LMFDB - Embedded newform 560.2.bl.a.267.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(267,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("560.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bl (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.20
Character	$\chi$	$=$	560.267
Dual form			560.2.bl.a.323.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.920909 - 1.07328i) q^{2} -1.27333 q^{3} +(-0.303853 + 1.97678i) q^{4} +(1.14059 - 1.92329i) q^{5} +(1.17262 + 1.36664i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.40146 - 1.49432i) q^{8} -1.37862 q^{9} +O(q^{10})$	\(q+(-0.920909 - 1.07328i) q^{2} -1.27333 q^{3} +(-0.303853 + 1.97678i) q^{4} +(1.14059 - 1.92329i) q^{5} +(1.17262 + 1.36664i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.40146 - 1.49432i) q^{8} -1.37862 q^{9} +(-3.11461 + 0.547008i) q^{10} +(3.26300 - 3.26300i) q^{11} +(0.386906 - 2.51710i) q^{12} +6.72886i q^{13} +(0.107741 - 1.41010i) q^{14} +(-1.45235 + 2.44899i) q^{15} +(-3.81535 - 1.20130i) q^{16} +(1.71563 + 1.71563i) q^{17} +(1.26959 + 1.47965i) q^{18} +(2.30052 - 2.30052i) q^{19} +(3.45536 + 2.83910i) q^{20} +(-0.900382 - 0.900382i) q^{21} +(-6.50703 - 0.497180i) q^{22} +(1.87556 - 1.87556i) q^{23} +(-3.05786 + 1.90277i) q^{24} +(-2.39811 - 4.38738i) q^{25} +(7.22194 - 6.19666i) q^{26} +5.57545 q^{27} +(-1.61265 + 1.18294i) q^{28} +(2.00799 + 2.00799i) q^{29} +(3.96593 - 0.696523i) q^{30} -6.13492i q^{31} +(2.22425 + 5.20122i) q^{32} +(-4.15488 + 4.15488i) q^{33} +(0.261409 - 3.42128i) q^{34} +(2.16649 - 0.553455i) q^{35} +(0.418899 - 2.72524i) q^{36} -2.72024i q^{37} +(-4.58767 - 0.350529i) q^{38} -8.56807i q^{39} +(-0.134933 - 6.32312i) q^{40} -10.0998i q^{41} +(-0.137191 + 1.79553i) q^{42} +1.44198i q^{43} +(5.45877 + 7.44171i) q^{44} +(-1.57244 + 2.65150i) q^{45} +(-3.74022 - 0.285778i) q^{46} +(7.89571 - 7.89571i) q^{47} +(4.85821 + 1.52966i) q^{48} +1.00000i q^{49} +(-2.50043 + 6.61421i) q^{50} +(-2.18456 - 2.18456i) q^{51} +(-13.3015 - 2.04458i) q^{52} -10.4902 q^{53} +(-5.13448 - 5.98400i) q^{54} +(-2.55396 - 9.99744i) q^{55} +(2.75473 + 0.641445i) q^{56} +(-2.92933 + 2.92933i) q^{57} +(0.305956 - 4.00431i) q^{58} +(-2.38194 - 2.38194i) q^{59} +(-4.39983 - 3.61512i) q^{60} +(4.82900 - 4.82900i) q^{61} +(-6.58447 + 5.64970i) q^{62} +(-0.974834 - 0.974834i) q^{63} +(3.53402 - 7.17710i) q^{64} +(12.9416 + 7.67486i) q^{65} +(8.28561 + 0.633076i) q^{66} +0.335471i q^{67} +(-3.91272 + 2.87013i) q^{68} +(-2.38821 + 2.38821i) q^{69} +(-2.58915 - 1.81557i) q^{70} +1.00678 q^{71} +(-3.31071 + 2.06010i) q^{72} +(8.26933 + 8.26933i) q^{73} +(-2.91957 + 2.50509i) q^{74} +(3.05359 + 5.58659i) q^{75} +(3.84861 + 5.24665i) q^{76} +4.61457 q^{77} +(-9.19593 + 7.89042i) q^{78} +1.97499 q^{79} +(-6.66220 + 5.96784i) q^{80} -2.96353 q^{81} +(-10.8399 + 9.30099i) q^{82} +1.82753 q^{83} +(2.05344 - 1.50628i) q^{84} +(5.25648 - 1.34283i) q^{85} +(1.54765 - 1.32793i) q^{86} +(-2.55684 - 2.55684i) q^{87} +(2.96000 - 12.7119i) q^{88} -6.29659 q^{89} +(4.29387 - 0.754117i) q^{90} +(-4.75802 + 4.75802i) q^{91} +(3.13768 + 4.27747i) q^{92} +7.81179i q^{93} +(-15.7455 - 1.20306i) q^{94} +(-1.80063 - 7.04853i) q^{95} +(-2.83222 - 6.62288i) q^{96} +(-1.69671 - 1.69671i) q^{97} +(1.07328 - 0.920909i) q^{98} +(-4.49844 + 4.49844i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 8 q^{4} + 144 q^{9}+O(q^{10}) $ 144 * q - 8 * q^4 + 144 * q^9	$ 144 q - 8 q^{4} + 144 q^{9} - 16 q^{12} + 8 q^{16} + 28 q^{18} + 16 q^{19} - 36 q^{22} + 32 q^{26} - 36 q^{30} - 40 q^{32} - 32 q^{34} - 32 q^{36} - 56 q^{38} - 48 q^{40} + 20 q^{42} + 56 q^{44} - 32 q^{46} - 24 q^{48} + 8 q^{50} - 16 q^{51} - 16 q^{52} - 32 q^{54} - 24 q^{56} - 52 q^{58} - 32 q^{60} - 32 q^{61} + 40 q^{62} - 32 q^{64} + 32 q^{66} + 80 q^{68} + 32 q^{69} + 40 q^{72} + 16 q^{73} + 32 q^{74} - 24 q^{75} - 28 q^{78} + 72 q^{80} + 144 q^{81} + 24 q^{82} - 80 q^{83} + 32 q^{86} - 112 q^{87} + 40 q^{88} + 32 q^{90} - 16 q^{92} + 8 q^{94} - 80 q^{95} + 32 q^{96} - 64 q^{99}+O(q^{100}) $ 144 * q - 8 * q^4 + 144 * q^9 - 16 * q^12 + 8 * q^16 + 28 * q^18 + 16 * q^19 - 36 * q^22 + 32 * q^26 - 36 * q^30 - 40 * q^32 - 32 * q^34 - 32 * q^36 - 56 * q^38 - 48 * q^40 + 20 * q^42 + 56 * q^44 - 32 * q^46 - 24 * q^48 + 8 * q^50 - 16 * q^51 - 16 * q^52 - 32 * q^54 - 24 * q^56 - 52 * q^58 - 32 * q^60 - 32 * q^61 + 40 * q^62 - 32 * q^64 + 32 * q^66 + 80 * q^68 + 32 * q^69 + 40 * q^72 + 16 * q^73 + 32 * q^74 - 24 * q^75 - 28 * q^78 + 72 * q^80 + 144 * q^81 + 24 * q^82 - 80 * q^83 + 32 * q^86 - 112 * q^87 + 40 * q^88 + 32 * q^90 - 16 * q^92 + 8 * q^94 - 80 * q^95 + 32 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.920909	−	1.07328i	−0.651181	−	0.758922i
$2$	−0.920909	−	1.07328i	−0.651181	−	0.758922i
$3$	−1.27333			−0.735159			−0.367580	−	0.929992i	$-0.619813\pi$
$3$	−1.27333			−0.735159			−0.367580	+	0.929992i	$0.619813\pi$
$4$	−0.303853	+	1.97678i	−0.151926	+	0.988392i
$5$	1.14059	−	1.92329i	0.510087	−	0.860123i
