LMFDB - Embedded newform 240.2.bl.a.229.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(109,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("240.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			229.22
Character	$\chi$	$=$	240.229
Dual form			240.2.bl.a.109.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36038 + 0.386472i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.70128 + 1.05150i) q^{4} +(-1.03097 - 1.98421i) q^{5} +(-0.688658 - 1.23521i) q^{6} +3.91927 q^{7} +(1.90801 + 2.08794i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(1.36038 + 0.386472i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.70128 + 1.05150i) q^{4} +(-1.03097 - 1.98421i) q^{5} +(-0.688658 - 1.23521i) q^{6} +3.91927 q^{7} +(1.90801 + 2.08794i) q^{8} +1.00000i q^{9} +(-0.635669 - 3.09773i) q^{10} +(-2.93423 - 2.93423i) q^{11} +(-0.459462 - 1.94651i) q^{12} +(0.732828 + 0.732828i) q^{13} +(5.33170 + 1.51469i) q^{14} +(-0.674045 + 2.13206i) q^{15} +(1.78869 + 3.57779i) q^{16} +2.89302i q^{17} +(-0.386472 + 1.36038i) q^{18} +(1.67534 - 1.67534i) q^{19} +(0.332434 - 4.45976i) q^{20} +(-2.77134 - 2.77134i) q^{21} +(-2.85767 - 5.12567i) q^{22} +1.73133 q^{23} +(0.127228 - 2.82556i) q^{24} +(-2.87420 + 4.09133i) q^{25} +(0.713708 + 1.28014i) q^{26} +(0.707107 - 0.707107i) q^{27} +(6.66776 + 4.12111i) q^{28} +(-4.99003 + 4.99003i) q^{29} +(-1.74094 + 2.63991i) q^{30} -10.8149 q^{31} +(1.05059 + 5.55844i) q^{32} +4.14963i q^{33} +(-1.11807 + 3.93561i) q^{34} +(-4.04065 - 7.77666i) q^{35} +(-1.05150 + 1.70128i) q^{36} +(-6.41524 + 6.41524i) q^{37} +(2.92658 - 1.63163i) q^{38} -1.03637i q^{39} +(2.17581 - 5.93850i) q^{40} -0.00577512i q^{41} +(-2.69904 - 4.84113i) q^{42} +(2.23930 - 2.23930i) q^{43} +(-1.90660 - 8.07728i) q^{44} +(1.98421 - 1.03097i) q^{45} +(2.35527 + 0.669110i) q^{46} -11.6451i q^{47} +(1.26508 - 3.79468i) q^{48} +8.36066 q^{49} +(-5.49120 + 4.45497i) q^{50} +(2.04567 - 2.04567i) q^{51} +(0.476175 + 2.01731i) q^{52} +(-5.55765 + 5.55765i) q^{53} +(1.23521 - 0.688658i) q^{54} +(-2.79703 + 8.84724i) q^{55} +(7.47801 + 8.18319i) q^{56} -2.36929 q^{57} +(-8.71685 + 4.85983i) q^{58} +(3.83290 + 3.83290i) q^{59} +(-3.38860 + 2.91846i) q^{60} +(9.30595 - 9.30595i) q^{61} +(-14.7123 - 4.17964i) q^{62} +3.91927i q^{63} +(-0.718981 + 7.96763i) q^{64} +(0.698563 - 2.20961i) q^{65} +(-1.60372 + 5.64508i) q^{66} +(3.85243 + 3.85243i) q^{67} +(-3.04201 + 4.92182i) q^{68} +(-1.22423 - 1.22423i) q^{69} +(-2.49136 - 12.1408i) q^{70} -1.15355i q^{71} +(-2.08794 + 1.90801i) q^{72} +7.98713 q^{73} +(-11.2065 + 6.24786i) q^{74} +(4.92537 - 0.860637i) q^{75} +(4.61185 - 1.08860i) q^{76} +(-11.5000 - 11.5000i) q^{77} +(0.400530 - 1.40987i) q^{78} +0.843960 q^{79} +(5.25501 - 7.23774i) q^{80} -1.00000 q^{81} +(0.00223193 - 0.00785637i) q^{82} +(5.20069 + 5.20069i) q^{83} +(-1.80076 - 7.62889i) q^{84} +(5.74036 - 2.98261i) q^{85} +(3.91173 - 2.18088i) q^{86} +7.05696 q^{87} +(0.527948 - 11.7250i) q^{88} +5.40896i q^{89} +(3.09773 - 0.635669i) q^{90} +(2.87215 + 2.87215i) q^{91} +(2.94547 + 1.82049i) q^{92} +(7.64726 + 7.64726i) q^{93} +(4.50051 - 15.8418i) q^{94} +(-5.05147 - 1.59701i) q^{95} +(3.18753 - 4.67329i) q^{96} -2.24154i q^{97} +(11.3737 + 3.23117i) q^{98} +(2.93423 - 2.93423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.36038	+	0.386472i	0.961935	+	0.273277i
$2$	1.36038	+	0.386472i	0.961935	+	0.273277i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.70128	+	1.05150i	0.850639	+	0.525750i
$5$	−1.03097	−	1.98421i	−0.461064	−	0.887367i
$5$	−1.03097	−	1.98421i	−0.461064	−	0.887367i
$6$	−0.688658	−	1.23521i	−0.281143	−	0.504273i
$7$	3.91927			1.48134			0.740672	−	0.671867i	$-0.234507\pi$
$7$	3.91927			1.48134			0.740672	+	0.671867i	$0.234507\pi$
$8$	1.90801	+	2.08794i	0.674584	+	0.738198i
$9$			1.00000i			0.333333i
$10$	−0.635669	−	3.09773i	−0.201016	−	0.979588i
$11$	−2.93423	−	2.93423i	−0.884703	−	0.884703i	0.109305	−	0.994008i	$-0.465138\pi$
$11$	−2.93423	−	2.93423i	−0.884703	−	0.884703i	−0.994008	+	0.109305i	$0.965138\pi$
$12$	−0.459462	−	1.94651i	−0.132635	−	0.561909i
$13$	0.732828	+	0.732828i	0.203250	+	0.203250i	0.801391	−	0.598141i	$-0.204094\pi$
$13$	0.732828	+	0.732828i	0.203250	+	0.203250i	−0.598141	+	0.801391i	$0.704094\pi$
$14$	5.33170	+	1.51469i	1.42496	+	0.404818i
$15$	−0.674045	+	2.13206i	−0.174038	+	0.550495i
$16$	1.78869	+	3.57779i	0.447173	+	0.894447i
$17$			2.89302i			0.701659i	0.936439	+	0.350830i	$0.114100\pi$
$17$			2.89302i			0.701659i	−0.936439	+	0.350830i	$0.885900\pi$
$18$	−0.386472	+	1.36038i	−0.0910924	+	0.320645i
$19$	1.67534	−	1.67534i	0.384350	−	0.384350i	−0.488316	−	0.872667i	$-0.662389\pi$
$19$	1.67534	−	1.67534i	0.384350	−	0.384350i	0.872667	+	0.488316i	$0.162389\pi$
$20$	0.332434	−	4.45976i	0.0743346	−	0.997233i
$21$	−2.77134	−	2.77134i	−0.604756	−	0.604756i
$22$	−2.85767	−	5.12567i	−0.609258	−	1.09280i
$23$	1.73133			0.361006			0.180503	−	0.983574i	$-0.442227\pi$
$23$	1.73133			0.361006			0.180503	+	0.983574i	$0.442227\pi$
$24$	0.127228	−	2.82556i	0.0259703	−	0.576766i
$25$	−2.87420	+	4.09133i	−0.574841	+	0.818265i
$26$	0.713708	+	1.28014i	0.139970	+	0.251057i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	6.66776	+	4.12111i	1.26009	+	0.778817i
$29$	−4.99003	+	4.99003i	−0.926625	+	0.926625i	−0.997486	−	0.0708617i	$-0.977425\pi$
$29$	−4.99003	+	4.99003i	−0.926625	+	0.926625i	0.0708617	+	0.997486i	$0.477425\pi$
$30$	−1.74094	+	2.63991i	−0.317851	+	0.481980i
$31$	−10.8149			−1.94241			−0.971203	−	0.238254i	$-0.923425\pi$
$31$	−10.8149			−1.94241			−0.971203	+	0.238254i	$0.923425\pi$
$32$	1.05059	+	5.55844i	0.185720	+	0.982603i
$33$			4.14963i			0.722357i
$34$	−1.11807	+	3.93561i	−0.191748	+	0.674951i
$35$	−4.04065	−	7.77666i	−0.682994	−	1.31450i
$36$	−1.05150	+	1.70128i	−0.175250	+	0.283546i
$37$	−6.41524	+	6.41524i	−1.05466	+	1.05466i	−0.0562413	+	0.998417i	$0.517912\pi$
$37$	−6.41524	+	6.41524i	−1.05466	+	1.05466i	−0.998417	+	0.0562413i	$0.982088\pi$
$38$	2.92658	−	1.63163i	0.474754	−	0.264686i
$39$		−	1.03637i		−	0.165953i
$40$	2.17581	−	5.93850i	0.344026	−	0.938960i
$41$		−	0.00577512i		−	0.000901923i	−1.00000		0.000450961i	$-0.999856\pi$
$41$		−	0.00577512i		−	0.000901923i	1.00000		0.000450961i	$-0.000143545\pi$
$42$	−2.69904	−	4.84113i	−0.416470	−	0.747002i
$43$	2.23930	−	2.23930i	0.341490	−	0.341490i	−0.515437	−	0.856927i	$-0.672370\pi$
$43$	2.23930	−	2.23930i	0.341490	−	0.341490i	0.856927	+	0.515437i	$0.172370\pi$
$44$	−1.90660	−	8.07728i	−0.287430	−	1.21770i
$45$	1.98421	−	1.03097i	0.295789	−	0.153688i
$46$	2.35527	+	0.669110i	0.347265	+	0.0986549i
$47$		−	11.6451i		−	1.69861i	−0.527900	−	0.849307i	$-0.677020\pi$
$47$		−	11.6451i		−	1.69861i	0.527900	−	0.849307i	$-0.322980\pi$
$48$	1.26508	−	3.79468i	0.182599	−	0.547714i
$49$	8.36066			1.19438
$50$	−5.49120	+	4.45497i	−0.776573	+	0.630028i
$51$	2.04567	−	2.04567i	0.286451	−	0.286451i
$52$	0.476175	+	2.01731i	0.0660336	+	0.279751i
$53$	−5.55765	+	5.55765i	−0.763402	+	0.763402i	−0.976936	−	0.213533i	$-0.931503\pi$
$53$	−5.55765	+	5.55765i	−0.763402	+	0.763402i	0.213533	+	0.976936i	$0.431503\pi$
$54$	1.23521	−	0.688658i	0.168091	−	0.0937145i
$55$	−2.79703	+	8.84724i	−0.377152	+	1.19296i
$56$	7.47801	+	8.18319i	0.999291	+	1.09353i
$57$	−2.36929			−0.313821
$58$	−8.71685	+	4.85983i	−1.14458	+	0.638127i
$59$	3.83290	+	3.83290i	0.499001	+	0.499001i	0.911127	−	0.412126i	$-0.135214\pi$
$59$	3.83290	+	3.83290i	0.499001	+	0.499001i	−0.412126	+	0.911127i	$0.635214\pi$
$60$	−3.38860	+	2.91846i	−0.437466	+	0.376772i
$61$	9.30595	−	9.30595i	1.19150	−	1.19150i	0.214859	−	0.976645i	$-0.431071\pi$
$61$	9.30595	−	9.30595i	1.19150	−	1.19150i	0.976645	−	0.214859i	$-0.0689293\pi$
$62$	−14.7123	−	4.17964i	−1.86847	−	0.530815i
$63$			3.91927i			0.493781i
$64$	−0.718981	+	7.96763i	−0.0898726	+	0.995953i
$65$	0.698563	−	2.20961i	0.0866461	−	0.274068i
$66$	−1.60372	+	5.64508i	−0.197404	+	0.694861i
$67$	3.85243	+	3.85243i	0.470649	+	0.470649i	0.902124	−	0.431476i	$-0.142007\pi$
$67$	3.85243	+	3.85243i	0.470649	+	0.470649i	−0.431476	+	0.902124i	$0.642007\pi$
$68$	−3.04201	+	4.92182i	−0.368898	+	0.596859i
$69$	−1.22423	−	1.22423i	−0.147380	−	0.147380i
$70$	−2.49136	−	12.1408i	−0.297774	−	1.45111i
$71$		−	1.15355i		−	0.136901i	−0.997655	−	0.0684504i	$-0.978195\pi$
$71$		−	1.15355i		−	0.136901i	0.997655	−	0.0684504i	$-0.0218055\pi$
$72$	−2.08794	+	1.90801i	−0.246066	+	0.224861i
$73$	7.98713			0.934823			0.467411	−	0.884040i	$-0.345187\pi$
$73$	7.98713			0.934823			0.467411	+	0.884040i	$0.345187\pi$
$74$	−11.2065	+	6.24786i	−1.30273	+	0.726299i
$75$	4.92537	−	0.860637i	0.568733	−	0.0993778i
$76$	4.61185	−	1.08860i	0.529016	−	0.124871i
$77$	−11.5000	−	11.5000i	−1.31055	−	1.31055i
$78$	0.400530	−	1.40987i	0.0453511	−	0.159636i
