LMFDB - Embedded newform 627.2.j.d.58.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [627,2,Mod(58,627)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("627.58"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(627, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.j (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			58.4
Character	$\chi$	$=$	627.58
Dual form			627.2.j.d.400.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.782102 + 0.568230i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.329236 + 1.01328i) q^{4} +(-0.534189 - 0.388111i) q^{5} +(-0.782102 - 0.568230i) q^{6} +(-1.56670 + 4.82180i) q^{7} +(-0.915756 - 2.81841i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.638327 q^{10} +(-2.30061 - 2.38898i) q^{11} -1.06543 q^{12} +(-0.634939 + 0.461310i) q^{13} +(-1.51458 - 4.66138i) q^{14} +(0.204042 - 0.627977i) q^{15} +(0.593815 + 0.431432i) q^{16} +(0.828222 + 0.601739i) q^{17} +(0.298736 - 0.919416i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(0.569141 - 0.413505i) q^{20} -5.06994 q^{21} +(3.15680 + 0.561150i) q^{22} +2.44192 q^{23} +(2.39748 - 1.74187i) q^{24} +(-1.41036 - 4.34063i) q^{25} +(0.234457 - 0.721583i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-4.37004 - 3.17502i) q^{28} +(-0.741993 + 2.28362i) q^{29} +(0.197254 + 0.607085i) q^{30} +(1.25306 - 0.910403i) q^{31} +5.21732 q^{32} +(1.56113 - 2.92624i) q^{33} -0.989680 q^{34} +(2.70831 - 1.96770i) q^{35} +(-0.329236 - 1.01328i) q^{36} +(-1.34706 + 4.14581i) q^{37} +(0.782102 + 0.568230i) q^{38} +(-0.634939 - 0.461310i) q^{39} +(-0.604668 + 1.86098i) q^{40} +(0.837053 + 2.57618i) q^{41} +(3.96521 - 2.88089i) q^{42} -5.29864 q^{43} +(3.17816 - 1.54463i) q^{44} +0.660294 q^{45} +(-1.90983 + 1.38757i) q^{46} +(-1.10564 - 3.40282i) q^{47} +(-0.226817 + 0.698072i) q^{48} +(-15.1321 - 10.9941i) q^{49} +(3.56952 + 2.59341i) q^{50} +(-0.316353 + 0.973634i) q^{51} +(-0.258394 - 0.795254i) q^{52} +(-9.47004 + 6.88039i) q^{53} +0.966731 q^{54} +(0.301770 + 2.16906i) q^{55} +15.0245 q^{56} +(0.809017 - 0.587785i) q^{57} +(-0.717308 - 2.20765i) q^{58} +(2.93223 - 9.02448i) q^{59} +(0.569141 + 0.413505i) q^{60} +(-0.711556 - 0.516976i) q^{61} +(-0.462704 + 1.42406i) q^{62} +(-1.56670 - 4.82180i) q^{63} +(-5.26811 + 3.82750i) q^{64} +0.518217 q^{65} +(0.441819 + 3.17570i) q^{66} +12.5757 q^{67} +(-0.882413 + 0.641111i) q^{68} +(0.754594 + 2.32240i) q^{69} +(-1.00006 + 3.07788i) q^{70} +(-5.05663 - 3.67386i) q^{71} +(2.39748 + 1.74187i) q^{72} +(-1.69571 + 5.21886i) q^{73} +(-1.30224 - 4.00788i) q^{74} +(3.69236 - 2.68266i) q^{75} +1.06543 q^{76} +(15.1235 - 7.35026i) q^{77} +0.758718 q^{78} +(-5.50789 + 4.00171i) q^{79} +(-0.149766 - 0.460932i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-2.11853 - 1.53920i) q^{82} +(-2.52786 - 1.83659i) q^{83} +(1.66921 - 5.13729i) q^{84} +(-0.208886 - 0.642884i) q^{85} +(4.14407 - 3.01085i) q^{86} -2.40114 q^{87} +(-4.62632 + 8.67176i) q^{88} -12.8059 q^{89} +(-0.516417 + 0.375199i) q^{90} +(-1.22959 - 3.78428i) q^{91} +(-0.803967 + 2.47436i) q^{92} +(1.25306 + 0.910403i) q^{93} +(2.79831 + 2.03309i) q^{94} +(-0.204042 + 0.627977i) q^{95} +(1.61224 + 4.96196i) q^{96} +(-8.40530 + 6.10681i) q^{97} +18.0820 q^{98} +(3.26543 + 0.580461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 3 q^{2} - 12 q^{3} - 21 q^{4} - 2 q^{5} + 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} + 2 q^{10} - 15 q^{11} + 74 q^{12} + 4 q^{13} - 24 q^{14} - 7 q^{15} - 25 q^{16} + 11 q^{17} - 2 q^{18} + 12 q^{19}+ \cdots - 5 q^{99}+O(q^{100}) $ 48 * q + 3 * q^2 - 12 * q^3 - 21 * q^4 - 2 * q^5 + 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 + 2 * q^10 - 15 * q^11 + 74 * q^12 + 4 * q^13 - 24 * q^14 - 7 * q^15 - 25 * q^16 + 11 * q^17 - 2 * q^18 + 12 * q^19 + 19 * q^20 - 6 * q^21 - 18 * q^22 + 60 * q^23 - 5 * q^24 - 8 * q^25 + 43 * q^26 - 12 * q^27 + 24 * q^28 + 9 * q^29 - 3 * q^30 - 16 * q^31 - 32 * q^32 + 5 * q^33 + 46 * q^34 + 22 * q^35 - 21 * q^36 - 23 * q^37 - 3 * q^38 + 4 * q^39 + 4 * q^40 - 10 * q^41 + 26 * q^42 + 2 * q^43 - 8 * q^44 + 18 * q^45 - 49 * q^46 - 57 * q^47 - 30 * q^48 - 22 * q^49 - 4 * q^50 - 14 * q^51 + 35 * q^52 - 22 * q^53 - 2 * q^54 - 22 * q^55 + 8 * q^56 + 12 * q^57 - 74 * q^58 + 29 * q^59 + 19 * q^60 - 24 * q^61 + 51 * q^62 + 4 * q^63 + 37 * q^64 - 60 * q^65 - 18 * q^66 + 92 * q^67 + 52 * q^68 - 20 * q^69 + 101 * q^70 - 38 * q^71 - 5 * q^72 - 24 * q^73 + 40 * q^74 - 43 * q^75 - 74 * q^76 + 53 * q^77 - 12 * q^78 + 11 * q^79 - 173 * q^80 - 12 * q^81 - 64 * q^82 - 20 * q^83 - 41 * q^84 + 29 * q^85 + 36 * q^86 - 26 * q^87 + 29 * q^88 + 42 * q^89 + 2 * q^90 - 35 * q^91 + 49 * q^92 - 16 * q^93 + 74 * q^94 + 7 * q^95 + 43 * q^96 - 45 * q^97 - 118 * q^98 - 5 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−0.782102	+	0.568230i	−0.553030	+	0.401800i	−0.828901	−	0.559395i	$-0.811034\pi$
$2$	−0.782102	+	0.568230i	−0.553030	+	0.401800i	0.275872	+	0.961194i	$0.411034\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.329236	+	1.01328i	−0.164618	+	0.506642i
$5$	−0.534189	−	0.388111i	−0.238897	−	0.173568i	0.461895	−	0.886935i	$-0.347170\pi$
$5$	−0.534189	−	0.388111i	−0.238897	−	0.173568i	−0.700792	+	0.713366i	$0.747170\pi$
$6$	−0.782102	−	0.568230i	−0.319292	−	0.231979i
$7$	−1.56670	+	4.82180i	−0.592156	+	1.82247i	−0.0237542	+	0.999718i	$0.507562\pi$
$7$	−1.56670	+	4.82180i	−0.592156	+	1.82247i	−0.568402	+	0.822751i	$0.692438\pi$
$8$	−0.915756	−	2.81841i	−0.323769	−	0.996457i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.638327			0.201857
$11$	−2.30061	−	2.38898i	−0.693659	−	0.720304i
$11$	−2.30061	−	2.38898i	−0.693659	−	0.720304i
$12$	−1.06543			−0.307563
$13$	−0.634939	+	0.461310i	−0.176100	+	0.127944i	−0.672344	−	0.740239i	$-0.734712\pi$
$13$	−0.634939	+	0.461310i	−0.176100	+	0.127944i	0.496243	+	0.868183i	$0.334712\pi$
$14$	−1.51458	−	4.66138i	−0.404787	−	1.24581i
$15$	0.204042	−	0.627977i	0.0526834	−	0.162143i
$16$	0.593815	+	0.431432i	0.148454	+	0.107858i
$17$	0.828222	+	0.601739i	0.200873	+	0.145943i	0.683675	−	0.729787i	$-0.260381\pi$
$17$	0.828222	+	0.601739i	0.200873	+	0.145943i	−0.482801	+	0.875730i	$0.660381\pi$
$18$	0.298736	−	0.919416i	0.0704128	−	0.216708i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	0.569141	−	0.413505i	0.127264	−	0.0924626i
$21$	−5.06994			−1.10635
$22$	3.15680	+	0.561150i	0.673032	+	0.119638i
$23$	2.44192			0.509175			0.254587	−	0.967050i	$-0.418060\pi$
$23$	2.44192			0.509175			0.254587	+	0.967050i	$0.418060\pi$
$24$	2.39748	−	1.74187i	0.489383	−	0.355558i
$25$	−1.41036	−	4.34063i	−0.282071	−	0.868127i
$26$	0.234457	−	0.721583i	0.0459807	−	0.141514i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−4.37004	−	3.17502i	−0.825860	−	0.600023i
$29$	−0.741993	+	2.28362i	−0.137785	+	0.424058i	−0.996013	−	0.0892108i	$-0.971566\pi$
$29$	−0.741993	+	2.28362i	−0.137785	+	0.424058i	0.858228	+	0.513269i	$0.171566\pi$
$30$	0.197254	+	0.607085i	0.0360134	+	0.110838i
$31$	1.25306	−	0.910403i	0.225057	−	0.163513i	−0.469543	−	0.882909i	$-0.655581\pi$
$31$	1.25306	−	0.910403i	0.225057	−	0.163513i	0.694600	+	0.719396i	$0.255581\pi$
$32$	5.21732			0.922300
$33$	1.56113	−	2.92624i	0.271757	−	0.509393i
$34$	−0.989680			−0.169729
$35$	2.70831	−	1.96770i	0.457787	−	0.332602i
$36$	−0.329236	−	1.01328i	−0.0548727	−	0.168881i
$37$	−1.34706	+	4.14581i	−0.221455	+	0.681567i	0.777178	+	0.629281i	$0.216651\pi$
$37$	−1.34706	+	4.14581i	−0.221455	+	0.681567i	−0.998632	+	0.0522857i	$0.983349\pi$
$38$	0.782102	+	0.568230i	0.126874	+	0.0921791i
$39$	−0.634939	−	0.461310i	−0.101672	−	0.0738688i
$40$	−0.604668	+	1.86098i	−0.0956064	+	0.294246i
$41$	0.837053	+	2.57618i	0.130726	+	0.402332i	0.994901	−	0.100859i	$-0.0321591\pi$
$41$	0.837053	+	2.57618i	0.130726	+	0.402332i	−0.864175	+	0.503191i	$0.832159\pi$
$42$	3.96521	−	2.88089i	0.611845	−	0.444532i
$43$	−5.29864			−0.808034			−0.404017	−	0.914751i	$-0.632386\pi$
$43$	−5.29864			−0.808034			−0.404017	+	0.914751i	$0.632386\pi$
$44$	3.17816	−	1.54463i	0.479125	−	0.232862i
$45$	0.660294			0.0984308
$46$	−1.90983	+	1.38757i	−0.281589	+	0.204586i
$47$	−1.10564	−	3.40282i	−0.161275	−	0.496352i	0.837468	−	0.546487i	$-0.184035\pi$
$47$	−1.10564	−	3.40282i	−0.161275	−	0.496352i	−0.998742	+	0.0501343i	$0.984035\pi$
$48$	−0.226817	+	0.698072i	−0.0327382	+	0.100758i
$49$	−15.1321	−	10.9941i	−2.16173	−	1.57059i
$50$	3.56952	+	2.59341i	0.504807	+	0.366764i
$51$	−0.316353	+	0.973634i	−0.0442982	+	0.136336i
$52$	−0.258394	−	0.795254i	−0.0358328	−	0.110282i
$53$	−9.47004	+	6.88039i	−1.30081	+	0.945094i	−0.999963	−	0.00857844i	$-0.997269\pi$
$53$	−9.47004	+	6.88039i	−1.30081	+	0.945094i	−0.300847	+	0.953672i	$0.597269\pi$
$54$	0.966731			0.131555
$55$	0.301770	+	2.16906i	0.0406906	+	0.292475i
$56$	15.0245			2.00773
$57$	0.809017	−	0.587785i	0.107157	−	0.0778541i
$58$	−0.717308	−	2.20765i	−0.0941872	−	0.289878i
$59$	2.93223	−	9.02448i	0.381744	−	1.17489i	−0.557071	−	0.830465i	$-0.688075\pi$
$59$	2.93223	−	9.02448i	0.381744	−	1.17489i	0.938815	−	0.344422i	$-0.111925\pi$
$60$	0.569141	+	0.413505i	0.0734758	+	0.0533833i
$61$	−0.711556	−	0.516976i	−0.0911055	−	0.0661920i	0.541300	−	0.840830i	$-0.317932\pi$
