LMFDB - Embedded newform 552.2.j.c.323.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(323,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.323"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [42,0,2,4,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.27
Character	$\chi$	$=$	552.323
Dual form			552.2.j.c.323.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.734855 - 1.20830i) q^{2} +(-1.73179 - 0.0302019i) q^{3} +(-0.919975 - 1.77585i) q^{4} +0.871841 q^{5} +(-1.30911 + 2.07032i) q^{6} -3.09231i q^{7} +(-2.82181 - 0.193388i) q^{8} +(2.99818 + 0.104607i) q^{9} +(0.640677 - 1.05344i) q^{10} -1.90350i q^{11} +(1.53957 + 3.10318i) q^{12} +1.23856i q^{13} +(-3.73644 - 2.27240i) q^{14} +(-1.50984 - 0.0263313i) q^{15} +(-2.30729 + 3.26748i) q^{16} -1.98300i q^{17} +(2.32962 - 3.54582i) q^{18} -4.96848 q^{19} +(-0.802072 - 1.54826i) q^{20} +(-0.0933936 + 5.35522i) q^{21} +(-2.29999 - 1.39879i) q^{22} -1.00000 q^{23} +(4.88093 + 0.420130i) q^{24} -4.23989 q^{25} +(1.49655 + 0.910161i) q^{26} +(-5.18904 - 0.271707i) q^{27} +(-5.49148 + 2.84485i) q^{28} -2.31109 q^{29} +(-1.14133 + 1.80499i) q^{30} -3.48492i q^{31} +(2.25257 + 5.18902i) q^{32} +(-0.0574892 + 3.29645i) q^{33} +(-2.39606 - 1.45722i) q^{34} -2.69600i q^{35} +(-2.57248 - 5.42055i) q^{36} +4.56655i q^{37} +(-3.65112 + 6.00341i) q^{38} +(0.0374068 - 2.14492i) q^{39} +(-2.46017 - 0.168603i) q^{40} -8.71457i q^{41} +(6.40208 + 4.04816i) q^{42} -3.26780 q^{43} +(-3.38032 + 1.75117i) q^{44} +(2.61393 + 0.0912003i) q^{45} +(-0.734855 + 1.20830i) q^{46} +7.68114 q^{47} +(4.09442 - 5.58889i) q^{48} -2.56238 q^{49} +(-3.11571 + 5.12306i) q^{50} +(-0.0598904 + 3.43414i) q^{51} +(2.19950 - 1.13944i) q^{52} +7.53051 q^{53} +(-4.14150 + 6.07025i) q^{54} -1.65955i q^{55} +(-0.598014 + 8.72591i) q^{56} +(8.60435 + 0.150058i) q^{57} +(-1.69832 + 2.79249i) q^{58} -12.2120i q^{59} +(1.34226 + 2.70548i) q^{60} +10.7975i q^{61} +(-4.21082 - 2.56091i) q^{62} +(0.323476 - 9.27129i) q^{63} +(7.92520 + 1.09141i) q^{64} +1.07983i q^{65} +(3.94085 + 2.49188i) q^{66} -0.0562647 q^{67} +(-3.52152 + 1.82431i) q^{68} +(1.73179 + 0.0302019i) q^{69} +(-3.25758 - 1.98117i) q^{70} +7.84847 q^{71} +(-8.44005 - 0.874989i) q^{72} -7.04796 q^{73} +(5.51775 + 3.35575i) q^{74} +(7.34259 + 0.128053i) q^{75} +(4.57088 + 8.82328i) q^{76} -5.88620 q^{77} +(-2.56422 - 1.62140i) q^{78} -5.10654i q^{79} +(-2.01159 + 2.84872i) q^{80} +(8.97811 + 0.627258i) q^{81} +(-10.5298 - 6.40395i) q^{82} -0.795490i q^{83} +(9.59600 - 4.76082i) q^{84} -1.72886i q^{85} +(-2.40136 + 3.94849i) q^{86} +(4.00232 + 0.0697994i) q^{87} +(-0.368112 + 5.37130i) q^{88} -17.3867i q^{89} +(2.03106 - 3.09139i) q^{90} +3.83001 q^{91} +(0.919975 + 1.77585i) q^{92} +(-0.105251 + 6.03513i) q^{93} +(5.64452 - 9.28111i) q^{94} -4.33173 q^{95} +(-3.74425 - 9.05431i) q^{96} +9.05221 q^{97} +(-1.88298 + 3.09612i) q^{98} +(0.199118 - 5.70701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25}+ \cdots - 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * q^96 + 20 * q^97 - 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.734855	−	1.20830i	0.519621	−	0.854397i
$2$	0.734855	−	1.20830i	0.519621	−	0.854397i
$3$	−1.73179	−	0.0302019i	−0.999848	−	0.0174371i
$3$	−1.73179	−	0.0302019i	−0.999848	−	0.0174371i
$4$	−0.919975	−	1.77585i	−0.459988	−	0.887925i
$5$	0.871841			0.389899			0.194950	−	0.980813i	$-0.437546\pi$
$5$	0.871841			0.389899			0.194950	+	0.980813i	$0.437546\pi$
$6$	−1.30911	+	2.07032i	−0.534440	+	0.845206i
$7$		−	3.09231i		−	1.16878i	−0.811472	−	0.584392i	$-0.801333\pi$
$7$		−	3.09231i		−	1.16878i	0.811472	−	0.584392i	$-0.198667\pi$
$8$	−2.82181	−	0.193388i	−0.997660	−	0.0683728i
$9$	2.99818	+	0.104607i	0.999392	+	0.0348688i
$10$	0.640677	−	1.05344i	0.202600	−	0.333129i
$11$		−	1.90350i		−	0.573926i	−0.957942	−	0.286963i	$-0.907354\pi$
$11$		−	1.90350i		−	0.573926i	0.957942	−	0.286963i	$-0.0926456\pi$
$12$	1.53957	+	3.10318i	0.444435	+	0.895811i
$13$			1.23856i			0.343514i	0.985139	+	0.171757i	$0.0549444\pi$
$13$			1.23856i			0.343514i	−0.985139	+	0.171757i	$0.945056\pi$
$14$	−3.73644	−	2.27240i	−0.998605	−	0.607325i
$15$	−1.50984	−	0.0263313i	−0.389840	−	0.00679870i
$16$	−2.30729	+	3.26748i	−0.576823	+	0.816869i
$17$		−	1.98300i		−	0.480949i	−0.970655	−	0.240474i	$-0.922697\pi$
$17$		−	1.98300i		−	0.480949i	0.970655	−	0.240474i	$-0.0773030\pi$
$18$	2.32962	−	3.54582i	0.549097	−	0.835759i
$19$	−4.96848			−1.13985			−0.569924	−	0.821697i	$-0.693027\pi$
$19$	−4.96848			−1.13985			−0.569924	+	0.821697i	$0.693027\pi$
$20$	−0.802072	−	1.54826i	−0.179349	−	0.346201i
$21$	−0.0933936	+	5.35522i	−0.0203802	+	1.16861i
$22$	−2.29999	−	1.39879i	−0.490360	−	0.298224i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	4.88093	+	0.420130i	0.996316	+	0.0857587i
$25$	−4.23989			−0.847979
$26$	1.49655	+	0.910161i	0.293498	+	0.178497i
$27$	−5.18904	−	0.271707i	−0.998632	−	0.0522900i
$28$	−5.49148	+	2.84485i	−1.03779	+	0.537626i
$29$	−2.31109			−0.429159			−0.214580	−	0.976706i	$-0.568838\pi$
$29$	−2.31109			−0.429159			−0.214580	+	0.976706i	$0.568838\pi$
$30$	−1.14133	+	1.80499i	−0.208378	+	0.329545i
$31$		−	3.48492i		−	0.625909i	−0.949768	−	0.312955i	$-0.898681\pi$
$31$		−	3.48492i		−	0.625909i	0.949768	−	0.312955i	$-0.101319\pi$
$32$	2.25257	+	5.18902i	0.398201	+	0.917298i
$33$	−0.0574892	+	3.29645i	−0.0100076	+	0.573838i
$34$	−2.39606	−	1.45722i	−0.410921	−	0.249911i
$35$		−	2.69600i		−	0.455708i
$36$	−2.57248	−	5.42055i	−0.428747	−	0.903425i
$37$			4.56655i			0.750735i	0.926876	+	0.375368i	$0.122484\pi$
$37$			4.56655i			0.750735i	−0.926876	+	0.375368i	$0.877516\pi$
$38$	−3.65112	+	6.00341i	−0.592289	+	0.973882i
$39$	0.0374068	−	2.14492i	0.00598989	−	0.343462i
$40$	−2.46017	−	0.168603i	−0.388987	−	0.0266585i
$41$		−	8.71457i		−	1.36099i	−0.732754	−	0.680493i	$-0.761766\pi$
$41$		−	8.71457i		−	1.36099i	0.732754	−	0.680493i	$-0.238234\pi$
$42$	6.40208	+	4.04816i	0.987863	+	0.624645i
$43$	−3.26780			−0.498336			−0.249168	−	0.968460i	$-0.580157\pi$
$43$	−3.26780			−0.498336			−0.249168	+	0.968460i	$0.580157\pi$
$44$	−3.38032	+	1.75117i	−0.509603	+	0.263999i
$45$	2.61393	+	0.0912003i	0.389662	+	0.0135953i
$46$	−0.734855	+	1.20830i	−0.108349	+	0.178154i
$47$	7.68114			1.12041			0.560205	−	0.828354i	$-0.310723\pi$
$47$	7.68114			1.12041			0.560205	+	0.828354i	$0.310723\pi$
$48$	4.09442	−	5.58889i	0.590979	−	0.806687i
$49$	−2.56238			−0.366054
$50$	−3.11571	+	5.12306i	−0.440628	+	0.724510i
$51$	−0.0598904	+	3.43414i	−0.00838634	+	0.480876i
$52$	2.19950	−	1.13944i	0.305015	−	0.158012i
$53$	7.53051			1.03439			0.517197	−	0.855866i	$-0.326975\pi$
$53$	7.53051			1.03439			0.517197	+	0.855866i	$0.326975\pi$
$54$	−4.14150	+	6.07025i	−0.563587	+	0.826057i
$55$		−	1.65955i		−	0.223773i
$56$	−0.598014	+	8.72591i	−0.0799130	+	1.16605i
$57$	8.60435	+	0.150058i	1.13967	+	0.0198756i
$58$	−1.69832	+	2.79249i	−0.223000	+	0.366672i
$59$		−	12.2120i		−	1.58986i	−0.606698	−	0.794932i	$-0.707506\pi$
$59$		−	12.2120i		−	1.58986i	0.606698	−	0.794932i	$-0.292494\pi$
$60$	1.34226	+	2.70548i	0.173285	+	0.349276i
$61$			10.7975i			1.38248i	0.722623	+	0.691242i	$0.242936\pi$
$61$			10.7975i			1.38248i	−0.722623	+	0.691242i	$0.757064\pi$
$62$	−4.21082	−	2.56091i	−0.534775	−	0.325236i
$63$	0.323476	−	9.27129i	0.0407541	−	1.16807i
$64$	7.92520	+	1.09141i	0.990650	+	0.136426i
$65$			1.07983i			0.133936i
$66$	3.94085	+	2.49188i	0.485085	+	0.306729i
$67$	−0.0562647			−0.00687383			−0.00343692	−	0.999994i	$-0.501094\pi$
$67$	−0.0562647			−0.00687383			−0.00343692	+	0.999994i	$0.501094\pi$
$68$	−3.52152	+	1.82431i	−0.427047	+	0.221231i
$69$	1.73179	+	0.0302019i	0.208483	+	0.00363588i
$70$	−3.25758	−	1.98117i	−0.389355	−	0.236795i
$71$	7.84847			0.931442			0.465721	−	0.884932i	$-0.345795\pi$
$71$	7.84847			0.931442			0.465721	+	0.884932i	$0.345795\pi$
$72$	−8.44005	−	0.874989i	−0.994669	−	0.103118i
$73$	−7.04796			−0.824902			−0.412451	−	0.910980i	$-0.635327\pi$
$73$	−7.04796			−0.824902			−0.412451	+	0.910980i	$0.635327\pi$
$74$	5.51775	+	3.35575i	0.641426	+	0.390098i
$75$	7.34259	+	0.128053i	0.847850	+	0.0147863i
$76$	4.57088	+	8.82328i	0.524316	+	1.01210i
