LMFDB - Embedded newform 630.2.r.a.59.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(59,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.59"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [48,-24] 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			59.9
Character	$\chi$	$=$	630.59
Dual form			630.2.r.a.299.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.07348 + 1.35928i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.28213 - 1.83198i) q^{5} +(-0.640430 - 1.60930i) q^{6} +(-2.37211 + 1.17179i) q^{7} +1.00000 q^{8} +(-0.695279 - 2.91832i) q^{9} +(0.945479 + 2.02634i) q^{10} +0.142115i q^{11} +(1.71391 + 0.250022i) q^{12} +(0.600465 - 1.04004i) q^{13} +(0.171260 - 2.64020i) q^{14} +(1.11384 + 3.70936i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0902992 - 0.0521342i) q^{17} +(2.87498 + 0.857030i) q^{18} +(5.02533 - 2.90137i) q^{19} +(-2.22760 - 0.194363i) q^{20} +(0.953633 - 4.48225i) q^{21} +(-0.123075 - 0.0710575i) q^{22} +4.30573 q^{23} +(-1.07348 + 1.35928i) q^{24} +(-1.71231 - 4.69766i) 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} +(-3.76932 - 0.890070i) q^{30} +(3.11572 - 1.79886i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.193174 - 0.152558i) q^{33} +(0.0902992 - 0.0521342i) q^{34} +(-0.894657 + 5.84804i) q^{35} +(-2.17970 + 2.06129i) q^{36} +(5.42899 - 3.13443i) q^{37} +5.80275i q^{38} +(0.769112 + 1.93266i) q^{39} +(1.28213 - 1.83198i) q^{40} +(-3.96636 + 6.86994i) q^{41} +(3.40493 + 3.06700i) q^{42} +(-1.49609 + 0.863766i) q^{43} +(0.123075 - 0.0710575i) q^{44} +(-6.23774 - 2.46791i) q^{45} +(-2.15286 + 3.72887i) q^{46} +(4.36959 + 2.52279i) q^{47} +(-0.640430 - 1.60930i) q^{48} +(4.25384 - 5.55921i) q^{49} +(4.92445 + 0.865927i) q^{50} +(0.167799 - 0.0667767i) q^{51} -1.20093 q^{52} +(1.34026 - 2.32140i) q^{53} +(-4.25118 + 2.98789i) q^{54} +(0.260352 + 0.182209i) q^{55} +(-2.37211 + 1.17179i) q^{56} +(-1.45081 + 9.94539i) q^{57} +3.70633i q^{58} +(4.90493 + 8.49559i) q^{59} +(2.65548 - 2.81929i) q^{60} +(-10.6579 - 6.15333i) q^{61} +3.59772i q^{62} +(5.06892 + 6.10786i) q^{63} +1.00000 q^{64} +(-1.13546 - 2.43350i) q^{65} +(0.228706 - 0.0910147i) q^{66} +(6.30254 - 3.63877i) q^{67} +0.104268i q^{68} +(-4.62211 + 5.85268i) q^{69} +(-4.61722 - 3.69882i) q^{70} +12.4507i q^{71} +(-0.695279 - 2.91832i) q^{72} +(4.01981 - 6.96252i) q^{73} +6.26885i q^{74} +(8.22356 + 2.71534i) q^{75} +(-5.02533 - 2.90137i) q^{76} +(-0.166528 - 0.337113i) q^{77} +(-2.05829 - 0.300259i) q^{78} +(4.20501 - 7.28330i) q^{79} +(0.945479 + 2.02634i) q^{80} +(-8.03317 + 4.05809i) q^{81} +(-3.96636 - 6.86994i) q^{82} +(2.03412 - 1.17440i) q^{83} +(-4.35856 + 1.41526i) q^{84} +(-0.211284 + 0.0985837i) q^{85} -1.72753i q^{86} +(-0.926663 + 6.35231i) q^{87} +0.142115i 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} +(-0.899509 + 6.16617i) q^{93} +(-4.36959 + 2.52279i) q^{94} +(1.12784 - 12.9262i) q^{95} +(1.71391 + 0.250022i) 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 - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{14} - 4 q^{15} - 24 q^{16} - 3 q^{18} + 5 q^{21} + 6 q^{22} - 6 q^{23} + 3 q^{24} - 3 q^{28} - 3 q^{29} + 5 q^{30} - 24 q^{32}+ \cdots - 26 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^14 - 4 * q^15 - 24 * q^16 - 3 * q^18 + 5 * q^21 + 6 * q^22 - 6 * q^23 + 3 * q^24 - 3 * q^28 - 3 * q^29 + 5 * q^30 - 24 * q^32 + 24 * q^33 + 18 * q^35 + 3 * q^41 + 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 + 42 * q^55 - 22 * q^57 - q^60 - 9 * q^61 - 10 * q^63 + 48 * q^64 - 33 * q^65 - 24 * q^66 - 33 * q^67 + 42 * q^69 - 6 * q^70 + 3 * q^72 + 18 * q^73 + 9 * q^75 + 6 * q^77 - 18 * q^78 - 37 * q^81 + 3 * q^82 - 9 * q^83 - 13 * q^84 - 33 * q^85 - 18 * q^87 + 33 * q^89 + 39 * q^90 + 3 * q^92 - 32 * q^93 + 33 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 26 * q^99

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.07348	+	1.35928i	−0.619774	+	0.784780i
$3$	−1.07348	+	1.35928i	−0.619774	+	0.784780i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.28213	−	1.83198i	0.573384	−	0.819287i
$5$	1.28213	−	1.83198i	0.573384	−	0.819287i
$6$	−0.640430	−	1.60930i	−0.261454	−	0.656994i
$7$	−2.37211	+	1.17179i	−0.896574	+	0.442893i
$7$	−2.37211	+	1.17179i	−0.896574	+	0.442893i
$8$	1.00000			0.353553
$9$	−0.695279	−	2.91832i	−0.231760	−	0.972773i
$10$	0.945479	+	2.02634i	0.298987	+	0.640786i
$11$			0.142115i			0.0428493i	0.999770	+	0.0214246i	$0.00682020\pi$
$11$			0.142115i			0.0428493i	−0.999770	+	0.0214246i	$0.993180\pi$
$12$	1.71391	+	0.250022i	0.494763	+	0.0721751i
$13$	0.600465	−	1.04004i	0.166539	−	0.288454i	−0.770662	−	0.637245i	$-0.780074\pi$
$13$	0.600465	−	1.04004i	0.166539	−	0.288454i	0.937201	+	0.348790i	$0.113407\pi$
$14$	0.171260	−	2.64020i	0.0457712	−	0.705624i
$15$	1.11384	+	3.70936i	0.287591	+	0.957753i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−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	$0.670692\pi$
$18$	2.87498	+	0.857030i	0.677639	+	0.202004i
$19$	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
$21$	0.953633	−	4.48225i	0.208100	−	0.978108i
$22$	−0.123075	−	0.0710575i	−0.0262397	−	0.0151495i
$23$	4.30573			0.897806			0.448903	−	0.893581i	$-0.351815\pi$
$23$	4.30573			0.897806			0.448903	+	0.893581i	$0.351815\pi$
$24$	−1.07348	+	1.35928i	−0.219123	+	0.277462i
$25$	−1.71231	−	4.69766i	−0.342462	−	0.939532i
$26$	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	−0.171442	−	0.985194i	$-0.554843\pi$
$29$	3.20977	−	1.85316i	0.596040	−	0.344124i	0.767482	+	0.641070i	$0.221509\pi$
$30$	−3.76932	−	0.890070i	−0.688181	−	0.162504i
$31$	3.11572	−	1.79886i	0.559599	−	0.323085i	−0.193385	−	0.981123i	$-0.561947\pi$
$31$	3.11572	−	1.79886i	0.559599	−	0.323085i	0.752985	+	0.658038i	$0.228613\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.193174	−	0.152558i	−0.0336273	−	0.0265569i
$34$	0.0902992	−	0.0521342i	0.0154862	−	0.00894095i
$35$	−0.894657	+	5.84804i	−0.151225	+	0.988499i
$36$	−2.17970	+	2.06129i	−0.363283	+	0.343548i
$37$	5.42899	−	3.13443i	0.892520	−	0.515296i	0.0177539	−	0.999842i	$-0.494348\pi$
$37$	5.42899	−	3.13443i	0.892520	−	0.515296i	0.874766	+	0.484546i	$0.161015\pi$
$38$			5.80275i			0.941330i
$39$	0.769112	+	1.93266i	0.123156	+	0.309473i
$40$	1.28213	−	1.83198i	0.202722	−	0.289662i
$41$	−3.96636	+	6.86994i	−0.619442	+	1.07290i	0.370146	+	0.928974i	$0.379308\pi$
$41$	−3.96636	+	6.86994i	−0.619442	+	1.07290i	−0.989588	+	0.143931i	$0.954026\pi$
$42$	3.40493	+	3.06700i	0.525392	+	0.473248i
$43$	−1.49609	+	0.863766i	−0.228151	+	0.131723i	−0.609719	−	0.792618i	$-0.708718\pi$
$43$	−1.49609	+	0.863766i	−0.228151	+	0.131723i	0.381568	+	0.924341i	$0.375384\pi$
$44$	0.123075	−	0.0710575i	0.0185543	−	0.0107123i
$45$	−6.23774	−	2.46791i	−0.929867	−	0.367895i
$46$	−2.15286	+	3.72887i	−0.317422	+	0.549792i
$47$	4.36959	+	2.52279i	0.637371	+	0.367986i	0.783601	−	0.621264i	$-0.213381\pi$
$47$	4.36959	+	2.52279i	0.637371	+	0.367986i	−0.146230	+	0.989251i	$0.546714\pi$
$48$	−0.640430	−	1.60930i	−0.0924381	−	0.232283i
$49$	4.25384	−	5.55921i	0.607691	−	0.794174i
$50$	4.92445	+	0.865927i	0.696422	+	0.122461i
$51$	0.167799	−	0.0667767i	0.0234966	−	0.00935060i
$52$	−1.20093			−0.166539
$53$	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	$0.107730\pi$
$54$	−4.25118	+	2.98789i	−0.578512	+	0.406601i
$55$	0.260352	+	0.182209i	0.0351059	+	0.0245691i
$56$	−2.37211	+	1.17179i	−0.316987	+	0.156586i
$57$	−1.45081	+	9.94539i	−0.192165	+	1.31730i
$58$			3.70633i			0.486665i
$59$	4.90493	+	8.49559i	0.638567	+	1.10603i	0.985747	+	0.168233i	$0.0538060\pi$
$59$	4.90493	+	8.49559i	0.638567	+	1.10603i	−0.347180	+	0.937799i	$0.612861\pi$
$60$	2.65548	−	2.81929i	0.342821	−	0.363969i
$61$	−10.6579	−	6.15333i	−1.36460	−	0.787853i	−0.374370	−	0.927280i	$-0.622141\pi$
$61$	−10.6579	−	6.15333i	−1.36460	−	0.787853i	−0.990232	+	0.139426i	$0.955474\pi$
$62$			3.59772i			0.456911i
$63$	5.06892	+	6.10786i	0.638624	+	0.769519i
$64$	1.00000			0.125000
$65$	−1.13546	−	2.43350i	−0.140836	−	0.301838i
$66$	0.228706	−	0.0910147i	0.0281517	−	0.0112031i
$67$	6.30254	−	3.63877i	0.769977	−	0.444547i	−0.0628891	−	0.998021i	$-0.520031\pi$
$67$	6.30254	−	3.63877i	0.769977	−	0.444547i	0.832867	+	0.553474i	$0.186698\pi$
$68$			0.104268i			0.0126444i
$69$	−4.62211	+	5.85268i	−0.556437	+	0.704580i
$70$	−4.61722	−	3.69882i	−0.551864	−	0.442093i
$71$			12.4507i			1.47762i	0.673912	+	0.738812i	$0.264613\pi$
$71$			12.4507i			1.47762i	−0.673912	+	0.738812i	$0.735387\pi$
$72$	−0.695279	−	2.91832i	−0.0819394	−	0.343927i
