LMFDB - Embedded newform 276.2.c.b.47.9

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			47.9
Character	$\chi$	$=$	276.47
Dual form			276.2.c.b.47.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.456308 - 1.33857i) q^{2} +(-0.784130 + 1.54439i) q^{3} +(-1.58357 + 1.22161i) q^{4} -1.42397i q^{5} +(2.42509 + 0.344899i) q^{6} -1.12562i q^{7} +(2.35780 + 1.56229i) q^{8} +(-1.77028 - 2.42200i) q^{9} +O(q^{10})$	\(q+(-0.456308 - 1.33857i) q^{2} +(-0.784130 + 1.54439i) q^{3} +(-1.58357 + 1.22161i) q^{4} -1.42397i q^{5} +(2.42509 + 0.344899i) 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} +(-0.644914 - 3.40354i) 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} +(-2.43424 + 3.47483i) 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} +(-4.26161 + 2.41633i) 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} +(0.491124 - 3.45324i) 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} +(5.76209 + 1.67282i) 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} +(0.388226 - 2.72973i) 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} +(5.17905 + 4.60190i) 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} +(-3.45774 - 6.48414i) 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} +(-4.84652 + 0.918335i) 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} +(4.08152 + 0.580479i) 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} +(-0.390094 - 8.47631i) 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} +(12.4732 + 1.77396i) 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} +(-3.83110 + 0.725929i) 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} +(4.94804 + 3.46627i) 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} +(3.79675 - 9.03242i) 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 + 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q + 9 * q^8 - 2 * q^9	$ 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) $ 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * 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	$-0.896852\pi$
$5$		−	1.42397i		−	0.636817i	0.947954	−	0.318408i	$-0.103148\pi$
$6$	2.42509	+	0.344899i	0.990037	+	0.140804i
$7$		−	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	$-0.418343\pi$
$11$	1.68304			0.507456			0.253728	+	0.967276i	$0.418343\pi$
$12$	−0.644914	−	3.40354i	−0.186171	−	0.982517i
$13$	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	$-0.809272\pi$
$17$		−	4.65065i		−	1.12795i	0.825793	−	0.563974i	$-0.190728\pi$
$18$	−2.43424	+	3.47483i	−0.573756	+	0.819026i
$19$		−	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
$24$	−4.26161	+	2.41633i	−0.869898	+	0.493231i
$25$	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	$-0.889250\pi$
$29$		−	3.67220i		−	0.681911i	0.940080	−	0.340955i	$-0.110750\pi$
$30$	0.491124	−	3.45324i	0.0896665	−	0.630472i
$31$			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
$36$	5.76209	+	1.67282i	0.960348	+	0.278803i
$37$	−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	$0.222417\pi$
$41$			8.23771i			1.28651i	−0.765650	+	0.643257i	$0.777583\pi$
$42$	0.388226	−	2.72973i	0.0599045	−	0.421207i
$43$			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	$-0.687668\pi$
$47$	−7.62360			−1.11202			−0.556008	+	0.831177i	$0.687668\pi$
$48$	5.17905	+	4.60190i	0.747531	+	0.664227i
$49$	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	$-0.951016\pi$
$53$		−	2.23179i		−	0.306560i	0.988183	−	0.153280i	$-0.0489837\pi$
$54$	−3.45774	−	6.48414i	−0.470539	−	0.882379i
$55$		−	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	$-0.416486\pi$
$59$	3.98448			0.518735			0.259367	+	0.965779i	$0.416486\pi$
$60$	−4.84652	+	0.918335i	−0.625683	+	0.118556i
$61$	−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
$66$	4.08152	+	0.580479i	0.502400	+	0.0714520i
$67$		−	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	$-0.432352\pi$
$71$	3.55458			0.421851			0.210925	+	0.977502i	$0.432352\pi$
$72$	−0.390094	−	8.47631i	−0.0459731	−	0.998943i
$73$	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
$78$	12.4732	+	1.77396i	1.41231	+	0.200861i
$79$			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	$-0.750629\pi$