$5$	1.14059	−	1.92329i	0.510087	−	0.860123i
$6$	1.17262	+	1.36664i	0.478722	+	0.557929i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	2.40146	−	1.49432i	0.849044	−	0.528322i
$9$	−1.37862			−0.459541
$10$	−3.11461	+	0.547008i	−0.984926	+	0.172979i
$11$	3.26300	−	3.26300i	0.983830	−	0.983830i	−0.0160411	−	0.999871i	$-0.505106\pi$
$11$	3.26300	−	3.26300i	0.983830	−	0.983830i	0.999871	+	0.0160411i	$0.00510626\pi$
$12$	0.386906	−	2.51710i	0.111690	−	0.726625i
$13$			6.72886i			1.86625i	0.359554	+	0.933124i	$0.382929\pi$
$13$			6.72886i			1.86625i	−0.359554	+	0.933124i	$0.617071\pi$
$14$	0.107741	−	1.41010i	0.0287951	−	0.376866i
$15$	−1.45235	+	2.44899i	−0.374995	+	0.632327i
$16$	−3.81535	−	1.20130i	−0.953837	−	0.300326i
$17$	1.71563	+	1.71563i	0.416101	+	0.416101i	0.883857	−	0.467757i	$-0.154938\pi$
$17$	1.71563	+	1.71563i	0.416101	+	0.416101i	−0.467757	+	0.883857i	$0.654938\pi$
$18$	1.26959	+	1.47965i	0.299244	+	0.348756i
$19$	2.30052	−	2.30052i	0.527776	−	0.527776i	−0.392133	−	0.919909i	$-0.628263\pi$
$19$	2.30052	−	2.30052i	0.527776	−	0.527776i	0.919909	+	0.392133i	$0.128263\pi$
$20$	3.45536	+	2.83910i	0.772642	+	0.634841i
$21$	−0.900382	−	0.900382i	−0.196480	−	0.196480i
$22$	−6.50703	−	0.497180i	−1.38730	−	0.105999i
$23$	1.87556	−	1.87556i	0.391082	−	0.391082i	−0.483991	−	0.875073i	$-0.660813\pi$
$23$	1.87556	−	1.87556i	0.391082	−	0.391082i	0.875073	+	0.483991i	$0.160813\pi$
$24$	−3.05786	+	1.90277i	−0.624183	+	0.388400i
$25$	−2.39811	−	4.38738i	−0.479622	−	0.877475i
$26$	7.22194	−	6.19666i	1.41634	−	1.21527i
$27$	5.57545			1.07299
$28$	−1.61265	+	1.18294i	−0.304763	+	0.223555i
$29$	2.00799	+	2.00799i	0.372874	+	0.372874i	0.868523	−	0.495649i	$-0.165070\pi$
$29$	2.00799	+	2.00799i	0.372874	+	0.372874i	−0.495649	+	0.868523i	$0.665070\pi$
$30$	3.96593	−	0.696523i	0.724077	−	0.127167i
$31$		−	6.13492i		−	1.10186i	−0.834550	−	0.550932i	$-0.814272\pi$
$31$		−	6.13492i		−	1.10186i	0.834550	−	0.550932i	$-0.185728\pi$
$32$	2.22425	+	5.20122i	0.393196	+	0.919454i
$33$	−4.15488	+	4.15488i	−0.723272	+	0.723272i
$34$	0.261409	−	3.42128i	0.0448313	−	0.586745i
$35$	2.16649	−	0.553455i	0.366204	−	0.0935509i
$36$	0.418899	−	2.72524i	0.0698165	−	0.454207i
$37$		−	2.72024i		−	0.447204i	−0.974681	−	0.223602i	$-0.928218\pi$
$37$		−	2.72024i		−	0.447204i	0.974681	−	0.223602i	$-0.0717816\pi$
$38$	−4.58767	−	0.350529i	−0.744219	−	0.0568633i
$39$		−	8.56807i		−	1.37199i
$40$	−0.134933	−	6.32312i	−0.0213347	−	0.999772i
