LMFDB - Embedded newform 804.2.j.a.499.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.20
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.325475 + 1.37625i) q^{2} -1.00000 q^{3} +(-1.78813 + 0.895869i) q^{4} -4.16950i q^{5} +(-0.325475 - 1.37625i) q^{6} +(-0.853071 + 1.47756i) q^{7} +(-1.81493 - 2.16934i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.325475 + 1.37625i) q^{2} -1.00000 q^{3} +(-1.78813 + 0.895869i) q^{4} -4.16950i q^{5} +(-0.325475 - 1.37625i) q^{6} +(-0.853071 + 1.47756i) q^{7} +(-1.81493 - 2.16934i) q^{8} +1.00000 q^{9} +(5.73827 - 1.35706i) q^{10} +(-2.31815 + 4.01516i) q^{11} +(1.78813 - 0.895869i) q^{12} +(1.43191 - 0.826711i) q^{13} +(-2.31115 - 0.693131i) q^{14} +4.16950i q^{15} +(2.39484 - 3.20387i) q^{16} +(2.55705 + 4.42894i) q^{17} +(0.325475 + 1.37625i) q^{18} +(3.35198 - 1.93527i) q^{19} +(3.73532 + 7.45561i) q^{20} +(0.853071 - 1.47756i) q^{21} +(-6.28037 - 1.88353i) q^{22} +(-4.99547 + 2.88414i) q^{23} +(1.81493 + 2.16934i) q^{24} -12.3847 q^{25} +(1.60381 + 1.70159i) q^{26} -1.00000 q^{27} +(0.201701 - 3.40632i) q^{28} +(-5.06928 + 8.78025i) q^{29} +(-5.73827 + 1.35706i) q^{30} +(-2.38328 + 4.12796i) q^{31} +(5.18878 + 2.25312i) q^{32} +(2.31815 - 4.01516i) q^{33} +(-5.26308 + 4.96065i) q^{34} +(6.16069 + 3.55688i) q^{35} +(-1.78813 + 0.895869i) q^{36} +(3.63265 + 6.29193i) q^{37} +(3.75440 + 3.98329i) q^{38} +(-1.43191 + 0.826711i) q^{39} +(-9.04504 + 7.56735i) q^{40} +(-7.26972 - 4.19717i) q^{41} +(2.31115 + 0.693131i) q^{42} +2.95503 q^{43} +(0.548108 - 9.25640i) q^{44} -4.16950i q^{45} +(-5.59519 - 5.93630i) q^{46} +(0.472829 + 0.272988i) q^{47} +(-2.39484 + 3.20387i) q^{48} +(2.04454 + 3.54125i) q^{49} +(-4.03090 - 17.0444i) q^{50} +(-2.55705 - 4.42894i) q^{51} +(-1.81981 + 2.76107i) q^{52} -3.50033i q^{53} +(-0.325475 - 1.37625i) q^{54} +(16.7412 + 9.66553i) q^{55} +(4.75360 - 0.831078i) q^{56} +(-3.35198 + 1.93527i) q^{57} +(-13.7338 - 4.11885i) q^{58} +10.5316i q^{59} +(-3.73532 - 7.45561i) q^{60} +(6.74319 - 3.89318i) q^{61} +(-6.45681 - 1.93644i) q^{62} +(-0.853071 + 1.47756i) q^{63} +(-1.41204 + 7.87440i) q^{64} +(-3.44697 - 5.97032i) q^{65} +(6.28037 + 1.88353i) q^{66} +(-7.70268 + 2.76925i) q^{67} +(-8.54010 - 5.62875i) q^{68} +(4.99547 - 2.88414i) q^{69} +(-2.89001 + 9.63633i) q^{70} +(-3.04145 - 1.75598i) q^{71} +(-1.81493 - 2.16934i) q^{72} +(-0.636897 - 1.10314i) q^{73} +(-7.47694 + 7.04730i) q^{74} +12.3847 q^{75} +(-4.26004 + 6.46346i) q^{76} +(-3.95510 - 6.85043i) q^{77} +(-1.60381 - 1.70159i) q^{78} +(7.40343 - 12.8231i) q^{79} +(-13.3585 - 9.98526i) q^{80} +1.00000 q^{81} +(3.41026 - 11.3710i) q^{82} +(-1.29893 + 0.749938i) q^{83} +(-0.201701 + 3.40632i) q^{84} +(18.4665 - 10.6616i) q^{85} +(0.961788 + 4.06687i) q^{86} +(5.06928 - 8.78025i) q^{87} +(12.9175 - 2.25839i) q^{88} -6.03812 q^{89} +(5.73827 - 1.35706i) q^{90} +2.82097i q^{91} +(6.34875 - 9.63250i) q^{92} +(2.38328 - 4.12796i) q^{93} +(-0.221806 + 0.739582i) q^{94} +(-8.06910 - 13.9761i) q^{95} +(-5.18878 - 2.25312i) q^{96} +(-13.8362 + 7.98831i) q^{97} +(-4.20820 + 3.96639i) q^{98} +(-2.31815 + 4.01516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.325475	+	1.37625i	0.230145	+	0.973156i
$2$	0.325475	+	1.37625i	0.230145	+	0.973156i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.78813	+	0.895869i	−0.894066	+	0.447935i
$5$		−	4.16950i		−	1.86466i	−0.361615	−	0.932328i	$-0.617774\pi$
$5$		−	4.16950i		−	1.86466i	0.361615	−	0.932328i	$-0.382226\pi$
$6$	−0.325475	−	1.37625i	−0.132874	−	0.561852i
$7$	−0.853071	+	1.47756i	−0.322431	+	0.558466i	−0.980989	−	0.194064i	$-0.937833\pi$
$7$	−0.853071	+	1.47756i	−0.322431	+	0.558466i	0.658558	+	0.752530i	$0.271167\pi$
$8$	−1.81493	−	2.16934i	−0.641676	−	0.766976i
$9$	1.00000			0.333333
$10$	5.73827	−	1.35706i	1.81460	−	0.429142i
$11$	−2.31815	+	4.01516i	−0.698950	+	1.21062i	0.269881	+	0.962894i	$0.413016\pi$
$11$	−2.31815	+	4.01516i	−0.698950	+	1.21062i	−0.968831	+	0.247723i	$0.920318\pi$
$12$	1.78813	−	0.895869i	0.516189	−	0.258615i
$13$	1.43191	−	0.826711i	0.397139	−	0.229288i	−0.288110	−	0.957597i	$-0.593027\pi$
$13$	1.43191	−	0.826711i	0.397139	−	0.229288i	0.685249	+	0.728309i	$0.259693\pi$
$14$	−2.31115	−	0.693131i	−0.617681	−	0.185247i
$15$			4.16950i			1.07656i
$16$	2.39484	−	3.20387i	0.598709	−	0.800967i
$17$	2.55705	+	4.42894i	0.620176	+	1.07418i	0.989453	+	0.144857i	$0.0462721\pi$
$17$	2.55705	+	4.42894i	0.620176	+	1.07418i	−0.369277	+	0.929319i	$0.620395\pi$
$18$	0.325475	+	1.37625i	0.0767151	+	0.324385i
$19$	3.35198	−	1.93527i	0.768998	−	0.443981i	−0.0635191	−	0.997981i	$-0.520232\pi$
$19$	3.35198	−	1.93527i	0.768998	−	0.443981i	0.832517	+	0.553999i	$0.186899\pi$
$20$	3.73532	+	7.45561i	0.835244	+	1.66713i
$21$	0.853071	−	1.47756i	0.186155	−	0.322431i
$22$	−6.28037	−	1.88353i	−1.33898	−	0.401570i
$23$	−4.99547	+	2.88414i	−1.04163	+	0.601384i	−0.920294	−	0.391228i	$-0.872050\pi$
$23$	−4.99547	+	2.88414i	−1.04163	+	0.601384i	−0.121333	+	0.992612i	$0.538717\pi$
$24$	1.81493	+	2.16934i	0.370472	+	0.442814i
$25$	−12.3847			−2.47694
$26$	1.60381	+	1.70159i	0.314533	+	0.333709i
$27$	−1.00000			−0.192450
$28$	0.201701	−	3.40632i	0.0381180	−	0.643733i
$29$	−5.06928	+	8.78025i	−0.941342	+	1.63045i	−0.178427	+	0.983953i	$0.557101\pi$
$29$	−5.06928	+	8.78025i	−0.941342	+	1.63045i	−0.762915	+	0.646499i	$0.776232\pi$
$30$	−5.73827	+	1.35706i	−1.04766	+	0.247765i
$31$	−2.38328	+	4.12796i	−0.428050	+	0.741404i	−0.996700	−	0.0811755i	$-0.974133\pi$
$31$	−2.38328	+	4.12796i	−0.428050	+	0.741404i	0.568650	+	0.822580i	$0.307466\pi$
$32$	5.18878	+	2.25312i	0.917256	+	0.398299i
$33$	2.31815	−	4.01516i	0.403539	−	0.698950i
$34$	−5.26308	+	4.96065i	−0.902611	+	0.850745i
$35$	6.16069	+	3.55688i	1.04135	+	0.601222i
$36$	−1.78813	+	0.895869i	−0.298022	+	0.149312i
$37$	3.63265	+	6.29193i	0.597204	+	1.03439i	0.993232	+	0.116149i	$0.0370549\pi$
$37$	3.63265	+	6.29193i	0.597204	+	1.03439i	−0.396028	+	0.918238i	$0.629612\pi$
$38$	3.75440	+	3.98329i	0.609044	+	0.646175i
$39$	−1.43191	+	0.826711i	−0.229288	+	0.132380i
$40$	−9.04504	+	7.56735i	−1.43015	+	1.19650i
$41$	−7.26972	−	4.19717i	−1.13534	−	0.655488i	−0.190067	−	0.981771i	$-0.560871\pi$
$41$	−7.26972	−	4.19717i	−1.13534	−	0.655488i	−0.945272	+	0.326283i	$0.894204\pi$
$42$	2.31115	+	0.693131i	0.356618	+	0.106952i
$43$	2.95503			0.450638			0.225319	−	0.974285i	$-0.427657\pi$
$43$	2.95503			0.450638			0.225319	+	0.974285i	$0.427657\pi$
$44$	0.548108	−	9.25640i	0.0826303	−	1.39546i
$45$		−	4.16950i		−	0.621552i
$46$	−5.59519	−	5.93630i	−0.824966	−	0.875260i
$47$	0.472829	+	0.272988i	0.0689692	+	0.0398194i	0.534088	−	0.845429i	$-0.320655\pi$
$47$	0.472829	+	0.272988i	0.0689692	+	0.0398194i	−0.465119	+	0.885248i	$0.653988\pi$
$48$	−2.39484	+	3.20387i	−0.345665	+	0.462438i
$49$	2.04454	+	3.54125i	0.292077	+	0.505892i
$50$	−4.03090	−	17.0444i	−0.570056	−	2.41045i
$51$	−2.55705	−	4.42894i	−0.358059	−	0.620176i
$52$	−1.81981	+	2.76107i	−0.252362	+	0.382891i
$53$		−	3.50033i		−	0.480807i	−0.970673	−	0.240404i	$-0.922720\pi$
$53$		−	3.50033i		−	0.480807i	0.970673	−	0.240404i	$-0.0772798\pi$
$54$	−0.325475	−	1.37625i	−0.0442915	−	0.187284i
$55$	16.7412	+	9.66553i	2.25738	+	1.30330i
$56$	4.75360	−	0.831078i	0.635226	−	0.111057i
$57$	−3.35198	+	1.93527i	−0.443981	+	0.256333i
$58$	−13.7338	−	4.11885i	−1.80333	−	0.540832i
$59$			10.5316i			1.37110i	0.728026	+	0.685550i	$0.240438\pi$
$59$			10.5316i			1.37110i	−0.728026	+	0.685550i	$0.759562\pi$
$60$	−3.73532	−	7.45561i	−0.482228	−	0.962515i
$61$	6.74319	−	3.89318i	0.863377	−	0.498471i	−0.00176477	−	0.999998i	$-0.500562\pi$
$61$	6.74319	−	3.89318i	0.863377	−	0.498471i	0.865142	+	0.501528i	$0.167228\pi$
$62$	−6.45681	−	1.93644i	−0.820016	−	0.245929i
$63$	−0.853071	+	1.47756i	−0.107477	+	0.186155i
$64$	−1.41204	+	7.87440i	−0.176505	+	0.984300i
$65$	−3.44697	−	5.97032i	−0.427544	−	0.740527i
$66$	6.28037	+	1.88353i	0.773060	+	0.231846i
$67$	−7.70268	+	2.76925i	−0.941032	+	0.338318i
$67$	−7.70268	+	2.76925i	−0.941032	+	0.338318i
$68$	−8.54010	−	5.62875i	−1.03564	−	0.682586i
$69$	4.99547	−	2.88414i	0.601384	−	0.347209i
$70$	−2.89001	+	9.63633i	−0.345422	+	1.15176i
$71$	−3.04145	−	1.75598i	−0.360953	−	0.208396i	0.308546	−	0.951210i	$-0.400158\pi$
$71$	−3.04145	−	1.75598i	−0.360953	−	0.208396i	−0.669499	+	0.742813i	$0.733491\pi$
$72$	−1.81493	−	2.16934i	−0.213892	−	0.255659i
$73$	−0.636897	−	1.10314i	−0.0745431	−	0.129113i	0.826344	−	0.563165i	$-0.190417\pi$
$73$	−0.636897	−	1.10314i	−0.0745431	−	0.129113i	−0.900888	+	0.434053i	$0.857083\pi$
$74$	−7.47694	+	7.04730i	−0.869177	+	0.819232i
$75$	12.3847			1.43006
$76$	−4.26004	+	6.46346i	−0.488661	+	0.741409i
$77$	−3.95510	−	6.85043i	−0.450726	−	0.780680i
$78$	−1.60381	−	1.70159i	−0.181596	−	0.192667i
