LMFDB - Embedded newform 630.2.bi.b.479.17

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			479.17
Character	$\chi$	$=$	630.479
Dual form			630.2.bi.b.509.17

$q$-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} +(0.640430 - 1.60930i) q^{3} +1.00000 q^{4} +(2.22760 - 0.194363i) q^{5} +(0.640430 - 1.60930i) q^{6} +(-2.20085 - 1.46842i) q^{7} +1.00000 q^{8} +(-2.17970 - 2.06129i) q^{9} +(2.22760 - 0.194363i) q^{10} +(-0.123075 + 0.0710575i) q^{11} +(0.640430 - 1.60930i) q^{12} +(-0.600465 - 1.04004i) q^{13} +(-2.20085 - 1.46842i) q^{14} +(1.11384 - 3.70936i) q^{15} +1.00000 q^{16} +(-0.0902992 - 0.0521342i) q^{17} +(-2.17970 - 2.06129i) q^{18} +(5.02533 - 2.90137i) q^{19} +(2.22760 - 0.194363i) q^{20} +(-3.77262 + 2.60142i) q^{21} +(-0.123075 + 0.0710575i) q^{22} +(-2.15286 + 3.72887i) q^{23} +(0.640430 - 1.60930i) q^{24} +(4.92445 - 0.865927i) q^{25} +(-0.600465 - 1.04004i) q^{26} +(-4.71318 + 2.18768i) q^{27} +(-2.20085 - 1.46842i) q^{28} +(3.20977 + 1.85316i) q^{29} +(1.11384 - 3.70936i) q^{30} +3.59772i q^{31} +1.00000 q^{32} +(0.0355319 + 0.243572i) q^{33} +(-0.0902992 - 0.0521342i) q^{34} +(-5.18803 - 2.84329i) q^{35} +(-2.17970 - 2.06129i) q^{36} +(-5.42899 + 3.13443i) q^{37} +(5.02533 - 2.90137i) q^{38} +(-2.05829 + 0.300259i) q^{39} +(2.22760 - 0.194363i) q^{40} +(3.96636 + 6.86994i) q^{41} +(-3.77262 + 2.60142i) q^{42} +(-1.49609 - 0.863766i) q^{43} +(-0.123075 + 0.0710575i) q^{44} +(-5.25615 - 4.16808i) q^{45} +(-2.15286 + 3.72887i) q^{46} -5.04557i q^{47} +(0.640430 - 1.60930i) q^{48} +(2.68750 + 6.46354i) q^{49} +(4.92445 - 0.865927i) q^{50} +(-0.141730 + 0.111930i) q^{51} +(-0.600465 - 1.04004i) q^{52} +(1.34026 - 2.32140i) q^{53} +(-4.71318 + 2.18768i) q^{54} +(-0.260352 + 0.182209i) q^{55} +(-2.20085 - 1.46842i) q^{56} +(-1.45081 - 9.94539i) q^{57} +(3.20977 + 1.85316i) q^{58} +9.80986 q^{59} +(1.11384 - 3.70936i) q^{60} +12.3067i q^{61} +3.59772i q^{62} +(1.77036 + 7.73730i) q^{63} +1.00000 q^{64} +(-1.53974 - 2.20008i) q^{65} +(0.0355319 + 0.243572i) q^{66} -7.27754i q^{67} +(-0.0902992 - 0.0521342i) q^{68} +(4.62211 + 5.85268i) q^{69} +(-5.18803 - 2.84329i) q^{70} -12.4507i q^{71} +(-2.17970 - 2.06129i) q^{72} +(-4.01981 + 6.96252i) q^{73} +(-5.42899 + 3.13443i) q^{74} +(1.76023 - 8.47948i) q^{75} +(5.02533 - 2.90137i) q^{76} +(0.375212 + 0.0243387i) q^{77} +(-2.05829 + 0.300259i) q^{78} -8.41003 q^{79} +(2.22760 - 0.194363i) q^{80} +(0.502177 + 8.98598i) q^{81} +(3.96636 + 6.86994i) q^{82} +(-2.03412 - 1.17440i) q^{83} +(-3.77262 + 2.60142i) q^{84} +(-0.211284 - 0.0985837i) q^{85} +(-1.49609 - 0.863766i) q^{86} +(5.03793 - 3.97867i) q^{87} +(-0.123075 + 0.0710575i) q^{88} +(-0.748203 - 1.29593i) q^{89} +(-5.25615 - 4.16808i) q^{90} +(-0.205672 + 3.17070i) q^{91} +(-2.15286 + 3.72887i) q^{92} +(5.78982 + 2.30409i) q^{93} -5.04557i q^{94} +(10.6305 - 7.43985i) q^{95} +(0.640430 - 1.60930i) q^{96} +(-2.01118 + 3.48347i) q^{97} +(2.68750 + 6.46354i) q^{98} +(0.414737 + 0.0988096i) 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} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 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 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * 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 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * 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 - 39 * 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
$3$	0.640430	−	1.60930i	0.369752	−	0.929130i
$3$	0.640430	−	1.60930i	0.369752	−	0.929130i
$4$	1.00000			0.500000
$5$	2.22760	−	0.194363i	0.996215	−	0.0869217i
$5$	2.22760	−	0.194363i	0.996215	−	0.0869217i
$6$	0.640430	−	1.60930i	0.261454	−	0.656994i
$7$	−2.20085	−	1.46842i	−0.831844	−	0.555009i
$7$	−2.20085	−	1.46842i	−0.831844	−	0.555009i
$8$	1.00000			0.353553
$9$	−2.17970	−	2.06129i	−0.726566	−	0.687096i
$10$	2.22760	−	0.194363i	0.704430	−	0.0614629i
$11$	−0.123075	+	0.0710575i	−0.0371086	+	0.0214246i	−0.518440	−	0.855114i	$-0.673487\pi$
$11$	−0.123075	+	0.0710575i	−0.0371086	+	0.0214246i	0.481331	+	0.876539i	$0.340154\pi$
$12$	0.640430	−	1.60930i	0.184876	−	0.464565i
$13$	−0.600465	−	1.04004i	−0.166539	−	0.288454i	0.770662	−	0.637245i	$-0.219926\pi$
$13$	−0.600465	−	1.04004i	−0.166539	−	0.288454i	−0.937201	+	0.348790i	$0.886593\pi$
$14$	−2.20085	−	1.46842i	−0.588203	−	0.392451i
$15$	1.11384	−	3.70936i	0.287591	−	0.957753i
$16$	1.00000			0.250000
$17$	−0.0902992	−	0.0521342i	−0.0219008	−	0.0126444i	0.489010	−	0.872278i	$-0.337358\pi$
$17$	−0.0902992	−	0.0521342i	−0.0219008	−	0.0126444i	−0.510910	+	0.859634i	$0.670692\pi$
$18$	−2.17970	−	2.06129i	−0.513760	−	0.485850i
$19$	5.02533	−	2.90137i	1.15289	−	0.665621i	0.203300	−	0.979117i	$-0.434833\pi$
$19$	5.02533	−	2.90137i	1.15289	−	0.665621i	0.949590	+	0.313495i	$0.101500\pi$
$20$	2.22760	−	0.194363i	0.498108	−	0.0434608i
$21$	−3.77262	+	2.60142i	−0.823252	+	0.567675i
$22$	−0.123075	+	0.0710575i	−0.0262397	+	0.0151495i
$23$	−2.15286	+	3.72887i	−0.448903	+	0.777523i	−0.998315	−	0.0580289i	$-0.981518\pi$
$23$	−2.15286	+	3.72887i	−0.448903	+	0.777523i	0.549412	+	0.835552i	$0.314852\pi$
$24$	0.640430	−	1.60930i	0.130727	−	0.328497i
$25$	4.92445	−	0.865927i	0.984889	−	0.173185i
$26$	−0.600465	−	1.04004i	−0.117761	−	0.203968i
$27$	−4.71318	+	2.18768i	−0.907052	+	0.421019i
$28$	−2.20085	−	1.46842i	−0.415922	−	0.277505i
$29$	3.20977	+	1.85316i	0.596040	+	0.344124i	0.767482	−	0.641070i	$-0.221509\pi$
$29$	3.20977	+	1.85316i	0.596040	+	0.344124i	−0.171442	+	0.985194i	$0.554843\pi$
$30$	1.11384	−	3.70936i	0.203358	−	0.677234i
$31$			3.59772i			0.646170i	0.946370	+	0.323085i	$0.104720\pi$
$31$			3.59772i			0.646170i	−0.946370	+	0.323085i	$0.895280\pi$
$32$	1.00000			0.176777
$33$	0.0355319	+	0.243572i	0.00618531	+	0.0424005i
$34$	−0.0902992	−	0.0521342i	−0.0154862	−	0.00894095i
$35$	−5.18803	−	2.84329i	−0.876938	−	0.480604i
$36$	−2.17970	−	2.06129i	−0.363283	−	0.343548i
$37$	−5.42899	+	3.13443i	−0.892520	+	0.515296i	−0.874766	−	0.484546i	$-0.838985\pi$
$37$	−5.42899	+	3.13443i	−0.892520	+	0.515296i	−0.0177539	+	0.999842i	$0.505652\pi$
$38$	5.02533	−	2.90137i	0.815216	−	0.470665i
$39$	−2.05829	+	0.300259i	−0.329590	+	0.0480799i
$40$	2.22760	−	0.194363i	0.352215	−	0.0307314i
$41$	3.96636	+	6.86994i	0.619442	+	1.07290i	0.989588	+	0.143931i	$0.0459743\pi$
$41$	3.96636	+	6.86994i	0.619442	+	1.07290i	−0.370146	+	0.928974i	$0.620692\pi$
$42$	−3.77262	+	2.60142i	−0.582127	+	0.401407i
$43$	−1.49609	−	0.863766i	−0.228151	−	0.131723i	0.381568	−	0.924341i	$-0.375384\pi$
$43$	−1.49609	−	0.863766i	−0.228151	−	0.131723i	−0.609719	+	0.792618i	$0.708718\pi$
$44$	−0.123075	+	0.0710575i	−0.0185543	+	0.0107123i
$45$	−5.25615	−	4.16808i	−0.783540	−	0.621341i
$46$	−2.15286	+	3.72887i	−0.317422	+	0.549792i
$47$		−	5.04557i		−	0.735973i	−0.929831	−	0.367986i	$-0.880047\pi$
$47$		−	5.04557i		−	0.735973i	0.929831	−	0.367986i	$-0.119953\pi$
$48$	0.640430	−	1.60930i	0.0924381	−	0.232283i
$49$	2.68750	+	6.46354i	0.383929	+	0.923363i
$50$	4.92445	−	0.865927i	0.696422	−	0.122461i
$51$	−0.141730	+	0.111930i	−0.0198462	+	0.0156734i
$52$	−0.600465	−	1.04004i	−0.0832696	−	0.144227i
$53$	1.34026	−	2.32140i	0.184099	−	0.318869i	−0.759174	−	0.650888i	$-0.774397\pi$
$53$	1.34026	−	2.32140i	0.184099	−	0.318869i	0.943273	+	0.332019i	$0.107730\pi$
$54$	−4.71318	+	2.18768i	−0.641382	+	0.297706i
$55$	−0.260352	+	0.182209i	−0.0351059	+	0.0245691i
$56$	−2.20085	−	1.46842i	−0.294101	−	0.196225i
$57$	−1.45081	−	9.94539i	−0.192165	−	1.31730i
$58$	3.20977	+	1.85316i	0.421464	+	0.243332i
$59$	9.80986			1.27713			0.638567	−	0.769566i	$-0.279527\pi$
$59$	9.80986			1.27713			0.638567	+	0.769566i	$0.279527\pi$
$60$	1.11384	−	3.70936i	0.143796	−	0.478877i
$61$			12.3067i			1.57571i	0.615863	+	0.787853i	$0.288808\pi$
$61$			12.3067i			1.57571i	−0.615863	+	0.787853i	$0.711192\pi$
$62$			3.59772i			0.456911i
$63$	1.77036	+	7.73730i	0.223045	+	0.974808i
$64$	1.00000			0.125000
$65$	−1.53974	−	2.20008i	−0.190982	−	0.272887i
$66$	0.0355319	+	0.243572i	0.00437367	+	0.0299817i
$67$		−	7.27754i		−	0.889093i	−0.895756	−	0.444547i	$-0.853365\pi$
$67$		−	7.27754i		−	0.889093i	0.895756	−	0.444547i	$-0.146635\pi$
$68$	−0.0902992	−	0.0521342i	−0.0109504	−	0.00632221i
$69$	4.62211	+	5.85268i	0.556437	+	0.704580i
$70$	−5.18803	−	2.84329i	−0.620089	−	0.339838i
$71$		−	12.4507i		−	1.47762i	−0.673912	−	0.738812i	$-0.735387\pi$
$71$		−	12.4507i		−	1.47762i	0.673912	−	0.738812i	$-0.264613\pi$
$72$	−2.17970	−	2.06129i	−0.256880	−	0.242925i
$73$	−4.01981	+	6.96252i	−0.470483	+	0.814901i	−0.999430	−	0.0337541i	$-0.989254\pi$
$73$	−4.01981	+	6.96252i	−0.470483	+	0.814901i	0.528947	+	0.848655i	$0.322587\pi$
$74$	−5.42899	+	3.13443i	−0.631107	+	0.364370i
$75$	1.76023	−	8.47948i	0.203253	−	0.979126i
$76$	5.02533	−	2.90137i	0.576445	−	0.332811i
$77$	0.375212	+	0.0243387i	0.0427594	+	0.00277365i
$78$	−2.05829	+	0.300259i	−0.233055	+	0.0339976i
$79$	−8.41003			−0.946202			−0.473101	−	0.881008i	$-0.656865\pi$
$79$	−8.41003			−0.946202			−0.473101	+	0.881008i	$0.656865\pi$