$83$	−12.9095			−1.41700			−0.708502	+	0.705709i	$0.750629\pi$
$84$	−3.83110	+	0.725929i	−0.418007	+	0.0792053i
$85$	−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	$0.319065\pi$
$89$			15.9010i			1.68550i	−0.538303	+	0.842751i	$0.680935\pi$
$90$	4.94804	+	3.46627i	0.521570	+	0.365377i
$91$		−	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
$96$	3.79675	−	9.03242i	0.387504	−	0.921868i
$97$	−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	$-0.982409\pi$
$101$		−	1.11023i		−	0.110472i	0.998473	−	0.0552362i	$-0.0175912\pi$
$102$	1.60400	−	11.2782i	0.158820	−	1.11671i
$103$		−	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	$-0.419504\pi$
$107$	5.17617			0.500400			0.250200	+	0.968194i	$0.419504\pi$
$108$	−7.10171	+	7.58721i	−0.683362	+	0.730079i
$109$	−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	$0.171141\pi$
$113$			10.8879i			1.02425i	−0.858911	+	0.512124i	$0.828859\pi$
$114$	2.02264	−	14.2218i	0.189437	−	1.33199i
$115$			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
$120$	3.44077	+	6.06839i	0.314098	+	0.553966i
$121$	−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
$126$	3.91135	+	2.74003i	0.348451	+	0.244102i
$127$			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	$-0.204219\pi$
$131$	18.3393			1.60231			0.801155	+	0.598457i	$0.204219\pi$
$132$	−1.08542	−	5.72830i	−0.0944734	−	0.498584i
$133$	−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	$-0.920782\pi$
$137$		−	5.76597i		−	0.492620i	0.969191	−	0.246310i	$-0.0792181\pi$
$138$	−2.42509	−	0.344899i	−0.206437	−	0.0293597i
$139$		−	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
$144$	−11.1682	+	4.38998i	−0.930681	+	0.365832i
$145$	−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	$0.246878\pi$
$149$			17.0925i			1.40027i	−0.714008	+	0.700137i	$0.753122\pi$
$150$	7.20814	+	1.02515i	0.588542	+	0.0837032i
$151$			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
$156$	−3.31705	−	17.5058i	−0.265577	−	1.40159i
$157$	−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
$162$	12.7254	−	0.255692i	0.999798	−	0.0200891i
$163$		−	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	$-0.195263\pi$
$167$	21.1334			1.63535			0.817674	+	0.575681i	$0.195263\pi$
$168$	2.71987	+	4.79697i	0.209843	+	0.370094i
$169$	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	$0.0201083\pi$
$173$			1.66069i			0.126260i	−0.998005	+	0.0631299i	$0.979892\pi$
$174$	1.26654	−	8.90540i	0.0960160	−	0.675117i
$175$		−	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	$-0.491747\pi$
$179$	0.693693			0.0518491			0.0259245	+	0.999664i	$0.491747\pi$
$180$	2.38204	−	8.20502i	0.177546	−	0.611566i
$181$	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
$186$	−1.30810	+	9.19765i	−0.0959146	+	0.674404i
$187$		−	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	$-0.642395\pi$
$191$	−11.9566			−0.865150			−0.432575	+	0.901598i	$0.642395\pi$
$192$	−13.8231	−	0.960665i	−0.997594	−	0.0693300i
$193$	−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	$0.0527915\pi$
$197$			4.63430i			0.330180i	−0.986278	+	0.165090i	$0.947208\pi$
$198$	−4.09693	+	5.84829i	−0.291156	+	0.415620i
$199$			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
$204$	−15.8287	+	2.99927i	−1.10823	+	0.209991i
$205$	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
$210$	−3.88704	−	0.552820i	−0.268231	−	0.0381482i
$211$			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
$216$	13.3966	+	6.04407i	0.911524	+	0.411247i
$217$	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
$222$	−6.11171	−	0.869215i	−0.410191	−	0.0583379i
$223$			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	$-0.216168\pi$
$227$	23.4475			1.55626			0.778132	+	0.628101i	$0.216168\pi$
$228$	−19.9599	+	3.78206i	−1.32187	+	0.250473i
$229$	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	$0.146541\pi$
$233$			13.5634i			0.888566i	−0.895887	+	0.444283i	$0.853459\pi$
$234$	−12.5203	+	17.8725i	−0.818477	+	1.16836i
$235$			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	$-0.915392\pi$
$239$	−29.8334			−1.92976			−0.964882	+	0.262683i	$0.915392\pi$
$240$	6.55295	−	7.37478i	0.422991	−	0.476040i
