LMFDB - Embedded newform 630.2.bi.a.479.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(479,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.479"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			479.23
Character	$\chi$	$=$	630.479
Dual form			630.2.bi.a.509.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(1.70170 + 0.322848i) q^{3} +1.00000 q^{4} +(-2.15016 + 0.613862i) q^{5} +(-1.70170 - 0.322848i) q^{6} +(1.39638 - 2.24725i) q^{7} -1.00000 q^{8} +(2.79154 + 1.09878i) q^{9} +(2.15016 - 0.613862i) q^{10} +(-4.57187 + 2.63957i) q^{11} +(1.70170 + 0.322848i) q^{12} +(2.80645 + 4.86092i) q^{13} +(-1.39638 + 2.24725i) q^{14} +(-3.85710 + 0.350434i) q^{15} +1.00000 q^{16} +(4.30888 + 2.48773i) q^{17} +(-2.79154 - 1.09878i) q^{18} +(-0.0258184 + 0.0149063i) q^{19} +(-2.15016 + 0.613862i) q^{20} +(3.10173 - 3.37332i) q^{21} +(4.57187 - 2.63957i) q^{22} +(2.13852 - 3.70403i) q^{23} +(-1.70170 - 0.322848i) q^{24} +(4.24635 - 2.63980i) q^{25} +(-2.80645 - 4.86092i) q^{26} +(4.39561 + 2.77103i) q^{27} +(1.39638 - 2.24725i) q^{28} +(6.48036 + 3.74144i) q^{29} +(3.85710 - 0.350434i) q^{30} +7.77478i q^{31} -1.00000 q^{32} +(-8.63211 + 3.01573i) q^{33} +(-4.30888 - 2.48773i) q^{34} +(-1.62293 + 5.68912i) q^{35} +(2.79154 + 1.09878i) q^{36} +(1.82734 - 1.05501i) q^{37} +(0.0258184 - 0.0149063i) q^{38} +(3.20639 + 9.17786i) q^{39} +(2.15016 - 0.613862i) q^{40} +(0.423283 + 0.733148i) q^{41} +(-3.10173 + 3.37332i) q^{42} +(-7.31735 - 4.22467i) q^{43} +(-4.57187 + 2.63957i) q^{44} +(-6.67674 - 0.648925i) q^{45} +(-2.13852 + 3.70403i) q^{46} -3.59113i q^{47} +(1.70170 + 0.322848i) q^{48} +(-3.10026 - 6.27602i) q^{49} +(-4.24635 + 2.63980i) q^{50} +(6.52924 + 5.62448i) q^{51} +(2.80645 + 4.86092i) q^{52} +(0.914662 - 1.58424i) q^{53} +(-4.39561 - 2.77103i) q^{54} +(8.20990 - 8.48199i) q^{55} +(-1.39638 + 2.24725i) q^{56} +(-0.0487476 + 0.0170305i) q^{57} +(-6.48036 - 3.74144i) q^{58} +2.43666 q^{59} +(-3.85710 + 0.350434i) q^{60} -4.23295i q^{61} -7.77478i q^{62} +(6.36727 - 4.73898i) q^{63} +1.00000 q^{64} +(-9.01825 - 8.72896i) q^{65} +(8.63211 - 3.01573i) q^{66} +14.2507i q^{67} +(4.30888 + 2.48773i) q^{68} +(4.83495 - 5.61271i) q^{69} +(1.62293 - 5.68912i) q^{70} +10.3996i q^{71} +(-2.79154 - 1.09878i) q^{72} +(-2.23753 + 3.87552i) q^{73} +(-1.82734 + 1.05501i) q^{74} +(8.07824 - 3.12121i) q^{75} +(-0.0258184 + 0.0149063i) q^{76} +(-0.452280 + 13.9600i) q^{77} +(-3.20639 - 9.17786i) q^{78} -4.22144 q^{79} +(-2.15016 + 0.613862i) q^{80} +(6.58537 + 6.13456i) q^{81} +(-0.423283 - 0.733148i) q^{82} +(-9.84730 - 5.68534i) q^{83} +(3.10173 - 3.37332i) q^{84} +(-10.7919 - 2.70396i) q^{85} +(7.31735 + 4.22467i) q^{86} +(9.81969 + 8.45896i) q^{87} +(4.57187 - 2.63957i) q^{88} +(-5.09947 - 8.83254i) q^{89} +(6.67674 + 0.648925i) q^{90} +(14.8426 + 0.480874i) q^{91} +(2.13852 - 3.70403i) q^{92} +(-2.51007 + 13.2303i) q^{93} +3.59113i q^{94} +(0.0463633 - 0.0478998i) q^{95} +(-1.70170 - 0.322848i) q^{96} +(6.01859 - 10.4245i) q^{97} +(3.10026 + 6.27602i) q^{98} +(-15.6629 + 2.34499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8} + 6 q^{11} + 3 q^{14} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39}+ \cdots - 26 q^{99}+O(q^{100}) $ 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8 + 6 * q^11 + 3 * q^14 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 + 42 * q^55 + 3 * q^56 + 22 * q^57 + 3 * q^58 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * q^70 + 18 * q^73 + 18 * q^75 + 12 * q^77 + 18 * q^78 + 8 * q^81 + 3 * q^82 - 9 * q^83 + 8 * q^84 + 33 * q^85 + 15 * q^87 - 6 * q^88 - 33 * q^89 - 15 * q^90 - 3 * q^92 + 8 * q^93 + 24 * q^97 - 3 * q^98 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.70170	+	0.322848i	0.982475	+	0.186396i
$3$	1.70170	+	0.322848i	0.982475	+	0.186396i
$4$	1.00000			0.500000
$5$	−2.15016	+	0.613862i	−0.961579	+	0.274528i
$5$	−2.15016	+	0.613862i	−0.961579	+	0.274528i
$6$	−1.70170	−	0.322848i	−0.694714	−	0.131802i
$7$	1.39638	−	2.24725i	0.527781	−	0.849381i
$7$	1.39638	−	2.24725i	0.527781	−	0.849381i
$8$	−1.00000			−0.353553
$9$	2.79154	+	1.09878i	0.930513	+	0.366259i
$10$	2.15016	−	0.613862i	0.679939	−	0.194120i
$11$	−4.57187	+	2.63957i	−1.37847	+	0.795860i	−0.991975	−	0.126431i	$-0.959648\pi$
$11$	−4.57187	+	2.63957i	−1.37847	+	0.795860i	−0.386495	+	0.922291i	$0.626314\pi$
$12$	1.70170	+	0.322848i	0.491237	+	0.0931982i
$13$	2.80645	+	4.86092i	0.778370	+	1.34818i	0.932881	+	0.360185i	$0.117286\pi$
$13$	2.80645	+	4.86092i	0.778370	+	1.34818i	−0.154511	+	0.987991i	$0.549380\pi$
$14$	−1.39638	+	2.24725i	−0.373197	+	0.600603i
$15$	−3.85710	+	0.350434i	−0.995898	+	0.0904815i
$16$	1.00000			0.250000
$17$	4.30888	+	2.48773i	1.04506	+	0.603364i	0.921261	−	0.388944i	$-0.127160\pi$
$17$	4.30888	+	2.48773i	1.04506	+	0.603364i	0.123796	+	0.992308i	$0.460493\pi$
$18$	−2.79154	−	1.09878i	−0.657972	−	0.258985i
$19$	−0.0258184	+	0.0149063i	−0.00592316	+	0.00341974i	−0.502959	−	0.864310i	$-0.667755\pi$
$19$	−0.0258184	+	0.0149063i	−0.00592316	+	0.00341974i	0.497035	+	0.867730i	$0.334422\pi$
$20$	−2.15016	+	0.613862i	−0.480790	+	0.137264i
$21$	3.10173	−	3.37332i	0.676853	−	0.736118i
$22$	4.57187	−	2.63957i	0.974726	−	0.562758i
$23$	2.13852	−	3.70403i	0.445912	−	0.772343i	−0.552203	−	0.833710i	$-0.686213\pi$
$23$	2.13852	−	3.70403i	0.445912	−	0.772343i	0.998115	+	0.0613667i	$0.0195459\pi$
$24$	−1.70170	−	0.322848i	−0.347357	−	0.0659011i
$25$	4.24635	−	2.63980i	0.849269	−	0.527960i
$26$	−2.80645	−	4.86092i	−0.550391	−	0.953304i
$27$	4.39561	+	2.77103i	0.845936	+	0.533285i
$28$	1.39638	−	2.24725i	0.263890	−	0.424690i
$29$	6.48036	+	3.74144i	1.20337	+	0.694768i	0.961304	−	0.275491i	$-0.0888405\pi$
$29$	6.48036	+	3.74144i	1.20337	+	0.694768i	0.242069	+	0.970259i	$0.422174\pi$
$30$	3.85710	−	0.350434i	0.704206	−	0.0639801i
$31$			7.77478i			1.39639i	0.715907	+	0.698196i	$0.246014\pi$
$31$			7.77478i			1.39639i	−0.715907	+	0.698196i	$0.753986\pi$
$32$	−1.00000			−0.176777
$33$	−8.63211	+	3.01573i	−1.50266	+	0.524971i
$34$	−4.30888	−	2.48773i	−0.738967	−	0.426643i
$35$	−1.62293	+	5.68912i	−0.274325	+	0.961637i
$36$	2.79154	+	1.09878i	0.465256	+	0.183130i
$37$	1.82734	−	1.05501i	0.300412	−	0.173443i	−0.342216	−	0.939621i	$-0.611177\pi$
$37$	1.82734	−	1.05501i	0.300412	−	0.173443i	0.642628	+	0.766178i	$0.277844\pi$
$38$	0.0258184	−	0.0149063i	0.00418830	−	0.00241812i
$39$	3.20639	+	9.17786i	0.513433	+	1.46963i
$40$	2.15016	−	0.613862i	0.339970	−	0.0970602i
$41$	0.423283	+	0.733148i	0.0661057	+	0.114498i	0.897184	−	0.441657i	$-0.145609\pi$
$41$	0.423283	+	0.733148i	0.0661057	+	0.114498i	−0.831078	+	0.556156i	$0.812276\pi$
$42$	−3.10173	+	3.37332i	−0.478607	+	0.520514i
$43$	−7.31735	−	4.22467i	−1.11589	−	0.644257i	−0.175538	−	0.984473i	$-0.556167\pi$
$43$	−7.31735	−	4.22467i	−1.11589	−	0.644257i	−0.940347	+	0.340216i	$0.889500\pi$
$44$	−4.57187	+	2.63957i	−0.689235	+	0.397930i
$45$	−6.67674	−	0.648925i	−0.995310	−	0.0967360i
$46$	−2.13852	+	3.70403i	−0.315308	+	0.546129i
$47$		−	3.59113i		−	0.523820i	−0.965092	−	0.261910i	$-0.915648\pi$
$47$		−	3.59113i		−	0.523820i	0.965092	−	0.261910i	$-0.0843524\pi$
$48$	1.70170	+	0.322848i	0.245619	+	0.0465991i
$49$	−3.10026	−	6.27602i	−0.442895	−	0.896574i
$50$	−4.24635	+	2.63980i	−0.600524	+	0.373324i
$51$	6.52924	+	5.62448i	0.914277	+	0.787585i
$52$	2.80645	+	4.86092i	0.389185	+	0.674088i
$53$	0.914662	−	1.58424i	0.125639	−	0.217612i	−0.796344	−	0.604844i	$-0.793235\pi$
$53$	0.914662	−	1.58424i	0.125639	−	0.217612i	0.921982	+	0.387232i	$0.126569\pi$
$54$	−4.39561	−	2.77103i	−0.598167	−	0.377089i
$55$	8.20990	−	8.48199i	1.10702	−	1.14371i
$56$	−1.39638	+	2.24725i	−0.186599	+	0.300301i
$57$	−0.0487476	+	0.0170305i	−0.00645678	+	0.00225575i
$58$	−6.48036	−	3.74144i	−0.850913	−	0.491275i
$59$	2.43666			0.317226			0.158613	−	0.987341i	$-0.449298\pi$
$59$	2.43666			0.317226			0.158613	+	0.987341i	$0.449298\pi$
$60$	−3.85710	+	0.350434i	−0.497949	+	0.0452408i
$61$		−	4.23295i		−	0.541974i	−0.962583	−	0.270987i	$-0.912650\pi$
$61$		−	4.23295i		−	0.541974i	0.962583	−	0.270987i	$-0.0873500\pi$
$62$		−	7.77478i		−	0.987398i
$63$	6.36727	−	4.73898i	0.802200	−	0.597055i
$64$	1.00000			0.125000
$65$	−9.01825	−	8.72896i	−1.11858	−	1.08269i
$66$	8.63211	−	3.01573i	1.06254	−	0.371210i
$67$			14.2507i			1.74099i	0.492174	+	0.870497i	$0.336203\pi$
$67$			14.2507i			1.74099i	−0.492174	+	0.870497i	$0.663797\pi$
$68$	4.30888	+	2.48773i	0.522529	+	0.301682i
$69$	4.83495	−	5.61271i	0.582060	−	0.675691i
$70$	1.62293	−	5.68912i	0.193977	−	0.679980i
$71$			10.3996i			1.23420i	0.786883	+	0.617102i	$0.211694\pi$
$71$			10.3996i			1.23420i	−0.786883	+	0.617102i	$0.788306\pi$
$72$	−2.79154	−	1.09878i	−0.328986	−	0.129492i
$73$	−2.23753	+	3.87552i	−0.261883	+	0.453595i	−0.966742	−	0.255752i	$-0.917677\pi$
$73$	−2.23753	+	3.87552i	−0.261883	+	0.453595i	0.704859	+	0.709347i	$0.251010\pi$
$74$	−1.82734	+	1.05501i	−0.212424	+	0.122643i
$75$	8.07824	−	3.12121i	0.932795	−	0.360407i
$76$	−0.0258184	+	0.0149063i	−0.00296158	+	0.00170987i