$77$	−5.88620			−0.670795
$78$	−2.56422	−	1.62140i	−0.290340	−	0.183588i
$79$		−	5.10654i		−	0.574531i	−0.957851	−	0.287265i	$-0.907254\pi$
$79$		−	5.10654i		−	0.574531i	0.957851	−	0.287265i	$-0.0927462\pi$
$80$	−2.01159	+	2.84872i	−0.224903	+	0.318497i
$81$	8.97811	+	0.627258i	0.997568	+	0.0696953i
$82$	−10.5298	−	6.40395i	−1.16282	−	0.707198i
$83$		−	0.795490i		−	0.0873163i	−0.999047	−	0.0436582i	$-0.986099\pi$
$83$		−	0.795490i		−	0.0873163i	0.999047	−	0.0436582i	$-0.0139012\pi$
$84$	9.59600	−	4.76082i	1.04701	−	0.519448i
$85$		−	1.72886i		−	0.187522i
$86$	−2.40136	+	3.94849i	−0.258946	+	0.425776i
$87$	4.00232	+	0.0697994i	0.429094	+	0.00748329i
$88$	−0.368112	+	5.37130i	−0.0392409	+	0.572582i
$89$		−	17.3867i		−	1.84298i	−0.388399	−	0.921491i	$-0.626972\pi$
$89$		−	17.3867i		−	1.84298i	0.388399	−	0.921491i	$-0.373028\pi$
$90$	2.03106	−	3.09139i	0.214092	−	0.325862i
$91$	3.83001			0.401494
$92$	0.919975	+	1.77585i	0.0959141	+	0.185145i
$93$	−0.105251	+	6.03513i	−0.0109140	+	0.625814i
$94$	5.64452	−	9.28111i	0.582188	−	0.957274i
$95$	−4.33173			−0.444426
$96$	−3.74425	−	9.05431i	−0.382146	−	0.924102i
$97$	9.05221			0.919113			0.459557	−	0.888149i	$-0.348008\pi$
$97$	9.05221			0.919113			0.459557	+	0.888149i	$0.348008\pi$
$98$	−1.88298	+	3.09612i	−0.190210	+	0.312756i
$99$	0.199118	−	5.70701i	0.0200121	−	0.573577i
$100$	3.90060	+	7.52942i	0.390060	+	0.752942i
$101$	19.5806			1.94835			0.974173	−	0.225803i	$-0.0725005\pi$
$101$	19.5806			1.94835			0.974173	+	0.225803i	$0.0725005\pi$
$102$	4.10546	+	2.59596i	0.406501	+	0.257038i
$103$		−	2.96013i		−	0.291670i	−0.989309	−	0.145835i	$-0.953413\pi$
$103$		−	2.96013i		−	0.291670i	0.989309	−	0.145835i	$-0.0465869\pi$
$104$	0.239522	−	3.49497i	0.0234870	−	0.342710i
$105$	−0.0814244	+	4.66890i	−0.00794621	+	0.455638i
$106$	5.53383	−	9.09911i	0.537494	−	0.883784i
$107$			8.95826i			0.866028i	0.901387	+	0.433014i	$0.142550\pi$
$107$			8.95826i			0.866028i	−0.901387	+	0.433014i	$0.857450\pi$
$108$	4.29128	+	9.46493i	0.412929	+	0.910763i
$109$		−	9.35024i		−	0.895591i	−0.894136	−	0.447795i	$-0.852209\pi$
$109$		−	9.35024i		−	0.895591i	0.894136	−	0.447795i	$-0.147791\pi$
$110$	−2.00523	−	1.21953i	−0.191191	−	0.116277i
$111$	0.137918	−	7.90829i	0.0130906	−	0.750621i
$112$	10.1041	+	7.13486i	0.954743	+	0.674181i
$113$		−	1.47151i		−	0.138428i	−0.997602	−	0.0692140i	$-0.977951\pi$
$113$		−	1.47151i		−	0.138428i	0.997602	−	0.0692140i	$-0.0220491\pi$
$114$	6.50427	−	10.2864i	0.609181	−	0.963406i
$115$	−0.871841			−0.0812996
$116$	2.12615	+	4.10416i	0.197408	+	0.381062i
$117$	−0.129561	+	3.71342i	−0.0119779	+	0.343305i
$118$	−14.7557	−	8.97404i	−1.35838	−	0.826127i
$119$	−6.13206			−0.562125
$120$	4.25540	+	0.366287i	0.388463	+	0.0334372i
$121$	7.37670			0.670609
$122$	13.0467	+	7.93463i	1.18119	+	0.718368i
$123$	−0.263196	+	15.0918i	−0.0237316	+	1.36078i
$124$	−6.18869	+	3.20604i	−0.555761	+	0.287911i
$125$	−8.05572			−0.720525
$126$	−10.9648	−	7.20391i	−0.976821	−	0.641775i
$127$			6.90921i			0.613093i	0.951856	+	0.306547i	$0.0991735\pi$
$127$			6.90921i			0.613093i	−0.951856	+	0.306547i	$0.900826\pi$
$128$	7.14262	−	8.77399i	0.631325	−	0.775519i
$129$	5.65914	+	0.0986939i	0.498260	+	0.00868951i
$130$	1.30475	+	0.793516i	0.114434	+	0.0695959i
$131$		−	12.5716i		−	1.09839i	−0.835695	−	0.549193i	$-0.814935\pi$
$131$		−	12.5716i		−	1.09839i	0.835695	−	0.549193i	$-0.185065\pi$
$132$	5.90689	−	2.93056i	0.514129	−	0.255073i
$133$			15.3641i			1.33224i
$134$	−0.0413464	+	0.0679846i	−0.00357179	+	0.00587298i
$135$	−4.52402	−	0.236885i	−0.389366	−	0.0203878i
$136$	−0.383488	+	5.59565i	−0.0328838	+	0.479823i
$137$			1.78484i			0.152490i	0.997089	+	0.0762448i	$0.0242930\pi$
$137$			1.78484i			0.152490i	−0.997089	+	0.0762448i	$0.975707\pi$
$138$	1.30911	−	2.07032i	0.111439	−	0.176238i
$139$	5.90847			0.501150			0.250575	−	0.968097i	$-0.419380\pi$
$139$	5.90847			0.501150			0.250575	+	0.968097i	$0.419380\pi$
$140$	−4.78770	+	2.48026i	−0.404634	+	0.209620i
$141$	−13.3021	−	0.231985i	−1.12024	−	0.0195367i
$142$	5.76749	−	9.48330i	0.483997	−	0.795821i
$143$	2.35759			0.197152
$144$	−7.25946	+	9.55511i	−0.604955	+	0.796259i
$145$	−2.01491			−0.167329
$146$	−5.17923	+	8.51605i	−0.428636	+	0.704793i
$147$	4.43750	+	0.0773888i	0.365999	+	0.00638292i
$148$	8.10950	−	4.20111i	0.666597	−	0.345329i
$149$	−18.3640			−1.50444			−0.752219	−	0.658914i	$-0.771016\pi$
$149$	−18.3640			−1.50444			−0.752219	+	0.658914i	$0.771016\pi$
$150$	5.55047	−	8.77795i	0.453194	−	0.716717i
$151$			5.65286i			0.460023i	0.973188	+	0.230012i	$0.0738764\pi$
$151$			5.65286i			0.460023i	−0.973188	+	0.230012i	$0.926124\pi$
$152$	14.0201	+	0.960843i	1.13718	+	0.0779346i
$153$	0.207435	−	5.94539i	0.0167701	−	0.480656i
$154$	−4.32550	+	7.11229i	−0.348559	+	0.573125i
$155$		−	3.03829i		−	0.244041i
$156$	−3.84347	+	1.90684i	−0.307724	+	0.152670i
$157$		−	17.6786i		−	1.41090i	−0.708758	−	0.705451i	$-0.750744\pi$
$157$		−	17.6786i		−	1.41090i	0.708758	−	0.705451i	$-0.249256\pi$
$158$	−6.17023	−	3.75257i	−0.490877	−	0.298538i
$159$	−13.0412	−	0.227436i	−1.03424	−	0.0180368i
$160$	1.96388	+	4.52400i	0.155258	+	0.357654i
$161$			3.09231i			0.243708i
$162$	7.35553	−	10.3873i	0.577905	−	0.816104i
$163$	−15.4158			−1.20746			−0.603728	−	0.797191i	$-0.706319\pi$
$163$	−15.4158			−1.20746			−0.603728	+	0.797191i	$0.706319\pi$
$164$	−15.4758	+	8.01719i	−1.20845	+	0.626037i
$165$	−0.0501214	+	2.87398i	−0.00390195	+	0.223739i
$166$	−0.961190	−	0.584570i	−0.0746028	−	0.0453714i
$167$	−9.04899			−0.700232			−0.350116	−	0.936706i	$-0.613858\pi$
$167$	−9.04899			−0.700232			−0.350116	+	0.936706i	$0.613858\pi$
$168$	1.29917	−	15.0934i	0.100233	−	1.16448i
$169$	11.4660			0.881998
$170$	−2.08898	−	1.27046i	−0.160218	−	0.0974401i
$171$	−14.8964	−	0.519736i	−1.13915	−	0.0397452i
$172$	3.00630	+	5.80313i	0.229228	+	0.442485i
$173$	−2.83727			−0.215714			−0.107857	−	0.994166i	$-0.534399\pi$
$173$	−2.83727			−0.215714			−0.107857	+	0.994166i	$0.534399\pi$
$174$	3.02547	−	4.78471i	0.229360	−	0.362728i
$175$			13.1111i			0.991103i
$176$	6.21963	+	4.39192i	0.468822	+	0.331053i
$177$	−0.368825	+	21.1486i	−0.0277226	+	1.58962i
$178$	−21.0083	−	12.7767i	−1.57464	−	0.957653i
$179$			10.5834i			0.791043i	0.918457	+	0.395521i	$0.129436\pi$
$179$			10.5834i			0.791043i	−0.918457	+	0.395521i	$0.870564\pi$
$180$	−2.24280	−	4.72586i	−0.167168	−	0.352244i
$181$		−	8.60505i		−	0.639608i	−0.947484	−	0.319804i	$-0.896383\pi$
$181$		−	8.60505i		−	0.639608i	0.947484	−	0.319804i	$-0.103617\pi$
$182$	2.81450	−	4.62780i	0.208625	−	0.343035i
$183$	0.326106	−	18.6991i	0.0241065	−	1.38227i
$184$	2.82181	+	0.193388i	0.208026	+	0.0142567i
$185$			3.98130i			0.292711i
$186$	7.21490	+	4.56212i	0.529022	+	0.334511i
$187$	−3.77464			−0.276029
$188$	−7.06646	−	13.6406i	−0.515374	−	0.994840i
$189$	−0.840202	+	16.0461i	−0.0611157	+	1.16718i
$190$	−3.18319	+	5.23402i	−0.230933	+	0.379716i
$191$	14.6068			1.05691			0.528454	−	0.848962i	$-0.322772\pi$
$191$	14.6068			1.05691			0.528454	+	0.848962i	$0.322772\pi$
$192$	−13.6918	−	2.12944i	−0.988121	−	0.153679i
$193$	−5.48507			−0.394824			−0.197412	−	0.980321i	$-0.563254\pi$
$193$	−5.48507			−0.394824			−0.197412	+	0.980321i	$0.563254\pi$
$194$	6.65207	−	10.9378i	0.477591	−	0.785287i
$195$	0.0326128	−	1.87003i	0.00233545	−	0.133916i
$196$	2.35733	+	4.55040i	0.168380	+	0.325029i
$197$	21.8619			1.55760			0.778798	−	0.627274i	$-0.215830\pi$
$197$	21.8619			1.55760			0.778798	+	0.627274i	$0.215830\pi$
$198$	−6.74946	−	4.43442i	−0.479663	−	0.315141i
$199$			19.5960i			1.38912i	0.719435	+	0.694560i	$0.244401\pi$
$199$			19.5960i			1.38912i	−0.719435	+	0.694560i	$0.755599\pi$
$200$	11.9642	+	0.819943i	0.845994	+	0.0579787i
$201$	0.0974385	+	0.00169930i	0.00687279	+	0.000119859i
$202$	14.3889	−	23.6593i	1.01240	−	1.66466i
$203$			7.14662i			0.501594i
$204$	6.15362	−	3.05297i	0.430839	−	0.213750i
$205$		−	7.59772i		−	0.530647i
$206$	−3.57672	−	2.17527i	−0.249202	−	0.151558i
$207$	−2.99818	−	0.104607i	−0.208388	−	0.00727066i
$208$	−4.04696	−	2.85771i	−0.280606	−	0.198147i
$209$			9.45748i			0.654188i