$79$	7.40343	−	12.8231i	0.832951	−	1.44271i	−0.0627362	−	0.998030i	$-0.519983\pi$
$79$	7.40343	−	12.8231i	0.832951	−	1.44271i	0.895688	−	0.444684i	$-0.146684\pi$
$80$	−13.3585	−	9.98526i	−1.49353	−	1.11639i
$81$	1.00000			0.111111
$82$	3.41026	−	11.3710i	0.376600	−	1.25572i
$83$	−1.29893	+	0.749938i	−0.142576	+	0.0823164i	−0.569591	−	0.821928i	$-0.692898\pi$
$83$	−1.29893	+	0.749938i	−0.142576	+	0.0823164i	0.427015	+	0.904245i	$0.359565\pi$
$84$	−0.201701	+	3.40632i	−0.0220074	+	0.371660i
$85$	18.4665	−	10.6616i	2.00297	−	1.15641i
$86$	0.961788	+	4.06687i	0.103712	+	0.438542i
$87$	5.06928	−	8.78025i	0.543484	−	0.941342i
$88$	12.9175	−	2.25839i	1.37701	−	0.240745i
$89$	−6.03812			−0.640039			−0.320020	−	0.947411i	$-0.603690\pi$
$89$	−6.03812			−0.640039			−0.320020	+	0.947411i	$0.603690\pi$
$90$	5.73827	−	1.35706i	0.604867	−	0.143047i
$91$			2.82097i			0.295718i
$92$	6.34875	−	9.63250i	0.661903	−	1.00426i
$93$	2.38328	−	4.12796i	0.247135	−	0.428050i
$94$	−0.221806	+	0.739582i	−0.0228776	+	0.0762821i
$95$	−8.06910	−	13.9761i	−0.827872	−	1.43392i
$96$	−5.18878	−	2.25312i	−0.529578	−	0.229958i
$97$	−13.8362	+	7.98831i	−1.40485	+	0.811090i	−0.994885	−	0.101012i	$-0.967792\pi$
$97$	−13.8362	+	7.98831i	−1.40485	+	0.811090i	−0.409963	+	0.912102i	$0.634459\pi$
$98$	−4.20820	+	3.96639i	−0.425092	+	0.400665i
$99$	−2.31815	+	4.01516i	−0.232983	+	0.403539i
$100$	22.1455	−	11.0951i	2.21455	−	1.10951i
$101$	13.2530	+	7.65165i	1.31873	+	0.761367i	0.983524	−	0.180778i	$-0.0578617\pi$
$101$	13.2530	+	7.65165i	1.31873	+	0.761367i	0.335203	+	0.942146i	$0.391195\pi$
$102$	5.26308	−	4.96065i	0.521123	−	0.491178i
$103$	6.64821	+	3.83835i	0.655068	+	0.378204i	0.790395	−	0.612597i	$-0.209875\pi$
$103$	6.64821	+	3.83835i	0.655068	+	0.378204i	−0.135327	+	0.990801i	$0.543209\pi$
$104$	−4.39222	−	1.60586i	−0.430693	−	0.157467i
$105$	−6.16069	−	3.55688i	−0.601222	−	0.347116i
$106$	4.81733	−	1.13927i	0.467901	−	0.110656i
$107$			0.478532i			0.0462614i	0.999732	+	0.0231307i	$0.00736339\pi$
$107$			0.478532i			0.0462614i	−0.999732	+	0.0231307i	$0.992637\pi$
$108$	1.78813	−	0.895869i	0.172063	−	0.0862051i
$109$			6.64012i			0.636008i	0.948089	+	0.318004i	$0.103013\pi$
$109$			6.64012i			0.636008i	−0.948089	+	0.318004i	$0.896987\pi$
$110$	−7.85337	+	26.1860i	−0.748789	+	2.49673i
$111$	−3.63265	−	6.29193i	−0.344796	−	0.597204i
$112$	2.69095	+	6.27164i	0.254271	+	0.592615i
$113$	−6.98854	−	4.03484i	−0.657427	−	0.379566i	0.133869	−	0.990999i	$-0.457260\pi$
$113$	−6.98854	−	4.03484i	−0.657427	−	0.379566i	−0.791296	+	0.611434i	$0.790593\pi$
$114$	−3.75440	−	3.98329i	−0.351632	−	0.373069i
$115$	12.0254	+	20.8286i	1.12137	+	1.94228i
$116$	1.19859	−	20.2417i	0.111286	−	1.87939i
$117$	1.43191	−	0.826711i	0.132380	−	0.0764294i
$118$	−14.4941	+	3.42777i	−1.33429	+	0.315552i
$119$	−8.72538			−0.799855
$120$	9.04504	−	7.56735i	0.825695	−	0.690802i
$121$	−5.24768	−	9.08925i	−0.477062	−	0.826295i
$122$	7.55273	+	8.01319i	0.683792	+	0.725480i
$123$	7.26972	+	4.19717i	0.655488	+	0.378446i
$124$	0.563506	−	9.51645i	0.0506043	−	0.854603i
$125$			30.7904i			2.75398i
$126$	−2.31115	−	0.693131i	−0.205894	−	0.0617490i
$127$	5.52839	+	3.19182i	0.490566	+	0.283228i	0.724809	−	0.688950i	$-0.241928\pi$
$127$	5.52839	+	3.19182i	0.490566	+	0.283228i	−0.234244	+	0.972178i	$0.575261\pi$
$128$	−11.2967	+	0.619596i	−0.998499	+	0.0547651i
$129$	−2.95503			−0.260176
$130$	7.09476	−	6.68708i	0.622252	−	0.586496i
$131$		−	12.7546i		−	1.11437i	−0.830387	−	0.557187i	$-0.811881\pi$
$131$		−	12.7546i		−	1.11437i	0.830387	−	0.557187i	$-0.188119\pi$
$132$	−0.548108	+	9.25640i	−0.0477066	+	0.805667i
$133$			6.60369i			0.572612i
$134$	−6.31821	−	9.69949i	−0.545811	−	0.837909i
$135$			4.16950i			0.358853i
$136$	4.96699	−	13.5853i	0.425916	−	1.16493i
$137$		−	5.96671i		−	0.509771i	−0.966971	−	0.254885i	$-0.917962\pi$
$137$		−	5.96671i		−	0.509771i	0.966971	−	0.254885i	$-0.0820377\pi$
$138$	5.59519	+	5.93630i	0.476294	+	0.505332i
$139$	8.17487			0.693383			0.346692	−	0.937979i	$-0.387305\pi$
$139$	8.17487			0.693383			0.346692	+	0.937979i	$0.387305\pi$
$140$	−14.2026	−	0.840993i	−1.20034	−	0.0710768i
$141$	−0.472829	−	0.272988i	−0.0398194	−	0.0229897i
$142$	1.42675	−	4.75732i	0.119731	−	0.399225i
$143$			7.66577i			0.641044i
$144$	2.39484	−	3.20387i	0.199570	−	0.266989i
$145$	36.6092	+	21.1363i	3.04023	+	1.75528i
$146$	1.31090	−	1.23557i	0.108491	−	0.102257i
$147$	−2.04454	−	3.54125i	−0.168631	−	0.292077i
$148$	−12.1324	−	7.99643i	−0.997278	−	0.657302i
$149$	14.2624			1.16842			0.584211	−	0.811601i	$-0.301404\pi$
$149$	14.2624			1.16842			0.584211	+	0.811601i	$0.301404\pi$
$150$	4.03090	+	17.0444i	0.329122	+	1.39167i
$151$	−5.11146	+	2.95110i	−0.415965	+	0.240157i	−0.693349	−	0.720602i	$-0.743866\pi$
$151$	−5.11146	+	2.95110i	−0.415965	+	0.240157i	0.277385	+	0.960759i	$0.410532\pi$
$152$	−10.2819	−	3.75920i	−0.833970	−	0.304911i
$153$	2.55705	+	4.42894i	0.206725	+	0.358059i
$154$	8.14063	−	7.67285i	0.655991	−	0.618296i
$155$	17.2115	+	9.93708i	1.38246	+	0.798165i
$156$	1.81981	−	2.76107i	0.145702	−	0.221062i
$157$	7.55154	+	13.0796i	0.602678	+	1.04387i	0.992414	+	0.122942i	$0.0392331\pi$
$157$	7.55154	+	13.0796i	0.602678	+	1.04387i	−0.389736	+	0.920927i	$0.627434\pi$
$158$	20.0575	+	6.01538i	1.59569	+	0.478558i
$159$			3.50033i			0.277594i
$160$	9.39437	−	21.6346i	0.742690	−	1.71037i
$161$		−	9.84149i		−	0.775618i
$162$	0.325475	+	1.37625i	0.0255717	+	0.108128i
$163$	−18.3058	−	10.5688i	−1.43382	−	0.827815i	−0.436408	−	0.899749i	$-0.643750\pi$
$163$	−18.3058	−	10.5688i	−1.43382	−	0.827815i	−0.997409	+	0.0719336i	$0.977083\pi$
$164$	16.7593	+	0.992386i	1.30868	+	0.0774923i
$165$	−16.7412	−	9.66553i	−1.30330	−	0.752461i
$166$	−1.45487	−	1.54357i	−0.112920	−	0.119804i
$167$	−3.00682	−	1.73599i	−0.232674	−	0.134335i	0.379131	−	0.925343i	$-0.376223\pi$
$167$	−3.00682	−	1.73599i	−0.232674	−	0.134335i	−0.611805	+	0.791008i	$0.709556\pi$
$168$	−4.75360	+	0.831078i	−0.366748	+	0.0641191i
$169$	−5.13310	+	8.89079i	−0.394854	+	0.683907i
$170$	20.6834	+	21.9444i	1.58635	+	1.68306i
$171$	3.35198	−	1.93527i	0.256333	−	0.147994i
$172$	−5.28399	+	2.64732i	−0.402901	+	0.201857i
$173$	−6.45025	−	11.1722i	−0.490403	−	0.849403i	0.509536	−	0.860449i	$-0.329817\pi$
$173$	−6.45025	−	11.1722i	−0.490403	−	0.849403i	−0.999939	+	0.0110462i	$0.996484\pi$
$174$	13.7338	+	4.11885i	1.04115	+	0.312249i
$175$	10.5650	−	18.2992i	0.798641	−	1.38329i
$176$	7.31244	+	17.0427i	0.551196	+	1.28464i
$177$		−	10.5316i		−	0.791605i
$178$	−1.96525	−	8.30997i	−0.147302	−	0.622858i
$179$	−25.2737			−1.88905			−0.944523	−	0.328446i	$-0.893475\pi$
$179$	−25.2737			−1.88905			−0.944523	+	0.328446i	$0.893475\pi$
$180$	3.73532	+	7.45561i	0.278415	+	0.555708i
$181$	5.09990	−	8.83329i	0.379073	−	0.656573i	−0.611855	−	0.790970i	$-0.709576\pi$
$181$	5.09990	−	8.83329i	0.379073	−	0.656573i	0.990928	+	0.134397i	$0.0429097\pi$
$182$	−3.88236	+	0.918155i	−0.287780	+	0.0680581i
$183$	−6.74319	+	3.89318i	−0.498471	+	0.287792i
$184$	15.3231	+	5.60234i	1.12963	+	0.413010i
$185$	26.2342	−	15.1463i	1.92878	−	1.11358i
$186$	6.45681	+	1.93644i	0.473436	+	0.141987i
$187$	−23.7106			−1.73389
$188$	−1.09004	−	0.0645457i	−0.0794995	−	0.00470748i
$189$	0.853071	−	1.47756i	0.0620518	−	0.107477i
$190$	16.6083	−	15.6540i	1.20489	−	1.13566i
$191$	4.28464	+	7.42121i	0.310026	+	0.536980i	0.978368	−	0.206874i	$-0.0663290\pi$
$191$	4.28464	+	7.42121i	0.310026	+	0.536980i	−0.668342	+	0.743854i	$0.732996\pi$
$192$	1.41204	−	7.87440i	0.101905	−	0.568286i
$193$	3.85697			0.277631			0.138816	−	0.990318i	$-0.455670\pi$
$193$	3.85697			0.277631			0.138816	+	0.990318i	$0.455670\pi$
$194$	−15.4972	−	16.4420i	−1.11264	−	1.18047i
$195$	3.44697	+	5.97032i	0.246842	+	0.427544i
$196$	−6.82840	−	4.50058i	−0.487743	−	0.321470i
$197$	0.862773	+	0.498122i	0.0614700	+	0.0354897i	0.530420	−	0.847735i	$-0.322034\pi$
$197$	0.862773	+	0.498122i	0.0614700	+	0.0354897i	−0.468950	+	0.883225i	$0.655368\pi$
$198$	−6.28037	−	1.88353i	−0.446326	−	0.133857i
$199$	−18.3581	+	10.5990i	−1.30137	+	0.751347i	−0.980639	−	0.195824i	$-0.937262\pi$
$199$	−18.3581	+	10.5990i	−1.30137	+	0.751347i	−0.320731	+	0.947170i	$0.603929\pi$
$200$	22.4774	+	26.8666i	1.58939	+	1.89975i
$201$	7.70268	−	2.76925i	0.543305	−	0.195328i
$202$	−6.21706	+	20.7299i	−0.437431	+	1.45855i
$203$	−8.64891	−	14.9804i	−0.607035	−	1.05141i
$204$	8.54010	+	5.62875i	0.597926	+	0.394091i
$205$	−17.5001	+	30.3111i	−1.22226	+	2.11702i
$206$	−3.11871	+	10.3989i	−0.217290	+	0.724525i
$207$	−4.99547	+	2.88414i	−0.347209	+	0.200461i
$208$	0.780507	−	6.56747i	0.0541184	−	0.455372i
$209$			17.9450i			1.24128i
$210$	2.89001	−	9.63633i	0.199429	−	0.664970i
$211$	−5.20080	+	3.00268i	−0.358038	+	0.206713i	−0.668220	−	0.743964i	$-0.732943\pi$
