LMFDB - Embedded newform 630.2.r.a.59.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(59,630)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.03057532734$
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			59.12
Character	$\chi$	$=$	630.59
Dual form			630.2.r.a.299.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.0618143 - 1.73095i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.717414 + 2.11786i) q^{5} +(1.52995 + 0.811941i) q^{6} +(-0.647443 - 2.56531i) q^{7} +1.00000 q^{8} +(-2.99236 + 0.213994i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.0618143 - 1.73095i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.717414 + 2.11786i) q^{5} +(1.52995 + 0.811941i) q^{6} +(-0.647443 - 2.56531i) q^{7} +1.00000 q^{8} +(-2.99236 + 0.213994i) q^{9} +(-1.47541 - 1.68023i) q^{10} +4.25348i q^{11} +(-1.46814 + 0.919006i) q^{12} +(1.61256 - 2.79304i) q^{13} +(2.54535 + 0.721953i) q^{14} +(3.71025 + 1.11089i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.68059 - 3.27969i) q^{17} +(1.31085 - 2.69846i) q^{18} +(2.46906 - 1.42551i) q^{19} +(2.19282 - 0.437630i) q^{20} +(-4.40040 + 1.27926i) q^{21} +(-3.68362 - 2.12674i) q^{22} -7.51895 q^{23} +(-0.0618143 - 1.73095i) q^{24} +(-3.97064 - 3.03876i) q^{25} +(1.61256 + 2.79304i) q^{26} +(0.555384 + 5.16639i) q^{27} +(-1.89790 + 1.84336i) q^{28} +(0.0500967 - 0.0289233i) q^{29} +(-2.81718 + 2.65772i) q^{30} +(-8.80647 + 5.08442i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(7.36254 - 0.262925i) q^{33} +(5.68059 - 3.27969i) q^{34} +(5.89744 + 0.469197i) q^{35} +(1.68150 + 2.48446i) q^{36} +(0.286737 - 0.165548i) q^{37} +2.85103i q^{38} +(-4.93429 - 2.61861i) q^{39} +(-0.717414 + 2.11786i) q^{40} +(-0.485297 + 0.840559i) q^{41} +(1.09232 - 4.45049i) q^{42} +(-5.85761 + 3.38189i) q^{43} +(3.68362 - 2.12674i) q^{44} +(1.69355 - 6.49091i) q^{45} +(3.75947 - 6.51160i) q^{46} +(-0.471402 - 0.272164i) q^{47} +(1.52995 + 0.811941i) q^{48} +(-6.16163 + 3.32179i) q^{49} +(4.61696 - 1.91929i) q^{50} +(-5.32583 + 10.0355i) q^{51} -3.22513 q^{52} +(0.951917 - 1.64877i) q^{53} +(-4.75191 - 2.10222i) q^{54} +(-9.00825 - 3.05150i) q^{55} +(-0.647443 - 2.56531i) q^{56} +(-2.62011 - 4.18570i) q^{57} +0.0578466i q^{58} +(-0.615269 - 1.06568i) q^{59} +(-0.893062 - 3.76861i) q^{60} +(-3.90523 - 2.25468i) q^{61} -10.1688i q^{62} +(2.48634 + 7.53778i) q^{63} +1.00000 q^{64} +(4.75838 + 5.41894i) q^{65} +(-3.45357 + 6.50761i) q^{66} +(-7.44867 + 4.30049i) q^{67} +6.55938i q^{68} +(0.464778 + 13.0149i) q^{69} +(-3.35506 + 4.87274i) q^{70} -3.35700i q^{71} +(-2.99236 + 0.213994i) q^{72} +(8.45840 - 14.6504i) q^{73} +0.331096i q^{74} +(-5.01449 + 7.06080i) q^{75} +(-2.46906 - 1.42551i) q^{76} +(10.9115 - 2.75388i) q^{77} +(4.73493 - 2.96391i) q^{78} +(1.71836 - 2.97629i) q^{79} +(-1.47541 - 1.68023i) q^{80} +(8.90841 - 1.28070i) q^{81} +(-0.485297 - 0.840559i) q^{82} +(-0.335938 + 0.193954i) q^{83} +(3.30807 + 3.17122i) q^{84} +(11.0212 - 9.67778i) q^{85} -6.76379i q^{86} +(-0.0531614 - 0.0849268i) q^{87} +4.25348i q^{88} +(-3.69936 - 6.40747i) q^{89} +(4.77452 + 4.71211i) q^{90} +(-8.20906 - 2.32839i) q^{91} +(3.75947 + 6.51160i) q^{92} +(9.34522 + 14.9292i) q^{93} +(0.471402 - 0.272164i) q^{94} +(1.24769 + 6.25180i) q^{95} +(-1.46814 + 0.919006i) q^{96} +(4.48327 + 7.76525i) q^{97} +(0.204066 - 6.99702i) q^{98} +(-0.910220 - 12.7279i) 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}+O(q^{10}) $ 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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
$3$	−0.0618143	−	1.73095i	−0.0356885	−	0.999363i
$3$	−0.0618143	−	1.73095i	−0.0356885	−	0.999363i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.717414	+	2.11786i	−0.320837	+	0.947134i
$5$	−0.717414	+	2.11786i	−0.320837	+	0.947134i
$6$	1.52995	+	0.811941i	0.624600	+	0.331474i
$7$	−0.647443	−	2.56531i	−0.244711	−	0.969596i
$7$	−0.647443	−	2.56531i	−0.244711	−	0.969596i
$8$	1.00000			0.353553
$9$	−2.99236	+	0.213994i	−0.997453	+	0.0713315i
$10$	−1.47541	−	1.68023i	−0.466566	−	0.531334i
$11$			4.25348i			1.28247i	0.767344	+	0.641236i	$0.221578\pi$
$11$			4.25348i			1.28247i	−0.767344	+	0.641236i	$0.778422\pi$
$12$	−1.46814	+	0.919006i	−0.423815	+	0.265294i
$13$	1.61256	−	2.79304i	0.447244	−	0.774650i	−0.550961	−	0.834531i	$-0.685739\pi$
$13$	1.61256	−	2.79304i	0.447244	−	0.774650i	0.998206	+	0.0598809i	$0.0190721\pi$
$14$	2.54535	+	0.721953i	0.680272	+	0.192950i
$15$	3.71025	+	1.11089i	0.957981	+	0.286831i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.68059	−	3.27969i	−1.37774	−	0.795441i	−0.385857	−	0.922559i	$-0.626094\pi$
$17$	−5.68059	−	3.27969i	−1.37774	−	0.795441i	−0.991888	+	0.127117i	$0.959428\pi$
$18$	1.31085	−	2.69846i	0.308971	−	0.636032i
$19$	2.46906	−	1.42551i	0.566442	−	0.327035i	−0.189285	−	0.981922i	$-0.560617\pi$
$19$	2.46906	−	1.42551i	0.566442	−	0.327035i	0.755727	+	0.654887i	$0.227284\pi$
$20$	2.19282	−	0.437630i	0.490331	−	0.0978570i
$21$	−4.40040	+	1.27926i	−0.960245	+	0.279158i
$22$	−3.68362	−	2.12674i	−0.785350	−	0.453422i
$23$	−7.51895			−1.56781			−0.783904	−	0.620882i	$-0.786775\pi$
$23$	−7.51895			−1.56781			−0.783904	+	0.620882i	$0.786775\pi$
$24$	−0.0618143	−	1.73095i	−0.0126178	−	0.353328i
$25$	−3.97064	−	3.03876i	−0.794127	−	0.607752i
$26$	1.61256	+	2.79304i	0.316250	+	0.547760i
$27$	0.555384	+	5.16639i	0.106884	+	0.994272i
$28$	−1.89790	+	1.84336i	−0.358670	+	0.348362i
$29$	0.0500967	−	0.0289233i	0.00930271	−	0.00537092i	−0.495341	−	0.868698i	$-0.664957\pi$
$29$	0.0500967	−	0.0289233i	0.00930271	−	0.00537092i	0.504644	+	0.863327i	$0.331624\pi$
$30$	−2.81718	+	2.65772i	−0.514345	+	0.485231i
$31$	−8.80647	+	5.08442i	−1.58169	+	0.913188i	−0.587075	+	0.809532i	$0.699721\pi$
$31$	−8.80647	+	5.08442i	−1.58169	+	0.913188i	−0.994613	+	0.103656i	$0.966946\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	7.36254	−	0.262925i	1.28165	−	0.0457694i
$34$	5.68059	−	3.27969i	0.974213	−	0.562462i
$35$	5.89744	+	0.469197i	0.996850	+	0.0793087i
$36$	1.68150	+	2.48446i	0.280251	+	0.414077i
$37$	0.286737	−	0.165548i	0.0471393	−	0.0272159i	−0.476245	−	0.879313i	$-0.658003\pi$
$37$	0.286737	−	0.165548i	0.0471393	−	0.0272159i	0.523384	+	0.852097i	$0.324669\pi$
$38$			2.85103i			0.462498i
$39$	−4.93429	−	2.61861i	−0.790118	−	0.419313i
$40$	−0.717414	+	2.11786i	−0.113433	+	0.334863i
$41$	−0.485297	+	0.840559i	−0.0757907	+	0.131273i	−0.901430	−	0.432925i	$-0.857481\pi$
$41$	−0.485297	+	0.840559i	−0.0757907	+	0.131273i	0.825639	+	0.564199i	$0.190815\pi$
$42$	1.09232	−	4.45049i	0.168549	−	0.686725i
$43$	−5.85761	+	3.38189i	−0.893277	+	0.515734i	−0.875013	−	0.484099i	$-0.839147\pi$
$43$	−5.85761	+	3.38189i	−0.893277	+	0.515734i	−0.0182643	+	0.999833i	$0.505814\pi$
$44$	3.68362	−	2.12674i	0.555326	−	0.320618i
$45$	1.69355	−	6.49091i	0.252459	−	0.967607i
$46$	3.75947	−	6.51160i	0.554304	−	0.960083i
$47$	−0.471402	−	0.272164i	−0.0687611	−	0.0396992i	0.465225	−	0.885192i	$-0.345973\pi$
$47$	−0.471402	−	0.272164i	−0.0687611	−	0.0396992i	−0.533986	+	0.845493i	$0.679307\pi$
$48$	1.52995	+	0.811941i	0.220829	+	0.117194i
$49$	−6.16163	+	3.32179i	−0.880233	+	0.474541i
$50$	4.61696	−	1.91929i	0.652937	−	0.271429i
$51$	−5.32583	+	10.0355i	−0.745765	+	1.40526i
$52$	−3.22513			−0.447244
$53$	0.951917	−	1.64877i	0.130756	−	0.226476i	−0.793212	−	0.608945i	$-0.791593\pi$
$53$	0.951917	−	1.64877i	0.130756	−	0.226476i	0.923968	+	0.382469i	$0.124926\pi$
$54$	−4.75191	−	2.10222i	−0.646654	−	0.286075i
$55$	−9.00825	−	3.05150i	−1.21467	−	0.411464i
$56$	−0.647443	−	2.56531i	−0.0865182	−	0.342804i
$57$	−2.62011	−	4.18570i	−0.347042	−	0.554409i
$58$			0.0578466i			0.00759563i
$59$	−0.615269	−	1.06568i	−0.0801012	−	0.138739i	0.823192	−	0.567763i	$-0.192191\pi$
$59$	−0.615269	−	1.06568i	−0.0801012	−	0.138739i	−0.903293	+	0.429024i	$0.858858\pi$
$60$	−0.893062	−	3.76861i	−0.115294	−	0.486526i
$61$	−3.90523	−	2.25468i	−0.500013	−	0.288683i	0.228706	−	0.973496i	$-0.426551\pi$
$61$	−3.90523	−	2.25468i	−0.500013	−	0.288683i	−0.728719	+	0.684813i	$0.759884\pi$
$62$		−	10.1688i		−	1.29144i
$63$	2.48634	+	7.53778i	0.313250	+	0.949671i
$64$	1.00000			0.125000
$65$	4.75838	+	5.41894i	0.590205	+	0.672137i
$66$	−3.45357	+	6.50761i	−0.425105	+	0.801032i
$67$	−7.44867	+	4.30049i	−0.910000	+	0.525389i	−0.880431	−	0.474174i	$-0.842747\pi$
$67$	−7.44867	+	4.30049i	−0.910000	+	0.525389i	−0.0295687	+	0.999563i	$0.509413\pi$
$68$			6.55938i			0.795441i
$69$	0.464778	+	13.0149i	0.0559527	+	1.56681i
$70$	−3.35506	+	4.87274i	−0.401006	+	0.582404i
$71$		−	3.35700i		−	0.398403i	−0.979959	−	0.199201i	$-0.936165\pi$
$71$		−	3.35700i		−	0.398403i	0.979959	−	0.199201i	$-0.0638348\pi$
$72$	−2.99236	+	0.213994i	−0.352653	+	0.0252195i
$73$	8.45840	−	14.6504i	0.989981	−	1.71470i	0.372710	−	0.927948i	$-0.378429\pi$
$73$	8.45840	−	14.6504i	0.989981	−	1.71470i	0.617272	−	0.786750i	$-0.288238\pi$
$74$			0.331096i			0.0384891i
$75$	−5.01449	+	7.06080i	−0.579023	+	0.815311i
$76$	−2.46906	−	1.42551i	−0.283221	−	0.163518i
$77$	10.9115	−	2.75388i	1.24348	−	0.313834i
$78$	4.73493	−	2.96391i	0.536125	−	0.335597i