$77$	−0.452280	+	13.9600i	−0.0515421	+	1.59089i
$78$	−3.20639	−	9.17786i	−0.363052	−	1.03919i
$79$	−4.22144			−0.474949			−0.237474	−	0.971394i	$-0.576320\pi$
$79$	−4.22144			−0.474949			−0.237474	+	0.971394i	$0.576320\pi$
$80$	−2.15016	+	0.613862i	−0.240395	+	0.0686319i
$81$	6.58537	+	6.13456i	0.731708	+	0.681618i
$82$	−0.423283	−	0.733148i	−0.0467438	−	0.0809626i
$83$	−9.84730	−	5.68534i	−1.08088	−	0.624047i	−0.149747	−	0.988724i	$-0.547846\pi$
$83$	−9.84730	−	5.68534i	−1.08088	−	0.624047i	−0.931134	+	0.364677i	$0.881179\pi$
$84$	3.10173	−	3.37332i	0.338426	−	0.368059i
$85$	−10.7919	−	2.70396i	−1.17055	−	0.293285i
$86$	7.31735	+	4.22467i	0.789050	+	0.455558i
$87$	9.81969	+	8.45896i	1.05278	+	0.906896i
$88$	4.57187	−	2.63957i	0.487363	−	0.281379i
$89$	−5.09947	−	8.83254i	−0.540543	−	0.936247i	−0.998873	−	0.0474654i	$-0.984886\pi$
$89$	−5.09947	−	8.83254i	−0.540543	−	0.936247i	0.458330	−	0.888782i	$-0.348448\pi$
$90$	6.67674	+	0.648925i	0.703791	+	0.0684027i
$91$	14.8426	+	0.480874i	1.55592	+	0.0504093i
$92$	2.13852	−	3.70403i	0.222956	−	0.386172i
$93$	−2.51007	+	13.2303i	−0.260282	+	1.37192i
$94$			3.59113i			0.370397i
$95$	0.0463633	−	0.0478998i	0.00475677	−	0.00491442i
$96$	−1.70170	−	0.322848i	−0.173679	−	0.0329505i
$97$	6.01859	−	10.4245i	0.611095	−	1.05845i	−0.379961	−	0.925002i	$-0.624063\pi$
$97$	6.01859	−	10.4245i	0.611095	−	1.05845i	0.991056	−	0.133445i	$-0.0426039\pi$
$98$	3.10026	+	6.27602i	0.313174	+	0.633973i
$99$	−15.6629	+	2.34499i	−1.57418	+	0.235680i
$100$	4.24635	−	2.63980i	0.424635	−	0.263980i
$101$	4.63929	+	8.03548i	0.461627	+	0.799561i	0.999042	−	0.0437569i	$-0.0139327\pi$
$101$	4.63929	+	8.03548i	0.461627	+	0.799561i	−0.537416	+	0.843318i	$0.680599\pi$
$102$	−6.52924	−	5.62448i	−0.646492	−	0.556906i
$103$	3.40899	−	5.90454i	0.335898	−	0.581792i	−0.647759	−	0.761845i	$-0.724294\pi$
$103$	3.40899	−	5.90454i	0.335898	−	0.581792i	0.983657	+	0.180053i	$0.0576270\pi$
$104$	−2.80645	−	4.86092i	−0.275195	−	0.476652i
$105$	−4.59845	+	9.15720i	−0.448763	+	0.893651i
$106$	−0.914662	+	1.58424i	−0.0888399	+	0.153875i
$107$	−2.94783	−	5.10579i	−0.284977	−	0.493595i	0.687626	−	0.726065i	$-0.258653\pi$
$107$	−2.94783	−	5.10579i	−0.284977	−	0.493595i	−0.972604	+	0.232470i	$0.925319\pi$
$108$	4.39561	+	2.77103i	0.422968	+	0.266642i
$109$	1.27384	−	2.20636i	0.122012	−	0.211331i	−0.798549	−	0.601930i	$-0.794399\pi$
$109$	1.27384	−	2.20636i	0.122012	−	0.211331i	0.920561	+	0.390599i	$0.127732\pi$
$110$	−8.20990	+	8.48199i	−0.782784	+	0.808726i
$111$	3.45018	−	1.20536i	0.327477	−	0.114408i
$112$	1.39638	−	2.24725i	0.131945	−	0.212345i
$113$	−6.04399	−	10.4685i	−0.568571	−	0.984793i	−0.996708	−	0.0810795i	$-0.974163\pi$
$113$	−6.04399	−	10.4685i	−0.568571	−	0.984793i	0.428137	−	0.903714i	$-0.359170\pi$
$114$	0.0487476	−	0.0170305i	0.00456563	−	0.00159506i
$115$	−2.32439	+	9.27700i	−0.216751	+	0.865084i
$116$	6.48036	+	3.74144i	0.601686	+	0.347384i
$117$	2.49325	+	16.6531i	0.230501	+	1.53958i
$118$	−2.43666			−0.224313
$119$	11.6074	−	6.20932i	1.06405	−	0.569207i
$120$	3.85710	−	0.350434i	0.352103	−	0.0319901i
$121$	8.43466	−	14.6093i	0.766788	−	1.32812i
$122$			4.23295i			0.383234i
$123$	0.483604	+	1.38425i	0.0436051	+	0.124814i
$124$			7.77478i			0.698196i
$125$	−7.50983	+	8.28266i	−0.671700	+	0.740823i
$126$	−6.36727	+	4.73898i	−0.567241	+	0.422181i
$127$			4.72029i			0.418858i	0.977824	+	0.209429i	$0.0671606\pi$
$127$			4.72029i			0.418858i	−0.977824	+	0.209429i	$0.932839\pi$
$128$	−1.00000			−0.0883883
$129$	−11.0880	−	9.55150i	−0.976242	−	0.840963i
$130$	9.01825	+	8.72896i	0.790953	+	0.765580i
$131$	4.92790	−	8.53537i	0.430553	−	0.745739i	−0.566368	−	0.824152i	$-0.691652\pi$
$131$	4.92790	−	8.53537i	0.430553	−	0.745739i	0.996921	+	0.0784133i	$0.0249854\pi$
$132$	−8.63211	+	3.01573i	−0.751329	+	0.262485i
$133$	−0.00255413	+	0.0788353i	−0.000221471	+	0.00683588i
$134$		−	14.2507i		−	1.23107i
$135$	−11.1523	−	3.25985i	−0.959836	−	0.280563i
$136$	−4.30888	−	2.48773i	−0.369483	−	0.213321i
$137$	−4.09746	−	7.09701i	−0.350069	−	0.606338i	0.636192	−	0.771531i	$-0.280509\pi$
$137$	−4.09746	−	7.09701i	−0.350069	−	0.606338i	−0.986261	+	0.165193i	$0.947175\pi$
$138$	−4.83495	+	5.61271i	−0.411578	+	0.477786i
$139$	−2.59638	+	1.49902i	−0.220222	+	0.127145i	−0.606053	−	0.795424i	$-0.707248\pi$
$139$	−2.59638	+	1.49902i	−0.220222	+	0.127145i	0.385831	+	0.922569i	$0.373915\pi$
$140$	−1.62293	+	5.68912i	−0.137162	+	0.480819i
$141$	1.15939	−	6.11101i	0.0976382	−	0.514640i
$142$		−	10.3996i		−	0.872715i
$143$	−25.6615	−	14.8157i	−2.14592	−	1.23895i
$144$	2.79154	+	1.09878i	0.232628	+	0.0915649i
$145$	−16.2305	−	4.06663i	−1.34787	−	0.337715i
$146$	2.23753	−	3.87552i	0.185179	−	0.320740i
$147$	−3.24951	−	11.6808i	−0.268015	−	0.963415i
$148$	1.82734	−	1.05501i	0.150206	−	0.0867216i
$149$	14.6204	+	8.44109i	1.19775	+	0.691521i	0.960053	−	0.279818i	$-0.0902741\pi$
$149$	14.6204	+	8.44109i	1.19775	+	0.691521i	0.237697	+	0.971339i	$0.423607\pi$
$150$	−8.07824	+	3.12121i	−0.659586	+	0.254846i
$151$	−9.49627	−	16.4480i	−0.772796	−	1.33852i	−0.936025	−	0.351933i	$-0.885524\pi$
$151$	−9.49627	−	16.4480i	−0.772796	−	1.33852i	0.163230	−	0.986588i	$-0.447809\pi$
$152$	0.0258184	−	0.0149063i	0.00209415	−	0.00120906i
$153$	9.29494	+	11.6791i	0.751451	+	0.944200i
$154$	0.452280	−	13.9600i	0.0364458	−	1.12493i
$155$	−4.77265	−	16.7170i	−0.383348	−	1.34274i
$156$	3.20639	+	9.17786i	0.256717	+	0.734817i
$157$	7.22541			0.576651			0.288325	−	0.957533i	$-0.406902\pi$
$157$	7.22541			0.576651			0.288325	+	0.957533i	$0.406902\pi$
$158$	4.22144			0.335839
$159$	2.06795	−	2.40060i	0.163999	−	0.190380i
$160$	2.15016	−	0.613862i	0.169985	−	0.0485301i
$161$	−5.33769	−	9.97801i	−0.420669	−	0.786377i
$162$	−6.58537	−	6.13456i	−0.517396	−	0.481977i
$163$	−18.7200	+	10.8080i	−1.46626	+	0.846546i	−0.999288	−	0.0377260i	$-0.987989\pi$
$163$	−18.7200	+	10.8080i	−1.46626	+	0.846546i	−0.466972	+	0.884272i	$0.654655\pi$
$164$	0.423283	+	0.733148i	0.0330528	+	0.0572492i
$165$	16.7092	−	11.7832i	1.30081	−	0.917322i
$166$	9.84730	+	5.68534i	0.764298	+	0.441268i
$167$	4.94362	−	2.85420i	0.382549	−	0.220865i	−0.296378	−	0.955071i	$-0.595779\pi$
$167$	4.94362	−	2.85420i	0.382549	−	0.220865i	0.678927	+	0.734206i	$0.262445\pi$
$168$	−3.10173	+	3.37332i	−0.239304	+	0.260257i
$169$	−9.25235	+	16.0255i	−0.711719	+	1.23273i
$170$	10.7919	+	2.70396i	0.827700	+	0.207384i
$171$	−0.0884519	+	0.0132427i	−0.00676408	+	0.00101270i
$172$	−7.31735	−	4.22467i	−0.557943	−	0.322128i
$173$		−	17.5004i		−	1.33053i	−0.746608	−	0.665264i	$-0.768319\pi$
$173$		−	17.5004i		−	1.33053i	0.746608	−	0.665264i	$-0.231681\pi$
$174$	−9.81969	−	8.45896i	−0.744429	−	0.641272i
$175$	−0.00279186	−	13.2288i	−0.000211044	−	1.00000i
$176$	−4.57187	+	2.63957i	−0.344618	+	0.198965i
$177$	4.14646	+	0.786671i	0.311667	+	0.0591298i
$178$	5.09947	+	8.83254i	0.382221	+	0.662027i
$179$	−8.01844	−	4.62945i	−0.599327	−	0.346021i	0.169450	−	0.985539i	$-0.445801\pi$
$179$	−8.01844	−	4.62945i	−0.599327	−	0.346021i	−0.768777	+	0.639517i	$0.779134\pi$
$180$	−6.67674	−	0.648925i	−0.497655	−	0.0483680i
$181$			5.45450i			0.405430i	0.979238	+	0.202715i	$0.0649764\pi$
$181$			5.45450i			0.405430i	−0.979238	+	0.202715i	$0.935024\pi$
$182$	−14.8426	−	0.480874i	−1.10020	−	0.0356448i
$183$	1.36660	−	7.20320i	0.101022	−	0.532476i
$184$	−2.13852	+	3.70403i	−0.157654	+	0.273065i
$185$	−3.28143	+	3.39018i	−0.241255	+	0.249251i
$186$	2.51007	−	13.2303i	0.184047	−	0.970094i
$187$	−26.2662			−1.92077
$188$		−	3.59113i		−	0.261910i
$189$	12.3651	−	6.00864i	0.899430	−	0.437064i
$190$	−0.0463633	+	0.0478998i	−0.00336355	+	0.00347502i
$191$		−	1.33175i		−	0.0963622i	−0.998839	−	0.0481811i	$-0.984658\pi$
$191$		−	1.33175i		−	0.0963622i	0.998839	−	0.0481811i	$-0.0153425\pi$
$192$	1.70170	+	0.322848i	0.122809	+	0.0232995i
$193$		−	13.0796i		−	0.941488i	−0.882270	−	0.470744i	$-0.843986\pi$
$193$		−	13.0796i		−	0.941488i	0.882270	−	0.470744i	$-0.156014\pi$
$194$	−6.01859	+	10.4245i	−0.432109	+	0.748435i
$195$	−12.5282	−	17.7656i	−0.897162	−	1.27222i
$196$	−3.10026	−	6.27602i	−0.221447	−	0.448287i
$197$	−14.3455			−1.02207			−0.511037	−	0.859559i	$-0.670738\pi$
$197$	−14.3455			−1.02207			−0.511037	+	0.859559i	$0.670738\pi$
$198$	15.6629	−	2.34499i	1.11311	−	0.166651i
$199$	−14.6558	−	8.46151i	−1.03892	−	0.599821i	−0.119393	−	0.992847i	$-0.538095\pi$
$199$	−14.6558	−	8.46151i	−1.03892	−	0.599821i	−0.919527	+	0.393026i	$0.871428\pi$
$200$	−4.24635	+	2.63980i	−0.300262	+	0.186662i
$201$	−4.60079	+	24.2503i	−0.324515	+	1.71048i
$202$	−4.63929	−	8.03548i	−0.326419	−	0.565375i
$203$	17.4570	−	9.33853i	1.22524	−	0.655436i
$204$	6.52924	+	5.62448i	0.457139	+	0.393792i
$205$	−1.36018	−	1.31654i	−0.0949988	−	0.0919515i
$206$	−3.40899	+	5.90454i	−0.237516	+	0.411389i
$207$	10.0397	−	7.99017i	0.697805	−	0.555355i
$208$	2.80645	+	4.86092i	0.194592	+	0.337044i
$209$	0.0786924	−	0.136299i	0.00544326	−	0.00942801i
$210$	4.59845	−	9.15720i	0.317323	−	0.631907i
$211$	−6.27315	−	10.8654i	−0.431861	−	0.748006i	0.565172	−	0.824973i	$-0.308810\pi$
