LMFDB - Embedded newform 630.2.r.a.299.22

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			299.22
Character	$\chi$	$=$	630.299
Dual form			630.2.r.a.59.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.60626 + 0.648019i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.09894 + 0.770998i) q^{5} +(-0.241929 - 1.71507i) q^{6} +(1.47445 + 2.19682i) q^{7} +1.00000 q^{8} +(2.16014 + 2.08177i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.60626 + 0.648019i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.09894 + 0.770998i) q^{5} +(-0.241929 - 1.71507i) q^{6} +(1.47445 + 2.19682i) q^{7} +1.00000 q^{8} +(2.16014 + 2.08177i) q^{9} +(1.71718 + 1.43224i) q^{10} +3.61095i q^{11} +(-1.36433 + 1.06705i) q^{12} +(-1.68621 - 2.92060i) q^{13} +(1.16527 - 2.37532i) q^{14} +(-3.87107 - 0.121732i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-6.40634 + 3.69870i) q^{17} +(0.722799 - 2.91163i) q^{18} +(-4.15471 - 2.39873i) q^{19} +(0.381768 - 2.20324i) q^{20} +(0.944768 + 4.48413i) q^{21} +(3.12718 - 1.80548i) q^{22} -7.98909 q^{23} +(1.60626 + 0.648019i) q^{24} +(3.81112 - 3.23656i) q^{25} +(-1.68621 + 2.92060i) q^{26} +(2.12072 + 4.74368i) q^{27} +(-2.63972 + 0.178501i) q^{28} +(7.66188 + 4.42359i) q^{29} +(1.83011 + 3.41331i) q^{30} +(5.58511 + 3.22456i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.33997 + 5.80013i) q^{33} +(6.40634 + 3.69870i) q^{34} +(-4.78852 - 3.47420i) q^{35} +(-2.88294 + 0.829851i) q^{36} +(5.56251 + 3.21152i) q^{37} +4.79745i q^{38} +(-0.815885 - 5.78394i) q^{39} +(-2.09894 + 0.770998i) q^{40} +(1.31158 + 2.27173i) q^{41} +(3.41099 - 3.06026i) q^{42} +(-0.660123 - 0.381122i) q^{43} +(-3.12718 - 1.80548i) q^{44} +(-6.13906 - 2.70406i) q^{45} +(3.99454 + 6.91875i) q^{46} +(7.12570 - 4.11402i) q^{47} +(-0.241929 - 1.71507i) q^{48} +(-2.65201 + 6.47818i) q^{49} +(-4.70851 - 1.68225i) q^{50} +(-12.6871 + 1.78965i) q^{51} +3.37242 q^{52} +(1.47706 + 2.55834i) q^{53} +(3.04779 - 4.20844i) q^{54} +(-2.78404 - 7.57918i) q^{55} +(1.47445 + 2.19682i) q^{56} +(-5.11913 - 6.54531i) q^{57} -8.84718i q^{58} +(0.562645 - 0.974530i) q^{59} +(2.04096 - 3.29158i) q^{60} +(1.45633 - 0.840811i) q^{61} -6.44913i q^{62} +(-1.38826 + 7.81490i) q^{63} +1.00000 q^{64} +(5.79103 + 4.83011i) q^{65} +(6.19304 - 0.873594i) q^{66} +(4.11272 + 2.37448i) q^{67} -7.39740i q^{68} +(-12.8325 - 5.17708i) q^{69} +(-0.614480 + 5.88408i) q^{70} +1.40979i q^{71} +(2.16014 + 2.08177i) q^{72} +(-2.78262 - 4.81964i) q^{73} -6.42303i q^{74} +(8.21901 - 2.72908i) q^{75} +(4.15471 - 2.39873i) q^{76} +(-7.93260 + 5.32416i) q^{77} +(-4.60109 + 3.59855i) q^{78} +(-0.0862526 - 0.149394i) q^{79} +(1.71718 + 1.43224i) q^{80} +(0.332429 + 8.99386i) q^{81} +(1.31158 - 2.27173i) q^{82} +(-11.5262 - 6.65467i) q^{83} +(-4.35575 - 1.42387i) q^{84} +(10.5948 - 12.7026i) q^{85} +0.762245i q^{86} +(9.44040 + 12.0705i) q^{87} +3.61095i q^{88} +(7.08044 - 12.2637i) q^{89} +(0.727745 + 6.66861i) q^{90} +(3.92979 - 8.01056i) q^{91} +(3.99454 - 6.91875i) q^{92} +(6.88156 + 8.79875i) q^{93} +(-7.12570 - 4.11402i) q^{94} +(10.5699 + 1.83151i) q^{95} +(-1.36433 + 1.06705i) q^{96} +(-4.18720 + 7.25244i) q^{97} +(6.93627 - 0.942388i) q^{98} +(-7.51719 + 7.80017i) 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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
$3$	1.60626	+	0.648019i	0.927375	+	0.374134i
$3$	1.60626	+	0.648019i	0.927375	+	0.374134i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.09894	+	0.770998i	−0.938676	+	0.344801i
$5$	−2.09894	+	0.770998i	−0.938676	+	0.344801i
$6$	−0.241929	−	1.71507i	−0.0987671	−	0.700175i
$7$	1.47445	+	2.19682i	0.557289	+	0.830319i
$7$	1.47445	+	2.19682i	0.557289	+	0.830319i
$8$	1.00000			0.353553
$9$	2.16014	+	2.08177i	0.720047	+	0.693925i
$10$	1.71718	+	1.43224i	0.543019	+	0.452914i
$11$			3.61095i			1.08874i	0.838844	+	0.544372i	$0.183232\pi$
$11$			3.61095i			1.08874i	−0.838844	+	0.544372i	$0.816768\pi$
$12$	−1.36433	+	1.06705i	−0.393848	+	0.308031i
$13$	−1.68621	−	2.92060i	−0.467670	−	0.810028i	0.531647	−	0.846966i	$-0.321573\pi$
$13$	−1.68621	−	2.92060i	−0.467670	−	0.810028i	−0.999318	+	0.0369373i	$0.988240\pi$
$14$	1.16527	−	2.37532i	0.311433	−	0.634830i
$15$	−3.87107	−	0.121732i	−0.999506	−	0.0314311i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.40634	+	3.69870i	−1.55377	+	0.897067i	−0.555935	+	0.831226i	$0.687640\pi$
$17$	−6.40634	+	3.69870i	−1.55377	+	0.897067i	−0.997830	+	0.0658408i	$0.979027\pi$
$18$	0.722799	−	2.91163i	0.170365	−	0.686277i
$19$	−4.15471	−	2.39873i	−0.953157	−	0.550305i	−0.0590966	−	0.998252i	$-0.518822\pi$
$19$	−4.15471	−	2.39873i	−0.953157	−	0.550305i	−0.894060	+	0.447947i	$0.852155\pi$
$20$	0.381768	−	2.20324i	0.0853658	−	0.492659i
$21$	0.944768	+	4.48413i	0.206165	+	0.978517i
$22$	3.12718	−	1.80548i	0.666716	−	0.384929i
$23$	−7.98909			−1.66584			−0.832920	−	0.553394i	$-0.813333\pi$
$23$	−7.98909			−1.66584			−0.832920	+	0.553394i	$0.813333\pi$
$24$	1.60626	+	0.648019i	0.327876	+	0.132276i
$25$	3.81112	−	3.23656i	0.762225	−	0.647312i
$26$	−1.68621	+	2.92060i	−0.330693	+	0.572777i
$27$	2.12072	+	4.74368i	0.408133	+	0.912923i
$28$	−2.63972	+	0.178501i	−0.498861	+	0.0337336i
$29$	7.66188	+	4.42359i	1.42278	+	0.821440i	0.996535	−	0.0831703i	$-0.0265045\pi$
$29$	7.66188	+	4.42359i	1.42278	+	0.821440i	0.426240	+	0.904610i	$0.359838\pi$
$30$	1.83011	+	3.41331i	0.334131	+	0.623182i
$31$	5.58511	+	3.22456i	1.00312	+	0.579149i	0.909169	−	0.416428i	$-0.136718\pi$
$31$	5.58511	+	3.22456i	1.00312	+	0.579149i	0.0939467	+	0.995577i	$0.470052\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.33997	+	5.80013i	−0.407336	+	1.00967i
$34$	6.40634	+	3.69870i	1.09868	+	0.634322i
$35$	−4.78852	−	3.47420i	−0.809408	−	0.587246i
$36$	−2.88294	+	0.829851i	−0.480490	+	0.138308i
$37$	5.56251	+	3.21152i	0.914471	+	0.527970i	0.881867	−	0.471498i	$-0.156287\pi$
$37$	5.56251	+	3.21152i	0.914471	+	0.527970i	0.0326040	+	0.999468i	$0.489620\pi$
$38$			4.79745i			0.778249i
$39$	−0.815885	−	5.78394i	−0.130646	−	0.926171i
$40$	−2.09894	+	0.770998i	−0.331872	+	0.121905i
$41$	1.31158	+	2.27173i	0.204835	+	0.354785i	0.950080	−	0.312006i	$-0.101001\pi$
$41$	1.31158	+	2.27173i	0.204835	+	0.354785i	−0.745245	+	0.666791i	$0.767668\pi$
$42$	3.41099	−	3.06026i	0.526327	−	0.472208i
$43$	−0.660123	−	0.381122i	−0.100668	−	0.0581206i	0.448821	−	0.893622i	$-0.351844\pi$
$43$	−0.660123	−	0.381122i	−0.100668	−	0.0581206i	−0.549489	+	0.835501i	$0.685177\pi$
$44$	−3.12718	−	1.80548i	−0.471440	−	0.272186i
$45$	−6.13906	−	2.70406i	−0.915157	−	0.403098i
$46$	3.99454	+	6.91875i	0.588963	+	1.02011i
$47$	7.12570	−	4.11402i	1.03939	−	0.600092i	0.119730	−	0.992807i	$-0.461797\pi$
$47$	7.12570	−	4.11402i	1.03939	−	0.600092i	0.919660	+	0.392714i	$0.128464\pi$
$48$	−0.241929	−	1.71507i	−0.0349194	−	0.247549i
$49$	−2.65201	+	6.47818i	−0.378858	+	0.925455i
$50$	−4.70851	−	1.68225i	−0.665883	−	0.237906i
$51$	−12.6871	+	1.78965i	−1.77655	+	0.250600i
$52$	3.37242			0.467670
$53$	1.47706	+	2.55834i	0.202889	+	0.351415i	0.949458	−	0.313893i	$-0.101633\pi$
$53$	1.47706	+	2.55834i	0.202889	+	0.351415i	−0.746569	+	0.665308i	$0.768300\pi$
$54$	3.04779	−	4.20844i	0.414752	−	0.572696i
$55$	−2.78404	−	7.57918i	−0.375399	−	1.02198i
$56$	1.47445	+	2.19682i	0.197031	+	0.293562i
$57$	−5.11913	−	6.54531i	−0.678045	−	0.866948i
$58$		−	8.84718i		−	1.16169i
$59$	0.562645	−	0.974530i	0.0732502	−	0.126873i	−0.827074	−	0.562093i	$-0.809996\pi$
$59$	0.562645	−	0.974530i	0.0732502	−	0.126873i	0.900324	+	0.435220i	$0.143330\pi$
$60$	2.04096	−	3.29158i	0.263487	−	0.424941i
$61$	1.45633	−	0.840811i	0.186464	−	0.107655i	−0.403862	−	0.914820i	$-0.632333\pi$
$61$	1.45633	−	0.840811i	0.186464	−	0.107655i	0.590326	+	0.807165i	$0.298999\pi$
$62$		−	6.44913i		−	0.819040i
$63$	−1.38826	+	7.81490i	−0.174904	+	0.984585i
$64$	1.00000			0.125000
$65$	5.79103	+	4.83011i	0.718289	+	0.599101i
$66$	6.19304	−	0.873594i	0.762311	−	0.107532i
$67$	4.11272	+	2.37448i	0.502448	+	0.290089i	0.729724	−	0.683742i	$-0.239649\pi$
$67$	4.11272	+	2.37448i	0.502448	+	0.290089i	−0.227276	+	0.973830i	$0.572982\pi$
$68$		−	7.39740i		−	0.897067i
$69$	−12.8325	−	5.17708i	−1.54486	−	0.623247i
$70$	−0.614480	+	5.88408i	−0.0734444	+	0.703282i
$71$			1.40979i			0.167311i	0.996495	+	0.0836554i	$0.0266595\pi$
$71$			1.40979i			0.167311i	−0.996495	+	0.0836554i	$0.973341\pi$
$72$	2.16014	+	2.08177i	0.254575	+	0.245339i
$73$	−2.78262	−	4.81964i	−0.325681	−	0.564096i	0.655969	−	0.754788i	$-0.272260\pi$
$73$	−2.78262	−	4.81964i	−0.325681	−	0.564096i	−0.981650	+	0.190692i	$0.938927\pi$
$74$		−	6.42303i		−	0.746662i
$75$	8.21901	−	2.72908i	0.949050	−	0.315127i
$76$	4.15471	−	2.39873i	0.476578	−	0.275153i
$77$	−7.93260	+	5.32416i	−0.904004	+	0.606745i
$78$	−4.60109	+	3.59855i	−0.520971	+	0.407455i
$79$	−0.0862526	−	0.149394i	−0.00970417	−	0.0168081i	0.861133	−	0.508381i	$-0.169756\pi$
