LMFDB - Embedded newform 560.2.bb.d.29.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(29,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("560.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bb (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.13
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.d.309.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.639532 - 1.26135i) q^{2} +(-0.819103 + 0.819103i) q^{3} +(-1.18200 + 1.61335i) q^{4} +(-2.21530 - 0.304027i) q^{5} +(1.55702 + 0.509331i) q^{6} +1.00000 q^{7} +(2.79091 + 0.459123i) q^{8} +1.65814i q^{9} +O(q^{10})$	\(q+(-0.639532 - 1.26135i) q^{2} +(-0.819103 + 0.819103i) q^{3} +(-1.18200 + 1.61335i) q^{4} +(-2.21530 - 0.304027i) q^{5} +(1.55702 + 0.509331i) q^{6} +1.00000 q^{7} +(2.79091 + 0.459123i) q^{8} +1.65814i q^{9} +(1.03327 + 2.98870i) q^{10} +(-0.276393 + 0.276393i) q^{11} +(-0.353319 - 2.28967i) q^{12} +(0.770831 - 0.770831i) q^{13} +(-0.639532 - 1.26135i) q^{14} +(2.06359 - 1.56553i) q^{15} +(-1.20577 - 3.81394i) q^{16} -4.40334i q^{17} +(2.09149 - 1.06043i) q^{18} +(-1.96757 - 1.96757i) q^{19} +(3.10898 - 3.21469i) q^{20} +(-0.819103 + 0.819103i) q^{21} +(0.525390 + 0.171865i) q^{22} -4.89424 q^{23} +(-2.66212 + 1.90998i) q^{24} +(4.81514 + 1.34702i) q^{25} +(-1.46526 - 0.479315i) q^{26} +(-3.81550 - 3.81550i) q^{27} +(-1.18200 + 1.61335i) q^{28} +(-1.08458 - 1.08458i) q^{29} +(-3.29441 - 1.60170i) q^{30} +1.82714 q^{31} +(-4.03958 + 3.96003i) q^{32} -0.452788i q^{33} +(-5.55414 + 2.81608i) q^{34} +(-2.21530 - 0.304027i) q^{35} +(-2.67515 - 1.95992i) q^{36} +(-8.29881 - 8.29881i) q^{37} +(-1.22346 + 3.74011i) q^{38} +1.26278i q^{39} +(-6.04314 - 1.86561i) q^{40} -9.95152i q^{41} +(1.55702 + 0.509331i) q^{42} +(5.40050 + 5.40050i) q^{43} +(-0.119222 - 0.772613i) q^{44} +(0.504119 - 3.67328i) q^{45} +(3.13002 + 6.17334i) q^{46} -6.02415i q^{47} +(4.11166 + 2.13636i) q^{48} +1.00000 q^{49} +(-1.38037 - 6.93503i) q^{50} +(3.60679 + 3.60679i) q^{51} +(0.332497 + 2.15474i) q^{52} +(-8.48035 - 8.48035i) q^{53} +(-2.37254 + 7.25280i) q^{54} +(0.696325 - 0.528263i) q^{55} +(2.79091 + 0.459123i) q^{56} +3.22328 q^{57} +(-0.674411 + 2.06166i) q^{58} +(1.47873 - 1.47873i) q^{59} +(0.0865865 + 5.17974i) q^{60} +(-2.65916 - 2.65916i) q^{61} +(-1.16851 - 2.30466i) q^{62} +1.65814i q^{63} +(7.57841 + 2.56275i) q^{64} +(-1.94198 + 1.47327i) q^{65} +(-0.571124 + 0.289573i) q^{66} +(-5.37037 + 5.37037i) q^{67} +(7.10411 + 5.20473i) q^{68} +(4.00888 - 4.00888i) q^{69} +(1.03327 + 2.98870i) q^{70} +3.80060i q^{71} +(-0.761290 + 4.62773i) q^{72} +8.12314 q^{73} +(-5.16033 + 15.7750i) q^{74} +(-5.04744 + 2.84074i) q^{75} +(5.50002 - 0.848707i) q^{76} +(-0.276393 + 0.276393i) q^{77} +(1.59281 - 0.807589i) q^{78} +13.0772 q^{79} +(1.51160 + 8.81561i) q^{80} +1.27615 q^{81} +(-12.5523 + 6.36432i) q^{82} +(-7.21840 + 7.21840i) q^{83} +(-0.353319 - 2.28967i) q^{84} +(-1.33873 + 9.75473i) q^{85} +(3.35812 - 10.2657i) q^{86} +1.77677 q^{87} +(-0.898287 + 0.644491i) q^{88} -4.21762i q^{89} +(-4.95569 + 1.71331i) q^{90} +(0.770831 - 0.770831i) q^{91} +(5.78497 - 7.89610i) q^{92} +(-1.49662 + 1.49662i) q^{93} +(-7.59855 + 3.85264i) q^{94} +(3.76056 + 4.95695i) q^{95} +(0.0651588 - 6.55250i) q^{96} +4.19134i q^{97} +(-0.639532 - 1.26135i) q^{98} +(-0.458298 - 0.458298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.639532	−	1.26135i	−0.452218	−	0.891908i
$2$	−0.639532	−	1.26135i	−0.452218	−	0.891908i
$3$	−0.819103	+	0.819103i	−0.472909	+	0.472909i	−0.902855	−	0.429946i	$-0.858533\pi$
$3$	−0.819103	+	0.819103i	−0.472909	+	0.472909i	0.429946	+	0.902855i	$0.358533\pi$
$4$	−1.18200	+	1.61335i	−0.590998	+	0.806673i
$5$	−2.21530	−	0.304027i	−0.990714	−	0.135965i
$5$	−2.21530	−	0.304027i	−0.990714	−	0.135965i
$6$	1.55702	+	0.509331i	0.635649	+	0.207934i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.79091	+	0.459123i	0.986737	+	0.162324i
$9$			1.65814i			0.552714i
$10$	1.03327	+	2.98870i	0.326750	+	0.945111i
$11$	−0.276393	+	0.276393i	−0.0833356	+	0.0833356i	−0.747546	−	0.664210i	$-0.768768\pi$
$11$	−0.276393	+	0.276393i	−0.0833356	+	0.0833356i	0.664210	+	0.747546i	$0.268768\pi$
$12$	−0.353319	−	2.28967i	−0.101994	−	0.660972i
$13$	0.770831	−	0.770831i	0.213790	−	0.213790i	−0.592085	−	0.805875i	$-0.701695\pi$
$13$	0.770831	−	0.770831i	0.213790	−	0.213790i	0.805875	+	0.592085i	$0.201695\pi$
$14$	−0.639532	−	1.26135i	−0.170922	−	0.337109i
$15$	2.06359	−	1.56553i	0.532817	−	0.404219i
$16$	−1.20577	−	3.81394i	−0.301442	−	0.953485i
$17$		−	4.40334i		−	1.06797i	−0.845495	−	0.533983i	$-0.820695\pi$
$17$		−	4.40334i		−	1.06797i	0.845495	−	0.533983i	$-0.179305\pi$
$18$	2.09149	−	1.06043i	0.492969	−	0.249947i
$19$	−1.96757	−	1.96757i	−0.451391	−	0.451391i	0.444425	−	0.895816i	$-0.353408\pi$
$19$	−1.96757	−	1.96757i	−0.451391	−	0.451391i	−0.895816	+	0.444425i	$0.853408\pi$
$20$	3.10898	−	3.21469i	0.695189	−	0.718827i
$21$	−0.819103	+	0.819103i	−0.178743	+	0.178743i
$22$	0.525390	+	0.171865i	0.112013	+	0.0366418i
$23$	−4.89424			−1.02052			−0.510260	−	0.860020i	$-0.670451\pi$
$23$	−4.89424			−1.02052			−0.510260	+	0.860020i	$0.670451\pi$
$24$	−2.66212	+	1.90998i	−0.543402	+	0.389873i
$25$	4.81514	+	1.34702i	0.963027	+	0.269404i
$26$	−1.46526	−	0.479315i	−0.287361	−	0.0940014i
$27$	−3.81550	−	3.81550i	−0.734293	−	0.734293i
$28$	−1.18200	+	1.61335i	−0.223376	+	0.304894i
$29$	−1.08458	−	1.08458i	−0.201402	−	0.201402i	0.599199	−	0.800600i	$-0.295486\pi$
$29$	−1.08458	−	1.08458i	−0.201402	−	0.201402i	−0.800600	+	0.599199i	$0.795486\pi$
$30$	−3.29441	−	1.60170i	−0.601475	−	0.292429i
$31$	1.82714			0.328164			0.164082	−	0.986447i	$-0.447534\pi$
$31$	1.82714			0.328164			0.164082	+	0.986447i	$0.447534\pi$
$32$	−4.03958	+	3.96003i	−0.714103	+	0.700041i
$33$		−	0.452788i		−	0.0788204i
$34$	−5.55414	+	2.81608i	−0.952527	+	0.482953i
$35$	−2.21530	−	0.304027i	−0.374455	−	0.0513899i
$36$	−2.67515	−	1.95992i	−0.445859	−	0.326653i
$37$	−8.29881	−	8.29881i	−1.36432	−	1.36432i	−0.868332	−	0.495984i	$-0.834808\pi$
$37$	−8.29881	−	8.29881i	−1.36432	−	1.36432i	−0.495984	−	0.868332i	$-0.665192\pi$
$38$	−1.22346	+	3.74011i	−0.198472	+	0.606726i
$39$			1.26278i			0.202207i
$40$	−6.04314	−	1.86561i	−0.955504	−	0.294979i
$41$		−	9.95152i		−	1.55417i	−0.629398	−	0.777083i	$-0.716698\pi$
$41$		−	9.95152i		−	1.55417i	0.629398	−	0.777083i	$-0.283302\pi$
$42$	1.55702	+	0.509331i	0.240253	+	0.0785915i
$43$	5.40050	+	5.40050i	0.823569	+	0.823569i	0.986618	−	0.163049i	$-0.0521329\pi$
$43$	5.40050	+	5.40050i	0.823569	+	0.823569i	−0.163049	+	0.986618i	$0.552133\pi$
$44$	−0.119222	−	0.772613i	−0.0179733	−	0.116476i
$45$	0.504119	−	3.67328i	0.0751496	−	0.547581i
$46$	3.13002	+	6.17334i	0.461497	+	0.910209i
$47$		−	6.02415i		−	0.878712i	−0.898313	−	0.439356i	$-0.855207\pi$
$47$		−	6.02415i		−	0.878712i	0.898313	−	0.439356i	$-0.144793\pi$
$48$	4.11166	+	2.13636i	0.593466	+	0.308357i
$49$	1.00000			0.142857
$50$	−1.38037	−	6.93503i	−0.195214	−	0.980761i
$51$	3.60679	+	3.60679i	0.505051	+	0.505051i
$52$	0.332497	+	2.15474i	0.0461090	+	0.298808i
$53$	−8.48035	−	8.48035i	−1.16487	−	1.16487i	−0.983397	−	0.181470i	$-0.941915\pi$
$53$	−8.48035	−	8.48035i	−1.16487	−	1.16487i	−0.181470	−	0.983397i	$-0.558085\pi$
$54$	−2.37254	+	7.25280i	−0.322861	+	0.986981i
$55$	0.696325	−	0.528263i	0.0938924	−	0.0712310i
$56$	2.79091	+	0.459123i	0.372952	+	0.0613529i
$57$	3.22328			0.426934
$58$	−0.674411	+	2.06166i	−0.0885545	+	0.270710i
$59$	1.47873	−	1.47873i	0.192514	−	0.192514i	−0.604268	−	0.796781i	$-0.706534\pi$
$59$	1.47873	−	1.47873i	0.192514	−	0.192514i	0.796781	+	0.604268i	$0.206534\pi$
$60$	0.0865865	+	5.17974i	0.0111783	+	0.668701i
$61$	−2.65916	−	2.65916i	−0.340470	−	0.340470i	0.516074	−	0.856544i	$-0.327393\pi$
$61$	−2.65916	−	2.65916i	−0.340470	−	0.340470i	−0.856544	+	0.516074i	$0.827393\pi$
$62$	−1.16851	−	2.30466i	−0.148402	−	0.292692i
$63$			1.65814i			0.208906i
$64$	7.57841	+	2.56275i	0.947302	+	0.320343i
$65$	−1.94198	+	1.47327i	−0.240873	+	0.182737i
$66$	−0.571124	+	0.289573i	−0.0703005	+	0.0356440i
$67$	−5.37037	+	5.37037i	−0.656096	+	0.656096i	−0.954454	−	0.298358i	$-0.903561\pi$
$67$	−5.37037	+	5.37037i	−0.656096	+	0.656096i	0.298358	+	0.954454i	$0.403561\pi$
$68$	7.10411	+	5.20473i	0.861499	+	0.631166i
$69$	4.00888	−	4.00888i	0.482613	−	0.482613i
$70$	1.03327	+	2.98870i	0.123500	+	0.357218i
$71$			3.80060i			0.451049i	0.974238	+	0.225524i	$0.0724095\pi$
$71$			3.80060i			0.451049i	−0.974238	+	0.225524i	$0.927590\pi$
$72$	−0.761290	+	4.62773i	−0.0897189	+	0.545383i
$73$	8.12314			0.950741			0.475371	−	0.879786i	$-0.342314\pi$
$73$	8.12314			0.950741			0.475371	+	0.879786i	$0.342314\pi$