$211$	−6.27315	−	10.8654i	−0.431861	−	0.748006i	−0.997034	+	0.0769670i	$0.975476\pi$
$212$	0.914662	−	1.58424i	0.0628193	−	0.108806i
$213$	−3.35749	+	17.6969i	−0.230051	+	1.21258i
$214$	2.94783	+	5.10579i	0.201509	+	0.349025i
$215$	18.3268	+	4.59186i	1.24988	+	0.313163i
$216$	−4.39561	−	2.77103i	−0.299083	−	0.188545i
$217$	17.4719	+	10.8565i	1.18607	+	0.736989i
$218$	−1.27384	+	2.20636i	−0.0862755	+	0.149433i
$219$	−5.05880	+	5.87257i	−0.341842	+	0.396831i
$220$	8.20990	−	8.48199i	0.553512	−	0.571856i
$221$			27.9268i			1.87856i
$222$	−3.45018	+	1.20536i	−0.231561	+	0.0808985i
$223$	7.34774	−	12.7267i	0.492041	−	0.852240i	−0.507917	−	0.861406i	$-0.669584\pi$
$223$	7.34774	−	12.7267i	0.492041	−	0.852240i	0.999958	+	0.00916616i	$0.00291772\pi$
$224$	−1.39638	+	2.24725i	−0.0932994	+	0.150151i
$225$	14.7544	−	2.70331i	0.983626	−	0.180221i
$226$	6.04399	+	10.4685i	0.402040	+	0.696354i
$227$	12.5560	−	7.24923i	0.833373	−	0.481148i	−0.0216333	−	0.999766i	$-0.506887\pi$
$227$	12.5560	−	7.24923i	0.833373	−	0.481148i	0.855006	+	0.518618i	$0.173553\pi$
$228$	−0.0487476	+	0.0170305i	−0.00322839	+	0.00112787i
$229$	18.5598	+	10.7155i	1.22647	+	0.708102i	0.966290	−	0.257458i	$-0.0828848\pi$
$229$	18.5598	+	10.7155i	1.22647	+	0.708102i	0.260180	+	0.965560i	$0.416218\pi$
$230$	2.32439	−	9.27700i	0.153266	−	0.611707i
$231$	−5.27659	+	23.6096i	−0.347174	+	1.55340i
$232$	−6.48036	−	3.74144i	−0.425457	−	0.245637i
$233$	9.49738	+	16.4499i	0.622194	+	1.07767i	0.989076	+	0.147404i	$0.0470918\pi$
$233$	9.49738	+	16.4499i	0.622194	+	1.07767i	−0.366882	+	0.930267i	$0.619575\pi$
$234$	−2.49325	−	16.6531i	−0.162989	−	1.08865i
$235$	2.20446	+	7.72149i	0.143803	+	0.503695i
$236$	2.43666			0.158613
$237$	−7.18360	−	1.36288i	−0.466625	−	0.0885287i
$238$	−11.6074	+	6.20932i	−0.752395	+	0.402490i
$239$	−7.44062	+	4.29585i	−0.481294	+	0.277875i	−0.720956	−	0.692981i	$-0.756297\pi$
$239$	−7.44062	+	4.29585i	−0.481294	+	0.277875i	0.239662	+	0.970856i	$0.422964\pi$
$240$	−3.85710	+	0.350434i	−0.248975	+	0.0226204i
$241$	17.1500	−	9.90158i	1.10473	−	0.637817i	0.167271	−	0.985911i	$-0.446504\pi$
$241$	17.1500	−	9.90158i	1.10473	−	0.637817i	0.937460	+	0.348094i	$0.113171\pi$
$242$	−8.43466	+	14.6093i	−0.542201	+	0.939119i
$243$	9.22577	+	12.5652i	0.591833	+	0.806060i
$244$		−	4.23295i		−	0.270987i
$245$	10.5187	+	11.5913i	0.672013	+	0.740540i
$246$	−0.483604	−	1.38425i	−0.0308334	−	0.0882566i
$247$	−0.144916	−	0.0836675i	−0.00922081	−	0.00532364i
$248$		−	7.77478i		−	0.493699i
$249$	−14.9216	−	12.8539i	−0.945618	−	0.814583i
$250$	7.50983	−	8.28266i	0.474964	−	0.523841i
$251$	−4.85874			−0.306681			−0.153340	−	0.988173i	$-0.549003\pi$
$251$	−4.85874			−0.306681			−0.153340	+	0.988173i	$0.549003\pi$
$252$	6.36727	−	4.73898i	0.401100	−	0.298527i
$253$			22.5791i			1.41954i
$254$		−	4.72029i		−	0.296178i
$255$	−17.4916	−	8.08545i	−1.09536	−	0.506331i
$256$	1.00000			0.0625000
$257$	−17.3248	−	10.0025i	−1.08069	−	0.623937i	−0.149608	−	0.988745i	$-0.547801\pi$
$257$	−17.3248	−	10.0025i	−1.08069	−	0.623937i	−0.931083	+	0.364808i	$0.881135\pi$
$258$	11.0880	+	9.55150i	0.690307	+	0.594651i
$259$	0.180772	−	5.57968i	0.0112327	−	0.346704i
$260$	−9.01825	−	8.72896i	−0.559288	−	0.541347i
$261$	13.9792	+	17.5648i	0.865289	+	1.08724i
$262$	−4.92790	+	8.53537i	−0.304447	+	0.527317i
$263$	1.76353	+	3.05452i	0.108744	+	0.188350i	0.915262	−	0.402860i	$-0.131984\pi$
$263$	1.76353	+	3.05452i	0.108744	+	0.188350i	−0.806518	+	0.591210i	$0.798651\pi$
$264$	8.63211	−	3.01573i	0.531270	−	0.185605i
$265$	−0.994161	+	3.96784i	−0.0610708	+	0.243743i
$266$	0.00255413	−	0.0788353i	0.000156604	−	0.00483370i
$267$	−5.82618	−	16.6767i	−0.356556	−	1.02059i
$268$			14.2507i			0.870497i
$269$	3.55670	−	6.16038i	0.216856	−	0.375605i	−0.736989	−	0.675904i	$-0.763753\pi$
$269$	3.55670	−	6.16038i	0.216856	−	0.375605i	0.953845	+	0.300299i	$0.0970865\pi$
$270$	11.1523	+	3.25985i	0.678706	+	0.198388i
$271$	−0.604546	+	0.349035i	−0.0367236	+	0.0212024i	−0.518249	−	0.855230i	$-0.673416\pi$
$271$	−0.604546	+	0.349035i	−0.0367236	+	0.0212024i	0.481526	+	0.876432i	$0.340083\pi$
$272$	4.30888	+	2.48773i	0.261264	+	0.150841i
$273$	25.1023	+	5.61019i	1.51926	+	0.339544i
$274$	4.09746	+	7.09701i	0.247536	+	0.428746i
$275$	−12.4458	+	23.2774i	−0.750510	+	1.40368i
$276$	4.83495	−	5.61271i	0.291030	−	0.337846i
$277$	−16.8512	+	9.72907i	−1.01249	+	0.584563i	−0.911921	−	0.410367i	$-0.865401\pi$
$277$	−16.8512	+	9.72907i	−1.01249	+	0.584563i	−0.100572	+	0.994930i	$0.532067\pi$
$278$	2.59638	−	1.49902i	0.155721	−	0.0899053i
$279$	−8.54276	+	21.7036i	−0.511442	+	1.29936i
$280$	1.62293	−	5.68912i	0.0969884	−	0.339990i
$281$	8.04686	+	4.64586i	0.480035	+	0.277149i	0.720431	−	0.693526i	$-0.243944\pi$
$281$	8.04686	+	4.64586i	0.480035	+	0.277149i	−0.240396	+	0.970675i	$0.577277\pi$
$282$	−1.15939	+	6.11101i	−0.0690406	+	0.363905i
$283$	−0.313268			−0.0186218			−0.00931091	−	0.999957i	$-0.502964\pi$
$283$	−0.313268			−0.0186218			−0.00931091	+	0.999957i	$0.502964\pi$
$284$			10.3996i			0.617102i
$285$	0.0943605	−	0.0665426i	0.00558944	−	0.00394164i
$286$	25.6615	+	14.8157i	1.51739	+	0.876068i
$287$	2.23863	+	0.0725278i	0.132142	+	0.00428118i
$288$	−2.79154	−	1.09878i	−0.164493	−	0.0647461i
$289$	3.87763	+	6.71626i	0.228096	+	0.395074i
$290$	16.2305	+	4.06663i	0.953089	+	0.238801i
$291$	13.6073	−	15.7962i	0.797676	−	0.925992i
$292$	−2.23753	+	3.87552i	−0.130942	+	0.226797i
$293$	11.3744	−	6.56701i	0.664499	−	0.383649i	−0.129490	−	0.991581i	$-0.541334\pi$
$293$	11.3744	−	6.56701i	0.664499	−	0.383649i	0.793989	+	0.607932i	$0.208001\pi$
$294$	3.24951	+	11.6808i	0.189515	+	0.681237i
$295$	−5.23920	+	1.49577i	−0.305038	+	0.0870874i
$296$	−1.82734	+	1.05501i	−0.106212	+	0.0613214i
$297$	−27.4105	−	1.06626i	−1.59052	−	0.0618707i
$298$	−14.6204	−	8.44109i	−0.846937	−	0.488979i
$299$	24.0066			1.38834
$300$	8.07824	−	3.12121i	0.466398	−	0.180203i
$301$	−19.7117	+	10.5447i	−1.13616	+	0.607785i
$302$	9.49627	+	16.4480i	0.546449	+	0.946477i
$303$	5.30042	+	15.1717i	0.304501	+	0.871594i
$304$	−0.0258184	+	0.0149063i	−0.00148079	+	0.000854934i
$305$	2.59845	+	9.10151i	0.148787	+	0.521151i
$306$	−9.29494	−	11.6791i	−0.531356	−	0.667650i
$307$	8.18498			0.467142			0.233571	−	0.972340i	$-0.424959\pi$
$307$	8.18498			0.467142			0.233571	+	0.972340i	$0.424959\pi$
$308$	−0.452280	+	13.9600i	−0.0257710	+	0.795443i
$309$	7.70734	−	8.94715i	0.438455	−	0.508986i
$310$	4.77265	+	16.7170i	0.271068	+	0.949462i
$311$	26.1476			1.48270			0.741348	−	0.671121i	$-0.234187\pi$
$311$	26.1476			1.48270			0.741348	+	0.671121i	$0.234187\pi$
$312$	−3.20639	−	9.17786i	−0.181526	−	0.519594i
$313$	4.72622			0.267142			0.133571	−	0.991039i	$-0.457356\pi$
$313$	4.72622			0.267142			0.133571	+	0.991039i	$0.457356\pi$
$314$	−7.22541			−0.407754
$315$	−10.7815	+	14.0982i	−0.607471	+	0.794342i
$316$	−4.22144			−0.237474
$317$	23.2386			1.30521			0.652604	−	0.757699i	$-0.273677\pi$
$317$	23.2386			1.30521			0.652604	+	0.757699i	$0.273677\pi$
$318$	−2.06795	+	2.40060i	−0.115965	+	0.134619i
$319$	−39.5032			−2.21175
$320$	−2.15016	+	0.613862i	−0.120197	+	0.0343160i
$321$	−3.36791	−	9.64020i	−0.187979	−	0.538063i
$322$	5.33769	+	9.97801i	0.297458	+	0.556053i
$323$	−0.148331			−0.00825338
$324$	6.58537	+	6.13456i	0.365854	+	0.340809i
$325$	24.7490	+	13.2327i	1.37283	+	0.734016i
$326$	18.7200	−	10.8080i	1.03680	−	0.598598i
$327$	2.88001	−	3.34329i	0.159265	−	0.184885i
$328$	−0.423283	−	0.733148i	−0.0233719	−	0.0404813i
$329$	−8.07017	−	5.01457i	−0.444923	−	0.276462i
$330$	−16.7092	+	11.7832i	−0.919809	+	0.648645i
$331$	−23.7985			−1.30808			−0.654042	−	0.756458i	$-0.726928\pi$
$331$	−23.7985			−1.30808			−0.654042	+	0.756458i	$0.726928\pi$
$332$	−9.84730	−	5.68534i	−0.540441	−	0.312024i
$333$	6.26031	−	0.937273i	0.343063	−	0.0513622i
$334$	−4.94362	+	2.85420i	−0.270503	+	0.156175i
$335$	−8.74794	−	30.6411i	−0.477951	−	1.67410i
$336$	3.10173	−	3.37332i	0.169213	−	0.184030i
$337$	27.9969	−	16.1640i	1.52509	−	0.880511i	0.525532	−	0.850774i	$-0.323866\pi$
$337$	27.9969	−	16.1640i	1.52509	−	0.880511i	0.999558	−	0.0297368i	$-0.00946692\pi$
$338$	9.25235	−	16.0255i	0.503261	−	0.871674i
$339$	−6.90530	−	19.7655i	−0.375044	−	1.07351i
$340$	−10.7919	−	2.70396i	−0.585273	−	0.146643i
$341$	−20.5221	−	35.5453i	−1.11133	−	1.92489i
$342$	0.0884519	−	0.0132427i	0.00478293	−	0.000716084i
$343$	−18.4329	−	1.79662i	−0.995284	−	0.0970083i
$344$	7.31735	+	4.22467i	0.394525	+	0.227779i
$345$	−6.95047	+	15.0362i	−0.374201	+	0.809522i
$346$			17.5004i			0.940825i
$347$	28.1271			1.50994			0.754970	−	0.655759i	$-0.227651\pi$
$347$	28.1271			1.50994			0.754970	+	0.655759i	$0.227651\pi$
$348$	9.81969	+	8.45896i	0.526391	+	0.453448i
$349$	24.7247	+	14.2748i	1.32348	+	0.764113i	0.984283	−	0.176601i	$-0.0565101\pi$
$349$	24.7247	+	14.2748i	1.32348	+	0.764113i	0.339201	+	0.940714i	$0.389843\pi$
$350$	0.00279186	+	13.2288i	0.000149231	+	0.707107i
$351$	−1.13367	+	29.1435i	−0.0605109	+	1.55556i
$352$	4.57187	−	2.63957i	0.243681	−	0.140690i
