LMFDB - Embedded newform 370.2.m.d.159.8

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			159.8
Root			$-2.85998i$ of defining polynomial
Character	$\chi$	$=$	370.159
Dual form			370.2.m.d.249.8

$q$-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} +(-0.654464 + 2.13815i) 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} +(-4.67851 + 4.35991i) 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} +(-1.52446 - 1.63586i) q^{20} +(-6.85436 - 11.8721i) q^{21} +(1.36333 + 2.36136i) q^{22} +7.02428 q^{23} +(-2.47681 - 1.42999i) q^{24} +(-4.14335 - 2.79868i) q^{25} -1.21778 q^{26} +6.23321i q^{27} +(4.15112 - 2.39665i) q^{28} -8.17947i q^{29} +(-6.11505 - 1.87175i) q^{30} +1.53078i q^{31} +(0.500000 - 0.866025i) q^{32} +(6.75343 + 3.89910i) q^{33} +(0.226399 - 0.392135i) q^{34} +(7.84115 - 7.30718i) q^{35} -5.17946 q^{36} +(5.22148 - 3.12028i) q^{37} +7.47310i q^{38} +(-3.01622 + 1.74141i) q^{39} +(0.654464 - 2.13815i) 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} +(0.352054 - 4.98759i) q^{50} -1.29499i q^{51} +(-0.608891 - 1.05463i) q^{52} +(-5.93485 + 3.42649i) q^{53} +(-5.39812 + 3.11660i) q^{54} +(-1.78450 + 5.83001i) 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} +(-1.85646 - 1.99212i) q^{65} +7.79819i q^{66} +(-0.0243958 - 0.0140849i) q^{67} +0.452798 q^{68} +(17.3978 + 10.0446i) q^{69} +(10.2488 + 3.13704i) 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} +(-7.89587 - 8.47286i) 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} +(-12.2249 + 11.3924i) 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} - 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^{20} - 6 q^{21} - 3 q^{22} - 22 q^{23}+ \cdots + 37 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 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^20 - 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 + 18 * q^35 - 26 * q^36 + 16 * q^37 + 15 * q^39 + 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 - 35 * 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 + 46 * q^65 + 24 * q^67 + 42 * q^69 + 12 * 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 - q^90 - 24 * q^91 + 11 * q^92 - 25 * q^93 - 27 * q^94 - 53 * q^95 - 3 * q^96 + 68 * q^97 - 4 * q^98 + 37 * q^99

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	0.997119	−	0.0758530i	$-0.0241680\pi$
$3$	2.47681	+	1.42999i	1.42999	+	0.825604i	0.432869	+	0.901457i	$0.357501\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.654464	+	2.13815i	−0.292685	+	0.956209i
$5$	−0.654464	+	2.13815i	−0.292685	+	0.956209i
$6$			2.85998i			1.16758i
$7$	−4.15112	−	2.39665i	−1.56897	−	0.905848i	−0.996289	−	0.0860730i	$-0.972568\pi$
$7$	−4.15112	−	2.39665i	−1.56897	−	0.905848i	−0.572686	−	0.819775i	$-0.694099\pi$
$8$	−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	−0.938025	−	0.346568i	$-0.887347\pi$
$13$	−0.608891	+	1.05463i	−0.168876	+	0.292502i	0.769149	+	0.639070i	$0.220680\pi$
$14$		−	4.79330i		−	1.28106i
$15$	−4.67851	+	4.35991i	−1.20799	+	1.12572i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.226399	−	0.392135i	−0.0549098	−	0.0951066i	0.837264	−	0.546799i	$-0.184154\pi$
$17$	−0.226399	−	0.392135i	−0.0549098	−	0.0951066i	−0.892174	+	0.451692i	$0.850820\pi$
$18$	−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	$0.338854\pi$
$20$	−1.52446	−	1.63586i	−0.340879	−	0.365789i
$21$	−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	$-0.238432\pi$
$23$	7.02428			1.46466			0.732332	+	0.680948i	$0.238432\pi$
$24$	−2.47681	−	1.42999i	−0.505577	−	0.291895i
$25$	−4.14335	−	2.79868i	−0.828671	−	0.559737i
$26$	−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	$-0.274529\pi$
$30$	−6.11505	−	1.87175i	−1.11645	−	0.341734i
$31$			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
$35$	7.84115	−	7.30718i	1.32540	−	1.23514i
$36$	−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
$40$	0.654464	−	2.13815i	0.103480	−	0.338071i
$41$	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	$-0.697471\pi$
$43$	−7.62420			−1.16268			−0.581340	+	0.813661i	$0.697471\pi$
$44$	−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	$-0.932788\pi$
$47$		−	2.87372i		−	0.419175i	0.977790	−	0.209588i	$-0.0672122\pi$
$48$		−	2.85998i		−	0.412802i
$49$	7.98785	+	13.8354i	1.14112	+	1.97648i
$50$	0.352054	−	4.98759i	0.0497880	−	0.705352i
$51$		−	1.29499i		−	0.181335i
$52$	−0.608891	−	1.05463i	−0.0844380	−	0.146251i
$53$	−5.93485	+	3.42649i	−0.815215	+	0.470664i	−0.848763	−	0.528773i	$-0.822652\pi$
$53$	−5.93485	+	3.42649i	−0.815215	+	0.470664i	0.0335488	+	0.999437i	$0.489319\pi$
