi$
$701$		−	7.50410i		−	0.283426i	0.989908	−	0.141713i	$-0.0452610\pi$
$702$	−6.28910	−	37.2693i	−0.237367	−	1.40664i
$703$			14.7796i			0.557422i
$704$	−5.24853	−	12.3992i	−0.197811	−	0.467314i
$705$	−16.7655	+	8.51231i	−0.631425	+	0.320592i
$706$	0.921860	−	0.314254i	0.0346947	−	0.0118271i
$707$	1.24970			0.0469999
$708$	12.4649	+	5.92789i	0.468458	+	0.222784i
$709$	38.2988			1.43834			0.719170	−	0.694834i	$-0.244522\pi$
$709$	38.2988			1.43834			0.719170	+	0.694834i	$0.244522\pi$
$710$	6.77532	−	2.30965i	0.254273	−	0.0866795i
$711$	−12.7712	−	9.33464i	−0.478956	−	0.350076i
$712$	−24.8420	+	37.4914i	−0.930994	+	1.40505i
$713$			3.79271i			0.142038i
$714$	−8.94889	+	9.18371i	−0.334904	+	0.343692i
$715$		−	12.3267i		−	0.460991i
$716$	1.09851	−	0.847419i	0.0410532	−	0.0316695i
$717$	23.3933	+	46.0745i	0.873638	+	1.72068i
$718$	−13.2522	−	38.8751i	−0.494566	−	1.45080i
$719$	−42.9789			−1.60284			−0.801422	−	0.598100i	$-0.795923\pi$
$719$	−42.9789			−1.60284			−0.801422	+	0.598100i	$0.795923\pi$
$720$	−13.2548	+	10.7840i	−0.493979	+	0.401896i
$721$	−18.7576			−0.698568
$722$	−7.02335	−	20.6029i	−0.261382	−	0.766761i
$723$	15.1169	+	29.7737i	0.562204	+	1.10729i
$724$	−13.7786	+	10.6292i	−0.512079	+	0.395032i
$725$			10.9150i			0.405372i
$726$	13.9619	−	14.3283i	0.518176	−	0.531773i
$727$			18.6182i			0.690511i	0.938509	+	0.345255i	$0.112208\pi$
$727$			18.6182i			0.690511i	−0.938509	+	0.345255i	$0.887792\pi$
$728$	−9.04495	+	13.6506i	−0.335228	+	0.505924i
$729$	25.6061	+	8.56319i	0.948374	+	0.317155i
$730$	−26.3321	+	8.97636i	−0.974593	+	0.332230i
$731$	−17.3235			−0.640733
$732$	22.3426	+	10.6254i	0.825805	+	0.392727i
$733$	−6.88546			−0.254320			−0.127160	−	0.991882i	$-0.540586\pi$
$733$	−6.88546			−0.254320			−0.127160	+	0.991882i	$0.540586\pi$
$734$	−16.9364	+	5.77346i	−0.625133	+	0.213102i
$735$	−12.6077	+	6.40129i	−0.465043	+	0.236115i
$736$	5.64224	−	0.406310i	0.207976	−	0.0149768i
$737$			20.6998i			0.762486i
$738$	−10.4164	+	33.3613i	−0.383432	+	1.22805i
$739$			4.21689i			0.155121i	0.996988	+	0.0775603i	$0.0247130\pi$
$739$			4.21689i			0.155121i	−0.996988	+	0.0775603i	$0.975287\pi$
$740$	4.38395	+	5.68291i	0.161157	+	0.208908i
$741$	46.5838	−	23.6519i	1.71130	−	0.868873i
$742$	1.14632	+	3.36271i	0.0420826	+	0.123449i
$743$	47.4143			1.73946			0.869731	−	0.493527i	$-0.164293\pi$
$743$	47.4143			1.73946			0.869731	+	0.493527i	$0.164293\pi$
$744$	18.4569	+	2.13896i	0.676662	+	0.0784181i
$745$	24.3392			0.891718