$74$	−5.16033	+	15.7750i	−0.599876	+	1.83381i
$75$	−5.04744	+	2.84074i	−0.582828	+	0.328021i
$76$	5.50002	−	0.848707i	0.630896	−	0.0973533i
$77$	−0.276393	+	0.276393i	−0.0314979	+	0.0314979i
$78$	1.59281	−	0.807589i	0.180350	−	0.0914414i
$79$	13.0772			1.47130			0.735650	−	0.677362i	$-0.236877\pi$
$79$	13.0772			1.47130			0.735650	+	0.677362i	$0.236877\pi$
$80$	1.51160	+	8.81561i	0.169002	+	0.985616i
$81$	1.27615			0.141794
$82$	−12.5523	+	6.36432i	−1.38617	+	0.702821i
$83$	−7.21840	+	7.21840i	−0.792322	+	0.792322i	−0.981871	−	0.189549i	$-0.939297\pi$
$83$	−7.21840	+	7.21840i	−0.792322	+	0.792322i	0.189549	+	0.981871i	$0.439297\pi$
$84$	−0.353319	−	2.28967i	−0.0385502	−	0.249824i
$85$	−1.33873	+	9.75473i	−0.145206	+	1.05805i
$86$	3.35812	−	10.2657i	0.362115	−	1.10698i
$87$	1.77677			0.190490
$88$	−0.898287	+	0.644491i	−0.0957578	+	0.0687029i
$89$		−	4.21762i		−	0.447067i	−0.974696	−	0.223533i	$-0.928241\pi$
$89$		−	4.21762i		−	0.447067i	0.974696	−	0.223533i	$-0.0717591\pi$
$90$	−4.95569	+	1.71331i	−0.522376	+	0.180599i
$91$	0.770831	−	0.770831i	0.0808051	−	0.0808051i
$92$	5.78497	−	7.89610i	0.603125	−	0.823225i
$93$	−1.49662	+	1.49662i	−0.155192	+	0.155192i
$94$	−7.59855	+	3.85264i	−0.783730	+	0.397369i
$95$	3.76056	+	4.95695i	0.385826	+	0.508572i
$96$	0.0651588	−	6.55250i	0.00665024	−	0.668762i
$97$			4.19134i			0.425566i	0.977099	+	0.212783i	$0.0682528\pi$
$97$			4.19134i			0.425566i	−0.977099	+	0.212783i	$0.931747\pi$
$98$	−0.639532	−	1.26135i	−0.0646025	−	0.127415i
$99$	−0.458298	−	0.458298i	−0.0460607	−	0.0460607i
$100$	−7.86469	+	6.17630i	−0.786469	+	0.617630i
$101$	11.7679	−	11.7679i	1.17095	−	1.17095i	0.188966	−	0.981984i	$-0.439487\pi$
$101$	11.7679	−	11.7679i	1.17095	−	1.17095i	0.981984	−	0.188966i	$-0.0605135\pi$
$102$	2.24276	−	6.85607i	0.222066	−	0.678852i
$103$	−2.72994			−0.268989			−0.134494	−	0.990914i	$-0.542941\pi$
$103$	−2.72994			−0.268989			−0.134494	+	0.990914i	$0.542941\pi$
$104$	2.50523	−	1.79742i	0.245658	−	0.176251i
$105$	2.06359	−	1.56553i	0.201386	−	0.152780i
$106$	−5.27322	+	16.1201i	−0.512180	+	1.56573i
$107$	3.53881	+	3.53881i	0.342110	+	0.342110i	0.857160	−	0.515050i	$-0.172227\pi$
$107$	3.53881	+	3.53881i	0.342110	+	0.342110i	−0.515050	+	0.857160i	$0.672227\pi$
$108$	10.6656	−	1.64581i	1.02630	−	0.158368i
$109$	−10.4757	−	10.4757i	−1.00339	−	1.00339i	−0.999994	−	0.00339441i	$-0.998920\pi$
$109$	−10.4757	−	10.4757i	−1.00339	−	1.00339i	−0.00339441	−	0.999994i	$-0.501080\pi$
$110$	−1.11165	−	0.540466i	−0.105991	−	0.0515315i
$111$	13.5952			1.29040
$112$	−1.20577	−	3.81394i	−0.113934	−	0.360383i
$113$		−	2.57164i		−	0.241919i	−0.992657	−	0.120960i	$-0.961403\pi$
$113$		−	2.57164i		−	0.241919i	0.992657	−	0.120960i	$-0.0385972\pi$
$114$	−2.06139	−	4.06568i	−0.193067	−	0.380785i
$115$	10.8422	+	1.48798i	1.01104	+	0.138755i
$116$	3.03178	−	0.467833i	0.281494	−	0.0434372i
$117$	1.27815	+	1.27815i	0.118165	+	0.118165i
$118$	−2.81088	−	0.919495i	−0.258763	−	0.0846464i
$119$		−	4.40334i		−	0.403653i
$120$	6.47808	−	3.42183i	0.591365	−	0.312369i
$121$			10.8472i			0.986110i
$122$	−1.65351	+	5.05474i	−0.149701	+	0.457635i
$123$	8.15132	+	8.15132i	0.734980	+	0.734980i
$124$	−2.15967	+	2.94781i	−0.193944	+	0.264721i
$125$	−10.2575	−	4.44799i	−0.917455	−	0.397841i
$126$	2.09149	−	1.06043i	0.186325	−	0.0944710i
$127$		−	9.97120i		−	0.884801i	−0.896818	−	0.442400i	$-0.854127\pi$
$127$		−	9.97120i		−	0.884801i	0.896818	−	0.442400i	$-0.145873\pi$
$128$	−1.61413	−	11.1980i	−0.142670	−	0.989770i
$129$	−8.84713			−0.778947
$130$	3.10027	+	1.50731i	0.271911	+	0.132199i
$131$	−2.24735	−	2.24735i	−0.196352	−	0.196352i	0.602082	−	0.798434i	$-0.294338\pi$
$131$	−2.24735	−	2.24735i	−0.196352	−	0.196352i	−0.798434	+	0.602082i	$0.794338\pi$
$132$	0.730504	+	0.535195i	0.0635822	+	0.0465827i
$133$	−1.96757	−	1.96757i	−0.170610	−	0.170610i
$134$	10.2084	+	3.33938i	0.881875	+	0.288479i
$135$	7.29247	+	9.61249i	0.627636	+	0.827312i
$136$	2.02167	−	12.2893i	0.173357	−	1.05380i
$137$	−5.74108			−0.490494			−0.245247	−	0.969461i	$-0.578869\pi$
$137$	−5.74108			−0.490494			−0.245247	+	0.969461i	$0.578869\pi$
$138$	−7.62041	−	2.49279i	−0.648692	−	0.212200i
$139$	7.71930	−	7.71930i	0.654743	−	0.654743i	−0.299389	−	0.954131i	$-0.596783\pi$
$139$	7.71930	−	7.71930i	0.654743	−	0.654743i	0.954131	+	0.299389i	$0.0967827\pi$
$140$	3.10898	−	3.21469i	0.262757	−	0.271691i
$141$	4.93440	+	4.93440i	0.415551	+	0.415551i
$142$	4.79388	−	2.43061i	0.402294	−	0.203972i
$143$			0.426105i			0.0356327i
$144$	6.32405	−	1.99933i	0.527004	−	0.166611i
$145$	2.07294	+	2.73242i	0.172148	+	0.226915i
$146$	−5.19501	−	10.2461i	−0.429942	−	0.847974i
$147$	−0.819103	+	0.819103i	−0.0675585	+	0.0675585i
$148$	23.1980	−	3.57968i	1.90686	−	0.294248i
$149$	3.76960	−	3.76960i	0.308818	−	0.308818i	−0.535633	−	0.844451i	$-0.679927\pi$
$149$	3.76960	−	3.76960i	0.308818	−	0.308818i	0.844451	+	0.535633i	$0.179927\pi$
$150$	6.81117	+	4.54983i	0.556129	+	0.371492i
$151$			23.7778i			1.93501i	0.252846	+	0.967507i	$0.418633\pi$
$151$			23.7778i			1.93501i	−0.252846	+	0.967507i	$0.581367\pi$
$152$	−4.58796	−	6.39466i	−0.372132	−	0.518676i
$153$	7.30135			0.590280
$154$	0.525390	+	0.171865i	0.0423371	+	0.0138493i
$155$	−4.04767	−	0.555499i	−0.325117	−	0.0446188i
$156$	−2.03730	−	1.49260i	−0.163115	−	0.119504i
$157$	6.56850	−	6.56850i	0.524223	−	0.524223i	−0.394621	−	0.918844i	$-0.629124\pi$
$157$	6.56850	−	6.56850i	0.524223	−	0.524223i	0.918844	+	0.394621i	$0.129124\pi$
$158$	−8.36329	−	16.4949i	−0.665348	−	1.31226i
$159$	13.8926			1.10175
$160$	10.1528	−	7.54452i	0.802653	−	0.596447i
$161$	−4.89424			−0.385720
$162$	−0.816138	−	1.60967i	−0.0641218	−	0.126467i
$163$	−8.81430	+	8.81430i	−0.690390	+	0.690390i	−0.962318	−	0.271928i	$-0.912339\pi$
$163$	−8.81430	+	8.81430i	−0.690390	+	0.690390i	0.271928	+	0.962318i	$0.412339\pi$
$164$	16.0552	+	11.7627i	1.25370	+	0.918510i
$165$	−0.137660	+	1.00306i	−0.0107168	+	0.0780884i
$166$	13.7213	+	4.48851i	1.06498	+	0.348376i
$167$	−19.6582			−1.52120			−0.760601	−	0.649220i	$-0.775095\pi$
$167$	−19.6582			−1.52120			−0.760601	+	0.649220i	$0.775095\pi$
$168$	−2.66212	+	1.90998i	−0.205387	+	0.147358i
$169$			11.8116i			0.908588i
$170$	13.1603	−	4.54986i	1.00935	−	0.348958i
$171$	3.26250	−	3.26250i	0.249490	−	0.249490i
$172$	−15.0963	+	2.32950i	−1.15108	+	0.177623i
$173$	−2.10601	+	2.10601i	−0.160117	+	0.160117i	−0.782619	−	0.622501i	$-0.786116\pi$
$173$	−2.10601	+	2.10601i	−0.160117	+	0.160117i	0.622501	+	0.782619i	$0.286116\pi$
$174$	−1.13630	−	2.24113i	−0.0861428	−	0.169899i
$175$	4.81514	+	1.34702i	0.363990	+	0.101825i
$176$	1.38741	+	0.720880i	0.104580	+	0.0543384i
$177$			2.42246i			0.182083i
$178$	−5.31988	+	2.69730i	−0.398742	+	0.202171i
$179$	−8.22517	−	8.22517i	−0.614778	−	0.614778i	0.329409	−	0.944187i	$-0.393150\pi$
$179$	−8.22517	−	8.22517i	−0.614778	−	0.614778i	−0.944187	+	0.329409i	$0.893150\pi$
$180$	5.33041	+	5.15513i	0.397305	+	0.384241i
$181$	−11.8314	+	11.8314i	−0.879420	+	0.879420i	−0.993474	−	0.114055i	$-0.963616\pi$
$181$	−11.8314	+	11.8314i	−0.879420	+	0.879420i	0.114055	+	0.993474i	$0.463616\pi$
$182$	−1.46526	−	0.479315i	−0.108612	−	0.0355292i
$183$	4.35625			0.322023
$184$	−13.6594	−	2.24706i	−1.00698	−	0.165655i
$185$	15.8613	+	20.9074i	1.16615	+	1.53714i
$186$	2.84489	+	0.930619i	0.208597	+	0.0682363i
$187$	1.21705	+	1.21705i	0.0889996	+	0.0889996i
$188$	9.71903	+	7.12053i	0.708833	+	0.519318i
$189$	−3.81550	−	3.81550i	−0.277537	−	0.277537i
$190$	3.84743	−	7.91351i	0.279122	−	0.574106i
$191$	−9.94443			−0.719554			−0.359777	−	0.933038i	$-0.617147\pi$
$191$	−9.94443			−0.719554			−0.359777	+	0.933038i	$0.617147\pi$
$192$	−8.30665	+	4.10835i	−0.599481	+	0.296494i
$193$		−	17.5635i		−	1.26425i	−0.774868	−	0.632123i	$-0.782184\pi$
$193$		−	17.5635i		−	1.26425i	0.774868	−	0.632123i	$-0.217816\pi$
$194$	5.28674	−	2.68050i	0.379566	−	0.192449i
$195$	0.383919	−	2.79744i	0.0274930	−	0.200329i
$196$	−1.18200	+	1.61335i	−0.0844284	+	0.115239i
$197$	13.2507	+	13.2507i	0.944074	+	0.944074i	0.998517	−	0.0544431i	$-0.0173384\pi$
$197$	13.2507	+	13.2507i	0.944074	+	0.944074i	−0.0544431	+	0.998517i	$0.517338\pi$
$198$	−0.284977	+	0.871170i	−0.0202524	+	0.0619114i
$199$		−	16.8348i		−	1.19339i	−0.802470	−	0.596693i	$-0.796481\pi$
$199$		−	16.8348i		−	1.19339i	0.802470	−	0.596693i	$-0.203519\pi$
$200$	12.8202	+	5.97016i	0.906524	+	0.422154i
$201$		−	8.79778i		−	0.620547i
$202$	−22.3694	−	7.31746i	−1.57390	−	0.514855i
$203$	−1.08458	−	1.08458i	−0.0761228	−	0.0761228i
$204$	−10.0822	+	1.55578i	−0.705896	+	0.108927i
$205$	−3.02553	+	22.0456i	−0.211312	+	1.53973i
$206$	1.74588	+	3.44340i	0.121641	+	0.239913i
$207$		−	8.11533i		−	0.564055i