$79$	−0.0862526	−	0.149394i	−0.00970417	−	0.0168081i	−0.870837	+	0.491572i	$0.836422\pi$
$80$	1.71718	+	1.43224i	0.191986	+	0.160129i
$81$	0.332429	+	8.99386i	0.0369366	+	0.999318i
$82$	1.31158	−	2.27173i	0.144840	−	0.250871i
$83$	−11.5262	−	6.65467i	−1.26517	−	0.730445i	−0.291098	−	0.956693i	$-0.594020\pi$
$83$	−11.5262	−	6.65467i	−1.26517	−	0.730445i	−0.974070	+	0.226249i	$0.927354\pi$
$84$	−4.35575	−	1.42387i	−0.475252	−	0.155357i
$85$	10.5948	−	12.7026i	1.14917	−	1.37779i
$86$			0.762245i			0.0821950i
$87$	9.44040	+	12.0705i	1.01212	+	1.29409i
$88$			3.61095i			0.384929i
$89$	7.08044	−	12.2637i	0.750525	−	1.29995i	−0.197043	−	0.980395i	$-0.563134\pi$
$89$	7.08044	−	12.2637i	0.750525	−	1.29995i	0.947568	−	0.319553i	$-0.103533\pi$
$90$	0.727745	+	6.66861i	0.0767110	+	0.702933i
$91$	3.92979	−	8.01056i	0.411954	−	0.839735i
$92$	3.99454	−	6.91875i	0.416460	−	0.721330i
$93$	6.88156	+	8.79875i	0.713584	+	0.912388i
$94$	−7.12570	−	4.11402i	−0.734960	−	0.424329i
$95$	10.5699	+	1.83151i	1.08445	+	0.187909i
$96$	−1.36433	+	1.06705i	−0.139246	+	0.108906i
$97$	−4.18720	+	7.25244i	−0.425145	+	0.736373i	−0.996434	−	0.0843759i	$-0.973110\pi$
$97$	−4.18720	+	7.25244i	−0.425145	+	0.736373i	0.571289	+	0.820749i	$0.306444\pi$
$98$	6.93627	−	0.942388i	0.700670	−	0.0951955i
$99$	−7.51719	+	7.80017i	−0.755506	+	0.783947i
$100$	0.897383	+	4.91881i	0.0897383	+	0.491881i
$101$	15.7774			1.56991			0.784954	−	0.619554i	$-0.212686\pi$
$101$	15.7774			1.56991			0.784954	+	0.619554i	$0.212686\pi$
$102$	7.89341	+	10.0925i	0.781564	+	0.999307i
$103$	4.00416			0.394542			0.197271	−	0.980349i	$-0.436792\pi$
$103$	4.00416			0.394542			0.197271	+	0.980349i	$0.436792\pi$
$104$	−1.68621	−	2.92060i	−0.165346	−	0.286388i
$105$	−5.44027	−	8.68352i	−0.530916	−	0.847425i
$106$	1.47706	−	2.55834i	0.143465	−	0.248488i
$107$	−1.60810	+	2.78531i	−0.155461	+	0.269266i	−0.933227	−	0.359288i	$-0.883020\pi$
$107$	−1.60810	+	2.78531i	−0.155461	+	0.269266i	0.777766	+	0.628554i	$0.216353\pi$
$108$	−5.16851	−	0.535245i	−0.497340	−	0.0515040i
$109$	3.65311	+	6.32737i	0.349904	+	0.606052i	0.986232	−	0.165367i	$-0.0528808\pi$
$109$	3.65311	+	6.32737i	0.349904	+	0.606052i	−0.636328	+	0.771419i	$0.719547\pi$
$110$	−5.17175	+	6.20064i	−0.493107	+	0.591208i
$111$	6.85371	+	8.76314i	0.650526	+	0.831761i
$112$	1.16527	−	2.37532i	0.110108	−	0.224446i
$113$	−6.81995	−	11.8125i	−0.641567	−	1.11123i	−0.985083	−	0.172079i	$-0.944951\pi$
$113$	−6.81995	−	11.8125i	−0.641567	−	1.11123i	0.343517	−	0.939147i	$-0.388382\pi$
$114$	−3.10884	+	7.70595i	−0.291170	+	0.721729i
$115$	16.7686	−	6.15957i	1.56368	−	0.574383i
$116$	−7.66188	+	4.42359i	−0.711388	+	0.410720i
$117$	2.43758	−	9.81922i	0.225354	−	0.907787i
$118$	−1.12529			−0.103591
$119$	−17.5712	−	8.62001i	−1.61075	−	0.790195i
$120$	−3.87107	−	0.121732i	−0.353379	−	0.0111126i
$121$	−2.03898			−0.185361
$122$	−1.45633	−	0.840811i	−0.131850	−	0.0761235i
$123$	0.634620	+	4.49892i	0.0572218	+	0.405654i
$124$	−5.58511	+	3.22456i	−0.501558	+	0.289574i
$125$	−5.50395	+	9.73173i	−0.492288	+	0.870432i
$126$	7.46204	−	2.70518i	0.664771	−	0.240997i
$127$			8.41042i			0.746304i	0.927770	+	0.373152i	$0.121723\pi$
$127$			8.41042i			0.746304i	−0.927770	+	0.373152i	$0.878277\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.813355	−	1.03995i	−0.0716119	−	0.0915629i
$130$	1.28748	−	7.43024i	0.112919	−	0.651675i
$131$	−5.79423			−0.506244			−0.253122	−	0.967434i	$-0.581457\pi$
$131$	−5.79423			−0.506244			−0.253122	+	0.967434i	$0.581457\pi$
$132$	−3.85308	−	4.92653i	−0.335367	−	0.428800i
$133$	−0.856351	−	12.6639i	−0.0742551	−	1.09810i
$134$		−	4.74896i		−	0.410247i
$135$	−8.10864	−	8.32165i	−0.697881	−	0.716214i
$136$	−6.40634	+	3.69870i	−0.549339	+	0.317161i
$137$	−7.45676			−0.637074			−0.318537	−	0.947910i	$-0.603192\pi$
$137$	−7.45676			−0.637074			−0.318537	+	0.947910i	$0.603192\pi$
$138$	1.93279	+	13.7019i	0.164530	+	1.16638i
$139$	7.19444	−	4.15371i	0.610225	−	0.352313i	−0.162829	−	0.986654i	$-0.552062\pi$
$139$	7.19444	−	4.15371i	0.610225	−	0.352313i	0.773053	+	0.634341i	$0.218728\pi$
$140$	5.40300	−	2.40989i	0.456637	−	0.203672i
$141$	14.1117	−	1.99060i	1.18842	−	0.167639i
$142$	1.22091	−	0.704893i	0.102456	−	0.0591533i
$143$	10.5461	−	6.08882i	0.881913	−	0.509173i
$144$	0.722799	−	2.91163i	0.0602332	−	0.242635i
$145$	−19.4924	−	3.37757i	−1.61876	−	0.280492i
$146$	−2.78262	+	4.81964i	−0.230291	+	0.398876i
$147$	−8.45780	+	8.68710i	−0.697587	+	0.716500i
$148$	−5.56251	+	3.21152i	−0.457236	+	0.263985i
$149$			11.6902i			0.957700i	0.877897	+	0.478850i	$0.158946\pi$
$149$			11.6902i			0.957700i	−0.877897	+	0.478850i	$0.841054\pi$
$150$	−6.47296	−	5.75333i	−0.528515	−	0.469758i
$151$	−9.06398			−0.737617			−0.368808	−	0.929505i	$-0.620234\pi$
$151$	−9.06398			−0.737617			−0.368808	+	0.929505i	$0.620234\pi$
$152$	−4.15471	−	2.39873i	−0.336992	−	0.194562i
$153$	−21.5385	−	5.34683i	−1.74128	−	0.432266i
$154$	8.57716	+	4.20775i	0.691167	+	0.339070i
$155$	−14.2090	−	2.46207i	−1.14129	−	0.197758i
$156$	5.41698	+	2.18539i	0.433705	+	0.174971i
$157$	9.89018	−	17.1303i	0.789322	−	1.36715i	−0.137060	−	0.990563i	$-0.543765\pi$
$157$	9.89018	−	17.1303i	0.789322	−	1.36715i	0.926383	−	0.376584i	$-0.122901\pi$
$158$	−0.0862526	+	0.149394i	−0.00686189	+	0.0118851i
$159$	0.714686	+	5.06652i	0.0566783	+	0.401801i
$160$	0.381768	−	2.20324i	0.0301814	−	0.174181i
$161$	−11.7795	−	17.5506i	−0.928354	−	1.38318i
$162$	7.62270	−	4.78482i	0.598896	−	0.375931i
$163$	11.4067	+	6.58566i	0.893442	+	0.515829i	0.875067	−	0.484002i	$-0.160817\pi$
$163$	11.4067	+	6.58566i	0.893442	+	0.515829i	0.0183750	+	0.999831i	$0.494151\pi$
$164$	−2.62317			−0.204835
$165$	0.439569	−	13.9782i	0.0342204	−	1.08821i
$166$			13.3093i			1.03300i
$167$	−1.88823	+	1.09017i	−0.146116	+	0.0843601i	−0.571276	−	0.820758i	$-0.693551\pi$
$167$	−1.88823	+	1.09017i	−0.146116	+	0.0843601i	0.425160	+	0.905118i	$0.360218\pi$
$168$	0.944768	+	4.48413i	0.0728904	+	0.345958i
$169$	0.813400	−	1.40885i	0.0625692	−	0.108373i
$170$	−16.2982	−	2.82409i	−1.25002	−	0.216598i
$171$	−3.98117	−	13.8308i	−0.304448	−	1.05767i
$172$	0.660123	−	0.381122i	0.0503339	−	0.0290603i
$173$	22.4575	−	12.9658i	1.70741	−	0.985773i	0.769665	−	0.638448i	$-0.220423\pi$
$173$	22.4575	−	12.9658i	1.70741	−	0.985773i	0.937745	−	0.347326i	$-0.112910\pi$
$174$	5.73314	−	14.2109i	0.434628	−	1.07732i
$175$	12.7294	+	3.60020i	0.962255	+	0.272149i
$176$	3.12718	−	1.80548i	0.235720	−	0.136093i
$177$	1.53527	−	1.20074i	0.115398	−	0.0902535i
$178$	−14.1609			−1.06140
$179$	12.3911	−	7.15401i	0.926155	−	0.534716i	0.0405613	−	0.999177i	$-0.487085\pi$
$179$	12.3911	−	7.15401i	0.926155	−	0.534716i	0.885593	+	0.464461i	$0.153752\pi$
$180$	5.41132	−	3.96455i	0.403336	−	0.295500i
$181$			4.19706i			0.311965i	0.987760	+	0.155982i	$0.0498543\pi$
$181$			4.19706i			0.311965i	−0.987760	+	0.155982i	$0.950146\pi$
$182$	−8.90225	+	0.601981i	−0.659879	+	0.0446218i
$183$	2.88410	−	0.406833i	0.213199	−	0.0300740i
$184$	−7.98909			−0.588963
$185$	−14.1515	−	2.45211i	−1.04044	−	0.180282i
$186$	4.17916	−	10.3590i	0.306431	−	0.759557i
$187$	−13.3558	−	23.1330i	−0.976675	−	1.69165i
$188$			8.22805i			0.600092i
$189$	−7.29411	+	11.6532i	−0.530569	+	0.847642i
$190$	−3.69883	−	10.0696i	−0.268341	−	0.730524i
$191$	16.2887	−	9.40430i	1.17861	−	0.680471i	0.222918	−	0.974837i	$-0.428442\pi$
$191$	16.2887	−	9.40430i	1.17861	−	0.680471i	0.955693	+	0.294366i	$0.0951084\pi$
$192$	1.60626	+	0.648019i	0.115922	+	0.0467668i
$193$	−4.76835	−	2.75301i	−0.343233	−	0.198166i	0.318468	−	0.947934i	$-0.396832\pi$
$193$	−4.76835	−	2.75301i	−0.343233	−	0.198166i	−0.661701	+	0.749768i	$0.730165\pi$
$194$	8.37439			0.601246
$195$	6.17190	+	11.5111i	0.441979	+	0.824328i
$196$	−4.28427	−	5.53580i	−0.306019	−	0.395414i
$197$	−13.1218			−0.934888			−0.467444	−	0.884023i	$-0.654825\pi$
$197$	−13.1218			−0.934888			−0.467444	+	0.884023i	$0.654825\pi$
$198$	10.5137	+	2.60999i	0.747179	+	0.185484i
$199$	−9.55302	+	5.51544i	−0.677195	+	0.390979i	−0.798797	−	0.601600i	$-0.794530\pi$
$199$	−9.55302	+	5.51544i	−0.677195	+	0.390979i	0.121602	+	0.992579i	$0.461197\pi$
$200$	3.81112	−	3.23656i	0.269487	−	0.228859i
$201$	5.06738	+	6.47915i	0.357426	+	0.457004i
$202$	−7.88869	−	13.6636i	−0.555047	−	0.961369i
$203$	1.57923	+	23.3541i	0.110840	+	1.63914i
$204$	4.79366	−	11.8821i	0.335623	−	0.831917i
$205$	−4.50444	−	3.75700i	−0.314604	−	0.262401i
$206$	−2.00208	−	3.46771i	−0.139492	−	0.241607i
$207$	−17.2576	−	16.6315i	−1.19948	−	1.15597i
$208$	−1.68621	+	2.92060i	−0.116918	+	0.202507i
$209$	8.66168	−	15.0025i	0.599141	−	1.03774i
$210$	−4.80001	+	9.05317i	−0.331232	+	0.624728i
$211$	7.09074	+	12.2815i	0.488147	+	0.845495i	0.999907	−	0.0136335i	$-0.00433983\pi$
$211$	7.09074	+	12.2815i	0.488147	+	0.845495i	−0.511761	+	0.859128i	$0.671006\pi$
$212$	−2.95411			−0.202889
$213$	−0.913568	+	2.26448i	−0.0625966	+	0.155160i
$214$	3.21620			0.219855
$215$	1.67941	+	0.291000i	0.114535	+	0.0198461i