$79$	0.843960			0.0949529			0.0474765	−	0.998872i	$-0.484882\pi$
$79$	0.843960			0.0949529			0.0474765	+	0.998872i	$0.484882\pi$
$80$	5.25501	−	7.23774i	0.587528	−	0.809204i
$81$	−1.00000			−0.111111
$82$	0.00223193	−	0.00785637i	0.000246475	−	0.000867591i
$83$	5.20069	+	5.20069i	0.570850	+	0.570850i	0.932366	−	0.361516i	$-0.117741\pi$
$83$	5.20069	+	5.20069i	0.570850	+	0.570850i	−0.361516	+	0.932366i	$0.617741\pi$
$84$	−1.80076	−	7.62889i	−0.196479	−	0.832380i
$85$	5.74036	−	2.98261i	0.622629	−	0.323510i
$86$	3.91173	−	2.18088i	0.421813	−	0.235170i
$87$	7.05696			0.756586
$88$	0.527948	−	11.7250i	0.0562794	−	1.24989i
$89$			5.40896i			0.573349i	0.958028	+	0.286674i	$0.0925498\pi$
$89$			5.40896i			0.573349i	−0.958028	+	0.286674i	$0.907450\pi$
$90$	3.09773	−	0.635669i	0.326529	−	0.0670054i
$91$	2.87215	+	2.87215i	0.301083	+	0.301083i
$92$	2.94547	+	1.82049i	0.307086	+	0.189799i
$93$	7.64726	+	7.64726i	0.792984	+	0.792984i
$94$	4.50051	−	15.8418i	0.464193	−	1.63396i
$95$	−5.05147	−	1.59701i	−0.518270	−	0.163850i
$96$	3.18753	−	4.67329i	0.325326	−	0.476966i
$97$		−	2.24154i		−	0.227594i	−0.993504	−	0.113797i	$-0.963699\pi$
$97$		−	2.24154i		−	0.227594i	0.993504	−	0.113797i	$-0.0363013\pi$
$98$	11.3737	+	3.23117i	1.14892	+	0.326397i
$99$	2.93423	−	2.93423i	0.294901	−	0.294901i
$100$	−9.19185	+	3.93826i	−0.919185	+	0.393826i
$101$	−7.50655	−	7.50655i	−0.746930	−	0.746930i	0.226972	−	0.973901i	$-0.427118\pi$
$101$	−7.50655	−	7.50655i	−0.746930	−	0.746930i	−0.973901	+	0.226972i	$0.927118\pi$
$102$	3.57349	−	1.99230i	0.353828	−	0.197267i
$103$	−3.91110			−0.385372			−0.192686	−	0.981260i	$-0.561720\pi$
$103$	−3.91110			−0.385372			−0.192686	+	0.981260i	$0.561720\pi$
$104$	−0.131856	+	2.92834i	−0.0129295	+	0.287148i
$105$	−2.64176	+	8.35610i	−0.257810	+	0.815472i
$106$	−9.70841	+	5.41265i	−0.942964	+	0.525723i
$107$	2.60233	−	2.60233i	0.251577	−	0.251577i	−0.570040	−	0.821617i	$-0.693072\pi$
$107$	2.60233	−	2.60233i	0.251577	−	0.251577i	0.821617	+	0.570040i	$0.193072\pi$
$108$	1.94651	−	0.459462i	0.187303	−	0.0442118i
$109$	−2.06635	+	2.06635i	−0.197920	+	0.197920i	−0.799108	−	0.601188i	$-0.794694\pi$
$109$	−2.06635	+	2.06635i	−0.197920	+	0.197920i	0.601188	+	0.799108i	$0.294694\pi$
$110$	−7.22425	+	10.9546i	−0.688805	+	1.04448i
$111$	9.07252			0.861125
$112$	7.01037	+	14.0223i	0.662418	+	1.32498i
$113$		−	8.13610i		−	0.765380i	−0.923877	−	0.382690i	$-0.874998\pi$
$113$		−	8.13610i		−	0.765380i	0.923877	−	0.382690i	$-0.125002\pi$
$114$	−3.22315	−	0.915667i	−0.301875	−	0.0857601i
$115$	−1.78495	−	3.43532i	−0.166447	−	0.320345i
$116$	−13.7364	+	3.24241i	−1.27540	+	0.301050i
$117$	−0.732828	+	0.732828i	−0.0677500	+	0.0677500i
$118$	3.73290	+	6.69551i	0.343641	+	0.616372i
$119$			11.3385i			1.03940i
$120$	−5.73769	+	2.66062i	−0.523777	+	0.242881i
$121$			6.21941i			0.565401i
$122$	16.2561	−	9.06315i	1.47176	−	0.820539i
$123$	−0.00408363	+	0.00408363i	−0.000368208	+	0.000368208i
$124$	−18.3991	−	11.3718i	−1.65229	−	1.02122i
$125$	11.0813	+	1.48500i	0.991140	+	0.132822i
$126$	−1.51469	+	5.33170i	−0.134939	+	0.474986i
$127$			16.0862i			1.42742i	0.700442	+	0.713709i	$0.252986\pi$
$127$			16.0862i			1.42742i	−0.700442	+	0.713709i	$0.747014\pi$
$128$	−4.05736	+	10.5611i	−0.358623	+	0.933482i
$129$	−3.16685			−0.278826
$130$	1.80427	−	2.73594i	0.158245	−	0.239958i
$131$	13.0407	−	13.0407i	1.13937	−	1.13937i	0.150808	−	0.988563i	$-0.451813\pi$
$131$	13.0407	−	13.0407i	1.13937	−	1.13937i	0.988563	−	0.150808i	$-0.0481875\pi$
$132$	−4.36333	+	7.05967i	−0.379780	+	0.614465i
$133$	6.56612	−	6.56612i	0.569355	−	0.569355i
$134$	3.75191	+	6.72963i	0.324116	+	0.581351i
$135$	−2.13206	−	0.674045i	−0.183498	−	0.0580125i
$136$	−6.04044	+	5.51991i	−0.517964	+	0.473328i
$137$	6.51614			0.556711			0.278356	−	0.960478i	$-0.410211\pi$
$137$	6.51614			0.556711			0.278356	+	0.960478i	$0.410211\pi$
$138$	−1.19229	−	2.13856i	−0.101495	−	0.182046i
$139$	−15.0953	−	15.0953i	−1.28036	−	1.28036i	−0.940461	−	0.339902i	$-0.889606\pi$
$139$	−15.0953	−	15.0953i	−1.28036	−	1.28036i	−0.339902	−	0.940461i	$-0.610394\pi$
$140$	1.30290	−	17.4790i	0.110115	−	1.47725i
$141$	−8.23434	+	8.23434i	−0.693456	+	0.693456i
$142$	0.445814	−	1.56926i	0.0374119	−	0.131690i
$143$		−	4.30057i		−	0.359632i
$144$	−3.57779	+	1.78869i	−0.298149	+	0.149058i
$145$	15.0458	+	4.75671i	1.24949	+	0.395023i
$146$	10.8655	+	3.08681i	0.899239	+	0.255466i
$147$	−5.91188	−	5.91188i	−0.487604	−	0.487604i
$148$	−17.6597	+	4.16848i	−1.45162	+	0.342647i
$149$	4.27402	+	4.27402i	0.350141	+	0.350141i	0.860162	−	0.510021i	$-0.170362\pi$
$149$	4.27402	+	4.27402i	0.350141	+	0.350141i	−0.510021	+	0.860162i	$0.670362\pi$
$150$	7.03300	+	0.732726i	0.574242	+	0.0598268i
$151$		−	8.39998i		−	0.683581i	−0.939776	−	0.341790i	$-0.888967\pi$
$151$		−	8.39998i		−	0.683581i	0.939776	−	0.341790i	$-0.111033\pi$
$152$	6.69459	+	0.301440i	0.543003	+	0.0244500i
$153$	−2.89302			−0.233886
$154$	−11.2000	−	20.0889i	−0.902521	−	1.61881i
$155$	11.1498	+	21.4590i	0.895573	+	1.72363i
$156$	1.08975	−	1.76316i	0.0872497	−	0.141166i
$157$	5.68893	+	5.68893i	0.454026	+	0.454026i	0.896689	−	0.442662i	$-0.145966\pi$
$157$	5.68893	+	5.68893i	0.454026	+	0.454026i	−0.442662	+	0.896689i	$0.645966\pi$
$158$	1.14811	+	0.326167i	0.0913386	+	0.0259485i
$159$	7.85971			0.623315
$160$	9.94600	−	7.81518i	0.786301	−	0.617844i
$161$	6.78553			0.534775
$162$	−1.36038	−	0.386472i	−0.106882	−	0.0303641i
$163$	−5.63869	−	5.63869i	−0.441656	−	0.441656i	0.450912	−	0.892568i	$-0.351099\pi$
$163$	−5.63869	−	5.63869i	−0.441656	−	0.441656i	−0.892568	+	0.450912i	$0.851099\pi$
$164$	0.00607254	−	0.00982509i	0.000474186	−	0.000767211i
$165$	8.23374	−	4.27814i	0.640996	−	0.333053i
$166$	5.06500	+	9.08485i	0.393120	+	0.705121i
$167$	6.45583			0.499567			0.249783	−	0.968302i	$-0.419641\pi$
$167$	6.45583			0.499567			0.249783	+	0.968302i	$0.419641\pi$
$168$	0.498640	−	11.0741i	0.0384709	−	0.854389i
$169$		−	11.9259i		−	0.917379i
$170$	8.96178	−	1.83900i	0.687337	−	0.141045i
$171$	1.67534	+	1.67534i	0.128117	+	0.128117i
$172$	6.16430	−	1.45505i	0.470023	−	0.110946i
$173$	−7.33664	−	7.33664i	−0.557795	−	0.557795i	0.370884	−	0.928679i	$-0.379055\pi$
$173$	−7.33664	−	7.33664i	−0.557795	−	0.557795i	−0.928679	+	0.370884i	$0.879055\pi$
$174$	9.60016	+	2.72732i	0.727787	+	0.206758i
$175$	−11.2648	+	16.0350i	−0.851537	+	1.21213i
$176$	5.24962	−	15.7465i	0.395705	−	1.18694i
$177$		−	5.42054i		−	0.407432i
$178$	−2.09042	+	7.35826i	−0.156683	+	0.551525i
$179$	−1.04377	+	1.04377i	−0.0780153	+	0.0780153i	−0.745038	−	0.667022i	$-0.767569\pi$
$179$	−1.04377	+	1.04377i	−0.0780153	+	0.0780153i	0.667022	+	0.745038i	$0.267569\pi$
$180$	4.45976	+	0.332434i	0.332411	+	0.0247782i
$181$	−12.1024	−	12.1024i	−0.899567	−	0.899567i	0.0958310	−	0.995398i	$-0.469449\pi$
$181$	−12.1024	−	12.1024i	−0.899567	−	0.899567i	−0.995398	+	0.0958310i	$0.969449\pi$
$182$	2.79721	+	5.01723i	0.207343	+	0.371901i
$183$	−13.1606			−0.972859
$184$	3.30339	+	3.61490i	0.243529	+	0.266494i
$185$	19.3431	+	6.11528i	1.42213	+	0.449604i
$186$	7.44774	+	13.3586i	0.546095	+	0.979504i
$187$	8.48877	−	8.48877i	0.620761	−	0.620761i
$188$	12.2448	−	19.8116i	0.893046	−	1.44491i
$189$	2.77134	−	2.77134i	0.201585	−	0.201585i
$190$	−6.25473	−	4.12480i	−0.453766	−	0.299244i
$191$	−21.2273			−1.53596			−0.767978	−	0.640477i	$-0.778737\pi$
$191$	−21.2273			−1.53596			−0.767978	+	0.640477i	$0.778737\pi$
$192$	6.14236	−	5.12557i	0.443287	−	0.369906i
$193$		−	19.2782i		−	1.38767i	−0.720132	−	0.693837i	$-0.755919\pi$
$193$		−	19.2782i		−	1.38767i	0.720132	−	0.693837i	$-0.244081\pi$
$194$	0.866292	−	3.04935i	0.0621961	−	0.218930i
$195$	−2.05639	+	1.06847i	−0.147261	+	0.0765148i
$196$	14.2238	+	8.79124i	1.01599	+	0.627946i
$197$	−9.48350	+	9.48350i	−0.675672	+	0.675672i	−0.959018	−	0.283346i	$-0.908556\pi$
$197$	−9.48350	+	9.48350i	−0.675672	+	0.675672i	0.283346	+	0.959018i	$0.408556\pi$
$198$	5.12567	−	2.85767i	0.364266	−	0.203086i
$199$			8.65421i			0.613481i	0.951793	+	0.306740i	$0.0992383\pi$
$199$			8.65421i			0.613481i	−0.951793	+	0.306740i	$0.900762\pi$
$200$	−14.0265	+	1.80514i	−0.991820	+	0.127643i
$201$		−	5.44815i		−	0.384283i
$202$	−7.31070	−	13.1129i	−0.514379	−	0.922617i
$203$	−19.5572	+	19.5572i	−1.37265	+	1.37265i
$204$	5.63128	−	1.32923i	0.394268	−	0.0930648i
$205$	−0.0114591	+	0.00595398i	−0.000800336	+	0.000415844i
$206$	−5.32059	−	1.51153i	−0.370703	−	0.105313i
$207$			1.73133i			0.120335i
$208$	−1.31110	+	3.93271i	−0.0909083	+	0.272684i
$209$	−9.83169			−0.680072
$210$	−6.82321	+	10.3465i	−0.470846	+	0.713978i
$211$	−0.875946	+	0.875946i	−0.0603026	+	0.0603026i	−0.736615	−	0.676312i	$-0.763577\pi$
$211$	−0.875946	+	0.875946i	−0.0603026	+	0.0603026i	0.676312	+	0.736615i	$0.263577\pi$
$212$	−15.2990	+	3.61124i	−1.05074	+	0.248021i
