LMFDB - Embedded newform 966.2.l.c.47.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.13
Character	$\chi$	$=$	966.47
Dual form			966.2.l.c.185.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.56059 + 0.751362i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.92458 + 3.33347i) q^{5} +(-0.975834 - 1.43100i) q^{6} +(0.526310 - 2.59287i) q^{7} -1.00000i q^{8} +(1.87091 + 2.34514i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.56059 + 0.751362i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.92458 + 3.33347i) q^{5} +(-0.975834 - 1.43100i) q^{6} +(0.526310 - 2.59287i) q^{7} -1.00000i q^{8} +(1.87091 + 2.34514i) q^{9} +(3.33347 - 1.92458i) q^{10} +(-4.47890 + 2.58589i) q^{11} +(0.129599 + 1.72720i) q^{12} +5.36500i q^{13} +(-1.75223 + 1.98234i) q^{14} +(-5.50813 + 3.75614i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.52828 - 6.11115i) q^{17} +(-0.447685 - 2.96641i) q^{18} +(-4.67791 - 2.70079i) q^{19} -3.84916 q^{20} +(2.76954 - 3.65098i) q^{21} +5.17179 q^{22} +(0.866025 + 0.500000i) q^{23} +(0.751362 - 1.56059i) q^{24} +(-4.90803 - 8.50095i) q^{25} +(2.68250 - 4.64622i) q^{26} +(1.15768 + 5.06555i) q^{27} +(2.50865 - 0.840639i) q^{28} -1.69376i q^{29} +(6.64826 - 0.498847i) q^{30} +(-0.119727 + 0.0691246i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-8.93269 + 0.670258i) q^{33} +7.05655i q^{34} +(7.63035 + 6.74464i) q^{35} +(-1.09550 + 2.79283i) q^{36} +(-1.41719 + 2.45464i) q^{37} +(2.70079 + 4.67791i) q^{38} +(-4.03105 + 8.37259i) q^{39} +(3.33347 + 1.92458i) q^{40} +5.70223 q^{41} +(-4.22398 + 1.77707i) q^{42} +3.94104 q^{43} +(-4.47890 - 2.58589i) q^{44} +(-11.4182 + 1.72321i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(2.14811 - 3.72064i) q^{47} +(-1.43100 + 0.975834i) q^{48} +(-6.44600 - 2.72931i) q^{49} +9.81605i q^{50} +(-0.914521 - 12.1880i) q^{51} +(-4.64622 + 2.68250i) q^{52} +(-8.28269 + 4.78201i) q^{53} +(1.53019 - 4.96573i) q^{54} -19.9071i q^{55} +(-2.59287 - 0.526310i) q^{56} +(-5.27105 - 7.72965i) q^{57} +(-0.846878 + 1.46684i) q^{58} +(-0.776799 - 1.34546i) q^{59} +(-6.00698 - 2.89211i) q^{60} +(1.50204 + 0.867201i) q^{61} +0.138249 q^{62} +(7.06534 - 3.61677i) q^{63} -1.00000 q^{64} +(-17.8841 - 10.3254i) q^{65} +(8.07106 + 3.88588i) q^{66} +(5.23869 + 9.07368i) q^{67} +(3.52828 - 6.11115i) q^{68} +(0.975834 + 1.43100i) q^{69} +(-3.23576 - 9.65620i) q^{70} +5.49401i q^{71} +(2.34514 - 1.87091i) q^{72} +(-12.5387 + 7.23923i) q^{73} +(2.45464 - 1.41719i) q^{74} +(-1.27215 - 16.9542i) q^{75} -5.40159i q^{76} +(4.34761 + 12.9742i) q^{77} +(7.67729 - 5.23534i) q^{78} +(-1.67489 + 2.90099i) q^{79} +(-1.92458 - 3.33347i) q^{80} +(-1.99939 + 8.77510i) q^{81} +(-4.93827 - 2.85111i) q^{82} -12.4904 q^{83} +(4.54661 + 0.573006i) q^{84} +27.1618 q^{85} +(-3.41304 - 1.97052i) q^{86} +(1.27262 - 2.64327i) q^{87} +(2.58589 + 4.47890i) q^{88} +(-2.12518 + 3.68093i) q^{89} +(10.7500 + 4.21675i) q^{90} +(13.9108 + 2.82365i) q^{91} +1.00000i q^{92} +(-0.238783 + 0.0179169i) q^{93} +(-3.72064 + 2.14811i) q^{94} +(18.0060 - 10.3958i) q^{95} +(1.72720 - 0.129599i) q^{96} +5.21678i q^{97} +(4.21774 + 5.58665i) q^{98} +(-14.4439 - 5.66568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.56059	+	0.751362i	0.901010	+	0.433799i
$3$	1.56059	+	0.751362i	0.901010	+	0.433799i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.92458	+	3.33347i	−0.860699	+	1.49077i	0.0105566	+	0.999944i	$0.496640\pi$
$5$	−1.92458	+	3.33347i	−0.860699	+	1.49077i	−0.871255	+	0.490830i	$0.836694\pi$
$6$	−0.975834	−	1.43100i	−0.398382	−	0.584202i
$7$	0.526310	−	2.59287i	0.198926	−	0.980014i
$7$	0.526310	−	2.59287i	0.198926	−	0.980014i
$8$		−	1.00000i		−	0.353553i
$9$	1.87091	+	2.34514i	0.623637	+	0.781714i
$10$	3.33347	−	1.92458i	1.05414	−	0.608606i
$11$	−4.47890	+	2.58589i	−1.35044	+	0.779676i	−0.988311	−	0.152452i	$-0.951283\pi$
$11$	−4.47890	+	2.58589i	−1.35044	+	0.779676i	−0.362128	+	0.932128i	$0.617950\pi$
$12$	0.129599	+	1.72720i	0.0374120	+	0.498598i
$13$			5.36500i			1.48798i	0.668189	+	0.743991i	$0.267070\pi$
$13$			5.36500i			1.48798i	−0.668189	+	0.743991i	$0.732930\pi$
$14$	−1.75223	+	1.98234i	−0.468304	+	0.529803i
$15$	−5.50813	+	3.75614i	−1.42219	+	0.969832i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.52828	−	6.11115i	−0.855732	−	1.48217i	−0.875964	−	0.482377i	$-0.839774\pi$
$17$	−3.52828	−	6.11115i	−0.855732	−	1.48217i	0.0202314	−	0.999795i	$-0.493560\pi$
$18$	−0.447685	−	2.96641i	−0.105520	−	0.699189i
$19$	−4.67791	−	2.70079i	−1.07319	−	0.619605i	−0.144136	−	0.989558i	$-0.546040\pi$
$19$	−4.67791	−	2.70079i	−1.07319	−	0.619605i	−0.929050	+	0.369953i	$0.879374\pi$
$20$	−3.84916			−0.860699
$21$	2.76954	−	3.65098i	0.604364	−	0.796708i
$22$	5.17179			1.10263
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$24$	0.751362	−	1.56059i	0.153371	−	0.318555i
$25$	−4.90803	−	8.50095i	−0.981605	−	1.70019i
$26$	2.68250	−	4.64622i	0.526081	−	0.911199i
$27$	1.15768	+	5.06555i	0.222796	+	0.974865i
$28$	2.50865	−	0.840639i	0.474090	−	0.158866i
$29$		−	1.69376i		−	0.314522i	−0.987557	−	0.157261i	$-0.949734\pi$
$29$		−	1.69376i		−	0.314522i	0.987557	−	0.157261i	$-0.0502665\pi$
$30$	6.64826	−	0.498847i	1.21380	−	0.0910766i
$31$	−0.119727	+	0.0691246i	−0.0215037	+	0.0124151i	−0.510713	−	0.859751i	$-0.670619\pi$
$31$	−0.119727	+	0.0691246i	−0.0215037	+	0.0124151i	0.489210	+	0.872166i	$0.337285\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−8.93269	+	0.670258i	−1.55498	+	0.116677i
$34$			7.05655i			1.21019i
$35$	7.63035	+	6.74464i	1.28976	+	1.14005i
$36$	−1.09550	+	2.79283i	−0.182583	+	0.465471i
$37$	−1.41719	+	2.45464i	−0.232984	+	0.403541i	−0.958685	−	0.284470i	$-0.908182\pi$
$37$	−1.41719	+	2.45464i	−0.232984	+	0.403541i	0.725701	+	0.688011i	$0.241516\pi$
$38$	2.70079	+	4.67791i	0.438127	+	0.758858i
$39$	−4.03105	+	8.37259i	−0.645485	+	1.34069i
$40$	3.33347	+	1.92458i	0.527068	+	0.304303i
$41$	5.70223			0.890538			0.445269	−	0.895397i	$-0.353108\pi$
$41$	5.70223			0.890538			0.445269	+	0.895397i	$0.353108\pi$
$42$	−4.22398	+	1.77707i	−0.651775	+	0.274207i
$43$	3.94104			0.601003			0.300501	−	0.953781i	$-0.402846\pi$
$43$	3.94104			0.601003			0.300501	+	0.953781i	$0.402846\pi$
$44$	−4.47890	−	2.58589i	−0.675220	−	0.389838i
$45$	−11.4182	+	1.72321i	−1.70212	+	0.256881i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	2.14811	−	3.72064i	0.313335	−	0.542712i	−0.665747	−	0.746177i	$-0.731887\pi$
$47$	2.14811	−	3.72064i	0.313335	−	0.542712i	0.979082	+	0.203466i	$0.0652205\pi$
$48$	−1.43100	+	0.975834i	−0.206546	+	0.140849i
$49$	−6.44600	−	2.72931i	−0.920857	−	0.389902i
$50$			9.81605i			1.38820i
$51$	−0.914521	−	12.1880i	−0.128059	−	1.70667i
$52$	−4.64622	+	2.68250i	−0.644315	+	0.371996i
$53$	−8.28269	+	4.78201i	−1.13771	+	0.656860i	−0.945864	−	0.324564i	$-0.894782\pi$
$53$	−8.28269	+	4.78201i	−1.13771	+	0.656860i	−0.191851	+	0.981424i	$0.561449\pi$
$54$	1.53019	−	4.96573i	0.208233	−	0.675751i
$55$		−	19.9071i		−	2.68427i
$56$	−2.59287	−	0.526310i	−0.346487	−	0.0703311i
$57$	−5.27105	−	7.72965i	−0.698168	−	1.02382i
$58$	−0.846878	+	1.46684i	−0.111200	+	0.192605i
$59$	−0.776799	−	1.34546i	−0.101131	−	0.175163i	0.811020	−	0.585018i	$-0.198913\pi$
$59$	−0.776799	−	1.34546i	−0.101131	−	0.175163i	−0.912151	+	0.409855i	$0.865579\pi$
$60$	−6.00698	−	2.89211i	−0.775498	−	0.373370i
$61$	1.50204	+	0.867201i	0.192316	+	0.111034i	0.593066	−	0.805154i	$-0.297917\pi$
$61$	1.50204	+	0.867201i	0.192316	+	0.111034i	−0.400750	+	0.916187i	$0.631251\pi$
$62$	0.138249			0.0175577
$63$	7.06534	−	3.61677i	0.890149	−	0.455670i
$64$	−1.00000			−0.125000
$65$	−17.8841	−	10.3254i	−2.21825	−	1.28070i
$66$	8.07106	+	3.88588i	0.993479	+	0.478319i
$67$	5.23869	+	9.07368i	0.640008	+	1.10853i	0.985430	+	0.170079i	$0.0544023\pi$
$67$	5.23869	+	9.07368i	0.640008	+	1.10853i	−0.345423	+	0.938447i	$0.612264\pi$
$68$	3.52828	−	6.11115i	0.427866	−	0.741086i
$69$	0.975834	+	1.43100i	0.117477	+	0.172272i
$70$	−3.23576	−	9.65620i	−0.386747	−	1.15414i
$71$			5.49401i			0.652019i	0.945367	+	0.326009i	$0.105704\pi$
$71$			5.49401i			0.652019i	−0.945367	+	0.326009i	$0.894296\pi$
$72$	2.34514	−	1.87091i	0.276378	−	0.220489i
$73$	−12.5387	+	7.23923i	−1.46755	+	0.847288i	−0.999340	−	0.0363321i	$-0.988433\pi$
$73$	−12.5387	+	7.23923i	−1.46755	+	0.847288i	−0.468205	+	0.883620i	$0.655099\pi$
$74$	2.45464	−	1.41719i	0.285347	−	0.164745i
$75$	−1.27215	−	16.9542i	−0.146895	−	1.95771i
$76$		−	5.40159i		−	0.619605i
$77$	4.34761	+	12.9742i	0.495456	+	1.47855i
$78$	7.67729	−	5.23534i	0.869282	−	0.592786i
$79$	−1.67489	+	2.90099i	−0.188440	+	0.326387i	−0.944730	−	0.327849i	$-0.893676\pi$
$79$	−1.67489	+	2.90099i	−0.188440	+	0.326387i	0.756291	+	0.654236i	$0.227010\pi$