$80$	2.22760	−	0.194363i	0.249054	−	0.0217304i
$81$	0.502177	+	8.98598i	0.0557975	+	0.998442i
$82$	3.96636	+	6.86994i	0.438011	+	0.758658i
$83$	−2.03412	−	1.17440i	−0.223274	−	0.128907i	0.384191	−	0.923253i	$-0.374480\pi$
$83$	−2.03412	−	1.17440i	−0.223274	−	0.128907i	−0.607465	+	0.794346i	$0.707814\pi$
$84$	−3.77262	+	2.60142i	−0.411626	+	0.283838i
$85$	−0.211284	−	0.0985837i	−0.0229169	−	0.0106929i
$86$	−1.49609	−	0.863766i	−0.161327	−	0.0931423i
$87$	5.03793	−	3.97867i	0.540123	−	0.426558i
$88$	−0.123075	+	0.0710575i	−0.0131199	+	0.00757476i
$89$	−0.748203	−	1.29593i	−0.0793094	−	0.137368i	0.823643	−	0.567109i	$-0.191938\pi$
$89$	−0.748203	−	1.29593i	−0.0793094	−	0.137368i	−0.902952	+	0.429741i	$0.858605\pi$
$90$	−5.25615	−	4.16808i	−0.554046	−	0.439355i
$91$	−0.205672	+	3.17070i	−0.0215603	+	0.332380i
$92$	−2.15286	+	3.72887i	−0.224451	+	0.388761i
$93$	5.78982	+	2.30409i	0.600376	+	0.238923i
$94$		−	5.04557i		−	0.520411i
$95$	10.6305	−	7.43985i	1.09067	−	0.763313i
$96$	0.640430	−	1.60930i	0.0653636	−	0.164249i
$97$	−2.01118	+	3.48347i	−0.204204	+	0.353693i	−0.949879	−	0.312618i	$-0.898794\pi$
$97$	−2.01118	+	3.48347i	−0.204204	+	0.353693i	0.745674	+	0.666310i	$0.232127\pi$
$98$	2.68750	+	6.46354i	0.271479	+	0.652916i
$99$	0.414737	+	0.0988096i	0.0416826	+	0.00993074i
$100$	4.92445	−	0.865927i	0.492445	−	0.0865927i
$101$	1.68050	+	2.91071i	0.167216	+	0.289626i	0.937440	−	0.348147i	$-0.113189\pi$
$101$	1.68050	+	2.91071i	0.167216	+	0.289626i	−0.770224	+	0.637773i	$0.779856\pi$
$102$	−0.141730	+	0.111930i	−0.0140334	+	0.0110827i
$103$	−9.57498	+	16.5843i	−0.943450	+	1.63410i	−0.184626	+	0.982809i	$0.559107\pi$
$103$	−9.57498	+	16.5843i	−0.943450	+	1.63410i	−0.758825	+	0.651295i	$0.774226\pi$
$104$	−0.600465	−	1.04004i	−0.0588805	−	0.101984i
$105$	−7.89828	+	6.52818i	−0.770793	+	0.637085i
$106$	1.34026	−	2.32140i	0.130178	−	0.225474i
$107$	−7.15043	−	12.3849i	−0.691258	−	1.19729i	−0.971426	−	0.237343i	$-0.923724\pi$
$107$	−7.15043	−	12.3849i	−0.691258	−	1.19729i	0.280168	−	0.959951i	$-0.409610\pi$
$108$	−4.71318	+	2.18768i	−0.453526	+	0.210510i
$109$	8.89823	−	15.4122i	0.852296	−	1.47622i	−0.0268351	−	0.999640i	$-0.508543\pi$
$109$	8.89823	−	15.4122i	0.852296	−	1.47622i	0.879131	−	0.476580i	$-0.158124\pi$
$110$	−0.260352	+	0.182209i	−0.0248236	+	0.0173730i
$111$	1.56735	+	10.7443i	0.148766	+	1.01980i
$112$	−2.20085	−	1.46842i	−0.207961	−	0.138752i
$113$	8.09024	+	14.0127i	0.761066	+	1.31820i	0.942302	+	0.334765i	$0.108657\pi$
$113$	8.09024	+	14.0127i	0.761066	+	1.31820i	−0.181236	+	0.983440i	$0.558010\pi$
$114$	−1.45081	−	9.94539i	−0.135881	−	0.931471i
$115$	−4.07097	+	8.72488i	−0.379620	+	0.813599i
$116$	3.20977	+	1.85316i	0.298020	+	0.172062i
$117$	−0.834982	+	3.50470i	−0.0771941	+	0.324010i
$118$	9.80986			0.903071
$119$	0.122180	+	0.247337i	0.0112003	+	0.0226733i
$120$	1.11384	−	3.70936i	0.101679	−	0.338617i
$121$	−5.48990	+	9.50879i	−0.499082	+	0.864435i
$122$			12.3067i			1.11419i
$123$	13.5960	−	1.98336i	1.22591	−	0.178833i
$124$			3.59772i			0.323085i
$125$	10.8014	−	2.88607i	0.966108	−	0.258138i
$126$	1.77036	+	7.73730i	0.157717	+	0.689293i
$127$			11.0556i			0.981023i	0.871435	+	0.490511i	$0.163190\pi$
$127$			11.0556i			0.981023i	−0.871435	+	0.490511i	$0.836810\pi$
$128$	1.00000			0.0883883
$129$	−2.34820	+	1.85447i	−0.206747	+	0.163277i
$130$	−1.53974	−	2.20008i	−0.135044	−	0.192960i
$131$	−4.68485	+	8.11440i	−0.409318	+	0.708959i	−0.994813	−	0.101717i	$-0.967567\pi$
$131$	−4.68485	+	8.11440i	−0.409318	+	0.708959i	0.585496	+	0.810675i	$0.300900\pi$
$132$	0.0355319	+	0.243572i	0.00309265	+	0.0212003i
$133$	−15.3204	−	0.993780i	−1.32845	−	0.0861717i
$134$		−	7.27754i		−	0.628684i
$135$	−10.0739	+	5.78936i	−0.867023	+	0.498268i
$136$	−0.0902992	−	0.0521342i	−0.00774309	−	0.00447047i
$137$	9.56078	+	16.5598i	0.816833	+	1.41480i	0.908004	+	0.418961i	$0.137605\pi$
$137$	9.56078	+	16.5598i	0.816833	+	1.41480i	−0.0911716	+	0.995835i	$0.529061\pi$
$138$	4.62211	+	5.85268i	0.393460	+	0.498213i
$139$	0.954315	−	0.550974i	0.0809439	−	0.0467330i	−0.458982	−	0.888446i	$-0.651786\pi$
$139$	0.954315	−	0.550974i	0.0809439	−	0.0467330i	0.539926	+	0.841713i	$0.318452\pi$
$140$	−5.18803	−	2.84329i	−0.438469	−	0.240302i
$141$	−8.11985	−	3.23134i	−0.683814	−	0.272128i
$142$		−	12.4507i		−	1.04484i
$143$	0.147805	+	0.0853352i	0.0123601	+	0.00713608i
$144$	−2.17970	−	2.06129i	−0.181642	−	0.171774i
$145$	7.51029	+	3.50426i	0.623696	+	0.291013i
$146$	−4.01981	+	6.96252i	−0.332682	+	0.576222i
$147$	12.1229	−	0.185558i	0.999883	−	0.0153045i
$148$	−5.42899	+	3.13443i	−0.446260	+	0.257648i
$149$	−12.1146	−	6.99438i	−0.992468	−	0.573002i	−0.0864572	−	0.996256i	$-0.527555\pi$
$149$	−12.1146	−	6.99438i	−0.992468	−	0.573002i	−0.906011	+	0.423254i	$0.860888\pi$
$150$	1.76023	−	8.47948i	0.143722	−	0.692347i
$151$	2.45666	+	4.25506i	0.199920	+	0.346272i	0.948502	−	0.316770i	$-0.102598\pi$
$151$	2.45666	+	4.25506i	0.199920	+	0.346272i	−0.748582	+	0.663042i	$0.769265\pi$
$152$	5.02533	−	2.90137i	0.407608	−	0.235333i
$153$	0.0893613	+	0.299770i	0.00722443	+	0.0242349i
$154$	0.375212	+	0.0243387i	0.0302355	+	0.00196126i
$155$	0.699263	+	8.01430i	0.0561662	+	0.643724i
$156$	−2.05829	+	0.300259i	−0.164795	+	0.0240400i
$157$	6.40902			0.511495			0.255748	−	0.966744i	$-0.417678\pi$
$157$	6.40902			0.511495			0.255748	+	0.966744i	$0.417678\pi$
$158$	−8.41003			−0.669066
$159$	−2.87749	−	3.64358i	−0.228200	−	0.288954i
$160$	2.22760	−	0.194363i	0.176108	−	0.0153657i
$161$	10.2137	−	5.04539i	0.804950	−	0.397632i
$162$	0.502177	+	8.98598i	0.0394548	+	0.706005i
$163$	0.970831	−	0.560510i	0.0760414	−	0.0439025i	−0.461497	−	0.887142i	$-0.652688\pi$
$163$	0.970831	−	0.560510i	0.0760414	−	0.0439025i	0.537539	+	0.843239i	$0.319354\pi$
$164$	3.96636	+	6.86994i	0.309721	+	0.536452i
$165$	0.126492	+	0.535677i	0.00984742	+	0.0417024i
$166$	−2.03412	−	1.17440i	−0.157879	−	0.0911512i
$167$	0.739056	−	0.426694i	0.0571899	−	0.0330186i	−0.471132	−	0.882062i	$-0.656155\pi$
$167$	0.739056	−	0.426694i	0.0571899	−	0.0330186i	0.528322	+	0.849044i	$0.322821\pi$
$168$	−3.77262	+	2.60142i	−0.291064	+	0.200704i
$169$	5.77888	−	10.0093i	0.444529	−	0.769948i
$170$	−0.211284	−	0.0985837i	−0.0162047	−	0.00756102i
$171$	−16.9343	−	4.03453i	−1.29500	−	0.308528i
$172$	−1.49609	−	0.863766i	−0.114076	−	0.0658615i
$173$		−	25.1821i		−	1.91456i	−0.289162	−	0.957280i	$-0.593377\pi$
$173$		−	25.1821i		−	1.91456i	0.289162	−	0.957280i	$-0.406623\pi$
$174$	5.03793	−	3.97867i	0.381925	−	0.301622i
$175$	−12.1095	−	5.32536i	−0.915394	−	0.402560i
$176$	−0.123075	+	0.0710575i	−0.00927714	+	0.00535616i
$177$	6.28253	−	15.7870i	0.472224	−	1.18662i
$178$	−0.748203	−	1.29593i	−0.0560802	−	0.0971337i
$179$	−14.0102	−	8.08881i	−1.04717	−	0.604586i	−0.125317	−	0.992117i	$-0.539995\pi$
$179$	−14.0102	−	8.08881i	−1.04717	−	0.604586i	−0.921857	+	0.387531i	$0.873328\pi$
$180$	−5.25615	−	4.16808i	−0.391770	−	0.310671i
$181$			17.0243i			1.26540i	0.774396	+	0.632701i	$0.218054\pi$
$181$			17.0243i			1.26540i	−0.774396	+	0.632701i	$0.781946\pi$
$182$	−0.205672	+	3.17070i	−0.0152454	+	0.235028i
$183$	19.8051	+	7.88155i	1.46404	+	0.582621i
$184$	−2.15286	+	3.72887i	−0.158711	+	0.274896i
$185$	−11.4844	+	8.03746i	−0.844351	+	0.590925i
$186$	5.78982	+	2.30409i	0.424530	+	0.168944i
$187$	0.0148181			0.00108361
$188$		−	5.04557i		−	0.367986i
$189$	13.5854	+	2.10615i	0.988195	+	0.153200i
$190$	10.6305	−	7.43985i	0.771220	−	0.539744i
$191$		−	3.96791i		−	0.287108i	−0.989643	−	0.143554i	$-0.954147\pi$
$191$		−	3.96791i		−	0.287108i	0.989643	−	0.143554i	$-0.0458530\pi$
$192$	0.640430	−	1.60930i	0.0462190	−	0.116141i
$193$		−	1.29203i		−	0.0930026i	−0.998918	−	0.0465013i	$-0.985193\pi$
$193$		−	1.29203i		−	0.0930026i	0.998918	−	0.0465013i	$-0.0148072\pi$
$194$	−2.01118	+	3.48347i	−0.144394	+	0.250098i
$195$	−4.52669	+	1.06891i	−0.324163	+	0.0765465i
$196$	2.68750	+	6.46354i	0.191964	+	0.461681i
$197$	0.983884			0.0700988			0.0350494	−	0.999386i	$-0.488841\pi$
$197$	0.983884			0.0700988			0.0350494	+	0.999386i	$0.488841\pi$
$198$	0.414737	+	0.0988096i	0.0294741	+	0.00702209i
$199$	−20.6241	−	11.9073i	−1.46200	−	0.844086i	−0.462897	−	0.886412i	$-0.653190\pi$
$199$	−20.6241	−	11.9073i	−1.46200	−	0.844086i	−0.999104	+	0.0423259i	$0.986523\pi$
$200$	4.92445	−	0.865927i	0.348211	−	0.0612303i
$201$	−11.7118	−	4.66076i	−0.826084	−	0.328744i
$202$	1.68050	+	2.91071i	0.118239	+	0.204797i
$203$	−4.34302	−	8.79183i	−0.304820	−	0.617065i
$204$	−0.141730	+	0.111930i	−0.00992308	+	0.00783668i
$205$	10.1707	+	14.5326i	0.710356	+	1.01500i
$206$	−9.57498	+	16.5843i	−0.667120	+	1.15549i
$207$	12.3789	−	3.69014i	0.860391	−	0.256482i
$208$	−0.600465	−	1.04004i	−0.0416348	−	0.0721136i
$209$	−0.412329	+	0.714175i	−0.0285214	+	0.0494005i
$210$	−7.89828	+	6.52818i	−0.545033	+	0.450487i
$211$	−11.2221	−	19.4372i	−0.772559	−	1.33811i	−0.936156	−	0.351585i	$-0.885643\pi$
$211$	−11.2221	−	19.4372i	−0.772559	−	1.33811i	0.163597	−	0.986527i	$-0.447690\pi$
