LMFDB - Embedded newform 720.2.cf.a.11.49

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.49
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.49

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.130543 + 1.40818i) q^{2} +(0.00582509 - 1.73204i) q^{3} +(-1.96592 + 0.367654i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.43978 - 0.217903i) q^{6} +(-1.28709 + 2.22930i) q^{7} +(-0.774358 - 2.72036i) q^{8} +(-2.99993 - 0.0201786i) q^{9} +O(q^{10})$	\(q+(0.130543 + 1.40818i) q^{2} +(0.00582509 - 1.73204i) q^{3} +(-1.96592 + 0.367654i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.43978 - 0.217903i) q^{6} +(-1.28709 + 2.22930i) q^{7} +(-0.774358 - 2.72036i) q^{8} +(-2.99993 - 0.0201786i) q^{9} +(-0.238368 + 1.39398i) q^{10} +(-1.49624 + 0.400915i) q^{11} +(0.625341 + 3.40719i) q^{12} +(-4.35804 - 1.16773i) q^{13} +(-3.30727 - 1.52143i) q^{14} +(0.453912 - 1.67152i) q^{15} +(3.72966 - 1.44556i) q^{16} -3.11083i q^{17} +(-0.363204 - 4.22707i) q^{18} +(0.356702 + 0.356702i) q^{19} +(-1.99409 - 0.153690i) q^{20} +(3.85375 + 2.24228i) q^{21} +(-0.759882 - 2.05463i) q^{22} +(-1.88714 + 1.08954i) q^{23} +(-4.71629 + 1.32537i) q^{24} +(0.866025 + 0.500000i) q^{25} +(1.07546 - 6.28932i) q^{26} +(-0.0524250 + 5.19589i) q^{27} +(1.71070 - 4.85583i) q^{28} +(-8.55924 + 2.29344i) q^{29} +(2.41304 + 0.420983i) q^{30} +(-3.82688 + 2.20945i) q^{31} +(2.52248 + 5.06331i) q^{32} +(0.685686 + 2.59388i) q^{33} +(4.38060 - 0.406096i) q^{34} +(-1.82022 + 1.82022i) q^{35} +(5.90504 - 1.06327i) q^{36} +(-6.60907 - 6.60907i) q^{37} +(-0.455734 + 0.548863i) q^{38} +(-2.04795 + 7.54150i) q^{39} +(-0.0438908 - 2.82809i) q^{40} +(-0.181889 - 0.315041i) q^{41} +(-2.65444 + 5.71946i) q^{42} +(-0.153996 - 0.574721i) q^{43} +(2.79408 - 1.33826i) q^{44} +(-2.89249 - 0.795931i) q^{45} +(-1.78062 - 2.51520i) q^{46} +(-3.01126 + 5.21566i) q^{47} +(-2.48204 - 6.46835i) q^{48} +(0.186807 + 0.323560i) q^{49} +(-0.591034 + 1.28479i) q^{50} +(-5.38809 - 0.0181209i) q^{51} +(8.99686 + 0.693415i) q^{52} +(0.622748 - 0.622748i) q^{53} +(-7.32357 + 0.604462i) q^{54} -1.54902 q^{55} +(7.06118 + 1.77507i) q^{56} +(0.619900 - 0.615744i) q^{57} +(-4.34692 - 11.7535i) q^{58} +(1.61378 - 6.02273i) q^{59} +(-0.277813 + 3.45294i) q^{60} +(-3.62605 - 13.5326i) q^{61} +(-3.61087 - 5.10049i) q^{62} +(3.90616 - 6.66178i) q^{63} +(-6.80074 + 4.21307i) q^{64} +(-3.90731 - 2.25589i) q^{65} +(-3.56313 + 1.30418i) q^{66} +(0.917458 - 3.42400i) q^{67} +(1.14371 + 6.11564i) q^{68} +(1.87614 + 3.27495i) q^{69} +(-2.80080 - 2.32557i) q^{70} +14.8581i q^{71} +(2.26813 + 8.17653i) q^{72} -9.34228i q^{73} +(8.44397 - 10.1695i) q^{74} +(0.871065 - 1.49708i) q^{75} +(-0.832389 - 0.570103i) q^{76} +(1.03203 - 3.85158i) q^{77} +(-10.8871 - 1.89938i) q^{78} +(9.07438 + 5.23909i) q^{79} +(3.97671 - 0.430992i) q^{80} +(8.99919 + 0.121069i) q^{81} +(0.419889 - 0.297258i) q^{82} +(3.29062 + 12.2808i) q^{83} +(-8.40053 - 2.99128i) q^{84} +(0.805142 - 3.00483i) q^{85} +(0.789205 - 0.291879i) q^{86} +(3.92248 + 14.8383i) q^{87} +(2.24926 + 3.75985i) q^{88} +1.43798 q^{89} +(0.743217 - 4.17704i) q^{90} +(8.21241 - 8.21241i) q^{91} +(3.30939 - 2.83577i) q^{92} +(3.80457 + 6.64119i) q^{93} +(-7.73766 - 3.55952i) q^{94} +(0.252226 + 0.436868i) q^{95} +(8.78456 - 4.33954i) q^{96} +(-4.05733 + 7.02749i) q^{97} +(-0.431243 + 0.305296i) q^{98} +(4.49670 - 1.17253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.130543	+	1.40818i	0.0923077	+	0.995731i
$2$	0.130543	+	1.40818i	0.0923077	+	0.995731i
$3$	0.00582509	−	1.73204i	0.00336312	−	0.999994i
$3$	0.00582509	−	1.73204i	0.00336312	−	0.999994i
$4$	−1.96592	+	0.367654i	−0.982959	+	0.183827i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	2.43978	−	0.217903i	0.996035	−	0.0889584i
$7$	−1.28709	+	2.22930i	−0.486474	+	0.842597i	−0.999879	−	0.0155491i	$-0.995050\pi$
$7$	−1.28709	+	2.22930i	−0.486474	+	0.842597i	0.513405	+	0.858146i	$0.328384\pi$
$8$	−0.774358	−	2.72036i	−0.273777	−	0.961793i
$9$	−2.99993	−	0.0201786i	−0.999977	−	0.00672619i
$10$	−0.238368	+	1.39398i	−0.0753786	+	0.440815i
$11$	−1.49624	+	0.400915i	−0.451132	+	0.120881i	−0.477229	−	0.878779i	$-0.658359\pi$
$11$	−1.49624	+	0.400915i	−0.451132	+	0.120881i	0.0260969	+	0.999659i	$0.491692\pi$
$12$	0.625341	+	3.40719i	0.180520	+	0.983571i
$13$	−4.35804	−	1.16773i	−1.20870	−	0.323871i	−0.402450	−	0.915442i	$-0.631841\pi$
$13$	−4.35804	−	1.16773i	−1.20870	−	0.323871i	−0.806253	+	0.591571i	$0.798508\pi$
$14$	−3.30727	−	1.52143i	−0.883905	−	0.406619i
$15$	0.453912	−	1.67152i	0.117200	−	0.431583i
$16$	3.72966	−	1.44556i	0.932415	−	0.361389i
$17$		−	3.11083i		−	0.754487i	−0.926114	−	0.377244i	$-0.876872\pi$
$17$		−	3.11083i		−	0.754487i	0.926114	−	0.377244i	$-0.123128\pi$
$18$	−0.363204	−	4.22707i	−0.0856081	−	0.996329i
$19$	0.356702	+	0.356702i	0.0818330	+	0.0818330i	0.746838	−	0.665006i	$-0.231571\pi$
$19$	0.356702	+	0.356702i	0.0818330	+	0.0818330i	−0.665006	+	0.746838i	$0.731571\pi$
$20$	−1.99409	−	0.153690i	−0.445891	−	0.0343662i
$21$	3.85375	+	2.24228i	0.840956	+	0.489305i
$22$	−0.759882	−	2.05463i	−0.162007	−	0.438048i
$23$	−1.88714	+	1.08954i	−0.393496	+	0.227185i	−0.683674	−	0.729788i	$-0.739619\pi$
$23$	−1.88714	+	1.08954i	−0.393496	+	0.227185i	0.290178	+	0.956973i	$0.406286\pi$
$24$	−4.71629	+	1.32537i	−0.962709	+	0.270541i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	1.07546	−	6.28932i	0.210916	−	1.23344i
$27$	−0.0524250	+	5.19589i	−0.0100892	+	0.999949i
$28$	1.71070	−	4.85583i	0.323291	−	0.917665i
$29$	−8.55924	+	2.29344i	−1.58941	+	0.425881i	−0.941823	−	0.336109i	$-0.890889\pi$
$29$	−8.55924	+	2.29344i	−1.58941	+	0.425881i	−0.647588	+	0.761990i	$0.724222\pi$
$30$	2.41304	+	0.420983i	0.440559	+	0.0768607i
$31$	−3.82688	+	2.20945i	−0.687328	+	0.396829i	−0.802610	−	0.596504i	$-0.796556\pi$
$31$	−3.82688	+	2.20945i	−0.687328	+	0.396829i	0.115282	+	0.993333i	$0.463223\pi$
$32$	2.52248	+	5.06331i	0.445915	+	0.895075i
$33$	0.685686	+	2.59388i	0.119363	+	0.451536i
$34$	4.38060	−	0.406096i	0.751266	−	0.0696450i
$35$	−1.82022	+	1.82022i	−0.307673	+	0.307673i
$36$	5.90504	−	1.06327i	0.984173	−	0.177211i
$37$	−6.60907	−	6.60907i	−1.08652	−	1.08652i	−0.995884	−	0.0906410i	$-0.971108\pi$
$37$	−6.60907	−	6.60907i	−1.08652	−	1.08652i	−0.0906410	−	0.995884i	$-0.528892\pi$
$38$	−0.455734	+	0.548863i	−0.0739298	+	0.0890374i
$39$	−2.04795	+	7.54150i	−0.327934	+	1.20761i
$40$	−0.0438908	−	2.82809i	−0.00693975	−	0.447160i
$41$	−0.181889	−	0.315041i	−0.0284063	−	0.0492012i	0.851473	−	0.524399i	$-0.175710\pi$
$41$	−0.181889	−	0.315041i	−0.0284063	−	0.0492012i	−0.879879	+	0.475198i	$0.842377\pi$
$42$	−2.65444	+	5.71946i	−0.409589	+	0.882532i
$43$	−0.153996	−	0.574721i	−0.0234842	−	0.0876441i	0.953189	−	0.302375i	$-0.0977793\pi$
$43$	−0.153996	−	0.574721i	−0.0234842	−	0.0876441i	−0.976673	+	0.214731i	$0.931113\pi$
$44$	2.79408	−	1.33826i	0.421223	−	0.201751i
$45$	−2.89249	−	0.795931i	−0.431187	−	0.118650i
$46$	−1.78062	−	2.51520i	−0.262538	−	0.370845i
$47$	−3.01126	+	5.21566i	−0.439238	+	0.760782i	−0.997631	−	0.0687943i	$-0.978085\pi$
$47$	−3.01126	+	5.21566i	−0.439238	+	0.760782i	0.558393	+	0.829577i	$0.311418\pi$
$48$	−2.48204	−	6.46835i	−0.358251	−	0.933625i
$49$	0.186807	+	0.323560i	0.0266868	+	0.0462228i
$50$	−0.591034	+	1.28479i	−0.0835849	+	0.181696i
$51$	−5.38809	−	0.0181209i	−0.754483	−	0.00253743i
$52$	8.99686	+	0.693415i	1.24764	+	0.0961593i
$53$	0.622748	−	0.622748i	0.0855410	−	0.0855410i	−0.663042	−	0.748583i	$-0.730735\pi$
$53$	0.622748	−	0.622748i	0.0855410	−	0.0855410i	0.748583	+	0.663042i	$0.230735\pi$
$54$	−7.32357	+	0.604462i	−0.996611	+	0.0822568i
$55$	−1.54902			−0.208870
$56$	7.06118	+	1.77507i	0.943589	+	0.237203i
$57$	0.619900	−	0.615744i	0.0821077	−	0.0815573i
$58$	−4.34692	−	11.7535i	−0.570778	−	1.54331i
$59$	1.61378	−	6.02273i	0.210097	−	0.784092i	−0.777738	−	0.628588i	$-0.783633\pi$
$59$	1.61378	−	6.02273i	0.210097	−	0.784092i	0.987835	−	0.155504i	$-0.0497002\pi$
$60$	−0.277813	+	3.45294i	−0.0358655	+	0.445773i
$61$	−3.62605	−	13.5326i	−0.464268	−	1.73267i	−0.659306	−	0.751875i	$-0.729150\pi$
$61$	−3.62605	−	13.5326i	−0.464268	−	1.73267i	0.195038	−	0.980796i	$-0.437517\pi$
$62$	−3.61087	−	5.10049i	−0.458581	−	0.647763i
$63$	3.90616	−	6.66178i	0.492130	−	0.839306i
$64$	−6.80074	+	4.21307i	−0.850092	+	0.526633i
$65$	−3.90731	−	2.25589i	−0.484642	−	0.279808i
$66$	−3.56313	+	1.30418i	−0.438590	+	0.160533i
$67$	0.917458	−	3.42400i	0.112085	−	0.418308i	−0.886967	−	0.461833i	$-0.847192\pi$
$67$	0.917458	−	3.42400i	0.112085	−	0.418308i	0.999052	+	0.0435246i	$0.0138587\pi$
$68$	1.14371	+	6.11564i	0.138695	+	0.741630i
$69$	1.87614	+	3.27495i	0.225861	+	0.394258i
$70$	−2.80080	−	2.32557i	−0.334760	−	0.277959i
$71$			14.8581i			1.76333i	0.471879	+	0.881664i	$0.343576\pi$
$71$			14.8581i			1.76333i	−0.471879	+	0.881664i	$0.656424\pi$
$72$	2.26813	+	8.17653i	0.267301	+	0.963613i
$73$		−	9.34228i		−	1.09343i	−0.837319	−	0.546715i	$-0.815878\pi$
$73$		−	9.34228i		−	1.09343i	0.837319	−	0.546715i	$-0.184122\pi$
$74$	8.44397	−	10.1695i	0.981591	−	1.18218i
$75$	0.871065	−	1.49708i	0.100582	−	0.172868i
$76$	−0.832389	−	0.570103i	−0.0954815	−	0.0653953i
$77$	1.03203	−	3.85158i	0.117610	−	0.438928i