$80$	−1.92458	−	3.33347i	−0.215175	−	0.372694i
$81$	−1.99939	+	8.77510i	−0.222154	+	0.975012i
$82$	−4.93827	−	2.85111i	−0.545341	−	0.314853i
$83$	−12.4904			−1.37099			−0.685497	−	0.728075i	$-0.740415\pi$
$83$	−12.4904			−1.37099			−0.685497	+	0.728075i	$0.740415\pi$
$84$	4.54661	+	0.573006i	0.496076	+	0.0625201i
$85$	27.1618			2.94611
$86$	−3.41304	−	1.97052i	−0.368038	−	0.212487i
$87$	1.27262	−	2.64327i	0.136440	−	0.283388i
$88$	2.58589	+	4.47890i	0.275657	+	0.477452i
$89$	−2.12518	+	3.68093i	−0.225269	+	0.390177i	−0.956400	−	0.292060i	$-0.905659\pi$
$89$	−2.12518	+	3.68093i	−0.225269	+	0.390177i	0.731131	+	0.682237i	$0.238993\pi$
$90$	10.7500	+	4.21675i	1.13315	+	0.444484i
$91$	13.9108	+	2.82365i	1.45824	+	0.295999i
$92$			1.00000i			0.104257i
$93$	−0.238783	+	0.0179169i	−0.0247607	+	0.00185790i
$94$	−3.72064	+	2.14811i	−0.383755	+	0.221561i
$95$	18.0060	−	10.3958i	1.84738	−	1.06659i
$96$	1.72720	−	0.129599i	0.176281	−	0.0132271i
$97$			5.21678i			0.529684i	0.964292	+	0.264842i	$0.0853198\pi$
$97$			5.21678i			0.529684i	−0.964292	+	0.264842i	$0.914680\pi$
$98$	4.21774	+	5.58665i	0.426056	+	0.564337i
$99$	−14.4439	−	5.66568i	−1.45167	−	0.569422i
$100$	4.90803	−	8.50095i	0.490803	−	0.850095i
$101$	−3.77208	−	6.53344i	−0.375336	−	0.650101i	0.615041	−	0.788495i	$-0.289139\pi$
$101$	−3.77208	−	6.53344i	−0.375336	−	0.650101i	−0.990377	+	0.138394i	$0.955806\pi$
$102$	−5.30202	+	11.0124i	−0.524978	+	1.09039i
$103$	−2.05103	−	1.18416i	−0.202094	−	0.116679i	0.395538	−	0.918450i	$-0.370558\pi$
$103$	−2.05103	−	1.18416i	−0.202094	−	0.116679i	−0.597632	+	0.801771i	$0.703892\pi$
$104$	5.36500			0.526081
$105$	6.84022	+	16.2588i	0.667537	+	1.58670i
$106$	9.56403			0.928940
$107$	9.07370	+	5.23870i	0.877187	+	0.506444i	0.869730	−	0.493528i	$-0.164293\pi$
$107$	9.07370	+	5.23870i	0.877187	+	0.506444i	0.00745730	+	0.999972i	$0.497626\pi$
$108$	−3.80805	+	3.53536i	−0.366430	+	0.340190i
$109$	−5.69643	−	9.86651i	−0.545619	−	0.945041i	−0.998568	−	0.0535037i	$-0.982961\pi$
$109$	−5.69643	−	9.86651i	−0.545619	−	0.945041i	0.452948	−	0.891537i	$-0.350372\pi$
$110$	−9.95353	+	17.2400i	−0.949031	+	1.64377i
$111$	−4.05598	+	2.76588i	−0.384977	+	0.262526i
$112$	1.98234	+	1.75223i	0.187314	+	0.165571i
$113$			13.6642i			1.28542i	0.766109	+	0.642711i	$0.222190\pi$
$113$			13.6642i			1.28542i	−0.766109	+	0.642711i	$0.777810\pi$
$114$	0.700040	+	9.32960i	0.0655647	+	0.873797i
$115$	−3.33347	+	1.92458i	−0.310848	+	0.179468i
$116$	1.46684	−	0.846878i	0.136192	−	0.0786306i
$117$	−12.5817	+	10.0374i	−1.16318	+	0.927961i
$118$			1.55360i			0.143020i
$119$	−17.7024	+	5.93202i	−1.62278	+	0.543787i
$120$	3.75614	+	5.50813i	0.342887	+	0.502822i
$121$	7.87370	−	13.6376i	0.715791	−	1.23979i
$122$	−0.867201	−	1.50204i	−0.0785127	−	0.135988i
$123$	8.89887	+	4.28444i	0.802384	+	0.386315i
$124$	−0.119727	−	0.0691246i	−0.0107518	−	0.00620757i
$125$	18.5378			1.65807
$126$	−7.92715	−	0.400459i	−0.706206	−	0.0356757i
$127$	12.9903			1.15270			0.576351	−	0.817202i	$-0.304476\pi$
$127$	12.9903			1.15270			0.576351	+	0.817202i	$0.304476\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	6.15036	+	2.96115i	0.541509	+	0.260714i
$130$	10.3254	+	17.8841i	0.905595	+	1.56854i
$131$	−5.81542	+	10.0726i	−0.508096	+	0.880048i	0.491860	+	0.870674i	$0.336317\pi$
$131$	−5.81542	+	10.0726i	−0.508096	+	0.880048i	−0.999956	+	0.00937364i	$0.997016\pi$
$132$	−5.04680	−	7.40081i	−0.439268	−	0.644158i
$133$	−9.46485	+	10.7078i	−0.820707	+	0.928483i
$134$		−	10.4774i		−	0.905108i
$135$	−19.1139	−	5.88995i	−1.64506	−	0.506926i
$136$	−6.11115	+	3.52828i	−0.524027	+	0.302547i
$137$	−9.19760	+	5.31024i	−0.785804	+	0.453684i	−0.838483	−	0.544927i	$-0.816557\pi$
$137$	−9.19760	+	5.31024i	−0.785804	+	0.453684i	0.0526793	+	0.998611i	$0.483224\pi$
$138$	−0.129599	−	1.72720i	−0.0110322	−	0.147029i
$139$			7.17631i			0.608687i	0.952562	+	0.304343i	$0.0984370\pi$
$139$			7.17631i			0.608687i	−0.952562	+	0.304343i	$0.901563\pi$
$140$	−2.02585	+	9.98039i	−0.171216	+	0.843497i
$141$	6.14788	−	4.19240i	0.517745	−	0.353064i
$142$	2.74700	−	4.75795i	0.230523	−	0.399278i
$143$	−13.8733	−	24.0293i	−1.16014	−	2.00943i
$144$	−2.96641	+	0.447685i	−0.247201	+	0.0373071i
$145$	5.64609	+	3.25977i	0.468882	+	0.270709i
$146$	14.4785			1.19825
$147$	−8.00889	−	9.10262i	−0.660562	−	0.750772i
$148$	−2.83438			−0.232984
$149$	7.41676	+	4.28207i	0.607605	+	0.350801i	0.772027	−	0.635589i	$-0.219243\pi$
$149$	7.41676	+	4.28207i	0.607605	+	0.350801i	−0.164423	+	0.986390i	$0.552576\pi$
$150$	−7.37541	+	15.3189i	−0.602199	+	1.25078i
$151$	5.42087	+	9.38922i	0.441144	+	0.764084i	0.997775	−	0.0666761i	$-0.0212394\pi$
$151$	5.42087	+	9.38922i	0.441144	+	0.764084i	−0.556631	+	0.830760i	$0.687906\pi$
$152$	−2.70079	+	4.67791i	−0.219063	+	0.379429i
$153$	7.73043	−	19.7077i	0.624968	−	1.59328i
$154$	2.72196	−	13.4098i	0.219342	−	1.08059i
$155$		−	0.532143i		−	0.0427428i
$156$	−9.26640	+	0.695298i	−0.741906	+	0.0556684i
$157$	−2.36632	+	1.36620i	−0.188853	+	0.109034i	−0.591445	−	0.806345i	$-0.701442\pi$
$157$	−2.36632	+	1.36620i	−0.188853	+	0.109034i	0.402593	+	0.915379i	$0.368109\pi$
$158$	2.90099	−	1.67489i	0.230790	−	0.133247i
$159$	−16.5189	+	1.23949i	−1.31004	+	0.0982977i
$160$			3.84916i			0.304303i
$161$	1.75223	−	1.98234i	0.138095	−	0.156230i
$162$	6.11907	−	6.59977i	0.480760	−	0.518527i
$163$	−6.17834	+	10.7012i	−0.483925	+	0.838183i	−0.999830	−	0.0184631i	$-0.994123\pi$
$163$	−6.17834	+	10.7012i	−0.483925	+	0.838183i	0.515904	+	0.856646i	$0.327456\pi$
$164$	2.85111	+	4.93827i	0.222635	+	0.385614i
$165$	14.9574	−	31.0668i	1.16443	−	2.41855i
$166$	10.8170	+	6.24518i	0.839559	+	0.484720i
$167$	1.96175			0.151805			0.0759023	−	0.997115i	$-0.475816\pi$
$167$	1.96175			0.151805			0.0759023	+	0.997115i	$0.475816\pi$
$168$	−3.65098	−	2.76954i	−0.281679	−	0.213675i
$169$	−15.7832			−1.21409
$170$	−23.5228	−	13.5809i	−1.80412	−	1.04161i
$171$	−2.41821	−	16.0233i	−0.184925	−	1.22533i
$172$	1.97052	+	3.41304i	0.150251	+	0.260242i
$173$	10.9822	−	19.0217i	0.834960	−	1.44619i	−0.0591022	−	0.998252i	$-0.518824\pi$
$173$	10.9822	−	19.0217i	0.834960	−	1.44619i	0.894063	−	0.447942i	$-0.147843\pi$
$174$	−2.42376	+	1.65282i	−0.183745	+	0.125300i
$175$	−24.6250	+	8.25176i	−1.86148	+	0.623774i
$176$		−	5.17179i		−	0.389838i
$177$	−0.201345	−	2.68337i	−0.0151340	−	0.201694i
$178$	3.68093	−	2.12518i	0.275897	−	0.159289i
$179$	18.0198	−	10.4038i	1.34686	−	0.777613i	0.359061	−	0.933314i	$-0.383097\pi$
$179$	18.0198	−	10.4038i	1.34686	−	0.777613i	0.987804	+	0.155701i	$0.0497637\pi$
$180$	−7.20144	−	9.02683i	−0.536764	−	0.672820i
$181$			10.0504i			0.747038i	0.927623	+	0.373519i	$0.121849\pi$
$181$			10.0504i			0.747038i	−0.927623	+	0.373519i	$0.878151\pi$
$182$	−10.6352	−	9.40074i	−0.788337	−	0.696829i
$183$	1.69249	+	2.48192i	0.125112	+	0.183469i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−5.45499	−	9.44832i	−0.401059	−	0.694654i
$186$	0.215751	+	0.103875i	0.0158196	+	0.00761649i
$187$	31.6056	+	18.2475i	2.31123	+	1.33439i
$188$	4.29623			0.313335
$189$	13.7436	−	0.335679i	0.999702	−	0.0244170i
$190$	−20.7916			−1.50838
$191$	14.7646	+	8.52435i	1.06833	+	0.616801i	0.927725	−	0.373265i	$-0.121762\pi$
$191$	14.7646	+	8.52435i	1.06833	+	0.616801i	0.140605	+	0.990066i	$0.455095\pi$
$192$	−1.56059	−	0.751362i	−0.112626	−	0.0542249i
$193$	7.09645	+	12.2914i	0.510814	+	0.884755i	0.999921	+	0.0125318i	$0.00398909\pi$
$193$	7.09645	+	12.2914i	0.510814	+	0.884755i	−0.489108	+	0.872223i	$0.662678\pi$
$194$	2.60839	−	4.51787i	0.187272	−	0.324364i
$195$	−20.1517	−	29.5511i	−1.44309	−	2.11620i
$196$	−0.859345	−	6.94705i	−0.0613818	−	0.496218i
$197$			4.83810i			0.344701i	0.985036	+	0.172350i	$0.0551361\pi$
$197$			4.83810i			0.344701i	−0.985036	+	0.172350i	$0.944864\pi$
$198$	9.67595	+	12.1286i	0.687640	+	0.861941i
$199$	0.381142	−	0.220052i	0.0270184	−	0.0155991i	−0.486430	−	0.873720i	$-0.661701\pi$
$199$	0.381142	−	0.220052i	0.0270184	−	0.0155991i	0.513448	+	0.858120i	$0.328368\pi$
$200$	−8.50095	+	4.90803i	−0.601108	+	0.347050i
$201$	1.35786	+	18.0965i	0.0957758	+	1.27643i
$202$			7.54416i			0.530805i
$203$	−4.39169	−	0.891440i	−0.308237	−	0.0625668i
$204$	10.0979	−	6.88602i	0.706994	−	0.482118i
$205$	−10.9744	+	19.0082i	−0.766485	+	1.32759i
$206$	1.18416	+	2.05103i	0.0825047	+	0.142902i
$207$	0.447685	+	2.96641i	0.0311163	+	0.206180i
$208$	−4.64622	−	2.68250i	−0.322158	−	0.185998i
$209$	27.9359			1.93236
$210$	2.20559	−	17.5006i	0.152201	−	1.20766i
$211$	24.3001			1.67289			0.836444	−	0.548053i	$-0.184631\pi$
$211$	24.3001			1.67289			0.836444	+	0.548053i	$0.184631\pi$
$212$	−8.28269	−	4.78201i	−0.568857	−	0.328430i