$79$	1.71836	−	2.97629i	0.193331	−	0.334859i	−0.753021	−	0.657996i	$-0.771404\pi$
$79$	1.71836	−	2.97629i	0.193331	−	0.334859i	0.946352	+	0.323137i	$0.104738\pi$
$80$	−1.47541	−	1.68023i	−0.164956	−	0.187855i
$81$	8.90841	−	1.28070i	0.989824	−	0.142300i
$82$	−0.485297	−	0.840559i	−0.0535921	−	0.0928242i
$83$	−0.335938	+	0.193954i	−0.0368739	+	0.0212892i	−0.518324	−	0.855185i	$-0.673444\pi$
$83$	−0.335938	+	0.193954i	−0.0368739	+	0.0212892i	0.481450	+	0.876474i	$0.340110\pi$
$84$	3.30807	+	3.17122i	0.360940	+	0.346009i
$85$	11.0212	−	9.67778i	1.19542	−	1.04970i
$86$		−	6.76379i		−	0.729358i
$87$	−0.0531614	−	0.0849268i	−0.00569950	−	0.00910511i
$88$			4.25348i			0.453422i
$89$	−3.69936	−	6.40747i	−0.392131	−	0.679191i	0.600600	−	0.799550i	$-0.294929\pi$
$89$	−3.69936	−	6.40747i	−0.392131	−	0.679191i	−0.992730	+	0.120359i	$0.961595\pi$
$90$	4.77452	+	4.71211i	0.503278	+	0.496700i
$91$	−8.20906	−	2.32839i	−0.860543	−	0.244081i
$92$	3.75947	+	6.51160i	0.391952	+	0.678881i
$93$	9.34522	+	14.9292i	0.969054	+	1.54809i
$94$	0.471402	−	0.272164i	0.0486214	−	0.0280716i
$95$	1.24769	+	6.25180i	0.128011	+	0.641421i
$96$	−1.46814	+	0.919006i	−0.149841	+	0.0937957i
$97$	4.48327	+	7.76525i	0.455207	+	0.788442i	0.998700	−	0.0509717i	$-0.0162318\pi$
$97$	4.48327	+	7.76525i	0.455207	+	0.788442i	−0.543493	+	0.839414i	$0.682899\pi$
$98$	0.204066	−	6.99702i	0.0206138	−	0.706806i
$99$	−0.910220	−	12.7279i	−0.0914806	−	1.27920i
$100$	−0.646325	+	4.95805i	−0.0646325	+	0.495805i
$101$	3.10315			0.308775			0.154388	−	0.988010i	$-0.450660\pi$
$101$	3.10315			0.308775			0.154388	+	0.988010i	$0.450660\pi$
$102$	−6.02811	−	9.63007i	−0.596872	−	0.953519i
$103$	12.5559			1.23717			0.618583	−	0.785720i	$-0.287707\pi$
$103$	12.5559			1.23717			0.618583	+	0.785720i	$0.287707\pi$
$104$	1.61256	−	2.79304i	0.158125	−	0.273880i
$105$	0.447609	−	10.2372i	0.0436821	−	0.999045i
$106$	0.951917	+	1.64877i	0.0924583	+	0.160143i
$107$	−1.14308	−	1.97987i	−0.110506	−	0.191401i	0.805469	−	0.592638i	$-0.201914\pi$
$107$	−1.14308	−	1.97987i	−0.110506	−	0.191401i	−0.915974	+	0.401237i	$0.868580\pi$
$108$	4.19653	−	3.06417i	0.403811	−	0.294850i
$109$	6.40462	−	11.0931i	0.613451	−	1.06253i	−0.377203	−	0.926131i	$-0.623114\pi$
$109$	6.40462	−	11.0931i	0.613451	−	1.06253i	0.990654	−	0.136398i	$-0.0435525\pi$
$110$	7.14680	−	6.27562i	0.681421	−	0.598357i
$111$	−0.304279	−	0.486094i	−0.0288809	−	0.0461380i
$112$	2.54535	+	0.721953i	0.240513	+	0.0682181i
$113$	−2.20016	+	3.81078i	−0.206973	+	0.358488i	−0.950760	−	0.309929i	$-0.899695\pi$
$113$	−2.20016	+	3.81078i	−0.206973	+	0.358488i	0.743786	+	0.668418i	$0.233028\pi$
$114$	4.93498	−	0.176234i	0.462203	−	0.0165058i
$115$	5.39420	−	15.9241i	0.503011	−	1.48493i
$116$	−0.0500967	−	0.0289233i	−0.00465136	−	0.00268546i
$117$	−4.22767	+	8.70286i	−0.390848	+	0.804579i
$118$	1.23054			0.113280
$119$	−4.73556	+	16.6959i	−0.434108	+	1.53051i
$120$	3.71025	+	1.11089i	0.338697	+	0.101410i
$121$	−7.09205			−0.644732
$122$	3.90523	−	2.25468i	0.353563	−	0.204130i
$123$	1.48496	+	0.788065i	0.133895	+	0.0710574i
$124$	8.80647	+	5.08442i	0.790844	+	0.456594i
$125$	9.28425	−	6.22919i	0.830408	−	0.557156i
$126$	−7.77108	−	1.61565i	−0.692303	−	0.143934i
$127$			3.43309i			0.304637i	0.988331	+	0.152319i	$0.0486740\pi$
$127$			3.43309i			0.304637i	−0.988331	+	0.152319i	$0.951326\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	6.21596	+	9.93017i	0.547285	+	0.874303i
$130$	−7.07213	+	1.41141i	−0.620267	+	0.123789i
$131$	20.2953			1.77321			0.886604	−	0.462528i	$-0.153058\pi$
$131$	20.2953			1.77321			0.886604	+	0.462528i	$0.153058\pi$
$132$	−3.90897	−	6.24469i	−0.340232	−	0.543530i
$133$	−5.25546	−	5.41097i	−0.455706	−	0.469191i
$134$		−	8.60098i		−	0.743012i
$135$	−11.3401	−	2.53021i	−0.976001	−	0.217766i
$136$	−5.68059	−	3.27969i	−0.487106	−	0.281231i
$137$	−22.2691			−1.90258			−0.951291	−	0.308295i	$-0.900242\pi$
$137$	−22.2691			−1.90258			−0.951291	+	0.308295i	$0.900242\pi$
$138$	−11.5036	−	6.10494i	−0.979253	−	0.519687i
$139$	−3.12764	−	1.80575i	−0.265283	−	0.153161i	0.361459	−	0.932388i	$-0.382279\pi$
$139$	−3.12764	−	1.80575i	−0.265283	−	0.153161i	−0.626742	+	0.779227i	$0.715612\pi$
$140$	−2.54239	−	5.34194i	−0.214871	−	0.451476i
$141$	−0.441963	+	0.832796i	−0.0372200	+	0.0701341i
$142$	2.90725	+	1.67850i	0.243971	+	0.140857i
$143$	11.8801	+	6.85899i	0.993466	+	0.573578i
$144$	1.31085	−	2.69846i	0.109238	−	0.224871i
$145$	0.0253154	+	0.126848i	0.00210233	+	0.0105341i
$146$	8.45840	+	14.6504i	0.700023	+	1.21247i
$147$	6.13071	+	10.4601i	0.505653	+	0.862737i
$148$	−0.286737	−	0.165548i	−0.0235697	−	0.0136080i
$149$		−	13.3639i		−	1.09481i	−0.836867	−	0.547406i	$-0.815615\pi$
$149$		−	13.3639i		−	1.09481i	0.836867	−	0.547406i	$-0.184385\pi$
$150$	−3.60759	−	7.87308i	−0.294558	−	0.642834i
$151$	0.890996			0.0725082			0.0362541	−	0.999343i	$-0.488457\pi$
$151$	0.890996			0.0725082			0.0362541	+	0.999343i	$0.488457\pi$
$152$	2.46906	−	1.42551i	0.200267	−	0.115624i
$153$	17.7002	+	8.59839i	1.43098	+	0.695138i
$154$	−3.07081	+	10.8266i	−0.247453	+	0.872429i
$155$	−4.45019	−	22.2985i	−0.357447	−	1.79106i
$156$	0.199359	+	5.58252i	0.0159615	+	0.446959i
$157$	8.11868	+	14.0620i	0.647941	+	1.12227i	0.983614	+	0.180288i	$0.0577031\pi$
$157$	8.11868	+	14.0620i	0.647941	+	1.12227i	−0.335673	+	0.941979i	$0.608964\pi$
$158$	1.71836	+	2.97629i	0.136706	+	0.236781i
$159$	−2.91277	−	1.54580i	−0.230998	−	0.122590i
$160$	2.19282	−	0.437630i	0.173358	−	0.0345977i
$161$	4.86809	+	19.2884i	0.383659	+	1.52014i
$162$	−3.34509	+	8.35526i	−0.262815	+	0.656451i
$163$	−10.6386	+	6.14217i	−0.833276	+	0.481092i	−0.854973	−	0.518672i	$-0.826426\pi$
$163$	−10.6386	+	6.14217i	−0.833276	+	0.481092i	0.0216970	+	0.999765i	$0.493093\pi$
$164$	0.970594			0.0757907
$165$	−4.72515	+	15.7814i	−0.367852	+	1.22858i
$166$		−	0.387907i		−	0.0301075i
$167$	14.8865	+	8.59473i	1.15195	+	0.665080i	0.949362	−	0.314183i	$-0.101731\pi$
$167$	14.8865	+	8.59473i	1.15195	+	0.665080i	0.202591	+	0.979264i	$0.435064\pi$
$168$	−4.40040	+	1.27926i	−0.339498	+	0.0986973i
$169$	1.29928	+	2.25043i	0.0999449	+	0.173110i
$170$	2.87058	+	14.3836i	0.220163	+	1.10317i
$171$	−7.08326	+	4.79401i	−0.541671	+	0.366607i
$172$	5.85761	+	3.38189i	0.446639	+	0.257867i
$173$	−5.70624	−	3.29450i	−0.433837	−	0.250476i	0.267143	−	0.963657i	$-0.413920\pi$
$173$	−5.70624	−	3.29450i	−0.433837	−	0.250476i	−0.700980	+	0.713181i	$0.747254\pi$
$174$	0.100129	−	0.00357575i	0.00759080	−	0.000271077i
$175$	−5.22460	+	12.1533i	−0.394943	+	0.918706i
$176$	−3.68362	−	2.12674i	−0.277663	−	0.160309i
$177$	−1.80660	+	1.13087i	−0.135792	+	0.0850015i
$178$	7.39871			0.554557
$179$	9.31118	+	5.37581i	0.695950	+	0.401807i	0.805837	−	0.592137i	$-0.201716\pi$
$179$	9.31118	+	5.37581i	0.695950	+	0.401807i	−0.109887	+	0.993944i	$0.535049\pi$
$180$	−6.46807	+	1.77880i	−0.482101	+	0.132584i
$181$			17.4543i			1.29737i	0.761057	+	0.648685i	$0.224681\pi$
$181$			17.4543i			1.29737i	−0.761057	+	0.648685i	$0.775319\pi$
$182$	6.12097	−	5.94506i	0.453717	−	0.440677i
$183$	−3.66134	+	6.89912i	−0.270654	+	0.509997i
$184$	−7.51895			−0.554304
$185$	0.144897	+	0.726035i	0.0106531	+	0.0533791i
$186$	−17.6017	+	0.628579i	−1.29062	+	0.0460896i
$187$	13.9501	−	24.1622i	1.02013	−	1.76692i
$188$			0.544329i			0.0396992i
$189$	12.8938	−	4.76967i	0.937886	−	0.346943i
$190$	−6.03807	−	2.04537i	−0.438047	−	0.148386i
$191$	−18.0983	−	10.4491i	−1.30955	−	0.756068i	−0.327528	−	0.944842i	$-0.606215\pi$
$191$	−18.0983	−	10.4491i	−1.30955	−	0.756068i	−0.982021	+	0.188773i	$0.939549\pi$
$192$	−0.0618143	−	1.73095i	−0.00446106	−	0.124920i
$193$	−3.03182	+	1.75042i	−0.218235	+	0.125998i	−0.605133	−	0.796125i	$-0.706880\pi$
$193$	−3.03182	+	1.75042i	−0.218235	+	0.125998i	0.386898	+	0.922123i	$0.373547\pi$
$194$	−8.96654			−0.643760
$195$	9.08577	−	8.57148i	0.650645	−	0.613817i
$196$	5.95757	+	3.67524i	0.425541	+	0.262517i
$197$	9.20124			0.655561			0.327781	−	0.944754i	$-0.393699\pi$
$197$	9.20124			0.655561			0.327781	+	0.944754i	$0.393699\pi$
$198$	11.4778	+	5.57569i	0.815693	+	0.396247i
$199$	9.22812	+	5.32786i	0.654164	+	0.377682i	0.790050	−	0.613043i	$-0.210055\pi$
$199$	9.22812	+	5.32786i	0.654164	+	0.377682i	−0.135886	+	0.990725i	$0.543388\pi$
$200$	−3.97064	−	3.03876i	−0.280766	−	0.214873i
$201$	7.90436	+	12.6274i	0.557530	+	0.890670i
$202$	−1.55158	+	2.68741i	−0.109169	+	0.189085i
$203$	−0.106632	−	0.109787i	−0.00748410	−	0.00770555i
$204$	11.3539	−	0.405463i	0.794935	−	0.0283881i
$205$	−1.43203	−	1.63082i	−0.100017	−	0.113901i
$206$	−6.27793	+	10.8737i	−0.437404	+	0.757606i
$207$	22.4994	−	1.60901i	1.56381	−	0.111834i
$208$	1.61256	+	2.79304i	0.111811	+	0.193663i
$209$	6.06339	+	10.5021i	0.419413	+	0.726445i
$210$	8.64184	+	5.50623i	0.596344	+	0.379966i
$211$	−4.37034	+	7.56965i	−0.300867	+	0.521116i	−0.976332	−	0.216275i	$-0.930609\pi$
$211$	−4.37034	+	7.56965i	−0.300867	+	0.521116i	0.675466	+	0.737391i	$0.263943\pi$
$212$	−1.90383			−0.130756
$213$	−5.81079	+	0.207510i	−0.398149	+	0.0142184i
$214$	2.28616			0.156279
$215$	−2.96004	−	14.8318i	−0.201873	−	1.01152i
$216$	0.555384	+	5.16639i	0.0377891	+	0.351528i
