LMFDB - Embedded newform 370.2.m.c.159.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(159,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("370.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.m (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 37x^{14} + 559x^{12} + 4431x^{10} + 19684x^{8} + 48248x^{6} + 58656x^{4} + 25392x^{2} + 256 $ x^16 + 37x^14 + 559x^12 + 4431x^10 + 19684x^8 + 48248x^6 + 58656x^4 + 25392*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			159.1
Root			$-2.85998i$ of defining polynomial
Character	$\chi$	$=$	370.159
Dual form			370.2.m.c.249.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-2.47681 - 1.42999i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.52446 - 1.63586i) q^{5} +2.85998i q^{6} +(4.15112 + 2.39665i) q^{7} +1.00000 q^{8} +(2.58973 + 4.48555i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-2.47681 - 1.42999i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.52446 - 1.63586i) q^{5} +2.85998i q^{6} +(4.15112 + 2.39665i) q^{7} +1.00000 q^{8} +(2.58973 + 4.48555i) q^{9} +(-2.17892 - 0.502291i) q^{10} +2.72666 q^{11} +(2.47681 - 1.42999i) q^{12} +(0.608891 - 1.05463i) q^{13} -4.79330i q^{14} +(-6.11505 + 1.87175i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.226399 + 0.392135i) q^{17} +(2.58973 - 4.48555i) q^{18} +(6.47189 + 3.73655i) q^{19} +(0.654464 + 2.13815i) q^{20} +(-6.85436 - 11.8721i) q^{21} +(-1.36333 - 2.36136i) q^{22} -7.02428 q^{23} +(-2.47681 - 1.42999i) q^{24} +(-0.352054 - 4.98759i) q^{25} -1.21778 q^{26} -6.23321i q^{27} +(-4.15112 + 2.39665i) q^{28} -8.17947i q^{29} +(4.67851 + 4.35991i) q^{30} +1.53078i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.75343 - 3.89910i) q^{33} +(0.226399 - 0.392135i) q^{34} +(10.2488 - 3.13704i) q^{35} -5.17946 q^{36} +(-5.22148 + 3.12028i) q^{37} -7.47310i q^{38} +(-3.01622 + 1.74141i) q^{39} +(1.52446 - 1.63586i) q^{40} +(2.40568 - 4.16675i) q^{41} +(-6.85436 + 11.8721i) q^{42} +7.62420 q^{43} +(-1.36333 + 2.36136i) q^{44} +(11.2856 + 2.60160i) q^{45} +(3.51214 + 6.08320i) q^{46} +2.87372i q^{47} +2.85998i q^{48} +(7.98785 + 13.8354i) q^{49} +(-4.14335 + 2.79868i) q^{50} -1.29499i q^{51} +(0.608891 + 1.05463i) q^{52} +(5.93485 - 3.42649i) q^{53} +(-5.39812 + 3.11660i) q^{54} +(4.15668 - 4.46043i) q^{55} +(4.15112 + 2.39665i) q^{56} +(-10.6864 - 18.5095i) q^{57} +(-7.08363 + 4.08974i) q^{58} +(-8.91923 + 5.14952i) q^{59} +(1.43654 - 6.23167i) q^{60} +(-5.44953 - 3.14629i) q^{61} +(1.32569 - 0.765390i) q^{62} +24.8267i q^{63} +1.00000 q^{64} +(-0.796995 - 2.60380i) q^{65} +7.79819i q^{66} +(0.0243958 + 0.0140849i) q^{67} -0.452798 q^{68} +(17.3978 + 10.0446i) q^{69} +(-7.84115 - 7.30718i) q^{70} +(-0.101250 + 0.175370i) q^{71} +(2.58973 + 4.48555i) q^{72} +1.18787i q^{73} +(5.31298 + 2.96180i) q^{74} +(-6.26022 + 12.8568i) q^{75} +(-6.47189 + 3.73655i) q^{76} +(11.3187 + 6.53485i) q^{77} +(3.01622 + 1.74141i) q^{78} +(-8.91394 - 5.14647i) q^{79} +(-2.17892 - 0.502291i) q^{80} +(-1.14422 + 1.98185i) q^{81} -4.81135 q^{82} +(5.78633 - 3.34074i) q^{83} +13.7087 q^{84} +(0.986612 + 0.227437i) q^{85} +(-3.81210 - 6.60275i) q^{86} +(-11.6965 + 20.2590i) q^{87} +2.72666 q^{88} +(3.24928 - 1.87597i) q^{89} +(-3.38977 - 11.0745i) q^{90} +(5.05516 - 2.91860i) q^{91} +(3.51214 - 6.08320i) q^{92} +(2.18900 - 3.79146i) q^{93} +(2.48872 - 1.43686i) q^{94} +(15.9786 - 4.89088i) q^{95} +(2.47681 - 1.42999i) q^{96} -15.7903 q^{97} +(7.98785 - 13.8354i) q^{98} +(7.06132 + 12.2306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−2.47681	−	1.42999i	−1.42999	−	0.825604i	−0.432869	−	0.901457i	$-0.642499\pi$
$3$	−2.47681	−	1.42999i	−1.42999	−	0.825604i	−0.997119	+	0.0758530i	$0.975832\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.52446	−	1.63586i	0.681758	−	0.731577i
$5$	1.52446	−	1.63586i	0.681758	−	0.731577i
$6$			2.85998i			1.16758i
$7$	4.15112	+	2.39665i	1.56897	+	0.905848i	0.996289	+	0.0860730i	$0.0274318\pi$
$7$	4.15112	+	2.39665i	1.56897	+	0.905848i	0.572686	+	0.819775i	$0.305901\pi$
$8$	1.00000			0.353553
$9$	2.58973	+	4.48555i	0.863244	+	1.49518i
$10$	−2.17892	−	0.502291i	−0.689036	−	0.158838i
$11$	2.72666			0.822120			0.411060	−	0.911608i	$-0.365159\pi$
$11$	2.72666			0.822120			0.411060	+	0.911608i	$0.365159\pi$
$12$	2.47681	−	1.42999i	0.714994	−	0.412802i
$13$	0.608891	−	1.05463i	0.168876	−	0.292502i	−0.769149	−	0.639070i	$-0.779320\pi$
$13$	0.608891	−	1.05463i	0.168876	−	0.292502i	0.938025	+	0.346568i	$0.112653\pi$
$14$		−	4.79330i		−	1.28106i
$15$	−6.11505	+	1.87175i	−1.57890	+	0.483284i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.226399	+	0.392135i	0.0549098	+	0.0951066i	0.892174	−	0.451692i	$-0.149180\pi$
$17$	0.226399	+	0.392135i	0.0549098	+	0.0951066i	−0.837264	+	0.546799i	$0.815846\pi$
$18$	2.58973	−	4.48555i	0.610405	−	1.05725i
$19$	6.47189	+	3.73655i	1.48475	+	0.857223i	0.999850	−	0.0173439i	$-0.00552102\pi$
$19$	6.47189	+	3.73655i	1.48475	+	0.857223i	0.484905	+	0.874567i	$0.338854\pi$
$20$	0.654464	+	2.13815i	0.146343	+	0.478104i
$21$	−6.85436	−	11.8721i	−1.49574	−	2.59070i
$22$	−1.36333	−	2.36136i	−0.290663	−	0.503444i
$23$	−7.02428			−1.46466			−0.732332	−	0.680948i	$-0.761568\pi$
$23$	−7.02428			−1.46466			−0.732332	+	0.680948i	$0.761568\pi$
$24$	−2.47681	−	1.42999i	−0.505577	−	0.291895i
$25$	−0.352054	−	4.98759i	−0.0704109	−	0.997518i
$26$	−1.21778			−0.238827
$27$		−	6.23321i		−	1.19958i
$28$	−4.15112	+	2.39665i	−0.784487	+	0.452924i
$29$		−	8.17947i		−	1.51889i	−0.650572	−	0.759445i	$-0.725471\pi$
$29$		−	8.17947i		−	1.51889i	0.650572	−	0.759445i	$-0.274529\pi$
$30$	4.67851	+	4.35991i	0.854175	+	0.796008i
$31$			1.53078i			0.274936i	0.990506	+	0.137468i	$0.0438965\pi$
$31$			1.53078i			0.274936i	−0.990506	+	0.137468i	$0.956104\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−6.75343	−	3.89910i	−1.17562	−	0.678745i
$34$	0.226399	−	0.392135i	0.0388271	−	0.0672506i
$35$	10.2488	−	3.13704i	1.73236	−	0.530257i
$36$	−5.17946			−0.863244
$37$	−5.22148	+	3.12028i	−0.858406	+	0.512971i
$37$	−5.22148	+	3.12028i	−0.858406	+	0.512971i
$38$		−	7.47310i		−	1.21230i
$39$	−3.01622	+	1.74141i	−0.482981	+	0.278849i
$40$	1.52446	−	1.63586i	0.241038	−	0.258652i
$41$	2.40568	−	4.16675i	0.375704	−	0.650738i	−0.614729	−	0.788739i	$-0.710734\pi$
$41$	2.40568	−	4.16675i	0.375704	−	0.650738i	0.990432	+	0.138001i	$0.0440678\pi$
$42$	−6.85436	+	11.8721i	−1.05765	+	1.83190i
$43$	7.62420			1.16268			0.581340	−	0.813661i	$-0.302529\pi$
$43$	7.62420			1.16268			0.581340	+	0.813661i	$0.302529\pi$
$44$	−1.36333	+	2.36136i	−0.205530	+	0.355988i
$45$	11.2856	+	2.60160i	1.68236	+	0.387823i
$46$	3.51214	+	6.08320i	0.517837	+	0.896920i
$47$			2.87372i			0.419175i	0.977790	+	0.209588i	$0.0672122\pi$
$47$			2.87372i			0.419175i	−0.977790	+	0.209588i	$0.932788\pi$
$48$			2.85998i			0.412802i
$49$	7.98785	+	13.8354i	1.14112	+	1.97648i
$50$	−4.14335	+	2.79868i	−0.585959	+	0.395794i
$51$		−	1.29499i		−	0.181335i
$52$	0.608891	+	1.05463i	0.0844380	+	0.146251i
$53$	5.93485	−	3.42649i	0.815215	−	0.470664i	−0.0335488	−	0.999437i	$-0.510681\pi$
$53$	5.93485	−	3.42649i	0.815215	−	0.470664i	0.848763	+	0.528773i	$0.177348\pi$
$54$	−5.39812	+	3.11660i	−0.734591	+	0.424116i
$55$	4.15668	−	4.46043i	0.560487	−	0.601444i
$56$	4.15112	+	2.39665i	0.554716	+	0.320266i
$57$	−10.6864	−	18.5095i	−1.41545	−	2.45164i
$58$	−7.08363	+	4.08974i	−0.930126	+	0.537009i
$59$	−8.91923	+	5.14952i	−1.16118	+	0.670410i	−0.951588	−	0.307378i	$-0.900548\pi$
$59$	−8.91923	+	5.14952i	−1.16118	+	0.670410i	−0.209597	+	0.977788i	$0.567215\pi$
$60$	1.43654	−	6.23167i	0.185457	−	0.804505i
$61$	−5.44953	−	3.14629i	−0.697741	−	0.402841i	0.108765	−	0.994068i	$-0.465311\pi$
$61$	−5.44953	−	3.14629i	−0.697741	−	0.402841i	−0.806505	+	0.591227i	$0.798644\pi$
$62$	1.32569	−	0.765390i	0.168363	−	0.0972047i
$63$			24.8267i			3.12787i
$64$	1.00000			0.125000
$65$	−0.796995	−	2.60380i	−0.0988551	−	0.322962i
$66$			7.79819i			0.959891i
$67$	0.0243958	+	0.0140849i	0.00298042	+	0.00172074i	0.501489	−	0.865164i	$-0.332786\pi$
$67$	0.0243958	+	0.0140849i	0.00298042	+	0.00172074i	−0.498509	+	0.866884i	$0.666119\pi$
$68$	−0.452798			−0.0549098
$69$	17.3978	+	10.0446i	2.09445	+	1.20923i
$70$	−7.84115	−	7.30718i	−0.937196	−	0.873375i
$71$	−0.101250	+	0.175370i	−0.0120162	+	0.0208126i	−0.871971	−	0.489558i	$-0.837158\pi$
$71$	−0.101250	+	0.175370i	−0.0120162	+	0.0208126i	0.859955	+	0.510370i	$0.170492\pi$
$72$	2.58973	+	4.48555i	0.305203	+	0.528627i
$73$			1.18787i			0.139030i	0.997581	+	0.0695150i	$0.0221452\pi$