$241$	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
$246$	−2.84118	+	19.9772i	−0.181147	+	1.27370i
$247$		−	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	$-0.368429\pi$
$251$	12.7274			0.803345			0.401673	+	0.915783i	$0.368429\pi$
$252$	1.88296	−	6.48593i	0.118615	−	0.408575i
$253$	−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	$0.164554\pi$
$257$			15.8466i			0.988484i	−0.869324	+	0.494242i	$0.835446\pi$
$258$	−1.28474	+	9.03337i	−0.0799842	+	0.562393i
$259$			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	$-0.772003\pi$
$263$	−24.4640			−1.50852			−0.754258	+	0.656578i	$0.772003\pi$
$264$	−7.17247	+	4.06678i	−0.441435	+	0.250293i
$265$	−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	$0.0200968\pi$
$269$			2.06964i			0.126188i	−0.998008	+	0.0630941i	$0.979903\pi$
$270$	−9.23319	+	4.92370i	−0.561914	+	0.299647i
$271$			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
$276$	0.644914	+	3.40354i	0.0388192	+	0.204869i
$277$	−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	$0.143400\pi$
$281$			14.5979i			0.870838i	−0.900228	+	0.435419i	$0.856600\pi$
$282$	−18.4879	−	2.62937i	−1.10094	−	0.156577i
$283$			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
$288$	10.9724	+	12.9463i	0.646557	+	0.762865i
$289$	−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	$-0.708873\pi$
$293$		−	27.1247i		−	1.58464i	0.610106	−	0.792320i	$-0.291127\pi$
$294$	13.9030	+	1.97730i	0.810837	+	0.115318i
$295$		−	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
$300$	−1.91689	−	10.1164i	−0.110672	−	0.584072i
$301$	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
$306$	16.1602	+	11.3208i	0.923819	+	0.647167i
$307$			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	$-0.643905\pi$
$311$	−15.4078			−0.873697			−0.436848	+	0.899535i	$0.643905\pi$
$312$	−21.9192	+	12.4282i	−1.24093	+	0.703606i
$313$	−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	$-0.955795\pi$
$317$		−	4.92932i		−	0.276858i	0.990372	−	0.138429i	$-0.0442053\pi$
$318$	0.769742	−	5.41229i	0.0431650	−	0.303506i
$319$		−	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
$324$	−6.14894	−	16.9172i	−0.341608	−	0.939843i
$325$	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
$330$	0.826582	−	5.81194i	0.0455018	−	0.319937i
$331$			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
$336$	5.18000	−	5.82965i	0.282592	−	0.318033i
$337$	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
$342$	20.3780	+	14.2755i	1.10191	+	0.771929i
$343$		−	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	$-0.514839\pi$
$347$	−1.73613			−0.0932006			−0.0466003	+	0.998914i	$0.514839\pi$
$348$	−12.4985	+	2.36825i	−0.669989	+	0.126952i
$349$	−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	$0.00583417\pi$
$353$			0.688688i			0.0366551i	−0.999832	+	0.0183276i	$0.994166\pi$
$354$	9.66270	+	1.37424i	0.513567	+	0.0730401i
$355$		−	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	$-0.222050\pi$
$359$	29.0421			1.53278			0.766392	+	0.642373i	$0.222050\pi$
$360$	−12.0700	+	0.555481i	−0.636143	+	0.0292764i
$361$	−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
$366$	−17.3199	−	2.46325i	−0.905323	−	0.128756i
$367$			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
$372$	12.9086	−	2.44597i	0.669282	−	0.126818i
$373$	−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
$378$	−7.29869	+	3.89211i	−0.375404	+	0.200188i
$379$			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	$-0.0807692\pi$
$383$	37.8875			1.93596			0.967979	+	0.251030i	$0.0807692\pi$
$384$	5.02165	+	18.9416i	0.256260	+	0.966608i
$385$	−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	$0.00750104\pi$
$389$			0.929471i			0.0471261i	−0.999722	+	0.0235630i	$0.992499\pi$
$390$	2.52605	−	17.7614i	0.127912	−	0.899384i
$391$			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
$396$	9.69783	+	2.81542i	0.487335	+	0.141480i
$397$	−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	$-0.907039\pi$
$401$		−	11.5308i		−	0.575823i	0.957657	−	0.287911i	$-0.0929609\pi$
$402$	4.24192	−	29.8262i	0.211568	−	1.48760i
$403$			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
$408$	11.2375	+	19.8193i	0.556339	+	0.981200i