$211$	−5.20080	+	3.00268i	−0.358038	+	0.206713i	0.310182	+	0.950677i	$0.399610\pi$
$212$	3.13584	+	6.25905i	0.215370	+	0.429874i
$213$	3.04145	+	1.75598i	0.208396	+	0.120318i
$214$	−0.658579	+	0.155750i	−0.0450196	+	0.0106468i
$215$		−	12.3210i		−	0.840285i
$216$	1.81493	+	2.16934i	0.123491	+	0.147605i
$217$	−4.06621	−	7.04289i	−0.276033	−	0.478103i
$218$	−9.13847	+	2.16119i	−0.618935	+	0.146374i
$219$	0.636897	+	1.10314i	0.0430375	+	0.0745431i
$220$	−38.5945	−	2.28533i	−2.60204	−	0.154077i
$221$	7.32291	+	4.22788i	0.492592	+	0.284398i
$222$	7.47694	−	7.04730i	0.501819	−	0.472984i
$223$		−	22.0870i		−	1.47905i	−0.673127	−	0.739527i	$-0.735049\pi$
$223$		−	22.0870i		−	1.47905i	0.673127	−	0.739527i	$-0.264951\pi$
$224$	−7.75552	+	5.74468i	−0.518188	+	0.383832i
$225$	−12.3847			−0.825646
$226$	3.27835	−	10.9312i	0.218073	−	0.727134i
$227$	−0.343477	−	0.198307i	−0.0227974	−	0.0131621i	0.488558	−	0.872531i	$-0.337523\pi$
$227$	−0.343477	−	0.198307i	−0.0227974	−	0.0131621i	−0.511355	+	0.859369i	$0.670856\pi$
$228$	4.26004	−	6.46346i	0.282128	−	0.428053i
$229$	14.4225	−	8.32684i	0.953066	−	0.550253i	0.0590341	−	0.998256i	$-0.481198\pi$
$229$	14.4225	−	8.32684i	0.953066	−	0.550253i	0.894032	+	0.448003i	$0.147865\pi$
$230$	−24.7514	+	23.3291i	−1.63206	+	1.53828i
$231$	3.95510	+	6.85043i	0.260227	+	0.450726i
$232$	28.2477	−	4.93859i	1.85455	−	0.324234i
$233$	−2.51365	−	1.45126i	−0.164675	−	0.0950751i	0.415398	−	0.909640i	$-0.363642\pi$
$233$	−2.51365	−	1.45126i	−0.164675	−	0.0950751i	−0.580073	+	0.814565i	$0.696976\pi$
$234$	1.60381	+	1.70159i	0.104844	+	0.111236i
$235$	1.13822	−	1.97146i	0.0742494	−	0.128604i
$236$	−9.43495	−	18.8319i	−0.614163	−	1.22585i
$237$	−7.40343	+	12.8231i	−0.480905	+	0.832951i
$238$	−2.83989	−	12.0083i	−0.184083	−	0.778383i
$239$	−11.8629	+	20.5472i	−0.767349	+	1.32909i	0.171646	+	0.985159i	$0.445091\pi$
$239$	−11.8629	+	20.5472i	−0.767349	+	1.32909i	−0.938995	+	0.343930i	$0.888242\pi$
$240$	13.3585	+	9.98526i	0.862288	+	0.644546i
$241$	−9.42863			−0.607351			−0.303676	−	0.952775i	$-0.598214\pi$
$241$	−9.42863			−0.607351			−0.303676	+	0.952775i	$0.598214\pi$
$242$	10.8011	−	10.1804i	0.694321	−	0.654424i
$243$	−1.00000			−0.0641500
$244$	−8.56993	+	13.0025i	−0.548634	+	0.832402i
$245$	14.7652	−	8.52470i	0.943315	−	0.544623i
$246$	−3.41026	+	11.3710i	−0.217430	+	0.724990i
$247$	3.19982	−	5.54224i	0.203599	−	0.352644i
$248$	13.2804	−	2.32184i	0.843308	−	0.147437i
$249$	1.29893	−	0.749938i	0.0823164	−	0.0475254i
$250$	−42.3754	+	10.0215i	−2.68005	+	0.633816i
$251$	1.99614	+	3.45742i	0.125995	+	0.218230i	0.922122	−	0.386900i	$-0.126454\pi$
$251$	1.99614	+	3.45742i	0.125995	+	0.218230i	−0.796126	+	0.605130i	$0.793121\pi$
$252$	0.201701	−	3.40632i	0.0127060	−	0.214578i
$253$		−	26.7435i		−	1.68135i
$254$	−2.59339	+	8.64731i	−0.162724	+	0.542581i
$255$	−18.4665	+	10.6616i	−1.15641	+	0.667656i
$256$	−4.52952	−	15.3455i	−0.283095	−	0.959092i
$257$	1.11377	−	1.92910i	0.0694749	−	0.120334i	−0.829195	−	0.558959i	$-0.811201\pi$
$257$	1.11377	−	1.92910i	0.0694749	−	0.120334i	0.898670	+	0.438625i	$0.144534\pi$
$258$	−0.961788	−	4.06687i	−0.0598783	−	0.253192i
$259$	−12.3956			−0.770227
$260$	11.5123	+	7.58769i	0.713960	+	0.470569i
$261$	−5.06928	+	8.78025i	−0.313781	+	0.543484i
$262$	17.5535	−	4.15129i	1.08446	−	0.256468i
$263$		−	11.3715i		−	0.701197i	−0.936526	−	0.350599i	$-0.885978\pi$
$263$		−	11.3715i		−	0.701197i	0.936526	−	0.350599i	$-0.114022\pi$
$264$	−12.9175	+	2.25839i	−0.795019	+	0.138994i
$265$	−14.5946			−0.896540
$266$	−9.08833	+	2.14933i	−0.557241	+	0.131784i
$267$	6.03812			0.369527
$268$	11.2925	−	11.8524i	0.689800	−	0.724000i
$269$	4.46275			0.272099			0.136049	−	0.990702i	$-0.456559\pi$
$269$	4.46275			0.272099			0.136049	+	0.990702i	$0.456559\pi$
$270$	−5.73827	+	1.35706i	−0.349220	+	0.0825883i
$271$	21.3867			1.29915			0.649574	−	0.760298i	$-0.274947\pi$
$271$	21.3867			1.29915			0.649574	+	0.760298i	$0.274947\pi$
$272$	20.3135	+	2.41414i	1.23168	+	0.146379i
$273$		−	2.82097i		−	0.170733i
$274$	8.21170	−	1.94201i	0.496087	−	0.117321i
$275$	28.7096	−	49.7265i	1.73126	−	2.99862i
$276$	−6.34875	+	9.63250i	−0.382150	+	0.579809i
$277$	−14.3293			−0.860966			−0.430483	−	0.902599i	$-0.641657\pi$
$277$	−14.3293			−0.860966			−0.430483	+	0.902599i	$0.641657\pi$
$278$	2.66071	+	11.2507i	0.159579	+	0.674770i
$279$	−2.38328	+	4.12796i	−0.142683	+	0.247135i
$280$	−3.46518	−	19.8201i	−0.207084	−	1.18448i
$281$	15.7947	−	9.11906i	0.942231	−	0.543998i	0.0515723	−	0.998669i	$-0.483577\pi$
$281$	15.7947	−	9.11906i	0.942231	−	0.543998i	0.890659	+	0.454672i	$0.150243\pi$
$282$	0.221806	−	0.739582i	0.0132084	−	0.0440415i
$283$		−	13.3972i		−	0.796378i	−0.917303	−	0.398189i	$-0.869639\pi$
$283$		−	13.3972i		−	0.796378i	0.917303	−	0.398189i	$-0.130361\pi$
$284$	7.01164	+	0.415186i	0.416064	+	0.0246368i
$285$	8.06910	+	13.9761i	0.477972	+	0.827872i
$286$	−10.5500	+	2.49501i	−0.623836	+	0.147533i
$287$	12.4032	−	7.16097i	0.732136	−	0.422699i
$288$	5.18878	+	2.25312i	0.305752	+	0.132766i
$289$	−4.57702	+	7.92762i	−0.269236	+	0.466331i
$290$	−17.1735	+	57.2628i	−1.00847	+	3.36259i
$291$	13.8362	−	7.98831i	0.811090	−	0.468283i
$292$	2.12712	+	1.40198i	0.124480	+	0.0820447i
$293$	−27.6590			−1.61586			−0.807929	−	0.589280i	$-0.799411\pi$
$293$	−27.6590			−1.61586			−0.807929	+	0.589280i	$0.799411\pi$
$294$	4.20820	−	3.96639i	0.245427	−	0.231324i
$295$	43.9115			2.55663
$296$	7.05630	−	19.2999i	0.410139	−	1.12178i
$297$	2.31815	−	4.01516i	0.134513	−	0.232983i
$298$	4.64206	+	19.6287i	0.268907	+	1.13706i
$299$	−4.76869	+	8.25961i	−0.275781	+	0.477666i
$300$	−22.1455	+	11.0951i	−1.27857	+	0.640574i
$301$	−2.52085	+	4.36625i	−0.145300	+	0.251666i
$302$	−5.72511	−	6.07414i	−0.329443	−	0.349528i
$303$	−13.2530	−	7.65165i	−0.761367	−	0.439576i
$304$	1.82711	−	15.3740i	0.104792	−	0.881757i
$305$	−16.2326	−	28.1157i	−0.929476	−	1.60990i
$306$	−5.26308	+	4.96065i	−0.300870	+	0.283582i
$307$	9.84151	−	5.68200i	0.561685	−	0.324289i	−0.192137	−	0.981368i	$-0.561542\pi$
$307$	9.84151	−	5.68200i	0.561685	−	0.324289i	0.753821	+	0.657079i	$0.228208\pi$
$308$	13.2093	+	8.70623i	0.752672	+	0.496084i
$309$	−6.64821	−	3.83835i	−0.378204	−	0.218356i
$310$	−8.07400	+	26.9216i	−0.458572	+	1.52905i
$311$	−13.9433			−0.790652			−0.395326	−	0.918541i	$-0.629368\pi$
$311$	−13.9433			−0.790652			−0.395326	+	0.918541i	$0.629368\pi$
$312$	4.39222	+	1.60586i	0.248661	+	0.0909139i
$313$		−	1.88468i		−	0.106529i	−0.998580	−	0.0532643i	$-0.983037\pi$
$313$		−	1.88468i		−	0.106529i	0.998580	−	0.0532643i	$-0.0169626\pi$
$314$	−15.5430	+	14.6499i	−0.877144	+	0.826742i
$315$	6.16069	+	3.55688i	0.347116	+	0.200407i
$316$	−1.75048	+	29.5620i	−0.0984721	+	1.66299i
$317$	2.47017	+	4.27846i	0.138739	+	0.240302i	0.927019	−	0.375013i	$-0.122362\pi$
$317$	2.47017	+	4.27846i	0.138739	+	0.240302i	−0.788281	+	0.615316i	$0.789029\pi$
$318$	−4.81733	+	1.13927i	−0.270143	+	0.0638870i
$319$	−23.5028	−	40.7080i	−1.31590	−	2.27921i
$320$	32.8323	+	5.88749i	1.83538	+	0.329121i
$321$		−	0.478532i		−	0.0267090i
$322$	13.5444	−	3.20315i	0.754797	−	0.178505i
$323$	17.1424	+	9.89716i	0.953828	+	0.550693i
$324$	−1.78813	+	0.895869i	−0.0993407	+	0.0497705i
$325$	−17.7337	+	10.2386i	−0.983689	+	0.567933i
$326$	8.58731	−	28.6332i	0.475607	−	1.58585i
$327$		−	6.64012i		−	0.367199i
$328$	4.08897	+	23.3881i	0.225775	+	1.29139i
$329$	−0.806713	+	0.465756i	−0.0444756	+	0.0256780i
$330$	7.85337	−	26.1860i	0.432314	−	1.44149i
$331$	0.946179	−	1.63883i	0.0520067	−	0.0900783i	−0.838850	−	0.544363i	$-0.816772\pi$
$331$	0.946179	−	1.63883i	0.0520067	−	0.0900783i	0.890857	+	0.454284i	$0.150105\pi$
$332$	1.65081	−	2.50466i	0.0906002	−	0.137461i
$333$	3.63265	+	6.29193i	0.199068	+	0.344796i
$334$	1.41051	−	4.70315i	0.0771797	−	0.257345i
$335$	11.5464	+	32.1163i	0.630847	+	1.75470i
$336$	−2.69095	−	6.27164i	−0.146803	−	0.342146i
$337$	7.02297	−	4.05471i	0.382565	−	0.220874i	−0.296368	−	0.955074i	$-0.595776\pi$
$337$	7.02297	−	4.05471i	0.382565	−	0.220874i	0.678934	+	0.734199i	$0.262442\pi$
$338$	−13.9066	−	4.17071i	−0.756422	−	0.226856i
$339$	6.98854	+	4.03484i	0.379566	+	0.219142i
$340$	−23.4691	+	35.6079i	−1.27279	+	1.93111i
$341$	−11.0496	−	19.1385i	−0.598371	−	1.03641i
$342$	3.75440	+	3.98329i	0.203015	+	0.215392i
$343$	−18.9195			−1.02156
$344$	−5.36319	−	6.41046i	−0.289164	−	0.345629i
$345$	−12.0254	−	20.8286i	−0.647425	−	1.12137i
$346$	13.2763	−	12.5134i	0.713738	−	0.672725i
$347$	5.03228	−	8.71616i	0.270147	−	0.467908i	−0.698753	−	0.715363i	$-0.746261\pi$
$347$	5.03228	−	8.71616i	0.270147	−	0.467908i	0.968899	+	0.247456i	$0.0795945\pi$
$348$	−1.19859	+	20.2417i	−0.0642511	+	1.08507i
$349$	34.7269			1.85889			0.929443	−	0.368965i	$-0.120288\pi$