$78$	−10.8871	−	1.89938i	−1.23272	−	0.215063i
$79$	9.07438	+	5.23909i	1.02095	+	0.589444i	0.914378	−	0.404861i	$-0.132680\pi$
$79$	9.07438	+	5.23909i	1.02095	+	0.589444i	0.106569	+	0.994305i	$0.466013\pi$
$80$	3.97671	−	0.430992i	0.444610	−	0.0481864i
$81$	8.99919	+	0.121069i	0.999910	+	0.0134521i
$82$	0.419889	−	0.297258i	0.0463690	−	0.0328267i
$83$	3.29062	+	12.2808i	0.361193	+	1.34799i	0.872510	+	0.488597i	$0.162491\pi$
$83$	3.29062	+	12.2808i	0.361193	+	1.34799i	−0.511317	+	0.859392i	$0.670842\pi$
$84$	−8.40053	−	2.99128i	−0.916573	−	0.326376i
$85$	0.805142	−	3.00483i	0.0873299	−	0.325920i
$86$	0.789205	−	0.291879i	0.0851021	−	0.0314741i
$87$	3.92248	+	14.8383i	0.420534	+	1.59083i
$88$	2.24926	+	3.75985i	0.239772	+	0.400802i
$89$	1.43798			0.152425			0.0762126	−	0.997092i	$-0.475717\pi$
$89$	1.43798			0.152425			0.0762126	+	0.997092i	$0.475717\pi$
$90$	0.743217	−	4.17704i	0.0783419	−	0.440298i
$91$	8.21241	−	8.21241i	0.860894	−	0.860894i
$92$	3.30939	−	2.83577i	0.345028	−	0.295649i
$93$	3.80457	+	6.64119i	0.394515	+	0.688659i
$94$	−7.73766	−	3.55952i	−0.798079	−	0.367136i
$95$	0.252226	+	0.436868i	0.0258779	+	0.0448218i
$96$	8.78456	−	4.33954i	0.896570	−	0.442902i
$97$	−4.05733	+	7.02749i	−0.411959	+	0.713534i	−0.995104	−	0.0988343i	$-0.968489\pi$
$97$	−4.05733	+	7.02749i	−0.411959	+	0.713534i	0.583145	+	0.812368i	$0.301822\pi$
$98$	−0.431243	+	0.305296i	−0.0435621	+	0.0308395i
$99$	4.49670	−	1.17253i	0.451935	−	0.117843i
$100$	−1.88636	−	0.664561i	−0.188636	−	0.0664561i
$101$	4.39210	+	16.3915i	0.437030	+	1.63102i	0.736161	+	0.676807i	$0.236637\pi$
$101$	4.39210	+	16.3915i	0.437030	+	1.63102i	−0.299130	+	0.954212i	$0.596697\pi$
$102$	−0.677858	−	7.58974i	−0.0671180	−	0.751496i
$103$	−2.05504	−	3.55943i	−0.202489	−	0.350721i	0.746841	−	0.665003i	$-0.231570\pi$
$103$	−2.05504	−	3.55943i	−0.202489	−	0.350721i	−0.949330	+	0.314282i	$0.898236\pi$
$104$	0.198025	+	12.7597i	0.0194180	+	1.25119i
$105$	3.14209	+	3.16329i	0.306636	+	0.308706i
$106$	0.958233	+	0.795643i	0.0930719	+	0.0772797i
$107$	−6.00195	−	6.00195i	−0.580231	−	0.580231i	0.354736	−	0.934967i	$-0.384571\pi$
$107$	−6.00195	−	6.00195i	−0.580231	−	0.580231i	−0.934967	+	0.354736i	$0.884571\pi$
$108$	−1.80723	−	10.2340i	−0.173900	−	0.984763i
$109$	2.39190	−	2.39190i	0.229103	−	0.229103i	−0.583215	−	0.812318i	$-0.698206\pi$
$109$	2.39190	−	2.39190i	0.229103	−	0.229103i	0.812318	+	0.583215i	$0.198206\pi$
$110$	−0.202213	−	2.18129i	−0.0192803	−	0.207978i
$111$	−11.4857	+	11.4087i	−1.09017	+	1.08286i
$112$	−1.57782	+	10.1751i	−0.149090	+	0.961456i
$113$	7.04348	−	4.06656i	0.662595	−	0.382549i	−0.130670	−	0.991426i	$-0.541713\pi$
$113$	7.04348	−	4.06656i	0.662595	−	0.382549i	0.793265	+	0.608876i	$0.208379\pi$
$114$	0.947999	+	0.792547i	0.0887882	+	0.0742288i
$115$	−2.10483	+	0.563988i	−0.196277	+	0.0525922i
$116$	15.9836	−	7.65556i	1.48404	−	0.710801i
$117$	13.0503	+	3.59106i	1.20650	+	0.331993i
$118$	8.69172	+	1.48627i	0.800138	+	0.136822i
$119$	6.93498	+	4.00391i	0.635729	+	0.367038i
$120$	−4.89862	+	0.0595469i	−0.447181	+	0.00543586i
$121$	−7.44829	+	4.30027i	−0.677117	+	0.390934i
$122$	18.5829	−	6.87269i	1.68242	−	0.622224i
$123$	−0.546724	+	0.313204i	−0.0492964	+	0.0282407i
$124$	6.71102	−	5.75057i	0.602667	−	0.516416i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	9.89088	+	4.63091i	0.881150	+	0.412555i
$127$		−	21.2692i		−	1.88734i	−0.330895	−	0.943668i	$-0.607351\pi$
$127$		−	21.2692i		−	1.88734i	0.330895	−	0.943668i	$-0.392649\pi$
$128$	−6.82053	−	9.02665i	−0.602855	−	0.797851i
$129$	−0.996337	+	0.263380i	−0.0877226	+	0.0231893i
$130$	2.66661	−	5.79667i	0.233877	−	0.508401i
$131$	6.35822	+	1.70368i	0.555520	+	0.148851i	0.525647	−	0.850703i	$-0.323823\pi$
$131$	6.35822	+	1.70368i	0.555520	+	0.148851i	0.0298726	+	0.999554i	$0.490490\pi$
$132$	−2.30165	−	4.84725i	−0.200333	−	0.421899i
$133$	−1.25430	+	0.336089i	−0.108762	+	0.0291426i
$134$	4.94136	+	0.844964i	0.426869	+	0.0729937i
$135$	−1.39543	+	5.00527i	−0.120100	+	0.430785i
$136$	−8.46259	+	2.40890i	−0.725661	+	0.206561i
$137$	6.53538	−	11.3196i	0.558355	−	0.967100i	−0.439279	−	0.898351i	$-0.644766\pi$
$137$	6.53538	−	11.3196i	0.558355	−	0.967100i	0.997634	−	0.0687491i	$-0.0219008\pi$
$138$	−4.36679	+	3.06945i	−0.371726	+	0.261289i
$139$	16.1767	+	4.33453i	1.37209	+	0.367650i	0.868241	−	0.496143i	$-0.165251\pi$
$139$	16.1767	+	4.33453i	1.37209	+	0.367650i	0.503847	+	0.863793i	$0.331918\pi$
$140$	2.90919	−	4.24761i	0.245871	−	0.358988i
$141$	9.01620	+	5.24601i	0.759301	+	0.441794i
$142$	−20.9228	+	1.93961i	−1.75580	+	0.162769i
$143$	6.98882			0.584434
$144$	−11.2179	+	4.26131i	−0.934825	+	0.355109i
$145$	−8.86118			−0.735881
$146$	13.1556	−	1.21957i	1.08876	−	0.100932i
$147$	0.561507	−	0.321673i	0.0463123	−	0.0265312i
$148$	15.4227	+	10.5630i	1.26774	+	0.868276i
$149$	−8.58949	−	2.30155i	−0.703678	−	0.188550i	−0.110801	−	0.993843i	$-0.535342\pi$
$149$	−8.58949	−	2.30155i	−0.703678	−	0.188550i	−0.592877	+	0.805293i	$0.702008\pi$
$150$	2.22186	+	1.03118i	0.181414	+	0.0841955i
$151$	−3.08414	+	5.34189i	−0.250984	+	0.434717i	−0.963797	−	0.266637i	$-0.914087\pi$
$151$	−3.08414	+	5.34189i	−0.250984	+	0.434717i	0.712813	+	0.701354i	$0.247421\pi$
$152$	0.694143	−	1.24657i	0.0563024	−	0.101110i
$153$	−0.0627721	+	9.33228i	−0.00507483	+	0.754470i
$154$	5.55842	+	0.950480i	0.447910	+	0.0765918i
$155$	−4.26833	+	1.14370i	−0.342841	+	0.0918639i
$156$	1.25343	−	15.5789i	0.100355	−	1.24731i
$157$	5.78439	+	1.54992i	0.461645	+	0.123697i	0.482143	−	0.876093i	$-0.339859\pi$
$157$	5.78439	+	1.54992i	0.461645	+	0.123697i	−0.0204982	+	0.999790i	$0.506525\pi$
$158$	−6.19297	+	13.4622i	−0.492686	+	1.07100i
$159$	−1.07500	−	1.08225i	−0.0852528	−	0.0858282i
$160$	1.12604	+	5.54365i	0.0890216	+	0.438264i
$161$		−	5.60935i		−	0.442078i
$162$	1.00429	+	12.6882i	0.0789047	+	0.996882i
$163$	−8.74624	−	8.74624i	−0.685059	−	0.685059i	0.276077	−	0.961136i	$-0.410966\pi$
$163$	−8.74624	−	8.74624i	−0.685059	−	0.685059i	−0.961136	+	0.276077i	$0.910966\pi$
$164$	0.473405	+	0.552473i	0.0369667	+	0.0431409i
$165$	−0.00902317	+	2.68296i	−0.000702453	+	0.208868i
$166$	−16.8639	+	6.23694i	−1.30889	+	0.484080i
$167$	−6.25635	+	3.61211i	−0.484131	+	0.279513i	−0.722136	−	0.691751i	$-0.756840\pi$
$167$	−6.25635	+	3.61211i	−0.484131	+	0.279513i	0.238005	+	0.971264i	$0.423506\pi$
$168$	3.11562	−	12.2199i	0.240376	−	0.942786i
$169$	6.37056	+	3.67805i	0.490043	+	0.282927i
$170$	4.33644	+	0.741523i	0.332589	+	0.0568722i
$171$	−1.06288	−	1.07728i	−0.0812807	−	0.0823815i
$172$	0.514042	+	1.07324i	0.0391953	+	0.0818335i
$173$	10.5121	−	2.81670i	0.799216	−	0.214149i	0.163977	−	0.986464i	$-0.447568\pi$
$173$	10.5121	−	2.81670i	0.799216	−	0.214149i	0.635240	+	0.772315i	$0.280901\pi$
$174$	−20.3829	+	7.46057i	−1.54522	+	0.565584i
$175$	−2.22930	+	1.28709i	−0.168519	+	0.0972947i
$176$	−5.00091	+	3.65817i	−0.376958	+	0.275745i
$177$	−10.4222	−	2.83022i	−0.783381	−	0.212733i
$178$	0.187717	+	2.02492i	0.0140700	+	0.151774i
$179$	−13.2765	+	13.2765i	−0.992329	+	0.992329i	−0.999971	−	0.00764192i	$-0.997567\pi$
$179$	−13.2765	+	13.2765i	−0.992329	+	0.992329i	0.00764192	+	0.999971i	$0.497567\pi$
$180$	5.97902	+	0.501298i	0.445650	+	0.0373645i
$181$	7.16449	+	7.16449i	0.532532	+	0.532532i	0.921325	−	0.388793i	$-0.127108\pi$
$181$	7.16449	+	7.16449i	0.532532	+	0.532532i	−0.388793	+	0.921325i	$0.627108\pi$
$182$	12.6366	+	10.4924i	0.936686	+	0.777752i
$183$	−23.4601	+	6.20163i	−1.73422	+	0.458438i
$184$	4.42527	+	4.29001i	0.326235	+	0.316264i
$185$	−4.67332	−	8.09443i	−0.343589	−	0.595114i
$186$	−8.85530	+	6.22446i	−0.649302	+	0.456400i
$187$	1.24718	+	4.65454i	0.0912028	+	0.340374i
$188$	4.00233	−	11.3607i	0.291900	−	0.828561i
$189$	−11.5157	−	6.80444i	−0.837646	−	0.494950i
$190$	−0.582261	+	0.412209i	−0.0422417	+	0.0299048i
$191$	−11.3716	+	19.6961i	−0.822818	+	1.42516i	0.0807567	+	0.996734i	$0.474266\pi$
$191$	−11.3716	+	19.6961i	−0.822818	+	1.42516i	−0.903575	+	0.428430i	$0.859067\pi$
$192$	7.25759	+	11.8037i	0.523772	+	0.851859i
$193$	2.14758	+	3.71971i	0.154586	+	0.267751i	0.932908	−	0.360114i	$-0.117262\pi$
$193$	2.14758	+	3.71971i	0.154586	+	0.267751i	−0.778322	+	0.627865i	$0.783929\pi$
$194$	−10.4256	−	4.79604i	−0.748514	−	0.344335i
$195$	−3.93005	+	6.75448i	−0.281437	+	0.483698i
$196$	−0.486206	−	0.567411i	−0.0347290	−	0.0405294i
$197$	14.3738	−	14.3738i	1.02409	−	1.02409i	0.0243860	−	0.999703i	$-0.492237\pi$
$197$	14.3738	−	14.3738i	1.02409	−	1.02409i	0.999703	−	0.0243860i	$-0.00776309\pi$
$198$	2.23814	+	6.17908i	0.159057	+	0.439128i
$199$	−8.65656			−0.613648			−0.306824	−	0.951766i	$-0.599266\pi$
$199$	−8.65656			−0.613648			−0.306824	+	0.951766i	$0.599266\pi$
$200$	0.689567	−	2.74308i	0.0487598	−	0.193965i
$201$	−5.92516	−	1.60902i	−0.417929	−	0.113492i
$202$	−22.5088	+	8.32464i	−1.58371	+	0.585720i
$203$	5.90372	−	22.0330i	0.414360	−	1.54641i
$204$	10.5992	−	1.94533i	0.742092	−	0.136200i
$205$	−0.0941527	−	0.351383i	−0.00657591	−	0.0245416i
$206$	4.74403	−	3.35851i	0.330532	−	0.233998i
$207$	5.68328	−	3.23047i	0.395016	−	0.224533i
$208$	−17.9420	+	1.94454i	−1.24406	+	0.134829i
$209$	−0.676717	−	0.390703i	−0.0468095	−	0.0270255i
$210$	−4.04430	+	4.83756i	−0.279083	+	0.333823i