$216$	2.12072	+	4.74368i	0.144297	+	0.322767i
$217$	1.15118	+	17.0239i	0.0781470	+	1.15566i
$218$	3.65311	−	6.32737i	0.247420	−	0.428543i
$219$	−1.34639	−	9.54478i	−0.0909807	−	0.644977i
$220$	7.95578	+	1.37854i	0.536379	+	0.0929415i
$221$	21.6048	+	12.4736i	1.45330	+	0.839063i
$222$	4.16225	−	10.3171i	0.279352	−	0.692436i
$223$	−1.85603	+	3.21474i	−0.124289	+	0.215275i	−0.921455	−	0.388485i	$-0.872998\pi$
$223$	−1.85603	+	3.21474i	−0.124289	+	0.215275i	0.797166	+	0.603761i	$0.206332\pi$
$224$	−2.63972	+	0.178501i	−0.176374	+	0.0119266i
$225$	14.9704	+	0.942466i	0.998024	+	0.0628311i
$226$	−6.81995	+	11.8125i	−0.453656	+	0.785755i
$227$			16.1336i			1.07083i	0.844591	+	0.535413i	$0.179844\pi$
$227$			16.1336i			1.07083i	−0.844591	+	0.535413i	$0.820156\pi$
$228$	8.22797	−	1.16064i	0.544911	−	0.0768654i
$229$		−	7.74473i		−	0.511786i	−0.966705	−	0.255893i	$-0.917631\pi$
$229$		−	7.74473i		−	0.511786i	0.966705	−	0.255893i	$-0.0823695\pi$
$230$	−13.7187	−	11.4423i	−0.904582	−	0.754482i
$231$	−16.1920	+	3.41151i	−1.06535	+	0.224461i
$232$	7.66188	+	4.42359i	0.503027	+	0.290423i
$233$	8.53036	−	14.7750i	0.558842	−	0.967944i	−0.438751	−	0.898609i	$-0.644579\pi$
$233$	8.53036	−	14.7750i	0.558842	−	0.967944i	0.997593	−	0.0693349i	$-0.0220877\pi$
$234$	−9.72248	+	2.79860i	−0.635578	+	0.182950i
$235$	−11.7845	+	14.1290i	−0.768738	+	0.921675i
$236$	0.562645	+	0.974530i	0.0366251	+	0.0634365i
$237$	−0.0417340	−	0.295859i	−0.00271091	−	0.0192181i
$238$	1.32045	+	19.5271i	0.0855918	+	1.26575i
$239$	−11.0069	+	6.35481i	−0.711975	+	0.411059i	−0.811792	−	0.583947i	$-0.801508\pi$
$239$	−11.0069	+	6.35481i	−0.711975	+	0.411059i	0.0998171	+	0.995006i	$0.468174\pi$
$240$	1.83011	+	3.41331i	0.118133	+	0.220328i
$241$			6.34032i			0.408416i	0.978928	+	0.204208i	$0.0654618\pi$
$241$			6.34032i			0.408416i	−0.978928	+	0.204208i	$0.934538\pi$
$242$	1.01949	+	1.76581i	0.0655352	+	0.113510i
$243$	−5.29423	+	14.6619i	−0.339625	+	0.940561i
$244$			1.68162i			0.107655i
$245$	0.571741	−	15.6420i	0.0365272	−	0.999333i
$246$	3.57887	−	2.79906i	0.228180	−	0.178461i
$247$			16.1790i			1.02945i
$248$	5.58511	+	3.22456i	0.354655	+	0.204760i
$249$	−14.2018	−	18.1583i	−0.900000	−	1.15074i
$250$	11.1799	−	0.0993046i	0.707079	−	0.00628058i
$251$	−16.1974			−1.02237			−0.511186	−	0.859470i	$-0.670794\pi$
$251$	−16.1974			−1.02237			−0.511186	+	0.859470i	$0.670794\pi$
$252$	−6.07378	−	5.10972i	−0.382612	−	0.321882i
$253$		−	28.8482i		−	1.81367i
$254$	7.28364	−	4.20521i	0.457016	−	0.263858i
$255$	25.2496	−	13.5381i	1.58119	−	0.847787i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		−	0.955954i		−	0.0596308i	−0.999555	−	0.0298154i	$-0.990508\pi$
$257$		−	0.955954i		−	0.0596308i	0.999555	−	0.0298154i	$-0.00949194\pi$
$258$	−0.493949	+	1.22436i	−0.0307519	+	0.0762255i
$259$	1.14652	+	16.9550i	0.0712413	+	1.05353i
$260$	−7.07851	+	2.60013i	−0.438991	+	0.161253i
$261$	7.34184	+	25.5059i	0.454448	+	1.57877i
$262$	2.89711	+	5.01795i	0.178984	+	0.310010i
$263$	16.4734			1.01579			0.507896	−	0.861419i	$-0.330423\pi$
$263$	16.4734			1.01579			0.507896	+	0.861419i	$0.330423\pi$
$264$	−2.33997	+	5.80013i	−0.144015	+	0.356973i
$265$	−5.07273	−	4.23100i	−0.311616	−	0.259908i
$266$	−10.5391	+	7.07359i	−0.646195	+	0.433710i
$267$	19.3201	−	15.1104i	1.18237	−	0.924742i
$268$	−4.11272	+	2.37448i	−0.251224	+	0.145044i
$269$	8.79451	+	15.2325i	0.536210	+	0.928744i	0.999104	+	0.0423298i	$0.0134780\pi$
$269$	8.79451	+	15.2325i	0.536210	+	0.928744i	−0.462893	+	0.886414i	$0.653189\pi$
$270$	−3.15244	+	11.1831i	−0.191851	+	0.680583i
$271$	−5.44818	−	3.14551i	−0.330953	−	0.191076i	0.325311	−	0.945607i	$-0.394531\pi$
$271$	−5.44818	−	3.14551i	−0.330953	−	0.191076i	−0.656264	+	0.754531i	$0.727864\pi$
$272$	6.40634	+	3.69870i	0.388441	+	0.224267i
$273$	11.5033	−	10.3205i	0.696209	−	0.624623i
$274$	3.72838	+	6.45775i	0.225240	+	0.390127i
$275$	11.6871	+	13.7618i	0.704757	+	0.829867i
$276$	10.8998	−	8.52477i	0.656088	−	0.513131i
$277$			2.76733i			0.166273i	0.996538	+	0.0831365i	$0.0264938\pi$
$277$			2.76733i			0.166273i	−0.996538	+	0.0831365i	$0.973506\pi$
$278$	−7.19444	−	4.15371i	−0.431494	−	0.249123i
$279$	5.35181	+	18.5925i	0.320405	+	1.11310i
$280$	−4.78852	−	3.47420i	−0.286169	−	0.207623i
$281$	3.01229	+	1.73915i	0.179698	+	0.103749i	0.587151	−	0.809477i	$-0.300249\pi$
$281$	3.01229	+	1.73915i	0.179698	+	0.103749i	−0.407453	+	0.913226i	$0.633583\pi$
$282$	−8.77976	−	11.2258i	−0.522827	−	0.668486i
$283$	−6.11408	+	10.5899i	−0.363444	+	0.629504i	−0.988525	−	0.151056i	$-0.951733\pi$
$283$	−6.11408	+	10.5899i	−0.363444	+	0.629504i	0.625081	+	0.780560i	$0.285066\pi$
$284$	−1.22091	−	0.704893i	−0.0724477	−	0.0418277i
$285$	15.7912	+	9.79139i	0.935389	+	0.579992i
$286$	−10.5461	−	6.08882i	−0.623607	−	0.360039i
$287$	−3.05671	+	6.23086i	−0.180432	+	0.367796i
$288$	−2.88294	+	0.829851i	−0.169879	+	0.0488994i
$289$	18.8608	−	32.6678i	1.10946	−	1.92164i
$290$	6.82116	+	18.5697i	0.400552	+	1.09045i
$291$	−11.4254	+	8.93591i	−0.669771	+	0.523833i
$292$	5.56524			0.325681
$293$	10.8450	−	6.26137i	0.633572	−	0.365793i	−0.148562	−	0.988903i	$-0.547464\pi$
$293$	10.8450	−	6.26137i	0.633572	−	0.365793i	0.782134	+	0.623110i	$0.214131\pi$
$294$	11.7521	+	2.98112i	0.685399	+	0.173862i
$295$	−0.429600	+	2.47928i	−0.0250123	+	0.144349i
$296$	5.56251	+	3.21152i	0.323314	+	0.186666i
$297$	−17.1292	+	7.65782i	−0.993938	+	0.444352i
$298$	10.1240	−	5.84511i	0.586469	−	0.338598i
$299$	13.4713	+	23.3329i	0.779064	+	1.34938i
$300$	−1.74605	+	8.48241i	−0.100808	+	0.489732i
$301$	−0.136062	−	2.01211i	−0.00784246	−	0.115976i
$302$	4.53199	+	7.84964i	0.260787	+	0.451696i
$303$	25.3426	+	10.2240i	1.45589	+	0.587356i
$304$			4.79745i			0.275153i
$305$	−2.40848	+	2.88764i	−0.137909	+	0.165346i
$306$	6.13874	+	21.3263i	0.350928	+	1.21914i
$307$	−7.45350			−0.425394			−0.212697	−	0.977118i	$-0.568225\pi$
$307$	−7.45350			−0.425394			−0.212697	+	0.977118i	$0.568225\pi$
$308$	−0.644560	−	9.53191i	−0.0367272	−	0.543131i
$309$	6.43173	+	2.59478i	0.365888	+	0.147612i
$310$	4.97227	+	13.5364i	0.282406	+	0.768813i
$311$	−11.2612	+	19.5049i	−0.638563	+	1.10602i	0.347186	+	0.937796i	$0.387137\pi$
$311$	−11.2612	+	19.5049i	−0.638563	+	1.10602i	−0.985748	+	0.168227i	$0.946196\pi$
$312$	−0.815885	−	5.78394i	−0.0461904	−	0.327451i
$313$	−10.2965	−	17.8341i	−0.581995	−	1.00804i	−0.995243	−	0.0974258i	$-0.968939\pi$
$313$	−10.2965	−	17.8341i	−0.581995	−	1.00804i	0.413248	−	0.910618i	$-0.364394\pi$
$314$	−19.7804			−1.11627
$315$	−3.11140	−	17.4734i	−0.175308	−	0.984514i
$316$	0.172505			0.00970417
$317$	4.35758	+	7.54755i	0.244746	+	0.423912i	0.962060	−	0.272837i	$-0.0879621\pi$
$317$	4.35758	+	7.54755i	0.244746	+	0.423912i	−0.717314	+	0.696750i	$0.754629\pi$
$318$	4.03039	−	3.15220i	0.226013	−	0.176766i
$319$	−15.9734	+	27.6667i	−0.894337	+	1.54904i
$320$	−2.09894	+	0.770998i	−0.117334	+	0.0431001i
$321$	−4.38796	+	3.43185i	−0.244912	+	0.191547i
$322$	−9.30948	+	18.9766i	−0.518797	+	1.05753i
$323$	35.4887			1.97464
$324$	−7.95512	−	4.20904i	−0.441951	−	0.233835i
$325$	−15.8791	−	5.67325i	−0.880811	−	0.314695i
$326$		−	13.1713i		−	0.729492i
$327$	1.76758	+	12.5307i	0.0977477	+	0.692948i
$328$	1.31158	+	2.27173i	0.0724201	+	0.125435i
$329$	19.5442	+	9.58794i	1.07751	+	0.528600i
$330$	−12.3253	+	6.60845i	−0.678486	+	0.363783i
$331$	7.18237	+	12.4402i	0.394779	+	0.683777i	0.993073	−	0.117500i	$-0.0374879\pi$
$331$	7.18237	+	12.4402i	0.394779	+	0.683777i	−0.598294	+	0.801276i	$0.704155\pi$
$332$	11.5262	−	6.65467i	0.632584	−	0.365222i
$333$	5.33016	+	18.5172i	0.292091	+	1.01474i
$334$	1.88823	+	1.09017i	0.103320	+	0.0596516i
$335$	−10.4631	−	1.81300i	−0.571659	−	0.0990546i
$336$	3.41099	−	3.06026i	0.186085	−	0.166951i
$337$	−9.09613	+	5.25165i	−0.495498	+	0.286076i	−0.726852	−	0.686794i	$-0.759018\pi$
$337$	−9.09613	+	5.25165i	−0.495498	+	0.286076i	0.231355	+	0.972870i	$0.425684\pi$
$338$	−1.62680			−0.0884863
$339$	−3.29988	−	23.3934i	−0.179225	−	1.27055i
$340$	5.70338	+	15.5267i	0.309309	+	0.842055i
$341$	−11.6437	+	20.1676i	−0.630544	+	1.09213i
$342$	−9.98721	+	10.3632i	−0.540046	+	0.560376i
$343$	−18.1416	+	3.72578i	−0.979556	+	0.201173i
$344$	−0.660123	−	0.381122i	−0.0355915	−	0.0205487i
$345$	30.9263	+	0.972528i	1.66502	+	0.0523591i
$346$	−22.4575	−	12.9658i	−1.20732	−	0.697047i
$347$	6.83069	−	11.8311i	0.366691	−	0.635127i	−0.622355	−	0.782735i	$-0.713824\pi$
$347$	6.83069	−	11.8311i	0.366691	−	0.635127i	0.989046	+	0.147608i	$0.0471574\pi$
$348$	−15.1735	+	2.14039i	−0.813387	+	0.114737i
$349$	−30.2742	−	17.4788i	−1.62054	−	0.935620i	−0.986775	−	0.162095i	$-0.948175\pi$
$349$	−30.2742	−	17.4788i	−1.62054	−	0.935620i	−0.633766	−	0.773525i	$-0.718492\pi$
$350$	−3.24686	−	12.8241i	−0.173552	−	0.685478i
$351$	10.2784	−	14.1926i	0.548622	−	0.757546i
$352$	−3.12718	−	1.80548i	−0.166679	−	0.0962322i
$353$			10.0636i			0.535633i	0.963470	+	0.267816i	$0.0863021\pi$