$210$	5.58160	+	3.52935i	0.385167	+	0.243549i
$211$	9.82214			0.676184			0.338092	−	0.941113i	$-0.390218\pi$
$211$	9.82214			0.676184			0.338092	+	0.941113i	$0.390218\pi$
$212$	−6.92788	−	13.3731i	−0.475809	−	0.918465i
$213$	−13.5919	−	0.237039i	−0.931300	−	0.0162416i
$214$	10.8243	+	6.58302i	0.739931	+	0.450006i
$215$	−2.84901			−0.194301
$216$	14.5899	+	1.77020i	0.992720	+	0.120447i
$217$	−10.7764			−0.731552
$218$	−11.2979	−	6.87107i	−0.765190	−	0.465368i
$219$	12.2056	+	0.212862i	0.824776	+	0.0143839i
$220$	−2.94710	+	1.52674i	−0.198694	+	0.102933i
$221$	2.45607			0.165213
$222$	−9.45423	−	5.97809i	−0.634526	−	0.401223i
$223$		−	5.37339i		−	0.359829i	−0.983682	−	0.179914i	$-0.942418\pi$
$223$		−	5.37339i		−	0.359829i	0.983682	−	0.179914i	$-0.0575821\pi$
$224$	16.0461	−	6.96563i	1.07212	−	0.465411i
$225$	−12.7119	−	0.443521i	−0.847463	−	0.0295680i
$226$	−1.77802	−	1.08135i	−0.118272	−	0.0719301i
$227$			23.0536i			1.53012i	0.643957	+	0.765061i	$0.277291\pi$
$227$			23.0536i			1.53012i	−0.643957	+	0.765061i	$0.722709\pi$
$228$	−7.64931	−	15.4181i	−0.506588	−	1.02109i
$229$		−	27.2263i		−	1.79916i	−0.436752	−	0.899582i	$-0.643871\pi$
$229$		−	27.2263i		−	1.79916i	0.436752	−	0.899582i	$-0.356129\pi$
$230$	−0.640677	+	1.05344i	−0.0422450	+	0.0694621i
$231$	10.1936	+	0.177774i	0.670693	+	0.0116967i
$232$	6.52147	+	0.446937i	0.428155	+	0.0293428i
$233$			21.6173i			1.41620i	0.706114	+	0.708098i	$0.250447\pi$
$233$			21.6173i			1.41620i	−0.706114	+	0.708098i	$0.749553\pi$
$234$	4.39171	+	2.88537i	0.287095	+	0.188623i
$235$	6.69673			0.436846
$236$	−21.6867	+	11.2347i	−1.41168	+	0.731318i
$237$	−0.154227	+	8.84345i	−0.0100181	+	0.574444i
$238$	−4.50618	+	7.40936i	−0.292092	+	0.480278i
$239$	−17.6777			−1.14348			−0.571738	−	0.820436i	$-0.693730\pi$
$239$	−17.6777			−1.14348			−0.571738	+	0.820436i	$0.693730\pi$
$240$	3.56968	−	4.87262i	0.230422	−	0.314527i
$241$	−16.3445			−1.05284			−0.526419	−	0.850225i	$-0.676466\pi$
$241$	−16.3445			−1.05284			−0.526419	+	0.850225i	$0.676466\pi$
$242$	5.42081	−	8.91327i	0.348463	−	0.572967i
$243$	−15.5292	−	1.35743i	−0.996201	−	0.0870794i
$244$	19.1748	−	9.93348i	1.22754	−	0.635926i
$245$	−2.23399			−0.142724
$246$	18.0420	+	11.4083i	1.15031	+	0.727366i
$247$		−	6.15376i		−	0.391554i
$248$	−0.673939	+	9.83376i	−0.0427952	+	0.624445i
$249$	−0.0240253	+	1.37762i	−0.00152254	+	0.0873030i
$250$	−5.91979	+	9.73372i	−0.374400	+	0.615614i
$251$		−	14.1286i		−	0.891791i	−0.895085	−	0.445896i	$-0.852885\pi$
$251$		−	14.1286i		−	0.891791i	0.895085	−	0.445896i	$-0.147115\pi$
$252$	−16.7620	+	7.95491i	−1.05591	+	0.501112i
$253$			1.90350i			0.119672i
$254$	8.34839	+	5.07727i	0.523825	+	0.318576i
$255$	−0.0522149	+	2.99402i	−0.00326983	+	0.187493i
$256$	−5.35282	−	15.0780i	−0.334551	−	0.942378i
$257$			13.2937i			0.829238i	0.909995	+	0.414619i	$0.136085\pi$
$257$			13.2937i			0.829238i	−0.909995	+	0.414619i	$0.863915\pi$
$258$	4.27790	−	6.76541i	0.266331	−	0.421196i
$259$	14.1212			0.877447
$260$	1.91761	−	0.993413i	0.118925	−	0.0616089i
$261$	−6.92907	−	0.241756i	−0.428898	−	0.0149643i
$262$	−15.1903	−	9.23832i	−0.938458	−	0.570745i
$263$	25.3919			1.56573			0.782865	−	0.622192i	$-0.213758\pi$
$263$	25.3919			1.56573			0.782865	+	0.622192i	$0.213758\pi$
$264$	0.799716	−	9.29083i	0.0492191	−	0.571811i
$265$	6.56541			0.403310
$266$	18.5644	+	11.2904i	1.13826	+	0.692258i
$267$	−0.525110	+	30.1100i	−0.0321362	+	1.84270i
$268$	0.0517622	+	0.0999177i	0.00316188	+	0.00610345i
$269$	2.58876			0.157840			0.0789198	−	0.996881i	$-0.474853\pi$
$269$	2.58876			0.157840			0.0789198	+	0.996881i	$0.474853\pi$
$270$	−3.61073	+	5.29230i	−0.219742	+	0.322079i
$271$			29.5135i			1.79282i	0.443226	+	0.896410i	$0.353834\pi$
$271$			29.5135i			1.79282i	−0.443226	+	0.896410i	$0.646166\pi$
$272$	6.47942	+	4.57536i	0.392872	+	0.277422i
$273$	−6.63276	−	0.115673i	−0.401433	−	0.00700088i
$274$	2.15663	+	1.31160i	0.130287	+	0.0792368i
$275$			8.07062i			0.486677i
$276$	−1.53957	−	3.10318i	−0.0926711	−	0.186790i
$277$		−	1.08750i		−	0.0653413i	−0.999466	−	0.0326707i	$-0.989599\pi$
$277$		−	1.08750i		−	0.0653413i	0.999466	−	0.0326707i	$-0.0104012\pi$
$278$	4.34187	−	7.13920i	0.260408	−	0.428181i
$279$	0.364545	−	10.4484i	0.0218247	−	0.625529i
$280$	−0.521373	+	7.60760i	−0.0311580	+	0.454641i
$281$			3.26761i			0.194929i	0.995239	+	0.0974647i	$0.0310733\pi$
$281$			3.26761i			0.194929i	−0.995239	+	0.0974647i	$0.968927\pi$
$282$	−10.0554	+	15.9024i	−0.598792	+	0.946977i
$283$	6.37119			0.378728			0.189364	−	0.981907i	$-0.439357\pi$
$283$	6.37119			0.378728			0.189364	+	0.981907i	$0.439357\pi$
$284$	−7.22040	−	13.9377i	−0.428452	−	0.827051i
$285$	7.50163	+	0.130826i	0.444358	+	0.00774948i
$286$	1.73249	−	2.84868i	0.102444	−	0.168446i
$287$	−26.9481			−1.59070
$288$	6.21078	+	15.7932i	0.365974	+	0.930625i
$289$	13.0677			0.768688
$290$	−1.48066	+	2.43461i	−0.0869476	+	0.142965i
$291$	−15.6765	−	0.273394i	−0.918973	−	0.0160266i
$292$	6.48395	+	12.5161i	0.379445	+	0.732451i
$293$	24.5319			1.43317			0.716584	−	0.697501i	$-0.245705\pi$
$293$	24.5319			1.43317			0.716584	+	0.697501i	$0.245705\pi$
$294$	3.35443	−	5.30496i	0.195634	−	0.309391i
$295$		−	10.6469i		−	0.619887i
$296$	0.883113	−	12.8859i	0.0513299	−	0.748979i
$297$	−0.517193	+	9.87732i	−0.0300106	+	0.573140i
$298$	−13.4949	+	22.1892i	−0.781738	+	1.28539i
$299$		−	1.23856i		−	0.0716277i
$300$	−6.52760	−	13.1572i	−0.376871	−	0.759629i
$301$			10.1051i			0.582446i
$302$	6.83035	+	4.15403i	0.393042	+	0.239038i
$303$	−33.9095	−	0.591372i	−1.94805	−	0.0339735i
$304$	11.4637	−	16.2344i	0.657490	−	0.931107i
$305$			9.41374i			0.539029i
$306$	−7.03138	−	4.61965i	−0.401957	−	0.264088i
$307$	6.49267			0.370556			0.185278	−	0.982686i	$-0.440681\pi$
$307$	6.49267			0.370556			0.185278	+	0.982686i	$0.440681\pi$
$308$	5.41516	+	10.4530i	0.308557	+	0.595615i
$309$	−0.0894015	+	5.12631i	−0.00508587	+	0.291626i
$310$	−3.67117	−	2.23271i	−0.208508	−	0.126809i
$311$	26.3522			1.49430			0.747149	−	0.664657i	$-0.231422\pi$
$311$	26.3522			1.49430			0.747149	+	0.664657i	$0.231422\pi$
$312$	−0.520356	+	6.04532i	−0.0294593	+	0.342249i
$313$	−33.2164			−1.87750			−0.938750	−	0.344599i	$-0.888015\pi$
$313$	−33.2164			−1.87750			−0.938750	+	0.344599i	$0.888015\pi$
$314$	−21.3610	−	12.9912i	−1.20547	−	0.733135i
$315$	0.282019	−	8.08309i	0.0158900	−	0.455430i
$316$	−9.06846	+	4.69789i	−0.510141	+	0.264277i
$317$	−21.3265			−1.19782			−0.598908	−	0.800818i	$-0.704399\pi$
$317$	−21.3265			−1.19782			−0.598908	+	0.800818i	$0.704399\pi$
$318$	−9.85824	+	15.5906i	−0.552822	+	0.874277i
$319$			4.39916i			0.246306i
$320$	6.90952	+	0.951532i	0.386254	+	0.0531922i
$321$	0.270556	−	15.5138i	0.0151010	−	0.865896i
$322$	3.73644	+	2.27240i	0.208223	+	0.126636i
$323$			9.85251i			0.548208i
$324$	−7.14573	−	16.5209i	−0.396985	−	0.917825i
$325$		−	5.25136i		−	0.291293i
$326$	−11.3284	+	18.6269i	−0.627419	+	1.03165i
$327$	−0.282395	+	16.1926i	−0.0156165	+	0.895454i
$328$	−1.68529	+	24.5908i	−0.0930545	+	1.35780i
$329$		−	23.7525i		−	1.30952i
$330$	3.43580	+	2.17252i	0.189134	+	0.119593i
$331$	−7.14989			−0.392994			−0.196497	−	0.980504i	$-0.562957\pi$
$331$	−7.14989			−0.392994			−0.196497	+	0.980504i	$0.562957\pi$
$332$	−1.41267	+	0.731831i	−0.0775304	+	0.0401644i
$333$	−0.477691	+	13.6913i	−0.0261773	+	0.750279i
$334$	−6.64970	+	10.9339i	−0.363855	+	0.598276i
$335$	−0.0490539			−0.00268010
$336$	−17.2826	−	12.6612i	−0.942842	−	0.690726i
$337$	7.67027			0.417826			0.208913	−	0.977934i	$-0.433007\pi$
$337$	7.67027			0.417826			0.208913	+	0.977934i	$0.433007\pi$
$338$	8.42583	−	13.8543i	0.458305	−	0.753576i
$339$	−0.0444424	+	2.54834i	−0.00241378	+	0.138407i
$340$	−3.07020	+	1.59051i	−0.166505	+	0.0862576i
$341$	−6.63352			−0.359225
$342$	−11.5747	+	17.6174i	−0.625887	+	0.952638i
$343$		−	13.7225i		−	0.740945i
$344$	9.22112	+	0.631953i	0.497169	+	0.0340726i
$345$	1.50984	+	0.0263313i	0.0812872	+	0.00141763i
$346$	−2.08498	+	3.42827i	−0.112089	+	0.184305i
$347$		−	27.3593i		−	1.46872i	−0.678759	−	0.734361i	$-0.737482\pi$
$347$		−	27.3593i		−	1.46872i	0.678759	−	0.734361i	$-0.262518\pi$
$348$	−3.55809	−	7.17174i	−0.190733	−	0.384446i