$211$	5.04976	−	18.8460i	0.347640	−	1.29741i	−0.541858	−	0.840470i	$-0.682279\pi$
$211$	5.04976	−	18.8460i	0.347640	−	1.29741i	0.889498	−	0.456939i	$-0.151054\pi$
$212$	−0.995315	+	1.45323i	−0.0683585	+	0.0998080i
$213$	25.7348	+	0.0865495i	1.76332	+	0.00593027i
$214$	7.66829	−	9.23531i	0.524194	−	0.631313i
$215$		−	0.594995i		−	0.0405783i
$216$	14.1753	−	3.88086i	0.964506	−	0.264059i
$217$		−	11.3750i		−	0.772188i
$218$	3.68046	+	3.05597i	0.249272	+	0.206977i
$219$	−16.1812	−	0.0544196i	−1.09342	−	0.00367733i
$220$	3.04524	−	0.569503i	0.205310	−	0.0383959i
$221$	−3.63262	+	13.5571i	−0.244356	+	0.911950i
$222$	−17.5648	−	14.6845i	−1.17887	−	0.985562i
$223$	1.21921	+	0.703910i	0.0816442	+	0.0471373i	0.540266	−	0.841494i	$-0.318323\pi$
$223$	1.21921	+	0.703910i	0.0816442	+	0.0471373i	−0.458622	+	0.888631i	$0.651657\pi$
$224$	−14.5343	−	0.893566i	−0.971114	−	0.0597039i
$225$	−2.58793	−	1.51744i	−0.172529	−	0.101163i
$226$	6.64590	+	9.38760i	0.442079	+	0.624454i
$227$	3.44025	+	12.8392i	0.228338	+	0.852168i	0.981040	+	0.193806i	$0.0620834\pi$
$227$	3.44025	+	12.8392i	0.228338	+	0.852168i	−0.752702	+	0.658361i	$0.771250\pi$
$228$	−0.992290	+	1.43841i	−0.0657160	+	0.0952611i
$229$	0.972777	−	3.63045i	0.0642829	−	0.239907i	−0.926307	−	0.376769i	$-0.877035\pi$
$229$	0.972777	−	3.63045i	0.0642829	−	0.239907i	0.990590	+	0.136862i	$0.0437017\pi$
$230$	−1.06897	−	2.89035i	−0.0704855	−	0.190584i
$231$	−6.66508	−	1.80995i	−0.438530	−	0.119086i
$232$	12.8669	+	21.5083i	0.844754	+	1.41209i
$233$	−27.2177			−1.78309			−0.891546	−	0.452930i	$-0.850379\pi$
$233$	−27.2177			−1.78309			−0.891546	+	0.452930i	$0.850379\pi$
$234$	−3.35322	+	18.8458i	−0.219207	+	1.23199i
$235$	−4.25857	+	4.25857i	−0.277798	+	0.277798i
$236$	−0.958286	+	12.4335i	−0.0623791	+	0.809352i
$237$	9.12718	−	15.6867i	0.592874	−	1.01896i
$238$	−4.73290	+	10.2884i	−0.306788	+	0.666895i
$239$	10.4675	+	18.1302i	0.677084	+	1.17274i	0.975855	+	0.218420i	$0.0700901\pi$
$239$	10.4675	+	18.1302i	0.677084	+	1.17274i	−0.298771	+	0.954325i	$0.596577\pi$
$240$	−0.723331	−	6.89034i	−0.0466908	−	0.444770i
$241$	−8.21444	+	14.2278i	−0.529139	+	0.916495i	0.470284	+	0.882515i	$0.344152\pi$
$241$	−8.21444	+	14.2278i	−0.529139	+	0.916495i	−0.999423	+	0.0339799i	$0.989182\pi$
$242$	−7.02786	−	9.92713i	−0.451768	−	0.638140i
$243$	0.262117	−	15.5863i	0.0168148	−	0.999859i
$244$	12.1038	+	25.2708i	0.774868	+	1.61780i
$245$	0.0966986	+	0.360884i	0.00617785	+	0.0230560i
$246$	−0.512417	−	0.728997i	−0.0326705	−	0.0464791i
$247$	−1.13799	−	1.97105i	−0.0724084	−	0.125415i
$248$	8.97389	+	8.69960i	0.569842	+	0.552425i
$249$	21.2900	−	5.62796i	1.34920	−	0.356657i
$250$	−0.903423	+	1.08804i	−0.0571375	+	0.0688136i
$251$	−3.99797	−	3.99797i	−0.252350	−	0.252350i	0.569584	−	0.821933i	$-0.307104\pi$
$251$	−3.99797	−	3.99797i	−0.252350	−	0.252350i	−0.821933	+	0.569584i	$0.807104\pi$
$252$	−5.22996	+	14.5326i	−0.329456	+	0.915470i
$253$	2.38680	−	2.38680i	0.150057	−	0.150057i
$254$	29.9508	−	2.77654i	1.87928	−	0.174216i
$255$	−5.19980	−	1.41204i	−0.325624	−	0.0884255i
$256$	11.8207	−	10.7829i	0.738796	−	0.673929i
$257$	5.45266	−	3.14810i	0.340128	−	0.196373i	−0.320201	−	0.947350i	$-0.603750\pi$
$257$	5.45266	−	3.14810i	0.340128	−	0.196373i	0.660328	+	0.750977i	$0.270417\pi$
$258$	−0.500949	−	1.36864i	−0.0311877	−	0.0852075i
$259$	23.2401	−	6.22716i	1.44407	−	0.386937i
$260$	8.51083	+	2.99835i	0.527819	+	0.185950i
$261$	25.7234	−	6.70746i	1.59224	−	0.415181i
$262$	−1.56906	+	9.17589i	−0.0969369	+	0.566888i
$263$	−14.4379	−	8.33575i	−0.890282	−	0.514004i	−0.0162472	−	0.999868i	$-0.505172\pi$
$263$	−14.4379	−	8.33575i	−0.890282	−	0.514004i	−0.874035	+	0.485864i	$0.838505\pi$
$264$	6.52532	−	3.87391i	0.401606	−	0.238422i
$265$	0.762707	−	0.440349i	0.0468527	−	0.0270504i
$266$	−0.637013	−	1.72240i	−0.0390578	−	0.105607i
$267$	0.00837634	−	2.49063i	0.000512623	−	0.152424i
$268$	−0.544798	+	7.06861i	−0.0332789	+	0.431784i
$269$	3.57389	+	3.57389i	0.217904	+	0.217904i	0.807615	−	0.589711i	$-0.200758\pi$
$269$	3.57389	+	3.57389i	0.217904	+	0.217904i	−0.589711	+	0.807615i	$0.700758\pi$
$270$	−7.23047	−	1.31161i	−0.440032	−	0.0798222i
$271$			13.7854i			0.837405i	0.908123	+	0.418703i	$0.137515\pi$
$271$			13.7854i			0.837405i	−0.908123	+	0.418703i	$0.862485\pi$
$272$	−4.49688	−	11.6023i	−0.272663	−	0.703495i
$273$	−14.1764	−	14.2721i	−0.857994	−	0.863785i
$274$	16.7932	+	7.72527i	1.01451	+	0.466701i
$275$	−1.49624	−	0.400915i	−0.0902265	−	0.0241761i
$276$	−4.89238	−	5.74852i	−0.294487	−	0.346020i
$277$	29.2286	−	7.83178i	1.75618	−	0.470566i	0.770250	−	0.637742i	$-0.220132\pi$
$277$	29.2286	−	7.83178i	1.75618	−	0.470566i	0.985927	+	0.167176i	$0.0534649\pi$
$278$	−3.99203	+	23.3454i	−0.239426	+	1.40017i
$279$	11.5250	−	6.55098i	0.689982	−	0.392197i
$280$	6.36115	+	3.54215i	0.380152	+	0.211684i
$281$	−7.28874	+	12.6245i	−0.434810	+	0.753113i	−0.997280	−	0.0737047i	$-0.976518\pi$
$281$	−7.28874	+	12.6245i	−0.434810	+	0.753113i	0.562470	+	0.826818i	$0.309851\pi$
$282$	−6.21031	+	13.3812i	−0.369818	+	0.796840i
$283$	−29.4828	−	7.89989i	−1.75257	−	0.469600i	−0.767399	−	0.641170i	$-0.778449\pi$
$283$	−29.4828	−	7.89989i	−1.75257	−	0.469600i	−0.985172	+	0.171570i	$0.945116\pi$
$284$	−5.46263	−	29.2097i	−0.324147	−	1.73328i
$285$	0.758143	−	0.434321i	0.0449085	−	0.0257270i
$286$	0.912339	+	9.84148i	0.0539478	+	0.581939i
$287$	0.936429			0.0552757
$288$	−7.46509	−	15.2405i	−0.439884	−	0.898054i
$289$	7.32273			0.430749
$290$	−1.15676	−	12.4781i	−0.0679274	−	0.732739i
$291$	12.1483	+	7.06839i	0.712144	+	0.414356i
$292$	3.43473	+	18.3661i	0.201002	+	1.07480i
$293$	−14.5067	−	3.88706i	−0.847491	−	0.227085i	−0.191161	−	0.981559i	$-0.561225\pi$
$293$	−14.5067	−	3.88706i	−0.847491	−	0.227085i	−0.656330	+	0.754474i	$0.727892\pi$
$294$	0.526273	+	0.748708i	0.0306929	+	0.0436656i
$295$	3.11759	−	5.39983i	0.181513	−	0.314390i
$296$	−12.8613	+	23.0969i	−0.747547	+	1.34248i
$297$	−2.00467	−	7.79530i	−0.116323	−	0.452329i
$298$	2.11969	−	12.3960i	0.122790	−	0.718078i
$299$	9.49653	−	2.54459i	0.549199	−	0.147157i
$300$	−1.16203	+	3.26338i	−0.0670901	+	0.188412i
$301$	1.47943	+	0.396413i	0.0852731	+	0.0228489i
$302$	−7.92493	−	3.64567i	−0.456029	−	0.209785i
$303$	28.4164	−	7.51181i	1.63248	−	0.431542i
$304$	1.84601	+	0.814744i	0.105876	+	0.0467288i
$305$		−	14.0100i		−	0.802208i
$306$	−13.1497	+	1.12987i	−0.751717	+	0.0645902i
$307$	−6.53156	−	6.53156i	−0.372776	−	0.372776i	0.495711	−	0.868487i	$-0.334907\pi$
$307$	−6.53156	−	6.53156i	−0.372776	−	0.372776i	−0.868487	+	0.495711i	$0.834907\pi$
$308$	−0.612831	+	7.95131i	−0.0349193	+	0.453068i
$309$	−6.17704	+	3.53867i	−0.351400	+	0.201308i
$310$	−2.16773	−	5.86126i	−0.123119	−	0.332897i
$311$	−4.93371	+	2.84848i	−0.279765	+	0.161523i	−0.633317	−	0.773892i	$-0.718307\pi$
$311$	−4.93371	+	2.84848i	−0.279765	+	0.161523i	0.353552	+	0.935415i	$0.384974\pi$
$312$	22.1014	−	0.268662i	1.25125	−	0.0152100i
$313$	−23.5701	−	13.6082i	−1.33226	−	0.769181i	−0.346615	−	0.938007i	$-0.612669\pi$
$313$	−23.5701	−	13.6082i	−1.33226	−	0.769181i	−0.985646	+	0.168826i	$0.946002\pi$
$314$	−1.42745	+	8.34777i	−0.0805559	+	0.471092i
$315$	5.49726	−	5.42380i	0.309735	−	0.305597i
$316$	−19.7656	−	6.96339i	−1.11190	−	0.391721i
$317$	−12.1693	+	3.26076i	−0.683496	+	0.183142i	−0.583827	−	0.811878i	$-0.698445\pi$
$317$	−12.1693	+	3.26076i	−0.683496	+	0.183142i	−0.0996695	+	0.995021i	$0.531779\pi$
$318$	1.38367	−	1.65506i	0.0775923	−	0.0928114i
$319$	11.8872	−	6.86306i	0.665554	−	0.384258i
$320$	−7.65943	+	2.30935i	−0.428175	+	0.129097i
$321$	−10.4306	+	10.3607i	−0.582179	+	0.578276i
$322$	7.89895	−	0.732260i	0.440191	−	0.0408072i
$323$	1.10964	−	1.10964i	0.0617419	−	0.0617419i
$324$	−17.7362	+	3.07058i	−0.985343	+	0.170588i
$325$	−3.19030	−	3.19030i	−0.176966	−	0.176966i
$326$	11.1745	−	13.4580i	0.618898	−	0.745370i
$327$	−4.12894	−	4.15680i	−0.228331	−	0.229872i
$328$	−0.716179	+	0.738759i	−0.0395444	+	0.0407911i
$329$	−7.75152	−	13.4260i	−0.427355	−	0.740201i
$330$	−3.77926	+	0.337535i	−0.208041	+	0.0185807i
$331$	0.353770	+	1.32029i	0.0194449	+	0.0725695i	0.974967	−	0.222352i	$-0.0713733\pi$
$331$	0.353770	+	1.32029i	0.0194449	+	0.0725695i	−0.955522	+	0.294921i	$0.904707\pi$
$332$	−10.9842	−	22.9332i	−0.602834	−	1.25862i
$333$	19.6934	+	19.9601i	1.07919	+	1.09381i
$334$	−5.90320	−	8.33851i	−0.323009	−	0.456263i
$335$	1.77239	−	3.06987i	0.0968362	−	0.167725i
$336$	17.6145	+	2.79212i	0.960950	+	0.152323i
$337$	8.63041	+	14.9483i	0.470128	+	0.814286i	0.999417	−	0.0341558i	$-0.0108743\pi$
$337$	8.63041	+	14.9483i	0.470128	+	0.814286i	−0.529288	+	0.848442i	$0.677541\pi$
$338$	−4.34770	+	9.45101i	−0.236484	+	0.514067i
$339$	−7.00241	−	12.2233i	−0.380319	−	0.663878i
$340$	−0.478104	+	6.20326i	−0.0259288	+	0.336419i
$341$	4.84012	−	4.84012i	0.262107	−	0.262107i
$342$	1.37825	−	1.63736i	0.0745270	−	0.0885381i
$343$	−18.9810			−1.02488
$344$	−1.44420	+	0.863964i	−0.0778661	+	0.0465818i
$345$	0.964590	+	3.64894i	0.0519318	+	0.196452i
$346$	5.33867	+	14.4351i	0.287009	+	0.776037i
$347$	3.47240	−	12.9592i	0.186408	−	0.695685i	−0.807916	−	0.589297i	$-0.799405\pi$
$347$	3.47240	−	12.9592i	0.186408	−	0.695685i	0.994325	−	0.106388i	$-0.0339286\pi$