$217$	18.7448	+	19.2995i	1.27248	+	1.31013i
$218$	6.40462	+	11.0931i	0.433775	+	0.751321i
$219$	−25.8819	−	13.7355i	−1.74894	−	0.928156i
$220$	1.86145	+	9.32713i	0.125499	+	0.628835i
$221$	−18.3206	+	10.5774i	−1.23238	+	0.711513i
$222$	0.573109	−	0.0204664i	0.0384646	−	0.00137362i
$223$	−14.6894	−	25.4429i	−0.983678	−	1.70378i	−0.647671	−	0.761920i	$-0.724257\pi$
$223$	−14.6894	−	25.4429i	−0.983678	−	1.70378i	−0.336006	−	0.941860i	$-0.609076\pi$
$224$	−1.89790	+	1.84336i	−0.126809	+	0.123165i
$225$	12.5318	+	8.24336i	0.835456	+	0.549557i
$226$	−2.20016	−	3.81078i	−0.146352	−	0.253490i
$227$			17.1538i			1.13854i	0.822152	+	0.569268i	$0.192773\pi$
$227$			17.1538i			1.13854i	−0.822152	+	0.569268i	$0.807227\pi$
$228$	−2.31487	+	4.36193i	−0.153306	+	0.288876i
$229$		−	11.0742i		−	0.731806i	−0.930653	−	0.365903i	$-0.880760\pi$
$229$		−	11.0742i		−	0.731806i	0.930653	−	0.365903i	$-0.119240\pi$
$230$	11.0935	+	12.6335i	0.731486	+	0.833031i
$231$	−5.44131	−	18.7170i	−0.358012	−	1.23149i
$232$	0.0500967	−	0.0289233i	0.00328901	−	0.00189891i
$233$	−11.7152	−	20.2913i	−0.767489	−	1.32933i	−0.938920	−	0.344134i	$-0.888172\pi$
$233$	−11.7152	−	20.2913i	−0.767489	−	1.32933i	0.171431	−	0.985196i	$-0.445161\pi$
$234$	−5.42306	−	8.01270i	−0.354517	−	0.523806i
$235$	0.914596	−	0.803108i	0.0596616	−	0.0523890i
$236$	−0.615269	+	1.06568i	−0.0400506	+	0.0693696i
$237$	−5.25802	−	2.79042i	−0.341545	−	0.181257i
$238$	−12.0913	−	12.4491i	−0.783761	−	0.806952i
$239$	−0.758949	−	0.438179i	−0.0490923	−	0.0283435i	0.475253	−	0.879849i	$-0.342357\pi$
$239$	−0.758949	−	0.438179i	−0.0490923	−	0.0283435i	−0.524345	+	0.851506i	$0.675690\pi$
$240$	−2.81718	+	2.65772i	−0.181848	+	0.171555i
$241$		−	16.9789i		−	1.09371i	−0.837228	−	0.546853i	$-0.815825\pi$
$241$		−	16.9789i		−	1.09371i	0.837228	−	0.546853i	$-0.184175\pi$
$242$	3.54603	−	6.14190i	0.227947	−	0.394816i
$243$	−2.76748	−	15.3408i	−0.177534	−	0.984115i
$244$			4.50937i			0.288683i
$245$	−2.61463	−	15.4326i	−0.167042	−	0.985950i
$246$	−1.42497	+	0.891982i	−0.0908525	+	0.0568707i
$247$		−	9.19492i		−	0.585059i
$248$	−8.80647	+	5.08442i	−0.559211	+	0.322861i
$249$	0.356489	+	0.569501i	0.0225916	+	0.0360907i
$250$	0.752513	+	11.1550i	0.0475931	+	0.705503i
$251$	−7.65250			−0.483022			−0.241511	−	0.970398i	$-0.577643\pi$
$251$	−7.65250			−0.483022			−0.241511	+	0.970398i	$0.577643\pi$
$252$	5.28473	−	5.92213i	0.332907	−	0.373059i
$253$		−	31.9817i		−	2.01067i
$254$	−2.97314	−	1.71654i	−0.186551	−	0.107705i
$255$	−17.4330	−	18.4790i	−1.09170	−	1.15720i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		−	6.58759i		−	0.410923i	−0.978665	−	0.205461i	$-0.934131\pi$
$257$		−	6.58759i		−	0.410923i	0.978665	−	0.205461i	$-0.0658695\pi$
$258$	−11.7078	+	0.418099i	−0.728893	+	0.0260297i
$259$	−0.610328	−	0.628387i	−0.0379239	−	0.0390461i
$260$	2.31375	−	6.83035i	0.143493	−	0.423601i
$261$	−0.143718	+	0.0972693i	−0.00889590	+	0.00602082i
$262$	−10.1477	+	17.5762i	−0.626924	+	1.08586i
$263$	−29.3620			−1.81054			−0.905270	−	0.424836i	$-0.860332\pi$
$263$	−29.3620			−1.81054			−0.905270	+	0.424836i	$0.860332\pi$
$264$	7.36254	−	0.262925i	0.453133	−	0.0161819i
$265$	2.80894	+	3.19887i	0.172552	+	0.196505i
$266$	7.31377	−	1.84588i	0.448436	−	0.113178i
$267$	−10.8623	+	6.79946i	−0.664763	+	0.416120i
$268$	7.44867	+	4.30049i	0.455000	+	0.262694i
$269$	−5.09477	+	8.82440i	−0.310633	+	0.538033i	−0.978500	−	0.206248i	$-0.933874\pi$
$269$	−5.09477	+	8.82440i	−0.310633	+	0.538033i	0.667866	+	0.744281i	$0.267208\pi$
$270$	7.86128	−	8.55571i	0.478422	−	0.520684i
$271$	24.6928	−	14.2564i	1.49998	−	0.866016i	0.499984	−	0.866035i	$-0.333339\pi$
$271$	24.6928	−	14.2564i	1.49998	−	0.866016i	1.00000		1.87784e-5i	$5.97736e-6\pi$
$272$	5.68059	−	3.27969i	0.344436	−	0.198860i
$273$	−3.52288	+	14.3534i	−0.213214	+	0.868706i
$274$	11.1346	−	19.2856i	0.672664	−	1.16509i
$275$	12.9253	−	16.8890i	0.779424	−	1.01844i
$276$	11.0388	−	6.90996i	0.664460	−	0.415931i
$277$			18.1943i			1.09319i	0.837397	+	0.546595i	$0.184076\pi$
$277$			18.1943i			1.09319i	−0.837397	+	0.546595i	$0.815924\pi$
$278$	3.12764	−	1.80575i	0.187584	−	0.108301i
$279$	25.2641	−	17.0989i	1.51252	−	1.02369i
$280$	5.89744	+	0.469197i	0.352440	+	0.0280399i
$281$	6.13073	−	3.53958i	0.365729	−	0.211154i	−0.305862	−	0.952076i	$-0.598945\pi$
$281$	6.13073	−	3.53958i	0.365729	−	0.211154i	0.671591	+	0.740922i	$0.265611\pi$
$282$	−0.500241	−	0.799149i	−0.0297889	−	0.0475886i
$283$	−13.0780	−	22.6517i	−0.777404	−	1.34650i	−0.933434	−	0.358750i	$-0.883203\pi$
$283$	−13.0780	−	22.6517i	−0.777404	−	1.34650i	0.156030	−	0.987752i	$-0.450130\pi$
$284$	−2.90725	+	1.67850i	−0.172513	+	0.0996007i
$285$	10.7444	−	2.54614i	0.636444	−	0.150821i
$286$	−11.8801	+	6.85899i	−0.702487	+	0.405581i
$287$	2.47050	+	0.700723i	0.145829	+	0.0413624i
$288$	1.68150	+	2.48446i	0.0990836	+	0.146398i
$289$	13.0127	+	22.5387i	0.765454	+	1.32580i
$290$	−0.122511	−	0.0415000i	−0.00719409	−	0.00243696i
$291$	13.1641	−	8.24031i	0.771694	−	0.483056i
$292$	−16.9168			−0.989981
$293$	−13.0082	−	7.51027i	−0.759945	−	0.438755i	0.0693308	−	0.997594i	$-0.477914\pi$
$293$	−13.0082	−	7.51027i	−0.759945	−	0.438755i	−0.829276	+	0.558839i	$0.811247\pi$
$294$	−12.1241	+	0.0792879i	−0.707092	+	0.00462417i
$295$	2.69835	−	0.538520i	0.157104	−	0.0313538i
$296$	0.286737	−	0.165548i	0.0166663	−	0.00962227i
$297$	−21.9751	+	2.36231i	−1.27512	+	0.137075i
$298$	11.5735	+	6.68194i	0.670433	+	0.387075i
$299$	−12.1248	+	21.0007i	−0.701194	+	1.21450i
$300$	8.62208	+	0.812277i	0.497796	+	0.0468968i
$301$	12.4681	+	12.8370i	0.718648	+	0.739913i
$302$	−0.445498	+	0.771625i	−0.0256355	+	0.0444021i
$303$	−0.191819	−	5.37139i	−0.0110197	−	0.308579i
$304$			2.85103i			0.163518i
$305$	7.57676	−	6.65317i	0.433844	−	0.380959i
$306$	−16.2965	+	11.0296i	−0.931610	+	0.630521i
$307$	−23.2295			−1.32578			−0.662890	−	0.748717i	$-0.730670\pi$
$307$	−23.2295			−1.32578			−0.662890	+	0.748717i	$0.730670\pi$
$308$	−7.84068	−	8.07268i	−0.446764	−	0.459984i
$309$	−0.776131	−	21.7335i	−0.0441526	−	1.23638i
$310$	21.5361	+	7.29526i	1.22317	+	0.414343i
$311$	−0.0992231	−	0.171859i	−0.00562642	−	0.00974525i	0.863198	−	0.504865i	$-0.168458\pi$
$311$	−0.0992231	−	0.171859i	−0.00562642	−	0.00974525i	−0.868825	+	0.495119i	$0.835124\pi$
$312$	−4.93429	−	2.61861i	−0.279349	−	0.148250i
$313$	−1.59131	+	2.75623i	−0.0899463	+	0.155791i	−0.907488	−	0.420078i	$-0.862003\pi$
$313$	−1.59131	+	2.75623i	−0.0899463	+	0.155791i	0.817542	+	0.575869i	$0.195336\pi$
$314$	−16.2374			−0.916327
$315$	−17.7477	−	0.141984i	−0.999968	−	0.00799990i
$316$	−3.43672			−0.193331
$317$	11.8116	−	20.4583i	0.663406	−	1.14905i	−0.316309	−	0.948656i	$-0.602444\pi$
$317$	11.8116	−	20.4583i	0.663406	−	1.14905i	0.979715	−	0.200396i	$-0.0642230\pi$
$318$	2.79509	−	1.74963i	0.156741	−	0.0981147i
$319$	0.123025	+	0.213085i	0.00688806	+	0.0119305i
$320$	−0.717414	+	2.11786i	−0.0401046	+	0.118392i
$321$	−3.35639	+	2.10099i	−0.187336	+	0.117266i
$322$	−19.1383	−	5.42832i	−1.06654	−	0.302509i
$323$	−18.7010			−1.04055
$324$	−5.56332	−	7.07456i	−0.309073	−	0.393031i
$325$	−14.8903	+	6.18995i	−0.825964	+	0.343357i
$326$		−	12.2843i		−	0.680367i
$327$	−19.5975	−	10.4003i	−1.08374	−	0.575140i
$328$	−0.485297	+	0.840559i	−0.0267960	+	0.0464121i
$329$	−0.392980	+	1.38550i	−0.0216657	+	0.0763853i
$330$	−11.3045	−	11.9828i	−0.622295	−	0.659632i
$331$	−11.8910	+	20.5958i	−0.653587	+	1.13205i	0.328659	+	0.944449i	$0.393403\pi$
$331$	−11.8910	+	20.5958i	−0.653587	+	1.13205i	−0.982246	+	0.187597i	$0.939930\pi$
$332$	0.335938	+	0.193954i	0.0184370	+	0.0106446i
$333$	−0.822594	+	0.556739i	−0.0450779	+	0.0305091i
$334$	−14.8865	+	8.59473i	−0.814554	+	0.470283i
$335$	−3.76405	−	18.8604i	−0.205652	−	1.03046i
$336$	1.09232	−	4.45049i	0.0595911	−	0.242794i
$337$	8.84127	+	5.10451i	0.481615	+	0.278060i	0.721089	−	0.692842i	$-0.243642\pi$
$337$	8.84127	+	5.10451i	0.481615	+	0.278060i	−0.239475	+	0.970903i	$0.576975\pi$
$338$	−2.59857			−0.141343
$339$	6.73227	+	3.57280i	0.365647	+	0.194048i
$340$	−13.8918	−	4.70579i	−0.753390	−	0.255207i
$341$	−21.6264	−	37.4581i	−1.17114	−	2.02847i
$342$	−0.610104	−	8.53129i	−0.0329906	−	0.461319i
$343$	12.5107	+	13.6558i	0.675515	+	0.737346i
$344$	−5.85761	+	3.38189i	−0.315821	+	0.182339i
$345$	−27.8971	−	8.35274i	−1.50193	−	0.449696i
$346$	5.70624	−	3.29450i	0.306769	−	0.177113i
$347$	7.10625	+	12.3084i	0.381483	+	0.660749i	0.991275	−	0.131813i	$-0.0420800\pi$
$347$	7.10625	+	12.3084i	0.381483	+	0.660749i	−0.609791	+	0.792562i	$0.708747\pi$
$348$	−0.0469681	+	0.0885025i	−0.00251775	+	0.00474423i
$349$	18.0147	−	10.4008i	0.964306	−	0.556742i	0.0668102	−	0.997766i	$-0.478718\pi$
$349$	18.0147	−	10.4008i	0.964306	−	0.556742i	0.897496	+	0.441023i	$0.145384\pi$
$350$	−7.91280	−	10.6013i	−0.422957	−	0.566664i
$351$	15.3255	+	6.77991i	0.818016	+	0.361885i
$352$	3.68362	−	2.12674i	0.196337	−	0.113355i
$353$			28.7177i			1.52849i	0.644927	+	0.764244i	$0.276888\pi$
$353$			28.7177i			1.52849i	−0.644927	+	0.764244i	$0.723112\pi$
$354$	−0.0760648	−	2.13000i	−0.00404280	−	0.113208i