$746$	−10.1957	−	29.9091i	−0.373292	−	1.09505i
$747$	−22.8535	+	31.2669i	−0.836165	+	1.14400i
$748$	9.56178	+	12.3949i	0.349613	+	0.453204i
$749$			5.82642i			0.212893i
$750$	−19.9157	−	19.4065i	−0.727220	−	0.708626i
$751$		−	12.0897i		−	0.441158i	−0.975369	−	0.220579i	$-0.929205\pi$
$751$		−	12.0897i		−	0.441158i	0.975369	−	0.220579i	$-0.0707947\pi$
$752$	7.74072	−	29.4956i	0.282275	−	1.07559i
$753$	−9.97992	−	19.6560i	−0.363689	−	0.716306i
$754$	−25.2825	+	8.61858i	−0.920735	+	0.313870i
$755$	−8.86096			−0.322483
$756$	−5.56413	−	10.2898i	−0.202365	−	0.374235i
$757$	3.14493			0.114304			0.0571522	−	0.998365i	$-0.481798\pi$
$757$	3.14493			0.114304			0.0571522	+	0.998365i	$0.481798\pi$
$758$	−4.37058	+	1.48989i	−0.158747	+	0.0541153i
$759$	−1.31972	−	2.59927i	−0.0479029	−	0.0943476i
$760$	−19.6895	−	13.0463i	−0.714212	−	0.473240i
$761$			20.3562i			0.737910i	0.929447	+	0.368955i	$0.120284\pi$
$761$			20.3562i			0.737910i	−0.929447	+	0.368955i	$0.879716\pi$
$762$	−15.4510	−	15.0559i	−0.559730	−	0.545418i
$763$			2.11757i			0.0766612i
$764$	−18.9341	+	14.6062i	−0.685011	+	0.528436i
$765$	11.7234	−	16.0394i	0.423862	−	0.579905i
$766$	−17.2884	−	50.7152i	−0.624654	−	1.83241i
$767$	−20.4938			−0.739988
$768$	1.20476	−	27.6866i	0.0434731	−	0.999055i
$769$	−29.0487			−1.04752			−0.523762	−	0.851865i	$-0.675472\pi$
$769$	−29.0487			−1.04752			−0.523762	+	0.851865i	$0.675472\pi$
$770$	−1.23096	−	3.61102i	−0.0443608	−	0.130132i
$771$	24.4733	−	12.4258i	0.881385	−	0.447504i
$772$	17.9842	−	13.8735i	0.647266	−	0.499319i
$773$		−	10.1707i		−	0.365813i	−0.983130	−	0.182907i	$-0.941449\pi$
$773$		−	10.1707i		−	0.365813i	0.983130	−	0.182907i	$-0.0585506\pi$
$774$	4.71013	−	15.0855i	0.169302	−	0.542236i
$775$			11.2732i			0.404944i
$776$	28.2030	+	18.6875i	1.01243	+	0.670841i
$777$	−4.38112	+	2.22442i	−0.157172	+	0.0798004i
$778$	1.24417	−	0.424125i	0.0446055	−	0.0152056i
$779$	−48.3096			−1.73087
$780$	10.8963	−	22.9122i	0.390150	−	0.820388i
$781$	5.98250			0.214071
$782$	−6.22524	+	2.12213i	−0.222614	+	0.0758871i
$783$	3.06570	−	18.8334i	0.109559	−	0.673052i
$784$	5.82105	−	22.1808i	0.207894	−	0.792171i
$785$		−	17.9690i		−	0.641342i
$786$	31.3506	−	32.1732i	1.11824	−	1.14758i
$787$		−	39.7585i		−	1.41724i	−0.705591	−	0.708619i	$-0.749319\pi$
$787$		−	39.7585i		−	1.41724i	0.705591	−	0.708619i	$-0.250681\pi$
$788$	5.66129	+	7.33872i	0.201675	+	0.261431i
$789$	19.1830	+	37.7820i	0.682931	+	1.34507i
$790$	−3.42620	−	10.0507i	−0.121899	−	0.357589i