$348$	−13.1666	−	27.7288i	−0.705806	−	1.48642i
$349$	−1.88963	−	7.05219i	−0.101150	−	0.377495i	0.896730	−	0.442577i	$-0.145936\pi$
$349$	−1.88963	−	7.05219i	−0.101150	−	0.377495i	−0.997880	+	0.0650820i	$0.979269\pi$
$350$	−2.10347	−	2.97123i	−0.112435	−	0.158819i
$351$	6.29588	−	22.5827i	0.336049	−	1.20537i
$352$	−5.80418	−	6.56461i	−0.309364	−	0.349895i
$353$	−3.50098	−	2.02129i	−0.186339	−	0.107583i	0.403929	−	0.914790i	$-0.367644\pi$
$353$	−3.50098	−	2.02129i	−0.186339	−	0.107583i	−0.590267	+	0.807208i	$0.700978\pi$
$354$	2.62491	−	15.0458i	0.139512	−	0.799673i
$355$	−3.84555	+	14.3518i	−0.204101	+	0.761714i
$356$	−2.82694	+	0.528678i	−0.149828	+	0.0280199i
$357$	6.97534	−	11.9884i	0.369174	−	0.634491i
$358$	−20.4287	−	16.9624i	−1.07969	−	0.896493i
$359$		−	21.3590i		−	1.12729i	−0.826019	−	0.563643i	$-0.809399\pi$
$359$		−	21.3590i		−	1.12729i	0.826019	−	0.563643i	$-0.190601\pi$
$360$	0.0746027	+	8.48495i	0.00393191	+	0.447196i
$361$		−	18.7455i		−	0.986607i
$362$	−9.15359	+	11.0241i	−0.481102	+	0.579416i
$363$	7.40486	+	12.9258i	0.388654	+	0.678428i
$364$	−13.1256	+	19.1642i	−0.687968	+	1.00448i
$365$	2.41796	−	9.02395i	0.126562	−	0.472335i
$366$	−11.7955	−	32.2264i	−0.616563	−	1.68450i
$367$	−10.9939	−	6.34735i	−0.573879	−	0.331329i	0.184818	−	0.982773i	$-0.440830\pi$
$367$	−10.9939	−	6.34735i	−0.573879	−	0.331329i	−0.758697	+	0.651444i	$0.774164\pi$
$368$	−5.46341	+	6.79159i	−0.284800	+	0.354036i
$369$	0.539298	+	0.948772i	0.0280747	+	0.0493911i
$370$	10.7883	−	7.63752i	0.560857	−	0.397056i
$371$	0.586762	+	2.18982i	0.0304632	+	0.113690i
$372$	−9.92113	−	11.6573i	−0.514387	−	0.604401i
$373$	−1.23411	+	4.60578i	−0.0639000	+	0.238478i	−0.990488	−	0.137600i	$-0.956061\pi$
$373$	−1.23411	+	4.60578i	−0.0639000	+	0.238478i	0.926588	+	0.376079i	$0.122728\pi$
$374$	−6.39160	+	2.36386i	−0.330502	+	0.122233i
$375$	1.22886	−	1.22062i	0.0634579	−	0.0630325i
$376$	16.5203	+	4.15294i	0.851968	+	0.214171i
$377$	39.9796			2.05906
$378$	8.07855	−	17.1044i	0.415516	−	0.879757i
$379$	17.9075	−	17.9075i	0.919848	−	0.919848i	−0.0771701	−	0.997018i	$-0.524588\pi$
$379$	17.9075	−	17.9075i	0.919848	−	0.919848i	0.997018	+	0.0771701i	$0.0245885\pi$
$380$	−0.656472	−	0.766115i	−0.0336763	−	0.0393009i
$381$	−36.8391	−	0.123895i	−1.88732	−	0.00634733i
$382$	−29.2201	−	13.4420i	−1.49503	−	0.687752i
$383$	9.49836	+	16.4516i	0.485344	+	0.840640i	0.999858	−	0.0168419i	$-0.00536119\pi$
$383$	9.49836	+	16.4516i	0.485344	+	0.840640i	−0.514515	+	0.857482i	$0.672028\pi$
$384$	−15.6743	+	11.7609i	−0.799874	+	0.600168i
$385$	1.99372	−	3.45323i	0.101610	−	0.175993i
$386$	−4.95766	+	3.50975i	−0.252338	+	0.178642i
$387$	0.450380	+	1.72723i	0.0228941	+	0.0878001i
$388$	5.39268	−	15.3072i	0.273772	−	0.777103i
$389$	−8.46953	−	31.6087i	−0.429422	−	1.60262i	−0.754073	−	0.656791i	$-0.771913\pi$
$389$	−8.46953	−	31.6087i	−0.429422	−	1.60262i	0.324651	−	0.945834i	$-0.394753\pi$
$390$	−10.0245	−	4.65245i	−0.507612	−	0.235586i
$391$	3.38938	+	5.87058i	0.171408	+	0.296888i
$392$	0.735544	−	0.758735i	0.0371506	−	0.0383219i
$393$	2.98788	−	11.0028i	0.150719	−	0.555016i
$394$	22.1172	+	18.3644i	1.11425	+	0.925185i
$395$	7.40920	+	7.40920i	0.372797	+	0.372797i
$396$	−8.40905	+	3.95832i	−0.422571	+	0.198913i
$397$	−22.3724	+	22.3724i	−1.12284	+	1.12284i	−0.131529	+	0.991312i	$0.541988\pi$
$397$	−22.3724	+	22.3724i	−1.12284	+	1.12284i	−0.991312	+	0.131529i	$0.958012\pi$
$398$	−1.13005	−	12.1900i	−0.0566444	−	0.611028i
$399$	0.574814	+	2.17446i	0.0287767	+	0.108859i
$400$	3.95276	+	0.612943i	0.197638	+	0.0306471i
$401$	−2.28643	+	1.32007i	−0.114179	+	0.0659213i	−0.556002	−	0.831181i	$-0.687665\pi$
$401$	−2.28643	+	1.32007i	−0.114179	+	0.0659213i	0.441823	+	0.897102i	$0.354332\pi$
$402$	1.49230	−	8.55372i	0.0744289	−	0.426621i
$403$	19.2577	−	5.16010i	0.959297	−	0.257043i
$404$	−14.6609	−	30.6096i	−0.729408	−	1.52289i
$405$	8.66121	+	2.44610i	0.430379	+	0.121548i
$406$	31.7970	+	5.43723i	1.57806	+	0.269845i
$407$	12.5384	+	7.23906i	0.621506	+	0.358827i
$408$	4.12301	+	14.6716i	0.204120	+	0.726351i
$409$	−15.0795	+	8.70614i	−0.745632	+	0.430491i	−0.824113	−	0.566425i	$-0.808326\pi$
$409$	−15.0795	+	8.70614i	−0.745632	+	0.430491i	0.0784816	+	0.996916i	$0.474993\pi$
$410$	0.482518	−	0.178454i	0.0238299	−	0.00881322i
$411$	−19.5680	−	11.3855i	−0.965217	−	0.561605i
$412$	5.34867	+	6.24200i	0.263510	+	0.307521i
$413$	11.3494	+	11.3494i	0.558467	+	0.558467i
$414$	5.29098	+	7.58135i	0.260038	+	0.372603i
$415$			12.7140i			0.624105i
$416$	−5.08045	−	25.0117i	−0.249090	−	1.22630i
$417$	7.60181	−	27.9934i	0.372262	−	1.37084i
$418$	0.461838	−	1.00394i	0.0225892	−	0.0491043i
$419$	−31.7857	−	8.51696i	−1.55283	−	0.416081i	−0.622448	−	0.782661i	$-0.713862\pi$
$419$	−31.7857	−	8.51696i	−1.55283	−	0.416081i	−0.930386	+	0.366581i	$0.880528\pi$
$420$	−7.34009	−	5.06357i	−0.358159	−	0.247077i
$421$	−35.0422	+	9.38954i	−1.70785	+	0.457618i	−0.974897	−	0.222656i	$-0.928527\pi$
$421$	−35.0422	+	9.38954i	−1.70785	+	0.457618i	−0.732957	+	0.680275i	$0.761861\pi$
$422$	27.1976	+	4.65074i	1.32396	+	0.226395i
$423$	9.13883	−	15.5859i	0.444345	−	0.757811i
$424$	−2.17633	−	1.21187i	−0.105692	−	0.0588536i
$425$	1.55542	−	2.69406i	0.0754487	−	0.130681i
$426$	3.23761	+	36.2504i	0.156863	+	1.75634i
$427$	34.8353	+	9.33408i	1.68580	+	0.451708i
$428$	14.0060	+	9.59270i	0.677005	+	0.463681i
$429$	0.0407105	−	12.1049i	0.00196552	−	0.584431i
$430$	0.837857	−	0.0776722i	0.0404051	−	0.00374569i
$431$	−2.13758			−0.102964			−0.0514819	−	0.998674i	$-0.516394\pi$
$431$	−2.13758			−0.102964			−0.0514819	+	0.998674i	$0.516394\pi$
$432$	7.31542	+	19.4547i	0.351963	+	0.936014i
$433$	−5.68795			−0.273345			−0.136673	−	0.990616i	$-0.543641\pi$
$433$	−5.68795			−0.273345			−0.136673	+	0.990616i	$0.543641\pi$
$434$	16.0181	−	1.48493i	0.768891	−	0.0712789i
$435$	−0.0516171	+	15.3479i	−0.00247485	+	0.735877i
$436$	−3.82289	+	5.58167i	−0.183083	+	0.267314i
$437$	−1.06179	−	0.284505i	−0.0507922	−	0.0136097i
$438$	−2.03571	−	22.7931i	−0.0972698	−	1.08910i
$439$	18.8900	−	32.7184i	0.901570	−	1.56156i	0.0761133	−	0.997099i	$-0.475749\pi$
$439$	18.8900	−	32.7184i	0.901570	−	1.56156i	0.825457	−	0.564466i	$-0.190918\pi$
$440$	1.19949	+	4.21389i	0.0571837	+	0.200889i
$441$	−0.553880	−	0.974427i	−0.0263753	−	0.0464013i
$442$	−19.5650	−	3.34558i	−0.930613	−	0.159133i
$443$	−17.1209	+	4.58754i	−0.813440	+	0.217961i	−0.641476	−	0.767143i	$-0.721678\pi$
$443$	−17.1209	+	4.58754i	−0.813440	+	0.217961i	−0.171963	+	0.985103i	$0.555011\pi$
$444$	18.3854	−	26.6513i	0.872535	−	1.26481i
$445$	1.38898	+	0.372176i	0.0658439	+	0.0176428i
$446$	−0.832070	+	1.80875i	−0.0393997	+	0.0856468i
$447$	−4.03641	+	14.8639i	−0.190915	+	0.703040i
$448$	−0.639050	−	20.5835i	−0.0301923	−	0.972479i
$449$			18.7225i			0.883570i	0.897121	+	0.441785i	$0.145655\pi$
$449$			18.7225i			0.883570i	−0.897121	+	0.441785i	$0.854345\pi$
$450$	1.79899	−	3.84235i	0.0848051	−	0.181130i
$451$	0.398454	+	0.398454i	0.0187625	+	0.0187625i
$452$	−12.3518	+	10.5841i	−0.580981	+	0.497833i
$453$	9.23441	+	5.37298i	0.433870	+	0.252445i
$454$	−17.6307	+	6.52055i	−0.827452	+	0.306024i
$455$	10.0581	−	5.80705i	0.471531	−	0.272239i
$456$	−2.15507	−	1.20955i	−0.100920	−	0.0566421i
$457$	−18.6423	−	10.7632i	−0.872052	−	0.503479i	−0.00402243	−	0.999992i	$-0.501280\pi$
$457$	−18.6423	−	10.7632i	−0.872052	−	0.503479i	−0.868030	+	0.496512i	$0.834614\pi$
$458$	5.23931	+	0.895912i	0.244817	+	0.0418632i
$459$	16.1635	+	0.163085i	0.754449	+	0.00761217i
$460$	3.93058	−	1.88261i	0.183264	−	0.0877769i
$461$	−32.6735	+	8.75485i	−1.52176	+	0.407754i	−0.920320	−	0.391165i	$-0.872072\pi$
$461$	−32.6735	+	8.75485i	−1.52176	+	0.407754i	−0.601438	+	0.798919i	$0.705405\pi$
$462$	1.67865	−	9.62188i	0.0780978	−	0.447650i
$463$	−20.8663	+	12.0472i	−0.969738	+	0.559879i	−0.899156	−	0.437627i	$-0.855819\pi$
$463$	−20.8663	+	12.0472i	−0.969738	+	0.559879i	−0.0705818	+	0.997506i	$0.522486\pi$
$464$	−28.6078	+	20.9266i	−1.32808	+	0.971494i
$465$	1.95607	+	7.39959i	0.0907104	+	0.343148i
$466$	−3.55308	−	38.3273i	−0.164593	−	1.77548i
$467$	−15.4673	+	15.4673i	−0.715740	+	0.715740i	−0.967730	−	0.251990i	$-0.918915\pi$
$467$	−15.4673	+	15.4673i	−0.715740	+	0.715740i	0.251990	+	0.967730i	$0.418915\pi$
$468$	−26.9760	−	2.26174i	−1.24697	−	0.104549i
$469$	6.45228	+	6.45228i	0.297939	+	0.297939i
$470$	−6.55274	−	5.44089i	−0.302255	−	0.250969i
$471$	2.71823	−	10.0098i	0.125249	−	0.461226i
$472$	−17.6336	+	0.273667i	−0.811654	+	0.0125966i
$473$	0.460829	+	0.798179i	0.0211889	+	0.0367003i
$474$	23.2811	+	10.8049i	1.06934	+	0.496285i
$475$	0.130562	+	0.487263i	0.00599059	+	0.0223572i
$476$	−15.1057	−	5.32169i	−0.692367	−	0.243919i
$477$	−1.88077	+	1.85563i	−0.0861144	+	0.0849637i
$478$	−24.1640	+	17.1068i	−1.10524	+	0.782447i
$479$	12.1204	−	20.9932i	0.553796	−	0.959202i	−0.444201	−	0.895927i	$-0.646512\pi$
$479$	12.1204	−	20.9932i	0.553796	−	0.959202i	0.997996	−	0.0632748i	$-0.0201544\pi$
$480$	9.60838	−	1.91806i	0.438561	−	0.0875471i
$481$	21.0850	+	36.5202i	0.961391	+	1.66518i
$482$	−21.1076	−	9.71004i	−0.961426	−	0.442280i
$483$	−9.71562	−	0.0326749i	−0.442076	−	0.00148676i
$484$	13.0617	−	11.1924i	0.593714	−	0.508744i