$349$	34.7269			1.85889			0.929443	+	0.368965i	$0.120288\pi$
$350$	28.6229	+	8.58421i	1.52996	+	0.458845i
$351$	−1.43191	+	0.826711i	−0.0764294	+	0.0441266i
$352$	−21.0750	+	15.6107i	−1.12330	+	0.832054i
$353$	−16.0075	+	9.24196i	−0.851996	+	0.491900i	−0.861324	−	0.508056i	$-0.830364\pi$
$353$	−16.0075	+	9.24196i	−0.851996	+	0.491900i	0.00932794	+	0.999956i	$0.497031\pi$
$354$	14.4941	−	3.42777i	0.770355	−	0.182184i
$355$	−7.32155	+	12.6813i	−0.388587	+	0.673053i
$356$	10.7970	−	5.40937i	0.572238	−	0.286696i
$357$	8.72538			0.461796
$358$	−8.22595	−	34.7830i	−0.434755	−	1.83834i
$359$			9.11105i			0.480863i	0.970666	+	0.240431i	$0.0772889\pi$
$359$			9.11105i			0.480863i	−0.970666	+	0.240431i	$0.922711\pi$
$360$	−9.04504	+	7.56735i	−0.476715	+	0.398835i
$361$	−2.00947	+	3.48050i	−0.105762	+	0.183184i
$362$	13.8167	+	4.14373i	0.726190	+	0.217790i
$363$	5.24768	+	9.08925i	0.275432	+	0.477062i
$364$	−2.52722	−	5.04427i	−0.132462	−	0.264392i
$365$	−4.59953	+	2.65554i	−0.240750	+	0.138997i
$366$	−7.55273	−	8.01319i	−0.394788	−	0.418856i
$367$	12.0486	−	20.8689i	0.628934	−	1.08935i	−0.358832	−	0.933402i	$-0.616825\pi$
$367$	12.0486	−	20.8689i	0.628934	−	1.08935i	0.987766	−	0.155943i	$-0.0498417\pi$
$368$	−2.72295	+	22.9118i	−0.141943	+	1.19436i
$369$	−7.26972	−	4.19717i	−0.378446	−	0.218496i
$370$	29.3837	+	31.1751i	1.52758	+	1.62071i
$371$	5.17195	+	2.98603i	0.268515	+	0.155027i
$372$	−0.563506	+	9.51645i	−0.0292164	+	0.493405i
$373$	15.1386	+	8.74029i	0.783848	+	0.452555i	0.837792	−	0.545989i	$-0.183846\pi$
$373$	15.1386	+	8.74029i	0.783848	+	0.452555i	−0.0539441	+	0.998544i	$0.517179\pi$
$374$	−7.71718	−	32.6317i	−0.399046	−	1.68734i
$375$		−	30.7904i		−	1.59001i
$376$	−0.265950	−	1.52118i	−0.0137153	−	0.0784489i
$377$			16.7633i			0.863355i
$378$	2.31115	+	0.693131i	0.118873	+	0.0356508i
$379$	10.3448	+	17.9177i	0.531377	+	0.920373i	0.999329	+	0.0366187i	$0.0116587\pi$
$379$	10.3448	+	17.9177i	0.531377	+	0.920373i	−0.467952	+	0.883754i	$0.655008\pi$
$380$	26.9494	+	17.7622i	1.38247	+	0.911183i
$381$	−5.52839	−	3.19182i	−0.283228	−	0.163522i
$382$	−8.81891	+	8.31216i	−0.451215	+	0.425287i
$383$	10.2473	+	17.7489i	0.523615	+	0.906928i	0.999622	+	0.0274863i	$0.00875026\pi$
$383$	10.2473	+	17.7489i	0.523615	+	0.906928i	−0.476007	+	0.879441i	$0.657916\pi$
$384$	11.2967	−	0.619596i	0.576484	−	0.0316186i
$385$	−28.5629	+	16.4908i	−1.45570	+	0.840448i
$386$	1.25535	+	5.30816i	0.0638955	+	0.270178i
$387$	2.95503			0.150213
$388$	17.5844	−	26.6795i	0.892713	−	1.35445i
$389$	−8.16640	−	14.1446i	−0.414053	−	0.717161i	0.581276	−	0.813707i	$-0.302554\pi$
$389$	−8.16640	−	14.1446i	−0.414053	−	0.717161i	−0.995329	+	0.0965459i	$0.969221\pi$
$390$	−7.09476	+	6.68708i	−0.359257	+	0.338613i
$391$	−25.5473	−	14.7498i	−1.29198	−	0.745927i
$392$	3.97145	−	10.8624i	0.200589	−	0.548635i
$393$			12.7546i			0.643384i
$394$	−0.404730	+	1.34952i	−0.0203900	+	0.0679877i
$395$	−53.4660	−	30.8686i	−2.69016	−	1.55317i
$396$	0.548108	−	9.25640i	0.0275434	−	0.465152i
$397$	7.46142			0.374478			0.187239	−	0.982314i	$-0.440046\pi$
$397$	7.46142			0.374478			0.187239	+	0.982314i	$0.440046\pi$
$398$	−20.5620	−	21.8156i	−1.03068	−	1.09352i
$399$		−	6.60369i		−	0.330598i
$400$	−29.6593	+	39.6789i	−1.48297	+	1.98395i
$401$			21.9869i			1.09797i	0.835831	+	0.548987i	$0.184986\pi$
$401$			21.9869i			1.09797i	−0.835831	+	0.548987i	$0.815014\pi$
$402$	6.31821	+	9.69949i	0.315124	+	0.483767i
$403$			7.88113i			0.392587i
$404$	−30.5531	−	1.80917i	−1.52007	−	0.0900094i
$405$		−	4.16950i		−	0.207184i
$406$	17.8017	−	16.7788i	0.883485	−	0.832718i
$407$	−33.6842			−1.66966
$408$	−4.96699	+	13.5853i	−0.245903	+	0.672574i
$409$	10.1078	+	5.83576i	0.499800	+	0.288560i	0.728631	−	0.684906i	$-0.240157\pi$
$409$	10.1078	+	5.83576i	0.499800	+	0.288560i	−0.228831	+	0.973466i	$0.573490\pi$
$410$	−47.4115	−	14.2190i	−2.34149	−	0.702229i
$411$			5.96671i			0.294316i
$412$	−15.3265	−	0.907544i	−0.755085	−	0.0447115i
$413$	−15.5611	−	8.98421i	−0.765712	−	0.442084i
$414$	−5.59519	−	5.93630i	−0.274989	−	0.291753i
$415$	3.12686	+	5.41589i	0.153492	+	0.265856i
$416$	9.29252	−	1.06337i	0.455603	−	0.0521360i
$417$	−8.17487			−0.400325
$418$	−24.6968	+	5.84064i	−1.20796	+	0.285675i
$419$	10.2137	−	5.89691i	0.498974	−	0.288083i	−0.229316	−	0.973352i	$-0.573649\pi$
$419$	10.2137	−	5.89691i	0.498974	−	0.288083i	0.728290	+	0.685269i	$0.240315\pi$
$420$	14.2026	+	0.840993i	0.693017	+	0.0410362i
$421$	6.61403	+	11.4558i	0.322348	+	0.558323i	0.980972	−	0.194149i	$-0.0621946\pi$
$421$	6.61403	+	11.4558i	0.322348	+	0.558323i	−0.658624	+	0.752472i	$0.728861\pi$
$422$	−5.82517	−	6.18031i	−0.283565	−	0.300853i
$423$	0.472829	+	0.272988i	0.0229897	+	0.0132731i
$424$	−7.59339	+	6.35286i	−0.368768	+	0.308522i
$425$	−31.6683	−	54.8511i	−1.53614	−	2.66067i
$426$	−1.42675	+	4.75732i	−0.0691265	+	0.230493i
$427$			13.2846i			0.642889i
$428$	−0.428702	−	0.855678i	−0.0207221	−	0.0413608i
$429$		−	7.66577i		−	0.370107i
$430$	16.9568	−	4.01017i	0.817729	−	0.193388i
$431$	33.9419	+	19.5964i	1.63492	+	0.943923i	0.982544	+	0.186030i	$0.0595621\pi$
$431$	33.9419	+	19.5964i	1.63492	+	0.943923i	0.652379	+	0.757893i	$0.273771\pi$
$432$	−2.39484	+	3.20387i	−0.115222	+	0.154146i
$433$	−27.8113	−	16.0569i	−1.33653	−	0.771643i	−0.350235	−	0.936662i	$-0.613898\pi$
$433$	−27.8113	−	16.0569i	−1.33653	−	0.771643i	−0.986290	+	0.165019i	$0.947232\pi$
$434$	8.36933	−	7.88841i	0.401741	−	0.378656i
$435$	−36.6092	−	21.1363i	−1.75528	−	1.01341i
$436$	−5.94868	−	11.8734i	−0.284890	−	0.568633i
$437$	−11.1632	+	19.3351i	−0.534006	+	0.924926i
$438$	−1.31090	+	1.23557i	−0.0626372	+	0.0590380i
$439$	−12.5976	+	7.27325i	−0.601253	+	0.347133i	−0.769534	−	0.638606i	$-0.779512\pi$
$439$	−12.5976	+	7.27325i	−0.601253	+	0.347133i	0.168282	+	0.985739i	$0.446178\pi$
$440$	−9.41635	−	53.8596i	−0.448907	−	2.56765i
$441$	2.04454	+	3.54125i	0.0973590	+	0.168631i
$442$	−3.43521	+	11.4542i	−0.163396	+	0.544822i
$443$	0.670339	−	1.16106i	0.0318488	−	0.0551637i	−0.849662	−	0.527328i	$-0.823194\pi$
$443$	0.670339	−	1.16106i	0.0318488	−	0.0551637i	0.881510	+	0.472165i	$0.156527\pi$
$444$	12.1324	+	7.99643i	0.575778	+	0.379494i
$445$			25.1759i			1.19345i
$446$	30.3972	−	7.18875i	1.43935	−	0.340397i
$447$	−14.2624			−0.674589
$448$	−10.4303	−	8.80380i	−0.492787	−	0.415940i
$449$	8.92592	−	15.4601i	0.421240	−	0.729609i	−0.574821	−	0.818279i	$-0.694928\pi$
$449$	8.92592	−	15.4601i	0.421240	−	0.729609i	0.996061	+	0.0886699i	$0.0282616\pi$
$450$	−4.03090	−	17.0444i	−0.190019	−	0.803483i
$451$	33.7047	−	19.4594i	1.58709	−	0.916307i
$452$	16.1111	+	0.954002i	0.757804	+	0.0448725i
$453$	5.11146	−	2.95110i	0.240157	−	0.138655i
$454$	0.161127	−	0.537254i	0.00756204	−	0.0252146i
$455$	11.7620			0.551412
$456$	10.2819	+	3.75920i	0.481493	+	0.176041i
$457$	12.1291	−	21.0083i	0.567377	−	0.982726i	−0.429447	−	0.903092i	$-0.641291\pi$
$457$	12.1291	−	21.0083i	0.567377	−	0.982726i	0.996824	−	0.0796341i	$-0.0253752\pi$
$458$	16.1540	+	17.1388i	0.754826	+	0.800844i
$459$	−2.55705	−	4.42894i	−0.119353	−	0.206725i
$460$	−40.1627	−	26.4711i	−1.87259	−	1.23422i
$461$	−10.1386			−0.472200			−0.236100	−	0.971729i	$-0.575869\pi$
$461$	−10.1386			−0.472200			−0.236100	+	0.971729i	$0.575869\pi$
$462$	−8.14063	+	7.67285i	−0.378736	+	0.356973i
$463$	−15.7638	−	27.3037i	−0.732605	−	1.26891i	−0.955766	−	0.294128i	$-0.904971\pi$
$463$	−15.7638	−	27.3037i	−0.732605	−	1.26891i	0.223161	−	0.974782i	$-0.428362\pi$
$464$	15.9907	+	37.2686i	0.742348	+	1.73015i
$465$	−17.2115	−	9.93708i	−0.798165	−	0.460821i
$466$	1.17917	−	3.93177i	0.0546238	−	0.182136i
$467$	−5.31715	+	3.06986i	−0.246049	+	0.142056i	−0.617954	−	0.786215i	$-0.712038\pi$
$467$	−5.31715	+	3.06986i	−0.246049	+	0.142056i	0.371905	+	0.928271i	$0.378705\pi$
$468$	−1.81981	+	2.76107i	−0.0841208	+	0.127630i
$469$	2.47918	−	13.7436i	0.114478	−	0.634618i
$470$	3.08368	+	0.924819i	0.142240	+	0.0426587i
$471$	−7.55154	−	13.0796i	−0.347956	−	0.602678i
$472$	22.8466	−	19.1142i	1.05160	−	0.879801i
$473$	−6.85022	+	11.8649i	−0.314974	+	0.545550i
$474$	−20.0575	−	6.01538i	−0.921270	−	0.276296i
$475$	−41.5133	+	23.9677i	−1.90476	+	1.09971i
$476$	15.6021	−	7.81680i	0.715123	−	0.358283i
$477$		−	3.50033i		−	0.160269i
$478$	−32.1392	−	9.63878i	−1.47001	−	0.440868i
$479$	−10.5122	+	6.06919i	−0.480312	+	0.277309i	−0.720547	−	0.693406i	$-0.756109\pi$
$479$	−10.5122	+	6.06919i	−0.480312	+	0.277309i	0.240234	+	0.970715i	$0.422776\pi$
$480$	−9.39437	+	21.6346i	−0.428792	+	0.987480i
$481$	10.4032	+	6.00630i	0.474346	+	0.273864i
$482$	−3.06878	−	12.9762i	−0.139779	−	0.591048i
$483$			9.84149i			0.447803i
$484$	17.5263	+	11.5515i	0.796651	+	0.525070i
$485$	33.3072	+	57.6898i	1.51240	+	2.61956i
$486$	−0.325475	−	1.37625i	−0.0147638	−	0.0624280i