$73$	4.01981	−	6.96252i	0.470483	−	0.814901i	−0.528947	−	0.848655i	$-0.677413\pi$
$73$	4.01981	−	6.96252i	0.470483	−	0.814901i	0.999430	+	0.0337541i	$0.0107463\pi$
$74$			6.26885i			0.728739i
$75$	8.22356	+	2.71534i	0.949575	+	0.313541i
$76$	−5.02533	−	2.90137i	−0.576445	−	0.332811i
$77$	−0.166528	−	0.337113i	−0.0189777	−	0.0384176i
$78$	−2.05829	−	0.300259i	−0.233055	−	0.0339976i
$79$	4.20501	−	7.28330i	0.473101	−	0.819435i	−0.526425	−	0.850222i	$-0.676468\pi$
$79$	4.20501	−	7.28330i	0.473101	−	0.819435i	0.999526	+	0.0307865i	$0.00980120\pi$
$80$	0.945479	+	2.02634i	0.105708	+	0.226552i
$81$	−8.03317	+	4.05809i	−0.892575	+	0.450899i
$82$	−3.96636	−	6.86994i	−0.438011	−	0.758658i
$83$	2.03412	−	1.17440i	0.223274	−	0.128907i	−0.384191	−	0.923253i	$-0.625520\pi$
$83$	2.03412	−	1.17440i	0.223274	−	0.128907i	0.607465	+	0.794346i	$0.292186\pi$
$84$	−4.35856	+	1.41526i	−0.475558	+	0.154417i
$85$	−0.211284	+	0.0985837i	−0.0229169	+	0.0106929i
$86$		−	1.72753i		−	0.186285i
$87$	−0.926663	+	6.35231i	−0.0993487	+	0.681040i
$88$			0.142115i			0.0151495i
$89$	0.748203	+	1.29593i	0.0793094	+	0.137368i	0.902952	−	0.429741i	$-0.141395\pi$
$89$	0.748203	+	1.29593i	0.0793094	+	0.137368i	−0.823643	+	0.567109i	$0.808062\pi$
$90$	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
$93$	−0.899509	+	6.16617i	−0.0932748	+	0.639402i
$94$	−4.36959	+	2.52279i	−0.450689	+	0.260206i
$95$	1.12784	−	12.9262i	0.115714	−	1.32620i
$96$	1.71391	+	0.250022i	0.174925	+	0.0255178i
$97$	2.01118	+	3.48347i	0.204204	+	0.353693i	0.949879	−	0.312618i	$-0.101206\pi$
$97$	2.01118	+	3.48347i	0.204204	+	0.353693i	−0.745674	+	0.666310i	$0.767873\pi$
$98$	2.68750	+	6.46354i	0.271479	+	0.652916i
$99$	0.414737	−	0.0988096i	0.0416826	−	0.00993074i
$100$	−3.21214	+	3.83173i	−0.321214	+	0.383173i
$101$	3.36100			0.334432			0.167216	−	0.985920i	$-0.446522\pi$
$101$	3.36100			0.334432			0.167216	+	0.985920i	$0.446522\pi$
$102$	−0.0260694	+	0.178707i	−0.00258126	+	0.0176946i
$103$	−19.1500			−1.88690			−0.943450	−	0.331514i	$-0.892441\pi$
$103$	−19.1500			−1.88690			−0.943450	+	0.331514i	$0.892441\pi$
$104$	0.600465	−	1.04004i	0.0588805	−	0.101984i
$105$	−6.98872	−	7.49385i	−0.682030	−	0.731325i
$106$	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	$-0.409610\pi$
$108$	−0.462002	−	5.17557i	−0.0444561	−	0.498020i
$109$	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	$-0.158124\pi$
$110$	−0.287974	+	0.134367i	−0.0274572	+	0.0128114i
$111$	−1.56735	+	10.7443i	−0.148766	+	1.01980i
$112$	0.171260	−	2.64020i	0.0161826	−	0.249476i
$113$	8.09024	−	14.0127i	0.761066	−	1.31820i	−0.181236	−	0.983440i	$-0.558010\pi$
$113$	8.09024	−	14.0127i	0.761066	−	1.31820i	0.942302	−	0.334765i	$-0.108657\pi$
$114$	−7.88756	−	6.22914i	−0.738737	−	0.583412i
$115$	5.52048	−	7.88801i	0.514787	−	0.735561i
$116$	−3.20977	−	1.85316i	−0.298020	−	0.172062i
$117$	−3.45265	−	1.02923i	−0.319198	−	0.0951527i
$118$	−9.80986			−0.903071
$119$	0.275290	+	0.0178570i	0.0252358	+	0.00163695i
$120$	1.11384	+	3.70936i	0.101679	+	0.338617i
$121$	10.9798			0.998164
$122$	10.6579	−	6.15333i	0.964919	−	0.557096i
$123$	−5.08035	−	12.7661i	−0.458080	−	1.15108i
$124$	−3.11572	−	1.79886i	−0.279800	−	0.161542i
$125$	−10.8014	−	2.88607i	−0.966108	−	0.258138i
$126$	−7.82403	+	1.33588i	−0.697020	+	0.119010i
$127$		−	11.0556i		−	0.981023i	−0.871435	−	0.490511i	$-0.836810\pi$
$127$		−	11.0556i		−	0.981023i	0.871435	−	0.490511i	$-0.163190\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	0.431921	−	2.96083i	0.0380285	−	0.260687i
$130$	2.67520	+	0.233416i	0.234631	+	0.0204720i
$131$	−9.36971			−0.818635			−0.409318	−	0.912392i	$-0.634233\pi$
$131$	−9.36971			−0.818635			−0.409318	+	0.912392i	$0.634233\pi$
$132$	−0.0355319	+	0.243572i	−0.00309265	+	0.0212003i
$133$	−8.52086	+	12.7710i	−0.738852	+	1.10739i
$134$			7.27754i			0.628684i
$135$	10.0507	−	5.82957i	0.865024	−	0.501730i
$136$	−0.0902992	−	0.0521342i	−0.00774309	−	0.00447047i
$137$	−19.1216			−1.63367			−0.816833	−	0.576875i	$-0.804272\pi$
$137$	−19.1216			−1.63367			−0.816833	+	0.576875i	$0.804272\pi$
$138$	−2.75752	−	6.92921i	−0.234735	−	0.589853i
$139$	−0.954315	−	0.550974i	−0.0809439	−	0.0467330i	0.458982	−	0.888446i	$-0.348214\pi$
$139$	−0.954315	−	0.550974i	−0.0809439	−	0.0467330i	−0.539926	+	0.841713i	$0.681548\pi$
$140$	5.51188	−	2.14922i	0.465839	−	0.181643i
$141$	−8.11985	+	3.23134i	−0.683814	+	0.272128i
$142$	−10.7826	−	6.22534i	−0.904856	−	0.522419i
$143$	0.147805	+	0.0853352i	0.0123601	+	0.00713608i
$144$	2.87498	+	0.857030i	0.239582	+	0.0714192i
$145$	0.720372	−	8.25623i	0.0598236	−	0.685643i
$146$	4.01981	+	6.96252i	0.332682	+	0.576222i
$147$	2.99011	+	11.7499i	0.246620	+	0.969112i
$148$	−5.42899	−	3.13443i	−0.446260	−	0.257648i
$149$		−	13.9888i		−	1.14600i	−0.819554	−	0.573002i	$-0.805779\pi$
$149$		−	13.9888i		−	1.14600i	0.819554	−	0.573002i	$-0.194221\pi$
$150$	−6.46333	+	5.76414i	−0.527729	+	0.470640i
$151$	−4.91333			−0.399841			−0.199920	−	0.979812i	$-0.564068\pi$
$151$	−4.91333			−0.399841			−0.199920	+	0.979812i	$0.564068\pi$
$152$	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
$156$	1.28918	−	1.63240i	0.103217	−	0.130697i
$157$	3.20451	+	5.55037i	0.255748	+	0.442968i	0.965098	−	0.261888i	$-0.0843450\pi$
$157$	3.20451	+	5.55037i	0.255748	+	0.442968i	−0.709351	+	0.704856i	$0.751012\pi$
$158$	4.20501	+	7.28330i	0.334533	+	0.579428i
$159$	1.71669	+	4.31377i	0.136142	+	0.342104i
$160$	−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	−0.537539	−	0.843239i	$-0.680646\pi$
$163$	−0.970831	+	0.560510i	−0.0760414	+	0.0439025i	0.461497	+	0.887142i	$0.347312\pi$
$164$	7.93272			0.619442
$165$	−0.527156	+	0.158293i	−0.0410390	+	0.0123231i
$166$			2.34880i			0.182302i
$167$	−0.739056	−	0.426694i	−0.0571899	−	0.0330186i	0.471132	−	0.882062i	$-0.343845\pi$
$167$	−0.739056	−	0.426694i	−0.0571899	−	0.0330186i	−0.528322	+	0.849044i	$0.677179\pi$
$168$	0.953633	−	4.48225i	0.0735744	−	0.345813i
$169$	5.77888	+	10.0093i	0.444529	+	0.769948i
$170$	0.0202659	−	0.232269i	0.00155432	−	0.0178142i
$171$	−11.9611	−	12.6482i	−0.914691	−	0.967236i
$172$	1.49609	+	0.863766i	0.114076	+	0.0658615i
$173$	21.8083	+	12.5911i	1.65806	+	0.957280i	0.973610	+	0.228218i	$0.0732899\pi$
$173$	21.8083	+	12.5911i	1.65806	+	0.957280i	0.684448	+	0.729062i	$0.260043\pi$
$174$	−5.03793	−	3.97867i	−0.381925	−	0.301622i
$175$	9.56644	+	9.13692i	0.723155	+	0.690686i
$176$	−0.123075	−	0.0710575i	−0.00927714	−	0.00535616i
$177$	−16.8132	−	2.45268i	−1.26376	−	0.184355i
$178$	−1.49641			−0.112160
$179$	14.0102	+	8.08881i	1.04717	+	0.604586i	0.921857	−	0.387531i	$-0.126672\pi$
$179$	14.0102	+	8.08881i	1.04717	+	0.604586i	0.125317	+	0.992117i	$0.460005\pi$
$180$	0.981594	+	6.63600i	0.0731637	+	0.494618i
$181$			17.0243i			1.26540i	0.774396	+	0.632701i	$0.218054\pi$
$181$			17.0243i			1.26540i	−0.774396	+	0.632701i	$0.781946\pi$
$182$	−2.64307	−	1.76347i	−0.195917	−	0.130717i
$183$	19.8051	−	7.88155i	1.46404	−	0.582621i
$184$	4.30573			0.317422
$185$	1.21843	−	13.9645i	0.0895809	−	1.02669i
$186$	−4.89031	−	3.86208i	−0.358575	−	0.283182i
$187$	0.00740906	−	0.0128329i	0.000541804	−	0.000938432i
$188$		−	5.04557i		−	0.367986i
$189$	−13.7437	+	0.333408i	−0.999706	+	0.0242519i
$190$	10.6305	+	7.43985i	0.771220	+	0.539744i
$191$	−3.43631	−	1.98395i	−0.248643	−	0.143554i	0.370500	−	0.928832i	$-0.379186\pi$
$191$	−3.43631	−	1.98395i	−0.248643	−	0.143554i	−0.619143	+	0.785279i	$0.712520\pi$
$192$	−1.07348	+	1.35928i	−0.0774718	+	0.0980975i
$193$	1.11893	−	0.646017i	0.0805426	−	0.0465013i	−0.459188	−	0.888339i	$-0.651859\pi$
$193$	1.11893	−	0.646017i	0.0805426	−	0.0465013i	0.539730	+	0.841838i	$0.318526\pi$
$194$	−4.02236			−0.288789
$195$	4.52669	+	1.06891i	0.324163	+	0.0765465i
$196$	−6.94134	−	0.904324i	−0.495810	−	0.0645945i
$197$	0.983884			0.0700988			0.0350494	−	0.999386i	$-0.488841\pi$
$197$	0.983884			0.0700988			0.0350494	+	0.999386i	$0.488841\pi$
$198$	−0.121797	+	0.408578i	−0.00865573	+	0.0290363i
$199$	−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	$0.986523\pi$
$200$	−1.71231	−	4.69766i	−0.121079	−	0.332175i
$201$	−1.81955	+	12.4731i	−0.128341	+	0.879782i
$202$	−1.68050	+	2.91071i	−0.118239	+	0.204797i
$203$	−5.44244	+	8.15708i	−0.381984	+	0.572515i
$204$	−0.141730	−	0.111930i	−0.00992308	−	0.00783668i
$205$	7.50023	+	16.0744i	0.523839	+	1.12269i
$206$	9.57498	−	16.5843i	0.667120	−	1.15549i
$207$	−2.99368	−	12.5655i	−0.208075	−	0.873361i
$208$	0.600465	+	1.04004i	0.0416348	+	0.0721136i