$791$	−12.2557			−0.435762
$792$	−13.3934	+	4.95641i	−0.475914	+	0.176118i
$793$	−36.7340			−1.30446
$794$	−5.75878	−	16.8933i	−0.204371	−	0.599521i
$795$	−2.49196	−	4.90806i	−0.0883807	−	0.174071i
$796$	−22.2027	−	28.7813i	−0.786953	−	1.02013i
$797$			1.92774i			0.0682842i	0.999417	+	0.0341421i	$0.0108699\pi$
$797$			1.92774i			0.0682842i	−0.999417	+	0.0341421i	$0.989130\pi$
$798$	11.2845	−	11.5806i	0.399467	−	0.409949i
$799$			35.4547i			1.25430i
$800$	16.7706	−	1.20769i	0.592929	−	0.0426982i
$801$	38.5123	+	28.1492i	1.36076	+	0.994604i
$802$	−15.4349	+	5.26162i	−0.545025	+	0.185794i
$803$	−23.2508			−0.820502
$804$	−18.2978	+	38.4757i	−0.645315	+	1.35693i
$805$	1.60285			0.0564929
$806$	−26.1122	+	8.90141i	−0.919762	+	0.313539i
$807$	3.19633	−	1.62287i	0.112516	−	0.0571276i
$808$	1.73451	−	2.61771i	0.0610198	−	0.0920908i
$809$			26.8795i			0.945032i	0.881322	+	0.472516i	$0.156654\pi$
$809$			26.8795i			0.945032i	−0.881322	+	0.472516i	$0.843346\pi$
$810$	10.7797	+	14.5699i	0.378761	+	0.511933i
$811$		−	33.4488i		−	1.17454i	−0.809389	−	0.587272i	$-0.800202\pi$
$811$		−	33.4488i		−	1.17454i	0.809389	−	0.587272i	$-0.199798\pi$
$812$	−6.54569	+	5.04952i	−0.229709	+	0.177203i
$813$	−36.6285	+	18.5973i	−1.28462	+	0.652236i
$814$	1.93548	+	5.67771i	0.0678385	+	0.199003i
$815$	20.9939			0.735383
$816$	6.81632	+	31.4914i	0.238619	+	1.10242i
$817$	21.8449			0.764255
$818$	10.5940	+	31.0773i	0.370409	+	1.08659i
$819$	14.0223	+	10.2491i	0.489978	+	0.358133i
$820$	−18.5756	+	14.3297i	−0.648687	+	0.500415i
$821$		−	6.68055i		−	0.233153i	−0.993182	−	0.116576i	$-0.962808\pi$
$821$		−	6.68055i		−	0.233153i	0.993182	−	0.116576i	$-0.0371920\pi$
$822$	−10.1154	−	9.85679i	−0.352816	−	0.343795i
$823$		−	3.67845i		−	0.128223i	−0.997943	−	0.0641113i	$-0.979579\pi$
$823$		−	3.67845i		−	0.128223i	0.997943	−	0.0641113i	$-0.0204213\pi$
$824$	−26.0343	+	39.2909i	−0.906949	+	1.36876i
$825$	−3.92264	−	7.72588i	−0.136569	−	0.268981i
$826$	−6.00353	+	2.04655i	−0.208889	+	0.0712085i
$827$	−29.3519			−1.02067			−0.510334	−	0.859977i	$-0.670478\pi$
$827$	−29.3519			−1.02067			−0.510334	+	0.859977i	$0.670478\pi$
$828$	−0.155376	−	5.99799i	−0.00539968	−	0.208444i
$829$	13.3676			0.464274			0.232137	−	0.972683i	$-0.425428\pi$
$829$	13.3676			0.464274			0.232137	+	0.972683i	$0.425428\pi$
$830$	−24.6066	+	8.38818i	−0.854109	+	0.291158i
$831$	−10.2218	−	20.1325i	−0.354591	−	0.698388i
$832$	16.0396	+	37.8923i	0.556073	+	1.31368i
$833$			26.6620i			0.923785i