$353$	5.19921	−	3.00176i	0.276726	−	0.159768i	−0.355214	−	0.934785i	$-0.615592\pi$
$353$	5.19921	−	3.00176i	0.276726	−	0.159768i	0.631940	+	0.775017i	$0.282259\pi$
$354$	−4.14646	−	0.786671i	−0.220382	−	0.0418111i
$355$	−6.38392	−	22.3608i	−0.338823	−	1.18679i
$356$	−5.09947	−	8.83254i	−0.270271	−	0.468124i
$357$	21.7569	−	6.81895i	1.15150	−	0.360897i
$358$	8.01844	+	4.62945i	0.423788	+	0.244674i
$359$	9.67555	−	5.58618i	0.510656	−	0.294827i	−0.222447	−	0.974945i	$-0.571405\pi$
$359$	9.67555	−	5.58618i	0.510656	−	0.294827i	0.733103	+	0.680117i	$0.238071\pi$
$360$	6.67674	+	0.648925i	0.351895	+	0.0342013i
$361$	−9.49956	+	16.4537i	−0.499977	+	0.865985i
$362$		−	5.45450i		−	0.286682i
$363$	19.0698	−	22.1374i	1.00091	−	1.16191i
$364$	14.8426	+	0.480874i	0.777962	+	0.0252047i
$365$	2.43201	−	9.70650i	0.127297	−	0.508061i
$366$	−1.36660	+	7.20320i	−0.0714333	+	0.376517i
$367$	6.40205	+	11.0887i	0.334185	+	0.578825i	0.983328	−	0.181842i	$-0.0582058\pi$
$367$	6.40205	+	11.0887i	0.334185	+	0.578825i	−0.649143	+	0.760666i	$0.724872\pi$
$368$	2.13852	−	3.70403i	0.111478	−	0.193086i
$369$	0.376044	+	2.51170i	0.0195761	+	0.130754i
$370$	3.28143	−	3.39018i	0.170593	−	0.176247i
$371$	−2.28297	−	4.26767i	−0.118526	−	0.221567i
$372$	−2.51007	+	13.2303i	−0.130141	+	0.685960i
$373$	−14.1942	−	8.19502i	−0.734947	−	0.424322i	0.0852821	−	0.996357i	$-0.472821\pi$
$373$	−14.1942	−	8.19502i	−0.734947	−	0.424322i	−0.820229	+	0.572035i	$0.806154\pi$
$374$	26.2662			1.35819
$375$	−15.4535	+	11.6700i	−0.798015	+	0.602638i
$376$			3.59113i			0.185198i
$377$			42.0007i			2.16314i
$378$	−12.3651	+	6.00864i	−0.635993	+	0.309051i
$379$	5.48486			0.281738			0.140869	−	0.990028i	$-0.455010\pi$
$379$	5.48486			0.281738			0.140869	+	0.990028i	$0.455010\pi$
$380$	0.0463633	−	0.0478998i	0.00237839	−	0.00245721i
$381$	−1.52394	+	8.03250i	−0.0780737	+	0.411518i
$382$			1.33175i			0.0681384i
$383$	17.8428	+	10.3015i	0.911722	+	0.526383i	0.880985	−	0.473144i	$-0.156881\pi$
$383$	17.8428	+	10.3015i	0.911722	+	0.526383i	0.0307374	+	0.999527i	$0.490214\pi$
$384$	−1.70170	−	0.322848i	−0.0868393	−	0.0164753i
$385$	−7.59703	−	30.2938i	−0.387180	−	1.54391i
$386$			13.0796i			0.665732i
$387$	−15.7847	−	19.8335i	−0.802381	−	1.00819i
$388$	6.01859	−	10.4245i	0.305547	−	0.529224i
$389$	−15.4245	+	8.90535i	−0.782054	+	0.451519i	−0.837158	−	0.546961i	$-0.815784\pi$
$389$	−15.4245	+	8.90535i	−0.782054	+	0.451519i	0.0551034	+	0.998481i	$0.482451\pi$
$390$	12.5282	+	17.7656i	0.634389	+	0.899594i
$391$	18.4293	−	10.6401i	0.932008	−	0.538095i
$392$	3.10026	+	6.27602i	0.156587	+	0.316987i
$393$	11.1414	−	12.9336i	0.562010	−	0.652416i
$394$	14.3455			0.722715
$395$	9.07675	−	2.59138i	0.456701	−	0.130387i
$396$	−15.6629	+	2.34499i	−0.787088	+	0.117840i
$397$	−1.81408	−	3.14208i	−0.0910462	−	0.157697i	0.816905	−	0.576772i	$-0.195688\pi$
$397$	−1.81408	−	3.14208i	−0.0910462	−	0.157697i	−0.907952	+	0.419075i	$0.862354\pi$
$398$	14.6558	+	8.46151i	0.734628	+	0.424137i
$399$	−0.0297982	+	0.133329i	−0.00149177	+	0.00667480i
$400$	4.24635	−	2.63980i	0.212317	−	0.131990i
$401$	−31.5305	−	18.2041i	−1.57456	−	0.909071i	−0.995599	−	0.0937125i	$-0.970127\pi$
$401$	−31.5305	−	18.2041i	−1.57456	−	0.909071i	−0.578957	−	0.815358i	$-0.696540\pi$
$402$	4.60079	−	24.2503i	0.229467	−	1.20949i
$403$	−37.7926	+	21.8196i	−1.88258	+	1.08691i
$404$	4.63929	+	8.03548i	0.230813	+	0.399780i
$405$	−17.9254	−	9.14776i	−0.890718	−	0.454556i
$406$	−17.4570	+	9.33853i	−0.866375	+	0.463464i
$407$	−5.56957	+	9.64677i	−0.276073	+	0.478173i
$408$	−6.52924	−	5.62448i	−0.323246	−	0.278453i
$409$			5.67091i			0.280408i	0.990123	+	0.140204i	$0.0447759\pi$
$409$			5.67091i			0.280408i	−0.990123	+	0.140204i	$0.955224\pi$
$410$	1.36018	+	1.31654i	0.0671743	+	0.0650195i
$411$	−4.68137	−	13.3998i	−0.230915	−	0.660963i
$412$	3.40899	−	5.90454i	0.167949	−	0.290896i
$413$	3.40250	−	5.47579i	0.167426	−	0.269446i
$414$	−10.0397	+	7.99017i	−0.493423	+	0.392696i
$415$	24.6632	+	6.17948i	1.21067	+	0.303339i
$416$	−2.80645	−	4.86092i	−0.137598	−	0.238326i
$417$	−4.90221	+	1.71264i	−0.240062	+	0.0838685i
$418$	−0.0786924	+	0.136299i	−0.00384897	+	0.00666661i
$419$	−13.5787	−	23.5190i	−0.663362	−	1.14898i	−0.979727	−	0.200339i	$-0.935796\pi$
$419$	−13.5787	−	23.5190i	−0.663362	−	1.14898i	0.316365	−	0.948638i	$-0.397538\pi$
$420$	−4.59845	+	9.15720i	−0.224381	+	0.446825i
$421$	−3.92131	+	6.79190i	−0.191113	+	0.331017i	−0.945619	−	0.325275i	$-0.894543\pi$
$421$	−3.92131	+	6.79190i	−0.191113	+	0.331017i	0.754506	+	0.656293i	$0.227876\pi$
$422$	6.27315	+	10.8654i	0.305372	+	0.528920i
$423$	3.94586	−	10.0248i	0.191854	−	0.487421i
$424$	−0.914662	+	1.58424i	−0.0444199	+	0.0769376i
$425$	24.8641	−	0.810809i	1.20609	−	0.0393300i
$426$	3.35749	−	17.6969i	0.162671	−	0.857420i
$427$	−9.51250	−	5.91080i	−0.460342	−	0.286044i
$428$	−2.94783	−	5.10579i	−0.142489	−	0.246798i
$429$	−38.8848	−	33.4965i	−1.87738	−	1.61723i
$430$	−18.3268	−	4.59186i	−0.883798	−	0.221439i
$431$	9.95046	+	5.74490i	0.479297	+	0.276722i	0.720123	−	0.693846i	$-0.244085\pi$
$431$	9.95046	+	5.74490i	0.479297	+	0.276722i	−0.240827	+	0.970568i	$0.577419\pi$
$432$	4.39561	+	2.77103i	0.211484	+	0.133321i
$433$	−33.0116			−1.58644			−0.793219	−	0.608937i	$-0.791596\pi$
$433$	−33.0116			−1.58644			−0.793219	+	0.608937i	$0.791596\pi$
$434$	−17.4719	−	10.8565i	−0.838677	−	0.521130i
$435$	−26.3065	−	12.1602i	−1.26130	−	0.583035i
$436$	1.27384	−	2.20636i	0.0610060	−	0.105665i
$437$			0.127510i			0.00609961i
$438$	5.05880	−	5.87257i	0.241719	−	0.280602i
$439$			36.8521i			1.75885i	0.476034	+	0.879427i	$0.342074\pi$
$439$			36.8521i			1.75885i	−0.476034	+	0.879427i	$0.657926\pi$
$440$	−8.20990	+	8.48199i	−0.391392	+	0.404363i
$441$	−1.75855	−	20.9262i	−0.0837406	−	0.996488i
$442$		−	27.9268i		−	1.32834i
$443$	6.89008			0.327358			0.163679	−	0.986514i	$-0.447664\pi$
$443$	6.89008			0.327358			0.163679	+	0.986514i	$0.447664\pi$
$444$	3.45018	−	1.20536i	0.163738	−	0.0572039i
$445$	16.3866	+	15.8610i	0.776800	+	0.751882i
$446$	−7.34774	+	12.7267i	−0.347925	+	0.602625i
$447$	22.1543	+	19.0843i	1.04786	+	0.902658i
$448$	1.39638	−	2.24725i	0.0659726	−	0.106173i
$449$			18.6394i			0.879650i	0.898084	+	0.439825i	$0.144960\pi$
$449$			18.6394i			0.879650i	−0.898084	+	0.439825i	$0.855040\pi$
$450$	−14.7544	+	2.70331i	−0.695529	+	0.127435i
$451$	−3.87039	−	2.23457i	−0.182250	−	0.105222i
$452$	−6.04399	−	10.4685i	−0.284285	−	0.492397i
$453$	−10.8496	−	31.0554i	−0.509756	−	1.45911i
$454$	−12.5560	+	7.24923i	−0.589284	+	0.340223i
$455$	−32.2090	+	8.07734i	−1.50998	+	0.378671i
$456$	0.0487476	−	0.0170305i	0.00228282	−	0.000797528i
$457$		−	19.5925i		−	0.916500i	−0.888823	−	0.458250i	$-0.848476\pi$
$457$		−	19.5925i		−	0.916500i	0.888823	−	0.458250i	$-0.151524\pi$
$458$	−18.5598	−	10.7155i	−0.867245	−	0.500704i
$459$	12.0466	+	22.8751i	0.562286	+	1.06772i
$460$	−2.32439	+	9.27700i	−0.108375	+	0.432542i
$461$	5.15453	−	8.92791i	0.240070	−	0.415814i	−0.720664	−	0.693285i	$-0.756163\pi$
$461$	5.15453	−	8.92791i	0.240070	−	0.415814i	0.960734	+	0.277471i	$0.0894961\pi$
$462$	5.27659	−	23.6096i	0.245489	−	1.09842i
$463$	−22.9305	+	13.2390i	−1.06567	+	0.615266i	−0.926996	−	0.375072i	$-0.877618\pi$
$463$	−22.9305	+	13.2390i	−1.06567	+	0.615266i	−0.138676	+	0.990338i	$0.544285\pi$
$464$	6.48036	+	3.74144i	0.300843	+	0.173692i
$465$	−2.72454	−	29.9881i	−0.126348	−	1.39066i
$466$	−9.49738	−	16.4499i	−0.439958	−	0.762029i
$467$	−7.88940	+	4.55495i	−0.365078	+	0.210778i	−0.671306	−	0.741180i	$-0.734266\pi$
$467$	−7.88940	+	4.55495i	−0.365078	+	0.210778i	0.306228	+	0.951958i	$0.400933\pi$
$468$	2.49325	+	16.6531i	0.115250	+	0.769790i
$469$	32.0248	+	19.8993i	1.47877	+	0.918863i
$470$	−2.20446	−	7.72149i	−0.101684	−	0.356166i
$471$	12.2955	+	2.33271i	0.566545	+	0.107486i
$472$	−2.43666			−0.112156
$473$	44.6053			2.05095
$474$	7.18360	+	1.36288i	0.329954	+	0.0625993i
$475$	−0.0702844	+	0.131453i	−0.00322487	+	0.00603147i
$476$	11.6074	−	6.20932i	0.532023	−	0.284604i
$477$	4.29405	−	3.41746i	0.196611	−	0.156475i
$478$	7.44062	−	4.29585i	0.340326	−	0.196487i
$479$	−0.511670	−	0.886239i	−0.0233788	−	0.0404933i	0.854099	−	0.520110i	$-0.174109\pi$
$479$	−0.511670	−	0.886239i	−0.0233788	−	0.0404933i	−0.877478	+	0.479617i	$0.840776\pi$
$480$	3.85710	−	0.350434i	0.176052	−	0.0159950i
$481$	10.2567	+	5.92169i	0.467664	+	0.270006i
$482$	−17.1500	+	9.90158i	−0.781163	+	0.451005i
$483$	−5.86175	−	18.7028i	−0.266719	−	0.851007i
$484$	8.43466	−	14.6093i	0.383394	−	0.664058i
$485$	−6.54169	+	26.1089i	−0.297043	+	1.18554i
$486$	−9.22577	−	12.5652i	−0.418489	−	0.569971i
$487$	2.98547	+	1.72366i	0.135285	+	0.0781066i	0.566115	−	0.824326i	$-0.308446\pi$
$487$	2.98547	+	1.72366i	0.135285	+	0.0781066i	−0.430830	+	0.902433i	$0.641779\pi$
$488$			4.23295i			0.191617i
$489$	−35.3450	+	12.3482i	−1.59836	+	0.558404i
$490$	−10.5187	−	11.5913i	−0.475185	−	0.523641i
$491$	−20.0862	+	11.5968i	−0.906479	+	0.523356i	−0.879297	−	0.476274i	$-0.841987\pi$
$491$	−20.0862	+	11.5968i	−0.906479	+	0.523356i	−0.0271826	+	0.999630i	$0.508654\pi$