$213$	−0.815681	+	0.815681i	−0.0558895	+	0.0558895i
$214$	4.54589	−	2.53443i	0.310751	−	0.173250i
$215$	−6.75190	−	2.13460i	−0.460476	−	0.145578i
$216$	2.82556	+	0.127228i	0.192255	+	0.00865675i
$217$	−42.3863			−2.87737
$218$	−3.60961	+	2.01243i	−0.244473	+	0.136299i
$219$	−5.64775	−	5.64775i	−0.381640	−	0.381640i
$220$	−14.0614	+	12.1105i	−0.948020	+	0.816492i
$221$	−2.12008	+	2.12008i	−0.142612	+	0.142612i
$222$	12.3421	+	3.50628i	0.828347	+	0.235326i
$223$		−	10.4375i		−	0.698946i	−0.936946	−	0.349473i	$-0.886361\pi$
$223$		−	10.4375i		−	0.698946i	0.936946	−	0.349473i	$-0.113639\pi$
$224$	4.11754	+	21.7850i	0.275115	+	1.45557i
$225$	−4.09133	−	2.87420i	−0.272755	−	0.191614i
$226$	3.14438	−	11.0682i	0.209161	−	0.736246i
$227$	13.7218	+	13.7218i	0.910747	+	0.910747i	0.996331	−	0.0855842i	$-0.0272757\pi$
$227$	13.7218	+	13.7218i	0.910747	+	0.910747i	−0.0855842	+	0.996331i	$0.527276\pi$
$228$	−4.03083	−	2.49131i	−0.266948	−	0.164991i
$229$	8.43878	+	8.43878i	0.557651	+	0.557651i	0.928638	−	0.370987i	$-0.120981\pi$
$229$	8.43878	+	8.43878i	0.557651	+	0.557651i	−0.370987	+	0.928638i	$0.620981\pi$
$230$	−1.10055	−	5.36318i	−0.0725681	−	0.353638i
$231$			16.2635i			1.07006i
$232$	−19.9399	−	0.897842i	−1.30912	−	0.0589462i
$233$	28.6100			1.87431			0.937153	−	0.348919i	$-0.113451\pi$
$233$	28.6100			1.87431			0.937153	+	0.348919i	$0.113451\pi$
$234$	−1.28014	+	0.713708i	−0.0836856	+	0.0466565i
$235$	−23.1064	+	12.0058i	−1.50729	+	0.783169i
$236$	2.49053	+	10.5511i	0.162120	+	0.686819i
$237$	−0.596770	−	0.596770i	−0.0387644	−	0.0387644i
$238$	−4.38202	+	15.4247i	−0.284044	+	0.999835i
$239$	21.4924			1.39023			0.695115	−	0.718899i	$-0.255354\pi$
$239$	21.4924			1.39023			0.695115	+	0.718899i	$0.255354\pi$
$240$	−8.83371	+	1.40201i	−0.570213	+	0.0904991i
$241$	−19.5943			−1.26218			−0.631091	−	0.775709i	$-0.717393\pi$
$241$	−19.5943			−1.26218			−0.631091	+	0.775709i	$0.717393\pi$
$242$	−2.40363	+	8.46077i	−0.154511	+	0.543879i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	25.6172	−	6.04680i	1.63997	−	0.387106i
$245$	−8.61959	−	16.5893i	−0.550685	−	1.05985i
$246$	−0.00713350	+	0.00397708i	−0.000454816	+	0.000253570i
$247$	2.45548			0.156238
$248$	−20.6349	−	22.5808i	−1.31032	−	1.43388i
$249$		−	7.35489i		−	0.466097i
$250$	14.5009	+	6.30277i	0.917115	+	0.398622i
$251$	−9.58072	−	9.58072i	−0.604730	−	0.604730i	0.336834	−	0.941564i	$-0.390644\pi$
$251$	−9.58072	−	9.58072i	−0.604730	−	0.604730i	−0.941564	+	0.336834i	$0.890644\pi$
$252$	−4.12111	+	6.66776i	−0.259606	+	0.420030i
$253$	−5.08011	−	5.08011i	−0.319384	−	0.319384i
$254$	−6.21687	+	21.8834i	−0.390081	+	1.37308i
$255$	−6.16807	−	1.95002i	−0.386260	−	0.122115i
$256$	−9.60115	+	12.7991i	−0.600072	+	0.799946i
$257$			13.2730i			0.827946i	0.910289	+	0.413973i	$0.135859\pi$
$257$			13.2730i			0.827946i	−0.910289	+	0.413973i	$0.864141\pi$
$258$	−4.30813	−	1.22390i	−0.268212	−	0.0761967i
$259$	−25.1430	+	25.1430i	−1.56231	+	1.56231i
$260$	3.51186	−	3.02462i	0.217796	−	0.187579i
$261$	−4.99003	−	4.99003i	−0.308875	−	0.308875i
$262$	22.7802	−	12.7005i	1.40737	−	0.784637i
$263$	−13.0606			−0.805349			−0.402675	−	0.915343i	$-0.631919\pi$
$263$	−13.0606			−0.805349			−0.402675	+	0.915343i	$0.631919\pi$
$264$	−8.66417	+	7.91754i	−0.533243	+	0.487291i
$265$	16.7573	+	5.29780i	1.02940	+	0.325441i
$266$	11.4701	−	6.39481i	0.703274	−	0.392091i
$267$	3.82471	−	3.82471i	0.234069	−	0.234069i
$268$	2.50322	+	10.6049i	0.152908	+	0.647796i
$269$	−12.4067	+	12.4067i	−0.756451	+	0.756451i	−0.975675	−	0.219224i	$-0.929647\pi$
$269$	−12.4067	+	12.4067i	−0.756451	+	0.756451i	0.219224	+	0.975675i	$0.429647\pi$
$270$	−2.63991	−	1.74094i	−0.160660	−	0.105950i
$271$	2.11193			0.128291			0.0641453	−	0.997941i	$-0.479568\pi$
$271$	2.11193			0.128291			0.0641453	+	0.997941i	$0.479568\pi$
$272$	−10.3506	+	5.17472i	−0.627597	+	0.313763i
$273$		−	4.06183i		−	0.245833i
$274$	8.86444	+	2.51831i	0.535520	+	0.152137i
$275$	20.4385	−	3.57132i	1.23249	−	0.215359i
$276$	−0.795479	−	3.37004i	−0.0478822	−	0.202853i
$277$	13.2116	−	13.2116i	0.793808	−	0.793808i	−0.188303	−	0.982111i	$-0.560299\pi$
$277$	13.2116	−	13.2116i	0.793808	−	0.793808i	0.982111	+	0.188303i	$0.0602988\pi$
$278$	−14.7014	−	26.3692i	−0.881732	−	1.58152i
$279$		−	10.8149i		−	0.647469i
$280$	8.52760	−	23.2746i	0.509621	−	1.39092i
$281$		−	3.78786i		−	0.225965i	−0.993597	−	0.112982i	$-0.963960\pi$
$281$		−	3.78786i		−	0.225965i	0.993597	−	0.112982i	$-0.0360404\pi$
$282$	−14.3842	+	8.01950i	−0.856566	+	0.477554i
$283$	3.16274	−	3.16274i	0.188005	−	0.188005i	−0.606828	−	0.794833i	$-0.707558\pi$
$283$	3.16274	−	3.16274i	0.188005	−	0.188005i	0.794833	+	0.606828i	$0.207558\pi$
$284$	1.21295	−	1.96250i	0.0719756	−	0.116453i
$285$	2.44267	+	4.70118i	0.144691	+	0.278474i
$286$	1.66205	−	5.85042i	0.0982792	−	0.345942i
$287$		−	0.0226343i		−	0.00133606i
$288$	−5.55844	+	1.05059i	−0.327534	+	0.0619066i
$289$	8.63046			0.507674
$290$	18.6298	+	12.2857i	1.09398	+	0.721444i
$291$	−1.58501	+	1.58501i	−0.0929147	+	0.0929147i
$292$	13.5883	+	8.39847i	0.795197	+	0.491483i
$293$	−8.51339	+	8.51339i	−0.497357	+	0.497357i	−0.910614	−	0.413257i	$-0.864391\pi$
$293$	−8.51339	+	8.51339i	−0.497357	+	0.497357i	0.413257	+	0.910614i	$0.364391\pi$
$294$	−5.75764	−	10.3272i	−0.335792	−	0.602294i
$295$	3.65368	−	11.5569i	0.212726	−	0.672868i
$296$	−25.6350	−	1.15428i	−1.49000	−	0.0670909i
$297$	−4.14963			−0.240786
$298$	4.16251	+	7.46609i	0.241128	+	0.432499i
$299$	1.26876	+	1.26876i	0.0733745	+	0.0733745i
$300$	9.28439	+	3.71485i	0.536035	+	0.214477i
$301$	8.77642	−	8.77642i	0.505864	−	0.505864i
$302$	3.24636	−	11.4272i	0.186807	−	0.657560i
$303$			10.6159i			0.609866i
$304$	8.99071	+	2.99735i	0.515652	+	0.171910i
$305$	−28.0591	−	8.87083i	−1.60666	−	0.507942i
$306$	−3.93561	−	1.11807i	−0.224984	−	0.0639159i
$307$	−7.12093	−	7.12093i	−0.406413	−	0.406413i	0.474073	−	0.880486i	$-0.342783\pi$
$307$	−7.12093	−	7.12093i	−0.406413	−	0.406413i	−0.880486	+	0.474073i	$0.842783\pi$
$308$	−7.47246	−	31.6570i	−0.425783	−	1.80383i
$309$	2.76557	+	2.76557i	0.157328	+	0.157328i
$310$	6.87467	+	33.5015i	0.390455	+	1.90276i
$311$		−	21.2980i		−	1.20770i	−0.797099	−	0.603849i	$-0.793633\pi$
$311$		−	21.2980i		−	1.20770i	0.797099	−	0.603849i	$-0.206367\pi$
$312$	2.16389	−	1.97742i	0.122506	−	0.111949i
$313$	−7.49789			−0.423806			−0.211903	−	0.977291i	$-0.567966\pi$
$313$	−7.49789			−0.423806			−0.211903	+	0.977291i	$0.567966\pi$
$314$	5.54051	+	9.93774i	0.312669	+	0.560819i
$315$	7.77666	−	4.04065i	0.438165	−	0.227665i
$316$	1.43581	+	0.887425i	0.0807707	+	0.0499215i
$317$	−2.35354	−	2.35354i	−0.132188	−	0.132188i	0.637917	−	0.770105i	$-0.279796\pi$
$317$	−2.35354	−	2.35354i	−0.132188	−	0.132188i	−0.770105	+	0.637917i	$0.779796\pi$
$318$	10.6922	+	3.03756i	0.599589	+	0.170338i
$319$	29.2838			1.63958
$320$	16.5507	−	6.78777i	0.925213	−	0.379448i
$321$	−3.68025			−0.205412
$322$	9.23091	+	2.62242i	0.514419	+	0.146142i
$323$	4.84680	+	4.84680i	0.269683	+	0.269683i
$324$	−1.70128	−	1.05150i	−0.0945154	−	0.0584167i
$325$	−5.10453	+	0.891943i	−0.283149	+	0.0494761i
$326$	−5.49157	−	9.84997i	−0.304150	−	0.545539i
$327$	2.92226			0.161601
$328$	0.0120581	−	0.0110190i	0.000665797	−	0.000608423i
$329$		−	45.6403i		−	2.51623i
$330$	12.8544	−	2.63779i	0.707613	−	0.145206i
$331$	22.6845	+	22.6845i	1.24685	+	1.24685i	0.957102	+	0.289753i	$0.0935730\pi$
$331$	22.6845	+	22.6845i	1.24685	+	1.24685i	0.289753	+	0.957102i	$0.406427\pi$
$332$	3.37929	+	14.3163i	0.185463	+	0.785712i
$333$	−6.41524	−	6.41524i	−0.351553	−	0.351553i
$334$	8.78239	+	2.49500i	0.480551	+	0.136520i
$335$	3.67230	−	11.6158i	0.200639	−	0.634637i
$336$	4.95819	−	14.8724i	0.270492	−	0.811353i
$337$		−	8.90357i		−	0.485008i	−0.970150	−	0.242504i	$-0.922031\pi$
$337$		−	8.90357i		−	0.485008i	0.970150	−	0.242504i	$-0.0779688\pi$
$338$	4.60904	−	16.2238i	0.250699	−	0.882459i
$339$	−5.75309	+	5.75309i	−0.312465	+	0.312465i
$340$	12.9022	+	0.961738i	0.699718	+	0.0521576i
$341$	31.7333	+	31.7333i	1.71845	+	1.71845i
$342$	1.63163	+	2.92658i	0.0882286	+	0.158251i
$343$	5.33279			0.287944
$344$	8.94814	+	0.402911i	0.482451	+	0.0217235i
$345$	−1.16699	+	3.69129i	−0.0628287	+	0.198732i
$346$	−7.14523	−	12.8160i	−0.384130	−	0.688995i
$347$	−8.87783	+	8.87783i	−0.476587	+	0.476587i	−0.904038	−	0.427451i	$-0.859412\pi$
$347$	−8.87783	+	8.87783i	−0.476587	+	0.476587i	0.427451	+	0.904038i	$0.359412\pi$
$348$	12.0059	+	7.42040i	0.643581	+	0.397775i
$349$	−8.23040	+	8.23040i	−0.440563	+	0.440563i	−0.892201	−	0.451638i	$-0.850840\pi$
$349$	−8.23040	+	8.23040i	−0.440563	+	0.440563i	0.451638	+	0.892201i	$0.350840\pi$
$350$	−21.5215	+	17.4602i	−1.15037	+	0.933288i
$351$	1.03637			0.0553176
$352$	13.2271	−	19.3924i	0.705005	−	1.03362i
$353$			34.7125i			1.84756i	0.382922	+	0.923781i	$0.374918\pi$