$208$	−3.86935	−	2.01046i	−0.268291	−	0.139400i
$209$	1.08764			0.0752338
$210$	−3.29441	−	1.60170i	−0.227336	−	0.110528i
$211$	4.23239	+	4.23239i	0.291370	+	0.291370i	0.837621	−	0.546251i	$-0.183946\pi$
$211$	4.23239	+	4.23239i	0.291370	+	0.291370i	−0.546251	+	0.837621i	$0.683946\pi$
$212$	23.7055	−	3.65799i	1.62810	−	0.251232i
$213$	−3.11309	−	3.11309i	−0.213305	−	0.213305i
$214$	2.20049	−	6.72685i	0.150422	−	0.459838i
$215$	−10.3219	−	13.6056i	−0.703945	−	0.927897i
$216$	−8.89695	−	12.4005i	−0.605360	−	0.843748i
$217$	1.82714			0.124034
$218$	−6.51394	+	19.9130i	−0.441180	+	1.34868i
$219$	−6.65369	+	6.65369i	−0.449614	+	0.449614i
$220$	0.0292172	+	1.74782i	0.00196982	+	0.117838i
$221$	−3.39423	−	3.39423i	−0.228321	−	0.228321i
$222$	−8.69454	−	17.1482i	−0.583539	−	1.15091i
$223$			2.97845i			0.199452i	0.995015	+	0.0997260i	$0.0317966\pi$
$223$			2.97845i			0.199452i	−0.995015	+	0.0997260i	$0.968203\pi$
$224$	−4.03958	+	3.96003i	−0.269906	+	0.264590i
$225$	−2.23355	+	7.98417i	−0.148903	+	0.532278i
$226$	−3.24373	+	1.64465i	−0.215770	+	0.109400i
$227$	−5.07819	+	5.07819i	−0.337051	+	0.337051i	−0.855256	−	0.518205i	$-0.826600\pi$
$227$	−5.07819	+	5.07819i	−0.337051	+	0.337051i	0.518205	+	0.855256i	$0.326600\pi$
$228$	−3.80991	+	5.20026i	−0.252317	+	0.344396i
$229$	5.00949	−	5.00949i	0.331037	−	0.331037i	−0.521943	−	0.852980i	$-0.674793\pi$
$229$	5.00949	−	5.00949i	0.331037	−	0.331037i	0.852980	+	0.521943i	$0.174793\pi$
$230$	−5.05709	−	14.6274i	−0.333455	−	0.964504i
$231$		−	0.452788i		−	0.0297913i
$232$	−2.52902	−	3.52494i	−0.166038	−	0.231423i
$233$	−1.46716			−0.0961169			−0.0480585	−	0.998845i	$-0.515303\pi$
$233$	−1.46716			−0.0961169			−0.0480585	+	0.998845i	$0.515303\pi$
$234$	0.794772	−	2.42960i	0.0519558	−	0.158828i
$235$	−1.83150	+	13.3453i	−0.119474	+	0.870552i
$236$	0.637846	+	4.13355i	0.0415202	+	0.269071i
$237$	−10.7116	+	10.7116i	−0.695791	+	0.695791i
$238$	−5.55414	+	2.81608i	−0.360022	+	0.182539i
$239$	−0.444418			−0.0287470			−0.0143735	−	0.999897i	$-0.504575\pi$
$239$	−0.444418			−0.0287470			−0.0143735	+	0.999897i	$0.504575\pi$
$240$	−8.45905	−	5.98274i	−0.546029	−	0.386184i
$241$	−22.5624			−1.45337			−0.726687	−	0.686968i	$-0.758941\pi$
$241$	−22.5624			−1.45337			−0.726687	+	0.686968i	$0.758941\pi$
$242$	13.6821	−	6.93714i	0.879519	−	0.445936i
$243$	10.4012	−	10.4012i	0.667237	−	0.667237i
$244$	7.43326	−	1.14702i	0.475865	−	0.0734306i
$245$	−2.21530	−	0.304027i	−0.141531	−	0.0194235i
$246$	5.06862	−	15.4947i	0.323163	−	0.987905i
$247$	−3.03332			−0.193006
$248$	5.09939	+	0.838882i	0.323812	+	0.0532690i
$249$		−	11.8252i		−	0.749393i
$250$	0.949507	+	15.7829i	0.0600521	+	0.998195i
$251$	−20.4677	+	20.4677i	−1.29191	+	1.29191i	−0.358308	+	0.933603i	$0.616646\pi$
$251$	−20.4677	+	20.4677i	−1.29191	+	1.29191i	−0.933603	+	0.358308i	$0.883354\pi$
$252$	−2.67515	−	1.95992i	−0.168519	−	0.123463i
$253$	1.35273	−	1.35273i	0.0850456	−	0.0850456i
$254$	−12.5771	+	6.37690i	−0.789160	+	0.400122i
$255$	−6.89357	−	9.08669i	−0.431692	−	0.569030i
$256$	−13.0923	+	9.19744i	−0.818266	+	0.574840i
$257$		−	4.57165i		−	0.285172i	−0.989782	−	0.142586i	$-0.954458\pi$
$257$		−	4.57165i		−	0.285172i	0.989782	−	0.142586i	$-0.0455417\pi$
$258$	5.65803	+	11.1593i	0.352253	+	0.694749i
$259$	−8.29881	−	8.29881i	−0.515663	−	0.515663i
$260$	−0.0814838	−	4.87448i	−0.00505341	−	0.302303i
$261$	1.79839	−	1.79839i	0.111318	−	0.111318i
$262$	−1.39744	+	4.27194i	−0.0863340	+	0.263922i
$263$	20.8906			1.28817			0.644085	−	0.764954i	$-0.277238\pi$
$263$	20.8906			1.28817			0.644085	+	0.764954i	$0.277238\pi$
$264$	0.207886	−	1.26369i	0.0127945	−	0.0777750i
$265$	16.2083	+	21.3648i	0.995668	+	1.31243i
$266$	−1.22346	+	3.74011i	−0.0750154	+	0.229321i
$267$	3.45466	+	3.45466i	0.211422	+	0.211422i
$268$	−2.31650	−	15.0120i	−0.141503	−	0.917006i
$269$	−12.4901	−	12.4901i	−0.761537	−	0.761537i	0.215063	−	0.976600i	$-0.431004\pi$
$269$	−12.4901	−	12.4901i	−0.761537	−	0.761537i	−0.976600	+	0.215063i	$0.931004\pi$
$270$	7.46093	−	15.3458i	0.454058	−	0.933918i
$271$	−29.6959			−1.80390			−0.901948	−	0.431845i	$-0.857863\pi$
$271$	−29.6959			−1.80390			−0.901948	+	0.431845i	$0.857863\pi$
$272$	−16.7941	+	5.30940i	−1.01829	+	0.321930i
$273$			1.26278i			0.0764270i
$274$	3.67161	+	7.24150i	0.221810	+	0.437475i
$275$	−1.70318	+	0.958562i	−0.102705	+	0.0578035i
$276$	1.72923	+	11.2062i	0.104087	+	0.674534i
$277$	−5.13014	−	5.13014i	−0.308240	−	0.308240i	0.535986	−	0.844227i	$-0.319940\pi$
$277$	−5.13014	−	5.13014i	−0.308240	−	0.308240i	−0.844227	+	0.535986i	$0.819940\pi$
$278$	−14.6735	−	4.79998i	−0.880056	−	0.287884i
$279$			3.02965i			0.181381i
$280$	−6.04314	−	1.86561i	−0.361147	−	0.111491i
$281$			18.0505i			1.07680i	0.842688	+	0.538402i	$0.180972\pi$
$281$			18.0505i			1.07680i	−0.842688	+	0.538402i	$0.819028\pi$
$282$	3.06829	−	9.37970i	0.182714	−	0.558553i
$283$	15.4887	+	15.4887i	0.920710	+	0.920710i	0.997080	−	0.0763692i	$-0.0243328\pi$
$283$	15.4887	+	15.4887i	0.920710	+	0.920710i	−0.0763692	+	0.997080i	$0.524333\pi$
$284$	−6.13168	−	4.49230i	−0.363849	−	0.266569i
$285$	−7.14054	−	0.979963i	−0.422969	−	0.0580480i
$286$	0.537466	−	0.272508i	0.0317810	−	0.0161137i
$287$		−	9.95152i		−	0.587420i
$288$	−6.56628	−	6.69819i	−0.386922	−	0.394694i
$289$	−2.38939			−0.140552
$290$	2.12082	−	4.36217i	0.124539	−	0.256155i
$291$	−3.43314	−	3.43314i	−0.201254	−	0.201254i
$292$	−9.60152	+	13.1054i	−0.561887	+	0.766937i
$293$	9.08634	+	9.08634i	0.530830	+	0.530830i	0.920819	−	0.389989i	$-0.127521\pi$
$293$	9.08634	+	9.08634i	0.530830	+	0.530830i	−0.389989	+	0.920819i	$0.627521\pi$
$294$	1.55702	+	0.509331i	0.0908071	+	0.0297048i
$295$	−3.72540	+	2.82625i	−0.216901	+	0.164551i
$296$	−19.3511	−	26.9714i	−1.12476	−	1.56768i
$297$	2.10915			0.122385
$298$	−7.16556	−	2.34400i	−0.415090	−	0.135784i
$299$	−3.77263	+	3.77263i	−0.218177	+	0.218177i
$300$	1.38296	−	11.5010i	0.0798454	−	0.664011i
$301$	5.40050	+	5.40050i	0.311280	+	0.311280i
$302$	29.9921	−	15.2067i	1.72585	−	0.875047i
$303$			19.2782i			1.10751i
$304$	−5.13175	+	9.87660i	−0.294326	+	0.566462i
$305$	5.08238	+	6.69929i	0.291017	+	0.383600i
$306$	−4.66945	−	9.20955i	−0.266935	−	0.526475i
$307$	−11.4806	+	11.4806i	−0.655231	+	0.655231i	−0.954248	−	0.299017i	$-0.903341\pi$
$307$	−11.4806	+	11.4806i	−0.655231	+	0.655231i	0.299017	+	0.954248i	$0.403341\pi$
$308$	−0.119222	−	0.772613i	−0.00679328	−	0.0440237i
$309$	2.23610	−	2.23610i	0.127207	−	0.127207i
$310$	1.88794	+	5.46078i	0.107228	+	0.310151i
$311$		−	10.4818i		−	0.594366i	−0.954820	−	0.297183i	$-0.903953\pi$
$311$		−	10.4818i		−	0.594366i	0.954820	−	0.297183i	$-0.0960472\pi$
$312$	−0.579771	+	3.52431i	−0.0328231	+	0.199525i
$313$	−8.55451			−0.483529			−0.241765	−	0.970335i	$-0.577726\pi$
$313$	−8.55451			−0.483529			−0.241765	+	0.970335i	$0.577726\pi$
$314$	−12.4859	−	4.08440i	−0.704622	−	0.230496i
$315$	0.504119	−	3.67328i	0.0284039	−	0.206966i
$316$	−15.4572	+	21.0980i	−0.869536	+	1.18686i
$317$	0.125178	−	0.125178i	0.00703068	−	0.00703068i	−0.703583	−	0.710613i	$-0.748418\pi$
$317$	0.125178	−	0.125178i	0.00703068	−	0.00703068i	0.710613	+	0.703583i	$0.248418\pi$
$318$	−8.88475	−	17.5234i	−0.498232	−	0.982661i
$319$	0.599542			0.0335679
$320$	−16.0093	−	7.98130i	−0.894949	−	0.446168i
$321$	−5.79730			−0.323574
$322$	3.13002	+	6.17334i	0.174429	+	0.344027i
$323$	−8.66386	+	8.66386i	−0.482070	+	0.482070i
$324$	−1.50840	+	2.05887i	−0.0838001	+	0.114381i
$325$	4.74998	−	2.67333i	0.263482	−	0.148290i
$326$	16.7549	+	5.48087i	0.927970	+	0.303557i
$327$	17.1613			0.949024
$328$	4.56897	−	27.7738i	0.252279	−	1.53355i
$329$		−	6.02415i		−	0.332122i
$330$	1.35325	−	0.467855i	0.0744940	−	0.0257546i
$331$	4.63127	−	4.63127i	0.254557	−	0.254557i	−0.568279	−	0.822836i	$-0.692390\pi$
$331$	4.63127	−	4.63127i	0.254557	−	0.254557i	0.822836	+	0.568279i	$0.192390\pi$
$332$	−3.11364	−	20.1779i	−0.170883	−	1.10741i
$333$	13.7606	−	13.7606i	0.754076	−	0.754076i
$334$	12.5721	+	24.7959i	0.687914	+	1.35677i
$335$	13.5297	−	10.2643i	0.739209	−	0.560797i
$336$	4.11166	+	2.13636i	0.224309	+	0.116548i
$337$		−	4.92436i		−	0.268247i	−0.990965	−	0.134124i	$-0.957178\pi$
$337$		−	4.92436i		−	0.268247i	0.990965	−	0.134124i	$-0.0428219\pi$
$338$	14.8986	−	7.55392i	0.810376	−	0.410879i
$339$	2.10644	+	2.10644i	0.114406	+	0.114406i
$340$	−14.1554	−	13.6899i	−0.767683	−	0.742439i
$341$	−0.505008	+	0.505008i	−0.0273477	+	0.0273477i
$342$	−6.20162	−	2.02867i	−0.335345	−	0.109698i
$343$	1.00000			0.0539949
$344$	12.5928	+	17.5518i	0.678961	+	0.946332i
$345$	−10.0997	+	7.66209i	−0.543750	+	0.412513i
$346$	4.00328	+	1.30955i	0.215218	+	0.0704020i
$347$	14.3448	+	14.3448i	0.770069	+	0.770069i	0.978118	−	0.208049i	$-0.0667113\pi$