$409$	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
$414$	2.43424	−	3.47483i	0.119636	−	0.170779i
$415$			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	$-0.245653\pi$
$419$	29.3409			1.43339			0.716697	+	0.697384i	$0.245653\pi$
$420$	1.03370	+	5.45535i	0.0504393	+	0.266194i
$421$	−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
$426$	8.62016	+	1.22597i	0.417648	+	0.0593984i
$427$			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	$-0.643499\pi$
$431$	−18.0908			−0.871401			−0.435700	+	0.900092i	$0.643499\pi$
$432$	1.97746	−	20.6903i	0.0951404	−	0.995464i
$433$	−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
$438$	33.5019	+	4.76469i	1.60078	+	0.227666i
$439$			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	$-0.473130\pi$
$443$	3.54917			0.168626			0.0843131	+	0.996439i	$0.473130\pi$
$444$	1.62531	+	8.57761i	0.0771339	+	0.407075i
$445$	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	$-0.907511\pi$
$449$		−	12.1412i		−	0.572980i	0.958083	−	0.286490i	$-0.0924885\pi$
$450$	−7.23535	+	10.3283i	−0.341078	+	0.486882i
$451$			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
$456$	14.1704	+	24.9920i	0.663591	+	1.17036i
$457$	−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	$-0.828622\pi$
$461$		−	22.0190i		−	1.02553i	0.858530	−	0.512763i	$-0.171378\pi$
$462$	0.653400	−	4.59425i	0.0303989	−	0.213744i
$463$		−	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	$-0.643624\pi$
$467$	−18.8463			−0.872105			−0.436052	+	0.899921i	$0.643624\pi$
$468$	29.6368	+	8.60399i	1.36996	+	0.397720i
$469$	−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
$474$	−1.81864	+	12.7874i	−0.0835329	+	0.587345i
$475$		−	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	$-0.500815\pi$
$479$	−0.112079			−0.00512102			−0.00256051	+	0.999997i	$0.500815\pi$
$480$	−12.8619	−	5.40644i	−0.587061	−	0.246769i
$481$	−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
$486$	−9.58344	+	19.8534i	−0.434714	+	0.900569i
$487$		−	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	$-0.581397\pi$
$491$	−11.2094			−0.505875			−0.252938	+	0.967483i	$0.581397\pi$
$492$	28.0374	−	5.31261i	1.26402	−	0.239511i
$493$	−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
$498$	−31.3067	−	4.45248i	−1.40289	−	0.199520i
$499$			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	$-0.774083\pi$
$503$	−34.0242			−1.51706			−0.758532	+	0.651636i	$0.774083\pi$
$504$	−9.54112	+	0.439099i	−0.424995	+	0.0195590i
$505$	−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	$-0.975964\pi$
$509$		−	3.40402i		−	0.150880i	0.997150	−	0.0754402i	$-0.0240362\pi$
$510$	−16.0598	−	2.28404i	−0.711140	−	0.101139i
$511$		−	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
$516$	12.6781	−	2.40228i	0.558121	−	0.105755i
$517$	−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	$0.130525\pi$
$521$			18.1993i			0.797324i	−0.917098	+	0.398662i	$0.869475\pi$
$522$	12.7603	+	8.93902i	0.558503	+	0.391250i
$523$		−	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
$528$	8.71655	+	7.74519i	0.379339	+	0.337066i
$529$	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
$534$	−5.48424	+	38.5613i	−0.237326	+	1.66871i
$535$		−	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
$540$	10.8039	+	10.1126i	0.464927	+	0.435177i
$541$	−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
$546$	1.99680	−	14.0401i	0.0854553	−	0.600862i
$547$		−	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
$552$	4.26161	−	2.41633i	0.181386	−	0.102846i
$553$	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	$0.0667081\pi$
$557$			9.81979i			0.416078i	−0.978121	+	0.208039i	$0.933292\pi$
$558$	−13.1790	−	9.23236i	−0.557913	−	0.390837i
$559$			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	$-0.173074\pi$
$563$	40.6115			1.71157			0.855786	+	0.517329i	$0.173074\pi$
$564$	4.91656	+	25.9472i	0.207025	+	1.09258i
$565$	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	$0.0625937\pi$
$569$			9.32103i			0.390758i	−0.980728	+	0.195379i	$0.937406\pi$
$570$	−20.2513	−	2.88017i	−0.848234	−	0.120637i
$571$		−	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