$61$	−0.711556	−	0.516976i	−0.0911055	−	0.0661920i	−0.632405	+	0.774638i	$0.717932\pi$
$62$	−0.462704	+	1.42406i	−0.0587635	+	0.180855i
$63$	−1.56670	−	4.82180i	−0.197385	−	0.607490i
$64$	−5.26811	+	3.82750i	−0.658513	+	0.478438i
$65$	0.518217			0.0642769
$66$	0.441819	+	3.17570i	0.0543842	+	0.390901i
$67$	12.5757			1.53637			0.768183	−	0.640230i	$-0.221161\pi$
$67$	12.5757			1.53637			0.768183	+	0.640230i	$0.221161\pi$
$68$	−0.882413	+	0.641111i	−0.107008	+	0.0777461i
$69$	0.754594	+	2.32240i	0.0908424	+	0.279584i
$70$	−1.00006	+	3.07788i	−0.119531	+	0.367877i
$71$	−5.05663	−	3.67386i	−0.600112	−	0.436007i	0.245807	−	0.969319i	$-0.420947\pi$
$71$	−5.05663	−	3.67386i	−0.600112	−	0.436007i	−0.845918	+	0.533312i	$0.820947\pi$
$72$	2.39748	+	1.74187i	0.282546	+	0.205281i
$73$	−1.69571	+	5.21886i	−0.198468	+	0.610821i	0.801451	+	0.598061i	$0.204062\pi$
$73$	−1.69571	+	5.21886i	−0.198468	+	0.610821i	−0.999919	+	0.0127606i	$0.995938\pi$
$74$	−1.30224	−	4.00788i	−0.151382	−	0.465907i
$75$	3.69236	−	2.68266i	0.426357	−	0.309767i
$76$	1.06543			0.122213
$77$	15.1235	−	7.35026i	1.72349	−	0.837639i
$78$	0.758718			0.0859079
$79$	−5.50789	+	4.00171i	−0.619686	+	0.450228i	−0.852812	−	0.522219i	$-0.825105\pi$
$79$	−5.50789	+	4.00171i	−0.619686	+	0.450228i	0.233126	+	0.972447i	$0.425105\pi$
$80$	−0.149766	−	0.460932i	−0.0167443	−	0.0515338i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−2.11853	−	1.53920i	−0.233952	−	0.169976i
$83$	−2.52786	−	1.83659i	−0.277468	−	0.201592i	0.440344	−	0.897829i	$-0.354856\pi$
$83$	−2.52786	−	1.83659i	−0.277468	−	0.201592i	−0.717812	+	0.696237i	$0.754856\pi$
$84$	1.66921	−	5.13729i	0.182126	−	0.560525i
$85$	−0.208886	−	0.642884i	−0.0226568	−	0.0697306i
$86$	4.14407	−	3.01085i	0.446867	−	0.324668i
$87$	−2.40114			−0.257429
$88$	−4.62632	+	8.67176i	−0.493167	+	0.924413i
$89$	−12.8059			−1.35742			−0.678712	−	0.734405i	$-0.737461\pi$
$89$	−12.8059			−1.35742			−0.678712	+	0.734405i	$0.737461\pi$
$90$	−0.516417	+	0.375199i	−0.0544351	+	0.0395494i
$91$	−1.22959	−	3.78428i	−0.128896	−	0.396701i
$92$	−0.803967	+	2.47436i	−0.0838194	+	0.257970i
$93$	1.25306	+	0.910403i	0.129937	+	0.0944044i
$94$	2.79831	+	2.03309i	0.288624	+	0.209697i
$95$	−0.204042	+	0.627977i	−0.0209343	+	0.0644290i
$96$	1.61224	+	4.96196i	0.164549	+	0.506428i
$97$	−8.40530	+	6.10681i	−0.853429	+	0.620052i	−0.926089	−	0.377304i	$-0.876851\pi$
$97$	−8.40530	+	6.10681i	−0.853429	+	0.620052i	0.0726605	+	0.997357i	$0.476851\pi$
$98$	18.0820			1.82656
$99$	3.26543	+	0.580461i	0.328189	+	0.0583385i
$100$	4.86264			0.486264
$101$	−9.78327	+	7.10796i	−0.973471	+	0.707268i	−0.956240	−	0.292583i	$-0.905485\pi$
$101$	−9.78327	+	7.10796i	−0.973471	+	0.707268i	−0.0172313	+	0.999852i	$0.505485\pi$
$102$	−0.305828	−	0.941242i	−0.0302815	−	0.0931969i
$103$	0.164846	−	0.507343i	0.0162427	−	0.0499900i	−0.942607	−	0.333905i	$-0.891633\pi$
$103$	0.164846	−	0.507343i	0.0162427	−	0.0499900i	0.958849	+	0.283915i	$0.0916334\pi$
$104$	1.88161	+	1.36707i	0.184507	+	0.134052i
$105$	2.70831	+	1.96770i	0.264304	+	0.192028i
$106$	3.49689	−	10.7623i	0.339648	−	1.04533i
$107$	2.25067	+	6.92686i	0.217581	+	0.669644i	0.998960	+	0.0455884i	$0.0145163\pi$
$107$	2.25067	+	6.92686i	0.217581	+	0.669644i	−0.781380	+	0.624056i	$0.785484\pi$
$108$	0.861952	−	0.626244i	0.0829413	−	0.0602604i
$109$	−9.77282			−0.936066			−0.468033	−	0.883711i	$-0.655037\pi$
$109$	−9.77282			−0.936066			−0.468033	+	0.883711i	$0.655037\pi$
$110$	−1.46854	−	1.52495i	−0.140020	−	0.145398i
$111$	−4.35916			−0.413753
$112$	−3.01061	+	2.18733i	−0.284476	+	0.206684i
$113$	−2.54708	−	7.83911i	−0.239609	−	0.737442i	−0.996476	−	0.0838730i	$-0.973271\pi$
$113$	−2.54708	−	7.83911i	−0.239609	−	0.737442i	0.756867	−	0.653569i	$-0.226729\pi$
$114$	−0.298736	+	0.919416i	−0.0279792	+	0.0861112i
$115$	−1.30444	−	0.947735i	−0.121640	−	0.0883767i
$116$	−2.06967	−	1.50370i	−0.192164	−	0.139615i
$117$	0.242525	−	0.746416i	0.0224215	−	0.0690062i
$118$	2.83468	+	8.72425i	0.260953	+	0.803132i
$119$	−4.19904	+	3.05078i	−0.384925	+	0.279664i
$120$	−1.95675			−0.178626
$121$	−0.414424	+	10.9922i	−0.0376749	+	0.999290i
$122$	0.850271			0.0769799
$123$	−2.19143	+	1.59217i	−0.197595	+	0.143561i
$124$	0.509944	+	1.56945i	0.0457943	+	0.140940i
$125$	−1.95146	+	6.00598i	−0.174544	+	0.537191i
$126$	3.96521	+	2.88089i	0.353249	+	0.256650i
$127$	12.3556	+	8.97684i	1.09638	+	0.796566i	0.980465	−	0.196693i	$-0.0630203\pi$
$127$	12.3556	+	8.97684i	1.09638	+	0.796566i	0.115914	+	0.993259i	$0.463020\pi$
$128$	−1.27919	+	3.93693i	−0.113065	+	0.347979i
$129$	−1.63737	−	5.03930i	−0.144162	−	0.443686i
$130$	−0.405298	+	0.294467i	−0.0355470	+	0.0258264i
$131$	11.4559			1.00091			0.500454	−	0.865763i	$-0.333167\pi$
$131$	11.4559			1.00091			0.500454	+	0.865763i	$0.333167\pi$
$132$	2.45114	+	2.54529i	0.213344	+	0.221539i
$133$	5.06994			0.439620
$134$	−9.83548	+	7.14590i	−0.849656	+	0.617311i
$135$	0.204042	+	0.627977i	0.0175611	+	0.0540476i
$136$	0.937495	−	2.88531i	0.0803895	−	0.247413i
$137$	−7.56987	−	5.49984i	−0.646738	−	0.469883i	0.215420	−	0.976521i	$-0.430888\pi$
$137$	−7.56987	−	5.49984i	−0.646738	−	0.469883i	−0.862158	+	0.506639i	$0.830888\pi$
$138$	−1.90983	−	1.38757i	−0.162575	−	0.118118i
$139$	−3.66165	+	11.2694i	−0.310577	+	0.955859i	0.666959	+	0.745094i	$0.267595\pi$
$139$	−3.66165	+	11.2694i	−0.310577	+	0.955859i	−0.977537	+	0.210765i	$0.932405\pi$
$140$	1.10217	+	3.39212i	0.0931501	+	0.286687i
$141$	2.89461	−	2.10306i	0.243770	−	0.177109i
$142$	6.04240			0.507067
$143$	2.56280	+	0.455562i	0.214312	+	0.0380960i
$144$	−0.733996			−0.0611663
$145$	1.28266	−	0.931909i	0.106519	−	0.0773908i
$146$	−1.63930	−	5.04524i	−0.135669	−	0.417547i
$147$	5.77994	−	17.7888i	0.476722	−	1.46720i
$148$	−3.75739	−	2.72990i	−0.308855	−	0.224397i
$149$	10.3853	+	7.54536i	0.850797	+	0.618140i	0.925366	−	0.379076i	$-0.123758\pi$
$149$	10.3853	+	7.54536i	0.850797	+	0.618140i	−0.0745687	+	0.997216i	$0.523758\pi$
$150$	−1.36344	+	4.19623i	−0.111324	+	0.342620i
$151$	5.04182	+	15.5171i	0.410297	+	1.26277i	0.916390	+	0.400287i	$0.131089\pi$
$151$	5.04182	+	15.5171i	0.410297	+	1.26277i	−0.506093	+	0.862479i	$0.668911\pi$
$152$	−2.39748	+	1.74187i	−0.194461	+	0.141284i
$153$	−1.02374			−0.0827644
$154$	−7.65150	+	14.3423i	−0.616575	+	1.15574i
$155$	−1.02271			−0.0821460
$156$	0.676484	−	0.491494i	0.0541620	−	0.0393510i
$157$	6.63298	+	20.4142i	0.529369	+	1.62923i	0.755511	+	0.655136i	$0.227389\pi$
$157$	6.63298	+	20.4142i	0.529369	+	1.62923i	−0.226141	+	0.974094i	$0.572611\pi$
$158$	2.03383	−	6.25950i	0.161803	−	0.497979i
$159$	−9.47004	−	6.88039i	−0.751023	−	0.545650i
$160$	−2.78703	−	2.02490i	−0.220334	−	0.160082i
$161$	−3.82575	+	11.7744i	−0.301511	+	0.927955i
$162$	0.298736	+	0.919416i	0.0234709	+	0.0722361i
$163$	16.3239	−	11.8600i	1.27859	−	0.928948i	0.279078	−	0.960268i	$-0.409971\pi$
$163$	16.3239	−	11.8600i	1.27859	−	0.928948i	0.999509	+	0.0313205i	$0.00997126\pi$
$164$	−2.88599			−0.225358
$165$	−1.96964	+	0.957275i	−0.153336	+	0.0745238i
$166$	3.02065			0.234448
$167$	−14.9960	+	10.8952i	−1.16043	+	0.843098i	−0.989832	−	0.142243i	$-0.954569\pi$
$167$	−14.9960	+	10.8952i	−1.16043	+	0.843098i	−0.170594	+	0.985341i	$0.554569\pi$
$168$	4.64283	+	14.2892i	0.358202	+	1.10243i
$169$	−3.82688	+	11.7779i	−0.294375	+	0.905994i
$170$	0.528676	+	0.384106i	0.0405476	+	0.0294596i
$171$	0.809017	+	0.587785i	0.0618671	+	0.0449491i
$172$	1.74450	−	5.36903i	0.133017	−	0.409385i
$173$	−0.284087	−	0.874331i	−0.0215988	−	0.0664741i	0.939676	−	0.342065i	$-0.111126\pi$
$173$	−0.284087	−	0.874331i	−0.0215988	−	0.0664741i	−0.961275	+	0.275591i	$0.911126\pi$
$174$	1.87794	−	1.36440i	0.142366	−	0.103435i
$175$	23.1393			1.74916
$176$	−0.335454	−	2.41117i	−0.0252858	−	0.181748i
$177$	9.48890			0.713229
$178$	10.0155	−	7.27670i	0.750695	−	0.545412i
$179$	6.60840	+	20.3386i	0.493935	+	1.52018i	0.818610	+	0.574350i	$0.194745\pi$
$179$	6.60840	+	20.3386i	0.493935	+	1.52018i	−0.324675	+	0.945826i	$0.605255\pi$
$180$	−0.217393	+	0.669066i	−0.0162035	+	0.0498692i
$181$	−11.8372	−	8.60021i	−0.879851	−	0.639249i	0.0533613	−	0.998575i	$-0.483006\pi$
$181$	−11.8372	−	8.60021i	−0.879851	−	0.639249i	−0.933212	+	0.359326i	$0.883006\pi$
$182$	3.11201	+	2.26101i	0.230677	+	0.167597i
$183$	0.271790	−	0.836485i	0.0200913	−	0.0618347i
$184$	−2.23620	−	6.88231i	−0.164855	−	0.507371i
$185$	2.32862	−	1.69184i	0.171203	−	0.124386i
$186$	−1.49734			−0.109790
$187$	−0.467873	−	3.36297i	−0.0342143	−	0.245925i
$188$	3.81204			0.278022
$189$	4.10167	−	2.98004i	0.298352	−	0.216766i
$190$	−0.197254	−	0.607085i	−0.0143103	−	0.0440425i
$191$	7.26038	−	22.3452i	0.525343	−	1.61684i	−0.238294	−	0.971193i	$-0.576588\pi$
$191$	7.26038	−	22.3452i	0.525343	−	1.61684i	0.763637	−	0.645646i	$-0.223412\pi$
$192$	−5.26811	−	3.82750i	−0.380193	−	0.276226i
$193$	−5.78919	−	4.20609i	−0.416715	−	0.302761i	0.359600	−	0.933107i	$-0.382913\pi$
$193$	−5.78919	−	4.20609i	−0.416715	−	0.302761i	−0.776315	+	0.630345i	$0.782913\pi$
$194$	3.10373	−	9.55229i	0.222835	−	0.685815i
$195$	0.160138	+	0.492854i	0.0114677	+	0.0352940i
$196$	16.1222	−	11.7135i	1.15159	−	0.836676i