$209$	0.412329	+	0.714175i	0.0285214	+	0.0494005i
$210$	9.98422	−	2.30549i	0.688977	−	0.159094i
$211$	−11.2221	+	19.4372i	−0.772559	+	1.33811i	0.163597	+	0.986527i	$0.447690\pi$
$211$	−11.2221	+	19.4372i	−0.772559	+	1.33811i	−0.936156	+	0.351585i	$0.885643\pi$
$212$	−2.68052			−0.184099
$213$	−16.9239	−	13.3656i	−1.15961	−	0.915793i
$214$	14.3009			0.977586
$215$	−0.335768	+	3.84826i	−0.0228992	+	0.262449i
$216$	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
$219$	5.14881	+	12.9382i	0.347925	+	0.874280i
$220$	0.0276219	−	0.316576i	0.00186227	−	0.0213436i
$221$	−0.108443	+	0.0626096i	−0.00729467	+	0.00421158i
$222$	−8.52112	−	6.72949i	−0.571900	−	0.451654i
$223$	8.99621	+	15.5819i	0.602430	+	1.04344i	0.992452	+	0.122634i	$0.0391343\pi$
$223$	8.99621	+	15.5819i	0.602430	+	1.04344i	−0.390021	+	0.920806i	$0.627532\pi$
$224$	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
$227$			20.2467i			1.34382i	0.740634	+	0.671909i	$0.234525\pi$
$227$			20.2467i			1.34382i	−0.740634	+	0.671909i	$0.765475\pi$
$228$	9.33837	−	3.71625i	0.618449	−	0.246115i
$229$			0.750689i			0.0496069i	0.999692	+	0.0248035i	$0.00789600\pi$
$229$			0.750689i			0.0496069i	−0.999692	+	0.0248035i	$0.992104\pi$
$230$	4.07097	+	8.72488i	0.268432	+	0.575302i
$231$	0.636995	+	0.135526i	0.0419112	+	0.00891693i
$232$	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	$-0.382575\pi$
$234$	2.61767	−	2.47547i	0.171122	−	0.161826i
$235$	10.2241	−	4.77049i	0.666945	−	0.311192i
$236$	4.90493	−	8.49559i	0.319284	−	0.553016i
$237$	5.38603	+	13.5343i	0.349860	+	0.879145i
$238$	−0.153110	+	0.229480i	−0.00992462	+	0.0148749i
$239$	1.15565	+	0.667217i	0.0747531	+	0.0431587i	0.536911	−	0.843639i	$-0.319591\pi$
$239$	1.15565	+	0.667217i	0.0747531	+	0.0431587i	−0.462158	+	0.886798i	$0.652925\pi$
$240$	−3.76932	−	0.890070i	−0.243309	−	0.0574538i
$241$		−	19.7785i		−	1.27405i	−0.770845	−	0.637023i	$-0.780166\pi$
$241$		−	19.7785i		−	1.27405i	0.770845	−	0.637023i	$-0.219834\pi$
$242$	−5.48990	+	9.50879i	−0.352904	+	0.611248i
$243$	3.10738	−	15.2756i	0.199338	−	0.979931i
$244$			12.3067i			0.787853i
$245$	−4.73042	−	14.9206i	−0.302216	−	0.953240i
$246$	13.5960	+	1.98336i	0.866848	+	0.126454i
$247$		−	6.96870i		−	0.443408i
$248$	3.11572	−	1.79886i	0.197848	−	0.114228i
$249$	−0.587252	+	4.02564i	−0.0372156	+	0.255114i
$250$	7.90012	−	7.91127i	0.499647	−	0.500352i
$251$	−28.8281			−1.81961			−0.909805	−	0.415035i	$-0.863769\pi$
$251$	−28.8281			−1.81961			−0.909805	+	0.415035i	$0.863769\pi$
$252$	2.75510	−	7.44375i	0.173555	−	0.468912i
$253$			0.611908i			0.0384703i
$254$	9.57440	+	5.52778i	0.600751	+	0.346844i
$255$	0.0928063	−	0.393021i	0.00581176	−	0.0246119i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$			17.9499i			1.11968i	0.828600	+	0.559841i	$0.189138\pi$
$257$			17.9499i			1.11968i	−0.828600	+	0.559841i	$0.810862\pi$
$258$	2.34820	+	1.85447i	0.146192	+	0.115454i
$259$	−9.20529	+	13.7968i	−0.571989	+	0.857293i
$260$	−1.53974	+	2.20008i	−0.0954909	+	0.136443i
$261$	−7.63981	−	8.07868i	−0.472892	−	0.500058i
$262$	4.68485	−	8.11440i	0.289431	−	0.501310i
$263$	15.8837			0.979430			0.489715	−	0.871883i	$-0.337101\pi$
$263$	15.8837			0.979430			0.489715	+	0.871883i	$0.337101\pi$
$264$	−0.193174	−	0.152558i	−0.0118890	−	0.00938928i
$265$	−2.53438	−	5.43166i	−0.155686	−	0.333664i
$266$	−6.79958	−	13.7648i	−0.416909	−	0.843973i
$267$	−2.56471	−	0.374134i	−0.156957	−	0.0228966i
$268$	−6.30254	−	3.63877i	−0.384989	−	0.222273i
$269$	−5.25345	+	9.09924i	−0.320308	+	0.554790i	−0.980552	−	0.196261i	$-0.937120\pi$
$269$	−5.25345	+	9.09924i	−0.320308	+	0.554790i	0.660243	+	0.751052i	$0.270453\pi$
$270$	0.0232189	+	11.6189i	0.00141306	+	0.707105i
$271$	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
$273$	−4.08908	−	3.68325i	−0.247483	−	0.222920i
$274$	9.56078	−	16.5598i	0.577588	−	1.00041i
$275$	0.667608	−	0.243345i	0.0402583	−	0.0146742i
$276$	7.37963	+	1.07653i	0.444201	+	0.0647993i
$277$			14.8920i			0.894773i	0.894341	+	0.447387i	$0.147645\pi$
$277$			14.8920i			0.894773i	−0.894341	+	0.447387i	$0.852355\pi$
$278$	0.954315	−	0.550974i	0.0572360	−	0.0330452i
$279$	−7.41594	−	7.84195i	−0.443981	−	0.469485i
$280$	−0.894657	+	5.84804i	−0.0534660	+	0.349487i
$281$	5.92114	−	3.41857i	0.353226	−	0.203935i	−0.312879	−	0.949793i	$-0.601294\pi$
$281$	5.92114	−	3.41857i	0.353226	−	0.203935i	0.666105	+	0.745858i	$0.267960\pi$
$282$	1.26150	−	8.64766i	0.0751215	−	0.514961i
$283$	−5.81467	−	10.0713i	−0.345646	−	0.598677i	0.639825	−	0.768521i	$-0.279007\pi$
$283$	−5.81467	−	10.0713i	−0.345646	−	0.598677i	−0.985471	+	0.169844i	$0.945674\pi$
$284$	10.7826	−	6.22534i	0.639830	−	0.369406i
$285$	16.3596	+	15.4091i	0.969062	+	0.912757i
$286$	−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
$290$	6.78992	+	4.75198i	0.398718	+	0.279046i
$291$	−6.89397	−	1.00568i	−0.404132	−	0.0589539i
$292$	−8.03962			−0.470483
$293$	8.60234	+	4.96657i	0.502554	+	0.290150i	0.729768	−	0.683695i	$-0.239628\pi$
$293$	8.60234	+	4.96657i	0.502554	+	0.290150i	−0.227213	+	0.973845i	$0.572962\pi$
$294$	−11.6707	−	3.28542i	−0.680651	−	0.191609i
$295$	21.8525	+	1.90667i	1.27230	+	0.111011i
$296$	5.42899	−	3.13443i	0.315553	−	0.182185i
$297$	−0.310902	+	0.669813i	−0.0180404	+	0.0388665i
$298$	12.1146	+	6.99438i	0.701781	+	0.405174i
$299$	2.58544	−	4.47811i	0.149520	−	0.258976i
$300$	−1.76023	−	8.47948i	−0.101627	−	0.489563i
$301$	2.53674	−	3.80204i	0.146215	−	0.219146i
$302$	2.45666	−	4.25506i	0.141365	−	0.244851i
$303$	−3.60796	+	4.56853i	−0.207272	+	0.262455i
$304$			5.80275i			0.332811i
$305$	−24.9375	+	11.6357i	−1.42792	+	0.666258i
$306$	−0.214927	−	0.227274i	−0.0122866	−	0.0129924i
$307$	−25.3226			−1.44524			−0.722618	−	0.691247i	$-0.757061\pi$
$307$	−25.3226			−1.44524			−0.722618	+	0.691247i	$0.757061\pi$
$308$	−0.208684	+	0.312774i	−0.0118909	+	0.0178220i
$309$	20.5571	−	26.0301i	1.16945	−	1.48080i
$310$	6.59096	+	4.61273i	0.374341	+	0.261985i
$311$	3.66138	+	6.34169i	0.207618	+	0.359604i	0.950964	−	0.309303i	$-0.100096\pi$
$311$	3.66138	+	6.34169i	0.207618	+	0.359604i	−0.743346	+	0.668907i	$0.766762\pi$
$312$	0.769112	+	1.93266i	0.0435424	+	0.109415i
$313$	−4.24352	+	7.34999i	−0.239858	+	0.415446i	−0.960673	−	0.277681i	$-0.910434\pi$
$313$	−4.24352	+	7.34999i	−0.239858	+	0.415446i	0.720815	+	0.693127i	$0.243767\pi$
$314$	−6.40902			−0.361682
$315$	17.6885	−	1.45512i	0.996633	−	0.0819870i
$316$	−8.41003			−0.473101
$317$	−1.12175	+	1.94293i	−0.0630039	+	0.109126i	−0.895807	−	0.444444i	$-0.853401\pi$
$317$	−1.12175	+	1.94293i	−0.0630039	+	0.109126i	0.832803	+	0.553570i	$0.186735\pi$
$318$	−4.59417	−	0.670189i	−0.257629	−	0.0375824i
$319$	0.263362	+	0.456157i	0.0147455	+	0.0255399i
$320$	1.28213	−	1.83198i	0.0716730	−	0.102411i
$321$	24.5104	+	3.57553i	1.36804	+	0.199566i
$322$	0.737400	−	11.3680i	0.0410937	−	0.633513i
$323$	−0.605044			−0.0336655
$324$	7.53100	+	4.92789i	0.418389	+	0.273772i
$325$	−5.91392	−	1.03992i	−0.328045	−	0.0576843i
$326$		−	1.12102i		−	0.0620875i
$327$	11.3974	+	28.6399i	0.630277	+	1.58379i
$328$	−3.96636	+	6.86994i	−0.219006	+	0.379329i
$329$	−13.3213	−	0.864106i	−0.734429	−	0.0476397i
$330$	0.126492	−	0.535677i	0.00696318	−	0.0294880i
$331$	2.52268	−	4.36942i	0.138659	−	0.240165i	−0.788330	−	0.615253i	$-0.789054\pi$
$331$	2.52268	−	4.36942i	0.138659	−	0.240165i	0.926989	+	0.375088i	$0.122387\pi$
$332$	−2.03412	−	1.17440i	−0.111637	−	0.0644536i
$333$	−12.9219	−	13.6642i	−0.708117	−	0.748794i
$334$	0.739056	−	0.426694i	0.0404394	−	0.0233477i
$335$	1.41448	−	16.2115i	0.0772815	−	0.885728i
$336$	3.40493	+	3.06700i	0.185754	+	0.167318i
$337$	30.0990	+	17.3777i	1.63960	+	0.946623i	0.980971	+	0.194155i	$0.0621965\pi$
$337$	30.0990	+	17.3777i	1.63960	+	0.946623i	0.658629	+	0.752468i	$0.271137\pi$
$338$	−11.5578			−0.628660
$339$	10.3625	+	26.0393i	0.562812	+	1.41426i
$340$	0.191018	+	0.133685i	0.0103594	+	0.00725010i
$341$	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
$345$	4.79587	+	15.9715i	0.258201	+	0.859877i
$346$	−21.8083	+	12.5911i	−1.17242	+	0.676899i
$347$	3.45072	+	5.97681i	0.185244	+	0.320852i	0.943659	−	0.330920i	$-0.107359\pi$
$347$	3.45072	+	5.97681i	0.185244	+	0.320852i	−0.758415	+	0.651772i	$0.774026\pi$
$348$	5.96460	−	2.37364i	0.319736	−	0.127241i
$349$	0.226488	−	0.130763i	0.0121237	−	0.00699959i	−0.493926	−	0.869504i	$-0.664439\pi$
$349$	0.226488	−	0.130763i	0.0121237	−	0.00699959i	0.506050	+	0.862504i	$0.331105\pi$
$350$	−12.6960	+	3.71632i	−0.678631	+	0.198646i
$351$	5.10537	−	3.58825i	0.272504	−	0.191527i