$353$			34.7125i			1.84756i	−0.382922	+	0.923781i	$0.625082\pi$
$354$	2.09489	−	7.37400i	0.111342	−	0.391924i
$355$	−2.28888	+	1.18927i	−0.121481	+	0.0631200i
$356$	−5.68753	+	9.20215i	−0.301438	+	0.487713i
$357$	8.01753	−	8.01753i	0.424333	−	0.424333i
$358$	−1.82332	+	1.01654i	−0.0963655	+	0.0537259i
$359$		−	2.81082i		−	0.148350i	−0.997245	−	0.0741748i	$-0.976368\pi$
$359$		−	2.81082i		−	0.148350i	0.997245	−	0.0741748i	$-0.0236323\pi$
$360$	5.93850	+	2.17581i	0.312987	+	0.114675i
$361$			13.3864i			0.704550i
$362$	−11.7867	−	21.1412i	−0.619494	−	1.11116i
$363$	4.39778	−	4.39778i	0.230824	−	0.230824i
$364$	1.86626	+	7.90639i	0.0978185	+	0.414407i
$365$	−8.23449	−	15.8482i	−0.431013	−	0.829531i
$366$	−17.9034	−	5.08621i	−0.935828	−	0.265860i
$367$			18.2835i			0.954392i	0.878797	+	0.477196i	$0.158347\pi$
$367$			18.2835i			0.954392i	−0.878797	+	0.477196i	$0.841653\pi$
$368$	3.09681	+	6.19432i	0.161433	+	0.322901i
$369$	0.00577512			0.000300641
$370$	23.9506	+	15.7947i	1.24513	+	0.821127i
$371$	−21.7819	+	21.7819i	−1.13086	+	1.13086i
$372$	4.96902	+	21.0512i	0.257632	+	1.09145i
$373$	23.4176	−	23.4176i	1.21252	−	1.21252i	0.242324	−	0.970195i	$-0.422090\pi$
$373$	23.4176	−	23.4176i	1.21252	−	1.21252i	0.970195	−	0.242324i	$-0.0779098\pi$
$374$	14.8287	−	8.26730i	0.766771	−	0.427492i
$375$	−6.78560	−	8.88570i	−0.350407	−	0.458856i
$376$	24.3143	−	22.2190i	1.25391	−	1.14586i
$377$	−7.31366			−0.376673
$378$	4.84113	−	2.69904i	0.249001	−	0.138823i
$379$	−6.20944	−	6.20944i	−0.318957	−	0.318957i	0.529409	−	0.848367i	$-0.322414\pi$
$379$	−6.20944	−	6.20944i	−0.318957	−	0.318957i	−0.848367	+	0.529409i	$0.822414\pi$
$380$	−6.91470	−	8.02858i	−0.354716	−	0.411857i
$381$	11.3746	−	11.3746i	0.582741	−	0.582741i
$382$	−28.8773	−	8.20378i	−1.47749	−	0.419742i
$383$		−	14.4005i		−	0.735832i	−0.929859	−	0.367916i	$-0.880071\pi$
$383$		−	14.4005i		−	0.735832i	0.929859	−	0.367916i	$-0.119929\pi$
$384$	10.3368	−	4.59888i	0.527500	−	0.234685i
$385$	−10.9623	+	34.6747i	−0.558692	+	1.76719i
$386$	7.45049	−	26.2257i	0.379220	−	1.33485i
$387$	2.23930	+	2.23930i	0.113830	+	0.113830i
$388$	2.35698	−	3.81348i	0.119657	−	0.193600i
$389$	15.4753	+	15.4753i	0.784630	+	0.784630i	0.980608	−	0.195978i	$-0.0627882\pi$
$389$	15.4753	+	15.4753i	0.784630	+	0.784630i	−0.195978	+	0.980608i	$0.562788\pi$
$390$	−3.21041	+	0.658791i	−0.162565	+	0.0333592i
$391$			5.00875i			0.253304i
$392$	15.9522	+	17.4566i	0.805710	+	0.881689i
$393$	−18.4423			−0.930292
$394$	−16.5663	+	9.23607i	−0.834598	+	0.465307i
$395$	−0.870098	−	1.67460i	−0.0437794	−	0.0842581i
$396$	8.07728	−	1.90660i	0.405899	−	0.0958101i
$397$	15.0440	+	15.0440i	0.755036	+	0.755036i	0.975414	−	0.220378i	$-0.0707292\pi$
$397$	15.0440	+	15.0440i	0.755036	+	0.755036i	−0.220378	+	0.975414i	$0.570729\pi$
$398$	−3.34461	+	11.7730i	−0.167650	+	0.590129i
$399$	−9.28590			−0.464876
$400$	−19.7790	−	2.96516i	−0.988949	−	0.148258i
$401$	28.7953			1.43797			0.718985	−	0.695026i	$-0.244607\pi$
$401$	28.7953			1.43797			0.718985	+	0.695026i	$0.244607\pi$
$402$	2.10556	−	7.41157i	0.105016	−	0.369655i
$403$	−7.92543	−	7.92543i	−0.394794	−	0.394794i
$404$	−4.87759	−	20.6639i	−0.242669	−	1.02807i
$405$	1.03097	+	1.98421i	0.0512293	+	0.0985963i
$406$	−34.1637	+	19.0470i	−1.69551	+	0.945286i
$407$	37.6476			1.86612
$408$	8.17440	+	0.368072i	0.404693	+	0.0182223i
$409$		−	23.3562i		−	1.15489i	−0.816430	−	0.577444i	$-0.804050\pi$
$409$		−	23.3562i		−	1.15489i	0.816430	−	0.577444i	$-0.195950\pi$
$410$	−0.0178898	+	0.00367107i	−0.000883512	+	0.000181301i
$411$	−4.60760	−	4.60760i	−0.227276	−	0.227276i
$412$	−6.65387	−	4.11252i	−0.327813	−	0.202610i
$413$	15.0222	+	15.0222i	0.739192	+	0.739192i
$414$	−0.669110	+	2.35527i	−0.0328850	+	0.115755i
$415$	4.95752	−	15.6810i	0.243355	−	0.769751i
$416$	−3.30348	+	4.84328i	−0.161966	+	0.237461i
$417$			21.3479i			1.04541i
$418$	−13.3749	−	3.79968i	−0.654185	−	0.185848i
$419$	−22.4332	+	22.4332i	−1.09594	+	1.09594i	−0.101055	+	0.994881i	$0.532222\pi$
$419$	−22.4332	+	22.4332i	−1.09594	+	1.09594i	−0.994881	+	0.101055i	$0.967778\pi$
$420$	−13.2808	+	11.4382i	−0.648037	+	0.558129i
$421$	14.7632	+	14.7632i	0.719513	+	0.719513i	0.968505	−	0.248993i	$-0.0800995\pi$
$421$	14.7632	+	14.7632i	0.719513	+	0.719513i	−0.248993	+	0.968505i	$0.580100\pi$
$422$	−1.53015	+	0.853092i	−0.0744865	+	0.0415279i
$423$	11.6451			0.566205
$424$	−22.2081	−	0.999973i	−1.07852	−	0.0485630i
$425$	−11.8363	−	8.31511i	−0.574144	−	0.403342i
$426$	−1.42488	+	0.794399i	−0.0690354	+	0.0384888i
$427$	36.4725	−	36.4725i	1.76503	−	1.76503i
$428$	7.16364	−	1.69094i	0.346268	−	0.0817345i
$429$	−3.04096	+	3.04096i	−0.146819	+	0.146819i
$430$	−8.36020	−	5.51329i	−0.403165	−	0.265875i
$431$	5.92220			0.285262			0.142631	−	0.989776i	$-0.454444\pi$
$431$	5.92220			0.285262			0.142631	+	0.989776i	$0.454444\pi$
$432$	3.79468	+	1.26508i	0.182571	+	0.0608662i
$433$			5.27026i			0.253272i	0.991949	+	0.126636i	$0.0404181\pi$
$433$			5.27026i			0.253272i	−0.991949	+	0.126636i	$0.959582\pi$
$434$	−57.6616	−	16.3811i	−2.76784	−	0.786320i
$435$	−7.27551	−	14.0025i	−0.348834	−	0.671369i
$436$	−5.68819	+	1.34267i	−0.272415	+	0.0643020i
$437$	2.90057	−	2.90057i	0.138753	−	0.138753i
$438$	−5.50040	−	9.86580i	−0.262819	−	0.471406i
$439$		−	17.8427i		−	0.851587i	−0.904820	−	0.425793i	$-0.859995\pi$
$439$		−	17.8427i		−	0.851587i	0.904820	−	0.425793i	$-0.140005\pi$
$440$	−23.8093	+	11.0406i	−1.13506	+	0.526340i
$441$			8.36066i			0.398127i
$442$	−3.70348	+	2.06477i	−0.176156	+	0.0982110i
$443$	5.89855	−	5.89855i	0.280248	−	0.280248i	−0.552960	−	0.833208i	$-0.686502\pi$
$443$	5.89855	−	5.89855i	0.280248	−	0.280248i	0.833208	+	0.552960i	$0.186502\pi$
$444$	15.4349	+	9.53975i	0.732507	+	0.452737i
$445$	10.7325	−	5.57648i	0.508771	−	0.264350i
$446$	4.03380	−	14.1990i	0.191006	−	0.672341i
$447$		−	6.04438i		−	0.285889i
$448$	−2.81788	+	31.2273i	−0.133132	+	1.47535i
$449$	8.12803			0.383586			0.191793	−	0.981435i	$-0.438570\pi$
$449$	8.12803			0.383586			0.191793	+	0.981435i	$0.438570\pi$
$450$	−4.45497	−	5.49120i	−0.210009	−	0.258858i
$451$	−0.0169455	+	0.0169455i	−0.000797934	+	0.000797934i
$452$	8.55511	−	13.8418i	0.402399	−	0.651062i
$453$	−5.93968	+	5.93968i	−0.279071	+	0.279071i
$454$	13.3638	+	23.9700i	0.627193	+	1.12497i
$455$	2.73786	−	8.66005i	0.128353	−	0.405990i
$456$	−4.52064	−	4.94694i	−0.211698	−	0.231662i
$457$	6.35488			0.297269			0.148634	−	0.988892i	$-0.452512\pi$
$457$	6.35488			0.297269			0.148634	+	0.988892i	$0.452512\pi$
$458$	8.21861	+	14.7413i	0.384030	+	0.688817i
$459$	2.04567	+	2.04567i	0.0954838	+	0.0954838i
$460$	0.575553	−	7.72131i	0.0268353	−	0.360008i
$461$	2.13085	−	2.13085i	0.0992438	−	0.0992438i	−0.655742	−	0.754985i	$-0.727644\pi$
$461$	2.13085	−	2.13085i	0.0992438	−	0.0992438i	0.754985	+	0.655742i	$0.227644\pi$
$462$	−6.28540	+	22.1246i	−0.292423	+	1.02933i
$463$		−	18.4540i		−	0.857630i	−0.903392	−	0.428815i	$-0.858931\pi$
$463$		−	18.4540i		−	0.857630i	0.903392	−	0.428815i	$-0.141069\pi$
$464$	−26.7789	−	8.92763i	−1.24318	−	0.414455i
$465$	7.28970	−	23.0579i	0.338052	−	1.06928i
$466$	38.9206	+	11.0570i	1.80296	+	0.512205i
$467$	5.63243	+	5.63243i	0.260638	+	0.260638i	0.825313	−	0.564675i	$-0.190999\pi$
$467$	5.63243	+	5.63243i	0.260638	+	0.260638i	−0.564675	+	0.825313i	$0.690999\pi$
$468$	−2.01731	+	0.476175i	−0.0932503	+	0.0220112i
$469$	15.0987	+	15.0987i	0.697193	+	0.697193i
$470$	−36.0734	+	7.40243i	−1.66394	+	0.341449i
$471$		−	8.04537i		−	0.370711i
$472$	−0.689643	+	15.3161i	−0.0317434	+	0.704979i
$473$	−13.1412			−0.604235
$474$	−0.581200	−	1.04247i	−0.0266954	−	0.0478822i
$475$	2.03910	+	11.6697i	0.0935604	+	0.535441i
$476$	−11.9224	+	19.2899i	−0.546464	+	0.884153i
$477$	−5.55765	−	5.55765i	−0.254467	−	0.254467i
$478$	29.2379	+	8.30623i	1.33731	+	0.379918i
$479$	21.4860			0.981720			0.490860	−	0.871239i	$-0.336683\pi$
$479$	21.4860			0.981720			0.490860	+	0.871239i	$0.336683\pi$
$480$	−12.5591	−	1.50672i	−0.573240	−	0.0687721i
$481$	−9.40253			−0.428718
$482$	−26.6558	−	7.57267i	−1.21414	−	0.344926i
$483$	−4.79810	−	4.79810i	−0.218321	−	0.218321i
$484$	−6.53971	+	10.5809i	−0.297259	+	0.480952i
$485$	−4.44769	+	2.31096i	−0.201959	+	0.104935i
$486$	0.688658	+	1.23521i	0.0312382	+	0.0560304i
$487$	−36.3297			−1.64626			−0.823128	−	0.567856i	$-0.807773\pi$
$487$	−36.3297			−1.64626			−0.823128	+	0.567856i	$0.807773\pi$
$488$	37.1861	+	1.67439i	1.68334	+	0.0757962i
$489$			7.97431i			0.360611i
$490$	−5.31461	−	25.8991i	−0.240090	−	1.17000i
$491$	1.63599	+	1.63599i	0.0738313	+	0.0738313i	0.743058	−	0.669227i	$-0.233375\pi$
$491$	1.63599	+	1.63599i	0.0738313	+	0.0738313i	−0.669227	+	0.743058i	$0.733375\pi$
$492$	−0.0112413	+	0.00265345i	−0.000506798	+	0.000119627i
$493$	−14.4362	−	14.4362i	−0.650175	−	0.650175i