$54$	−5.39812	+	3.11660i	−0.734591	+	0.424116i
$55$	−1.78450	+	5.83001i	−0.240622	+	0.786118i
$56$	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
$65$	−1.85646	−	1.99212i	−0.230265	−	0.247092i
$66$			7.79819i			0.959891i
$67$	−0.0243958	−	0.0140849i	−0.00298042	−	0.00172074i	0.498509	−	0.866884i	$-0.333881\pi$
$67$	−0.0243958	−	0.0140849i	−0.00298042	−	0.00172074i	−0.501489	+	0.865164i	$0.667214\pi$
$68$	0.452798			0.0549098
$69$	17.3978	+	10.0446i	2.09445	+	1.20923i
$70$	10.2488	+	3.13704i	1.22496	+	0.374948i
$71$	−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	$-0.977855\pi$
$73$		−	1.18787i		−	0.139030i	0.997581	−	0.0695150i	$-0.0221452\pi$
$74$	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	−0.782737	−	0.622353i	$-0.786177\pi$
$83$	−5.78633	+	3.34074i	−0.635132	+	0.366694i	0.147605	+	0.989046i	$0.452844\pi$
$84$	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	$0.269612\pi$
$90$	−7.89587	−	8.47286i	−0.832298	−	0.893118i
$91$	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
$95$	−12.2249	+	11.3924i	−1.25425	+	1.16884i
$96$	2.47681	−	1.42999i	0.252789	−	0.145948i
$97$	15.7903			1.60326			0.801630	−	0.597820i	$-0.203966\pi$
$97$	15.7903			1.60326			0.801630	+	0.597820i	$0.203966\pi$
$98$	−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	$-0.361999\pi$
$103$	8.52688			0.840179			0.420089	+	0.907483i	$0.361999\pi$
$104$	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	0.196715	−	0.980461i	$-0.436973\pi$
$107$	−5.73095	−	3.30877i	−0.554032	−	0.319871i	−0.750747	+	0.660590i	$0.770306\pi$
$108$	−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	0.898179	−	0.439630i	$-0.144890\pi$
$113$	0.726663	+	1.25862i	0.0683588	+	0.118401i	−0.829820	+	0.558031i	$0.811557\pi$
$114$	−10.6864	+	18.5095i	−1.00088	+	1.73357i
$115$	−4.59714	+	15.0189i	−0.428686	+	1.40052i
$116$	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
$120$	4.67851	−	4.35991i	0.427088	−	0.398004i
$121$	−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	−0.916760	−	0.399438i	$-0.869205\pi$
$127$	−11.5987	+	6.69650i	−1.02922	+	0.594218i	−0.112456	+	0.993657i	$0.535872\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−18.8837	−	10.9025i	−1.66262	−	0.959913i
$130$	0.796995	−	2.60380i	0.0699011	−	0.228368i
$131$	−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
$135$	−13.3275	−	4.07941i	−1.14705	−	0.351100i
$136$	0.226399	+	0.392135i	0.0194136	+	0.0336253i
$137$		−	9.41845i		−	0.804673i	−0.915492	−	0.402336i	$-0.868198\pi$
$137$		−	9.41845i		−	0.804673i	0.915492	−	0.402336i	$-0.131802\pi$
$138$			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
$145$	17.4889	+	5.35317i	1.45238	+	0.444557i
$146$	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	$0.443640\pi$
$150$	8.00417	−	11.8499i	0.653537	−	0.967539i
$151$	−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
$155$	−3.27304	−	1.00184i	−0.262897	−	0.0804698i
$156$		−	3.48283i		−	0.278849i
$157$	0.603380	−	0.348361i	0.0481549	−	0.0278023i	−0.475729	−	0.879592i	$-0.657816\pi$
$157$	0.603380	−	0.348361i	0.0481549	−	0.0278023i	0.523884	+	0.851789i	$0.324482\pi$
$158$		−	10.2929i		−	0.818862i
$159$	−19.5993			−1.55433
$160$	1.52446	+	1.63586i	0.120519	+	0.129326i
$161$	−29.1586	−	16.8347i	−2.29802	−	1.32676i
$162$	−2.28844			−0.179797
$163$	−4.94299	−	8.56151i	−0.387165	−	0.670589i	0.604902	−	0.796300i	$-0.293212\pi$
$163$	−4.94299	−	8.56151i	−0.387165	−	0.670589i	−0.992067	+	0.125711i	$0.959879\pi$
$164$	2.40568	+	4.16675i	0.187852	+	0.325369i
$165$	−12.7567	+	11.8880i	−0.993110	+	0.925481i
$166$	−5.78633	−	3.34074i	−0.449106	−	0.259292i
$167$	7.01504	−	12.1504i	0.542840	−	0.940227i	−0.455899	−	0.890032i	$-0.650682\pi$
$167$	7.01504	−	12.1504i	0.542840	−	0.940227i	0.998739	−	0.0501957i	$-0.0159845\pi$
$168$	6.85436	+	11.8721i	0.528825	+	0.915952i
$169$	5.75850	+	9.97402i	0.442962	+	0.767232i
$170$	0.690272	+	0.740713i	0.0529414	+	0.0568101i
$171$			38.7066i			2.95997i
$172$	3.81210	−	6.60275i	0.290670	−	0.503455i
$173$	−3.44700	+	1.99013i	−0.262071	+	0.151307i	−0.625279	−	0.780401i	$-0.715015\pi$
$173$	−3.44700	+	1.99013i	−0.262071	+	0.151307i	0.363208	+	0.931708i	$0.381681\pi$
$174$	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	$-0.0967974\pi$
$180$	3.38977	−	11.0745i	0.252659	−	0.825441i
$181$	−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
$185$	3.25435	+	13.2064i	0.239264	+	0.970954i
$186$	−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
$190$	−15.9786	−	4.89088i	−1.15921	−	0.354821i
$191$			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	$-0.320875\pi$