$492$	0.483604	+	1.38425i	0.0218025	+	0.0624068i
$493$	18.6154	+	32.2428i	0.838395	+	1.45214i
$494$	0.144916	+	0.0836675i	0.00652010	+	0.00376438i
$495$	32.2381	−	14.6569i	1.44899	−	0.658780i
$496$			7.77478i			0.349098i
$497$	23.3705	+	14.5218i	1.04831	+	0.651390i
$498$	14.9216	+	12.8539i	0.668653	+	0.575997i
$499$	−5.15759	+	8.93321i	−0.230885	+	0.399905i	−0.958069	−	0.286538i	$-0.907496\pi$
$499$	−5.15759	+	8.93321i	−0.230885	+	0.399905i	0.727184	+	0.686443i	$0.240829\pi$
$500$	−7.50983	+	8.28266i	−0.335850	+	0.370412i
$501$	9.33401	−	3.26094i	0.417013	−	0.145688i
$502$	4.85874			0.216856
$503$		−	28.2092i		−	1.25779i	−0.777492	−	0.628893i	$-0.783508\pi$
$503$		−	28.2092i		−	1.25779i	0.777492	−	0.628893i	$-0.216492\pi$
$504$	−6.36727	+	4.73898i	−0.283621	+	0.211091i
$505$	−14.9079	−	14.4297i	−0.663392	−	0.642112i
$506$		−	22.5791i		−	1.00376i
$507$	−20.9185	+	24.2835i	−0.929023	+	1.07847i
$508$			4.72029i			0.209429i
$509$	0.464334	−	0.804250i	0.0205813	−	0.0356478i	−0.855551	−	0.517718i	$-0.826782\pi$
$509$	0.464334	−	0.804250i	0.0205813	−	0.0356478i	0.876133	+	0.482070i	$0.160115\pi$
$510$	17.4916	+	8.08545i	0.774539	+	0.358030i
$511$	5.58482	+	10.4400i	0.247058	+	0.461837i
$512$	−1.00000			−0.0441942
$513$	−0.154794	−	0.00602142i	−0.00683430	−	0.000265852i
$514$	17.3248	+	10.0025i	0.764164	+	0.441190i
$515$	−3.70528	+	14.7883i	−0.163274	+	0.651652i
$516$	−11.0880	−	9.55150i	−0.488121	−	0.420482i
$517$	9.47904	+	16.4182i	0.416888	+	0.722071i
$518$	−0.180772	+	5.57968i	−0.00794268	+	0.245157i
$519$	5.64996	−	29.7803i	0.248006	−	1.30721i
$520$	9.01825	+	8.72896i	0.395476	+	0.382790i
$521$	2.36411	−	4.09476i	0.103574	−	0.179395i	−0.809581	−	0.587008i	$-0.800306\pi$
$521$	2.36411	−	4.09476i	0.103574	−	0.179395i	0.913155	+	0.407614i	$0.133639\pi$
$522$	−13.9792	−	17.5648i	−0.611851	−	0.768793i
$523$	−6.27036	−	10.8606i	−0.274184	−	0.474900i	0.695745	−	0.718289i	$-0.255074\pi$
$523$	−6.27036	−	10.8606i	−0.274184	−	0.474900i	−0.969929	+	0.243388i	$0.921741\pi$
$524$	4.92790	−	8.53537i	0.215276	−	0.372869i
$525$	4.26613	−	22.5122i	0.186189	−	0.982514i
$526$	−1.76353	−	3.05452i	−0.0768934	−	0.133183i
$527$	−19.3416	+	33.5006i	−0.842533	+	1.45931i
$528$	−8.63211	+	3.01573i	−0.375665	+	0.131243i
$529$	2.35345	+	4.07630i	0.102324	+	0.177231i
$530$	0.994161	−	3.96784i	0.0431836	−	0.172352i
$531$	6.80203	+	2.67735i	0.295183	+	0.116187i
$532$	−0.00255413	+	0.0788353i	−0.000110736	+	0.00341794i
$533$	−2.37585	+	4.11509i	−0.102909	+	0.178244i
$534$	5.82618	+	16.6767i	0.252123	+	0.721669i
$535$	9.47254	+	9.16868i	0.409534	+	0.396397i
$536$		−	14.2507i		−	0.615534i
$537$	−12.1503	−	10.4667i	−0.524326	−	0.451669i
$538$	−3.55670	+	6.16038i	−0.153340	+	0.265593i
$539$	30.7400	+	20.5098i	1.32406	+	0.883418i
$540$	−11.1523	−	3.25985i	−0.479918	−	0.140281i
$541$	−19.5668	−	33.8907i	−0.841243	−	1.45708i	−0.888844	−	0.458210i	$-0.848491\pi$
$541$	−19.5668	−	33.8907i	−0.841243	−	1.45708i	0.0476006	−	0.998866i	$-0.484843\pi$
$542$	0.604546	−	0.349035i	0.0259675	−	0.0149923i
$543$	−1.76097	+	9.28190i	−0.0755706	+	0.398324i
$544$	−4.30888	−	2.48773i	−0.184742	−	0.106661i
$545$	−1.38456	+	5.52598i	−0.0593080	+	0.236707i
$546$	−25.1023	−	5.61019i	−1.07428	−	0.240094i
$547$	25.0270	+	14.4493i	1.07008	+	0.617808i	0.928202	−	0.372076i	$-0.121354\pi$
$547$	25.0270	+	14.4493i	1.07008	+	0.617808i	0.141873	+	0.989885i	$0.454687\pi$
$548$	−4.09746	−	7.09701i	−0.175035	−	0.303169i
$549$	4.65108	−	11.8164i	0.198503	−	0.504314i
$550$	12.4458	−	23.2774i	0.530691	−	0.992550i
$551$	−0.223084			−0.00950369
$552$	−4.83495	+	5.61271i	−0.205789	+	0.238893i
$553$	−5.89472	+	9.48662i	−0.250669	+	0.403412i
$554$	16.8512	−	9.72907i	0.715941	−	0.413349i
$555$	−6.67851	+	4.70965i	−0.283487	+	0.199914i
$556$	−2.59638	+	1.49902i	−0.110111	+	0.0635727i
$557$	−1.24187	+	2.15098i	−0.0526196	+	0.0911398i	−0.891135	−	0.453737i	$-0.850090\pi$
$557$	−1.24187	+	2.15098i	−0.0526196	+	0.0911398i	0.838516	+	0.544877i	$0.183424\pi$
$558$	8.54276	−	21.7036i	0.361644	−	0.918787i
$559$		−	47.4254i		−	2.00588i
$560$	−1.62293	+	5.68912i	−0.0685812	+	0.240409i
$561$	−44.6971	−	8.47999i	−1.88711	−	0.358025i
$562$	−8.04686	−	4.64586i	−0.339436	−	0.195974i
$563$		−	39.5457i		−	1.66665i	−0.552783	−	0.833325i	$-0.686434\pi$
$563$		−	39.5457i		−	1.66665i	0.552783	−	0.833325i	$-0.313566\pi$
$564$	1.15939	−	6.11101i	0.0488191	−	0.257320i
$565$	19.4217	+	18.7987i	0.817079	+	0.790868i
$566$	0.313268			0.0131676
$567$	22.9816	−	6.23281i	0.965135	−	0.261754i
$568$		−	10.3996i		−	0.436357i
$569$		−	8.79625i		−	0.368758i	−0.982855	−	0.184379i	$-0.940973\pi$
$569$		−	8.79625i		−	0.368758i	0.982855	−	0.184379i	$-0.0590274\pi$
$570$	−0.0943605	+	0.0665426i	−0.00395233	+	0.00278716i
$571$	15.5917			0.652494			0.326247	−	0.945284i	$-0.394216\pi$
$571$	15.5917			0.652494			0.326247	+	0.945284i	$0.394216\pi$
$572$	−25.6615	−	14.8157i	−1.07296	−	0.619474i
$573$	0.429954	−	2.26624i	0.0179616	−	0.0946734i
$574$	−2.23863	−	0.0725278i	−0.0934385	−	0.00302725i
$575$	−0.696993	−	21.3739i	−0.0290666	−	0.891351i
$576$	2.79154	+	1.09878i	0.116314	+	0.0457824i
$577$	−3.78855	+	6.56196i	−0.157719	+	0.273178i	−0.934046	−	0.357153i	$-0.883747\pi$
$577$	−3.78855	+	6.56196i	−0.157719	+	0.273178i	0.776327	+	0.630331i	$0.217081\pi$
$578$	−3.87763	−	6.71626i	−0.161288	−	0.279360i
$579$	4.22271	−	22.2574i	0.175490	−	0.924988i
$580$	−16.2305	−	4.06663i	−0.673936	−	0.168858i
$581$	−26.5269	+	14.1905i	−1.10052	+	0.588719i
$582$	−13.6073	+	15.7962i	−0.564042	+	0.654775i
$583$			9.65726i			0.399963i
$584$	2.23753	−	3.87552i	0.0925896	−	0.160370i
$585$	−15.5836	−	34.2763i	−0.644302	−	1.41715i
$586$	−11.3744	+	6.56701i	−0.469872	+	0.271281i
$587$	−30.2467	−	17.4630i	−1.24842	−	0.720774i	−0.277623	−	0.960690i	$-0.589547\pi$
$587$	−30.2467	−	17.4630i	−1.24842	−	0.720774i	−0.970794	+	0.239917i	$0.922880\pi$
$588$	−3.24951	−	11.6808i	−0.134007	−	0.481707i
$589$	−0.115893	−	0.200733i	−0.00477529	−	0.00827105i
$590$	5.23920	−	1.49577i	0.215695	−	0.0615801i
$591$	−24.4117	−	4.63141i	−1.00416	−	0.190511i
$592$	1.82734	−	1.05501i	0.0751031	−	0.0433608i
$593$	−8.23683	+	4.75554i	−0.338246	+	0.195286i	−0.659496	−	0.751708i	$-0.729230\pi$
$593$	−8.23683	+	4.75554i	−0.338246	+	0.195286i	0.321250	+	0.946994i	$0.395897\pi$
$594$	27.4105	+	1.06626i	1.12467	+	0.0437492i
$595$	−21.1460	+	20.4763i	−0.866902	+	0.839448i
$596$	14.6204	+	8.44109i	0.598875	+	0.345761i
$597$	−22.2079	−	19.1305i	−0.908908	−	0.782960i
$598$	−24.0066			−0.981704
$599$		−	14.2978i		−	0.584192i	−0.956389	−	0.292096i	$-0.905647\pi$
$599$		−	14.2978i		−	0.584192i	0.956389	−	0.292096i	$-0.0943527\pi$
$600$	−8.07824	+	3.12121i	−0.329793	+	0.127423i
$601$	17.7858	+	10.2686i	0.725496	+	0.418865i	0.816772	−	0.576960i	$-0.195761\pi$
$601$	17.7858	+	10.2686i	0.725496	+	0.418865i	−0.0912761	+	0.995826i	$0.529095\pi$
$602$	19.7117	−	10.5447i	0.803388	−	0.429769i
$603$	−15.6583	+	39.7812i	−0.637656	+	1.62002i
$604$	−9.49627	−	16.4480i	−0.386398	−	0.669261i
$605$	−9.16777	+	36.5899i	−0.372723	+	1.48759i
$606$	−5.30042	−	15.1717i	−0.215315	−	0.616310i
$607$	−1.31765	+	2.28224i	−0.0534819	+	0.0926333i	−0.891527	−	0.452968i	$-0.850365\pi$
$607$	−1.31765	+	2.28224i	−0.0534819	+	0.0926333i	0.838045	+	0.545601i	$0.183699\pi$
$608$	0.0258184	−	0.0149063i	0.00104708	−	0.000604530i
$609$	32.7214	−	10.2554i	1.32594	−	0.415570i
$610$	−2.59845	−	9.10151i	−0.105208	−	0.368509i
$611$	17.4562	−	10.0783i	0.706202	−	0.407726i
$612$	9.29494	+	11.6791i	0.375726	+	0.472100i
$613$	−6.11616	−	3.53116i	−0.247029	−	0.142622i	0.371374	−	0.928483i	$-0.378887\pi$
$613$	−6.11616	−	3.53116i	−0.247029	−	0.142622i	−0.618403	+	0.785861i	$0.712220\pi$
$614$	−8.18498			−0.330319
$615$	−1.88956	−	2.67949i	−0.0761945	−	0.108047i
$616$	0.452280	−	13.9600i	0.0182229	−	0.562463i
$617$	8.01842	+	13.8883i	0.322810	+	0.559122i	0.981067	−	0.193671i	$-0.0620393\pi$
$617$	8.01842	+	13.8883i	0.322810	+	0.559122i	−0.658257	+	0.752793i	$0.728706\pi$
$618$	−7.70734	+	8.94715i	−0.310035	+	0.359907i
$619$	1.05485	−	0.609018i	0.0423980	−	0.0244785i	−0.478651	−	0.878005i	$-0.658874\pi$
$619$	1.05485	−	0.609018i	0.0423980	−	0.0244785i	0.521049	+	0.853527i	$0.325541\pi$
$620$	−4.77265	−	16.7170i	−0.191674	−	0.671371i
$621$	19.6641	−	10.3556i	0.789092	−	0.415554i
$622$	−26.1476			−1.04842
$623$	−26.9697	−	0.873774i	−1.08052	−	0.0350070i
$624$	3.20639	+	9.17786i	0.128358	+	0.367409i
$625$	11.0629	−	22.4190i	0.442516	−	0.896760i
$626$	−4.72622			−0.188898
$627$	0.177914	−	0.206534i	0.00710522	−	0.00824818i
$628$	7.22541			0.288325
$629$	10.4984			0.418597
$630$	10.7815	−	14.0982i	0.429547	−	0.561684i
$631$	48.3010			1.92283			0.961417	−	0.275095i	$-0.0887092\pi$
$631$	48.3010			1.92283			0.961417	+	0.275095i	$0.0887092\pi$
$632$	4.22144			0.167920
$633$	−7.16712	−	20.5149i	−0.284867	−	0.815394i
$634$	−23.2386			−0.922921
$635$	−2.89761	−	10.1494i	−0.114988	−	0.402765i
$636$	2.06795	−	2.40060i	0.0819994	−	0.0951900i
$637$	21.8065	−	32.6835i	0.864003	−	1.29497i