$494$	3.34039	+	0.948974i	0.150291	+	0.0426964i
$495$	−8.84724	−	2.79703i	−0.397654	−	0.125717i
$496$	−19.3445	−	38.6933i	−0.868592	−	1.73738i
$497$		−	4.52106i		−	0.202797i
$498$	2.84246	−	10.0055i	0.127374	−	0.448355i
$499$	18.7955	−	18.7955i	0.841402	−	0.841402i	−0.147639	−	0.989041i	$-0.547167\pi$
$499$	18.7955	−	18.7955i	0.841402	−	0.841402i	0.989041	+	0.147639i	$0.0471674\pi$
$500$	17.2909	+	14.1784i	0.773271	+	0.634076i
$501$	−4.56496	−	4.56496i	−0.203947	−	0.203947i
$502$	−9.33076	−	16.7361i	−0.416452	−	0.746970i
$503$	−13.8118			−0.615838			−0.307919	−	0.951413i	$-0.599633\pi$
$503$	−13.8118			−0.615838			−0.307919	+	0.951413i	$0.599633\pi$
$504$	−8.18319	+	7.47801i	−0.364508	+	0.333097i
$505$	−7.15557	+	22.6336i	−0.318419	+	1.00718i
$506$	−4.94757	−	8.87421i	−0.219946	−	0.394507i
$507$	−8.43290	+	8.43290i	−0.374518	+	0.374518i
$508$	−16.9146	+	27.3671i	−0.750465	+	1.21422i
$509$	−5.40184	+	5.40184i	−0.239432	+	0.239432i	−0.816615	−	0.577183i	$-0.804152\pi$
$509$	−5.40184	+	5.40184i	−0.239432	+	0.239432i	0.577183	+	0.816615i	$0.304152\pi$
$510$	−7.63730	−	5.03657i	−0.338186	−	0.223023i
$511$	31.3037			1.38479
$512$	−18.0077	+	13.7011i	−0.795837	+	0.605510i
$513$		−	2.36929i		−	0.104607i
$514$	−5.12964	+	18.0563i	−0.226259	+	0.796431i
$515$	4.03223	+	7.76046i	0.177681	+	0.341967i
$516$	−5.38769	−	3.32994i	−0.237180	−	0.146593i
$517$	−34.1694	+	34.1694i	−1.50277	+	1.50277i
$518$	−43.9212	+	24.4870i	−1.92979	+	1.07590i
$519$			10.3756i			0.455437i
$520$	5.94640	−	2.75740i	0.260767	−	0.120920i
$521$			33.6969i			1.47629i	0.674642	+	0.738145i	$0.264298\pi$
$521$			33.6969i			1.47629i	−0.674642	+	0.738145i	$0.735702\pi$
$522$	−4.85983	−	8.71685i	−0.212709	−	0.381526i
$523$	4.31481	−	4.31481i	0.188673	−	0.188673i	−0.606449	−	0.795122i	$-0.707407\pi$
$523$	4.31481	−	4.31481i	0.188673	−	0.188673i	0.795122	+	0.606449i	$0.207407\pi$
$524$	35.8981	−	8.47355i	1.56822	−	0.370169i
$525$	19.3039	−	3.37307i	0.842489	−	0.147213i
$526$	−17.7674	−	5.04755i	−0.774694	−	0.220084i
$527$		−	31.2876i		−	1.36291i
$528$	−14.8465	+	7.42241i	−0.646111	+	0.323019i
$529$	−20.0025			−0.869674
$530$	20.7489	+	13.6833i	0.901276	+	0.594364i
$531$	−3.83290	+	3.83290i	−0.166334	+	0.166334i
$532$	18.0751	−	4.26652i	0.783654	−	0.184977i
$533$	0.00423217	−	0.00423217i	0.000183316	−	0.000183316i
$534$	6.68122	−	3.72493i	0.289125	−	0.161193i
$535$	−7.84650	−	2.48065i	−0.339234	−	0.107248i
$536$	−0.693156	+	15.3941i	−0.0299398	+	0.664924i
$537$	1.47612			0.0636993
$538$	−21.6727	+	12.0830i	−0.934377	+	0.520936i
$539$	−24.5321	−	24.5321i	−1.05667	−	1.05667i
$540$	−2.91846	−	3.38860i	−0.125591	−	0.145822i
$541$	−22.8010	+	22.8010i	−0.980290	+	0.980290i	−0.999809	−	0.0195198i	$-0.993786\pi$
$541$	−22.8010	+	22.8010i	−0.980290	+	0.980290i	0.0195198	+	0.999809i	$0.493786\pi$
$542$	2.87303	+	0.816203i	0.123407	+	0.0350589i
$543$			17.1154i			0.734493i
$544$	−16.0807	+	3.03937i	−0.689452	+	0.130312i
$545$	6.23041	+	1.96973i	0.266882	+	0.0843740i
$546$	1.56979	−	5.52564i	0.0671806	−	0.236476i
$547$	5.56014	+	5.56014i	0.237735	+	0.237735i	0.815911	−	0.578177i	$-0.196236\pi$
$547$	5.56014	+	5.56014i	0.237735	+	0.237735i	−0.578177	+	0.815911i	$0.696236\pi$
$548$	11.0858	+	6.85172i	0.473560	+	0.292691i
$549$	9.30595	+	9.30595i	0.397168	+	0.397168i
$550$	29.1843	+	3.04054i	1.24442	+	0.129649i
$551$			16.7200i			0.712297i
$552$	0.220273	−	4.89197i	0.00937543	−	0.208216i
$553$	3.30771			0.140658
$554$	23.0787	−	12.8669i	0.980521	−	0.546662i
$555$	−9.35349	−	18.0018i	−0.397034	−	0.764134i
$556$	−9.80856	−	41.5539i	−0.415976	−	1.76228i
$557$	−12.2628	−	12.2628i	−0.519591	−	0.519591i	0.397857	−	0.917447i	$-0.369754\pi$
$557$	−12.2628	−	12.2628i	−0.519591	−	0.519591i	−0.917447	+	0.397857i	$0.869754\pi$
$558$	4.17964	−	14.7123i	0.176938	−	0.622823i
$559$	3.28204			0.138816
$560$	20.5958	−	28.3667i	0.870330	−	1.19871i
$561$	−12.0049			−0.506849
$562$	1.46390	−	5.15294i	0.0617510	−	0.217363i
$563$	−0.327630	−	0.327630i	−0.0138079	−	0.0138079i	0.700169	−	0.713977i	$-0.253108\pi$
$563$	−0.327630	−	0.327630i	−0.0138079	−	0.0138079i	−0.713977	+	0.700169i	$0.753108\pi$
$564$	−22.6673	+	5.35049i	−0.954465	+	0.225296i
$565$	−16.1438	+	8.38807i	−0.679173	+	0.352889i
$566$	5.52484	−	3.08022i	0.232226	−	0.129471i
$567$	−3.91927			−0.164594
$568$	2.40853	−	2.20098i	0.101060	−	0.0923511i
$569$		−	35.6010i		−	1.49247i	−0.665681	−	0.746237i	$-0.731859\pi$
$569$		−	35.6010i		−	1.49247i	0.665681	−	0.746237i	$-0.268141\pi$
$570$	1.50609	+	7.33943i	0.0630830	+	0.307415i
$571$	3.57427	+	3.57427i	0.149579	+	0.149579i	0.777930	−	0.628351i	$-0.216270\pi$
$571$	3.57427	+	3.57427i	0.149579	+	0.149579i	−0.628351	+	0.777930i	$0.716270\pi$
$572$	4.52205	−	7.31646i	0.189076	−	0.305917i
$573$	15.0100	+	15.0100i	0.627051	+	0.627051i
$574$	0.00874752	−	0.0307912i	0.000365114	−	0.00128520i
$575$	−4.97618	+	7.08342i	−0.207521	+	0.295399i
$576$	−7.96763	−	0.718981i	−0.331984	−	0.0299575i
$577$		−	8.80260i		−	0.366457i	−0.983070	−	0.183229i	$-0.941345\pi$
$577$		−	8.80260i		−	0.366457i	0.983070	−	0.183229i	$-0.0586548\pi$
$578$	11.7407	+	3.33543i	0.488350	+	0.138736i
$579$	−13.6317	+	13.6317i	−0.566515	+	0.566515i
$580$	20.5955	+	23.9132i	0.855181	+	0.992941i
$581$	20.3829	+	20.3829i	0.845625	+	0.845625i
$582$	−2.76877	+	1.54365i	−0.114769	+	0.0639864i
$583$	32.6149			1.35077
$584$	15.2395	+	16.6766i	0.630616	+	0.690084i
$585$	2.20961	+	0.698563i	0.0913561	+	0.0288820i
$586$	−14.8716	+	8.29127i	−0.614342	+	0.342509i
$587$	−17.9887	+	17.9887i	−0.742475	+	0.742475i	−0.973054	−	0.230579i	$-0.925938\pi$
$587$	−17.9887	+	17.9887i	−0.742475	+	0.742475i	0.230579	+	0.973054i	$0.425938\pi$
$588$	−3.84141	−	16.2741i	−0.158417	−	0.671132i
$589$	−18.1186	+	18.1186i	−0.746564	+	0.746564i
$590$	9.43682	−	14.3097i	0.388508	−	0.589122i
$591$	13.4117			0.551684
$592$	−34.4273	−	11.4775i	−1.41495	−	0.471721i
$593$		−	25.4791i		−	1.04630i	−0.852240	−	0.523150i	$-0.824757\pi$
$593$		−	25.4791i		−	1.04630i	0.852240	−	0.523150i	$-0.175243\pi$
$594$	−5.64508	−	1.60372i	−0.231620	−	0.0658013i
$595$	22.4980	−	11.6897i	0.922328	−	0.479229i
$596$	2.77716	+	11.7654i	0.113757	+	0.481931i
$597$	6.11945	−	6.11945i	0.250452	−	0.250452i
$598$	1.23566	+	2.21635i	0.0505299	+	0.0906331i
$599$		−	14.6977i		−	0.600532i	−0.953856	−	0.300266i	$-0.902925\pi$
$599$		−	14.6977i		−	0.600532i	0.953856	−	0.300266i	$-0.0970754\pi$
$600$	11.1946	+	8.64177i	0.457019	+	0.352799i
$601$		−	12.2790i		−	0.500869i	−0.968134	−	0.250434i	$-0.919427\pi$
$601$		−	12.2790i		−	0.500869i	0.968134	−	0.250434i	$-0.0805735\pi$
$602$	15.3311	−	8.54744i	0.624850	−	0.348368i
$603$	−3.85243	+	3.85243i	−0.156883	+	0.156883i
$604$	8.83258	−	14.2907i	0.359393	−	0.581480i
$605$	12.3406	−	6.41202i	0.501718	−	0.260686i
$606$	−4.10274	+	14.4416i	−0.166662	+	0.586651i
$607$		−	26.2195i		−	1.06421i	−0.846677	−	0.532107i	$-0.821400\pi$
$607$		−	26.2195i		−	1.06421i	0.846677	−	0.532107i	$-0.178600\pi$
$608$	11.0724	+	7.55220i	0.449045	+	0.306282i
$609$	27.6581			1.12076
$610$	−34.7428	−	22.9118i	−1.40669	−	0.927672i
$611$	8.53386	−	8.53386i	0.345243	−	0.345243i
$612$	−4.92182	−	3.04201i	−0.198953	−	0.122966i
$613$	−23.4055	+	23.4055i	−0.945340	+	0.945340i	−0.998582	−	0.0532416i	$-0.983045\pi$
$613$	−23.4055	+	23.4055i	−0.945340	+	0.945340i	0.0532416	+	0.998582i	$0.483045\pi$
$614$	−6.93514	−	12.4392i	−0.279880	−	0.502007i
$615$	0.0123129	+	0.00389269i	0.000496503	+	0.000156968i
$616$	2.06917	−	45.9536i	0.0833692	−	1.85152i
$617$	27.5735			1.11007			0.555033	−	0.831828i	$-0.312706\pi$
$617$	27.5735			1.11007			0.555033	+	0.831828i	$0.312706\pi$
$618$	2.69341	+	4.83104i	0.108345	+	0.194333i
$619$	−12.2452	−	12.2452i	−0.492176	−	0.492176i	0.416815	−	0.908991i	$-0.363146\pi$
$619$	−12.2452	−	12.2452i	−0.492176	−	0.492176i	−0.908991	+	0.416815i	$0.863146\pi$
$620$	−3.59523	+	48.2317i	−0.144388	+	1.93703i
$621$	1.22423	−	1.22423i	0.0491268	−	0.0491268i
$622$	8.23108	−	28.9734i	0.330036	−	1.16173i
$623$			21.1992i			0.849327i
$624$	3.70793	−	1.85376i	0.148436	−	0.0742097i
$625$	−8.47792	−	23.5186i	−0.339117	−	0.940744i
$626$	−10.2000	−	2.89773i	−0.407673	−	0.115816i
$627$	6.95205	+	6.95205i	0.277638	+	0.277638i
$628$	3.69654	+	15.6604i	0.147508	+	0.624917i
$629$	−18.5594	−	18.5594i	−0.740011	−	0.740011i
$630$	12.1408	−	2.49136i	0.483702	−	0.0992580i
$631$			25.5846i			1.01851i	0.860617	+	0.509253i	$0.170078\pi$
$631$			25.5846i			1.01851i	−0.860617	+	0.509253i	$0.829922\pi$
$632$	1.61029	+	1.76214i	0.0640537	+	0.0700941i
$633$	1.23877			0.0492369
$634$	−2.29214	−	4.11130i	−0.0910324	−	0.163281i
$635$	31.9184	−	16.5844i	1.26664	−	0.658131i
$636$	13.3716	+	8.26449i	0.530216	+	0.327708i
$637$	6.12692	+	6.12692i	0.242758	+	0.242758i
$638$	39.8371	+	11.3174i	1.57717	+	0.448059i
$639$	1.15355			0.0456336