$485$	−5.73792	+	5.73792i	−0.260546	+	0.260546i
$486$	21.9824	−	1.66557i	0.997142	−	0.0755516i
$487$	−2.89338			−0.131112			−0.0655558	−	0.997849i	$-0.520882\pi$
$487$	−2.89338			−0.131112			−0.0655558	+	0.997849i	$0.520882\pi$
$488$	−34.0057	+	20.3432i	−1.53937	+	0.920895i
$489$	−15.1998	+	15.0979i	−0.687359	+	0.682751i
$490$	−0.495565	+	0.183279i	−0.0223873	+	0.00827972i
$491$	1.38806	−	5.18031i	0.0626423	−	0.233784i	−0.927506	−	0.373809i	$-0.878052\pi$
$491$	1.38806	−	5.18031i	0.0626423	−	0.233784i	0.990148	+	0.140025i	$0.0447182\pi$
$492$	0.959663	−	0.816739i	0.0432649	−	0.0368214i
$493$	7.13451	+	26.6264i	0.321322	+	1.19919i
$494$	2.62703	−	1.85979i	0.118196	−	0.0836760i
$495$	4.64695	+	0.0312570i	0.208865	+	0.00140490i
$496$	−11.0791	+	13.7725i	−0.497466	+	0.618402i
$497$	−33.1231	−	19.1236i	−1.48577	−	0.857812i
$498$	10.7044	+	29.2453i	0.479676	+	1.31051i
$499$	4.24677	−	15.8492i	0.190112	−	0.709506i	−0.803367	−	0.595485i	$-0.796960\pi$
$499$	4.24677	−	15.8492i	0.190112	−	0.709506i	0.993478	−	0.114022i	$-0.0363733\pi$
$500$	−1.65008	−	1.13014i	−0.0737940	−	0.0505415i
$501$	6.21987	+	10.8573i	0.277883	+	0.485068i
$502$	5.10794	−	6.15176i	0.227979	−	0.274566i
$503$			37.4609i			1.67030i	0.550022	+	0.835150i	$0.314619\pi$
$503$			37.4609i			1.67030i	−0.550022	+	0.835150i	$0.685381\pi$
$504$	−21.1472	−	5.46757i	−0.941973	−	0.243545i
$505$			16.9698i			0.755145i
$506$	3.67261	+	3.04945i	0.163267	+	0.135565i
$507$	6.40764	−	11.0126i	0.284573	−	0.489089i
$508$	7.81971	+	41.8135i	0.346943	+	1.85517i
$509$	2.28234	−	8.51783i	0.101163	−	0.377546i	−0.896719	−	0.442601i	$-0.854056\pi$
$509$	2.28234	−	8.51783i	0.101163	−	0.377546i	0.997882	+	0.0650553i	$0.0207224\pi$
$510$	1.30961	−	7.50657i	0.0579904	−	0.332396i
$511$	20.8268	+	12.0243i	0.921322	+	0.531925i
$512$	16.7273	+	15.2381i	0.739248	+	0.673433i
$513$	−1.87208	+	1.83468i	−0.0826544	+	0.0810032i
$514$	5.14488	+	7.26734i	0.226931	+	0.320549i
$515$	−1.06377	−	3.97003i	−0.0468751	−	0.174940i
$516$	1.86188	−	0.884090i	0.0819648	−	0.0389199i
$517$	2.41452	−	9.01112i	0.106191	−	0.396309i
$518$	11.8028	+	31.9132i	0.518583	+	1.40219i
$519$	−4.81740	−	18.2237i	−0.211460	−	0.799932i
$520$	−3.11117	+	12.3762i	−0.136434	+	0.542731i
$521$	−26.4730			−1.15980			−0.579901	−	0.814687i	$-0.696909\pi$
$521$	−26.4730			−1.15980			−0.579901	+	0.814687i	$0.696909\pi$
$522$	12.8033	+	35.3475i	0.560385	+	1.54712i
$523$	19.9244	−	19.9244i	0.871234	−	0.871234i	−0.121373	−	0.992607i	$-0.538730\pi$
$523$	19.9244	−	19.9244i	0.871234	−	0.871234i	0.992607	+	0.121373i	$0.0387296\pi$
$524$	−13.1261	−	1.01167i	−0.573416	−	0.0441949i
$525$	2.21630	+	3.86874i	0.0967274	+	0.168846i
$526$	9.85343	−	21.4193i	0.429630	−	0.933927i
$527$	6.87323	+	11.9048i	0.299403	+	0.518580i
$528$	6.30697	+	8.68309i	0.274476	+	0.377883i
$529$	−9.12580	+	15.8063i	−0.396774	+	0.687232i
$530$	0.719655	+	1.01654i	0.0312598	+	0.0441557i
$531$	−4.96277	+	18.0352i	−0.215366	+	0.782661i
$532$	2.34229	−	1.12187i	0.101551	−	0.0486394i
$533$	0.424796	+	1.58536i	0.0183999	+	0.0686695i
$534$	3.50834	−	0.313339i	0.151821	−	0.0135595i
$535$	−4.24402	−	7.35086i	−0.183485	−	0.317805i
$536$	−10.0250	+	0.155584i	−0.433012	+	0.00672019i
$537$	22.9180	+	23.0727i	0.988986	+	0.995661i
$538$	−4.56612	+	5.49921i	−0.196859	+	0.237088i
$539$	−0.409228	−	0.409228i	−0.0176267	−	0.0176267i
$540$	0.903096	−	10.3530i	0.0388631	−	0.445522i
$541$	3.69250	−	3.69250i	0.158753	−	0.158753i	−0.623261	−	0.782014i	$-0.714193\pi$
$541$	3.69250	−	3.69250i	0.158753	−	0.158753i	0.782014	+	0.623261i	$0.214193\pi$
$542$	−19.4123	+	1.79959i	−0.833830	+	0.0772989i
$543$	12.4509	−	12.3675i	0.534320	−	0.530738i
$544$	15.7511	−	7.84700i	0.675323	−	0.336437i
$545$	2.92947	−	1.69133i	0.125485	−	0.0724486i
$546$	18.2470	−	21.8260i	0.780897	−	0.934065i
$547$	29.4157	−	7.88191i	1.25772	−	0.337006i	0.432408	−	0.901678i	$-0.357664\pi$
$547$	29.4157	−	7.88191i	1.25772	−	0.337006i	0.825315	+	0.564672i	$0.190997\pi$
$548$	−8.68632	+	24.6562i	−0.371061	+	1.05326i
$549$	10.6048	+	40.6700i	0.452603	+	1.73575i
$550$	0.369236	−	2.15930i	0.0157443	−	0.0920729i
$551$	−3.87117	−	2.23502i	−0.164917	−	0.0952151i
$552$	7.45626	−	7.63976i	0.317359	−	0.325170i
$553$	−23.3590	+	13.4864i	−0.993328	+	0.573498i
$554$	14.8441	+	40.1366i	0.630666	+	1.70524i
$555$	−14.0471	+	8.04723i	−0.596266	+	0.341586i
$556$	−33.3956	−	2.57390i	−1.41629	−	0.109158i
$557$	29.3791	+	29.3791i	1.24483	+	1.24483i	0.957972	+	0.286861i	$0.0926119\pi$
$557$	29.3791	+	29.3791i	1.24483	+	1.24483i	0.286861	+	0.957972i	$0.407388\pi$
$558$	10.7294	+	15.3740i	0.454213	+	0.650833i
$559$			2.68448i			0.113541i
$560$	−4.15757	+	9.42002i	−0.175689	+	0.398069i
$561$	8.06912	−	2.13305i	0.340678	−	0.0900576i
$562$	−18.7290	−	8.61580i	−0.790034	−	0.363435i
$563$	16.8496	+	4.51484i	0.710127	+	0.190278i	0.595762	−	0.803161i	$-0.296850\pi$
$563$	16.8496	+	4.51484i	0.710127	+	0.190278i	0.114365	+	0.993439i	$0.463517\pi$
$564$	−19.6538	−	6.99838i	−0.827575	−	0.294685i
$565$	7.85598	−	2.10500i	0.330504	−	0.0885582i
$566$	7.27567	−	42.5482i	0.305819	−	1.78844i
$567$	−11.8526	+	19.9061i	−0.497764	+	0.835977i
$568$	40.4193	−	11.5055i	1.69596	−	0.482758i
$569$	8.72565	−	15.1133i	0.365798	−	0.633581i	−0.623106	−	0.782138i	$-0.714129\pi$
$569$	8.72565	−	15.1133i	0.365798	−	0.633581i	0.988904	+	0.148557i	$0.0474627\pi$
$570$	0.710571	+	1.01090i	0.0297625	+	0.0423420i
$571$	−1.01310	−	0.271460i	−0.0423970	−	0.0113602i	0.237558	−	0.971373i	$-0.423653\pi$
$571$	−1.01310	−	0.271460i	−0.0423970	−	0.0113602i	−0.279955	+	0.960013i	$0.590320\pi$
$572$	−13.7394	+	2.56947i	−0.574475	+	0.107435i
$573$	34.0483	+	19.8108i	1.42239	+	0.827607i
$574$	0.122244	+	1.31866i	0.00510237	+	0.0550397i
$575$	−2.17908			−0.0908741
$576$	20.4868	−	12.5017i	0.853615	−	0.520904i
$577$	22.6611			0.943395			0.471698	−	0.881760i	$-0.343641\pi$
$577$	22.6611			0.943395			0.471698	+	0.881760i	$0.343641\pi$
$578$	0.955930	+	10.3117i	0.0397614	+	0.428910i
$579$	6.45521	−	3.69803i	0.268269	−	0.153685i
$580$	17.4203	−	3.25785i	0.723340	−	0.135275i
$581$	−31.6129	−	8.47064i	−1.31152	−	0.351421i
$582$	−8.36767	+	18.0296i	−0.346851	+	0.747352i
$583$	−0.682109	+	1.18145i	−0.0282501	+	0.0489305i
$584$	−25.4144	+	7.23427i	−1.05165	+	0.299356i
$585$	11.6761	+	6.84635i	0.482749	+	0.283062i
$586$	3.57992	−	20.9354i	0.147885	−	0.864834i
$587$	−34.4031	+	9.21829i	−1.41997	+	0.380479i	−0.885473	−	0.464692i	$-0.846165\pi$
$587$	−34.4031	+	9.21829i	−1.41997	+	0.380479i	−0.534496	+	0.845171i	$0.679499\pi$
$588$	−0.985612	+	0.838823i	−0.0406459	+	0.0345925i
$589$	−2.15317	−	0.576940i	−0.0887198	−	0.0237724i
$590$	8.01089	+	3.68521i	0.329803	+	0.151718i
$591$	−24.8122	−	24.9797i	−1.02064	−	1.02753i
$592$	−34.2034	−	15.0958i	−1.40575	−	0.620434i
$593$		−	26.2004i		−	1.07592i	−0.842970	−	0.537961i	$-0.819195\pi$
$593$		−	26.2004i		−	1.07592i	0.842970	−	0.537961i	$-0.180805\pi$
$594$	10.7155	−	3.84055i	0.439660	−	0.157580i
$595$	5.66239	+	5.66239i	0.232135	+	0.232135i
$596$	17.7324	+	1.36669i	0.726347	+	0.0559817i
$597$	−0.0504252	+	14.9935i	−0.00206377	+	0.613644i
$598$	4.82293	+	13.0406i	0.197224	+	0.533270i
$599$	−0.876558	+	0.506081i	−0.0358152	+	0.0206779i	−0.517801	−	0.855501i	$-0.673249\pi$
$599$	−0.876558	+	0.506081i	−0.0358152	+	0.0206779i	0.481986	+	0.876179i	$0.339916\pi$
$600$	−4.74711	−	1.21034i	−0.193800	−	0.0494118i
$601$	−30.0737	−	17.3631i	−1.22673	−	0.708254i	−0.260387	−	0.965504i	$-0.583850\pi$
$601$	−30.0737	−	17.3631i	−1.22673	−	0.708254i	−0.966345	+	0.257250i	$0.917184\pi$
$602$	−0.365090	+	2.13505i	−0.0148799	+	0.0870181i
$603$	−2.82140	+	10.2533i	−0.114896	+	0.417545i
$604$	4.09920	−	11.6356i	0.166794	−	0.473446i
$605$	−8.30749	+	2.22598i	−0.337747	+	0.0904991i
$606$	14.2875	+	39.0347i	0.580390	+	1.58568i
$607$	−33.5181	+	19.3517i	−1.36046	+	0.785461i	−0.989685	−	0.143263i	$-0.954241\pi$
$607$	−33.5181	+	19.3517i	−1.36046	+	0.785461i	−0.370773	+	0.928724i	$0.620907\pi$
$608$	−0.906320	+	2.70586i	−0.0367561	+	0.109737i
$609$	−38.1277	−	10.3538i	−1.54501	−	0.419559i
$610$	19.7285	−	1.82890i	0.798783	−	0.0740500i
$611$	19.2137	−	19.2137i	0.777303	−	0.777303i
$612$	−3.30765	−	18.3696i	−0.133704	−	0.742546i
$613$	10.9098	+	10.9098i	0.440641	+	0.440641i	0.892227	−	0.451586i	$-0.149142\pi$
$613$	10.9098	+	10.9098i	0.440641	+	0.440641i	−0.451586	+	0.892227i	$0.649142\pi$
$614$	8.34494	−	10.0502i	0.336774	−	0.405595i
$615$	−0.609158	+	0.161030i	−0.0245636	+	0.00649334i
$616$	−11.2768	+	0.175012i	−0.454357	+	0.00705145i
$617$	6.74400	+	11.6809i	0.271503	+	0.470257i	0.969247	−	0.246090i	$-0.0791459\pi$
$617$	6.74400	+	11.6809i	0.271503	+	0.470257i	−0.697744	+	0.716347i	$0.745813\pi$
$618$	−5.78944	−	8.23642i	−0.232885	−	0.331317i
$619$	5.80618	+	21.6689i	0.233370	+	0.870948i	0.978877	+	0.204451i	$0.0655408\pi$
$619$	5.80618	+	21.6689i	0.233370	+	0.870948i	−0.745507	+	0.666498i	$0.767793\pi$
$620$	7.97070	−	3.81768i	0.320111	−	0.153322i
$621$	−5.56220	−	9.86250i	−0.223204	−	0.395768i
$622$	−4.65522	−	6.57569i	−0.186657	−	0.263661i
$623$	−1.85080	+	3.20568i	−0.0741508	+	0.128433i
$624$	3.26351	+	31.0876i	0.130645	+	1.24450i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	16.0858	−	34.9673i	0.642919	−	1.39757i