$41$		−	10.0998i		−	1.57732i	−0.614828	−	0.788661i	$-0.710775\pi$
$41$		−	10.0998i		−	1.57732i	0.614828	−	0.788661i	$-0.289225\pi$
$42$	−0.137191	+	1.79553i	−0.0211690	+	0.277056i
$43$			1.44198i			0.219900i	0.993937	+	0.109950i	$0.0350691\pi$
$43$			1.44198i			0.219900i	−0.993937	+	0.109950i	$0.964931\pi$
$44$	5.45877	+	7.44171i	0.822940	+	1.12188i
$45$	−1.57244	+	2.65150i	−0.234406	+	0.395262i
$46$	−3.74022	−	0.285778i	−0.551466	−	0.0421357i
$47$	7.89571	−	7.89571i	1.15171	−	1.15171i	0.165498	−	0.986210i	$-0.447077\pi$
$47$	7.89571	−	7.89571i	1.15171	−	1.15171i	0.986210	−	0.165498i	$-0.0529232\pi$
$48$	4.85821	+	1.52966i	0.701222	+	0.220787i
$49$			1.00000i			0.142857i
$50$	−2.50043	+	6.61421i	−0.353615	+	0.935391i
$51$	−2.18456	−	2.18456i	−0.305900	−	0.305900i
$52$	−13.3015	−	2.04458i	−1.84459	−	0.283533i
$53$	−10.4902			−1.44094			−0.720471	−	0.693485i	$-0.756074\pi$
$53$	−10.4902			−1.44094			−0.720471	+	0.693485i	$0.756074\pi$
$54$	−5.13448	−	5.98400i	−0.698714	−	0.814320i
$55$	−2.55396	−	9.99744i	−0.344375	−	1.34805i
$56$	2.75473	+	0.641445i	0.368117	+	0.0857168i
$57$	−2.92933	+	2.92933i	−0.387999	+	0.387999i
$58$	0.305956	−	4.00431i	0.0401740	−	0.525791i
$59$	−2.38194	−	2.38194i	−0.310102	−	0.310102i	0.534847	−	0.844949i	$-0.320369\pi$
$59$	−2.38194	−	2.38194i	−0.310102	−	0.310102i	−0.844949	+	0.534847i	$0.820369\pi$
$60$	−4.39983	−	3.61512i	−0.568015	−	0.466709i
$61$	4.82900	−	4.82900i	0.618291	−	0.618291i	−0.326802	−	0.945093i	$-0.605971\pi$
$61$	4.82900	−	4.82900i	0.618291	−	0.618291i	0.945093	+	0.326802i	$0.105971\pi$
$62$	−6.58447	+	5.64970i	−0.836229	+	0.717513i
$63$	−0.974834	−	0.974834i	−0.122818	−	0.122818i
$64$	3.53402	−	7.17710i	0.441753	−	0.897137i
$65$	12.9416	+	7.67486i	1.60520	+	0.951950i
$66$	8.28561	+	0.633076i	1.01989	+	0.0779263i
$67$			0.335471i			0.0409844i	0.999790	+	0.0204922i	$0.00652332\pi$
$67$			0.335471i			0.0409844i	−0.999790	+	0.0204922i	$0.993477\pi$
$68$	−3.91272	+	2.87013i	−0.474487	+	0.348054i
$69$	−2.38821	+	2.38821i	−0.287507	+	0.287507i
$70$	−2.58915	−	1.81557i	−0.309463	−	0.217002i
$71$	1.00678			0.119483			0.0597416	−	0.998214i	$-0.480972\pi$
$71$	1.00678			0.119483			0.0597416	+	0.998214i	$0.480972\pi$
$72$	−3.31071	+	2.06010i	−0.390171	+	0.242786i
$73$	8.26933	+	8.26933i	0.967852	+	0.967852i	0.999499	−	0.0316470i	$-0.0100752\pi$
$73$	8.26933	+	8.26933i	0.967852	+	0.967852i	−0.0316470	+	0.999499i	$0.510075\pi$
$74$	−2.91957	+	2.50509i	−0.339393	+	0.291211i
$75$	3.05359	+	5.58659i	0.352599	+	0.645084i