$640$	25.1386	−	2.83757i	0.993690	−	0.112165i
$641$	−3.52020			−0.139040			−0.0695198	−	0.997581i	$-0.522147\pi$
$641$	−3.52020			−0.139040			−0.0695198	+	0.997581i	$0.522147\pi$
$642$	−5.00655	−	1.42232i	−0.197593	−	0.0561343i
$643$	19.0869	+	19.0869i	0.752715	+	0.752715i	0.974985	−	0.222270i	$-0.0713466\pi$
$643$	19.0869	+	19.0869i	0.752715	+	0.752715i	−0.222270	+	0.974985i	$0.571347\pi$
$644$	11.5441	+	7.13499i	0.454900	+	0.281158i
$645$	3.26493	+	6.28370i	0.128556	+	0.247421i
$646$	4.72034	+	8.46665i	0.185719	+	0.333116i
$647$	−5.02456			−0.197536			−0.0987678	−	0.995111i	$-0.531490\pi$
$647$	−5.02456			−0.197536			−0.0987678	+	0.995111i	$0.531490\pi$
$648$	−1.90801	−	2.08794i	−0.0749538	−	0.0820220i
$649$		−	22.4932i		−	0.882935i
$650$	−7.28883	−	0.759379i	−0.285891	−	0.0297853i
$651$	29.9717	+	29.9717i	1.17468	+	1.17468i
$652$	−3.66389	−	15.5221i	−0.143489	−	0.607891i
$653$	6.07220	+	6.07220i	0.237623	+	0.237623i	0.815865	−	0.578242i	$-0.196261\pi$
$653$	6.07220	+	6.07220i	0.237623	+	0.237623i	−0.578242	+	0.815865i	$0.696261\pi$
$654$	3.97538	+	1.12937i	0.155450	+	0.0441619i
$655$	−39.3201	−	12.4310i	−1.53636	−	0.485718i
$656$	0.0206622	−	0.0103299i	0.000806722	−	0.000403316i
$657$			7.98713i			0.311608i
$658$	17.6387	−	62.0882i	0.687629	−	2.42045i
$659$	−5.88182	+	5.88182i	−0.229123	+	0.229123i	−0.812326	−	0.583203i	$-0.801799\pi$
$659$	−5.88182	+	5.88182i	−0.229123	+	0.229123i	0.583203	+	0.812326i	$0.301799\pi$
$660$	18.5064	+	1.37948i	0.720359	+	0.0536962i
$661$	−24.0275	−	24.0275i	−0.934562	−	0.934562i	0.0634242	−	0.997987i	$-0.479798\pi$
$661$	−24.0275	−	24.0275i	−0.934562	−	0.934562i	−0.997987	+	0.0634242i	$0.979798\pi$
$662$	22.0927	+	39.6266i	0.858656	+	1.54013i
$663$	2.99825			0.116442
$664$	−0.935746	+	20.7817i	−0.0363140	+	0.806486i
$665$	−19.7981	−	6.25911i	−0.767736	−	0.242718i
$666$	−6.24786	−	11.2065i	−0.242100	−	0.434243i
$667$	−8.63936	+	8.63936i	−0.334517	+	0.334517i
$668$	10.9832	+	6.78831i	0.424951	+	0.262647i
$669$	−7.38042	+	7.38042i	−0.285344	+	0.285344i
$670$	9.48490	−	14.3826i	0.366434	−	0.555650i
$671$	−54.6116			−2.10826
$672$	12.4928	−	18.3159i	0.481920	−	0.706550i
$673$			36.5327i			1.40823i	0.710084	+	0.704117i	$0.248657\pi$
$673$			36.5327i			1.40823i	−0.710084	+	0.704117i	$0.751343\pi$
$674$	3.44098	−	12.1123i	0.132542	−	0.466546i
$675$	0.860637	+	4.92537i	0.0331259	+	0.189578i
$676$	12.5401	−	20.2893i	0.482312	−	0.780358i
$677$	−20.5460	+	20.5460i	−0.789645	+	0.789645i	−0.981436	−	0.191791i	$-0.938571\pi$
$677$	−20.5460	+	20.5460i	−0.789645	+	0.789645i	0.191791	+	0.981436i	$0.438571\pi$
$678$	−10.0498	+	5.60299i	−0.385961	+	0.215182i
$679$		−	8.78518i		−	0.337144i
$680$	17.1802	+	6.29466i	0.658830	+	0.241389i
$681$		−	19.4055i		−	0.743622i
$682$	30.9053	+	55.4334i	1.18343	+	2.12265i
$683$	18.2074	−	18.2074i	0.696688	−	0.696688i	−0.267007	−	0.963695i	$-0.586035\pi$
$683$	18.2074	−	18.2074i	0.696688	−	0.696688i	0.963695	+	0.267007i	$0.0860346\pi$
$684$	1.08860	+	4.61185i	0.0416237	+	0.176339i
$685$	−6.71794	−	12.9294i	−0.256679	−	0.494007i
$686$	7.25464	+	2.06098i	0.276983	+	0.0786885i
$687$		−	11.9342i		−	0.455320i
$688$	12.0172	+	4.00632i	0.458150	+	0.152740i
$689$	−8.14561			−0.310323
$690$	−3.01413	+	4.57055i	−0.114746	+	0.173998i
$691$	11.5350	−	11.5350i	0.438811	−	0.438811i	−0.452801	−	0.891612i	$-0.649575\pi$
$691$	11.5350	−	11.5350i	0.438811	−	0.438811i	0.891612	+	0.452801i	$0.149575\pi$
$692$	−4.76719	−	20.1962i	−0.181221	−	0.767743i
$693$	11.5000	−	11.5000i	0.436850	−	0.436850i
$694$	−15.5083	+	8.64620i	−0.588686	+	0.328205i
$695$	−14.3894	+	45.5149i	−0.545823	+	1.72648i
$696$	13.4648	+	14.7345i	0.510381	+	0.558510i
$697$	0.0167075			0.000632842
$698$	−14.3773	+	8.01567i	−0.544189	+	0.303397i
$699$	−20.2304	−	20.2304i	−0.765182	−	0.765182i
$700$	−36.0253	+	15.4351i	−1.36163	+	0.583392i
$701$	16.5440	−	16.5440i	0.624859	−	0.624859i	−0.321911	−	0.946770i	$-0.604325\pi$
$701$	16.5440	−	16.5440i	0.624859	−	0.624859i	0.946770	+	0.321911i	$0.104325\pi$
$702$	1.40987	+	0.400530i	0.0532120	+	0.0151170i
$703$			21.4955i			0.810717i
$704$	25.4885	−	21.2692i	0.960634	−	0.801613i
$705$	24.8280	+	7.84932i	0.935078	+	0.295623i
$706$	−13.4154	+	47.2223i	−0.504897	+	1.77723i
$707$	−29.4202	−	29.4202i	−1.10646	−	1.10646i
$708$	5.69970	−	9.22184i	0.214208	−	0.346578i
$709$	−8.47518	−	8.47518i	−0.318292	−	0.318292i	0.529819	−	0.848111i	$-0.322260\pi$
$709$	−8.47518	−	8.47518i	−0.318292	−	0.318292i	−0.848111	+	0.529819i	$0.822260\pi$
$710$	−3.57337	+	0.733274i	−0.134106	+	0.0275193i
$711$			0.843960i			0.0316510i
$712$	−11.2936	+	10.3204i	−0.423245	+	0.386772i
$713$	−18.7240			−0.701221
$714$	14.0055	−	7.80835i	0.524141	−	0.292220i
$715$	−8.53325	+	4.43376i	−0.319125	+	0.165813i
$716$	−2.87328	+	0.678221i	−0.107379	+	0.0253463i
$717$	−15.1974	−	15.1974i	−0.567559	−	0.567559i
$718$	1.08631	−	3.82380i	0.0405406	−	0.142703i
$719$	−11.5303			−0.430008			−0.215004	−	0.976613i	$-0.568976\pi$
$719$	−11.5303			−0.430008			−0.215004	+	0.976613i	$0.568976\pi$
$720$	7.23774	+	5.25501i	0.269735	+	0.195843i
$721$	−15.3287			−0.570869
$722$	−5.17349	+	18.2107i	−0.192537	+	0.677731i
$723$	13.8553	+	13.8553i	0.515284	+	0.515284i
$724$	−7.86389	−	33.3153i	−0.292259	−	1.23815i
$725$	−6.07348	−	34.7582i	−0.225564	−	1.29089i
$726$	7.68229	−	4.28304i	0.285116	−	0.158959i
$727$	−32.2855			−1.19740			−0.598702	−	0.800972i	$-0.704316\pi$
$727$	−32.2855			−1.19740			−0.598702	+	0.800972i	$0.704316\pi$
$728$	−0.516778	+	11.4770i	−0.0191531	+	0.425365i
$729$		−	1.00000i		−	0.0370370i
$730$	−5.07717	−	24.7420i	−0.187914	−	0.915741i
$731$	6.47833	+	6.47833i	0.239610	+	0.239610i
$732$	−22.3898	−	13.8384i	−0.827552	−	0.511481i
$733$	33.6309	+	33.6309i	1.24219	+	1.24219i	0.959092	+	0.283094i	$0.0913609\pi$
$733$	33.6309	+	33.6309i	1.24219	+	1.24219i	0.283094	+	0.959092i	$0.408639\pi$
$734$	−7.06607	+	24.8726i	−0.260814	+	0.918063i
$735$	−5.63546	+	17.8254i	−0.207867	+	0.657500i
$736$	1.81891	+	9.62347i	0.0670461	+	0.354726i
$737$		−	22.6078i		−	0.832769i
$738$	0.00785637	+	0.00223193i	0.000289197	+	8.21583e-5i
$739$	−11.6806	+	11.6806i	−0.429676	+	0.429676i	−0.888518	−	0.458842i	$-0.848264\pi$
$739$	−11.6806	+	11.6806i	−0.429676	+	0.429676i	0.458842	+	0.888518i	$0.348264\pi$
$740$	26.4778	+	30.7431i	0.973343	+	1.13014i
$741$	−1.73628	−	1.73628i	−0.0637840	−	0.0637840i
$742$	−38.0499	+	21.2136i	−1.39685	+	0.778777i
$743$	11.7641			0.431582			0.215791	−	0.976440i	$-0.430767\pi$
$743$	11.7641			0.431582			0.215791	+	0.976440i	$0.430767\pi$
$744$	−1.37595	+	30.5581i	−0.0504448	+	1.12031i
$745$	4.07418	−	12.8870i	0.149266	−	0.472142i
$746$	40.9072	−	22.8067i	1.49772	−	0.835011i
$747$	−5.20069	+	5.20069i	−0.190283	+	0.190283i
$748$	23.3677	−	5.51582i	0.854408	−	0.201678i
$749$	10.1992	−	10.1992i	0.372672	−	0.372672i
$750$	−5.79693	−	14.7104i	−0.211674	−	0.537148i
$751$	9.89062			0.360914			0.180457	−	0.983583i	$-0.442242\pi$
$751$	9.89062			0.360914			0.180457	+	0.983583i	$0.442242\pi$
$752$	41.6637	−	20.8295i	1.51932	−	0.759575i
$753$			13.5492i			0.493760i
$754$	−9.94937	−	2.82653i	−0.362335	−	0.102936i
$755$	−16.6673	+	8.66012i	−0.606587	+	0.315174i
$756$	7.62889	−	1.80076i	0.277460	−	0.0654928i
$757$	19.7078	−	19.7078i	0.716291	−	0.716291i	−0.251553	−	0.967844i	$-0.580941\pi$
$757$	19.7078	−	19.7078i	0.716291	−	0.716291i	0.967844	+	0.251553i	$0.0809413\pi$
$758$	−6.04743	−	10.8470i	−0.219653	−	0.393980i
$759$			7.18436i			0.260776i
$760$	−6.30380	−	13.5943i	−0.228663	−	0.493116i
$761$			48.2102i			1.74762i	0.486270	+	0.873808i	$0.338357\pi$
$761$			48.2102i			1.74762i	−0.486270	+	0.873808i	$0.661643\pi$
$762$	19.8699	−	11.0779i	0.719809	−	0.401309i
$763$	−8.09857	+	8.09857i	−0.293188	+	0.293188i
$764$	−36.1136	−	22.3205i	−1.30654	−	0.807529i
$765$	2.98261	+	5.74036i	0.107837	+	0.207543i
$766$	5.56540	−	19.5902i	0.201086	−	0.707823i
$767$			5.61771i			0.202844i
$768$	15.8394	−	2.26132i	0.571555	−	0.0815984i
$769$	−30.7814			−1.11000			−0.555002	−	0.831849i	$-0.687283\pi$
$769$	−30.7814			−1.11000			−0.555002	+	0.831849i	$0.687283\pi$
$770$	−28.3138	+	42.9342i	−1.02036	+	1.54724i
$771$	9.38542	−	9.38542i	0.338008	−	0.338008i
$772$	20.2710	−	32.7975i	0.729570	−	1.18041i
$773$	31.7802	−	31.7802i	1.14306	−	1.14306i	0.155167	−	0.987888i	$-0.450408\pi$
$773$	31.7802	−	31.7802i	1.14306	−	1.14306i	0.987888	−	0.155167i	$-0.0495916\pi$
$774$	2.18088	+	3.91173i	0.0783900	+	0.140604i
$775$	31.0841	−	44.2471i	1.11657	−	1.58940i
$776$	4.68019	−	4.27688i	0.168009	−	0.153531i
$777$	35.5576			1.27562
$778$	15.0716	+	27.0331i	0.540342	+	0.969185i
$779$	−0.00967532	−	0.00967532i	−0.000346654	−	0.000346654i
$780$	−4.62199	−	0.344527i	−0.165494	−	0.0123360i
$781$	−3.38477	+	3.38477i	−0.121117	+	0.121117i
$782$	−1.93575	+	6.81382i	−0.0692221	+	0.243662i