$353$			10.0636i			0.535633i	−0.963470	+	0.267816i	$0.913698\pi$
$354$	−1.80751	−	0.729210i	−0.0960681	−	0.0387571i
$355$	−1.08694	−	2.95906i	−0.0576889	−	0.157051i
$356$	7.08044	+	12.2637i	0.375263	+	0.649974i
$357$	−22.6380	−	25.2324i	−1.19813	−	1.33544i
$358$	−12.3911	−	7.15401i	−0.654890	−	0.378101i
$359$	3.51811	+	2.03118i	0.185679	+	0.107202i	0.589958	−	0.807434i	$-0.299144\pi$
$359$	3.51811	+	2.03118i	0.185679	+	0.107202i	−0.404279	+	0.914636i	$0.632478\pi$
$360$	−6.13906	−	2.70406i	−0.323557	−	0.142517i
$361$	2.00777	+	3.47755i	0.105672	+	0.183029i
$362$	3.63476	−	2.09853i	0.191039	−	0.110296i
$363$	−3.27513	−	1.32130i	−0.171900	−	0.0693500i
$364$	4.97245	+	7.40858i	0.260627	+	0.388315i
$365$	9.55649	+	7.97075i	0.500210	+	0.417208i
$366$	−1.79438	−	2.29429i	−0.0937937	−	0.119924i
$367$	15.4047			0.804120			0.402060	−	0.915613i	$-0.368294\pi$
$367$	15.4047			0.804120			0.402060	+	0.915613i	$0.368294\pi$
$368$	3.99454	+	6.91875i	0.208230	+	0.360665i
$369$	−1.89602	+	7.63768i	−0.0987030	+	0.397602i
$370$	4.95215	+	13.4816i	0.257450	+	0.700874i
$371$	−3.44236	+	7.01696i	−0.178718	+	0.364303i
$372$	−11.0607	+	1.56023i	−0.573471	+	0.0808942i
$373$			29.2392i			1.51395i	0.653444	+	0.756974i	$0.273323\pi$
$373$			29.2392i			1.51395i	−0.653444	+	0.756974i	$0.726677\pi$
$374$	−13.3558	+	23.1330i	−0.690614	+	1.19618i
$375$	−15.1471	+	12.0650i	−0.782194	+	0.623035i
$376$	7.12570	−	4.11402i	0.367480	−	0.212165i
$377$		−	29.8364i		−	1.53665i
$378$	13.7390	+	0.490312i	0.706657	+	0.0252189i
$379$	32.1478			1.65132			0.825662	−	0.564166i	$-0.190802\pi$
$379$	32.1478			1.65132			0.825662	+	0.564166i	$0.190802\pi$
$380$	−6.87110	+	8.23806i	−0.352480	+	0.422604i
$381$	−5.45012	+	13.5093i	−0.279218	+	0.692104i
$382$	−16.2887	−	9.40430i	−0.833404	−	0.481166i
$383$			6.34301i			0.324112i	0.986782	+	0.162056i	$0.0518126\pi$
$383$			6.34301i			0.324112i	−0.986782	+	0.162056i	$0.948187\pi$
$384$	−0.241929	−	1.71507i	−0.0123459	−	0.0875219i
$385$	12.5452	−	17.2911i	0.639360	−	0.881238i
$386$			5.50601i			0.280249i
$387$	−0.632549	−	2.19751i	−0.0321543	−	0.111706i
$388$	−4.18720	−	7.25244i	−0.212573	−	0.368187i
$389$		−	24.2709i		−	1.23058i	−0.788299	−	0.615292i	$-0.789038\pi$
$389$		−	24.2709i		−	1.23058i	0.788299	−	0.615292i	$-0.210962\pi$
$390$	6.88296	−	11.1006i	0.348532	−	0.562100i
$391$	51.1808	−	29.5492i	2.58832	−	1.49437i
$392$	−2.65201	+	6.47818i	−0.133947	+	0.327198i
$393$	−9.30703	−	3.75477i	−0.469478	−	0.189403i
$394$	6.56089	+	11.3638i	0.330533	+	0.572500i
$395$	0.296222	+	0.247069i	0.0149045	+	0.0124314i
$396$	−2.99655	−	10.4102i	−0.150582	−	0.523130i
$397$	3.23274	−	5.59927i	0.162246	−	0.281019i	−0.773428	−	0.633885i	$-0.781459\pi$
$397$	3.23274	−	5.59927i	0.162246	−	0.281019i	0.935674	+	0.352866i	$0.114793\pi$
$398$	9.55302	+	5.51544i	0.478849	+	0.276464i
$399$	6.83095	−	20.8965i	0.341975	−	1.04613i
$400$	−4.70851	−	1.68225i	−0.235425	−	0.0841125i
$401$		−	36.0669i		−	1.80109i	−0.434759	−	0.900547i	$-0.643167\pi$
$401$		−	36.0669i		−	1.80109i	0.434759	−	0.900547i	$-0.356833\pi$
$402$	3.07741	−	7.62806i	0.153488	−	0.380453i
$403$		−	21.7492i		−	1.08340i
$404$	−7.88869	+	13.6636i	−0.392477	+	0.679790i
$405$	−7.63200	−	18.6213i	−0.379237	−	0.925300i
$406$	19.4356	−	13.0447i	0.964574	−	0.647398i
$407$	−11.5966	+	20.0860i	−0.574824	+	0.995624i
$408$	−12.6871	+	1.78965i	−0.628104	+	0.0886006i
$409$	−30.8153	−	17.7912i	−1.52372	−	0.879718i	−0.999606	−	0.0280674i	$-0.991065\pi$
$409$	−30.8153	−	17.7912i	−1.52372	−	0.879718i	−0.524110	−	0.851651i	$-0.675602\pi$
$410$	−1.00144	+	5.77946i	−0.0494576	+	0.285427i
$411$	−11.9775	−	4.83212i	−0.590806	−	0.238351i
$412$	−2.00208	+	3.46771i	−0.0986355	+	0.170842i
$413$	2.97046	−	0.200866i	0.146167	−	0.00988396i
$414$	−5.77450	+	23.2612i	−0.283801	+	1.14323i
$415$	29.3236	+	5.08107i	1.43944	+	0.249420i
$416$	3.37242			0.165346
$417$	14.2478	−	2.00981i	0.697719	−	0.0984206i
$418$	−17.3234			−0.847313
$419$	9.77575	+	16.9321i	0.477576	+	0.827187i	0.999670	−	0.0257018i	$-0.00818203\pi$
$419$	9.77575	+	16.9321i	0.477576	+	0.827187i	−0.522093	+	0.852888i	$0.674849\pi$
$420$	10.2403	−	0.369652i	0.499675	−	0.0180372i
$421$	6.82851	−	11.8273i	0.332801	−	0.576428i	−0.650259	−	0.759713i	$-0.725340\pi$
$421$	6.82851	−	11.8273i	0.332801	−	0.576428i	0.983060	+	0.183284i	$0.0586729\pi$
$422$	7.09074	−	12.2815i	0.345172	−	0.597855i
$423$	23.9570	+	5.94722i	1.16483	+	0.289164i
$424$	1.47706	+	2.55834i	0.0717323	+	0.124244i
$425$	−12.4443	+	34.8307i	−0.603636	+	1.68954i
$426$	2.41788	−	0.341068i	0.117147	−	0.0165248i
$427$	3.99439	+	1.95955i	0.193302	+	0.0948294i
$428$	−1.60810	−	2.78531i	−0.0777304	−	0.134633i
$429$	20.8855	−	2.94612i	1.00836	−	0.142240i
$430$	−0.587689	−	1.59991i	−0.0283409	−	0.0771544i
$431$	6.33629	−	3.65826i	0.305208	−	0.176212i	−0.339572	−	0.940580i	$-0.610282\pi$
$431$	6.33629	−	3.65826i	0.305208	−	0.176212i	0.644780	+	0.764368i	$0.276949\pi$
$432$	3.04779	−	4.20844i	0.146637	−	0.202479i
$433$	−7.45007			−0.358027			−0.179014	−	0.983847i	$-0.557291\pi$
$433$	−7.45007			−0.358027			−0.179014	+	0.983847i	$0.557291\pi$
$434$	14.1676	−	9.50891i	0.680064	−	0.456442i
$435$	−29.1212	−	18.0567i	−1.39625	−	0.865753i
$436$	−7.30622			−0.349904
$437$	33.1924	+	19.1636i	1.58781	+	0.916720i
$438$	−7.59283	+	5.93840i	−0.362799	+	0.283748i
$439$	13.2005	−	7.62131i	0.630025	−	0.363745i	−0.150737	−	0.988574i	$-0.548165\pi$
$439$	13.2005	−	7.62131i	0.630025	−	0.363745i	0.780762	+	0.624829i	$0.214831\pi$
$440$	−2.78404	−	7.57918i	−0.132724	−	0.361323i
$441$	−19.2148	+	8.47292i	−0.914992	+	0.403472i
$442$		−	24.9471i		−	1.18661i
$443$	−1.09863	−	1.90288i	−0.0521974	−	0.0904086i	0.838746	−	0.544523i	$-0.183289\pi$
$443$	−1.09863	−	1.90288i	−0.0521974	−	0.0904086i	−0.890944	+	0.454114i	$0.849956\pi$
$444$	−11.0160	+	1.55392i	−0.522794	+	0.0737457i
$445$	−5.40617	+	31.1998i	−0.256277	+	1.47901i
$446$	3.71206			0.175771
$447$	−7.57549	+	18.7775i	−0.358308	+	0.888147i
$448$	1.47445	+	2.19682i	0.0696611	+	0.103790i
$449$		−	11.6919i		−	0.551773i	−0.961190	−	0.275886i	$-0.911029\pi$
$449$		−	11.6919i		−	0.551773i	0.961190	−	0.275886i	$-0.0889713\pi$
$450$	−6.66898	−	13.4359i	−0.314379	−	0.633377i
$451$	−8.20311	+	4.73607i	−0.386269	+	0.223013i
$452$	13.6399			0.641567
$453$	−14.5591	−	5.87364i	−0.684047	−	0.275967i
$454$	13.9721	−	8.06681i	0.655744	−	0.378594i
$455$	−2.07228	+	19.8436i	−0.0971502	+	0.930281i
$456$	−5.11913	−	6.54531i	−0.239725	−	0.306512i
$457$	−18.8329	+	10.8732i	−0.880964	+	0.508625i	−0.870976	−	0.491325i	$-0.836513\pi$
$457$	−18.8329	+	10.8732i	−0.880964	+	0.508625i	−0.00998773	+	0.999950i	$0.503179\pi$
$458$	−6.70713	+	3.87236i	−0.313404	+	0.180944i
$459$	−31.1315	−	22.5457i	−1.45309	−	1.05234i
$460$	−3.04997	+	17.6019i	−0.142206	+	0.820691i
$461$	−7.88022	+	13.6489i	−0.367019	+	0.635695i	−0.989098	−	0.147259i	$-0.952955\pi$
$461$	−7.88022	+	13.6489i	−0.367019	+	0.635695i	0.622079	+	0.782954i	$0.286288\pi$
$462$	11.0504	+	12.3169i	0.514113	+	0.573034i
$463$	−6.80572	+	3.92928i	−0.316288	+	0.182609i	−0.649737	−	0.760159i	$-0.725121\pi$
$463$	−6.80572	+	3.92928i	−0.316288	+	0.182609i	0.333449	+	0.942768i	$0.391788\pi$
$464$		−	8.84718i		−	0.410720i
$465$	−21.2278	−	13.1624i	−0.984416	−	0.610392i
$466$	−17.0607			−0.790323
$467$	−22.1423	−	12.7839i	−1.02462	−	0.591567i	−0.109184	−	0.994022i	$-0.534824\pi$
$467$	−22.1423	−	12.7839i	−1.02462	−	0.591567i	−0.915440	+	0.402455i	$0.868157\pi$
$468$	7.28490	+	7.02061i	0.336745	+	0.324528i
$469$	0.847695	+	12.5359i	0.0391429	+	0.578855i
$470$	18.1283	+	3.14120i	0.836198	+	0.144893i
$471$	26.9870	−	21.1067i	1.24349	−	0.972544i
$472$	0.562645	−	0.974530i	0.0258979	−	0.0448564i
$473$	1.37621	−	2.38367i	0.0632784	−	0.109601i
$474$	−0.235354	+	0.184072i	−0.0108102	+	0.00845471i
$475$	−23.5978	+	4.30515i	−1.08274	+	0.197534i
$476$	16.2507	−	10.9071i	0.744851	−	0.499925i
$477$	−2.13523	+	8.60128i	−0.0977655	+	0.393825i
$478$	11.0069	+	6.35481i	0.503442	+	0.290662i
$479$	−7.96636			−0.363992			−0.181996	−	0.983299i	$-0.558256\pi$
$479$	−7.96636			−0.363992			−0.181996	+	0.983299i	$0.558256\pi$
$480$	2.04096	−	3.29158i	0.0931566	−	0.150239i
$481$		−	21.6612i		−	0.987663i
$482$	5.49087	−	3.17016i	0.250102	−	0.144397i
$483$	−7.54783	−	35.8241i	−0.343438	−	1.63005i
$484$	1.01949	−	1.76581i	0.0463404	−	0.0802639i
$485$	3.19707	−	18.4508i	0.145172	−	0.837806i
$486$	15.3447	−	2.74601i	0.696049	−	0.124562i
$487$	1.35301	−	0.781161i	0.0613108	−	0.0353978i	−0.469031	−	0.883182i	$-0.655397\pi$
$487$	1.35301	−	0.781161i	0.0613108	−	0.0353978i	0.530342	+	0.847784i	$0.322064\pi$
$488$	1.45633	−	0.840811i	0.0659248	−	0.0380617i
$489$	14.0545	+	17.9700i	0.635566	+	0.812633i
$490$	−13.8323	+	7.32587i	−0.624878	+	0.330949i
$491$	−3.63710	+	2.09988i	−0.164140	+	0.0947663i	−0.579820	−	0.814745i	$-0.696877\pi$
$491$	−3.63710	+	2.09988i	−0.164140	+	0.0947663i	0.415680	+	0.909511i	$0.363544\pi$