$834$	4.23875	+	4.13037i	0.146776	+	0.143023i
$835$		−	30.0932i		−	1.04142i
$836$	−12.0574	−	15.6300i	−0.417013	−	0.540573i
$837$	3.16630	−	19.4515i	0.109443	−	0.672341i
$838$	−13.3885	−	39.2749i	−0.462497	−	1.35673i
$839$	7.53668			0.260195			0.130098	−	0.991501i	$-0.458471\pi$
$839$	7.53668			0.260195			0.130098	+	0.991501i	$0.458471\pi$
$840$	0.903952	−	7.80011i	0.0311893	−	0.269129i
$841$	15.5149			0.534998
$842$	−11.6769	−	34.2542i	−0.402414	−	1.18048i
$843$	22.5449	−	11.4467i	0.776487	−	0.394244i
$844$	−15.8147	−	20.5006i	−0.544366	−	0.705661i
$845$			19.1590i			0.659088i
$846$	−30.8743	−	9.63985i	−1.06148	−	0.331425i
$847$			9.19337i			0.315888i
$848$	8.63477	+	2.26608i	0.296519	+	0.0778174i
$849$	−35.1999	+	17.8719i	−1.20806	+	0.613364i
$850$	−18.5034	+	6.30765i	−0.634662	+	0.216351i
$851$	−2.52020			−0.0863914
$852$	11.1200	+	5.28831i	0.380964	+	0.181175i
$853$	36.6618			1.25528			0.627638	−	0.778506i	$-0.284022\pi$
$853$	36.6618			1.25528			0.627638	+	0.778506i	$0.284022\pi$
$854$	−10.7610	+	3.66832i	−0.368234	+	0.125527i
$855$	−14.7832	+	20.2256i	−0.505575	+	0.691700i
$856$	12.2044	+	8.08670i	0.417138	+	0.276398i
$857$		−	22.2605i		−	0.760404i	−0.924903	−	0.380202i	$-0.875854\pi$
$857$		−	22.2605i		−	0.760404i	0.924903	−	0.380202i	$-0.124146\pi$
$858$	14.7982	−	15.1865i	0.505202	−	0.518459i
$859$		−	19.7600i		−	0.674201i	−0.941469	−	0.337100i	$-0.890554\pi$
$859$		−	19.7600i		−	0.674201i	0.941469	−	0.337100i	$-0.109446\pi$
$860$	8.39959	−	6.47967i	0.286424	−	0.220955i
$861$	−7.27088	−	14.3204i	−0.247791	−	0.488039i
$862$	8.25496	+	24.2158i	0.281165	+	0.824794i
$863$	40.1334			1.36616			0.683078	−	0.730345i	$-0.260641\pi$
$863$	40.1334			1.36616			0.683078	+	0.730345i	$0.260641\pi$
$864$	−29.2763	−	2.62654i	−0.996000	−	0.0893568i
$865$	2.36476			0.0804044
$866$	−1.31131	−	3.84671i	−0.0445600	−	0.130716i
$867$	−3.62935	−	7.14823i	−0.123259	−	0.242766i
$868$	−6.76049	+	5.21522i	−0.229466	+	0.177016i
$869$		−	8.87462i		−	0.301051i
$870$	8.93900	−	9.17356i	0.303061	−	0.311013i
$871$		−	63.2589i		−	2.14345i
$872$	4.43561	+	2.93906i	0.150209	+	0.0995290i
$873$	21.1753	−	28.9709i	0.716676	−	0.980518i
$874$	7.85000	−	2.67599i	0.265530	−	0.0905168i
$875$	12.7784			0.431989
$876$	−43.2174	−	20.5528i	−1.46018	−	0.694416i
$877$	−6.22608			−0.210240			−0.105120	−	0.994460i	$-0.533523\pi$
$877$	−6.22608			−0.210240			−0.105120	+	0.994460i	$0.533523\pi$
$878$	−37.2420	+	12.6955i	−1.25686	+	0.428451i