$73$			1.18787i			0.139030i	−0.997581	+	0.0695150i	$0.977855\pi$
$74$	5.31298	+	2.96180i	0.617622	+	0.344302i
$75$	−6.26022	+	12.8568i	−0.722868	+	1.48457i
$76$	−6.47189	+	3.73655i	−0.742377	+	0.428612i
$77$	11.3187	+	6.53485i	1.28989	+	0.744716i
$78$	3.01622	+	1.74141i	0.341519	+	0.197176i
$79$	−8.91394	−	5.14647i	−1.00290	−	0.579023i	−0.0937929	−	0.995592i	$-0.529899\pi$
$79$	−8.91394	−	5.14647i	−1.00290	−	0.579023i	−0.909104	+	0.416569i	$0.863232\pi$
$80$	−2.17892	−	0.502291i	−0.243611	−	0.0561579i
$81$	−1.14422	+	1.98185i	−0.127135	+	0.220205i
$82$	−4.81135			−0.531325
$83$	5.78633	−	3.34074i	0.635132	−	0.366694i	−0.147605	−	0.989046i	$-0.547156\pi$
$83$	5.78633	−	3.34074i	0.635132	−	0.366694i	0.782737	+	0.622353i	$0.213823\pi$
$84$	13.7087			1.49574
$85$	0.986612	+	0.227437i	0.107013	+	0.0246690i
$86$	−3.81210	−	6.60275i	−0.411070	−	0.711993i
$87$	−11.6965	+	20.2590i	−1.25400	+	2.17199i
$88$	2.72666			0.290663
$89$	3.24928	−	1.87597i	0.344423	−	0.198853i	−0.317803	−	0.948157i	$-0.602945\pi$
$89$	3.24928	−	1.87597i	0.344423	−	0.198853i	0.662226	+	0.749304i	$0.269612\pi$
$90$	−3.38977	−	11.0745i	−0.357313	−	1.16735i
$91$	5.05516	−	2.91860i	0.529925	−	0.305952i
$92$	3.51214	−	6.08320i	0.366166	−	0.634218i
$93$	2.18900	−	3.79146i	0.226988	−	0.393156i
$94$	2.48872	−	1.43686i	0.256691	−	0.148201i
$95$	15.9786	−	4.89088i	1.63937	−	0.501793i
$96$	2.47681	−	1.42999i	0.252789	−	0.145948i
$97$	−15.7903			−1.60326			−0.801630	−	0.597820i	$-0.796034\pi$
$97$	−15.7903			−1.60326			−0.801630	+	0.597820i	$0.796034\pi$
$98$	7.98785	−	13.8354i	0.806894	−	1.39758i
$99$	7.06132	+	12.2306i	0.709690	+	1.22922i
$100$	4.49541	+	2.18891i	0.449541	+	0.218891i
$101$	−6.29744			−0.626619			−0.313310	−	0.949651i	$-0.601438\pi$
$101$	−6.29744			−0.626619			−0.313310	+	0.949651i	$0.601438\pi$
$102$	−1.12150	+	0.647496i	−0.111045	+	0.0641117i
$103$	−8.52688			−0.840179			−0.420089	−	0.907483i	$-0.638001\pi$
$103$	−8.52688			−0.840179			−0.420089	+	0.907483i	$0.638001\pi$
$104$	0.608891	−	1.05463i	0.0597067	−	0.103415i
$105$	−29.8702	−	6.88577i	−2.91504	−	0.671982i
$106$	−5.93485	−	3.42649i	−0.576444	−	0.332810i
$107$	5.73095	+	3.30877i	0.554032	+	0.319871i	0.750747	−	0.660590i	$-0.229694\pi$
$107$	5.73095	+	3.30877i	0.554032	+	0.319871i	−0.196715	+	0.980461i	$0.563027\pi$
$108$	5.39812	+	3.11660i	0.519434	+	0.299895i
$109$	12.9732	−	7.49007i	1.24261	−	0.717418i	0.272981	−	0.962019i	$-0.411990\pi$
$109$	12.9732	−	7.49007i	1.24261	−	0.717418i	0.969624	+	0.244601i	$0.0786570\pi$
$110$	−5.94119	−	1.36958i	−0.566470	−	0.130584i
$111$	17.3946	−	0.261690i	1.65102	−	0.0248385i
$112$		−	4.79330i		−	0.452924i
$113$	−0.726663	−	1.25862i	−0.0683588	−	0.118401i	0.829820	−	0.558031i	$-0.188443\pi$
$113$	−0.726663	−	1.25862i	−0.0683588	−	0.118401i	−0.898179	+	0.439630i	$0.855110\pi$
$114$	−10.6864	+	18.5095i	−1.00088	+	1.73357i
$115$	−10.7082	+	11.4907i	−0.998547	+	1.07151i
$116$	7.08363	+	4.08974i	0.657698	+	0.379722i
$117$	6.30746			0.583125
$118$	8.91923	+	5.14952i	0.821081	+	0.474052i
$119$			2.17040i			0.198960i
$120$	−6.11505	+	1.87175i	−0.558225	+	0.170867i
$121$	−3.56531			−0.324119
$122$			6.29258i			0.569703i
$123$	−11.9168	+	6.88018i	−1.07450	+	0.620365i
$124$	−1.32569	−	0.765390i	−0.119051	−	0.0687341i
$125$	−8.69568	−	7.02746i	−0.777765	−	0.628555i
$126$	21.5006	−	12.4133i	1.91542	−	1.10587i
$127$	11.5987	−	6.69650i	1.02922	−	0.594218i	0.112456	−	0.993657i	$-0.464128\pi$
$127$	11.5987	−	6.69650i	1.02922	−	0.594218i	0.916760	+	0.399438i	$0.130795\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−18.8837	−	10.9025i	−1.66262	−	0.959913i
$130$	−1.85646	+	1.99212i	−0.162822	+	0.174720i
$131$	−5.49133	+	3.17042i	−0.479780	+	0.277001i	−0.720325	−	0.693637i	$-0.756007\pi$
$131$	−5.49133	+	3.17042i	−0.479780	+	0.277001i	0.240545	+	0.970638i	$0.422674\pi$
$132$	6.75343	−	3.89910i	0.587811	−	0.339373i
$133$	17.9104	+	31.0217i	1.55303	+	2.68992i
$134$		−	0.0281698i		−	0.00243350i
$135$	−10.1966	−	9.50226i	−0.877587	−	0.817825i
$136$	0.226399	+	0.392135i	0.0194136	+	0.0336253i
$137$			9.41845i			0.804673i	0.915492	+	0.402336i	$0.131802\pi$
$137$			9.41845i			0.804673i	−0.915492	+	0.402336i	$0.868198\pi$
$138$		−	20.0893i		−	1.71011i
$139$	−4.32653	−	7.49376i	−0.366971	−	0.635613i	0.622119	−	0.782922i	$-0.286272\pi$
$139$	−4.32653	−	7.49376i	−0.366971	−	0.635613i	−0.989090	+	0.147310i	$0.952939\pi$
$140$	−2.40763	+	10.4442i	−0.203482	+	0.882698i
$141$	4.10939	−	7.11767i	0.346073	−	0.599416i
$142$	0.202500			0.0169934
$143$	1.66024	−	2.87562i	0.138836	−	0.240472i
$144$	2.58973	−	4.48555i	0.215811	−	0.373795i
$145$	−13.3804	−	12.4693i	−1.11119	−	1.03552i
$146$	1.02873	−	0.593937i	0.0851382	−	0.0491545i
$147$		−	45.6901i		−	3.76846i
$148$	−0.0915007	−	6.08207i	−0.00752131	−	0.499943i
$149$	4.30003			0.352272			0.176136	−	0.984366i	$-0.443640\pi$
$149$	4.30003			0.352272			0.176136	+	0.984366i	$0.443640\pi$
$150$	14.2644	−	1.00687i	1.16468	−	0.0822104i
$151$	−0.465325	+	0.805967i	−0.0378677	+	0.0655887i	−0.884338	−	0.466847i	$-0.845390\pi$
$151$	−0.465325	+	0.805967i	−0.0378677	+	0.0655887i	0.846470	+	0.532436i	$0.178723\pi$
$152$	6.47189	+	3.73655i	0.524940	+	0.303074i
$153$	−1.17263	+	2.03105i	−0.0948012	+	0.164200i
$154$		−	13.0697i		−	1.05319i
$155$	2.50414	+	2.33361i	0.201137	+	0.187440i
$156$		−	3.48283i		−	0.278849i
$157$	−0.603380	+	0.348361i	−0.0481549	+	0.0278023i	−0.523884	−	0.851789i	$-0.675518\pi$
$157$	−0.603380	+	0.348361i	−0.0481549	+	0.0278023i	0.475729	+	0.879592i	$0.342184\pi$
$158$			10.2929i			0.818862i
$159$	−19.5993			−1.55433
$160$	0.654464	+	2.13815i	0.0517400	+	0.169035i
$161$	−29.1586	−	16.8347i	−2.29802	−	1.32676i
$162$	2.28844			0.179797
$163$	4.94299	+	8.56151i	0.387165	+	0.670589i	0.992067	−	0.125711i	$-0.0401212\pi$
$163$	4.94299	+	8.56151i	0.387165	+	0.670589i	−0.604902	+	0.796300i	$0.706788\pi$
$164$	2.40568	+	4.16675i	0.187852	+	0.325369i
$165$	−16.6737	+	5.10364i	−1.29804	+	0.397318i
$166$	−5.78633	−	3.34074i	−0.449106	−	0.259292i
$167$	−7.01504	+	12.1504i	−0.542840	+	0.940227i	0.455899	+	0.890032i	$0.349318\pi$
$167$	−7.01504	+	12.1504i	−0.542840	+	0.940227i	−0.998739	+	0.0501957i	$0.984016\pi$
$168$	−6.85436	−	11.8721i	−0.528825	−	0.915952i
$169$	5.75850	+	9.97402i	0.442962	+	0.767232i
$170$	−0.296340	−	0.968150i	−0.0227283	−	0.0742537i
$171$			38.7066i			2.95997i
$172$	−3.81210	+	6.60275i	−0.290670	+	0.503455i
$173$	3.44700	−	1.99013i	0.262071	−	0.151307i	−0.363208	−	0.931708i	$-0.618319\pi$
$173$	3.44700	−	1.99013i	0.262071	−	0.151307i	0.625279	+	0.780401i	$0.284985\pi$
$174$	23.3931			1.77343
$175$	10.4921	−	21.5478i	0.793127	−	1.62886i
$176$	−1.36333	−	2.36136i	−0.102765	−	0.177994i
$177$	29.4550			2.21397
$178$	−3.24928	−	1.87597i	−0.243544	−	0.140610i
$179$		−	8.01227i		−	0.598866i	−0.954117	−	0.299433i	$-0.903203\pi$
$179$		−	8.01227i		−	0.598866i	0.954117	−	0.299433i	$-0.0967974\pi$
$180$	−7.89587	+	8.47286i	−0.588524	+	0.631529i
$181$	−12.3988	+	21.4754i	−0.921599	+	1.59626i	−0.124656	+	0.992200i	$0.539783\pi$
$181$	−12.3988	+	21.4754i	−0.921599	+	1.59626i	−0.796942	+	0.604055i	$0.793551\pi$
$182$	−5.05516	−	2.91860i	−0.374713	−	0.216341i
$183$	8.99831	+	15.5855i	0.665174	+	1.15212i
$184$	−7.02428			−0.517837
$185$	−2.85560	+	13.2983i	−0.209948	+	0.977713i
$186$	−4.37800			−0.321010
$187$	0.617314	+	1.06922i	0.0451425	+	0.0781891i
$188$	−2.48872	−	1.43686i	−0.181508	−	0.104794i
$189$	14.9388	−	25.8748i	1.08664	−	1.88211i
$190$	−12.2249	−	11.3924i	−0.886889	−	0.826493i
$191$			6.28982i			0.455116i	0.973765	+	0.227558i	$0.0730741\pi$
$191$			6.28982i			0.455116i	−0.973765	+	0.227558i	$0.926926\pi$
$192$	−2.47681	−	1.42999i	−0.178748	−	0.103200i
$193$	−14.8233			−1.06701			−0.533503	−	0.845798i	$-0.679125\pi$
$193$	−14.8233			−1.06701			−0.533503	+	0.845798i	$0.679125\pi$
$194$	7.89514	+	13.6748i	0.566838	+	0.981793i
$195$	−1.74939	+	7.58881i	−0.125277	+	0.543446i
$196$	−15.9757			−1.14112
$197$	16.3592	−	9.44497i	1.16554	−	0.672926i	0.212916	−	0.977070i	$-0.431704\pi$
$197$	16.3592	−	9.44497i	1.16554	−	0.672926i	0.952626	+	0.304145i	$0.0983706\pi$
$198$	7.06132	−	12.2306i	0.501826	−	0.869189i
$199$			17.7101i			1.25544i	0.778441	+	0.627718i	$0.216011\pi$
$199$			17.7101i			1.25544i	−0.778441	+	0.627718i	$0.783989\pi$
$200$	−0.352054	−	4.98759i	−0.0248940	−	0.352676i
$201$	−0.0402825	−	0.0697713i	−0.00284131	−	0.00492129i
$202$	3.14872	+	5.45375i	0.221543	+	0.383724i
$203$	19.6033	−	33.9539i	1.37588	−	2.38310i
$204$	1.12150	+	0.647496i	0.0785204	+	0.0453338i
$205$	−3.14886	−	10.2874i	−0.219926	−	0.718502i