$627$	−0.680655	+	1.16983i	−0.0271828	+	0.0467183i
$628$	−11.9415	−	0.920365i	−0.476517	−	0.0367265i
$629$	−20.5597	+	20.5597i	−0.819769	+	0.819769i
$630$	8.35529	+	7.03307i	0.332883	+	0.280204i
$631$	37.3930			1.48859			0.744296	−	0.667850i	$-0.232785\pi$
$631$	37.3930			1.48859			0.744296	+	0.667850i	$0.232785\pi$
$632$	7.22542	−	28.7425i	0.287412	−	1.14332i
$633$	−32.6126	−	8.85617i	−1.29623	−	0.352001i
$634$	−6.18033	−	16.7108i	−0.245452	−	0.663673i
$635$	5.50487	−	20.5445i	0.218454	−	0.815282i
$636$	2.51125	+	1.73239i	0.0995775	+	0.0686938i
$637$	−0.436282	−	1.62823i	−0.0172861	−	0.0645127i
$638$	11.2162	+	15.8433i	0.444053	+	0.627243i
$639$	0.299815	−	44.5732i	0.0118605	−	1.76329i
$640$	−4.25185	−	10.4844i	−0.168069	−	0.414431i
$641$	8.05618	+	4.65124i	0.318200	+	0.183713i	0.650590	−	0.759429i	$-0.274522\pi$
$641$	8.05618	+	4.65124i	0.318200	+	0.183713i	−0.332390	+	0.943142i	$0.607855\pi$
$642$	−15.9513	−	13.3356i	−0.629547	−	0.526314i
$643$	4.58413	−	17.1082i	0.180780	−	0.674681i	−0.814714	−	0.579863i	$-0.803106\pi$
$643$	4.58413	−	17.1082i	0.180780	−	0.674681i	0.995495	−	0.0948187i	$-0.0302271\pi$
$644$	2.06230	+	11.0275i	0.0812660	+	0.434545i
$645$	−1.03056	−	0.00346590i	−0.0405781	−	0.000136470i
$646$	1.70742	+	1.41771i	0.0671776	+	0.0557791i
$647$			24.8891i			0.978493i	0.872146	+	0.489246i	$0.162728\pi$
$647$			24.8891i			0.978493i	−0.872146	+	0.489246i	$0.837272\pi$
$648$	−6.63924	−	24.5748i	−0.260814	−	0.965389i
$649$			9.65841i			0.379126i
$650$	4.07604	−	4.90898i	0.159875	−	0.192546i
$651$	−19.7020	−	0.0662606i	−0.772183	−	0.00259696i
$652$	20.4100	+	13.9788i	0.799317	+	0.547452i
$653$	5.47711	−	20.4409i	0.214336	−	0.799912i	−0.772063	−	0.635546i	$-0.780775\pi$
$653$	5.47711	−	20.4409i	0.214336	−	0.799912i	0.986399	−	0.164367i	$-0.0525581\pi$
$654$	5.31451	−	6.35691i	0.207814	−	0.248575i
$655$	5.70062	+	3.29125i	0.222742	+	0.128600i
$656$	−1.13379	−	0.912066i	−0.0442672	−	0.0356102i
$657$	−0.188514	+	28.0262i	−0.00735463	+	1.09341i
$658$	17.8943	−	12.6682i	0.697593	−	0.493857i
$659$	0.581885	+	2.17162i	0.0226670	+	0.0845945i	0.976333	−	0.216274i	$-0.0693903\pi$
$659$	0.581885	+	2.17162i	0.0226670	+	0.0845945i	−0.953666	+	0.300868i	$0.902724\pi$
$660$	−0.968664	−	5.27780i	−0.0377052	−	0.205438i
$661$	9.92827	−	37.0528i	0.386165	−	1.44119i	−0.450158	−	0.892949i	$-0.648632\pi$
$661$	9.92827	−	37.0528i	0.386165	−	1.44119i	0.836323	−	0.548238i	$-0.184701\pi$
$662$	−1.81301	+	0.670524i	−0.0704648	+	0.0260607i
$663$	23.4603	+	6.37082i	0.911123	+	0.247422i
$664$	30.8600	−	18.4614i	1.19760	−	0.716441i
$665$	−1.29855			−0.0503556
$666$	−25.5365	+	30.3374i	−0.989521	+	1.17555i
$667$	13.6537	−	13.6537i	0.528674	−	0.528674i
$668$	10.9715	−	9.40128i	0.424499	−	0.363746i
$669$	1.22630	−	2.10762i	0.0474116	−	0.0814852i
$670$	4.55430	+	2.09509i	0.175948	+	0.0809404i
$671$	10.8508	+	18.7942i	0.418892	+	0.725543i
$672$	−1.63236	+	25.1688i	−0.0629695	+	0.970907i
$673$	−8.83129	+	15.2962i	−0.340421	+	0.589627i	−0.984511	−	0.175323i	$-0.943903\pi$
$673$	−8.83129	+	15.2962i	−0.340421	+	0.589627i	0.644090	+	0.764950i	$0.277236\pi$
$674$	−19.9232	+	14.1045i	−0.767413	+	0.543286i
$675$	−2.64335	+	4.47356i	−0.101742	+	0.172187i
$676$	−13.8762	−	4.88857i	−0.533702	−	0.188022i
$677$	−4.25903	−	15.8949i	−0.163688	−	0.610891i	−0.998204	−	0.0599074i	$-0.980919\pi$
$677$	−4.25903	−	15.8949i	−0.163688	−	0.610891i	0.834516	−	0.550983i	$-0.185747\pi$
$678$	16.2984	−	11.4563i	0.625937	−	0.439976i
$679$	−10.4443	−	18.0900i	−0.400814	−	0.694231i
$680$	−8.79770	+	0.136537i	−0.337376	+	0.00523595i
$681$	22.2581	−	5.88387i	0.852931	−	0.225470i
$682$	7.44758	+	6.18389i	0.285183	+	0.236794i
$683$	−11.0699	−	11.0699i	−0.423578	−	0.423578i	0.462856	−	0.886434i	$-0.346825\pi$
$683$	−11.0699	−	11.0699i	−0.423578	−	0.423578i	−0.886434	+	0.462856i	$0.846825\pi$
$684$	2.48561	+	1.72707i	0.0950395	+	0.0660360i
$685$	9.24243	−	9.24243i	0.353135	−	0.353135i
$686$	−2.47783	−	26.7286i	−0.0946040	−	1.02050i
$687$	−6.28243	−	1.70604i	−0.239690	−	0.0650894i
$688$	−1.40514	−	1.92090i	−0.0535706	−	0.0732338i
$689$	−3.44116	+	1.98676i	−0.131098	+	0.0756894i
$690$	−5.01243	+	1.83466i	−0.190820	+	0.0698441i
$691$	11.4986	−	3.08103i	0.437426	−	0.117208i	−0.0333842	−	0.999443i	$-0.510628\pi$
$691$	11.4986	−	3.08103i	0.437426	−	0.117208i	0.470810	+	0.882235i	$0.343962\pi$
$692$	−19.6303	+	9.40219i	−0.746230	+	0.357418i
$693$	−3.17373	+	11.5336i	−0.120560	+	0.438127i
$694$	18.7021	+	3.19802i	0.709922	+	0.121395i
$695$	14.5036	+	8.37366i	0.550153	+	0.317631i
$696$	37.3282	−	22.1607i	1.41492	−	0.840000i
$697$	−0.980040	+	0.565826i	−0.0371217	+	0.0214322i
$698$	9.68405	−	3.58154i	0.366547	−	0.135563i
$699$	−0.158546	+	47.1422i	−0.00599675	+	1.78308i
$700$	3.90942	−	3.34992i	0.147762	−	0.126615i
$701$	27.0773	+	27.0773i	1.02270	+	1.02270i	0.999736	+	0.0229600i	$0.00730903\pi$
$701$	27.0773	+	27.0773i	1.02270	+	1.02270i	0.0229600	+	0.999736i	$0.492691\pi$
$702$	32.6222	+	5.91770i	1.23125	+	0.223349i
$703$		−	4.71493i		−	0.177827i
$704$	8.48643	−	9.03027i	0.319844	−	0.340341i
$705$	7.35121	+	7.40082i	0.276863	+	0.278731i
$706$	2.38931	−	5.19387i	0.0899228	−	0.195474i
$707$	−42.1947	−	11.3060i	−1.58690	−	0.425207i
$708$	21.5297	+	1.73222i	0.809137	+	0.0651007i
$709$	−25.3703	+	6.79795i	−0.952801	+	0.255302i	−0.701550	−	0.712620i	$-0.747508\pi$
$709$	−25.3703	+	6.79795i	−0.952801	+	0.255302i	−0.251250	+	0.967922i	$0.580842\pi$
$710$	−20.7118	−	3.54169i	−0.777301	−	0.132917i
$711$	−27.1168	−	15.9000i	−1.01696	−	0.596298i
$712$	−1.11351	−	3.91182i	−0.0417305	−	0.146601i
$713$	4.81458	−	8.33910i	0.180307	−	0.312302i
$714$	17.7923	+	8.25751i	0.665859	+	0.309030i
$715$	6.75068	+	1.80884i	0.252461	+	0.0676467i
$716$	21.2193	−	30.9816i	0.793001	−	1.15784i
$717$	31.4632	−	18.0245i	1.17502	−	0.673136i
$718$	30.0772	−	2.78826i	1.12247	−	0.104057i
$719$	4.76649			0.177760			0.0888800	−	0.996042i	$-0.471671\pi$
$719$	4.76649			0.177760			0.0888800	+	0.996042i	$0.471671\pi$
$720$	−11.9386	+	1.21270i	−0.444924	+	0.0451948i
$721$	10.5801			0.394022
$722$	26.3970	−	2.44709i	0.982394	−	0.0910714i
$723$	24.5953	+	14.3106i	0.914710	+	0.532218i
$724$	−16.7188	−	11.4507i	−0.621351	−	0.425563i
$725$	−8.55924	−	2.29344i	−0.317882	−	0.0851763i
$726$	−17.2351	+	12.1147i	−0.639656	+	0.449619i
$727$	−2.92361	+	5.06385i	−0.108431	+	0.187808i	−0.915135	−	0.403148i	$-0.867916\pi$
$727$	−2.92361	+	5.06385i	−0.108431	+	0.187808i	0.806704	+	0.590956i	$0.201249\pi$
$728$	−28.7001	−	15.9814i	−1.06370	−	0.592309i
$729$	−26.9945	−	0.544789i	−0.999796	−	0.0201774i
$730$	13.0229	+	2.22690i	0.482001	+	0.0824213i
$731$	−1.78786	+	0.479055i	−0.0661264	+	0.0177185i
$732$	43.8406	−	20.8171i	1.62040	−	0.769423i
$733$	−11.3348	−	3.03716i	−0.418661	−	0.112180i	0.0433374	−	0.999060i	$-0.486201\pi$
$733$	−11.3348	−	3.03716i	−0.418661	−	0.112180i	−0.461999	+	0.886880i	$0.652868\pi$
$734$	7.50301	−	16.3100i	0.276941	−	0.602013i
$735$	0.625629	−	0.165384i	0.0230767	−	0.00610027i
$736$	−10.2770	−	6.80684i	−0.378814	−	0.250904i
$737$			5.49094i			0.202261i
$738$	−1.26564	+	0.883282i	−0.0465887	+	0.0325140i
$739$	−9.91629	−	9.91629i	−0.364777	−	0.364777i	0.500791	−	0.865568i	$-0.333042\pi$
$739$	−9.91629	−	9.91629i	−0.364777	−	0.364777i	−0.865568	+	0.500791i	$0.833042\pi$
$740$	12.1633	+	14.1948i	0.447132	+	0.521811i
$741$	−3.42057	+	1.95956i	−0.125658	+	0.0719862i
$742$	−3.00706	+	1.11213i	−0.110393	+	0.0408275i
$743$	32.8301	−	18.9545i	1.20442	−	0.695372i	0.242885	−	0.970055i	$-0.421906\pi$
$743$	32.8301	−	18.9545i	1.20442	−	0.695372i	0.961535	+	0.274682i	$0.0885727\pi$
$744$	15.1203	−	15.4925i	0.554338	−	0.567981i
$745$	−7.70112	−	4.44625i	−0.282147	−	0.162898i
$746$	−6.64685	−	1.13660i	−0.243358	−	0.0416139i
$747$	−9.62383	−	36.9079i	−0.352118	−	1.35039i
$748$	−4.16311	−	8.69191i	−0.152218	−	0.317808i
$749$	21.1052	−	5.65512i	0.771168	−	0.206634i
$750$	1.87926	+	1.57110i	0.0686210	+	0.0573686i
$751$	−25.6238	+	14.7939i	−0.935024	+	0.539837i	−0.888397	−	0.459076i	$-0.848181\pi$
$751$	−25.6238	+	14.7939i	−0.935024	+	0.539837i	−0.0466273	+	0.998912i	$0.514847\pi$
$752$	−3.69146	+	23.8056i	−0.134614	+	0.868101i
$753$	−6.94794	+	6.90137i	−0.253197	+	0.251500i
$754$	5.21905	+	56.2983i	0.190067	+	2.05026i
$755$	−4.36164	+	4.36164i	−0.158736	+	0.158736i
$756$	25.1407	+	9.14315i	0.914357	+	0.332533i
$757$	−12.5836	−	12.5836i	−0.457358	−	0.457358i	0.440430	−	0.897787i	$-0.354826\pi$
$757$	−12.5836	−	12.5836i	−0.457358	−	0.457358i	−0.897787	+	0.440430i	$0.854826\pi$
$758$	27.5546	+	22.8792i	1.00083	+	0.831012i
$759$	−4.12013	−	4.14793i	−0.149551	−	0.150560i
$760$	0.993127	−	1.02444i	0.0360245	−	0.0371603i
$761$	14.5441	+	25.1912i	0.527225	+	0.913180i	0.999497	+	0.0317273i	$0.0101008\pi$
$761$	14.5441	+	25.1912i	0.527225	+	0.913180i	−0.472272	+	0.881453i	$0.656566\pi$
$762$	−4.63461	−	51.8921i	−0.167894	−	1.87985i
$763$	2.25368	+	8.41086i	0.0815888	+	0.304494i
$764$	15.1142	−	42.9018i	0.546813	−	1.55213i
$765$	−2.47601	+	8.99804i	−0.0895202	+	0.325325i
$766$	−21.9269	+	15.5230i	−0.792250	+	0.560869i
$767$	−14.0659	+	24.3628i	−0.507889	+	0.879690i
$768$	−18.6075	−	20.5368i	−0.671440	−	0.741058i
$769$	24.9374	+	43.1928i	0.899265	+	1.55757i	0.828436	+	0.560084i	$0.189231\pi$