$352$	0.123075	−	0.0710575i	0.00655993	−	0.00378738i
$353$			28.5457i			1.51934i	0.650311	+	0.759668i	$0.274639\pi$
$353$			28.5457i			1.51934i	−0.650311	+	0.759668i	$0.725361\pi$
$354$	10.5307	−	13.3343i	0.559700	−	0.708712i
$355$	22.8094	+	15.9633i	1.21060	+	0.847246i
$356$	0.748203	−	1.29593i	0.0396547	−	0.0686839i
$357$	−0.319791	+	0.355027i	−0.0169251	+	0.0187900i
$358$	−14.0102	+	8.08881i	−0.740464	+	0.427507i
$359$	10.5441	−	6.08767i	0.556499	−	0.321295i	−0.195240	−	0.980755i	$-0.562549\pi$
$359$	10.5441	−	6.08767i	0.556499	−	0.321295i	0.751739	+	0.659461i	$0.229215\pi$
$360$	−6.23774	−	2.46791i	−0.328758	−	0.130070i
$361$	7.33595	−	12.7062i	0.386103	−	0.668750i
$362$	−14.7434	−	8.51213i	−0.774898	−	0.447387i
$363$	−11.7866	+	14.9246i	−0.618636	+	0.783339i
$364$	2.84874	−	1.40723i	0.149315	−	0.0737591i
$365$	−7.60130	−	16.2910i	−0.397870	−	0.852712i
$366$	−3.07694	+	21.0925i	−0.160834	+	1.10252i
$367$	22.2397			1.16090			0.580451	−	0.814295i	$-0.302876\pi$
$367$	22.2397			1.16090			0.580451	+	0.814295i	$0.302876\pi$
$368$	−2.15286	+	3.72887i	−0.112226	+	0.194381i
$369$	22.8064	+	6.79859i	1.18725	+	0.353920i
$370$	11.4844	+	8.03746i	0.597046	+	0.417847i
$371$	−0.459067	+	7.07712i	−0.0238336	+	0.367426i
$372$	5.78982	−	2.30409i	0.300188	−	0.119461i
$373$		−	3.83418i		−	0.198526i	−0.995061	−	0.0992631i	$-0.968351\pi$
$373$		−	3.83418i		−	0.198526i	0.995061	−	0.0992631i	$-0.0316485\pi$
$374$	0.00740906	+	0.0128329i	0.000383113	+	0.000663572i
$375$	15.5181	−	11.5840i	0.801351	−	0.598195i
$376$	4.36959	+	2.52279i	0.225345	+	0.130103i
$377$		−	4.45104i		−	0.229240i
$378$	6.58310	−	12.0691i	0.338598	−	0.620767i
$379$	−29.0957			−1.49454			−0.747272	−	0.664519i	$-0.768637\pi$
$379$	−29.0957			−1.49454			−0.747272	+	0.664519i	$0.768637\pi$
$380$	−11.7584	+	5.48638i	−0.603191	+	0.281445i
$381$	15.0276	+	11.8679i	0.769887	+	0.608013i
$382$	3.43631	−	1.98395i	0.175817	−	0.101508i
$383$			14.1500i			0.723032i	0.932366	+	0.361516i	$0.117741\pi$
$383$			14.1500i			0.723032i	−0.932366	+	0.361516i	$0.882259\pi$
$384$	−0.640430	−	1.60930i	−0.0326818	−	0.0821243i
$385$	−0.831095	−	0.127144i	−0.0423565	−	0.00647987i
$386$			1.29203i			0.0657628i
$387$	3.56094	+	3.76550i	0.181013	+	0.191411i
$388$	2.01118	−	3.48347i	0.102102	−	0.176846i
$389$			34.5798i			1.75327i	0.481160	+	0.876633i	$0.340216\pi$
$389$			34.5798i			1.75327i	−0.481160	+	0.876633i	$0.659784\pi$
$390$	−3.18905	+	3.38577i	−0.161484	+	0.171445i
$391$	−0.388803	−	0.224476i	−0.0196626	−	0.0113522i
$392$	4.25384	−	5.55921i	0.214851	−	0.280783i
$393$	10.0582	−	12.7360i	0.507369	−	0.642449i
$394$	−0.491942	+	0.852068i	−0.0247837	+	0.0429266i
$395$	−7.95151	−	17.0416i	−0.400084	−	0.857456i
$396$	−0.292940	−	0.309768i	−0.0147208	−	0.0155664i
$397$	14.6731	+	25.4146i	0.736422	+	1.27552i	0.954096	+	0.299500i	$0.0968197\pi$
$397$	14.6731	+	25.4146i	0.736422	+	1.27552i	−0.217674	+	0.976022i	$0.569847\pi$
$398$	20.6241	−	11.9073i	1.03379	−	0.596859i
$399$	−8.21237	−	25.2916i	−0.411133	−	1.26617i
$400$	4.92445	+	0.865927i	0.246222	+	0.0432963i
$401$		−	26.3817i		−	1.31744i	−0.752389	−	0.658719i	$-0.771099\pi$
$401$		−	26.3817i		−	1.31744i	0.752389	−	0.658719i	$-0.228901\pi$
$402$	−9.89221	−	7.81230i	−0.493379	−	0.389642i
$403$		−	4.32061i		−	0.215225i
$404$	−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
$408$	0.167799	−	0.0667767i	0.00830731	−	0.00330594i
$409$	−11.1253	+	6.42321i	−0.550112	+	0.317607i	−0.749167	−	0.662381i	$-0.769546\pi$
$409$	−11.1253	+	6.42321i	−0.550112	+	0.317607i	0.199055	+	0.979988i	$0.436213\pi$
$410$	−17.6710	−	1.54183i	−0.872707	−	0.0761454i
$411$	20.5266	−	25.9915i	1.01250	−	1.28207i
$412$	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
$415$	0.456520	−	5.23220i	0.0224097	−	0.256839i
$416$	−1.20093			−0.0588805
$417$	1.77337	−	0.705720i	0.0868421	−	0.0345593i
$418$	−0.824658			−0.0403353
$419$	5.13440	−	8.89304i	0.250832	−	0.434453i	−0.712923	−	0.701242i	$-0.752629\pi$
$419$	5.13440	−	8.89304i	0.250832	−	0.434453i	0.963755	+	0.266789i	$0.0859626\pi$
$420$	−2.99550	+	9.79934i	−0.146165	+	0.478159i
$421$	3.18306	+	5.51323i	0.155133	+	0.268698i	0.933107	−	0.359598i	$-0.117086\pi$
$421$	3.18306	+	5.51323i	0.155133	+	0.268698i	−0.777974	+	0.628296i	$0.783753\pi$
$422$	−11.2221	−	19.4372i	−0.546282	−	0.946188i
$423$	4.32421	−	14.5059i	0.210250	−	0.705302i
$424$	1.34026	−	2.32140i	0.0650888	−	0.112737i
$425$	−0.0902889	+	0.513465i	−0.00437965	+	0.0249067i
$426$	20.0369	−	7.97379i	0.970791	−	0.386331i
$427$	32.4921	+	2.10764i	1.57240	+	0.101996i
$428$	−7.15043	+	12.3849i	−0.345629	+	0.598647i
$429$	−0.274660	+	0.109302i	−0.0132607	+	0.00527717i
$430$	−3.16481	−	2.21491i	−0.152620	−	0.106813i
$431$	3.37653	+	1.94944i	0.162642	+	0.0939012i	0.579112	−	0.815248i	$-0.303400\pi$
$431$	3.37653	+	1.94944i	0.162642	+	0.0939012i	−0.416470	+	0.909149i	$0.636733\pi$
$432$	−4.25118	+	2.98789i	−0.204535	+	0.143755i
$433$	−20.9340			−1.00603			−0.503013	−	0.864279i	$-0.667775\pi$
$433$	−20.9340			−1.00603			−0.503013	+	0.864279i	$0.667775\pi$
$434$	−4.21576	−	8.53420i	−0.202363	−	0.409655i
$435$	10.4492	+	9.84209i	0.501002	+	0.471892i
$436$	−17.7965			−0.852296
$437$	21.6377	−	12.4925i	1.03507	−	0.597599i
$438$	−13.7792	−	2.01008i	−0.658395	−	0.0960454i
$439$	14.2043	+	8.20086i	0.677934	+	0.391406i	0.799076	−	0.601230i	$-0.205322\pi$
$439$	14.2043	+	8.20086i	0.677934	+	0.391406i	−0.121142	+	0.992635i	$0.538656\pi$
$440$	0.260352	+	0.182209i	0.0124118	+	0.00868649i
$441$	−19.1812	−	8.54885i	−0.913389	−	0.407088i
$442$		−	0.125219i		−	0.00595607i
$443$	−13.1926	+	22.8503i	−0.626800	+	1.08565i	0.361390	+	0.932415i	$0.382302\pi$
$443$	−13.1926	+	22.8503i	−0.626800	+	1.08565i	−0.988190	+	0.153235i	$0.951031\pi$
$444$	10.0885	−	4.01476i	0.478778	−	0.190532i
$445$	3.33340	+	0.290846i	0.158018	+	0.0137874i
$446$	−17.9924			−0.851965
$447$	19.0146	+	15.0167i	0.899361	+	0.710264i
$448$	−2.37211	+	1.17179i	−0.112072	+	0.0553617i
$449$		−	32.5310i		−	1.53523i	−0.640911	−	0.767615i	$-0.721443\pi$
$449$		−	32.5310i		−	1.53523i	0.640911	−	0.767615i	$-0.278557\pi$
$450$	−0.896813	−	14.9732i	−0.0422762	−	0.705842i
$451$	−0.976322	−	0.563680i	−0.0459732	−	0.0265426i
$452$	−16.1805			−0.761066
$453$	5.27436	−	6.67858i	0.247811	−	0.313787i
$454$	−17.5341	−	10.1233i	−0.822917	−	0.475111i
$455$	5.54497	+	4.44202i	0.259952	+	0.208245i
$456$	−1.45081	+	9.94539i	−0.0679406	+	0.465736i
$457$	−30.3183	−	17.5043i	−1.41823	−	0.818814i	−0.422085	−	0.906556i	$-0.638702\pi$
$457$	−30.3183	−	17.5043i	−1.41823	−	0.818814i	−0.996143	+	0.0877418i	$0.972035\pi$
$458$	−0.650116	−	0.375345i	−0.0303779	−	0.0175387i
$459$	−0.311543	−	0.443264i	−0.0145416	−	0.0206898i
$460$	−9.59146	−	0.836873i	−0.447204	−	0.0390194i
$461$	5.08610	+	8.80939i	0.236883	+	0.410294i	0.959818	−	0.280622i	$-0.0905407\pi$
$461$	5.08610	+	8.80939i	0.236883	+	0.410294i	−0.722935	+	0.690916i	$0.757207\pi$
$462$	−0.435866	+	0.483891i	−0.0202783	+	0.0225127i
$463$	−27.5356	−	15.8977i	−1.27969	−	0.738828i	−0.302897	−	0.953023i	$-0.597954\pi$
$463$	−27.5356	−	15.8977i	−1.27969	−	0.738828i	−0.976791	+	0.214195i	$0.931287\pi$
$464$			3.70633i			0.172062i
$465$	10.1430	+	9.55369i	0.470372	+	0.443042i
$466$	19.1557			0.887373
$467$	−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
$471$	−10.9845	−	1.60240i	−0.506138	−	0.0738345i
$472$	4.90493	+	8.49559i	0.225768	+	0.391041i
$473$	−0.122754	−	0.212616i	−0.00564424	−	0.00977611i
$474$	−14.4140	−	2.10269i	−0.662059	−	0.0965798i
$475$	−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
$479$	9.62036			0.439565			0.219783	−	0.975549i	$-0.429465\pi$
$479$	9.62036			0.439565			0.219783	+	0.975549i	$0.429465\pi$
$480$	2.65548	−	2.81929i	0.121206	−	0.128682i
$481$		−	7.52846i		−	0.343268i
$482$	17.1287	+	9.88925i	0.780191	+	0.450443i
$483$	4.10608	−	19.2993i	0.186833	−	0.878151i
$484$	−5.48990	−	9.50879i	−0.249541	−	0.432218i
$485$	8.96023	+	0.781797i	0.406863	+	0.0354996i
$486$	11.6754	+	10.3289i	0.529606	+	0.468527i
$487$	8.50444	+	4.91004i	0.385373	+	0.222495i	0.680153	−	0.733070i	$-0.261913\pi$
$487$	8.50444	+	4.91004i	0.385373	+	0.222495i	−0.294781	+	0.955565i	$0.595247\pi$
$488$	−10.6579	−	6.15333i	−0.482460	−	0.278548i
$489$	0.280280	−	1.92133i	0.0126747	−	0.0868854i
$490$	15.2868	+	3.36361i	0.690587	+	0.151953i
$491$	24.7333	+	14.2798i	1.11620	+	0.644437i	0.940428	−	0.339994i	$-0.110425\pi$
$491$	24.7333	+	14.2798i	1.11620	+	0.644437i	0.175770	+	0.984431i	$0.443758\pi$
$492$	−8.51563	+	10.7828i	−0.383914	+	0.486126i