$206$	4.26344	+	7.38450i	0.297048	+	0.514502i
$207$	−18.1910	−	31.5077i	−1.26436	−	2.18994i
$208$	−1.21778			−0.0844380
$209$	17.6467	+	10.1883i	1.22065	+	0.704740i
$210$	8.97186	+	29.3113i	0.619117	+	2.02267i
$211$	−8.54618			−0.588344			−0.294172	−	0.955753i	$-0.595044\pi$
$211$	−8.54618			−0.588344			−0.294172	+	0.955753i	$0.595044\pi$
$212$			6.85298i			0.470664i
$213$	0.501555	−	0.289573i	0.0343660	−	0.0198412i
$214$		−	6.61753i		−	0.452365i
$215$	11.6228	−	12.4721i	0.792667	−	0.850591i
$216$		−	6.23321i		−	0.424116i
$217$	−3.66874	+	6.35445i	−0.249051	+	0.431368i
$218$	−12.9732	−	7.49007i	−0.878654	−	0.507291i
$219$	1.69864	−	2.94214i	0.114784	−	0.198811i
$220$	1.78450	+	5.83001i	0.120311	+	0.393059i
$221$	0.551410			0.0370918
$222$	−8.92392	−	14.9333i	−0.598934	−	1.00226i
$223$		−	23.2869i		−	1.55940i	−0.626150	−	0.779702i	$-0.715370\pi$
$223$		−	23.2869i		−	1.55940i	0.626150	−	0.779702i	$-0.284630\pi$
$224$	−4.15112	+	2.39665i	−0.277358	+	0.160133i
$225$	21.4603	−	14.4957i	1.43069	−	0.966378i
$226$	−0.726663	+	1.25862i	−0.0483369	+	0.0837220i
$227$	−1.50747	+	2.61101i	−0.100054	+	0.173299i	−0.911707	−	0.410842i	$-0.865235\pi$
$227$	−1.50747	+	2.61101i	−0.100054	+	0.173299i	0.811653	+	0.584140i	$0.198568\pi$
$228$	21.3729			1.41545
$229$	−0.804843	+	1.39403i	−0.0531855	+	0.0921201i	−0.891392	−	0.453232i	$-0.850271\pi$
$229$	−0.804843	+	1.39403i	−0.0531855	+	0.0921201i	0.838207	+	0.545352i	$0.183604\pi$
$230$	15.3054	+	3.52823i	1.00921	+	0.232645i
$231$	−18.6895	−	32.3712i	−1.22968	−	2.12987i
$232$		−	8.17947i		−	0.537009i
$233$			19.5213i			1.27888i	0.768839	+	0.639442i	$0.220835\pi$
$233$			19.5213i			1.27888i	−0.768839	+	0.639442i	$0.779165\pi$
$234$	−3.15373	−	5.46242i	−0.206166	−	0.357090i
$235$	4.70100	+	4.38087i	0.306659	+	0.285776i
$236$		−	10.2990i		−	0.670410i
$237$	14.7188	+	25.4937i	0.956087	+	1.65599i
$238$	1.87962	−	1.08520i	0.121838	−	0.0703429i
$239$	−5.67805	+	3.27822i	−0.367282	+	0.212051i	−0.672271	−	0.740306i	$-0.734681\pi$
$239$	−5.67805	+	3.27822i	−0.367282	+	0.212051i	0.304988	+	0.952356i	$0.401347\pi$
$240$	4.67851	+	4.35991i	0.301997	+	0.281431i
$241$	8.41117	+	4.85619i	0.541811	+	0.312815i	0.745813	−	0.666156i	$-0.232061\pi$
$241$	8.41117	+	4.85619i	0.541811	+	0.312815i	−0.204002	+	0.978971i	$0.565395\pi$
$242$	1.78265	+	3.08765i	0.114593	+	0.198481i
$243$	−10.5263	+	6.07737i	−0.675264	+	0.389864i
$244$	5.44953	−	3.14629i	0.348870	−	0.201420i
$245$	34.8098	+	8.02445i	2.22392	+	0.512663i
$246$	11.9168	+	6.88018i	0.759788	+	0.438664i
$247$	7.88136	−	4.55030i	0.501479	−	0.289529i
$248$			1.53078i			0.0972047i
$249$	−19.1089			−1.21098
$250$	−1.73812	+	11.0444i	−0.109929	+	0.698510i
$251$		−	17.8028i		−	1.12371i	−0.827237	−	0.561853i	$-0.810089\pi$
$251$		−	17.8028i		−	1.12371i	0.827237	−	0.561853i	$-0.189911\pi$
$252$	−21.5006	−	12.4133i	−1.35441	−	0.781967i
$253$	−19.1528			−1.20413
$254$	−11.5987	−	6.69650i	−0.727766	−	0.420176i
$255$	−2.11842	−	1.97416i	−0.132661	−	0.123627i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.3090	+	17.8557i	0.643058	+	1.11381i	0.984746	+	0.173996i	$0.0556680\pi$
$257$	10.3090	+	17.8557i	0.643058	+	1.11381i	−0.341688	+	0.939813i	$0.610999\pi$
$258$			21.8050i			1.35752i
$259$	−29.1532	+	0.438590i	−1.81149	+	0.0272527i
$260$	2.65345	+	0.611681i	0.164560	+	0.0379349i
$261$	36.6894	−	21.1826i	2.27102	−	1.31117i
$262$	5.49133	+	3.17042i	0.339255	+	0.195869i
$263$	−24.0090	−	13.8616i	−1.48046	−	0.854743i	−0.480704	−	0.876883i	$-0.659619\pi$
$263$	−24.0090	−	13.8616i	−1.48046	−	0.854743i	−0.999755	+	0.0221398i	$0.992952\pi$
$264$	−6.75343	−	3.89910i	−0.415645	−	0.239973i
$265$	3.44219	−	14.9321i	0.211452	−	0.917272i
$266$	17.9104	−	31.0217i	1.09816	−	1.90206i
$267$	−10.7305			−0.656694
$268$	−0.0243958	+	0.0140849i	−0.00149021	+	0.000860372i
$269$	−15.7739			−0.961749			−0.480875	−	0.876789i	$-0.659681\pi$
$269$	−15.7739			−0.961749			−0.480875	+	0.876789i	$0.659681\pi$
$270$	−3.13089	+	13.5817i	−0.190540	+	0.826555i
$271$	12.0183	+	20.8164i	0.730063	+	1.26451i	0.956856	+	0.290563i	$0.0938424\pi$
$271$	12.0183	+	20.8164i	0.730063	+	1.26451i	−0.226793	+	0.973943i	$0.572824\pi$
$272$	0.226399	−	0.392135i	0.0137275	−	0.0237767i
$273$	−16.6942			−1.01038
$274$	8.15662	−	4.70923i	0.492759	−	0.284495i
$275$	−0.959934	−	13.5995i	−0.0578862	−	0.820080i
$276$	−17.3978	+	10.0446i	−1.04723	+	0.604616i
$277$	−8.49982	+	14.7221i	−0.510705	+	0.884567i	0.489218	+	0.872161i	$0.337282\pi$
$277$	−8.49982	+	14.7221i	−0.510705	+	0.884567i	−0.999923	+	0.0124054i	$0.996051\pi$
$278$	−4.32653	+	7.49376i	−0.259488	+	0.449446i
$279$	−6.86639	+	3.96431i	−0.411080	+	0.237337i
$280$	10.2488	−	3.13704i	0.612482	−	0.187474i
$281$	16.1845	−	9.34413i	0.965486	−	0.557424i	0.0676291	−	0.997711i	$-0.478457\pi$
$281$	16.1845	−	9.34413i	0.965486	−	0.557424i	0.897857	+	0.440287i	$0.145123\pi$
$282$	−8.21877			−0.489421
$283$	−0.220942	+	0.382682i	−0.0131336	+	0.0227481i	−0.872518	−	0.488583i	$-0.837514\pi$
$283$	−0.220942	+	0.382682i	−0.0131336	+	0.0227481i	0.859384	+	0.511331i	$0.170847\pi$
$284$	−0.101250	−	0.175370i	−0.00600809	−	0.0104063i
$285$	−46.5699	−	10.7354i	−2.75856	−	0.635911i
$286$	−3.32048			−0.196344
$287$	19.9725	−	11.5311i	1.17894	−	0.680661i
$288$	−5.17946			−0.305203
$289$	8.39749	−	14.5449i	0.493970	−	0.855581i
$290$	−4.10848	+	17.8224i	−0.241258	+	1.04657i
$291$	39.1096	+	22.5799i	2.29264	+	1.32366i
$292$	−1.02873	−	0.593937i	−0.0602018	−	0.0347575i
$293$	−4.12530	−	2.38174i	−0.241003	−	0.139143i	0.374635	−	0.927172i	$-0.377768\pi$
$293$	−4.12530	−	2.38174i	−0.241003	−	0.139143i	−0.615637	+	0.788030i	$0.711101\pi$
$294$	−39.5688	+	22.8450i	−2.30770	+	1.33235i
$295$	−5.17311	+	22.4408i	−0.301190	+	1.30655i
$296$	−5.22148	+	3.12028i	−0.303492	+	0.181363i
$297$		−	16.9959i		−	0.986200i
$298$	−2.15001	−	3.72393i	−0.124547	−	0.215722i
$299$	−4.27702	+	7.40802i	−0.247347	+	0.428417i
$300$	−8.00417	−	11.8499i	−0.462121	−	0.684154i
$301$	31.6490	+	18.2725i	1.82422	+	1.05321i
$302$	0.930651			0.0535529
$303$	15.5976	+	9.00527i	0.896058	+	0.517339i
$304$		−	7.47310i		−	0.428612i
$305$	−13.4545	+	4.11827i	−0.770400	+	0.235811i
$306$	2.34525			0.134069
$307$		−	2.96816i		−	0.169402i	−0.996406	−	0.0847009i	$-0.973007\pi$
$307$		−	2.96816i		−	0.169402i	0.996406	−	0.0847009i	$-0.0269935\pi$
$308$	−11.3187	+	6.53485i	−0.644943	+	0.372358i
$309$	21.1195	+	12.1933i	1.20145	+	0.693655i
$310$	0.768898	−	3.33545i	0.0436704	−	0.189441i
$311$	−21.7036	+	12.5306i	−1.23070	+	0.710544i	−0.967176	−	0.254109i	$-0.918218\pi$
$311$	−21.7036	+	12.5306i	−1.23070	+	0.710544i	−0.263523	+	0.964653i	$0.584884\pi$
$312$	−3.01622	+	1.74141i	−0.170760	+	0.0985882i
$313$	−8.91834	−	15.4470i	−0.504095	−	0.873117i	−0.999989	−	0.00473445i	$-0.998493\pi$
$313$	−8.91834	−	15.4470i	−0.504095	−	0.873117i	0.495894	−	0.868383i	$-0.334840\pi$
$314$	0.603380	+	0.348361i	0.0340507	+	0.0196592i
$315$	40.6129	+	37.8473i	2.28828	+	2.13245i
$316$	8.91394	−	5.14647i	0.501449	−	0.289511i
$317$	3.90982	−	2.25733i	0.219597	−	0.126785i	−0.386167	−	0.922429i	$-0.626201\pi$
$317$	3.90982	−	2.25733i	0.219597	−	0.126785i	0.605764	+	0.795645i	$0.292868\pi$
$318$	9.79967	+	16.9735i	0.549538	+	0.951829i
$319$		−	22.3027i		−	1.24871i
$320$	1.52446	−	1.63586i	0.0852198	−	0.0914472i
$321$	−9.46299	−	16.3904i	−0.528173	−	0.914822i
$322$			33.6695i			1.87633i
$323$			3.38381i			0.188280i
$324$	−1.14422	−	1.98185i	−0.0635677	−	0.110103i
$325$	−5.47443	−	2.66561i	−0.303667	−	0.147862i
$326$	4.94299	−	8.56151i	0.273767	−	0.474178i
$327$	−42.8428			−2.36921
$328$	2.40568	−	4.16675i	0.132831	−	0.230070i
$329$	−6.88730	+	11.9292i	−0.379709	+	0.657676i
$330$	12.7567	+	11.8880i	0.702235	+	0.654414i
$331$	−19.8565	+	11.4642i	−1.09141	+	0.630127i	−0.933952	−	0.357399i	$-0.883664\pi$
$331$	−19.8565	+	11.4642i	−1.09141	+	0.630127i	−0.157460	+	0.987525i	$0.550330\pi$
$332$			6.68148i			0.366694i
$333$	−27.5184	−	15.3405i	−1.50800	−	0.840654i
$334$	14.0301			0.767692
$335$	0.0602312	−	0.0184361i	0.00329078	−	0.00100727i
$336$	−6.85436	+	11.8721i	−0.373936	+	0.647676i
$337$	9.93107	+	5.73371i	0.540980	+	0.312335i	0.745476	−	0.666532i	$-0.232222\pi$
$337$	9.93107	+	5.73371i	0.540980	+	0.312335i	−0.204496	+	0.978867i	$0.565556\pi$
$338$	5.75850	−	9.97402i	0.313221	−	0.542515i
$339$			4.15648i			0.225749i
$340$	−0.690272	+	0.740713i	−0.0374353	+	0.0401708i
$341$			4.17392i			0.226031i
$342$	33.5209	−	19.3533i	1.81260	−	1.04651i
$343$			43.0232i			2.32303i
$344$	7.62420			0.411070
$345$	42.9538	−	13.1477i	2.31256	−	0.707849i
$346$	−3.44700	−	1.99013i	−0.185312	−	0.106990i