$769$	24.9374	+	43.1928i	0.899265	+	1.55757i	0.0708295	+	0.997488i	$0.477435\pi$
$770$	5.12302	+	2.35672i	0.184621	+	0.0849302i
$771$	−5.42087	−	9.46257i	−0.195228	−	0.340786i
$772$	−5.58953	−	6.52308i	−0.201172	−	0.234771i
$773$	−14.9664	+	14.9664i	−0.538305	+	0.538305i	−0.923031	−	0.384726i	$-0.874296\pi$
$773$	−14.9664	+	14.9664i	−0.538305	+	0.538305i	0.384726	+	0.923031i	$0.374296\pi$
$774$	−2.37345	+	0.859692i	−0.0853119	+	0.0309010i
$775$	−4.41890			−0.158732
$776$	22.2591	+	5.59560i	0.799057	+	0.200870i
$777$	−10.6503	−	40.2890i	−0.382078	−	1.44536i
$778$	43.4050	−	16.0529i	1.55614	−	0.575523i
$779$	0.0474956	−	0.177256i	0.00170170	−	0.00635085i
$780$	5.24284	−	14.7236i	0.187724	−	0.527191i
$781$	−5.95682	−	22.2312i	−0.213152	−	0.795494i
$782$	−7.82435	+	5.53920i	−0.279798	+	0.198082i
$783$	−11.4677	−	44.5931i	−0.409824	−	1.59363i
$784$	1.16445	+	0.936728i	0.0415876	+	0.0334546i
$785$	5.18615	+	2.99422i	0.185101	+	0.106868i
$786$	15.8839	+	2.77113i	0.566559	+	0.0988428i
$787$	−5.43805	+	20.2951i	−0.193846	+	0.723442i	0.798717	+	0.601707i	$0.205512\pi$
$787$	−5.43805	+	20.2951i	−0.193846	+	0.723442i	−0.992563	+	0.121735i	$0.961154\pi$
$788$	−22.9731	+	33.5422i	−0.818381	+	1.19489i
$789$	−14.5220	+	24.9586i	−0.516996	+	0.888548i
$790$	−9.46623	+	11.4007i	−0.336794	+	0.405618i
$791$			20.9361i			0.744401i
$792$	−6.67175	−	11.3247i	−0.237070	−	0.402405i
$793$			63.2098i			2.24465i
$794$	−34.4249	−	28.5838i	−1.22169	−	1.01440i
$795$	−0.758260	−	1.32361i	−0.0268927	−	0.0469434i
$796$	17.0181	−	3.18262i	0.603190	−	0.112805i
$797$	3.12230	−	11.6526i	0.110598	−	0.412756i	−0.888322	−	0.459220i	$-0.848129\pi$
$797$	3.12230	−	11.6526i	0.110598	−	0.412756i	0.998920	+	0.0464645i	$0.0147955\pi$
$798$	−2.98698	+	1.09330i	−0.105738	+	0.0387024i
$799$	16.2250	+	9.36753i	0.574000	+	0.331399i
$800$	−0.347127	+	5.64619i	−0.0122728	+	0.199623i
$801$	−4.31383	−	0.0290163i	−0.152422	−	0.00102524i
$802$	−2.15737	−	3.04737i	−0.0761794	−	0.107606i
$803$	3.74546	+	13.9783i	0.132174	+	0.493282i
$804$	12.2399	+	0.984788i	0.431670	+	0.0347308i
$805$	1.45181	−	5.41821i	0.0511694	−	0.190967i
$806$	9.78028	+	26.4447i	0.344496	+	0.931474i
$807$	6.21094	−	6.16931i	0.218636	−	0.217170i
$808$	41.1899	−	24.6410i	1.44905	−	0.866868i
$809$	47.7721			1.67958			0.839789	−	0.542913i	$-0.182679\pi$
$809$	47.7721			1.67958			0.839789	+	0.542913i	$0.182679\pi$
$810$	−2.31389	+	12.5158i	−0.0813017	+	0.439761i
$811$	−2.62127	+	2.62127i	−0.0920453	+	0.0920453i	−0.751630	−	0.659585i	$-0.770732\pi$
$811$	−2.62127	+	2.62127i	−0.0920453	+	0.0920453i	0.659585	+	0.751630i	$0.270732\pi$
$812$	−3.50571	+	45.4856i	−0.123026	+	1.59623i
$813$	23.8769	+	0.0803013i	0.837401	+	0.00281629i
$814$	−8.55706	+	18.6013i	−0.299925	+	0.651975i
$815$	−6.18453	−	10.7119i	−0.216635	−	0.375222i
$816$	−20.1219	+	7.72119i	−0.704408	+	0.270296i
$817$	0.150073	−	0.259934i	0.00525040	−	0.00909395i
$818$	−14.2283	−	20.0980i	−0.497480	−	0.702711i
$819$	−24.8024	+	24.4710i	−0.866665	+	0.855084i
$820$	0.314284	+	0.656174i	0.0109753	+	0.0229146i
$821$	−3.73241	−	13.9295i	−0.130262	−	0.486144i	0.869711	−	0.493562i	$-0.164305\pi$
$821$	−3.73241	−	13.9295i	−0.130262	−	0.486144i	−0.999972	+	0.00741809i	$0.997639\pi$
$822$	13.4783	−	29.0414i	0.470110	−	1.01294i
$823$	6.93703	+	12.0153i	0.241810	+	0.418826i	0.961230	−	0.275749i	$-0.0889257\pi$
$823$	6.93703	+	12.0153i	0.241810	+	0.418826i	−0.719420	+	0.694575i	$0.755592\pi$
$824$	−8.09160	+	8.34671i	−0.281884	+	0.290772i
$825$	−0.703118	+	2.58921i	−0.0244794	+	0.0901446i
$826$	−14.5004	+	17.4635i	−0.504532	+	0.607634i
$827$	1.72998	+	1.72998i	0.0601572	+	0.0601572i	0.736545	−	0.676388i	$-0.236456\pi$
$827$	1.72998	+	1.72998i	0.0601572	+	0.0601572i	−0.676388	+	0.736545i	$0.736456\pi$
$828$	−9.98517	+	8.44032i	−0.347009	+	0.293322i
$829$	−36.1956	+	36.1956i	−1.25713	+	1.25713i	−0.304668	+	0.952459i	$0.598546\pi$
$829$	−36.1956	+	36.1956i	−1.25713	+	1.25713i	−0.952459	+	0.304668i	$0.901454\pi$
$830$	−17.9035	+	1.65972i	−0.621440	+	0.0576097i
$831$	−13.3947	−	50.6708i	−0.464657	−	1.75775i
$832$	34.5576	−	10.4193i	1.19807	−	0.361223i
$833$	1.00654	−	0.581126i	0.0348745	−	0.0201348i
$834$	40.4120	+	7.05034i	1.39935	+	0.244133i
$835$	−6.97805	+	1.86976i	−0.241485	+	0.0647058i
$836$	1.47401	+	0.519291i	0.0509798	+	0.0179601i
$837$	−11.2794	−	19.9999i	−0.389874	−	0.691297i
$838$	7.84398	−	45.8717i	0.270966	−	1.58461i
$839$	−34.5636	−	19.9553i	−1.19327	−	0.688933i	−0.234220	−	0.972184i	$-0.575254\pi$
$839$	−34.5636	−	19.9553i	−1.19327	−	0.688933i	−0.959046	+	0.283251i	$0.908587\pi$
$840$	6.17221	−	10.9971i	0.212961	−	0.379437i
$841$	42.8860	−	24.7603i	1.47883	−	0.853802i
$842$	−17.7966	−	48.1199i	−0.613312	−	1.65832i
$843$	21.8236	+	12.6979i	0.751646	+	0.437340i
$844$	−2.99861	+	38.9062i	−0.103216	+	1.33920i
$845$	5.20154	+	5.20154i	0.178938	+	0.178938i
$846$	23.1406	+	10.8345i	0.795592	+	0.372496i
$847$		−	22.1393i		−	0.760716i
$848$	1.42242	−	3.22285i	0.0488462	−	0.110673i
$849$	−13.8547	+	51.0194i	−0.475491	+	1.75098i
$850$	3.99676	+	1.83861i	0.137088	+	0.0630637i
$851$	19.6731	+	5.27140i	0.674386	+	0.180701i
$852$	−50.6242	+	9.29135i	−1.73436	+	0.318316i
$853$	−37.3961	+	10.0203i	−1.28042	+	0.343087i	−0.834013	−	0.551745i	$-0.813962\pi$
$853$	−37.3961	+	10.0203i	−1.28042	+	0.343087i	−0.446404	+	0.894831i	$0.647296\pi$
$854$	−8.59654	+	50.2727i	−0.294167	+	1.72030i
$855$	−0.747846	−	1.31567i	−0.0255758	−	0.0449948i
$856$	−11.6798	+	20.9751i	−0.399208	+	0.716916i
$857$	16.2379	−	28.1249i	0.554677	−	0.960729i	−0.443251	−	0.896397i	$-0.646175\pi$
$857$	16.2379	−	28.1249i	0.554677	−	0.960729i	0.997929	−	0.0643319i	$-0.0204916\pi$
$858$	17.0512	−	1.52288i	0.582117	−	0.0519903i
$859$	−42.2035	−	11.3084i	−1.43997	−	0.385837i	−0.547444	−	0.836843i	$-0.684399\pi$
$859$	−42.2035	−	11.3084i	−1.43997	−	0.385837i	−0.892521	+	0.451005i	$0.851066\pi$
$860$	0.218752	+	1.16971i	0.00745939	+	0.0398868i
$861$	0.00545478	−	1.62193i	0.000185899	−	0.0552754i
$862$	−0.279046	−	3.01009i	−0.00950435	−	0.102524i
$863$	2.29309			0.0780576			0.0390288	−	0.999238i	$-0.487574\pi$
$863$	2.29309			0.0780576			0.0390288	+	0.999238i	$0.487574\pi$
$864$	−26.4406	+	12.8411i	−0.899529	+	0.436862i
$865$	10.8829			0.370029
$866$	−0.742520	−	8.00963i	−0.0252319	−	0.272178i
$867$	0.0426556	−	12.6833i	0.00144866	−	0.430747i
$868$	4.18208	+	22.3624i	0.141949	+	0.759029i
$869$	−15.6778	−	4.20087i	−0.531835	−	0.142505i
$870$	−21.6193	+	1.93087i	−0.732963	+	0.0654628i
$871$	−7.99663	+	13.8506i	−0.270956	+	0.469309i
$872$	−8.35903	−	4.65465i	−0.283072	−	0.157626i
$873$	12.3135	−	21.0001i	0.416749	−	0.710747i
$874$	0.262025	−	1.53232i	0.00886311	−	0.0518316i
$875$	−2.48646	+	0.666246i	−0.0840578	+	0.0225232i
$876$	31.8309	−	5.84210i	1.07547	−	0.197386i
$877$	−12.9818	−	3.47845i	−0.438363	−	0.117459i	0.0328861	−	0.999459i	$-0.489530\pi$
$877$	−12.9818	−	3.47845i	−0.438363	−	0.117459i	−0.471249	+	0.882000i	$0.656197\pi$
$878$	48.5392	+	22.3293i	1.63812	+	0.753576i
$879$	−6.81705	+	25.1036i	−0.229933	+	0.846722i
$880$	−5.77731	+	2.23919i	−0.194753	+	0.0754831i
$881$		−	32.9257i		−	1.10929i	−0.832086	−	0.554647i	$-0.812853\pi$
$881$		−	32.9257i		−	1.10929i	0.832086	−	0.554647i	$-0.187147\pi$
$882$	1.29986	−	0.907165i	0.0437685	−	0.0305458i
$883$	36.8244	+	36.8244i	1.23924	+	1.23924i	0.960312	+	0.278927i	$0.0899786\pi$
$883$	36.8244	+	36.8244i	1.23924	+	1.23924i	0.278927	+	0.960312i	$0.410021\pi$
$884$	2.15710	−	27.9877i	0.0725510	−	0.941329i
$885$	−9.33456	−	5.43125i	−0.313778	−	0.182570i
$886$	−8.69507	−	23.5104i	−0.292117	−	0.789847i
$887$	27.6388	−	15.9572i	0.928019	−	0.535792i	0.0418345	−	0.999125i	$-0.486680\pi$
$887$	27.6388	−	15.9572i	0.928019	−	0.535792i	0.886184	+	0.463333i	$0.153346\pi$
$888$	39.9298	+	22.4108i	1.33996	+	0.752057i
$889$	47.4155	+	27.3753i	1.59026	+	0.918139i
$890$	−0.342768	+	2.00451i	−0.0114896	+	0.0671913i
$891$	−13.5134	+	3.42676i	−0.452718	+	0.114801i
$892$	−2.65566	−	0.935582i	−0.0889180	−	0.0313256i
$893$	−2.93456	+	0.786312i	−0.0982012	+	0.0263129i
$894$	−21.4580	−	3.74359i	−0.717661	−	0.125204i
$895$	−16.2603	+	9.38787i	−0.543521	+	0.313802i
$896$	28.9018	−	3.58692i	0.965540	−	0.119831i
$897$	−4.35201	−	16.4632i	−0.145309	−	0.549690i
$898$	−26.3646	+	2.44409i	−0.879797	+	0.0815603i
$899$	27.6880	−	27.6880i	0.923445	−	0.923445i
$900$	5.64555	+	2.03170i	0.188185	+	0.0677234i
$901$	−1.93726	−	1.93726i	−0.0645396	−	0.0645396i
$902$	−0.509078	+	0.613109i	−0.0169504	+	0.0204143i
$903$	0.695221	−	2.56013i	0.0231355	−	0.0851958i
$904$	−16.5167	−	16.0119i	−0.549337	−	0.532546i
$905$	5.06606	+	8.77467i	0.168402	+	0.291680i
$906$	−6.36061	+	13.7051i	−0.211317	+	0.455321i
$907$	4.40133	+	16.4260i	0.146144	+	0.545416i	0.999702	+	0.0244183i	$0.00777335\pi$
$907$	4.40133	+	16.4260i	0.146144	+	0.545416i	−0.853558	+	0.520998i	$0.825560\pi$
$908$	−11.4836	−	23.9760i	−0.381098	−	0.795671i
$909$	−12.8452	−	49.2621i	−0.426050	−	1.63392i
$910$	9.49036	+	13.4055i	0.314602	+	0.444388i
$911$	13.9747	−	24.2049i	0.463002	−	0.801943i	−0.536107	−	0.844150i	$-0.680106\pi$
$911$	13.9747	−	24.2049i	0.463002	−	0.801943i	0.999109	+	0.0422074i	$0.0134390\pi$
$912$	1.42192	−	3.19262i	0.0470846	−	0.105718i