$576$	12.3227	−	20.5949i	0.513447	−	0.858122i
$577$	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
$582$	−29.0078	−	4.12553i	−1.20241	−	0.171009i
$583$		−	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	$-0.468422\pi$
$587$	4.79917			0.198083			0.0990415	+	0.995083i	$0.468422\pi$
$588$	−3.69727	−	19.5124i	−0.152473	−	0.804678i
$589$	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	$-0.718220\pi$
$593$		−	37.6994i		−	1.54813i	0.633106	−	0.774065i	$-0.281780\pi$
$594$	−5.81952	−	10.9131i	−0.238778	−	0.447769i
$595$			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	$-0.809057\pi$
$599$	−40.4030			−1.65082			−0.825411	+	0.564532i	$0.809057\pi$
$600$	−12.6669	+	7.18211i	−0.517124	+	0.293208i
$601$	−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
$606$	0.382918	−	2.69241i	0.0155550	−	0.109372i
$607$		−	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
$612$	7.77969	−	26.7974i	0.314475	−	1.08322i
$613$	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	$0.370431\pi$
$617$			45.6198i			1.83658i	−0.395905	+	0.918292i	$0.629569\pi$
$618$	5.74746	−	40.4121i	0.231197	−	1.62561i
$619$			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
$624$	26.6379	+	23.6695i	1.06637	+	0.947537i
$625$	−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
$630$	3.90171	−	5.56963i	0.155448	−	0.221899i
$631$			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
$636$	−7.59599	+	1.43931i	−0.301201	+	0.0570725i
$637$	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	$-0.787658\pi$
$641$		−	31.3286i		−	1.23741i	0.785625	−	0.618704i	$-0.212342\pi$
$642$	12.5527	+	1.78526i	0.495414	+	0.0704584i
$643$		−	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	$-0.352858\pi$
$647$	22.6877			0.891944			0.445972	+	0.895047i	$0.352858\pi$
$648$	−19.8391	+	15.9503i	−0.779353	+	0.626585i
$649$	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	$0.380111\pi$
$653$			47.5253i			1.85981i	−0.367799	+	0.929905i	$0.619889\pi$
$654$	−4.56218	−	0.648839i	−0.178395	−	0.0253716i
$655$		−	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	$-0.378975\pi$
$659$	19.0539			0.742236			0.371118	+	0.928586i	$0.378975\pi$
$660$	−8.15690	+	1.54559i	−0.317507	+	0.0601622i
$661$	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
$666$	6.13478	−	8.75728i	0.237718	−	0.339338i
$667$			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
$672$	−10.1671	−	4.27370i	−0.392204	−	0.164862i
$673$	−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	$-0.602720\pi$
$677$		−	49.3523i		−	1.89676i	0.317133	−	0.948381i	$-0.397280\pi$
$678$	−3.75523	+	26.4041i	−0.144219	+	1.01404i
$679$			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	$-0.464993\pi$
$683$	5.73685			0.219514			0.109757	+	0.993958i	$0.464993\pi$
$684$	9.81015	−	33.7914i	0.375100	−	1.29205i
$685$	−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
$690$	−0.491124	+	3.45324i	−0.0186968	+	0.131463i
$691$			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
$696$	8.87324	+	15.6495i	0.336339	+	0.593193i
$697$	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	$0.0452610\pi$
$701$			7.50410i			0.283426i	−0.989908	+	0.141713i	$0.954739\pi$
$702$	−17.7846	−	33.3506i	−0.671235	−	1.25874i
$703$			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
$708$	−2.56964	−	13.5613i	−0.0965731	−	0.509666i
$709$	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
$714$	−12.6950	−	1.80550i	−0.475099	−	0.0675691i
$715$		−	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	$-0.204077\pi$
$719$	42.9789			1.60284			0.801422	+	0.598100i	$0.204077\pi$
$720$	6.25118	+	15.9031i	0.232968	+	0.592673i
$721$	−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
$726$	−19.8066	−	2.81692i	−0.735091	−	0.104546i
$727$			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
$732$	4.60594	+	24.3079i	0.170241	+	0.898447i
$733$	−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
$738$	−28.6247	−	20.0526i	−1.05369	−	0.738146i
$739$			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	$-0.835707\pi$
$743$	−47.4143			−1.73946			−0.869731	+	0.493527i	$0.835707\pi$
$744$	−9.16443	−	16.1631i	−0.335984	−	0.592567i