$212$	1.34026	−	2.32140i	0.0920495	−	0.159434i
$213$	−20.0369	−	7.97379i	−1.37291	−	0.546355i
$214$	−7.15043	−	12.3849i	−0.488793	−	0.846614i
$215$	−3.50057	−	1.63335i	−0.238737	−	0.111393i
$216$	−4.71318	+	2.18768i	−0.320691	+	0.148853i
$217$	5.28296	−	7.91805i	0.358630	−	0.537513i
$218$	8.89823	−	15.4122i	0.602664	−	1.04385i
$219$	8.63038	+	10.9281i	0.583187	+	0.738452i
$220$	−0.260352	+	0.182209i	−0.0175529	+	0.0122845i
$221$			0.125219i			0.00842316i
$222$	1.56735	+	10.7443i	0.105194	+	0.721107i
$223$	−8.99621	+	15.5819i	−0.602430	+	1.04344i	0.390021	+	0.920806i	$0.372468\pi$
$223$	−8.99621	+	15.5819i	−0.602430	+	1.04344i	−0.992452	+	0.122634i	$0.960866\pi$
$224$	−2.20085	−	1.46842i	−0.147051	−	0.0981127i
$225$	−12.5187	−	8.26325i	−0.834582	−	0.550883i
$226$	8.09024	+	14.0127i	0.538155	+	0.932111i
$227$	17.5341	−	10.1233i	1.16378	−	0.671909i	0.211573	−	0.977362i	$-0.432141\pi$
$227$	17.5341	−	10.1233i	1.16378	−	0.671909i	0.952207	+	0.305453i	$0.0988080\pi$
$228$	−1.45081	−	9.94539i	−0.0960826	−	0.658650i
$229$	−0.650116	−	0.375345i	−0.0429609	−	0.0248035i	0.478366	−	0.878161i	$-0.341229\pi$
$229$	−0.650116	−	0.375345i	−0.0429609	−	0.0248035i	−0.521327	+	0.853357i	$0.674563\pi$
$230$	−4.07097	+	8.72488i	−0.268432	+	0.575302i
$231$	0.279465	−	0.588243i	0.0183875	−	0.0387035i
$232$	3.20977	+	1.85316i	0.210732	+	0.121666i
$233$	−9.57787	−	16.5894i	−0.627467	−	1.08681i	−0.988058	−	0.154081i	$-0.950758\pi$
$233$	−9.57787	−	16.5894i	−0.627467	−	1.08681i	0.360591	−	0.932724i	$-0.382575\pi$
$234$	−0.834982	+	3.50470i	−0.0545845	+	0.229109i
$235$	−0.980671	−	11.2395i	−0.0639720	−	0.733187i
$236$	9.80986			0.638567
$237$	−5.38603	+	13.5343i	−0.349860	+	0.879145i
$238$	0.122180	+	0.247337i	0.00791977	+	0.0160325i
$239$	1.15565	−	0.667217i	0.0747531	−	0.0431587i	−0.462158	−	0.886798i	$-0.652925\pi$
$239$	1.15565	−	0.667217i	0.0747531	−	0.0431587i	0.536911	+	0.843639i	$0.319591\pi$
$240$	1.11384	−	3.70936i	0.0718978	−	0.239438i
$241$	−17.1287	+	9.88925i	−1.10336	+	0.637023i	−0.937100	−	0.349060i	$-0.886501\pi$
$241$	−17.1287	+	9.88925i	−1.10336	+	0.637023i	−0.166256	+	0.986083i	$0.553168\pi$
$242$	−5.48990	+	9.50879i	−0.352904	+	0.611248i
$243$	14.7828	+	4.94674i	0.948314	+	0.317333i
$244$			12.3067i			0.787853i
$245$	7.24296	+	13.8759i	0.462736	+	0.886496i
$246$	13.5960	−	1.98336i	0.866848	−	0.126454i
$247$	−6.03507	−	3.48435i	−0.384002	−	0.221704i
$248$			3.59772i			0.228456i
$249$	−3.19268	+	2.52139i	−0.202328	+	0.159787i
$250$	10.8014	−	2.88607i	0.683142	−	0.182531i
$251$	28.8281			1.81961			0.909805	−	0.415035i	$-0.136231\pi$
$251$	28.8281			1.81961			0.909805	+	0.415035i	$0.136231\pi$
$252$	1.77036	+	7.73730i	0.111522	+	0.487404i
$253$		−	0.611908i		−	0.0384703i
$254$			11.0556i			0.693688i
$255$	−0.293963	+	0.276883i	−0.0184087	+	0.0173391i
$256$	1.00000			0.0625000
$257$	−15.5450	−	8.97493i	−0.969672	−	0.559841i	−0.0705361	−	0.997509i	$-0.522471\pi$
$257$	−15.5450	−	8.97493i	−0.969672	−	0.559841i	−0.899136	+	0.437669i	$0.855804\pi$
$258$	−2.34820	+	1.85447i	−0.146192	+	0.115454i
$259$	16.5510	+	1.07361i	1.02843	+	0.0667106i
$260$	−1.53974	−	2.20008i	−0.0954909	−	0.136443i
$261$	−3.17644	−	10.6556i	−0.196616	−	0.659566i
$262$	−4.68485	+	8.11440i	−0.289431	+	0.501310i
$263$	−7.94184	−	13.7557i	−0.489715	−	0.848211i	0.510215	−	0.860047i	$-0.329566\pi$
$263$	−7.94184	−	13.7557i	−0.489715	−	0.848211i	−0.999930	+	0.0118356i	$0.996233\pi$
$264$	0.0355319	+	0.243572i	0.00218684	+	0.0149908i
$265$	2.53438	−	5.43166i	0.155686	−	0.333664i
$266$	−15.3204	−	0.993780i	−0.939356	−	0.0609326i
$267$	−2.56471	+	0.374134i	−0.156957	+	0.0228966i
$268$		−	7.27754i		−	0.444547i
$269$	5.25345	−	9.09924i	0.320308	−	0.554790i	−0.660243	−	0.751052i	$-0.729547\pi$
$269$	5.25345	−	9.09924i	0.320308	−	0.554790i	0.980552	+	0.196261i	$0.0628801\pi$
$270$	−10.0739	+	5.78936i	−0.613078	+	0.352329i
$271$	10.9732	−	6.33540i	0.666577	−	0.384848i	−0.128202	−	0.991748i	$-0.540920\pi$
$271$	10.9732	−	6.33540i	0.666577	−	0.384848i	0.794778	+	0.606900i	$0.207587\pi$
$272$	−0.0902992	−	0.0521342i	−0.00547519	−	0.00316110i
$273$	4.97089	+	2.36160i	0.300852	+	0.142930i
$274$	9.56078	+	16.5598i	0.577588	+	1.00041i
$275$	−0.544547	+	0.456493i	−0.0328374	+	0.0275276i
$276$	4.62211	+	5.85268i	0.278219	+	0.352290i
$277$	−12.8968	+	7.44600i	−0.774896	+	0.447387i	−0.834619	−	0.550828i	$-0.814312\pi$
$277$	−12.8968	+	7.44600i	−0.774896	+	0.447387i	0.0597221	+	0.998215i	$0.480979\pi$
$278$	0.954315	−	0.550974i	0.0572360	−	0.0330452i
$279$	7.41594	−	7.84195i	0.443981	−	0.469485i
$280$	−5.18803	−	2.84329i	−0.310044	−	0.169919i
$281$	5.92114	+	3.41857i	0.353226	+	0.203935i	0.666105	−	0.745858i	$-0.267960\pi$
$281$	5.92114	+	3.41857i	0.353226	+	0.203935i	−0.312879	+	0.949793i	$0.601294\pi$
$282$	−8.11985	−	3.23134i	−0.483530	−	0.192423i
$283$	−11.6293			−0.691292			−0.345646	−	0.938365i	$-0.612340\pi$
$283$	−11.6293			−0.691292			−0.345646	+	0.938365i	$0.612340\pi$
$284$		−	12.4507i		−	0.738812i
$285$	−5.16486	−	21.8724i	−0.305940	−	1.29561i
$286$	0.147805	+	0.0853352i	0.00873988	+	0.00504597i
$287$	1.35856	−	20.9440i	0.0801933	−	1.23629i
$288$	−2.17970	−	2.06129i	−0.128440	−	0.121463i
$289$	−8.49456	−	14.7130i	−0.499680	−	0.865472i
$290$	7.51029	+	3.50426i	0.441020	+	0.205777i
$291$	4.31793	+	5.46751i	0.253121	+	0.320511i
$292$	−4.01981	+	6.96252i	−0.235242	+	0.407450i
$293$	−8.60234	+	4.96657i	−0.502554	+	0.290150i	−0.729768	−	0.683695i	$-0.760372\pi$
$293$	−8.60234	+	4.96657i	−0.502554	+	0.290150i	0.227213	+	0.973845i	$0.427038\pi$
$294$	12.1229	−	0.185558i	0.707024	−	0.0108219i
$295$	21.8525	−	1.90667i	1.27230	−	0.111011i
$296$	−5.42899	+	3.13443i	−0.315553	+	0.182185i
$297$	0.424624	−	0.604156i	0.0246392	−	0.0350567i
$298$	−12.1146	−	6.99438i	−0.701781	−	0.405174i
$299$	5.17088			0.299040
$300$	1.76023	−	8.47948i	0.101627	−	0.489563i
$301$	2.02430	+	4.09790i	0.116679	+	0.236199i
$302$	2.45666	+	4.25506i	0.141365	+	0.244851i
$303$	5.76045	−	0.840323i	0.330929	−	0.0482753i
$304$	5.02533	−	2.90137i	0.288222	−	0.166405i
$305$	2.39196	+	27.4144i	0.136963	+	1.56974i
$306$	0.0893613	+	0.299770i	0.00510844	+	0.0171367i
$307$	25.3226			1.44524			0.722618	−	0.691247i	$-0.242939\pi$
$307$	25.3226			1.44524			0.722618	+	0.691247i	$0.242939\pi$
$308$	0.375212	+	0.0243387i	0.0213797	+	0.00138682i
$309$	20.5571	+	26.0301i	1.16945	+	1.48080i
$310$	0.699263	+	8.01430i	0.0397155	+	0.455182i
$311$	7.32275			0.415235			0.207618	−	0.978210i	$-0.433429\pi$
$311$	7.32275			0.415235			0.207618	+	0.978210i	$0.433429\pi$
$312$	−2.05829	+	0.300259i	−0.116528	+	0.0169988i
$313$	−8.48704			−0.479716			−0.239858	−	0.970808i	$-0.577101\pi$
$313$	−8.48704			−0.479716			−0.239858	+	0.970808i	$0.577101\pi$
$314$	6.40902			0.361682
$315$	5.44752	+	16.8916i	0.306933	+	0.951731i
$316$	−8.41003			−0.473101
$317$	2.24351			0.126008			0.0630039	−	0.998013i	$-0.479932\pi$
$317$	2.24351			0.126008			0.0630039	+	0.998013i	$0.479932\pi$
$318$	−2.87749	−	3.64358i	−0.161362	−	0.204322i
$319$	−0.526725			−0.0294909
$320$	2.22760	−	0.194363i	0.124527	−	0.0108652i
$321$	−24.5104	+	3.57553i	−1.36804	+	0.199566i
$322$	10.2137	−	5.04539i	0.569185	−	0.281168i
$323$	−0.605044			−0.0336655
$324$	0.502177	+	8.98598i	0.0278987	+	0.499221i
$325$	−3.85756	−	4.60165i	−0.213979	−	0.255253i
$326$	0.970831	−	0.560510i	0.0537694	−	0.0310438i
$327$	−19.1042	−	24.1904i	−1.05646	−	1.33773i
$328$	3.96636	+	6.86994i	0.219006	+	0.379329i
$329$	−7.40901	+	11.1046i	−0.408472	+	0.612214i
$330$	0.126492	+	0.535677i	0.00696318	+	0.0294880i
$331$	−5.04537			−0.277319			−0.138659	−	0.990340i	$-0.544279\pi$
$331$	−5.04537			−0.277319			−0.138659	+	0.990340i	$0.544279\pi$
$332$	−2.03412	−	1.17440i	−0.111637	−	0.0644536i
$333$	18.2945	+	4.35860i	1.00253	+	0.238850i
$334$	0.739056	−	0.426694i	0.0404394	−	0.0233477i
$335$	−1.41448	−	16.2115i	−0.0772815	−	0.885728i
$336$	−3.77262	+	2.60142i	−0.205813	+	0.141919i
$337$	30.0990	−	17.3777i	1.63960	−	0.946623i	0.658629	−	0.752468i	$-0.271137\pi$
$337$	30.0990	−	17.3777i	1.63960	−	0.946623i	0.980971	−	0.194155i	$-0.0621965\pi$
$338$	5.77888	−	10.0093i	0.314330	−	0.544435i
$339$	27.7319	−	4.04547i	1.50619	−	0.219720i
$340$	−0.211284	−	0.0985837i	−0.0114585	−	0.00534645i
$341$	−0.255645	−	0.442790i	−0.0138440	−	0.0239784i
$342$	−16.9343	−	4.03453i	−0.915701	−	0.218162i
$343$	3.57637	−	18.1717i	0.193106	−	0.981178i
$344$	−1.49609	−	0.863766i	−0.0806636	−	0.0465711i
$345$	11.4338	+	12.1391i	0.615574	+	0.653547i
$346$		−	25.1821i		−	1.35380i
$347$	−6.90143			−0.370488			−0.185244	−	0.982693i	$-0.559308\pi$
$347$	−6.90143			−0.370488			−0.185244	+	0.982693i	$0.559308\pi$
$348$	5.03793	−	3.97867i	0.270062	−	0.213279i
$349$	−0.226488	−	0.130763i	−0.0121237	−	0.00699959i	0.493926	−	0.869504i	$-0.335561\pi$
$349$	−0.226488	−	0.130763i	−0.0121237	−	0.00699959i	−0.506050	+	0.862504i	$0.668895\pi$
$350$	−12.1095	−	5.32536i	−0.647281	−	0.284653i
$351$	5.10537	+	3.58825i	0.272504	+	0.191527i
$352$	−0.123075	+	0.0710575i	−0.00655993	+	0.00378738i