$487$	6.63771	+	11.4968i	0.300783	+	0.520972i	0.976314	−	0.216360i	$-0.0694186\pi$
$487$	6.63771	+	11.4968i	0.300783	+	0.520972i	−0.675530	+	0.737332i	$0.736085\pi$
$488$	−20.6841	−	7.56238i	−0.936323	−	0.342333i
$489$	18.3058	+	10.5688i	0.827815	+	0.477939i
$490$	16.5378	+	17.5461i	0.747103	+	0.792650i
$491$			11.5281i			0.520256i	0.965574	+	0.260128i	$0.0837648\pi$
$491$			11.5281i			0.520256i	−0.965574	+	0.260128i	$0.916235\pi$
$492$	−16.7593	−	0.992386i	−0.755569	−	0.0447402i
$493$	−51.8496			−2.33519
$494$	8.66897	+	2.59989i	0.390036	+	0.116975i
$495$	16.7412	+	9.66553i	0.752461	+	0.434433i
$496$	7.51788	+	17.5215i	0.337563	+	0.786739i
$497$	5.18914	−	2.99595i	0.232765	−	0.134387i
$498$	1.45487	+	1.54357i	0.0651944	+	0.0691690i
$499$	−2.18106	−	3.77771i	−0.0976378	−	0.169114i	0.813069	−	0.582168i	$-0.197795\pi$
$499$	−2.18106	−	3.77771i	−0.0976378	−	0.169114i	−0.910706	+	0.413054i	$0.864462\pi$
$500$	−27.5842	−	55.0574i	−1.23360	−	2.46224i
$501$	3.00682	+	1.73599i	0.134335	+	0.0775581i
$502$	−4.10858	+	3.87249i	−0.183375	+	0.172838i
$503$	−0.541291	+	0.937543i	−0.0241350	+	0.0418030i	−0.877841	−	0.478953i	$-0.841016\pi$
$503$	−0.541291	+	0.937543i	−0.0241350	+	0.0418030i	0.853706	+	0.520756i	$0.174350\pi$
$504$	4.75360	−	0.831078i	0.211742	−	0.0370192i
$505$	31.9035	−	55.2585i	1.41969	−	2.45897i
$506$	36.8057	−	8.70432i	1.63621	−	0.386954i
$507$	5.13310	−	8.89079i	0.227969	−	0.394854i
$508$	−12.7450	−	0.754678i	−0.565466	−	0.0334834i
$509$	11.2846			0.500180			0.250090	−	0.968223i	$-0.419540\pi$
$509$	11.2846			0.500180			0.250090	+	0.968223i	$0.419540\pi$
$510$	−20.6834	−	21.9444i	−0.915877	−	0.971714i
$511$	2.17327			0.0961399
$512$	19.6450	−	11.2283i	0.868193	−	0.496226i
$513$	−3.35198	+	1.93527i	−0.147994	+	0.0854442i
$514$	3.01743	+	0.904950i	0.133093	+	0.0399156i
$515$	16.0040	−	27.7197i	0.705219	−	1.22148i
$516$	5.28399	−	2.64732i	0.232615	−	0.116542i
$517$	−2.19218	+	1.26566i	−0.0964120	+	0.0556635i
$518$	−4.03446	−	17.0595i	−0.177264	−	0.749551i
$519$	6.45025	+	11.1722i	0.283134	+	0.490403i
$520$	−6.69562	+	18.3134i	−0.293622	+	0.803094i
$521$		−	30.7942i		−	1.34912i	−0.738221	−	0.674559i	$-0.764334\pi$
$521$		−	30.7942i		−	1.34912i	0.738221	−	0.674559i	$-0.235666\pi$
$522$	−13.7338	−	4.11885i	−0.601110	−	0.180277i
$523$	−33.7241	+	19.4706i	−1.47465	+	0.851391i	−0.999592	−	0.0285614i	$-0.990907\pi$
$523$	−33.7241	+	19.4706i	−1.47465	+	0.851391i	−0.475061	+	0.879953i	$0.657574\pi$
$524$	11.4264	+	22.8069i	0.499166	+	0.996324i
$525$	−10.5650	+	18.2992i	−0.461095	+	0.798641i
$526$	15.6500	−	3.70114i	0.682375	−	0.161377i
$527$	−24.3767			−1.06186
$528$	−7.31244	−	17.0427i	−0.318233	−	0.741689i
$529$	5.13647	−	8.89663i	0.223325	−	0.386810i
$530$	−4.75017	−	20.0858i	−0.206334	−	0.872473i
$531$			10.5316i			0.457033i
$532$	−5.91604	−	11.8083i	−0.256493	−	0.511953i
$533$	−13.8794			−0.601183
$534$	1.96525	+	8.30997i	0.0850449	+	0.359607i
$535$	1.99524			0.0862615
$536$	19.9873	+	11.6837i	0.863319	+	0.504658i
$537$	25.2737			1.09064
$538$	1.45251	+	6.14186i	0.0626222	+	0.264795i
$539$	−18.9582			−0.816589
$540$	−3.73532	−	7.45561i	−0.160743	−	0.320838i
$541$			19.0662i			0.819722i	0.912148	+	0.409861i	$0.134423\pi$
$541$			19.0662i			0.819722i	−0.912148	+	0.409861i	$0.865577\pi$
$542$	6.96082	+	29.4334i	0.298993	+	1.26427i
$543$	−5.09990	+	8.83329i	−0.218858	+	0.379073i
$544$	3.28905	+	28.7421i	0.141017	+	1.23231i
$545$	27.6859			1.18594
$546$	3.88236	−	0.918155i	0.166150	−	0.0392934i
$547$	−8.86084	+	15.3474i	−0.378862	+	0.656208i	−0.990897	−	0.134622i	$-0.957018\pi$
$547$	−8.86084	+	15.3474i	−0.378862	+	0.656208i	0.612035	+	0.790831i	$0.290351\pi$
$548$	5.34540	+	10.6693i	0.228344	+	0.455769i
$549$	6.74319	−	3.89318i	0.287792	−	0.166157i
$550$	77.7805	+	23.3269i	3.31657	+	0.994664i
$551$			39.2417i			1.67175i
$552$	−15.3231	−	5.60234i	−0.652194	−	0.238451i
$553$	12.6313	+	21.8781i	0.537138	+	0.930350i
$554$	−4.66383	−	19.7208i	−0.198147	−	0.837855i
$555$	−26.2342	+	15.1463i	−1.11358	+	0.642925i
$556$	−14.6177	+	7.32361i	−0.619930	+	0.310590i
$557$	−17.4038	+	30.1442i	−0.737421	+	1.27725i	0.216232	+	0.976342i	$0.430623\pi$
$557$	−17.4038	+	30.1442i	−0.737421	+	1.27725i	−0.953653	+	0.300909i	$0.902710\pi$
$558$	−6.45681	−	1.93644i	−0.273339	−	0.0819762i
$559$	4.23133	−	2.44296i	0.178966	−	0.103326i
$560$	26.1496	−	11.2199i	1.10502	−	0.474127i
$561$	23.7106			1.00106
$562$	17.6909	+	18.7694i	0.746245	+	0.791740i
$563$	12.4444			0.524467			0.262234	−	0.965004i	$-0.415541\pi$
$563$	12.4444			0.524467			0.262234	+	0.965004i	$0.415541\pi$
$564$	1.09004	+	0.0645457i	0.0458991	+	0.00271786i
$565$	−16.8232	+	29.1387i	−0.707759	+	1.22587i
$566$	18.4378	−	4.36043i	0.775000	−	0.183283i
$567$	−0.853071	+	1.47756i	−0.0358256	+	0.0620518i
$568$	1.71071	+	9.78490i	0.0717798	+	0.410565i
$569$	−7.94945	+	13.7688i	−0.333258	+	0.577220i	−0.983149	−	0.182808i	$-0.941481\pi$
$569$	−7.94945	+	13.7688i	−0.333258	+	0.577220i	0.649890	+	0.760028i	$0.274815\pi$
$570$	−16.6083	+	15.6540i	−0.695646	+	0.655672i
$571$	−2.35850	−	1.36168i	−0.0987002	−	0.0569846i	0.449837	−	0.893110i	$-0.351482\pi$
$571$	−2.35850	−	1.36168i	−0.0987002	−	0.0569846i	−0.548538	+	0.836126i	$0.684815\pi$
$572$	−6.86753	−	13.7074i	−0.287146	−	0.573136i
$573$	−4.28464	−	7.42121i	−0.178993	−	0.310026i
$574$	13.8922	+	14.7392i	0.579850	+	0.615201i
$575$	61.8673	−	35.7191i	2.58005	−	1.48959i
$576$	−1.41204	+	7.87440i	−0.0588350	+	0.328100i
$577$	−7.93997	−	4.58414i	−0.330545	−	0.190840i	0.325538	−	0.945529i	$-0.394455\pi$
$577$	−7.93997	−	4.58414i	−0.330545	−	0.190840i	−0.656083	+	0.754689i	$0.727788\pi$
$578$	−12.4001	−	3.71888i	−0.515776	−	0.154685i
$579$	−3.85697			−0.160290
$580$	−84.3976	−	4.99751i	−3.50442	−	0.207510i
$581$		−	2.55900i		−	0.106165i
$582$	15.4972	+	16.4420i	0.642381	+	0.681544i
$583$	14.0544	+	8.11430i	0.582073	+	0.336060i
$584$	−1.23715	+	3.38376i	−0.0511937	+	0.140021i
$585$	−3.44697	−	5.97032i	−0.142515	−	0.246842i
$586$	−9.00231	−	38.0657i	−0.371882	−	1.57248i
$587$	8.50625	+	14.7333i	0.351091	+	0.608107i	0.986441	−	0.164117i	$-0.0524776\pi$
$587$	8.50625	+	14.7333i	0.351091	+	0.608107i	−0.635350	+	0.772224i	$0.719144\pi$
$588$	6.82840	+	4.50058i	0.281599	+	0.185601i
$589$			18.4492i			0.760184i
$590$	14.2921	+	60.4333i	0.588396	+	2.48800i
$591$	−0.862773	−	0.498122i	−0.0354897	−	0.0204900i
$592$	28.8581	+	3.42963i	1.18606	+	0.140957i
$593$	−6.59437	+	3.80726i	−0.270798	+	0.156345i	−0.629250	−	0.777203i	$-0.716638\pi$
$593$	−6.59437	+	3.80726i	−0.270798	+	0.156345i	0.358452	+	0.933548i	$0.383305\pi$
$594$	6.28037	+	1.88353i	0.257687	+	0.0772821i
$595$			36.3804i			1.49145i
$596$	−25.5031	+	12.7773i	−1.04465	+	0.523377i
$597$	18.3581	−	10.5990i	0.751347	−	0.433790i
$598$	−12.9194	−	3.87462i	−0.528313	−	0.158445i
$599$	10.0070	−	17.3326i	0.408875	−	0.708192i	−0.585889	−	0.810391i	$-0.699255\pi$
$599$	10.0070	−	17.3326i	0.408875	−	0.708192i	0.994764	+	0.102199i	$0.0325879\pi$
$600$	−22.4774	−	26.8666i	−0.917635	−	1.09682i
$601$	18.9857	+	32.8842i	0.774443	+	1.34138i	0.935107	+	0.354366i	$0.115303\pi$
$601$	18.9857	+	32.8842i	0.774443	+	1.34138i	−0.160663	+	0.987009i	$0.551363\pi$
$602$	−6.82952	−	2.04822i	−0.278351	−	0.0834794i
$603$	−7.70268	+	2.76925i	−0.313677	+	0.112773i
$604$	6.49617	−	9.85617i	0.264325	−	0.401042i
$605$	−37.8976	+	21.8802i	−1.54076	+	0.889556i
$606$	6.21706	−	20.7299i	0.252551	−	0.842096i
$607$	16.1381	+	9.31735i	0.655026	+	0.378179i	0.790379	−	0.612618i	$-0.209884\pi$
$607$	16.1381	+	9.31735i	0.655026	+	0.378179i	−0.135353	+	0.990797i	$0.543217\pi$
$608$	21.7531	−	2.48927i	0.882205	−	0.100953i
$609$	8.64891	+	14.9804i	0.350472	+	0.607035i
$610$	33.4110	−	31.4911i	1.35277	−	1.27504i
$611$	0.902728			0.0365205
$612$	−8.54010	−	5.62875i	−0.345213	−	0.227529i
$613$	15.9728	+	27.6657i	0.645136	+	1.11741i	0.984270	+	0.176670i	$0.0565326\pi$
$613$	15.9728	+	27.6657i	0.645136	+	1.11741i	−0.339134	+	0.940738i	$0.610134\pi$
$614$	11.0230	+	11.6950i	0.444853	+	0.471974i
$615$	17.5001	−	30.3111i	0.705672	−	1.22226i
$616$	−7.68266	+	21.0130i	−0.309543	+	0.846639i
$617$	−29.2728			−1.17848			−0.589239	−	0.807959i	$-0.700572\pi$
$617$	−29.2728			−1.17848			−0.589239	+	0.807959i	$0.700572\pi$
$618$	3.11871	−	10.3989i	0.125453	−	0.418305i
$619$	33.9365	−	19.5933i	1.36402	−	0.787520i	0.373868	−	0.927482i	$-0.378031\pi$
$619$	33.9365	−	19.5933i	1.36402	−	0.787520i	0.990157	+	0.139962i	$0.0446980\pi$
$620$	−39.6788	−	2.34954i	−1.59354	−	0.0943597i
$621$	4.99547	−	2.88414i	0.200461	−	0.115736i
$622$	−4.53819	−	19.1895i	−0.181965	−	0.769428i
$623$	5.15094	−	8.92170i	0.206368	−	0.357440i
$624$	−0.780507	+	6.56747i	−0.0312453	+	0.262909i
$625$	66.4572			2.65829
$626$	2.59380	−	0.613416i	0.103669	−	0.0245171i