$349$			6.07938i			0.325422i	0.986674	+	0.162711i	$0.0520238\pi$
$349$			6.07938i			0.325422i	−0.986674	+	0.162711i	$0.947976\pi$
$350$	15.8421	+	9.63474i	0.846795	+	0.514998i
$351$	0.336525	−	6.42693i	0.0179624	−	0.343044i
$352$	9.87728	−	4.28775i	0.526461	−	0.228538i
$353$		−	25.6872i		−	1.36719i	−0.729861	−	0.683595i	$-0.760415\pi$
$353$		−	25.6872i		−	1.36719i	0.729861	−	0.683595i	$-0.239585\pi$
$354$	25.2828	+	15.9868i	1.34376	+	0.849688i
$355$	6.84262			0.363168
$356$	−30.8761	+	15.9953i	−1.63643	+	0.847749i
$357$	10.6194	+	0.185200i	0.562039	+	0.00980181i
$358$	12.7880	+	7.77729i	0.675864	+	0.411042i
$359$	17.9590			0.947838			0.473919	−	0.880568i	$-0.342839\pi$
$359$	17.9590			0.947838			0.473919	+	0.880568i	$0.342839\pi$
$360$	−7.35838	−	0.762852i	−0.387821	−	0.0402058i
$361$	5.68581			0.299253
$362$	−10.3975	−	6.32347i	−0.546479	−	0.332354i
$363$	−12.7749	−	0.222790i	−0.670508	−	0.0116935i
$364$	−3.52351	−	6.80152i	−0.184682	−	0.356497i
$365$	−6.14470			−0.321628
$366$	−22.3544	−	14.1351i	−1.16848	−	0.738855i
$367$		−	22.5647i		−	1.17787i	−0.808180	−	0.588935i	$-0.799547\pi$
$367$		−	22.5647i		−	1.17787i	0.808180	−	0.588935i	$-0.200453\pi$
$368$	2.30729	−	3.26748i	0.120276	−	0.170329i
$369$	0.911601	−	26.1278i	0.0474560	−	1.36016i
$370$	4.81060	+	2.92568i	0.250091	+	0.152099i
$371$		−	23.2867i		−	1.20898i
$372$	10.8143	−	5.36526i	0.560697	−	0.278176i
$373$			19.6359i			1.01671i	0.861147	+	0.508355i	$0.169746\pi$
$373$			19.6359i			1.01671i	−0.861147	+	0.508355i	$0.830254\pi$
$374$	−2.77381	+	4.56089i	−0.143430	+	0.235838i
$375$	13.9508	+	0.243298i	0.720416	+	0.0125639i
$376$	−21.6747	−	1.48544i	−1.11779	−	0.0766055i
$377$		−	2.86243i		−	0.147422i
$378$	18.7711	+	12.8068i	0.965481	+	0.658711i
$379$	−13.9167			−0.714855			−0.357428	−	0.933941i	$-0.616346\pi$
$379$	−13.9167			−0.714855			−0.357428	+	0.933941i	$0.616346\pi$
$380$	3.98508	+	7.69250i	0.204430	+	0.394617i
$381$	0.208671	−	11.9653i	0.0106905	−	0.613000i
$382$	10.7339	−	17.6493i	0.549192	−	0.903019i
$383$	−27.2328			−1.39153			−0.695766	−	0.718269i	$-0.744935\pi$
$383$	−27.2328			−1.39153			−0.695766	+	0.718269i	$0.744935\pi$
$384$	−12.6345	+	14.9790i	−0.644751	+	0.764392i
$385$	−5.13183			−0.261542
$386$	−4.03073	+	6.62761i	−0.205159	+	0.337336i
$387$	−9.79745	−	0.341834i	−0.498032	−	0.0173764i
$388$	−8.32781	−	16.0754i	−0.422781	−	0.816104i
$389$	−0.198260			−0.0100522			−0.00502608	−	0.999987i	$-0.501600\pi$
$389$	−0.198260			−0.0100522			−0.00502608	+	0.999987i	$0.501600\pi$
$390$	−2.23559	−	1.41361i	−0.113203	−	0.0715808i
$391$			1.98300i			0.100285i
$392$	7.23055	+	0.495532i	0.365198	+	0.0250282i
$393$	−0.379687	+	21.7714i	−0.0191527	+	1.09822i
$394$	16.0653	−	26.4157i	0.809360	−	1.33081i
$395$		−	4.45209i		−	0.224009i
$396$	−10.3180	+	4.89671i	−0.518498	+	0.246069i
$397$		−	12.8510i		−	0.644971i	−0.946574	−	0.322485i	$-0.895482\pi$
$397$		−	12.8510i		−	0.644971i	0.946574	−	0.322485i	$-0.104518\pi$
$398$	23.6778	+	14.4002i	1.18686	+	0.721816i
$399$	0.464025	−	26.6073i	0.0232303	−	1.33203i
$400$	9.78267	−	13.8538i	0.489133	−	0.692688i
$401$		−	23.3200i		−	1.16454i	−0.812994	−	0.582272i	$-0.802164\pi$
$401$		−	23.3200i		−	1.16454i	0.812994	−	0.582272i	$-0.197836\pi$
$402$	0.0736565	−	0.116486i	0.00367365	−	0.00580980i
$403$	4.31627			0.215009
$404$	−18.0137	−	34.7723i	−0.896215	−	1.72999i
$405$	7.82749	+	0.546869i	0.388951	+	0.0271741i
$406$	8.63526	+	5.25173i	0.428561	+	0.260639i
$407$	8.69240			0.430866
$408$	0.833119	−	9.67890i	0.0412455	−	0.479177i
$409$	2.90989			0.143885			0.0719425	−	0.997409i	$-0.477080\pi$
$409$	2.90989			0.143885			0.0719425	+	0.997409i	$0.477080\pi$
$410$	−9.18032	−	5.58322i	−0.453383	−	0.275736i
$411$	0.0539057	−	3.09097i	0.00265897	−	0.152466i
$412$	−5.25674	+	2.72324i	−0.258981	+	0.134165i
$413$	−37.7632			−1.85821
$414$	−2.32962	+	3.54582i	−0.114495	+	0.174268i
$415$		−	0.693540i		−	0.0340446i
$416$	−6.42691	+	2.78994i	−0.315105	+	0.136788i
$417$	−10.2322	−	0.178447i	−0.501074	−	0.00873859i
$418$	11.4275	+	6.94988i	0.558936	+	0.339930i
$419$		−	15.9445i		−	0.778941i	−0.921039	−	0.389470i	$-0.872658\pi$
$419$		−	15.9445i		−	0.778941i	0.921039	−	0.389470i	$-0.127342\pi$
$420$	8.36618	−	4.15068i	0.408228	−	0.202532i
$421$		−	30.6791i		−	1.49521i	−0.664144	−	0.747604i	$-0.731204\pi$
$421$		−	30.6791i		−	1.49521i	0.664144	−	0.747604i	$-0.268796\pi$
$422$	7.21785	−	11.8681i	0.351360	−	0.577730i
$423$	23.0294	+	0.803497i	1.11973	+	0.0390674i
$424$	−21.2497	−	1.45631i	−1.03197	−	0.0707245i
$425$			8.40772i			0.407834i
$426$	−10.2745	+	16.2489i	−0.497800	+	0.787260i
$427$	33.3894			1.61582
$428$	15.9085	−	8.24138i	0.768968	−	0.398362i
$429$	−4.08285	−	0.0712037i	−0.197122	−	0.00343775i
$430$	−2.09361	+	3.44245i	−0.100963	+	0.166010i
$431$	−35.6205			−1.71578			−0.857890	−	0.513833i	$-0.828225\pi$
$431$	−35.6205			−1.71578			−0.857890	+	0.513833i	$0.828225\pi$
$432$	12.8604	−	16.3282i	0.618748	−	0.785590i
$433$	3.15606			0.151670			0.0758352	−	0.997120i	$-0.475838\pi$
$433$	3.15606			0.151670			0.0758352	+	0.997120i	$0.475838\pi$
$434$	−7.91912	+	13.0212i	−0.380130	+	0.625036i
$435$	3.48939	+	0.0608540i	0.167303	+	0.00291773i
$436$	−16.6046	+	8.60199i	−0.795218	+	0.411961i
$437$	4.96848			0.237675
$438$	9.22653	−	14.5916i	0.440861	−	0.697212i
$439$			27.8197i			1.32776i	0.747839	+	0.663880i	$0.231092\pi$
$439$			27.8197i			1.32776i	−0.747839	+	0.663880i	$0.768908\pi$
$440$	−0.320935	+	4.68292i	−0.0153000	+	0.223249i
$441$	−7.68247	−	0.268042i	−0.365832	−	0.0127639i
$442$	1.80485	−	2.96766i	0.0858481	−	0.141157i
$443$		−	6.53287i		−	0.310386i	−0.987884	−	0.155193i	$-0.950400\pi$
$443$		−	6.53287i		−	0.310386i	0.987884	−	0.155193i	$-0.0496000\pi$
$444$	−14.1708	+	7.03051i	−0.672517	+	0.333653i
$445$		−	15.1584i		−	0.718577i
$446$	−6.49267	−	3.94867i	−0.307437	−	0.186975i
$447$	31.8025	+	0.554628i	1.50421	+	0.0262330i
$448$	3.37496	−	24.5072i	0.159452	−	1.15786i
$449$			25.4871i			1.20281i	0.798943	+	0.601406i	$0.205393\pi$
$449$			25.4871i			1.20281i	−0.798943	+	0.601406i	$0.794607\pi$
$450$	−9.87735	+	15.0339i	−0.465623	+	0.708705i
$451$	−16.5881			−0.781105
$452$	−2.61318	+	1.35375i	−0.122914	+	0.0636752i
$453$	0.170727	−	9.78955i	0.00802146	−	0.459953i
$454$	27.8557	+	16.9411i	1.30733	+	0.795084i
$455$	3.33916			0.156542
$456$	−24.2508	−	2.08741i	−1.13565	−	0.0977519i
$457$	2.40286			0.112401			0.0562004	−	0.998420i	$-0.482101\pi$
$457$	2.40286			0.112401			0.0562004	+	0.998420i	$0.482101\pi$
$458$	−32.8975	−	20.0074i	−1.53720	−	0.934884i
$459$	−0.538796	+	10.2899i	−0.0251488	+	0.480291i
$460$	0.802072	+	1.54826i	0.0373968	+	0.0721880i
$461$	14.0637			0.655013			0.327506	−	0.944849i	$-0.393792\pi$
$461$	14.0637			0.655013			0.327506	+	0.944849i	$0.393792\pi$
$462$	7.70566	−	12.1863i	0.358500	−	0.566960i
$463$			35.7689i			1.66232i	0.556031	+	0.831161i	$0.312323\pi$
$463$			35.7689i			1.66232i	−0.556031	+	0.831161i	$0.687677\pi$
$464$	5.33237	−	7.55145i	0.247549	−	0.350567i
$465$	−0.0917622	+	5.26168i	−0.00425537	+	0.244004i
$466$	26.1202	+	15.8856i	1.20999	+	0.735886i
$467$			39.3360i			1.82025i	0.414331	+	0.910126i	$0.364015\pi$
$467$			39.3360i			1.82025i	−0.414331	+	0.910126i	$0.635985\pi$
$468$	6.71367	−	3.18617i	0.310339	−	0.147281i
$469$			0.173988i			0.00803402i
$470$	4.92113	−	8.09165i	0.226995	−	0.373240i
$471$	−0.533926	+	30.6155i	−0.0246020	+	1.41069i
$472$	−2.36165	+	34.4599i	−0.108704	+	1.58614i
$473$			6.22025i			0.286007i
$474$	10.5722	+	6.68501i	0.485597	+	0.307053i
$475$	21.0658			0.966567
$476$	5.64134	+	10.8896i	0.258571	+	0.499125i
$477$	22.5778	+	0.787740i	1.03377	+	0.0360682i
$478$	−12.9906	+	21.3600i	−0.594174	+	0.976982i
$479$	−2.16149			−0.0987611			−0.0493805	−	0.998780i	$-0.515725\pi$
$479$	−2.16149			−0.0987611			−0.0493805	+	0.998780i	$0.515725\pi$
$480$	−3.26439	−	7.89392i	−0.148998	−	0.360307i
$481$	−5.65593			−0.257888
$482$	−12.0108	+	19.7490i	−0.547077	+	0.899542i
$483$	0.0933936	−	5.35522i	0.00424956	−	0.243671i
$484$	−6.78639	−	13.0999i	−0.308472	−	0.595451i
$485$	7.89209			0.358361
$486$	−13.0519	+	17.7665i	−0.592048	+	0.805903i