$193$	14.8233			1.06701			0.533503	+	0.845798i	$0.320875\pi$
$194$	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	−0.952626	−	0.304145i	$-0.901629\pi$
$197$	−16.3592	+	9.44497i	−1.16554	+	0.672926i	−0.212916	+	0.977070i	$0.568296\pi$
$198$	−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	$0.783989\pi$
$200$	4.14335	+	2.79868i	0.292979	+	0.197897i
$201$	−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
$205$	7.33471	+	7.87068i	0.512278	+	0.549712i
$206$	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
$210$	20.8984	+	22.4255i	1.44212	+	1.54751i
$211$	−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
$215$	4.98977	−	16.3017i	0.340299	−	1.11177i
$216$		−	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
$220$	−4.15668	−	4.46043i	−0.280244	−	0.300722i
$221$	0.551410			0.0370918
$222$	8.92392	+	14.9333i	0.598934	+	1.00226i
$223$			23.2869i			1.55940i	0.626150	+	0.779702i	$0.284630\pi$
$223$			23.2869i			1.55940i	−0.626150	+	0.779702i	$0.715370\pi$
$224$	−4.15112	+	2.39665i	−0.277358	+	0.160133i
$225$	1.82345	−	25.8330i	0.121563	−	1.72220i
$226$	−0.726663	+	1.25862i	−0.0483369	+	0.0837220i
$227$	1.50747	−	2.61101i	0.100054	−	0.173299i	−0.811653	−	0.584140i	$-0.801432\pi$
$227$	1.50747	−	2.61101i	0.100054	−	0.173299i	0.911707	+	0.410842i	$0.134765\pi$
$228$	−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	$-0.779165\pi$
$233$		−	19.5213i		−	1.27888i	0.768839	−	0.639442i	$-0.220835\pi$
$234$	−3.15373	−	5.46242i	−0.206166	−	0.357090i
$235$	6.14444	+	1.88075i	0.400819	+	0.122686i
$236$		−	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	$0.401347\pi$
$240$	6.11505	+	1.87175i	0.394725	+	0.120821i
$241$	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
$250$	10.4338	+	4.01694i	0.659891	+	0.254054i
$251$		−	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
$255$	2.76888	+	0.847526i	0.173394	+	0.0530741i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.3090	−	17.8557i	−0.643058	−	1.11381i	−0.984746	−	0.173996i	$-0.944332\pi$
$257$	−10.3090	−	17.8557i	−0.643058	−	1.11381i	0.341688	−	0.939813i	$-0.389001\pi$
$258$		−	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	0.999755	−	0.0221398i	$-0.00704789\pi$
$263$	24.0090	+	13.8616i	1.48046	+	0.854743i	0.480704	+	0.876883i	$0.340381\pi$
$264$	−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
$275$	−11.2975	−	7.63107i	−0.681267	−	0.460171i
$276$	−17.3978	+	10.0446i	−1.04723	+	0.604616i
$277$	8.49982	−	14.7221i	0.510705	−	0.884567i	−0.489218	−	0.872161i	$-0.662718\pi$
$277$	8.49982	−	14.7221i	0.510705	−	0.884567i	0.999923	−	0.0124054i	$-0.00394888\pi$
$278$	4.32653	−	7.49376i	0.259488	−	0.449446i
$279$	−6.86639	+	3.96431i	−0.411080	+	0.237337i
$280$	−7.84115	+	7.30718i	−0.468598	+	0.436688i
$281$	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	−0.859384	−	0.511331i	$-0.829153\pi$
$283$	0.220942	−	0.382682i	0.0131336	−	0.0227481i	0.872518	+	0.488583i	$0.162486\pi$
$284$	−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	0.615637	−	0.788030i	$-0.288899\pi$
$293$	4.12530	+	2.38174i	0.241003	+	0.139143i	−0.374635	+	0.927172i	$0.622232\pi$
$294$	−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
$300$	14.2644	+	1.00687i	0.823555	+	0.0581315i
$301$	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
$305$	10.2938	−	9.59277i	0.589419	−	0.549280i
$306$	2.34525			0.134069
$307$			2.96816i			0.169402i	0.996406	+	0.0847009i	$0.0269935\pi$
$307$			2.96816i			0.169402i	−0.996406	+	0.0847009i	$0.973007\pi$
$308$	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	$0.00150703\pi$
$313$	8.91834	+	15.4470i	0.504095	+	0.873117i	−0.495894	+	0.868383i	$0.665160\pi$
$314$	0.603380	+	0.348361i	0.0340507	+	0.0196592i
$315$	53.0832	+	16.2482i	2.99090	+	0.915482i
$316$	8.91394	−	5.14647i	0.501449	−	0.289511i
$317$	−3.90982	+	2.25733i	−0.219597	+	0.126785i	−0.605764	−	0.795645i	$-0.707132\pi$
$317$	−3.90982	+	2.25733i	−0.219597	+	0.126785i	0.386167	+	0.922429i	$0.373799\pi$
$318$	−9.79967	−	16.9735i	−0.549538	−	0.951829i
$319$		−	22.3027i		−	1.24871i
$320$	−0.654464	+	2.13815i	−0.0365857	+	0.119526i
$321$	−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
$330$	−16.6737	−	5.10364i	−0.917856	−	0.280946i
$331$	−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
$335$	0.0460818	−	0.0429437i	0.00251772	−	0.00234626i
$336$	−6.85436	+	11.8721i	−0.373936	+	0.647676i
$337$	−9.93107	−	5.73371i	−0.540980	−	0.312335i	0.204496	−	0.978867i	$-0.434444\pi$
$337$	−9.93107	−	5.73371i	−0.540980	−	0.312335i	−0.745476	+	0.666532i	$0.767778\pi$
$338$	−5.75850	+	9.97402i	−0.313221	+	0.542515i