$783$			7.05696i			0.252195i
$784$	14.9547	+	29.9127i	0.534095	+	1.06831i
$785$	5.42294	−	17.1532i	0.193553	−	0.612223i
$786$	−25.0886	−	7.12745i	−0.894881	−	0.254228i
$787$	21.8749	+	21.8749i	0.779754	+	0.779754i	0.979789	−	0.200035i	$-0.0641054\pi$
$787$	21.8749	+	21.8749i	0.779754	+	0.779754i	−0.200035	+	0.979789i	$0.564105\pi$
$788$	−26.1060	+	6.16217i	−0.929987	+	0.219518i
$789$	9.23522	+	9.23522i	0.328782	+	0.328782i
$790$	−0.536479	−	2.61436i	−0.0190871	−	0.0930148i
$791$		−	31.8876i		−	1.13379i
$792$	11.7250	+	0.527948i	0.416631	+	0.0187598i
$793$	13.6393			0.484346
$794$	14.6515	+	26.2797i	0.519962	+	0.932630i
$795$	−8.10312	−	15.5953i	−0.287388	−	0.553110i
$796$	−9.09990	+	14.7232i	−0.322538	+	0.521850i
$797$	−16.0370	−	16.0370i	−0.568058	−	0.568058i	0.363526	−	0.931584i	$-0.381573\pi$
$797$	−16.0370	−	16.0370i	−0.568058	−	0.568058i	−0.931584	+	0.363526i	$0.881573\pi$
$798$	−12.6324	−	3.58874i	−0.447181	−	0.127040i
$799$	33.6895			1.19185
$800$	−25.7610	−	11.6778i	−0.910789	−	0.412872i
$801$	−5.40896			−0.191116
$802$	39.1726	+	11.1286i	1.38323	+	0.392964i
$803$	−23.4361	−	23.4361i	−0.827041	−	0.827041i
$804$	5.72873	−	9.26882i	0.202037	−	0.326886i
$805$	−6.99568	−	13.4639i	−0.246565	−	0.474542i
$806$	−7.71865	−	13.8446i	−0.271878	−	0.487654i
$807$	17.5457			0.617639
$808$	1.35063	−	29.9958i	0.0475151	−	1.05525i
$809$			37.0836i			1.30379i	0.758309	+	0.651895i	$0.226026\pi$
$809$			37.0836i			1.30379i	−0.758309	+	0.651895i	$0.773974\pi$
$810$	0.635669	+	3.09773i	0.0223351	+	0.108843i
$811$	−11.8858	−	11.8858i	−0.417369	−	0.417369i	0.466927	−	0.884296i	$-0.345361\pi$
$811$	−11.8858	−	11.8858i	−0.417369	−	0.417369i	−0.884296	+	0.466927i	$0.845361\pi$
$812$	−53.8368	+	12.7079i	−1.88930	+	0.445959i
$813$	−1.49336	−	1.49336i	−0.0523744	−	0.0523744i
$814$	51.2151	+	14.5497i	1.79509	+	0.509968i
$815$	−5.37504	+	17.0017i	−0.188279	+	0.595543i
$816$	10.9781	+	3.65990i	0.384309	+	0.128122i
$817$		−	7.50320i		−	0.262504i
$818$	9.02651	−	31.7733i	0.315605	−	1.11093i
$819$	−2.87215	+	2.87215i	−0.100361	+	0.100361i
$820$	−0.0257557	−	0.00191985i	−0.000899427	−	6.70441e-5i
$821$	−18.0568	−	18.0568i	−0.630186	−	0.630186i	0.317928	−	0.948115i	$-0.397013\pi$
$821$	−18.0568	−	18.0568i	−0.630186	−	0.630186i	−0.948115	+	0.317928i	$0.897013\pi$
$822$	−4.48739	−	8.04881i	−0.156516	−	0.280735i
$823$	9.66750			0.336988			0.168494	−	0.985703i	$-0.446110\pi$
$823$	9.66750			0.336988			0.168494	+	0.985703i	$0.446110\pi$
$824$	−7.46243	−	8.16614i	−0.259966	−	0.284481i
$825$	−16.9775	−	11.9269i	−0.591080	−	0.415240i
$826$	14.6302	+	26.2415i	0.509050	+	0.913059i
$827$	−15.9204	+	15.9204i	−0.553607	+	0.553607i	−0.927480	−	0.373873i	$-0.878030\pi$
$827$	−15.9204	+	15.9204i	−0.553607	+	0.553607i	0.373873	+	0.927480i	$0.378030\pi$
$828$	−1.82049	+	2.94547i	−0.0632664	+	0.102362i
$829$	6.21199	−	6.21199i	0.215751	−	0.215751i	−0.590954	−	0.806705i	$-0.701249\pi$
$829$	6.21199	−	6.21199i	0.215751	−	0.215751i	0.806705	+	0.590954i	$0.201249\pi$
$830$	12.8044	−	19.4162i	0.444448	−	0.673948i
$831$	−18.6840			−0.648141
$832$	−6.36579	+	5.31201i	−0.220694	+	0.184161i
$833$			24.1875i			0.838048i
$834$	−8.25038	+	29.0413i	−0.285687	+	1.00562i
$835$	−6.65576	−	12.8097i	−0.230332	−	0.443299i
$836$	−16.7264	−	10.3380i	−0.578496	−	0.357548i
$837$	−7.64726	+	7.64726i	−0.264328	+	0.264328i
$838$	−39.1876	+	21.8479i	−1.35371	+	0.754725i
$839$			11.4138i			0.394047i	0.980399	+	0.197023i	$0.0631275\pi$
$839$			11.4138i			0.394047i	−0.980399	+	0.197023i	$0.936873\pi$
$840$	−22.4875	+	10.4277i	−0.775894	+	0.359790i
$841$		−	20.8007i		−	0.717266i
$842$	14.3780	+	25.7891i	0.495498	+	0.888751i
$843$	−2.67842	+	2.67842i	−0.0922497	+	0.0922497i
$844$	−2.41128	+	0.569170i	−0.0829998	+	0.0195916i
$845$	−23.6636	+	12.2953i	−0.814052	+	0.422970i
$846$	15.8418	+	4.50051i	0.544652	+	0.154731i
$847$			24.3755i			0.837553i
$848$	−29.8251	−	9.94317i	−1.02420	−	0.341450i
$849$	−4.47278			−0.153506
$850$	−12.8883	−	15.8861i	−0.442065	−	0.544890i
$851$	−11.1069	+	11.1069i	−0.380739	+	0.380739i
$852$	−2.24539	+	0.530011i	−0.0769257	+	0.0181579i
$853$	12.1530	−	12.1530i	0.416110	−	0.416110i	−0.467751	−	0.883861i	$-0.654935\pi$
$853$	12.1530	−	12.1530i	0.416110	−	0.416110i	0.883861	+	0.467751i	$0.154935\pi$
$854$	63.7121	−	35.5209i	2.18018	−	1.21550i
$855$	1.59701	−	5.05147i	0.0546166	−	0.172757i
$856$	10.3988	+	0.468230i	0.355423	+	0.0160038i
$857$	23.6445			0.807681			0.403840	−	0.914829i	$-0.367675\pi$
$857$	23.6445			0.807681			0.403840	+	0.914829i	$0.367675\pi$
$858$	−5.31212	+	2.96162i	−0.181353	+	0.101108i
$859$	18.9186	+	18.9186i	0.645494	+	0.645494i	0.951901	−	0.306407i	$-0.0991268\pi$
$859$	18.9186	+	18.9186i	0.645494	+	0.645494i	−0.306407	+	0.951901i	$0.599127\pi$
$860$	−9.24233	−	10.7312i	−0.315161	−	0.365930i
$861$	−0.0160048	+	0.0160048i	−0.000545443	+	0.000545443i
$862$	8.05645	+	2.28877i	0.274404	+	0.0779557i
$863$			32.1371i			1.09396i	0.837146	+	0.546980i	$0.184223\pi$
$863$			32.1371i			1.09396i	−0.837146	+	0.546980i	$0.815777\pi$
$864$	4.67329	+	3.18753i	0.158989	+	0.108442i
$865$	−6.99361	+	22.1213i	−0.237790	+	0.752148i
$866$	−2.03681	+	7.16956i	−0.0692136	+	0.243632i
$867$	−6.10266	−	6.10266i	−0.207257	−	0.207257i
$868$	−72.1109	−	44.5692i	−2.44760	−	1.51278i
$869$	−2.47637	−	2.47637i	−0.0840052	−	0.0840052i
$870$	−4.48589	−	21.8606i	−0.152086	−	0.741142i
$871$			5.64633i			0.191319i
$872$	−8.25702	−	0.371792i	−0.279618	−	0.0125905i
$873$	2.24154			0.0758645
$874$	5.06687	−	2.82489i	0.171389	−	0.0955533i
$875$	43.4305	+	5.82010i	1.46822	+	0.196755i
$876$	−3.66978	−	15.5470i	−0.123990	−	0.525285i
$877$	33.5598	+	33.5598i	1.13323	+	1.13323i	0.989636	+	0.143597i	$0.0458670\pi$
$877$	33.5598	+	33.5598i	1.13323	+	1.13323i	0.143597	+	0.989636i	$0.454133\pi$
$878$	6.89572	−	24.2729i	0.232719	−	0.819171i
$879$	12.0397			0.406091
$880$	−36.6566	+	5.81780i	−1.23569	+	0.196118i
$881$	3.11390			0.104910			0.0524550	−	0.998623i	$-0.483295\pi$
$881$	3.11390			0.104910			0.0524550	+	0.998623i	$0.483295\pi$
$882$	−3.23117	+	11.3737i	−0.108799	+	0.382972i
$883$	−36.1043	−	36.1043i	−1.21501	−	1.21501i	−0.969359	−	0.245647i	$-0.921000\pi$
$883$	−36.1043	−	36.1043i	−1.21501	−	1.21501i	−0.245647	−	0.969359i	$-0.579000\pi$
$884$	−5.83612	+	1.37758i	−0.196290	+	0.0463331i
$885$	−10.7555	+	5.58841i	−0.361542	+	0.187852i
$886$	10.3039	−	5.74465i	0.346166	−	0.192995i
$887$	−38.4317			−1.29041			−0.645206	−	0.764009i	$-0.723228\pi$
$887$	−38.4317			−1.29041			−0.645206	+	0.764009i	$0.723228\pi$
$888$	17.3105	+	18.9429i	0.580901	+	0.635681i
$889$			63.0461i			2.11450i
$890$	16.7555	−	3.43831i	0.561646	−	0.115252i
$891$	2.93423	+	2.93423i	0.0983004	+	0.0983004i
$892$	10.9750	−	17.7571i	0.367471	−	0.594551i
$893$	−19.5096	−	19.5096i	−0.652863	−	0.652863i
$894$	2.33599	−	8.22266i	0.0781271	−	0.275007i
$895$	3.14717	+	0.994971i	0.105198	+	0.0332582i
$896$	−15.9019	+	41.3920i	−0.531244	+	1.38281i
$897$		−	1.79430i		−	0.0599100i
$898$	11.0572	+	3.14126i	0.368985	+	0.104825i
$899$	53.9664	−	53.9664i	1.79988	−	1.79988i
$900$	−3.93826	−	9.19185i	−0.131275	−	0.306395i
$901$	−16.0784	−	16.0784i	−0.535649	−	0.535649i
$902$	−0.0296014	+	0.0165034i	−0.000985618	+	0.000549504i
$903$	−12.4117			−0.413037
$904$	16.9877	−	15.5238i	0.565002	−	0.516313i
$905$	−11.5366	+	36.4910i	−0.383488	+	1.21300i
$906$	−10.3758	+	5.78471i	−0.344712	+	0.192184i
$907$	−37.6279	+	37.6279i	−1.24941	+	1.24941i	−0.293436	+	0.955979i	$0.594799\pi$
$907$	−37.6279	+	37.6279i	−1.24941	+	1.24941i	−0.955979	+	0.293436i	$0.905201\pi$
$908$	8.91611	+	37.7730i	0.295891	+	1.25354i
$909$	7.50655	−	7.50655i	0.248977	−	0.248977i
$910$	7.07140	−	10.7229i	0.234415	−	0.355460i
$911$	−11.8631			−0.393042			−0.196521	−	0.980500i	$-0.562964\pi$
$911$	−11.8631			−0.393042			−0.196521	+	0.980500i	$0.562964\pi$
$912$	−4.23794	−	8.47684i	−0.140332	−	0.280696i
$913$		−	30.5200i		−	1.01007i
$914$	8.64506	+	2.45599i	0.285953	+	0.0812368i
$915$	13.5682	+	26.1134i	0.448550	+	0.863283i
$916$	5.48333	+	23.2301i	0.181174	+	0.767544i
$917$	51.1100	−	51.1100i	1.68780	−	1.68780i
$918$	1.99230	+	3.57349i	0.0657556	+	0.117943i
$919$			46.4906i			1.53358i	0.641895	+	0.766792i	$0.278148\pi$
$919$			46.4906i			1.53358i	−0.641895	+	0.766792i	$0.721852\pi$
$920$	3.76704	−	10.2815i	0.124196	−	0.338971i
$921$			10.0705i			0.331835i
$922$	3.72229	−	2.07526i	0.122587	−	0.0683450i
$923$	0.845351	−	0.845351i	0.0278251	−	0.0278251i
$924$	−17.1011	+	27.6687i	−0.562584	+	0.910235i
$925$	−7.80814	−	44.6855i	−0.256730	−	1.46925i
$926$	7.13196	−	25.1045i	0.234371	−	0.824985i
$927$		−	3.91110i		−	0.128457i
$928$	−32.9792	−	22.4943i	−1.08260	−	0.738411i
$929$	3.18351			0.104448			0.0522238	−	0.998635i	$-0.483369\pi$
$929$	3.18351			0.104448			0.0522238	+	0.998635i	$0.483369\pi$