$213$	−4.12799	+	8.57392i	−0.282845	+	0.587475i
$214$	−5.23870	−	9.07370i	−0.358110	−	0.620265i
$215$	−7.58485	+	13.1373i	−0.517282	+	0.895960i
$216$	5.06555	−	1.15768i	0.344667	−	0.0787703i
$217$	0.116218	+	0.346819i	0.00788937	+	0.0235436i
$218$			11.3929i			0.771622i
$219$	−25.0071	+	1.87639i	−1.68982	+	0.126795i
$220$	17.2400	−	9.95353i	1.16232	−	0.671067i
$221$	32.7863	−	18.9292i	2.20545	−	1.27331i
$222$	4.89553	−	0.367332i	0.328566	−	0.0246537i
$223$		−	16.5686i		−	1.10951i	−0.832012	−	0.554757i	$-0.812811\pi$
$223$		−	16.5686i		−	1.10951i	0.832012	−	0.554757i	$-0.187189\pi$
$224$	−0.840639	−	2.50865i	−0.0561676	−	0.167616i
$225$	10.7535	−	27.4145i	0.716897	−	1.82764i
$226$	6.83211	−	11.8336i	0.454465	−	0.787157i
$227$	1.82471	+	3.16049i	0.121110	+	0.209769i	0.920206	−	0.391435i	$-0.128021\pi$
$227$	1.82471	+	3.16049i	0.121110	+	0.209769i	−0.799096	+	0.601204i	$0.794688\pi$
$228$	4.05855	−	8.42969i	0.268784	−	0.558270i
$229$	−4.59154	−	2.65093i	−0.303417	−	0.175178i	0.340560	−	0.940223i	$-0.389383\pi$
$229$	−4.59154	−	2.65093i	−0.303417	−	0.175178i	−0.643977	+	0.765045i	$0.722717\pi$
$230$	3.84916			0.253806
$231$	−2.96347	+	23.5141i	−0.194982	+	1.54711i
$232$	−1.69376			−0.111200
$233$	−11.8030	−	6.81444i	−0.773237	−	0.446429i	0.0607909	−	0.998151i	$-0.480638\pi$
$233$	−11.8030	−	6.81444i	−0.773237	−	0.446429i	−0.834028	+	0.551722i	$0.813971\pi$
$234$	15.9148	−	2.40183i	1.04038	−	0.157013i
$235$	8.26844	+	14.3214i	0.539374	+	0.934223i
$236$	0.776799	−	1.34546i	0.0505653	−	0.0875817i
$237$	−4.79351	+	3.26882i	−0.311372	+	0.212333i
$238$	18.2968	+	3.71393i	1.18600	+	0.240738i
$239$			14.8003i			0.957349i	0.877992	+	0.478674i	$0.158883\pi$
$239$			14.8003i			0.957349i	−0.877992	+	0.478674i	$0.841117\pi$
$240$	−0.498847	−	6.64826i	−0.0322004	−	0.429143i
$241$	4.99910	−	2.88623i	0.322020	−	0.185918i	−0.330272	−	0.943886i	$-0.607141\pi$
$241$	4.99910	−	2.88623i	0.322020	−	0.185918i	0.652293	+	0.757967i	$0.273807\pi$
$242$	−13.6376	+	7.87370i	−0.876661	+	0.506140i
$243$	−9.71351	+	12.1921i	−0.623122	+	0.782125i
$244$			1.73440i			0.111034i
$245$	21.5039	−	16.2348i	1.37384	−	1.03720i
$246$	−5.56443	−	8.15986i	−0.354775	−	0.520254i
$247$	14.4898	−	25.0970i	0.921961	−	1.59688i
$248$	0.0691246	+	0.119727i	0.00438941	+	0.00760269i
$249$	−19.4924	−	9.38477i	−1.23528	−	0.594736i
$250$	−16.0542	−	9.26888i	−1.01536	−	0.586216i
$251$	3.09196			0.195163			0.0975813	−	0.995228i	$-0.468889\pi$
$251$	3.09196			0.195163			0.0975813	+	0.995228i	$0.468889\pi$
$252$	6.66488	+	4.31038i	0.419848	+	0.271528i
$253$	−5.17179			−0.325148
$254$	−11.2499	−	6.49515i	−0.705883	−	0.407542i
$255$	42.3886	+	20.4083i	2.65448	+	1.27802i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.27846	+	12.6067i	−0.454018	+	0.786382i	−0.998631	−	0.0523050i	$-0.983343\pi$
$257$	−7.27846	+	12.6067i	−0.454018	+	0.786382i	0.544613	+	0.838687i	$0.316677\pi$
$258$	−3.84580	−	5.63961i	−0.239429	−	0.351107i
$259$	5.61870	+	4.96650i	0.349129	+	0.308603i
$260$		−	20.6507i		−	1.28070i
$261$	3.97210	−	3.16887i	0.245867	−	0.196148i
$262$	10.0726	−	5.81542i	0.622288	−	0.359278i
$263$	−6.91106	+	3.99010i	−0.426154	+	0.246040i	−0.697707	−	0.716383i	$-0.745796\pi$
$263$	−6.91106	+	3.99010i	−0.426154	+	0.246040i	0.271553	+	0.962424i	$0.412463\pi$
$264$	0.670258	+	8.93269i	0.0412515	+	0.549769i
$265$		−	36.8135i		−	2.26143i
$266$	13.5507	−	4.54079i	0.830846	−	0.278414i
$267$	−6.08226	+	4.14765i	−0.372228	+	0.253832i
$268$	−5.23869	+	9.07368i	−0.320004	+	0.554263i
$269$	−11.0314	−	19.1069i	−0.672595	−	1.16497i	−0.977166	−	0.212479i	$-0.931846\pi$
$269$	−11.0314	−	19.1069i	−0.672595	−	1.16497i	0.304571	−	0.952490i	$-0.401487\pi$
$270$	13.6082	+	14.6578i	0.828166	+	0.892046i
$271$	3.74537	+	2.16239i	0.227515	+	0.131356i	0.609425	−	0.792844i	$-0.291400\pi$
$271$	3.74537	+	2.16239i	0.227515	+	0.131356i	−0.381910	+	0.924200i	$0.624734\pi$
$272$	7.05655			0.427866
$273$	19.5875	+	14.8586i	1.18549	+	0.899283i
$274$	10.6205			0.641606
$275$	43.9651	+	25.3833i	2.65120	+	1.53067i
$276$	−0.751362	+	1.56059i	−0.0452267	+	0.0939368i
$277$	−8.32951	−	14.4271i	−0.500472	−	0.866843i	−1.00000		0.000544827i	$-0.999827\pi$
$277$	−8.32951	−	14.4271i	−0.500472	−	0.866843i	0.499528	−	0.866298i	$-0.333507\pi$
$278$	3.58816	−	6.21487i	0.215203	−	0.372743i
$279$	−0.386106	−	0.151452i	−0.0231156	−	0.00906717i
$280$	6.74464	−	7.63035i	0.403069	−	0.456001i
$281$		−	21.5710i		−	1.28682i	−0.765523	−	0.643408i	$-0.777520\pi$
$281$		−	21.5710i		−	1.28682i	0.765523	−	0.643408i	$-0.222480\pi$
$282$	−7.42043	+	0.556786i	−0.441880	+	0.0331561i
$283$	−3.71734	+	2.14621i	−0.220973	+	0.127579i	−0.606401	−	0.795159i	$-0.707387\pi$
$283$	−3.71734	+	2.14621i	−0.220973	+	0.127579i	0.385428	+	0.922738i	$0.374054\pi$
$284$	−4.75795	+	2.74700i	−0.282332	+	0.163005i
$285$	35.9111	−	2.69457i	2.12719	−	0.159612i
$286$			27.7466i			1.64069i
$287$	3.00114	−	14.7852i	0.177152	−	0.872740i
$288$	2.79283	+	1.09550i	0.164569	+	0.0645528i
$289$	−16.3975	+	28.4012i	−0.964556	+	1.67066i
$290$	−3.25977	−	5.64609i	−0.191420	−	0.331550i
$291$	−3.91969	+	8.14129i	−0.229776	+	0.477251i
$292$	−12.5387	−	7.23923i	−0.733773	−	0.423644i
$293$	14.3378			0.837622			0.418811	−	0.908073i	$-0.362447\pi$
$293$	14.3378			0.837622			0.418811	+	0.908073i	$0.362447\pi$
$294$	2.38459	+	11.8875i	0.139072	+	0.693296i
$295$	5.98005			0.348172
$296$	2.45464	+	1.41719i	0.142673	+	0.0823725i
$297$	−18.2841	−	19.6944i	−1.06095	−	1.14279i
$298$	−4.28207	−	7.41676i	−0.248054	−	0.429641i
$299$	−2.68250	+	4.64622i	−0.155133	+	0.268698i
$300$	14.0467	−	9.57883i	0.810988	−	0.553034i
$301$	2.07421	−	10.2186i	0.119555	−	0.588991i
$302$		−	10.8417i		−	0.623872i
$303$	−0.977715	−	13.0302i	−0.0561683	−	0.748568i
$304$	4.67791	−	2.70079i	0.268297	−	0.154901i
$305$	−5.78158	+	3.33800i	−0.331052	+	0.191133i
$306$	−16.5486	+	13.2022i	−0.946021	+	0.754718i
$307$		−	9.61028i		−	0.548488i	−0.961660	−	0.274244i	$-0.911572\pi$
$307$		−	9.61028i		−	0.548488i	0.961660	−	0.274244i	$-0.0884275\pi$
$308$	−9.06219	+	10.2522i	−0.516366	+	0.584176i
$309$	−2.31110	−	3.38907i	−0.131474	−	0.192797i
$310$	−0.266072	+	0.460850i	−0.0151119	+	0.0261745i
$311$	−3.29501	−	5.70713i	−0.186843	−	0.323622i	0.757353	−	0.653006i	$-0.226492\pi$
$311$	−3.29501	−	5.70713i	−0.186843	−	0.323622i	−0.944196	+	0.329384i	$0.893159\pi$
$312$	8.37259	+	4.03105i	0.474004	+	0.228213i
$313$	−17.1423	−	9.89710i	−0.968938	−	0.559417i	−0.0700260	−	0.997545i	$-0.522308\pi$
$313$	−17.1423	−	9.89710i	−0.968938	−	0.559417i	−0.898912	+	0.438128i	$0.855642\pi$
$314$	2.73239			0.154198
$315$	−1.54143	+	30.5129i	−0.0868498	+	1.71921i
$316$	−3.34978			−0.188440
$317$	24.8720	+	14.3599i	1.39695	+	0.806530i	0.994072	−	0.108723i	$-0.0346761\pi$
$317$	24.8720	+	14.3599i	1.39695	+	0.806530i	0.402879	+	0.915253i	$0.368009\pi$
$318$	14.9256	+	7.18604i	0.836984	+	0.402973i
$319$	4.37987	+	7.58616i	0.245226	+	0.424743i
$320$	1.92458	−	3.33347i	0.107587	−	0.186347i
$321$	10.2242	+	14.9931i	0.570659	+	0.836834i
$322$	−2.50865	+	0.840639i	−0.139802	+	0.0468470i
$323$			38.1166i			2.12086i
$324$	−8.59916	+	2.65603i	−0.477731	+	0.147557i
$325$	45.6076	−	26.3315i	2.52985	−	1.46061i
$326$	10.7012	−	6.17834i	0.592685	−	0.342187i
$327$	−1.47650	−	19.6777i	−0.0816508	−	1.08818i
$328$		−	5.70223i		−	0.314853i
$329$	−8.51659	−	7.52800i	−0.469535	−	0.415032i
$330$	−28.4869	+	19.4260i	−1.56815	+	1.06936i
$331$	−0.750411	+	1.29975i	−0.0412463	+	0.0714407i	−0.885912	−	0.463854i	$-0.846466\pi$
$331$	−0.750411	+	1.29975i	−0.0412463	+	0.0714407i	0.844665	+	0.535295i	$0.179800\pi$
$332$	−6.24518	−	10.8170i	−0.342749	−	0.593658i
$333$	−8.40792	+	1.26891i	−0.460751	+	0.0695358i
$334$	−1.69892	−	0.980874i	−0.0929610	−	0.0536711i
$335$	−40.3291			−2.20342
$336$	1.77707	+	4.22398i	0.0969469	+	0.230437i
$337$	0.0754879			0.00411209			0.00205604	−	0.999998i	$-0.499346\pi$
$337$	0.0754879			0.00411209			0.00205604	+	0.999998i	$0.499346\pi$
$338$	13.6686	+	7.89160i	0.743476	+	0.429246i
$339$	−10.2668	+	21.3243i	−0.557614	+	1.15818i
$340$	13.5809	+	23.5228i	0.736528	+	1.27570i
$341$	0.357498	−	0.619204i	0.0193596	−	0.0335318i
$342$	−5.91743	+	15.0857i	−0.319978	+	0.815741i
$343$	−10.4694	+	15.2772i	−0.565292	+	0.824891i
$344$		−	3.94104i		−	0.212487i
$345$	−6.64826	+	0.498847i	−0.357930	+	0.0268570i
$346$	−19.0217	+	10.9822i	−1.02261	+	0.590406i
$347$	−12.9453	+	7.47398i	−0.694941	+	0.401224i	−0.805460	−	0.592650i	$-0.798082\pi$
$347$	−12.9453	+	7.47398i	−0.694941	+	0.401224i	0.110520	+	0.993874i	$0.464749\pi$
$348$	2.92545	−	0.219509i	0.156820	−	0.0117669i
$349$			31.5104i			1.68671i	0.537355	+	0.843356i	$0.319423\pi$
$349$			31.5104i			1.68671i	−0.537355	+	0.843356i	$0.680577\pi$