$339$			4.15648i			0.225749i
$340$	−0.296340	+	0.968150i	−0.0160713	+	0.0525053i
$341$			4.17392i			0.226031i
$342$	−33.5209	+	19.3533i	−1.81260	+	1.04651i
$343$		−	43.0232i		−	2.32303i
$344$	7.62420			0.411070
$345$	−32.8632	+	30.6253i	−1.76929	+	1.64881i
$346$	−3.44700	−	1.99013i	−0.185312	−	0.106990i
$347$	11.3700			0.610373			0.305187	−	0.952293i	$-0.401281\pi$
$347$	11.3700			0.610373			0.305187	+	0.952293i	$0.401281\pi$
$348$	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	$0.790080\pi$
$350$	−13.4149	+	19.8603i	−0.717058	+	1.06158i
$351$	−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	$-0.986450\pi$
$353$	−10.0780	−	17.4557i	−0.536400	−	0.929072i	0.462694	−	0.886518i	$-0.346883\pi$
$354$	−14.7275	−	25.5088i	−0.782758	−	1.35578i
$355$	−0.308703	−	0.331262i	−0.0163843	−	0.0175815i
$356$			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
$365$	2.53985	+	0.777421i	0.132942	+	0.0406921i
$366$	8.99831	−	15.5855i	0.470349	−	0.814668i
$367$	−19.0638	−	11.0065i	−0.995123	−	0.574535i	−0.0883215	−	0.996092i	$-0.528150\pi$
$367$	−19.0638	−	11.0065i	−0.995123	−	0.574535i	−0.906802	+	0.421557i	$0.861484\pi$
$368$	−3.51214	−	6.08320i	−0.183083	−	0.317109i
$369$	24.9202			1.29729
$370$	−9.80991	+	9.42155i	−0.509993	+	0.489803i
$371$	32.8484			1.70540
$372$	−2.18900	−	3.79146i	−0.113494	−	0.196578i
$373$	−0.696232	−	0.401970i	−0.0360495	−	0.0208132i	0.481867	−	0.876244i	$-0.339959\pi$
$373$	−0.696232	−	0.401970i	−0.0360495	−	0.0208132i	−0.517916	+	0.855431i	$0.673292\pi$
$374$	0.617314	−	1.06922i	0.0319206	−	0.0552880i
$375$	31.5867	−	4.97099i	1.63113	−	0.256701i
$376$			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	−0.856693	−	0.515827i	$-0.827485\pi$
$383$	0.359573	−	0.622798i	0.0183733	−	0.0318235i	0.875066	+	0.484004i	$0.160818\pi$
$384$			2.85998i			0.145948i
$385$	21.3802	−	19.9242i	1.08963	−	1.01543i
$386$	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	$0.779173\pi$
$390$	5.69741	−	5.30943i	0.288500	−	0.268853i
$391$	−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
$395$	16.8378	−	15.6912i	0.847200	−	0.789507i
$396$	−14.1226			−0.709690
$397$		−	15.3780i		−	0.771802i	−0.922540	−	0.385901i	$-0.873891\pi$
$397$		−	15.3780i		−	0.771802i	0.922540	−	0.385901i	$-0.126109\pi$
$398$	−15.3374	+	8.85505i	−0.768794	+	0.443863i
$399$		−	102.447i		−	5.12874i
$400$	−0.352054	+	4.98759i	−0.0176027	+	0.249380i
$401$			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
$405$	−3.48863	−	3.74356i	−0.173351	−	0.186019i
$406$	−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	$0.397753\pi$
$410$	−3.14886	+	10.2874i	−0.155511	+	0.508058i
$411$	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	$0.917707\pi$
$420$	−8.97186	+	29.3113i	−0.437782	+	1.43024i
$421$		−	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
$425$	−0.159410	+	2.25837i	−0.00773250	+	0.109547i
$426$	−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	$0.270525\pi$
$433$			31.2629i			1.50240i	−0.660075	+	0.751200i	$0.729475\pi$
$434$	7.33749			0.352211
$435$	35.6618	+	38.2677i	1.70985	+	1.83480i
$436$			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	$0.482787\pi$
$440$	1.78450	−	5.83001i	0.0850729	−	0.277935i
$441$	−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	$-0.988661\pi$
$443$		−	1.49918i		−	0.0712281i	0.999366	−	0.0356141i	$-0.0113387\pi$
$444$	−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	$0.440659\pi$
$457$	−16.2116	+	28.0793i	−0.758346	+	1.31349i	−0.943693	+	0.330821i	$0.892674\pi$
$458$	−1.60969			−0.0752157
$459$	2.44426	−	1.41119i	0.114088	−	0.0658688i
$460$	−10.7082	−	11.4907i	−0.499273	−	0.535757i
$461$	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	−0.990667	−	0.136302i	$-0.956478\pi$
$463$	−8.11837	+	14.0614i	−0.377293	+	0.653490i	0.613375	+	0.789792i	$0.289812\pi$
$464$	−7.08363	+	4.08974i	−0.328849	+	0.189861i
$465$	−6.67407	−	7.16177i	−0.309503	−	0.332119i
$466$	16.9060	−	9.76067i	0.783154	−	0.452154i
$467$	3.44377			0.159358			0.0796792	−	0.996821i	$-0.474610\pi$
$467$	3.44377			0.159358			0.0796792	+	0.996821i	$0.474610\pi$
$468$	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
$485$	−10.3342	+	33.7620i	−0.469251	+	1.53305i
$486$	10.5263	+	6.07737i	0.477483	+	0.275675i
$487$	−4.97590			−0.225479			−0.112740	−	0.993625i	$-0.535963\pi$
$487$	−4.97590			−0.225479			−0.112740	+	0.993625i	$0.535963\pi$
$488$	5.44953	+	3.14629i	0.246689	+	0.142426i
$489$		−	28.2736i		−	1.27858i
$490$	−24.3543	−	26.1339i	−1.10021	−	1.18061i
$491$	−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	$0.760411\pi$