$355$	7.10965	+	2.40836i	0.377341	+	0.127822i
$356$	−3.69936	+	6.40747i	−0.196065	+	0.339595i
$357$	29.1924	+	7.16496i	1.54503	+	0.379210i
$358$	−9.31118	+	5.37581i	−0.492111	+	0.284121i
$359$	−4.11171	+	2.37390i	−0.217008	+	0.125289i	−0.604564	−	0.796557i	$-0.706653\pi$
$359$	−4.11171	+	2.37390i	−0.217008	+	0.125289i	0.387556	+	0.921846i	$0.373319\pi$
$360$	1.69355	−	6.49091i	0.0892579	−	0.342101i
$361$	−5.43582	+	9.41512i	−0.286096	+	0.495533i
$362$	−15.1159	−	8.72717i	−0.794474	−	0.458690i
$363$	0.438390	+	12.2760i	0.0230095	+	0.644321i
$364$	2.08809	+	8.27345i	0.109445	+	0.433646i
$365$	24.9592	+	28.4241i	1.30643	+	1.48778i
$366$	−4.14414	−	6.62037i	−0.216618	−	0.346052i
$367$	25.5470			1.33354			0.666770	−	0.745263i	$-0.267676\pi$
$367$	25.5470			1.33354			0.666770	+	0.745263i	$0.267676\pi$
$368$	3.75947	−	6.51160i	0.195976	−	0.339441i
$369$	1.27231	−	2.61910i	0.0662337	−	0.136345i
$370$	−0.701213	−	0.237533i	−0.0364543	−	0.0123487i
$371$	−4.84591	−	1.37448i	−0.251587	−	0.0713593i
$372$	8.25649	−	15.5578i	0.428079	−	0.806636i
$373$		−	36.9589i		−	1.91366i	−0.290650	−	0.956829i	$-0.593872\pi$
$373$		−	36.9589i		−	1.91366i	0.290650	−	0.956829i	$-0.406128\pi$
$374$	13.9501	+	24.1622i	0.721341	+	1.24940i
$375$	−11.3563	−	15.6855i	−0.586437	−	0.809995i
$376$	−0.471402	−	0.272164i	−0.0243107	−	0.0140358i
$377$		−	0.186563i		−	0.00960846i
$378$	−2.31624	+	13.5512i	−0.119135	+	0.696999i
$379$	−12.7446			−0.654645			−0.327322	−	0.944913i	$-0.606146\pi$
$379$	−12.7446			−0.654645			−0.327322	+	0.944913i	$0.606146\pi$
$380$	4.79037	−	4.20644i	0.245741	−	0.215786i
$381$	5.94249	−	0.212214i	0.304443	−	0.0108720i
$382$	18.0983	−	10.4491i	0.925991	−	0.534621i
$383$			31.5647i			1.61288i	0.591317	+	0.806439i	$0.298608\pi$
$383$			31.5647i			1.61288i	−0.591317	+	0.806439i	$0.701392\pi$
$384$	1.52995	+	0.811941i	0.0780750	+	0.0414342i
$385$	−1.99572	+	25.0846i	−0.101711	+	1.27843i
$386$		−	3.50084i		−	0.178188i
$387$	16.8044	−	11.3733i	0.854214	−	0.578139i
$388$	4.48327	−	7.76525i	0.227604	−	0.394221i
$389$		−	37.7841i		−	1.91573i	−0.287219	−	0.957865i	$-0.592731\pi$
$389$		−	37.7841i		−	1.91573i	0.287219	−	0.957865i	$-0.407269\pi$
$390$	2.88024	+	12.1542i	0.145846	+	0.615454i
$391$	42.7120	+	24.6598i	2.16004	+	1.24710i
$392$	−6.16163	+	3.32179i	−0.311210	+	0.167776i
$393$	−1.25454	−	35.1301i	−0.0632831	−	1.77208i
$394$	−4.60062	+	7.96851i	−0.231776	+	0.401448i
$395$	5.07058	+	5.77448i	0.255129	+	0.290546i
$396$	−10.5676	+	7.15223i	−0.531041	+	0.359413i
$397$	−8.08256	−	13.9994i	−0.405652	−	0.702610i	0.588745	−	0.808319i	$-0.299622\pi$
$397$	−8.08256	−	13.9994i	−0.405652	−	0.702610i	−0.994397	+	0.105709i	$0.966289\pi$
$398$	−9.22812	+	5.32786i	−0.462564	+	0.267061i
$399$	−9.04124	+	9.43140i	−0.452628	+	0.472161i
$400$	4.61696	−	1.91929i	0.230848	−	0.0959646i
$401$			9.36761i			0.467796i	0.972261	+	0.233898i	$0.0751482\pi$
$401$			9.36761i			0.467796i	−0.972261	+	0.233898i	$0.924852\pi$
$402$	−14.8878	+	0.531663i	−0.742538	+	0.0265170i
$403$			32.7958i			1.63367i
$404$	−1.55158	−	2.68741i	−0.0771938	−	0.133704i
$405$	−3.67869	+	19.7855i	−0.182795	+	0.983151i
$406$	0.148395	−	0.0374524i	0.00736470	−	0.00185873i
$407$	0.704154	+	1.21963i	0.0349036	+	0.0604548i
$408$	−5.32583	+	10.0355i	−0.263668	+	0.496833i
$409$	−15.8045	+	9.12476i	−0.781485	+	0.451190i	−0.836956	−	0.547270i	$-0.815667\pi$
$409$	−15.8045	+	9.12476i	−0.781485	+	0.451190i	0.0554716	+	0.998460i	$0.482334\pi$
$410$	2.12834	−	0.424761i	0.105111	−	0.0209774i
$411$	1.37655	+	38.5467i	0.0679002	+	1.90137i
$412$	−6.27793	−	10.8737i	−0.309291	−	0.535708i
$413$	−2.33544	+	2.26832i	−0.114919	+	0.111617i
$414$	−9.85624	+	20.2895i	−0.484408	+	0.997176i
$415$	−0.169760	−	0.850613i	−0.00833318	−	0.0417549i
$416$	−3.22513			−0.158125
$417$	−2.93232	+	5.52541i	−0.143596	+	0.270580i
$418$	−12.1268			−0.593140
$419$	5.45769	−	9.45300i	0.266626	−	0.461809i	−0.701362	−	0.712805i	$-0.747425\pi$
$419$	5.45769	−	9.45300i	0.266626	−	0.461809i	0.967988	+	0.250995i	$0.0807579\pi$
$420$	−9.08945	+	4.73094i	−0.443520	+	0.230846i
$421$	−4.79701	−	8.30867i	−0.233792	−	0.404940i	0.725129	−	0.688613i	$-0.241780\pi$
$421$	−4.79701	−	8.30867i	−0.233792	−	0.404940i	−0.958921	+	0.283674i	$0.908447\pi$
$422$	−4.37034	−	7.56965i	−0.212745	−	0.368485i
$423$	1.46885	+	0.713535i	0.0714178	+	0.0346933i
$424$	0.951917	−	1.64877i	0.0462292	−	0.0800713i
$425$	12.5894	+	30.2844i	0.610673	+	1.46901i
$426$	2.72569	−	5.13605i	0.132060	−	0.248842i
$427$	−3.25555	+	11.4779i	−0.157547	+	0.555455i
$428$	−1.14308	+	1.97987i	−0.0552528	+	0.0957007i
$429$	11.1382	−	20.9879i	0.537757	−	1.01330i
$430$	14.3247	+	4.85243i	0.690800	+	0.234005i
$431$	−17.0044	−	9.81749i	−0.819072	−	0.472892i	0.0310241	−	0.999519i	$-0.490123\pi$
$431$	−17.0044	−	9.81749i	−0.819072	−	0.472892i	−0.850096	+	0.526627i	$0.823456\pi$
$432$	−4.75191	−	2.10222i	−0.228627	−	0.101143i
$433$	28.7386			1.38109			0.690545	−	0.723290i	$-0.257371\pi$
$433$	28.7386			1.38109			0.690545	+	0.723290i	$0.257371\pi$
$434$	−26.0862	+	6.58374i	−1.25218	+	0.316030i
$435$	0.218002	−	0.0516606i	0.0104524	−	0.00247694i
$436$	−12.8092			−0.613451
$437$	−18.5647	+	10.7184i	−0.888072	+	0.512729i
$438$	24.8362	−	15.5467i	1.18672	−	0.742848i
$439$	−14.7853	−	8.53628i	−0.705662	−	0.407414i	0.103791	−	0.994599i	$-0.466903\pi$
$439$	−14.7853	−	8.53628i	−0.705662	−	0.407414i	−0.809453	+	0.587185i	$0.800236\pi$
$440$	−9.00825	−	3.05150i	−0.429452	−	0.145475i
$441$	17.7270	−	11.2585i	0.844142	−	0.536120i
$442$		−	21.1548i		−	1.00623i
$443$	−14.9365	+	25.8707i	−0.709652	+	1.22915i	0.255334	+	0.966853i	$0.417815\pi$
$443$	−14.9365	+	25.8707i	−0.709652	+	1.22915i	−0.964986	+	0.262301i	$0.915519\pi$
$444$	−0.268830	+	0.506560i	−0.0127581	+	0.0240403i
$445$	16.2241	−	3.23790i	0.769095	−	0.153491i
$446$	29.3789			1.39113
$447$	−23.1322	+	0.826079i	−1.09411	+	0.0390722i
$448$	−0.647443	−	2.56531i	−0.0305888	−	0.121200i
$449$			30.0088i			1.41620i	0.706110	+	0.708102i	$0.250448\pi$
$449$			30.0088i			1.41620i	−0.706110	+	0.708102i	$0.749552\pi$
$450$	−13.4049	+	6.73121i	−0.631912	+	0.317312i
$451$	−3.57530	−	2.06420i	−0.168354	−	0.0971993i
$452$	4.40032			0.206973
$453$	−0.0550763	−	1.54227i	−0.00258771	−	0.0724621i
$454$	−14.8556	−	8.57689i	−0.697208	−	0.402533i
$455$	10.8205	−	15.7152i	0.507272	−	0.736740i
$456$	−2.62011	−	4.18570i	−0.122698	−	0.196013i
$457$	−0.248131	−	0.143259i	−0.0116071	−	0.00670135i	0.494185	−	0.869357i	$-0.335466\pi$
$457$	−0.248131	−	0.143259i	−0.0116071	−	0.00670135i	−0.505792	+	0.862655i	$0.668800\pi$
$458$	9.59057	+	5.53712i	0.448138	+	0.258733i
$459$	13.7892	−	31.1696i	0.643626	−	1.45487i
$460$	−16.4877	+	3.29052i	−0.768744	+	0.153421i
$461$	−10.0357	−	17.3823i	−0.467409	−	0.809576i	0.531897	−	0.846809i	$-0.321479\pi$
$461$	−10.0357	−	17.3823i	−0.467409	−	0.809576i	−0.999307	+	0.0372323i	$0.988146\pi$
$462$	18.9300	+	4.64617i	0.880705	+	0.216159i
$463$	13.2014	+	7.62183i	0.613521	+	0.354216i	0.774342	−	0.632767i	$-0.218081\pi$
$463$	13.2014	+	7.62183i	0.613521	+	0.354216i	−0.160821	+	0.986984i	$0.551414\pi$
$464$			0.0578466i			0.00268546i
$465$	−38.3224	+	9.08140i	−1.77716	+	0.421140i
$466$	23.4304			1.08539
$467$	−12.6675	+	7.31361i	−0.586184	+	0.338434i	−0.763587	−	0.645705i	$-0.776564\pi$
$467$	−12.6675	+	7.31361i	−0.586184	+	0.338434i	0.177403	+	0.984138i	$0.443230\pi$
$468$	9.65073	−	0.690159i	0.446105	−	0.0319026i
$469$	15.8547	+	16.3238i	0.732101	+	0.753764i
$470$	0.238214	+	1.19362i	0.0109880	+	0.0550575i
$471$	23.8387	−	14.9222i	1.09843	−	0.687580i
$472$	−0.615269	−	1.06568i	−0.0283200	−	0.0490517i
$473$	−14.3848	−	24.9152i	−0.661414	−	1.14560i
$474$	5.04558	−	3.15837i	0.231751	−	0.145069i
$475$	−14.1355	−	1.84269i	−0.648583	−	0.0845484i
$476$	16.8268	−	4.24682i	0.771257	−	0.194653i
$477$	−2.49565	+	5.13741i	−0.114268	+	0.235226i
$478$	0.758949	−	0.438179i	0.0347135	−	0.0200419i
$479$	6.57154			0.300261			0.150131	−	0.988666i	$-0.452031\pi$
$479$	6.57154			0.300261			0.150131	+	0.988666i	$0.452031\pi$
$480$	−0.893062	−	3.76861i	−0.0407625	−	0.172013i
$481$		−	1.06783i		−	0.0486886i
$482$	14.7042	+	8.48945i	0.669756	+	0.386684i
$483$	33.0863	−	9.61871i	1.50548	−	0.437666i
$484$	3.54603	+	6.14190i	0.161183	+	0.279177i
$485$	−19.6621	+	3.92403i	−0.892808	+	0.178181i
$486$	14.6693	+	5.27370i	0.665412	+	0.239220i
$487$	−11.8823	−	6.86022i	−0.538436	−	0.310866i	0.206009	−	0.978550i	$-0.433952\pi$
$487$	−11.8823	−	6.86022i	−0.538436	−	0.310866i	−0.744445	+	0.667684i	$0.767286\pi$
$488$	−3.90523	−	2.25468i	−0.176781	−	0.102065i
$489$	11.2894	+	18.0351i	0.510524	+	0.815576i
$490$	14.6723	+	5.45195i	0.662827	+	0.246294i
$491$	−10.5069	−	6.06619i	−0.474172	−	0.273763i	0.243813	−	0.969822i	$-0.421602\pi$
$491$	−10.5069	−	6.06619i	−0.474172	−	0.273763i	−0.717985	+	0.696059i	$0.754935\pi$
$492$	−0.0599966	−	1.68005i	−0.00270485	−	0.0757424i
$493$	−0.379438			−0.0170890
$494$	7.96303	+	4.59746i	0.358274	+	0.206849i
$495$	27.6089	+	7.20347i	1.24093	+	0.323772i
$496$		−	10.1688i		−	0.456594i
$497$	−8.61175	+	2.17347i	−0.386290	+	0.0974933i
$498$	−0.671447	+	0.0239782i	−0.0300883	+	0.00107449i