$350$	25.4518	+	5.16628i	1.36046	+	0.276150i
$351$	−27.1766	+	6.21097i	−1.45058	+	0.331517i
$352$	−2.58589	+	4.47890i	−0.137829	+	0.238726i
$353$	11.9629	+	20.7204i	0.636723	+	1.10284i	0.986147	+	0.165872i	$0.0530437\pi$
$353$	11.9629	+	20.7204i	0.636723	+	1.10284i	−0.349425	+	0.936964i	$0.613623\pi$
$354$	−1.16731	+	2.42454i	−0.0620421	+	0.128863i
$355$	−18.3141	−	10.5737i	−0.972013	−	0.561192i
$356$	−4.25037			−0.225269
$357$	−32.0834	−	4.04345i	−1.69803	−	0.214002i
$358$	−20.8075			−1.09971
$359$	−11.9881	−	6.92136i	−0.632710	−	0.365295i	0.149091	−	0.988824i	$-0.452365\pi$
$359$	−11.9881	−	6.92136i	−0.632710	−	0.365295i	−0.781801	+	0.623528i	$0.785699\pi$
$360$	1.72321	+	11.4182i	0.0908213	+	0.601791i
$361$	5.08858	+	8.81367i	0.267820	+	0.463878i
$362$	5.02518	−	8.70387i	0.264118	−	0.457465i
$363$	22.5345	−	15.3668i	1.18275	−	0.806550i
$364$	4.51003	+	13.4589i	0.236390	+	0.705438i
$365$		−	55.7299i		−	2.91704i
$366$	−0.224777	−	2.99565i	−0.0117493	−	0.156585i
$367$	22.5909	−	13.0429i	1.17924	−	0.680833i	0.223399	−	0.974727i	$-0.428285\pi$
$367$	22.5909	−	13.0429i	1.17924	−	0.680833i	0.955838	+	0.293894i	$0.0949513\pi$
$368$	−0.866025	+	0.500000i	−0.0451447	+	0.0260643i
$369$	10.6684	+	13.3725i	0.555373	+	0.696146i
$370$			10.9100i			0.567183i
$371$	8.03990	+	23.9928i	0.417411	+	1.24564i
$372$	−0.134908	−	0.197834i	−0.00699466	−	0.0102572i
$373$	15.4877	−	26.8255i	0.801924	−	1.38897i	−0.116424	−	0.993200i	$-0.537143\pi$
$373$	15.4877	−	26.8255i	0.801924	−	1.38897i	0.918348	−	0.395773i	$-0.129523\pi$
$374$	−18.2475	−	31.6056i	−0.943555	−	1.63429i
$375$	28.9299	+	13.9286i	1.49394	+	0.719268i
$376$	−3.72064	−	2.14811i	−0.191878	−	0.110781i
$377$	9.08699			0.468004
$378$	−12.0702	−	6.58111i	−0.620823	−	0.338496i
$379$	−6.11799			−0.314260			−0.157130	−	0.987578i	$-0.550224\pi$
$379$	−6.11799			−0.314260			−0.157130	+	0.987578i	$0.550224\pi$
$380$	18.0060	+	10.3958i	0.923691	+	0.533293i
$381$	20.2726	+	9.76041i	1.03860	+	0.500041i
$382$	−8.52435	−	14.7646i	−0.436144	−	0.755423i
$383$	4.40072	−	7.62227i	0.224866	−	0.389480i	−0.731413	−	0.681935i	$-0.761139\pi$
$383$	4.40072	−	7.62227i	0.224866	−	0.389480i	0.956279	+	0.292455i	$0.0944721\pi$
$384$	0.975834	+	1.43100i	0.0497978	+	0.0730252i
$385$	−51.6165	−	10.4773i	−2.63062	−	0.533972i
$386$		−	14.1929i		−	0.722399i
$387$	7.37333	+	9.24230i	0.374808	+	0.469812i
$388$	−4.51787	+	2.60839i	−0.229360	+	0.132421i
$389$	28.1066	−	16.2273i	1.42506	−	0.822758i	0.428334	−	0.903621i	$-0.359101\pi$
$389$	28.1066	−	16.2273i	1.42506	−	0.822758i	0.996725	+	0.0808627i	$0.0257675\pi$
$390$	2.67631	+	35.6679i	0.135520	+	1.80611i
$391$		−	7.05655i		−	0.356865i
$392$	−2.72931	+	6.44600i	−0.137851	+	0.325572i
$393$	−16.6437	+	11.3498i	−0.839563	+	0.572520i
$394$	2.41905	−	4.18992i	0.121870	−	0.211085i
$395$	−6.44692	−	11.1664i	−0.324379	−	0.561842i
$396$	−2.31533	−	15.3416i	−0.116350	−	0.770946i
$397$	−19.4760	−	11.2445i	−0.977472	−	0.564344i	−0.0759659	−	0.997110i	$-0.524204\pi$
$397$	−19.4760	−	11.2445i	−0.977472	−	0.564344i	−0.901506	+	0.432767i	$0.857537\pi$
$398$	−0.440105			−0.0220605
$399$	−22.8162	+	9.59898i	−1.14224	+	0.480550i
$400$	9.81605			0.490803
$401$	−25.4935	−	14.7187i	−1.27309	−	0.735016i	−0.297518	−	0.954716i	$-0.596159\pi$
$401$	−25.4935	−	14.7187i	−1.27309	−	0.735016i	−0.975567	+	0.219700i	$0.929492\pi$
$402$	7.87230	−	16.3509i	0.392635	−	0.815511i
$403$	−0.370853	−	0.642336i	−0.0184735	−	0.0319971i
$404$	3.77208	−	6.53344i	0.187668	−	0.325051i
$405$	−25.4036	−	23.5533i	−1.26231	−	1.17037i
$406$	3.35760	+	2.96786i	0.166635	+	0.147292i
$407$		−	14.6588i		−	0.726610i
$408$	−12.1880	+	0.914521i	−0.603398	+	0.0452755i
$409$	−20.2489	+	11.6907i	−1.00124	+	0.578068i	−0.908616	−	0.417633i	$-0.862860\pi$
$409$	−20.2489	+	11.6907i	−1.00124	+	0.578068i	−0.0926273	+	0.995701i	$0.529527\pi$
$410$	19.0082	−	10.9744i	0.938749	−	0.541987i
$411$	−18.3436	+	1.37640i	−0.904825	+	0.0678929i
$412$		−	2.36833i		−	0.116679i
$413$	−3.89744	+	1.30602i	−0.191780	+	0.0642649i
$414$	1.09550	−	2.79283i	0.0538408	−	0.137260i
$415$	24.0387	−	41.6362i	1.18001	−	2.04384i
$416$	2.68250	+	4.64622i	0.131520	+	0.227800i
$417$	−5.39201	+	11.1993i	−0.264048	+	0.548433i
$418$	−24.1932	−	13.9679i	−1.18333	−	0.683194i
$419$	15.8613			0.774876			0.387438	−	0.921896i	$-0.373360\pi$
$419$	15.8613			0.774876			0.387438	+	0.921896i	$0.373360\pi$
$420$	−10.6604	+	14.0532i	−0.520175	+	0.685726i
$421$	10.3457			0.504218			0.252109	−	0.967699i	$-0.418876\pi$
$421$	10.3457			0.504218			0.252109	+	0.967699i	$0.418876\pi$
$422$	−21.0445	−	12.1500i	−1.02443	−	0.591455i
$423$	12.7444	−	1.92336i	0.619652	−	0.0935169i
$424$	4.78201	+	8.28269i	0.232235	+	0.402243i
$425$	−34.6337	+	59.9874i	−1.67998	+	2.90982i
$426$	7.86190	−	5.36124i	0.380910	−	0.259753i
$427$	3.03908	−	3.43818i	0.147071	−	0.166385i
$428$			10.4774i			0.506444i
$429$	−3.59593	−	47.9238i	−0.173613	−	2.31379i
$430$	13.1373	−	7.58485i	0.633539	−	0.365774i
$431$	7.11052	−	4.10526i	0.342502	−	0.197743i	−0.318876	−	0.947796i	$-0.603305\pi$
$431$	7.11052	−	4.10526i	0.342502	−	0.197743i	0.661378	+	0.750053i	$0.269972\pi$
$432$	−4.96573	−	1.53019i	−0.238914	−	0.0736213i
$433$			11.9801i			0.575728i	0.957671	+	0.287864i	$0.0929451\pi$
$433$			11.9801i			0.575728i	−0.957671	+	0.287864i	$0.907055\pi$
$434$	0.0727619	−	0.358463i	0.00349268	−	0.0172068i
$435$	6.36199	+	9.32943i	0.305034	+	0.447312i
$436$	5.69643	−	9.86651i	0.272810	−	0.472520i
$437$	−2.70079	−	4.67791i	−0.129197	−	0.223775i
$438$	22.5950	+	10.8786i	1.07963	+	0.519798i
$439$	6.28205	+	3.62694i	0.299826	+	0.173104i	0.642365	−	0.766399i	$-0.277954\pi$
$439$	6.28205	+	3.62694i	0.299826	+	0.173104i	−0.342539	+	0.939504i	$0.611287\pi$
$440$	−19.9071			−0.949031
$441$	−5.65926	−	20.2231i	−0.269489	−	0.963004i
$442$	−37.8584			−1.80074
$443$	−28.2503	−	16.3103i	−1.34221	−	0.774927i	−0.355081	−	0.934835i	$-0.615547\pi$
$443$	−28.2503	−	16.3103i	−1.34221	−	0.774927i	−0.987132	+	0.159908i	$0.948880\pi$
$444$	−4.42332	−	2.12964i	−0.209921	−	0.101068i
$445$	−8.18018	−	14.1685i	−0.387778	−	0.671650i
$446$	−8.28429	+	14.3488i	−0.392272	+	0.679436i
$447$	8.35717	+	12.2552i	0.395281	+	0.579653i
$448$	−0.526310	+	2.59287i	−0.0248658	+	0.122502i
$449$			9.63798i			0.454844i	0.973796	+	0.227422i	$0.0730297\pi$
$449$			9.63798i			0.454844i	−0.973796	+	0.227422i	$0.926970\pi$
$450$	−23.0200	+	18.3650i	−1.08517	+	0.865732i
$451$	−25.5397	+	14.7454i	−1.20262	+	0.694332i
$452$	−11.8336	+	6.83211i	−0.556604	+	0.321355i
$453$	1.40508	+	18.7258i	0.0660163	+	0.879815i
$454$		−	3.64942i		−	0.171276i
$455$	−36.1850	+	40.9368i	−1.69638	+	1.91915i
$456$	−7.72965	+	5.27105i	−0.361974	+	0.246840i
$457$	17.4655	−	30.2512i	0.817004	−	1.41509i	−0.0908768	−	0.995862i	$-0.528967\pi$
$457$	17.4655	−	30.2512i	0.817004	−	1.41509i	0.907880	−	0.419229i	$-0.137700\pi$
$458$	2.65093	+	4.59154i	0.123870	+	0.214548i
$459$	26.8717	−	24.9474i	1.25426	−	1.16445i
$460$	−3.33347	−	1.92458i	−0.155424	−	0.0897341i
$461$	−23.8237			−1.10958			−0.554791	−	0.831990i	$-0.687202\pi$
$461$	−23.8237			−1.10958			−0.554791	+	0.831990i	$0.687202\pi$
$462$	14.3235	−	18.8821i	0.666389	−	0.878474i
$463$	−10.4748			−0.486807			−0.243403	−	0.969925i	$-0.578264\pi$
$463$	−10.4748			−0.486807			−0.243403	+	0.969925i	$0.578264\pi$
$464$	1.46684	+	0.846878i	0.0680961	+	0.0393153i
$465$	0.399832	−	0.830460i	0.0185418	−	0.0385117i
$466$	6.81444	+	11.8030i	0.315673	+	0.546761i
$467$	−12.0113	+	20.8042i	−0.555818	+	0.962706i	0.442021	+	0.897005i	$0.354262\pi$
$467$	−12.0113	+	20.8042i	−0.555818	+	0.962706i	−0.997839	+	0.0657011i	$0.979072\pi$
$468$	−14.9835	−	5.87734i	−0.692613	−	0.271680i
$469$	26.2841	−	8.80770i	1.21369	−	0.406702i
$470$		−	16.5369i		−	0.762789i
$471$	−4.71937	+	0.354115i	−0.217457	+	0.0163167i
$472$	−1.34546	+	0.776799i	−0.0619296	+	0.0357551i
$473$	−17.6515	+	10.1911i	−0.811618	+	0.468588i
$474$	5.78572	−	0.434127i	0.265747	−	0.0199401i
$475$			53.0223i			2.43283i
$476$	−13.9885	−	12.3647i	−0.641161	−	0.566737i
$477$	−26.7107	−	10.4774i	−1.22300	−	0.479726i
$478$	7.40013	−	12.8174i	0.338474	−	0.586254i
$479$	16.5610	+	28.6845i	0.756691	+	1.31063i	0.944529	+	0.328428i	$0.106519\pi$
$479$	16.5610	+	28.6845i	0.756691	+	1.31063i	−0.187838	+	0.982200i	$0.560148\pi$
$480$	−2.89211	+	6.00698i	−0.132006	+	0.274180i
$481$	−13.1692	−	7.60322i	−0.600462	−	0.346677i
$482$	−5.77246			−0.262928
$483$	4.22398	−	1.77707i	0.192198	−	0.0808593i
$484$	15.7474			0.715791
$485$	−17.3900	−	10.0401i	−0.789640	−	0.455899i
$486$	14.5082	−	5.70193i	0.658106	−	0.258645i
$487$	−7.22550	−	12.5149i	−0.327419	−	0.567106i	0.654580	−	0.755993i	$-0.272845\pi$