$353$	24.7213	−	14.2729i	1.31578	−	0.759668i	0.332737	−	0.943020i	$-0.392028\pi$
$353$	24.7213	−	14.2729i	1.31578	−	0.759668i	0.983047	+	0.183351i	$0.0586946\pi$
$354$	6.28253	−	15.7870i	0.333913	−	0.839070i
$355$	−2.41995	−	27.7352i	−0.128438	−	1.47203i
$356$	−0.748203	−	1.29593i	−0.0396547	−	0.0686839i
$357$	0.476287	−	0.0382231i	0.0252078	−	0.00202298i
$358$	−14.0102	−	8.08881i	−0.740464	−	0.427507i
$359$	−10.5441	+	6.08767i	−0.556499	+	0.321295i	−0.751739	−	0.659461i	$-0.770785\pi$
$359$	−10.5441	+	6.08767i	−0.556499	+	0.321295i	0.195240	+	0.980755i	$0.437451\pi$
$360$	−5.25615	−	4.16808i	−0.277023	−	0.219677i
$361$	7.33595	−	12.7062i	0.386103	−	0.668750i
$362$			17.0243i			0.894775i
$363$	11.7866	+	14.9246i	0.618636	+	0.783339i
$364$	−0.205672	+	3.17070i	−0.0107801	+	0.166190i
$365$	−7.60130	+	16.2910i	−0.397870	+	0.852712i
$366$	19.8051	+	7.88155i	1.03523	+	0.411975i
$367$	11.1198	+	19.2601i	0.580451	+	1.00537i	0.995426	+	0.0955375i	$0.0304570\pi$
$367$	11.1198	+	19.2601i	0.580451	+	1.00537i	−0.414975	+	0.909833i	$0.636210\pi$
$368$	−2.15286	+	3.72887i	−0.112226	+	0.194381i
$369$	5.51546	−	23.1502i	0.287123	−	1.20515i
$370$	−11.4844	+	8.03746i	−0.597046	+	0.417847i
$371$	−6.35850	+	3.14100i	−0.330117	+	0.163072i
$372$	5.78982	+	2.30409i	0.300188	+	0.119461i
$373$	−3.32049	−	1.91709i	−0.171929	−	0.0992631i	0.411566	−	0.911380i	$-0.364982\pi$
$373$	−3.32049	−	1.91709i	−0.171929	−	0.0992631i	−0.583495	+	0.812117i	$0.698315\pi$
$374$	0.0148181			0.000766227
$375$	2.27299	−	19.2311i	0.117377	−	0.993087i
$376$		−	5.04557i		−	0.260206i
$377$		−	4.45104i		−	0.229240i
$378$	13.5854	+	2.10615i	0.698760	+	0.108329i
$379$	−29.0957			−1.49454			−0.747272	−	0.664519i	$-0.768637\pi$
$379$	−29.0957			−1.49454			−0.747272	+	0.664519i	$0.768637\pi$
$380$	10.6305	−	7.43985i	0.545335	−	0.381656i
$381$	17.7917	+	7.08031i	0.911498	+	0.362735i
$382$		−	3.96791i		−	0.203016i
$383$	−12.2543	−	7.07501i	−0.626164	−	0.361516i	0.153101	−	0.988211i	$-0.451074\pi$
$383$	−12.2543	−	7.07501i	−0.626164	−	0.361516i	−0.779265	+	0.626695i	$0.784407\pi$
$384$	0.640430	−	1.60930i	0.0326818	−	0.0821243i
$385$	0.840556	−	0.0187104i	0.0428387	−	0.000953571i
$386$		−	1.29203i		−	0.0657628i
$387$	1.48055	+	4.96662i	0.0752605	+	0.252467i
$388$	−2.01118	+	3.48347i	−0.102102	+	0.176846i
$389$	−29.9470	+	17.2899i	−1.51837	+	0.876633i	−0.518606	+	0.855013i	$0.673549\pi$
$389$	−29.9470	+	17.2899i	−1.51837	+	0.876633i	−0.999766	+	0.0216198i	$0.993118\pi$
$390$	−4.52669	+	1.06891i	−0.229218	+	0.0541265i
$391$	0.388803	−	0.224476i	0.0196626	−	0.0113522i
$392$	2.68750	+	6.46354i	0.135739	+	0.326458i
$393$	10.0582	+	12.7360i	0.507369	+	0.642449i
$394$	0.983884			0.0495674
$395$	−18.7342	+	1.63460i	−0.942621	+	0.0822455i
$396$	0.414737	+	0.0988096i	0.0208413	+	0.00496537i
$397$	−14.6731	−	25.4146i	−0.736422	−	1.27552i	−0.954096	−	0.299500i	$-0.903180\pi$
$397$	−14.6731	−	25.4146i	−0.736422	−	1.27552i	0.217674	−	0.976022i	$-0.430153\pi$
$398$	−20.6241	−	11.9073i	−1.03379	−	0.596859i
$399$	−11.4110	+	24.0187i	−0.571262	+	1.20244i
$400$	4.92445	−	0.865927i	0.246222	−	0.0432963i
$401$	−22.8472	−	13.1908i	−1.14093	−	0.658719i	−0.194273	−	0.980948i	$-0.562235\pi$
$401$	−22.8472	−	13.1908i	−1.14093	−	0.658719i	−0.946662	+	0.322229i	$0.895568\pi$
$402$	−11.7118	−	4.66076i	−0.584129	−	0.232457i
$403$	3.74176	−	2.16031i	0.186390	−	0.107613i
$404$	1.68050	+	2.91071i	0.0836079	+	0.144813i
$405$	2.86519	+	19.9196i	0.142373	+	0.989813i
$406$	−4.34302	−	8.79183i	−0.215541	−	0.436331i
$407$	0.445449	−	0.771540i	0.0220801	−	0.0382438i
$408$	−0.141730	+	0.111930i	−0.00701668	+	0.00554137i
$409$		−	12.8464i		−	0.635215i	−0.948222	−	0.317607i	$-0.897121\pi$
$409$		−	12.8464i		−	0.635215i	0.948222	−	0.317607i	$-0.102879\pi$
$410$	10.1707	+	14.5326i	0.502297	+	0.717714i
$411$	32.7726	−	4.78081i	1.61656	−	0.235820i
$412$	−9.57498	+	16.5843i	−0.471725	+	0.817052i
$413$	−21.5901	−	14.4050i	−1.06238	−	0.708822i
$414$	12.3789	−	3.69014i	0.608388	−	0.181360i
$415$	−4.75948	−	2.22074i	−0.233634	−	0.109012i
$416$	−0.600465	−	1.04004i	−0.0294402	−	0.0509920i
$417$	−0.275511	−	1.88864i	−0.0134918	−	0.0924871i
$418$	−0.412329	+	0.714175i	−0.0201677	+	0.0349314i
$419$	−5.13440	−	8.89304i	−0.250832	−	0.434453i	0.712923	−	0.701242i	$-0.247371\pi$
$419$	−5.13440	−	8.89304i	−0.250832	−	0.434453i	−0.963755	+	0.266789i	$0.914037\pi$
$420$	−7.89828	+	6.52818i	−0.385397	+	0.318543i
$421$	3.18306	−	5.51323i	0.155133	−	0.268698i	−0.777974	−	0.628296i	$-0.783753\pi$
$421$	3.18306	−	5.51323i	0.155133	−	0.268698i	0.933107	+	0.359598i	$0.117086\pi$
$422$	−11.2221	−	19.4372i	−0.546282	−	0.946188i
$423$	−10.4004	+	10.9978i	−0.505684	+	0.534733i
$424$	1.34026	−	2.32140i	0.0650888	−	0.112737i
$425$	−0.489818	−	0.178540i	−0.0237597	−	0.00866045i
$426$	−20.0369	−	7.97379i	−0.970791	−	0.386331i
$427$	18.0713	−	27.0851i	0.874532	−	1.31074i
$428$	−7.15043	−	12.3849i	−0.345629	−	0.598647i
$429$	0.231989	−	0.183211i	0.0112005	−	0.00884552i
$430$	−3.50057	−	1.63335i	−0.168813	−	0.0787669i
$431$	−3.37653	−	1.94944i	−0.162642	−	0.0939012i	0.416470	−	0.909149i	$-0.363267\pi$
$431$	−3.37653	−	1.94944i	−0.162642	−	0.0939012i	−0.579112	+	0.815248i	$0.696600\pi$
$432$	−4.71318	+	2.18768i	−0.226763	+	0.105255i
$433$	20.9340			1.00603			0.503013	−	0.864279i	$-0.332225\pi$
$433$	20.9340			1.00603			0.503013	+	0.864279i	$0.332225\pi$
$434$	5.28296	−	7.91805i	0.253590	−	0.380079i
$435$	10.4492	−	9.84209i	0.501002	−	0.471892i
$436$	8.89823	−	15.4122i	0.426148	−	0.738110i
$437$			24.9851i			1.19520i
$438$	8.63038	+	10.9281i	0.412375	+	0.522164i
$439$		−	16.4017i		−	0.782811i	−0.920218	−	0.391406i	$-0.871989\pi$
$439$		−	16.4017i		−	0.782811i	0.920218	−	0.391406i	$-0.128011\pi$
$440$	−0.260352	+	0.182209i	−0.0124118	+	0.00868649i
$441$	7.46527	−	19.6283i	0.355489	−	0.934680i
$442$			0.125219i			0.00595607i
$443$	26.3852			1.25360			0.626800	−	0.779180i	$-0.284364\pi$
$443$	26.3852			1.25360			0.626800	+	0.779180i	$0.284364\pi$
$444$	1.56735	+	10.7443i	0.0743832	+	0.509900i
$445$	−1.91858	−	2.74139i	−0.0909494	−	0.129954i
$446$	−8.99621	+	15.5819i	−0.425983	+	0.737824i
$447$	−19.0146	+	15.0167i	−0.899361	+	0.710264i
$448$	−2.20085	−	1.46842i	−0.103981	−	0.0693762i
$449$			32.5310i			1.53523i	0.640911	+	0.767615i	$0.278557\pi$
$449$			32.5310i			1.53523i	−0.640911	+	0.767615i	$0.721443\pi$
$450$	−12.5187	−	8.26325i	−0.590139	−	0.389533i
$451$	−0.976322	−	0.563680i	−0.0459732	−	0.0265426i
$452$	8.09024	+	14.0127i	0.380533	+	0.659102i
$453$	8.42100	−	1.22844i	0.395653	−	0.0577171i
$454$	17.5341	−	10.1233i	0.822917	−	0.475111i
$455$	0.158111	+	7.10304i	0.00741235	+	0.332996i
$456$	−1.45081	−	9.94539i	−0.0679406	−	0.465736i
$457$		−	35.0085i		−	1.63763i	−0.574058	−	0.818814i	$-0.694632\pi$
$457$		−	35.0085i		−	1.63763i	0.574058	−	0.818814i	$-0.305368\pi$
$458$	−0.650116	−	0.375345i	−0.0303779	−	0.0175387i
$459$	0.539649	+	0.0481722i	0.0251887	+	0.00224849i
$460$	−4.07097	+	8.72488i	−0.189810	+	0.406800i
$461$	−5.08610	+	8.80939i	−0.236883	+	0.410294i	−0.959818	−	0.280622i	$-0.909459\pi$
$461$	−5.08610	+	8.80939i	−0.236883	+	0.410294i	0.722935	+	0.690916i	$0.242793\pi$
$462$	0.279465	−	0.588243i	0.0130019	−	0.0273675i
$463$	−27.5356	+	15.8977i	−1.27969	+	0.738828i	−0.976791	−	0.214195i	$-0.931287\pi$
$463$	−27.5356	+	15.8977i	−1.27969	+	0.738828i	−0.302897	+	0.953023i	$0.597954\pi$
$464$	3.20977	+	1.85316i	0.149010	+	0.0860310i
$465$	13.3453	+	4.00727i	0.618871	+	0.185833i
$466$	−9.57787	−	16.5894i	−0.443686	−	0.768487i
$467$	−19.5141	+	11.2665i	−0.903006	+	0.521351i	−0.878174	−	0.478341i	$-0.841238\pi$
$467$	−19.5141	+	11.2665i	−0.903006	+	0.521351i	−0.0248321	+	0.999692i	$0.507905\pi$
$468$	−0.834982	+	3.50470i	−0.0385970	+	0.162005i
$469$	−10.6865	+	16.0168i	−0.493455	+	0.739587i
$470$	−0.980671	−	11.2395i	−0.0452350	−	0.518441i
$471$	4.10453	−	10.3140i	0.189127	−	0.475246i
$472$	9.80986			0.451535
$473$	0.245508			0.0112885
$474$	−5.38603	+	13.5343i	−0.247389	+	0.621650i
$475$	22.2346	−	18.6392i	1.02019	−	0.855227i
$476$	0.122180	+	0.247337i	0.00560013	+	0.0113367i
$477$	−7.70644	+	2.29729i	−0.352854	+	0.105186i
$478$	1.15565	−	0.667217i	0.0528584	−	0.0305178i
$479$	4.81018	+	8.33147i	0.219783	+	0.380675i	0.954741	−	0.297437i	$-0.0961318\pi$
$479$	4.81018	+	8.33147i	0.219783	+	0.380675i	−0.734959	+	0.678112i	$0.762799\pi$
$480$	1.11384	−	3.70936i	0.0508394	−	0.169308i
$481$	6.51984	+	3.76423i	0.297279	+	0.171634i
$482$	−17.1287	+	9.88925i	−0.780191	+	0.450443i
$483$	−1.57841	−	19.6681i	−0.0718201	−	0.894929i
$484$	−5.48990	+	9.50879i	−0.249541	+	0.432218i
$485$	−3.80306	+	8.15069i	−0.172688	+	0.370104i
$486$	14.7828	+	4.94674i	0.670559	+	0.224388i
$487$	−8.50444	−	4.91004i	−0.385373	−	0.222495i	0.294781	−	0.955565i	$-0.404753\pi$
$487$	−8.50444	−	4.91004i	−0.385373	−	0.222495i	−0.680153	+	0.733070i	$0.738087\pi$
$488$			12.3067i			0.557096i
$489$	−0.280280	−	1.92133i	−0.0126747	−	0.0868854i
$490$	7.24296	+	13.8759i	0.327204	+	0.626847i
$491$	24.7333	−	14.2798i	1.11620	−	0.644437i	0.175770	−	0.984431i	$-0.443758\pi$