$500$	1.73812	+	11.0444i	0.0777312	+	0.493921i
$501$	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	$0.231207\pi$
$503$	21.2832	+	36.8636i	0.948971	+	1.64367i	0.201372	+	0.979515i	$0.435460\pi$
$504$			24.8267i			1.10587i
$505$	4.12145	−	13.4649i	0.183402	−	0.599179i
$506$	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
$515$	−5.58054	+	18.2317i	−0.245908	+	0.803386i
$516$	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
$520$	1.85646	+	1.99212i	0.0814111	+	0.0873602i
$521$	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	−0.984716	−	0.174166i	$-0.944277\pi$
$523$	−7.81043	+	13.5281i	−0.341526	+	0.591541i	0.643190	+	0.765706i	$0.277610\pi$
$524$		−	6.34084i		−	0.277001i
$525$	−4.82621	+	68.3734i	−0.210633	+	2.98406i
$526$			27.7232i			1.20879i
$527$	0.600272	−	0.346567i	0.0261483	−	0.0150967i
$528$		−	7.79819i		−	0.339373i
$529$	26.3405			1.14524
$530$	11.2105	−	10.4471i	0.486953	−	0.453792i
$531$	−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
$535$	10.8253	−	10.0882i	0.468020	−	0.436149i
$536$	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
$540$	10.1966	−	9.50226i	0.438793	−	0.408912i
$541$		−	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	$-0.482898\pi$
$547$	2.51196			0.107404			0.0537018	+	0.998557i	$0.482898\pi$
$548$	8.15662	+	4.70923i	0.348434	+	0.201168i
$549$		−	32.5922i		−	1.39100i
$550$	0.959934	−	13.5995i	0.0409317	−	0.579884i
$551$	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
$555$	−10.8246	+	37.3635i	−0.459479	+	1.58599i
$556$	8.65305			0.366971
$557$	12.6417	+	21.8961i	0.535646	+	0.927766i	0.999132	+	0.0416616i	$0.0132651\pi$
$557$	12.6417	+	21.8961i	0.535646	+	0.927766i	−0.463486	+	0.886104i	$0.653402\pi$
$558$	−6.86639	−	3.96431i	−0.290677	−	0.167823i
$559$	4.64231	−	8.04072i	0.196349	−	0.340086i
$560$	−10.2488	−	3.13704i	−0.433090	−	0.132564i
$561$		−	3.53101i		−	0.149079i
$562$	16.1845	+	9.34413i	0.682702	+	0.394158i
$563$	−7.66929			−0.323222			−0.161611	−	0.986855i	$-0.551669\pi$
$563$	−7.66929			−0.323222			−0.161611	+	0.986855i	$0.551669\pi$
$564$	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	$-0.0970113\pi$
$570$	−32.5821	−	34.9630i	−1.36471	−	1.46444i
$571$	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
$575$	−29.1041	−	19.6587i	−1.21372	−	0.819826i
$576$	2.58973	+	4.48555i	0.107905	+	0.186898i
$577$	−11.0994	−	19.2247i	−0.462073	−	0.800335i	0.536991	−	0.843588i	$-0.319561\pi$
$577$	−11.0994	−	19.2247i	−0.462073	−	0.800335i	−0.999064	+	0.0432535i	$0.986228\pi$
$578$	16.7950			0.698579
$579$	36.7146	+	21.1972i	1.52581	+	0.880924i
$580$	−13.3804	+	12.4693i	−0.555593	+	0.517758i
$581$	32.0263			1.32868
$582$			45.1598i			1.87194i
$583$	−16.1823	+	9.34288i	−0.670204	+	0.386943i
$584$			1.18787i			0.0491545i
$585$	4.12801	−	13.4863i	0.170672	−	0.557589i
$586$			4.76349i			0.196778i
$587$	6.18890	−	10.7195i	0.255443	−	0.442441i	−0.709572	−	0.704632i	$-0.751112\pi$
$587$	6.18890	−	10.7195i	0.255443	−	0.442441i	0.965016	+	0.262192i	$0.0844452\pi$
$588$	−39.5688	−	22.8450i	−1.63179	−	0.942114i
$589$	−5.71984	+	9.90705i	−0.235682	+	0.408213i
$590$	16.8477	−	15.7005i	0.693611	−	0.646377i
$591$	−54.0248			−2.22228
$592$	−5.31298	−	2.96180i	−0.218362	−	0.121729i
$593$		−	44.0752i		−	1.80995i	−0.425463	−	0.904976i	$-0.639889\pi$
$593$		−	44.0752i		−	1.80995i	0.425463	−	0.904976i	$-0.360111\pi$
$594$	−14.7188	+	8.49793i	−0.603922	+	0.348674i
$595$	−4.64063	−	1.42045i	−0.190247	−	0.0582326i
$596$	−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
$605$	2.33337	−	7.62315i	0.0948648	−	0.309925i
$606$		−	18.0105i		−	0.731628i
$607$	12.6098	+	21.8408i	0.511815	+	0.886490i	0.999906	+	0.0136974i	$0.00436017\pi$
$607$	12.6098	+	21.8408i	0.511815	+	0.886490i	−0.488091	+	0.872793i	$0.662307\pi$
$608$	6.47189	−	3.73655i	0.262470	−	0.151537i
$609$	−97.1074	+	56.0650i	−3.93499	+	2.27187i
$610$	13.4545	+	4.11827i	0.544755	+	0.166744i
$611$	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	−0.989532	−	0.144315i	$-0.953902\pi$
$613$	−33.6551	+	19.4308i	−1.35932	+	0.784802i	−0.369785	+	0.929117i	$0.620569\pi$
$614$	−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	0.433320	−	0.901240i	$-0.357342\pi$
$617$	35.5323	−	20.5146i	1.43048	−	0.825886i	0.997157	+	0.0753540i	$0.0240087\pi$
$618$			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	$0.251496\pi$
$620$	2.50414	−	2.33361i	0.100569	−	0.0937201i
$621$			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
$625$	9.33474	+	23.1919i	0.373390	+	0.927675i
$626$	−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	$-0.195104\pi$