$347$	−11.3700			−0.610373			−0.305187	−	0.952293i	$-0.598719\pi$
$347$	−11.3700			−0.610373			−0.305187	+	0.952293i	$0.598719\pi$
$348$	−11.6965	−	20.2590i	−0.627001	−	1.08600i
$349$	2.53073	+	4.38336i	0.135467	+	0.234636i	0.925776	−	0.378073i	$-0.123413\pi$
$349$	2.53073	+	4.38336i	0.135467	+	0.234636i	−0.790309	+	0.612709i	$0.790080\pi$
$350$	−23.9070	+	1.68750i	−1.27788	+	0.0902007i
$351$	−6.57373	−	3.79535i	−0.350880	−	0.202581i
$352$	−1.36333	+	2.36136i	−0.0726658	+	0.125861i
$353$	10.0780	+	17.4557i	0.536400	+	0.929072i	0.999094	+	0.0425542i	$0.0135495\pi$
$353$	10.0780	+	17.4557i	0.536400	+	0.929072i	−0.462694	+	0.886518i	$0.653117\pi$
$354$	−14.7275	−	25.5088i	−0.782758	−	1.35578i
$355$	0.132529	+	0.432976i	0.00703392	+	0.0229800i
$356$			3.75194i			0.198853i
$357$	3.10364	−	5.37566i	0.164262	−	0.284510i
$358$	−6.93883	+	4.00614i	−0.366729	+	0.211731i
$359$	−4.76781			−0.251635			−0.125818	−	0.992053i	$-0.540155\pi$
$359$	−4.76781			−0.251635			−0.125818	+	0.992053i	$0.540155\pi$
$360$	11.2856	+	2.60160i	0.594806	+	0.137116i
$361$	18.4236	+	31.9106i	0.969663	+	1.67951i
$362$	24.7977			1.30334
$363$	8.83059	+	5.09834i	0.463486	+	0.267594i
$364$			5.83719i			0.305952i
$365$	1.94319	+	1.81086i	0.101711	+	0.0947849i
$366$	8.99831	−	15.5855i	0.470349	−	0.814668i
$367$	19.0638	+	11.0065i	0.995123	+	0.574535i	0.906802	−	0.421557i	$-0.138516\pi$
$367$	19.0638	+	11.0065i	0.995123	+	0.574535i	0.0883215	+	0.996092i	$0.471850\pi$
$368$	3.51214	+	6.08320i	0.183083	+	0.317109i
$369$	24.9202			1.29729
$370$	12.9445	−	4.17614i	0.672952	−	0.217107i
$371$	32.8484			1.70540
$372$	2.18900	+	3.79146i	0.113494	+	0.196578i
$373$	0.696232	+	0.401970i	0.0360495	+	0.0208132i	0.517916	−	0.855431i	$-0.326708\pi$
$373$	0.696232	+	0.401970i	0.0360495	+	0.0208132i	−0.481867	+	0.876244i	$0.660041\pi$
$374$	0.617314	−	1.06922i	0.0319206	−	0.0552880i
$375$	11.4884	+	29.8404i	0.593257	+	1.54095i
$376$			2.87372i			0.148201i
$377$	−8.62632	−	4.98041i	−0.444278	−	0.256504i
$378$	−29.8776			−1.53674
$379$	0.189378	+	0.328013i	0.00972771	+	0.0168489i	0.870848	−	0.491552i	$-0.163570\pi$
$379$	0.189378	+	0.328013i	0.00972771	+	0.0168489i	−0.861121	+	0.508401i	$0.830237\pi$
$380$	−3.75367	+	16.2833i	−0.192559	+	0.835316i
$381$	−38.3037			−1.96236
$382$	5.44715	−	3.14491i	0.278700	−	0.160908i
$383$	−0.359573	+	0.622798i	−0.0183733	+	0.0318235i	−0.875066	−	0.484004i	$-0.839182\pi$
$383$	−0.359573	+	0.622798i	−0.0183733	+	0.0318235i	0.856693	+	0.515827i	$0.172515\pi$
$384$			2.85998i			0.145948i
$385$	27.9450	−	8.55366i	1.42421	−	0.435935i
$386$	7.41166	+	12.8374i	0.377243	+	0.653405i
$387$	19.7446	+	34.1987i	1.00368	+	1.73842i
$388$	7.89514	−	13.6748i	0.400815	−	0.694232i
$389$	−11.8245	−	6.82689i	−0.599527	−	0.346137i	0.169328	−	0.985560i	$-0.445840\pi$
$389$	−11.8245	−	6.82689i	−0.599527	−	0.346137i	−0.768855	+	0.639423i	$0.779173\pi$
$390$	7.44680	−	2.27939i	0.377084	−	0.115421i
$391$	−1.59029	−	2.75446i	−0.0804244	−	0.139299i
$392$	7.98785	+	13.8354i	0.403447	+	0.698791i
$393$	18.1346			0.914772
$394$	−16.3592	−	9.44497i	−0.824163	−	0.475831i
$395$	−22.0078	+	6.73636i	−1.10733	+	0.338943i
$396$	−14.1226			−0.709690
$397$			15.3780i			0.771802i	0.922540	+	0.385901i	$0.126109\pi$
$397$			15.3780i			0.771802i	−0.922540	+	0.385901i	$0.873891\pi$
$398$	15.3374	−	8.85505i	0.768794	−	0.443863i
$399$		−	102.447i		−	5.12874i
$400$	−4.14335	+	2.79868i	−0.207168	+	0.139934i
$401$			30.7247i			1.53432i	0.641457	+	0.767159i	$0.278330\pi$
$401$			30.7247i			1.53432i	−0.641457	+	0.767159i	$0.721670\pi$
$402$	−0.0402825	+	0.0697713i	−0.00200911	+	0.00347988i
$403$	1.61441	+	0.932079i	0.0804194	+	0.0464302i
$404$	3.14872	−	5.45375i	0.156655	−	0.271334i
$405$	1.49770	+	4.89302i	0.0744214	+	0.243136i
$406$	−39.2066			−1.94579
$407$	−14.2372	+	8.50795i	−0.705713	+	0.421723i
$408$		−	1.29499i		−	0.0641117i
$409$	−7.04079	+	4.06500i	−0.348144	+	0.201001i	−0.663868	−	0.747850i	$-0.731086\pi$
$409$	−7.04079	+	4.06500i	−0.348144	+	0.201001i	0.315723	+	0.948851i	$0.397753\pi$
$410$	−7.33471	+	7.87068i	−0.362235	+	0.388705i
$411$	13.4683	−	23.3277i	0.664341	−	1.15067i
$412$	4.26344	−	7.38450i	0.210045	−	0.363808i
$413$	−49.3663			−2.42916
$414$	−18.1910	+	31.5077i	−0.894038	+	1.54852i
$415$	3.35605	−	14.5584i	0.164742	−	0.714645i
$416$	0.608891	+	1.05463i	0.0298534	+	0.0517075i
$417$			24.7475i			1.21189i
$418$		−	20.3766i		−	0.996653i
$419$	−5.36246	−	9.28806i	−0.261973	−	0.453751i	0.704793	−	0.709413i	$-0.251040\pi$
$419$	−5.36246	−	9.28806i	−0.261973	−	0.453751i	−0.966766	+	0.255662i	$0.917707\pi$
$420$	20.8984	−	22.4255i	1.01974	−	1.09425i
$421$		−	35.7769i		−	1.74366i	−0.489809	−	0.871830i	$-0.662934\pi$
$421$		−	35.7769i		−	1.74366i	0.489809	−	0.871830i	$-0.337066\pi$
$422$	4.27309	+	7.40121i	0.208011	+	0.360285i
$423$	−12.8902	+	7.44216i	−0.626743	+	0.361850i
$424$	5.93485	−	3.42649i	0.288222	−	0.166405i
$425$	1.87610	−	1.26724i	0.0910043	−	0.0614701i
$426$	−0.501555	−	0.289573i	−0.0243004	−	0.0140299i
$427$	−15.0811	−	26.1212i	−0.729825	−	1.26409i
$428$	−5.73095	+	3.30877i	−0.277016	+	0.159935i
$429$	−8.22421	+	4.74825i	−0.397069	+	0.229248i
$430$	−16.6126	−	3.82957i	−0.801128	−	0.184678i
$431$	−2.13125	−	1.23048i	−0.102659	−	0.0592700i	0.447792	−	0.894138i	$-0.352211\pi$
$431$	−2.13125	−	1.23048i	−0.102659	−	0.0592700i	−0.550450	+	0.834868i	$0.685544\pi$
$432$	−5.39812	+	3.11660i	−0.259717	+	0.149948i
$433$		−	31.2629i		−	1.50240i	−0.660075	−	0.751200i	$-0.729475\pi$
$433$		−	31.2629i		−	1.50240i	0.660075	−	0.751200i	$-0.270525\pi$
$434$	7.33749			0.352211
$435$	15.3099	+	50.0179i	0.734056	+	2.39817i
$436$			14.9801i			0.717418i
$437$	−45.4604	−	26.2466i	−2.17467	−	1.25554i
$438$	−3.39729			−0.162329
$439$	19.8174	+	11.4416i	0.945835	+	0.546078i	0.891785	−	0.452460i	$-0.149453\pi$
$439$	19.8174	+	11.4416i	0.945835	+	0.546078i	0.0540505	+	0.998538i	$0.482787\pi$
$440$	4.15668	−	4.46043i	0.198162	−	0.212643i
$441$	−41.3727	+	71.6597i	−1.97013	+	3.41237i
$442$	−0.275705	−	0.477535i	−0.0131139	−	0.0227140i
$443$			1.49918i			0.0712281i	0.999366	+	0.0356141i	$0.0113387\pi$
$443$			1.49918i			0.0712281i	−0.999366	+	0.0356141i	$0.988661\pi$
$444$	−8.47066	+	15.1950i	−0.402000	+	0.721123i
$445$	1.88457	−	8.17520i	0.0893371	−	0.387541i
$446$	−20.1670	+	11.6434i	−0.954936	+	0.551333i
$447$	−10.6504	−	6.14898i	−0.503744	−	0.290837i
$448$	4.15112	+	2.39665i	0.196122	+	0.113231i
$449$	−22.7095	−	13.1113i	−1.07173	−	0.618761i	−0.143074	−	0.989712i	$-0.545699\pi$
$449$	−22.7095	−	13.1113i	−1.07173	−	0.618761i	−0.928653	+	0.370951i	$0.879032\pi$
$450$	−23.2838	−	11.3374i	−1.09761	−	0.534448i
$451$	6.55947	−	11.3613i	0.308873	−	0.534984i
$452$	1.45333			0.0683588
$453$	2.30505	−	1.33082i	0.108301	−	0.0625274i
$454$	3.01493			0.141498
$455$	2.93197	−	12.7188i	0.137453	−	0.596266i
$456$	−10.6864	−	18.5095i	−0.500438	−	0.866785i
$457$	16.2116	−	28.0793i	0.758346	−	1.31349i	−0.185347	−	0.982673i	$-0.559341\pi$
$457$	16.2116	−	28.0793i	0.758346	−	1.31349i	0.943693	−	0.330821i	$-0.107326\pi$
$458$	1.60969			0.0752157
$459$	2.44426	−	1.41119i	0.114088	−	0.0658688i
$460$	−4.59714	−	15.0189i	−0.214343	−	0.700262i
$461$	6.96252	−	4.01982i	0.324277	−	0.187221i	−0.329020	−	0.944323i	$-0.606718\pi$
$461$	6.96252	−	4.01982i	0.324277	−	0.187221i	0.653297	+	0.757101i	$0.273385\pi$
$462$	−18.6895	+	32.3712i	−0.869515	+	1.50604i
$463$	8.11837	−	14.0614i	0.377293	−	0.653490i	−0.613375	−	0.789792i	$-0.710188\pi$
$463$	8.11837	−	14.0614i	0.377293	−	0.653490i	0.990667	+	0.136302i	$0.0435218\pi$
$464$	−7.08363	+	4.08974i	−0.328849	+	0.189861i
$465$	−2.86524	−	9.36080i	−0.132872	−	0.434097i
$466$	16.9060	−	9.76067i	0.783154	−	0.452154i
$467$	−3.44377			−0.159358			−0.0796792	−	0.996821i	$-0.525390\pi$
$467$	−3.44377			−0.159358			−0.0796792	+	0.996821i	$0.525390\pi$
$468$	−3.15373	+	5.46242i	−0.145781	+	0.252500i
$469$	0.0675131	+	0.116936i	0.00311747	+	0.00539961i
$470$	1.44344	−	6.26162i	0.0665811	−	0.288827i
$471$	1.99261			0.0918147
$472$	−8.91923	+	5.14952i	−0.410541	+	0.237026i
$473$	20.7886			0.955863
$474$	14.7188	−	25.4937i	0.676056	−	1.17096i
$475$	16.3579	−	33.5946i	0.750553	−	1.54143i
$476$	−1.87962	−	1.08520i	−0.0861522	−	0.0497400i
$477$	30.7393	+	17.7474i	1.40746	+	0.812596i
$478$	5.67805	+	3.27822i	0.259708	+	0.149942i
$479$	5.67506	−	3.27650i	0.259300	−	0.149707i	−0.364715	−	0.931119i	$-0.618834\pi$
$479$	5.67506	−	3.27650i	0.259300	−	0.149707i	0.624015	+	0.781412i	$0.285500\pi$
$480$	1.43654	−	6.23167i	0.0655688	−	0.284435i
$481$	0.111428	+	7.40664i	0.00508068	+	0.337714i