$347$	14.3448	+	14.3448i	0.770069	+	0.770069i	−0.208049	+	0.978118i	$0.566711\pi$
$348$	−2.10014	+	2.86654i	−0.112579	+	0.153663i
$349$	14.1407	+	14.1407i	0.756934	+	0.756934i	0.975763	−	0.218829i	$-0.0702237\pi$
$349$	14.1407	+	14.1407i	0.756934	+	0.756934i	−0.218829	+	0.975763i	$0.570224\pi$
$350$	−1.38037	−	6.93503i	−0.0737839	−	0.370693i
$351$	−5.88221			−0.313969
$352$	0.0219868	−	2.21103i	0.00117190	−	0.117849i
$353$			12.1107i			0.644586i	0.946640	+	0.322293i	$0.104454\pi$
$353$			12.1107i			0.644586i	−0.946640	+	0.322293i	$0.895546\pi$
$354$	3.05556	−	1.54924i	0.162401	−	0.0823412i
$355$	1.15548	−	8.41949i	0.0613268	−	0.446860i
$356$	6.80447	+	4.98521i	0.360636	+	0.264216i
$357$	3.60679	+	3.60679i	0.190891	+	0.190891i
$358$	−5.11454	+	15.6351i	−0.270312	+	0.826338i
$359$		−	12.6636i		−	0.668359i	−0.942509	−	0.334180i	$-0.891541\pi$
$359$		−	12.6636i		−	0.668359i	0.942509	−	0.334180i	$-0.108459\pi$
$360$	3.09344	−	10.0204i	0.163039	−	0.528120i
$361$		−	11.2574i		−	0.592493i
$362$	22.4900	+	7.35694i	1.18205	+	0.386672i
$363$	−8.88499	−	8.88499i	−0.466341	−	0.466341i
$364$	0.332497	+	2.15474i	0.0174276	+	0.112939i
$365$	−17.9952	−	2.46965i	−0.941913	−	0.129267i
$366$	−2.78596	−	5.49474i	−0.145625	−	0.287215i
$367$		−	36.6205i		−	1.91158i	−0.294057	−	0.955788i	$-0.595006\pi$
$367$		−	36.6205i		−	1.91158i	0.294057	−	0.955788i	$-0.404994\pi$
$368$	5.90131	+	18.6663i	0.307627	+	0.973049i
$369$	16.5010			0.859009
$370$	16.2277	−	33.3776i	0.843639	−	1.73522i
$371$	−8.48035	−	8.48035i	−0.440278	−	0.440278i
$372$	−0.645563	−	4.18355i	−0.0334709	−	0.216907i
$373$	−21.8149	−	21.8149i	−1.12953	−	1.12953i	−0.990253	−	0.139282i	$-0.955520\pi$
$373$	−21.8149	−	21.8149i	−1.12953	−	1.12953i	−0.139282	−	0.990253i	$-0.544480\pi$
$374$	0.756782	−	2.31347i	0.0391322	−	0.119627i
$375$	12.0453	−	4.75855i	0.622015	−	0.245730i
$376$	2.76582	−	16.8129i	0.142637	−	0.867058i
$377$	−1.67206			−0.0861155
$378$	−2.37254	+	7.25280i	−0.122030	+	0.373044i
$379$	2.81110	−	2.81110i	0.144396	−	0.144396i	−0.631213	−	0.775610i	$-0.717443\pi$
$379$	2.81110	−	2.81110i	0.144396	−	0.144396i	0.775610	+	0.631213i	$0.217443\pi$
$380$	−12.4422	+	0.207989i	−0.638274	+	0.0106696i
$381$	8.16744	+	8.16744i	0.418430	+	0.418430i
$382$	6.35978	+	12.5434i	0.325395	+	0.641775i
$383$			28.6819i			1.46558i	0.680457	+	0.732788i	$0.261781\pi$
$383$			28.6819i			1.46558i	−0.680457	+	0.732788i	$0.738219\pi$
$384$	10.4944	+	7.85016i	0.535542	+	0.400602i
$385$	0.696325	−	0.528263i	0.0354880	−	0.0269228i
$386$	−22.1536	+	11.2324i	−1.12759	+	0.571714i
$387$	−8.95479	+	8.95479i	−0.455198	+	0.455198i
$388$	−6.76208	−	4.95416i	−0.343293	−	0.251509i
$389$	20.9755	−	20.9755i	1.06350	−	1.06350i	0.0656593	−	0.997842i	$-0.479085\pi$
$389$	20.9755	−	20.9755i	1.06350	−	1.06350i	0.997842	−	0.0656593i	$-0.0209151\pi$
$390$	−3.77408	+	1.30480i	−0.191108	+	0.0660711i
$391$			21.5510i			1.08988i
$392$	2.79091	+	0.459123i	0.140962	+	0.0231892i
$393$	3.68162			0.185713
$394$	8.23950	−	25.1880i	0.415100	−	1.26895i
$395$	−28.9700	−	3.97582i	−1.45764	−	0.200045i
$396$	1.28110	−	0.197686i	0.0643777	−	0.00993411i
$397$	−13.4361	+	13.4361i	−0.674337	+	0.674337i	−0.958713	−	0.284376i	$-0.908214\pi$
$397$	−13.4361	+	13.4361i	−0.674337	+	0.674337i	0.284376	+	0.958713i	$0.408214\pi$
$398$	−21.2345	+	10.7664i	−1.06439	+	0.539670i
$399$	3.22328			0.161366
$400$	−0.668469	−	19.9888i	−0.0334234	−	0.999441i
$401$	11.9920			0.598851			0.299426	−	0.954120i	$-0.403205\pi$
$401$	11.9920			0.598851			0.299426	+	0.954120i	$0.403205\pi$
$402$	−11.0971	+	5.62646i	−0.553471	+	0.280622i
$403$	1.40842	−	1.40842i	0.0701582	−	0.0701582i
$404$	5.07606	+	32.8953i	0.252544	+	1.63660i
$405$	−2.82705	−	0.387983i	−0.140477	−	0.0192790i
$406$	−0.674411	+	2.06166i	−0.0334704	+	0.102319i
$407$	4.58746			0.227392
$408$	8.41028	+	11.7222i	0.416371	+	0.580335i
$409$			19.4349i			0.960995i	0.876996	+	0.480497i	$0.159544\pi$
$409$			19.4349i			0.960995i	−0.876996	+	0.480497i	$0.840456\pi$
$410$	29.7421	−	10.2827i	1.46886	−	0.507824i
$411$	4.70254	−	4.70254i	0.231959	−	0.231959i
$412$	3.22678	−	4.40433i	0.158972	−	0.216986i
$413$	1.47873	−	1.47873i	0.0727634	−	0.0727634i
$414$	−10.2363	+	5.19002i	−0.503085	+	0.255075i
$415$	18.1855	−	13.7964i	0.892692	−	0.677236i
$416$	−0.0613188	+	6.16635i	−0.00300640	+	0.302330i
$417$			12.6458i			0.619268i
$418$	−0.695583	−	1.37190i	−0.0340221	−	0.0671016i
$419$	−1.49967	−	1.49967i	−0.0732636	−	0.0732636i	0.669525	−	0.742789i	$-0.266497\pi$
$419$	−1.49967	−	1.49967i	−0.0732636	−	0.0732636i	−0.742789	+	0.669525i	$0.766497\pi$
$420$	0.0865865	+	5.17974i	0.00422499	+	0.252745i
$421$	−0.620238	+	0.620238i	−0.0302286	+	0.0302286i	−0.722060	−	0.691831i	$-0.756804\pi$
$421$	−0.620238	+	0.620238i	−0.0302286	+	0.0302286i	0.691831	+	0.722060i	$0.256804\pi$
$422$	2.63177	−	8.04527i	0.128112	−	0.391638i
$423$	9.98889			0.485676
$424$	−19.7744	−	27.5615i	−0.960331	−	1.33850i
$425$	5.93139	−	21.2027i	0.287715	−	1.02848i
$426$	−1.93576	+	5.91760i	−0.0937881	+	0.286709i
$427$	−2.65916	−	2.65916i	−0.128686	−	0.128686i
$428$	−9.89219	+	1.52646i	−0.478157	+	0.0737842i
$429$	−0.349024	−	0.349024i	−0.0168510	−	0.0168510i
$430$	−10.5603	+	21.7207i	−0.509263	+	1.04747i
$431$	−14.1084			−0.679576			−0.339788	−	0.940502i	$-0.610355\pi$
$431$	−14.1084			−0.679576			−0.339788	+	0.940502i	$0.610355\pi$
$432$	−9.95147	+	19.1527i	−0.478790	+	0.921483i
$433$		−	21.3170i		−	1.02443i	−0.858857	−	0.512215i	$-0.828825\pi$
$433$		−	21.3170i		−	1.02443i	0.858857	−	0.512215i	$-0.171175\pi$
$434$	−1.16851	−	2.30466i	−0.0560905	−	0.110627i
$435$	−3.93608	−	0.540185i	−0.188721	−	0.0258999i
$436$	29.2831	−	4.51867i	1.40241	−	0.216405i
$437$	9.62974	+	9.62974i	0.460653	+	0.460653i
$438$	12.6479	+	4.13737i	0.604338	+	0.197691i
$439$		−	15.1624i		−	0.723664i	−0.932243	−	0.361832i	$-0.882151\pi$
$439$		−	15.1624i		−	0.723664i	0.932243	−	0.361832i	$-0.117849\pi$
$440$	2.18592	−	1.15464i	0.104210	−	0.0550453i
$441$			1.65814i			0.0789591i
$442$	−2.11059	+	6.45203i	−0.100390	+	0.306892i
$443$	5.90825	+	5.90825i	0.280709	+	0.280709i	0.833392	−	0.552683i	$-0.186396\pi$
$443$	5.90825	+	5.90825i	0.280709	+	0.280709i	−0.552683	+	0.833392i	$0.686396\pi$
$444$	−16.0694	+	21.9337i	−0.762622	+	1.04093i
$445$	−1.28227	+	9.34330i	−0.0607853	+	0.442915i
$446$	3.75687	−	1.90482i	0.177893	−	0.0901957i
$447$			6.17539i			0.292086i
$448$	7.57841	+	2.56275i	0.358046	+	0.121078i
$449$	31.4819			1.48572			0.742861	−	0.669446i	$-0.233468\pi$
$449$	31.4819			1.48572			0.742861	+	0.669446i	$0.233468\pi$
$450$	11.4992	−	2.28885i	0.542080	−	0.107897i
$451$	2.75053	+	2.75053i	0.129517	+	0.129517i
$452$	4.14894	+	3.03967i	0.195150	+	0.142974i
$453$	−19.4765	−	19.4765i	−0.915086	−	0.915086i
$454$	9.65303	+	3.15770i	0.453039	+	0.148198i
$455$	−1.94198	+	1.47327i	−0.0910413	+	0.0690680i
$456$	8.99590	+	1.47988i	0.421271	+	0.0693018i
$457$	4.00635			0.187409			0.0937046	−	0.995600i	$-0.470129\pi$
$457$	4.00635			0.187409			0.0937046	+	0.995600i	$0.470129\pi$
$458$	−9.52244	−	3.11498i	−0.444955	−	0.145553i
$459$	−16.8009	+	16.8009i	−0.784200	+	0.784200i
$460$	−15.2161	+	15.7335i	−0.709454	+	0.733576i
$461$	11.9582	+	11.9582i	0.556947	+	0.556947i	0.928437	−	0.371490i	$-0.121153\pi$
$461$	11.9582	+	11.9582i	0.556947	+	0.556947i	−0.371490	+	0.928437i	$0.621153\pi$
$462$	−0.571124	+	0.289573i	−0.0265711	+	0.0134721i
$463$		−	25.6285i		−	1.19106i	−0.803334	−	0.595528i	$-0.796943\pi$
$463$		−	25.6285i		−	1.19106i	0.803334	−	0.595528i	$-0.203057\pi$
$464$	−2.82878	+	5.44429i	−0.131323	+	0.252745i
$465$	3.77047	−	2.86045i	0.174851	−	0.132650i
$466$	0.938297	+	1.85060i	0.0434658	+	0.0857274i
$467$	26.6077	−	26.6077i	1.23126	−	1.23126i	0.267773	−	0.963482i	$-0.413712\pi$
$467$	26.6077	−	26.6077i	1.23126	−	1.23126i	0.963482	−	0.267773i	$-0.0862878\pi$
$468$	−3.57286	+	0.551327i	−0.165155	+	0.0254851i
$469$	−5.37037	+	5.37037i	−0.247981	+	0.247981i
$470$	18.0044	−	6.22460i	0.830481	−	0.287119i
$471$			10.7606i			0.495820i
$472$	4.80592	−	3.44808i	0.221210	−	0.158711i
$473$	−2.98532			−0.137265
$474$	20.3614	+	6.66062i	0.935231	+	0.305933i
$475$	−6.82374	−	12.1245i	−0.313095	−	0.556308i
$476$	7.10411	+	5.20473i	0.325616	+	0.238559i
$477$	14.0616	−	14.0616i	0.643837	−	0.643837i
$478$	0.284220	+	0.560566i	0.0129999	+	0.0256397i
$479$	−23.0291			−1.05222			−0.526112	−	0.850415i	$-0.676351\pi$
$479$	−23.0291			−1.05222			−0.526112	+	0.850415i	$0.676351\pi$
$480$	−2.13648	+	14.4960i	−0.0975166	+	0.661647i
$481$	−12.7940			−0.583354
$482$	14.4294	+	28.4591i	0.657242	+	1.29628i
$483$	4.00888	−	4.00888i	0.182411	−	0.182411i
$484$	−17.5003	−	12.8214i	−0.795468	−	0.582790i