$487$			28.2115i			1.27839i	0.769046	+	0.639193i	$0.220732\pi$
$487$			28.2115i			1.27839i	−0.769046	+	0.639193i	$0.779268\pi$
$488$	2.08811	−	30.4686i	0.0945244	−	1.37925i
$489$	26.6968	+	0.465585i	1.20727	+	0.0210545i
$490$	−1.64166	+	2.69933i	−0.0741625	+	0.121943i
$491$			5.65453i			0.255185i	0.991827	+	0.127593i	$0.0407250\pi$
$491$			5.65453i			0.255185i	−0.991827	+	0.127593i	$0.959275\pi$
$492$	27.0429	−	13.4167i	1.21919	−	0.604870i
$493$			4.58291i			0.206404i
$494$	−7.43558	−	4.52212i	−0.334543	−	0.203460i
$495$	0.173599	−	4.97561i	0.00780271	−	0.223637i
$496$	11.3869	+	8.04071i	0.511286	+	0.361039i
$497$		−	24.2699i		−	1.08865i
$498$	1.64692	+	1.04138i	0.0738003	+	0.0466654i
$499$	31.1605			1.39494			0.697468	−	0.716616i	$-0.254310\pi$
$499$	31.1605			1.39494			0.697468	+	0.716616i	$0.254310\pi$
$500$	7.41106	+	14.3057i	0.331433	+	0.639773i
$501$	15.6709	+	0.273297i	0.700125	+	0.0122100i
$502$	−17.0716	−	10.3825i	−0.761944	−	0.463394i
$503$	0.784770			0.0349912			0.0174956	−	0.999847i	$-0.494431\pi$
$503$	0.784770			0.0349912			0.0174956	+	0.999847i	$0.494431\pi$
$504$	−2.70574	+	26.0992i	−0.120523	+	1.16255i
$505$	17.0712			0.759658
$506$	2.29999	+	1.39879i	0.102247	+	0.0621840i
$507$	−19.8566	−	0.346294i	−0.881864	−	0.0153795i
$508$	12.2697	−	6.35630i	0.544381	−	0.282015i
$509$	−1.62618			−0.0720790			−0.0360395	−	0.999350i	$-0.511474\pi$
$509$	−1.62618			−0.0720790			−0.0360395	+	0.999350i	$0.511474\pi$
$510$	3.57931	+	2.26327i	0.158494	+	0.100219i
$511$			21.7945i			0.964131i
$512$	−22.1523	−	4.61237i	−0.979004	−	0.203840i
$513$	25.7817	+	1.34997i	1.13829	+	0.0596027i
$514$	16.0628	+	9.76895i	0.708499	+	0.430890i
$515$		−	2.58076i		−	0.113722i
$516$	−5.03101	−	10.1406i	−0.221478	−	0.446415i
$517$		−	14.6210i		−	0.643031i
$518$	10.3770	−	17.0626i	0.455940	−	0.749688i
$519$	4.91355	+	0.0856910i	0.215681	+	0.00376142i
$520$	0.208825	−	3.04706i	0.00915758	−	0.133623i
$521$		−	22.0363i		−	0.965429i	−0.875778	−	0.482715i	$-0.839651\pi$
$521$		−	22.0363i		−	0.965429i	0.875778	−	0.482715i	$-0.160349\pi$
$522$	−5.38397	+	8.19473i	−0.235650	+	0.358674i
$523$	−0.873026			−0.0381748			−0.0190874	−	0.999818i	$-0.506076\pi$
$523$	−0.873026			−0.0381748			−0.0190874	+	0.999818i	$0.506076\pi$
$524$	−22.3253	+	11.5656i	−0.975286	+	0.505244i
$525$	0.395979	−	22.7056i	0.0172819	−	0.990953i
$526$	18.6593	−	30.6810i	0.813586	−	1.33775i
$527$	−6.91060			−0.301030
$528$	−10.6384	−	7.79371i	−0.462978	−	0.339178i
$529$	1.00000			0.0434783
$530$	4.82462	−	7.93298i	0.209568	−	0.344586i
$531$	1.27745	−	36.6137i	0.0554368	−	1.58890i
$532$	27.2843	−	14.1346i	1.18293	−	0.612812i
$533$	10.7935			0.467518
$534$	35.9960	+	22.7610i	1.55770	+	0.984964i
$535$			7.81018i			0.337663i
$536$	0.158768	+	0.0108809i	0.00685774	+	0.000469983i
$537$	0.319640	−	18.3282i	0.0137935	−	0.790922i
$538$	1.90236	−	3.12800i	0.0820168	−	0.134858i
$539$			4.87748i			0.210088i
$540$	3.74131	+	8.25191i	0.161001	+	0.355106i
$541$		−	40.4127i		−	1.73748i	−0.495269	−	0.868739i	$-0.664931\pi$
$541$		−	40.4127i		−	1.73748i	0.495269	−	0.868739i	$-0.335069\pi$
$542$	35.6612	+	21.6882i	1.53178	+	0.931587i
$543$	−0.259889	+	14.9021i	−0.0111529	+	0.639511i
$544$	10.2898	−	4.46685i	0.441173	−	0.191514i
$545$		−	8.15192i		−	0.349190i
$546$	−5.01389	+	7.92935i	−0.214574	+	0.339345i
$547$	26.3268			1.12565			0.562825	−	0.826576i	$-0.309714\pi$
$547$	26.3268			1.12565			0.562825	+	0.826576i	$0.309714\pi$
$548$	3.16962	−	1.64201i	0.135399	−	0.0701433i
$549$	−1.12949	+	32.3729i	−0.0482056	+	1.38164i
$550$	9.75172	+	5.93074i	0.415815	+	0.252887i
$551$	11.4826			0.489176
$552$	−4.88093	−	0.420130i	−0.207746	−	0.0178819i
$553$	−15.7910			−0.671502
$554$	−1.31402	−	0.799152i	−0.0558274	−	0.0339527i
$555$	0.120243	−	6.89477i	0.00510402	−	0.292667i
$556$	−5.43565	−	10.4926i	−0.230523	−	0.444984i
$557$	−26.7166			−1.13202			−0.566009	−	0.824399i	$-0.691513\pi$
$557$	−26.7166			−1.13202			−0.566009	+	0.824399i	$0.691513\pi$
$558$	−12.3569	−	8.11853i	−0.523109	−	0.343685i
$559$		−	4.04737i		−	0.171185i
$560$	8.80913	+	6.22046i	0.372254	+	0.262862i
$561$	6.53687	+	0.114001i	0.275987	+	0.00481313i
$562$	3.94825	+	2.40122i	0.166547	+	0.101289i
$563$			13.0343i			0.549330i	0.961540	+	0.274665i	$0.0885669\pi$
$563$			13.0343i			0.549330i	−0.961540	+	0.274665i	$0.911433\pi$
$564$	11.8256	+	23.8360i	0.497949	+	1.00367i
$565$		−	1.28292i		−	0.0539729i
$566$	4.68191	−	7.69831i	0.196795	−	0.323584i
$567$	1.93967	−	27.7631i	0.0814587	−	1.16594i
$568$	−22.1469	−	1.51780i	−0.929262	−	0.0636853i
$569$			38.2253i			1.60249i	0.598338	+	0.801244i	$0.295828\pi$
$569$			38.2253i			1.60249i	−0.598338	+	0.801244i	$0.704172\pi$
$570$	5.67069	−	8.96807i	0.237519	−	0.375631i
$571$	25.1413			1.05213			0.526066	−	0.850444i	$-0.323667\pi$
$571$	25.1413			1.05213			0.526066	+	0.850444i	$0.323667\pi$
$572$	−2.16893	−	4.18673i	−0.0906873	−	0.175056i
$573$	−25.2958	−	0.441152i	−1.05675	−	0.0184294i
$574$	−19.8030	+	32.5614i	−0.826561	+	1.35909i
$575$	4.23989			0.176816
$576$	23.6470	+	4.10125i	0.985291	+	0.170886i
$577$	−20.3082			−0.845442			−0.422721	−	0.906260i	$-0.638925\pi$
$577$	−20.3082			−0.845442			−0.422721	+	0.906260i	$0.638925\pi$
$578$	9.60287	−	15.7897i	0.399427	−	0.656765i
$579$	9.49898	+	0.165660i	0.394764	+	0.00688458i
$580$	1.85366	+	3.57817i	0.0769692	+	0.148576i
$581$	−2.45990			−0.102054
$582$	−11.8503	+	18.7410i	−0.491211	+	0.776840i
$583$		−	14.3343i		−	0.593666i
$584$	19.8880	+	1.36299i	0.822971	+	0.0564009i
$585$	−0.112957	+	3.23751i	−0.00467019	+	0.133854i
$586$	18.0274	−	29.6419i	0.744705	−	1.22449i
$587$		−	15.5366i		−	0.641263i	−0.947204	−	0.320631i	$-0.896105\pi$
$587$		−	15.5366i		−	0.641263i	0.947204	−	0.320631i	$-0.103895\pi$
$588$	−3.94496	−	7.95153i	−0.162687	−	0.327916i
$589$			17.3147i			0.713441i
$590$	−12.8647	−	7.82394i	−0.529629	−	0.322106i
$591$	−37.8602	−	0.660271i	−1.55736	−	0.0271599i
$592$	−14.9211	−	10.5363i	−0.613253	−	0.433041i
$593$			6.77501i			0.278216i	0.990277	+	0.139108i	$0.0444236\pi$
$593$			6.77501i			0.278216i	−0.990277	+	0.139108i	$0.955576\pi$
$594$	11.5547	+	7.88333i	0.474095	+	0.323457i
$595$	−5.34618			−0.219172
$596$	16.8944	+	32.6117i	0.692023	+	1.33583i
$597$	0.591835	−	33.9360i	0.0242222	−	1.38891i
$598$	−1.49655	−	0.910161i	−0.0611985	−	0.0372193i
$599$	32.7522			1.33822			0.669109	−	0.743164i	$-0.266676\pi$
$599$	32.7522			1.33822			0.669109	+	0.743164i	$0.266676\pi$
$600$	−20.6946	−	1.78131i	−0.844855	−	0.0727216i
$601$	−7.83996			−0.319799			−0.159899	−	0.987133i	$-0.551117\pi$
$601$	−7.83996			−0.319799			−0.159899	+	0.987133i	$0.551117\pi$
$602$	12.2099	+	7.42576i	0.497640	+	0.302651i
$603$	−0.168692	−	0.00588566i	−0.00686965	−	0.000239683i
$604$	10.0386	−	5.20049i	0.408466	−	0.211605i
$605$	6.43131			0.261470
$606$	−25.6331	+	40.5383i	−1.04127	+	1.64675i
$607$			11.1151i			0.451147i	0.974226	+	0.225574i	$0.0724256\pi$
$607$			11.1151i			0.451147i	−0.974226	+	0.225574i	$0.927574\pi$
$608$	−11.1918	−	25.7816i	−0.453889	−	1.04558i
$609$	0.215841	−	12.3764i	0.00874634	−	0.501518i
$610$	11.3746	+	6.91774i	0.460545	+	0.280091i
$611$			9.51354i			0.384877i
$612$	−10.7490	+	5.10124i	−0.434501	+	0.206205i
$613$		−	2.83979i		−	0.114698i	−0.998354	−	0.0573490i	$-0.981735\pi$
$613$		−	2.83979i		−	0.114698i	0.998354	−	0.0573490i	$-0.0182648\pi$
$614$	4.77117	−	7.84509i	0.192549	−	0.316602i
$615$	−0.229465	+	13.1576i	−0.00925294	+	0.530567i
$616$	16.6097	+	1.13832i	0.669225	+	0.0458641i
$617$			2.11914i			0.0853133i	0.999090	+	0.0426566i	$0.0135822\pi$
$617$			2.11914i			0.0853133i	−0.999090	+	0.0426566i	$0.986418\pi$
$618$	6.12842	+	3.87512i	0.246521	+	0.155880i
$619$	−19.2856			−0.775154			−0.387577	−	0.921837i	$-0.626688\pi$
$619$	−19.2856			−0.775154			−0.387577	+	0.921837i	$0.626688\pi$
$620$	−5.39555	+	2.79515i	−0.216691	+	0.112256i
$621$	5.18904	+	0.271707i	0.208229	+	0.0109032i
$622$	19.3651	−	31.8414i	0.776469	−	1.27672i
$623$	−53.7649			−2.15405
$624$	6.92217	+	5.07118i	0.277109	+	0.203010i
$625$	14.1762			0.567047
$626$	−24.4092	+	40.1353i	−0.975589	+	1.60413i
$627$	0.285634	−	16.3784i	0.0114071	−	0.654088i
$628$	−31.3945	+	16.2638i	−1.25278	+	0.648998i