$491$	24.7333	−	14.2798i	1.11620	−	0.644437i	0.940428	+	0.339994i	$0.110425\pi$
$492$	13.5960	−	1.98336i	0.612954	−	0.0894166i
$493$	−0.193227	−	0.334678i	−0.00870249	−	0.0150732i
$494$	−6.03507	−	3.48435i	−0.271531	−	0.156768i
$495$	0.943075	+	0.139499i	0.0423881	+	0.00627002i
$496$			3.59772i			0.161542i
$497$	−18.2828	+	27.4021i	−0.820095	+	1.22915i
$498$	−3.19268	+	2.52139i	−0.143067	+	0.112986i
$499$	−10.3032	+	17.8456i	−0.461232	+	0.798878i	−0.999023	−	0.0442006i	$-0.985926\pi$
$499$	−10.3032	+	17.8456i	−0.461232	+	0.798878i	0.537790	+	0.843079i	$0.319259\pi$
$500$	10.8014	−	2.88607i	0.483054	−	0.129069i
$501$	−0.213366	−	1.46263i	−0.00953248	−	0.0653456i
$502$	28.8281			1.28666
$503$		−	5.19287i		−	0.231539i	−0.993276	−	0.115769i	$-0.963067\pi$
$503$		−	5.19287i		−	0.231539i	0.993276	−	0.115769i	$-0.0369333\pi$
$504$	1.77036	+	7.73730i	0.0788583	+	0.344647i
$505$	4.30922	+	6.15728i	0.191758	+	0.273995i
$506$		−	0.611908i		−	0.0272026i
$507$	−12.4070	−	15.7102i	−0.551016	−	0.697716i
$508$			11.0556i			0.490511i
$509$	−17.7208	+	30.6933i	−0.785461	+	1.36046i	0.143263	+	0.989685i	$0.454241\pi$
$509$	−17.7208	+	30.6933i	−0.785461	+	1.36046i	−0.928724	+	0.370773i	$0.879093\pi$
$510$	−0.293963	+	0.276883i	−0.0130169	+	0.0122606i
$511$	19.0709	−	9.42071i	0.843646	−	0.416748i
$512$	1.00000			0.0441942
$513$	−17.3380	+	24.6685i	−0.765491	+	1.08914i
$514$	−15.5450	−	8.97493i	−0.685662	−	0.395867i
$515$	−18.1059	+	38.8044i	−0.797840	+	1.70993i
$516$	−2.34820	+	1.85447i	−0.103374	+	0.0816386i
$517$	0.358526	+	0.620985i	0.0157680	+	0.0273109i
$518$	16.5510	+	1.07361i	0.727211	+	0.0471715i
$519$	−40.5256	−	16.1274i	−1.77888	−	0.707913i
$520$	−1.53974	−	2.20008i	−0.0675222	−	0.0964800i
$521$	−5.23647	+	9.06983i	−0.229414	+	0.397356i	−0.957635	−	0.287986i	$-0.907014\pi$
$521$	−5.23647	+	9.06983i	−0.229414	+	0.397356i	0.728221	+	0.685343i	$0.240348\pi$
$522$	−3.17644	−	10.6556i	−0.139029	−	0.466383i
$523$	16.1085	+	27.9007i	0.704375	+	1.22001i	0.966916	+	0.255093i	$0.0821062\pi$
$523$	16.1085	+	27.9007i	0.704375	+	1.22001i	−0.262541	+	0.964921i	$0.584560\pi$
$524$	−4.68485	+	8.11440i	−0.204659	+	0.354479i
$525$	−16.3254	+	16.0773i	−0.712499	+	0.701673i
$526$	−7.94184	−	13.7557i	−0.346281	−	0.599776i
$527$	0.187564	−	0.324871i	0.00817044	−	0.0141516i
$528$	0.0355319	+	0.243572i	0.00154633	+	0.0106001i
$529$	2.23036	+	3.86310i	0.0969723	+	0.167961i
$530$	2.53438	−	5.43166i	0.110086	−	0.235936i
$531$	−21.3825	−	20.2210i	−0.927923	−	0.877515i
$532$	−15.3204	−	0.993780i	−0.664225	−	0.0430858i
$533$	4.76333	−	8.25032i	0.206323	−	0.357361i
$534$	−2.56471	+	0.374134i	−0.110986	+	0.0161904i
$535$	−18.3355	−	26.1989i	−0.792712	−	1.13268i
$536$		−	7.27754i		−	0.314342i
$537$	−21.9899	+	17.3664i	−0.948934	+	0.749414i
$538$	5.25345	−	9.09924i	0.226492	−	0.392296i
$539$	−0.790048	−	0.604534i	−0.0340298	−	0.0260391i
$540$	−10.0739	+	5.78936i	−0.433511	+	0.249134i
$541$	12.4544	+	21.5717i	0.535457	+	0.927439i	0.999141	+	0.0414381i	$0.0131939\pi$
$541$	12.4544	+	21.5717i	0.535457	+	0.927439i	−0.463684	+	0.886001i	$0.653473\pi$
$542$	10.9732	−	6.33540i	0.471341	−	0.272129i
$543$	27.3972	+	10.9028i	1.17572	+	0.467886i
$544$	−0.0902992	−	0.0521342i	−0.00387154	−	0.00223524i
$545$	16.8262	−	36.0617i	0.720755	−	1.54472i
$546$	4.97089	+	2.36160i	0.212735	+	0.101067i
$547$	23.6806	+	13.6720i	1.01251	+	0.584574i	0.911926	−	0.410355i	$-0.134595\pi$
$547$	23.6806	+	13.6720i	1.01251	+	0.584574i	0.100585	+	0.994928i	$0.467928\pi$
$548$	9.56078	+	16.5598i	0.408416	+	0.707398i
$549$	25.3676	−	26.8248i	1.08266	−	1.14486i
$550$	−0.544547	+	0.456493i	−0.0232195	+	0.0194649i
$551$	21.5069			0.916224
$552$	4.62211	+	5.85268i	0.196730	+	0.249107i
$553$	18.5092	+	12.3494i	0.787093	+	0.525151i
$554$	−12.8968	+	7.44600i	−0.547935	+	0.316350i
$555$	5.57972	+	23.6293i	0.236846	+	1.00301i
$556$	0.954315	−	0.550974i	0.0404720	−	0.0233665i
$557$	−8.95463	+	15.5099i	−0.379420	+	0.657175i	−0.990978	−	0.134025i	$-0.957210\pi$
$557$	−8.95463	+	15.5099i	−0.379420	+	0.657175i	0.611558	+	0.791200i	$0.290543\pi$
$558$	7.41594	−	7.84195i	0.313942	−	0.331976i
$559$			2.07465i			0.0877482i
$560$	−5.18803	−	2.84329i	−0.219234	−	0.120151i
$561$	0.00948997	−	0.0238468i	0.000400667	−	0.00100681i
$562$	5.92114	+	3.41857i	0.249768	+	0.144204i
$563$		−	30.4638i		−	1.28390i	−0.766748	−	0.641948i	$-0.778126\pi$
$563$		−	30.4638i		−	1.28390i	0.766748	−	0.641948i	$-0.221874\pi$
$564$	−8.11985	−	3.23134i	−0.341907	−	0.136064i
$565$	20.7454	+	29.6423i	0.872766	+	1.24706i
$566$	−11.6293			−0.488817
$567$	12.0899	−	20.5142i	0.507730	−	0.861516i
$568$		−	12.4507i		−	0.522419i
$569$		−	39.6736i		−	1.66320i	−0.555371	−	0.831602i	$-0.687424\pi$
$569$		−	39.6736i		−	1.66320i	0.555371	−	0.831602i	$-0.312576\pi$
$570$	−5.16486	−	21.8724i	−0.216332	−	0.916135i
$571$	3.24837			0.135940			0.0679699	−	0.997687i	$-0.478348\pi$
$571$	3.24837			0.135940			0.0679699	+	0.997687i	$0.478348\pi$
$572$	0.147805	+	0.0853352i	0.00618003	+	0.00356804i
$573$	−6.38556	−	2.54117i	−0.266760	−	0.106159i
$574$	1.35856	−	20.9440i	0.0567052	−	0.874186i
$575$	−7.37273	+	20.2268i	−0.307464	+	0.843517i
$576$	−2.17970	−	2.06129i	−0.0908208	−	0.0858870i
$577$	0.0635247	−	0.110028i	0.00264457	−	0.00458053i	−0.864700	−	0.502289i	$-0.832492\pi$
$577$	0.0635247	−	0.110028i	0.00264457	−	0.00458053i	0.867345	+	0.497708i	$0.165825\pi$
$578$	−8.49456	−	14.7130i	−0.353327	−	0.611981i
$579$	−2.07927	−	0.827457i	−0.0864116	−	0.0343879i
$580$	7.51029	+	3.50426i	0.311848	+	0.145506i
$581$	2.75229	+	5.57162i	0.114184	+	0.231150i
$582$	4.31793	+	5.46751i	0.178984	+	0.226636i
$583$			0.380942i			0.0157770i
$584$	−4.01981	+	6.96252i	−0.166341	+	0.288111i
$585$	−1.17883	+	7.96938i	−0.0487385	+	0.329493i
$586$	−8.60234	+	4.96657i	−0.355360	+	0.205167i
$587$	−2.49693	−	1.44160i	−0.103059	−	0.0595014i	0.447584	−	0.894242i	$-0.352284\pi$
$587$	−2.49693	−	1.44160i	−0.103059	−	0.0595014i	−0.550644	+	0.834740i	$0.685618\pi$
$588$	12.1229	−	0.185558i	0.499941	−	0.00765227i
$589$	10.4383	+	18.0797i	0.430104	+	0.744962i
$590$	21.8525	−	1.90667i	0.899653	−	0.0784964i
$591$	0.630109	−	1.58337i	0.0259192	−	0.0651309i
$592$	−5.42899	+	3.13443i	−0.223130	+	0.128824i
$593$	40.6636	−	23.4772i	1.66986	−	0.964092i	0.702143	−	0.712036i	$-0.252227\pi$
$593$	40.6636	−	23.4772i	1.66986	−	0.964092i	0.967713	−	0.252055i	$-0.0811065\pi$
$594$	0.424624	−	0.604156i	0.0174225	−	0.0247888i
$595$	0.320242	+	0.527221i	0.0131287	+	0.0216139i
$596$	−12.1146	−	6.99438i	−0.496234	−	0.286501i
$597$	−32.3707	+	25.5645i	−1.32484	+	1.04629i
$598$	5.17088			0.211453
$599$		−	5.67416i		−	0.231840i	−0.993259	−	0.115920i	$-0.963018\pi$
$599$		−	5.67416i		−	0.231840i	0.993259	−	0.115920i	$-0.0369816\pi$
$600$	1.76023	−	8.47948i	0.0718609	−	0.346173i
$601$	−28.9131	−	16.6930i	−1.17939	−	0.680921i	−0.223516	−	0.974700i	$-0.571753\pi$
$601$	−28.9131	−	16.6930i	−1.17939	−	0.680921i	−0.955873	+	0.293780i	$0.905087\pi$
$602$	2.02430	+	4.09790i	0.0825042	+	0.167018i
$603$	−15.0011	+	15.8629i	−0.610893	+	0.645985i
$604$	2.45666	+	4.25506i	0.0999602	+	0.173136i
$605$	−10.3812	+	22.2489i	−0.422055	+	0.904545i
$606$	5.76045	−	0.840323i	0.234002	−	0.0341358i
$607$	−22.3763	+	38.7570i	−0.908228	+	1.57310i	−0.0917027	+	0.995786i	$0.529231\pi$
$607$	−22.3763	+	38.7570i	−0.908228	+	1.57310i	−0.816525	+	0.577310i	$0.804102\pi$
$608$	5.02533	−	2.90137i	0.203804	−	0.117666i
$609$	−16.9301	+	1.35868i	−0.686042	+	0.0550565i
$610$	2.39196	+	27.4144i	0.0968475	+	1.10998i
$611$	−5.24758	+	3.02969i	−0.212294	+	0.122568i
$612$	0.0893613	+	0.299770i	0.00361222	+	0.0121175i
$613$	−27.0024	−	15.5899i	−1.09062	−	0.629668i	−0.156877	−	0.987618i	$-0.550143\pi$
$613$	−27.0024	−	15.5899i	−1.09062	−	0.629668i	−0.933741	+	0.357950i	$0.883476\pi$
$614$	25.3226			1.02194
$615$	29.9010	−	7.06068i	1.20572	−	0.284714i
$616$	0.375212	+	0.0243387i	0.0151177	+	0.000980632i
$617$	0.359684	+	0.622991i	0.0144803	+	0.0250807i	0.873175	−	0.487407i	$-0.162057\pi$
$617$	0.359684	+	0.622991i	0.0144803	+	0.0250807i	−0.858694	+	0.512488i	$0.828724\pi$
$618$	20.5571	+	26.0301i	0.826928	+	1.04709i
$619$	31.7674	−	18.3409i	1.27684	−	0.737184i	0.300574	−	0.953758i	$-0.402822\pi$
$619$	31.7674	−	18.3409i	1.27684	−	0.737184i	0.976266	+	0.216574i	$0.0694884\pi$
$620$	0.699263	+	8.01430i	0.0280831	+	0.321862i
$621$	1.98925	−	22.2846i	0.0798260	−	0.894250i
$622$	7.32275			0.293616
$623$	−0.256275	+	3.95081i	−0.0102674	+	0.158286i
$624$	−2.05829	+	0.300259i	−0.0823975	+	0.0120200i
$625$	23.5003	−	8.52842i	0.940014	−	0.341137i
$626$	−8.48704			−0.339210
$627$	0.885254	+	1.12094i	0.0353536	+	0.0447660i
$628$	6.40902			0.255748
$629$	0.653644			0.0260625
$630$	5.44752	+	16.8916i	0.217034	+	0.672976i
$631$	−15.5643			−0.619603			−0.309802	−	0.950801i	$-0.600263\pi$
$631$	−15.5643			−0.619603			−0.309802	+	0.950801i	$0.600263\pi$
$632$	−8.41003			−0.334533
$633$	−38.4673	+	5.61153i	−1.52894	+	0.223038i
$634$	2.24351			0.0891010
$635$	2.14879	+	24.6274i	0.0852721	+	0.977310i