$643$	41.4828			1.63592			0.817962	+	0.575273i	$0.195104\pi$
$644$	29.1586	−	16.8347i	1.14901	−	0.663381i
$645$	35.6699	−	33.2409i	1.40450	−	1.30886i
$646$	2.93046	−	1.69190i	0.115297	−	0.0665670i
$647$	15.5065	−	26.8580i	0.609622	−	1.05590i	−0.381681	−	0.924294i	$-0.624655\pi$
$647$	15.5065	−	26.8580i	0.609622	−	1.05590i	0.991303	−	0.131602i	$-0.0420120\pi$
$648$	1.14422	−	1.98185i	0.0449492	−	0.0778543i
$649$	−24.3197	+	14.0410i	−0.954633	+	0.551158i
$650$	5.04570	+	3.40819i	0.197909	+	0.133680i
$651$	18.1736	−	10.4925i	0.712278	−	0.411234i
$652$	9.88597			0.387165
$653$	−4.23528	+	7.33571i	−0.165739	+	0.287069i	−0.936918	−	0.349551i	$-0.886334\pi$
$653$	−4.23528	+	7.33571i	−0.165739	+	0.287069i	0.771178	+	0.636619i	$0.219668\pi$
$654$	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
$670$	0.0602312	+	0.0184361i	0.00232693	+	0.000712250i
$671$	−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	$-0.990486\pi$
$673$	−39.5674	−	22.8442i	−1.52521	−	0.880580i	−0.525656	−	0.850697i	$-0.676180\pi$
$674$		−	11.4674i		−	0.441708i
$675$	17.4448	−	25.8264i	0.671450	−	0.994058i
$676$	−11.5170			−0.442962
$677$		−	34.8450i		−	1.33920i	−0.742722	−	0.669600i	$-0.766465\pi$
$677$		−	34.8450i		−	1.33920i	0.742722	−	0.669600i	$-0.233535\pi$
$678$	−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	0.825891	−	0.563829i	$-0.190672\pi$
$683$	−1.96909	−	3.41056i	−0.0753450	−	0.130501i	−0.901236	+	0.433328i	$0.857339\pi$
$684$	−33.5209	−	19.3533i	−1.28170	−	0.739992i
$685$	20.1380	+	6.16404i	0.769435	+	0.235516i
$686$	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
$690$	−42.9538	−	13.1477i	−1.63522	−	0.500525i
$691$	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
$700$	−23.9070	−	1.68750i	−0.903600	−	0.0637816i
$701$	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
$705$	12.5292	+	13.4447i	0.471876	+	0.506358i
$706$	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	$0.984375\pi$
$710$	0.132529	−	0.432976i	0.00497373	−	0.0162493i
$711$		−	53.3119i		−	1.99935i
$712$	−3.24928	+	1.87597i	−0.121772	+	0.0703050i
$713$			10.7526i			0.402689i
$714$	−6.20728			−0.232302
$715$	−5.06194	−	5.43184i	−0.189306	−	0.203139i
$716$	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	$0.903266\pi$
$720$	7.89587	+	8.47286i	0.294262	+	0.315765i
$721$	−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
$725$	−22.8917	+	33.8904i	−0.850178	+	1.25866i
$726$		−	10.1967i		−	0.378435i
$727$	10.9295	−	18.9305i	0.405354	−	0.702093i	−0.589009	−	0.808127i	$-0.700482\pi$
$727$	10.9295	−	18.9305i	0.405354	−	0.702093i	0.994363	+	0.106033i	$0.0338150\pi$
$728$	−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	0.458586	−	0.888650i	$-0.348356\pi$
$733$	−2.21236	−	1.27731i	−0.0817153	−	0.0471784i	−0.540301	+	0.841472i	$0.681690\pi$
$734$		−	22.0130i		−	0.812515i
$735$	−97.6922	−	29.9025i	−3.60343	−	1.10297i
$736$	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	$0.553242\pi$
$740$	−13.0643	−	3.78486i	−0.480252	−	0.139134i
$741$	−26.0275			−0.956145
$742$	16.4242	+	28.4475i	0.602950	+	1.04434i
$743$	13.0291	+	7.52236i	0.477992	+	0.275969i	0.719579	−	0.694410i	$-0.244335\pi$
$743$	13.0291	+	7.52236i	0.477992	+	0.275969i	−0.241587	+	0.970379i	$0.577668\pi$
$744$	2.18900	−	3.79146i	0.0802526	−	0.139001i
$745$	−2.81421	+	9.19409i	−0.103105	+	0.336845i
$746$		−	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
$755$	−1.41874	−	1.52241i	−0.0516332	−	0.0554062i
$756$	14.9388	+	25.8748i	0.543319	+	0.941056i
$757$	9.72544	+	16.8450i	0.353477	+	0.612241i	0.986856	−	0.161601i	$-0.0516658\pi$
$757$	9.72544	+	16.8450i	0.353477	+	0.612241i	−0.633379	+	0.773842i	$0.718333\pi$
$758$	−0.189378	+	0.328013i	−0.00687853	+	0.0119140i
$759$	47.4380	+	27.3883i	1.72189	+	0.994134i
$760$	12.2249	−	11.3924i	0.443444	−	0.413247i
$761$	−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
$765$	3.57524	+	3.83649i	0.129263	+	0.138709i
$766$	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	$-0.0389978\pi$
$770$	27.9450	+	8.55366i	1.00707	+	0.308252i
$771$		−	58.9670i		−	2.12365i
$772$	−7.41166	+	12.8374i	−0.266751	+	0.462027i
$773$	23.2941	+	13.4489i	0.837831	+	0.483722i	0.856526	−	0.516103i	$-0.172618\pi$
$773$	23.2941	+	13.4489i	0.837831	+	0.483722i	−0.0186952	+	0.999825i	$0.505951\pi$
$774$	19.7446	−	34.1987i	0.709706	−	1.22925i
$775$	4.28417	−	6.34256i	0.153892	−	0.227832i
$776$	−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
$780$	7.44680	+	2.27939i	0.266638	+	0.0816152i
$781$	−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	$0.198741\pi$
$787$			32.7991i			1.16916i	−0.811335	+	0.584581i	$0.801259\pi$