$629$	9.05547			0.361065
$630$	−9.55955	−	6.28066i	−0.380862	−	0.250228i
$631$			12.4518i			0.495696i	0.968799	+	0.247848i	$0.0797234\pi$
$631$			12.4518i			0.495696i	−0.968799	+	0.247848i	$0.920277\pi$
$632$	−0.987542	+	14.4097i	−0.0392823	+	0.573186i
$633$	−17.0099	−	0.296647i	−0.676081	−	0.0117907i
$634$	−15.6719	+	25.7688i	−0.622411	+	1.02341i
$635$			6.02373i			0.239044i
$636$	11.5937	+	23.3685i	0.459721	+	0.926623i
$637$		−	3.17366i		−	0.125745i
$638$	5.31550	+	3.23274i	0.210443	+	0.127986i
$639$	23.5311	+	0.821001i	0.930875	+	0.0324783i
$640$	6.22723	−	7.64953i	0.246153	−	0.302374i
$641$		−	18.3406i		−	0.724411i	−0.932098	−	0.362205i	$-0.882024\pi$
$641$		−	18.3406i		−	0.724411i	0.932098	−	0.362205i	$-0.117976\pi$
$642$	−18.5465	−	11.7273i	−0.731972	−	0.462840i
$643$	42.8115			1.68832			0.844160	−	0.536091i	$-0.180100\pi$
$643$	42.8115			1.68832			0.844160	+	0.536091i	$0.180100\pi$
$644$	5.49148	−	2.84485i	0.216395	−	0.112103i
$645$	4.93387	+	0.0860454i	0.194271	+	0.00338803i
$646$	11.9048	+	7.24017i	0.468388	+	0.284861i
$647$	24.2136			0.951935			0.475968	−	0.879463i	$-0.342098\pi$
$647$	24.2136			0.951935			0.475968	+	0.879463i	$0.342098\pi$
$648$	−25.2132	−	3.50626i	−0.990469	−	0.137739i
$649$	−23.2455			−0.912464
$650$	−6.34521	−	3.85899i	−0.248880	−	0.151362i
$651$	18.6625	+	0.325469i	0.731441	+	0.0127561i
$652$	14.1821	+	27.3761i	0.555415	+	1.07213i
$653$	37.6716			1.47420			0.737101	−	0.675782i	$-0.236194\pi$
$653$	37.6716			1.47420			0.737101	+	0.675782i	$0.236194\pi$
$654$	19.3580	+	12.2405i	0.756959	+	0.478640i
$655$		−	10.9604i		−	0.428260i
$656$	28.4747	+	20.1070i	1.11175	+	0.785048i
$657$	−21.1310	−	0.737263i	−0.824400	−	0.0287634i
$658$	−28.7001	−	17.4546i	−1.11885	−	0.680452i
$659$			24.6271i			0.959337i	0.877450	+	0.479669i	$0.159243\pi$
$659$			24.6271i			0.959337i	−0.877450	+	0.479669i	$0.840757\pi$
$660$	5.14987	−	2.55498i	0.200458	−	0.0994526i
$661$		−	43.8276i		−	1.70470i	−0.522976	−	0.852348i	$-0.675178\pi$
$661$		−	43.8276i		−	1.70470i	0.522976	−	0.852348i	$-0.324822\pi$
$662$	−5.25414	+	8.63921i	−0.204208	+	0.335773i
$663$	−4.25338	−	0.0741778i	−0.165188	−	0.00288083i
$664$	−0.153838	+	2.24472i	−0.00597006	+	0.0871120i
$665$			13.3950i			0.519437i
$666$	16.1922	+	10.6383i	0.627434	+	0.412227i
$667$	2.31109			0.0894859
$668$	8.32484	+	16.0696i	0.322098	+	0.621753i
$669$	−0.162287	+	9.30557i	−0.00627436	+	0.359774i
$670$	−0.0360475	+	0.0592718i	−0.00139264	+	0.00228987i
$671$	20.5531			0.793443
$672$	−27.9987	+	11.5784i	−1.08008	+	0.446646i
$673$	−33.5022			−1.29142			−0.645708	−	0.763584i	$-0.723438\pi$
$673$	−33.5022			−1.29142			−0.645708	+	0.763584i	$0.723438\pi$
$674$	5.63654	−	9.26799i	0.217111	−	0.356989i
$675$	22.0010	+	1.15201i	0.846819	+	0.0443408i
$676$	−10.5484	−	20.3619i	−0.405708	−	0.783148i
$677$	14.9572			0.574850			0.287425	−	0.957803i	$-0.407201\pi$
$677$	14.9572			0.574850			0.287425	+	0.957803i	$0.407201\pi$
$678$	3.04650	+	1.92636i	0.117000	+	0.0739815i
$679$		−	27.9923i		−	1.07424i
$680$	−0.334341	+	4.87852i	−0.0128214	+	0.187083i
$681$	0.696263	−	39.9240i	0.0266809	−	1.52989i
$682$	−4.87468	+	8.01528i	−0.186661	+	0.306921i
$683$			4.05767i			0.155262i	0.996982	+	0.0776312i	$0.0247357\pi$
$683$			4.05767i			0.155262i	−0.996982	+	0.0776312i	$0.975264\pi$
$684$	12.7813	+	26.9319i	0.488706	+	1.02977i
$685$			1.55610i			0.0594555i
$686$	−16.5809	−	10.0840i	−0.633061	−	0.385011i
$687$	−0.822286	+	47.1502i	−0.0313722	+	1.79889i
$688$	7.53978	−	10.6775i	0.287451	−	0.407075i
$689$			9.32698i			0.355329i
$690$	1.14133	−	1.80499i	0.0434498	−	0.0687149i
$691$	−23.0400			−0.876485			−0.438242	−	0.898857i	$-0.644399\pi$
$691$	−23.0400			−0.876485			−0.438242	+	0.898857i	$0.644399\pi$
$692$	2.61022	+	5.03857i	0.0992257	+	0.191538i
$693$	−17.6479	−	0.615735i	−0.670387	−	0.0233898i
$694$	−33.0582	−	20.1051i	−1.25487	−	0.763179i
$695$	5.15125			0.195398
$696$	−11.2803	−	0.970960i	−0.427578	−	0.0368042i
$697$	−17.2810			−0.654565
$698$	7.34572	+	4.46747i	0.278040	+	0.169096i
$699$	0.652884	−	37.4366i	0.0246943	−	1.41598i
$700$	23.2833	−	12.0619i	0.880026	−	0.455895i
$701$	−22.3112			−0.842683			−0.421342	−	0.906902i	$-0.638441\pi$
$701$	−22.3112			−0.842683			−0.421342	+	0.906902i	$0.638441\pi$
$702$	−7.51836	−	5.12949i	−0.283762	−	0.193600i
$703$		−	22.6888i		−	0.855724i
$704$	2.07749	−	15.0856i	0.0782982	−	0.568560i
$705$	−11.5973	−	0.202254i	−0.436780	−	0.00761732i
$706$	−31.0378	−	18.8764i	−1.16812	−	0.710421i
$707$		−	60.5494i		−	2.27719i
$708$	37.8960	−	18.8012i	1.42422	−	0.706591i
$709$			17.9668i			0.674758i	0.941369	+	0.337379i	$0.109540\pi$
$709$			17.9668i			0.674758i	−0.941369	+	0.337379i	$0.890460\pi$
$710$	5.02833	−	8.26793i	0.188710	−	0.310290i
$711$	0.534178	−	15.3103i	0.0200332	−	0.574182i
$712$	−3.36236	+	49.0618i	−0.126010	+	1.83867i
$713$			3.48492i			0.130511i
$714$	8.02752	−	12.6953i	0.300422	−	0.475111i
$715$	2.05544			0.0768693
$716$	18.7946	−	9.73649i	0.702387	−	0.363870i
$717$	30.6140	+	0.533900i	1.14330	+	0.0199389i
$718$	13.1972	−	21.6998i	0.492517	−	0.809830i
$719$	−34.2271			−1.27646			−0.638228	−	0.769848i	$-0.720332\pi$
$719$	−34.2271			−1.27646			−0.638228	+	0.769848i	$0.720332\pi$
$720$	−6.32910	+	8.33054i	−0.235871	+	0.310461i
$721$	−9.15363			−0.340899
$722$	4.17825	−	6.87016i	0.155498	−	0.255681i
$723$	28.3051	+	0.493634i	1.05268	+	0.0183584i
$724$	−15.2813	+	7.91644i	−0.567925	+	0.294212i
$725$	9.79879			0.363918
$726$	−9.65689	+	15.2722i	−0.358401	+	0.566803i
$727$			19.2864i			0.715293i	0.933857	+	0.357646i	$0.116421\pi$
$727$			19.2864i			0.715293i	−0.933857	+	0.357646i	$0.883579\pi$
$728$	−10.8075	−	0.740676i	−0.400554	−	0.0274513i
$729$	26.8524	+	2.81980i	0.994532	+	0.104437i
$730$	−4.51547	+	7.42464i	−0.167125	+	0.274798i
$731$			6.48007i			0.239674i
$732$	−33.5067	+	16.6236i	−1.23844	+	0.614424i
$733$			13.7227i			0.506860i	0.967354	+	0.253430i	$0.0815587\pi$
$733$			13.7227i			0.506860i	−0.967354	+	0.253430i	$0.918441\pi$
$734$	−27.2650	−	16.5818i	−1.00637	−	0.612046i
$735$	3.86879	+	0.0674707i	0.142703	+	0.00248869i
$736$	−2.25257	−	5.18902i	−0.0830307	−	0.191270i
$737$			0.107100i			0.00394507i
$738$	−30.9003	−	20.3016i	−1.13746	−	0.747314i
$739$	−21.1541			−0.778167			−0.389083	−	0.921203i	$-0.627208\pi$
$739$	−21.1541			−0.778167			−0.389083	+	0.921203i	$0.627208\pi$
$740$	7.07020	−	3.66270i	0.259906	−	0.134643i
$741$	−0.185855	+	10.6570i	−0.00682756	+	0.391495i
$742$	−28.1373	−	17.1123i	−1.03295	−	0.628213i
$743$	26.8675			0.985673			0.492837	−	0.870122i	$-0.335960\pi$
$743$	26.8675			0.985673			0.492837	+	0.870122i	$0.335960\pi$
$744$	1.46412	−	17.0096i	0.0536772	−	0.623603i
$745$	−16.0105			−0.586579
$746$	23.7261	+	14.4296i	0.868674	+	0.528304i
$747$	0.0832134	−	2.38502i	0.00304462	−	0.0872632i
$748$	3.47257	+	6.70319i	0.126970	+	0.245093i
$749$	27.7017			1.01220
$750$	10.5458	−	16.6779i	0.385078	−	0.608992i
$751$			6.80908i			0.248467i	0.992253	+	0.124233i	$0.0396472\pi$
$751$			6.80908i			0.248467i	−0.992253	+	0.124233i	$0.960353\pi$
$752$	−17.7226	+	25.0979i	−0.646277	+	0.915228i
$753$	−0.426711	+	24.4678i	−0.0155502	+	0.891656i
$754$	−3.45867	−	2.10347i	−0.125957	−	0.0766038i
$755$			4.92839i			0.179363i
$756$	29.2685	−	13.2700i	1.06448	−	0.482624i
$757$		−	5.76958i		−	0.209699i	−0.994488	−	0.104849i	$-0.966564\pi$
$757$		−	5.76958i		−	0.209699i	0.994488	−	0.104849i	$-0.0334361\pi$
$758$	−10.2268	+	16.8156i	−0.371454	+	0.610770i
$759$	0.0574892	−	3.29645i	0.00208673	−	0.119654i
$760$	12.2233	+	0.837702i	0.443386	+	0.0303866i
$761$			39.7502i			1.44095i	0.693483	+	0.720473i	$0.256075\pi$
$761$			39.7502i			1.44095i	−0.693483	+	0.720473i	$0.743925\pi$
$762$	−14.3043	−	9.04489i	−0.518190	−	0.327662i
$763$	−28.9138			−1.04675
$764$	−13.4379	−	25.9394i	−0.486165	−	0.938455i
$765$	0.180850	−	5.18343i	0.00653866	−	0.187407i
$766$	−20.0122	+	32.9054i	−0.723069	+	1.18892i
$767$	15.1253			0.546141
$768$	8.81456	+	26.2736i	0.318068	+	0.948068i
$769$	44.3637			1.59980			0.799898	−	0.600136i	$-0.204887\pi$
$769$	44.3637			1.59980			0.799898	+	0.600136i	$0.204887\pi$
$770$	−3.77115	+	6.20079i	−0.135903	+	0.223461i