$636$	−2.87749	−	3.64358i	−0.114100	−	0.144477i
$637$	5.10856	−	6.67623i	0.202409	−	0.264522i
$638$	−0.526725			−0.0208532
$639$	−25.6644	+	27.1387i	−1.01527	+	1.07359i
$640$	2.22760	−	0.194363i	0.0880538	−	0.00768286i
$641$	−16.3208	+	9.42280i	−0.644632	+	0.372178i	−0.786396	−	0.617722i	$-0.788056\pi$
$641$	−16.3208	+	9.42280i	−0.644632	+	0.372178i	0.141765	+	0.989900i	$0.454722\pi$
$642$	−24.5104	+	3.57553i	−0.967348	+	0.141115i
$643$	−5.39558	−	9.34542i	−0.212781	−	0.368548i	0.739803	−	0.672824i	$-0.234919\pi$
$643$	−5.39558	−	9.34542i	−0.212781	−	0.368548i	−0.952584	+	0.304276i	$0.901585\pi$
$644$	10.2137	−	5.04539i	0.402475	−	0.198816i
$645$	−4.87042	+	4.58743i	−0.191772	+	0.180630i
$646$	−0.605044			−0.0238051
$647$	43.7372	+	25.2517i	1.71949	+	0.992747i	0.919856	+	0.392256i	$0.128305\pi$
$647$	43.7372	+	25.2517i	1.71949	+	0.992747i	0.799632	+	0.600491i	$0.205028\pi$
$648$	0.502177	+	8.98598i	0.0197274	+	0.353003i
$649$	−1.20735	+	0.697064i	−0.0473927	+	0.0273622i
$650$	−3.85756	−	4.60165i	−0.151306	−	0.180491i
$651$	−9.35917	−	13.5728i	−0.366815	−	0.531961i
$652$	0.970831	−	0.560510i	0.0380207	−	0.0219513i
$653$	−18.0024	+	31.1811i	−0.704490	+	1.22021i	0.262385	+	0.964963i	$0.415491\pi$
$653$	−18.0024	+	31.1811i	−0.704490	+	1.22021i	−0.966875	+	0.255249i	$0.917842\pi$
$654$	−19.1042	−	24.1904i	−0.747032	−	0.945918i
$655$	−8.85886	+	18.9862i	−0.346144	+	0.741854i
$656$	3.96636	+	6.86994i	0.154860	+	0.268226i
$657$	23.1137	−	6.89020i	0.901753	−	0.268812i
$658$	−7.40901	+	11.1046i	−0.288833	+	0.432901i
$659$	4.91626	+	2.83840i	0.191510	+	0.110568i	0.592689	−	0.805431i	$-0.298066\pi$
$659$	4.91626	+	2.83840i	0.191510	+	0.110568i	−0.401179	+	0.916000i	$0.631400\pi$
$660$	0.126492	+	0.535677i	0.00492371	+	0.0208512i
$661$			21.4910i			0.835902i	0.908470	+	0.417951i	$0.137252\pi$
$661$			21.4910i			0.835902i	−0.908470	+	0.417951i	$0.862748\pi$
$662$	−5.04537			−0.196094
$663$	0.201515	+	0.0801941i	0.00782621	+	0.00311448i
$664$	−2.03412	−	1.17440i	−0.0789393	−	0.0455756i
$665$	−34.3210	+	0.763972i	−1.33091	+	0.0296255i
$666$	18.2945	+	4.35860i	0.708898	+	0.168892i
$667$	−13.8204	+	7.97922i	−0.535128	+	0.308956i
$668$	0.739056	−	0.426694i	0.0285949	−	0.0165093i
$669$	19.3145	+	24.4567i	0.746742	+	0.945551i
$670$	−1.41448	−	16.2115i	−0.0546462	−	0.626304i
$671$	−0.874481	−	1.51465i	−0.0337590	−	0.0584722i
$672$	−3.77262	+	2.60142i	−0.145532	+	0.100352i
$673$	−6.60209	−	3.81172i	−0.254492	−	0.146931i	0.367327	−	0.930092i	$-0.380273\pi$
$673$	−6.60209	−	3.81172i	−0.254492	−	0.146931i	−0.621819	+	0.783161i	$0.713606\pi$
$674$	30.0990	−	17.3777i	1.15937	−	0.669364i
$675$	−21.3154	+	14.8544i	−0.820431	+	0.571746i
$676$	5.77888	−	10.0093i	0.222265	−	0.384974i
$677$			30.8268i			1.18477i	0.805654	+	0.592386i	$0.201814\pi$
$677$			30.8268i			1.18477i	−0.805654	+	0.592386i	$0.798186\pi$
$678$	27.7319	−	4.04547i	1.06504	−	0.155366i
$679$	9.54150	−	4.71335i	0.366169	−	0.180882i
$680$	−0.211284	−	0.0985837i	−0.00810236	−	0.00378051i
$681$	−5.06211	−	34.7010i	−0.193980	−	1.32974i
$682$	−0.255645	−	0.442790i	−0.00978916	−	0.0169553i
$683$	−18.8176	+	32.5930i	−0.720036	+	1.24714i	0.240949	+	0.970538i	$0.422541\pi$
$683$	−18.8176	+	32.5930i	−0.720036	+	1.24714i	−0.960985	+	0.276601i	$0.910792\pi$
$684$	−16.9343	−	4.03453i	−0.647498	−	0.154264i
$685$	24.5162	+	35.0303i	0.936718	+	1.33844i
$686$	3.57637	−	18.1717i	0.136547	−	0.693798i
$687$	−1.02040	+	0.805850i	−0.0389305	+	0.0307451i
$688$	−1.49609	−	0.863766i	−0.0570378	−	0.0329308i
$689$	−3.21912			−0.122639
$690$	11.4338	+	12.1391i	0.435277	+	0.462128i
$691$			11.9246i			0.453633i	0.973938	+	0.226816i	$0.0728317\pi$
$691$			11.9246i			0.453633i	−0.973938	+	0.226816i	$0.927168\pi$
$692$		−	25.1821i		−	0.957280i
$693$	−0.767681	−	0.826472i	−0.0291618	−	0.0313951i
$694$	−6.90143			−0.261975
$695$	2.01875	−	1.41284i	0.0765755	−	0.0535919i
$696$	5.03793	−	3.97867i	0.190962	−	0.150811i
$697$		−	0.827133i		−	0.0313299i
$698$	−0.226488	−	0.130763i	−0.00857272	−	0.00494946i
$699$	−32.8312	+	4.78936i	−1.24179	+	0.181150i
$700$	−12.1095	−	5.32536i	−0.457697	−	0.201280i
$701$		−	12.4716i		−	0.471046i	−0.971869	−	0.235523i	$-0.924320\pi$
$701$		−	12.4716i		−	0.471046i	0.971869	−	0.235523i	$-0.0756803\pi$
$702$	5.10537	+	3.58825i	0.192690	+	0.135430i
$703$	−18.1883	+	31.5030i	−0.685984	+	1.18816i
$704$	−0.123075	+	0.0710575i	−0.00463857	+	0.00267808i
$705$	−18.7159	−	5.61994i	−0.704880	−	0.211659i
$706$	24.7213	−	14.2729i	0.930400	−	0.537167i
$707$	0.575605	−	8.87371i	0.0216479	−	0.333730i
$708$	6.28253	−	15.7870i	0.236112	−	0.593312i
$709$	28.2913			1.06250			0.531251	−	0.847215i	$-0.321722\pi$
$709$	28.2913			1.06250			0.531251	+	0.847215i	$0.321722\pi$
$710$	−2.41995	−	27.7352i	−0.0908190	−	1.04088i
$711$	18.3313	+	17.3355i	0.687479	+	0.650132i
$712$	−0.748203	−	1.29593i	−0.0280401	−	0.0485669i
$713$	−13.4154	−	7.74540i	−0.502412	−	0.290068i
$714$	0.476287	−	0.0382231i	0.0178246	−	0.00143047i
$715$	0.345837	+	0.161365i	0.0129336	+	0.00603472i
$716$	−14.0102	−	8.08881i	−0.523587	−	0.302293i
$717$	−0.333638	−	2.28710i	−0.0124599	−	0.0854134i
$718$	−10.5441	+	6.08767i	−0.393504	+	0.227190i
$719$	3.47046	+	6.01101i	0.129426	+	0.224173i	0.923454	−	0.383708i	$-0.125353\pi$
$719$	3.47046	+	6.01101i	0.129426	+	0.224173i	−0.794028	+	0.607881i	$0.792020\pi$
$720$	−5.25615	−	4.16808i	−0.195885	−	0.155335i
$721$	45.4258	−	22.4396i	1.69175	−	0.835696i
$722$	7.33595	−	12.7062i	0.273016	−	0.472877i
$723$	4.94506	+	33.8986i	0.183909	+	1.26070i
$724$			17.0243i			0.632701i
$725$	17.4111	+	6.34638i	0.646631	+	0.235699i
$726$	11.7866	+	14.9246i	0.437442	+	0.553904i
$727$	8.87166	−	15.3662i	0.329032	−	0.569899i	−0.653288	−	0.757109i	$-0.726611\pi$
$727$	8.87166	−	15.3662i	0.329032	−	0.569899i	0.982320	+	0.187210i	$0.0599444\pi$
$728$	−0.205672	+	3.17070i	−0.00762270	+	0.117514i
$729$	17.4281	−	20.6219i	0.645485	−	0.763773i
$730$	−7.60130	+	16.2910i	−0.281337	+	0.602958i
$731$	0.0900636	+	0.155995i	0.00333112	+	0.00576967i
$732$	19.8051	+	7.88155i	0.732018	+	0.291311i
$733$	9.39300	−	16.2692i	0.346939	−	0.600915i	−0.638765	−	0.769402i	$-0.720555\pi$
$733$	9.39300	−	16.2692i	0.346939	−	0.600915i	0.985704	+	0.168486i	$0.0538879\pi$
$734$	11.1198	+	19.2601i	0.410441	+	0.710904i
$735$	26.9690	−	2.76960i	0.994768	−	0.102158i
$736$	−2.15286	+	3.72887i	−0.0793556	+	0.137448i
$737$	0.517124	+	0.895685i	0.0190485	+	0.0329930i
$738$	5.51546	−	23.1502i	0.203027	−	0.852171i
$739$	−19.5906	+	33.9320i	−0.720653	+	1.24821i	0.240085	+	0.970752i	$0.422825\pi$
$739$	−19.5906	+	33.9320i	−0.720653	+	1.24821i	−0.960738	+	0.277456i	$0.910509\pi$
$740$	−11.4844	+	8.03746i	−0.422176	+	0.295463i
$741$	−9.47241	+	7.48077i	−0.347978	+	0.274813i
$742$	−6.35850	+	3.14100i	−0.233428	+	0.115310i
$743$	−3.04957	−	5.28201i	−0.111878	−	0.193778i	0.804650	−	0.593750i	$-0.202353\pi$
$743$	−3.04957	−	5.28201i	−0.111878	−	0.193778i	−0.916527	+	0.399972i	$0.869020\pi$
$744$	5.78982	+	2.30409i	0.212265	+	0.0844720i
$745$	−28.3460	−	13.2261i	−1.03852	−	0.484566i
$746$	−3.32049	−	1.91709i	−0.121572	−	0.0701896i
$747$	2.01300	+	6.75276i	0.0736517	+	0.247070i
$748$	0.0148181			0.000541804
$749$	−2.44917	+	37.7571i	−0.0894906	+	1.37962i
$750$	2.27299	−	19.2311i	0.0829979	−	0.702219i
$751$	−26.9458	+	46.6715i	−0.983266	+	1.70307i	−0.333862	+	0.942622i	$0.608352\pi$
$751$	−26.9458	+	46.6715i	−0.983266	+	1.70307i	−0.649404	+	0.760444i	$0.724981\pi$
$752$		−	5.04557i		−	0.183993i
$753$	18.4623	−	46.3930i	0.672805	−	1.69066i
$754$		−	4.45104i		−	0.162097i
$755$	6.29950	+	9.00112i	0.229262	+	0.327584i
$756$	13.5854	+	2.10615i	0.494098	+	0.0765999i
$757$		−	18.1765i		−	0.660637i	−0.943870	−	0.330318i	$-0.892844\pi$
$757$		−	18.1765i		−	0.660637i	0.943870	−	0.330318i	$-0.107156\pi$
$758$	−29.0957			−1.05680
$759$	−0.984745	−	0.391884i	−0.0357440	−	0.0142245i
$760$	10.6305	−	7.43985i	0.385610	−	0.269872i
$761$	14.9924	−	25.9677i	0.543476	−	0.941328i	−0.455225	−	0.890376i	$-0.650441\pi$
$761$	14.9924	−	25.9677i	0.543476	−	0.941328i	0.998701	−	0.0509513i	$-0.0162253\pi$
$762$	17.7917	+	7.08031i	0.644526	+	0.256493i
$763$	−42.2152	+	20.8536i	−1.52829	+	0.754952i
$764$		−	3.96791i		−	0.143554i
$765$	0.257326	+	0.650400i	0.00930363	+	0.0235153i
$766$	−12.2543	−	7.07501i	−0.442765	−	0.255630i
$767$	−5.89048	−	10.2026i	−0.212693	−	0.368395i
$768$	0.640430	−	1.60930i	0.0231095	−	0.0580706i
$769$	−29.1902	+	16.8530i	−1.05263	+	0.607734i	−0.923383	−	0.383879i	$-0.874588\pi$
$769$	−29.1902	+	16.8530i	−1.05263	+	0.607734i	−0.129242	+	0.991613i	$0.541255\pi$
$770$	0.840556	−	0.0187104i	0.0302915	−	0.000674276i
$771$	−24.3989	+	19.2688i	−0.878704	+	0.693950i
$772$		−	1.29203i		−	0.0465013i
$773$	27.1549	+	15.6779i	0.976694	+	0.563895i	0.901270	−	0.433257i	$-0.142636\pi$
$773$	27.1549	+	15.6779i	0.976694	+	0.563895i	0.0754237	+	0.997152i	$0.475969\pi$
$774$	1.48055	+	4.96662i	0.0532172	+	0.178521i
$775$	3.11536	+	17.7168i	0.111907	+	0.636406i
$776$	−2.01118	+	3.48347i	−0.0721972	+	0.125049i