$745$	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
$750$	3.91540	−	27.5303i	0.142970	−	1.00527i
$751$		−	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
$756$	8.54033	+	7.99384i	0.310609	+	0.290733i
$757$	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	$-0.879716\pi$
$761$		−	20.3562i		−	0.737910i	0.929447	−	0.368955i	$-0.120284\pi$
$762$	−3.03763	+	21.3585i	−0.110042	+	0.773737i
$763$			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
$768$	23.0633	−	15.3651i	0.832225	−	0.554438i
$769$	−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	$0.0585506\pi$
$773$			10.1707i			0.365813i	−0.983130	+	0.182907i	$0.941449\pi$
$774$	−12.9436	−	9.06747i	−0.465250	−	0.325923i
$775$			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
$780$	−24.9276	+	4.72337i	−0.892553	+	0.169124i
$781$	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
$786$	44.4743	+	6.32519i	1.58635	+	0.225612i
$787$		−	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
$792$	−0.656545	−	14.2660i	−0.0233293	−	0.506919i
$793$	−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	$-0.989130\pi$
$797$		−	1.92774i		−	0.0682842i	0.999417	−	0.0341421i	$-0.0108699\pi$
$798$	−16.0083	−	2.27673i	−0.566689	−	0.0805953i
$799$			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
$804$	−41.8602	+	7.93181i	−1.47630	+	0.279733i
$805$	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	$-0.843346\pi$
$809$		−	26.8795i		−	0.945032i	0.881322	−	0.472516i	$-0.156654\pi$
$810$	−0.364097	−	18.1205i	−0.0127931	−	0.636688i
$811$		−	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
$816$	21.4018	−	24.0859i	0.749213	−	0.843175i
$817$	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	$0.0371920\pi$
$821$			6.68055i			0.233153i	−0.993182	+	0.116576i	$0.962808\pi$
$822$	1.98868	−	13.9830i	0.0693630	−	0.487712i
$823$		−	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	$-0.329522\pi$
$827$	29.3519			1.02067			0.510334	+	0.859977i	$0.329522\pi$
$828$	−5.76209	−	1.67282i	−0.200246	−	0.0581345i
$829$	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
$834$	0.833331	−	5.85940i	0.0288559	−	0.202894i
$835$		−	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	$-0.541529\pi$
$839$	−7.53668			−0.260195			−0.130098	+	0.991501i	$0.541529\pi$
$840$	6.83071	−	3.87300i	0.235682	−	0.133631i
$841$	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
$846$	18.5577	−	26.4908i	0.638026	−	0.910771i
$847$			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
$852$	−2.29240	−	12.0981i	−0.0785362	−	0.414476i
$853$	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	$0.124146\pi$
$857$			22.2605i			0.760404i	−0.924903	+	0.380202i	$0.875854\pi$
$858$	20.9929	+	2.98564i	0.716687	+	0.101928i
$859$		−	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	$-0.739359\pi$
$863$	−40.1334			−1.36616			−0.683078	+	0.730345i	$0.739359\pi$
$864$	−28.5979	+	6.79419i	−0.972920	+	0.231143i
$865$	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
$870$	−12.6810	−	1.80351i	−0.429926	−	0.0611446i
$871$		−	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
$876$	−8.90932	−	47.0190i	−0.301018	−	1.58863i
$877$	−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	$0.0989066\pi$
$881$			18.1502i			0.611496i	−0.952112	+	0.305748i	$0.901093\pi$
$882$	−13.9554	+	19.9211i	−0.469904	+	0.670780i
$883$			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	$-0.556387\pi$
$887$	−10.4966			−0.352443			−0.176221	+	0.984351i	$0.556387\pi$
$888$	10.7401	−	6.08964i	0.360415	−	0.204355i
$889$	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
$894$	−5.89519	+	41.4509i	−0.197165	+	1.38632i
$895$		−	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
$900$	17.1268	+	4.97216i	0.570893	+	0.165739i
$901$	−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
$906$	−2.14621	+	15.0907i	−0.0713032	+	0.501354i
$907$			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	$-0.667800\pi$
$911$	−30.3688			−1.00616			−0.503081	+	0.864239i	$0.667800\pi$
$912$	26.9876	−	30.3722i	0.893648	−	1.00572i
$913$	−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
$918$	−30.1554	+	16.0807i	−0.995278	+	0.530743i
$919$			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