$879$	−41.8911	+	21.2693i	−1.41295	+	0.717394i
$880$	−9.27238	−	2.43341i	−0.312572	−	0.0820302i
$881$		−	18.1502i		−	0.611496i	−0.952112	−	0.305748i	$-0.901093\pi$
$881$		−	18.1502i		−	0.611496i	0.952112	−	0.305748i	$-0.0989066\pi$
$882$	−23.2176	−	7.24920i	−0.781776	−	0.244093i
$883$			7.83604i			0.263704i	0.991269	+	0.131852i	$0.0420923\pi$
$883$			7.83604i			0.263704i	−0.991269	+	0.131852i	$0.957908\pi$
$884$	−29.2210	−	37.8792i	−0.982809	−	1.27401i
$885$	8.76249	−	4.44896i	0.294548	−	0.149550i
$886$	−1.61952	−	4.75083i	−0.0544087	−	0.159607i
$887$	10.4966			0.352443			0.176221	−	0.984351i	$-0.443613\pi$
$887$	10.4966			0.352443			0.176221	+	0.984351i	$0.443613\pi$
$888$	−1.42131	+	12.2643i	−0.0476960	+	0.411564i
$889$	9.91371			0.332495
$890$	10.3319	+	30.3086i	0.346327	+	1.01595i
$891$	4.59842	+	14.4325i	0.154053	+	0.483507i
$892$	−1.43808	−	1.86418i	−0.0481504	−	0.0624174i
$893$		−	44.7082i		−	1.49610i
$894$	29.9860	+	29.2193i	1.00288	+	0.977239i
$895$		−	0.987795i		−	0.0330184i
$896$	8.48270	+	9.49858i	0.283387	+	0.317325i
$897$	4.03310	+	7.94343i	0.134661	+	0.265223i
$898$	−16.2519	+	5.54014i	−0.542334	+	0.184877i
$899$	−13.9276			−0.464511
$900$	−0.461827	−	17.8280i	−0.0153942	−	0.594265i
$901$	−10.3793			−0.345784
$902$	−18.5586	+	6.32644i	−0.617932	+	0.210648i
$903$	3.28778	+	6.47548i	0.109411	+	0.215491i
$904$	−17.0101	+	25.6716i	−0.565748	+	0.853823i
$905$			12.3900i			0.411856i
$906$	−10.9168	−	10.6376i	−0.362685	−	0.353412i
$907$			5.19923i			0.172637i	0.996268	+	0.0863187i	$0.0275103\pi$
$907$			5.19923i			0.172637i	−0.996268	+	0.0863187i	$0.972490\pi$
$908$	37.1306	−	28.6436i	1.23222	−	0.950570i
$909$	−2.68899	−	1.96542i	−0.0891881	−	0.0651890i
$910$	3.76185	+	11.0353i	0.124704	+	0.365818i
$911$	30.3688			1.00616			0.503081	−	0.864239i	$-0.332200\pi$
$911$	30.3688			1.00616			0.503081	+	0.864239i	$0.332200\pi$
$912$	−8.59534	−	39.7105i	−0.284620	−	1.31494i
$913$	−21.7273			−0.719067
$914$	−13.1080	−	38.4523i	−0.433575	−	1.27189i
$915$	15.7063	−	7.97452i	0.519234	−	0.263629i
$916$	−43.8084	+	33.7949i	−1.44747	+	1.11662i
$917$			20.6431i			0.681695i
$918$	33.6987	−	5.68657i	1.11222	−	0.187685i
$919$			11.0039i			0.362984i	0.983392	+	0.181492i	$0.0580926\pi$
$919$			11.0039i			0.362984i	−0.983392	+	0.181492i	$0.941907\pi$
$920$	2.22465	−	3.35743i	0.0733446	−	0.110691i
$921$	−27.8295	+	14.1298i	−0.917014	+	0.465593i
$922$	−29.4741	+	10.0474i	−0.970677	+	0.330895i
$923$	−18.2826			−0.601781
$924$	2.81849	−	5.92657i	0.0927215	−	0.194970i