$788$		−	18.8899i		−	0.672926i
$789$	39.6439	+	68.6652i	1.41136	+	2.44454i
$790$	22.0078	+	6.73636i	0.783003	+	0.239669i
$791$		−	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
$795$	12.8271	−	41.9063i	0.454929	−	1.48626i
$796$	−15.3374	−	8.85505i	−0.543619	−	0.313859i
$797$	−18.6926	−	32.3766i	−0.662127	−	1.14684i	−0.980056	−	0.198723i	$-0.936321\pi$
$797$	−18.6926	−	32.3766i	−0.662127	−	1.14684i	0.317929	−	0.948115i	$-0.397013\pi$
$798$	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
$805$	55.0784	−	51.3277i	1.94126	−	1.80906i
$806$		−	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	$0.642499\pi$
$810$	1.49770	−	4.89302i	0.0526239	−	0.171923i
$811$	−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	−0.137992	−	0.990433i	$-0.544065\pi$
$823$	18.6688	−	10.7784i	0.650753	−	0.375712i	0.788745	+	0.614721i	$0.210731\pi$
$824$	−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	$0.539723\pi$
$827$	−26.5009	+	45.9009i	−0.921526	+	1.59613i	−0.797055	+	0.603907i	$0.793610\pi$
$828$	−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	$0.449522\pi$
$830$	10.9299	−	10.1856i	0.379384	−	0.353549i
$831$	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
$835$	21.3883	+	22.9512i	0.740172	+	0.794260i
$836$	−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	0.695215	−	0.718802i	$-0.255309\pi$
$853$	−8.02858	−	13.9059i	−0.274893	−	0.476129i	−0.970108	+	0.242673i	$0.921976\pi$
$854$	−15.0811	+	26.1212i	−0.516064	+	0.893850i
$855$	−82.7605	−	25.3321i	−2.83035	−	0.866340i
$856$	5.73095	+	3.30877i	0.195880	+	0.113091i
$857$	50.9495			1.74040			0.870202	−	0.492696i	$-0.163988\pi$
$857$	50.9495			1.74040			0.870202	+	0.492696i	$0.163988\pi$
$858$	−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	$0.758717\pi$
$860$	11.6228	+	12.4721i	0.396334	+	0.425295i
$861$	−65.9575			−2.24782
$862$		−	2.46095i		−	0.0838205i
$863$	2.94309	−	1.69919i	0.100184	−	0.0578411i	−0.449071	−	0.893496i	$-0.648245\pi$
$863$	2.94309	−	1.69919i	0.100184	−	0.0578411i	0.549255	+	0.835655i	$0.314912\pi$
$864$	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
$870$	−15.3099	+	50.0179i	−0.519056	+	1.69577i
$871$	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
$875$	−52.9391	+	8.33134i	−1.78967	+	0.281651i
$876$	1.69864	+	2.94214i	0.0573919	+	0.0994056i
$877$			24.2792i			0.819851i	0.912119	+	0.409925i	$0.134445\pi$
$877$			24.2792i			0.819851i	−0.912119	+	0.409925i	$0.865555\pi$
$878$			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	−0.837318	−	0.546716i	$-0.815878\pi$
$883$	1.62873	−	2.82104i	0.0548111	−	0.0949356i	0.892129	+	0.451781i	$0.149211\pi$
$884$	−0.275705	+	0.477535i	−0.00927296	+	0.0160612i
$885$	19.2772	−	62.9791i	0.647997	−	2.11702i
$886$	1.29833	−	0.749589i	0.0436181	−	0.0251829i
$887$		−	34.5745i		−	1.16090i	−0.814296	−	0.580450i	$-0.802877\pi$
$887$		−	34.5745i		−	1.16090i	0.814296	−	0.580450i	$-0.197123\pi$
$888$	−17.3946	+	0.261690i	−0.583724	+	0.00878174i
$889$	64.1966			2.15309
$890$	−6.13764	+	5.71968i	−0.205734	+	0.191724i
$891$	−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
$895$	17.1314	+	5.24375i	0.572640	+	0.175279i
$896$		−	4.79330i		−	0.160133i
$897$	−21.1868	+	12.2322i	−0.707405	+	0.408421i
$898$		−	26.2226i		−	0.875061i
$899$	12.5210			0.417598
$900$	21.4603	+	14.4957i	0.715345	+	0.483189i
$901$	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
$905$	−37.8030	−	40.5655i	−1.25662	−	1.34844i
$906$	−2.30505	−	1.33082i	−0.0765801	−	0.0442135i
$907$	−15.9340	+	27.5984i	−0.529078	+	0.916390i	0.470347	+	0.882482i	$0.344129\pi$
$907$	−15.9340	+	27.5984i	−0.529078	+	0.916390i	−0.999425	+	0.0339085i	$0.989205\pi$
$908$	1.50747	+	2.61101i	0.0500270	+	0.0866493i
$909$	−16.3087	−	28.2475i	−0.540925	−	0.936910i
$910$	−9.54881	+	8.89856i	−0.316540	+	0.294984i
$911$			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	$-0.241173\pi$
$920$	4.59714	−	15.0189i	0.151563	−	0.495160i
$921$	−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
$925$	−30.3671	−	1.68485i	−0.998464	−	0.0553976i
$926$	−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	$0.0740737\pi$
$930$	2.86524	−	9.36080i	0.0939550	−	0.306953i
$931$			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	−0.402553	−	0.915397i	$-0.631877\pi$
$937$	5.78313	−	3.33889i	0.188927	−	0.109077i	0.591480	+	0.806320i	$0.298544\pi$
$938$	−0.0675131	+	0.116936i	−0.00220438	+	0.00381810i
$939$			51.0125i			1.66473i
$940$	−4.70100	+	4.38087i	−0.153330	+	0.142888i
$941$	−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
$945$	45.5472	+	48.8755i	1.48165	+	1.58992i