$76$	3.84861	+	5.24665i	0.441466	+	0.601832i
$77$	4.61457			0.525879
$78$	−9.19593	+	7.89042i	−1.04123	+	0.893414i
$79$	1.97499			0.222204			0.111102	−	0.993809i	$-0.464562\pi$
$79$	1.97499			0.222204			0.111102	+	0.993809i	$0.464562\pi$
$80$	−6.66220	+	5.96784i	−0.744857	+	0.667224i
$81$	−2.96353			−0.329281
$82$	−10.8399	+	9.30099i	−1.19707	+	1.02712i
$83$	1.82753			0.200597			0.100299	−	0.994957i	$-0.468020\pi$
$83$	1.82753			0.200597			0.100299	+	0.994957i	$0.468020\pi$
$84$	2.05344	−	1.50628i	0.224049	−	0.164348i
$85$	5.25648	−	1.34283i	0.570145	−	0.145650i
$86$	1.54765	−	1.32793i	0.166887	−	0.143195i
$87$	−2.55684	−	2.55684i	−0.274122	−	0.274122i
$88$	2.96000	−	12.7119i	0.315537	−	1.35509i
$89$	−6.29659			−0.667437			−0.333719	−	0.942673i	$-0.608304\pi$
$89$	−6.29659			−0.667437			−0.333719	+	0.942673i	$0.608304\pi$
$90$	4.29387	−	0.754117i	0.452614	−	0.0794909i
$91$	−4.75802	+	4.75802i	−0.498776	+	0.498776i
$92$	3.13768	+	4.27747i	0.327126	+	0.445957i
$93$			7.81179i			0.810045i
$94$	−15.7455	−	1.20306i	−1.62403	−	0.124087i
$95$	−1.80063	−	7.04853i	−0.184740	−	0.723164i
$96$	−2.83222	−	6.62288i	−0.289062	−	0.675945i
$97$	−1.69671	−	1.69671i	−0.172274	−	0.172274i	0.615704	−	0.787978i	$-0.288872\pi$
$97$	−1.69671	−	1.69671i	−0.172274	−	0.172274i	−0.787978	+	0.615704i	$0.788872\pi$
$98$	1.07328	−	0.920909i	0.108417	−	0.0930259i
$99$	−4.49844	+	4.49844i	−0.452110	+	0.452110i
$100$	9.40157	−	3.40743i	0.940157	−	0.340743i
$101$	12.8706	+	12.8706i	1.28067	+	1.28067i	0.940287	+	0.340384i	$0.110557\pi$
$101$	12.8706	+	12.8706i	1.28067	+	1.28067i	0.340384	+	0.940287i	$0.389443\pi$
$102$	−0.332861	+	4.35643i	−0.0329581	+	0.431351i
$103$	7.23217	−	7.23217i	0.712607	−	0.712607i	−0.254473	−	0.967080i	$-0.581902\pi$
$103$	7.23217	−	7.23217i	0.712607	−	0.712607i	0.967080	+	0.254473i	$0.0819019\pi$
$104$	10.0551	+	16.1591i	0.985980	+	1.58453i
$105$	−2.75867	+	0.704732i	−0.269218	+	0.0687748i
$106$	9.66053	+	11.2589i	0.938314	+	1.09356i
$107$	−17.6332			−1.70466			−0.852331	−	0.523003i	$-0.824812\pi$
$107$	−17.6332			−1.70466			−0.852331	+	0.523003i	$0.824812\pi$
$108$	−1.69412	+	11.0214i	−0.163016	+	1.06054i
$109$	10.7301	+	10.7301i	1.02775	+	1.02775i	0.999604	+	0.0281500i	$0.00896162\pi$
$109$	10.7301	+	10.7301i	1.02775	+	1.02775i	0.0281500	+	0.999604i	$0.491038\pi$
$110$	−8.37807	+	11.9478i	−0.798818	+	1.13918i
$111$			3.46377i			0.328766i
$112$	−1.84841	−	3.54731i	−0.174658	−	0.335189i
$113$	6.09130	−	6.09130i	0.573021	−	0.573021i	−0.359950	−	0.932971i	$-0.617206\pi$