$499$	−15.0271			−0.672706			−0.336353	−	0.941736i	$-0.609193\pi$
$499$	−15.0271			−0.672706			−0.336353	+	0.941736i	$0.609193\pi$
$500$	−10.0368	−	4.92580i	−0.448857	−	0.220288i
$501$	13.9568	−	26.2990i	0.623545	−	1.17495i
$502$	3.82625	−	6.62726i	0.170774	−	0.295789i
$503$		−	8.31165i		−	0.370598i	−0.982682	−	0.185299i	$-0.940675\pi$
$503$		−	8.31165i		−	0.370598i	0.982682	−	0.185299i	$-0.0593254\pi$
$504$	2.48634	+	7.53778i	0.110751	+	0.335759i
$505$	−2.22624	+	6.57203i	−0.0990666	+	0.292452i
$506$	27.6969	+	15.9908i	1.23128	+	0.710879i
$507$	3.81505	−	2.38810i	0.169432	−	0.106059i
$508$	2.97314	−	1.71654i	0.131912	−	0.0761593i
$509$	−20.5051			−0.908871			−0.454436	−	0.890780i	$-0.650159\pi$
$509$	−20.5051			−0.908871			−0.454436	+	0.890780i	$0.650159\pi$
$510$	24.7198	−	5.85793i	1.09461	−	0.259394i
$511$	−43.0591	−	12.2131i	−1.90482	−	0.540277i
$512$	1.00000			0.0441942
$513$	8.73603	+	11.9644i	0.385705	+	0.528242i
$514$	5.70502	+	3.29380i	0.251638	+	0.145283i
$515$	−9.00775	+	26.5915i	−0.396929	+	1.17176i
$516$	5.49180	−	10.3483i	0.241763	−	0.455557i
$517$	1.15764	−	2.00510i	0.0509131	−	0.0881841i
$518$	0.849363	−	0.214366i	0.0373189	−	0.00941869i
$519$	−5.34988	+	10.0808i	−0.234834	+	0.442500i
$520$	4.75838	+	5.41894i	0.208669	+	0.237636i
$521$	−11.0285	+	19.1019i	−0.483166	+	0.836869i	−0.999813	−	0.0193301i	$-0.993847\pi$
$521$	−11.0285	+	19.1019i	−0.483166	+	0.836869i	0.516647	+	0.856199i	$0.327180\pi$
$522$	−0.0123789	−	0.173098i	−0.000541808	−	0.00757629i
$523$	−11.6387	−	20.1588i	−0.508924	−	0.881483i	−0.999947	−	0.0103357i	$-0.996710\pi$
$523$	−11.6387	−	20.1588i	−0.508924	−	0.881483i	0.491022	−	0.871147i	$-0.336623\pi$
$524$	−10.1477	−	17.5762i	−0.443302	−	0.767822i
$525$	21.3597	+	8.29226i	0.932215	+	0.361904i
$526$	14.6810	−	25.4283i	0.640123	−	1.10873i
$527$	66.7012			2.90555
$528$	−3.45357	+	6.50761i	−0.150297	+	0.283207i
$529$	33.5346			1.45802
$530$	−4.17477	+	0.833174i	−0.181341	+	0.0361908i
$531$	2.06915	+	3.05722i	0.0897936	+	0.132672i
$532$	−2.05831	+	7.25685i	−0.0892389	+	0.314624i
$533$	1.56514	+	2.71091i	0.0677939	+	0.117422i
$534$	−0.457346	−	12.8068i	−0.0197913	−	0.554204i
$535$	5.01314	−	1.00049i	0.216737	−	0.0432550i
$536$	−7.44867	+	4.30049i	−0.321733	+	0.185753i
$537$	8.72968	−	16.4495i	0.376714	−	0.709847i
$538$	−5.09477	−	8.82440i	−0.219651	−	0.380447i
$539$	−14.1291	−	26.2084i	−0.608585	−	1.12887i
$540$	3.47882	+	11.0859i	0.149705	+	0.477062i
$541$	2.50191	+	4.33344i	0.107566	+	0.186309i	0.914784	−	0.403944i	$-0.132361\pi$
$541$	2.50191	+	4.33344i	0.107566	+	0.186309i	−0.807218	+	0.590254i	$0.799028\pi$
$542$			28.5128i			1.22473i
$543$	30.2125	−	1.07893i	1.29654	−	0.0463012i
$544$			6.55938i			0.281231i
$545$	18.8989	+	21.5224i	0.809539	+	0.921919i
$546$	−10.6689	−	10.2276i	−0.456589	−	0.437701i
$547$	−36.7469	+	21.2159i	−1.57119	+	0.907124i	−0.575162	+	0.818040i	$0.695061\pi$
$547$	−36.7469	+	21.2159i	−1.57119	+	0.907124i	−0.996024	+	0.0890846i	$0.971606\pi$
$548$	11.1346	+	19.2856i	0.475645	+	0.823842i
$549$	12.1683	+	5.91113i	0.519332	+	0.252281i
$550$	8.16366	+	19.6381i	0.348100	+	0.837372i
$551$	0.0824611	−	0.142827i	0.00351296	−	0.00608463i
$552$	0.464778	+	13.0149i	0.0197823	+	0.553951i
$553$	−8.74765	−	2.48115i	−0.371988	−	0.105509i
$554$	−15.7567	−	9.09715i	−0.669439	−	0.386501i
$555$	1.24777	−	0.295689i	0.0529650	−	0.0125513i
$556$			3.61149i			0.153161i
$557$	−12.7850	+	22.1443i	−0.541718	+	0.938284i	0.457087	+	0.889422i	$0.348893\pi$
$557$	−12.7850	+	22.1443i	−0.541718	+	0.938284i	−0.998806	+	0.0488618i	$0.984441\pi$
$558$	2.17607	+	30.4288i	0.0921206	+	1.28815i
$559$			21.8141i			0.922636i
$560$	−3.35506	+	4.87274i	−0.141777	+	0.205911i
$561$	−42.6859	−	22.6533i	−1.80220	−	0.956422i
$562$			7.07916i			0.298616i
$563$	−23.9827	+	13.8464i	−1.01075	+	0.583557i	−0.911411	−	0.411497i	$-0.865006\pi$
$563$	−23.9827	+	13.8464i	−1.01075	+	0.583557i	−0.0993391	+	0.995054i	$0.531673\pi$
$564$	0.942204	−	0.0336473i	0.0396740	−	0.00141681i
$565$	−6.49227	−	7.39353i	−0.273132	−	0.311048i
$566$	26.1559			1.09941
$567$	−9.05307	−	22.0237i	−0.380193	−	0.924907i
$568$		−	3.35700i		−	0.140857i
$569$	16.3160	+	9.42003i	0.684001	+	0.394908i	0.801361	−	0.598181i	$-0.204110\pi$
$569$	16.3160	+	9.42003i	0.684001	+	0.394908i	−0.117360	+	0.993089i	$0.537443\pi$
$570$	−3.16718	+	10.5780i	−0.132659	+	0.443064i
$571$	5.23363	+	9.06492i	0.219021	+	0.379355i	0.954509	−	0.298183i	$-0.0963805\pi$
$571$	5.23363	+	9.06492i	0.219021	+	0.379355i	−0.735488	+	0.677538i	$0.763047\pi$
$572$		−	13.7180i		−	0.573578i
$573$	−16.9681	+	31.9731i	−0.708851	+	1.33570i
$574$	−1.84209	+	1.78915i	−0.0768875	+	0.0746778i
$575$	29.8550	+	22.8483i	1.24504	+	0.952839i
$576$	−2.99236	+	0.213994i	−0.124682	+	0.00891644i
$577$	12.1563	−	21.0553i	0.506073	−	0.876544i	−0.493902	−	0.869517i	$-0.664430\pi$
$577$	12.1563	−	21.0553i	0.506073	−	0.876544i	0.999975	−	0.00702671i	$-0.00223669\pi$
$578$	−26.0254			−1.08252
$579$	3.21730	+	5.13972i	0.133706	+	0.213599i
$580$	0.0971955	−	0.0853475i	0.00403582	−	0.00354386i
$581$	0.715052	+	0.736210i	0.0296654	+	0.0305431i
$582$	0.554260	+	15.5206i	0.0229748	+	0.643350i
$583$	7.01299	+	4.04895i	0.290449	+	0.167691i
$584$	8.45840	−	14.6504i	0.350011	−	0.606237i
$585$	−15.3984	−	15.1971i	−0.636646	−	0.628325i
$586$	13.0082	−	7.51027i	0.537363	−	0.310246i
$587$	−13.8270	+	7.98305i	−0.570703	+	0.329496i	−0.757430	−	0.652916i	$-0.773545\pi$
$587$	−13.8270	+	7.98305i	−0.570703	+	0.329496i	0.186727	+	0.982412i	$0.440212\pi$
$588$	5.99338	−	10.5394i	0.247163	−	0.434638i
$589$	−14.4958	+	25.1075i	−0.597289	+	1.03454i
$590$	−0.882805	+	2.60610i	−0.0363445	+	0.107292i
$591$	−0.568768	−	15.9269i	−0.0233960	−	0.655144i
$592$			0.331096i			0.0136080i
$593$	15.2225	−	8.78872i	0.625114	−	0.360910i	−0.153743	−	0.988111i	$-0.549133\pi$
$593$	15.2225	−	8.78872i	0.625114	−	0.360910i	0.778857	+	0.627201i	$0.215800\pi$
$594$	8.94173	−	20.2121i	0.366884	−	0.829314i
$595$	−31.9621	−	22.0071i	−1.31032	−	0.902203i
$596$	−11.5735	+	6.68194i	−0.474068	+	0.273703i
$597$	8.65181	−	16.3027i	0.354095	−	0.667226i
$598$	−12.1248	−	21.0007i	−0.495819	−	0.858783i
$599$	−8.55345	+	4.93833i	−0.349484	+	0.201775i	−0.664458	−	0.747325i	$-0.731338\pi$
$599$	−8.55345	+	4.93833i	−0.349484	+	0.201775i	0.314974	+	0.949100i	$0.398004\pi$
$600$	−5.01449	+	7.06080i	−0.204716	+	0.288256i
$601$	−27.9885	+	16.1592i	−1.14168	+	0.659147i	−0.946845	−	0.321689i	$-0.895749\pi$
$601$	−27.9885	+	16.1592i	−1.14168	+	0.659147i	−0.194831	+	0.980837i	$0.562416\pi$
$602$	−17.3512	+	4.37917i	−0.707183	+	0.178482i
$603$	21.3688	−	14.4626i	0.870205	−	0.588962i
$604$	−0.445498	−	0.771625i	−0.0181271	−	0.0313970i
$605$	5.08793	−	15.0199i	0.206854	−	0.610648i
$606$	4.74767	+	2.51958i	0.192861	+	0.102351i
$607$	−32.4088			−1.31543			−0.657716	−	0.753266i	$-0.728477\pi$
$607$	−32.4088			−1.31543			−0.657716	+	0.753266i	$0.728477\pi$
$608$	−2.46906	−	1.42551i	−0.100134	−	0.0578122i
$609$	−0.183445	+	0.191361i	−0.00743355	+	0.00775433i
$610$	1.97343	+	9.88825i	0.0799020	+	0.400364i
$611$	−1.52033	+	0.877764i	−0.0615060	+	0.0355105i
$612$	−1.40367	−	19.6280i	−0.0567400	−	0.793415i
$613$	28.5172	+	16.4644i	1.15180	+	0.664992i	0.949325	−	0.314296i	$-0.101768\pi$
$613$	28.5172	+	16.4644i	1.15180	+	0.664992i	0.202474	+	0.979288i	$0.435102\pi$
$614$	11.6148	−	20.1174i	0.468734	−	0.811871i
$615$	−2.73434	+	2.57957i	−0.110259	+	0.104018i
$616$	10.9115	−	2.75388i	0.439636	−	0.110957i
$617$	10.9432	−	18.9542i	0.440558	−	0.763069i	−0.557173	−	0.830396i	$-0.688114\pi$
$617$	10.9432	−	18.9542i	0.440558	−	0.763069i	0.997731	+	0.0673277i	$0.0214473\pi$
$618$	19.2099	+	10.1946i	0.772734	+	0.410088i
$619$		−	16.3846i		−	0.658551i	−0.944234	−	0.329276i	$-0.893195\pi$
$619$		−	16.3846i		−	0.658551i	0.944234	−	0.329276i	$-0.106805\pi$
$620$	−17.0859	+	15.0032i	−0.686188	+	0.602543i
$621$	−4.17590	−	38.8458i	−0.167573	−	1.55883i
$622$	0.198446			0.00795696
$623$	−14.0420	+	13.6385i	−0.562582	+	0.546414i
$624$	4.73493	−	2.96391i	0.189549	−	0.118651i
$625$	6.53188	+	24.1316i	0.261275	+	0.965264i
$626$	−1.59131	−	2.75623i	−0.0636016	−	0.110161i
$627$	17.8038	−	11.1446i	0.711014	−	0.445072i
$628$	8.11868	−	14.0620i	0.323971	−	0.561134i
$629$	−2.17178			−0.0865946
$630$	8.99680	−	15.2989i	0.358441	−	0.609524i
$631$	3.75165			0.149351			0.0746755	−	0.997208i	$-0.476208\pi$
$631$	3.75165			0.149351			0.0746755	+	0.997208i	$0.476208\pi$
$632$	1.71836	−	2.97629i	0.0683528	−	0.118390i
$633$	13.3728	+	7.09692i	0.531522	+	0.282077i
$634$	11.8116	+	20.4583i	0.469099	+	0.812503i
$635$	−7.27079	−	2.46294i	−0.288532	−	0.0977389i
$636$	0.117684	+	3.29544i	0.00466648	+	0.130673i
$637$	−0.658139	+	22.5663i	−0.0260764	+	0.894109i
$638$	−0.246049			−0.00974118
$639$	0.718379	+	10.0453i	0.0284187	+	0.397388i
$640$	−1.47541	−	1.68023i	−0.0583207	−	0.0664168i
$641$			0.643043i			0.0253987i	0.999919	+	0.0126993i	$0.00404243\pi$
$641$			0.643043i			0.0253987i	−0.999919	+	0.0126993i	$0.995958\pi$
$642$	−0.141317	−	3.95722i	−0.00557734	−	0.156179i
$643$	9.73259	−	16.8573i	0.383816	−	0.664789i	−0.607788	−	0.794099i	$-0.707943\pi$