$925$	−7.49086			−0.246298
$926$	34.4308	−	11.7371i	1.13147	−	0.385706i
$927$	40.3607	+	29.5003i	1.32562	+	0.968916i
$928$	1.49205	+	20.7195i	0.0489791	+	0.680149i
$929$			56.7119i			1.86066i	0.366729	+	0.930328i	$0.380478\pi$
$929$			56.7119i			1.86066i	−0.366729	+	0.930328i	$0.619522\pi$
$930$	9.23235	−	9.47460i	0.302741	−	0.310685i
$931$		−	33.6207i		−	1.10187i
$932$	16.5691	+	21.4785i	0.542738	+	0.703551i
$933$	12.0817	+	23.7957i	0.395538	+	0.779035i
$934$	8.59974	+	25.2272i	0.281392	+	0.825461i
$935$	11.1457			0.364503
$936$	40.9305	−	15.1469i	1.33786	−	0.495092i
$937$	−34.7161			−1.13413			−0.567064	−	0.823674i	$-0.691921\pi$
$937$	−34.7161			−1.13413			−0.567064	+	0.823674i	$0.691921\pi$
$938$	−6.31715	−	18.5313i	−0.206262	−	0.605069i
$939$	−0.936982	−	1.84544i	−0.0305773	−	0.0602237i
$940$	−13.2614	−	17.1908i	−0.432540	−	0.560702i
$941$			10.5373i			0.343507i	0.985140	+	0.171754i	$0.0549433\pi$
$941$			10.5373i			0.343507i	−0.985140	+	0.171754i	$0.945057\pi$
$942$	21.5719	−	22.1379i	0.702850	−	0.721293i
$943$		−	8.23771i		−	0.268257i
$944$	−4.04569	+	15.4159i	−0.131676	+	0.501744i
$945$	−8.22044	−	1.33812i	−0.267411	−	0.0435290i
$946$	8.39190	−	2.86072i	0.272844	−	0.0930101i
$947$	−4.19362			−0.136274			−0.0681372	−	0.997676i	$-0.521706\pi$
$947$	−4.19362			−0.136274			−0.0681372	+	0.997676i	$0.521706\pi$
$948$	7.84484	−	16.4957i	0.254789	−	0.535756i
$949$	71.0549			2.30654
$950$	23.3327	−	7.95391i	0.757013	−	0.258059i
$951$	−7.61280	+	3.86523i	−0.246862	+	0.125339i
$952$	−12.3428	−	8.17840i	−0.400032	−	0.265064i
$953$			2.24336i			0.0726695i	0.999340	+	0.0363347i	$0.0115683\pi$
$953$			2.24336i			0.0726695i	−0.999340	+	0.0363347i	$0.988432\pi$
$954$	2.82204	−	9.03837i	0.0913670	−	0.292628i
$955$			17.0258i			0.550942i
$956$	−47.2432	+	36.4447i	−1.52795	+	1.17870i
$957$	9.54505	−	4.84629i	0.308548	−	0.156658i
$958$	0.0511425	+	0.150026i	0.00165234	+	0.00484712i
$959$	6.49030			0.209583
$960$	−15.0840	−	12.7195i	−0.486834	−	0.410521i
$961$	16.6154			0.535979
$962$	−5.91486	−	17.3512i	−0.190703	−	0.559425i
$963$	9.16328	−	12.5367i	0.295283	−	0.403990i
$964$	−30.5289	+	23.5508i	−0.983270	+	0.758521i
$965$		−	16.1717i		−	0.520585i
$966$	1.97472	+	1.92423i	0.0635355	+	0.0619109i
$967$		−	6.60501i		−	0.212403i	−0.994345	−	0.106201i	$-0.966131\pi$
$967$		−	6.60501i		−	0.212403i	0.994345	−	0.106201i	$-0.0338688\pi$
$968$	19.2571	+	12.7598i	0.618945	+	0.410117i
$969$	21.3859	+	42.1208i	0.687015	+	1.35312i