$771$	0.401495	−	23.0219i	0.0144595	−	0.829112i
$772$	5.04613	+	9.74067i	0.181614	+	0.350574i
$773$	−20.9167			−0.752321			−0.376161	−	0.926554i	$-0.622756\pi$
$773$	−20.9167			−0.752321			−0.376161	+	0.926554i	$0.622756\pi$
$774$	−7.61275	+	11.5871i	−0.273635	+	0.416488i
$775$			14.7757i			0.530758i
$776$	−25.5436	−	1.75059i	−0.916962	−	0.0628424i
$777$	−24.4549	−	0.426486i	−0.877314	−	0.0153001i
$778$	−0.145692	+	0.239557i	−0.00522332	+	0.00858854i
$779$			43.2982i			1.55132i
$780$	−3.35090	+	1.66247i	−0.119981	+	0.0595258i
$781$		−	14.9395i		−	0.534578i
$782$	2.39606	+	1.45722i	0.0856830	+	0.0521101i
$783$	11.9924	+	0.627940i	0.428572	+	0.0224408i
$784$	5.91216	−	8.37252i	0.211148	−	0.299019i
$785$		−	15.4129i		−	0.550110i
$786$	26.0273	+	16.4576i	0.928363	+	0.587022i
$787$	−52.1207			−1.85790			−0.928951	−	0.370202i	$-0.879289\pi$
$787$	−52.1207			−1.85790			−0.928951	+	0.370202i	$0.879289\pi$
$788$	−20.1124	−	38.8235i	−0.716475	−	1.38303i
$789$	−43.9733	−	0.766883i	−1.56549	−	0.0273017i
$790$	−5.37946	−	3.27164i	−0.191393	−	0.116400i
$791$	−4.55036			−0.161792
$792$	−1.66554	+	16.0656i	−0.0591823	+	0.570866i
$793$	−13.3734			−0.474903
$794$	−15.5278	−	9.44359i	−0.551061	−	0.335140i
$795$	−11.3699	−	0.198288i	−0.403248	−	0.00703254i
$796$	34.7995	−	18.0278i	1.23343	−	0.638978i
$797$	−35.1231			−1.24412			−0.622062	−	0.782968i	$-0.713705\pi$
$797$	−35.1231			−1.24412			−0.622062	+	0.782968i	$0.713705\pi$
$798$	−31.8086	−	20.1132i	−1.12601	−	0.712000i
$799$		−	15.2317i		−	0.538859i
$800$	−9.55064	−	22.0009i	−0.337666	−	0.777849i
$801$	1.81876	−	52.1283i	0.0642627	−	1.84186i
$802$	−28.1775	−	17.1368i	−0.994983	−	0.605122i
$803$			13.4158i			0.473432i
$804$	−0.0866234	−	0.174600i	−0.00305497	−	0.00615765i
$805$			2.69600i			0.0950216i
$806$	3.17184	−	5.21535i	0.111723	−	0.183703i
$807$	−4.48318	−	0.0781855i	−0.157816	−	0.00275226i
$808$	−55.2528	−	3.78665i	−1.94379	−	0.133214i
$809$			11.2110i			0.394157i	0.980388	+	0.197078i	$0.0631454\pi$
$809$			11.2110i			0.394157i	−0.980388	+	0.197078i	$0.936855\pi$
$810$	6.41285	−	9.05608i	0.225325	−	0.318198i
$811$	−23.2309			−0.815746			−0.407873	−	0.913039i	$-0.633729\pi$
$811$	−23.2309			−0.815746			−0.407873	+	0.913039i	$0.633729\pi$
$812$	12.6913	−	6.57471i	0.445378	−	0.230727i
$813$	0.891365	−	51.1112i	0.0312615	−	1.79255i
$814$	6.38766	−	10.5030i	0.223887	−	0.368131i
$815$	−13.4401			−0.470786
$816$	−11.0828	−	8.11925i	−0.387975	−	0.284231i
$817$	16.2360			0.568027
$818$	2.13835	−	3.51602i	0.0747657	−	0.122935i
$819$	11.4830	+	0.400644i	0.401250	+	0.0139996i
$820$	−13.4924	+	6.98971i	−0.471175	+	0.244091i
$821$	8.28219			0.289050			0.144525	−	0.989501i	$-0.453835\pi$
$821$	8.28219			0.289050			0.144525	+	0.989501i	$0.453835\pi$
$822$	−3.69521	−	2.33655i	−0.128885	−	0.0814966i
$823$			17.0583i			0.594616i	0.954782	+	0.297308i	$0.0960889\pi$
$823$			17.0583i			0.594616i	−0.954782	+	0.297308i	$0.903911\pi$
$824$	−0.572452	+	8.35291i	−0.0199423	+	0.290987i
$825$	0.243748	−	13.9766i	0.00848622	−	0.486603i
$826$	−27.7505	+	45.6293i	−0.965564	+	1.58765i
$827$		−	11.3622i		−	0.395101i	−0.980293	−	0.197551i	$-0.936701\pi$
$827$		−	11.3622i		−	0.395101i	0.980293	−	0.197551i	$-0.0632987\pi$
$828$	2.57248	+	5.42055i	0.0893999	+	0.188377i
$829$			33.5403i			1.16490i	0.812865	+	0.582452i	$0.197906\pi$
$829$			33.5403i			1.16490i	−0.812865	+	0.582452i	$0.802094\pi$
$830$	−0.838004	−	0.509652i	−0.0290876	−	0.0176903i
$831$	−0.0328444	+	1.88331i	−0.00113936	+	0.0653314i
$832$	−1.35177	+	9.81583i	−0.0468642	+	0.340303i
$833$			5.08121i			0.176053i
$834$	−7.73482	+	12.2325i	−0.267835	+	0.423575i
$835$	−7.88928			−0.273020
$836$	16.7951	−	8.70065i	0.580870	−	0.300918i
$837$	−0.946876	+	18.0834i	−0.0327288	+	0.625053i
$838$	−19.2658	−	11.7169i	−0.665524	−	0.404754i
$839$	0.880528			0.0303992			0.0151996	−	0.999884i	$-0.495162\pi$
$839$	0.880528			0.0303992			0.0151996	+	0.999884i	$0.495162\pi$
$840$	1.13267	−	13.1590i	0.0390809	−	0.454029i
$841$	−23.6588			−0.815822
$842$	−37.0696	−	22.5447i	−1.27750	−	0.776942i
$843$	0.0986881	−	5.65881i	0.00339900	−	0.194900i
$844$	−9.03613	−	17.4427i	−0.311036	−	0.600401i
$845$	9.99650			0.343890
$846$	17.8941	−	27.2360i	0.615213	−	0.936391i
$847$		−	22.8111i		−	0.783797i
$848$	−17.3751	+	24.6058i	−0.596662	+	0.844966i
$849$	−11.0336	−	0.192422i	−0.378671	−	0.00660391i
$850$	10.1590	+	6.17846i	0.348452	+	0.211919i
$851$		−	4.56655i		−	0.156539i
$852$	12.0832	+	24.3552i	0.413965	+	0.834396i
$853$			51.3054i			1.75666i	0.478052	+	0.878331i	$0.341343\pi$
$853$			51.3054i			1.75666i	−0.478052	+	0.878331i	$0.658657\pi$
$854$	24.5363	−	40.3443i	0.839617	−	1.38056i
$855$	−12.9873	−	0.453127i	−0.444155	−	0.0154966i
$856$	1.73242	−	25.2785i	0.0592128	−	0.864001i
$857$		−	20.2353i		−	0.691224i	−0.938378	−	0.345612i	$-0.887671\pi$
$857$		−	20.2353i		−	0.691224i	0.938378	−	0.345612i	$-0.112329\pi$
$858$	−3.08634	+	4.88098i	−0.105366	+	0.166634i
$859$	−23.4886			−0.801421			−0.400710	−	0.916205i	$-0.631237\pi$
$859$	−23.4886			−0.801421			−0.400710	+	0.916205i	$0.631237\pi$
$860$	2.62101	+	5.05941i	0.0893759	+	0.172524i
$861$	46.6685	+	0.813885i	1.59046	+	0.0277371i
$862$	−26.1759	+	43.0403i	−0.891556	+	1.46596i
$863$	−4.02794			−0.137113			−0.0685563	−	0.997647i	$-0.521839\pi$
$863$	−4.02794			−0.137113			−0.0685563	+	0.997647i	$0.521839\pi$
$864$	−10.2788	−	27.5381i	−0.349691	−	0.936865i
$865$	−2.47365			−0.0841066
$866$	2.31924	−	3.81346i	0.0788111	−	0.129587i
$867$	−22.6305	−	0.394669i	−0.768571	−	0.0134037i
$868$	9.91406	+	19.1373i	0.336505	+	0.649564i
$869$	−9.72028			−0.329738
$870$	2.63773	−	4.17151i	0.0894273	−	0.141427i
$871$		−	0.0696872i		−	0.00236126i
$872$	−1.80822	+	26.3846i	−0.0612341	+	0.893495i
$873$	27.1401	+	0.946921i	0.918554	+	0.0320484i
$874$	3.65112	−	6.00341i	0.123501	−	0.203068i
$875$			24.9108i			0.842138i
$876$	−10.8508	−	21.8711i	−0.366615	−	0.738956i
$877$			37.8678i			1.27870i	0.768914	+	0.639352i	$0.220798\pi$
$877$			37.8678i			1.27870i	−0.768914	+	0.639352i	$0.779202\pi$
$878$	33.6145	+	20.4434i	1.13443	+	0.689933i
$879$	−42.4840	−	0.740910i	−1.43295	−	0.0249903i
$880$	5.42253	+	3.82905i	0.182793	+	0.129077i
$881$		−	48.6628i		−	1.63949i	−0.572727	−	0.819746i	$-0.694115\pi$
$881$		−	48.6628i		−	1.63949i	0.572727	−	0.819746i	$-0.305885\pi$
$882$	−5.96938	+	9.08575i	−0.200999	+	0.305933i
$883$	−6.80087			−0.228868			−0.114434	−	0.993431i	$-0.536505\pi$
$883$	−6.80087			−0.228868			−0.114434	+	0.993431i	$0.536505\pi$
$884$	−2.25952	−	4.36160i	−0.0759959	−	0.146697i
$885$	−0.321557	+	18.4382i	−0.0108090	+	0.619793i
$886$	−7.89367	−	4.80072i	−0.265193	−	0.161283i
$887$	2.86430			0.0961737			0.0480869	−	0.998843i	$-0.484688\pi$
$887$	2.86430			0.0961737			0.0480869	+	0.998843i	$0.484688\pi$
$888$	−1.91854	+	22.2890i	−0.0643821	+	0.747970i
$889$	21.3654			0.716573
$890$	−18.3159	−	11.1392i	−0.613950	−	0.373388i
$891$	1.19398	−	17.0898i	0.0399999	−	0.572530i
$892$	−9.54234	+	4.94339i	−0.319501	+	0.165517i
$893$	−38.1636			−1.27710
$894$	24.0404	−	38.0194i	0.804032	−	1.27156i
$895$			9.22707i			0.308427i
$896$	−27.1319	−	22.0872i	−0.906413	−	0.737882i
$897$	−0.0374068	+	2.14492i	−0.00124898	+	0.0716168i
$898$	30.7961	+	18.7294i	1.02768	+	0.625007i
$899$			8.05397i			0.268615i
$900$	10.9070	+	22.9825i	0.363568	+	0.766085i
$901$		−	14.9330i		−	0.497491i
$902$	−12.1899	+	20.0434i	−0.405879	+	0.667374i
$903$	0.305192	−	17.4998i	0.0101562	−	0.582358i
$904$	−0.284572	+	4.15232i	−0.00946471	+	0.138104i
$905$		−	7.50224i		−	0.249383i
$906$	−11.7033	−	7.40019i	−0.388814	−	0.245855i
$907$	−19.3695			−0.643153			−0.321576	−	0.946884i	$-0.604213\pi$
$907$	−19.3695			−0.643153			−0.321576	+	0.946884i	$0.604213\pi$
$908$	40.9398	−	21.2088i	1.35863	−	0.703838i
$909$	58.7062	+	2.04826i	1.94716	+	0.0679366i
$910$	2.45380	−	4.03470i	0.0813426	−	0.133749i
$911$	22.5365			0.746668			0.373334	−	0.927697i	$-0.378215\pi$
$911$	22.5365			0.746668			0.373334	+	0.927697i	$0.378215\pi$
$912$	−20.3431	+	27.7683i	−0.673626	+	0.919501i
$913$	−1.51421			−0.0501131
$914$	1.76575	−	2.90337i	0.0584059	−	0.0960349i
$915$	0.284313	−	16.3026i	0.00939909	−	0.538947i