$492$	−4.21349	−	1.69986i	−0.189959	−	0.0766358i
$493$	−65.4461			−2.94754
$494$	14.0114	−	8.08950i	0.630404	−	0.363964i
$495$	9.76423	−	22.1679i	0.438870	−	0.996371i
$496$		−	6.44913i		−	0.289574i
$497$	−3.09704	+	2.07866i	−0.138921	+	0.0932404i
$498$	−8.62470	+	21.3782i	−0.386482	+	0.957982i
$499$	−11.1563			−0.499427			−0.249713	−	0.968320i	$-0.580336\pi$
$499$	−11.1563			−0.499427			−0.249713	+	0.968320i	$0.580336\pi$
$500$	−5.67595	−	9.63242i	−0.253836	−	0.430775i
$501$	−3.73945	+	0.527488i	−0.167066	+	0.0235664i
$502$	8.09871	+	14.0274i	0.361463	+	0.626072i
$503$		−	15.9146i		−	0.709598i	−0.934943	−	0.354799i	$-0.884549\pi$
$503$		−	15.9146i		−	0.709598i	0.934943	−	0.354799i	$-0.115451\pi$
$504$	−1.38826	+	7.81490i	−0.0618380	+	0.348104i
$505$	−33.1158	+	12.1643i	−1.47364	+	0.541306i
$506$	−24.9833	+	14.4241i	−1.11064	+	0.641230i
$507$	2.21949	−	1.73588i	0.0985712	−	0.0770932i
$508$	−7.28364	−	4.20521i	−0.323159	−	0.186576i
$509$	−14.0765			−0.623930			−0.311965	−	0.950094i	$-0.600987\pi$
$509$	−14.0765			−0.623930			−0.311965	+	0.950094i	$0.600987\pi$
$510$	−24.3491	−	15.0978i	−1.07820	−	0.668541i
$511$	6.48503	−	13.2192i	0.286881	−	0.584783i
$512$	1.00000			0.0441942
$513$	2.56781	−	24.7957i	0.113372	−	1.09476i
$514$	−0.827880	+	0.477977i	−0.0365162	+	0.0210827i
$515$	−8.40451	+	3.08720i	−0.370347	+	0.136038i
$516$	1.30730	−	0.184409i	0.0575509	−	0.00811815i
$517$	14.8555	+	25.7306i	0.653346	+	1.13163i
$518$	14.1102	−	9.47043i	0.619968	−	0.416107i
$519$	44.4746	−	6.27362i	1.95222	−	0.275381i
$520$	5.79103	+	4.83011i	0.253954	+	0.211814i
$521$	15.9369	+	27.6036i	0.698209	+	1.20933i	0.969087	+	0.246720i	$0.0793529\pi$
$521$	15.9369	+	27.6036i	0.698209	+	1.20933i	−0.270877	+	0.962614i	$0.587314\pi$
$522$	18.4178	−	19.1112i	0.806126	−	0.836473i
$523$	−5.99562	+	10.3847i	−0.262170	+	0.454092i	−0.966818	−	0.255465i	$-0.917771\pi$
$523$	−5.99562	+	10.3847i	−0.262170	+	0.454092i	0.704648	+	0.709557i	$0.251105\pi$
$524$	2.89711	−	5.01795i	0.126561	−	0.219210i
$525$	18.1138	+	14.0318i	0.790551	+	0.612397i
$526$	−8.23669	−	14.2664i	−0.359137	−	0.622043i
$527$	−47.7068			−2.07814
$528$	6.19304	−	0.873594i	0.269518	−	0.0380183i
$529$	40.8255			1.77502
$530$	−1.12779	+	6.50862i	−0.0489879	+	0.282716i
$531$	3.24415	−	0.933823i	0.140784	−	0.0405245i
$532$	11.3955	+	5.59035i	0.494056	+	0.242372i
$533$	4.42321	−	7.66122i	0.191590	−	0.331844i
$534$	−22.7461	−	9.17653i	−0.984318	−	0.397107i
$535$	1.22784	−	7.08605i	0.0530842	−	0.306356i
$536$	4.11272	+	2.37448i	0.177642	+	0.102562i
$537$	24.5393	−	3.46152i	1.05895	−	0.149376i
$538$	8.79451	−	15.2325i	0.379158	−	0.656721i
$539$	−23.3924	−	9.57627i	−1.00758	−	0.412479i
$540$	11.2611	−	2.86146i	0.484600	−	0.123138i
$541$	−8.92677	+	15.4616i	−0.383792	+	0.664747i	−0.991601	−	0.129336i	$-0.958715\pi$
$541$	−8.92677	+	15.4616i	−0.383792	+	0.664747i	0.607809	+	0.794083i	$0.292049\pi$
$542$			6.29101i			0.270222i
$543$	−2.71977	+	6.74157i	−0.116717	+	0.289308i
$544$		−	7.39740i		−	0.317161i
$545$	−12.5461	−	10.4642i	−0.537414	−	0.448239i
$546$	−14.6894	−	4.80189i	−0.628649	−	0.205502i
$547$	16.3179	+	9.42113i	0.697702	+	0.402818i	0.806491	−	0.591247i	$-0.201364\pi$
$547$	16.3179	+	9.42113i	0.697702	+	0.402818i	−0.108789	+	0.994065i	$0.534697\pi$
$548$	3.72838	−	6.45775i	0.159269	−	0.275861i
$549$	4.89625	+	1.21547i	0.208967	+	0.0518752i
$550$	6.07452	−	17.0022i	0.259018	−	0.724976i
$551$	−21.2219	−	36.7575i	−0.904085	−	1.56592i
$552$	−12.8325	−	5.17708i	−0.546190	−	0.220351i
$553$	0.201016	−	0.409754i	0.00854806	−	0.0174245i
$554$	2.39658	−	1.38367i	0.101821	−	0.0587864i
$555$	−21.1419	−	13.1091i	−0.897425	−	0.556452i
$556$			8.30743i			0.352313i
$557$	16.8982	+	29.2685i	0.716000	+	1.24015i	0.962573	+	0.271024i	$0.0873622\pi$
$557$	16.8982	+	29.2685i	0.716000	+	1.24015i	−0.246573	+	0.969124i	$0.579304\pi$
$558$	13.4256	−	13.9310i	0.568352	−	0.589748i
$559$			2.57061i			0.108725i
$560$	−0.614480	+	5.88408i	−0.0259665	+	0.248648i
$561$	−6.46232	−	45.8124i	−0.272840	−	1.93420i
$562$		−	3.47830i		−	0.146723i
$563$	−19.5776	−	11.3032i	−0.825100	−	0.476371i	0.0270723	−	0.999633i	$-0.491382\pi$
$563$	−19.5776	−	11.3032i	−0.825100	−	0.476371i	−0.852172	+	0.523262i	$0.824715\pi$
$564$	−5.33193	+	13.2164i	−0.224515	+	0.556510i
$565$	23.4221	+	19.5356i	0.985375	+	0.821868i
$566$	12.2282			0.513988
$567$	−19.2677	+	13.9913i	−0.809168	+	0.587578i
$568$			1.40979i			0.0591533i
$569$	−11.3581	+	6.55760i	−0.476156	+	0.274909i	−0.718813	−	0.695203i	$-0.755314\pi$
$569$	−11.3581	+	6.55760i	−0.476156	+	0.274909i	0.242657	+	0.970112i	$0.421981\pi$
$570$	0.584003	−	18.5713i	0.0244612	−	0.777865i
$571$	−18.7178	+	32.4202i	−0.783317	+	1.35674i	0.146683	+	0.989184i	$0.453140\pi$
$571$	−18.7178	+	32.4202i	−0.783317	+	1.35674i	−0.930000	+	0.367561i	$0.880193\pi$
$572$			12.1776i			0.509173i
$573$	32.2581	−	4.55035i	1.34760	−	0.190093i
$574$	6.92444	−	0.468239i	0.289020	−	0.0195439i
$575$	−30.4474	+	25.8572i	−1.26974	+	1.07832i
$576$	2.16014	+	2.08177i	0.0900059	+	0.0867406i
$577$	9.64764	+	16.7102i	0.401636	+	0.695655i	0.993924	−	0.110072i	$-0.0351082\pi$
$577$	9.64764	+	16.7102i	0.401636	+	0.695655i	−0.592287	+	0.805727i	$0.701775\pi$
$578$	−37.7215			−1.56901
$579$	−5.87520	−	7.51202i	−0.244165	−	0.312189i
$580$	12.6713	−	15.1922i	0.526146	−	0.630820i
$581$	−2.37573	−	35.1330i	−0.0985620	−	1.45756i
$582$	13.4515	+	5.42677i	0.557581	+	0.224947i
$583$	−9.23804	+	5.33358i	−0.382600	+	0.220894i
$584$	−2.78262	−	4.81964i	−0.115146	−	0.199438i
$585$	2.45426	+	22.4893i	0.101471	+	0.929820i
$586$	−10.8450	−	6.26137i	−0.448003	−	0.258655i
$587$	20.0370	+	11.5683i	0.827014	+	0.477477i	0.852829	−	0.522190i	$-0.174885\pi$
$587$	20.0370	+	11.5683i	0.827014	+	0.477477i	−0.0258152	+	0.999667i	$0.508218\pi$
$588$	−3.29435	−	11.6682i	−0.135857	−	0.481189i
$589$	−15.4697	−	26.7943i	−0.637417	−	1.10404i
$590$	2.36192	−	0.867597i	0.0972388	−	0.0357184i
$591$	−21.0770	−	8.50317i	−0.866992	−	0.349774i
$592$		−	6.42303i		−	0.263985i
$593$	12.4103	+	7.16507i	0.509629	+	0.294234i	0.732681	−	0.680572i	$-0.238269\pi$
$593$	12.4103	+	7.16507i	0.509629	+	0.294234i	−0.223052	+	0.974806i	$0.571602\pi$
$594$	15.1965	+	11.0054i	0.623519	+	0.451558i
$595$	43.5269	+	4.54556i	1.78443	+	0.186350i
$596$	−10.1240	−	5.84511i	−0.414696	−	0.239425i
$597$	−18.9187	+	2.66869i	−0.774292	+	0.109222i
$598$	13.4713	−	23.3329i	0.550881	−	0.954154i
$599$	−4.89074	−	2.82367i	−0.199830	−	0.115372i	0.396746	−	0.917928i	$-0.370139\pi$
$599$	−4.89074	−	2.82367i	−0.199830	−	0.115372i	−0.596576	+	0.802556i	$0.703473\pi$
$600$	8.21901	−	2.72908i	0.335540	−	0.111414i
$601$	11.9185	+	6.88116i	0.486167	+	0.280688i	0.722983	−	0.690866i	$-0.242771\pi$
$601$	11.9185	+	6.88116i	0.486167	+	0.280688i	−0.236816	+	0.971554i	$0.576104\pi$
$602$	−1.67451	+	1.12389i	−0.0682480	+	0.0458063i
$603$	3.94093	+	13.6910i	0.160487	+	0.557539i
$604$	4.53199	−	7.84964i	0.184404	−	0.319397i
$605$	4.27969	−	1.57205i	0.173994	−	0.0639128i
$606$	−3.81701	−	27.0593i	−0.155055	−	1.09921i
$607$	5.66533			0.229949			0.114974	−	0.993368i	$-0.463321\pi$
$607$	5.66533			0.229949			0.114974	+	0.993368i	$0.463321\pi$
$608$	4.15471	−	2.39873i	0.168496	−	0.0972812i
$609$	−12.5972	+	38.5361i	−0.510466	+	1.56156i
$610$	3.70501	+	0.641989i	0.150012	+	0.0259934i
$611$	−24.0308	−	13.8742i	−0.972183	−	0.561290i
$612$	15.3997	−	15.9794i	0.622497	−	0.645931i
$613$	4.30137	−	2.48340i	0.173731	−	0.100304i	−0.410613	−	0.911810i	$-0.634685\pi$
$613$	4.30137	−	2.48340i	0.173731	−	0.100304i	0.584344	+	0.811506i	$0.301352\pi$
$614$	3.72675	+	6.45492i	0.150399	+	0.260499i
$615$	−4.80069	−	8.95369i	−0.193583	−	0.361048i
$616$	−7.93260	+	5.32416i	−0.319614	+	0.214517i
$617$	12.3417	+	21.3765i	0.496858	+	0.860584i	0.999993	−	0.00362388i	$-0.00115352\pi$
$617$	12.3417	+	21.3765i	0.496858	+	0.860584i	−0.503135	+	0.864208i	$0.667820\pi$
$618$	−0.968723	−	6.86743i	−0.0389678	−	0.276249i
$619$			31.9421i			1.28386i	0.766763	+	0.641930i	$0.221866\pi$
$619$			31.9421i			1.28386i	−0.766763	+	0.641930i	$0.778134\pi$
$620$	9.23669	−	11.0743i	0.370955	−	0.444754i
$621$	−16.9426	−	37.8977i	−0.679884	−	1.52078i
$622$	22.5224			0.903064
$623$	37.3808	−	2.52774i	1.49763	−	0.101272i
$624$	−4.60109	+	3.59855i	−0.184191	+	0.144057i
$625$	4.04933	−	24.6699i	0.161973	−	0.986795i
$626$	−10.2965	+	17.8341i	−0.411532	+	0.712795i
$627$	23.6348	−	18.4849i	0.943883	−	0.738217i
$628$	9.89018	+	17.1303i	0.394661	+	0.683573i
$629$	−47.5138			−1.89450
$630$	−13.5767	+	11.4312i	−0.540909	+	0.455432i
$631$	−29.5217			−1.17524			−0.587620	−	0.809137i	$-0.699935\pi$
$631$	−29.5217			−1.17524			−0.587620	+	0.809137i	$0.699935\pi$
$632$	−0.0862526	−	0.149394i	−0.00343094	−	0.00594257i
$633$	3.43091	+	24.3222i	0.136366	+	0.966722i
$634$	4.35758	−	7.54755i	0.173062	−	0.299751i
$635$	−6.48442	−	17.6530i	−0.257326	−	0.700538i
$636$	−4.74508	−	1.91432i	−0.188155	−	0.0759079i