$627$		−	17.9450i		−	0.716655i
$628$	−25.2208	−	16.6229i	−1.00642	−	0.663328i
$629$	−18.5777	+	32.1776i	−0.740743	+	1.28300i
$630$	−2.89001	+	9.63633i	−0.115141	+	0.383920i
$631$	18.5384	+	32.1094i	0.738000	+	1.27825i	0.953394	+	0.301727i	$0.0975631\pi$
$631$	18.5384	+	32.1094i	0.738000	+	1.27825i	−0.215394	+	0.976527i	$0.569104\pi$
$632$	−41.2544	+	7.21257i	−1.64101	+	0.286901i
$633$	5.20080	−	3.00268i	0.206713	−	0.119346i
$634$	−5.08426	+	4.79210i	−0.201922	+	0.190319i
$635$	13.3083	−	23.0506i	0.528123	−	0.914736i
$636$	−3.13584	−	6.25905i	−0.124344	−	0.248188i
$637$	5.85517	+	3.38049i	0.231990	+	0.133940i
$638$	48.3748	−	45.5951i	1.91518	−	1.80513i
$639$	−3.04145	−	1.75598i	−0.120318	−	0.0694655i
$640$	2.58340	+	47.1017i	0.102118	+	1.86186i
$641$	17.1212	+	9.88492i	0.676246	+	0.390431i	0.798439	−	0.602076i	$-0.205659\pi$
$641$	17.1212	+	9.88492i	0.676246	+	0.390431i	−0.122193	+	0.992506i	$0.538993\pi$
$642$	0.658579	−	0.155750i	0.0259921	−	0.00614696i
$643$			38.1300i			1.50370i	0.659333	+	0.751851i	$0.270839\pi$
$643$			38.1300i			1.50370i	−0.659333	+	0.751851i	$0.729161\pi$
$644$	8.81669	+	17.5979i	0.347426	+	0.693454i
$645$			12.3210i			0.485139i
$646$	−8.04156	+	26.8135i	−0.316391	+	1.05496i
$647$	−21.5950	−	37.4036i	−0.848986	−	1.47049i	−0.882114	−	0.471035i	$-0.843880\pi$
$647$	−21.5950	−	37.4036i	−0.848986	−	1.47049i	0.0331286	−	0.999451i	$-0.489453\pi$
$648$	−1.81493	−	2.16934i	−0.0712973	−	0.0852196i
$649$	−42.2861	−	24.4139i	−1.65988	−	0.958330i
$650$	−19.8627	−	21.0736i	−0.779079	−	0.826576i
$651$	4.06621	+	7.04289i	0.159368	+	0.276033i
$652$	42.2014	+	2.49891i	1.65274	+	0.0978649i
$653$	16.7917	−	9.69467i	0.657108	−	0.379382i	−0.134066	−	0.990972i	$-0.542803\pi$
$653$	16.7917	−	9.69467i	0.657108	−	0.379382i	0.791174	+	0.611591i	$0.209470\pi$
$654$	9.13847	−	2.16119i	0.357342	−	0.0845092i
$655$	−53.1802			−2.07792
$656$	−30.8570	+	13.2397i	−1.20476	+	0.516922i
$657$	−0.636897	−	1.10314i	−0.0248477	−	0.0430375i
$658$	−0.903562	−	0.958648i	−0.0352245	−	0.0373720i
$659$	16.2607	+	9.38809i	0.633425	+	0.365708i	0.782077	−	0.623181i	$-0.214160\pi$
$659$	16.2607	+	9.38809i	0.633425	+	0.365708i	−0.148652	+	0.988890i	$0.547493\pi$
$660$	38.5945	+	2.28533i	1.50229	+	0.0889564i
$661$		−	7.15199i		−	0.278180i	−0.990280	−	0.139090i	$-0.955582\pi$
$661$		−	7.15199i		−	0.278180i	0.990280	−	0.139090i	$-0.0444177\pi$
$662$	2.56340	+	0.768782i	0.0996293	+	0.0298796i
$663$	−7.32291	−	4.22788i	−0.284398	−	0.164197i
$664$	3.98434	+	1.45673i	0.154622	+	0.0565321i
$665$	27.5340			1.06772
$666$	−7.47694	+	7.04730i	−0.289726	+	0.273077i
$667$		−	58.4820i		−	2.26443i
$668$	6.93180	+	0.410459i	0.268200	+	0.0158811i
$669$			22.0870i			0.853932i
$670$	−40.4420	+	26.3438i	−1.56241	+	1.01775i
$671$			36.1000i			1.39362i
$672$	7.75552	−	5.74468i	0.299176	−	0.221606i
$673$		−	7.78300i		−	0.300013i	−0.988685	−	0.150006i	$-0.952071\pi$
$673$		−	7.78300i		−	0.300013i	0.988685	−	0.150006i	$-0.0479294\pi$
$674$	7.86610	+	8.34566i	0.302991	+	0.321463i
$675$	12.3847			0.476687
$676$	1.21368	−	20.4965i	0.0466799	−	0.788327i
$677$	−36.6838	−	21.1794i	−1.40987	−	0.813990i	−0.414497	−	0.910051i	$-0.636042\pi$
$677$	−36.6838	−	21.1794i	−1.40987	−	0.813990i	−0.995375	+	0.0960607i	$0.969376\pi$
$678$	−3.27835	+	10.9312i	−0.125904	+	0.419811i
$679$		−	27.2584i		−	1.04608i
$680$	−56.6440	−	20.7098i	−2.17220	−	0.794186i
$681$	0.343477	+	0.198307i	0.0131621	+	0.00759913i
$682$	22.7430	−	21.4362i	0.870875	−	0.820833i
$683$	15.9567	+	27.6378i	0.610566	+	1.05753i	0.991145	+	0.132783i	$0.0423913\pi$
$683$	15.9567	+	27.6378i	0.610566	+	1.05753i	−0.380579	+	0.924748i	$0.624275\pi$
$684$	−4.26004	+	6.46346i	−0.162887	+	0.247136i
$685$	−24.8782			−0.950547
$686$	−6.15783	−	26.0380i	−0.235107	−	0.994137i
$687$	−14.4225	+	8.32684i	−0.550253	+	0.317689i
$688$	7.07682	−	9.46753i	0.269801	−	0.360946i
$689$	−2.89376	−	5.01214i	−0.110243	−	0.190947i
$690$	24.7514	−	23.3291i	0.942270	−	0.888125i
$691$	−18.2527	−	10.5382i	−0.694367	−	0.400893i	0.110879	−	0.993834i	$-0.464633\pi$
$691$	−18.2527	−	10.5382i	−0.694367	−	0.400893i	−0.805246	+	0.592941i	$0.797967\pi$
$692$	21.5427	+	14.1987i	0.818930	+	0.539754i
$693$	−3.95510	−	6.85043i	−0.150242	−	0.260227i
$694$	13.6335	+	4.08879i	0.517520	+	0.155208i
$695$		−	34.0851i		−	1.29292i
$696$	−28.2477	+	4.93859i	−1.07073	+	0.187197i
$697$		−	42.9295i		−	1.62607i
$698$	11.3027	+	47.7929i	0.427814	+	1.80899i
$699$	2.51365	+	1.45126i	0.0950751	+	0.0548916i
$700$	−2.49801	+	42.1862i	−0.0944158	+	1.59449i
$701$	30.4377	+	17.5732i	1.14961	+	0.663730i	0.948793	−	0.315898i	$-0.102306\pi$
$701$	30.4377	+	17.5732i	1.14961	+	0.663730i	0.200821	+	0.979628i	$0.435639\pi$
$702$	−1.60381	−	1.70159i	−0.0605319	−	0.0642223i
$703$	24.3532	+	14.0603i	0.918497	+	0.530294i
$704$	−28.3437	−	23.9236i	−1.06824	−	0.901656i
$705$	−1.13822	+	1.97146i	−0.0428679	+	0.0742494i
$706$	−17.9293	−	19.0224i	−0.674778	−	0.715917i
$707$	−22.6116	+	13.0548i	−0.850396	+	0.490976i
$708$	9.43495	+	18.8319i	0.354587	+	0.707747i
$709$	−3.69484	−	6.39965i	−0.138763	−	0.240344i	0.788266	−	0.615335i	$-0.210979\pi$
$709$	−3.69484	−	6.39965i	−0.138763	−	0.240344i	−0.927029	+	0.374991i	$0.877646\pi$
$710$	−19.8356	−	5.94885i	−0.744418	−	0.223256i
$711$	7.40343	−	12.8231i	0.277650	−	0.480905i
$712$	10.9588	+	13.0987i	0.410698	+	0.490895i
$713$		−	27.4948i		−	1.02969i
$714$	2.83989	+	12.0083i	0.106280	+	0.449400i
$715$	31.9624			1.19533
$716$	45.1927	−	22.6419i	1.68893	−	0.846169i
$717$	11.8629	−	20.5472i	0.443029	−	0.767349i
$718$	−12.5391	+	2.96542i	−0.467955	+	0.110668i
$719$	9.46958	−	5.46727i	0.353156	−	0.203895i	−0.312918	−	0.949780i	$-0.601307\pi$
$719$	9.46958	−	5.46727i	0.353156	−	0.203895i	0.666074	+	0.745885i	$0.267973\pi$
$720$	−13.3585	−	9.98526i	−0.497842	−	0.372129i
$721$	−11.3428	+	6.54877i	−0.422428	+	0.243889i
$722$	−5.44407	−	1.63272i	−0.202607	−	0.0607635i
$723$	9.42863			0.350654
$724$	−1.20583	+	20.3639i	−0.0448142	+	0.756820i
$725$	62.7815	−	108.741i	2.33165	−	4.03853i
$726$	−10.8011	+	10.1804i	−0.400866	+	0.377832i
$727$	8.20134	+	14.2051i	0.304171	+	0.526839i	0.977076	−	0.212889i	$-0.0682873\pi$
$727$	8.20134	+	14.2051i	0.304171	+	0.526839i	−0.672906	+	0.739728i	$0.734954\pi$
$728$	6.11964	−	5.11987i	0.226809	−	0.189755i
$729$	1.00000			0.0370370
$730$	−5.15172	−	5.46579i	−0.190674	−	0.202298i
$731$	7.55617	+	13.0877i	0.279475	+	0.484065i
$732$	8.56993	−	13.0025i	0.316754	−	0.480588i
$733$	23.0097	+	13.2847i	0.849884	+	0.490681i	0.860612	−	0.509262i	$-0.170082\pi$
$733$	23.0097	+	13.2847i	0.849884	+	0.490681i	−0.0107280	+	0.999942i	$0.503415\pi$
$734$	32.6423	+	9.78967i	1.20485	+	0.361343i
$735$	−14.7652	+	8.52470i	−0.544623	+	0.314438i
$736$	−32.4187	+	3.70977i	−1.19497	+	0.136744i
$737$	6.73699	−	37.3470i	0.248160	−	1.37570i
$738$	3.41026	−	11.3710i	0.125533	−	0.418573i
$739$	14.7697	+	25.5818i	0.543311	+	0.941042i	0.998711	+	0.0507555i	$0.0161629\pi$
$739$	14.7697	+	25.5818i	0.543311	+	0.941042i	−0.455400	+	0.890287i	$0.650504\pi$
$740$	−33.3411	+	50.5860i	−1.22564	+	1.85958i
$741$	−3.19982	+	5.54224i	−0.117548	+	0.203599i
$742$	−2.42619	+	8.08978i	−0.0890681	+	0.296985i
$743$	31.7258	−	18.3169i	1.16391	−	0.671981i	0.211669	−	0.977341i	$-0.432110\pi$
$743$	31.7258	−	18.3169i	1.16391	−	0.671981i	0.952237	+	0.305360i	$0.0987769\pi$
$744$	−13.2804	+	2.32184i	−0.486884	+	0.0851227i
$745$		−	59.4671i		−	2.17871i
$746$	−7.10159	+	23.6793i	−0.260008	+	0.866960i
$747$	−1.29893	+	0.749938i	−0.0475254	+	0.0274388i
$748$	42.3976	−	21.2416i	1.55021	−	0.776668i
$749$	−0.707060	−	0.408221i	−0.0258354	−	0.0149161i
$750$	42.3754	−	10.0215i	1.54733	−	0.365934i
$751$			2.16041i			0.0788346i	0.999223	+	0.0394173i	$0.0125502\pi$
$751$			2.16041i			0.0788346i	−0.999223	+	0.0394173i	$0.987450\pi$
$752$	2.00697	−	0.861120i	0.0731865	−	0.0314018i
$753$	−1.99614	−	3.45742i	−0.0727434	−	0.125995i
$754$	−23.0705	+	5.45603i	−0.840179	+	0.198697i
$755$	12.3046	+	21.3122i	0.447811	+	0.775631i
$756$	−0.201701	+	3.40632i	−0.00733580	+	0.123887i
$757$	−6.76318	−	3.90473i	−0.245812	−	0.141920i	0.372033	−	0.928219i	$-0.378661\pi$
$757$	−6.76318	−	3.90473i	−0.245812	−	0.141920i	−0.617845	+	0.786300i	$0.711994\pi$
$758$	−21.2923	+	20.0688i	−0.773372	+	0.728933i
$759$			26.7435i			0.970727i
$760$	−15.6740	+	42.8702i	−0.568554	+	1.55507i
$761$	1.59990			0.0579963			0.0289982	−	0.999579i	$-0.490768\pi$
$761$	1.59990			0.0579963			0.0289982	+	0.999579i	$0.490768\pi$
$762$	2.59339	−	8.64731i	0.0939487	−	0.313259i
$763$	−9.81119	−	5.66449i	−0.355189	−	0.205068i
$764$	−14.3099	−	9.43164i	−0.517716	−	0.341225i
$765$	18.4665	−	10.6616i	0.667656	−	0.385471i
$766$	−21.0917	+	19.8797i	−0.762075	+	0.718284i
$767$	8.70660	+	15.0803i	0.314377	+	0.544517i