$482$		−	9.71238i		−	0.442387i
$483$	48.1469	+	83.3929i	2.19076	+	3.79451i
$484$	1.78265	−	3.08765i	0.0810297	−	0.140348i
$485$	−24.0716	+	25.8306i	−1.09304	+	1.17291i
$486$	10.5263	+	6.07737i	0.477483	+	0.275675i
$487$	4.97590			0.225479			0.112740	−	0.993625i	$-0.464037\pi$
$487$	4.97590			0.225479			0.112740	+	0.993625i	$0.464037\pi$
$488$	−5.44953	−	3.14629i	−0.246689	−	0.142426i
$489$		−	28.2736i		−	1.27858i
$490$	−10.4555	−	34.1584i	−0.472332	−	1.54312i
$491$	−13.1607			−0.593934			−0.296967	−	0.954888i	$-0.595975\pi$
$491$	−13.1607			−0.593934			−0.296967	+	0.954888i	$0.595975\pi$
$492$		−	13.7604i		−	0.620365i
$493$	3.20745	−	1.85182i	0.144456	−	0.0834020i
$494$	−7.88136	−	4.55030i	−0.354599	−	0.204728i
$495$	30.7722	+	7.09368i	1.38311	+	0.318837i
$496$	1.32569	−	0.765390i	0.0595255	−	0.0343670i
$497$	−0.840602	+	0.485322i	−0.0377062	+	0.0217697i
$498$	9.55443	+	16.5488i	0.428144	+	0.741568i
$499$	−11.2307	−	6.48407i	−0.502757	−	0.290267i	0.227094	−	0.973873i	$-0.427077\pi$
$499$	−11.2307	−	6.48407i	−0.502757	−	0.290267i	−0.729851	+	0.683606i	$0.760411\pi$
$500$	10.4338	−	4.01694i	0.466614	−	0.179643i
$501$	34.7499	−	20.0629i	1.55251	−	0.896342i
$502$	−15.4177	+	8.90142i	−0.688127	+	0.397290i
$503$	−21.2832	−	36.8636i	−0.948971	−	1.64367i	−0.747598	−	0.664151i	$-0.768793\pi$
$503$	−21.2832	−	36.8636i	−0.948971	−	1.64367i	−0.201372	−	0.979515i	$-0.564540\pi$
$504$			24.8267i			1.10587i
$505$	−9.60019	+	10.3017i	−0.427203	+	0.458420i
$506$	9.57642	+	16.5869i	0.425724	+	0.737375i
$507$		−	32.9384i		−	1.46284i
$508$			13.3930i			0.594218i
$509$	−8.09471	−	14.0204i	−0.358791	−	0.621445i	0.628968	−	0.777431i	$-0.283478\pi$
$509$	−8.09471	−	14.0204i	−0.358791	−	0.621445i	−0.987759	+	0.155986i	$0.950144\pi$
$510$	−0.650463	+	2.82169i	−0.0288030	+	0.124946i
$511$	−2.84691	+	4.93100i	−0.125940	+	0.218135i
$512$	1.00000			0.0441942
$513$	23.2907	−	40.3407i	1.02831	−	1.78108i
$514$	10.3090	−	17.8557i	0.454711	−	0.787582i
$515$	−12.9989	+	13.9488i	−0.572799	+	0.614656i
$516$	18.8837	−	10.9025i	0.831309	−	0.479957i
$517$			7.83567i			0.344612i
$518$	14.9564	+	25.0281i	0.657148	+	1.09967i
$519$	−11.3834			−0.499677
$520$	−0.796995	−	2.60380i	−0.0349506	−	0.114184i
$521$	0.175072	−	0.303234i	0.00767006	−	0.0132849i	−0.862165	−	0.506628i	$-0.830892\pi$
$521$	0.175072	−	0.303234i	0.00767006	−	0.0132849i	0.869835	+	0.493343i	$0.164225\pi$
$522$	−36.6894	−	21.1826i	−1.60585	−	0.927138i
$523$	7.81043	−	13.5281i	0.341526	−	0.591541i	−0.643190	−	0.765706i	$-0.722390\pi$
$523$	7.81043	−	13.5281i	0.341526	−	0.591541i	0.984716	+	0.174166i	$0.0557229\pi$
$524$		−	6.34084i		−	0.277001i
$525$	−56.8000	+	38.3663i	−2.47896	+	1.67444i
$526$			27.7232i			1.20879i
$527$	−0.600272	+	0.346567i	−0.0261483	+	0.0150967i
$528$			7.79819i			0.339373i
$529$	26.3405			1.14524
$530$	−14.6527	+	4.48503i	−0.636472	+	0.194817i
$531$	−46.1968	−	26.6717i	−2.00477	−	1.15745i
$532$	−35.8208			−1.55303
$533$	−2.92959	−	5.07420i	−0.126895	−	0.219788i
$534$	5.36524	+	9.29286i	0.232176	+	0.402141i
$535$	14.1493	−	4.33094i	0.611726	−	0.187243i
$536$	0.0243958	+	0.0140849i	0.00105374	+	0.000608375i
$537$	−11.4575	+	19.8449i	−0.494426	+	0.856370i
$538$	7.88693	+	13.6606i	0.340030	+	0.588949i
$539$	21.7802	+	37.7244i	0.938138	+	1.62490i
$540$	13.3275	−	4.07941i	0.573525	−	0.175550i
$541$		−	20.4656i		−	0.879886i	−0.898026	−	0.439943i	$-0.854999\pi$
$541$		−	20.4656i		−	0.879886i	0.898026	−	0.439943i	$-0.145001\pi$
$542$	12.0183	−	20.8164i	0.516232	−	0.894140i
$543$	61.4192	−	35.4604i	2.63575	−	1.52175i
$544$	−0.452798			−0.0194136
$545$	7.52439	−	32.6406i	0.322309	−	1.39817i
$546$	8.34712	+	14.4576i	0.357224	+	0.618729i
$547$	−2.51196			−0.107404			−0.0537018	−	0.998557i	$-0.517102\pi$
$547$	−2.51196			−0.107404			−0.0537018	+	0.998557i	$0.517102\pi$
$548$	−8.15662	−	4.70923i	−0.348434	−	0.201168i
$549$		−	32.5922i		−	1.39100i
$550$	−11.2975	+	7.63107i	−0.481728	+	0.325390i
$551$	30.5630	−	52.9367i	1.30203	−	2.25518i
$552$	17.3978	+	10.0446i	0.740500	+	0.427528i
$553$	−24.6685	−	42.7272i	−1.04901	−	1.81694i
$554$	16.9996			0.722246
$555$	26.0892	−	28.8540i	1.10743	−	1.22478i
$556$	8.65305			0.366971
$557$	−12.6417	−	21.8961i	−0.535646	−	0.927766i	−0.999132	−	0.0416616i	$-0.986735\pi$
$557$	−12.6417	−	21.8961i	−0.535646	−	0.927766i	0.463486	−	0.886104i	$-0.346598\pi$
$558$	6.86639	+	3.96431i	0.290677	+	0.167823i
$559$	4.64231	−	8.04072i	0.196349	−	0.340086i
$560$	−7.84115	−	7.30718i	−0.331349	−	0.308785i
$561$		−	3.53101i		−	0.149079i
$562$	−16.1845	−	9.34413i	−0.682702	−	0.394158i
$563$	7.66929			0.323222			0.161611	−	0.986855i	$-0.448331\pi$
$563$	7.66929			0.323222			0.161611	+	0.986855i	$0.448331\pi$
$564$	4.10939	+	7.11767i	0.173036	+	0.299708i
$565$	−3.16669	−	0.729993i	−0.133224	−	0.0307110i
$566$	0.441884			0.0185738
$567$	−9.49957	+	5.48458i	−0.398945	+	0.230331i
$568$	−0.101250	+	0.175370i	−0.00424836	+	0.00735838i
$569$		−	14.3157i		−	0.600147i	−0.953916	−	0.300074i	$-0.902989\pi$
$569$		−	14.3157i		−	0.600147i	0.953916	−	0.300074i	$-0.0970113\pi$
$570$	13.9878	+	45.6984i	0.585884	+	1.91409i
$571$	19.3284	+	33.4777i	0.808867	+	1.40100i	0.913649	+	0.406504i	$0.133252\pi$
$571$	19.3284	+	33.4777i	0.808867	+	1.40100i	−0.104782	+	0.994495i	$0.533415\pi$
$572$	1.66024	+	2.87562i	0.0694182	+	0.120236i
$573$	8.99437	−	15.5787i	0.375745	−	0.650810i
$574$	−19.9725	−	11.5311i	−0.833635	−	0.481300i
$575$	2.47293	+	35.0342i	0.103128	+	1.46103i
$576$	2.58973	+	4.48555i	0.107905	+	0.186898i
$577$	11.0994	+	19.2247i	0.462073	+	0.800335i	0.999064	−	0.0432535i	$-0.0137723\pi$
$577$	11.0994	+	19.2247i	0.462073	+	0.800335i	−0.536991	+	0.843588i	$0.680439\pi$
$578$	−16.7950			−0.698579
$579$	36.7146	+	21.1972i	1.52581	+	0.880924i
$580$	17.4889	−	5.35317i	0.726188	−	0.222278i
$581$	32.0263			1.32868
$582$		−	45.1598i		−	1.87194i
$583$	16.1823	−	9.34288i	0.670204	−	0.386943i
$584$			1.18787i			0.0491545i
$585$	9.61546	−	10.3181i	0.397550	−	0.426601i
$586$			4.76349i			0.196778i
$587$	−6.18890	+	10.7195i	−0.255443	+	0.442441i	−0.965016	−	0.262192i	$-0.915555\pi$
$587$	−6.18890	+	10.7195i	−0.255443	+	0.442441i	0.709572	+	0.704632i	$0.248888\pi$
$588$	39.5688	+	22.8450i	1.63179	+	0.942114i
$589$	−5.71984	+	9.90705i	−0.235682	+	0.408213i
$590$	22.0209	−	6.74035i	0.906585	−	0.277496i
$591$	−54.0248			−2.22228
$592$	5.31298	+	2.96180i	0.218362	+	0.121729i
$593$			44.0752i			1.80995i	0.425463	+	0.904976i	$0.360111\pi$
$593$			44.0752i			1.80995i	−0.425463	+	0.904976i	$0.639889\pi$
$594$	−14.7188	+	8.49793i	−0.603922	+	0.348674i
$595$	3.55046	+	3.30868i	0.145555	+	0.135643i
$596$	−2.15001	+	3.72393i	−0.0880679	+	0.152538i
$597$	25.3252	−	43.8646i	1.03649	−	1.79526i
$598$	8.55405			0.349801
$599$	−20.8173	+	36.0565i	−0.850570	+	1.47323i	0.0301245	+	0.999546i	$0.490410\pi$
$599$	−20.8173	+	36.0565i	−0.850570	+	1.47323i	−0.880695	+	0.473685i	$0.842924\pi$
$600$	−6.26022	+	12.8568i	−0.255572	+	0.524875i
$601$	−2.02155	−	3.50143i	−0.0824607	−	0.142826i	0.821846	−	0.569710i	$-0.192945\pi$
$601$	−2.02155	−	3.50143i	−0.0824607	−	0.142826i	−0.904306	+	0.426884i	$0.859611\pi$
$602$		−	36.5451i		−	1.48947i
$603$			0.145904i			0.00594169i
$604$	−0.465325	−	0.805967i	−0.0189338	−	0.0327943i
$605$	−5.43516	+	5.83233i	−0.220971	+	0.237118i
$606$		−	18.0105i		−	0.731628i
$607$	−12.6098	−	21.8408i	−0.511815	−	0.886490i	−0.999906	−	0.0136974i	$-0.995640\pi$
$607$	−12.6098	−	21.8408i	−0.511815	−	0.886490i	0.488091	−	0.872793i	$-0.337693\pi$
$608$	−6.47189	+	3.73655i	−0.262470	+	0.151537i
$609$	−97.1074	+	56.0650i	−3.93499	+	2.27187i
$610$	10.2938	+	9.59277i	0.416782	+	0.388400i
$611$	3.03071	+	1.74978i	0.122610	+	0.0707887i
$612$	−1.17263	−	2.03105i	−0.0474006	−	0.0821002i
$613$	33.6551	−	19.4308i	1.35932	−	0.784802i	0.369785	−	0.929117i	$-0.379431\pi$
$613$	33.6551	−	19.4308i	1.35932	−	0.784802i	0.989532	+	0.144315i	$0.0460978\pi$
$614$	−2.57050	+	1.48408i	−0.103737	+	0.0598926i
$615$	−6.91170	+	29.9827i	−0.278707	+	1.20902i
$616$	11.3187	+	6.53485i	0.456043	+	0.263297i
$617$	−35.5323	+	20.5146i	−1.43048	+	0.825886i	−0.997157	−	0.0753540i	$-0.975991\pi$
$617$	−35.5323	+	20.5146i	−1.43048	+	0.825886i	−0.433320	+	0.901240i	$0.642658\pi$
$618$		−	24.3867i		−	0.980976i
$619$	35.0195			1.40755			0.703775	−	0.710423i	$-0.251496\pi$
$619$	35.0195			1.40755			0.703775	+	0.710423i	$0.251496\pi$
$620$	−3.27304	+	1.00184i	−0.131448	+	0.0402349i
$621$			43.7838i			1.75698i
$622$	21.7036	+	12.5306i	0.870235	+	0.502430i
$623$	17.9842			0.720521
$624$	3.01622	+	1.74141i	0.120745	+	0.0697124i