$485$	1.27428	−	9.28510i	0.0578621	−	0.421615i
$486$	−19.7714	−	6.46762i	−0.896850	−	0.293377i
$487$	20.0047			0.906498			0.453249	−	0.891384i	$-0.350265\pi$
$487$	20.0047			0.906498			0.453249	+	0.891384i	$0.350265\pi$
$488$	−6.20060	−	8.64236i	−0.280688	−	0.391221i
$489$		−	14.4396i		−	0.652983i
$490$	1.03327	+	2.98870i	0.0466786	+	0.135016i
$491$	30.1419	−	30.1419i	1.36028	−	1.36028i	0.486733	−	0.873551i	$-0.338188\pi$
$491$	30.1419	−	30.1419i	1.36028	−	1.36028i	0.873551	−	0.486733i	$-0.161812\pi$
$492$	−22.7857	+	3.51606i	−1.02726	+	0.158516i
$493$	−4.77579	+	4.77579i	−0.215091	+	0.215091i
$494$	1.93991	+	3.82608i	0.0872806	+	0.172143i
$495$	0.875935	+	1.15460i	0.0393703	+	0.0518956i
$496$	−2.20310	−	6.96860i	−0.0989223	−	0.312899i
$497$			3.80060i			0.170480i
$498$	−14.9157	+	7.56261i	−0.668389	+	0.338889i
$499$	−3.44442	−	3.44442i	−0.154193	−	0.154193i	0.625795	−	0.779988i	$-0.284775\pi$
$499$	−3.44442	−	3.44442i	−0.154193	−	0.154193i	−0.779988	+	0.625795i	$0.784775\pi$
$500$	19.3004	−	11.2913i	0.863141	−	0.504962i
$501$	16.1021	−	16.1021i	0.719390	−	0.719390i
$502$	38.9067	+	12.7272i	1.73649	+	0.568041i
$503$	−10.4197			−0.464593			−0.232296	−	0.972645i	$-0.574624\pi$
$503$	−10.4197			−0.464593			−0.232296	+	0.972645i	$0.574624\pi$
$504$	−0.761290	+	4.62773i	−0.0339106	+	0.206135i
$505$	−29.6472	+	22.4917i	−1.31928	+	1.00087i
$506$	−2.57138	−	0.841150i	−0.114312	−	0.0373937i
$507$	−9.67495	−	9.67495i	−0.429680	−	0.429680i
$508$	16.0870	+	11.7859i	0.713744	+	0.522916i
$509$	−3.93441	−	3.93441i	−0.174390	−	0.174390i	0.614515	−	0.788905i	$-0.289352\pi$
$509$	−3.93441	−	3.93441i	−0.174390	−	0.174390i	−0.788905	+	0.614515i	$0.789352\pi$
$510$	−7.05281	+	14.5064i	−0.312304	+	0.642355i
$511$	8.12314			0.359346
$512$	19.9741	+	10.6318i	0.882738	+	0.469865i
$513$			15.0145i			0.662906i
$514$	−5.76644	+	2.92372i	−0.254347	+	0.128960i
$515$	6.04764	+	0.829973i	0.266491	+	0.0365730i
$516$	10.4573	−	14.2735i	0.460356	−	0.628355i
$517$	1.66503	+	1.66503i	0.0732280	+	0.0732280i
$518$	−5.16033	+	15.7750i	−0.226732	+	0.693115i
$519$		−	3.45008i		−	0.151442i
$520$	−6.09631	+	3.22017i	−0.267341	+	0.141214i
$521$		−	11.1639i		−	0.489098i	−0.969637	−	0.244549i	$-0.921360\pi$
$521$		−	11.1639i		−	0.489098i	0.969637	−	0.244549i	$-0.0786400\pi$
$522$	−3.41853	−	1.11827i	−0.149625	−	0.0489452i
$523$	14.8552	+	14.8552i	0.649571	+	0.649571i	0.952889	−	0.303318i	$-0.0980946\pi$
$523$	14.8552	+	14.8552i	0.649571	+	0.649571i	−0.303318	+	0.952889i	$0.598095\pi$
$524$	6.28211	−	0.969391i	0.274435	−	0.0423480i
$525$	−5.04744	+	2.84074i	−0.220288	+	0.123980i
$526$	−13.3602	−	26.3503i	−0.582533	−	1.14893i
$527$		−	8.04551i		−	0.350468i
$528$	−1.72691	+	0.545957i	−0.0751540	+	0.0237597i
$529$	0.953562			0.0414592
$530$	16.5827	−	34.1078i	0.720308	−	1.48155i
$531$	2.45194	+	2.45194i	0.106405	+	0.106405i
$532$	5.50002	−	0.848707i	0.238456	−	0.0367961i
$533$	−7.67094	−	7.67094i	−0.332265	−	0.332265i
$534$	2.14816	−	6.56690i	0.0929601	−	0.284178i
$535$	−6.76364	−	8.91543i	−0.292418	−	0.385448i
$536$	−17.4539	+	12.5226i	−0.753894	+	0.540894i
$537$	13.4745			0.581468
$538$	−7.76656	+	23.7422i	−0.334840	+	1.02360i
$539$	−0.276393	+	0.276393i	−0.0119051	+	0.0119051i
$540$	−24.1279	+	0.403332i	−1.03830	+	0.0173567i
$541$	29.7161	+	29.7161i	1.27759	+	1.27759i	0.942010	+	0.335585i	$0.108934\pi$
$541$	29.7161	+	29.7161i	1.27759	+	1.27759i	0.335585	+	0.942010i	$0.391066\pi$
$542$	18.9915	+	37.4568i	0.815754	+	1.60891i
$543$		−	19.3822i		−	0.831772i
$544$	17.4373	+	17.7876i	0.747620	+	0.762638i
$545$	20.0219	+	26.3917i	0.857645	+	1.13050i
$546$	1.59281	−	0.807589i	0.0681658	−	0.0345616i
$547$	−5.61365	+	5.61365i	−0.240022	+	0.240022i	−0.816859	−	0.576837i	$-0.804287\pi$
$547$	−5.61365	+	5.61365i	−0.240022	+	0.240022i	0.576837	+	0.816859i	$0.304287\pi$
$548$	6.78594	−	9.26234i	0.289881	−	0.395668i
$549$	4.40926	−	4.40926i	0.188183	−	0.188183i
$550$	2.29832	+	1.53527i	0.0980005	+	0.0654640i
$551$			4.26798i			0.181822i
$552$	13.0290	−	9.34788i	0.554552	−	0.397872i
$553$	13.0772			0.556099
$554$	−3.19000	+	9.75179i	−0.135530	+	0.414314i
$555$	−30.1174	−	4.13329i	−1.27841	−	0.175448i
$556$	3.32971	+	21.5781i	0.141211	+	0.915115i
$557$	−9.31394	+	9.31394i	−0.394644	+	0.394644i	−0.876339	−	0.481695i	$-0.840021\pi$
$557$	−9.31394	+	9.31394i	−0.394644	+	0.394644i	0.481695	+	0.876339i	$0.340021\pi$
$558$	3.82145	−	1.93756i	0.161775	−	0.0820235i
$559$	8.32575			0.352142
$560$	1.51160	+	8.81561i	0.0638767	+	0.372528i
$561$	−1.99378			−0.0841775
$562$	22.7680	−	11.5439i	0.960410	−	0.486950i
$563$	−27.7113	+	27.7113i	−1.16789	+	1.16789i	−0.185190	+	0.982703i	$0.559290\pi$
$563$	−27.7113	+	27.7113i	−1.16789	+	1.16789i	−0.982703	+	0.185190i	$0.940710\pi$
$564$	−13.7933	+	2.12844i	−0.580804	+	0.0896237i
$565$	−0.781847	+	5.69696i	−0.0328925	+	0.239673i
$566$	9.63114	−	29.4423i	0.404827	−	1.23755i
$567$	1.27615			0.0535932
$568$	−1.74494	+	10.6072i	−0.0732162	+	0.445067i
$569$			5.57279i			0.233623i	0.993154	+	0.116812i	$0.0372674\pi$
$569$			5.57279i			0.233623i	−0.993154	+	0.116812i	$0.962733\pi$
$570$	3.33053	+	9.63342i	0.139501	+	0.403500i
$571$	20.8873	−	20.8873i	0.874108	−	0.874108i	−0.118809	−	0.992917i	$-0.537908\pi$
$571$	20.8873	−	20.8873i	0.874108	−	0.874108i	0.992917	+	0.118809i	$0.0379077\pi$
$572$	−0.687454	−	0.503654i	−0.0287439	−	0.0210588i
$573$	8.14551	−	8.14551i	0.340284	−	0.340284i
$574$	−12.5523	+	6.36432i	−0.523924	+	0.265642i
$575$	−23.5664	−	6.59265i	−0.982788	−	0.274932i
$576$	−4.24939	+	12.5661i	−0.177058	+	0.523586i
$577$			38.8294i			1.61649i	0.588848	+	0.808244i	$0.299582\pi$
$577$			38.8294i			1.61649i	−0.588848	+	0.808244i	$0.700418\pi$
$578$	1.52809	+	3.01385i	0.0635602	+	0.125360i
$579$	14.3863	+	14.3863i	0.597873	+	0.597873i
$580$	−6.85855	+	0.114650i	−0.284786	+	0.00476059i
$581$	−7.21840	+	7.21840i	−0.299470	+	0.299470i
$582$	−2.13478	+	6.52599i	−0.0884895	+	0.270511i
$583$	4.68782			0.194150
$584$	22.6710	+	3.72952i	0.938132	+	0.154329i
$585$	−2.44289	−	3.22007i	−0.101001	−	0.133134i
$586$	5.65003	−	17.2720i	0.233401	−	0.713502i
$587$	−9.79173	−	9.79173i	−0.404148	−	0.404148i	0.475544	−	0.879692i	$-0.342251\pi$
$587$	−9.79173	−	9.79173i	−0.404148	−	0.404148i	−0.879692	+	0.475544i	$0.842251\pi$
$588$	−0.353319	−	2.28967i	−0.0145706	−	0.0944245i
$589$	−3.59502	−	3.59502i	−0.148130	−	0.148130i
$590$	5.94740	+	2.89154i	0.244851	+	0.119043i
$591$	−21.7074			−0.892923
$592$	−21.6447	+	41.6576i	−0.889592	+	1.71212i
$593$		−	41.3902i		−	1.69969i	−0.527030	−	0.849846i	$-0.676695\pi$
$593$		−	41.3902i		−	1.69969i	0.527030	−	0.849846i	$-0.323305\pi$
$594$	−1.34887	−	2.66038i	−0.0553449	−	0.109157i
$595$	−1.33873	+	9.75473i	−0.0548827	+	0.399905i
$596$	1.62601	+	10.5373i	0.0666041	+	0.431626i
$597$	13.7894	+	13.7894i	0.564363	+	0.564363i
$598$	7.17132	+	2.34588i	0.293257	+	0.0959302i
$599$		−	4.53114i		−	0.185138i	−0.995706	−	0.0925688i	$-0.970492\pi$
$599$		−	4.53114i		−	0.185138i	0.995706	−	0.0925688i	$-0.0295078\pi$
$600$	−15.3912	+	5.61087i	−0.628344	+	0.229063i
$601$		−	10.6569i		−	0.434703i	−0.976093	−	0.217352i	$-0.930258\pi$
$601$		−	10.6569i		−	0.434703i	0.976093	−	0.217352i	$-0.0697418\pi$
$602$	3.35812	−	10.2657i	0.136867	−	0.418399i
$603$	−8.90484	−	8.90484i	−0.362633	−	0.362633i
$604$	−38.3619	−	28.1053i	−1.56092	−	1.14359i
$605$	3.29784	−	24.0299i	0.134076	−	0.976953i
$606$	24.3166	−	12.3291i	0.987793	−	0.500834i
$607$			24.7206i			1.00338i	0.865048	+	0.501689i	$0.167288\pi$
$607$			24.7206i			1.00338i	−0.865048	+	0.501689i	$0.832712\pi$
$608$	15.7398	+	0.156518i	0.638331	+	0.00634764i
$609$	1.77677			0.0719984
$610$	5.19979	−	10.6951i	0.210533	−	0.433031i
$611$	−4.64360	−	4.64360i	−0.187860	−	0.187860i
$612$	−8.63018	+	11.7796i	−0.348854	+	0.476162i
$613$	−13.5018	−	13.5018i	−0.545333	−	0.545333i	0.379754	−	0.925087i	$-0.376009\pi$
$613$	−13.5018	−	13.5018i	−0.545333	−	0.545333i	−0.925087	+	0.379754i	$0.876009\pi$
$614$	21.8232	+	7.13880i	0.880712	+	0.288098i
$615$	−15.5794	−	20.5359i	−0.628223	−	0.828086i
$616$	−0.898287	+	0.644491i	−0.0361930	+	0.0259673i
$617$	−26.4452			−1.06464			−0.532321	−	0.846543i	$-0.678680\pi$
$617$	−26.4452			−1.06464			−0.532321	+	0.846543i	$0.678680\pi$
$618$	−4.25056	−	1.39044i	−0.170982	−	0.0559317i
$619$	25.9846	−	25.9846i	1.04441	−	1.04441i	0.0454409	−	0.998967i	$-0.485531\pi$
$619$	25.9846	−	25.9846i	1.04441	−	1.04441i	0.998967	−	0.0454409i	$-0.0144693\pi$
$620$	5.68054	−	5.87369i	0.228136	−	0.235893i
$621$	18.6739	+	18.6739i	0.749360	+	0.749360i
$622$	−13.2212	+	6.70343i	−0.530120	+	0.268783i
$623$		−	4.21762i		−	0.168975i
$624$	4.81617	−	1.52262i	0.192801	−	0.0609535i