$197$	10.4955			0.747774			0.373887	−	0.927474i	$-0.378025\pi$
$197$	10.4955			0.747774			0.373887	+	0.927474i	$0.378025\pi$
$198$	−2.88374	+	1.40154i	−0.204938	+	0.0996031i
$199$	−16.7269			−1.18574			−0.592870	−	0.805298i	$-0.702005\pi$
$199$	−16.7269			−1.18574			−0.592870	+	0.805298i	$0.702005\pi$
$200$	−10.9421	+	7.94992i	−0.773725	+	0.562144i
$201$	3.88611	+	11.9602i	0.274105	+	0.843608i
$202$	3.61255	−	11.1183i	0.254178	−	0.782281i
$203$	−9.84868	−	7.15549i	−0.691242	−	0.502217i
$204$	−0.882413	−	0.641111i	−0.0617813	−	0.0448867i
$205$	0.552701	−	1.70104i	0.0386023	−	0.118806i
$206$	0.159362	+	0.490464i	0.0111032	+	0.0341723i
$207$	−1.97555	+	1.43532i	−0.137310	+	0.0997618i
$208$	−0.576060			−0.0399426
$209$	−1.56113	+	2.92624i	−0.107985	+	0.202412i
$210$	−3.23628			−0.223324
$211$	−6.94412	+	5.04520i	−0.478053	+	0.347326i	−0.800571	−	0.599237i	$-0.795471\pi$
$211$	−6.94412	+	5.04520i	−0.478053	+	0.347326i	0.322518	+	0.946563i	$0.395471\pi$
$212$	−3.85391	−	11.8611i	−0.264688	−	0.814625i
$213$	1.93146	−	5.94442i	0.132341	−	0.407305i
$214$	−5.69630	−	4.13861i	−0.389391	−	0.282909i
$215$	2.83047	+	2.05646i	0.193037	+	0.140249i
$216$	−0.915756	+	2.81841i	−0.0623093	+	0.191768i
$217$	2.42661	+	7.46834i	0.164729	+	0.506984i
$218$	7.64334	−	5.55321i	0.517672	−	0.376111i
$219$	−5.48744			−0.370807
$220$	−2.29722	−	0.408353i	−0.154879	−	0.0275311i
$221$	−0.803459			−0.0540465
$222$	3.40931	−	2.47701i	0.228818	−	0.166246i
$223$	6.92668	+	21.3181i	0.463845	+	1.42757i	0.860429	+	0.509570i	$0.170195\pi$
$223$	6.92668	+	21.3181i	0.463845	+	1.42757i	−0.396584	+	0.917998i	$0.629805\pi$
$224$	−8.17396	+	25.1569i	−0.546146	+	1.68086i
$225$	3.69236	+	2.68266i	0.246158	+	0.178844i
$226$	6.44650	+	4.68366i	0.428815	+	0.311552i
$227$	6.18935	−	19.0489i	0.410802	−	1.26432i	−0.505151	−	0.863031i	$-0.668563\pi$
$227$	6.18935	−	19.0489i	0.410802	−	1.26432i	0.915953	−	0.401286i	$-0.131437\pi$
$228$	0.329236	+	1.01328i	0.0218042	+	0.0671064i
$229$	17.8907	−	12.9983i	1.18225	−	0.858953i	0.189824	−	0.981818i	$-0.439208\pi$
$229$	17.8907	−	12.9983i	1.18225	−	0.858953i	0.992423	+	0.122865i	$0.0392082\pi$
$230$	1.55874			0.102780
$231$	11.6639	+	12.1120i	0.767431	+	0.796909i
$232$	7.11566			0.467166
$233$	−14.4695	+	10.5127i	−0.947931	+	0.688712i	−0.950317	−	0.311285i	$-0.899241\pi$
$233$	−14.4695	+	10.5127i	−0.947931	+	0.688712i	0.00238565	+	0.999997i	$0.499241\pi$
$234$	0.234457	+	0.721583i	0.0153269	+	0.0471714i
$235$	−0.730049	+	2.24686i	−0.0476232	+	0.146569i
$236$	8.17897	+	5.94237i	0.532406	+	0.386815i
$237$	−5.50789	−	4.00171i	−0.357776	−	0.259939i
$238$	1.55053	−	4.77204i	0.100506	−	0.309325i
$239$	1.07966	+	3.32286i	0.0698377	+	0.214938i	0.979884	−	0.199569i	$-0.0639541\pi$
$239$	1.07966	+	3.32286i	0.0698377	+	0.214938i	−0.910046	+	0.414507i	$0.863954\pi$
$240$	0.392092	−	0.284872i	0.0253095	−	0.0183884i
$241$	−23.0182			−1.48273			−0.741365	−	0.671102i	$-0.765821\pi$
$241$	−23.0182			−1.48273			−0.741365	+	0.671102i	$0.765821\pi$
$242$	−5.92197	−	8.83250i	−0.380679	−	0.567775i
$243$	1.00000			0.0641500
$244$	0.758114	−	0.550802i	0.0485333	−	0.0352615i
$245$	3.81646	+	11.7459i	0.243825	+	0.750415i
$246$	0.809205	−	2.49048i	0.0515930	−	0.158787i
$247$	0.634939	+	0.461310i	0.0404002	+	0.0293525i
$248$	−3.71338	−	2.69793i	−0.235800	−	0.171319i
$249$	0.965555	−	2.97167i	0.0611896	−	0.188322i
$250$	−1.88654	−	5.80616i	−0.119315	−	0.367214i
$251$	10.2678	−	7.46002i	0.648100	−	0.470872i	−0.214523	−	0.976719i	$-0.568820\pi$
$251$	10.2678	−	7.46002i	0.648100	−	0.470872i	0.862623	+	0.505847i	$0.168820\pi$
$252$	5.40167			0.340273
$253$	−5.61789	−	5.83368i	−0.353194	−	0.366761i
$254$	−14.7642			−0.926390
$255$	0.546870	−	0.397324i	0.0342463	−	0.0248814i
$256$	−5.26111	−	16.1920i	−0.328819	−	1.01200i
$257$	1.09778	−	3.37861i	0.0684775	−	0.210752i	−0.910962	−	0.412490i	$-0.864659\pi$
$257$	1.09778	−	3.37861i	0.0684775	−	0.210752i	0.979439	+	0.201738i	$0.0646591\pi$
$258$	4.14407	+	3.01085i	0.257999	+	0.187447i
$259$	−17.8798	−	12.9905i	−1.11100	−	0.807188i
$260$	−0.170616	+	0.525101i	−0.0105811	+	0.0325654i
$261$	−0.741993	−	2.28362i	−0.0459282	−	0.141353i
$262$	−8.95969	+	6.50960i	−0.553532	+	0.402164i
$263$	−7.41293			−0.457101			−0.228550	−	0.973532i	$-0.573399\pi$
$263$	−7.41293			−0.457101			−0.228550	+	0.973532i	$0.573399\pi$
$264$	−9.67695	−	1.72017i	−0.595575	−	0.105869i
$265$	7.72914			0.474798
$266$	−3.96521	+	2.88089i	−0.243123	+	0.176639i
$267$	−3.95724	−	12.1791i	−0.242179	−	0.745351i
$268$	−4.14038	+	12.7428i	−0.252914	+	0.778388i
$269$	−17.9175	−	13.0178i	−1.09245	−	0.793712i	−0.112640	−	0.993636i	$-0.535931\pi$
$269$	−17.9175	−	13.0178i	−1.09245	−	0.793712i	−0.979811	+	0.199924i	$0.935931\pi$
$270$	−0.516417	−	0.375199i	−0.0314281	−	0.0228339i
$271$	−3.53941	+	10.8932i	−0.215004	+	0.661715i	0.784149	+	0.620572i	$0.213100\pi$
$271$	−3.53941	+	10.8932i	−0.215004	+	0.661715i	−0.999153	+	0.0411422i	$0.986900\pi$
$272$	0.232202	+	0.714643i	0.0140793	+	0.0433316i
$273$	3.21910	−	2.33882i	0.194829	−	0.141552i
$274$	9.04559			0.546464
$275$	−7.12500	+	13.3554i	−0.429654	+	0.805361i
$276$	−2.60169			−0.156604
$277$	7.26942	−	5.28154i	0.436777	−	0.317337i	−0.347576	−	0.937652i	$-0.612995\pi$
$277$	7.26942	−	5.28154i	0.436777	−	0.317337i	0.784353	+	0.620315i	$0.212995\pi$
$278$	−3.53984	−	10.8945i	−0.212305	−	0.653408i
$279$	−0.478627	+	1.47306i	−0.0286547	+	0.0881900i
$280$	−8.02592	−	5.83117i	−0.479641	−	0.348479i
$281$	9.02417	+	6.55644i	0.538337	+	0.391124i	0.823467	−	0.567364i	$-0.192037\pi$
$281$	9.02417	+	6.55644i	0.538337	+	0.391124i	−0.285130	+	0.958489i	$0.592037\pi$
$282$	−1.06886	+	3.28961i	−0.0636497	+	0.195894i
$283$	−4.07949	−	12.5554i	−0.242500	−	0.746339i	−0.996038	−	0.0889340i	$-0.971654\pi$
$283$	−4.07949	−	12.5554i	−0.242500	−	0.746339i	0.753537	−	0.657405i	$-0.228346\pi$
$284$	5.38749	−	3.91424i	0.319689	−	0.232267i
$285$	−0.660294			−0.0391124
$286$	−2.26324	+	1.09997i	−0.133828	+	0.0650424i
$287$	−13.7332			−0.810648
$288$	−4.22090	+	3.06666i	−0.248719	+	0.180705i
$289$	−4.92943	−	15.1712i	−0.289966	−	0.892424i
$290$	−0.473634	+	1.45770i	−0.0278127	+	0.0855988i
$291$	−8.40530	−	6.10681i	−0.492727	−	0.357987i
$292$	−4.72990	−	3.43648i	−0.276797	−	0.201105i
$293$	4.11970	−	12.6791i	0.240676	−	0.740723i	−0.755642	−	0.654985i	$-0.772675\pi$
$293$	4.11970	−	12.6791i	0.240676	−	0.740723i	0.996318	−	0.0857385i	$-0.0273250\pi$
$294$	5.58765	+	17.1970i	0.325879	+	1.00295i
$295$	−5.06887	+	3.68275i	−0.295121	+	0.214418i
$296$	12.9182			0.750852
$297$	0.457024	+	3.28499i	0.0265192	+	0.190614i
$298$	−12.4099			−0.718884
$299$	−1.55047	+	1.12648i	−0.0896659	+	0.0651461i
$300$	1.50264	+	4.62464i	0.0867548	+	0.267004i
$301$	8.30136	−	25.5490i	0.478483	−	1.47262i
$302$	−12.7605	−	9.27106i	−0.734285	−	0.533490i
$303$	−9.78327	−	7.10796i	−0.562034	−	0.408342i
$304$	0.226817	−	0.698072i	0.0130089	−	0.0400372i
$305$	0.179461	+	0.552326i	0.0102759	+	0.0316261i
$306$	0.800668	−	0.581720i	0.0457712	−	0.0332547i
$307$	−10.1142			−0.577248			−0.288624	−	0.957443i	$-0.593198\pi$
$307$	−10.1142			−0.577248			−0.288624	+	0.957443i	$0.593198\pi$
$308$	2.46869	+	17.7444i	0.140667	+	1.01108i
$309$	0.533452			0.0303470
$310$	0.799863	−	0.581134i	0.0454292	−	0.0330062i
$311$	−1.18075	−	3.63396i	−0.0669540	−	0.206063i	0.911982	−	0.410230i	$-0.134552\pi$
$311$	−1.18075	−	3.63396i	−0.0669540	−	0.206063i	−0.978936	+	0.204167i	$0.934552\pi$
$312$	−0.718711	+	2.21196i	−0.0406890	+	0.125228i
$313$	4.12697	+	2.99842i	0.233270	+	0.169480i	0.698280	−	0.715825i	$-0.253949\pi$
$313$	4.12697	+	2.99842i	0.233270	+	0.169480i	−0.465010	+	0.885306i	$0.653949\pi$
$314$	−16.7876	−	12.1969i	−0.947381	−	0.688313i
$315$	−1.03448	+	3.18380i	−0.0582864	+	0.179387i
$316$	−2.24148	−	6.89857i	−0.126093	−	0.388075i
$317$	4.60252	−	3.34393i	0.258503	−	0.187814i	−0.450984	−	0.892532i	$-0.648927\pi$
$317$	4.60252	−	3.34393i	0.258503	−	0.187814i	0.709487	+	0.704719i	$0.248927\pi$
$318$	11.3162			0.634580
$319$	7.16255	−	3.48111i	0.401026	−	0.194905i
$320$	4.29966			0.240358
$321$	−5.89234	+	4.28103i	−0.328878	+	0.238944i
$322$	−3.69847	−	11.3827i	−0.206108	−	0.634334i
$323$	0.316353	−	0.973634i	0.0176023	−	0.0541744i
$324$	0.861952	+	0.626244i	0.0478862	+	0.0347914i
$325$	2.89787	+	2.10543i	0.160745	+	0.116788i
$326$	−6.02774	+	18.5515i	−0.333846	+	1.02747i
$327$	−3.01997	−	9.29450i	−0.167005	−	0.513987i
$328$	6.49419	−	4.71831i	0.358582	−	0.260525i
$329$	18.1399			1.00009
$330$	0.996508	−	1.86790i	0.0548560	−	0.102824i
$331$	25.9116			1.42423			0.712114	−	0.702064i	$-0.247738\pi$
$331$	25.9116			1.42423			0.712114	+	0.702064i	$0.247738\pi$
$332$	2.69326	−	1.95676i	0.147812	−	0.107391i
$333$	−1.34706	−	4.14581i	−0.0738182	−	0.227189i
$334$	5.53740	−	17.0424i	0.302993	−	0.932517i
$335$	−6.71780	−	4.88077i	−0.367033	−	0.266665i
$336$	−3.01061	−	2.18733i	−0.164242	−	0.119329i
$337$	0.174615	−	0.537409i	0.00951188	−	0.0292746i	−0.946188	−	0.323618i	$-0.895101\pi$
$337$	0.174615	−	0.537409i	0.00951188	−	0.0292746i	0.955700	+	0.294343i	$0.0951008\pi$
$338$	−3.69956	−	11.3861i	−0.201230	−	0.619322i
$339$	6.66835	−	4.84484i	0.362175	−	0.263136i