$113$	6.09130	−	6.09130i	0.573021	−	0.573021i	0.932971	+	0.359950i	$0.117206\pi$
$114$	5.84163	+	0.446340i	0.547119	+	0.0418036i
$115$	−1.46801	−	5.74650i	−0.136892	−	0.535864i
$116$	−4.57949	+	3.35923i	−0.425195	+	0.311896i
$117$		−	9.27656i		−	0.857618i
$118$	−0.362934	+	4.75003i	−0.0334108	+	0.437276i
$119$			2.42626i			0.222415i
$120$	0.171814	+	8.05143i	0.0156844	+	0.734992i
$121$		−	10.2943i		−	0.935844i
$122$	−9.62994	−	0.735792i	−0.871854	−	0.0666155i
$123$			12.8604i			1.15958i
$124$	12.1274	+	1.86411i	1.08907	+	0.167402i
$125$	−11.1735	−	0.391928i	−0.999385	−	0.0350551i
$126$	−0.148535	+	1.94400i	−0.0132325	+	0.173185i
$127$	−10.3424	+	10.3424i	−0.917740	+	0.917740i	−0.996865	−	0.0791248i	$-0.974787\pi$
$127$	−10.3424	+	10.3424i	−0.917740	+	0.917740i	0.0791248	+	0.996865i	$0.474787\pi$
$128$	−10.9575	+	2.81646i	−0.968518	+	0.248943i
$129$		−	1.83612i		−	0.161662i
$130$	−3.68073	−	20.9577i	−0.322822	−	1.83812i
$131$	6.55920	+	6.55920i	0.573080	+	0.573080i	0.932988	−	0.359908i	$-0.117192\pi$
$131$	6.55920	+	6.55920i	0.573080	+	0.573080i	−0.359908	+	0.932988i	$0.617192\pi$
$132$	−6.95083	−	9.47577i	−0.604992	−	0.824760i
$133$	3.25343			0.282108
$134$	0.360054	−	0.308939i	0.0311039	−	0.0266882i
$135$	6.35930	−	10.7232i	0.547321	−	0.922907i
$136$	6.68370	+	1.55632i	0.573123	+	0.133453i
$137$	9.09364	−	9.09364i	0.776922	−	0.776922i	−0.202384	−	0.979306i	$-0.564869\pi$
$137$	9.09364	−	9.09364i	0.776922	−	0.776922i	0.979306	+	0.202384i	$0.0648690\pi$
$138$	4.76255	+	0.363891i	0.405415	+	0.0309764i
$139$	3.37410	+	3.37410i	0.286187	+	0.286187i	0.835571	−	0.549383i	$-0.185137\pi$
$139$	3.37410	+	3.37410i	0.286187	+	0.286187i	−0.549383	+	0.835571i	$0.685137\pi$
$140$	0.435765	+	4.45085i	0.0368289	+	0.376166i
$141$	−10.0539	+	10.0539i	−0.846689	+	0.846689i
$142$	−0.927156	−	1.08056i	−0.0778052	−	0.0906785i
$143$	21.9562	+	21.9562i	1.83607	+	1.83607i
$144$	5.25993	+	1.65614i	0.438327	+	0.138012i
$145$	6.15224	−	1.57166i	0.510916	−	0.130519i
$146$	1.25999	−	16.4906i	0.104278	−	1.36477i
$147$		−	1.27333i		−	0.105023i
$148$	5.37732	+	0.826552i	0.442013	+	0.0679421i
$149$	−8.73456	+	8.73456i	−0.715563	+	0.715563i	−0.967693	−	0.252130i	$-0.918869\pi$
$149$	−8.73456	+	8.73456i	−0.715563	+	0.715563i	0.252130	+	0.967693i	$0.418869\pi$
$150$	3.18389	−	8.42210i	0.259963	−	0.687661i
$151$	2.84338			0.231391			0.115695	−	0.993285i	$-0.463090\pi$
$151$	2.84338			0.231391			0.115695	+	0.993285i	$0.463090\pi$