$625$	21.3711	+	12.9722i	0.854842	+	0.518888i
$626$	5.47088	+	10.7902i	0.218660	+	0.431264i
$627$	−0.890891	+	0.890891i	−0.0355788	+	0.0355788i
$628$	2.83331	+	18.3612i	0.113061	+	0.732692i
$629$	−36.5425	+	36.5425i	−1.45704	+	1.45704i
$630$	−4.95569	+	1.71331i	−0.197439	+	0.0682601i
$631$		−	30.4265i		−	1.21126i	−0.795746	−	0.605631i	$-0.792921\pi$
$631$		−	30.4265i		−	1.21126i	0.795746	−	0.605631i	$-0.207079\pi$
$632$	36.4974	+	6.00404i	1.45179	+	0.238828i
$633$	−6.93353			−0.275583
$634$	−0.237948	−	0.0778374i	−0.00945011	−	0.00309132i
$635$	−3.03151	+	22.0892i	−0.120302	+	0.876584i
$636$	−16.4210	+	22.4135i	−0.651134	+	0.888753i
$637$	0.770831	−	0.770831i	0.0305414	−	0.0305414i
$638$	−0.383426	−	0.756231i	−0.0151800	−	0.0299395i
$639$	−6.30193			−0.249301
$640$	0.171294	+	25.2976i	0.00677100	+	0.999977i
$641$	14.7899			0.584167			0.292084	−	0.956393i	$-0.405651\pi$
$641$	14.7899			0.584167			0.292084	+	0.956393i	$0.405651\pi$
$642$	3.70756	+	7.31241i	0.146326	+	0.288598i
$643$	21.0055	−	21.0055i	0.828375	−	0.828375i	−0.158917	−	0.987292i	$-0.550800\pi$
$643$	21.0055	−	21.0055i	0.828375	−	0.828375i	0.987292	+	0.158917i	$0.0508003\pi$
$644$	5.78497	−	7.89610i	0.227960	−	0.311150i
$645$	19.5991	+	2.68976i	0.771713	+	0.105909i
$646$	16.4690	+	5.38732i	0.647962	+	0.211961i
$647$	−16.3851			−0.644165			−0.322082	−	0.946712i	$-0.604383\pi$
$647$	−16.3851			−0.644165			−0.322082	+	0.946712i	$0.604383\pi$
$648$	3.56162	+	0.585909i	0.139914	+	0.0230167i
$649$			0.817419i			0.0320865i
$650$	−6.40977	−	4.28170i	−0.251412	−	0.167942i
$651$	−1.49662	+	1.49662i	−0.0586570	+	0.0586570i
$652$	−3.80204	−	24.6390i	−0.148899	−	0.964938i
$653$	−28.8108	+	28.8108i	−1.12746	+	1.12746i	−0.136866	+	0.990590i	$0.543703\pi$
$653$	−28.8108	+	28.8108i	−1.12746	+	1.12746i	−0.990590	+	0.136866i	$0.956297\pi$
$654$	−10.9752	−	21.6464i	−0.429165	−	0.846441i
$655$	4.29531	+	5.66182i	0.167832	+	0.221225i
$656$	−37.9545	+	11.9992i	−1.48187	+	0.468490i
$657$			13.4693i			0.525488i
$658$	−7.59855	+	3.85264i	−0.296222	+	0.150191i
$659$	27.0373	+	27.0373i	1.05322	+	1.05322i	0.998502	+	0.0547230i	$0.0174276\pi$
$659$	27.0373	+	27.0373i	1.05322	+	1.05322i	0.0547230	+	0.998502i	$0.482572\pi$
$660$	−1.45557	−	1.40771i	−0.0566582	−	0.0547951i
$661$	−4.12831	+	4.12831i	−0.160573	+	0.160573i	−0.782820	−	0.622248i	$-0.786220\pi$
$661$	−4.12831	+	4.12831i	−0.160573	+	0.160573i	0.622248	+	0.782820i	$0.286220\pi$
$662$	−8.80348	−	2.87979i	−0.342157	−	0.111926i
$663$	5.56045			0.215950
$664$	−23.4601	+	16.8318i	−0.910427	+	0.653200i
$665$	3.76056	+	4.95695i	0.145828	+	0.192222i
$666$	−26.1572	−	8.55655i	−1.01357	−	0.331560i
$667$	5.30821	+	5.30821i	0.205535	+	0.205535i
$668$	23.2360	−	31.7155i	0.899027	−	1.22711i
$669$	−2.43966	−	2.43966i	−0.0943228	−	0.0943228i
$670$	−21.5995	−	10.5014i	−0.834462	−	0.405704i
$671$	1.46994			0.0567466
$672$	0.0651588	−	6.55250i	0.00251355	−	0.252768i
$673$		−	14.0450i		−	0.541396i	−0.962664	−	0.270698i	$-0.912746\pi$
$673$		−	14.0450i		−	0.541396i	0.962664	−	0.270698i	$-0.0872545\pi$
$674$	−6.21133	+	3.14929i	−0.239252	+	0.121306i
$675$	−13.2326	−	23.5117i	−0.509322	−	0.904966i
$676$	−19.0563	−	13.9613i	−0.732933	−	0.536974i
$677$	8.10443	+	8.10443i	0.311479	+	0.311479i	0.845482	−	0.534004i	$-0.179313\pi$
$677$	8.10443	+	8.10443i	0.311479	+	0.311479i	−0.534004	+	0.845482i	$0.679313\pi$
$678$	1.30982	−	4.00408i	0.0503031	−	0.153776i
$679$			4.19134i			0.160849i
$680$	−8.21491	+	26.6100i	−0.315027	+	1.02045i
$681$		−	8.31912i		−	0.318789i
$682$	0.959961	+	0.314022i	0.0367588	+	0.0120245i
$683$	0.109456	+	0.109456i	0.00418820	+	0.00418820i	0.709198	−	0.705010i	$-0.249057\pi$
$683$	0.109456	+	0.109456i	0.00418820	+	0.00418820i	−0.705010	+	0.709198i	$0.749057\pi$
$684$	1.40727	+	9.11981i	0.0538085	+	0.348705i
$685$	12.7182	+	1.74544i	0.485939	+	0.0666899i
$686$	−0.639532	−	1.26135i	−0.0244175	−	0.0481585i
$687$			8.20658i			0.313101i
$688$	14.0854	−	27.1089i	0.537002	−	1.03352i
$689$	−13.0738			−0.498074
$690$	16.1236	+	7.83909i	0.613817	+	0.298429i
$691$	−20.5435	−	20.5435i	−0.781512	−	0.781512i	0.198574	−	0.980086i	$-0.436369\pi$
$691$	−20.5435	−	20.5435i	−0.781512	−	0.781512i	−0.980086	+	0.198574i	$0.936369\pi$
$692$	−0.908426	−	5.88703i	−0.0345332	−	0.223791i
$693$	−0.458298	−	0.458298i	−0.0174093	−	0.0174093i
$694$	8.91982	−	27.2678i	0.338592	−	1.03507i
$695$	−19.4475	+	14.7537i	−0.737685	+	0.559641i
$696$	4.95881	+	0.815756i	0.187963	+	0.0309211i
$697$	−43.8199			−1.65980
$698$	8.79291	−	26.8798i	0.332816	−	1.01741i
$699$	1.20176	−	1.20176i	0.0454546	−	0.0454546i
$700$	−7.86469	+	6.17630i	−0.297257	+	0.233442i
$701$	5.39493	+	5.39493i	0.203764	+	0.203764i	0.801610	−	0.597847i	$-0.203977\pi$
$701$	5.39493	+	5.39493i	0.203764	+	0.203764i	−0.597847	+	0.801610i	$0.703977\pi$
$702$	3.76186	+	7.41951i	0.141982	+	0.280031i
$703$			32.6569i			1.23168i
$704$	−2.80294	+	1.38629i	−0.105640	+	0.0522479i
$705$	−9.43100	−	12.4314i	−0.355192	−	0.468193i
$706$	15.2758	−	7.74516i	0.574911	−	0.291493i
$707$	11.7679	−	11.7679i	0.442577	−	0.442577i
$708$	−3.90826	−	2.86334i	−0.146881	−	0.107611i
$709$	10.7172	−	10.7172i	0.402492	−	0.402492i	−0.476618	−	0.879110i	$-0.658138\pi$
$709$	10.7172	−	10.7172i	0.402492	−	0.402492i	0.879110	+	0.476618i	$0.158138\pi$
$710$	−11.3589	+	3.92707i	−0.426291	+	0.147380i
$711$			21.6838i			0.813207i
$712$	1.93640	−	11.7710i	0.0725698	−	0.441137i
$713$	−8.94246			−0.334898
$714$	2.24276	−	6.85607i	0.0839331	−	0.256582i
$715$	0.129547	−	0.943951i	0.00484479	−	0.0353018i
$716$	22.9922	−	3.54791i	0.859257	−	0.132592i
$717$	0.364024	−	0.364024i	0.0135947	−	0.0135947i
$718$	−15.9732	+	8.09878i	−0.596115	+	0.302244i
$719$	24.8704			0.927511			0.463755	−	0.885963i	$-0.346502\pi$
$719$	24.8704			0.927511			0.463755	+	0.885963i	$0.346502\pi$
$720$	−14.6175	+	2.50644i	−0.544763	+	0.0934097i
$721$	−2.72994			−0.101668
$722$	−14.1995	+	7.19945i	−0.528449	+	0.267936i
$723$	18.4810	−	18.4810i	0.687315	−	0.687315i
$724$	−5.10345	−	33.0728i	−0.189668	−	1.22914i
$725$	−3.76146	−	6.68337i	−0.139697	−	0.248214i
$726$	−5.52482	+	16.8893i	−0.205045	+	0.626820i
$727$	−12.4099			−0.460259			−0.230130	−	0.973160i	$-0.573915\pi$
$727$	−12.4099			−0.460259			−0.230130	+	0.973160i	$0.573915\pi$
$728$	2.50523	−	1.79742i	0.0928500	−	0.0666168i
$729$			20.8677i			0.772879i
$730$	8.39343	+	24.2776i	0.310655	+	0.898556i
$731$	23.7802	−	23.7802i	0.879544	−	0.879544i
$732$	−5.14907	+	7.02813i	−0.190315	+	0.259767i
$733$	8.78765	−	8.78765i	0.324579	−	0.324579i	−0.525941	−	0.850521i	$-0.676287\pi$
$733$	8.78765	−	8.78765i	0.324579	−	0.324579i	0.850521	+	0.525941i	$0.176287\pi$
$734$	−46.1912	+	23.4200i	−1.70495	+	0.864448i
$735$	2.06359	−	1.56553i	0.0761167	−	0.0577455i
$736$	19.7706	−	19.3813i	0.728756	−	0.714405i
$737$		−	2.96867i		−	0.109352i
$738$	−10.5529	−	20.8135i	−0.388459	−	0.766157i
$739$	−30.0208	−	30.0208i	−1.10433	−	1.10433i	−0.993882	−	0.110451i	$-0.964770\pi$
$739$	−30.0208	−	30.0208i	−1.10433	−	1.10433i	−0.110451	−	0.993882i	$-0.535230\pi$
$740$	−52.4789	+	0.877258i	−1.92916	+	0.0322487i
$741$	2.48460	−	2.48460i	0.0912742	−	0.0912742i
$742$	−5.27322	+	16.1201i	−0.193586	+	0.591789i
$743$	−42.7793			−1.56942			−0.784710	−	0.619863i	$-0.787188\pi$
$743$	−42.7793			−1.56942			−0.784710	+	0.619863i	$0.787188\pi$
$744$	−4.86406	+	3.48980i	−0.178325	+	0.127942i
$745$	−9.49687	+	7.20475i	−0.347939	+	0.263962i
$746$	−13.5649	+	41.4676i	−0.496645	+	1.51824i
$747$	−11.9691	−	11.9691i	−0.437927	−	0.437927i
$748$	−3.40208	+	0.524973i	−0.124392	+	0.0191949i
$749$	3.53881	+	3.53881i	0.129305	+	0.129305i
$750$	−13.7055	−	12.1500i	−0.500455	−	0.443657i
$751$	15.2985			0.558251			0.279125	−	0.960255i	$-0.409956\pi$
$751$	15.2985			0.558251			0.279125	+	0.960255i	$0.409956\pi$
$752$	−22.9757	+	7.26372i	−0.837839	+	0.264881i
$753$		−	33.5304i		−	1.22191i
$754$	1.06934	+	2.10905i	0.0389430	+	0.0768071i
$755$	7.22910	−	52.6751i	0.263094	−	1.91704i
$756$	10.6656	−	1.64581i	0.387905	−	0.0598575i
$757$	17.2990	+	17.2990i	0.628744	+	0.628744i	0.947752	−	0.319008i	$-0.103350\pi$
$757$	17.2990	+	17.2990i	0.628744	+	0.628744i	−0.319008	+	0.947752i	$0.603350\pi$
$758$	−5.34356	−	1.74799i	−0.194087	−	0.0634897i
$759$			2.21605i			0.0804377i
$760$	8.21956	+	15.5610i	0.298155	+	0.564456i
$761$		−	38.7329i		−	1.40407i	−0.712143	−	0.702034i	$-0.752275\pi$
$761$		−	38.7329i		−	1.40407i	0.712143	−	0.702034i	$-0.247725\pi$
$762$	5.07864	−	15.5253i	0.183980	−	0.562423i
$763$	−10.4757	−	10.4757i	−0.379245	−	0.379245i
$764$	11.7543	−	16.0438i	0.425255	−	0.580444i
$765$	−16.1747	−	2.21981i	−0.584798	−	0.0802573i
$766$	36.1778	−	18.3430i	1.30716	−	0.662759i
$767$		−	2.27970i		−	0.0823151i