$913$	−9.84710	−	17.0557i	−0.325891	−	0.564460i
$914$	12.7228	−	27.6567i	0.420833	−	0.914804i
$915$	−24.2658	−	0.0816093i	−0.802204	−	0.00269792i
$916$	−0.577648	+	7.49482i	−0.0190860	+	0.247636i
$917$	−11.9816	+	11.9816i	−0.395667	+	0.395667i
$918$	1.88038	+	22.7824i	0.0620617	+	0.751930i
$919$	−9.53539			−0.314544			−0.157272	−	0.987555i	$-0.550270\pi$
$919$	−9.53539			−0.314544			−0.157272	+	0.987555i	$0.550270\pi$
$920$	3.16415	+	5.28918i	0.104319	+	0.174379i
$921$	−11.3510	+	11.2749i	−0.374028	+	0.371520i
$922$	−16.5937	−	44.8672i	−0.546483	−	1.47762i
$923$	17.3502	−	64.7520i	0.571090	−	2.13134i
$924$	13.7684	+	1.10777i	0.452948	+	0.0364428i
$925$	−2.41909	−	9.02816i	−0.0795391	−	0.296844i
$926$	−19.6884	−	27.8107i	−0.647003	−	0.913917i
$927$	6.09314	+	10.7195i	0.200125	+	0.352075i
$928$	−33.2029	−	37.5529i	−1.08994	−	1.23274i
$929$	21.3978	+	12.3540i	0.702037	+	0.405322i	0.808106	−	0.589037i	$-0.200493\pi$
$929$	21.3978	+	12.3540i	0.702037	+	0.405322i	−0.106068	+	0.994359i	$0.533826\pi$
$930$	−10.1646	+	3.72045i	−0.333309	+	0.121998i
$931$	−0.0487798	+	0.182049i	−0.00159869	+	0.00596641i
$932$	53.5078	−	10.0067i	1.75271	−	0.327781i
$933$	4.90495	+	8.56199i	0.160581	+	0.280307i
$934$	−23.7998	−	19.7615i	−0.778752	−	0.646616i
$935$			4.81873i			0.157589i
$936$	−0.336591	−	38.2822i	−0.0110018	−	1.25129i
$937$			42.9287i			1.40242i	0.712956	+	0.701209i	$0.247356\pi$
$937$			42.9287i			1.40242i	−0.712956	+	0.701209i	$0.752644\pi$
$938$	−8.24365	+	9.92824i	−0.269165	+	0.324169i
$939$	−23.7073	+	40.7451i	−0.773658	+	1.32967i
$940$	6.80631	−	9.93767i	0.221997	−	0.324131i
$941$	−1.85985	+	6.94105i	−0.0606293	+	0.226272i	−0.989592	−	0.143902i	$-0.954035\pi$
$941$	−1.85985	+	6.94105i	−0.0606293	+	0.226272i	0.928963	+	0.370173i	$0.120702\pi$
$942$	14.4504	+	2.52104i	0.470818	+	0.0821398i
$943$	0.686501	+	0.396352i	0.0223556	+	0.0129070i
$944$	−2.68732	−	24.7955i	−0.0874647	−	0.807026i
$945$	−9.36222	−	9.55307i	−0.304553	−	0.310761i
$946$	−1.06382	+	0.753124i	−0.0345877	+	0.0244862i
$947$	10.6480	+	39.7387i	0.346012	+	1.29133i	0.891425	+	0.453168i	$0.149706\pi$
$947$	10.6480	+	39.7387i	0.346012	+	1.29133i	−0.545413	+	0.838167i	$0.683627\pi$
$948$	−12.1760	+	34.1944i	−0.395459	+	1.11058i
$949$	−10.9093	+	40.7140i	−0.354130	+	1.32163i
$950$	−0.669109	+	0.247463i	−0.0217087	+	0.00802875i
$951$	5.57687	+	21.0967i	0.180843	+	0.684108i
$952$	5.52194	−	21.9661i	0.178967	−	0.711926i
$953$	−7.87451			−0.255080			−0.127540	−	0.991833i	$-0.540708\pi$
$953$	−7.87451			−0.255080			−0.127540	+	0.991833i	$0.540708\pi$
$954$	−2.85858	−	2.40621i	−0.0925500	−	0.0779040i
$955$	−16.0818	+	16.0818i	−0.520396	+	0.520396i
$956$	−27.2438	−	31.7940i	−0.881128	−	1.02829i
$957$	−11.8179	−	20.6291i	−0.382017	−	0.666843i
$958$	31.1443	+	14.3272i	1.00623	+	0.462890i
$959$	16.8232	+	29.1387i	0.543250	+	0.940937i
$960$	3.95527	+	13.2799i	0.127656	+	0.428607i
$961$	−5.73665	+	9.93616i	−0.185053	+	0.320521i
$962$	−48.6744	+	34.4588i	−1.56933	+	1.11100i
$963$	17.8843	+	18.1266i	0.576315	+	0.584120i
$964$	10.9180	−	30.9908i	0.351645	−	0.998147i
$965$	1.11167	+	4.14880i	0.0357859	+	0.133555i
$966$	−1.22229	−	13.6856i	−0.0393266	−	0.440326i
$967$	−3.24446	−	5.61956i	−0.104335	−	0.180713i	0.809132	−	0.587628i	$-0.199938\pi$
$967$	−3.24446	−	5.61956i	−0.104335	−	0.180713i	−0.913466	+	0.406915i	$0.866605\pi$
$968$	17.4659	+	16.9321i	0.561376	+	0.544218i
$969$	−1.91548	−	1.92840i	−0.0615339	−	0.0619492i
$970$	−8.82905	−	7.33096i	−0.283484	−	0.235383i
$971$	27.1755	+	27.1755i	0.872103	+	0.872103i	0.992701	−	0.120598i	$-0.0384812\pi$
$971$	27.1755	+	27.1755i	0.872103	+	0.872103i	−0.120598	+	0.992701i	$0.538481\pi$
$972$	5.21505	+	30.7377i	0.167273	+	0.985911i
$973$	−30.4838	+	30.4838i	−0.977265	+	0.977265i
$974$	−0.377710	−	4.07439i	−0.0121026	−	0.130552i
$975$	−5.54432	+	5.50716i	−0.177560	+	0.176370i
$976$	−33.0860	−	45.2303i	−1.05906	−	1.44779i
$977$	17.8419	−	10.3010i	0.570814	−	0.329560i	−0.186660	−	0.982425i	$-0.559766\pi$
$977$	17.8419	−	10.3010i	0.570814	−	0.329560i	0.757474	+	0.652865i	$0.226433\pi$
$978$	−23.2447	−	19.4331i	−0.743284	−	0.621401i
$979$	−2.15155	+	0.576507i	−0.0687639	+	0.0184252i
$980$	−0.322782	−	0.673917i	−0.0103109	−	0.0215275i
$981$	−7.22381	+	7.12728i	−0.230638	+	0.227556i
$982$	7.47599	+	1.27838i	0.238569	+	0.0407948i
$983$	6.25769	+	3.61288i	0.199589	+	0.115233i	0.596464	−	0.802640i	$-0.296572\pi$
$983$	6.25769	+	3.61288i	0.199589	+	0.115233i	−0.396875	+	0.917873i	$0.629905\pi$
$984$	1.27539	+	1.24475i	0.0406579	+	0.0396813i
$985$	17.6042	−	10.1638i	0.560916	−	0.323845i
$986$	−36.5632	+	13.5225i	−1.16441	+	0.430645i
$987$	−23.2996	+	13.3477i	−0.741634	+	0.424863i
$988$	2.96185	+	3.45654i	0.0942291	+	0.109967i
$989$	0.916795	+	0.916795i	0.0291524	+	0.0291524i
$990$	0.562610	+	6.54780i	0.0178809	+	0.208103i
$991$			24.0146i			0.762848i	0.924400	+	0.381424i	$0.124566\pi$
$991$			24.0146i			0.762848i	−0.924400	+	0.381424i	$0.875434\pi$
$992$	−20.8404	−	13.8034i	−0.661682	−	0.438259i
$993$	2.28885	−	0.605053i	0.0726345	−	0.0192008i
$994$	22.6055	−	49.1396i	0.717001	−	1.55861i
$995$	−8.36160	−	2.24048i	−0.265081	−	0.0710281i
$996$	−39.7852	+	18.8914i	−1.26064	+	0.598598i
$997$	26.3428	−	7.05853i	0.834284	−	0.223546i	0.183702	−	0.982982i	$-0.441192\pi$
$997$	26.3428	−	7.05853i	0.834284	−	0.223546i	0.650582	+	0.759436i	$0.274525\pi$
$998$	22.8728	+	3.91121i	0.724026	+	0.123807i
$999$	34.6865	−	33.9935i	1.09743	−	1.07551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.49	✓	384
9.5	odd	6	inner	720.2.cf.a.491.82	yes	384
16.3	odd	4	inner	720.2.cf.a.371.82	yes	384
144.131	even	12	inner	720.2.cf.a.131.49	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.49	✓	384	1.1	even	1	trivial
720.2.cf.a.131.49	yes	384	144.131	even	12	inner
720.2.cf.a.371.82	yes	384	16.3	odd	4	inner
720.2.cf.a.491.82	yes	384	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.130543 + 1.40818i) q^{2} +(0.00582509 - 1.73204i) q^{3} +(-1.96592 + 0.367654i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.43978 - 0.217903i) q^{6} +(-1.28709 + 2.22930i) q^{7} +(-0.774358 - 2.72036i) q^{8} +(-2.99993 - 0.0201786i) q^{9} +O(q^{10})\)	\(q+(0.130543 + 1.40818i) q^{2} +(0.00582509 - 1.73204i) q^{3} +(-1.96592 + 0.367654i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.43978 - 0.217903i) q^{6} +(-1.28709 + 2.22930i) q^{7} +(-0.774358 - 2.72036i) q^{8} +(-2.99993 - 0.0201786i) q^{9} +(-0.238368 + 1.39398i) q^{10} +(-1.49624 + 0.400915i) q^{11} +(0.625341 + 3.40719i) q^{12} +(-4.35804 - 1.16773i) q^{13} +(-3.30727 - 1.52143i) q^{14} +(0.453912 - 1.67152i) q^{15} +(3.72966 - 1.44556i) q^{16} -3.11083i q^{17} +(-0.363204 - 4.22707i) q^{18} +(0.356702 + 0.356702i) q^{19} +(-1.99409 - 0.153690i) q^{20} +(3.85375 + 2.24228i) q^{21} +(-0.759882 - 2.05463i) q^{22} +(-1.88714 + 1.08954i) q^{23} +(-4.71629 + 1.32537i) q^{24} +(0.866025 + 0.500000i) q^{25} +(1.07546 - 6.28932i) q^{26} +(-0.0524250 + 5.19589i) q^{27} +(1.71070 - 4.85583i) q^{28} +(-8.55924 + 2.29344i) q^{29} +(2.41304 + 0.420983i) q^{30} +(-3.82688 + 2.20945i) q^{31} +(2.52248 + 5.06331i) q^{32} +(0.685686 + 2.59388i) q^{33} +(4.38060 - 0.406096i) q^{34} +(-1.82022 + 1.82022i) q^{35} +(5.90504 - 1.06327i) q^{36} +(-6.60907 - 6.60907i) q^{37} +(-0.455734 + 0.548863i) q^{38} +(-2.04795 + 7.54150i) q^{39} +(-0.0438908 - 2.82809i) q^{40} +(-0.181889 - 0.315041i) q^{41} +(-2.65444 + 5.71946i) q^{42} +(-0.153996 - 0.574721i) q^{43} +(2.79408 - 1.33826i) q^{44} +(-2.89249 - 0.795931i) q^{45} +(-1.78062 - 2.51520i) q^{46} +(-3.01126 + 5.21566i) q^{47} +(-2.48204 - 6.46835i) q^{48} +(0.186807 + 0.323560i) q^{49} +(-0.591034 + 1.28479i) q^{50} +(-5.38809 - 0.0181209i) q^{51} +(8.99686 + 0.693415i) q^{52} +(0.622748 - 0.622748i) q^{53} +(-7.32357 + 0.604462i) q^{54} -1.54902 q^{55} +(7.06118 + 1.77507i) q^{56} +(0.619900 - 0.615744i) q^{57} +(-4.34692 - 11.7535i) q^{58} +(1.61378 - 6.02273i) q^{59} +(-0.277813 + 3.45294i) q^{60} +(-3.62605 - 13.5326i) q^{61} +(-3.61087 - 5.10049i) q^{62} +(3.90616 - 6.66178i) q^{63} +(-6.80074 + 4.21307i) q^{64} +(-3.90731 - 2.25589i) q^{65} +(-3.56313 + 1.30418i) q^{66} +(0.917458 - 3.42400i) q^{67} +(1.14371 + 6.11564i) q^{68} +(1.87614 + 3.27495i) q^{69} +(-2.80080 - 2.32557i) q^{70} +14.8581i q^{71} +(2.26813 + 8.17653i) q^{72} -9.34228i q^{73} +(8.44397 - 10.1695i) q^{74} +(0.871065 - 1.49708i) q^{75} +(-0.832389 - 0.570103i) q^{76} +(1.03203 - 3.85158i) q^{77} +(-10.8871 - 1.89938i) q^{78} +(9.07438 + 5.23909i) q^{79} +(3.97671 - 0.430992i) q^{80} +(8.99919 + 0.121069i) q^{81} +(0.419889 - 0.297258i) q^{82} +(3.29062 + 12.2808i) q^{83} +(-8.40053 - 2.99128i) q^{84} +(0.805142 - 3.00483i) q^{85} +(0.789205 - 0.291879i) q^{86} +(3.92248 + 14.8383i) q^{87} +(2.24926 + 3.75985i) q^{88} +1.43798 q^{89} +(0.743217 - 4.17704i) q^{90} +(8.21241 - 8.21241i) q^{91} +(3.30939 - 2.83577i) q^{92} +(3.80457 + 6.64119i) q^{93} +(-7.73766 - 3.55952i) q^{94} +(0.252226 + 0.436868i) q^{95} +(8.78456 - 4.33954i) q^{96} +(-4.05733 + 7.02749i) q^{97} +(-0.431243 + 0.305296i) q^{98} +(4.49670 - 1.17253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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