$625$	−24.7521	+	3.51181i	−0.990085	+	0.140472i
$626$	−8.91834	+	15.4470i	−0.356449	+	0.617387i
$627$	−29.1383	−	50.4691i	−1.16367	−	2.01554i
$628$		−	0.696723i		−	0.0278023i
$629$	−2.40571	−	1.34110i	−0.0959219	−	0.0534730i
$630$	12.4702	−	54.0955i	0.496826	−	2.15521i
$631$	−10.5341	+	6.08185i	−0.419355	+	0.242115i	−0.694801	−	0.719202i	$-0.744508\pi$
$631$	−10.5341	+	6.08185i	−0.419355	+	0.242115i	0.275446	+	0.961316i	$0.411174\pi$
$632$	−8.91394	−	5.14647i	−0.354578	−	0.204715i
$633$	21.1673	+	12.2209i	0.841324	+	0.485739i
$634$	−3.90982	−	2.25733i	−0.155279	−	0.0896502i
$635$	6.72719	−	29.1823i	0.266960	−	1.15806i
$636$	9.79967	−	16.9735i	0.388582	−	0.673044i
$637$	19.4549			0.770832
$638$	−19.3147	+	11.1513i	−0.764675	+	0.441485i
$639$	−1.04884			−0.0414916
$640$	−2.17892	−	0.502291i	−0.0861295	−	0.0198548i
$641$	−5.79442	−	10.0362i	−0.228866	−	0.396407i	0.728606	−	0.684933i	$-0.240168\pi$
$641$	−5.79442	−	10.0362i	−0.228866	−	0.396407i	−0.957472	+	0.288525i	$0.906835\pi$
$642$	−9.46299	+	16.3904i	−0.373475	+	0.646877i
$643$	−41.4828			−1.63592			−0.817962	−	0.575273i	$-0.804896\pi$
$643$	−41.4828			−1.63592			−0.817962	+	0.575273i	$0.804896\pi$
$644$	29.1586	−	16.8347i	1.14901	−	0.663381i
$645$	−46.6224	+	14.2706i	−1.83576	+	0.561905i
$646$	2.93046	−	1.69190i	0.115297	−	0.0665670i
$647$	−15.5065	+	26.8580i	−0.609622	+	1.05590i	0.381681	+	0.924294i	$0.375345\pi$
$647$	−15.5065	+	26.8580i	−0.609622	+	1.05590i	−0.991303	+	0.131602i	$0.957988\pi$
$648$	−1.14422	+	1.98185i	−0.0449492	+	0.0778543i
$649$	−24.3197	+	14.0410i	−0.954633	+	0.551158i
$650$	0.428726	+	6.07380i	0.0168160	+	0.238234i
$651$	18.1736	−	10.4925i	0.712278	−	0.411234i
$652$	−9.88597			−0.387165
$653$	4.23528	−	7.33571i	0.165739	−	0.287069i	−0.771178	−	0.636619i	$-0.780332\pi$
$653$	4.23528	−	7.33571i	0.165739	−	0.287069i	0.936918	+	0.349551i	$0.113666\pi$
$654$	21.4214	+	37.1030i	0.837643	+	1.45084i
$655$	−3.18495	+	13.8162i	−0.124446	+	0.539844i
$656$	−4.81135			−0.187852
$657$	−5.32826	+	3.07627i	−0.207875	+	0.120017i
$658$	13.7746			0.536990
$659$	−6.79380	+	11.7672i	−0.264649	+	0.458385i	−0.967472	−	0.252980i	$-0.918589\pi$
$659$	−6.79380	+	11.7672i	−0.264649	+	0.458385i	0.702823	+	0.711365i	$0.251923\pi$
$660$	3.91696	−	16.9917i	0.152468	−	0.661399i
$661$	21.0739	+	12.1670i	0.819679	+	0.473242i	0.850306	−	0.526289i	$-0.176417\pi$
$661$	21.0739	+	12.1670i	0.819679	+	0.473242i	−0.0306266	+	0.999531i	$0.509750\pi$
$662$	19.8565	+	11.4642i	0.771745	+	0.445567i
$663$	−1.36574	−	0.788509i	−0.0530409	−	0.0306232i
$664$	5.78633	−	3.34074i	0.224553	−	0.129646i
$665$	78.0507	+	17.9925i	3.02668	+	0.697718i
$666$	0.473924	+	31.5019i	0.0183642	+	1.22067i
$667$			57.4549i			2.22466i
$668$	−7.01504	−	12.1504i	−0.271420	−	0.470114i
$669$	−33.3000	+	57.6772i	−1.28745	+	2.22993i
$670$	−0.0460818	−	0.0429437i	−0.00178029	−	0.00165906i
$671$	−14.8590	−	8.57887i	−0.573627	−	0.331184i
$672$	13.7087			0.528825
$673$	39.5674	+	22.8442i	1.52521	+	0.880580i	0.999553	+	0.0298833i	$0.00951356\pi$
$673$	39.5674	+	22.8442i	1.52521	+	0.880580i	0.525656	+	0.850697i	$0.323820\pi$
$674$		−	11.4674i		−	0.441708i
$675$	−31.0887	+	2.19443i	−1.19660	+	0.0844636i
$676$	−11.5170			−0.442962
$677$			34.8450i			1.33920i	0.742722	+	0.669600i	$0.233535\pi$
$677$			34.8450i			1.33920i	−0.742722	+	0.669600i	$0.766465\pi$
$678$	3.59962	−	2.07824i	0.138242	−	0.0798143i
$679$	−65.5473	−	37.8438i	−2.51548	−	1.45231i
$680$	0.986612	+	0.227437i	0.0378349	+	0.00872179i
$681$	7.46742	−	4.31132i	0.286152	−	0.165210i
$682$	3.61472	−	2.08696i	0.138415	−	0.0799139i
$683$	1.96909	+	3.41056i	0.0753450	+	0.130501i	0.901236	−	0.433328i	$-0.142661\pi$
$683$	1.96909	+	3.41056i	0.0753450	+	0.130501i	−0.825891	+	0.563829i	$0.809328\pi$
$684$	−33.5209	−	19.3533i	−1.28170	−	0.739992i
$685$	15.4072	+	14.3580i	0.588680	+	0.548592i
$686$	37.2592	−	21.5116i	1.42256	−	0.821316i
$687$	3.98689	−	2.30183i	0.152109	−	0.0878204i
$688$	−3.81210	−	6.60275i	−0.145335	−	0.251728i
$689$		−	8.34544i		−	0.317936i
$690$	−32.8632	−	30.6253i	−1.25108	−	1.16588i
$691$	4.62702	+	8.01424i	0.176020	+	0.304876i	0.940514	−	0.339755i	$-0.110344\pi$
$691$	4.62702	+	8.01424i	0.176020	+	0.304876i	−0.764494	+	0.644631i	$0.777011\pi$
$692$			3.98026i			0.151307i
$693$			67.6940i			2.57148i
$694$	5.68500	+	9.84670i	0.215800	+	0.373776i
$695$	−18.8543	−	4.34635i	−0.715186	−	0.164867i
$696$	−11.6965	+	20.2590i	−0.443356	+	0.767916i
$697$	2.17857			0.0825193
$698$	2.53073	−	4.38336i	0.0957896	−	0.165913i
$699$	27.9153	−	48.3507i	1.05585	−	1.82879i
$700$	13.4149	+	19.8603i	0.507036	+	0.750650i
$701$	27.8917	−	16.1033i	1.05346	−	0.608213i	0.129841	−	0.991535i	$-0.458553\pi$
$701$	27.8917	−	16.1033i	1.05346	−	0.608213i	0.923615	+	0.383321i	$0.125220\pi$
$702$			7.59069i			0.286492i
$703$	−45.4519	+	0.683794i	−1.71425	+	0.0257898i
$704$	2.72666			0.102765
$705$	−5.37889	−	17.5730i	−0.202581	−	0.661836i
$706$	10.0780	−	17.4557i	0.379292	−	0.656953i
$707$	−26.1414	−	15.0928i	−0.983150	−	0.567622i
$708$	−14.7275	+	25.5088i	−0.553493	+	0.958678i
$709$			2.61309i			0.0981367i	0.998795	+	0.0490683i	$0.0156252\pi$
$709$			2.61309i			0.0981367i	−0.998795	+	0.0490683i	$0.984375\pi$
$710$	0.308703	−	0.331262i	0.0115854	−	0.0124320i
$711$		−	53.3119i		−	1.99935i
$712$	3.24928	−	1.87597i	0.121772	−	0.0703050i
$713$		−	10.7526i		−	0.402689i
$714$	−6.20728			−0.232302
$715$	−2.17314	−	7.09968i	−0.0812708	−	0.265513i
$716$	6.93883	+	4.00614i	0.259316	+	0.149716i
$717$	18.7513			0.700279
$718$	2.38391	+	4.12905i	0.0889666	+	0.154095i
$719$	−5.84379	−	10.1217i	−0.217937	−	0.377477i	0.736240	−	0.676720i	$-0.236599\pi$
$719$	−5.84379	−	10.1217i	−0.217937	−	0.377477i	−0.954177	+	0.299243i	$0.903266\pi$
$720$	−3.38977	−	11.0745i	−0.126329	−	0.412721i
$721$	−35.3961	−	20.4359i	−1.31822	−	0.761074i
$722$	18.4236	−	31.9106i	0.685655	−	1.18759i
$723$	−13.8886	−	24.0557i	−0.516522	−	0.894643i
$724$	−12.3988	−	21.4754i	−0.460799	−	0.798128i
$725$	−40.7959	+	2.87962i	−1.51512	+	0.106946i
$726$		−	10.1967i		−	0.378435i
$727$	−10.9295	+	18.9305i	−0.405354	+	0.702093i	−0.994363	−	0.106033i	$-0.966185\pi$
$727$	−10.9295	+	18.9305i	−0.405354	+	0.702093i	0.589009	+	0.808127i	$0.299518\pi$
$728$	5.05516	−	2.91860i	0.187357	−	0.108170i
$729$	41.6276			1.54176
$730$	0.596658	−	2.58828i	0.0220833	−	0.0957967i
$731$	1.72611	+	2.98972i	0.0638426	+	0.110579i
$732$	−17.9966			−0.665174
$733$	2.21236	+	1.27731i	0.0817153	+	0.0471784i	0.540301	−	0.841472i	$-0.318310\pi$
$733$	2.21236	+	1.27731i	0.0817153	+	0.0471784i	−0.458586	+	0.888650i	$0.651644\pi$
$734$		−	22.0130i		−	0.812515i
$735$	−74.7425	−	69.6526i	−2.75692	−	2.56918i
$736$	3.51214	−	6.08320i	0.129459	−	0.224230i
$737$	0.0665190	+	0.0384048i	0.00245026	+	0.00141466i
$738$	−12.4601	−	21.5815i	−0.458663	−	0.794427i
$739$	−9.05174			−0.332974			−0.166487	−	0.986044i	$-0.553242\pi$
$739$	−9.05174			−0.332974			−0.166487	+	0.986044i	$0.553242\pi$
$740$	−10.0889	−	9.12219i	−0.370875	−	0.335338i
$741$	−26.0275			−0.956145
$742$	−16.4242	−	28.4475i	−0.602950	−	1.04434i
$743$	−13.0291	−	7.52236i	−0.477992	−	0.275969i	0.241587	−	0.970379i	$-0.422332\pi$
$743$	−13.0291	−	7.52236i	−0.477992	−	0.275969i	−0.719579	+	0.694410i	$0.755665\pi$
$744$	2.18900	−	3.79146i	0.0802526	−	0.139001i
$745$	6.55521	−	7.03423i	0.240164	−	0.257714i
$746$		−	0.803940i		−	0.0294343i
$747$	29.9701	+	17.3032i	1.09655	+	0.633092i
$748$	−1.23463			−0.0451425
$749$	15.8599	+	27.4702i	0.579508	+	1.00374i
$750$	20.0984	−	24.8694i	0.733889	−	0.908103i
$751$	−53.5679			−1.95472			−0.977360	−	0.211582i	$-0.932139\pi$
$751$	−53.5679			−1.95472			−0.977360	+	0.211582i	$0.932139\pi$
$752$	2.48872	−	1.43686i	0.0907541	−	0.0523969i
$753$	−25.4579	+	44.0943i	−0.927736	+	1.60689i
$754$			9.96082i			0.362752i
$755$	0.609078	+	1.98987i	0.0221666	+	0.0724188i
$756$	14.9388	+	25.8748i	0.543319	+	0.941056i
$757$	−9.72544	−	16.8450i	−0.353477	−	0.612241i	0.633379	−	0.773842i	$-0.281667\pi$
$757$	−9.72544	−	16.8450i	−0.353477	−	0.612241i	−0.986856	+	0.161601i	$0.948334\pi$
$758$	0.189378	−	0.328013i	0.00687853	−	0.0119140i
$759$	47.4380	+	27.3883i	1.72189	+	0.994134i
$760$	15.9786	−	4.89088i	0.579604	−	0.177411i
$761$	−16.5499	−	28.6652i	−0.599932	−	1.03911i	−0.992830	−	0.119531i	$-0.961861\pi$
$761$	−16.5499	−	28.6652i	−0.599932	−	1.03911i	0.392898	−	0.919582i	$-0.371472\pi$
$762$	19.1518	+	33.1719i	0.693798	+	1.20169i
$763$	71.8042			2.59949
$764$	−5.44715	−	3.14491i	−0.197071	−	0.113779i
$765$	1.53488	+	5.01449i	0.0554938	+	0.181299i
$766$	0.719146			0.0259838
$767$			12.5420i			0.452865i