$768$	3.19026	−	18.2576i	0.115118	−	0.658813i
$769$	23.8664			0.860644			0.430322	−	0.902676i	$-0.358400\pi$
$769$	23.8664			0.860644			0.430322	+	0.902676i	$0.358400\pi$
$770$	−1.11165	−	0.540466i	−0.0400609	−	0.0194771i
$771$	3.74465	+	3.74465i	0.134860	+	0.134860i
$772$	28.3359	+	20.7600i	1.01983	+	0.747167i
$773$	32.7532	+	32.7532i	1.17805	+	1.17805i	0.980240	+	0.197811i	$0.0633832\pi$
$773$	32.7532	+	32.7532i	1.17805	+	1.17805i	0.197811	+	0.980240i	$0.436617\pi$
$774$	17.0220	+	5.56823i	0.611843	+	0.200146i
$775$	8.79793	+	2.46120i	0.316031	+	0.0884088i
$776$	−1.92434	+	11.6977i	−0.0690798	+	0.419922i
$777$	13.5952			0.487723
$778$	−39.8720	−	13.0429i	−1.42948	−	0.467611i
$779$	−19.5803	+	19.5803i	−0.701536	+	0.701536i
$780$	4.05945	+	3.92596i	0.145352	+	0.140572i
$781$	−1.05046	−	1.05046i	−0.0375884	−	0.0375884i
$782$	27.1833	−	13.7825i	0.972072	−	0.492863i
$783$			8.27645i			0.295776i
$784$	−1.20577	−	3.81394i	−0.0430631	−	0.136212i
$785$	−16.5482	+	12.5542i	−0.590631	+	0.448079i
$786$	−2.35452	−	4.64381i	−0.0839828	−	0.165639i
$787$	31.4499	−	31.4499i	1.12107	−	1.12107i	0.129487	−	0.991581i	$-0.458667\pi$
$787$	31.4499	−	31.4499i	1.12107	−	1.12107i	0.991581	−	0.129487i	$-0.0413330\pi$
$788$	−37.0403	+	5.71567i	−1.31950	+	0.203612i
$789$	−17.1115	+	17.1115i	−0.609187	+	0.609187i
$790$	13.5123	+	39.0839i	0.480747	+	1.39054i
$791$		−	2.57164i		−	0.0914369i
$792$	−1.06866	−	1.48949i	−0.0379730	−	0.0529266i
$793$	−4.09952			−0.145578
$794$	25.5404	+	8.35476i	0.906394	+	0.296499i
$795$	−30.7762	−	4.22371i	−1.09152	−	0.149800i
$796$	27.1603	+	19.8987i	0.962672	+	0.705289i
$797$	3.41184	−	3.41184i	0.120854	−	0.120854i	−0.644093	−	0.764947i	$-0.722765\pi$
$797$	3.41184	−	3.41184i	0.120854	−	0.120854i	0.764947	+	0.644093i	$0.222765\pi$
$798$	−2.06139	−	4.06568i	−0.0729724	−	0.143923i
$799$	−26.5264			−0.938435
$800$	−24.7854	+	13.6267i	−0.876295	+	0.481776i
$801$	6.99340			0.247100
$802$	−7.66926	−	15.1261i	−0.270811	−	0.534120i
$803$	−2.24518	+	2.24518i	−0.0792306	+	0.0792306i
$804$	14.1939	+	10.3989i	0.500579	+	0.366743i
$805$	10.8422	+	1.48798i	0.382138	+	0.0524444i
$806$	−2.67723	−	0.875775i	−0.0943014	−	0.0308479i
$807$	20.4614			0.720276
$808$	38.2461	−	27.4403i	1.34549	−	0.965346i
$809$			3.51379i			0.123538i	0.998090	+	0.0617692i	$0.0196743\pi$
$809$			3.51379i			0.123538i	−0.998090	+	0.0617692i	$0.980326\pi$
$810$	1.31861	+	3.81403i	0.0463313	+	0.134011i
$811$	36.6400	−	36.6400i	1.28660	−	1.28660i	0.349765	−	0.936837i	$-0.386261\pi$
$811$	36.6400	−	36.6400i	1.28660	−	1.28660i	0.936837	−	0.349765i	$-0.113739\pi$
$812$	3.03178	−	0.467833i	0.106395	−	0.0164177i
$813$	24.3240	−	24.3240i	0.853079	−	0.853079i
$814$	−2.93383	−	5.78639i	−0.102831	−	0.202813i
$815$	22.2061	−	16.8466i	0.777847	−	0.590110i
$816$	9.40712	−	18.1050i	0.329315	−	0.633802i
$817$		−	21.2517i		−	0.743503i
$818$	24.5142	−	12.4293i	0.857118	−	0.434579i
$819$	1.27815	+	1.27815i	0.0446621	+	0.0446621i
$820$	−31.9911	−	30.9391i	−1.11718	−	1.08044i
$821$	−30.8002	+	30.8002i	−1.07493	+	1.07493i	−0.0779783	+	0.996955i	$0.524846\pi$
$821$	−30.8002	+	30.8002i	−1.07493	+	1.07493i	−0.996955	+	0.0779783i	$0.975154\pi$
$822$	−8.93896	−	2.92411i	−0.311782	−	0.101990i
$823$	31.2844			1.09051			0.545253	−	0.838272i	$-0.316434\pi$
$823$	31.2844			1.09051			0.545253	+	0.838272i	$0.316434\pi$
$824$	−7.61902	−	1.25338i	−0.265421	−	0.0436634i
$825$	0.609916	−	2.18024i	0.0212346	−	0.0759061i
$826$	−2.81088	−	0.919495i	−0.0978031	−	0.0319933i
$827$	−0.438302	−	0.438302i	−0.0152412	−	0.0152412i	0.699445	−	0.714686i	$-0.253431\pi$
$827$	−0.438302	−	0.438302i	−0.0152412	−	0.0152412i	−0.714686	+	0.699445i	$0.753431\pi$
$828$	13.0928	+	9.59230i	0.455008	+	0.333355i
$829$	−13.0661	−	13.0661i	−0.453805	−	0.453805i	0.442810	−	0.896615i	$-0.353982\pi$
$829$	−13.0661	−	13.0661i	−0.453805	−	0.453805i	−0.896615	+	0.442810i	$0.853982\pi$
$830$	−29.0322	−	14.1151i	−1.00772	−	0.489941i
$831$	8.40423			0.291539
$832$	7.81712	−	3.86623i	0.271010	−	0.134038i
$833$		−	4.40334i		−	0.152567i
$834$	15.9508	−	8.08740i	0.552330	−	0.280044i
$835$	43.5490	+	5.97663i	1.50707	+	0.206830i
$836$	−1.28559	+	1.75474i	−0.0444631	+	0.0606891i
$837$	−6.97145	−	6.97145i	−0.240968	−	0.240968i
$838$	−0.932517	+	2.85069i	−0.0322133	+	0.0984754i
$839$		−	27.6794i		−	0.955598i	−0.878469	−	0.477799i	$-0.841435\pi$
$839$		−	27.6794i		−	0.955598i	0.878469	−	0.477799i	$-0.158565\pi$
$840$	6.47808	−	3.42183i	0.223515	−	0.118064i
$841$		−	26.6474i		−	0.918874i
$842$	1.17900	+	0.385674i	0.0406310	+	0.0132912i
$843$	−14.7852	−	14.7852i	−0.509231	−	0.509231i
$844$	−11.8310	+	1.82564i	−0.407239	+	0.0628410i
$845$	3.59105	−	26.1664i	0.123536	−	0.900150i
$846$	−6.38822	−	12.5995i	−0.219631	−	0.433178i
$847$			10.8472i			0.372715i
$848$	−22.1182	+	42.5689i	−0.759543	+	1.46182i
$849$	−25.3738			−0.870825
$850$	−30.5373	+	6.07824i	−1.04742	+	0.208482i
$851$	40.6163	+	40.6163i	1.39231	+	1.39231i
$852$	8.70214	−	1.34282i	0.298130	−	0.0460044i
$853$	−10.2786	−	10.2786i	−0.351931	−	0.351931i	0.508897	−	0.860828i	$-0.330054\pi$
$853$	−10.2786	−	10.2786i	−0.351931	−	0.351931i	−0.860828	+	0.508897i	$0.830054\pi$
$854$	−1.65351	+	5.05474i	−0.0565818	+	0.172970i
$855$	−8.21932	+	6.23554i	−0.281095	+	0.213251i
$856$	8.25177	+	11.5013i	0.282040	+	0.393105i
$857$	−14.3929			−0.491651			−0.245826	−	0.969314i	$-0.579059\pi$
$857$	−14.3929			−0.491651			−0.245826	+	0.969314i	$0.579059\pi$
$858$	−0.217028	+	0.663452i	−0.00740922	+	0.0226499i
$859$	−32.9472	+	32.9472i	−1.12414	+	1.12414i	−0.133033	+	0.991112i	$0.542472\pi$
$859$	−32.9472	+	32.9472i	−1.12414	+	1.12414i	−0.991112	+	0.133033i	$0.957528\pi$
$860$	34.1510	−	0.570881i	1.16454	−	0.0194669i
$861$	8.15132	+	8.15132i	0.277796	+	0.277796i
$862$	9.02276	+	17.7956i	0.307316	+	0.606119i
$863$			43.5111i			1.48114i	0.671982	+	0.740568i	$0.265443\pi$
$863$			43.5111i			1.48114i	−0.671982	+	0.740568i	$0.734557\pi$
$864$	30.5225	+	0.303519i	1.03840	+	0.0103259i
$865$	5.30574	−	4.02517i	0.180401	−	0.136860i
$866$	−26.8882	+	13.6329i	−0.913697	+	0.463265i
$867$	1.95715	−	1.95715i	0.0664684	−	0.0664684i
$868$	−2.15967	+	2.94781i	−0.0733041	+	0.100055i
$869$	−3.61445	+	3.61445i	−0.122612	+	0.122612i
$870$	1.83589	+	5.31024i	0.0622425	+	0.180034i
$871$			8.27931i			0.280534i
$872$	−24.4271	−	34.0464i	−0.827207	−	1.15296i
$873$	−6.94984			−0.235216
$874$	5.98792	−	18.3050i	0.202544	−	0.619175i
$875$	−10.2575	−	4.44799i	−0.346765	−	0.150370i
$876$	−2.87006	−	18.5993i	−0.0969702	−	0.628413i
$877$	37.4565	−	37.4565i	1.26482	−	1.26482i	0.316085	−	0.948731i	$-0.397631\pi$
$877$	37.4565	−	37.4565i	1.26482	−	1.26482i	0.948731	−	0.316085i	$-0.102369\pi$
$878$	−19.1251	+	9.69687i	−0.645441	+	0.327253i
$879$	−14.8853			−0.502069
$880$	−2.85437	−	2.01878i	−0.0962208	−	0.0680530i
$881$	−47.6944			−1.60687			−0.803433	−	0.595395i	$-0.796995\pi$
$881$	−47.6944			−1.60687			−0.803433	+	0.595395i	$0.796995\pi$
$882$	2.09149	−	1.06043i	0.0704242	−	0.0357067i
$883$	11.1286	−	11.1286i	0.374507	−	0.374507i	−0.494609	−	0.869116i	$-0.664689\pi$
$883$	11.1286	−	11.1286i	0.374507	−	0.374507i	0.869116	+	0.494609i	$0.164689\pi$
$884$	9.48804	−	1.46410i	0.319117	−	0.0492429i
$885$	0.736492	−	5.36648i	0.0247569	−	0.180392i
$886$	3.67384	−	11.2309i	0.123425	−	0.377309i
$887$	12.5582			0.421661			0.210831	−	0.977523i	$-0.432383\pi$
$887$	12.5582			0.421661			0.210831	+	0.977523i	$0.432383\pi$
$888$	37.9429	+	6.24185i	1.27328	+	0.209463i
$889$		−	9.97120i		−	0.334423i
$890$	12.6052	−	4.35796i	0.422527	−	0.146079i
$891$	−0.352718	+	0.352718i	−0.0118165	+	0.0118165i
$892$	−4.80528	−	3.52052i	−0.160893	−	0.117876i
$893$	−11.8529	+	11.8529i	−0.396643	+	0.396643i
$894$	7.78931	−	3.94936i	0.260513	−	0.132086i
$895$	15.7206	+	20.7219i	0.525481	+	0.692657i
$896$	−1.61413	−	11.1980i	−0.0539241	−	0.374098i
$897$		−	6.18035i		−	0.206356i
$898$	−20.1337	−	39.7096i	−0.671870	−	1.32513i
$899$	−1.98168	−	1.98168i	−0.0660929	−	0.0660929i
$900$	−10.2412	−	13.0408i	−0.341372	−	0.434692i
$901$	−37.3419	+	37.3419i	−1.24404	+	1.24404i
$902$	1.71032	−	5.22843i	0.0569475	−	0.174088i
$903$	−8.84713			−0.294414
$904$	1.18070	−	7.17722i	0.0392694	−	0.238711i
$905$	29.8072	−	22.6130i	0.990823	−	0.751683i
$906$	−12.1108	+	37.0225i	−0.402354	+	1.22999i
$907$	22.8903	+	22.8903i	0.760059	+	0.760059i	0.976333	−	0.216274i	$-0.0693903\pi$
$907$	22.8903	+	22.8903i	0.760059	+	0.760059i	−0.216274	+	0.976333i	$0.569390\pi$
$908$	−2.19047	−	14.1953i	−0.0726933	−	0.471087i
$909$	19.5128	+	19.5128i	0.647200	+	0.647200i
$910$	3.10027	+	1.50731i	0.102773	+	0.0499667i
$911$	−37.3668			−1.23802			−0.619009	−	0.785384i	$-0.712466\pi$
$911$	−37.3668			−1.23802			−0.619009	+	0.785384i	$0.712466\pi$