$487$	−7.22550	−	12.5149i	−0.327419	−	0.567106i	−0.981999	+	0.188887i	$0.939512\pi$
$488$	0.867201	−	1.50204i	0.0392564	−	0.0679940i
$489$	−17.6824	+	12.0581i	−0.799624	+	0.545285i
$490$	−26.7403	+	3.30776i	−1.20800	+	0.149429i
$491$			35.1014i			1.58410i	0.610454	+	0.792052i	$0.290987\pi$
$491$			35.1014i			1.58410i	−0.610454	+	0.792052i	$0.709013\pi$
$492$	0.739002	+	9.84886i	0.0333168	+	0.444021i
$493$	−10.3508	+	5.97603i	−0.466176	+	0.269147i
$494$	−25.0970	+	14.4898i	−1.12917	+	0.651925i
$495$	46.6849	−	37.2443i	2.09833	−	1.67401i
$496$		−	0.138249i		−	0.00620757i
$497$	14.2453	+	2.89155i	0.638988	+	0.129704i
$498$	12.1885	+	17.8736i	0.546180	+	0.800937i
$499$	−15.4372	+	26.7380i	−0.691063	+	1.19696i	0.280428	+	0.959875i	$0.409524\pi$
$499$	−15.4372	+	26.7380i	−0.691063	+	1.19696i	−0.971490	+	0.237080i	$0.923810\pi$
$500$	9.26888	+	16.0542i	0.414517	+	0.717964i
$501$	3.06149	+	1.47398i	0.136777	+	0.0658527i
$502$	−2.67771	−	1.54598i	−0.119512	−	0.0690004i
$503$	8.36818			0.373119			0.186559	−	0.982444i	$-0.440266\pi$
$503$	8.36818			0.373119			0.186559	+	0.982444i	$0.440266\pi$
$504$	−3.61677	−	7.06534i	−0.161104	−	0.314715i
$505$	29.0387			1.29221
$506$	4.47890	+	2.58589i	0.199111	+	0.114957i
$507$	−24.6312	−	11.8589i	−1.09391	−	0.526672i
$508$	6.49515	+	11.2499i	0.288175	+	0.499135i
$509$	−5.97810	+	10.3544i	−0.264974	+	0.458949i	−0.967557	−	0.252653i	$-0.918697\pi$
$509$	−5.97810	+	10.3544i	−0.264974	+	0.458949i	0.702582	+	0.711602i	$0.252030\pi$
$510$	−26.5054	−	38.8684i	−1.17368	−	1.72112i
$511$	12.1712	+	36.3214i	0.538421	+	1.60676i
$512$			1.00000i			0.0441942i
$513$	8.26546	−	26.8229i	0.364929	−	1.18426i
$514$	12.6067	−	7.27846i	0.556056	−	0.321039i
$515$	7.89476	−	4.55804i	0.347885	−	0.200851i
$516$	0.510754	+	6.80695i	0.0224847	+	0.299659i
$517$			22.2192i			0.977199i
$518$	−2.38269	−	7.11046i	−0.104689	−	0.312416i
$519$	31.4309	−	21.4336i	1.37966	−	0.940830i
$520$	−10.3254	+	17.8841i	−0.452798	+	0.784268i
$521$	3.95641	+	6.85271i	0.173334	+	0.300223i	0.939583	−	0.342320i	$-0.111213\pi$
$521$	3.95641	+	6.85271i	0.173334	+	0.300223i	−0.766250	+	0.642543i	$0.777879\pi$
$522$	−5.02437	+	0.758269i	−0.219911	+	0.0331885i
$523$	13.1596	+	7.59767i	0.575427	+	0.332223i	0.759314	−	0.650724i	$-0.225535\pi$
$523$	13.1596	+	7.59767i	0.575427	+	0.332223i	−0.183887	+	0.982947i	$0.558868\pi$
$524$	−11.6308			−0.508096
$525$	−44.6298	−	5.62466i	−1.94780	−	0.245480i
$526$	7.98020			0.347953
$527$	0.844861	+	0.487781i	0.0368027	+	0.0212481i
$528$	3.88588	−	8.07106i	0.169111	−	0.351248i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	−18.4067	+	31.8814i	−0.799538	+	1.38484i
$531$	1.70196	−	4.33893i	0.0738589	−	0.188294i
$532$	−14.0056	−	2.84291i	−0.607222	−	0.123256i
$533$			30.5924i			1.32511i
$534$	7.34121	−	0.550843i	0.317685	−	0.0238373i
$535$	−34.9261	+	20.1646i	−1.50999	+	0.871792i
$536$	9.07368	−	5.23869i	0.391923	−	0.226277i
$537$	35.9386	−	2.69663i	1.55087	−	0.116368i
$538$			22.0628i			0.951193i
$539$	35.9287	−	4.44435i	1.54756	−	0.191432i
$540$	−4.45611	−	19.4981i	−0.191760	−	0.839065i
$541$	5.43252	−	9.40940i	0.233562	−	0.404542i	−0.725292	−	0.688442i	$-0.758295\pi$
$541$	5.43252	−	9.40940i	0.233562	−	0.404542i	0.958854	+	0.283900i	$0.0916284\pi$
$542$	−2.16239	−	3.74537i	−0.0928827	−	0.160878i
$543$	−7.55146	+	15.6845i	−0.324064	+	0.673088i
$544$	−6.11115	−	3.52828i	−0.262013	−	0.151274i
$545$	43.8530			1.87846
$546$	−9.53396	−	22.6617i	−0.408016	−	0.969829i
$547$	2.26342			0.0967768			0.0483884	−	0.998829i	$-0.484591\pi$
$547$	2.26342			0.0967768			0.0483884	+	0.998829i	$0.484591\pi$
$548$	−9.19760	−	5.31024i	−0.392902	−	0.226842i
$549$	0.776466	+	5.14495i	0.0331388	+	0.219581i
$550$	−25.3833	−	43.9651i	−1.08235	−	1.87468i
$551$	−4.57448	+	7.92324i	−0.194880	+	0.337541i
$552$	1.43100	−	0.975834i	0.0609072	−	0.0415342i
$553$	6.64039	+	5.86959i	0.282378	+	0.249601i
$554$			16.6590i			0.707774i
$555$	−1.41392	−	18.8437i	−0.0600176	−	0.799869i
$556$	−6.21487	+	3.58816i	−0.263569	+	0.152172i
$557$	−17.8890	+	10.3282i	−0.757980	+	0.437620i	−0.828570	−	0.559886i	$-0.810845\pi$
$557$	−17.8890	+	10.3282i	−0.757980	+	0.437620i	0.0705903	+	0.997505i	$0.477512\pi$
$558$	0.258652	+	0.324214i	0.0109496	+	0.0137251i
$559$			21.1437i			0.894282i
$560$	−9.65620	+	3.23576i	−0.408049	+	0.136736i
$561$	35.6130	+	52.2242i	1.50358	+	2.20491i
$562$	−10.7855	+	18.6810i	−0.454958	+	0.788011i
$563$	4.26604	+	7.38900i	0.179792	+	0.311409i	0.941809	−	0.336148i	$-0.109124\pi$
$563$	4.26604	+	7.38900i	0.179792	+	0.311409i	−0.762017	+	0.647557i	$0.775791\pi$
$564$	6.70467	+	3.22802i	0.282318	+	0.135924i
$565$	−45.5493	−	26.2979i	−1.91627	−	1.10636i
$566$	4.29241			0.180423
$567$	21.7004	+	9.80258i	0.911333	+	0.411670i
$568$	5.49401			0.230523
$569$	0.106589	+	0.0615389i	0.00446842	+	0.00257985i	0.502233	−	0.864733i	$-0.332512\pi$
$569$	0.106589	+	0.0615389i	0.00446842	+	0.00257985i	−0.497764	+	0.867312i	$0.665845\pi$
$570$	−32.4472	−	15.6220i	−1.35907	−	0.654334i
$571$	−10.7476	−	18.6154i	−0.449772	−	0.779028i	0.548599	−	0.836086i	$-0.315161\pi$
$571$	−10.7476	−	18.6154i	−0.449772	−	0.779028i	−0.998371	+	0.0570575i	$0.981828\pi$
$572$	13.8733	−	24.0293i	0.580072	−	1.00471i
$573$	16.6367	+	24.3966i	0.695008	+	1.01918i
$574$	−9.99164	+	11.3038i	−0.417043	+	0.471810i
$575$		−	9.81605i		−	0.409358i
$576$	−1.87091	−	2.34514i	−0.0779546	−	0.0977143i
$577$	−32.9754	+	19.0384i	−1.37278	+	0.792577i	−0.991278	−	0.131789i	$-0.957928\pi$
$577$	−32.9754	+	19.0384i	−1.37278	+	0.792577i	−0.381507	+	0.924366i	$0.624595\pi$
$578$	28.4012	−	16.3975i	1.18134	−	0.682044i
$579$	1.83938	+	24.5139i	0.0764422	+	1.01876i
$580$			6.51954i			0.270709i
$581$	−6.57380	+	32.3859i	−0.272727	+	1.34359i
$582$	7.46520	−	5.09071i	0.309442	−	0.211017i
$583$	24.7316	−	42.8363i	1.02428	−	1.77410i
$584$	7.23923	+	12.5387i	0.299561	+	0.518856i
$585$	−9.24503	−	61.2585i	−0.382235	−	2.53273i
$586$	−12.4169	−	7.16889i	−0.512936	−	0.296144i
$587$	−38.2357			−1.57816			−0.789078	−	0.614293i	$-0.789441\pi$
$587$	−38.2357			−1.57816			−0.789078	+	0.614293i	$0.789441\pi$
$588$	3.87866	−	11.4872i	0.159953	−	0.473725i
$589$	0.746765			0.0307699
$590$	−5.17888	−	2.99003i	−0.213211	−	0.123097i
$591$	−3.63517	+	7.55032i	−0.149531	+	0.310579i
$592$	−1.41719	−	2.45464i	−0.0582461	−	0.100885i
$593$	19.1445	−	33.1592i	0.786170	−	1.36169i	−0.142128	−	0.989848i	$-0.545395\pi$
$593$	19.1445	−	33.1592i	0.786170	−	1.36169i	0.928298	−	0.371837i	$-0.121272\pi$
$594$	5.98729	+	26.1979i	0.245662	+	1.07491i
$595$	14.2955	−	70.4272i	0.586060	−	2.88723i
$596$			8.56413i			0.350801i
$597$	0.760147	−	0.0570371i	0.0311108	−	0.00233437i
$598$	4.64622	−	2.68250i	0.189998	−	0.109696i
$599$	−4.16597	+	2.40522i	−0.170217	+	0.0982748i	−0.582688	−	0.812696i	$-0.697999\pi$
$599$	−4.16597	+	2.40522i	−0.170217	+	0.0982748i	0.412471	+	0.910971i	$0.364666\pi$
$600$	−16.9542	+	1.27215i	−0.692154	+	0.0519353i
$601$			28.3259i			1.15544i	0.816235	+	0.577720i	$0.196057\pi$
$601$			28.3259i			1.15544i	−0.816235	+	0.577720i	$0.803943\pi$
$602$	−6.90563	+	7.81248i	−0.281452	+	0.318413i
$603$	−11.4779	+	29.2615i	−0.467418	+	1.19162i
$604$	−5.42087	+	9.38922i	−0.220572	+	0.382042i
$605$	30.3071	+	52.4935i	1.23216	+	2.13416i
$606$	−5.66840	+	11.7734i	−0.230263	+	0.478261i
$607$	10.3352	+	5.96704i	0.419494	+	0.242195i	0.694861	−	0.719144i	$-0.255466\pi$
$607$	10.3352	+	5.96704i	0.419494	+	0.242195i	−0.275367	+	0.961339i	$0.588799\pi$
$608$	−5.40159			−0.219063
$609$	−6.18386	−	4.69093i	−0.250583	−	0.190086i
$610$	6.67600			0.270303
$611$	19.9612	+	11.5246i	0.807545	+	0.466237i
$612$	20.9326	−	3.15911i	0.846151	−	0.127700i
$613$	1.26028	+	2.18287i	0.0509023	+	0.0881654i	0.890354	−	0.455269i	$-0.150457\pi$
$613$	1.26028	+	2.18287i	0.0509023	+	0.0881654i	−0.839452	+	0.543435i	$0.817124\pi$
$614$	−4.80514	+	8.32275i	−0.193920	+	0.335879i
$615$	−31.4086	+	21.4184i	−1.26652	+	0.863672i
$616$	12.9742	−	4.34761i	0.522746	−	0.175170i
$617$		−	42.2311i		−	1.70016i	−0.526654	−	0.850080i	$-0.676553\pi$
$617$		−	42.2311i		−	1.70016i	0.526654	−	0.850080i	$-0.323447\pi$
$618$	0.306933	+	4.09057i	0.0123466	+	0.164547i
$619$	−24.6184	+	14.2135i	−0.989499	+	0.571288i	−0.905124	−	0.425147i	$-0.860223\pi$
$619$	−24.6184	+	14.2135i	−0.989499	+	0.571288i	−0.0843745	+	0.996434i	$0.526889\pi$
$620$	0.460850	−	0.266072i	0.0185082	−	0.0106857i
$621$	−1.53019	+	4.96573i	−0.0614044	+	0.199268i
$622$			6.59002i			0.264236i
$623$	8.42567	+	7.44764i	0.337567	+	0.298383i
$624$	−5.23534	−	7.67729i	−0.209582	−	0.307337i
$625$	−11.1373	+	19.2904i	−0.445492	+	0.771615i
$626$	9.89710	+	17.1423i	0.395567	+	0.685143i
$627$	43.5966	+	20.9899i	1.74108	+	0.838258i
$628$	−2.36632	−	1.36620i	−0.0944264	−	0.0545171i