$340$	0.720198			0.0390582
$341$	−5.05774	−	0.899059i	−0.273892	−	0.0486868i
$342$	−0.966731			−0.0522748
$343$	48.0071	−	34.8792i	2.59214	−	1.88330i
$344$	4.85226	+	14.9337i	0.261616	+	0.805172i
$345$	0.498254	−	1.53347i	0.0268251	−	0.0825591i
$346$	0.719006	+	0.522389i	0.0386540	+	0.0280838i
$347$	−29.6991	−	21.5777i	−1.59433	−	1.15835i	−0.897406	−	0.441206i	$-0.854551\pi$
$347$	−29.6991	−	21.5777i	−1.59433	−	1.15835i	−0.696926	−	0.717143i	$-0.745449\pi$
$348$	0.790542	−	2.43304i	0.0423775	−	0.130425i
$349$	8.15428	+	25.0963i	0.436488	+	1.34337i	0.891554	+	0.452915i	$0.149616\pi$
$349$	8.15428	+	25.0963i	0.436488	+	1.34337i	−0.455065	+	0.890458i	$0.650384\pi$
$350$	−18.0973	+	13.1484i	−0.967340	+	0.702813i
$351$	0.784828			0.0418910
$352$	−12.0030	−	12.4641i	−0.639762	−	0.664336i
$353$	31.6359			1.68381			0.841905	−	0.539626i	$-0.181434\pi$
$353$	31.6359			1.68381			0.841905	+	0.539626i	$0.181434\pi$
$354$	−7.42129	+	5.39188i	−0.394437	+	0.286575i
$355$	1.27533	+	3.92507i	0.0676876	+	0.208321i
$356$	4.21617	−	12.9760i	0.223456	−	0.687728i
$357$	−4.19904	−	3.05078i	−0.222237	−	0.161464i
$358$	−16.7254	−	12.1517i	−0.883967	−	0.642239i
$359$	4.08678	−	12.5778i	0.215692	−	0.663831i	−0.783412	−	0.621503i	$-0.786522\pi$
$359$	4.08678	−	12.5778i	0.215692	−	0.663831i	0.999104	−	0.0423285i	$-0.0134776\pi$
$360$	−0.604668	−	1.86098i	−0.0318688	−	0.0980820i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	14.1448			0.743433
$363$	−10.5823	+	3.00263i	−0.555425	+	0.157597i
$364$	4.23938			0.222204
$365$	2.93133	−	2.12973i	0.153433	−	0.111475i
$366$	0.262748	+	0.808656i	0.0137341	+	0.0422691i
$367$	6.68667	−	20.5795i	0.349041	−	1.07424i	−0.610343	−	0.792137i	$-0.708968\pi$
$367$	6.68667	−	20.5795i	0.349041	−	1.07424i	0.959385	−	0.282102i	$-0.0910315\pi$
$368$	1.45005	+	1.05352i	0.0755889	+	0.0549186i
$369$	−2.19143	−	1.59217i	−0.114081	−	0.0828850i
$370$	−0.859861	+	2.64638i	−0.0447021	+	0.137579i
$371$	−18.3392	−	56.4421i	−0.952122	−	2.93033i
$372$	−1.33505	+	0.969971i	−0.0692192	+	0.0502907i
$373$	−5.30074			−0.274462			−0.137231	−	0.990539i	$-0.543820\pi$
$373$	−5.30074			−0.274462			−0.137231	+	0.990539i	$0.543820\pi$
$374$	2.27686	+	2.36432i	0.117734	+	0.122256i
$375$	−6.31506			−0.326108
$376$	−8.57803	+	6.23230i	−0.442378	+	0.321407i
$377$	−0.582337	−	1.79225i	−0.0299919	−	0.0923055i
$378$	−1.51458	+	4.66138i	−0.0779014	+	0.239756i
$379$	4.55336	+	3.30821i	0.233890	+	0.169931i	0.698557	−	0.715554i	$-0.253826\pi$
$379$	4.55336	+	3.30821i	0.233890	+	0.169931i	−0.464667	+	0.885486i	$0.653826\pi$
$380$	−0.569141	−	0.413505i	−0.0291963	−	0.0212124i
$381$	−4.71941	+	14.5248i	−0.241783	+	0.744130i
$382$	7.01884	+	21.6018i	0.359115	+	1.10524i
$383$	−4.77423	+	3.46868i	−0.243952	+	0.177241i	−0.703042	−	0.711148i	$-0.748175\pi$
$383$	−4.77423	+	3.46868i	−0.243952	+	0.177241i	0.459090	+	0.888390i	$0.348175\pi$
$384$	−4.13954			−0.211245
$385$	−10.9315	−	1.94318i	−0.557122	−	0.0990336i
$386$	6.91777			0.352105
$387$	4.28669	−	3.11446i	0.217905	−	0.158317i
$388$	−3.42061	−	10.5275i	−0.173655	−	0.534455i
$389$	−9.17316	+	28.2321i	−0.465098	+	1.43142i	0.393762	+	0.919213i	$0.371174\pi$
$389$	−9.17316	+	28.2321i	−0.465098	+	1.43142i	−0.858859	+	0.512211i	$0.828826\pi$
$390$	−0.405298	−	0.294467i	−0.0205231	−	0.0149109i
$391$	2.02245	+	1.46940i	0.102280	+	0.0743105i
$392$	−17.1286	+	52.7163i	−0.865123	+	2.66257i
$393$	3.54007	+	10.8952i	0.178573	+	0.549591i
$394$	−8.20856	+	5.96387i	−0.413541	+	0.300455i
$395$	4.49536			0.226186
$396$	−1.66327	+	3.11771i	−0.0835825	+	0.156671i
$397$	37.5054			1.88234			0.941172	−	0.337928i	$-0.109726\pi$
$397$	37.5054			1.88234			0.941172	+	0.337928i	$0.109726\pi$
$398$	13.0822	−	9.50475i	0.655750	−	0.476430i
$399$	1.56670	+	4.82180i	0.0784330	+	0.241392i
$400$	1.03520	−	3.18601i	0.0517598	−	0.159300i
$401$	−17.5147	−	12.7251i	−0.874640	−	0.635463i	0.0571876	−	0.998363i	$-0.481787\pi$
$401$	−17.5147	−	12.7251i	−0.874640	−	0.635463i	−0.931828	+	0.362900i	$0.881787\pi$
$402$	−9.83548	−	7.14590i	−0.490549	−	0.356405i
$403$	−0.375640	+	1.15610i	−0.0187120	+	0.0575895i
$404$	−3.98138	−	12.2534i	−0.198081	−	0.609631i
$405$	−0.534189	+	0.388111i	−0.0265441	+	0.0192854i
$406$	11.7686			0.584068
$407$	13.0033	−	6.31979i	0.644549	−	0.313260i
$408$	3.03380			0.150195
$409$	−1.85385	+	1.34690i	−0.0916668	+	0.0665998i	−0.632675	−	0.774418i	$-0.718043\pi$
$409$	−1.85385	+	1.34690i	−0.0916668	+	0.0665998i	0.541008	+	0.841018i	$0.318043\pi$
$410$	0.534313	+	1.64445i	0.0263878	+	0.0812134i
$411$	2.89143	−	8.89892i	0.142624	−	0.438951i
$412$	0.459810	+	0.334071i	0.0226532	+	0.0164585i
$413$	38.9203	+	28.2773i	1.91514	+	1.39143i
$414$	0.729489	−	2.24514i	0.0358524	−	0.110342i
$415$	0.637550	+	1.96218i	0.0312961	+	0.0963195i
$416$	−3.31268	+	2.40680i	−0.162417	+	0.118003i
$417$	−11.8494			−0.580266
$418$	−0.441819	−	3.17570i	−0.0216101	−	0.155328i
$419$	−30.6434			−1.49703			−0.748513	−	0.663120i	$-0.769232\pi$
$419$	−30.6434			−1.49703			−0.748513	+	0.663120i	$0.769232\pi$
$420$	−2.88551	+	2.09645i	−0.140799	+	0.102296i
$421$	−2.34122	−	7.20554i	−0.114104	−	0.351177i	0.877655	−	0.479293i	$-0.159107\pi$
$421$	−2.34122	−	7.20554i	−0.114104	−	0.351177i	−0.991759	+	0.128116i	$0.959107\pi$
$422$	2.56418	−	7.89172i	0.124822	−	0.384163i
$423$	2.89461	+	2.10306i	0.140741	+	0.102254i
$424$	28.0640	+	20.3897i	1.36291	+	0.990210i
$425$	1.44384	−	4.44368i	0.0700364	−	0.215550i
$426$	1.86720	+	5.74666i	0.0904663	+	0.278427i
$427$	3.60755	−	2.62104i	0.174581	−	0.126841i
$428$	−7.75988			−0.375088
$429$	0.358685	+	2.57815i	0.0173175	+	0.124474i
$430$	−3.38226			−0.163107
$431$	−30.2206	+	21.9566i	−1.45568	+	1.05761i	−0.471212	+	0.882020i	$0.656183\pi$
$431$	−30.2206	+	21.9566i	−1.45568	+	1.05761i	−0.984463	+	0.175590i	$0.943817\pi$
$432$	−0.226817	−	0.698072i	−0.0109127	−	0.0335860i
$433$	−7.11726	+	21.9047i	−0.342034	+	1.05267i	0.621119	+	0.783716i	$0.286678\pi$
$433$	−7.11726	+	21.9047i	−0.342034	+	1.05267i	−0.963153	+	0.268955i	$0.913322\pi$
$434$	−6.14160	−	4.46213i	−0.294806	−	0.214189i
$435$	1.28266	+	0.931909i	0.0614990	+	0.0446816i
$436$	3.21756	−	9.90265i	0.154093	−	0.474251i
$437$	−0.754594	−	2.32240i	−0.0360971	−	0.111096i
$438$	4.29173	−	3.11813i	0.205067	−	0.148990i
$439$	−2.61385			−0.124752			−0.0623762	−	0.998053i	$-0.519868\pi$
$439$	−2.61385			−0.124752			−0.0623762	+	0.998053i	$0.519868\pi$
$440$	5.83693	−	2.83683i	0.278265	−	0.135241i
$441$	18.7043			0.890681
$442$	0.628387	−	0.456550i	0.0298893	−	0.0217159i
$443$	3.19590	+	9.83598i	0.151842	+	0.467321i	0.997827	−	0.0658848i	$-0.0209870\pi$
$443$	3.19590	+	9.83598i	0.151842	+	0.467321i	−0.845985	+	0.533206i	$0.820987\pi$
$444$	1.43519	−	4.41707i	0.0681113	−	0.209625i
$445$	6.84077	+	4.97011i	0.324284	+	0.235606i
$446$	−17.5310	−	12.7370i	−0.830116	−	0.603115i
$447$	−3.96683	+	12.2087i	−0.187625	+	0.577449i
$448$	−10.2019	−	31.3983i	−0.481996	−	1.48343i
$449$	−4.54112	+	3.29932i	−0.214309	+	0.155705i	−0.689761	−	0.724037i	$-0.742284\pi$
$449$	−4.54112	+	3.29932i	−0.214309	+	0.155705i	0.475452	+	0.879742i	$0.342284\pi$
$450$	−4.41217			−0.207992
$451$	4.22871	−	7.92648i	0.199122	−	0.373243i
$452$	8.78185			0.413063
$453$	−13.1997	+	9.59011i	−0.620174	+	0.450583i
$454$	5.98344	+	18.4151i	0.280817	+	0.864265i
$455$	−0.811889	+	2.49874i	−0.0380620	+	0.117143i
$456$	−2.39748	−	1.74187i	−0.112272	−	0.0815706i
$457$	26.3566	+	19.1492i	1.23291	+	0.895762i	0.997105	−	0.0760378i	$-0.0242270\pi$
$457$	26.3566	+	19.1492i	1.23291	+	0.895762i	0.235806	+	0.971800i	$0.424227\pi$
$458$	−6.60627	+	20.3320i	−0.308691	+	0.950053i
$459$	−0.316353	−	0.973634i	−0.0147661	−	0.0454453i
$460$	1.38980	−	1.00975i	0.0647995	−	0.0470796i
$461$	1.18043			0.0549782			0.0274891	−	0.999622i	$-0.491249\pi$
$461$	1.18043			0.0549782			0.0274891	+	0.999622i	$0.491249\pi$
$462$	−16.0048	−	2.84500i	−0.744610	−	0.132361i
$463$	−4.95377			−0.230221			−0.115111	−	0.993353i	$-0.536722\pi$
$463$	−4.95377			−0.230221			−0.115111	+	0.993353i	$0.536722\pi$
$464$	−1.42583	+	1.03593i	−0.0661927	+	0.0480918i
$465$	−0.316035	−	0.972654i	−0.0146558	−	0.0451058i
$466$	5.34300	−	16.4441i	0.247510	−	0.761756i
$467$	16.9012	+	12.2794i	0.782094	+	0.568225i	0.905607	−	0.424118i	$-0.139416\pi$
$467$	16.9012	+	12.2794i	0.782094	+	0.568225i	−0.123512	+	0.992343i	$0.539416\pi$
$468$	0.676484	+	0.491494i	0.0312705	+	0.0227193i
$469$	−19.7023	+	60.6375i	−0.909769	+	2.79998i
$470$	−0.705761	−	2.17211i	−0.0325543	−	0.100192i
$471$	−17.3654	+	12.6167i	−0.800154	+	0.581346i
$472$	−28.1199			−1.29432
$473$	12.1901	+	12.6583i	0.560500	+	0.582030i
$474$	6.58162			0.302304
$475$	−3.69236	+	2.68266i	−0.169417	+	0.123089i
$476$	−1.70883	−	5.25925i	−0.0783242	−	0.241057i
$477$	3.61723	−	11.1327i	0.165622	−	0.509731i
$478$	−2.73256	−	1.98532i	−0.124984	−	0.0908065i
$479$	18.3288	+	13.3167i	0.837465	+	0.608454i	0.921661	−	0.387995i	$-0.126832\pi$
$479$	18.3288	+	13.3167i	0.837465	+	0.608454i	−0.0841963	+	0.996449i	$0.526832\pi$
$480$	1.06455	−	3.27635i	0.0485899	−	0.149544i
$481$	−1.05721	−	3.25375i	−0.0482045	−	0.148358i
$482$	18.0025	−	13.0796i	0.819994	−	0.595760i