$912$	−3.88652	−	12.2934i	−0.128696	−	0.407075i
$913$		−	3.99023i		−	0.132057i
$914$	−2.56219	−	5.05340i	−0.0847498	−	0.167152i
$915$	−9.65041	−	1.32442i	−0.319033	−	0.0437838i
$916$	2.16084	+	14.0032i	0.0713960	+	0.462680i
$917$	−2.24735	−	2.24735i	−0.0742140	−	0.0742140i
$918$	31.9365	+	10.4471i	1.05406	+	0.344805i
$919$			25.5946i			0.844288i	0.906529	+	0.422144i	$0.138722\pi$
$919$			25.5946i			0.844288i	−0.906529	+	0.422144i	$0.861278\pi$
$920$	29.5765	+	9.13073i	0.975110	+	0.301031i
$921$		−	18.8075i		−	0.619730i
$922$	7.43578	−	22.7310i	0.244884	−	0.748607i
$923$	2.92962	+	2.92962i	0.0964297	+	0.0964297i
$924$	0.730504	+	0.535195i	0.0240318	+	0.0176066i
$925$	−28.7812	−	51.1386i	−0.946320	−	1.68143i
$926$	−32.3264	+	16.3902i	−1.06231	+	0.538617i
$927$		−	4.52662i		−	0.148674i
$928$	8.67623	+	0.0862774i	0.284811	+	0.00283220i
$929$	55.7757			1.82994			0.914971	−	0.403520i	$-0.132214\pi$
$929$	55.7757			1.82994			0.914971	+	0.403520i	$0.132214\pi$
$930$	−6.01935	−	2.92652i	−0.197382	−	0.0959645i
$931$	−1.96757	−	1.96757i	−0.0644844	−	0.0644844i
$932$	1.73418	−	2.36704i	0.0568050	−	0.0775349i
$933$	8.58565	+	8.58565i	0.281081	+	0.281081i
$934$	−50.5780	−	16.5451i	−1.65496	−	0.541371i
$935$	−2.32612	−	3.06615i	−0.0760723	−	0.100274i
$936$	2.98037	+	4.15403i	0.0974165	+	0.135779i
$937$	43.3861			1.41736			0.708680	−	0.705530i	$-0.249291\pi$
$937$	43.3861			1.41736			0.708680	+	0.705530i	$0.249291\pi$
$938$	10.2084	+	3.33938i	0.333317	+	0.109035i
$939$	7.00702	−	7.00702i	0.228666	−	0.228666i
$940$	−19.3658	−	18.7290i	−0.631642	−	0.610872i
$941$	8.36888	+	8.36888i	0.272818	+	0.272818i	0.830234	−	0.557416i	$-0.188207\pi$
$941$	8.36888	+	8.36888i	0.272818	+	0.272818i	−0.557416	+	0.830234i	$0.688207\pi$
$942$	13.5728	−	6.88172i	0.442226	−	0.224219i
$943$			48.7051i			1.58606i
$944$	−7.42277	−	3.85677i	−0.241591	−	0.125527i
$945$	7.29247	+	9.61249i	0.237224	+	0.312694i
$946$	1.90921	+	3.76553i	0.0620737	+	0.122428i
$947$	−4.06481	+	4.06481i	−0.132088	+	0.132088i	−0.770060	−	0.637972i	$-0.779774\pi$
$947$	−4.06481	+	4.06481i	−0.132088	+	0.132088i	0.637972	+	0.770060i	$0.279774\pi$
$948$	−4.62042	−	29.9425i	−0.150064	−	0.972488i
$949$	6.26157	−	6.26157i	0.203259	−	0.203259i
$950$	−10.9292	+	16.3611i	−0.354588	+	0.530824i
$951$			0.205067i			0.00664975i
$952$	2.02167	−	12.2893i	0.0655228	−	0.398300i
$953$	−40.0218			−1.29643			−0.648217	−	0.761455i	$-0.724485\pi$
$953$	−40.0218			−1.29643			−0.648217	+	0.761455i	$0.724485\pi$
$954$	−26.7295	−	8.74374i	−0.865398	−	0.283089i
$955$	22.0299	+	3.02337i	0.712872	+	0.0978340i
$956$	0.525301	−	0.717000i	0.0169895	−	0.0231895i
$957$	−0.491087	+	0.491087i	−0.0158746	+	0.0158746i
$958$	14.7278	+	29.0477i	0.475834	+	0.938487i
$959$	−5.74108			−0.185389
$960$	19.6508	−	6.57579i	0.634227	−	0.212233i
$961$	−27.6616			−0.892308
$962$	8.18215	+	16.1376i	0.263803	+	0.520298i
$963$	−5.86784	+	5.86784i	−0.189089	+	0.189089i
$964$	26.6687	−	36.4010i	0.858942	−	1.17240i
$965$	−5.33976	+	38.9084i	−0.171893	+	1.25251i
$966$	−7.62041	−	2.49279i	−0.245183	−	0.0802041i
$967$	−20.7433			−0.667059			−0.333530	−	0.942740i	$-0.608240\pi$
$967$	−20.7433			−0.667059			−0.333530	+	0.942740i	$0.608240\pi$
$968$	−4.98020	+	30.2737i	−0.160070	+	0.973032i
$969$		−	14.1932i		−	0.455951i
$970$	−12.5267	+	4.33081i	−0.402207	+	0.139054i
$971$	−2.46682	+	2.46682i	−0.0791640	+	0.0791640i	−0.745580	−	0.666416i	$-0.767827\pi$
$971$	−2.46682	+	2.46682i	−0.0791640	+	0.0791640i	0.666416	+	0.745580i	$0.267827\pi$
$972$	4.48654	+	29.0749i	0.143906	+	0.932578i
$973$	7.71930	−	7.71930i	0.247470	−	0.247470i
$974$	−12.7936	−	25.2328i	−0.409934	−	0.808512i
$975$	−1.70099	+	6.08046i	−0.0544754	+	0.194731i
$976$	−6.93554	+	13.3482i	−0.222001	+	0.427265i
$977$			7.92103i			0.253416i	0.991940	+	0.126708i	$0.0404411\pi$
$977$			7.92103i			0.253416i	−0.991940	+	0.126708i	$0.959559\pi$
$978$	−18.2134	+	9.23462i	−0.582401	+	0.295291i
$979$	1.16572	+	1.16572i	0.0372566	+	0.0372566i
$980$	3.10898	−	3.21469i	0.0993128	−	0.102690i
$981$	17.3702	−	17.3702i	0.554587	−	0.554587i
$982$	−57.2961	−	18.7427i	−1.82839	−	0.598103i
$983$	−57.9992			−1.84989			−0.924943	−	0.380105i	$-0.875888\pi$
$983$	−57.9992			−1.84989			−0.924943	+	0.380105i	$0.875888\pi$
$984$	19.0072	+	26.4921i	0.605927	+	0.844537i
$985$	−25.3258	−	33.3829i	−0.806946	−	1.06367i
$986$	9.07820	+	2.96966i	0.289109	+	0.0945732i
$987$	4.93440	+	4.93440i	0.157064	+	0.157064i
$988$	3.58538	−	4.89380i	0.114066	−	0.155692i
$989$	−26.4313	−	26.4313i	−0.840468	−	0.840468i
$990$	0.896169	−	1.84327i	0.0284821	−	0.0585828i
$991$	−51.7541			−1.64402			−0.822011	−	0.569472i	$-0.807148\pi$
$991$	−51.7541			−1.64402			−0.822011	+	0.569472i	$0.807148\pi$
$992$	−7.38087	+	7.23552i	−0.234343	+	0.229728i
$993$			7.58697i			0.240765i
$994$	4.79388	−	2.43061i	0.152053	−	0.0770942i
$995$	−5.11822	+	37.2941i	−0.162259	+	1.18230i
$996$	19.0782	+	13.9774i	0.604515	+	0.442890i
$997$	3.89462	+	3.89462i	0.123344	+	0.123344i	0.766084	−	0.642740i	$-0.222203\pi$
$997$	3.89462	+	3.89462i	0.123344	+	0.123344i	−0.642740	+	0.766084i	$0.722203\pi$
$998$	−2.14179	+	6.54742i	−0.0677973	+	0.207255i
$999$			63.3281i			2.00361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.d.29.13	yes	70
5.4	even	2		560.2.bb.c.29.23	✓	70
16.5	even	4		560.2.bb.c.309.23	yes	70
80.69	even	4	inner	560.2.bb.d.309.13	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.23	✓	70	5.4	even	2
560.2.bb.c.309.23	yes	70	16.5	even	4
560.2.bb.d.29.13	yes	70	1.1	even	1	trivial
560.2.bb.d.309.13	yes	70	80.69	even	4	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.639532 - 1.26135i) q^{2} +(-0.819103 + 0.819103i) q^{3} +(-1.18200 + 1.61335i) q^{4} +(-2.21530 - 0.304027i) q^{5} +(1.55702 + 0.509331i) q^{6} +1.00000 q^{7} +(2.79091 + 0.459123i) q^{8} +1.65814i q^{9} +O(q^{10})\)	\(q+(-0.639532 - 1.26135i) q^{2} +(-0.819103 + 0.819103i) q^{3} +(-1.18200 + 1.61335i) q^{4} +(-2.21530 - 0.304027i) q^{5} +(1.55702 + 0.509331i) q^{6} +1.00000 q^{7} +(2.79091 + 0.459123i) q^{8} +1.65814i q^{9} +(1.03327 + 2.98870i) q^{10} +(-0.276393 + 0.276393i) q^{11} +(-0.353319 - 2.28967i) q^{12} +(0.770831 - 0.770831i) q^{13} +(-0.639532 - 1.26135i) q^{14} +(2.06359 - 1.56553i) q^{15} +(-1.20577 - 3.81394i) q^{16} -4.40334i q^{17} +(2.09149 - 1.06043i) q^{18} +(-1.96757 - 1.96757i) q^{19} +(3.10898 - 3.21469i) q^{20} +(-0.819103 + 0.819103i) q^{21} +(0.525390 + 0.171865i) q^{22} -4.89424 q^{23} +(-2.66212 + 1.90998i) q^{24} +(4.81514 + 1.34702i) q^{25} +(-1.46526 - 0.479315i) q^{26} +(-3.81550 - 3.81550i) q^{27} +(-1.18200 + 1.61335i) q^{28} +(-1.08458 - 1.08458i) q^{29} +(-3.29441 - 1.60170i) q^{30} +1.82714 q^{31} +(-4.03958 + 3.96003i) q^{32} -0.452788i q^{33} +(-5.55414 + 2.81608i) q^{34} +(-2.21530 - 0.304027i) q^{35} +(-2.67515 - 1.95992i) q^{36} +(-8.29881 - 8.29881i) q^{37} +(-1.22346 + 3.74011i) q^{38} +1.26278i q^{39} +(-6.04314 - 1.86561i) q^{40} -9.95152i q^{41} +(1.55702 + 0.509331i) q^{42} +(5.40050 + 5.40050i) q^{43} +(-0.119222 - 0.772613i) q^{44} +(0.504119 - 3.67328i) q^{45} +(3.13002 + 6.17334i) q^{46} -6.02415i q^{47} +(4.11166 + 2.13636i) q^{48} +1.00000 q^{49} +(-1.38037 - 6.93503i) q^{50} +(3.60679 + 3.60679i) q^{51} +(0.332497 + 2.15474i) q^{52} +(-8.48035 - 8.48035i) q^{53} +(-2.37254 + 7.25280i) q^{54} +(0.696325 - 0.528263i) q^{55} +(2.79091 + 0.459123i) q^{56} +3.22328 q^{57} +(-0.674411 + 2.06166i) q^{58} +(1.47873 - 1.47873i) q^{59} +(0.0865865 + 5.17974i) q^{60} +(-2.65916 - 2.65916i) q^{61} +(-1.16851 - 2.30466i) q^{62} +1.65814i q^{63} +(7.57841 + 2.56275i) q^{64} +(-1.94198 + 1.47327i) q^{65} +(-0.571124 + 0.289573i) q^{66} +(-5.37037 + 5.37037i) q^{67} +(7.10411 + 5.20473i) q^{68} +(4.00888 - 4.00888i) q^{69} +(1.03327 + 2.98870i) q^{70} +3.80060i q^{71} +(-0.761290 + 4.62773i) q^{72} +8.12314 q^{73} +(-5.16033 + 15.7750i) q^{74} +(-5.04744 + 2.84074i) q^{75} +(5.50002 - 0.848707i) q^{76} +(-0.276393 + 0.276393i) q^{77} +(1.59281 - 0.807589i) q^{78} +13.0772 q^{79} +(1.51160 + 8.81561i) q^{80} +1.27615 q^{81} +(-12.5523 + 6.36432i) q^{82} +(-7.21840 + 7.21840i) q^{83} +(-0.353319 - 2.28967i) q^{84} +(-1.33873 + 9.75473i) q^{85} +(3.35812 - 10.2657i) q^{86} +1.77677 q^{87} +(-0.898287 + 0.644491i) q^{88} -4.21762i q^{89} +(-4.95569 + 1.71331i) q^{90} +(0.770831 - 0.770831i) q^{91} +(5.78497 - 7.89610i) q^{92} +(-1.49662 + 1.49662i) q^{93} +(-7.59855 + 3.85264i) q^{94} +(3.76056 + 4.95695i) q^{95} +(0.0651588 - 6.55250i) q^{96} +4.19134i q^{97} +(-0.639532 - 1.26135i) q^{98} +(-0.458298 - 0.458298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

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