$970$	22.7997	−	7.77222i	0.732055	−	0.249551i
$971$	31.3795			1.00702			0.503508	−	0.863990i	$-0.332042\pi$
$971$	31.3795			1.00702			0.503508	+	0.863990i	$0.332042\pi$
$972$	−4.21049	+	30.8913i	−0.135051	+	0.990839i
$973$	−2.71968			−0.0871890
$974$	36.7669	−	12.5335i	1.17809	−	0.401599i
$975$	11.9877	+	23.6104i	0.383913	+	0.756139i
$976$	−7.25167	+	27.6321i	−0.232120	+	0.884482i
$977$			33.9220i			1.08526i	0.839971	+	0.542631i	$0.182572\pi$
$977$			33.9220i			1.08526i	−0.839971	+	0.542631i	$0.817428\pi$
$978$	25.8646	+	25.2032i	0.827058	+	0.805911i
$979$			26.7620i			0.855318i
$980$	−9.97264	−	12.9275i	−0.318564	−	0.412955i
$981$	3.33033	−	4.55638i	0.106329	−	0.145474i
$982$	5.11496	+	15.0047i	0.163225	+	0.478819i
$983$	−47.8056			−1.52476			−0.762381	−	0.647128i	$-0.775970\pi$
$983$	−47.8056			−1.52476			−0.762381	+	0.647128i	$0.775970\pi$
$984$	−40.0881	−	4.64579i	−1.27796	−	0.148102i
$985$	6.59908			0.210264
$986$	−7.79288	−	22.8603i	−0.248176	−	0.728021i
$987$	13.2529	−	6.72885i	0.421843	−	0.214182i
$988$	36.8475	+	47.7655i	1.17228	+	1.51962i
$989$			3.72497i			0.118447i
$990$	−3.03043	+	9.70579i	−0.0963133	+	0.308470i
$991$			58.8306i			1.86881i	0.356207	+	0.934407i	$0.384070\pi$
$991$			58.8306i			1.86881i	−0.356207	+	0.934407i	$0.615930\pi$
$992$	1.54102	+	21.3994i	0.0489273	+	0.679431i
$993$	−19.3773	+	9.83838i	−0.614919	+	0.312212i
$994$	−5.35579	+	1.82574i	−0.169875	+	0.0579089i
$995$	−25.8806			−0.820469
$996$	−40.3856	−	19.2061i	−1.27967	−	0.608569i
$997$	7.97211			0.252479			0.126240	−	0.992000i	$-0.459709\pi$
$997$	7.97211			0.252479			0.126240	+	0.992000i	$0.459709\pi$
$998$	−0.0392296	+	0.0133730i	−0.00124179	+	0.000423315i
$999$	12.9252	+	2.10396i	0.408936	+	0.0665665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.c.a.47.14	yes	22
3.2	odd	2		276.2.c.b.47.9	yes	22
4.3	odd	2		276.2.c.b.47.10	yes	22
12.11	even	2	inner	276.2.c.a.47.13	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.c.a.47.13	✓	22	12.11	even	2	inner
276.2.c.a.47.14	yes	22	1.1	even	1	trivial
276.2.c.b.47.9	yes	22	3.2	odd	2
276.2.c.b.47.10	yes	22	4.3	odd	2

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.456308 + 1.33857i) q^{2} +(0.784130 + 1.54439i) q^{3} +(-1.58357 + 1.22161i) q^{4} +1.42397i q^{5} +(-1.70948 + 1.75433i) q^{6} -1.12562i q^{7} +(-2.35780 - 1.56229i) q^{8} +(-1.77028 + 2.42200i) q^{9} +O(q^{10})\)	\(q+(0.456308 + 1.33857i) q^{2} +(0.784130 + 1.54439i) q^{3} +(-1.58357 + 1.22161i) q^{4} +1.42397i q^{5} +(-1.70948 + 1.75433i) q^{6} -1.12562i q^{7} +(-2.35780 - 1.56229i) q^{8} +(-1.77028 + 2.42200i) q^{9} +(-1.90608 + 0.649767i) q^{10} -1.68304 q^{11} +(-3.12836 - 1.48775i) q^{12} +5.14341 q^{13} +(1.50673 - 0.513630i) q^{14} +(-2.19916 + 1.11657i) q^{15} +(1.01536 - 3.86898i) q^{16} +4.65065i q^{17} +(-4.04983 - 1.26447i) q^{18} -5.86444i q^{19} +(-1.73952 - 2.25494i) q^{20} +(1.73840 - 0.882634i) q^{21} +(-0.767985 - 2.25288i) q^{22} +1.00000 q^{23} +(0.563966 - 4.86641i) q^{24} +2.97232 q^{25} +(2.34698 + 6.88484i) q^{26} +(-5.12865 - 0.834839i) q^{27} +(1.37507 + 1.78250i) q^{28} +3.67220i q^{29} +(-2.49811 - 2.43424i) q^{30} +3.79271i q^{31} +(5.64224 - 0.406310i) q^{32} +(-1.31972 - 2.59927i) q^{33} +(-6.22524 + 2.12213i) q^{34} +1.60285 q^{35} +(-0.155376 - 5.99799i) q^{36} -2.52020 q^{37} +(7.85000 - 2.67599i) q^{38} +(4.03310 + 7.94343i) q^{39} +(2.22465 - 3.35743i) q^{40} -8.23771i q^{41} +(1.97472 + 1.92423i) q^{42} +3.72497i q^{43} +(2.66521 - 2.05601i) q^{44} +(-3.44885 - 2.52082i) q^{45} +(0.456308 + 1.33857i) q^{46} +7.62360 q^{47} +(6.77140 - 1.46567i) q^{48} +5.73298 q^{49} +(1.35629 + 3.97868i) q^{50} +(-7.18241 + 3.64671i) q^{51} +(-8.14493 + 6.28321i) q^{52} +2.23179i q^{53} +(-1.22275 - 7.24603i) q^{54} -2.39659i q^{55} +(-1.75855 + 2.65400i) q^{56} +(9.05699 - 4.59848i) q^{57} +(-4.91552 + 1.67565i) q^{58} -3.98448 q^{59} +(2.11850 - 4.45467i) q^{60} -7.14195 q^{61} +(-5.07682 + 1.73064i) q^{62} +(2.72626 + 1.99267i) q^{63} +(3.11848 + 7.36716i) q^{64} +7.32404i q^{65} +(2.87712 - 2.95262i) q^{66} -12.2990i q^{67} +(-5.68125 - 7.36460i) q^{68} +(0.784130 + 1.54439i) q^{69} +(0.731392 + 2.14553i) q^{70} -3.55458 q^{71} +(7.95786 - 2.94491i) q^{72} +13.8147 q^{73} +(-1.14999 - 3.37348i) q^{74} +(2.33069 + 4.59043i) q^{75} +(7.16403 + 9.28673i) q^{76} +1.89447i q^{77} +(-8.79254 + 9.02326i) q^{78} +5.27297i q^{79} +(5.50930 + 1.44584i) q^{80} +(-2.73221 - 8.57526i) q^{81} +(11.0268 - 3.75894i) q^{82} +12.9095 q^{83} +(-1.67464 + 3.52135i) q^{84} -6.62236 q^{85} +(-4.98615 + 1.69973i) q^{86} +(-5.67131 + 2.87948i) q^{87} +(3.96828 + 2.62940i) q^{88} -15.9010i q^{89} +(1.80057 - 5.76681i) q^{90} -5.78953i q^{91} +(-1.58357 + 1.22161i) q^{92} +(-5.85742 + 2.97398i) q^{93} +(3.47871 + 10.2048i) q^{94} +8.35076 q^{95} +(5.05175 + 8.39522i) q^{96} -11.9616 q^{97} +(2.61600 + 7.67402i) q^{98} +(2.97946 - 4.07633i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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