$637$	23.3920	−	3.17813i	0.926825	−	0.125922i
$638$	31.9467			1.26478
$639$	−2.93485	+	3.04534i	−0.116101	+	0.120472i
$640$	1.71718	+	1.43224i	0.0678773	+	0.0566142i
$641$		−	30.6755i		−	1.21161i	−0.795614	−	0.605804i	$-0.792851\pi$
$641$		−	30.6755i		−	1.21161i	0.795614	−	0.605804i	$-0.207149\pi$
$642$	5.16605	+	2.08416i	0.203888	+	0.0822551i
$643$	9.01650	+	15.6170i	0.355576	+	0.615876i	0.987216	−	0.159386i	$-0.0509514\pi$
$643$	9.01650	+	15.6170i	0.355576	+	0.615876i	−0.631640	+	0.775262i	$0.717618\pi$
$644$	21.0890	−	1.42606i	0.831022	−	0.0561947i
$645$	2.50899	+	1.55571i	0.0987913	+	0.0612560i
$646$	−17.7443	−	30.7341i	−0.698141	−	1.20922i
$647$	−0.566867	+	0.327281i	−0.0222858	+	0.0128667i	−0.511102	−	0.859520i	$-0.670762\pi$
$647$	−0.566867	+	0.327281i	−0.0222858	+	0.0128667i	0.488816	+	0.872387i	$0.337429\pi$
$648$	0.332429	+	8.99386i	0.0130591	+	0.353312i
$649$	3.51898	+	2.03169i	0.138132	+	0.0797506i
$650$	3.02635	+	16.5883i	0.118703	+	0.650646i
$651$	−9.18273	+	28.0908i	−0.359900	+	1.10097i
$652$	−11.4067	+	6.58566i	−0.446721	+	0.257914i
$653$	8.32983			0.325971			0.162986	−	0.986628i	$-0.447888\pi$
$653$	8.32983			0.325971			0.162986	+	0.986628i	$0.447888\pi$
$654$	9.96810	−	7.79612i	0.389783	−	0.304852i
$655$	12.1617	−	4.46734i	0.475199	−	0.174553i
$656$	1.31158	−	2.27173i	0.0512088	−	0.0886962i
$657$	4.02255	−	16.2039i	0.156934	−	0.632174i
$658$	−1.46872	−	21.7198i	−0.0572566	−	0.846725i
$659$	32.1220	+	18.5456i	1.25129	+	0.722435i	0.971367	−	0.237586i	$-0.0763561\pi$
$659$	32.1220	+	18.5456i	1.25129	+	0.722435i	0.279928	+	0.960021i	$0.409689\pi$
$660$	11.8857	+	7.36980i	0.462652	+	0.286869i
$661$	−11.4479	−	6.60942i	−0.445270	−	0.257077i	0.260560	−	0.965458i	$-0.416093\pi$
$661$	−11.4479	−	6.60942i	−0.445270	−	0.257077i	−0.705831	+	0.708381i	$0.749426\pi$
$662$	7.18237	−	12.4402i	0.279151	−	0.483503i
$663$	26.6199	+	34.0361i	1.03383	+	1.32185i
$664$	−11.5262	−	6.65467i	−0.447304	−	0.258251i
$665$	11.5613	+	25.9206i	0.448328	+	1.00516i
$666$	13.3713	−	13.8747i	0.518128	−	0.537632i
$667$	−61.2114	−	35.3404i	−2.37012	−	1.36839i
$668$		−	2.18034i		−	0.0843601i
$669$	−5.06448	+	3.96097i	−0.195804	+	0.153140i
$670$	3.66144	+	9.96779i	0.141454	+	0.385089i
$671$	3.03613	+	5.25873i	0.117208	+	0.203011i
$672$	−4.35575	−	1.42387i	−0.168027	−	0.0549270i
$673$	25.9475	+	14.9808i	1.00020	+	0.577466i	0.908308	−	0.418302i	$-0.137375\pi$
$673$	25.9475	+	14.9808i	1.00020	+	0.577466i	0.0918934	+	0.995769i	$0.470708\pi$
$674$	9.09613	+	5.25165i	0.350370	+	0.202286i
$675$	23.4356	+	11.2149i	0.902035	+	0.431663i
$676$	0.813400	+	1.40885i	0.0312846	+	0.0541865i
$677$	36.3274	−	20.9737i	1.39618	−	0.806083i	0.402187	−	0.915557i	$-0.368250\pi$
$677$	36.3274	−	20.9737i	1.39618	−	0.806083i	0.993990	+	0.109474i	$0.0349168\pi$
$678$	−18.6093	+	14.5545i	−0.714687	+	0.558961i
$679$	−22.1061	+	1.49484i	−0.848353	+	0.0573667i
$680$	10.5948	−	12.7026i	0.406294	−	0.487124i
$681$	−10.4549	+	25.9148i	−0.400632	+	0.993057i
$682$	23.2875			0.891724
$683$	17.3451	+	30.0426i	0.663691	+	1.14955i	0.979638	+	0.200770i	$0.0643444\pi$
$683$	17.3451	+	30.0426i	0.663691	+	1.14955i	−0.315947	+	0.948777i	$0.602322\pi$
$684$	13.9684	+	3.46759i	0.534094	+	0.132587i
$685$	15.6513	−	5.74915i	0.598006	−	0.219664i
$686$	12.2974	+	13.8482i	0.469518	+	0.528728i
$687$	5.01873	−	12.4400i	0.191477	−	0.474617i
$688$			0.762245i			0.0290603i
$689$	4.98125	−	8.62779i	0.189771	−	0.328692i
$690$	−14.6209	−	27.2692i	−0.556609	−	1.03812i
$691$	10.2119	−	5.89584i	0.388479	−	0.224288i	−0.293022	−	0.956106i	$-0.594661\pi$
$691$	10.2119	−	5.89584i	0.388479	−	0.224288i	0.681501	+	0.731817i	$0.261328\pi$
$692$			25.9317i			0.985773i
$693$	−28.2192	−	5.01294i	−1.07196	−	0.190426i
$694$	−13.6614			−0.518579
$695$	−11.8982	+	14.2653i	−0.451325	+	0.541114i
$696$	9.44040	+	12.0705i	0.357837	+	0.457530i
$697$	−16.8049	−	9.70231i	−0.636531	−	0.367501i
$698$			34.9576i			1.32317i
$699$	23.2765	−	18.2047i	0.880397	−	0.688564i
$700$	−9.48258	+	9.22392i	−0.358408	+	0.348631i
$701$		−	32.3472i		−	1.22174i	−0.791732	−	0.610869i	$-0.790820\pi$
$701$		−	32.3472i		−	1.22174i	0.791732	−	0.610869i	$-0.209180\pi$
$702$	−17.4304	−	1.80507i	−0.657867	−	0.0681279i
$703$	−15.4071	−	26.6859i	−0.581089	−	1.00648i
$704$			3.61095i			0.136093i
$705$	−28.0849	+	15.0582i	−1.05774	+	0.567126i
$706$	8.71536	−	5.03181i	0.328007	−	0.189375i
$707$	23.2629	+	34.6600i	0.874893	+	1.30352i
$708$	0.272240	+	1.92995i	0.0102314	+	0.0725321i
$709$	11.9774	+	20.7454i	0.449820	+	0.779111i	0.998374	−	0.0570043i	$-0.0181549\pi$
$709$	11.9774	+	20.7454i	0.449820	+	0.779111i	−0.548554	+	0.836115i	$0.684822\pi$
$710$	−2.01915	+	2.42085i	−0.0757773	+	0.0908528i
$711$	0.124686	−	0.502270i	0.00467611	−	0.0188366i
$712$	7.08044	−	12.2637i	0.265351	−	0.459601i
$713$	−44.6199	−	25.7613i	−1.67103	−	0.964769i
$714$	−10.5329	+	32.2213i	−0.394186	+	1.20585i
$715$	−17.4413	+	20.9111i	−0.652267	+	0.782032i
$716$			14.3080i			0.534716i
$717$	−21.7979	+	3.07483i	−0.814058	+	0.114832i
$718$		−	4.06236i		−	0.151606i
$719$	10.7973	−	18.7015i	0.402672	−	0.697448i	−0.591376	−	0.806396i	$-0.701415\pi$
$719$	10.7973	−	18.7015i	0.402672	−	0.697448i	0.994047	+	0.108948i	$0.0347482\pi$
$720$	0.727745	+	6.66861i	0.0271214	+	0.248525i
$721$	5.90393	+	8.79642i	0.219874	+	0.327596i
$722$	2.00777	−	3.47755i	0.0747213	−	0.129421i
$723$	−4.10865	+	10.1842i	−0.152802	+	0.378754i
$724$	−3.63476	−	2.09853i	−0.135085	−	0.0779912i
$725$	43.5176	−	7.93931i	1.61620	−	0.294858i
$726$	0.493287	+	3.49699i	0.0183076	+	0.129785i
$727$	16.1191	−	27.9190i	0.597823	−	1.03546i	−0.395319	−	0.918544i	$-0.629366\pi$
$727$	16.1191	−	27.9190i	0.597823	−	1.03546i	0.993142	−	0.116916i	$-0.0373008\pi$
$728$	3.92979	−	8.01056i	0.145648	−	0.296891i
$729$	−18.0051	+	20.1201i	−0.666855	+	0.745187i
$730$	2.12463	−	12.2615i	0.0786360	−	0.453820i
$731$	5.63863			0.208552
$732$	−1.08972	+	2.70112i	−0.0402773	+	0.0998363i
$733$	−19.6399			−0.725416			−0.362708	−	0.931903i	$-0.618148\pi$
$733$	−19.6399			−0.725416			−0.362708	+	0.931903i	$0.618148\pi$
$734$	−7.70236	−	13.3409i	−0.284299	−	0.492421i
$735$	11.0547	−	24.7547i	0.407759	−	0.913090i
$736$	3.99454	−	6.91875i	0.147241	−	0.255029i
$737$	−8.57413	+	14.8508i	−0.315832	+	0.547037i
$738$	7.56244	−	2.17684i	0.278377	−	0.0801305i
$739$	−18.6678	−	32.3336i	−0.686706	−	1.18941i	−0.972897	−	0.231237i	$-0.925723\pi$
$739$	−18.6678	−	32.3336i	−0.686706	−	1.18941i	0.286191	−	0.958172i	$-0.407611\pi$
$740$	9.19932	−	11.0295i	0.338174	−	0.405452i
$741$	−10.4843	+	25.9877i	−0.385151	+	0.954682i
$742$	7.79805	−	0.527313i	0.286275	−	0.0193583i
$743$	−6.11862	−	10.5978i	−0.224470	−	0.388794i	0.731690	−	0.681637i	$-0.238732\pi$
$743$	−6.11862	−	10.5978i	−0.224470	−	0.388794i	−0.956160	+	0.292843i	$0.905399\pi$
$744$	6.88156	+	8.79875i	0.252290	+	0.322578i
$745$	−9.01314	−	24.5371i	−0.330216	−	0.898970i
$746$	25.3219	−	14.6196i	0.927101	−	0.535262i
$747$	−11.0448	−	38.3700i	−0.404107	−	1.40389i
$748$	26.7117			0.976675
$749$	−8.48987	+	0.574095i	−0.310213	+	0.0209770i
$750$	18.0222	+	7.08528i	0.658077	+	0.258718i
$751$	16.0433			0.585427			0.292713	−	0.956200i	$-0.405442\pi$
$751$	16.0433			0.585427			0.292713	+	0.956200i	$0.405442\pi$
$752$	−7.12570	−	4.11402i	−0.259848	−	0.150023i
$753$	−26.0173	−	10.4962i	−0.948121	−	0.382504i
$754$	−25.8391	+	14.9182i	−0.941003	+	0.543288i
$755$	19.0248	−	6.98831i	0.692383	−	0.254331i
$756$	−6.44487	−	12.1435i	−0.234398	−	0.441653i
$757$			5.92914i			0.215498i	0.994178	+	0.107749i	$0.0343643\pi$
$757$			5.92914i			0.215498i	−0.994178	+	0.107749i	$0.965636\pi$
$758$	−16.0739	−	27.8408i	−0.583831	−	1.01122i
$759$	18.6942	−	46.3377i	0.678556	−	1.68195i
$760$	10.5699	+	1.83151i	0.383411	+	0.0664359i
$761$	−14.5872			−0.528786			−0.264393	−	0.964415i	$-0.585172\pi$
$761$	−14.5872			−0.528786			−0.264393	+	0.964415i	$0.585172\pi$
$762$	14.4245	−	2.03472i	0.522544	−	0.0737103i
$763$	−8.51375	+	17.3546i	−0.308218	+	0.628278i
$764$			18.8086i			0.680471i
$765$	49.3304	−	5.38342i	1.78354	−	0.194638i
$766$	5.49320	−	3.17150i	0.198478	−	0.114591i
$767$	−3.79495			−0.137028
$768$	−1.36433	+	1.06705i	−0.0492311	+	0.0385039i
$769$	−28.3116	+	16.3457i	−1.02094	+	0.589441i	−0.914377	−	0.404865i	$-0.867319\pi$
$769$	−28.3116	+	16.3457i	−1.02094	+	0.589441i	−0.106565	+	0.994306i	$0.533985\pi$
$770$	−21.2471	−	2.21886i	−0.765694	−	0.0799621i
$771$	0.619476	−	1.53551i	0.0223099	−	0.0553000i
$772$	4.76835	−	2.75301i	0.171617	−	0.0990828i
$773$	−14.5424	+	8.39605i	−0.523053	+	0.301985i	−0.738183	−	0.674601i	$-0.764316\pi$
$773$	−14.5424	+	8.39605i	−0.523053	+	0.301985i	0.215130	+	0.976585i	$0.430983\pi$
$774$	−1.58682	+	1.64656i	−0.0570371	+	0.0591843i
$775$	31.7220	−	5.78734i	1.13949	−	0.207887i
$776$	−4.18720	+	7.25244i	−0.150312	+	0.260347i
$777$	−9.14558	+	27.9772i	−0.328096	+	1.00367i
$778$	−21.0192	+	12.1355i	−0.753576	+	0.435077i
$779$		−	12.5845i		−	0.450887i