$768$	4.52952	+	15.3455i	0.163445	+	0.553732i
$769$	28.0130	+	16.1733i	1.01017	+	0.583225i	0.911243	−	0.411870i	$-0.135124\pi$
$769$	28.0130	+	16.1733i	1.01017	+	0.583225i	0.0989319	+	0.995094i	$0.468457\pi$
$770$	−31.9919	−	33.9423i	−1.15291	−	1.22320i
$771$	−1.11377	+	1.92910i	−0.0401114	+	0.0694749i
$772$	−6.89678	+	3.45534i	−0.248221	+	0.124361i
$773$	9.20107	−	15.9367i	0.330940	−	0.573204i	−0.651757	−	0.758428i	$-0.725968\pi$
$773$	9.20107	−	15.9367i	0.330940	−	0.573204i	0.982696	+	0.185224i	$0.0593010\pi$
$774$	0.961788	+	4.06687i	0.0345708	+	0.146181i
$775$	29.5162	−	51.1236i	1.06025	−	1.83641i
$776$	42.4410	+	15.5170i	1.52354	+	0.557029i
$777$	12.3956			0.444691
$778$	16.8086	−	15.8427i	0.602617	−	0.567989i
$779$	−32.4906			−1.16410
$780$	−11.5123	−	7.58769i	−0.412205	−	0.271683i
$781$	14.1011	−	8.14126i	0.504576	−	0.291317i
$782$	11.9844	−	39.9602i	0.428560	−	1.42897i
$783$	5.06928	−	8.78025i	0.181161	−	0.313781i
$784$	16.2420	+	1.93027i	0.580072	+	0.0689384i
$785$	54.5355	−	31.4861i	1.94646	−	1.12379i
$786$	−17.5535	+	4.15129i	−0.626113	+	0.148072i
$787$	−11.2554	−	19.4950i	−0.401212	−	0.694920i	0.592660	−	0.805453i	$-0.298078\pi$
$787$	−11.2554	−	19.4950i	−0.401212	−	0.694920i	−0.993873	+	0.110532i	$0.964744\pi$
$788$	−1.98900	−	0.117777i	−0.0708554	−	0.00419562i
$789$			11.3715i			0.404836i
$790$	25.0811	−	83.6295i	0.892346	−	2.97540i
$791$	11.9234	−	6.88400i	0.423949	−	0.244767i
$792$	12.9175	−	2.25839i	0.459004	−	0.0802484i
$793$	6.43707	−	11.1493i	0.228587	−	0.395924i
$794$	2.42850	+	10.2688i	0.0861843	+	0.364425i
$795$	14.5946			0.517617
$796$	23.3313	−	35.3990i	0.826957	−	1.25468i
$797$	16.4943	−	28.5689i	0.584257	−	1.01196i	−0.410710	−	0.911766i	$-0.634719\pi$
$797$	16.4943	−	28.5689i	0.584257	−	1.01196i	0.994968	−	0.100197i	$-0.0319474\pi$
$798$	9.08833	−	2.14933i	0.321723	−	0.0760855i
$799$			2.79218i			0.0987801i
$800$	−64.2615	−	27.9042i	−2.27199	−	0.986562i
$801$	−6.03812			−0.213346
$802$	−30.2595	+	7.15618i	−1.06850	+	0.252694i
$803$	5.90570			0.208408
$804$	−11.2925	+	11.8524i	−0.398256	+	0.418001i
$805$	−41.0340			−1.44626
$806$	−10.8464	+	2.56511i	−0.382049	+	0.0903521i
$807$	−4.46275			−0.157096
$808$	−7.45438	−	42.6375i	−0.262244	−	1.49998i
$809$			30.9716i			1.08890i	0.838792	+	0.544452i	$0.183262\pi$
$809$			30.9716i			1.08890i	−0.838792	+	0.544452i	$0.816738\pi$
$810$	5.73827	−	1.35706i	0.201622	−	0.0476824i
$811$	3.96469	−	6.86705i	0.139219	−	0.241135i	−0.787982	−	0.615698i	$-0.788874\pi$
$811$	3.96469	−	6.86705i	0.139219	−	0.241135i	0.927201	+	0.374564i	$0.122207\pi$
$812$	28.8858	+	19.0386i	1.01369	+	0.668123i
$813$	−21.3867			−0.750064
$814$	−10.9633	−	46.3579i	−0.384265	−	1.62484i
$815$	−44.0667	+	76.3258i	−1.54359	+	2.67358i
$816$	−20.3135	−	2.41414i	−0.711113	−	0.0845119i
$817$	9.90523	−	5.71879i	0.346540	−	0.200075i
$818$	−4.74163	+	15.8103i	−0.165787	+	0.552794i
$819$			2.82097i			0.0985727i
$820$	4.13775	−	69.8780i	0.144496	−	2.44025i
$821$	7.63477	+	13.2238i	0.266455	+	0.461514i	0.967944	−	0.251167i	$-0.0808142\pi$
$821$	7.63477	+	13.2238i	0.266455	+	0.461514i	−0.701489	+	0.712681i	$0.747481\pi$
$822$	−8.21170	+	1.94201i	−0.286416	+	0.0677355i
$823$	−41.4942	+	23.9567i	−1.44640	+	0.835077i	−0.998264	−	0.0588909i	$-0.981244\pi$
$823$	−41.4942	+	23.9567i	−1.44640	+	0.835077i	−0.448131	+	0.893968i	$0.647910\pi$
$824$	−3.73939	−	21.3886i	−0.130268	−	0.745106i
$825$	−28.7096	+	49.7265i	−0.999541	+	1.73126i
$826$	7.29978	−	24.3401i	0.253992	−	0.846901i
$827$	44.2782	−	25.5640i	1.53970	−	0.888948i	0.540848	−	0.841121i	$-0.318104\pi$
$827$	44.2782	−	25.5640i	1.53970	−	0.888948i	0.998856	−	0.0478275i	$-0.0152298\pi$
$828$	6.34875	−	9.63250i	0.220634	−	0.334753i
$829$	−53.6112			−1.86199			−0.930996	−	0.365028i	$-0.881059\pi$
$829$	−53.6112			−1.86199			−0.930996	+	0.365028i	$0.881059\pi$
$830$	−6.43591	+	6.06608i	−0.223394	+	0.210557i
$831$	14.3293			0.497079
$832$	4.48794	+	12.4427i	0.155591	+	0.431374i
$833$	−10.4560	+	18.1103i	−0.362278	+	0.627485i
$834$	−2.66071	−	11.2507i	−0.0921329	−	0.389579i
$835$	−7.23819	+	12.5369i	−0.250488	+	0.433858i
$836$	−16.0764	−	32.0881i	−0.556013	−	1.10979i
$837$	2.38328	−	4.12796i	0.0823782	−	0.142683i
$838$	11.4399	+	12.1374i	0.395186	+	0.419279i
$839$	21.7923	+	12.5818i	0.752354	+	0.434372i	0.826544	−	0.562873i	$-0.190304\pi$
$839$	21.7923	+	12.5818i	0.752354	+	0.434372i	−0.0741901	+	0.997244i	$0.523637\pi$
$840$	3.46518	+	19.8201i	0.119560	+	0.683858i
$841$	−36.8952	−	63.9044i	−1.27225	−	2.20360i
$842$	−13.6134	+	12.8311i	−0.469149	+	0.442190i
$843$	−15.7947	+	9.11906i	−0.543998	+	0.314077i
$844$	6.60971	−	10.0284i	0.227516	−	0.345193i
$845$	37.0701	+	21.4024i	1.27525	+	0.736266i
$846$	−0.221806	+	0.739582i	−0.00762585	+	0.0254274i
$847$	17.9066			0.615277
$848$	−11.2146	−	8.38272i	−0.385111	−	0.287864i
$849$			13.3972i			0.459789i
$850$	65.1816	−	61.4361i	2.23571	−	2.10724i
$851$	−36.2936	−	20.9541i	−1.24413	−	0.718297i
$852$	−7.01164	−	0.415186i	−0.240215	−	0.0142240i
$853$	18.7245	+	32.4318i	0.641115	+	1.11044i	0.985184	+	0.171499i	$0.0548610\pi$
$853$	18.7245	+	32.4318i	0.641115	+	1.11044i	−0.344070	+	0.938944i	$0.611806\pi$
$854$	−18.2830	+	4.32381i	−0.625631	+	0.147958i
$855$	−8.06910	−	13.9761i	−0.275957	−	0.477972i
$856$	1.03810	−	0.868503i	0.0354814	−	0.0296848i
$857$		−	4.88340i		−	0.166814i	−0.996516	−	0.0834069i	$-0.973420\pi$
$857$		−	4.88340i		−	0.166814i	0.996516	−	0.0834069i	$-0.0265801\pi$
$858$	10.5500	−	2.49501i	0.360172	−	0.0851784i
$859$	−15.6722	−	9.04836i	−0.534729	−	0.308726i	0.208211	−	0.978084i	$-0.433236\pi$
$859$	−15.6722	−	9.04836i	−0.534729	−	0.308726i	−0.742940	+	0.669358i	$0.766569\pi$
$860$	11.0380	+	22.0316i	0.376393	+	0.751271i
$861$	−12.4032	+	7.16097i	−0.422699	+	0.244045i
$862$	−15.9223	+	53.0907i	−0.542315	+	1.80827i
$863$			11.9646i			0.407281i	0.979046	+	0.203640i	$0.0652773\pi$
$863$			11.9646i			0.407281i	−0.979046	+	0.203640i	$0.934723\pi$
$864$	−5.18878	−	2.25312i	−0.176526	−	0.0766526i
$865$	−46.5823	+	26.8943i	−1.58384	+	0.914433i
$866$	13.0464	−	43.5014i	0.443335	−	1.47824i
$867$	4.57702	−	7.92762i	0.155444	−	0.269236i
$868$	13.5804	+	8.95083i	0.460950	+	0.303811i
$869$	34.3246	+	59.4520i	1.16438	+	2.01677i
$870$	17.1735	−	57.2628i	0.582238	−	1.94139i
$871$	−8.74013	+	10.3332i	−0.296148	+	0.350127i
$872$	14.4047	−	12.0514i	0.487803	−	0.408111i
$873$	−13.8362	+	7.98831i	−0.468283	+	0.270363i
$874$	−30.2433	−	9.07020i	−1.02300	−	0.306804i
$875$	−45.4948	−	26.2664i	−1.53801	−	0.887968i
$876$	−2.12712	−	1.40198i	−0.0718688	−	0.0473685i
$877$	−2.65364	−	4.59623i	−0.0896069	−	0.155204i	0.817738	−	0.575590i	$-0.195228\pi$
$877$	−2.65364	−	4.59623i	−0.0896069	−	0.155204i	−0.907345	+	0.420387i	$0.861894\pi$
$878$	−14.1100	−	14.9703i	−0.476190	−	0.505222i
$879$	27.6590			0.932916
$880$	71.0595	−	30.4892i	2.39542	−	1.02779i
$881$	26.4430	+	45.8006i	0.890886	+	1.54306i	0.838815	+	0.544416i	$0.183249\pi$
$881$	26.4430	+	45.8006i	0.890886	+	1.54306i	0.0520710	+	0.998643i	$0.483418\pi$
$882$	−4.20820	+	3.96639i	−0.141697	+	0.133555i
$883$	5.23475	−	9.06686i	0.176163	−	0.305124i	−0.764400	−	0.644743i	$-0.776965\pi$
$883$	5.23475	−	9.06686i	0.176163	−	0.305124i	0.940563	+	0.339618i	$0.110298\pi$
$884$	−16.8820	−	0.999646i	−0.567802	−	0.0336217i
$885$	−43.9115			−1.47607
$886$	1.81609	+	0.544658i	0.0610127	+	0.0182982i
$887$	−33.6020	+	19.4001i	−1.12825	+	0.651393i	−0.943493	−	0.331392i	$-0.892482\pi$
$887$	−33.6020	+	19.4001i	−1.12825	+	0.651393i	−0.184753	+	0.982785i	$0.559148\pi$
$888$	−7.05630	+	19.2999i	−0.236794	+	0.647661i
$889$	−9.43222	+	5.44570i	−0.316347	+	0.182643i
$890$	−34.6484	+	8.19412i	−1.16142	+	0.274668i
$891$	−2.31815	+	4.01516i	−0.0776611	+	0.134513i
$892$	19.7870	+	39.4944i	0.662519	+	1.32237i
$893$	2.11322			0.0707162
$894$	−4.64206	−	19.6287i	−0.155254	−	0.656481i
$895$			105.379i			3.52242i
$896$	8.72142	−	17.2202i	0.291362	−	0.575286i
$897$	4.76869	−	8.25961i	0.159222	−	0.275781i
$898$	24.1822	+	7.25242i	0.806970	+	0.242016i
$899$	−24.1630	−	41.8516i	−0.805883	−	1.39583i
$900$	22.1455	−	11.0951i	0.738182	−	0.369836i
$901$	15.5028	−	8.95052i	0.516472	−	0.298185i
$902$	37.7510	+	40.0525i	1.25697	+	1.33360i
$903$	2.52085	−	4.36625i	0.0838888	−	0.145300i
$904$	3.93082	+	22.4835i	0.130737	+	0.747789i
$905$	−36.8303	−	21.2640i	−1.22428	−	0.706840i
$906$	5.72511	+	6.07414i	0.190204	+	0.201800i
$907$	−4.47580	−	2.58411i	−0.148617	−	0.0858038i	0.423848	−	0.905733i	$-0.360679\pi$
$907$	−4.47580	−	2.58411i	−0.148617	−	0.0858038i	−0.572464	+	0.819930i	$0.694013\pi$
$908$	0.791839	+	0.0468879i	0.0262781	+	0.00155603i
$909$	13.2530	+	7.65165i	0.439576	+	0.253789i
$910$	3.82824	+	16.1875i	0.126905	+	0.536610i
$911$		−	49.6189i		−	1.64395i	−0.569524	−	0.821974i	$-0.692873\pi$