$483$	−12.3804			−0.563326
$484$	−11.0018	−	4.03896i	−0.500081	−	0.183589i
$485$	6.86014			0.311503
$486$	−0.782102	+	0.568230i	−0.0354769	+	0.0257755i
$487$	−10.6753	−	32.8552i	−0.483744	−	1.48881i	−0.833792	−	0.552079i	$-0.813835\pi$
$487$	−10.6753	−	32.8552i	−0.483744	−	1.48881i	0.350048	−	0.936732i	$-0.386165\pi$
$488$	−0.805436	+	2.47888i	−0.0364604	+	0.112214i
$489$	16.3239	+	11.8600i	0.738193	+	0.536328i
$490$	−9.65922	−	7.01783i	−0.436359	−	0.317033i
$491$	−1.13835	+	3.50350i	−0.0513732	+	0.158111i	−0.973452	−	0.228892i	$-0.926490\pi$
$491$	−1.13835	+	3.50350i	−0.0513732	+	0.158111i	0.922079	+	0.387003i	$0.126490\pi$
$492$	−0.891821	−	2.74474i	−0.0402064	−	0.123743i
$493$	−1.98868	+	1.44486i	−0.0895656	+	0.0650732i
$494$	−0.758718			−0.0341363
$495$	−1.51908	−	1.57743i	−0.0682774	−	0.0709001i
$496$	1.13686			0.0510467
$497$	25.6368	−	18.6262i	1.14997	−	0.835501i
$498$	0.933432	+	2.87281i	0.0418281	+	0.128734i
$499$	4.65386	−	14.3231i	0.208335	−	0.641190i	−0.791225	−	0.611526i	$-0.790556\pi$
$499$	4.65386	−	14.3231i	0.208335	−	0.641190i	0.999560	−	0.0296643i	$-0.00944384\pi$
$500$	−5.44327	−	3.95477i	−0.243431	−	0.176863i
$501$	−14.9960	−	10.8952i	−0.669972	−	0.486763i
$502$	−3.79149	+	11.6690i	−0.169222	+	0.520813i
$503$	8.01060	+	24.6541i	0.357175	+	1.09927i	0.954738	+	0.297449i	$0.0961359\pi$
$503$	8.01060	+	24.6541i	0.357175	+	1.09927i	−0.597563	+	0.801822i	$0.703864\pi$
$504$	−12.1551	+	8.83118i	−0.541430	+	0.393372i
$505$	7.98479			0.355318
$506$	7.70864	+	1.37028i	0.342691	+	0.0609164i
$507$	−12.3840			−0.549995
$508$	−13.1640	+	9.56421i	−0.584058	+	0.424343i
$509$	6.91090	+	21.2696i	0.306320	+	0.942757i	0.979181	+	0.202988i	$0.0650653\pi$
$509$	6.91090	+	21.2696i	0.306320	+	0.942757i	−0.672861	+	0.739769i	$0.734935\pi$
$510$	−0.201936	+	0.621496i	−0.00894189	+	0.0275203i
$511$	−22.5076	−	16.3528i	−0.995679	−	0.723403i
$512$	6.61760	+	4.80797i	0.292460	+	0.212484i
$513$	−0.309017	+	0.951057i	−0.0136434	+	0.0419902i
$514$	1.06126	+	3.26621i	0.0468100	+	0.144066i
$515$	−0.284964	+	0.207039i	−0.0125570	+	0.00912321i
$516$	5.64533			0.248522
$517$	−5.58561	+	10.4699i	−0.245655	+	0.460466i
$518$	21.3654			0.938743
$519$	0.743750	−	0.540366i	0.0326470	−	0.0237194i
$520$	−0.474560	−	1.46055i	−0.0208108	−	0.0640492i
$521$	−4.91225	+	15.1184i	−0.215210	+	0.662347i	0.783929	+	0.620850i	$0.213213\pi$
$521$	−4.91225	+	15.1184i	−0.215210	+	0.662347i	−0.999139	+	0.0414966i	$0.986787\pi$
$522$	1.87794	+	1.36440i	0.0821951	+	0.0597182i
$523$	17.7321	+	12.8831i	0.775371	+	0.563340i	0.903586	−	0.428407i	$-0.140925\pi$
$523$	17.7321	+	12.8831i	0.775371	+	0.563340i	−0.128215	+	0.991746i	$0.540925\pi$
$524$	−3.77170	+	11.6081i	−0.164768	+	0.507102i
$525$	7.15043	+	22.0068i	0.312070	+	0.960453i
$526$	5.79766	−	4.21225i	0.252790	−	0.183663i
$527$	1.58564			0.0690715
$528$	2.18949	−	1.06413i	0.0952855	−	0.0463102i
$529$	−17.0370			−0.740741
$530$	−6.04498	+	4.39193i	−0.262577	+	0.190773i
$531$	2.93223	+	9.02448i	0.127248	+	0.391629i
$532$	−1.66921	+	5.13729i	−0.0723693	+	0.222730i
$533$	−1.71990	−	1.24958i	−0.0744970	−	0.0541252i
$534$	10.0155	+	7.27670i	0.433414	+	0.314894i
$535$	1.48610	−	4.57376i	0.0642499	−	0.197741i
$536$	−11.5163	−	35.4434i	−0.497427	−	1.53092i
$537$	−17.3010	+	12.5699i	−0.746594	+	0.542432i
$538$	21.4105			0.923071
$539$	8.54831	+	61.4433i	0.368202	+	2.64655i
$540$	−0.703497			−0.0302737
$541$	23.4715	−	17.0531i	1.00912	−	0.733169i	0.0450959	−	0.998983i	$-0.485641\pi$
$541$	23.4715	−	17.0531i	1.00912	−	0.733169i	0.964024	+	0.265814i	$0.0856407\pi$
$542$	−3.42166	−	10.5308i	−0.146973	−	0.452336i
$543$	4.52140	−	13.9154i	0.194032	−	0.597169i
$544$	4.32110	+	3.13946i	0.185266	+	0.134603i
$545$	5.22053	+	3.79294i	0.223623	+	0.162472i
$546$	−1.18868	+	3.65838i	−0.0508709	+	0.156564i
$547$	1.03924	+	3.19845i	0.0444347	+	0.136756i	0.970813	−	0.239839i	$-0.0770947\pi$
$547$	1.03924	+	3.19845i	0.0444347	+	0.136756i	−0.926378	+	0.376595i	$0.877095\pi$
$548$	8.06518	−	5.85969i	0.344527	−	0.250314i
$549$	0.879532			0.0375375
$550$	−2.01647	−	14.4939i	−0.0859825	−	0.618023i
$551$	2.40114			0.102292
$552$	5.85445	−	4.25350i	0.249182	−	0.181041i
$553$	−10.6663	−	32.8274i	−0.453576	−	1.39596i
$554$	−2.68429	+	8.26141i	−0.114045	+	0.350994i
$555$	2.32862	+	1.69184i	0.0988443	+	0.0718146i
$556$	−10.2136	−	7.42060i	−0.433152	−	0.314703i
$557$	−4.13716	+	12.7329i	−0.175297	+	0.539508i	−0.999647	−	0.0265720i	$-0.991541\pi$
$557$	−4.13716	+	12.7329i	−0.175297	+	0.539508i	0.824350	+	0.566080i	$0.191541\pi$
$558$	−0.462704	−	1.42406i	−0.0195878	−	0.0602851i
$559$	3.36431	−	2.44432i	0.142295	−	0.103384i
$560$	2.45716			0.103834
$561$	3.05379	−	1.48419i	0.128931	−	0.0626625i
$562$	−10.7834			−0.454870
$563$	25.4002	−	18.4543i	1.07049	−	0.777758i	0.0944909	−	0.995526i	$-0.469878\pi$
$563$	25.4002	−	18.4543i	1.07049	−	0.777758i	0.976001	+	0.217768i	$0.0698777\pi$
$564$	1.17799	+	3.62547i	0.0496022	+	0.152660i
$565$	−1.68182	+	5.17612i	−0.0707548	+	0.217761i
$566$	10.3249	+	7.50149i	0.433989	+	0.315311i
$567$	4.10167	+	2.98004i	0.172254	+	0.125150i
$568$	−5.72378	+	17.6160i	−0.240165	+	0.739151i
$569$	−13.1866	−	40.5841i	−0.552810	−	1.70137i	−0.701658	−	0.712514i	$-0.747556\pi$
$569$	−13.1866	−	40.5841i	−0.552810	−	1.70137i	0.148848	−	0.988860i	$-0.452444\pi$
$570$	0.516417	−	0.375199i	0.0216303	−	0.0157154i
$571$	23.4617			0.981842			0.490921	−	0.871204i	$-0.336660\pi$
$571$	23.4617			0.981842			0.490921	+	0.871204i	$0.336660\pi$
$572$	−1.30538	+	2.44686i	−0.0545808	+	0.102308i
$573$	23.4951			0.981521
$574$	10.7408	−	7.80365i	0.448312	−	0.325718i
$575$	−3.44398	−	10.5995i	−0.143624	−	0.442028i
$576$	2.01224	−	6.19303i	0.0838432	−	0.258043i
$577$	−5.92581	−	4.30535i	−0.246695	−	0.179234i	0.457566	−	0.889176i	$-0.348721\pi$
$577$	−5.92581	−	4.30535i	−0.246695	−	0.179234i	−0.704261	+	0.709941i	$0.748721\pi$
$578$	12.4761	+	9.06439i	0.518936	+	0.377029i
$579$	2.21127	−	6.80560i	0.0918974	−	0.282831i
$580$	0.521990	+	1.60652i	0.0216745	+	0.0667071i
$581$	12.8161	−	9.31143i	0.531700	−	0.386303i
$582$	10.0439			0.416332
$583$	38.2239	+	6.79465i	1.58307	+	0.281406i
$584$	16.2617			0.672915
$585$	−0.419246	+	0.304600i	−0.0173337	+	0.0125937i
$586$	3.98265	+	12.2573i	0.164522	+	0.506345i
$587$	−2.15858	+	6.64343i	−0.0890942	+	0.274204i	−0.985670	−	0.168687i	$-0.946047\pi$
$587$	−2.15858	+	6.64343i	−0.0890942	+	0.274204i	0.896575	+	0.442891i	$0.146047\pi$
$588$	16.1222	+	11.7135i	0.664868	+	0.483055i
$589$	−1.25306	−	0.910403i	−0.0516315	−	0.0375125i
$590$	1.87172	−	5.76057i	0.0770575	−	0.237159i
$591$	3.24329	+	9.98183i	0.133411	+	0.410597i
$592$	−2.58854	+	1.88068i	−0.106388	+	0.0772956i
$593$	2.43142			0.0998463			0.0499232	−	0.998753i	$-0.484102\pi$
$593$	2.43142			0.0998463			0.0499232	+	0.998753i	$0.484102\pi$
$594$	−2.22407	−	2.30950i	−0.0912546	−	0.0947599i
$595$	3.42712			0.140498
$596$	−11.0648	+	8.03906i	−0.453233	+	0.329293i
$597$	−5.16890	−	15.9083i	−0.211549	−	0.651081i
$598$	0.572524	−	1.76205i	0.0234122	−	0.0720554i
$599$	19.3208	+	14.0374i	0.789428	+	0.573553i	0.907794	−	0.419417i	$-0.137766\pi$
$599$	19.3208	+	14.0374i	0.789428	+	0.573553i	−0.118366	+	0.992970i	$0.537766\pi$
$600$	−10.9421	−	7.94992i	−0.446710	−	0.324554i
$601$	−12.4466	+	38.3066i	−0.507706	+	1.56256i	0.288469	+	0.957489i	$0.406854\pi$
$601$	−12.4466	+	38.3066i	−0.507706	+	1.56256i	−0.796174	+	0.605068i	$0.793146\pi$
$602$	8.02519	+	24.6990i	0.327082	+	1.00666i
$603$	−10.1740	+	7.39181i	−0.414316	+	0.301018i
$604$	−17.3832			−0.707313
$605$	4.48757	−	5.71106i	0.182446	−	0.232188i
$606$	11.6905			0.474893
$607$	7.14083	−	5.18812i	0.289837	−	0.210579i	−0.433359	−	0.901221i	$-0.642672\pi$
$607$	7.14083	−	5.18812i	0.289837	−	0.210579i	0.723197	+	0.690642i	$0.242672\pi$
$608$	−1.61224	−	4.96196i	−0.0653850	−	0.201234i
$609$	3.76186	−	11.5778i	0.152438	−	0.469157i
$610$	−0.454205	−	0.329999i	−0.0183902	−	0.0133613i
$611$	2.27177	+	1.65054i	0.0919060	+	0.0667737i
$612$	0.337052	−	1.03734i	0.0136245	−	0.0419320i
$613$	4.44423	+	13.6779i	0.179501	+	0.552447i	0.999810	−	0.0194731i	$-0.00619888\pi$
$613$	4.44423	+	13.6779i	0.179501	+	0.552447i	−0.820310	+	0.571920i	$0.806199\pi$
$614$	7.91034	−	5.74720i	0.319235	−	0.231938i
$615$	1.78858			0.0721224
$616$	−34.5655	−	35.8932i	−1.39268	−	1.44618i
$617$	−26.8000			−1.07893			−0.539464	−	0.842009i	$-0.681373\pi$
$617$	−26.8000			−1.07893			−0.539464	+	0.842009i	$0.681373\pi$
$618$	−0.417214	+	0.303124i	−0.0167828	+	0.0121934i
$619$	8.36578	+	25.7472i	0.336249	+	1.03487i	0.966104	+	0.258155i	$0.0831145\pi$
$619$	8.36578	+	25.7472i	0.336249	+	1.03487i	−0.629855	+	0.776713i	$0.716886\pi$
$620$	0.336713	−	1.03630i	0.0135227	−	0.0416186i
$621$	−1.97555	−	1.43532i	−0.0792762	−	0.0575975i
$622$	2.98839	+	2.17119i	0.119824	+	0.0870570i
$623$	20.0630	−	61.7475i	0.803806	−	2.47386i
$624$	−0.178012	−	0.547866i	−0.00712620	−	0.0219322i
$625$	−15.0884	+	10.9624i	−0.603535	+	0.438494i
$626$	−4.93150			−0.197102
$627$	−3.26543	−	0.580461i	−0.130409	−	0.0231814i
$628$	−22.8692			−0.912581
$629$	−3.61036	+	2.62308i	−0.143954	+	0.104589i
$630$	−1.00006	−	3.07788i	−0.0398435	−	0.122626i