$629$	20.0009			0.797490
$630$	16.5914	−	25.6542i	0.661015	−	1.02209i
$631$	10.6219			0.422852			0.211426	−	0.977394i	$-0.432189\pi$
$631$	10.6219			0.422852			0.211426	+	0.977394i	$0.432189\pi$
$632$	2.90099	+	1.67489i	0.115395	+	0.0666235i
$633$	37.9226	+	18.2582i	1.50729	+	0.725697i
$634$	−14.3599	−	24.8720i	−0.570303	−	0.987794i
$635$	−25.0009	+	43.3028i	−0.992129	+	1.71842i
$636$	−9.33290	−	13.6861i	−0.370073	−	0.542688i
$637$	14.6427	−	34.5827i	0.580167	−	1.37022i
$638$		−	8.75974i		−	0.346802i
$639$	−12.8842	+	10.2788i	−0.509692	+	0.406623i
$640$	−3.33347	+	1.92458i	−0.131767	+	0.0760758i
$641$	24.4430	−	14.1122i	0.965441	−	0.557398i	0.0675976	−	0.997713i	$-0.478467\pi$
$641$	24.4430	−	14.1122i	0.965441	−	0.557398i	0.897843	+	0.440315i	$0.145133\pi$
$642$	−1.35786	−	18.0965i	−0.0535904	−	0.714213i
$643$			4.64662i			0.183245i	0.995794	+	0.0916223i	$0.0292053\pi$
$643$			4.64662i			0.183245i	−0.995794	+	0.0916223i	$0.970795\pi$
$644$	2.59287	+	0.526310i	0.102174	+	0.0207395i
$645$	−21.7078	+	14.8031i	−0.854743	+	0.582872i
$646$	19.0583	−	33.0099i	0.749838	−	1.29876i
$647$	1.21464	+	2.10382i	0.0477525	+	0.0827097i	0.888914	−	0.458075i	$-0.151461\pi$
$647$	1.21464	+	2.10382i	0.0477525	+	0.0827097i	−0.841161	+	0.540784i	$0.818127\pi$
$648$	8.77510	+	1.99939i	0.344719	+	0.0785433i
$649$	6.95841	+	4.01744i	0.273142	+	0.157698i
$650$	−52.6631			−2.06562
$651$	−0.0792176	+	0.628565i	−0.00310478	+	0.0246354i
$652$	−12.3567			−0.483925
$653$	35.0689	+	20.2470i	1.37235	+	0.792327i	0.991224	−	0.132196i	$-0.0422027\pi$
$653$	35.0689	+	20.2470i	1.37235	+	0.792327i	0.381127	+	0.924523i	$0.375536\pi$
$654$	−8.56017	+	17.7796i	−0.334729	+	0.695239i
$655$	−22.3845	−	38.7711i	−0.874635	−	1.51491i
$656$	−2.85111	+	4.93827i	−0.111317	+	0.192807i
$657$	−40.4358	−	15.8611i	−1.57755	−	0.618801i
$658$	3.61158	+	10.7777i	0.140794	+	0.420160i
$659$		−	6.34104i		−	0.247012i	−0.992344	−	0.123506i	$-0.960586\pi$
$659$		−	6.34104i		−	0.247012i	0.992344	−	0.123506i	$-0.0394138\pi$
$660$	34.3834	−	2.57993i	1.33837	−	0.100424i
$661$	−1.74356	+	1.00665i	−0.0678167	+	0.0391540i	−0.533525	−	0.845784i	$-0.679133\pi$
$661$	−1.74356	+	1.00665i	−0.0678167	+	0.0391540i	0.465708	+	0.884938i	$0.345800\pi$
$662$	1.29975	−	0.750411i	0.0505162	−	0.0291655i
$663$	65.3888	−	4.90640i	2.53949	−	0.190549i
$664$			12.4904i			0.484720i
$665$	−17.4782	−	52.1588i	−0.677777	−	2.02263i
$666$	7.91593	+	3.10505i	0.306736	+	0.120318i
$667$	0.846878	−	1.46684i	0.0327912	−	0.0567961i
$668$	0.980874	+	1.69892i	0.0379512	+	0.0657333i
$669$	12.4490	−	25.8568i	0.481306	−	0.999683i
$670$	34.9261	+	20.1646i	1.34931	+	0.779025i
$671$	−8.96996			−0.346282
$672$	0.573006	−	4.54661i	0.0221042	−	0.175389i
$673$	4.60388			0.177467			0.0887333	−	0.996055i	$-0.471718\pi$
$673$	4.60388			0.177467			0.0887333	+	0.996055i	$0.471718\pi$
$674$	−0.0653745	−	0.0377440i	−0.00251813	−	0.00145384i
$675$	37.3800	−	34.7032i	1.43876	−	1.33573i
$676$	−7.89160	−	13.6686i	−0.303523	−	0.525717i
$677$	−5.40197	+	9.35649i	−0.207615	+	0.359599i	−0.950963	−	0.309306i	$-0.899903\pi$
$677$	−5.40197	+	9.35649i	−0.207615	+	0.359599i	0.743348	+	0.668905i	$0.233237\pi$
$678$	19.5534	−	13.3340i	0.750945	−	0.512089i
$679$	13.5265	+	2.74565i	0.519098	+	0.105368i
$680$		−	27.1618i		−	1.04161i
$681$	0.472961	+	6.30326i	0.0181239	+	0.241541i
$682$	−0.619204	+	0.357498i	−0.0237105	+	0.0136893i
$683$	35.1048	−	20.2678i	1.34325	−	0.775525i	0.355967	−	0.934499i	$-0.384152\pi$
$683$	35.1048	−	20.2678i	1.34325	−	0.775525i	0.987283	+	0.158973i	$0.0508184\pi$
$684$	12.6675	−	10.1059i	0.484354	−	0.386408i
$685$		−	40.8799i		−	1.56194i
$686$	16.7053	−	7.99576i	0.637812	−	0.305280i
$687$	−5.17373	−	7.58693i	−0.197390	−	0.289459i
$688$	−1.97052	+	3.41304i	−0.0751254	+	0.130121i
$689$	−25.6555	−	44.4366i	−0.977396	−	1.69290i
$690$	6.00698	+	2.89211i	0.228682	+	0.110101i
$691$	−24.6725	−	14.2447i	−0.938586	−	0.541893i	−0.0490695	−	0.998795i	$-0.515626\pi$
$691$	−24.6725	−	14.2447i	−0.938586	−	0.541893i	−0.889517	+	0.456902i	$0.848959\pi$
$692$	21.9644			0.834960
$693$	−22.2924	+	34.4693i	−0.846817	+	1.30938i
$694$	14.9480			0.567417
$695$	−23.9220	−	13.8114i	−0.907415	−	0.523896i
$696$	−2.64327	−	1.27262i	−0.100193	−	0.0482387i
$697$	−20.1190	−	34.8472i	−0.762063	−	1.31993i
$698$	15.7552	−	27.2888i	0.596343	−	1.03290i
$699$	−13.2995	−	19.5029i	−0.503034	−	0.737666i
$700$	−19.4588	−	17.2000i	−0.735472	−	0.650100i
$701$			11.1854i			0.422466i	0.977436	+	0.211233i	$0.0677479\pi$
$701$			11.1854i			0.422466i	−0.977436	+	0.211233i	$0.932252\pi$
$702$	26.6411	+	8.20947i	1.00551	+	0.309846i
$703$	13.2590	−	7.65507i	0.500072	−	0.288717i
$704$	4.47890	−	2.58589i	0.168805	−	0.0974595i
$705$	2.14316	+	28.5624i	0.0807161	+	1.07572i
$706$		−	23.9259i		−	0.900462i
$707$	−18.9257	+	6.34192i	−0.711773	+	0.238513i
$708$	2.22319	−	1.51605i	0.0835527	−	0.0569768i
$709$	−25.4725	+	44.1197i	−0.956640	+	1.65695i	−0.226069	+	0.974111i	$0.572588\pi$
$709$	−25.4725	+	44.1197i	−0.956640	+	1.65695i	−0.730571	+	0.682837i	$0.760746\pi$
$710$	10.5737	+	18.3141i	0.396823	+	0.687317i
$711$	−9.93680	+	1.49964i	−0.372659	+	0.0562411i
$712$	3.68093	+	2.12518i	0.137949	+	0.0796446i
$713$	−0.138249			−0.00517747
$714$	25.7633	+	19.5434i	0.964167	+	0.731394i
$715$	106.801			3.99414
$716$	18.0198	+	10.4038i	0.673432	+	0.388806i
$717$	−11.1203	+	23.0972i	−0.415297	+	0.862581i
$718$	6.92136	+	11.9881i	0.258303	+	0.447394i
$719$	15.3180	−	26.5316i	0.571265	−	0.989460i	−0.425171	−	0.905113i	$-0.639786\pi$
$719$	15.3180	−	26.5316i	0.571265	−	0.989460i	0.996436	−	0.0843474i	$-0.0268806\pi$
$720$	4.21675	−	10.7500i	0.157149	−	0.400631i
$721$	−4.14987	+	4.69483i	−0.154549	+	0.174845i
$722$		−	10.1772i		−	0.378754i
$723$	9.97017	−	0.748105i	0.370795	−	0.0278223i
$724$	−8.70387	+	5.02518i	−0.323477	+	0.186759i
$725$	−14.3985	+	8.31299i	−0.534748	+	0.308737i
$726$	−27.1988	+	2.04084i	−1.00944	+	0.0757428i
$727$		−	39.9378i		−	1.48121i	−0.671939	−	0.740606i	$-0.734538\pi$
$727$		−	39.9378i		−	1.48121i	0.671939	−	0.740606i	$-0.265462\pi$
$728$	2.82365	−	13.9108i	0.104651	−	0.515567i
$729$	−24.3195	+	11.7286i	−0.900724	+	0.434392i
$730$	−27.8650	+	48.2635i	−1.03133	+	1.78631i
$731$	−13.9051	−	24.0843i	−0.514298	−	0.890790i
$732$	−1.30316	+	2.70670i	−0.0481663	+	0.100042i
$733$	−37.2895	−	21.5291i	−1.37732	−	0.795196i	−0.385484	−	0.922714i	$-0.625966\pi$
$733$	−37.2895	−	21.5291i	−1.37732	−	0.795196i	−0.991836	+	0.127518i	$0.959299\pi$
$734$	−26.0858			−0.962843
$735$	45.7571	−	9.17866i	1.68778	−	0.338560i
$736$	1.00000			0.0368605
$737$	−46.9271	−	27.0934i	−1.72858	−	0.997998i
$738$	−2.55280	−	16.9151i	−0.0939700	−	0.622655i
$739$	18.6886	+	32.3696i	0.687470	+	1.19073i	0.972654	+	0.232261i	$0.0746122\pi$
$739$	18.6886	+	32.3696i	0.687470	+	1.19073i	−0.285183	+	0.958473i	$0.592054\pi$
$740$	5.45499	−	9.44832i	0.200529	−	0.347327i
$741$	41.4695	−	28.2792i	1.52342	−	1.03886i
$742$	5.03364	−	24.7983i	0.184791	−	0.910375i
$743$			38.1630i			1.40006i	0.714112	+	0.700032i	$0.246831\pi$
$743$			38.1630i			1.40006i	−0.714112	+	0.700032i	$0.753169\pi$
$744$	0.0179169	+	0.238783i	0.000656867	+	0.00875422i
$745$	−28.5483	+	16.4824i	−1.04593	+	0.603867i
$746$	−26.8255	+	15.4877i	−0.982152	+	0.567046i
$747$	−23.3683	−	29.2917i	−0.855003	−	1.07173i
$748$			36.4950i			1.33439i
$749$	18.3589	−	20.7698i	0.670818	−	0.758911i
$750$	−18.0898	−	26.5275i	−0.660545	−	0.968646i
$751$	−1.49013	+	2.58097i	−0.0543755	+	0.0941811i	−0.891932	−	0.452170i	$-0.850650\pi$
$751$	−1.49013	+	2.58097i	−0.0543755	+	0.0941811i	0.837556	+	0.546351i	$0.183983\pi$
$752$	2.14811	+	3.72064i	0.0783337	+	0.135678i
$753$	4.82529	+	2.32318i	0.175843	+	0.0846613i
$754$	−7.86957	−	4.54350i	−0.286593	−	0.165464i
$755$	−41.7316			−1.51877
$756$	7.16252	+	11.7345i	0.260498	+	0.426779i
$757$	−32.6178			−1.18551			−0.592756	−	0.805382i	$-0.701960\pi$
$757$	−32.6178			−1.18551			−0.592756	+	0.805382i	$0.701960\pi$
$758$	5.29834	+	3.05900i	0.192444	+	0.111108i
$759$	−8.07106	−	3.88588i	−0.292961	−	0.141049i
$760$	−10.3958	−	18.0060i	−0.377095	−	0.653148i
$761$	4.83134	−	8.36813i	0.175136	−	0.303344i	−0.765072	−	0.643944i	$-0.777297\pi$
$761$	4.83134	−	8.36813i	0.175136	−	0.303344i	0.940208	+	0.340600i	$0.110630\pi$
$762$	−12.6764	−	18.5891i	−0.459216	−	0.673410i
$763$	−28.5807	+	9.57729i	−1.03469	+	0.346721i
$764$			17.0487i			0.616801i
$765$	50.8173	+	63.6983i	1.83730	+	2.30302i
$766$	−7.62227	+	4.40072i	−0.275404	+	0.159005i
$767$	7.21837	−	4.16753i	0.260640	−	0.150481i
$768$	−0.129599	−	1.72720i	−0.00467650	−	0.0623248i
$769$		−	21.5467i		−	0.776993i	−0.921450	−	0.388497i	$-0.872994\pi$
$769$		−	21.5467i		−	0.776993i	0.921450	−	0.388497i	$-0.127006\pi$