$493$	−0.386453			−0.0174050
$494$	6.03507	+	3.48435i	0.271531	+	0.156768i
$495$	0.350728	−	0.886477i	0.0157640	−	0.0398442i
$496$			3.59772i			0.161542i
$497$	−14.5895	−	29.5344i	−0.654430	−	1.32480i
$498$	−3.19268	−	2.52139i	−0.143067	−	0.112986i
$499$	20.6063			0.922465			0.461232	−	0.887279i	$-0.347407\pi$
$499$	20.6063			0.922465			0.461232	+	0.887279i	$0.347407\pi$
$500$	2.90130	+	10.7973i	0.129750	+	0.482872i
$501$	1.37336	−	0.546536i	0.0613572	−	0.0244174i
$502$	14.4140	−	24.9658i	0.643329	−	1.11428i
$503$		−	5.19287i		−	0.231539i	−0.993276	−	0.115769i	$-0.963067\pi$
$503$		−	5.19287i		−	0.231539i	0.993276	−	0.115769i	$-0.0369333\pi$
$504$	5.06892	+	6.10786i	0.225788	+	0.272066i
$505$	4.30922	−	6.15728i	0.191758	−	0.273995i
$506$	−0.529928	−	0.305954i	−0.0235582	−	0.0136013i
$507$	−19.8090	−	2.88970i	−0.879747	−	0.128336i
$508$	−9.57440	+	5.52778i	−0.424795	+	0.245256i
$509$	−35.4416			−1.57092			−0.785461	−	0.618912i	$-0.787574\pi$
$509$	−35.4416			−1.57092			−0.785461	+	0.618912i	$0.787574\pi$
$510$	0.293963	+	0.276883i	0.0130169	+	0.0122606i
$511$	−1.37687	+	21.2262i	−0.0609090	+	0.938993i
$512$	1.00000			0.0441942
$513$	30.0326	−	2.68088i	1.32597	−	0.118364i
$514$	−15.5450	−	8.97493i	−0.685662	−	0.395867i
$515$	−24.5526	+	35.0823i	−1.08192	+	1.54591i
$516$	−2.78012	+	1.10636i	−0.122388	+	0.0487049i
$517$	−0.358526	+	0.620985i	−0.0157680	+	0.0273109i
$518$	−7.34575	−	14.8704i	−0.322754	−	0.653369i
$519$	−40.5256	+	16.1274i	−1.77888	+	0.707913i
$520$	−1.13546	−	2.43350i	−0.0497930	−	0.106716i
$521$	5.23647	−	9.06983i	0.229414	−	0.397356i	−0.728221	−	0.685343i	$-0.759652\pi$
$521$	5.23647	−	9.06983i	0.229414	−	0.397356i	0.957635	+	0.287986i	$0.0929858\pi$
$522$	10.8162	−	2.57693i	0.473414	−	0.112789i
$523$	−16.1085	−	27.9007i	−0.704375	−	1.22001i	−0.966916	−	0.255093i	$-0.917894\pi$
$523$	−16.1085	−	27.9007i	−0.704375	−	1.22001i	0.262541	−	0.964921i	$-0.415440\pi$
$524$	4.68485	+	8.11440i	0.204659	+	0.354479i
$525$	−22.6890	+	3.19515i	−0.990229	+	0.139448i
$526$	−7.94184	+	13.7557i	−0.346281	+	0.599776i
$527$	−0.375129			−0.0163409
$528$	0.228706	−	0.0910147i	0.00995314	−	0.00396091i
$529$	−4.46072			−0.193945
$530$	5.97114	+	0.520994i	0.259370	+	0.0226305i
$531$	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
$534$	1.60636	−	2.03403i	0.0695141	−	0.0880212i
$535$	−31.8566	−	2.77955i	−1.37728	−	0.120171i
$536$	6.30254	−	3.63877i	0.272228	−	0.157171i
$537$	−26.0347	+	10.3606i	−1.12348	+	0.447094i
$538$	−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	$0.653473\pi$
$542$			12.6708i			0.544258i
$543$	−23.1407	−	18.2752i	−0.993063	−	0.784264i
$544$			0.104268i			0.00447047i
$545$	−16.8262	−	36.0617i	−0.720755	−	1.54472i
$546$	5.23433	−	1.69962i	0.224009	−	0.0727372i
$547$	23.6806	−	13.6720i	1.01251	−	0.584574i	0.100585	−	0.994928i	$-0.467928\pi$
$547$	23.6806	−	13.6720i	1.01251	−	0.584574i	0.911926	+	0.410355i	$0.134595\pi$
$548$	9.56078	+	16.5598i	0.408416	+	0.707398i
$549$	−10.5472	+	35.3814i	−0.450143	+	1.51004i
$550$	−0.123061	+	0.699838i	−0.00524735	+	0.0298412i
$551$	10.7534	−	18.6255i	0.458112	−	0.793474i
$552$	−4.62211	+	5.85268i	−0.196730	+	0.249107i
$553$	−1.44030	+	22.2042i	−0.0612480	+	0.944218i
$554$	−12.8968	−	7.44600i	−0.547935	−	0.316350i
$555$	17.6737	+	16.6468i	0.750208	+	0.706619i
$556$			1.10195i			0.0467330i
$557$	−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	$0.290543\pi$
$558$	10.4993	−	2.50142i	0.444471	−	0.105894i
$559$			2.07465i			0.0877482i
$560$	−4.61722	−	3.69882i	−0.195113	−	0.156304i
$561$	0.00948997	+	0.0238468i	0.000400667	+	0.00100681i
$562$			6.83715i			0.288408i
$563$	−26.3824	+	15.2319i	−1.11189	+	0.641948i	−0.939318	−	0.343049i	$-0.888540\pi$
$563$	−26.3824	+	15.2319i	−1.11189	+	0.641948i	−0.172570	+	0.984997i	$0.555207\pi$
$564$	6.85834	+	5.41633i	0.288788	+	0.228068i
$565$	−15.2983	−	32.7872i	−0.643605	−	1.37937i
$566$	11.6293			0.488817
$567$	14.3004	−	19.0394i	0.600560	−	0.799580i
$568$			12.4507i			0.522419i
$569$	−34.3584	−	19.8368i	−1.44038	−	0.831602i	−0.442503	−	0.896767i	$-0.645909\pi$
$569$	−34.3584	−	19.8368i	−1.44038	−	0.831602i	−0.997875	+	0.0651645i	$0.979243\pi$
$570$	−21.5245	+	6.46331i	−0.901562	+	0.270718i
$571$	−1.62418	−	2.81317i	−0.0679699	−	0.117727i	0.830038	−	0.557707i	$-0.188319\pi$
$571$	−1.62418	−	2.81317i	−0.0679699	−	0.117727i	−0.898008	+	0.439980i	$0.854986\pi$
$572$		−	0.170670i		−	0.00713608i
$573$	6.38556	−	2.54117i	0.266760	−	0.106159i
$574$	17.4588	+	11.6485i	0.728714	+	0.486201i
$575$	−7.37273	−	20.2268i	−0.307464	−	0.843517i
$576$	−0.695279	−	2.91832i	−0.0289700	−	0.121597i
$577$	−0.0635247	+	0.110028i	−0.00264457	+	0.00458053i	−0.867345	−	0.497708i	$-0.834175\pi$
$577$	−0.0635247	+	0.110028i	−0.00264457	+	0.00458053i	0.864700	+	0.502289i	$0.167508\pi$
$578$	16.9891			0.706655
$579$	−0.323037	+	2.21443i	−0.0134250	+	0.0920286i
$580$	−7.51029	+	3.50426i	−0.311848	+	0.145506i
$581$	−3.44902	+	5.16937i	−0.143090	+	0.214462i
$582$	4.31793	−	5.46751i	0.178984	−	0.226636i
$583$	0.329906	+	0.190471i	0.0136633	+	0.00788851i
$584$	4.01981	−	6.96252i	0.166341	−	0.288111i
$585$	−6.31227	+	5.00558i	−0.260980	+	0.206955i
$586$	−8.60234	+	4.96657i	−0.355360	+	0.205167i
$587$	2.49693	−	1.44160i	0.103059	−	0.0595014i	−0.447584	−	0.894242i	$-0.647716\pi$
$587$	2.49693	−	1.44160i	0.103059	−	0.0595014i	0.550644	+	0.834740i	$0.314382\pi$
$588$	8.68062	−	8.46444i	0.357983	−	0.349068i
$589$	10.4383	−	18.0797i	0.430104	−	0.744962i
$590$	−12.5775	+	17.9715i	−0.517806	+	0.739874i
$591$	−1.05618	+	1.33737i	−0.0434455	+	0.0550122i
$592$			6.26885i			0.257648i
$593$	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
$595$	0.385670	−	0.481431i	0.0158109	−	0.0197367i
$596$	−12.1146	+	6.99438i	−0.496234	+	0.286501i
$597$	38.3249	−	15.2516i	1.56853	−	0.624206i
$598$	2.58544	+	4.47811i	0.105726	+	0.183124i
$599$	4.91397	−	2.83708i	0.200779	−	0.115920i	−0.396240	−	0.918147i	$-0.629685\pi$
$599$	4.91397	−	2.83708i	0.200779	−	0.115920i	0.597019	+	0.802227i	$0.296352\pi$
$600$	8.22356	+	2.71534i	0.335725	+	0.110853i
$601$	28.9131	−	16.6930i	1.17939	−	0.680921i	0.223516	−	0.974700i	$-0.428247\pi$
$601$	28.9131	−	16.6930i	1.17939	−	0.680921i	0.955873	+	0.293780i	$0.0949132\pi$
$602$	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
$605$	14.0775	−	20.1148i	0.572331	−	0.817783i
$606$	−2.15248	−	5.40886i	−0.0874386	−	0.219720i
$607$	−44.7527			−1.81646			−0.908228	−	0.418476i	$-0.862564\pi$
$607$	−44.7527			−1.81646			−0.908228	+	0.418476i	$0.862564\pi$
$608$	−5.02533	−	2.90137i	−0.203804	−	0.117666i
$609$	−5.24540	−	16.1543i	−0.212554	−	0.654603i
$610$	2.39196	−	27.4144i	0.0968475	−	1.10998i
$611$	5.24758	−	3.02969i	0.212294	−	0.122568i
$612$	0.304289	−	0.0724957i	0.0123001	−	0.00293046i
$613$	27.0024	+	15.5899i	1.09062	+	0.629668i	0.933741	−	0.357950i	$-0.116524\pi$
$613$	27.0024	+	15.5899i	1.09062	+	0.629668i	0.156877	+	0.987618i	$0.449857\pi$
$614$	12.6613	−	21.9300i	0.510968	−	0.885023i
$615$	−29.9010	−	7.06068i	−1.20572	−	0.284714i
$616$	−0.166528	−	0.337113i	−0.00670962	−	0.0135827i
$617$	0.359684	−	0.622991i	0.0144803	−	0.0250807i	−0.858694	−	0.512488i	$-0.828724\pi$
$617$	0.359684	−	0.622991i	0.0144803	−	0.0250807i	0.873175	+	0.487407i	$0.162057\pi$
$618$	12.2642	+	30.8180i	0.493338	+	1.23968i
$619$			36.6819i			1.47437i	0.675692	+	0.737184i	$0.263845\pi$
$619$			36.6819i			1.47437i	−0.675692	+	0.737184i	$0.736155\pi$
$620$	−7.29022	+	3.40157i	−0.292782	+	0.136610i
$621$	20.2937	+	9.41956i	0.814356	+	0.377994i
$622$	−7.32275			−0.293616
$623$	−3.29337	−	2.19735i	−0.131946	−	0.0880349i
$624$	−2.05829	−	0.300259i	−0.0823975	−	0.0120200i
$625$	−19.1360	+	16.0877i	−0.765440	+	0.643507i
$626$	−4.24352	−	7.34999i	−0.169605	−	0.293765i
$627$	−1.41339	−	0.206183i	−0.0564454	−	0.00823414i
$628$	3.20451	−	5.55037i	0.127874	−	0.221484i
$629$	−0.653644			−0.0260625
$630$	−7.58407	+	16.0462i	−0.302157	+	0.639298i
$631$	−15.5643			−0.619603			−0.309802	−	0.950801i	$-0.600263\pi$
$631$	−15.5643			−0.619603			−0.309802	+	0.950801i	$0.600263\pi$
$632$	4.20501	−	7.28330i	0.167266	−	0.289714i
$633$	−14.3739	−	36.1194i	−0.571311	−	1.43562i
$634$	−1.12175	−	1.94293i	−0.0445505	−	0.0771637i
$635$	−20.2536	−	14.1746i	−0.803739	−	0.562503i
$636$	2.87749	−	3.64358i	0.114100	−	0.144477i
$637$	−3.22750	−	7.76226i	−0.127878	−	0.307552i
$638$	−0.526725			−0.0208532
$639$	36.3351	−	8.65670i	1.43739	−	0.342454i
$640$	0.945479	+	2.02634i	0.0373734	+	0.0800983i
$641$			18.8456i			0.744356i	0.928161	+	0.372178i	$0.121389\pi$