$638$	39.5032			1.56395
$639$	−11.4268	+	29.0309i	−0.452039	+	1.14844i
$640$	2.15016	−	0.613862i	0.0849924	−	0.0242650i
$641$	−31.9313	+	18.4356i	−1.26121	+	0.728161i	−0.973309	−	0.229499i	$-0.926291\pi$
$641$	−31.9313	+	18.4356i	−1.26121	+	0.728161i	−0.287902	+	0.957660i	$0.592958\pi$
$642$	3.36791	+	9.64020i	0.132921	+	0.380468i
$643$	−20.4508	−	35.4219i	−0.806502	−	1.39690i	−0.915272	−	0.402835i	$-0.868025\pi$
$643$	−20.4508	−	35.4219i	−0.806502	−	1.39690i	0.108771	−	0.994067i	$-0.465309\pi$
$644$	−5.33769	−	9.97801i	−0.210335	−	0.393189i
$645$	29.7042	+	13.7307i	1.16960	+	0.540647i
$646$	0.148331			0.00583602
$647$	32.3274	+	18.6642i	1.27092	+	0.733767i	0.975162	−	0.221495i	$-0.0710936\pi$
$647$	32.3274	+	18.6642i	1.27092	+	0.733767i	0.295761	+	0.955262i	$0.404427\pi$
$648$	−6.58537	−	6.13456i	−0.258698	−	0.240988i
$649$	−11.1401	+	6.43174i	−0.437287	+	0.252468i
$650$	−24.7490	−	13.2327i	−0.970736	−	0.519028i
$651$	26.2268	+	24.1153i	1.02791	+	0.945152i
$652$	−18.7200	+	10.8080i	−0.733130	+	0.423273i
$653$	−22.3398	+	38.6937i	−0.874224	+	1.51420i	−0.0166362	+	0.999862i	$0.505296\pi$
$653$	−22.3398	+	38.6937i	−0.874224	+	1.51420i	−0.857587	+	0.514338i	$0.828038\pi$
$654$	−2.88001	+	3.34329i	−0.112617	+	0.130733i
$655$	−5.35621	+	21.3774i	−0.209284	+	0.835286i
$656$	0.423283	+	0.733148i	0.0165264	+	0.0286246i
$657$	−10.5045	+	8.36010i	−0.409819	+	0.326159i
$658$	8.07017	+	5.01457i	0.314608	+	0.195488i
$659$	1.20746	+	0.697128i	0.0470360	+	0.0271562i	0.523334	−	0.852128i	$-0.324688\pi$
$659$	1.20746	+	0.697128i	0.0470360	+	0.0271562i	−0.476298	+	0.879284i	$0.658022\pi$
$660$	16.7092	−	11.7832i	0.650403	−	0.458661i
$661$		−	11.4011i		−	0.443450i	−0.975109	−	0.221725i	$-0.928831\pi$
$661$		−	11.4011i		−	0.443450i	0.975109	−	0.221725i	$-0.0711687\pi$
$662$	23.7985			0.924956
$663$	−9.01612	+	47.5230i	−0.350157	+	1.84564i
$664$	9.84730	+	5.68534i	0.382149	+	0.220634i
$665$	−0.0429022	−	0.171076i	−0.00166368	−	0.00663404i
$666$	−6.26031	+	0.937273i	−0.242582	+	0.0363186i
$667$	27.7168	−	16.0023i	1.07320	−	0.619611i
$668$	4.94362	−	2.85420i	0.191274	−	0.110432i
$669$	16.6124	−	19.2847i	0.642272	−	0.745589i
$670$	8.74794	+	30.6411i	0.337962	+	1.18377i
$671$	11.1732	+	19.3525i	0.431336	+	0.747095i
$672$	−3.10173	+	3.37332i	−0.119652	+	0.130129i
$673$	−4.09954	−	2.36687i	−0.158025	−	0.0912361i	0.418902	−	0.908031i	$-0.362415\pi$
$673$	−4.09954	−	2.36687i	−0.158025	−	0.0912361i	−0.576927	+	0.816795i	$0.695748\pi$
$674$	−27.9969	+	16.1640i	−1.07840	+	0.622615i
$675$	25.9802	+	0.163211i	0.999980	+	0.00628200i
$676$	−9.25235	+	16.0255i	−0.355860	+	0.616367i
$677$			28.7024i			1.10312i	0.834134	+	0.551561i	$0.185968\pi$
$677$			28.7024i			1.10312i	−0.834134	+	0.551561i	$0.814032\pi$
$678$	6.90530	+	19.7655i	0.265196	+	0.759089i
$679$	−15.0222	−	28.0818i	−0.576500	−	1.07768i
$680$	10.7919	+	2.70396i	0.413850	+	0.103692i
$681$	23.7069	−	8.28229i	0.908452	−	0.317378i
$682$	20.5221	+	35.5453i	0.785831	+	1.36110i
$683$	−17.0772	+	29.5785i	−0.653440	+	1.13179i	0.328843	+	0.944385i	$0.393341\pi$
$683$	−17.0772	+	29.5785i	−0.653440	+	1.13179i	−0.982282	+	0.187406i	$0.939992\pi$
$684$	−0.0884519	+	0.0132427i	−0.00338204	+	0.000506348i
$685$	13.1668	+	12.7444i	0.503076	+	0.486938i
$686$	18.4329	+	1.79662i	0.703772	+	0.0685952i
$687$	28.1237	+	24.2266i	1.07299	+	0.924302i
$688$	−7.31735	−	4.22467i	−0.278971	−	0.161064i
$689$	10.2678			0.391173
$690$	6.95047	−	15.0362i	0.264600	−	0.572418i
$691$		−	24.7129i		−	0.940122i	−0.882634	−	0.470061i	$-0.844232\pi$
$691$		−	24.7129i		−	0.940122i	0.882634	−	0.470061i	$-0.155768\pi$
$692$		−	17.5004i		−	0.665264i
$693$	−16.6015	+	38.4728i	−0.630638	+	1.46146i
$694$	−28.1271			−1.06769
$695$	4.66243	−	4.81695i	0.176856	−	0.182717i
$696$	−9.81969	−	8.45896i	−0.372214	−	0.320636i
$697$			4.21206i			0.159543i
$698$	−24.7247	−	14.2748i	−0.935844	−	0.540310i
$699$	10.8508	+	31.0590i	0.410416	+	1.17476i
$700$	−0.00279186	−	13.2288i	−0.000105522	−	0.500000i
$701$			25.0887i			0.947587i	0.880636	+	0.473793i	$0.157116\pi$
$701$			25.0887i			0.947587i	−0.880636	+	0.473793i	$0.842884\pi$
$702$	1.13367	−	29.1435i	0.0427877	−	1.09995i
$703$	−0.0314527	+	0.0544776i	−0.00118626	+	0.00205466i
$704$	−4.57187	+	2.63957i	−0.172309	+	0.0994826i
$705$	1.25845	+	13.8513i	0.0473960	+	0.521671i
$706$	−5.19921	+	3.00176i	−0.195675	+	0.112973i
$707$	24.5359	+	0.794924i	0.922769	+	0.0298962i
$708$	4.14646	+	0.786671i	0.155833	+	0.0295649i
$709$	32.1693			1.20815			0.604073	−	0.796929i	$-0.293544\pi$
$709$	32.1693			1.20815			0.604073	+	0.796929i	$0.293544\pi$
$710$	6.38392	+	22.3608i	0.239584	+	0.839184i
$711$	−11.7843	−	4.63842i	−0.441946	−	0.173954i
$712$	5.09947	+	8.83254i	0.191111	+	0.331013i
$713$	28.7980	+	16.6265i	1.07849	+	0.622669i
$714$	−21.7569	+	6.81895i	−0.814231	+	0.255193i
$715$	64.2710	+	16.1034i	2.40360	+	0.602232i
$716$	−8.01844	−	4.62945i	−0.299663	−	0.173011i
$717$	−14.0486	+	4.90803i	−0.524654	+	0.183294i
$718$	−9.67555	+	5.58618i	−0.361088	+	0.208474i
$719$	−15.8662	−	27.4810i	−0.591708	−	1.02487i	−0.994002	−	0.109357i	$-0.965121\pi$
$719$	−15.8662	−	27.4810i	−0.591708	−	1.02487i	0.402295	−	0.915510i	$-0.368213\pi$
$720$	−6.67674	−	0.648925i	−0.248828	−	0.0241840i
$721$	−8.50875	−	15.9058i	−0.316882	−	0.592364i
$722$	9.49956	−	16.4537i	0.353537	−	0.612344i
$723$	32.3809	−	11.3126i	1.20426	−	0.420721i
$724$			5.45450i			0.202715i
$725$	37.3945	−	1.21942i	1.38880	−	0.0452881i
$726$	−19.0698	+	22.1374i	−0.707747	+	0.821597i
$727$	−4.37774	+	7.58247i	−0.162361	+	0.281218i	−0.935715	−	0.352757i	$-0.885244\pi$
$727$	−4.37774	+	7.58247i	−0.162361	+	0.281218i	0.773354	+	0.633975i	$0.218578\pi$
$728$	−14.8426	−	0.480874i	−0.550102	−	0.0178224i
$729$	11.6428	+	24.3607i	0.431215	+	0.902249i
$730$	−2.43201	+	9.70650i	−0.0900126	+	0.359254i
$731$	−21.0197	−	36.4072i	−0.777443	−	1.34657i
$732$	1.36660	−	7.20320i	0.0505110	−	0.266238i
$733$	−6.74214	+	11.6777i	−0.249027	+	0.431327i	−0.963256	−	0.268585i	$-0.913444\pi$
$733$	−6.74214	+	11.6777i	−0.249027	+	0.431327i	0.714229	+	0.699912i	$0.246777\pi$
$734$	−6.40205	−	11.0887i	−0.236304	−	0.409291i
$735$	14.1573	+	23.1208i	0.522201	+	0.852822i
$736$	−2.13852	+	3.70403i	−0.0788269	+	0.136532i
$737$	−37.6156	−	65.1521i	−1.38559	−	2.39991i
$738$	−0.376044	−	2.51170i	−0.0138424	−	0.0924571i
$739$	16.5844	−	28.7251i	0.610068	−	1.05667i	−0.381161	−	0.924509i	$-0.624476\pi$
$739$	16.5844	−	28.7251i	0.610068	−	1.05667i	0.991228	−	0.132159i	$-0.0421911\pi$
$740$	−3.28143	+	3.39018i	−0.120628	+	0.124625i
$741$	−0.219592	−	0.189163i	−0.00806691	−	0.00694906i
$742$	2.28297	+	4.26767i	0.0838106	+	0.156671i
$743$	−14.0246	−	24.2913i	−0.514513	−	0.891163i	−0.999858	−	0.0168402i	$-0.994639\pi$
$743$	−14.0246	−	24.2913i	−0.514513	−	0.891163i	0.485345	−	0.874323i	$-0.338694\pi$
$744$	2.51007	−	13.2303i	0.0920237	−	0.485047i
$745$	−36.6178	−	9.17476i	−1.34157	−	0.336137i
$746$	14.1942	+	8.19502i	0.519686	+	0.300041i
$747$	−21.2422	−	26.6908i	−0.777211	−	0.976567i
$748$	−26.2662			−0.960387
$749$	−15.5903	−	0.505099i	−0.569656	−	0.0184559i
$750$	15.4535	−	11.6700i	0.564282	−	0.426129i
$751$	−4.20623	+	7.28541i	−0.153488	+	0.265848i	−0.932507	−	0.361151i	$-0.882384\pi$
$751$	−4.20623	+	7.28541i	−0.153488	+	0.265848i	0.779020	+	0.626999i	$0.215717\pi$
$752$		−	3.59113i		−	0.130955i
$753$	−8.26810	−	1.56863i	−0.301306	−	0.0571642i
$754$		−	42.0007i		−	1.52957i
$755$	30.5153	+	29.5364i	1.11057	+	1.07494i
$756$	12.3651	−	6.00864i	0.449715	−	0.218532i
$757$			14.2416i			0.517618i	0.965928	+	0.258809i	$0.0833301\pi$
$757$			14.2416i			0.517618i	−0.965928	+	0.258809i	$0.916670\pi$
$758$	−5.48486			−0.199219
$759$	−7.28962	+	38.4228i	−0.264596	+	1.39466i
$760$	−0.0463633	+	0.0478998i	−0.00168177	+	0.00173751i
$761$	−0.524330	+	0.908166i	−0.0190070	+	0.0329210i	−0.875372	−	0.483449i	$-0.839384\pi$
$761$	−0.524330	+	0.908166i	−0.0190070	+	0.0329210i	0.856365	+	0.516370i	$0.172717\pi$
$762$	1.52394	−	8.03250i	0.0552064	−	0.290987i
$763$	−3.17948	−	5.94355i	−0.115105	−	0.215171i
$764$		−	1.33175i		−	0.0481811i
$765$	−27.1549	−	19.4061i	−0.981789	−	0.701629i
$766$	−17.8428	−	10.3015i	−0.644685	−	0.372209i
$767$	6.83837	+	11.8444i	0.246919	+	0.427677i
$768$	1.70170	+	0.322848i	0.0614047	+	0.0116498i
$769$	−41.5385	+	23.9823i	−1.49792	+	0.864823i	−0.999997	−	0.00240052i	$-0.999236\pi$
$769$	−41.5385	+	23.9823i	−1.49792	+	0.864823i	−0.497920	+	0.867223i	$0.665903\pi$
$770$	7.59703	+	30.2938i	0.273778	+	1.09171i
$771$	−26.2522	−	22.6144i	−0.945452	−	0.814439i
$772$		−	13.0796i		−	0.470744i
$773$	−10.8239	−	6.24918i	−0.389309	−	0.224767i	0.292552	−	0.956250i	$-0.405496\pi$
$773$	−10.8239	−	6.24918i	−0.389309	−	0.224767i	−0.681861	+	0.731482i	$0.738829\pi$
$774$	15.7847	+	19.8335i	0.567369	+	0.712900i
$775$	20.5239	+	33.0144i	0.737239	+	1.18591i
$776$	−6.01859	+	10.4245i	−0.216055	+	0.374218i
$777$	2.10901	−	9.43656i	0.0756603	−	0.338535i
$778$	15.4245	−	8.90535i	0.552996	−	0.319272i
$779$	−0.0218570	−	0.0126191i	−0.000783109	−	0.000452128i