$946$	−10.3943	−	18.0035i	−0.337948	−	0.585344i
$947$	−6.35306	−	11.0038i	−0.206447	−	0.357576i	0.744146	−	0.668017i	$-0.232857\pi$
$947$	−6.35306	−	11.0038i	−0.206447	−	0.357576i	−0.950593	+	0.310441i	$0.899523\pi$
$948$	29.4375			0.956087
$949$	1.25277	+	0.723286i	0.0406666	+	0.0234788i
$950$	20.9148	−	30.9637i	0.678567	−	1.00459i
$951$	−12.9118			−0.418695
$952$		−	2.17040i		−	0.0703429i
$953$	−7.63027	+	4.40534i	−0.247169	+	0.142703i	−0.618467	−	0.785811i	$-0.712246\pi$
$953$	−7.63027	+	4.40534i	−0.247169	+	0.142703i	0.371298	+	0.928514i	$0.378913\pi$
$954$		−	35.4947i		−	1.14918i
$955$	−13.4486	−	4.11647i	−0.435186	−	0.133206i
$956$		−	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
$960$	−4.67851	+	4.35991i	−0.150998	+	0.140716i
$961$	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
$965$	−9.70133	+	31.6944i	−0.312297	+	1.02028i
$966$	48.1469	−	83.3929i	1.54910	−	2.68312i
$967$	−28.7222	+	49.7484i	−0.923645	+	1.59980i	−0.129918	+	0.991525i	$0.541471\pi$
$967$	−28.7222	+	49.7484i	−0.923645	+	1.59980i	−0.793727	+	0.608275i	$0.791862\pi$
$968$	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
$975$	17.3709	+	1.22615i	0.556315	+	0.0392681i
$976$			6.29258i			0.201420i
$977$	5.86092	+	10.1514i	0.187507	+	0.324772i	0.944419	−	0.328745i	$-0.106626\pi$
$977$	5.86092	+	10.1514i	0.187507	+	0.324772i	−0.756911	+	0.653518i	$0.773292\pi$
$978$	24.4857	−	14.1368i	0.782966	−	0.452046i
$979$	8.85969	−	5.11514i	0.283157	−	0.163481i
$980$	10.4555	−	34.1584i	0.333989	−	1.09115i
$981$	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	−0.133314	−	0.991074i	$-0.542562\pi$
$983$	20.6403	−	11.9167i	0.658324	−	0.380083i	0.791638	+	0.610990i	$0.209229\pi$
$984$	−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
$990$	−21.5294	−	23.1026i	−0.684249	−	0.734250i
$991$			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
$995$	−37.8668	−	11.5906i	−1.20046	−	0.367448i
$996$	9.55443	−	16.5488i	0.302744	−	0.524368i
$997$	12.0633	+	20.8943i	0.382050	+	0.661730i	0.991355	−	0.131206i	$-0.0418849\pi$
$997$	12.0633	+	20.8943i	0.382050	+	0.661730i	−0.609305	+	0.792936i	$0.708552\pi$
$998$		−	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.d.159.8	yes	16
5.4	even	2		370.2.m.c.159.1	✓	16
37.27	even	6		370.2.m.c.249.1	yes	16
185.64	even	6	inner	370.2.m.d.249.8	yes	16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
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} +(-0.654464 + 2.13815i) 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} +(-4.67851 + 4.35991i) 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} +(-1.52446 - 1.63586i) q^{20} +(-6.85436 - 11.8721i) q^{21} +(1.36333 + 2.36136i) q^{22} +7.02428 q^{23} +(-2.47681 - 1.42999i) q^{24} +(-4.14335 - 2.79868i) q^{25} -1.21778 q^{26} +6.23321i q^{27} +(4.15112 - 2.39665i) q^{28} -8.17947i q^{29} +(-6.11505 - 1.87175i) q^{30} +1.53078i q^{31} +(0.500000 - 0.866025i) q^{32} +(6.75343 + 3.89910i) q^{33} +(0.226399 - 0.392135i) q^{34} +(7.84115 - 7.30718i) q^{35} -5.17946 q^{36} +(5.22148 - 3.12028i) q^{37} +7.47310i q^{38} +(-3.01622 + 1.74141i) q^{39} +(0.654464 - 2.13815i) 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} +(0.352054 - 4.98759i) q^{50} -1.29499i q^{51} +(-0.608891 - 1.05463i) q^{52} +(-5.93485 + 3.42649i) q^{53} +(-5.39812 + 3.11660i) q^{54} +(-1.78450 + 5.83001i) 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} +(-1.85646 - 1.99212i) q^{65} +7.79819i q^{66} +(-0.0243958 - 0.0140849i) q^{67} +0.452798 q^{68} +(17.3978 + 10.0446i) q^{69} +(10.2488 + 3.13704i) 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} +(-7.89587 - 8.47286i) 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} +(-12.2249 + 11.3924i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 12 q^{7} - 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} + 3 q^{12} - 6 q^{13} + 9 q^{15} - 8 q^{16} - 13 q^{18} - 3 q^{19} - 6 q^{20} - 6 q^{21} - 3 q^{22} - 22 q^{23}+ \cdots + 37 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 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^20 - 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 + 18 * q^35 - 26 * q^36 + 16 * q^37 + 15 * q^39 + 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 - 35 * 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 + 46 * q^65 + 24 * q^67 + 42 * q^69 + 12 * 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 - q^90 - 24 * q^91 + 11 * q^92 - 25 * q^93 - 27 * q^94 - 53 * q^95 - 3 * q^96 + 68 * q^97 - 4 * q^98 + 37 * q^99

Introduction

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