$641$			18.8456i			0.744356i	−0.928161	+	0.372178i	$0.878611\pi$
$642$	−15.3517	+	19.4388i	−0.605883	+	0.767190i
$643$	5.39558	−	9.34542i	0.212781	−	0.368548i	−0.739803	−	0.672824i	$-0.765081\pi$
$643$	5.39558	−	9.34542i	0.212781	−	0.368548i	0.952584	+	0.304276i	$0.0984146\pi$
$644$	9.47627	+	6.32260i	0.373417	+	0.249145i
$645$	−4.87042	−	4.58743i	−0.191772	−	0.180630i
$646$	0.302522	−	0.523983i	0.0119026	−	0.0206159i
$647$	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	$0.205028\pi$
$648$	−8.03317	+	4.05809i	−0.315573	+	0.159417i
$649$	−1.20735	+	0.697064i	−0.0473927	+	0.0273622i
$650$	3.85756	−	4.60165i	0.151306	−	0.180491i
$651$	−5.09169	−	15.6809i	−0.199559	−	0.614582i
$652$	0.970831	+	0.560510i	0.0380207	+	0.0219513i
$653$	36.0049			1.40898			0.704490	−	0.709714i	$-0.251176\pi$
$653$	36.0049			1.40898			0.704490	+	0.709714i	$0.251176\pi$
$654$	−30.5015	−	4.44951i	−1.19270	−	0.173989i
$655$	−12.0131	+	17.1651i	−0.469392	+	0.670697i
$656$	−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	−0.401179	−	0.916000i	$-0.631400\pi$
$659$	4.91626	−	2.83840i	0.191510	−	0.110568i	0.592689	+	0.805431i	$0.298066\pi$
$660$	0.400664	+	0.377384i	0.0155958	+	0.0146897i
$661$	18.6117	−	10.7455i	0.723913	−	0.417951i	−0.0922785	−	0.995733i	$-0.529415\pi$
$661$	18.6117	−	10.7455i	0.723913	−	0.417951i	0.816191	+	0.577782i	$0.196082\pi$
$662$	2.52268	+	4.36942i	0.0980469	+	0.169822i
$663$	0.0313076	−	0.214615i	0.00121588	−	0.00833494i
$664$	2.03412	−	1.17440i	0.0789393	−	0.0455756i
$665$	12.4714	+	31.9841i	0.483621	+	1.24029i
$666$	18.2945	−	4.35860i	0.708898	−	0.168892i
$667$	13.8204	−	7.97922i	0.535128	−	0.308956i
$668$			0.853389i			0.0330186i
$669$	−30.8374	−	4.49850i	−1.19224	−	0.173922i
$670$	13.3323	+	9.33072i	0.515072	+	0.360477i
$671$	0.874481	−	1.51465i	0.0337590	−	0.0584722i
$672$	−4.35856	+	1.41526i	−0.168135	+	0.0545947i
$673$	−6.60209	+	3.81172i	−0.254492	+	0.146931i	−0.621819	−	0.783161i	$-0.713606\pi$
$673$	−6.60209	+	3.81172i	−0.254492	+	0.146931i	0.367327	+	0.930092i	$0.380273\pi$
$674$	−30.0990	+	17.3777i	−1.15937	+	0.669364i
$675$	2.20656	−	25.8869i	0.0849307	−	0.996387i
$676$	5.77888	−	10.0093i	0.222265	−	0.384974i
$677$	−26.6968	−	15.4134i	−1.02604	−	0.592386i	−0.110194	−	0.993910i	$-0.535147\pi$
$677$	−26.6968	−	15.4134i	−1.02604	−	0.592386i	−0.915848	+	0.401524i	$0.868481\pi$
$678$	−27.7319	−	4.04547i	−1.06504	−	0.155366i
$679$	−8.85263	−	5.90651i	−0.339733	−	0.226671i
$680$	−0.211284	+	0.0985837i	−0.00810236	+	0.00378051i
$681$	−27.5209	−	21.7344i	−1.05460	−	0.832864i
$682$	−0.511290			−0.0195783
$683$	−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	$0.910792\pi$
$684$	−4.97313	+	16.6828i	−0.190153	+	0.637882i
$685$	−24.5162	+	35.0303i	−0.936718	+	1.33844i
$686$	−13.9489	−	12.1831i	−0.532573	−	0.465152i
$687$	−1.02040	−	0.805850i	−0.0389305	−	0.0307451i
$688$		−	1.72753i		−	0.0658615i
$689$	−1.60956	−	2.78784i	−0.0613194	−	0.106208i
$690$	−16.2297	−	3.83240i	−0.617853	−	0.145897i
$691$	−10.3270	−	5.96230i	−0.392858	−	0.226816i	0.290540	−	0.956863i	$-0.406165\pi$
$691$	−10.3270	−	5.96230i	−0.392858	−	0.226816i	−0.683398	+	0.730046i	$0.739498\pi$
$692$		−	25.1821i		−	0.957280i
$693$	−0.868019	+	0.720370i	−0.0329733	+	0.0273646i
$694$	−6.90143			−0.261975
$695$	−2.23292	+	1.04187i	−0.0846997	+	0.0395203i
$696$	−0.926663	+	6.35231i	−0.0351251	+	0.240784i
$697$	0.716318	−	0.413567i	0.0271325	−	0.0156650i
$698$			0.261526i			0.00989892i
$699$	32.8312	+	4.78936i	1.24179	+	0.181150i
$700$	3.12958	−	12.8532i	0.118287	−	0.485807i
$701$			12.4716i			0.471046i	0.971869	+	0.235523i	$0.0756803\pi$
$701$			12.4716i			0.471046i	−0.971869	+	0.235523i	$0.924320\pi$
$702$	0.554832	+	6.21551i	0.0209408	+	0.234589i
$703$	18.1883	−	31.5030i	0.685984	−	1.18816i
$704$			0.142115i			0.00535616i
$705$	−4.49092	+	19.0184i	−0.169138	+	0.716274i
$706$	−24.7213	−	14.2729i	−0.930400	−	0.537167i
$707$	−7.97266	+	3.93837i	−0.299843	+	0.148118i
$708$	6.28253	+	15.7870i	0.236112	+	0.593312i
$709$	−14.1456	+	24.5010i	−0.531251	+	0.920153i	0.468084	+	0.883684i	$0.344944\pi$
$709$	−14.1456	+	24.5010i	−0.531251	+	0.920153i	−0.999335	+	0.0364694i	$0.988389\pi$
$710$	−25.2294	+	11.7719i	−0.946841	+	0.441790i
$711$	−24.1786	−	7.20765i	−0.906770	−	0.270308i
$712$	0.748203	+	1.29593i	0.0280401	+	0.0485669i
$713$	13.4154	−	7.74540i	0.502412	−	0.290068i
$714$	−0.147567	−	0.454461i	−0.00552254	−	0.0170078i
$715$	0.345837	−	0.161365i	0.0129336	−	0.00603472i
$716$		−	16.1776i		−	0.604586i
$717$	−2.14751	+	0.854612i	−0.0802001	+	0.0319161i
$718$			12.1753i			0.454379i
$719$	−3.47046	−	6.01101i	−0.129426	−	0.224173i	0.794028	−	0.607881i	$-0.207980\pi$
$719$	−3.47046	−	6.01101i	−0.129426	−	0.224173i	−0.923454	+	0.383708i	$0.874647\pi$
$720$	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
$723$	26.8845	+	21.2318i	0.999846	+	0.789621i
$724$	14.7434	−	8.51213i	0.547936	−	0.316351i
$725$	−14.2017	−	11.9052i	−0.527436	−	0.442149i
$726$	−7.03179	−	17.6698i	−0.260974	−	0.655788i
$727$	−8.87166	−	15.3662i	−0.329032	−	0.569899i	0.653288	−	0.757109i	$-0.273389\pi$
$727$	−8.87166	−	15.3662i	−0.329032	−	0.569899i	−0.982320	+	0.187210i	$0.940056\pi$
$728$	−0.205672	+	3.17070i	−0.00762270	+	0.117514i
$729$	17.4281	+	20.6219i	0.645485	+	0.763773i
$730$	17.9091	+	1.56260i	0.662845	+	0.0578345i
$731$	0.180127			0.00666224
$732$	−16.7282	−	13.2110i	−0.618292	−	0.488291i
$733$	18.7860			0.693877			0.346939	−	0.937888i	$-0.387221\pi$
$733$	18.7860			0.693877			0.346939	+	0.937888i	$0.387221\pi$
$734$	−11.1198	+	19.2601i	−0.410441	+	0.710904i
$735$	25.3592	+	9.58697i	0.935389	+	0.353621i
$736$	−2.15286	−	3.72887i	−0.0793556	−	0.137448i
$737$	0.517124	+	0.895685i	0.0190485	+	0.0329930i
$738$	−17.2910	+	16.3516i	−0.636489	+	0.601912i
$739$	−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	$0.910509\pi$
$740$	−12.7028	+	5.92707i	−0.466966	+	0.217883i
$741$	9.47241	+	7.48077i	0.347978	+	0.274813i
$742$	−5.89943	−	3.93612i	−0.216575	−	0.144500i
$743$	−3.04957	+	5.28201i	−0.111878	+	0.193778i	−0.916527	−	0.399972i	$-0.869020\pi$
$743$	−3.04957	+	5.28201i	−0.111878	+	0.193778i	0.804650	+	0.593750i	$0.202353\pi$
$744$	−0.899509	+	6.16617i	−0.0329776	+	0.226063i
$745$	−25.6271	−	17.9353i	−0.938906	−	0.657100i
$746$	3.32049	+	1.91709i	0.121572	+	0.0701896i
$747$	−4.84156	−	5.11968i	−0.177143	−	0.187319i
$748$	−0.0148181			−0.000541804
$749$	31.4741	+	20.9996i	1.15004	+	0.767309i
$750$	2.27299	+	19.2311i	0.0829979	+	0.702219i
$751$	53.8916			1.96653			0.983266	−	0.182178i	$-0.0583148\pi$
$751$	53.8916			1.96653			0.983266	+	0.182178i	$0.0583148\pi$
$752$	−4.36959	+	2.52279i	−0.159343	+	0.0919966i
$753$	30.9464	−	39.1854i	1.12775	−	1.42799i
$754$	3.85472	+	2.22552i	0.140381	+	0.0810487i
$755$	−6.29950	+	9.00112i	−0.229262	+	0.327584i
$756$	7.16058	+	11.7357i	0.260428	+	0.426822i
$757$			18.1765i			0.660637i	0.943870	+	0.330318i	$0.107156\pi$
$757$			18.1765i			0.660637i	−0.943870	+	0.330318i	$0.892844\pi$
$758$	14.5478	−	25.1976i	0.528401	−	0.915217i
$759$	−0.831754	−	0.656872i	−0.0301908	−	0.0238429i
$760$	1.12784	−	12.9262i	0.0409110	−	0.468884i
$761$	29.9849			1.08695			0.543476	−	0.839425i	$-0.317108\pi$
$761$	29.9849			1.08695			0.543476	+	0.839425i	$0.317108\pi$
$762$	−17.7917	+	7.08031i	−0.644526	+	0.256493i
$763$	−3.04783	+	46.9863i	−0.110339	+	1.70102i
$764$			3.96791i			0.143554i
$765$	0.434600	+	0.548050i	0.0157130	+	0.0198148i
$766$	−12.2543	−	7.07501i	−0.442765	−	0.255630i
$767$	11.7810			0.425386
$768$	1.71391	+	0.250022i	0.0618454	+	0.00902189i
$769$	29.1902	+	16.8530i	1.05263	+	0.607734i	0.923383	−	0.383879i	$-0.125412\pi$
$769$	29.1902	+	16.8530i	1.05263	+	0.607734i	0.129242	+	0.991613i	$0.458745\pi$
$770$	0.525657	−	0.656177i	0.0189434	−	0.0236470i
$771$	−24.3989	−	19.2688i	−0.878704	−	0.693950i
$772$	−1.11893	−	0.646017i	−0.0402713	−	0.0232507i
$773$	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	$0.475969\pi$
$774$	−5.04149	+	1.20112i	−0.181213	+	0.0431732i
$775$	−13.7855	−	11.5564i	−0.495190	−	0.415117i
$776$	2.01118	+	3.48347i	0.0721972	+	0.125049i
$777$	−8.87203	−	27.3232i	−0.318282	−	0.980213i
$778$	−29.9470	−	17.2899i	−1.07365	−	0.619873i
$779$			46.0316i			1.64925i
$780$	−1.33764	−	4.45469i	−0.0478952	−	0.159503i
$781$	−1.76943			−0.0633151
$782$	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
$786$	6.00064	+	15.0787i	0.214036	+	0.537839i
$787$	−16.6879	−	28.9043i	−0.594859	−	1.03033i	−0.993567	−	0.113248i	$-0.963874\pi$
$787$	−16.6879	−	28.9043i	−0.594859	−	1.03033i	0.398707	−	0.917078i	$-0.369459\pi$