$770$	39.4625	+	34.8818i	1.42213	+	1.25705i
$771$	−20.8309	+	14.2051i	−0.750207	+	0.511586i
$772$	−7.09645	+	12.2914i	−0.255407	+	0.442378i
$773$	−7.66598	−	13.2779i	−0.275726	−	0.477572i	0.694592	−	0.719404i	$-0.255585\pi$
$773$	−7.66598	−	13.2779i	−0.275726	−	0.477572i	−0.970318	+	0.241832i	$0.922252\pi$
$774$	−1.76434	−	11.6907i	−0.0634181	−	0.420215i
$775$	1.17525	+	0.678530i	0.0422162	+	0.0243735i
$776$	5.21678			0.187272
$777$	5.03688	+	11.9724i	0.180697	+	0.429506i
$778$	−32.4547			−1.16356
$779$	−26.6745	−	15.4005i	−0.955714	−	0.551782i
$780$	15.5162	−	32.2274i	0.555568	−	1.15393i
$781$	−14.2069	−	24.6071i	−0.508364	−	0.880512i
$782$	−3.52828	+	6.11115i	−0.126171	+	0.218534i
$783$	8.57980	−	1.96083i	0.306617	−	0.0700744i
$784$	5.58665	−	4.21774i	0.199523	−	0.150634i
$785$		−	10.5174i		−	0.375383i
$786$	20.0887	−	1.50734i	0.716542	−	0.0537652i
$787$	−36.5005	+	21.0736i	−1.30110	+	0.751192i	−0.980593	−	0.196053i	$-0.937187\pi$
$787$	−36.5005	+	21.0736i	−1.30110	+	0.751192i	−0.320509	+	0.947245i	$0.603854\pi$
$788$	−4.18992	+	2.41905i	−0.149260	+	0.0861751i
$789$	−13.7834	+	1.03423i	−0.490701	+	0.0368194i
$790$			12.8938i			0.458742i
$791$	35.4296	+	7.19161i	1.25973	+	0.255704i
$792$	−5.66568	+	14.4439i	−0.201321	+	0.513242i
$793$	−4.65253	+	8.05842i	−0.165216	+	0.286163i
$794$	11.2445	+	19.4760i	0.399051	+	0.691177i
$795$	27.6602	−	57.4509i	0.981008	−	2.03757i
$796$	0.381142	+	0.220052i	0.0135092	+	0.00779955i
$797$	−20.8475			−0.738456			−0.369228	−	0.929339i	$-0.620378\pi$
$797$	−20.8475			−0.738456			−0.369228	+	0.929339i	$0.620378\pi$
$798$	24.5589	+	3.09515i	0.869376	+	0.109567i
$799$	−30.3166			−1.07252
$800$	−8.50095	−	4.90803i	−0.300554	−	0.173525i
$801$	−12.6083	+	1.90283i	−0.445493	+	0.0672331i
$802$	14.7187	+	25.4935i	0.519735	+	0.900207i
$803$	37.4398	−	64.8476i	1.32122	−	2.28842i
$804$	−14.9931	+	10.2242i	−0.528765	+	0.360579i
$805$	3.23576	+	9.65620i	0.114045	+	0.340336i
$806$			0.741706i			0.0261255i
$807$	−2.85931	−	38.1067i	−0.100652	−	1.34142i
$808$	−6.53344	+	3.77208i	−0.229846	+	0.132701i
$809$	5.55454	−	3.20692i	0.195287	−	0.112749i	−0.399168	−	0.916878i	$-0.630701\pi$
$809$	5.55454	−	3.20692i	0.195287	−	0.112749i	0.594455	+	0.804129i	$0.297368\pi$
$810$	10.2235	+	33.0995i	0.359217	+	1.16300i
$811$		−	7.47635i		−	0.262530i	−0.991347	−	0.131265i	$-0.958096\pi$
$811$		−	7.47635i		−	0.262530i	0.991347	−	0.131265i	$-0.0419039\pi$
$812$	−1.42384	−	4.24904i	−0.0499669	−	0.149112i
$813$	4.22027	+	6.18875i	0.148011	+	0.217049i
$814$	−7.32940	+	12.6949i	−0.256895	+	0.444956i
$815$	−23.7815	−	41.1907i	−0.833028	−	1.44285i
$816$	11.0124	+	5.30202i	0.385512	+	0.185608i
$817$	−18.4358	−	10.6439i	−0.644988	−	0.372384i
$818$	23.3814			0.817512
$819$	19.4039	+	37.9055i	0.678028	+	1.32453i
$820$	−21.9488			−0.766485
$821$	18.6188	+	10.7496i	0.649802	+	0.375163i	0.788380	−	0.615188i	$-0.210920\pi$
$821$	18.6188	+	10.7496i	0.649802	+	0.375163i	−0.138578	+	0.990351i	$0.544253\pi$
$822$	16.5743	+	7.97982i	0.578093	+	0.278328i
$823$	2.24607	+	3.89030i	0.0782930	+	0.135607i	0.902514	−	0.430662i	$-0.141720\pi$
$823$	2.24607	+	3.89030i	0.0782930	+	0.135607i	−0.824221	+	0.566269i	$0.808386\pi$
$824$	−1.18416	+	2.05103i	−0.0412523	+	0.0714511i
$825$	49.5397	+	72.6467i	1.72475	+	2.52923i
$826$	4.02829	+	0.817674i	0.140162	+	0.0284505i
$827$		−	13.9682i		−	0.485724i	−0.970061	−	0.242862i	$-0.921914\pi$
$827$		−	13.9682i		−	0.485724i	0.970061	−	0.242862i	$-0.0780862\pi$
$828$	−2.34514	+	1.87091i	−0.0814993	+	0.0650186i
$829$	44.5098	−	25.6977i	1.54589	−	0.892520i	0.547441	−	0.836845i	$-0.315602\pi$
$829$	44.5098	−	25.6977i	1.54589	−	0.892520i	0.998449	−	0.0556751i	$-0.0177311\pi$
$830$	−41.6362	+	24.0387i	−1.44522	+	0.834395i
$831$	−2.15899	−	28.7734i	−0.0748945	−	0.998138i
$832$		−	5.36500i		−	0.185998i
$833$	6.06401	+	49.0222i	0.210106	+	1.69852i
$834$	10.2693	−	7.00289i	0.355596	−	0.242490i
$835$	−3.77554	+	6.53943i	−0.130658	+	0.226306i
$836$	13.9679	+	24.1932i	0.483091	+	0.836738i
$837$	−0.488760	−	0.526460i	−0.0168940	−	0.0181971i
$838$	−13.7363	−	7.93065i	−0.474512	−	0.273960i
$839$	53.3594			1.84217			0.921085	−	0.389361i	$-0.127304\pi$
$839$	53.3594			1.84217			0.921085	+	0.389361i	$0.127304\pi$
$840$	16.2588	−	6.84022i	0.560982	−	0.236010i
$841$	26.1312			0.901076
$842$	−8.95963	−	5.17285i	−0.308769	−	0.178268i
$843$	16.2076	−	33.6635i	0.558220	−	1.15943i
$844$	12.1500	+	21.0445i	0.418222	+	0.724381i
$845$	30.3760	−	52.6128i	1.04497	−	1.80994i
$846$	−11.9986	−	4.70651i	−0.412521	−	0.161813i
$847$	−31.2167	−	27.5931i	−1.07262	−	0.948111i
$848$		−	9.56403i		−	0.328430i
$849$	−7.41383	+	0.556292i	−0.254442	+	0.0190919i
$850$	59.9874	−	34.6337i	2.05755	−	1.18793i
$851$	−2.45464	+	1.41719i	−0.0841441	+	0.0485806i
$852$	−9.48923	+	0.712017i	−0.325095	+	0.0243933i
$853$		−	10.0611i		−	0.344484i	−0.985055	−	0.172242i	$-0.944899\pi$
$853$		−	10.0611i		−	0.344484i	0.985055	−	0.172242i	$-0.0551011\pi$
$854$	−4.35101	+	1.45801i	−0.148888	+	0.0498920i
$855$	58.0673	+	22.7771i	1.98586	+	0.778962i
$856$	5.23870	−	9.07370i	0.179055	−	0.310133i
$857$	−26.6322	−	46.1284i	−0.909740	−	1.57572i	−0.814426	−	0.580268i	$-0.802948\pi$
$857$	−26.6322	−	46.1284i	−0.909740	−	1.57572i	−0.0953142	−	0.995447i	$-0.530386\pi$
$858$	−20.8478	+	43.3012i	−0.711731	+	1.47828i
$859$	−7.54022	−	4.35335i	−0.257269	−	0.148534i	0.365819	−	0.930686i	$-0.380789\pi$
$859$	−7.54022	−	4.35335i	−0.257269	−	0.148534i	−0.623088	+	0.782152i	$0.714122\pi$
$860$	−15.1697			−0.517282
$861$	15.7926	−	20.8187i	0.538209	−	0.709499i
$862$	−8.21052			−0.279652
$863$	−3.10463	−	1.79246i	−0.105683	−	0.0610159i	0.446227	−	0.894920i	$-0.352767\pi$
$863$	−3.10463	−	1.79246i	−0.105683	−	0.0610159i	−0.551910	+	0.833904i	$0.686101\pi$
$864$	3.53536	+	3.80805i	0.120275	+	0.129553i
$865$	42.2722	+	73.2177i	1.43730	+	2.48947i
$866$	5.99006	−	10.3751i	0.203550	−	0.352560i
$867$	−46.9294	+	32.0024i	−1.59381	+	1.08686i
$868$	−0.242245	+	0.274057i	−0.00822233	+	0.00930209i
$869$		−	17.3243i		−	0.587688i
$870$	−0.844925	−	11.2605i	−0.0286456	−	0.381767i
$871$	−48.6803	+	28.1056i	−1.64947	+	0.952321i
$872$	−9.86651	+	5.69643i	−0.334122	+	0.192906i
$873$	−12.2341	+	9.76014i	−0.414062	+	0.330331i
$874$			5.40159i			0.182711i
$875$	9.75661	−	48.0661i	0.329834	−	1.62493i
$876$	−14.1286	−	20.7186i	−0.477360	−	0.700017i
$877$	0.184926	−	0.320301i	0.00624451	−	0.0108158i	−0.862886	−	0.505398i	$-0.831346\pi$
$877$	0.184926	−	0.320301i	0.00624451	−	0.0108158i	0.869131	+	0.494582i	$0.164679\pi$
$878$	−3.62694	−	6.28205i	−0.122403	−	0.212009i
$879$	22.3755	+	10.7729i	0.754705	+	0.363359i
$880$	17.2400	+	9.95353i	0.581161	+	0.335533i
$881$	34.7678			1.17136			0.585679	−	0.810543i	$-0.300828\pi$
$881$	34.7678			1.17136			0.585679	+	0.810543i	$0.300828\pi$
$882$	−5.21047	+	20.3433i	−0.175446	+	0.684995i
$883$	1.71306			0.0576490			0.0288245	−	0.999584i	$-0.490824\pi$
$883$	1.71306			0.0576490			0.0288245	+	0.999584i	$0.490824\pi$
$884$	32.7863	+	18.9292i	1.10272	+	0.636657i
$885$	9.33244	+	4.49318i	0.313707	+	0.151037i
$886$	16.3103	+	28.2503i	0.547956	+	0.949088i
$887$	−9.85440	+	17.0683i	−0.330878	+	0.573098i	−0.982684	−	0.185288i	$-0.940678\pi$
$887$	−9.85440	+	17.0683i	−0.330878	+	0.573098i	0.651806	+	0.758386i	$0.274012\pi$
$888$	2.76588	+	4.05598i	0.0928169	+	0.136110i
$889$	6.83692	−	33.6822i	0.229303	−	1.12966i
$890$			16.3604i			0.548400i
$891$	−13.7364	−	44.4730i	−0.460188	−	1.48990i
$892$	14.3488	−	8.28429i	0.480434	−	0.277378i
$893$	−20.0974	+	11.6032i	−0.672533	+	0.388287i
$894$	−1.10990	−	14.7919i	−0.0371207	−	0.494716i
$895$			80.0915i			2.67716i
$896$	1.75223	−	1.98234i	0.0585381	−	0.0662253i
$897$	−7.67729	+	5.23534i	−0.256337	+	0.174803i
$898$	4.81899	−	8.34673i	0.160812	−	0.278534i
$899$	0.117080	+	0.202789i	0.00390484	+	0.00676338i
$900$	29.1184	−	4.39450i	0.970614	−	0.146483i
$901$	58.4472	+	33.7445i	1.94716	+	1.12419i
$902$	29.4907			0.981933
$903$	10.9149	−	14.3886i	0.363224	−	0.478824i
$904$	13.6642			0.454465
$905$	−33.5026	−	19.3427i	−1.11366	−	0.642974i
$906$	8.14607	−	16.9196i	0.270635	−	0.562115i
$907$	24.8606	+	43.0599i	0.825484	+	1.42978i	0.901549	+	0.432677i	$0.142431\pi$
$907$	24.8606	+	43.0599i	0.825484	+	1.42978i	−0.0760653	+	0.997103i	$0.524236\pi$
$908$	−1.82471	+	3.16049i	−0.0605551	+	0.104885i
$909$	8.26461	−	21.0695i	0.274120	−	0.698833i
$910$	51.8055	−	17.3598i	1.71734	−	0.575473i
$911$		−	57.1990i		−	1.89509i	−0.319624	−	0.947545i	$-0.603557\pi$
$911$		−	57.1990i		−	1.89509i	0.319624	−	0.947545i	$-0.396443\pi$
$912$	9.32960	−	0.700040i	0.308934	−	0.0231806i
$913$	55.9430	−	32.2987i	1.85144	−	1.06893i
$914$	−30.2512	+	17.4655i	−1.00062	+	0.577709i