$768$	2.47681	−	1.42999i	0.0893742	−	0.0516002i
$769$		−	6.77792i		−	0.244418i	−0.992504	−	0.122209i	$-0.961002\pi$
$769$		−	6.77792i		−	0.244418i	0.992504	−	0.122209i	$-0.0389978\pi$
$770$	−21.3802	−	19.9242i	−0.770488	−	0.718019i
$771$		−	58.9670i		−	2.12365i
$772$	7.41166	−	12.8374i	0.266751	−	0.462027i
$773$	−23.2941	−	13.4489i	−0.837831	−	0.483722i	0.0186952	−	0.999825i	$-0.494049\pi$
$773$	−23.2941	−	13.4489i	−0.837831	−	0.483722i	−0.856526	+	0.516103i	$0.827382\pi$
$774$	19.7446	−	34.1987i	0.709706	−	1.22925i
$775$	7.63491	−	0.538918i	0.274254	−	0.0193585i
$776$	−15.7903			−0.566838
$777$	72.8341	+	40.6024i	2.61291	+	1.45660i
$778$			13.6538i			0.489512i
$779$	31.1386	−	17.9779i	1.11565	−	0.644124i
$780$	−5.69741	−	5.30943i	−0.204000	−	0.190108i
$781$	−0.276075	+	0.478176i	−0.00987874	+	0.0171105i
$782$	−1.59029	+	2.75446i	−0.0568687	+	0.0984994i
$783$	−50.9843			−1.82203
$784$	7.98785	−	13.8354i	0.285280	−	0.494120i
$785$	−0.349958	+	1.51811i	−0.0124905	+	0.0541835i
$786$	−9.06732	−	15.7051i	−0.323421	−	0.560181i
$787$		−	32.7991i		−	1.16916i	−0.811335	−	0.584581i	$-0.801259\pi$
$787$		−	32.7991i		−	1.16916i	0.811335	−	0.584581i	$-0.198741\pi$
$788$			18.8899i			0.672926i
$789$	39.6439	+	68.6652i	1.41136	+	2.44454i
$790$	16.8378	+	15.6912i	0.599061	+	0.558266i
$791$		−	6.96623i		−	0.247691i
$792$	7.06132	+	12.2306i	0.250913	+	0.434594i
$793$	−6.63634	+	3.83149i	−0.235663	+	0.136060i
$794$	13.3178	−	7.68902i	0.472630	−	0.272873i
$795$	−29.8784	+	32.0617i	−1.05968	+	1.13711i
$796$	−15.3374	−	8.85505i	−0.543619	−	0.313859i
$797$	18.6926	+	32.3766i	0.662127	+	1.14684i	0.980056	+	0.198723i	$0.0636795\pi$
$797$	18.6926	+	32.3766i	0.662127	+	1.14684i	−0.317929	+	0.948115i	$0.602987\pi$
$798$	−88.7213	+	51.2233i	−3.14070	+	1.81328i
$799$	−1.12689	+	0.650608i	−0.0398664	+	0.0230169i
$800$	4.49541	+	2.18891i	0.158937	+	0.0773896i
$801$	16.8295	+	9.71653i	0.594642	+	0.343317i
$802$	26.6084	−	15.3624i	0.939574	−	0.542463i
$803$			3.23893i			0.114299i
$804$	0.0805650			0.00284131
$805$	−71.9903	+	22.0355i	−2.53732	+	0.776648i
$806$		−	1.86416i		−	0.0656622i
$807$	39.0689	+	22.5564i	1.37529	+	0.794024i
$808$	−6.29744			−0.221543
$809$	3.73688	+	2.15749i	0.131382	+	0.0758533i	0.564250	−	0.825604i	$-0.309165\pi$
$809$	3.73688	+	2.15749i	0.131382	+	0.0758533i	−0.432869	+	0.901457i	$0.642499\pi$
$810$	3.48863	−	3.74356i	0.122578	−	0.131535i
$811$	−12.2356	+	21.1926i	−0.429649	+	0.744173i	−0.996842	−	0.0794116i	$-0.974696\pi$
$811$	−12.2356	+	21.1926i	−0.429649	+	0.744173i	0.567193	+	0.823585i	$0.308029\pi$
$812$	19.6033	+	33.9539i	0.687942	+	1.19155i
$813$		−	68.7444i		−	2.41097i
$814$	14.4867	+	8.07582i	0.507759	+	0.283057i
$815$	21.5408	+	4.96564i	0.754540	+	0.173939i
$816$	−1.12150	+	0.647496i	−0.0392602	+	0.0226669i
$817$	49.3430	+	28.4882i	1.72629	+	0.996676i
$818$	7.04079	+	4.06500i	0.246175	+	0.142129i
$819$	26.1830	+	15.1168i	0.914908	+	0.528222i
$820$	10.4836	+	2.41670i	0.366102	+	0.0843948i
$821$	4.53720	−	7.85866i	0.158349	−	0.274269i	−0.775924	−	0.630826i	$-0.782716\pi$
$821$	4.53720	−	7.85866i	0.158349	−	0.274269i	0.934274	+	0.356557i	$0.116049\pi$
$822$	−26.9365			−0.939520
$823$	−18.6688	+	10.7784i	−0.650753	+	0.375712i	−0.788745	−	0.614721i	$-0.789269\pi$
$823$	−18.6688	+	10.7784i	−0.650753	+	0.375712i	0.137992	+	0.990433i	$0.455935\pi$
$824$	−8.52688			−0.297048
$825$	−17.0695	+	35.0560i	−0.594284	+	1.22049i
$826$	24.6832	+	42.7525i	0.858837	+	1.48755i
$827$	26.5009	−	45.9009i	0.921526	−	1.59613i	0.124471	−	0.992223i	$-0.460277\pi$
$827$	26.5009	−	45.9009i	0.921526	−	1.59613i	0.797055	−	0.603907i	$-0.206390\pi$
$828$	36.3820			1.26436
$829$	−17.8018	+	10.2779i	−0.618283	+	0.356966i	−0.776200	−	0.630487i	$-0.782855\pi$
$829$	−17.8018	+	10.2779i	−0.618283	+	0.356966i	0.157917	+	0.987452i	$0.449522\pi$
$830$	−14.2860	+	4.37279i	−0.495874	+	0.151782i
$831$	42.1049	−	24.3093i	1.46060	−	0.843280i
$832$	0.608891	−	1.05463i	0.0211095	−	0.0365627i
$833$	−3.61688	+	6.26462i	−0.125318	+	0.217056i
$834$	21.4320	−	12.3738i	0.742129	−	0.428468i
$835$	9.18219	+	29.9984i	0.317763	+	1.03814i
$836$	−17.6467	+	10.1883i	−0.610323	+	0.352370i
$837$	9.54167			0.329808
$838$	−5.36246	+	9.28806i	−0.185243	+	0.320851i
$839$	22.5116	+	38.9912i	0.777186	+	1.34612i	0.933558	+	0.358427i	$0.116687\pi$
$839$	22.5116	+	38.9912i	0.777186	+	1.34612i	−0.156372	+	0.987698i	$0.549980\pi$
$840$	−29.8702	−	6.88577i	−1.03062	−	0.237581i
$841$	−37.9037			−1.30703
$842$	−30.9837	+	17.8884i	−1.06777	+	0.616477i
$843$	−53.4479			−1.84085
$844$	4.27309	−	7.40121i	0.147086	−	0.254760i
$845$	25.0947	+	5.78489i	0.863283	+	0.199006i
$846$	12.8902	+	7.44216i	0.443174	+	0.255867i
$847$	−14.8000	−	8.54479i	−0.508534	−	0.293602i
$848$	−5.93485	−	3.42649i	−0.203804	−	0.117666i
$849$	1.09446	−	0.631888i	0.0375619	−	0.0216864i
$850$	−2.03551	−	0.991133i	−0.0698175	−	0.0339956i
$851$	36.6771	−	21.9177i	1.25728	−	0.751329i
$852$			0.579146i			0.0198412i
$853$	8.02858	+	13.9059i	0.274893	+	0.476129i	0.970108	−	0.242673i	$-0.0780242\pi$
$853$	8.02858	+	13.9059i	0.274893	+	0.476129i	−0.695215	+	0.718802i	$0.744691\pi$
$854$	−15.0811	+	26.1212i	−0.516064	+	0.893850i
$855$	63.3185	+	59.0066i	2.16545	+	2.01798i
$856$	5.73095	+	3.30877i	0.195880	+	0.113091i
$857$	−50.9495			−1.74040			−0.870202	−	0.492696i	$-0.836012\pi$
$857$	−50.9495			−1.74040			−0.870202	+	0.492696i	$0.836012\pi$
$858$	8.22421	+	4.74825i	0.280770	+	0.162103i
$859$			40.2983i			1.37496i	0.726203	+	0.687480i	$0.241283\pi$
$859$			40.2983i			1.37496i	−0.726203	+	0.687480i	$0.758717\pi$
$860$	4.98977	+	16.3017i	0.170150	+	0.555883i
$861$	−65.9575			−2.24782
$862$			2.46095i			0.0838205i
$863$	−2.94309	+	1.69919i	−0.100184	+	0.0578411i	−0.549255	−	0.835655i	$-0.685088\pi$
$863$	−2.94309	+	1.69919i	−0.100184	+	0.0578411i	0.449071	+	0.893496i	$0.351755\pi$
$864$	5.39812	+	3.11660i	0.183648	+	0.106029i
$865$	1.99925	−	8.67267i	0.0679764	−	0.294880i
$866$	−27.0745	+	15.6315i	−0.920028	+	0.531178i
$867$	−41.5980	+	24.0166i	−1.41274	+	0.815647i
$868$	−3.66874	−	6.35445i	−0.124525	−	0.215684i
$869$	−24.3053	−	14.0327i	−0.824502	−	0.476026i
$870$	35.6618	−	38.2677i	1.20905	−	1.29740i
$871$	0.0297087	−	0.0171523i	0.00100664	−	0.000581185i
$872$	12.9732	−	7.49007i	0.439327	−	0.253646i
$873$	−40.8926	−	70.8280i	−1.38400	−	2.39717i
$874$			52.4931i			1.77561i
$875$	−19.2544	−	50.0123i	−0.650918	−	1.69072i
$876$	1.69864	+	2.94214i	0.0573919	+	0.0994056i
$877$		−	24.2792i		−	0.819851i	−0.912119	−	0.409925i	$-0.865555\pi$
$877$		−	24.2792i		−	0.819851i	0.912119	−	0.409925i	$-0.134445\pi$
$878$		−	22.8832i		−	0.772271i
$879$	6.81173	+	11.7983i	0.229754	+	0.397945i
$880$	−5.94119	−	1.36958i	−0.200277	−	0.0461685i
$881$	−27.2517	+	47.2013i	−0.918132	+	1.59025i	−0.115881	+	0.993263i	$0.536969\pi$
$881$	−27.2517	+	47.2013i	−0.918132	+	1.59025i	−0.802251	+	0.596987i	$0.796364\pi$
$882$	82.7455			2.78619
$883$	−1.62873	+	2.82104i	−0.0548111	+	0.0949356i	−0.892129	−	0.451781i	$-0.850789\pi$
$883$	−1.62873	+	2.82104i	−0.0548111	+	0.0949356i	0.837318	+	0.546716i	$0.184122\pi$
$884$	−0.275705	+	0.477535i	−0.00927296	+	0.0160612i
$885$	44.9029	−	48.1842i	1.50939	−	1.61969i
$886$	1.29833	−	0.749589i	0.0436181	−	0.0251829i
$887$			34.5745i			1.16090i	0.814296	+	0.580450i	$0.197123\pi$
$887$			34.5745i			1.16090i	−0.814296	+	0.580450i	$0.802877\pi$
$888$	17.3946	−	0.261690i	0.583724	−	0.00878174i
$889$	64.1966			2.15309
$890$	−8.02221	+	2.45551i	−0.268905	+	0.0823090i
$891$	−3.11990	+	5.40383i	−0.104521	+	0.181035i
$892$	20.1670	+	11.6434i	0.675242	+	0.389851i
$893$	−10.7378	+	18.5984i	−0.359327	+	0.622372i
$894$			12.2980i			0.411306i
$895$	−13.1069	−	12.2144i	−0.438116	−	0.408282i
$896$		−	4.79330i		−	0.160133i
$897$	21.1868	−	12.2322i	0.707405	−	0.408421i
$898$			26.2226i			0.875061i
$899$	12.5210			0.417598
$900$	1.82345	+	25.8330i	0.0607817	+	0.861101i
$901$	2.68729	+	1.55151i	0.0895266	+	0.0516882i
$902$	−13.1189			−0.436813
$903$	−52.2590	−	90.5153i	−1.73907	−	3.01216i
$904$	−0.726663	−	1.25862i	−0.0241685	−	0.0418610i
$905$	16.2292	+	53.0211i	0.539477	+	1.76248i
$906$	−2.30505	−	1.33082i	−0.0765801	−	0.0442135i
$907$	15.9340	−	27.5984i	0.529078	−	0.916390i	−0.470347	−	0.882482i	$-0.655871\pi$
$907$	15.9340	−	27.5984i	0.529078	−	0.916390i	0.999425	−	0.0339085i	$-0.0107955\pi$
$908$	−1.50747	−	2.61101i	−0.0500270	−	0.0866493i
$909$	−16.3087	−	28.2475i	−0.540925	−	0.936910i
$910$	−12.4808	+	3.82024i	−0.413734	+	0.126640i
$911$			16.4317i			0.544406i	0.962240	+	0.272203i	$0.0877523\pi$