$631$	10.1794	−	31.3290i	0.405236	−	1.24719i	−0.515463	−	0.856912i	$-0.672380\pi$
$631$	10.1794	−	31.3290i	0.405236	−	1.24719i	0.920698	−	0.390275i	$-0.127620\pi$
$632$	16.3223	+	11.8589i	0.649268	+	0.471721i
$633$	−6.94412	−	5.04520i	−0.276004	−	0.200529i
$634$	−1.69952	+	5.23058i	−0.0674965	+	0.207733i
$635$	−3.11619	−	9.59066i	−0.123662	−	0.380594i
$636$	10.0897	−	7.33058i	0.400082	−	0.290676i
$637$	14.6796			0.581629
$638$	−3.62378	+	6.79256i	−0.143467	+	0.268920i
$639$	6.25034			0.247260
$640$	2.21129	−	1.60660i	0.0874091	−	0.0635064i
$641$	7.40106	+	22.7781i	0.292324	+	0.899682i	0.984107	+	0.177576i	$0.0568255\pi$
$641$	7.40106	+	22.7781i	0.292324	+	0.899682i	−0.691783	+	0.722106i	$0.743174\pi$
$642$	2.17579	−	6.69641i	0.0858718	−	0.264286i
$643$	10.7378	+	7.80148i	0.423458	+	0.307661i	0.779028	−	0.626989i	$-0.215713\pi$
$643$	10.7378	+	7.80148i	0.423458	+	0.307661i	−0.355569	+	0.934650i	$0.615713\pi$
$644$	−10.6713	−	7.75314i	−0.420507	−	0.305517i
$645$	−1.08114	+	3.32742i	−0.0425700	+	0.131017i
$646$	0.305828	+	0.941242i	0.0120326	+	0.0370327i
$647$	−0.0497632	+	0.0361551i	−0.00195639	+	0.00142140i	−0.588763	−	0.808306i	$-0.700385\pi$
$647$	−0.0497632	+	0.0361551i	−0.00195639	+	0.00142140i	0.586807	+	0.809727i	$0.300385\pi$
$648$	−2.96345			−0.116415
$649$	−28.3052	+	13.7567i	−1.11108	+	0.539999i
$650$	−3.46280			−0.135822
$651$	−6.35295	+	4.61569i	−0.248992	+	0.180903i
$652$	6.64315	+	20.4455i	0.260166	+	0.800708i
$653$	−5.26091	+	16.1914i	−0.205875	+	0.633619i	0.793801	+	0.608178i	$0.208099\pi$
$653$	−5.26091	+	16.1914i	−0.205875	+	0.633619i	−0.999676	+	0.0254414i	$0.991901\pi$
$654$	7.64334	+	5.55321i	0.298878	+	0.217148i
$655$	−6.11962	−	4.44616i	−0.239113	−	0.173726i
$656$	−0.614393	+	1.89091i	−0.0239880	+	0.0738275i
$657$	−1.69571	−	5.21886i	−0.0661560	−	0.203607i
$658$	−14.1873	+	10.3077i	−0.553077	+	0.401834i
$659$	−30.6063			−1.19225			−0.596126	−	0.802891i	$-0.703294\pi$
$659$	−30.6063			−1.19225			−0.596126	+	0.802891i	$0.703294\pi$
$660$	−0.321515	−	2.31098i	−0.0125150	−	0.0899547i
$661$	37.5019			1.45866			0.729328	−	0.684164i	$-0.239833\pi$
$661$	37.5019			1.45866			0.729328	+	0.684164i	$0.239833\pi$
$662$	−20.2655	+	14.7237i	−0.787640	+	0.572254i
$663$	−0.248282	−	0.764135i	−0.00964249	−	0.0296765i
$664$	−2.86137	+	8.80640i	−0.111043	+	0.341754i
$665$	−2.70831	−	1.96770i	−0.105024	−	0.0763041i
$666$	3.40931	+	2.47701i	0.132108	+	0.0959821i
$667$	−1.81189	+	5.57641i	−0.0701565	+	0.215920i
$668$	−6.10275	−	18.7823i	−0.236122	−	0.726710i
$669$	−18.1343	+	13.1753i	−0.701112	+	0.509388i
$670$	8.02740			0.310126
$671$	0.401967	+	2.88925i	0.0155178	+	0.111538i
$672$	−26.4515			−1.02039
$673$	−20.7638	+	15.0858i	−0.800385	+	0.581514i	−0.911027	−	0.412346i	$-0.864709\pi$
$673$	−20.7638	+	15.0858i	−0.800385	+	0.581514i	0.110642	+	0.993860i	$0.464709\pi$
$674$	0.168806	+	0.519530i	0.00650215	+	0.0200116i
$675$	−1.41036	+	4.34063i	−0.0542847	+	0.167071i
$676$	−10.6744	−	7.75544i	−0.410556	−	0.298286i
$677$	−7.21648	−	5.24308i	−0.277352	−	0.201508i	0.440410	−	0.897797i	$-0.354833\pi$
$677$	−7.21648	−	5.24308i	−0.277352	−	0.201508i	−0.717762	+	0.696289i	$0.754833\pi$
$678$	−2.46234	+	7.57832i	−0.0945658	+	0.291043i
$679$	−16.2772	−	50.0962i	−0.624663	−	1.92252i
$680$	−1.62062	+	1.17745i	−0.0621480	+	0.0451531i
$681$	20.0292			0.767519
$682$	4.46654	−	2.17080i	0.171033	−	0.0831243i
$683$	4.63728			0.177441			0.0887204	−	0.996057i	$-0.471722\pi$
$683$	4.63728			0.177441			0.0887204	+	0.996057i	$0.471722\pi$
$684$	−0.861952	+	0.626244i	−0.0329575	+	0.0239451i
$685$	1.90920	+	5.87590i	0.0729466	+	0.224507i
$686$	−17.7270	+	54.5582i	−0.676821	+	2.08304i
$687$	17.8907	+	12.9983i	0.682571	+	0.495917i
$688$	−3.14641	−	2.28600i	−0.119956	−	0.0871530i
$689$	2.83891	−	8.73725i	0.108154	−	0.332863i
$690$	0.481677	+	1.48245i	0.0183371	+	0.0564359i
$691$	−7.81291	+	5.67641i	−0.297217	+	0.215941i	−0.726392	−	0.687280i	$-0.758804\pi$
$691$	−7.81291	+	5.67641i	−0.297217	+	0.215941i	0.429175	+	0.903221i	$0.358804\pi$
$692$	0.979478			0.0372342
$693$	−7.91482	+	14.8359i	−0.300659	+	0.563568i
$694$	35.4888			1.34714
$695$	6.32980	−	4.59887i	0.240103	−	0.174445i
$696$	2.19886	+	6.76739i	0.0833475	+	0.256517i
$697$	−0.856923	+	2.63734i	−0.0324583	+	0.0998963i
$698$	−20.6379	−	14.9943i	−0.781158	−	0.567544i
$699$	−14.4695	−	10.5127i	−0.547288	−	0.397628i
$700$	−7.61828	+	23.4467i	−0.287944	+	0.886201i
$701$	−7.18047	−	22.0992i	−0.271202	−	0.834675i	−0.990199	−	0.139662i	$-0.955398\pi$
$701$	−7.18047	−	22.0992i	−0.271202	−	0.834675i	0.718997	−	0.695013i	$-0.244602\pi$
$702$	−0.613815	+	0.445963i	−0.0231670	+	0.0168318i
$703$	4.35916			0.164409
$704$	21.2637	+	3.77981i	0.801404	+	0.142457i
$705$	−2.36249			−0.0889765
$706$	−24.7425	+	17.9765i	−0.931197	+	0.676554i
$707$	−18.9457	−	58.3090i	−0.712528	−	2.19293i
$708$	−3.12409	+	9.61496i	−0.117410	+	0.361352i
$709$	−28.0221	−	20.3593i	−1.05239	−	0.764609i	−0.0797275	−	0.996817i	$-0.525405\pi$
$709$	−28.0221	−	20.3593i	−1.05239	−	0.764609i	−0.972666	+	0.232208i	$0.925405\pi$
$710$	−3.22778	−	2.34512i	−0.121136	−	0.0880108i
$711$	2.10383	−	6.47491i	0.0788996	−	0.242828i
$712$	11.7271	+	36.0922i	0.439491	+	1.35261i
$713$	3.05987	−	2.22313i	0.114593	−	0.0832568i
$714$	5.01762			0.187780
$715$	−1.19221	−	1.23801i	−0.0445862	−	0.0462989i
$716$	−22.7845			−0.851496
$717$	−2.82660	+	2.05364i	−0.105561	+	0.0766947i
$718$	3.95082	+	12.1594i	0.147443	+	0.453783i
$719$	−9.80521	+	30.1773i	−0.365673	+	1.12543i	0.583886	+	0.811836i	$0.301532\pi$
$719$	−9.80521	+	30.1773i	−0.365673	+	1.12543i	−0.949559	+	0.313589i	$0.898468\pi$
$720$	0.392092	+	0.284872i	0.0146124	+	0.0106165i
$721$	2.18804	+	1.58971i	0.0814870	+	0.0592038i
$722$	0.298736	−	0.919416i	0.0111178	−	0.0342171i
$723$	−7.11300	−	21.8916i	−0.264535	−	0.814156i
$724$	12.6117	−	9.16293i	0.468710	−	0.340538i
$725$	10.9588			0.407001
$726$	6.57022	−	8.36153i	0.243844	−	0.310325i
$727$	33.6517			1.24807			0.624036	−	0.781396i	$-0.285492\pi$
$727$	33.6517			1.24807			0.624036	+	0.781396i	$0.285492\pi$
$728$	−9.53964	+	6.93096i	−0.353563	+	0.256878i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−1.08242	+	3.33134i	−0.0400621	+	0.123298i
$731$	−4.38845	−	3.18839i	−0.162313	−	0.117927i
$732$	0.758114	+	0.550802i	0.0280207	+	0.0203582i
$733$	14.0180	−	43.1430i	0.517767	−	1.59352i	−0.260424	−	0.965494i	$-0.583862\pi$
$733$	14.0180	−	43.1430i	0.517767	−	1.59352i	0.778190	−	0.628028i	$-0.216138\pi$
$734$	6.46421	+	19.8948i	0.238598	+	0.734330i
$735$	−9.99162	+	7.25934i	−0.368547	+	0.267765i
$736$	12.7403			0.469612
$737$	−28.9317	−	30.0431i	−1.06571	−	1.10665i
$738$	2.61864			0.0963935
$739$	−13.2223	+	9.60656i	−0.486390	+	0.353383i	−0.803794	−	0.594907i	$-0.797189\pi$
$739$	−13.2223	+	9.60656i	−0.486390	+	0.353383i	0.317404	+	0.948290i	$0.397189\pi$
$740$	0.947650	+	2.91657i	0.0348363	+	0.107215i
$741$	−0.242525	+	0.746416i	−0.00890938	+	0.0274203i
$742$	46.4152	+	33.7226i	1.70396	+	1.23800i
$743$	−31.8534	−	23.1428i	−1.16859	−	0.849028i	−0.177747	−	0.984076i	$-0.556881\pi$
$743$	−31.8534	−	23.1428i	−1.16859	−	0.849028i	−0.990839	+	0.135049i	$0.956881\pi$
$744$	1.41839	−	4.36535i	0.0520006	−	0.160041i
$745$	−2.61927	−	8.06130i	−0.0959628	−	0.295343i
$746$	4.14572	−	3.01204i	0.151786	−	0.110279i
$747$	3.12460			0.114323
$748$	3.56168	+	0.633122i	0.130228	+	0.0231492i
$749$	−36.9260			−1.34925
$750$	4.93902	−	3.58841i	0.180347	−	0.131030i
$751$	11.4611	+	35.2736i	0.418221	+	1.28715i	0.909338	+	0.416059i	$0.136589\pi$
$751$	11.4611	+	35.2736i	0.418221	+	1.28715i	−0.491116	+	0.871094i	$0.663411\pi$
$752$	0.811538	−	2.49766i	0.0295937	−	0.0910801i
$753$	10.2678	+	7.46002i	0.374181	+	0.271858i
$754$	1.47386	+	1.07082i	0.0536747	+	0.0389970i
$755$	3.32908	−	10.2459i	0.121158	−	0.372885i
$756$	1.66921	+	5.13729i	0.0607085	+	0.186842i
$757$	8.98196	−	6.52577i	0.326455	−	0.237183i	−0.412470	−	0.910971i	$-0.635334\pi$
$757$	8.98196	−	6.52577i	0.326455	−	0.237183i	0.738925	+	0.673788i	$0.235334\pi$
$758$	−5.44102			−0.197627
$759$	3.81214	−	7.14564i	0.138372	−	0.259370i
$760$	1.95675			0.0709786
$761$	35.7112	−	25.9457i	1.29453	−	0.940531i	0.294643	−	0.955607i	$-0.404799\pi$
$761$	35.7112	−	25.9457i	1.29453	−	0.940531i	0.999886	+	0.0150763i	$0.00479912\pi$
$762$	−4.56240	−	14.0416i	−0.165278	−	0.508674i
$763$	15.3110	−	47.1226i	0.554297	−	1.70595i
$764$	20.2516	+	14.7137i	0.732678	+	0.532322i
$765$	0.546870	+	0.397324i	0.0197721	+	0.0143653i
$766$	1.76293	−	5.42573i	0.0636971	−	0.196039i
$767$	2.30130	+	7.08266i	0.0830950	+	0.255740i
$768$	13.7738	−	10.0072i	0.497017	−	0.361104i
$769$	−23.0500			−0.831203			−0.415601	−	0.909547i	$-0.636429\pi$
$769$	−23.0500			−0.831203			−0.415601	+	0.909547i	$0.636429\pi$
$770$	9.65375	−	4.69186i	0.347897	−	0.169083i
$771$	3.55248			0.127939
$772$	6.16798	−	4.48130i	0.221990	−	0.161286i
$773$	−1.61026	−	4.95586i	−0.0579169	−	0.178250i	0.917913	−	0.396782i	$-0.129873\pi$
$773$	−1.61026	−	4.95586i	−0.0579169	−	0.178250i	−0.975830	+	0.218532i	$0.929873\pi$
$774$	−1.58290	+	4.87165i	−0.0568960	+	0.175108i
$775$	−5.71899	−	4.15509i	−0.205432	−	0.149255i
$776$	24.9087	+	18.0972i	0.894169	+	0.649652i