$788$	−0.491942	−	0.852068i	−0.0175247	−	0.0303537i
$789$	−17.0508	+	21.5904i	−0.607026	+	0.768637i
$790$	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
$794$	−29.3462			−1.04146
$795$	10.1037	+	2.38585i	0.358343	+	0.0846175i
$796$			23.8146i			0.844086i
$797$	−4.60415	−	2.65821i	−0.163087	−	0.0941585i	0.416235	−	0.909257i	$-0.363349\pi$
$797$	−4.60415	−	2.65821i	−0.163087	−	0.0941585i	−0.579322	+	0.815099i	$0.696683\pi$
$798$	26.0094	+	5.53370i	0.920722	+	0.195891i
$799$	−0.263047	−	0.455611i	−0.00930594	−	0.0161184i
$800$	−3.21214	+	3.83173i	−0.113566	+	0.135472i
$801$	3.26171	−	3.08452i	0.115247	−	0.108986i
$802$	22.8472	+	13.1908i	0.806762	+	0.465785i
$803$	0.989478	+	0.571275i	0.0349179	+	0.0201599i
$804$	11.7118	−	4.66076i	0.413042	−	0.164372i
$805$	−3.85215	+	25.1801i	−0.135770	+	0.887481i
$806$	3.74176	+	2.16031i	0.131798	+	0.0760936i
$807$	−6.72893	−	16.9088i	−0.236870	−	0.595217i
$808$	3.36100			0.118239
$809$	−13.1171	−	7.57314i	−0.461171	−	0.266257i	0.251365	−	0.967892i	$-0.419120\pi$
$809$	−13.1171	−	7.57314i	−0.461171	−	0.266257i	−0.712537	+	0.701635i	$0.752454\pi$
$810$	−15.8183	−	12.4411i	−0.555798	−	0.437137i
$811$		−	25.5538i		−	0.897316i	−0.893704	−	0.448658i	$-0.851902\pi$
$811$		−	25.5538i		−	0.897316i	0.893704	−	0.448658i	$-0.148098\pi$
$812$	9.78546	+	0.634747i	0.343402	+	0.0222752i
$813$	−3.16798	+	21.7166i	−0.111106	+	0.761635i
$814$	−0.890898			−0.0312260
$815$	−0.217884	+	2.49719i	−0.00763216	+	0.0874727i
$816$	−0.0260694	+	0.178707i	−0.000912612	+	0.00625599i
$817$	−5.01222	+	8.68142i	−0.175355	+	0.303724i
$818$		−	12.8464i		−	0.449164i
$819$	9.39612	−	1.60431i	0.328327	−	0.0560590i
$820$	10.1707	−	14.5326i	0.355178	−	0.507500i
$821$	−26.2300	−	15.1439i	−0.915432	−	0.528525i	−0.0332572	−	0.999447i	$-0.510588\pi$
$821$	−26.2300	−	15.1439i	−0.915432	−	0.528525i	−0.882175	+	0.470922i	$0.843921\pi$
$822$	12.2460	+	30.7724i	0.427129	+	1.07331i
$823$	−38.4513	+	22.1999i	−1.34033	+	0.773838i	−0.986855	−	0.161607i	$-0.948332\pi$
$823$	−38.4513	+	22.1999i	−1.34033	+	0.773838i	−0.353472	+	0.935445i	$0.614999\pi$
$824$	−19.1500			−0.667120
$825$	−0.385891	+	1.16869i	−0.0134350	+	0.0406886i
$826$	23.2701	−	11.4951i	0.809670	−	0.399964i
$827$	8.05224			0.280004			0.140002	−	0.990151i	$-0.455289\pi$
$827$	8.05224			0.280004			0.140002	+	0.990151i	$0.455289\pi$
$828$	−9.38519	+	8.87534i	−0.326158	+	0.308440i
$829$	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	$0.607156\pi$
$830$	4.30296	+	3.01146i	0.149358	+	0.104529i
$831$	−20.2424	−	15.9863i	−0.702200	−	0.554558i
$832$	0.600465	−	1.04004i	0.0208174	−	0.0360568i
$833$	−0.673943	+	0.280222i	−0.0233508	+	0.00970911i
$834$	−0.275511	+	1.88864i	−0.00954017	+	0.0653982i
$835$	−1.72926	+	0.806861i	−0.0598435	+	0.0279226i
$836$	0.412329	−	0.714175i	0.0142607	−	0.0247002i
$837$	18.6203	−	1.66215i	0.643611	−	0.0574524i
$838$	5.13440	+	8.89304i	0.177365	+	0.307205i
$839$	−24.9171	−	43.1577i	−0.860234	−	1.48997i	−0.871703	−	0.490034i	$-0.836984\pi$
$839$	−24.9171	−	43.1577i	−0.860234	−	1.48997i	0.0114693	−	0.999934i	$-0.496349\pi$
$840$	−6.98872	−	7.49385i	−0.241134	−	0.258562i
$841$	−7.63157	+	13.2183i	−0.263157	+	0.455802i
$842$	−6.36613			−0.219391
$843$	−1.70944	+	11.7183i	−0.0588761	+	0.403598i
$844$	22.4441			0.772559
$845$	25.7461	+	2.24640i	0.885694	+	0.0772785i
$846$	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
$849$	19.9316	+	2.90759i	0.684052	+	0.0997882i
$850$	−0.399529	−	0.334925i	−0.0137037	−	0.0114878i
$851$	23.3757	−	13.4960i	0.801309	−	0.462636i
$852$	−3.11294	+	21.3394i	−0.106648	+	0.731074i
$853$	−9.14863	−	15.8459i	−0.313243	−	0.542553i	0.665819	−	0.746113i	$-0.268082\pi$
$853$	−9.14863	−	15.8459i	−0.313243	−	0.542553i	−0.979062	+	0.203560i	$0.934749\pi$
$854$	−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
$857$		−	13.9051i		−	0.474991i	−0.971389	−	0.237495i	$-0.923674\pi$
$857$		−	13.9051i		−	0.474991i	0.971389	−	0.237495i	$-0.0763265\pi$
$858$	0.0426713	−	0.292514i	0.00145678	−	0.00998625i
$859$		−	39.1336i		−	1.33522i	−0.744511	−	0.667611i	$-0.767317\pi$
$859$		−	39.1336i		−	1.33522i	0.744511	−	0.667611i	$-0.232683\pi$
$860$	3.50057	−	1.63335i	0.119369	−	0.0556966i
$861$	27.0103	+	24.3296i	0.920510	+	0.829152i
$862$	−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	$0.827727\pi$
$864$	−0.462002	−	5.17557i	−0.0157176	−	0.176077i
$865$	51.0276	−	23.8092i	1.73499	−	0.809536i
$866$	10.4670	−	18.1294i	0.355684	−	0.616062i
$867$	29.1178	+	4.24766i	0.988894	+	0.144258i
$868$	9.49871	+	0.616147i	0.322407	+	0.0209134i
$869$	1.03507	+	0.597596i	0.0351122	+	0.0202720i
$870$	−13.7481	+	4.12824i	−0.466105	+	0.139961i
$871$		−	8.73983i		−	0.296138i
$872$	8.89823	−	15.4122i	0.301332	−	0.521923i
$873$	8.76754	−	8.29125i	0.296736	−	0.280616i
$874$			24.9851i			0.845132i
$875$	29.0040	−	5.81086i	0.980515	−	0.196443i
$876$	8.63038	−	10.9281i	0.291593	−	0.369226i
$877$			1.55515i			0.0525137i	0.999655	+	0.0262568i	$0.00835877\pi$
$877$			1.55515i			0.0525137i	−0.999655	+	0.0262568i	$0.991641\pi$
$878$	−14.2043	+	8.20086i	−0.479372	+	0.276766i
$879$	−15.9854	+	6.36147i	−0.539174	+	0.214567i
$880$	−0.287974	+	0.134367i	−0.00970760	+	0.00452950i
$881$	11.9598			0.402937			0.201469	−	0.979495i	$-0.435429\pi$
$881$	11.9598			0.402937			0.201469	+	0.979495i	$0.435429\pi$
$882$	16.9941	−	12.3370i	0.572221	−	0.415407i
$883$			10.7656i			0.362292i	0.983456	+	0.181146i	$0.0579806\pi$
$883$			10.7656i			0.362292i	−0.983456	+	0.181146i	$0.942019\pi$
$884$	0.108443	+	0.0626096i	0.00364733	+	0.00210579i
$885$	−26.0499	+	27.6569i	−0.875659	+	0.929675i
$886$	−13.1926	−	22.8503i	−0.443214	−	0.767670i
$887$			26.6394i			0.894465i	0.894418	+	0.447232i	$0.147590\pi$
$887$			26.6394i			0.894465i	−0.894418	+	0.447232i	$0.852410\pi$
$888$	−1.56735	+	10.7443i	−0.0525968	+	0.360553i
$889$	12.9548	+	26.2250i	0.434488	+	0.879560i
$890$	−1.91858	+	2.74139i	−0.0643110	+	0.0918915i
$891$	−0.576716	−	1.14163i	−0.0193207	−	0.0382462i
$892$	8.99621	−	15.5819i	0.301215	−	0.521720i
$893$	29.2782			0.979758
$894$	−22.5121	+	8.95882i	−0.752918	+	0.299628i
$895$	32.7814	−	15.2956i	1.09576	−	0.511276i
$896$	0.171260	−	2.64020i	0.00572140	−	0.0882030i
$897$	3.31159	+	8.32150i	0.110571	+	0.277847i
$898$	28.1726	+	16.2655i	0.940133	+	0.542786i
$899$	6.66717	−	11.5479i	0.222362	−	0.385143i
$900$	13.4155	+	6.70992i	0.447185	+	0.223664i
$901$	−0.242049	+	0.139747i	−0.00806382	+	0.00465565i
$902$	0.976322	−	0.563680i	0.0325080	−	0.0187685i
$903$	2.44490	+	7.52955i	0.0813611	+	0.250568i
$904$	8.09024	−	14.0127i	0.269077	−	0.466056i
$905$	31.1881	+	21.8272i	1.03673	+	0.725562i
$906$	3.14664	+	7.90702i	0.104540	+	0.262693i
$907$			7.55211i			0.250764i	0.992109	+	0.125382i	$0.0400156\pi$
$907$			7.55211i			0.250764i	−0.992109	+	0.125382i	$0.959984\pi$
$908$	17.5341	−	10.1233i	0.581890	−	0.335954i
$909$	−2.33683	−	9.80846i	−0.0775078	−	0.325326i
$910$	−6.61939	+	2.58107i	−0.219431	+	0.0855617i
$911$	21.2685	−	12.2794i	0.704656	−	0.406834i	−0.104423	−	0.994533i	$-0.533300\pi$
$911$	21.2685	−	12.2794i	0.704656	−	0.406834i	0.809079	+	0.587699i	$0.199966\pi$
$912$	−7.88756	−	6.22914i	−0.261183	−	0.206267i
$913$	0.166900	+	0.289079i	0.00552359	+	0.00956713i
$914$	30.3183	−	17.5043i	1.00284	−	0.578989i
$915$	10.9538	−	46.3877i	0.362121	−	1.53353i
$916$	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	$-0.358177\pi$
$920$	5.52048	−	7.88801i	0.182005	−	0.260060i
$921$	27.1833	−	34.4205i	0.895720	−	1.13419i
$922$	−10.1722			−0.335004
$923$	12.9492	+	7.47620i	0.426227	+	0.246082i
$924$	−0.201129	−	0.619417i	−0.00661666	−	0.0203773i
$925$	−24.0206	−	20.1364i	−0.789791	−	0.662081i
$926$	27.5356	−	15.8977i	0.904876	−	0.522430i
$927$	13.3146	+	55.8857i	0.437307	+	1.83553i
$928$	−3.20977	−	1.85316i	−0.105366	−	0.0608331i
$929$	11.0156	−	19.0796i	0.361411	−	0.625982i	−0.626783	−	0.779194i	$-0.715629\pi$
$929$	11.0156	−	19.0796i	0.361411	−	0.625982i	0.988193	+	0.153213i	$0.0489619\pi$
$930$	−13.3453	+	4.00727i	−0.437608	+	0.131404i
$931$	5.24756	−	40.2789i	0.171982	−	1.32009i
$932$	−9.57787	+	16.5894i	−0.313734	+	0.543403i
$933$	−12.5505	−	1.83085i	−0.410886	−	0.0599393i
$934$		−	22.5330i		−	0.737302i
$935$	−0.0140102	−	0.0300266i	−0.000458183	−	0.000981975i
$936$	−3.45265	−	1.02923i	−0.112853	−	0.0336416i
$937$	−36.9235			−1.20624			−0.603120	−	0.797651i	$-0.706076\pi$
$937$	−36.9235			−1.20624			−0.603120	+	0.797651i	$0.706076\pi$
$938$	−8.52772	−	17.2632i	−0.278440	−	0.563662i