$780$	−12.5282	−	17.7656i	−0.448581	−	0.636109i
$781$	−27.4505	−	47.5456i	−0.982255	−	1.70132i
$782$	−18.4293	+	10.6401i	−0.659029	+	0.380491i
$783$	18.1175	+	34.4032i	0.647467	+	1.22947i
$784$	−3.10026	−	6.27602i	−0.110724	−	0.224143i
$785$	−15.5358	+	4.43541i	−0.554495	+	0.158307i
$786$	−11.1414	+	12.9336i	−0.397401	+	0.461328i
$787$	43.6003			1.55418			0.777091	−	0.629388i	$-0.216694\pi$
$787$	43.6003			1.55418			0.777091	+	0.629388i	$0.216694\pi$
$788$	−14.3455			−0.511037
$789$	2.01484	+	5.76721i	0.0717302	+	0.205318i
$790$	−9.07675	+	2.59138i	−0.322936	+	0.0921972i
$791$	−31.9650	−	1.03561i	−1.13655	−	0.0368222i
$792$	15.6629	−	2.34499i	0.556555	−	0.0833256i
$793$	20.5760	−	11.8796i	0.730676	−	0.421856i
$794$	1.81408	+	3.14208i	0.0643794	+	0.111508i
$795$	−2.97277	+	6.43110i	−0.105433	+	0.228088i
$796$	−14.6558	−	8.46151i	−0.519460	−	0.299910i
$797$	−38.9021	+	22.4601i	−1.37798	+	0.795578i	−0.991916	−	0.126894i	$-0.959499\pi$
$797$	−38.9021	+	22.4601i	−1.37798	+	0.795578i	−0.386065	+	0.922472i	$0.626166\pi$
$798$	0.0297982	−	0.133329i	0.00105484	−	0.00471980i
$799$	8.93377	−	15.4737i	0.316054	−	0.547422i
$800$	−4.24635	+	2.63980i	−0.150131	+	0.0933310i
$801$	−4.53036	−	30.2596i	−0.160072	−	1.06917i
$802$	31.5305	+	18.2041i	1.11338	+	0.642810i
$803$		−	23.6245i		−	0.833689i
$804$	−4.60079	+	24.2503i	−0.162258	+	0.855241i
$805$	17.6020	+	18.1777i	0.620389	+	0.640679i
$806$	37.7926	−	21.8196i	1.33119	−	0.768561i
$807$	8.04129	−	9.33483i	0.283067	−	0.328601i
$808$	−4.63929	−	8.03548i	−0.163210	−	0.282687i
$809$	25.9011	+	14.9540i	0.910635	+	0.525755i	0.880635	−	0.473795i	$-0.157116\pi$
$809$	25.9011	+	14.9540i	0.910635	+	0.525755i	0.0299994	+	0.999550i	$0.490449\pi$
$810$	17.9254	+	9.14776i	0.629833	+	0.321419i
$811$		−	22.6858i		−	0.796607i	−0.917254	−	0.398303i	$-0.869599\pi$
$811$		−	22.6858i		−	0.796607i	0.917254	−	0.398303i	$-0.130401\pi$
$812$	17.4570	−	9.33853i	0.612620	−	0.327718i
$813$	−1.14144	+	0.398775i	−0.0400320	+	0.0139856i
$814$	5.56957	−	9.64677i	0.195213	−	0.338119i
$815$	33.6162	−	34.7303i	1.17753	−	1.21655i
$816$	6.52924	+	5.62448i	0.228569	+	0.196896i
$817$	0.251897			0.00881275
$818$		−	5.67091i		−	0.198279i
$819$	40.9052	+	17.6511i	1.42934	+	0.616778i
$820$	−1.36018	−	1.31654i	−0.0474994	−	0.0459757i
$821$		−	24.7257i		−	0.862933i	−0.902129	−	0.431467i	$-0.857996\pi$
$821$		−	24.7257i		−	0.862933i	0.902129	−	0.431467i	$-0.142004\pi$
$822$	4.68137	+	13.3998i	0.163282	+	0.467372i
$823$		−	51.0056i		−	1.77794i	−0.457963	−	0.888971i	$-0.651421\pi$
$823$		−	51.0056i		−	1.77794i	0.457963	−	0.888971i	$-0.348579\pi$
$824$	−3.40899	+	5.90454i	−0.118758	+	0.205695i
$825$	−28.6940	+	35.5929i	−0.998998	+	1.23918i
$826$	−3.40250	+	5.47579i	−0.118388	+	0.190527i
$827$	−10.5632			−0.367317			−0.183659	−	0.982990i	$-0.558794\pi$
$827$	−10.5632			−0.367317			−0.183659	+	0.982990i	$0.558794\pi$
$828$	10.0397	−	7.99017i	0.348903	−	0.277678i
$829$	−28.1683	−	16.2630i	−0.978325	−	0.564836i	−0.0765613	−	0.997065i	$-0.524394\pi$
$829$	−28.1683	−	16.2630i	−0.978325	−	0.564836i	−0.901764	+	0.432228i	$0.857727\pi$
$830$	−24.6632	−	6.17948i	−0.856074	−	0.214493i
$831$	−31.8167	+	11.1155i	−1.10371	+	0.385593i
$832$	2.80645	+	4.86092i	0.0972962	+	0.168522i
$833$	2.25439	−	34.7552i	0.0781100	−	1.20420i
$834$	4.90221	−	1.71264i	0.169750	−	0.0593040i
$835$	−8.87747	+	9.17167i	−0.307217	+	0.317399i
$836$	0.0786924	−	0.136299i	0.00272163	−	0.00471401i
$837$	−21.5441	+	34.1749i	−0.744675	+	1.18126i
$838$	13.5787	+	23.5190i	0.469067	+	0.812449i
$839$	−11.6589	+	20.1938i	−0.402509	+	0.697166i	−0.994028	−	0.109125i	$-0.965195\pi$
$839$	−11.6589	+	20.1938i	−0.402509	+	0.697166i	0.591519	+	0.806291i	$0.298529\pi$
$840$	4.59845	−	9.15720i	0.158662	−	0.315953i
$841$	13.4967	+	23.3770i	0.465404	+	0.806104i
$842$	3.92131	−	6.79190i	0.135137	−	0.234064i
$843$	12.1934	+	10.5037i	0.419963	+	0.361768i
$844$	−6.27315	−	10.8654i	−0.215931	−	0.374003i
$845$	10.0565	−	40.1371i	0.345955	−	1.38076i
$846$	−3.94586	+	10.0248i	−0.135661	+	0.344659i
$847$	−21.0527	−	39.3548i	−0.723379	−	1.35225i
$848$	0.914662	−	1.58424i	0.0314096	−	0.0544031i
$849$	−0.533086	−	0.101138i	−0.0182955	−	0.00347104i
$850$	−24.8641	+	0.810809i	−0.852832	+	0.0278105i
$851$		−	9.02468i		−	0.309362i
$852$	−3.35749	+	17.6969i	−0.115026	+	0.606288i
$853$	16.4172	−	28.4354i	0.562114	−	0.973609i	−0.435198	−	0.900335i	$-0.643322\pi$
$853$	16.4172	−	28.4354i	0.562114	−	0.973609i	0.997312	−	0.0732747i	$-0.0233450\pi$
$854$	9.51250	+	5.91080i	0.325511	+	0.202263i
$855$	0.182056	−	0.0827712i	0.00622619	−	0.00283071i
$856$	2.94783	+	5.10579i	0.100755	+	0.174512i
$857$	8.43621	−	4.87065i	0.288175	−	0.166378i	−0.348943	−	0.937144i	$-0.613459\pi$
$857$	8.43621	−	4.87065i	0.288175	−	0.166378i	0.637119	+	0.770766i	$0.280126\pi$
$858$	38.8848	+	33.4965i	1.32751	+	1.14355i
$859$	−3.10405	−	1.79213i	−0.105909	−	0.0611466i	0.446110	−	0.894978i	$-0.352809\pi$
$859$	−3.10405	−	1.79213i	−0.105909	−	0.0611466i	−0.552019	+	0.833832i	$0.686142\pi$
$860$	18.3268	+	4.59186i	0.624939	+	0.156581i
$861$	3.78605	+	0.846157i	0.129028	+	0.0288370i
$862$	−9.95046	−	5.74490i	−0.338914	−	0.195672i
$863$	−23.0657	−	39.9510i	−0.785165	−	1.35995i	−0.928900	−	0.370330i	$-0.879245\pi$
$863$	−23.0657	−	39.9510i	−0.785165	−	1.35995i	0.143735	−	0.989616i	$-0.454089\pi$
$864$	−4.39561	−	2.77103i	−0.149542	−	0.0942723i
$865$	10.7428	+	37.6285i	0.365267	+	1.27941i
$866$	33.0116			1.12178
$867$	4.43022	+	12.6809i	0.150458	+	0.430667i
$868$	17.4719	+	10.8565i	0.593034	+	0.368495i
$869$	19.2999	−	11.1428i	0.654703	−	0.377993i
$870$	26.3065	+	12.1602i	0.891874	+	0.412268i
$871$	−69.2713	+	39.9938i	−2.34717	+	1.35514i
$872$	−1.27384	+	2.20636i	−0.0431377	+	0.0747167i
$873$	28.2553	−	22.4873i	0.956298	−	0.761079i
$874$		−	0.127510i		−	0.00431308i
$875$	8.12664	+	28.4422i	0.274731	+	0.961521i
$876$	−5.05880	+	5.87257i	−0.170921	+	0.198416i
$877$	−35.1752	−	20.3084i	−1.18778	−	0.685766i	−0.229980	−	0.973195i	$-0.573866\pi$
$877$	−35.1752	−	20.3084i	−1.18778	−	0.685766i	−0.957802	+	0.287429i	$0.907199\pi$
$878$		−	36.8521i		−	1.24370i
$879$	21.4759	−	7.50285i	0.724364	−	0.253065i
$880$	8.20990	−	8.48199i	0.276756	−	0.285928i
$881$	−49.0514			−1.65258			−0.826292	−	0.563243i	$-0.809554\pi$
$881$	−49.0514			−1.65258			−0.826292	+	0.563243i	$0.809554\pi$
$882$	1.75855	+	20.9262i	0.0592136	+	0.704623i
$883$			49.0178i			1.64958i	0.565438	+	0.824791i	$0.308707\pi$
$883$			49.0178i			1.64958i	−0.565438	+	0.824791i	$0.691293\pi$
$884$			27.9268i			0.939281i
$885$	−9.39844	+	0.853888i	−0.315925	+	0.0287031i
$886$	−6.89008			−0.231477
$887$	−16.1307	−	9.31309i	−0.541617	−	0.312703i	0.204117	−	0.978947i	$-0.434568\pi$
$887$	−16.1307	−	9.31309i	−0.541617	−	0.312703i	−0.745734	+	0.666244i	$0.767901\pi$
$888$	−3.45018	+	1.20536i	−0.115781	+	0.0404492i
$889$	10.6077	+	6.59131i	0.355770	+	0.221065i
$890$	−16.3866	−	15.8610i	−0.549281	−	0.531661i
$891$	−46.3001	−	10.6639i	−1.55111	−	0.357253i
$892$	7.34774	−	12.7267i	0.246020	−	0.426120i
$893$	0.0535304	+	0.0927174i	0.00179133	+	0.00310267i
$894$	−22.1543	−	19.0843i	−0.740950	−	0.638276i
$895$	20.0828	+	5.03182i	0.671292	+	0.168195i
$896$	−1.39638	+	2.24725i	−0.0466497	+	0.0750753i
$897$	40.8520	+	7.75049i	1.36401	+	0.258781i
$898$		−	18.6394i		−	0.622006i
$899$	−29.0889	+	50.3834i	−0.970168	+	1.68038i
$900$	14.7544	−	2.70331i	0.491813	−	0.0901104i
$901$	7.88234	−	4.55087i	0.262599	−	0.151612i
$902$	3.87039	+	2.23457i	0.128870	+	0.0744030i
$903$	−36.9476	+	11.5800i	−1.22954	+	0.385357i
$904$	6.04399	+	10.4685i	0.201020	+	0.348177i
$905$	−3.34831	−	11.7280i	−0.111302	−	0.389853i
$906$	10.8496	+	31.0554i	0.360452	+	1.03175i
$907$	−8.12112	+	4.68873i	−0.269657	+	0.155687i	−0.628732	−	0.777622i	$-0.716426\pi$
$907$	−8.12112	+	4.68873i	−0.269657	+	0.155687i	0.359075	+	0.933309i	$0.383092\pi$
$908$	12.5560	−	7.24923i	0.416686	−	0.240574i
$909$	4.12154	+	27.5289i	0.136703	+	0.913076i
$910$	32.2090	−	8.07734i	1.06772	−	0.267761i
$911$	−19.1619	−	11.0631i	−0.634862	−	0.366538i	0.147770	−	0.989022i	$-0.452790\pi$
$911$	−19.1619	−	11.0631i	−0.634862	−	0.366538i	−0.782633	+	0.622484i	$0.786124\pi$
$912$	−0.0487476	+	0.0170305i	−0.00161419	+	0.000563937i
$913$	60.0274			1.98662
$914$			19.5925i			0.648063i
$915$	1.48337	+	16.3269i	0.0490386	+	0.539751i
$916$	18.5598	+	10.7155i	0.613235	+	0.354051i
$917$	−12.2999	−	22.9928i	−0.406179	−	0.759290i
$918$	−12.0466	−	22.8751i	−0.397596	−	0.754992i
$919$	−5.93693	−	10.2831i	−0.195841	−	0.339207i	0.751335	−	0.659921i	$-0.229410\pi$
$919$	−5.93693	−	10.2831i	−0.195841	−	0.339207i	−0.947176	+	0.320714i	$0.896077\pi$
$920$	2.32439	−	9.27700i	0.0766329	−	0.305854i
$921$	13.9284	+	2.64250i	0.458955	+	0.0870735i
$922$	−5.15453	+	8.92791i	−0.169755	+	0.294025i
$923$	−50.5516	+	29.1860i	−1.66393	+	0.960668i
$924$	−5.27659	+	23.6096i	−0.173587	+	0.776699i
$925$	4.97448	−	9.30376i	0.163560	−	0.305906i
$926$	22.9305	−	13.2390i	0.753544	−	0.435059i
$927$	16.0041	−	12.7370i	0.525644	−	0.418339i
$928$	−6.48036	−	3.74144i	−0.212728	−	0.122819i