$643$	9.73259	−	16.8573i	0.383816	−	0.664789i	0.991604	+	0.129310i	$0.0412764\pi$
$644$	14.2702	−	13.8601i	0.562326	−	0.546165i
$645$	−25.4901	+	6.04048i	−1.00367	+	0.237844i
$646$	9.35048	−	16.1955i	0.367890	−	0.637204i
$647$	16.9629	+	9.79351i	0.666879	+	0.385023i	0.794893	−	0.606750i	$-0.207527\pi$
$647$	16.9629	+	9.79351i	0.666879	+	0.385023i	−0.128014	+	0.991772i	$0.540860\pi$
$648$	8.90841	−	1.28070i	0.349956	−	0.0503105i
$649$	4.53283	−	2.61703i	0.177929	−	0.102727i
$650$	2.08448	−	15.9903i	0.0817600	−	0.627192i
$651$	32.2476	−	33.6392i	1.26388	−	1.31843i
$652$	10.6386	+	6.14217i	0.416638	+	0.240546i
$653$	−44.4545			−1.73964			−0.869820	−	0.493370i	$-0.835765\pi$
$653$	−44.4545			−1.73964			−0.869820	+	0.493370i	$0.835765\pi$
$654$	18.8057	−	11.7718i	0.735362	−	0.460313i
$655$	−14.5601	+	42.9825i	−0.568911	+	1.67947i
$656$	−0.485297	−	0.840559i	−0.0189477	−	0.0328183i
$657$	−22.1755	+	45.6493i	−0.865148	+	1.78095i
$658$	−1.00339	−	1.03308i	−0.0391163	−	0.0402737i
$659$	38.2434	−	22.0798i	1.48975	−	0.860108i	0.489819	−	0.871824i	$-0.337063\pi$
$659$	38.2434	−	22.0798i	1.48975	−	0.860108i	0.999931	+	0.0117165i	$0.00372956\pi$
$660$	16.0297	−	3.79862i	0.623955	−	0.147861i
$661$	27.2188	−	15.7148i	1.05869	−	0.611233i	0.133618	−	0.991033i	$-0.457340\pi$
$661$	27.2188	−	15.7148i	1.05869	−	0.611233i	0.925069	+	0.379800i	$0.124007\pi$
$662$	−11.8910	−	20.5958i	−0.462156	−	0.800477i
$663$	19.4414	+	31.0582i	0.755042	+	1.20620i
$664$	−0.335938	+	0.193954i	−0.0130369	+	0.00752686i
$665$	15.2300	−	7.24841i	0.590594	−	0.281081i
$666$	−0.0708527	−	0.990757i	−0.00274548	−	0.0383911i
$667$	−0.376674	+	0.217473i	−0.0145849	+	0.00842058i
$668$		−	17.1895i		−	0.665080i
$669$	−43.1322	+	26.9994i	−1.66759	+	1.04386i
$670$	18.2156	+	6.17046i	0.703732	+	0.238386i
$671$	9.59024	−	16.6108i	0.370227	−	0.641252i
$672$	3.30807	+	3.17122i	0.127612	+	0.122333i
$673$	30.4994	−	17.6088i	1.17567	−	0.678771i	0.220657	−	0.975351i	$-0.429180\pi$
$673$	30.4994	−	17.6088i	1.17567	−	0.678771i	0.955008	+	0.296581i	$0.0958464\pi$
$674$	−8.84127	+	5.10451i	−0.340553	+	0.196618i
$675$	13.4942	−	22.2015i	0.519391	−	0.854537i
$676$	1.29928	−	2.25043i	0.0499725	−	0.0865548i
$677$	23.9797	+	13.8447i	0.921615	+	0.532094i	0.884150	−	0.467203i	$-0.154738\pi$
$677$	23.9797	+	13.8447i	0.921615	+	0.532094i	0.0374649	+	0.999298i	$0.488072\pi$
$678$	−6.46027	+	4.04392i	−0.248105	+	0.155306i
$679$	17.0176	−	16.5285i	0.653076	−	0.634307i
$680$	11.0212	−	9.67778i	0.422645	−	0.371126i
$681$	29.6923	−	1.06035i	1.13781	−	0.0406326i
$682$	43.2529			1.65624
$683$	3.51121	−	6.08159i	0.134353	−	0.232706i	−0.790997	−	0.611820i	$-0.790438\pi$
$683$	3.51121	−	6.08159i	0.134353	−	0.232706i	0.925350	+	0.379114i	$0.123771\pi$
$684$	7.69337	+	3.73728i	0.294163	+	0.142898i
$685$	15.9762	−	47.1629i	0.610419	−	1.80200i
$686$	−18.0817	+	4.00668i	−0.690361	+	0.152976i
$687$	−19.1689	+	0.684546i	−0.731340	+	0.0261171i
$688$		−	6.76379i		−	0.257867i
$689$	−3.07005	−	5.31748i	−0.116960	−	0.202580i
$690$	21.1822	−	19.9833i	0.806394	−	0.760750i
$691$	0.310049	+	0.179007i	0.0117948	+	0.00680974i	0.505886	−	0.862600i	$-0.331166\pi$
$691$	0.310049	+	0.179007i	0.0117948	+	0.00680974i	−0.494091	+	0.869410i	$0.664499\pi$
$692$			6.58900i			0.250476i
$693$	−32.0618	+	10.5756i	−1.21793	+	0.401734i
$694$	−14.2125			−0.539499
$695$	6.06812	−	5.32843i	0.230177	−	0.202119i
$696$	−0.0531614	−	0.0849268i	−0.00201508	−	0.00321914i
$697$	5.51354	−	3.18325i	0.208840	−	0.120574i
$698$			20.8016i			0.787352i
$699$	−34.3991	+	21.5327i	−1.30109	+	0.814442i
$700$	13.1374	−	1.55203i	0.496547	−	0.0586613i
$701$		−	37.7652i		−	1.42637i	−0.700975	−	0.713186i	$-0.747251\pi$
$701$		−	37.7652i		−	1.42637i	0.700975	−	0.713186i	$-0.252749\pi$
$702$	−13.5343	+	9.88233i	−0.510821	+	0.372985i
$703$	0.471981	−	0.817496i	0.0178011	−	0.0308324i
$704$			4.25348i			0.160309i
$705$	−1.44667	−	1.53347i	−0.0544849	−	0.0577539i
$706$	−24.8702	−	14.3588i	−0.936004	−	0.540402i
$707$	−2.00912	−	7.96055i	−0.0755606	−	0.299387i
$708$	1.88266	+	0.999124i	0.0707548	+	0.0375494i
$709$	5.33508	−	9.24063i	0.200363	−	0.347039i	−0.748282	−	0.663380i	$-0.769121\pi$
$709$	5.33508	−	9.24063i	0.200363	−	0.347039i	0.948645	+	0.316341i	$0.102454\pi$
$710$	−5.64052	+	4.95295i	−0.211685	+	0.185881i
$711$	−4.50505	+	9.27385i	−0.168952	+	0.347796i
$712$	−3.69936	−	6.40747i	−0.138639	−	0.240130i
$713$	66.2154	−	38.2295i	2.47978	−	1.43170i
$714$	−20.8012	+	21.6989i	−0.778467	+	0.812061i
$715$	−23.0493	+	20.2397i	−0.861996	+	0.756921i
$716$		−	10.7516i		−	0.401807i
$717$	−0.711552	+	1.34079i	−0.0265734	+	0.0500726i
$718$		−	4.74779i		−	0.177186i
$719$	14.8805	+	25.7738i	0.554950	+	0.961202i	0.997907	+	0.0646590i	$0.0205960\pi$
$719$	14.8805	+	25.7738i	0.554950	+	0.961202i	−0.442957	+	0.896543i	$0.646071\pi$
$720$	4.77452	+	4.71211i	0.177936	+	0.175610i
$721$	−8.12921	−	32.2097i	−0.302747	−	1.19955i
$722$	−5.43582	−	9.41512i	−0.202300	−	0.350395i
$723$	−29.3896	+	1.04954i	−1.09301	+	0.0390327i
$724$	15.1159	−	8.72717i	0.561778	−	0.324343i
$725$	−0.286807	−	0.0373877i	−0.0106517	−	0.00138855i
$726$	−10.8505	−	5.75833i	−0.402700	−	0.213712i
$727$	−15.8270	−	27.4132i	−0.586992	−	1.01670i	−0.994624	−	0.103554i	$-0.966979\pi$
$727$	−15.8270	−	27.4132i	−0.586992	−	1.01670i	0.407632	−	0.913146i	$-0.366355\pi$
$728$	−8.20906	−	2.32839i	−0.304248	−	0.0862958i
$729$	−26.3831	+	5.73865i	−0.977152	+	0.212543i
$730$	−37.0956	+	7.40330i	−1.37297	+	0.274008i
$731$	44.3662			1.64094
$732$	7.80548	−	0.278743i	0.288499	−	0.0103026i
$733$	5.32798			0.196794			0.0983968	−	0.995147i	$-0.468629\pi$
$733$	5.32798			0.196794			0.0983968	+	0.995147i	$0.468629\pi$
$734$	−12.7735	+	22.1243i	−0.471478	+	0.816624i
$735$	−26.5513	+	5.47973i	−0.979360	+	0.202123i
$736$	3.75947	+	6.51160i	0.138576	+	0.240021i
$737$	−18.2920	−	31.6827i	−0.673796	−	1.16705i
$738$	1.63206	+	2.41140i	0.0600769	+	0.0887650i
$739$	4.81913	−	8.34698i	0.177275	−	0.307049i	−0.763672	−	0.645605i	$-0.776605\pi$
$739$	4.81913	−	8.34698i	0.177275	−	0.307049i	0.940946	+	0.338556i	$0.109939\pi$
$740$	0.556316	−	0.488502i	0.0204506	−	0.0179577i
$741$	−15.9159	+	0.568377i	−0.584686	+	0.0208799i
$742$	3.61329	−	3.50945i	0.132648	−	0.128836i
$743$	−6.25928	+	10.8414i	−0.229631	+	0.397732i	−0.957699	−	0.287773i	$-0.907085\pi$
$743$	−6.25928	+	10.8414i	−0.229631	+	0.397732i	0.728068	+	0.685505i	$0.240419\pi$
$744$	9.34522	+	14.9292i	0.342613	+	0.547333i
$745$	28.3028	+	9.58744i	1.03693	+	0.351257i
$746$	32.0073	+	18.4794i	1.17187	+	0.676581i
$747$	0.963741	−	0.652268i	0.0352614	−	0.0238652i
$748$	−27.9001			−1.02013
$749$	−4.33891	+	4.21421i	−0.158540	+	0.153984i
$750$	19.2622	−	1.99210i	0.703355	−	0.0727411i
$751$	30.5684			1.11546			0.557728	−	0.830024i	$-0.311673\pi$
$751$	30.5684			1.11546			0.557728	+	0.830024i	$0.311673\pi$
$752$	0.471402	−	0.272164i	0.0171903	−	0.00992481i
$753$	0.473034	+	13.2461i	0.0172383	+	0.482714i
$754$	0.161568	+	0.0932813i	0.00588396	+	0.00339710i
$755$	−0.639213	+	1.88700i	−0.0232633	+	0.0686751i
$756$	−10.5776	−	8.78153i	−0.384702	−	0.319381i
$757$			5.43126i			0.197403i	0.995117	+	0.0987013i	$0.0314688\pi$
$757$			5.43126i			0.197403i	−0.995117	+	0.0987013i	$0.968531\pi$
$758$	6.37229	−	11.0371i	0.231452	−	0.400886i
$759$	−55.3586	+	1.97692i	−2.00939	+	0.0717577i
$760$	1.24769	+	6.25180i	0.0452586	+	0.226777i
$761$	−14.2887			−0.517964			−0.258982	−	0.965882i	$-0.583387\pi$
$761$	−14.2887			−0.517964			−0.258982	+	0.965882i	$0.583387\pi$
$762$	−2.78746	+	5.25246i	−0.100979	+	0.190276i
$763$	−32.6039	−	9.24766i	−1.18034	−	0.334788i
$764$			20.8981i			0.756068i
$765$	−30.9085	+	31.3179i	−1.11750	+	1.13230i
$766$	−27.3358	−	15.7823i	−0.987682	−	0.570239i
$767$	−3.96864			−0.143299
$768$	−1.46814	+	0.919006i	−0.0529768	+	0.0331618i
$769$	−20.9348	−	12.0867i	−0.754928	−	0.435858i	0.0725437	−	0.997365i	$-0.476888\pi$
$769$	−20.9348	−	12.0867i	−0.754928	−	0.435858i	−0.827472	+	0.561507i	$0.810222\pi$
$770$	−20.7261	−	14.2707i	−0.746916	−	0.514279i
$771$	−11.4028	+	0.407207i	−0.410661	+	0.0146652i
$772$	3.03182	+	1.75042i	0.109118	+	0.0629990i
$773$	4.26935	+	2.46491i	0.153558	+	0.0886567i	0.574810	−	0.818287i	$-0.305076\pi$
$773$	4.26935	+	2.46491i	0.153558	+	0.0886567i	−0.421252	+	0.906944i	$0.638409\pi$
$774$	1.44741	+	20.2397i	0.0520262	+	0.727500i
$775$	50.4176	+	6.57237i	1.81105	+	0.236087i
$776$	4.48327	+	7.76525i	0.160940	+	0.278756i
$777$	−1.04998	+	1.09529i	−0.0376678	+	0.0392933i
$778$	32.7220	+	18.8920i	1.17314	+	0.677313i
$779$			2.76719i			0.0991449i
$780$	−11.9660	−	3.58276i	−0.428452	−	0.128284i
$781$	14.2789			0.510940
$782$	−42.7120	+	24.6598i	−1.52738	+	0.881833i
$783$	0.177252	+	0.242755i	0.00633447	+	0.00867536i
$784$	0.204066	−	6.99702i	0.00728808	−	0.249894i
$785$	−35.6057	+	7.10595i	−1.27082	+	0.253622i
$786$	31.0508	+	16.4786i	1.10755	+	0.587772i
$787$	14.4124	+	24.9631i	0.513748	+	0.889838i	0.999873	+	0.0159482i	$0.00507668\pi$
$787$	14.4124	+	24.9631i	0.513748	+	0.889838i	−0.486125	+	0.873889i	$0.661590\pi$
$788$	−4.60062	−	7.96851i	−0.163890	−	0.283866i