$777$	12.3275	−	25.9480i	0.442248	−	0.930881i
$778$	−29.9470	+	17.2899i	−1.07365	+	0.619873i
$779$	39.8645	+	23.0158i	1.42830	+	0.824627i
$780$	−4.52669	+	1.06891i	−0.162082	+	0.0382732i
$781$	0.884714	+	1.53237i	0.0316576	+	0.0548325i
$782$	0.388803	−	0.224476i	0.0139036	−	0.00802724i
$783$	−19.1824	−	1.71233i	−0.685522	−	0.0611937i
$784$	2.68750	+	6.46354i	0.0959822	+	0.230841i
$785$	14.2768	−	1.24567i	0.509559	−	0.0444600i
$786$	10.0582	+	12.7360i	0.358764	+	0.454280i
$787$	−33.3758			−1.18972			−0.594859	−	0.803830i	$-0.702792\pi$
$787$	−33.3758			−1.18972			−0.594859	+	0.803830i	$0.702792\pi$
$788$	0.983884			0.0350494
$789$	−27.2232	+	3.97127i	−0.969172	+	0.141381i
$790$	−18.7342	+	1.63460i	−0.666534	+	0.0581563i
$791$	2.77107	−	42.7197i	0.0985280	−	1.51894i
$792$	0.414737	+	0.0988096i	0.0147370	+	0.00351105i
$793$	12.7994	−	7.38973i	0.454519	−	0.262417i
$794$	−14.6731	−	25.4146i	−0.520729	−	0.901930i
$795$	−7.11808	−	7.55717i	−0.252452	−	0.268025i
$796$	−20.6241	−	11.9073i	−0.731000	−	0.422043i
$797$	4.60415	−	2.65821i	0.163087	−	0.0941585i	−0.416235	−	0.909257i	$-0.636651\pi$
$797$	4.60415	−	2.65821i	0.163087	−	0.0941585i	0.579322	+	0.815099i	$0.303317\pi$
$798$	−11.4110	+	24.0187i	−0.403943	+	0.850254i
$799$	−0.263047	+	0.455611i	−0.00930594	+	0.0161184i
$800$	4.92445	−	0.865927i	0.174105	−	0.0306151i
$801$	−1.04042	+	4.36699i	−0.0367614	+	0.154300i
$802$	−22.8472	−	13.1908i	−0.806762	−	0.465785i
$803$		−	1.14255i		−	0.0403197i
$804$	−11.7118	−	4.66076i	−0.413042	−	0.164372i
$805$	21.7714	−	13.2243i	0.767340	−	0.466095i
$806$	3.74176	−	2.16031i	0.131798	−	0.0760936i
$807$	−11.2790	−	14.2818i	−0.397038	−	0.502743i
$808$	1.68050	+	2.91071i	0.0591197	+	0.102398i
$809$	13.1171	+	7.57314i	0.461171	+	0.266257i	0.712537	−	0.701635i	$-0.247546\pi$
$809$	13.1171	+	7.57314i	0.461171	+	0.266257i	−0.251365	+	0.967892i	$0.580880\pi$
$810$	2.86519	+	19.9196i	0.100673	+	0.699904i
$811$		−	25.5538i		−	0.897316i	−0.893704	−	0.448658i	$-0.851902\pi$
$811$		−	25.5538i		−	0.897316i	0.893704	−	0.448658i	$-0.148098\pi$
$812$	−4.34302	−	8.79183i	−0.152410	−	0.308533i
$813$	−3.16798	−	21.7166i	−0.111106	−	0.761635i
$814$	0.445449	−	0.771540i	0.0156130	−	0.0270425i
$815$	2.05369	−	1.43729i	0.0719375	−	0.0503460i
$816$	−0.141730	+	0.111930i	−0.00496154	+	0.00391834i
$817$	−10.0244			−0.350711
$818$		−	12.8464i		−	0.449164i
$819$	6.98403	−	6.48723i	0.244042	−	0.226682i
$820$	10.1707	+	14.5326i	0.355178	+	0.507500i
$821$		−	30.2878i		−	1.05705i	−0.848918	−	0.528525i	$-0.822745\pi$
$821$		−	30.2878i		−	1.05705i	0.848918	−	0.528525i	$-0.177255\pi$
$822$	32.7726	−	4.78081i	1.14308	−	0.166750i
$823$			44.3997i			1.54768i	0.633383	+	0.773838i	$0.281666\pi$
$823$			44.3997i			1.54768i	−0.633383	+	0.773838i	$0.718334\pi$
$824$	−9.57498	+	16.5843i	−0.333560	+	0.577743i
$825$	0.385891	+	1.16869i	0.0134350	+	0.0406886i
$826$	−21.5901	−	14.4050i	−0.751214	−	0.501213i
$827$	8.05224			0.280004			0.140002	−	0.990151i	$-0.455289\pi$
$827$	8.05224			0.280004			0.140002	+	0.990151i	$0.455289\pi$
$828$	12.3789	−	3.69014i	0.430195	−	0.128241i
$829$	9.26932	+	5.35164i	0.321937	+	0.185870i	0.652255	−	0.757999i	$-0.273823\pi$
$829$	9.26932	+	5.35164i	0.321937	+	0.185870i	−0.330319	+	0.943869i	$0.607156\pi$
$830$	−4.75948	−	2.22074i	−0.165204	−	0.0770832i
$831$	3.72333	+	25.5235i	0.129161	+	0.885402i
$832$	−0.600465	−	1.04004i	−0.0208174	−	0.0360568i
$833$	0.0942925	−	0.723763i	0.00326704	−	0.0250769i
$834$	−0.275511	−	1.88864i	−0.00954017	−	0.0653982i
$835$	1.56339	−	1.09415i	0.0541034	−	0.0378647i
$836$	−0.412329	+	0.714175i	−0.0142607	+	0.0247002i
$837$	−7.87067	−	16.9567i	−0.272050	−	0.586109i
$838$	−5.13440	−	8.89304i	−0.177365	−	0.307205i
$839$	24.9171	−	43.1577i	0.860234	−	1.48997i	−0.0114693	−	0.999934i	$-0.503651\pi$
$839$	24.9171	−	43.1577i	0.860234	−	1.48997i	0.871703	−	0.490034i	$-0.163016\pi$
$840$	−7.89828	+	6.52818i	−0.272517	+	0.225244i
$841$	−7.63157	−	13.2183i	−0.263157	−	0.455802i
$842$	3.18306	−	5.51323i	0.109696	−	0.189998i
$843$	9.29359	−	7.33954i	0.320088	−	0.252787i
$844$	−11.2221	−	19.4372i	−0.386280	−	0.669056i
$845$	10.9276	−	23.4200i	0.375922	−	0.805673i
$846$	−10.4004	+	10.9978i	−0.357573	+	0.378113i
$847$	26.0453	−	12.8660i	0.894928	−	0.442080i
$848$	1.34026	−	2.32140i	0.0460248	−	0.0797172i
$849$	−7.44777	+	18.7151i	−0.255607	+	0.642301i
$850$	−0.489818	−	0.178540i	−0.0168006	−	0.00612387i
$851$		−	26.9920i		−	0.925272i
$852$	−20.0369	−	7.97379i	−0.686453	−	0.273177i
$853$	9.14863	−	15.8459i	0.313243	−	0.542553i	−0.665819	−	0.746113i	$-0.731918\pi$
$853$	9.14863	−	15.8459i	0.313243	−	0.542553i	0.979062	+	0.203560i	$0.0652512\pi$
$854$	18.0713	−	27.0851i	0.618388	−	0.926835i
$855$	−38.5070	−	5.69594i	−1.31691	−	0.194797i
$856$	−7.15043	−	12.3849i	−0.244397	−	0.423307i
$857$	−12.0422	+	6.95257i	−0.411354	+	0.237495i	−0.691371	−	0.722500i	$-0.742993\pi$
$857$	−12.0422	+	6.95257i	−0.411354	+	0.237495i	0.280017	+	0.959995i	$0.409660\pi$
$858$	0.231989	−	0.183211i	0.00791996	−	0.00625473i
$859$	33.8907	+	19.5668i	1.15634	+	0.667611i	0.950423	−	0.310960i	$-0.100650\pi$
$859$	33.8907	+	19.5668i	1.15634	+	0.667611i	0.205912	+	0.978570i	$0.433984\pi$
$860$	−3.50057	−	1.63335i	−0.119369	−	0.0556966i
$861$	−32.8351	−	15.5995i	−1.11902	−	0.531629i
$862$	−3.37653	−	1.94944i	−0.115005	−	0.0663982i
$863$	0.517393	+	0.896150i	0.0176122	+	0.0305053i	0.874697	−	0.484670i	$-0.161060\pi$
$863$	0.517393	+	0.896150i	0.0176122	+	0.0305053i	−0.857085	+	0.515175i	$0.827727\pi$
$864$	−4.71318	+	2.18768i	−0.160346	+	0.0744264i
$865$	−4.89446	−	56.0958i	−0.166417	−	1.90731i
$866$	20.9340			0.711367
$867$	−29.1178	+	4.24766i	−0.988894	+	0.144258i
$868$	5.28296	−	7.91805i	0.179315	−	0.268756i
$869$	1.03507	−	0.597596i	0.0351122	−	0.0202720i
$870$	10.4492	−	9.84209i	0.354262	−	0.333678i
$871$	−7.56891	+	4.36991i	−0.256463	+	0.148069i
$872$	8.89823	−	15.4122i	0.301332	−	0.521923i
$873$	11.5642	−	3.44729i	0.391389	−	0.116673i
$874$			24.9851i			0.845132i
$875$	−28.0103	−	9.50917i	−0.946920	−	0.321469i
$876$	8.63038	+	10.9281i	0.291593	+	0.369226i
$877$	1.34680	+	0.777575i	0.0454782	+	0.0262568i	0.522567	−	0.852598i	$-0.324975\pi$
$877$	1.34680	+	0.777575i	0.0454782	+	0.0262568i	−0.477089	+	0.878855i	$0.658308\pi$
$878$		−	16.4017i		−	0.553531i
$879$	2.48350	+	17.0245i	0.0837664	+	0.574222i
$880$	−0.260352	+	0.182209i	−0.00877646	+	0.00614227i
$881$	−11.9598			−0.402937			−0.201469	−	0.979495i	$-0.564571\pi$
$881$	−11.9598			−0.402937			−0.201469	+	0.979495i	$0.564571\pi$
$882$	7.46527	−	19.6283i	0.251369	−	0.660919i
$883$		−	10.7656i		−	0.362292i	−0.983456	−	0.181146i	$-0.942019\pi$
$883$		−	10.7656i		−	0.362292i	0.983456	−	0.181146i	$-0.0579806\pi$
$884$			0.125219i			0.00421158i
$885$	10.9266	−	36.3883i	0.367293	−	1.22318i
$886$	26.3852			0.886429
$887$	−23.0704	−	13.3197i	−0.774629	−	0.447232i	0.0598943	−	0.998205i	$-0.480924\pi$
$887$	−23.0704	−	13.3197i	−0.774629	−	0.447232i	−0.834524	+	0.550972i	$0.814257\pi$
$888$	1.56735	+	10.7443i	0.0525968	+	0.360553i
$889$	16.2342	−	24.3317i	0.544477	−	0.816058i
$890$	−1.91858	−	2.74139i	−0.0643110	−	0.0918915i
$891$	−0.700327	−	1.07027i	−0.0234618	−	0.0358553i
$892$	−8.99621	+	15.5819i	−0.301215	+	0.521720i
$893$	−14.6391	−	25.3557i	−0.489879	−	0.848495i
$894$	−19.0146	+	15.0167i	−0.635944	+	0.502232i
$895$	−32.7814	−	15.2956i	−1.09576	−	0.511276i
$896$	−2.20085	−	1.46842i	−0.0735253	−	0.0490564i
$897$	3.31159	−	8.32150i	0.110571	−	0.277847i
$898$			32.5310i			1.08557i
$899$	−6.66717	+	11.5479i	−0.222362	+	0.385143i
$900$	−12.5187	−	8.26325i	−0.417291	−	0.275442i
$901$	−0.242049	+	0.139747i	−0.00806382	+	0.00465565i
$902$	−0.976322	−	0.563680i	−0.0325080	−	0.0187685i
$903$	7.89117	−	0.633285i	0.262602	−	0.0210744i
$904$	8.09024	+	14.0127i	0.269077	+	0.466056i
$905$	3.30888	+	37.9233i	0.109991	+	1.26061i
$906$	8.42100	−	1.22844i	0.279769	−	0.0408122i
$907$	−6.54032	+	3.77606i	−0.217168	+	0.125382i	−0.604638	−	0.796500i	$-0.706682\pi$
$907$	−6.54032	+	3.77606i	−0.217168	+	0.125382i	0.387470	+	0.921882i	$0.373349\pi$
$908$	17.5341	−	10.1233i	0.581890	−	0.335954i
$909$	2.33683	−	9.80846i	0.0775078	−	0.325326i
$910$	0.158111	+	7.10304i	0.00524132	+	0.235464i
$911$	21.2685	+	12.2794i	0.704656	+	0.406834i	0.809079	−	0.587699i	$-0.199966\pi$
$911$	21.2685	+	12.2794i	0.704656	+	0.406834i	−0.104423	+	0.994533i	$0.533300\pi$
$912$	−1.45081	−	9.94539i	−0.0480413	−	0.329325i
$913$	0.333800			0.0110472
$914$		−	35.0085i		−	1.15798i
$915$	45.6499	+	13.7076i	1.50914	+	0.453160i
$916$	−0.650116	−	0.375345i	−0.0214804	−	0.0124017i
$917$	22.2260	−	10.9793i	0.733967	−	0.362568i
$918$	0.539649	+	0.0481722i	0.0178111	+	0.00158992i
$919$	−17.1584	−	29.7192i	−0.566003	−	0.980345i	−0.996956	−	0.0779709i	$-0.975156\pi$
$919$	−17.1584	−	29.7192i	−0.566003	−	0.980345i	0.430953	−	0.902374i	$-0.358177\pi$
$920$	−4.07097	+	8.72488i	−0.134216	+	0.287651i
$921$	16.2173	−	40.7517i	0.534380	−	1.34281i
$922$	−5.08610	+	8.80939i	−0.167502	+	0.290122i
$923$	−12.9492	+	7.47620i	−0.426227	+	0.246082i