$929$	−15.4622			−0.507299			−0.253649	−	0.967296i	$-0.581631\pi$
$929$	−15.4622			−0.507299			−0.253649	+	0.967296i	$0.581631\pi$
$930$	2.72454	+	29.9881i	0.0893413	+	0.983348i
$931$	0.173596	+	0.115824i	0.00568938	+	0.00379596i
$932$	9.49738	+	16.4499i	0.311097	+	0.538836i
$933$	44.4953	+	8.44171i	1.45671	+	0.276369i
$934$	7.88940	−	4.55495i	0.258149	−	0.149042i
$935$	56.4764	−	16.1238i	1.84698	−	0.527306i
$936$	−2.49325	−	16.6531i	−0.0814944	−	0.544324i
$937$	17.1241			0.559421			0.279711	−	0.960084i	$-0.409761\pi$
$937$	17.1241			0.559421			0.279711	+	0.960084i	$0.409761\pi$
$938$	−32.0248	−	19.8993i	−1.04565	−	0.649735i
$939$	8.04259	+	1.52585i	0.262460	+	0.0497943i
$940$	2.20446	+	7.72149i	0.0719015	+	0.251847i
$941$	25.5399			0.832575			0.416288	−	0.909233i	$-0.363331\pi$
$941$	25.5399			0.832575			0.416288	+	0.909233i	$0.363331\pi$
$942$	−12.2955	−	2.33271i	−0.400607	−	0.0760038i
$943$	3.62080			0.117909
$944$	2.43666			0.0793066
$945$	−22.8985	+	20.5100i	−0.744888	+	0.667190i
$946$	−44.6053			−1.45024
$947$	13.8371			0.449645			0.224822	−	0.974400i	$-0.427820\pi$
$947$	13.8371			0.449645			0.224822	+	0.974400i	$0.427820\pi$
$948$	−7.18360	−	1.36288i	−0.233313	−	0.0442644i
$949$	−25.1181			−0.815367
$950$	0.0702844	−	0.131453i	0.00228033	−	0.00426489i
$951$	39.5450	+	7.50252i	1.28233	+	0.243286i
$952$	−11.6074	+	6.20932i	−0.376197	+	0.201245i
$953$	18.9540			0.613982			0.306991	−	0.951712i	$-0.400678\pi$
$953$	18.9540			0.613982			0.306991	+	0.951712i	$0.400678\pi$
$954$	−4.29405	+	3.41746i	−0.139025	+	0.110644i
$955$	0.817513	+	2.86348i	0.0264541	+	0.0926599i
$956$	−7.44062	+	4.29585i	−0.240647	+	0.138938i
$957$	−67.2224	−	12.7535i	−2.17299	−	0.412263i
$958$	0.511670	+	0.886239i	0.0165313	+	0.0286331i
$959$	−21.6703	−	0.702083i	−0.699772	−	0.0226714i
$960$	−3.85710	+	0.350434i	−0.124487	+	0.0113102i
$961$	−29.4472			−0.949911
$962$	−10.2567	−	5.92169i	−0.330688	−	0.190923i
$963$	−2.61885	−	17.4920i	−0.0843911	−	0.563672i
$964$	17.1500	−	9.90158i	0.552365	−	0.318908i
$965$	8.02905	+	28.1231i	0.258464	+	0.905315i
$966$	5.86175	+	18.7028i	0.188599	+	0.601753i
$967$	−34.2125	+	19.7526i	−1.10020	+	0.635200i	−0.936273	−	0.351273i	$-0.885749\pi$
$967$	−34.2125	+	19.7526i	−1.10020	+	0.635200i	−0.163926	+	0.986473i	$0.552416\pi$
$968$	−8.43466	+	14.6093i	−0.271100	+	0.469560i
$969$	−0.252415	−	0.0478885i	−0.00810874	−	0.00153840i
$970$	6.54169	−	26.1089i	0.210041	−	0.838306i
$971$	13.7224	+	23.7679i	0.440373	+	0.762748i	0.997717	−	0.0675336i	$-0.0215130\pi$
$971$	13.7224	+	23.7679i	0.440373	+	0.762748i	−0.557344	+	0.830281i	$0.688180\pi$
$972$	9.22577	+	12.5652i	0.295917	+	0.403030i
$973$	−0.256851	+	7.92792i	−0.00823428	+	0.254157i
$974$	−2.98547	−	1.72366i	−0.0956607	−	0.0552297i
$975$	37.8432	+	30.5081i	1.21195	+	0.977043i
$976$		−	4.23295i		−	0.135494i
$977$	−21.2690			−0.680456			−0.340228	−	0.940343i	$-0.610504\pi$
$977$	−21.2690			−0.680456			−0.340228	+	0.940343i	$0.610504\pi$
$978$	35.3450	−	12.3482i	1.13021	−	0.394851i
$979$	46.6282	+	26.9208i	1.49024	+	0.860393i
$980$	10.5187	+	11.5913i	0.336006	+	0.370270i
$981$	5.98028	−	4.75947i	0.190936	−	0.151958i
$982$	20.0862	−	11.5968i	0.640978	−	0.370069i
$983$	9.52638	−	5.50006i	0.303844	−	0.175425i	−0.340324	−	0.940308i	$-0.610537\pi$
$983$	9.52638	−	5.50006i	0.303844	−	0.175425i	0.644169	+	0.764884i	$0.277204\pi$
$984$	−0.483604	−	1.38425i	−0.0154167	−	0.0441283i
$985$	30.8450	−	8.80615i	0.982805	−	0.280587i
$986$	−18.6154	−	32.2428i	−0.592835	−	1.02682i
$987$	−12.1140	−	11.1387i	−0.385594	−	0.354549i
$988$	−0.144916	−	0.0836675i	−0.00461041	−	0.00266182i
$989$	−31.2966	+	18.0691i	−0.995175	+	0.574564i
$990$	−32.2381	+	14.6569i	−1.02459	+	0.465828i
$991$	4.84786	−	8.39675i	0.153997	−	0.266731i	−0.778696	−	0.627401i	$-0.784119\pi$
$991$	4.84786	−	8.39675i	0.153997	−	0.266731i	0.932694	+	0.360670i	$0.117452\pi$
$992$		−	7.77478i		−	0.246850i
$993$	−40.4978	−	7.68330i	−1.28516	−	0.243822i
$994$	−23.3705	−	14.5218i	−0.741267	−	0.460602i
$995$	36.7064	+	9.19695i	1.16367	+	0.291563i
$996$	−14.9216	−	12.8539i	−0.472809	−	0.407291i
$997$	−10.5919	−	18.3456i	−0.335447	−	0.581012i	0.648123	−	0.761535i	$-0.275554\pi$
$997$	−10.5919	−	18.3456i	−0.335447	−	0.581012i	−0.983571	+	0.180524i	$0.942221\pi$
$998$	5.15759	−	8.93321i	0.163261	−	0.282776i
$999$	10.9557	+	0.426175i	0.346624	+	0.0134836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.a.479.23	yes	48
3.2	odd	2		1890.2.bi.b.899.23		48
5.4	even	2		630.2.bi.b.479.2	yes	48
7.5	odd	6		630.2.r.b.299.19	yes	48
9.4	even	3		1890.2.r.b.1529.18		48
9.5	odd	6		630.2.r.a.59.6	✓	48
15.14	odd	2		1890.2.bi.a.899.10		48
21.5	even	6		1890.2.r.a.89.18		48
35.19	odd	6		630.2.r.a.299.6	yes	48
45.4	even	6		1890.2.r.a.1529.18		48
45.14	odd	6		630.2.r.b.59.19	yes	48
63.5	even	6		630.2.bi.b.509.2	yes	48
63.40	odd	6		1890.2.bi.a.719.10		48
105.89	even	6		1890.2.r.b.89.18		48
315.194	even	6	inner	630.2.bi.a.509.23	yes	48
315.229	odd	6		1890.2.bi.b.719.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.6	✓	48	9.5	odd	6
630.2.r.a.299.6	yes	48	35.19	odd	6
630.2.r.b.59.19	yes	48	45.14	odd	6
630.2.r.b.299.19	yes	48	7.5	odd	6
630.2.bi.a.479.23	yes	48	1.1	even	1	trivial
630.2.bi.a.509.23	yes	48	315.194	even	6	inner
630.2.bi.b.479.2	yes	48	5.4	even	2
630.2.bi.b.509.2	yes	48	63.5	even	6
1890.2.r.a.89.18		48	21.5	even	6
1890.2.r.a.1529.18		48	45.4	even	6
1890.2.r.b.89.18		48	105.89	even	6
1890.2.r.b.1529.18		48	9.4	even	3
1890.2.bi.a.719.10		48	63.40	odd	6
1890.2.bi.a.899.10		48	15.14	odd	2
1890.2.bi.b.719.23		48	315.229	odd	6
1890.2.bi.b.899.23		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.70170 + 0.322848i) q^{3} +1.00000 q^{4} +(-2.15016 + 0.613862i) q^{5} +(-1.70170 - 0.322848i) q^{6} +(1.39638 - 2.24725i) q^{7} -1.00000 q^{8} +(2.79154 + 1.09878i) q^{9} +(2.15016 - 0.613862i) q^{10} +(-4.57187 + 2.63957i) q^{11} +(1.70170 + 0.322848i) q^{12} +(2.80645 + 4.86092i) q^{13} +(-1.39638 + 2.24725i) q^{14} +(-3.85710 + 0.350434i) q^{15} +1.00000 q^{16} +(4.30888 + 2.48773i) q^{17} +(-2.79154 - 1.09878i) q^{18} +(-0.0258184 + 0.0149063i) q^{19} +(-2.15016 + 0.613862i) q^{20} +(3.10173 - 3.37332i) q^{21} +(4.57187 - 2.63957i) q^{22} +(2.13852 - 3.70403i) q^{23} +(-1.70170 - 0.322848i) q^{24} +(4.24635 - 2.63980i) q^{25} +(-2.80645 - 4.86092i) q^{26} +(4.39561 + 2.77103i) q^{27} +(1.39638 - 2.24725i) q^{28} +(6.48036 + 3.74144i) q^{29} +(3.85710 - 0.350434i) q^{30} +7.77478i q^{31} -1.00000 q^{32} +(-8.63211 + 3.01573i) q^{33} +(-4.30888 - 2.48773i) q^{34} +(-1.62293 + 5.68912i) q^{35} +(2.79154 + 1.09878i) q^{36} +(1.82734 - 1.05501i) q^{37} +(0.0258184 - 0.0149063i) q^{38} +(3.20639 + 9.17786i) q^{39} +(2.15016 - 0.613862i) q^{40} +(0.423283 + 0.733148i) q^{41} +(-3.10173 + 3.37332i) q^{42} +(-7.31735 - 4.22467i) q^{43} +(-4.57187 + 2.63957i) q^{44} +(-6.67674 - 0.648925i) q^{45} +(-2.13852 + 3.70403i) q^{46} -3.59113i q^{47} +(1.70170 + 0.322848i) q^{48} +(-3.10026 - 6.27602i) q^{49} +(-4.24635 + 2.63980i) q^{50} +(6.52924 + 5.62448i) q^{51} +(2.80645 + 4.86092i) q^{52} +(0.914662 - 1.58424i) q^{53} +(-4.39561 - 2.77103i) q^{54} +(8.20990 - 8.48199i) q^{55} +(-1.39638 + 2.24725i) q^{56} +(-0.0487476 + 0.0170305i) q^{57} +(-6.48036 - 3.74144i) q^{58} +2.43666 q^{59} +(-3.85710 + 0.350434i) q^{60} -4.23295i q^{61} -7.77478i q^{62} +(6.36727 - 4.73898i) q^{63} +1.00000 q^{64} +(-9.01825 - 8.72896i) q^{65} +(8.63211 - 3.01573i) q^{66} +14.2507i q^{67} +(4.30888 + 2.48773i) q^{68} +(4.83495 - 5.61271i) q^{69} +(1.62293 - 5.68912i) q^{70} +10.3996i q^{71} +(-2.79154 - 1.09878i) q^{72} +(-2.23753 + 3.87552i) q^{73} +(-1.82734 + 1.05501i) q^{74} +(8.07824 - 3.12121i) q^{75} +(-0.0258184 + 0.0149063i) q^{76} +(-0.452280 + 13.9600i) q^{77} +(-3.20639 - 9.17786i) q^{78} -4.22144 q^{79} +(-2.15016 + 0.613862i) q^{80} +(6.58537 + 6.13456i) q^{81} +(-0.423283 - 0.733148i) q^{82} +(-9.84730 - 5.68534i) q^{83} +(3.10173 - 3.37332i) q^{84} +(-10.7919 - 2.70396i) q^{85} +(7.31735 + 4.22467i) q^{86} +(9.81969 + 8.45896i) q^{87} +(4.57187 - 2.63957i) q^{88} +(-5.09947 - 8.83254i) q^{89} +(6.67674 + 0.648925i) q^{90} +(14.8426 + 0.480874i) q^{91} +(2.13852 - 3.70403i) q^{92} +(-2.51007 + 13.2303i) q^{93} +3.59113i q^{94} +(0.0463633 - 0.0478998i) q^{95} +(-1.70170 - 0.322848i) q^{96} +(6.01859 - 10.4245i) q^{97} +(3.10026 + 6.27602i) q^{98} +(-15.6629 + 2.34499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8} + 6 q^{11} + 3 q^{14} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39}+ \cdots - 26 q^{99}+O(q^{100}) \) 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8 + 6 * q^11 + 3 * q^14 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 + 42 * q^55 + 3 * q^56 + 22 * q^57 + 3 * q^58 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * q^70 + 18 * q^73 + 18 * q^75 + 12 * q^77 + 18 * q^78 + 8 * q^81 + 3 * q^82 - 9 * q^83 + 8 * q^84 + 33 * q^85 + 15 * q^87 - 6 * q^88 - 33 * q^89 - 15 * q^90 - 3 * q^92 + 8 * q^93 + 24 * q^97 - 3 * q^98 - 26 * q^99

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