$789$	1.81499	+	50.8241i	0.0646154	+	1.80939i
$790$	−7.53614	+	1.50401i	−0.268124	+	0.0535104i
$791$	11.2003	+	3.17682i	0.398238	+	0.112955i
$792$	−0.910220	−	12.7279i	−0.0323433	−	0.452267i
$793$	−12.5948	+	7.27164i	−0.447256	+	0.258223i
$794$	16.1651			0.573679
$795$	5.36345	−	5.05986i	0.190222	−	0.179455i
$796$		−	10.6557i		−	0.377682i
$797$	3.98408	+	2.30021i	0.141123	+	0.0814776i	0.568899	−	0.822407i	$-0.307369\pi$
$797$	3.98408	+	2.30021i	0.141123	+	0.0814776i	−0.427776	+	0.903885i	$0.640703\pi$
$798$	−3.64721	−	12.5456i	−0.129110	−	0.444111i
$799$	1.78523	+	3.09211i	0.0631568	+	0.109391i
$800$	−0.646325	+	4.95805i	−0.0228510	+	0.175294i
$801$	12.4410	+	18.3818i	0.439580	+	0.649489i
$802$	−8.11259	−	4.68380i	−0.286465	−	0.165391i
$803$	62.3151	+	35.9776i	2.19905	+	1.26962i
$804$	6.98349	−	13.1591i	0.246289	−	0.464085i
$805$	−44.3426	−	3.52787i	−1.56287	−	0.124341i
$806$	−28.4020	−	16.3979i	−1.00042	−	0.577591i
$807$	15.5895	+	8.27330i	0.548776	+	0.291234i
$808$	3.10315			0.109169
$809$	9.00006	+	5.19619i	0.316425	+	0.182688i	0.649798	−	0.760107i	$-0.274853\pi$
$809$	9.00006	+	5.19619i	0.316425	+	0.182688i	−0.333373	+	0.942795i	$0.608187\pi$
$810$	−15.2954	−	13.0786i	−0.537427	−	0.459535i
$811$			37.3233i			1.31060i	0.755369	+	0.655299i	$0.227457\pi$
$811$			37.3233i			1.31060i	−0.755369	+	0.655299i	$0.772543\pi$
$812$	−0.0417625	+	0.147240i	−0.00146558	+	0.00516710i
$813$	−26.2035	−	41.8608i	−0.918996	−	1.46812i
$814$	−1.40831			−0.0493612
$815$	−5.37600	−	26.9374i	−0.188313	−	0.943577i
$816$	−6.02811	−	9.63007i	−0.211026	−	0.337120i
$817$	−9.64187	+	16.7002i	−0.337326	+	0.584266i
$818$		−	18.2495i		−	0.638079i
$819$	25.0627	+	5.21068i	0.875762	+	0.182076i
$820$	−0.696318	+	2.05558i	−0.0243165	+	0.0717839i
$821$	8.33276	+	4.81092i	0.290815	+	0.167902i	0.638310	−	0.769780i	$-0.279634\pi$
$821$	8.33276	+	4.81092i	0.290815	+	0.167902i	−0.347494	+	0.937682i	$0.612967\pi$
$822$	−34.0707	−	18.0812i	−1.18835	−	0.630655i
$823$	−29.2450	+	16.8846i	−1.01941	+	0.588560i	−0.913934	−	0.405862i	$-0.866971\pi$
$823$	−29.2450	+	16.8846i	−1.01941	+	0.588560i	−0.105481	+	0.994421i	$0.533638\pi$
$824$	12.5559			0.437404
$825$	−30.0329	−	21.3290i	−1.04561	−	0.742581i
$826$	−0.796703	−	3.15671i	−0.0277209	−	0.109836i
$827$	3.56688			0.124032			0.0620162	−	0.998075i	$-0.480247\pi$
$827$	3.56688			0.124032			0.0620162	+	0.998075i	$0.480247\pi$
$828$	−12.6431	−	18.6805i	−0.439379	−	0.649193i
$829$	−26.6295	−	15.3746i	−0.924881	−	0.533980i	−0.0396920	−	0.999212i	$-0.512638\pi$
$829$	−26.6295	−	15.3746i	−0.924881	−	0.533980i	−0.885189	+	0.465232i	$0.845971\pi$
$830$	0.821532	+	0.278290i	0.0285158	+	0.00965959i
$831$	31.4934	−	1.12467i	1.09249	−	0.0390143i
$832$	1.61256	−	2.79304i	0.0559055	−	0.0968313i
$833$	45.8961	+	1.33855i	1.59021	+	0.0463779i
$834$	−3.31898	−	5.30216i	−0.114927	−	0.183599i
$835$	−28.8822	+	25.3615i	−0.999510	+	0.877672i
$836$	6.06339	−	10.5021i	0.209707	−	0.363222i
$837$	−31.1590	−	42.6738i	−1.07701	−	1.47502i
$838$	5.45769	+	9.45300i	0.188533	+	0.326549i
$839$	−24.9770	−	43.2615i	−0.862302	−	1.49355i	−0.869701	−	0.493578i	$-0.835689\pi$
$839$	−24.9770	−	43.2615i	−0.862302	−	1.49355i	0.00739911	−	0.999973i	$-0.497645\pi$
$840$	0.447609	−	10.2372i	0.0154440	−	0.353216i
$841$	−14.4983	+	25.1118i	−0.499942	+	0.865925i
$842$	9.59402			0.330632
$843$	−6.50579	−	10.3932i	−0.224071	−	0.357960i
$844$	8.74068			0.300867
$845$	−5.69820	+	1.13721i	−0.196024	+	0.0391212i
$846$	−1.35236	+	0.915290i	−0.0464952	+	0.0314683i
$847$	4.59170	+	18.1933i	0.157773	+	0.625130i
$848$	0.951917	+	1.64877i	0.0326890	+	0.0566189i
$849$	−38.4005	+	24.0374i	−1.31790	+	0.824963i
$850$	−32.5217	−	4.23949i	−1.11549	−	0.145413i
$851$	−2.15596	+	1.24475i	−0.0739054	+	0.0426693i
$852$	3.08510	+	4.92854i	0.105694	+	0.168849i
$853$	6.54348	+	11.3336i	0.224044	+	0.388056i	0.956032	−	0.293261i	$-0.0947406\pi$
$853$	6.54348	+	11.3336i	0.224044	+	0.388056i	−0.731988	+	0.681318i	$0.761407\pi$
$854$	−8.31238	−	8.55834i	−0.284444	−	0.292860i
$855$	−5.07140	−	18.4406i	−0.173438	−	0.630656i
$856$	−1.14308	−	1.97987i	−0.0390696	−	0.0676706i
$857$			36.4596i			1.24544i	0.782447	+	0.622718i	$0.213972\pi$
$857$			36.4596i			1.24544i	−0.782447	+	0.622718i	$0.786028\pi$
$858$	12.6069	+	20.1399i	0.430393	+	0.687565i
$859$		−	11.4104i		−	0.389319i	−0.980871	−	0.194660i	$-0.937640\pi$
$859$		−	11.4104i		−	0.389319i	0.980871	−	0.194660i	$-0.0623602\pi$
$860$	−11.3647	+	9.97937i	−0.387533	+	0.340294i
$861$	1.06020	−	4.31962i	0.0361316	−	0.147212i
$862$	17.0044	−	9.81749i	0.579172	−	0.334385i
$863$	16.1265	+	27.9320i	0.548954	+	0.950816i	0.998347	+	0.0574817i	$0.0183071\pi$
$863$	16.1265	+	27.9320i	0.548954	+	0.950816i	−0.449393	+	0.893334i	$0.648360\pi$
$864$	4.19653	−	3.06417i	0.142769	−	0.104245i
$865$	11.0710	−	9.72148i	0.376426	−	0.330540i
$866$	−14.3693	+	24.8884i	−0.488289	+	0.845741i
$867$	38.2089	−	23.9175i	1.29764	−	0.812282i
$868$	7.34142	−	25.8832i	0.249184	−	0.878533i
$869$	12.6596	+	7.30901i	0.429447	+	0.247941i
$870$	−0.0642613	+	0.214625i	−0.00217866	+	0.00727648i
$871$			27.7392i			0.939908i
$872$	6.40462	−	11.0931i	0.216888	−	0.375661i
$873$	−15.0773	−	22.2770i	−0.510288	−	0.753963i
$874$		−	21.4367i		−	0.725108i
$875$	−21.9908	−	19.7839i	−0.743426	−	0.668819i
$876$	1.04570	+	29.2821i	0.0353309	+	0.989351i
$877$		−	12.9822i		−	0.438379i	−0.975682	−	0.219189i	$-0.929659\pi$
$877$		−	12.9822i		−	0.438379i	0.975682	−	0.219189i	$-0.0703412\pi$
$878$	14.7853	−	8.53628i	0.498978	−	0.288085i
$879$	−12.1958	+	22.9807i	−0.411354	+	0.775120i
$880$	7.14680	−	6.27562i	0.240919	−	0.211551i
$881$	13.5811			0.457560			0.228780	−	0.973478i	$-0.426526\pi$
$881$	13.5811			0.457560			0.228780	+	0.973478i	$0.426526\pi$
$882$	0.886685	+	20.9813i	0.0298562	+	0.706476i
$883$			15.6250i			0.525823i	0.964820	+	0.262911i	$0.0846827\pi$
$883$			15.6250i			0.525823i	−0.964820	+	0.262911i	$0.915317\pi$
$884$	18.3206	+	10.5774i	0.616189	+	0.355757i
$885$	−1.09895	−	4.63742i	−0.0369407	−	0.155885i
$886$	−14.9365	−	25.8707i	−0.501800	−	0.869143i
$887$		−	31.2381i		−	1.04887i	−0.851449	−	0.524437i	$-0.824276\pi$
$887$		−	31.2381i		−	1.04887i	0.851449	−	0.524437i	$-0.175724\pi$
$888$	−0.304279	−	0.486094i	−0.0102109	−	0.0163122i
$889$	8.80693	−	2.22273i	0.295375	−	0.0745479i
$890$	−5.30794	+	15.6694i	−0.177922	+	0.525240i
$891$	5.44741	+	37.8917i	0.182495	+	1.26942i
$892$	−14.6894	+	25.4429i	−0.491839	+	0.851890i
$893$	−1.55190			−0.0519322
$894$	10.8507	−	20.4461i	0.362901	−	0.683820i
$895$	−18.0652	+	15.8631i	−0.603852	+	0.530244i
$896$	2.54535	+	0.721953i	0.0850340	+	0.0241188i
$897$	37.1006	+	19.6892i	1.23875	+	0.657403i
$898$	−25.9884	−	15.0044i	−0.867244	−	0.500704i
$899$	−0.294116	+	0.509424i	−0.00980933	+	0.0169903i
$900$	0.873041	−	14.9746i	0.0291014	−	0.499152i
$901$	−10.8149	+	6.24398i	−0.360296	+	0.208017i
$902$	3.57530	−	2.06420i	0.119044	−	0.0687303i
$903$	21.4495	−	22.3751i	0.713794	−	0.744597i
$904$	−2.20016	+	3.81078i	−0.0731762	+	0.126745i
$905$	−36.9658	−	12.5220i	−1.22878	−	0.416245i
$906$	1.36318	+	0.723436i	0.0452887	+	0.0240346i
$907$			17.9546i			0.596173i	0.954539	+	0.298086i	$0.0963484\pi$
$907$			17.9546i			0.596173i	−0.954539	+	0.298086i	$0.903652\pi$
$908$	14.8556	−	8.57689i	0.493001	−	0.284634i
$909$	−9.28574	+	0.664058i	−0.307989	+	0.0220254i
$910$	8.19951	+	17.2284i	0.271811	+	0.571116i
$911$	2.41770	−	1.39586i	0.0801020	−	0.0462469i	−0.459414	−	0.888222i	$-0.651941\pi$
$911$	2.41770	−	1.39586i	0.0801020	−	0.0462469i	0.539516	+	0.841975i	$0.318607\pi$
$912$	4.93498	−	0.176234i	0.163413	−	0.00583569i
$913$	−0.824977	−	1.42890i	−0.0273028	−	0.0472898i
$914$	0.248131	−	0.143259i	0.00820744	−	0.00473857i
$915$	−11.9846	−	12.7037i	−0.396200	−	0.419972i
$916$	−9.59057	+	5.53712i	−0.316882	+	0.182952i
$917$	−13.1401	−	52.0638i	−0.433923	−	1.71930i
$918$	20.0990	+	27.5266i	0.663367	+	0.908514i
$919$	9.73375	+	16.8593i	0.321087	+	0.556139i	0.980713	−	0.195456i	$-0.0626185\pi$
$919$	9.73375	+	16.8593i	0.321087	+	0.556139i	−0.659626	+	0.751594i	$0.729285\pi$
$920$	5.39420	−	15.9241i	0.177841	−	0.525000i
$921$	1.43592	+	40.2091i	0.0473151	+	1.32493i
$922$	20.0714			0.661016
$923$	−9.37624	−	5.41337i	−0.308623	−	0.178183i
$924$	−13.4887	+	14.0708i	−0.443746	+	0.462895i
$925$	−1.64159	−	0.213996i	−0.0539751	−	0.00703613i
$926$	−13.2014	+	7.62183i	−0.433825	+	0.250469i
$927$	−37.5716	+	2.68688i	−1.23401	+	0.0882489i
$928$	−0.0500967	−	0.0289233i	−0.00164450	−	0.000949454i
$929$	−8.15506	+	14.1250i	−0.267559	+	0.463426i	−0.968231	−	0.250058i	$-0.919550\pi$
$929$	−8.15506	+	14.1250i	−0.267559	+	0.463426i	0.700672	+	0.713484i	$0.252884\pi$
$930$	11.2965	−	37.7289i	0.370426	−	1.23718i
$931$	−10.4782	+	16.9852i	−0.343409	+	0.556667i
$932$	−11.7152	+	20.2913i	−0.383745	+	0.664665i
$933$	−0.291346	+	0.182373i	−0.00953825	+	0.00597063i
$934$		−	14.6272i		−	0.478617i
$935$	41.1642	+	46.8786i	1.34621	+	1.53309i
$936$	−4.22767	+	8.70286i	−0.138186	+	0.284462i
$937$	−22.1662			−0.724138			−0.362069	−	0.932151i	$-0.617930\pi$
$937$	−22.1662			−0.724138			−0.362069	+	0.932151i	$0.617930\pi$