$939$	−5.43535	−	13.6582i	−0.177376	−	0.445718i
$940$	−9.24339	−	6.46906i	−0.301486	−	0.210997i
$941$	7.87587	+	13.6414i	0.256746	+	0.444697i	0.965368	−	0.260891i	$-0.0840162\pi$
$941$	7.87587	+	13.6414i	0.256746	+	0.444697i	−0.708622	+	0.705588i	$0.750683\pi$
$942$	6.87996	−	8.71164i	0.224161	−	0.283841i
$943$	−17.0781	+	29.5801i	−0.556138	+	0.963260i
$944$	−9.80986			−0.319284
$945$	−17.0103	+	25.6056i	−0.553346	+	0.832951i
$946$	0.245508			0.00798216
$947$	−9.61807	+	16.6590i	−0.312545	+	0.541344i	−0.978913	−	0.204279i	$-0.934515\pi$
$947$	−9.61807	+	16.6590i	−0.312545	+	0.541344i	0.666367	+	0.745624i	$0.267848\pi$
$948$	9.02800	−	11.4316i	0.293216	−	0.371280i
$949$	−4.82751	−	8.36150i	−0.156708	−	0.271426i
$950$	27.2593	−	9.93610i	0.884410	−	0.322370i
$951$	−1.43681	−	3.61048i	−0.0465917	−	0.117078i
$952$	0.275290	+	0.0178570i	0.00892220	+	0.000578750i
$953$	21.0241			0.681036			0.340518	−	0.940238i	$-0.389398\pi$
$953$	21.0241			0.681036			0.340518	+	0.940238i	$0.389398\pi$
$954$	5.84273	−	5.52533i	0.189165	−	0.178889i
$955$	−8.04034	+	3.75157i	−0.260179	+	0.121398i
$956$		−	1.33443i		−	0.0431587i
$957$	−0.902759	−	0.131693i	−0.0291821	−	0.00425702i
$958$	−4.81018	+	8.33147i	−0.155410	+	0.269178i
$959$	45.3585	−	22.4064i	1.46470	−	0.723540i
$960$	1.11384	+	3.70936i	0.0359489	+	0.119719i
$961$	−9.02820	+	15.6373i	−0.291232	+	0.504429i
$962$	6.51984	+	3.76423i	0.210208	+	0.121364i
$963$	−31.1716	+	29.4782i	−1.00449	+	0.949921i
$964$	−17.1287	+	9.88925i	−0.551678	+	0.318511i
$965$	0.251123	−	2.87814i	0.00808394	−	0.0926506i
$966$	14.6607	+	13.2056i	0.471700	+	0.424885i
$967$	−31.4041	−	18.1311i	−1.00989	−	0.583058i	−0.0987282	−	0.995114i	$-0.531477\pi$
$967$	−31.4041	−	18.1311i	−1.00989	−	0.583058i	−0.911158	+	0.412056i	$0.864811\pi$
$968$	10.9798			0.352904
$969$	0.649503	−	0.822424i	0.0208650	−	0.0264200i
$970$	−5.15717	+	7.36889i	−0.165587	+	0.236601i
$971$	19.6361	+	34.0108i	0.630153	+	1.09146i	0.987520	+	0.157493i	$0.0503412\pi$
$971$	19.6361	+	34.0108i	0.630153	+	1.09146i	−0.357367	+	0.933964i	$0.616325\pi$
$972$	−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
$975$	7.76202	−	6.92233i	0.248583	−	0.221692i
$976$	10.6579	−	6.15333i	0.341150	−	0.196963i
$977$	−18.6475	−	32.2985i	−0.596587	−	1.03332i	−0.993321	−	0.115386i	$-0.963190\pi$
$977$	−18.6475	−	32.2985i	−0.596587	−	1.03332i	0.396734	−	0.917934i	$-0.370144\pi$
$978$	1.52378	+	1.20339i	0.0487251	+	0.0384803i
$979$	−0.184170	+	0.106331i	−0.00588611	+	0.00339835i
$980$	−10.5564	+	11.5569i	−0.337211	+	0.369173i
$981$	−51.1644	−	15.2521i	−1.63355	−	0.486962i
$982$	−24.7333	+	14.2798i	−0.789271	+	0.455686i
$983$			41.0158i			1.30820i	0.756408	+	0.654100i	$0.226953\pi$
$983$			41.0158i			1.30820i	−0.756408	+	0.654100i	$0.773047\pi$
$984$	−5.08035	−	12.7661i	−0.161956	−	0.406970i
$985$	1.26146	−	1.80246i	0.0401935	−	0.0574310i
$986$	0.193227	−	0.334678i	0.00615359	−	0.0106583i
$987$	15.4748	−	17.1798i	0.492567	−	0.546839i
$988$	−6.03507	+	3.48435i	−0.192001	+	0.110852i
$989$	−6.44174	+	3.71914i	−0.204835	+	0.118262i
$990$	0.592347	+	0.746977i	0.0188260	+	0.0237405i
$991$	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	$0.0687858\pi$
$992$	−3.11572	−	1.79886i	−0.0989241	−	0.0571139i
$993$	3.23121	+	8.11952i	0.102539	+	0.257665i
$994$	32.8723	+	2.13231i	1.04265	+	0.0676327i
$995$	−48.2566	+	22.5162i	−1.52984	+	0.713812i
$996$	3.77993	−	1.50424i	0.119772	−	0.0476638i
$997$	35.6508			1.12907			0.564536	−	0.825408i	$-0.309055\pi$
$997$	35.6508			1.12907			0.564536	+	0.825408i	$0.309055\pi$
$998$	−10.3032	+	17.8456i	−0.326141	+	0.564892i
$999$	32.4449	−	2.89622i	1.02651	−	0.0916324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.r.a.59.9	✓	48
3.2	odd	2		1890.2.r.b.1529.8		48
5.4	even	2		630.2.r.b.59.16	yes	48
7.5	odd	6		630.2.bi.b.509.17	yes	48
9.2	odd	6		630.2.bi.a.479.8	yes	48
9.7	even	3		1890.2.bi.b.899.15		48
15.14	odd	2		1890.2.r.a.1529.8		48
21.5	even	6		1890.2.bi.a.719.1		48
35.19	odd	6		630.2.bi.a.509.8	yes	48
45.29	odd	6		630.2.bi.b.479.17	yes	48
45.34	even	6		1890.2.bi.a.899.1		48
63.47	even	6		630.2.r.b.299.16	yes	48
63.61	odd	6		1890.2.r.a.89.8		48
105.89	even	6		1890.2.bi.b.719.15		48
315.124	odd	6		1890.2.r.b.89.8		48
315.299	even	6	inner	630.2.r.a.299.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.9	✓	48	1.1	even	1	trivial
630.2.r.a.299.9	yes	48	315.299	even	6	inner
630.2.r.b.59.16	yes	48	5.4	even	2
630.2.r.b.299.16	yes	48	63.47	even	6
630.2.bi.a.479.8	yes	48	9.2	odd	6
630.2.bi.a.509.8	yes	48	35.19	odd	6
630.2.bi.b.479.17	yes	48	45.29	odd	6
630.2.bi.b.509.17	yes	48	7.5	odd	6
1890.2.r.a.89.8		48	63.61	odd	6
1890.2.r.a.1529.8		48	15.14	odd	2
1890.2.r.b.89.8		48	315.124	odd	6
1890.2.r.b.1529.8		48	3.2	odd	2
1890.2.bi.a.719.1		48	21.5	even	6
1890.2.bi.a.899.1		48	45.34	even	6
1890.2.bi.b.719.15		48	105.89	even	6
1890.2.bi.b.899.15		48	9.7	even	3

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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.07348 + 1.35928i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.28213 - 1.83198i) q^{5} +(-0.640430 - 1.60930i) q^{6} +(-2.37211 + 1.17179i) q^{7} +1.00000 q^{8} +(-0.695279 - 2.91832i) q^{9} +(0.945479 + 2.02634i) q^{10} +0.142115i q^{11} +(1.71391 + 0.250022i) q^{12} +(0.600465 - 1.04004i) q^{13} +(0.171260 - 2.64020i) q^{14} +(1.11384 + 3.70936i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0902992 - 0.0521342i) q^{17} +(2.87498 + 0.857030i) q^{18} +(5.02533 - 2.90137i) q^{19} +(-2.22760 - 0.194363i) q^{20} +(0.953633 - 4.48225i) q^{21} +(-0.123075 - 0.0710575i) q^{22} +4.30573 q^{23} +(-1.07348 + 1.35928i) q^{24} +(-1.71231 - 4.69766i) 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} +(-3.76932 - 0.890070i) q^{30} +(3.11572 - 1.79886i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.193174 - 0.152558i) q^{33} +(0.0902992 - 0.0521342i) q^{34} +(-0.894657 + 5.84804i) q^{35} +(-2.17970 + 2.06129i) q^{36} +(5.42899 - 3.13443i) q^{37} +5.80275i q^{38} +(0.769112 + 1.93266i) q^{39} +(1.28213 - 1.83198i) q^{40} +(-3.96636 + 6.86994i) q^{41} +(3.40493 + 3.06700i) q^{42} +(-1.49609 + 0.863766i) q^{43} +(0.123075 - 0.0710575i) q^{44} +(-6.23774 - 2.46791i) q^{45} +(-2.15286 + 3.72887i) q^{46} +(4.36959 + 2.52279i) q^{47} +(-0.640430 - 1.60930i) q^{48} +(4.25384 - 5.55921i) q^{49} +(4.92445 + 0.865927i) q^{50} +(0.167799 - 0.0667767i) q^{51} -1.20093 q^{52} +(1.34026 - 2.32140i) q^{53} +(-4.25118 + 2.98789i) q^{54} +(0.260352 + 0.182209i) q^{55} +(-2.37211 + 1.17179i) q^{56} +(-1.45081 + 9.94539i) q^{57} +3.70633i q^{58} +(4.90493 + 8.49559i) q^{59} +(2.65548 - 2.81929i) q^{60} +(-10.6579 - 6.15333i) q^{61} +3.59772i q^{62} +(5.06892 + 6.10786i) q^{63} +1.00000 q^{64} +(-1.13546 - 2.43350i) q^{65} +(0.228706 - 0.0910147i) q^{66} +(6.30254 - 3.63877i) q^{67} +0.104268i q^{68} +(-4.62211 + 5.85268i) q^{69} +(-4.61722 - 3.69882i) q^{70} +12.4507i q^{71} +(-0.695279 - 2.91832i) q^{72} +(4.01981 - 6.96252i) q^{73} +6.26885i q^{74} +(8.22356 + 2.71534i) q^{75} +(-5.02533 - 2.90137i) q^{76} +(-0.166528 - 0.337113i) q^{77} +(-2.05829 - 0.300259i) q^{78} +(4.20501 - 7.28330i) q^{79} +(0.945479 + 2.02634i) q^{80} +(-8.03317 + 4.05809i) q^{81} +(-3.96636 - 6.86994i) q^{82} +(2.03412 - 1.17440i) q^{83} +(-4.35856 + 1.41526i) q^{84} +(-0.211284 + 0.0985837i) q^{85} -1.72753i q^{86} +(-0.926663 + 6.35231i) q^{87} +0.142115i 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} +(-0.899509 + 6.16617i) q^{93} +(-4.36959 + 2.52279i) q^{94} +(1.12784 - 12.9262i) q^{95} +(1.71391 + 0.250022i) q^{96} +(2.01118 + 3.48347i) q^{97} +(2.68750 + 6.46354i) q^{98} +(0.414737 - 0.0988096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{14} - 4 q^{15} - 24 q^{16} - 3 q^{18} + 5 q^{21} + 6 q^{22} - 6 q^{23} + 3 q^{24} - 3 q^{28} - 3 q^{29} + 5 q^{30} - 24 q^{32}+ \cdots - 26 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^14 - 4 * q^15 - 24 * q^16 - 3 * q^18 + 5 * q^21 + 6 * q^22 - 6 * q^23 + 3 * q^24 - 3 * q^28 - 3 * q^29 + 5 * q^30 - 24 * q^32 + 24 * q^33 + 18 * q^35 + 3 * q^41 + 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 + 42 * q^55 - 22 * q^57 - q^60 - 9 * q^61 - 10 * q^63 + 48 * q^64 - 33 * q^65 - 24 * q^66 - 33 * q^67 + 42 * q^69 - 6 * q^70 + 3 * q^72 + 18 * q^73 + 9 * q^75 + 6 * q^77 - 18 * q^78 - 37 * q^81 + 3 * q^82 - 9 * q^83 - 13 * q^84 - 33 * q^85 - 18 * q^87 + 33 * q^89 + 39 * q^90 + 3 * q^92 - 32 * q^93 + 33 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 26 * q^99

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