$916$	−48.3498	+	25.0475i	−1.59752	+	0.827593i
$917$	−38.8753			−1.28378
$918$	12.0373	+	8.21261i	0.397291	+	0.271056i
$919$		−	47.7774i		−	1.57603i	−0.615656	−	0.788015i	$-0.711109\pi$
$919$		−	47.7774i		−	1.57603i	0.615656	−	0.788015i	$-0.288891\pi$
$920$	2.46017	+	0.168603i	0.0811093	+	0.00555868i
$921$	−11.2439	−	0.196091i	−0.370500	−	0.00646142i
$922$	10.3348	−	16.9932i	0.340359	−	0.559641i
$923$			9.72079i			0.319964i
$924$	−9.06220	−	18.2659i	−0.298125	−	0.600905i
$925$		−	19.3617i		−	0.636608i
$926$	43.2196	+	26.2850i	1.42028	+	0.863778i
$927$	0.309649	−	8.87498i	0.0101702	−	0.291493i
$928$	−5.20589	−	11.9923i	−0.170892	−	0.393667i
$929$			40.9144i			1.34236i	0.741295	+	0.671179i	$0.234212\pi$
$929$			40.9144i			1.34236i	−0.741295	+	0.671179i	$0.765788\pi$
$930$	6.29025	+	3.97745i	0.206265	+	0.130426i
$931$	12.7311			0.417246
$932$	38.3891	−	19.8874i	1.25748	−	0.651433i
$933$	−45.6365	−	0.795887i	−1.49407	−	0.0260562i
$934$	47.5296	+	28.9063i	1.55522	+	0.945842i
$935$	−3.29088			−0.107623
$936$	1.08373	−	10.4535i	0.0354227	−	0.341683i
$937$	27.6662			0.903814			0.451907	−	0.892065i	$-0.350744\pi$
$937$	27.6662			0.903814			0.451907	+	0.892065i	$0.350744\pi$
$938$	0.210230	+	0.127856i	0.00686424	+	0.00417465i
$939$	57.5237	+	1.00320i	1.87721	+	0.0327381i
$940$	−6.16083	−	11.8924i	−0.200944	−	0.387887i
$941$	6.59325			0.214934			0.107467	−	0.994209i	$-0.465726\pi$
$941$	6.59325			0.214934			0.107467	+	0.994209i	$0.465726\pi$
$942$	36.6003	+	23.1431i	1.19250	+	0.754043i
$943$			8.71457i			0.283785i
$944$	39.9024	+	28.1766i	1.29871	+	0.917070i
$945$	−0.732522	+	13.9897i	−0.0238290	+	0.455084i
$946$	7.51593	+	4.57099i	0.244364	+	0.148616i
$947$		−	48.2638i		−	1.56836i	−0.620531	−	0.784182i	$-0.713083\pi$
$947$		−	48.2638i		−	1.56836i	0.620531	−	0.784182i	$-0.286917\pi$
$948$	15.8465	−	7.86187i	0.514671	−	0.255342i
$949$		−	8.72931i		−	0.283366i
$950$	15.4803	−	25.4538i	0.502249	−	0.825831i
$951$	36.9330	+	0.644101i	1.19763	+	0.0208864i
$952$	17.3035	+	1.18586i	0.560809	+	0.0384341i
$953$			48.2640i			1.56342i	0.623640	+	0.781712i	$0.285653\pi$
$953$			48.2640i			1.56342i	−0.623640	+	0.781712i	$0.714347\pi$
$954$	17.5432	−	26.7019i	0.567983	−	0.864504i
$955$	12.7348			0.412087
$956$	16.2630	+	31.3930i	0.525985	+	1.01532i
$957$	0.132863	−	7.61841i	0.00429485	−	0.246268i
$958$	−1.58838	+	2.61173i	−0.0513184	+	0.0843812i
$959$	5.51929			0.178227
$960$	−11.9371	−	1.85653i	−0.385267	−	0.0599193i
$961$	18.8554			0.608237
$962$	−4.15629	+	6.83406i	−0.134004	+	0.220339i
$963$	−0.937092	+	26.8584i	−0.0301974	+	0.865501i
$964$	15.0365	+	29.0253i	0.484293	+	0.934842i
$965$	−4.78211			−0.153942
$966$	−6.40208	−	4.04816i	−0.205984	−	0.130247i
$967$			51.1796i			1.64583i	0.568168	+	0.822913i	$0.307652\pi$
$967$			51.1796i			1.64583i	−0.568168	+	0.822913i	$0.692348\pi$
$968$	−20.8156	−	1.42656i	−0.669040	−	0.0458515i
$969$	0.297565	−	17.0625i	0.00955915	−	0.548125i
$970$	5.79954	−	9.53601i	0.186212	−	0.306183i
$971$			31.6471i			1.01560i	0.861474	+	0.507802i	$0.169542\pi$
$971$			31.6471i			1.01560i	−0.861474	+	0.507802i	$0.830458\pi$
$972$	11.8759	+	28.8264i	0.380920	+	0.924608i
$973$		−	18.2708i		−	0.585736i
$974$	34.0880	+	20.7314i	1.09225	+	0.664277i
$975$	−0.158601	+	9.09423i	−0.00507929	+	0.291249i
$976$	−35.2807	−	24.9131i	−1.12931	−	0.797448i
$977$			25.9886i			0.831448i	0.909491	+	0.415724i	$0.136472\pi$
$977$			25.9886i			0.831448i	−0.909491	+	0.415724i	$0.863528\pi$
$978$	20.1809	−	31.9156i	0.645313	−	1.02055i
$979$	−33.0954			−1.05773
$980$	2.05521	+	3.96723i	0.0656514	+	0.126728i
$981$	0.978096	−	28.0337i	0.0312282	−	0.895046i
$982$	6.83236	+	4.15526i	0.218029	+	0.132600i
$983$	−39.6637			−1.26507			−0.632537	−	0.774530i	$-0.717986\pi$
$983$	−39.6637			−1.26507			−0.632537	+	0.774530i	$0.717986\pi$
$984$	3.66125	−	42.5352i	0.116716	−	1.35597i
$985$	19.0601			0.607305
$986$	5.53752	+	3.36777i	0.176351	+	0.107252i
$987$	−0.717369	+	41.1342i	−0.0228341	+	1.30932i
$988$	−10.9282	+	5.66130i	−0.347671	+	0.180110i
$989$	3.26780			0.103910
$990$	−5.88446	−	3.86611i	−0.187020	−	0.122873i
$991$			13.4539i			0.427378i	0.976902	+	0.213689i	$0.0685480\pi$
$991$			13.4539i			0.427378i	−0.976902	+	0.213689i	$0.931452\pi$
$992$	18.0833	−	7.85000i	0.574145	−	0.249238i
$993$	12.3821	+	0.215940i	0.392934	+	0.00685266i
$994$	−29.3253	−	17.8349i	−0.930142	−	0.565687i
$995$			17.0846i			0.541617i
$996$	2.46855	−	1.22471i	0.0782189	−	0.0388064i
$997$			57.2452i			1.81297i	0.422234	+	0.906487i	$0.361246\pi$
$997$			57.2452i			1.81297i	−0.422234	+	0.906487i	$0.638754\pi$
$998$	22.8985	−	37.6512i	0.724838	−	1.19183i
$999$	1.24076	−	23.6960i	0.0392560	−	0.749708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.c.323.27	✓	42
3.2	odd	2		552.2.j.d.323.16	yes	42
4.3	odd	2		2208.2.j.c.47.42		42
8.3	odd	2		552.2.j.d.323.15	yes	42
8.5	even	2		2208.2.j.d.47.42		42
12.11	even	2		2208.2.j.d.47.41		42
24.5	odd	2		2208.2.j.c.47.41		42
24.11	even	2	inner	552.2.j.c.323.28	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.27	✓	42	1.1	even	1	trivial
552.2.j.c.323.28	yes	42	24.11	even	2	inner
552.2.j.d.323.15	yes	42	8.3	odd	2
552.2.j.d.323.16	yes	42	3.2	odd	2
2208.2.j.c.47.41		42	24.5	odd	2
2208.2.j.c.47.42		42	4.3	odd	2
2208.2.j.d.47.41		42	12.11	even	2
2208.2.j.d.47.42		42	8.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.734855 - 1.20830i) q^{2} +(-1.73179 - 0.0302019i) q^{3} +(-0.919975 - 1.77585i) q^{4} +0.871841 q^{5} +(-1.30911 + 2.07032i) q^{6} -3.09231i q^{7} +(-2.82181 - 0.193388i) q^{8} +(2.99818 + 0.104607i) q^{9} +(0.640677 - 1.05344i) q^{10} -1.90350i q^{11} +(1.53957 + 3.10318i) q^{12} +1.23856i q^{13} +(-3.73644 - 2.27240i) q^{14} +(-1.50984 - 0.0263313i) q^{15} +(-2.30729 + 3.26748i) q^{16} -1.98300i q^{17} +(2.32962 - 3.54582i) q^{18} -4.96848 q^{19} +(-0.802072 - 1.54826i) q^{20} +(-0.0933936 + 5.35522i) q^{21} +(-2.29999 - 1.39879i) q^{22} -1.00000 q^{23} +(4.88093 + 0.420130i) q^{24} -4.23989 q^{25} +(1.49655 + 0.910161i) q^{26} +(-5.18904 - 0.271707i) q^{27} +(-5.49148 + 2.84485i) q^{28} -2.31109 q^{29} +(-1.14133 + 1.80499i) q^{30} -3.48492i q^{31} +(2.25257 + 5.18902i) q^{32} +(-0.0574892 + 3.29645i) q^{33} +(-2.39606 - 1.45722i) q^{34} -2.69600i q^{35} +(-2.57248 - 5.42055i) q^{36} +4.56655i q^{37} +(-3.65112 + 6.00341i) q^{38} +(0.0374068 - 2.14492i) q^{39} +(-2.46017 - 0.168603i) q^{40} -8.71457i q^{41} +(6.40208 + 4.04816i) q^{42} -3.26780 q^{43} +(-3.38032 + 1.75117i) q^{44} +(2.61393 + 0.0912003i) q^{45} +(-0.734855 + 1.20830i) q^{46} +7.68114 q^{47} +(4.09442 - 5.58889i) q^{48} -2.56238 q^{49} +(-3.11571 + 5.12306i) q^{50} +(-0.0598904 + 3.43414i) q^{51} +(2.19950 - 1.13944i) q^{52} +7.53051 q^{53} +(-4.14150 + 6.07025i) q^{54} -1.65955i q^{55} +(-0.598014 + 8.72591i) q^{56} +(8.60435 + 0.150058i) q^{57} +(-1.69832 + 2.79249i) q^{58} -12.2120i q^{59} +(1.34226 + 2.70548i) q^{60} +10.7975i q^{61} +(-4.21082 - 2.56091i) q^{62} +(0.323476 - 9.27129i) q^{63} +(7.92520 + 1.09141i) q^{64} +1.07983i q^{65} +(3.94085 + 2.49188i) q^{66} -0.0562647 q^{67} +(-3.52152 + 1.82431i) q^{68} +(1.73179 + 0.0302019i) q^{69} +(-3.25758 - 1.98117i) q^{70} +7.84847 q^{71} +(-8.44005 - 0.874989i) q^{72} -7.04796 q^{73} +(5.51775 + 3.35575i) q^{74} +(7.34259 + 0.128053i) q^{75} +(4.57088 + 8.82328i) q^{76} -5.88620 q^{77} +(-2.56422 - 1.62140i) q^{78} -5.10654i q^{79} +(-2.01159 + 2.84872i) q^{80} +(8.97811 + 0.627258i) q^{81} +(-10.5298 - 6.40395i) q^{82} -0.795490i q^{83} +(9.59600 - 4.76082i) q^{84} -1.72886i q^{85} +(-2.40136 + 3.94849i) q^{86} +(4.00232 + 0.0697994i) q^{87} +(-0.368112 + 5.37130i) q^{88} -17.3867i q^{89} +(2.03106 - 3.09139i) q^{90} +3.83001 q^{91} +(0.919975 + 1.77585i) q^{92} +(-0.105251 + 6.03513i) q^{93} +(5.64452 - 9.28111i) q^{94} -4.33173 q^{95} +(-3.74425 - 9.05431i) q^{96} +9.05221 q^{97} +(-1.88298 + 3.09612i) q^{98} +(0.199118 - 5.70701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25}+ \cdots - 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * q^96 + 20 * q^97 - 64 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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