$930$	18.8280	−	28.5503i	0.617395	−	0.936200i
$931$	14.0070	−	14.0070i	0.459060	−	0.459060i
$932$	48.6736	+	30.0835i	1.59436	+	0.985417i
$933$	−15.0599	+	15.0599i	−0.493040	+	0.493040i
$934$	5.48548	+	9.83903i	0.179490	+	0.321943i
$935$	−25.5952	−	8.09187i	−0.837053	−	0.264632i
$936$	−2.92834	−	0.131856i	−0.0957159	−	0.00430984i
$937$	27.2455			0.890072			0.445036	−	0.895513i	$-0.353191\pi$
$937$	27.2455			0.890072			0.445036	+	0.895513i	$0.353191\pi$
$938$	14.7048	+	26.3752i	0.480127	+	0.861181i
$939$	5.30181	+	5.30181i	0.173018	+	0.173018i
$940$	−51.9344	−	3.87124i	−1.69391	−	0.126266i
$941$	4.15297	−	4.15297i	0.135383	−	0.135383i	−0.636168	−	0.771551i	$-0.719481\pi$
$941$	4.15297	−	4.15297i	0.135383	−	0.135383i	0.771551	+	0.636168i	$0.219481\pi$
$942$	3.10931	−	10.9448i	0.101307	−	0.356600i
$943$		−	0.00999862i		−	0.000325600i
$944$	−6.85742	+	20.5692i	−0.223190	+	0.669470i
$945$	−8.35610	−	2.64176i	−0.271824	−	0.0859365i
$946$	−17.8771	−	5.07873i	−0.581235	−	0.165124i
$947$	−18.3519	−	18.3519i	−0.596358	−	0.596358i	0.342984	−	0.939341i	$-0.388562\pi$
$947$	−18.3519	−	18.3519i	−0.596358	−	0.596358i	−0.939341	+	0.342984i	$0.888562\pi$
$948$	−0.387768	−	1.64278i	−0.0125941	−	0.0533549i
$949$	5.85319	+	5.85319i	0.190003	+	0.190003i
$950$	−1.73604	+	16.6633i	−0.0563247	+	0.540627i
$951$			3.32841i			0.107931i
$952$	−23.6741	+	21.6340i	−0.767282	+	0.701162i
$953$	−52.0669			−1.68661			−0.843307	−	0.537433i	$-0.819394\pi$
$953$	−52.0669			−1.68661			−0.843307	+	0.537433i	$0.819394\pi$
$954$	−5.41265	−	9.70841i	−0.175241	−	0.314321i
$955$	21.8847	+	42.1195i	0.708173	+	1.36296i
$956$	36.5646	+	22.5993i	1.18258	+	0.730913i
$957$	−20.7067	−	20.7067i	−0.669354	−	0.669354i
$958$	29.2291	+	8.30374i	0.944351	+	0.268282i
$959$	25.5385			0.824681
$960$	−16.5028	−	6.90344i	−0.532626	−	0.222808i
$961$	85.9611			2.77294
$962$	−12.7910	−	3.63382i	−0.412399	−	0.117159i
$963$	2.60233	+	2.60233i	0.0838589	+	0.0838589i
$964$	−33.3354	−	20.6035i	−1.07366	−	0.663593i
$965$	−38.2520	+	19.8752i	−1.23138	+	0.639806i
$966$	−4.67291	−	8.38157i	−0.150348	−	0.269673i
$967$	−32.8074			−1.05502			−0.527508	−	0.849550i	$-0.676873\pi$
$967$	−32.8074			−1.05502			−0.527508	+	0.849550i	$0.676873\pi$
$968$	−12.9857	+	11.8667i	−0.417378	+	0.381410i
$969$		−	6.85441i		−	0.220195i
$970$	−6.94367	+	1.42487i	−0.222948	+	0.0457500i
$971$	−25.4682	−	25.4682i	−0.817314	−	0.817314i	0.168404	−	0.985718i	$-0.446139\pi$
$971$	−25.4682	−	25.4682i	−0.817314	−	0.817314i	−0.985718	+	0.168404i	$0.946139\pi$
$972$	0.459462	+	1.94651i	0.0147373	+	0.0624343i
$973$	−59.1623	−	59.1623i	−1.89666	−	1.89666i
$974$	−49.4223	−	14.0404i	−1.58359	−	0.449884i
$975$	4.24015	+	2.97875i	0.135793	+	0.0953964i
$976$	49.9402	+	16.6492i	1.59855	+	0.532929i
$977$			2.69863i			0.0863367i	0.999068	+	0.0431684i	$0.0137452\pi$
$977$			2.69863i			0.0863367i	−0.999068	+	0.0431684i	$0.986255\pi$
$978$	−3.08185	+	10.8481i	−0.0985467	+	0.346884i
$979$	15.8711	−	15.8711i	0.507244	−	0.507244i
$980$	2.77937	−	37.2866i	0.0887838	−	1.19108i
$981$	−2.06635	−	2.06635i	−0.0659734	−	0.0659734i
$982$	1.59331	+	2.85784i	0.0508445	+	0.0911973i
$983$	25.2037			0.803875			0.401937	−	0.915667i	$-0.368337\pi$
$983$	25.2037			0.803875			0.401937	+	0.915667i	$0.368337\pi$
$984$	−0.0163180		0.000734756i	−0.000520198		2.34232e-5i
$985$	28.5945	+	9.04009i	0.911097	+	0.288041i
$986$	−14.0596	−	25.2180i	−0.447748	−	0.803104i
$987$	−32.2726	+	32.2726i	−1.02725	+	1.02725i
$988$	4.17745	+	2.58194i	0.132902	+	0.0821423i
$989$	3.87696	−	3.87696i	0.123280	−	0.123280i
$990$	−10.9546	−	7.22425i	−0.348162	−	0.229602i
$991$	−9.06410			−0.287931			−0.143965	−	0.989583i	$-0.545985\pi$
$991$	−9.06410			−0.287931			−0.143965	+	0.989583i	$0.545985\pi$
$992$	−11.3620	−	60.1137i	−0.360743	−	1.90861i
$993$		−	32.0808i		−	1.01805i
$994$	1.74726	−	6.15037i	0.0554199	−	0.195078i
$995$	17.1718	−	8.92223i	0.544382	−	0.282854i
$996$	7.73366	−	12.5127i	0.245051	−	0.396480i
$997$	25.5035	−	25.5035i	0.807703	−	0.807703i	−0.176583	−	0.984286i	$-0.556504\pi$
$997$	25.5035	−	25.5035i	0.807703	−	0.807703i	0.984286	+	0.176583i	$0.0565044\pi$
$998$	32.8330	−	18.3051i	1.03931	−	0.579438i
$999$			9.07252i			0.287042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.229.22	yes	48
3.2	odd	2		720.2.bm.h.469.3		48
4.3	odd	2		960.2.bl.a.49.17		48
5.4	even	2	inner	240.2.bl.a.229.3	yes	48
8.3	odd	2		1920.2.bl.b.1249.2		48
8.5	even	2		1920.2.bl.a.1249.23		48
15.14	odd	2		720.2.bm.h.469.22		48
16.3	odd	4		960.2.bl.a.529.2		48
16.5	even	4		1920.2.bl.a.289.2		48
16.11	odd	4		1920.2.bl.b.289.23		48
16.13	even	4	inner	240.2.bl.a.109.3	✓	48
20.19	odd	2		960.2.bl.a.49.2		48
40.19	odd	2		1920.2.bl.b.1249.23		48
40.29	even	2		1920.2.bl.a.1249.2		48
48.29	odd	4		720.2.bm.h.109.22		48
80.19	odd	4		960.2.bl.a.529.17		48
80.29	even	4	inner	240.2.bl.a.109.22	yes	48
80.59	odd	4		1920.2.bl.b.289.2		48
80.69	even	4		1920.2.bl.a.289.23		48
240.29	odd	4		720.2.bm.h.109.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.3	✓	48	16.13	even	4	inner
240.2.bl.a.109.22	yes	48	80.29	even	4	inner
240.2.bl.a.229.3	yes	48	5.4	even	2	inner
240.2.bl.a.229.22	yes	48	1.1	even	1	trivial
720.2.bm.h.109.3		48	240.29	odd	4
720.2.bm.h.109.22		48	48.29	odd	4
720.2.bm.h.469.3		48	3.2	odd	2
720.2.bm.h.469.22		48	15.14	odd	2
960.2.bl.a.49.2		48	20.19	odd	2
960.2.bl.a.49.17		48	4.3	odd	2
960.2.bl.a.529.2		48	16.3	odd	4
960.2.bl.a.529.17		48	80.19	odd	4
1920.2.bl.a.289.2		48	16.5	even	4
1920.2.bl.a.289.23		48	80.69	even	4
1920.2.bl.a.1249.2		48	40.29	even	2
1920.2.bl.a.1249.23		48	8.5	even	2
1920.2.bl.b.289.2		48	80.59	odd	4
1920.2.bl.b.289.23		48	16.11	odd	4
1920.2.bl.b.1249.2		48	8.3	odd	2
1920.2.bl.b.1249.23		48	40.19	odd	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36038 + 0.386472i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.70128 + 1.05150i) q^{4} +(-1.03097 - 1.98421i) q^{5} +(-0.688658 - 1.23521i) q^{6} +3.91927 q^{7} +(1.90801 + 2.08794i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(1.36038 + 0.386472i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.70128 + 1.05150i) q^{4} +(-1.03097 - 1.98421i) q^{5} +(-0.688658 - 1.23521i) q^{6} +3.91927 q^{7} +(1.90801 + 2.08794i) q^{8} +1.00000i q^{9} +(-0.635669 - 3.09773i) q^{10} +(-2.93423 - 2.93423i) q^{11} +(-0.459462 - 1.94651i) q^{12} +(0.732828 + 0.732828i) q^{13} +(5.33170 + 1.51469i) q^{14} +(-0.674045 + 2.13206i) q^{15} +(1.78869 + 3.57779i) q^{16} +2.89302i q^{17} +(-0.386472 + 1.36038i) q^{18} +(1.67534 - 1.67534i) q^{19} +(0.332434 - 4.45976i) q^{20} +(-2.77134 - 2.77134i) q^{21} +(-2.85767 - 5.12567i) q^{22} +1.73133 q^{23} +(0.127228 - 2.82556i) q^{24} +(-2.87420 + 4.09133i) q^{25} +(0.713708 + 1.28014i) q^{26} +(0.707107 - 0.707107i) q^{27} +(6.66776 + 4.12111i) q^{28} +(-4.99003 + 4.99003i) q^{29} +(-1.74094 + 2.63991i) q^{30} -10.8149 q^{31} +(1.05059 + 5.55844i) q^{32} +4.14963i q^{33} +(-1.11807 + 3.93561i) q^{34} +(-4.04065 - 7.77666i) q^{35} +(-1.05150 + 1.70128i) q^{36} +(-6.41524 + 6.41524i) q^{37} +(2.92658 - 1.63163i) q^{38} -1.03637i q^{39} +(2.17581 - 5.93850i) q^{40} -0.00577512i q^{41} +(-2.69904 - 4.84113i) q^{42} +(2.23930 - 2.23930i) q^{43} +(-1.90660 - 8.07728i) q^{44} +(1.98421 - 1.03097i) q^{45} +(2.35527 + 0.669110i) q^{46} -11.6451i q^{47} +(1.26508 - 3.79468i) q^{48} +8.36066 q^{49} +(-5.49120 + 4.45497i) q^{50} +(2.04567 - 2.04567i) q^{51} +(0.476175 + 2.01731i) q^{52} +(-5.55765 + 5.55765i) q^{53} +(1.23521 - 0.688658i) q^{54} +(-2.79703 + 8.84724i) q^{55} +(7.47801 + 8.18319i) q^{56} -2.36929 q^{57} +(-8.71685 + 4.85983i) q^{58} +(3.83290 + 3.83290i) q^{59} +(-3.38860 + 2.91846i) q^{60} +(9.30595 - 9.30595i) q^{61} +(-14.7123 - 4.17964i) q^{62} +3.91927i q^{63} +(-0.718981 + 7.96763i) q^{64} +(0.698563 - 2.20961i) q^{65} +(-1.60372 + 5.64508i) q^{66} +(3.85243 + 3.85243i) q^{67} +(-3.04201 + 4.92182i) q^{68} +(-1.22423 - 1.22423i) q^{69} +(-2.49136 - 12.1408i) q^{70} -1.15355i q^{71} +(-2.08794 + 1.90801i) q^{72} +7.98713 q^{73} +(-11.2065 + 6.24786i) q^{74} +(4.92537 - 0.860637i) q^{75} +(4.61185 - 1.08860i) q^{76} +(-11.5000 - 11.5000i) q^{77} +(0.400530 - 1.40987i) q^{78} +0.843960 q^{79} +(5.25501 - 7.23774i) q^{80} -1.00000 q^{81} +(0.00223193 - 0.00785637i) q^{82} +(5.20069 + 5.20069i) q^{83} +(-1.80076 - 7.62889i) q^{84} +(5.74036 - 2.98261i) q^{85} +(3.91173 - 2.18088i) q^{86} +7.05696 q^{87} +(0.527948 - 11.7250i) q^{88} +5.40896i q^{89} +(3.09773 - 0.635669i) q^{90} +(2.87215 + 2.87215i) q^{91} +(2.94547 + 1.82049i) q^{92} +(7.64726 + 7.64726i) q^{93} +(4.50051 - 15.8418i) q^{94} +(-5.05147 - 1.59701i) q^{95} +(3.18753 - 4.67329i) q^{96} -2.24154i q^{97} +(11.3737 + 3.23117i) q^{98} +(2.93423 - 2.93423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

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