$924$	0.279465	−	0.588243i	0.00919374	−	0.0193518i
$925$	−24.0206	+	20.1364i	−0.789791	+	0.662081i
$926$	−27.5356	+	15.8977i	−0.904876	+	0.522430i
$927$	55.0557	−	16.4121i	1.80827	−	0.539044i
$928$	3.20977	+	1.85316i	0.105366	+	0.0608331i
$929$	22.0312			0.722821			0.361411	−	0.932407i	$-0.382295\pi$
$929$	22.0312			0.722821			0.361411	+	0.932407i	$0.382295\pi$
$930$	13.3453	+	4.00727i	0.437608	+	0.131404i
$931$	32.2587	+	24.6840i	1.05724	+	0.808984i
$932$	−9.57787	−	16.5894i	−0.313734	−	0.543403i
$933$	4.68971	−	11.7845i	0.153534	−	0.385808i
$934$	−19.5141	+	11.2665i	−0.638522	+	0.368651i
$935$	0.0330089	−	0.00288009i	0.00107951	−	9.41890e-5i
$936$	−0.834982	+	3.50470i	−0.0272922	+	0.114555i
$937$	36.9235			1.20624			0.603120	−	0.797651i	$-0.293924\pi$
$937$	36.9235			1.20624			0.603120	+	0.797651i	$0.293924\pi$
$938$	−10.6865	+	16.0168i	−0.348926	+	0.522967i
$939$	−5.43535	+	13.6582i	−0.177376	+	0.445718i
$940$	−0.980671	−	11.2395i	−0.0319860	−	0.366593i
$941$	15.7517			0.513492			0.256746	−	0.966479i	$-0.417350\pi$
$941$	15.7517			0.513492			0.256746	+	0.966479i	$0.417350\pi$
$942$	4.10453	−	10.3140i	0.133733	−	0.336050i
$943$	−34.1561			−1.11228
$944$	9.80986			0.319284
$945$	30.6723	+	2.05116i	0.997771	+	0.0667243i
$946$	0.245508			0.00798216
$947$	19.2361			0.625090			0.312545	−	0.949903i	$-0.398818\pi$
$947$	19.2361			0.625090			0.312545	+	0.949903i	$0.398818\pi$
$948$	−5.38603	+	13.5343i	−0.174930	+	0.439573i
$949$	9.65503			0.313415
$950$	22.2346	−	18.6392i	0.721385	−	0.604737i
$951$	1.43681	−	3.61048i	0.0465917	−	0.117078i
$952$	0.122180	+	0.247337i	0.00395989	+	0.00801623i
$953$	21.0241			0.681036			0.340518	−	0.940238i	$-0.389398\pi$
$953$	21.0241			0.681036			0.340518	+	0.940238i	$0.389398\pi$
$954$	−7.70644	+	2.29729i	−0.249505	+	0.0743775i
$955$	−0.771213	−	8.83893i	−0.0249559	−	0.286021i
$956$	1.15565	−	0.667217i	0.0373765	−	0.0215794i
$957$	−0.337330	+	0.847659i	−0.0109043	+	0.0274009i
$958$	4.81018	+	8.33147i	0.155410	+	0.269178i
$959$	3.27476	−	50.4848i	0.105748	−	1.63024i
$960$	1.11384	−	3.70936i	0.0359489	−	0.119719i
$961$	18.0564			0.582465
$962$	6.51984	+	3.76423i	0.210208	+	0.121364i
$963$	−9.94308	+	41.7345i	−0.320411	+	1.34487i
$964$	−17.1287	+	9.88925i	−0.551678	+	0.318511i
$965$	−0.251123	−	2.87814i	−0.00808394	−	0.0926506i
$966$	−1.57841	−	19.6681i	−0.0507845	−	0.632810i
$967$	−31.4041	+	18.1311i	−1.00989	+	0.583058i	−0.911158	−	0.412056i	$-0.864811\pi$
$967$	−31.4041	+	18.1311i	−1.00989	+	0.583058i	−0.0987282	+	0.995114i	$0.531477\pi$
$968$	−5.48990	+	9.50879i	−0.176452	+	0.305624i
$969$	−0.387488	+	0.973698i	−0.0124479	+	0.0312797i
$970$	−3.80306	+	8.15069i	−0.122109	+	0.261703i
$971$	−19.6361	−	34.0108i	−0.630153	−	1.09146i	−0.987520	−	0.157493i	$-0.949659\pi$
$971$	−19.6361	−	34.0108i	−0.630153	−	1.09146i	0.357367	−	0.933964i	$-0.383675\pi$
$972$	14.7828	+	4.94674i	0.474157	+	0.158667i
$973$	−2.90937	−	0.188720i	−0.0932700	−	0.00605008i
$974$	−8.50444	−	4.91004i	−0.272500	−	0.157328i
$975$	−9.87593	+	3.26094i	−0.316283	+	0.104434i
$976$			12.3067i			0.393927i
$977$	37.2951			1.19317			0.596587	−	0.802548i	$-0.296523\pi$
$977$	37.2951			1.19317			0.596587	+	0.802548i	$0.296523\pi$
$978$	−0.280280	−	1.92133i	−0.00896235	−	0.0614373i
$979$	0.184170	+	0.106331i	0.00588611	+	0.00339835i
$980$	7.24296	+	13.8759i	0.231368	+	0.443248i
$981$	−51.1644	+	15.2521i	−1.63355	+	0.486962i
$982$	24.7333	−	14.2798i	0.789271	−	0.455686i
$983$	35.5207	−	20.5079i	1.13293	−	0.654100i	0.188264	−	0.982119i	$-0.439714\pi$
$983$	35.5207	−	20.5079i	1.13293	−	0.654100i	0.944671	+	0.328018i	$0.106381\pi$
$984$	13.5960	−	1.98336i	0.433424	−	0.0632271i
$985$	2.19170	−	0.191230i	0.0698335	−	0.00609311i
$986$	−0.193227	−	0.334678i	−0.00615359	−	0.0106583i
$987$	13.1256	+	19.0350i	0.417794	+	0.605891i
$988$	−6.03507	−	3.48435i	−0.192001	−	0.110852i
$989$	6.44174	−	3.71914i	0.204835	−	0.118262i
$990$	0.943075	+	0.139499i	0.0299729	+	0.00443358i
$991$	9.52837	−	16.5036i	0.302679	−	0.524255i	−0.674063	−	0.738674i	$-0.735452\pi$
$991$	9.52837	−	16.5036i	0.302679	−	0.524255i	0.976742	+	0.214419i	$0.0687858\pi$
$992$			3.59772i			0.114228i
$993$	−3.23121	+	8.11952i	−0.102539	+	0.257665i
$994$	−18.2828	+	27.4021i	−0.579895	+	0.869142i
$995$	−48.2566	−	22.5162i	−1.52984	−	0.713812i
$996$	−3.19268	+	2.52139i	−0.101164	+	0.0798934i
$997$	17.8254	+	30.8745i	0.564536	+	0.977806i	0.997093	+	0.0761986i	$0.0242783\pi$
$997$	17.8254	+	30.8745i	0.564536	+	0.977806i	−0.432556	+	0.901607i	$0.642388\pi$
$998$	−10.3032	+	17.8456i	−0.326141	+	0.564892i
$999$	18.7307	−	26.6500i	0.592612	−	0.843169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.b.479.17	yes	48
3.2	odd	2		1890.2.bi.a.899.1		48
5.4	even	2		630.2.bi.a.479.8	yes	48
7.5	odd	6		630.2.r.a.299.9	yes	48
9.4	even	3		1890.2.r.a.1529.8		48
9.5	odd	6		630.2.r.b.59.16	yes	48
15.14	odd	2		1890.2.bi.b.899.15		48
21.5	even	6		1890.2.r.b.89.8		48
35.19	odd	6		630.2.r.b.299.16	yes	48
45.4	even	6		1890.2.r.b.1529.8		48
45.14	odd	6		630.2.r.a.59.9	✓	48
63.5	even	6		630.2.bi.a.509.8	yes	48
63.40	odd	6		1890.2.bi.b.719.15		48
105.89	even	6		1890.2.r.a.89.8		48
315.194	even	6	inner	630.2.bi.b.509.17	yes	48
315.229	odd	6		1890.2.bi.a.719.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.9	✓	48	45.14	odd	6
630.2.r.a.299.9	yes	48	7.5	odd	6
630.2.r.b.59.16	yes	48	9.5	odd	6
630.2.r.b.299.16	yes	48	35.19	odd	6
630.2.bi.a.479.8	yes	48	5.4	even	2
630.2.bi.a.509.8	yes	48	63.5	even	6
630.2.bi.b.479.17	yes	48	1.1	even	1	trivial
630.2.bi.b.509.17	yes	48	315.194	even	6	inner
1890.2.r.a.89.8		48	105.89	even	6
1890.2.r.a.1529.8		48	9.4	even	3
1890.2.r.b.89.8		48	21.5	even	6
1890.2.r.b.1529.8		48	45.4	even	6
1890.2.bi.a.719.1		48	315.229	odd	6
1890.2.bi.a.899.1		48	3.2	odd	2
1890.2.bi.b.719.15		48	63.40	odd	6
1890.2.bi.b.899.15		48	15.14	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} +(0.640430 - 1.60930i) q^{3} +1.00000 q^{4} +(2.22760 - 0.194363i) q^{5} +(0.640430 - 1.60930i) q^{6} +(-2.20085 - 1.46842i) q^{7} +1.00000 q^{8} +(-2.17970 - 2.06129i) q^{9} +(2.22760 - 0.194363i) q^{10} +(-0.123075 + 0.0710575i) q^{11} +(0.640430 - 1.60930i) q^{12} +(-0.600465 - 1.04004i) q^{13} +(-2.20085 - 1.46842i) q^{14} +(1.11384 - 3.70936i) q^{15} +1.00000 q^{16} +(-0.0902992 - 0.0521342i) q^{17} +(-2.17970 - 2.06129i) q^{18} +(5.02533 - 2.90137i) q^{19} +(2.22760 - 0.194363i) q^{20} +(-3.77262 + 2.60142i) q^{21} +(-0.123075 + 0.0710575i) q^{22} +(-2.15286 + 3.72887i) q^{23} +(0.640430 - 1.60930i) q^{24} +(4.92445 - 0.865927i) q^{25} +(-0.600465 - 1.04004i) q^{26} +(-4.71318 + 2.18768i) q^{27} +(-2.20085 - 1.46842i) q^{28} +(3.20977 + 1.85316i) q^{29} +(1.11384 - 3.70936i) q^{30} +3.59772i q^{31} +1.00000 q^{32} +(0.0355319 + 0.243572i) q^{33} +(-0.0902992 - 0.0521342i) q^{34} +(-5.18803 - 2.84329i) q^{35} +(-2.17970 - 2.06129i) q^{36} +(-5.42899 + 3.13443i) q^{37} +(5.02533 - 2.90137i) q^{38} +(-2.05829 + 0.300259i) q^{39} +(2.22760 - 0.194363i) q^{40} +(3.96636 + 6.86994i) q^{41} +(-3.77262 + 2.60142i) q^{42} +(-1.49609 - 0.863766i) q^{43} +(-0.123075 + 0.0710575i) q^{44} +(-5.25615 - 4.16808i) q^{45} +(-2.15286 + 3.72887i) q^{46} -5.04557i q^{47} +(0.640430 - 1.60930i) q^{48} +(2.68750 + 6.46354i) q^{49} +(4.92445 - 0.865927i) q^{50} +(-0.141730 + 0.111930i) q^{51} +(-0.600465 - 1.04004i) q^{52} +(1.34026 - 2.32140i) q^{53} +(-4.71318 + 2.18768i) q^{54} +(-0.260352 + 0.182209i) q^{55} +(-2.20085 - 1.46842i) q^{56} +(-1.45081 - 9.94539i) q^{57} +(3.20977 + 1.85316i) q^{58} +9.80986 q^{59} +(1.11384 - 3.70936i) q^{60} +12.3067i q^{61} +3.59772i q^{62} +(1.77036 + 7.73730i) q^{63} +1.00000 q^{64} +(-1.53974 - 2.20008i) q^{65} +(0.0355319 + 0.243572i) q^{66} -7.27754i q^{67} +(-0.0902992 - 0.0521342i) q^{68} +(4.62211 + 5.85268i) q^{69} +(-5.18803 - 2.84329i) q^{70} -12.4507i q^{71} +(-2.17970 - 2.06129i) q^{72} +(-4.01981 + 6.96252i) q^{73} +(-5.42899 + 3.13443i) q^{74} +(1.76023 - 8.47948i) q^{75} +(5.02533 - 2.90137i) q^{76} +(0.375212 + 0.0243387i) q^{77} +(-2.05829 + 0.300259i) q^{78} -8.41003 q^{79} +(2.22760 - 0.194363i) q^{80} +(0.502177 + 8.98598i) q^{81} +(3.96636 + 6.86994i) q^{82} +(-2.03412 - 1.17440i) q^{83} +(-3.77262 + 2.60142i) q^{84} +(-0.211284 - 0.0985837i) q^{85} +(-1.49609 - 0.863766i) q^{86} +(5.03793 - 3.97867i) q^{87} +(-0.123075 + 0.0710575i) q^{88} +(-0.748203 - 1.29593i) q^{89} +(-5.25615 - 4.16808i) q^{90} +(-0.205672 + 3.17070i) q^{91} +(-2.15286 + 3.72887i) q^{92} +(5.78982 + 2.30409i) q^{93} -5.04557i q^{94} +(10.6305 - 7.43985i) q^{95} +(0.640430 - 1.60930i) q^{96} +(-2.01118 + 3.48347i) q^{97} +(2.68750 + 6.46354i) q^{98} +(0.414737 + 0.0988096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39}+ \cdots - 26 q^{99}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * 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 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * 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 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more