$915$	−11.5308	+	0.865202i	−0.381195	+	0.0286027i
$916$		−	5.30185i		−	0.175178i
$917$	23.0563	+	20.3800i	0.761386	+	0.673006i
$918$	−35.7453	+	8.16925i	−1.17977	+	0.269625i
$919$	12.3675	−	21.4211i	0.407965	−	0.706616i	−0.586697	−	0.809807i	$-0.699572\pi$
$919$	12.3675	−	21.4211i	0.407965	−	0.706616i	0.994662	+	0.103191i	$0.0329052\pi$
$920$	1.92458	+	3.33347i	0.0634516	+	0.109901i
$921$	7.22080	−	14.9978i	0.237933	−	0.494193i
$922$	20.6320	+	11.9119i	0.679477	+	0.392296i
$923$	−29.4753			−0.970192
$924$	−21.8455	+	9.19061i	−0.718666	+	0.302349i
$925$	27.8224			0.914795
$926$	9.07147	+	5.23741i	0.298107	+	0.172112i
$927$	−1.06027	−	7.02543i	−0.0348237	−	0.230745i
$928$	−0.846878	−	1.46684i	−0.0278001	−	0.0481512i
$929$	5.33811	−	9.24587i	0.175138	−	0.303347i	−0.765071	−	0.643946i	$-0.777296\pi$
$929$	5.33811	−	9.24587i	0.175138	−	0.303347i	0.940209	+	0.340598i	$0.110630\pi$
$930$	−0.761495	+	0.519283i	−0.0249704	+	0.0170280i
$931$	22.7825	+	30.1768i	0.746666	+	0.989004i
$932$		−	13.6289i		−	0.446429i
$933$	−0.854060	−	11.3823i	−0.0279607	−	0.372638i
$934$	20.8042	−	12.0113i	0.680736	−	0.393023i
$935$	−121.655	+	70.2376i	−3.97854	+	2.29701i
$936$	10.0374	+	12.5817i	0.328084	+	0.411245i
$937$			18.1921i			0.594311i	0.954829	+	0.297155i	$0.0960379\pi$
$937$			18.1921i			0.594311i	−0.954829	+	0.297155i	$0.903962\pi$
$938$	−27.1665	−	5.51435i	−0.887019	−	0.180050i
$939$	−19.3158	−	28.3254i	−0.630349	−	0.924365i
$940$	−8.26844	+	14.3214i	−0.269687	+	0.467111i
$941$	19.0947	+	33.0730i	0.622470	+	1.07815i	0.989024	+	0.147753i	$0.0472041\pi$
$941$	19.0947	+	33.0730i	0.622470	+	1.07815i	−0.366554	+	0.930397i	$0.619463\pi$
$942$	4.26415	+	2.05301i	0.138934	+	0.0668908i
$943$	4.93827	+	2.85111i	0.160812	+	0.0928450i
$944$	1.55360			0.0505653
$945$	−25.3318	+	46.4600i	−0.824042	+	1.51135i
$946$	20.3822			0.662683
$947$	14.6954	+	8.48441i	0.477537	+	0.275706i	0.719390	−	0.694607i	$-0.244422\pi$
$947$	14.6954	+	8.48441i	0.477537	+	0.275706i	−0.241852	+	0.970313i	$0.577755\pi$
$948$	−5.22764	−	2.51689i	−0.169786	−	0.0817449i
$949$	−38.8384	−	67.2701i	−1.26075	−	2.18368i
$950$	26.5111	−	45.9186i	0.860135	−	1.48980i
$951$	28.0257	+	41.0978i	0.908795	+	1.33269i
$952$	5.93202	+	17.7024i	0.192258	+	0.573739i
$953$		−	19.2791i		−	0.624510i	−0.949998	−	0.312255i	$-0.898916\pi$
$953$		−	19.2791i		−	0.624510i	0.949998	−	0.312255i	$-0.101084\pi$
$954$	17.8934	+	22.4290i	0.579321	+	0.726166i
$955$	−56.8314	+	32.8116i	−1.83902	+	1.06176i
$956$	−12.8174	+	7.40013i	−0.414544	+	0.239337i
$957$	1.13525	+	15.1298i	0.0366975	+	0.489077i
$958$		−	33.1220i		−	1.07012i
$959$	8.92799	+	26.6431i	0.288300	+	0.860349i
$960$	5.50813	−	3.75614i	0.177774	−	0.121229i
$961$	−15.4904	+	26.8302i	−0.499692	+	0.865491i
$962$	7.60322	+	13.1692i	0.245138	+	0.424591i
$963$	4.69058	+	31.0802i	0.151152	+	1.00155i
$964$	4.99910	+	2.88623i	0.161010	+	0.0929592i
$965$	−54.6308			−1.75863
$966$	−4.54661	−	0.573006i	−0.146285	−	0.0184362i
$967$	−33.3423			−1.07222			−0.536108	−	0.844149i	$-0.680106\pi$
$967$	−33.3423			−1.07222			−0.536108	+	0.844149i	$0.680106\pi$
$968$	−13.6376	−	7.87370i	−0.438330	−	0.253070i
$969$	−28.6393	+	59.4845i	−0.920028	+	1.91092i
$970$	10.0401	+	17.3900i	0.322369	+	0.558359i
$971$	1.98291	−	3.43450i	0.0636346	−	0.110218i	−0.832453	−	0.554096i	$-0.813064\pi$
$971$	1.98291	−	3.43450i	0.0636346	−	0.110218i	0.896087	+	0.443877i	$0.146397\pi$
$972$	−15.4154	−	2.31609i	−0.494450	−	0.0742885i
$973$	18.6073	+	3.77696i	0.596522	+	0.121084i
$974$			14.4510i			0.463040i
$975$	90.9594	−	6.82508i	2.91303	−	0.218577i
$976$	−1.50204	+	0.867201i	−0.0480790	+	0.0277584i
$977$	10.7580	−	6.21115i	0.344180	−	0.198712i	−0.317939	−	0.948111i	$-0.602991\pi$
$977$	10.7580	−	6.21115i	0.344180	−	0.198712i	0.662119	+	0.749399i	$0.269657\pi$
$978$	21.3424	−	1.60141i	0.682455	−	0.0512075i
$979$		−	21.9820i		−	0.702548i
$980$	24.8117	+	10.5056i	0.792580	+	0.335588i
$981$	12.4809	−	31.8183i	0.398483	−	1.01588i
$982$	17.5507	−	30.3987i	0.560065	−	0.970062i
$983$	17.7439	+	30.7334i	0.565944	+	0.980244i	0.996961	+	0.0778999i	$0.0248214\pi$
$983$	17.7439	+	30.7334i	0.565944	+	0.980244i	−0.431017	+	0.902344i	$0.641845\pi$
$984$	4.28444	−	8.89887i	0.136583	−	0.283685i
$985$	−16.1277	−	9.31132i	−0.513871	−	0.296683i
$986$	11.9521			0.380631
$987$	−7.63469	−	18.1472i	−0.243015	−	0.577632i
$988$	28.9795			0.921961
$989$	3.41304	+	1.97052i	0.108528	+	0.0626589i
$990$	−59.0524	+	8.91209i	−1.87681	+	0.283245i
$991$	−18.9540	−	32.8293i	−0.602095	−	1.04286i	−0.992503	−	0.122217i	$-0.961000\pi$
$991$	−18.9540	−	32.8293i	−0.602095	−	1.04286i	0.390409	−	0.920642i	$-0.372334\pi$
$992$	−0.0691246	+	0.119727i	−0.00219471	+	0.00380134i
$993$	−2.14767	+	1.46455i	−0.0681542	+	0.0464762i
$994$	−10.8910	−	9.62679i	−0.345441	−	0.305343i
$995$			1.69404i			0.0537045i
$996$	−1.61874	−	21.5733i	−0.0512916	−	0.683575i
$997$	16.9504	−	9.78632i	0.536825	−	0.309936i	−0.206966	−	0.978348i	$-0.566359\pi$
$997$	16.9504	−	9.78632i	0.536825	−	0.309936i	0.743791	+	0.668412i	$0.233026\pi$
$998$	26.7380	−	15.4372i	0.846375	−	0.488655i
$999$	−14.0748	−	4.33714i	−0.445306	−	0.137221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.c.47.13	✓	56
3.2	odd	2	inner	966.2.l.c.47.22	yes	56
7.3	odd	6	inner	966.2.l.c.185.22	yes	56
21.17	even	6	inner	966.2.l.c.185.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.c.47.13	✓	56	1.1	even	1	trivial
966.2.l.c.47.22	yes	56	3.2	odd	2	inner
966.2.l.c.185.13	yes	56	21.17	even	6	inner
966.2.l.c.185.22	yes	56	7.3	odd	6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.56059 + 0.751362i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.92458 + 3.33347i) q^{5} +(-0.975834 - 1.43100i) q^{6} +(0.526310 - 2.59287i) q^{7} -1.00000i q^{8} +(1.87091 + 2.34514i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.56059 + 0.751362i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.92458 + 3.33347i) q^{5} +(-0.975834 - 1.43100i) q^{6} +(0.526310 - 2.59287i) q^{7} -1.00000i q^{8} +(1.87091 + 2.34514i) q^{9} +(3.33347 - 1.92458i) q^{10} +(-4.47890 + 2.58589i) q^{11} +(0.129599 + 1.72720i) q^{12} +5.36500i q^{13} +(-1.75223 + 1.98234i) q^{14} +(-5.50813 + 3.75614i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.52828 - 6.11115i) q^{17} +(-0.447685 - 2.96641i) q^{18} +(-4.67791 - 2.70079i) q^{19} -3.84916 q^{20} +(2.76954 - 3.65098i) q^{21} +5.17179 q^{22} +(0.866025 + 0.500000i) q^{23} +(0.751362 - 1.56059i) q^{24} +(-4.90803 - 8.50095i) q^{25} +(2.68250 - 4.64622i) q^{26} +(1.15768 + 5.06555i) q^{27} +(2.50865 - 0.840639i) q^{28} -1.69376i q^{29} +(6.64826 - 0.498847i) q^{30} +(-0.119727 + 0.0691246i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-8.93269 + 0.670258i) q^{33} +7.05655i q^{34} +(7.63035 + 6.74464i) q^{35} +(-1.09550 + 2.79283i) q^{36} +(-1.41719 + 2.45464i) q^{37} +(2.70079 + 4.67791i) q^{38} +(-4.03105 + 8.37259i) q^{39} +(3.33347 + 1.92458i) q^{40} +5.70223 q^{41} +(-4.22398 + 1.77707i) q^{42} +3.94104 q^{43} +(-4.47890 - 2.58589i) q^{44} +(-11.4182 + 1.72321i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(2.14811 - 3.72064i) q^{47} +(-1.43100 + 0.975834i) q^{48} +(-6.44600 - 2.72931i) q^{49} +9.81605i q^{50} +(-0.914521 - 12.1880i) q^{51} +(-4.64622 + 2.68250i) q^{52} +(-8.28269 + 4.78201i) q^{53} +(1.53019 - 4.96573i) q^{54} -19.9071i q^{55} +(-2.59287 - 0.526310i) q^{56} +(-5.27105 - 7.72965i) q^{57} +(-0.846878 + 1.46684i) q^{58} +(-0.776799 - 1.34546i) q^{59} +(-6.00698 - 2.89211i) q^{60} +(1.50204 + 0.867201i) q^{61} +0.138249 q^{62} +(7.06534 - 3.61677i) q^{63} -1.00000 q^{64} +(-17.8841 - 10.3254i) q^{65} +(8.07106 + 3.88588i) q^{66} +(5.23869 + 9.07368i) q^{67} +(3.52828 - 6.11115i) q^{68} +(0.975834 + 1.43100i) q^{69} +(-3.23576 - 9.65620i) q^{70} +5.49401i q^{71} +(2.34514 - 1.87091i) q^{72} +(-12.5387 + 7.23923i) q^{73} +(2.45464 - 1.41719i) q^{74} +(-1.27215 - 16.9542i) q^{75} -5.40159i q^{76} +(4.34761 + 12.9742i) q^{77} +(7.67729 - 5.23534i) q^{78} +(-1.67489 + 2.90099i) q^{79} +(-1.92458 - 3.33347i) q^{80} +(-1.99939 + 8.77510i) q^{81} +(-4.93827 - 2.85111i) q^{82} -12.4904 q^{83} +(4.54661 + 0.573006i) q^{84} +27.1618 q^{85} +(-3.41304 - 1.97052i) q^{86} +(1.27262 - 2.64327i) q^{87} +(2.58589 + 4.47890i) q^{88} +(-2.12518 + 3.68093i) q^{89} +(10.7500 + 4.21675i) q^{90} +(13.9108 + 2.82365i) q^{91} +1.00000i q^{92} +(-0.238783 + 0.0179169i) q^{93} +(-3.72064 + 2.14811i) q^{94} +(18.0060 - 10.3958i) q^{95} +(1.72720 - 0.129599i) q^{96} +5.21678i q^{97} +(4.21774 + 5.58665i) q^{98} +(-14.4439 - 5.66568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Introduction

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