$780$	−13.0549	−	0.410531i	−0.467439	−	0.0146994i
$781$	−5.09067			−0.182158
$782$	−51.1808	−	29.5492i	−1.83022	−	1.05668i
$783$	−4.73541	+	45.7267i	−0.169230	+	1.63414i
$784$	6.93627	−	0.942388i	0.247724	−	0.0336567i
$785$	−7.55150	+	43.5808i	−0.269525	+	1.55547i
$786$	1.40179	+	9.93751i	0.0500002	+	0.354459i
$787$	−10.9653	+	18.9925i	−0.390872	+	0.677010i	−0.992565	−	0.121717i	$-0.961160\pi$
$787$	−10.9653	+	18.9925i	−0.390872	+	0.677010i	0.601693	+	0.798728i	$0.294493\pi$
$788$	6.56089	−	11.3638i	0.233722	−	0.404818i
$789$	26.4605	+	10.6751i	0.942019	+	0.380042i
$790$	0.0658569	−	0.380070i	0.00234308	−	0.0135223i
$791$	15.8942	−	32.3991i	0.565133	−	1.15198i
$792$	−7.51719	+	7.80017i	−0.267112	+	0.277167i
$793$	−4.91134	−	2.83557i	−0.174407	−	0.100694i
$794$	−6.46548			−0.229451
$795$	−5.40636	−	10.0833i	−0.191744	−	0.357618i
$796$		−	11.0309i		−	0.390979i
$797$	19.5566	−	11.2910i	0.692730	−	0.399948i	−0.111904	−	0.993719i	$-0.535695\pi$
$797$	19.5566	−	11.2910i	0.692730	−	0.399948i	0.804634	+	0.593771i	$0.202362\pi$
$798$	−21.5124	+	4.53248i	−0.761530	+	0.160448i
$799$	−30.4331	+	52.7117i	−1.07665	+	1.86480i
$800$	0.897383	+	4.91881i	0.0317273	+	0.173906i
$801$	40.8250	−	11.7514i	1.44248	−	0.415216i
$802$	−31.2348	+	18.0334i	−1.10294	+	0.636783i
$803$	17.4035	−	10.0479i	0.614155	−	0.354583i
$804$	−8.14480	+	1.14891i	−0.287245	+	0.0405189i
$805$	38.2559	+	27.7557i	1.34834	+	0.978258i
$806$	−18.8353	+	10.8746i	−0.663446	+	0.383041i
$807$	4.25529	+	30.1664i	0.149793	+	1.06191i
$808$	15.7774			0.555047
$809$	−13.7016	+	7.91060i	−0.481721	+	0.278122i	−0.721133	−	0.692796i	$-0.756379\pi$
$809$	−13.7016	+	7.91060i	−0.481721	+	0.278122i	0.239412	+	0.970918i	$0.423045\pi$
$810$	−12.3105	+	15.9202i	−0.432547	+	0.559377i
$811$		−	20.5447i		−	0.721421i	−0.932678	−	0.360710i	$-0.882534\pi$
$811$		−	20.5447i		−	0.721421i	0.932678	−	0.360710i	$-0.117466\pi$
$812$	−21.0149	−	10.3094i	−0.737477	−	0.361789i
$813$	−6.71284	−	8.58302i	−0.235430	−	0.301020i
$814$	23.1933			0.812924
$815$	−29.0195	−	5.02838i	−1.01651	−	0.176137i
$816$	7.89341	+	10.0925i	0.276325	+	0.353308i
$817$	1.82842	+	3.16691i	0.0639682	+	0.110796i
$818$			35.5824i			1.24411i
$819$	25.1651	−	9.12301i	0.879340	−	0.318784i
$820$	5.50588	−	2.02246i	0.192274	−	0.0706273i
$821$	11.7506	−	6.78423i	0.410100	−	0.236771i	−0.280733	−	0.959786i	$-0.590578\pi$
$821$	11.7506	−	6.78423i	0.410100	−	0.236771i	0.690833	+	0.723015i	$0.257244\pi$
$822$	1.80401	+	12.7889i	0.0629219	+	0.446063i
$823$	−16.4510	−	9.49800i	−0.573446	−	0.331079i	0.185078	−	0.982724i	$-0.440746\pi$
$823$	−16.4510	−	9.49800i	−0.573446	−	0.331079i	−0.758525	+	0.651644i	$0.774079\pi$
$824$	4.00416			0.139492
$825$	9.85457	+	29.6785i	0.343092	+	1.03327i
$826$	−1.65918	−	2.47206i	−0.0577304	−	0.0860139i
$827$	−45.9391			−1.59746			−0.798730	−	0.601689i	$-0.794495\pi$
$827$	−45.9391			−1.59746			−0.798730	+	0.601689i	$0.794495\pi$
$828$	23.0321	−	6.62975i	0.800420	−	0.230400i
$829$	23.0544	−	13.3105i	0.800714	−	0.462292i	−0.0430068	−	0.999075i	$-0.513694\pi$
$829$	23.0544	−	13.3105i	0.800714	−	0.462292i	0.843721	+	0.536782i	$0.180360\pi$
$830$	−10.2615	−	27.9355i	−0.356181	−	0.969656i
$831$	−1.79329	+	4.44506i	−0.0622084	+	0.154197i
$832$	−1.68621	−	2.92060i	−0.0584588	−	0.101254i
$833$	−6.97122	−	51.3104i	−0.241538	−	1.77780i
$834$	−8.86446	−	11.3341i	−0.306951	−	0.392467i
$835$	3.12277	−	3.74403i	0.108068	−	0.129568i
$836$	8.66168	+	15.0025i	0.299571	+	0.518871i
$837$	−3.45186	+	33.3324i	−0.119314	+	1.15214i
$838$	9.77575	−	16.9321i	0.337698	−	0.584909i
$839$	−11.2983	+	19.5693i	−0.390062	+	0.675607i	−0.992457	−	0.122591i	$-0.960880\pi$
$839$	−11.2983	+	19.5693i	−0.390062	+	0.675607i	0.602396	+	0.798198i	$0.294213\pi$
$840$	−5.44027	−	8.68352i	−0.187707	−	0.299610i
$841$	24.6363	+	42.6713i	0.849527	+	1.47142i
$842$	−13.6570			−0.470652
$843$	3.71153	+	4.74555i	0.127832	+	0.163445i
$844$	−14.1815			−0.488147
$845$	−0.621060	+	3.58423i	−0.0213651	+	0.123301i
$846$	−6.82805	−	23.7210i	−0.234753	−	0.815544i
$847$	−3.00636	−	4.47926i	−0.103300	−	0.153909i
$848$	1.47706	−	2.55834i	0.0507224	−	0.0878537i
$849$	−16.6833	+	13.0481i	−0.572568	+	0.447809i
$850$	36.3864	−	6.63830i	1.24804	−	0.227692i
$851$	−44.4394	−	25.6571i	−1.52336	−	0.879514i
$852$	−1.50431	−	1.92341i	−0.0515370	−	0.0658951i
$853$	5.34386	−	9.25584i	0.182970	−	0.316914i	−0.759920	−	0.650016i	$-0.774762\pi$
$853$	5.34386	−	9.25584i	0.182970	−	0.316914i	0.942891	+	0.333102i	$0.108095\pi$
$854$	−0.300172	−	4.43902i	−0.0102717	−	0.151900i
$855$	19.0197	+	25.9605i	0.650461	+	0.887831i
$856$	−1.60810	+	2.78531i	−0.0549637	+	0.0951999i
$857$		−	27.2333i		−	0.930273i	−0.885239	−	0.465137i	$-0.846005\pi$
$857$		−	27.2333i		−	0.930273i	0.885239	−	0.465137i	$-0.153995\pi$
$858$	−12.9942	−	16.6143i	−0.443614	−	0.567204i
$859$		−	26.1550i		−	0.892397i	−0.894934	−	0.446198i	$-0.852778\pi$
$859$		−	26.1550i		−	0.892397i	0.894934	−	0.446198i	$-0.147222\pi$
$860$	−1.09172	+	1.30891i	−0.0372272	+	0.0446334i
$861$	−8.94759	+	8.02757i	−0.304933	+	0.273579i
$862$	−6.33629	−	3.65826i	−0.215815	−	0.124601i
$863$	25.1857	−	43.6229i	0.857331	−	1.48494i	−0.0171355	−	0.999853i	$-0.505455\pi$
$863$	25.1857	−	43.6229i	0.857331	−	1.48494i	0.874466	−	0.485087i	$-0.161212\pi$
$864$	−5.16851	−	0.535245i	−0.175836	−	0.0182094i
$865$	−37.1403	+	44.5292i	−1.26281	+	1.51404i
$866$	3.72503	+	6.45195i	0.126582	+	0.219246i
$867$	51.4647	−	40.2509i	1.74783	−	1.36699i
$868$	−15.3187	−	7.51501i	−0.519952	−	0.255076i
$869$	0.539454	−	0.311454i	0.0182997	−	0.0105653i
$870$	−1.07698	+	34.2480i	−0.0365132	+	1.16112i
$871$		−	16.0155i		−	0.542663i
$872$	3.65311	+	6.32737i	0.123710	+	0.214272i
$873$	−24.1429	+	6.94950i	−0.817113	+	0.235205i
$874$		−	38.3272i		−	1.29644i
$875$	−29.4941	+	2.25776i	−0.997083	+	0.0763263i
$876$	8.93922	+	3.60638i	0.302028	+	0.121848i
$877$		−	34.2640i		−	1.15701i	−0.815677	−	0.578507i	$-0.803636\pi$
$877$		−	34.2640i		−	1.15701i	0.815677	−	0.578507i	$-0.196364\pi$
$878$	−13.2005	−	7.62131i	−0.445495	−	0.257207i
$879$	21.4774	−	3.02961i	0.724415	−	0.102186i
$880$	−5.17175	+	6.20064i	−0.174340	+	0.209023i
$881$	−8.34204			−0.281050			−0.140525	−	0.990077i	$-0.544879\pi$
$881$	−8.34204			−0.281050			−0.140525	+	0.990077i	$0.544879\pi$
$882$	16.9452	+	12.4041i	0.570574	+	0.417667i
$883$			32.5885i			1.09669i	0.836252	+	0.548345i	$0.184742\pi$
$883$			32.5885i			1.09669i	−0.836252	+	0.548345i	$0.815258\pi$
$884$	−21.6048	+	12.4736i	−0.726650	+	0.419531i
$885$	−2.29667	+	3.70398i	−0.0772018	+	0.124508i
$886$	−1.09863	+	1.90288i	−0.0369091	+	0.0639285i
$887$		−	22.6116i		−	0.759222i	−0.925146	−	0.379611i	$-0.876058\pi$
$887$		−	22.6116i		−	0.759222i	0.925146	−	0.379611i	$-0.123942\pi$
$888$	6.85371	+	8.76314i	0.229996	+	0.294072i
$889$	−18.4762	+	12.4007i	−0.619670	+	0.415907i
$890$	29.7229	−	10.9180i	0.996314	−	0.365973i
$891$	−32.4764	+	1.20039i	−1.08800	+	0.0402144i
$892$	−1.85603	−	3.21474i	−0.0621446	−	0.107638i
$893$	−39.4737			−1.32094
$894$	20.0496	−	2.82820i	0.670558	−	0.0945892i
$895$	−20.4925	+	24.5694i	−0.684989	+	0.821264i
$896$	1.16527	−	2.37532i	0.0389291	−	0.0793538i
$897$	6.51818	+	46.2084i	0.217636	+	1.54285i
$898$	−10.1254	+	5.84593i	−0.337890	+	0.195081i
$899$	28.5283	+	49.4125i	0.951472	+	1.64800i
$900$	−8.30138	+	12.4935i	−0.276713	+	0.416449i
$901$	−18.9251	−	10.9264i	−0.630485	−	0.364011i
$902$	8.20311	+	4.73607i	0.273134	+	0.157694i
$903$	1.08534	−	3.32015i	0.0361178	−	0.110488i
$904$	−6.81995	−	11.8125i	−0.226828	−	0.392878i
$905$	−3.23592	−	8.80939i	−0.107566	−	0.292834i
$906$	2.19284	+	15.5454i	0.0728522	+	0.516461i
$907$			4.76791i			0.158316i	0.996862	+	0.0791578i	$0.0252231\pi$
$907$			4.76791i			0.158316i	−0.996862	+	0.0791578i	$0.974777\pi$
$908$	−13.9721	−	8.06681i	−0.463681	−	0.267706i
$909$	34.0814	+	32.8450i	1.13041	+	1.08940i
$910$	18.2212	−	8.12714i	0.604026	−	0.269412i
$911$	−45.4053	−	26.2148i	−1.50434	−	0.868534i	−0.999987	−	0.00503892i	$-0.998396\pi$
$911$	−45.4053	−	26.2148i	−1.50434	−	0.868534i	−0.504357	−	0.863495i	$-0.668271\pi$
$912$	−3.10884	+	7.70595i	−0.102944	+	0.255170i
$913$	24.0297	−	41.6206i	0.795266	−	1.37744i
$914$	18.8329	+	10.8732i	0.622935	+	0.359652i
$915$	−5.73990	+	3.07756i	−0.189755	+	0.101741i
$916$	6.70713	+	3.87236i	0.221610	+	0.127946i
$917$	−8.54328	−	12.7289i	−0.282124	−	0.420344i
$918$	−3.95942	+	38.2336i	−0.130680	+	1.26190i
$919$	11.9138	−	20.6354i	0.393001	−	0.680698i	−0.599842	−	0.800118i	$-0.704770\pi$
$919$	11.9138	−	20.6354i	0.393001	−	0.680698i	0.992844	+	0.119420i	$0.0381034\pi$
$920$	16.7686	−	6.15957i	0.552846	−	0.203075i
$921$	−11.9723	−	4.83001i	−0.394499	−	0.159154i
$922$	15.7604			0.519043
$923$	4.11742	−	2.37719i	0.135526	−	0.0782462i
$924$	5.14153	−	15.7284i	0.169144	−	0.517427i
$925$	31.5937	−	5.76392i	1.03879	−	0.189517i
$926$	6.80572	+	3.92928i	0.223650	+	0.129124i
$927$	8.64957	+	8.33577i	0.284089	+	0.273783i