$777$	6.82949	−	21.0190i	0.245007	−	0.754053i
$778$	−8.86798	−	27.2928i	−0.317933	−	0.978496i
$779$	2.19143	−	1.59217i	0.0785162	−	0.0570454i
$780$	−0.552124			−0.0197692
$781$	2.85655	+	20.5323i	0.102215	+	0.734702i
$782$	−2.41672			−0.0864216
$783$	1.94256	−	1.41136i	0.0694216	−	0.0504377i
$784$	−4.24246	−	13.0569i	−0.151516	−	0.466319i
$785$	4.37971	−	13.4794i	0.156319	−	0.481099i
$786$	−8.95969	−	6.50960i	−0.319582	−	0.232190i
$787$	13.4560	+	9.77633i	0.479653	+	0.348488i	0.801191	−	0.598408i	$-0.204200\pi$
$787$	13.4560	+	9.77633i	0.479653	+	0.348488i	−0.321538	+	0.946897i	$0.604200\pi$
$788$	−3.45550	+	10.6349i	−0.123097	+	0.378854i
$789$	−2.29072	−	7.05011i	−0.0815518	−	0.250991i
$790$	−3.51583	+	2.55440i	−0.125088	+	0.0908815i
$791$	41.7891			1.48585
$792$	−1.35437	−	9.73488i	−0.0481253	−	0.345914i
$793$	0.690281			0.0245126
$794$	−29.3331	+	21.3117i	−1.04099	+	0.756325i
$795$	2.38844	+	7.35085i	0.0847091	+	0.260708i
$796$	5.50711	−	16.9491i	0.195194	−	0.600746i
$797$	25.4970	+	18.5246i	0.903150	+	0.656177i	0.939273	−	0.343171i	$-0.111501\pi$
$797$	25.4970	+	18.5246i	0.903150	+	0.656177i	−0.0361235	+	0.999347i	$0.511501\pi$
$798$	−3.96521	−	2.88089i	−0.140367	−	0.101983i
$799$	1.13189	−	3.48360i	0.0400434	−	0.123241i
$800$	−7.35828	−	22.6465i	−0.260155	−	0.800674i
$801$	10.3602	−	7.52712i	0.366060	−	0.265958i
$802$	20.9291			0.739031
$803$	16.3689	−	7.95553i	0.577646	−	0.280745i
$804$	−13.3985			−0.472530
$805$	6.61346	−	4.80496i	0.233094	−	0.169353i
$806$	−0.363143	−	1.11764i	−0.0127912	−	0.0393672i
$807$	6.84389	−	21.0633i	0.240916	−	0.741464i
$808$	28.9922	+	21.0641i	1.01994	+	0.741031i
$809$	12.7930	+	9.29465i	0.449777	+	0.326782i	0.789508	−	0.613740i	$-0.210336\pi$
$809$	12.7930	+	9.29465i	0.449777	+	0.326782i	−0.339730	+	0.940523i	$0.610336\pi$
$810$	0.197254	−	0.607085i	0.00693079	−	0.0213308i
$811$	10.4935	+	32.2956i	0.368476	+	1.13405i	0.947776	+	0.318938i	$0.103326\pi$
$811$	10.4935	+	32.2956i	0.368476	+	1.13405i	−0.579300	+	0.815115i	$0.696674\pi$
$812$	10.4931	−	7.62367i	0.368235	−	0.267539i
$813$	−11.4538			−0.401702
$814$	−6.57880	+	12.3316i	−0.230587	+	0.432222i
$815$	−13.3231			−0.466686
$816$	−0.607912	+	0.441674i	−0.0212812	+	0.0154617i
$817$	1.63737	+	5.03930i	0.0572843	+	0.176303i
$818$	0.684548	−	2.10682i	0.0239347	−	0.0736633i
$819$	3.21910	+	2.33882i	0.112485	+	0.0817248i
$820$	1.54167	+	1.12009i	0.0538373	+	0.0391151i
$821$	8.92763	−	27.4764i	0.311577	−	0.958934i	−0.665564	−	0.746341i	$-0.731809\pi$
$821$	8.92763	−	27.4764i	0.311577	−	0.958934i	0.977141	−	0.212593i	$-0.0681910\pi$
$822$	2.79524	+	8.60286i	0.0974952	+	0.300059i
$823$	14.0989	−	10.2435i	0.491457	−	0.357065i	−0.314287	−	0.949328i	$-0.601765\pi$
$823$	14.0989	−	10.2435i	0.491457	−	0.357065i	0.805744	+	0.592263i	$0.201765\pi$
$824$	−1.58086			−0.0550718
$825$	−14.9035	−	2.64923i	−0.518873	−	0.0922344i
$826$	−46.5077			−1.61821
$827$	−4.35935	+	3.16725i	−0.151590	+	0.110136i	−0.660995	−	0.750391i	$-0.729865\pi$
$827$	−4.35935	+	3.16725i	−0.151590	+	0.110136i	0.509405	+	0.860527i	$0.329865\pi$
$828$	−0.803967	−	2.47436i	−0.0279398	−	0.0859899i
$829$	−5.90051	+	18.1599i	−0.204933	+	0.630720i	0.794783	+	0.606894i	$0.207585\pi$
$829$	−5.90051	+	18.1599i	−0.204933	+	0.630720i	−0.999716	+	0.0238259i	$0.992415\pi$
$830$	−1.61360	−	1.17235i	−0.0560088	−	0.0406928i
$831$	7.26942	+	5.28154i	0.252173	+	0.183215i
$832$	1.57926	−	4.86046i	0.0547510	−	0.168506i
$833$	−5.91715	−	18.2111i	−0.205017	−	0.630978i
$834$	9.26741	−	6.73317i	0.320904	−	0.233151i
$835$	12.2393			0.423557
$836$	−2.45114	−	2.54529i	−0.0847743	−	0.0880307i
$837$	−1.54887			−0.0535368
$838$	23.9662	−	17.4125i	0.827900	−	0.601505i
$839$	5.04294	+	15.5206i	0.174102	+	0.535830i	0.999591	−	0.0285875i	$-0.00910093\pi$
$839$	5.04294	+	15.5206i	0.174102	+	0.535830i	−0.825490	+	0.564417i	$0.809101\pi$
$840$	3.06563	−	9.43504i	0.105774	−	0.325540i
$841$	18.7971	+	13.6569i	0.648177	+	0.470928i
$842$	5.92548	+	4.30511i	0.204206	+	0.148364i
$843$	−3.44692	+	10.6085i	−0.118718	+	0.365378i
$844$	−2.82597	−	8.69744i	−0.0972739	−	0.299378i
$845$	6.61542	−	4.80638i	0.227577	−	0.165345i
$846$	−3.45890			−0.118920
$847$	−52.3529	−	19.2197i	−1.79887	−	0.660397i
$848$	−8.59187			−0.295046
$849$	10.6802	−	7.75964i	0.366545	−	0.266310i
$850$	1.39580	+	4.29584i	0.0478757	+	0.147346i
$851$	−3.28940	+	10.1237i	−0.112759	+	0.347037i
$852$	5.38749	+	3.91424i	0.184572	+	0.134100i
$853$	16.7865	+	12.1961i	0.574759	+	0.417587i	0.836831	−	0.547461i	$-0.184406\pi$
$853$	16.7865	+	12.1961i	0.574759	+	0.417587i	−0.262072	+	0.965048i	$0.584406\pi$
$854$	−1.33212	+	4.09984i	−0.0455841	+	0.140294i
$855$	−0.204042	−	0.627977i	−0.00697809	−	0.0214763i
$856$	17.4616	−	12.6866i	0.596826	−	0.433620i
$857$	9.28903			0.317307			0.158654	−	0.987334i	$-0.449285\pi$
$857$	9.28903			0.317307			0.158654	+	0.987334i	$0.449285\pi$
$858$	−1.74551	−	1.81256i	−0.0595907	−	0.0618797i
$859$	−43.1947			−1.47378			−0.736891	−	0.676011i	$-0.763707\pi$
$859$	−43.1947			−1.47378			−0.736891	+	0.676011i	$0.763707\pi$
$860$	−3.01567	+	2.19101i	−0.102834	+	0.0747130i
$861$	−4.24381	−	13.0611i	−0.144629	−	0.445121i
$862$	11.1592	−	34.3445i	0.380084	−	1.16978i
$863$	−14.5688	−	10.5849i	−0.495929	−	0.360313i	0.311531	−	0.950236i	$-0.399158\pi$
$863$	−14.5688	−	10.5849i	−0.495929	−	0.360313i	−0.807460	+	0.589923i	$0.799158\pi$
$864$	−4.22090	−	3.06666i	−0.143598	−	0.104330i
$865$	−0.187581	+	0.577315i	−0.00637795	+	0.0196293i
$866$	−6.88048	−	21.1759i	−0.233808	−	0.719588i
$867$	12.9054	−	9.37633i	0.438291	−	0.318437i
$868$	−8.36649			−0.283977
$869$	22.2315	+	3.95185i	0.754151	+	0.134057i
$870$	−1.53271			−0.0519638
$871$	−7.98480	+	5.80130i	−0.270555	+	0.196570i
$872$	8.94951	+	27.5438i	0.303069	+	0.932750i
$873$	3.21054	−	9.88102i	0.108660	−	0.334422i
$874$	1.90983	+	1.38757i	0.0646009	+	0.0469353i
$875$	−25.9023	−	18.8191i	−0.875656	−	0.636202i
$876$	1.80666	−	5.56033i	0.0610415	−	0.187866i
$877$	11.3114	+	34.8130i	0.381960	+	1.17555i	0.938661	+	0.344840i	$0.112067\pi$
$877$	11.3114	+	34.8130i	0.381960	+	1.17555i	−0.556701	+	0.830713i	$0.687933\pi$
$878$	2.04430	−	1.48527i	0.0689918	−	0.0501255i
$879$	13.3316			0.449665
$880$	−0.756604	+	1.41821i	−0.0255051	+	0.0478079i
$881$	−55.7564			−1.87848			−0.939240	−	0.343261i	$-0.888468\pi$
$881$	−55.7564			−1.87848			−0.939240	+	0.343261i	$0.888468\pi$
$882$	−14.6287	+	10.6283i	−0.492573	+	0.357875i
$883$	−1.84260	−	5.67093i	−0.0620084	−	0.190842i	0.915253	−	0.402879i	$-0.131990\pi$
$883$	−1.84260	−	5.67093i	−0.0620084	−	0.190842i	−0.977262	+	0.212037i	$0.931990\pi$
$884$	0.264528	−	0.814133i	0.00889703	−	0.0273822i
$885$	−5.06887	−	3.68275i	−0.170388	−	0.123794i
$886$	−8.08862	−	5.87673i	−0.271743	−	0.197433i
$887$	8.89246	−	27.3682i	0.298580	−	0.918934i	−0.683416	−	0.730029i	$-0.739506\pi$
$887$	8.89246	−	27.3682i	0.298580	−	0.918934i	0.981995	−	0.188904i	$-0.0604936\pi$
$888$	3.99193	+	12.2859i	0.133960	+	0.412288i
$889$	−62.6420	+	45.5121i	−2.10094	+	1.52643i
$890$	−8.17435			−0.274005
$891$	−2.98298	+	1.44977i	−0.0999335	+	0.0485692i
$892$	−23.8819			−0.799624
$893$	−2.89461	+	2.10306i	−0.0968645	+	0.0703762i
$894$	−3.83486	−	11.8025i	−0.128257	−	0.394734i
$895$	4.36349	−	13.4294i	0.145855	−	0.448896i
$896$	−16.9790	−	12.3360i	−0.567229	−	0.412116i
$897$	−1.55047	−	1.12648i	−0.0517686	−	0.0376121i
$898$	1.67685	−	5.16081i	0.0559572	−	0.172218i
$899$	1.14925	+	3.53703i	0.0383297	+	0.117967i
$900$	−3.93396	+	2.85819i	−0.131132	+	0.0952729i
$901$	−11.9835			−0.399228
$902$	1.19678	+	8.60220i	0.0398485	+	0.286422i
$903$	26.8638			0.893970
$904$	−19.7613	+	14.3574i	−0.657251	+	0.477521i
$905$	2.98545	+	9.18828i	0.0992398	+	0.305429i
$906$	4.87408	−	15.0009i	0.161931	−	0.498371i
$907$	−20.1720	−	14.6558i	−0.669799	−	0.486638i	0.200159	−	0.979764i	$-0.435854\pi$
$907$	−20.1720	−	14.6558i	−0.669799	−	0.486638i	−0.869958	+	0.493126i	$0.835854\pi$
$908$	17.2642	+	12.5431i	0.572931	+	0.416259i
$909$	3.73687	−	11.5009i	0.123944	−	0.381461i
$910$	−0.784879	−	2.41561i	−0.0260185	−	0.0800766i
$911$	−15.8863	+	11.5420i	−0.526335	+	0.382405i	−0.818985	−	0.573815i	$-0.805463\pi$
$911$	−15.8863	+	11.5420i	−0.526335	+	0.382405i	0.292650	+	0.956220i	$0.405463\pi$
$912$	0.733996			0.0243050
$913$	1.42802	+	10.2643i	0.0472605	+	0.339698i
$914$	−31.4947			−1.04175
$915$	−0.469836	+	0.341356i	−0.0155323	+	0.0112849i
$916$	7.28075	+	22.4078i	0.240563	+	0.740376i
$917$	−17.9479	+	55.2381i	−0.592694	+	1.82412i
$918$	0.800668	+	0.581720i	0.0264260	+	0.0191996i
$919$	−25.7532	−	18.7108i	−0.849520	−	0.617212i	0.0754938	−	0.997146i	$-0.475947\pi$
$919$	−25.7532	−	18.7108i	−0.849520	−	0.617212i	−0.925014	+	0.379934i	$0.875947\pi$
$920$	−1.47655	+	4.54435i	−0.0486804	+	0.149823i
$921$	−3.12546	−	9.61918i	−0.102987	−	0.316963i
$922$	−0.923218	+	0.670757i	−0.0304046	+	0.0220902i
$923$	4.90544			0.161464
$924$	−16.1131	+	7.83119i	−0.530081	+	0.257627i
$925$	19.8953			0.654153
$926$	3.87436	−	2.81488i	0.127319	−	0.0925029i
$927$	0.164846	+	0.507343i	0.00541424	+	0.0166633i
$928$	−3.87122	+	11.9144i	−0.127079	+	0.391109i
$929$	−33.2718	−	24.1734i	−1.09161	−	0.793103i	−0.111942	−	0.993715i	$-0.535707\pi$