$924$	−6.44790	+	1.22177i	−0.212120	+	0.0401932i
$925$	−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	$-0.619522\pi$
$929$		−	56.7119i		−	1.86066i	0.366729	−	0.930328i	$-0.380478\pi$
$930$	13.0971	+	1.86269i	0.429472	+	0.0610800i
$931$		−	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
$936$	−2.00641	−	43.5971i	−0.0655817	−	1.42502i
$937$	−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	$-0.945057\pi$
$941$		−	10.5373i		−	0.343507i	0.985140	−	0.171754i	$-0.0549433\pi$
$942$	−30.6022	−	4.35228i	−0.997072	−	0.141805i
$943$		−	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	$-0.478294\pi$
$947$	4.19362			0.136274			0.0681372	+	0.997676i	$0.478294\pi$
$948$	17.9468	−	3.40061i	0.582884	−	0.110447i
$949$	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	$-0.988432\pi$
$953$		−	2.24336i		−	0.0726695i	0.999340	−	0.0363347i	$-0.0115683\pi$
$954$	7.75511	+	5.43272i	0.251081	+	0.175891i
$955$			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
$960$	−1.36795	+	19.6836i	−0.0441505	+	0.635284i
$961$	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
$966$	−0.388226	+	2.72973i	−0.0124910	+	0.0878276i
$967$		−	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	$-0.667958\pi$
$971$	−31.3795			−1.00702			−0.503508	+	0.863990i	$0.667958\pi$
$972$	30.9483	+	3.76888i	0.992666	+	0.120887i
$973$	−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	$-0.817428\pi$
$977$		−	33.9220i		−	1.08526i	0.839971	−	0.542631i	$-0.182572\pi$
$978$	5.08493	−	35.7536i	0.162598	−	1.14328i
$979$			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	$-0.224030\pi$
$983$	47.8056			1.52476			0.762381	+	0.647128i	$0.224030\pi$
$984$	−19.9050	−	35.1060i	−0.634549	−	1.11914i
$985$	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
$990$	8.32776	+	5.83388i	0.264674	+	0.185413i
$991$			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
$996$	8.32553	+	43.9381i	0.263804	+	1.39223i
$997$	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.b.47.9	yes	22
3.2	odd	2		276.2.c.a.47.14	yes	22
4.3	odd	2		276.2.c.a.47.13	✓	22
12.11	even	2	inner	276.2.c.b.47.10	yes	22

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

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)

\(f(q)\)	\(=\)	\(q+(-0.456308 - 1.33857i) q^{2} +(-0.784130 + 1.54439i) q^{3} +(-1.58357 + 1.22161i) q^{4} -1.42397i q^{5} +(2.42509 + 0.344899i) q^{6} -1.12562i q^{7} +(2.35780 + 1.56229i) q^{8} +(-1.77028 - 2.42200i) q^{9} +O(q^{10})\)	\(q+(-0.456308 - 1.33857i) q^{2} +(-0.784130 + 1.54439i) q^{3} +(-1.58357 + 1.22161i) q^{4} -1.42397i q^{5} +(2.42509 + 0.344899i) 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} +(-0.644914 - 3.40354i) 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} +(-2.43424 + 3.47483i) 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} +(-4.26161 + 2.41633i) 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} +(0.491124 - 3.45324i) 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} +(5.76209 + 1.67282i) 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} +(0.388226 - 2.72973i) 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} +(5.17905 + 4.60190i) 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} +(-3.45774 - 6.48414i) 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} +(-4.84652 + 0.918335i) 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} +(4.08152 + 0.580479i) 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} +(-0.390094 - 8.47631i) 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} +(12.4732 + 1.77396i) 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} +(-3.83110 + 0.725929i) 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} +(4.94804 + 3.46627i) 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} +(3.79675 - 9.03242i) q^{96} -11.9616 q^{97} +(-2.61600 - 7.67402i) q^{98} +(-2.97946 - 4.07633i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q + 9 * q^8 - 2 * q^9	\( 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) \) 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * 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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