$928$	−7.66188	+	4.42359i	−0.251514	+	0.145211i
$929$	5.24880	+	9.09118i	0.172207	+	0.298272i	0.939191	−	0.343394i	$-0.111577\pi$
$929$	5.24880	+	9.09118i	0.172207	+	0.298272i	−0.766984	+	0.641666i	$0.778243\pi$
$930$	−0.785066	+	24.9650i	−0.0257433	+	0.818635i
$931$	26.5577	−	20.5536i	0.870394	−	0.673616i
$932$	8.53036	+	14.7750i	0.279421	+	0.483972i
$933$	−30.7279	+	24.0325i	−1.00599	+	0.786790i
$934$			25.5677i			0.836602i
$935$	45.8686	+	38.2575i	1.50006	+	1.25115i
$936$	2.43758	−	9.81922i	0.0796747	−	0.320951i
$937$	21.2575			0.694452			0.347226	−	0.937781i	$-0.387124\pi$
$937$	21.2575			0.694452			0.347226	+	0.937781i	$0.387124\pi$
$938$	10.4326	−	7.00209i	0.340636	−	0.228626i
$939$	−4.98206	−	35.3186i	−0.162583	−	1.15258i
$940$	−6.34381	−	17.2702i	−0.206912	−	0.563292i
$941$	30.0733	−	52.0884i	0.980361	−	1.69803i	0.319389	−	0.947624i	$-0.396522\pi$
$941$	30.0733	−	52.0884i	0.980361	−	1.69803i	0.660972	−	0.750411i	$-0.270144\pi$
$942$	−31.7724	−	12.8181i	−1.03520	−	0.417635i
$943$	−10.4784	−	18.1490i	−0.341222	−	0.591014i
$944$	−1.12529			−0.0366251
$945$	6.32537	−	30.0830i	0.205764	−	0.978602i
$946$	−2.75243			−0.0894892
$947$	−25.7890	−	44.6679i	−0.838030	−	1.45151i	−0.891539	−	0.452944i	$-0.850374\pi$
$947$	−25.7890	−	44.6679i	−0.838030	−	1.45151i	0.0535089	−	0.998567i	$-0.482959\pi$
$948$	0.277088	+	0.111787i	0.00899940	+	0.00363066i
$949$	−9.38415	+	16.2538i	−0.304622	+	0.527622i
$950$	15.5272	+	18.2837i	0.503770	+	0.593201i
$951$	2.10845	+	14.9471i	0.0683711	+	0.484693i
$952$	−17.5712	−	8.62001i	−0.569485	−	0.279376i
$953$	−21.6816			−0.702337			−0.351169	−	0.936312i	$-0.614216\pi$
$953$	−21.6816			−0.702337			−0.351169	+	0.936312i	$0.614216\pi$
$954$	8.51654	−	2.45147i	0.275733	−	0.0793694i
$955$	−26.9384	+	32.2977i	−0.871707	+	1.04513i
$956$		−	12.7096i		−	0.411059i
$957$	−43.5859	+	34.0888i	−1.40893	+	1.10194i
$958$	3.98318	+	6.89907i	0.128691	+	0.222899i
$959$	−10.9946	−	16.3811i	−0.355034	−	0.528975i
$960$	−3.87107	−	0.121732i	−0.124938	−	0.00392888i
$961$	5.29563	+	9.17230i	0.170827	+	0.295881i
$962$	−18.7591	+	10.8306i	−0.604818	+	0.349192i
$963$	−9.27211	+	2.66896i	−0.298789	+	0.0860062i
$964$	−5.49087	−	3.17016i	−0.176849	−	0.102104i
$965$	12.1310	+	2.10202i	0.390512	+	0.0676663i
$966$	−27.2507	+	24.4487i	−0.876776	+	0.786623i
$967$	24.9910	−	14.4286i	0.803657	−	0.463992i	−0.0410912	−	0.999155i	$-0.513083\pi$
$967$	24.9910	−	14.4286i	0.803657	−	0.463992i	0.844748	+	0.535164i	$0.179750\pi$
$968$	−2.03898			−0.0655352
$969$	57.0040	+	22.9973i	1.83123	+	0.738781i
$970$	−17.5774	+	6.45664i	−0.564375	+	0.207310i
$971$	−14.9307	+	25.8608i	−0.479150	+	0.829911i	−0.999714	−	0.0239109i	$-0.992388\pi$
$971$	−14.9307	+	25.8608i	−0.479150	+	0.829911i	0.520565	+	0.853822i	$0.325722\pi$
$972$	−10.0505	−	11.9159i	−0.322369	−	0.382202i
$973$	19.7328	+	9.68043i	0.632604	+	0.310340i
$974$	−1.35301	−	0.781161i	−0.0433533	−	0.0250300i
$975$	−21.8295	−	19.4026i	−0.699104	−	0.621382i
$976$	−1.45633	−	0.840811i	−0.0466159	−	0.0269137i
$977$	−0.215010	+	0.372408i	−0.00687877	+	0.0119144i	−0.869444	−	0.494031i	$-0.835523\pi$
$977$	−0.215010	+	0.372408i	−0.00687877	+	0.0119144i	0.862566	+	0.505945i	$0.168856\pi$
$978$	8.53527	−	21.1566i	0.272928	−	0.676512i
$979$	44.2836	+	25.5671i	1.41531	+	0.817129i
$980$	13.2605	+	8.31616i	0.423592	+	0.265650i
$981$	−5.28092	+	21.2730i	−0.168607	+	0.679193i
$982$	3.63710	+	2.09988i	0.116065	+	0.0670099i
$983$		−	7.98937i		−	0.254821i	−0.991850	−	0.127411i	$-0.959333\pi$
$983$		−	7.98937i		−	0.254821i	0.991850	−	0.127411i	$-0.0406666\pi$
$984$	0.634620	+	4.49892i	0.0202310	+	0.143420i
$985$	27.5419	−	10.1169i	0.877557	−	0.322350i
$986$	32.7231	+	56.6780i	1.04211	+	1.80500i
$987$	25.1799	+	28.0658i	0.801487	+	0.893343i
$988$	−14.0114	−	8.08950i	−0.445763	−	0.257361i
$989$	5.27378	+	3.04482i	0.167697	+	0.0968196i
$990$	−24.0800	+	2.62785i	−0.765314	+	0.0835186i
$991$	28.7067	+	49.7215i	0.911900	+	1.57946i	0.811378	+	0.584522i	$0.198718\pi$
$991$	28.7067	+	49.7215i	0.911900	+	1.57946i	0.100522	+	0.994935i	$0.467949\pi$
$992$	−5.58511	+	3.22456i	−0.177327	+	0.102380i
$993$	3.47524	+	24.6366i	0.110284	+	0.781817i
$994$	3.34869	+	1.64279i	0.106214	+	0.0521060i
$995$	15.7988	−	18.9419i	0.500857	−	0.600500i
$996$	22.8265	−	3.21991i	0.723284	−	0.102027i
$997$	25.2757			0.800490			0.400245	−	0.916408i	$-0.368925\pi$
$997$	25.2757			0.800490			0.400245	+	0.916408i	$0.368925\pi$
$998$	5.57817	+	9.66168i	0.176574	+	0.305835i
$999$	−3.43790	+	33.1975i	−0.108770	+	1.05032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.r.a.299.22	yes	48
3.2	odd	2		1890.2.r.b.89.23		48
5.4	even	2		630.2.r.b.299.3	yes	48
7.3	odd	6		630.2.bi.b.479.13	yes	48
9.4	even	3		1890.2.bi.b.719.18		48
9.5	odd	6		630.2.bi.a.509.12	yes	48
15.14	odd	2		1890.2.r.a.89.23		48
21.17	even	6		1890.2.bi.a.899.15		48
35.24	odd	6		630.2.bi.a.479.12	yes	48
45.4	even	6		1890.2.bi.a.719.15		48
45.14	odd	6		630.2.bi.b.509.13	yes	48
63.31	odd	6		1890.2.r.a.1529.23		48
63.59	even	6		630.2.r.b.59.3	yes	48
105.59	even	6		1890.2.bi.b.899.18		48
315.59	even	6	inner	630.2.r.a.59.22	✓	48
315.94	odd	6		1890.2.r.b.1529.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.22	✓	48	315.59	even	6	inner
630.2.r.a.299.22	yes	48	1.1	even	1	trivial
630.2.r.b.59.3	yes	48	63.59	even	6
630.2.r.b.299.3	yes	48	5.4	even	2
630.2.bi.a.479.12	yes	48	35.24	odd	6
630.2.bi.a.509.12	yes	48	9.5	odd	6
630.2.bi.b.479.13	yes	48	7.3	odd	6
630.2.bi.b.509.13	yes	48	45.14	odd	6
1890.2.r.a.89.23		48	15.14	odd	2
1890.2.r.a.1529.23		48	63.31	odd	6
1890.2.r.b.89.23		48	3.2	odd	2
1890.2.r.b.1529.23		48	315.94	odd	6
1890.2.bi.a.719.15		48	45.4	even	6
1890.2.bi.a.899.15		48	21.17	even	6
1890.2.bi.b.719.18		48	9.4	even	3
1890.2.bi.b.899.18		48	105.59	even	6

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.60626 + 0.648019i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.09894 + 0.770998i) q^{5} +(-0.241929 - 1.71507i) q^{6} +(1.47445 + 2.19682i) q^{7} +1.00000 q^{8} +(2.16014 + 2.08177i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.60626 + 0.648019i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.09894 + 0.770998i) q^{5} +(-0.241929 - 1.71507i) q^{6} +(1.47445 + 2.19682i) q^{7} +1.00000 q^{8} +(2.16014 + 2.08177i) q^{9} +(1.71718 + 1.43224i) q^{10} +3.61095i q^{11} +(-1.36433 + 1.06705i) q^{12} +(-1.68621 - 2.92060i) q^{13} +(1.16527 - 2.37532i) q^{14} +(-3.87107 - 0.121732i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-6.40634 + 3.69870i) q^{17} +(0.722799 - 2.91163i) q^{18} +(-4.15471 - 2.39873i) q^{19} +(0.381768 - 2.20324i) q^{20} +(0.944768 + 4.48413i) q^{21} +(3.12718 - 1.80548i) q^{22} -7.98909 q^{23} +(1.60626 + 0.648019i) q^{24} +(3.81112 - 3.23656i) q^{25} +(-1.68621 + 2.92060i) q^{26} +(2.12072 + 4.74368i) q^{27} +(-2.63972 + 0.178501i) q^{28} +(7.66188 + 4.42359i) q^{29} +(1.83011 + 3.41331i) q^{30} +(5.58511 + 3.22456i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.33997 + 5.80013i) q^{33} +(6.40634 + 3.69870i) q^{34} +(-4.78852 - 3.47420i) q^{35} +(-2.88294 + 0.829851i) q^{36} +(5.56251 + 3.21152i) q^{37} +4.79745i q^{38} +(-0.815885 - 5.78394i) q^{39} +(-2.09894 + 0.770998i) q^{40} +(1.31158 + 2.27173i) q^{41} +(3.41099 - 3.06026i) q^{42} +(-0.660123 - 0.381122i) q^{43} +(-3.12718 - 1.80548i) q^{44} +(-6.13906 - 2.70406i) q^{45} +(3.99454 + 6.91875i) q^{46} +(7.12570 - 4.11402i) q^{47} +(-0.241929 - 1.71507i) q^{48} +(-2.65201 + 6.47818i) q^{49} +(-4.70851 - 1.68225i) q^{50} +(-12.6871 + 1.78965i) q^{51} +3.37242 q^{52} +(1.47706 + 2.55834i) q^{53} +(3.04779 - 4.20844i) q^{54} +(-2.78404 - 7.57918i) q^{55} +(1.47445 + 2.19682i) q^{56} +(-5.11913 - 6.54531i) q^{57} -8.84718i q^{58} +(0.562645 - 0.974530i) q^{59} +(2.04096 - 3.29158i) q^{60} +(1.45633 - 0.840811i) q^{61} -6.44913i q^{62} +(-1.38826 + 7.81490i) q^{63} +1.00000 q^{64} +(5.79103 + 4.83011i) q^{65} +(6.19304 - 0.873594i) q^{66} +(4.11272 + 2.37448i) q^{67} -7.39740i q^{68} +(-12.8325 - 5.17708i) q^{69} +(-0.614480 + 5.88408i) q^{70} +1.40979i q^{71} +(2.16014 + 2.08177i) q^{72} +(-2.78262 - 4.81964i) q^{73} -6.42303i q^{74} +(8.21901 - 2.72908i) q^{75} +(4.15471 - 2.39873i) q^{76} +(-7.93260 + 5.32416i) q^{77} +(-4.60109 + 3.59855i) q^{78} +(-0.0862526 - 0.149394i) q^{79} +(1.71718 + 1.43224i) q^{80} +(0.332429 + 8.99386i) q^{81} +(1.31158 - 2.27173i) q^{82} +(-11.5262 - 6.65467i) q^{83} +(-4.35575 - 1.42387i) q^{84} +(10.5948 - 12.7026i) q^{85} +0.762245i q^{86} +(9.44040 + 12.0705i) q^{87} +3.61095i q^{88} +(7.08044 - 12.2637i) q^{89} +(0.727745 + 6.66861i) q^{90} +(3.92979 - 8.01056i) q^{91} +(3.99454 - 6.91875i) q^{92} +(6.88156 + 8.79875i) q^{93} +(-7.12570 - 4.11402i) q^{94} +(10.5699 + 1.83151i) q^{95} +(-1.36433 + 1.06705i) q^{96} +(-4.18720 + 7.25244i) q^{97} +(6.93627 - 0.942388i) q^{98} +(-7.51719 + 7.80017i) 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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