$938$	−22.0642	+	5.56865i	−0.720421	+	0.181823i
$939$	4.86926	+	2.58410i	0.158902	+	0.0843290i
$940$	−1.15281	−	0.390509i	−0.0376005	−	0.0127370i
$941$	−1.98371	−	3.43589i	−0.0646671	−	0.112007i	0.831879	−	0.554957i	$-0.187265\pi$
$941$	−1.98371	−	3.43589i	−0.0646671	−	0.112007i	−0.896546	+	0.442950i	$0.853932\pi$
$942$	1.00370	+	28.1060i	0.0327023	+	0.915743i
$943$	3.64892	−	6.32012i	0.118825	−	0.205811i
$944$	1.23054			0.0400506
$945$	0.851292	+	30.7291i	0.0276925	+	0.999616i
$946$	28.7696			0.935380
$947$	27.1246	−	46.9812i	0.881431	−	1.52668i	0.0316810	−	0.999498i	$-0.489914\pi$
$947$	27.1246	−	46.9812i	0.881431	−	1.52668i	0.849750	−	0.527186i	$-0.176753\pi$
$948$	0.212439	+	5.94879i	0.00689969	+	0.193208i
$949$	−27.2794	−	47.2493i	−0.885527	−	1.53378i
$950$	8.66358	−	11.3204i	0.281084	−	0.367282i
$951$	−36.1424	−	19.1807i	−1.17200	−	0.621975i
$952$	−4.73556	+	16.6959i	−0.153480	+	0.541117i
$953$	−22.6579			−0.733960			−0.366980	−	0.930229i	$-0.619608\pi$
$953$	−22.6579			−0.733960			−0.366980	+	0.930229i	$0.619608\pi$
$954$	−3.20130	−	4.73000i	−0.103646	−	0.153139i
$955$	35.1136	−	30.8333i	1.13625	−	0.997744i
$956$			0.876359i			0.0283435i
$957$	0.361234	−	0.226121i	0.0116770	−	0.00730945i
$958$	−3.28577	+	5.69112i	−0.106158	+	0.183872i
$959$	14.4180	+	57.1273i	0.465582	+	1.84474i
$960$	3.71025	+	1.11089i	0.119748	+	0.0358539i
$961$	36.2026	−	62.7047i	1.16783	−	2.02273i
$962$	0.924764	+	0.533913i	0.0298156	+	0.0172140i
$963$	3.84418	+	5.67987i	0.123877	+	0.183031i
$964$	−14.7042	+	8.48945i	−0.473589	+	0.273427i
$965$	−1.53207	−	7.67673i	−0.0493192	−	0.247123i
$966$	−8.21312	+	33.4630i	−0.264253	+	1.07665i
$967$	41.1433	+	23.7541i	1.32308	+	0.763880i	0.984219	−	0.176957i	$-0.0566252\pi$
$967$	41.1433	+	23.7541i	1.32308	+	0.763880i	0.338860	+	0.940837i	$0.389959\pi$
$968$	−7.09205			−0.227947
$969$	1.15599	+	32.3704i	0.0371356	+	1.03989i
$970$	6.43272	−	18.9899i	0.206542	−	0.609727i
$971$	−16.4415	−	28.4776i	−0.527634	−	0.913888i	−0.999481	−	0.0322080i	$-0.989746\pi$
$971$	−16.4415	−	28.4776i	−0.527634	−	0.913888i	0.471848	−	0.881680i	$-0.343587\pi$
$972$	−11.9018	+	10.0671i	−0.381751	+	0.322903i
$973$	−2.60733	+	9.19249i	−0.0835870	+	0.294698i
$974$	11.8823	−	6.86022i	0.380732	−	0.219816i
$975$	11.6349	+	25.3917i	0.372616	+	0.813184i
$976$	3.90523	−	2.25468i	0.125003	−	0.0721707i
$977$	−12.6826	−	21.9669i	−0.405752	−	0.702783i	0.588657	−	0.808383i	$-0.299657\pi$
$977$	−12.6826	−	21.9669i	−0.405752	−	0.702783i	−0.994409	+	0.105600i	$0.966324\pi$
$978$	−21.2636	+	0.759348i	−0.679934	+	0.0242813i
$979$	27.2540	−	15.7351i	0.871042	−	0.502896i
$980$	−12.0577	+	9.98061i	−0.385168	+	0.318819i
$981$	−16.7910	+	34.5651i	−0.536097	+	1.10358i
$982$	10.5069	−	6.06619i	0.335290	−	0.193580i
$983$		−	45.9352i		−	1.46511i	−0.680710	−	0.732553i	$-0.738329\pi$
$983$		−	45.9352i		−	1.46511i	0.680710	−	0.732553i	$-0.261671\pi$
$984$	1.48496	+	0.788065i	0.0473389	+	0.0251226i
$985$	−6.60110	+	19.4869i	−0.210329	+	0.620905i
$986$	0.189719	−	0.328603i	0.00604188	−	0.0104648i
$987$	2.42253	+	0.594583i	0.0771099	+	0.0189258i
$988$	−7.96303	+	4.59746i	−0.253338	+	0.146265i
$989$	44.0431	−	25.4283i	1.40049	−	0.808572i
$990$	−20.0428	+	20.3083i	−0.637003	+	0.645440i
$991$	7.89796	−	13.6797i	0.250887	−	0.434549i	−0.712883	−	0.701283i	$-0.752611\pi$
$991$	7.89796	−	13.6797i	0.250887	−	0.434549i	0.963770	+	0.266734i	$0.0859444\pi$
$992$	8.80647	+	5.08442i	0.279606	+	0.161430i
$993$	36.3852	+	19.3095i	1.15465	+	0.612770i
$994$	2.42360	−	8.54473i	0.0768718	−	0.271022i
$995$	−17.9040	+	15.7216i	−0.567596	+	0.498407i
$996$	0.314958	−	0.593479i	0.00997982	−	0.0188051i
$997$	−24.1022			−0.763324			−0.381662	−	0.924302i	$-0.624648\pi$
$997$	−24.1022			−0.763324			−0.381662	+	0.924302i	$0.624648\pi$
$998$	7.51355	−	13.0139i	0.237837	−	0.411946i
$999$	1.01453	+	1.38945i	0.0320984	+	0.0439604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.r.a.59.12	✓	48
3.2	odd	2		1890.2.r.b.1529.15		48
5.4	even	2		630.2.r.b.59.13	yes	48
7.5	odd	6		630.2.bi.b.509.4	yes	48
9.2	odd	6		630.2.bi.a.479.21	yes	48
9.7	even	3		1890.2.bi.b.899.7		48
15.14	odd	2		1890.2.r.a.1529.15		48
21.5	even	6		1890.2.bi.a.719.23		48
35.19	odd	6		630.2.bi.a.509.21	yes	48
45.29	odd	6		630.2.bi.b.479.4	yes	48
45.34	even	6		1890.2.bi.a.899.23		48
63.47	even	6		630.2.r.b.299.13	yes	48
63.61	odd	6		1890.2.r.a.89.15		48
105.89	even	6		1890.2.bi.b.719.7		48
315.124	odd	6		1890.2.r.b.89.15		48
315.299	even	6	inner	630.2.r.a.299.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.12	✓	48	1.1	even	1	trivial
630.2.r.a.299.12	yes	48	315.299	even	6	inner
630.2.r.b.59.13	yes	48	5.4	even	2
630.2.r.b.299.13	yes	48	63.47	even	6
630.2.bi.a.479.21	yes	48	9.2	odd	6
630.2.bi.a.509.21	yes	48	35.19	odd	6
630.2.bi.b.479.4	yes	48	45.29	odd	6
630.2.bi.b.509.4	yes	48	7.5	odd	6
1890.2.r.a.89.15		48	63.61	odd	6
1890.2.r.a.1529.15		48	15.14	odd	2
1890.2.r.b.89.15		48	315.124	odd	6
1890.2.r.b.1529.15		48	3.2	odd	2
1890.2.bi.a.719.23		48	21.5	even	6
1890.2.bi.a.899.23		48	45.34	even	6
1890.2.bi.b.719.7		48	105.89	even	6
1890.2.bi.b.899.7		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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.0618143 - 1.73095i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.717414 + 2.11786i) q^{5} +(1.52995 + 0.811941i) q^{6} +(-0.647443 - 2.56531i) q^{7} +1.00000 q^{8} +(-2.99236 + 0.213994i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.0618143 - 1.73095i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.717414 + 2.11786i) q^{5} +(1.52995 + 0.811941i) q^{6} +(-0.647443 - 2.56531i) q^{7} +1.00000 q^{8} +(-2.99236 + 0.213994i) q^{9} +(-1.47541 - 1.68023i) q^{10} +4.25348i q^{11} +(-1.46814 + 0.919006i) q^{12} +(1.61256 - 2.79304i) q^{13} +(2.54535 + 0.721953i) q^{14} +(3.71025 + 1.11089i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.68059 - 3.27969i) q^{17} +(1.31085 - 2.69846i) q^{18} +(2.46906 - 1.42551i) q^{19} +(2.19282 - 0.437630i) q^{20} +(-4.40040 + 1.27926i) q^{21} +(-3.68362 - 2.12674i) q^{22} -7.51895 q^{23} +(-0.0618143 - 1.73095i) q^{24} +(-3.97064 - 3.03876i) q^{25} +(1.61256 + 2.79304i) q^{26} +(0.555384 + 5.16639i) q^{27} +(-1.89790 + 1.84336i) q^{28} +(0.0500967 - 0.0289233i) q^{29} +(-2.81718 + 2.65772i) q^{30} +(-8.80647 + 5.08442i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(7.36254 - 0.262925i) q^{33} +(5.68059 - 3.27969i) q^{34} +(5.89744 + 0.469197i) q^{35} +(1.68150 + 2.48446i) q^{36} +(0.286737 - 0.165548i) q^{37} +2.85103i q^{38} +(-4.93429 - 2.61861i) q^{39} +(-0.717414 + 2.11786i) q^{40} +(-0.485297 + 0.840559i) q^{41} +(1.09232 - 4.45049i) q^{42} +(-5.85761 + 3.38189i) q^{43} +(3.68362 - 2.12674i) q^{44} +(1.69355 - 6.49091i) q^{45} +(3.75947 - 6.51160i) q^{46} +(-0.471402 - 0.272164i) q^{47} +(1.52995 + 0.811941i) q^{48} +(-6.16163 + 3.32179i) q^{49} +(4.61696 - 1.91929i) q^{50} +(-5.32583 + 10.0355i) q^{51} -3.22513 q^{52} +(0.951917 - 1.64877i) q^{53} +(-4.75191 - 2.10222i) q^{54} +(-9.00825 - 3.05150i) q^{55} +(-0.647443 - 2.56531i) q^{56} +(-2.62011 - 4.18570i) q^{57} +0.0578466i q^{58} +(-0.615269 - 1.06568i) q^{59} +(-0.893062 - 3.76861i) q^{60} +(-3.90523 - 2.25468i) q^{61} -10.1688i q^{62} +(2.48634 + 7.53778i) q^{63} +1.00000 q^{64} +(4.75838 + 5.41894i) q^{65} +(-3.45357 + 6.50761i) q^{66} +(-7.44867 + 4.30049i) q^{67} +6.55938i q^{68} +(0.464778 + 13.0149i) q^{69} +(-3.35506 + 4.87274i) q^{70} -3.35700i q^{71} +(-2.99236 + 0.213994i) q^{72} +(8.45840 - 14.6504i) q^{73} +0.331096i q^{74} +(-5.01449 + 7.06080i) q^{75} +(-2.46906 - 1.42551i) q^{76} +(10.9115 - 2.75388i) q^{77} +(4.73493 - 2.96391i) q^{78} +(1.71836 - 2.97629i) q^{79} +(-1.47541 - 1.68023i) q^{80} +(8.90841 - 1.28070i) q^{81} +(-0.485297 - 0.840559i) q^{82} +(-0.335938 + 0.193954i) q^{83} +(3.30807 + 3.17122i) q^{84} +(11.0212 - 9.67778i) q^{85} -6.76379i q^{86} +(-0.0531614 - 0.0849268i) q^{87} +4.25348i q^{88} +(-3.69936 - 6.40747i) q^{89} +(4.77452 + 4.71211i) q^{90} +(-8.20906 - 2.32839i) q^{91} +(3.75947 + 6.51160i) q^{92} +(9.34522 + 14.9292i) q^{93} +(0.471402 - 0.272164i) q^{94} +(1.24769 + 6.25180i) q^{95} +(-1.46814 + 0.919006i) q^{96} +(4.48327 + 7.76525i) q^{97} +(0.204066 - 6.99702i) q^{98} +(-0.910220 - 12.7279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9}+O(q^{10}) \) 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9	\( 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{14} - 4 q^{15} - 24 q^{16} - 3 q^{18} + 5 q^{21} + 6 q^{22} - 6 q^{23} + 3 q^{24} - 3 q^{28} - 3 q^{29} + 5 q^{30} - 24 q^{32} + 24 q^{33} + 18 q^{35} + 3 q^{41} + 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} + 42 q^{55} - 22 q^{57} - q^{60} - 9 q^{61} - 10 q^{63} + 48 q^{64} - 33 q^{65} - 24 q^{66} - 33 q^{67} + 42 q^{69} - 6 q^{70} + 3 q^{72} + 18 q^{73} + 9 q^{75} + 6 q^{77} - 18 q^{78} - 37 q^{81} + 3 q^{82} - 9 q^{83} - 13 q^{84} - 33 q^{85} - 18 q^{87} + 33 q^{89} + 39 q^{90} + 3 q^{92} - 32 q^{93} + 33 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) \) 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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