$911$		−	49.6189i		−	1.64395i	0.569524	−	0.821974i	$-0.307127\pi$
$912$	−1.82711	+	15.3740i	−0.0605017	+	0.509083i
$913$		−	6.95389i		−	0.230140i
$914$	32.8604	+	9.85507i	1.08693	+	0.325977i
$915$	16.2326	+	28.1157i	0.536633	+	0.929476i
$916$	−18.3296	+	27.8102i	−0.605627	+	0.918874i
$917$	18.8457	+	10.8806i	0.622340	+	0.359308i
$918$	5.26308	−	4.96065i	0.173708	−	0.163726i
$919$	−5.22770	−	9.05464i	−0.172446	−	0.298685i	0.766828	−	0.641852i	$-0.221834\pi$
$919$	−5.22770	−	9.05464i	−0.172446	−	0.298685i	−0.939274	+	0.343167i	$0.888500\pi$
$920$	23.3589	−	63.8896i	0.770121	−	2.10638i
$921$	−9.84151	+	5.68200i	−0.324289	+	0.187228i
$922$	−3.29985	−	13.9532i	−0.108675	−	0.459525i
$923$	−5.80675			−0.191131
$924$	−13.2093	−	8.70623i	−0.434555	−	0.286414i
$925$	−44.9892	−	77.9236i	−1.47924	−	2.56211i
$926$	32.4460	−	30.5816i	1.06624	−	1.00497i
$927$	6.64821	+	3.83835i	0.218356	+	0.126068i
$928$	−46.0863	+	34.1371i	−1.51286	+	1.12061i
$929$			10.4003i			0.341224i	0.985338	+	0.170612i	$0.0545744\pi$
$929$			10.4003i			0.341224i	−0.985338	+	0.170612i	$0.945426\pi$
$930$	8.07400	−	26.9216i	0.264757	−	0.882795i
$931$	13.7065	+	7.91347i	0.449213	+	0.259353i
$932$	5.79488	+	0.343138i	0.189818	+	0.0112398i
$933$	13.9433			0.456483
$934$	−5.95550	−	6.31858i	−0.194870	−	0.206750i
$935$			98.8610i			3.23310i
$936$	−4.39222	−	1.60586i	−0.143564	−	0.0524891i
$937$		−	3.29602i		−	0.107676i	−0.998550	−	0.0538381i	$-0.982854\pi$
$937$		−	3.29602i		−	0.107676i	0.998550	−	0.0538381i	$-0.0171455\pi$
$938$	19.7215	−	1.06120i	0.643929	−	0.0346493i
$939$			1.88468i			0.0615043i
$940$	−0.269123	+	4.54493i	−0.00877782	+	0.148239i
$941$			17.2797i			0.563301i	0.959517	+	0.281651i	$0.0908819\pi$
$941$			17.2797i			0.563301i	−0.959517	+	0.281651i	$0.909118\pi$
$942$	15.5430	−	14.6499i	0.506420	−	0.477320i
$943$	48.4209			1.57680
$944$	33.7419	+	25.2215i	1.09820	+	0.820890i
$945$	−6.16069	−	3.55688i	−0.200407	−	0.115705i
$946$	−18.5587	−	5.56589i	−0.603396	−	0.180963i
$947$		−	33.4709i		−	1.08766i	−0.839196	−	0.543829i	$-0.816974\pi$
$947$		−	33.4709i		−	1.08766i	0.839196	−	0.543829i	$-0.183026\pi$
$948$	1.75048	−	29.5620i	0.0568529	−	0.960128i
$949$	−1.82395	−	1.05306i	−0.0592080	−	0.0341837i
$950$	−46.4971	−	49.3318i	−1.50857	−	1.60054i
$951$	−2.47017	−	4.27846i	−0.0801008	−	0.138739i
$952$	15.8360	+	18.9283i	0.513247	+	0.613469i
$953$	−13.6873			−0.443376			−0.221688	−	0.975118i	$-0.571157\pi$
$953$	−13.6873			−0.443376			−0.221688	+	0.975118i	$0.571157\pi$
$954$	4.81733	−	1.13927i	0.155967	−	0.0368852i
$955$	30.9427	−	17.8648i	1.00128	−	0.578091i
$956$	2.80489	−	47.3688i	0.0907166	−	1.53202i
$957$	23.5028	+	40.7080i	0.759736	+	1.31590i
$958$	−11.7742	−	12.4920i	−0.380406	−	0.403598i
$959$	8.81619	+	5.09003i	0.284690	+	0.164366i
$960$	−32.8323	−	5.88749i	−1.05966	−	0.190018i
$961$	4.13995	+	7.17060i	0.133547	+	0.231310i
$962$	−4.88019	+	16.2723i	−0.157344	+	0.524641i
$963$			0.478532i			0.0154205i
$964$	16.8596	−	8.44682i	0.543012	−	0.272054i
$965$		−	16.0816i		−	0.517686i
$966$	−13.5444	+	3.20315i	−0.435782	+	0.103060i
$967$	−26.1761	−	15.1128i	−0.841768	−	0.485995i	0.0160967	−	0.999870i	$-0.494876\pi$
$967$	−26.1761	−	15.1128i	−0.841768	−	0.485995i	−0.857865	+	0.513875i	$0.828209\pi$
$968$	−10.1934	+	27.8804i	−0.327630	+	0.896109i
$969$	−17.1424	−	9.89716i	−0.550693	−	0.317943i
$970$	−68.5550	+	64.6156i	−2.20117	+	2.07468i
$971$	51.9851	+	30.0136i	1.66828	+	0.963183i	0.968564	+	0.248764i	$0.0800242\pi$
$971$	51.9851	+	30.0136i	1.66828	+	0.963183i	0.699718	+	0.714419i	$0.253309\pi$
$972$	1.78813	−	0.895869i	0.0573544	−	0.0287350i
$973$	−6.97374	+	12.0789i	−0.223568	+	0.387231i
$974$	−13.6621	+	12.8771i	−0.437763	+	0.412608i
$975$	17.7337	−	10.2386i	0.567933	−	0.327896i
$976$	3.67560	−	30.9278i	0.117653	−	0.989975i
$977$	25.7852	+	44.6613i	0.824943	+	1.42884i	0.901963	+	0.431813i	$0.142126\pi$
$977$	25.7852	+	44.6613i	0.824943	+	1.42884i	−0.0770207	+	0.997029i	$0.524541\pi$
$978$	−8.58731	+	28.6332i	−0.274592	+	0.915589i
$979$	13.9973	−	24.2440i	0.447355	−	0.774842i
$980$	−18.7651	+	28.4710i	−0.599430	+	0.909473i
$981$			6.64012i			0.212003i
$982$	−15.8656	+	3.75211i	−0.506291	+	0.119735i
$983$	8.71918			0.278099			0.139049	−	0.990285i	$-0.455595\pi$
$983$	8.71918			0.278099			0.139049	+	0.990285i	$0.455595\pi$
$984$	−4.08897	−	23.3881i	−0.130352	−	0.745584i
$985$	2.07692	−	3.59733i	0.0661761	−	0.114620i
$986$	−16.8757	−	71.3581i	−0.537433	−	2.27251i
$987$	0.806713	−	0.465756i	0.0256780	−	0.0148252i
$988$	−0.756569	+	12.7769i	−0.0240697	+	0.406487i
$989$	−14.7618	+	8.52272i	−0.469397	+	0.271007i
$990$	−7.85337	+	26.1860i	−0.249596	+	0.832245i
$991$	−2.48474			−0.0789305			−0.0394653	−	0.999221i	$-0.512565\pi$
$991$	−2.48474			−0.0789305			−0.0394653	+	0.999221i	$0.512565\pi$
$992$	−21.6671	+	16.0493i	−0.687932	+	0.509565i
$993$	−0.946179	+	1.63883i	−0.0300261	+	0.0520067i
$994$	5.81211	+	6.16645i	0.184349	+	0.195588i
$995$	44.1927	+	76.5440i	1.40100	+	2.42661i
$996$	−1.65081	+	2.50466i	−0.0523081	+	0.0793633i
$997$	−1.00170			−0.0317242			−0.0158621	−	0.999874i	$-0.505049\pi$
$997$	−1.00170			−0.0317242			−0.0158621	+	0.999874i	$0.505049\pi$
$998$	4.48920	−	4.23124i	0.142103	−	0.133938i
$999$	−3.63265	−	6.29193i	−0.114932	−	0.199068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.20	✓	68
4.3	odd	2		804.2.j.b.499.9	yes	68
67.38	odd	6		804.2.j.b.775.9	yes	68
268.239	even	6	inner	804.2.j.a.775.20	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.20	✓	68	1.1	even	1	trivial
804.2.j.a.775.20	yes	68	268.239	even	6	inner
804.2.j.b.499.9	yes	68	4.3	odd	2
804.2.j.b.775.9	yes	68	67.38	odd	6

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.325475 + 1.37625i) q^{2} -1.00000 q^{3} +(-1.78813 + 0.895869i) q^{4} -4.16950i q^{5} +(-0.325475 - 1.37625i) q^{6} +(-0.853071 + 1.47756i) q^{7} +(-1.81493 - 2.16934i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.325475 + 1.37625i) q^{2} -1.00000 q^{3} +(-1.78813 + 0.895869i) q^{4} -4.16950i q^{5} +(-0.325475 - 1.37625i) q^{6} +(-0.853071 + 1.47756i) q^{7} +(-1.81493 - 2.16934i) q^{8} +1.00000 q^{9} +(5.73827 - 1.35706i) q^{10} +(-2.31815 + 4.01516i) q^{11} +(1.78813 - 0.895869i) q^{12} +(1.43191 - 0.826711i) q^{13} +(-2.31115 - 0.693131i) q^{14} +4.16950i q^{15} +(2.39484 - 3.20387i) q^{16} +(2.55705 + 4.42894i) q^{17} +(0.325475 + 1.37625i) q^{18} +(3.35198 - 1.93527i) q^{19} +(3.73532 + 7.45561i) q^{20} +(0.853071 - 1.47756i) q^{21} +(-6.28037 - 1.88353i) q^{22} +(-4.99547 + 2.88414i) q^{23} +(1.81493 + 2.16934i) q^{24} -12.3847 q^{25} +(1.60381 + 1.70159i) q^{26} -1.00000 q^{27} +(0.201701 - 3.40632i) q^{28} +(-5.06928 + 8.78025i) q^{29} +(-5.73827 + 1.35706i) q^{30} +(-2.38328 + 4.12796i) q^{31} +(5.18878 + 2.25312i) q^{32} +(2.31815 - 4.01516i) q^{33} +(-5.26308 + 4.96065i) q^{34} +(6.16069 + 3.55688i) q^{35} +(-1.78813 + 0.895869i) q^{36} +(3.63265 + 6.29193i) q^{37} +(3.75440 + 3.98329i) q^{38} +(-1.43191 + 0.826711i) q^{39} +(-9.04504 + 7.56735i) q^{40} +(-7.26972 - 4.19717i) q^{41} +(2.31115 + 0.693131i) q^{42} +2.95503 q^{43} +(0.548108 - 9.25640i) q^{44} -4.16950i q^{45} +(-5.59519 - 5.93630i) q^{46} +(0.472829 + 0.272988i) q^{47} +(-2.39484 + 3.20387i) q^{48} +(2.04454 + 3.54125i) q^{49} +(-4.03090 - 17.0444i) q^{50} +(-2.55705 - 4.42894i) q^{51} +(-1.81981 + 2.76107i) q^{52} -3.50033i q^{53} +(-0.325475 - 1.37625i) q^{54} +(16.7412 + 9.66553i) q^{55} +(4.75360 - 0.831078i) q^{56} +(-3.35198 + 1.93527i) q^{57} +(-13.7338 - 4.11885i) q^{58} +10.5316i q^{59} +(-3.73532 - 7.45561i) q^{60} +(6.74319 - 3.89318i) q^{61} +(-6.45681 - 1.93644i) q^{62} +(-0.853071 + 1.47756i) q^{63} +(-1.41204 + 7.87440i) q^{64} +(-3.44697 - 5.97032i) q^{65} +(6.28037 + 1.88353i) q^{66} +(-7.70268 + 2.76925i) q^{67} +(-8.54010 - 5.62875i) q^{68} +(4.99547 - 2.88414i) q^{69} +(-2.89001 + 9.63633i) q^{70} +(-3.04145 - 1.75598i) q^{71} +(-1.81493 - 2.16934i) q^{72} +(-0.636897 - 1.10314i) q^{73} +(-7.47694 + 7.04730i) q^{74} +12.3847 q^{75} +(-4.26004 + 6.46346i) q^{76} +(-3.95510 - 6.85043i) q^{77} +(-1.60381 - 1.70159i) q^{78} +(7.40343 - 12.8231i) q^{79} +(-13.3585 - 9.98526i) q^{80} +1.00000 q^{81} +(3.41026 - 11.3710i) q^{82} +(-1.29893 + 0.749938i) q^{83} +(-0.201701 + 3.40632i) q^{84} +(18.4665 - 10.6616i) q^{85} +(0.961788 + 4.06687i) q^{86} +(5.06928 - 8.78025i) q^{87} +(12.9175 - 2.25839i) q^{88} -6.03812 q^{89} +(5.73827 - 1.35706i) q^{90} +2.82097i q^{91} +(6.34875 - 9.63250i) q^{92} +(2.38328 - 4.12796i) q^{93} +(-0.221806 + 0.739582i) q^{94} +(-8.06910 - 13.9761i) q^{95} +(-5.18878 - 2.25312i) q^{96} +(-13.8362 + 7.98831i) q^{97} +(-4.20820 + 3.96639i) q^{98} +(-2.31815 + 4.01516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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