$911$			16.4317i			0.544406i	−0.962240	+	0.272203i	$0.912248\pi$
$912$	−10.6864	+	18.5095i	−0.353863	+	0.612909i
$913$	15.7774	−	9.10907i	0.522155	−	0.301466i
$914$	−32.4232			−1.07246
$915$	39.2132	+	9.03954i	1.29635	+	0.298838i
$916$	−0.804843	−	1.39403i	−0.0265928	−	0.0460600i
$917$	−30.3935			−1.00368
$918$	−2.44426	−	1.41119i	−0.0806725	−	0.0465763i
$919$		−	41.6667i		−	1.37446i	−0.726440	−	0.687229i	$-0.758827\pi$
$919$		−	41.6667i		−	1.37446i	0.726440	−	0.687229i	$-0.241173\pi$
$920$	−10.7082	+	11.4907i	−0.353040	+	0.378838i
$921$	−4.24443	+	7.35157i	−0.139859	+	0.242243i
$922$	−6.96252	−	4.01982i	−0.229299	−	0.132386i
$923$	0.123301	+	0.213563i	0.00405849	+	0.00702951i
$924$	37.3790			1.22968
$925$	17.4009	+	24.9441i	0.572139	+	0.820157i
$926$	−16.2367			−0.533572
$927$	−22.0823	−	38.2477i	−0.725279	−	1.25622i
$928$	7.08363	+	4.08974i	0.232532	+	0.134252i
$929$	8.74165	−	15.1410i	0.286804	−	0.496760i	−0.686241	−	0.727374i	$-0.740740\pi$
$929$	8.74165	−	15.1410i	0.286804	−	0.496760i	0.973045	+	0.230615i	$0.0740737\pi$
$930$	−6.67407	+	7.16177i	−0.218851	+	0.234844i
$931$			119.388i			3.91278i
$932$	−16.9060	−	9.76067i	−0.553773	−	0.319721i
$933$	71.6743			2.34651
$934$	1.72188	+	2.98239i	0.0563417	+	0.0975867i
$935$	2.69016	+	0.620143i	0.0879776	+	0.0202808i
$936$	6.30746			0.206166
$937$	−5.78313	+	3.33889i	−0.188927	+	0.109077i	−0.591480	−	0.806320i	$-0.701456\pi$
$937$	−5.78313	+	3.33889i	−0.188927	+	0.109077i	0.402553	+	0.915397i	$0.368123\pi$
$938$	0.0675131	−	0.116936i	0.00220438	−	0.00381810i
$939$			51.0125i			1.66473i
$940$	−6.14444	+	1.88075i	−0.200410	+	0.0613432i
$941$	−9.59102	−	16.6121i	−0.312658	−	0.541540i	0.666279	−	0.745703i	$-0.267886\pi$
$941$	−9.59102	−	16.6121i	−0.312658	−	0.541540i	−0.978937	+	0.204163i	$0.934553\pi$
$942$	−0.996305	−	1.72565i	−0.0324614	−	0.0562248i
$943$	−16.8981	+	29.2684i	−0.550279	+	0.953112i
$944$	8.91923	+	5.14952i	0.290296	+	0.167603i
$945$	−19.5538	−	63.8828i	−0.636086	−	2.07811i
$946$	−10.3943	−	18.0035i	−0.337948	−	0.585344i
$947$	6.35306	+	11.0038i	0.206447	+	0.357576i	0.950593	−	0.310441i	$-0.100477\pi$
$947$	6.35306	+	11.0038i	0.206447	+	0.357576i	−0.744146	+	0.668017i	$0.767143\pi$
$948$	−29.4375			−0.956087
$949$	1.25277	+	0.723286i	0.0406666	+	0.0234788i
$950$	−37.2728	+	2.63094i	−1.20929	+	0.0853589i
$951$	−12.9118			−0.418695
$952$			2.17040i			0.0703429i
$953$	7.63027	−	4.40534i	0.247169	−	0.142703i	−0.371298	−	0.928514i	$-0.621087\pi$
$953$	7.63027	−	4.40534i	0.247169	−	0.142703i	0.618467	+	0.785811i	$0.287754\pi$
$954$		−	35.4947i		−	1.14918i
$955$	10.2892	+	9.58857i	0.332952	+	0.310279i
$956$		−	6.55644i		−	0.212051i
$957$	−31.8925	+	55.2395i	−1.03094	+	1.78564i
$958$	−5.67506	−	3.27650i	−0.183353	−	0.105859i
$959$	−22.5727	+	39.0971i	−0.728911	+	1.26251i
$960$	−6.11505	+	1.87175i	−0.197362	+	0.0604105i
$961$	28.6567			0.924410
$962$	6.35863	−	3.79982i	0.205010	−	0.122511i
$963$			34.2753i			1.10450i
$964$	−8.41117	+	4.85619i	−0.270905	+	0.156407i
$965$	−22.5975	+	24.2488i	−0.727440	+	0.780597i
$966$	48.1469	−	83.3929i	1.54910	−	2.68312i
$967$	28.7222	−	49.7484i	0.923645	−	1.59980i	0.129918	−	0.991525i	$-0.458529\pi$
$967$	28.7222	−	49.7484i	0.923645	−	1.59980i	0.793727	−	0.608275i	$-0.208138\pi$
$968$	−3.56531			−0.114593
$969$	4.83880	−	8.38105i	0.155445	−	0.269238i
$970$	34.4058	+	7.93132i	1.10470	+	0.254659i
$971$	1.39588	+	2.41774i	0.0447959	+	0.0775888i	0.887554	−	0.460704i	$-0.152403\pi$
$971$	1.39588	+	2.41774i	0.0447959	+	0.0775888i	−0.842758	+	0.538292i	$0.819070\pi$
$972$		−	12.1547i		−	0.389864i
$973$		−	41.4766i		−	1.32968i
$974$	−2.48795	−	4.30925i	−0.0797190	−	0.138077i
$975$	9.74734	+	14.4306i	0.312165	+	0.462149i
$976$			6.29258i			0.201420i
$977$	−5.86092	−	10.1514i	−0.187507	−	0.324772i	0.756911	−	0.653518i	$-0.226708\pi$
$977$	−5.86092	−	10.1514i	−0.187507	−	0.324772i	−0.944419	+	0.328745i	$0.893374\pi$
$978$	−24.4857	+	14.1368i	−0.782966	+	0.452046i
$979$	8.85969	−	5.11514i	0.283157	−	0.163481i
$980$	−24.3543	+	26.1339i	−0.777969	+	0.834818i
$981$	67.1941	+	38.7945i	2.14534	+	1.23861i
$982$	6.58035	+	11.3975i	0.209987	+	0.363709i
$983$	−20.6403	+	11.9167i	−0.658324	+	0.380083i	−0.791638	−	0.610990i	$-0.790771\pi$
$983$	−20.6403	+	11.9167i	−0.658324	+	0.380083i	0.133314	+	0.991074i	$0.457438\pi$
$984$	−11.9168	+	6.88018i	−0.379894	+	0.219332i
$985$	9.48825	−	41.1597i	0.302321	−	1.31146i
$986$	−3.20745	−	1.85182i	−0.102146	−	0.0589741i
$987$	34.1171	−	19.6975i	1.08596	−	0.626979i
$988$			9.10061i			0.289529i
$989$	−53.5545			−1.70294
$990$	−9.24277	−	30.1963i	−0.293755	−	0.959702i
$991$			22.9383i			0.728660i	0.931270	+	0.364330i	$0.118702\pi$
$991$			22.9383i			0.728660i	−0.931270	+	0.364330i	$0.881298\pi$
$992$	−1.32569	−	0.765390i	−0.0420909	−	0.0243012i
$993$	65.5744			2.08094
$994$	0.840602	+	0.485322i	0.0266623	+	0.0153935i
$995$	28.9712	+	26.9983i	0.918448	+	0.855904i
$996$	9.55443	−	16.5488i	0.302744	−	0.524368i
$997$	−12.0633	−	20.8943i	−0.382050	−	0.661730i	0.609305	−	0.792936i	$-0.291448\pi$
$997$	−12.0633	−	20.8943i	−0.382050	−	0.661730i	−0.991355	+	0.131206i	$0.958115\pi$
$998$			12.9681i			0.410499i
$999$	19.4493	+	32.5466i	0.615350	+	1.02973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.m.c.159.1	✓	16
5.4	even	2		370.2.m.d.159.8	yes	16
37.27	even	6		370.2.m.d.249.8	yes	16
185.64	even	6	inner	370.2.m.c.249.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.c.159.1	✓	16	1.1	even	1	trivial
370.2.m.c.249.1	yes	16	185.64	even	6	inner
370.2.m.d.159.8	yes	16	5.4	even	2
370.2.m.d.249.8	yes	16	37.27	even	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-2.47681 - 1.42999i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.52446 - 1.63586i) q^{5} +2.85998i q^{6} +(4.15112 + 2.39665i) q^{7} +1.00000 q^{8} +(2.58973 + 4.48555i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-2.47681 - 1.42999i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.52446 - 1.63586i) q^{5} +2.85998i q^{6} +(4.15112 + 2.39665i) q^{7} +1.00000 q^{8} +(2.58973 + 4.48555i) q^{9} +(-2.17892 - 0.502291i) q^{10} +2.72666 q^{11} +(2.47681 - 1.42999i) q^{12} +(0.608891 - 1.05463i) q^{13} -4.79330i q^{14} +(-6.11505 + 1.87175i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.226399 + 0.392135i) q^{17} +(2.58973 - 4.48555i) q^{18} +(6.47189 + 3.73655i) q^{19} +(0.654464 + 2.13815i) q^{20} +(-6.85436 - 11.8721i) q^{21} +(-1.36333 - 2.36136i) q^{22} -7.02428 q^{23} +(-2.47681 - 1.42999i) q^{24} +(-0.352054 - 4.98759i) q^{25} -1.21778 q^{26} -6.23321i q^{27} +(-4.15112 + 2.39665i) q^{28} -8.17947i q^{29} +(4.67851 + 4.35991i) q^{30} +1.53078i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.75343 - 3.89910i) q^{33} +(0.226399 - 0.392135i) q^{34} +(10.2488 - 3.13704i) q^{35} -5.17946 q^{36} +(-5.22148 + 3.12028i) q^{37} -7.47310i q^{38} +(-3.01622 + 1.74141i) q^{39} +(1.52446 - 1.63586i) q^{40} +(2.40568 - 4.16675i) q^{41} +(-6.85436 + 11.8721i) q^{42} +7.62420 q^{43} +(-1.36333 + 2.36136i) q^{44} +(11.2856 + 2.60160i) q^{45} +(3.51214 + 6.08320i) q^{46} +2.87372i q^{47} +2.85998i q^{48} +(7.98785 + 13.8354i) q^{49} +(-4.14335 + 2.79868i) q^{50} -1.29499i q^{51} +(0.608891 + 1.05463i) q^{52} +(5.93485 - 3.42649i) q^{53} +(-5.39812 + 3.11660i) q^{54} +(4.15668 - 4.46043i) q^{55} +(4.15112 + 2.39665i) q^{56} +(-10.6864 - 18.5095i) q^{57} +(-7.08363 + 4.08974i) q^{58} +(-8.91923 + 5.14952i) q^{59} +(1.43654 - 6.23167i) q^{60} +(-5.44953 - 3.14629i) q^{61} +(1.32569 - 0.765390i) q^{62} +24.8267i q^{63} +1.00000 q^{64} +(-0.796995 - 2.60380i) q^{65} +7.79819i q^{66} +(0.0243958 + 0.0140849i) q^{67} -0.452798 q^{68} +(17.3978 + 10.0446i) q^{69} +(-7.84115 - 7.30718i) q^{70} +(-0.101250 + 0.175370i) q^{71} +(2.58973 + 4.48555i) q^{72} +1.18787i q^{73} +(5.31298 + 2.96180i) q^{74} +(-6.26022 + 12.8568i) q^{75} +(-6.47189 + 3.73655i) q^{76} +(11.3187 + 6.53485i) q^{77} +(3.01622 + 1.74141i) q^{78} +(-8.91394 - 5.14647i) q^{79} +(-2.17892 - 0.502291i) q^{80} +(-1.14422 + 1.98185i) q^{81} -4.81135 q^{82} +(5.78633 - 3.34074i) q^{83} +13.7087 q^{84} +(0.986612 + 0.227437i) q^{85} +(-3.81210 - 6.60275i) q^{86} +(-11.6965 + 20.2590i) q^{87} +2.72666 q^{88} +(3.24928 - 1.87597i) q^{89} +(-3.38977 - 11.0745i) q^{90} +(5.05516 - 2.91860i) q^{91} +(3.51214 - 6.08320i) q^{92} +(2.18900 - 3.79146i) q^{93} +(2.48872 - 1.43686i) q^{94} +(15.9786 - 4.89088i) q^{95} +(2.47681 - 1.42999i) q^{96} -15.7903 q^{97} +(7.98785 - 13.8354i) q^{98} +(7.06132 + 12.2306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

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