$929$	−33.2718	−	24.1734i	−1.09161	−	0.793103i	−0.979671	+	0.200611i	$0.935707\pi$
$930$	0.799863	+	0.581134i	0.0262285	+	0.0190562i
$931$	−5.77994	+	17.7888i	−0.189430	+	0.583006i
$932$	−5.88850	−	18.1229i	−0.192884	−	0.593637i
$933$	3.09123	−	2.24591i	0.101202	−	0.0735279i
$934$	−20.1960			−0.660834
$935$	−1.05527	+	1.97805i	−0.0345111	+	0.0646890i
$936$	−2.32580			−0.0760210
$937$	−22.0254	+	16.0024i	−0.719537	+	0.522775i	−0.886236	−	0.463233i	$-0.846689\pi$
$937$	−22.0254	+	16.0024i	−0.719537	+	0.522775i	0.166699	+	0.986008i	$0.446689\pi$
$938$	−19.0469	−	58.6202i	−0.621902	−	1.91402i
$939$	−1.57636	+	4.85154i	−0.0514426	+	0.158324i
$940$	−2.03635	−	1.47950i	−0.0664184	−	0.0482558i
$941$	17.4423	+	12.6725i	0.568601	+	0.413113i	0.834597	−	0.550861i	$-0.185701\pi$
$941$	17.4423	+	12.6725i	0.568601	+	0.413113i	−0.265995	+	0.963974i	$0.585701\pi$
$942$	6.41231	−	19.7350i	0.208924	−	0.643003i
$943$	2.04401	+	6.29082i	0.0665622	+	0.204857i
$944$	5.63465	−	4.09382i	0.183392	−	0.133242i
$945$	−3.34765			−0.108899
$946$	−16.7267	−	2.97333i	−0.543833	−	0.0966712i
$947$	−22.7301			−0.738628			−0.369314	−	0.929305i	$-0.620407\pi$
$947$	−22.7301			−0.738628			−0.369314	+	0.929305i	$0.620407\pi$
$948$	5.86827	−	4.26355i	0.190593	−	0.138474i
$949$	−1.33084	−	4.09591i	−0.0432009	−	0.132959i
$950$	1.36344	−	4.19623i	0.0442357	−	0.136144i
$951$	4.60252	+	3.34393i	0.149247	+	0.108434i
$952$	12.4436	+	9.04082i	0.403300	+	0.293015i
$953$	9.57162	−	29.4584i	0.310055	−	0.954252i	−0.667687	−	0.744442i	$-0.732716\pi$
$953$	9.57162	−	29.4584i	0.310055	−	0.954252i	0.977742	−	0.209810i	$-0.0672845\pi$
$954$	3.49689	+	10.7623i	0.113216	+	0.348443i
$955$	−12.5508	+	9.11870i	−0.406135	+	0.295074i
$956$	−3.72247			−0.120393
$957$	5.52408	+	5.73627i	0.178568	+	0.185427i
$958$	−21.9019			−0.707620
$959$	38.3788	−	27.8838i	1.23932	−	0.900416i
$960$	1.32867	+	4.08922i	0.0428826	+	0.131979i
$961$	−8.83820	+	27.2012i	−0.285103	+	0.877457i
$962$	2.67572	+	1.94403i	0.0862687	+	0.0626779i
$963$	−5.89234	−	4.28103i	−0.189878	−	0.137954i
$964$	7.57841	−	23.3239i	0.244084	−	0.751214i
$965$	1.46009	+	4.49370i	0.0470020	+	0.144657i
$966$	9.68271	−	7.03490i	0.311536	−	0.226344i
$967$	−2.82731			−0.0909203			−0.0454601	−	0.998966i	$-0.514475\pi$
$967$	−2.82731			−0.0909203			−0.0454601	+	0.998966i	$0.514475\pi$
$968$	31.3600	−	8.89814i	1.00795	−	0.285997i
$969$	1.02374			0.0328872
$970$	−5.36533	+	3.89814i	−0.172270	+	0.125162i
$971$	18.5371	+	57.0515i	0.594885	+	1.83087i	0.555297	+	0.831652i	$0.312605\pi$
$971$	18.5371	+	57.0515i	0.594885	+	1.83087i	0.0395881	+	0.999216i	$0.487395\pi$
$972$	−0.329236	+	1.01328i	−0.0105603	+	0.0325011i
$973$	−48.6021	−	35.3115i	−1.55811	−	1.13204i
$974$	27.0185	+	19.6301i	0.865728	+	0.628988i
$975$	−1.10689	+	3.40665i	−0.0354488	+	0.109100i
$976$	−0.199493	−	0.613976i	−0.00638562	−	0.0196529i
$977$	−6.57633	+	4.77798i	−0.210395	+	0.152861i	−0.687993	−	0.725718i	$-0.741508\pi$
$977$	−6.57633	+	4.77798i	−0.210395	+	0.152861i	0.477597	+	0.878579i	$0.341508\pi$
$978$	−19.5062			−0.623739
$979$	29.4613	+	30.5930i	0.941589	+	0.977757i
$980$	−13.1584			−0.420330
$981$	7.90637	−	5.74432i	0.252431	−	0.183402i
$982$	−1.10048	−	3.38694i	−0.0351178	−	0.108082i
$983$	−12.9607	+	39.8890i	−0.413383	+	1.27226i	0.500306	+	0.865849i	$0.333221\pi$
$983$	−12.9607	+	39.8890i	−0.413383	+	1.27226i	−0.913689	+	0.406414i	$0.866779\pi$
$984$	6.49419	+	4.71831i	0.207027	+	0.150414i
$985$	−5.60659	−	4.07342i	−0.178641	−	0.129790i
$986$	0.734336	−	2.26005i	0.0233860	−	0.0719748i
$987$	5.60554	+	17.2521i	0.178426	+	0.549140i
$988$	−0.676484	+	0.491494i	−0.0215218	+	0.0156365i
$989$	−12.9388			−0.411431
$990$	2.08441	+	0.370524i	0.0662470	+	0.0117760i
$991$	27.2520			0.865689			0.432844	−	0.901469i	$-0.357510\pi$
$991$	27.2520			0.865689			0.432844	+	0.901469i	$0.357510\pi$
$992$	6.53763	−	4.74986i	0.207570	−	0.150808i
$993$	8.00711	+	24.6434i	0.254098	+	0.782033i
$994$	−9.46661	+	29.1352i	−0.300263	+	0.924113i
$995$	8.93534	+	6.49190i	0.283269	+	0.205807i
$996$	2.69326	+	1.95676i	0.0853391	+	0.0620025i
$997$	7.60738	−	23.4131i	0.240928	−	0.741500i	−0.755351	−	0.655320i	$-0.772534\pi$
$997$	7.60738	−	23.4131i	0.240928	−	0.741500i	0.996280	−	0.0861805i	$-0.0274662\pi$
$998$	4.49903	+	13.8466i	0.142414	+	0.438306i
$999$	3.52664	−	2.56225i	0.111578	−	0.0810661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.j.d.58.4	✓	48
11.2	odd	10		6897.2.a.bq.1.8		24
11.4	even	5	inner	627.2.j.d.400.4	yes	48
11.9	even	5		6897.2.a.bp.1.17		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.j.d.58.4	✓	48	1.1	even	1	trivial
627.2.j.d.400.4	yes	48	11.4	even	5	inner
6897.2.a.bp.1.17		24	11.9	even	5
6897.2.a.bq.1.8		24	11.2	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.782102 + 0.568230i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.329236 + 1.01328i) q^{4} +(-0.534189 - 0.388111i) q^{5} +(-0.782102 - 0.568230i) q^{6} +(-1.56670 + 4.82180i) q^{7} +(-0.915756 - 2.81841i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.638327 q^{10} +(-2.30061 - 2.38898i) q^{11} -1.06543 q^{12} +(-0.634939 + 0.461310i) q^{13} +(-1.51458 - 4.66138i) q^{14} +(0.204042 - 0.627977i) q^{15} +(0.593815 + 0.431432i) q^{16} +(0.828222 + 0.601739i) q^{17} +(0.298736 - 0.919416i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(0.569141 - 0.413505i) q^{20} -5.06994 q^{21} +(3.15680 + 0.561150i) q^{22} +2.44192 q^{23} +(2.39748 - 1.74187i) q^{24} +(-1.41036 - 4.34063i) q^{25} +(0.234457 - 0.721583i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-4.37004 - 3.17502i) q^{28} +(-0.741993 + 2.28362i) q^{29} +(0.197254 + 0.607085i) q^{30} +(1.25306 - 0.910403i) q^{31} +5.21732 q^{32} +(1.56113 - 2.92624i) q^{33} -0.989680 q^{34} +(2.70831 - 1.96770i) q^{35} +(-0.329236 - 1.01328i) q^{36} +(-1.34706 + 4.14581i) q^{37} +(0.782102 + 0.568230i) q^{38} +(-0.634939 - 0.461310i) q^{39} +(-0.604668 + 1.86098i) q^{40} +(0.837053 + 2.57618i) q^{41} +(3.96521 - 2.88089i) q^{42} -5.29864 q^{43} +(3.17816 - 1.54463i) q^{44} +0.660294 q^{45} +(-1.90983 + 1.38757i) q^{46} +(-1.10564 - 3.40282i) q^{47} +(-0.226817 + 0.698072i) q^{48} +(-15.1321 - 10.9941i) q^{49} +(3.56952 + 2.59341i) q^{50} +(-0.316353 + 0.973634i) q^{51} +(-0.258394 - 0.795254i) q^{52} +(-9.47004 + 6.88039i) q^{53} +0.966731 q^{54} +(0.301770 + 2.16906i) q^{55} +15.0245 q^{56} +(0.809017 - 0.587785i) q^{57} +(-0.717308 - 2.20765i) q^{58} +(2.93223 - 9.02448i) q^{59} +(0.569141 + 0.413505i) q^{60} +(-0.711556 - 0.516976i) q^{61} +(-0.462704 + 1.42406i) q^{62} +(-1.56670 - 4.82180i) q^{63} +(-5.26811 + 3.82750i) q^{64} +0.518217 q^{65} +(0.441819 + 3.17570i) q^{66} +12.5757 q^{67} +(-0.882413 + 0.641111i) q^{68} +(0.754594 + 2.32240i) q^{69} +(-1.00006 + 3.07788i) q^{70} +(-5.05663 - 3.67386i) q^{71} +(2.39748 + 1.74187i) q^{72} +(-1.69571 + 5.21886i) q^{73} +(-1.30224 - 4.00788i) q^{74} +(3.69236 - 2.68266i) q^{75} +1.06543 q^{76} +(15.1235 - 7.35026i) q^{77} +0.758718 q^{78} +(-5.50789 + 4.00171i) q^{79} +(-0.149766 - 0.460932i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-2.11853 - 1.53920i) q^{82} +(-2.52786 - 1.83659i) q^{83} +(1.66921 - 5.13729i) q^{84} +(-0.208886 - 0.642884i) q^{85} +(4.14407 - 3.01085i) q^{86} -2.40114 q^{87} +(-4.62632 + 8.67176i) q^{88} -12.8059 q^{89} +(-0.516417 + 0.375199i) q^{90} +(-1.22959 - 3.78428i) q^{91} +(-0.803967 + 2.47436i) q^{92} +(1.25306 + 0.910403i) q^{93} +(2.79831 + 2.03309i) q^{94} +(-0.204042 + 0.627977i) q^{95} +(1.61224 + 4.96196i) q^{96} +(-8.40530 + 6.10681i) q^{97} +18.0820 q^{98} +(3.26543 + 0.580461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 3 q^{2} - 12 q^{3} - 21 q^{4} - 2 q^{5} + 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} + 2 q^{10} - 15 q^{11} + 74 q^{12} + 4 q^{13} - 24 q^{14} - 7 q^{15} - 25 q^{16} + 11 q^{17} - 2 q^{18} + 12 q^{19}+ \cdots - 5 q^{99}+O(q^{100}) \) 48 * q + 3 * q^2 - 12 * q^3 - 21 * q^4 - 2 * q^5 + 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 + 2 * q^10 - 15 * q^11 + 74 * q^12 + 4 * q^13 - 24 * q^14 - 7 * q^15 - 25 * q^16 + 11 * q^17 - 2 * q^18 + 12 * q^19 + 19 * q^20 - 6 * q^21 - 18 * q^22 + 60 * q^23 - 5 * q^24 - 8 * q^25 + 43 * q^26 - 12 * q^27 + 24 * q^28 + 9 * q^29 - 3 * q^30 - 16 * q^31 - 32 * q^32 + 5 * q^33 + 46 * q^34 + 22 * q^35 - 21 * q^36 - 23 * q^37 - 3 * q^38 + 4 * q^39 + 4 * q^40 - 10 * q^41 + 26 * q^42 + 2 * q^43 - 8 * q^44 + 18 * q^45 - 49 * q^46 - 57 * q^47 - 30 * q^48 - 22 * q^49 - 4 * q^50 - 14 * q^51 + 35 * q^52 - 22 * q^53 - 2 * q^54 - 22 * q^55 + 8 * q^56 + 12 * q^57 - 74 * q^58 + 29 * q^59 + 19 * q^60 - 24 * q^61 + 51 * q^62 + 4 * q^63 + 37 * q^64 - 60 * q^65 - 18 * q^66 + 92 * q^67 + 52 * q^68 - 20 * q^69 + 101 * q^70 - 38 * q^71 - 5 * q^72 - 24 * q^73 + 40 * q^74 - 43 * q^75 - 74 * q^76 + 53 * q^77 - 12 * q^78 + 11 * q^79 - 173 * q^80 - 12 * q^81 - 64 * q^82 - 20 * q^83 - 41 * q^84 + 29 * q^85 + 36 * q^86 - 26 * q^87 + 29 * q^88 + 42 * q^89 + 2 * q^90 - 35 * q^91 + 49 * q^92 - 16 * q^93 + 74 * q^94 + 7 * q^95 + 43 * q^96 - 45 * q^97 - 118 * q^98 - 5 * q^99

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