$152$	2.08690	−	8.96232i	0.169270	−	0.726940i
$153$	−2.36520	−	2.36520i	−0.191215	−	0.191215i
$154$	−4.24960	−	4.95272i	−0.342443	−	0.399102i
$155$	−11.7992	−	6.99742i	−0.947738	−	0.562046i
$156$	16.9372	+	2.60343i	1.35606	+	0.208442i
$157$	5.81437			0.464037			0.232018	−	0.972711i	$-0.425467\pi$
$157$	5.81437			0.464037			0.232018	+	0.972711i	$0.425467\pi$
$158$	−1.81879	−	2.11971i	−0.144695	−	0.168635i
$159$	13.3575			1.05932
$160$	12.5404	+	1.65456i	0.991408	+	0.130805i
$161$	2.65244			0.209042
$162$	2.72914	+	3.18069i	0.214421	+	0.249899i
$163$	−4.09873			−0.321037			−0.160519	−	0.987033i	$-0.551317\pi$
$163$	−4.09873			−0.321037			−0.160519	+	0.987033i	$0.551317\pi$
$164$	19.9651	+	3.06885i	1.55901	+	0.239637i
$165$	3.25204	+	12.7301i	0.253171	+	0.991034i
$166$	−1.68299	−	1.96145i	−0.130625	−	0.152238i
$167$	8.80222	+	8.80222i	0.681136	+	0.681136i	0.960256	−	0.279120i	$-0.0900428\pi$
$167$	8.80222	+	8.80222i	0.681136	+	0.681136i	−0.279120	+	0.960256i	$0.590043\pi$
$168$	−3.50769	−	0.816774i	−0.270624	−	0.0630154i
$169$	−32.2775			−2.48288
$170$	−6.28197	−	4.40505i	−0.481805	−	0.337852i
$171$	−3.17155	+	3.17155i	−0.242535	+	0.242535i
$172$	−2.85049	−	0.438150i	−0.217348	−	0.0334087i
$173$			10.4031i			0.790934i	0.918480	+	0.395467i	$0.129417\pi$
$173$			10.4031i			0.790934i	−0.918480	+	0.395467i	$0.870583\pi$
$174$	−0.389584	+	5.09882i	−0.0295343	+	0.386540i
$175$	1.40662	−	4.79806i	0.106331	−	0.362699i
$176$	−16.3693	+	8.52961i	−1.23388	+	0.642944i
$177$	3.03300	+	3.03300i	0.227974	+	0.227974i
$178$	5.79859	+	6.75799i	0.434622	+	0.506533i
$179$	5.56325	−	5.56325i	0.415817	−	0.415817i	−0.467942	−	0.883759i	$-0.655004\pi$
$179$	5.56325	−	5.56325i	0.415817	−	0.415817i	0.883759	+	0.467942i	$0.155004\pi$
$180$	−4.76364	−	3.91405i	−0.355061	−	0.291736i
$181$	−2.09167	−	2.09167i	−0.155473	−	0.155473i	0.625084	−	0.780557i	$-0.285065\pi$
$181$	−2.09167	−	2.09167i	−0.155473	−	0.155473i	−0.780557	+	0.625084i	$0.785065\pi$
$182$	9.48838	+	0.724976i	0.703326	+	0.0537388i
$183$	−6.14893	+	6.14893i	−0.454542	+	0.454542i
$184$	1.70140	−	7.30677i	0.125429	−	0.538662i
$185$	−5.23181	−	3.10267i	−0.384650	−	0.228113i
$186$	8.38423	−	7.19395i	0.614761	−	0.527486i
$187$	11.1962			0.818745
$188$	13.2090	+	18.0073i	0.963364	+	1.31331i
$189$	3.94244	+	3.94244i	0.286770	+	0.286770i
$190$	−5.90682	+	8.42363i	−0.428526	+	0.611114i
$191$			17.3158i			1.25293i	0.779450	+	0.626464i	$0.215499\pi$
$191$			17.3158i			1.25293i	−0.779450	+	0.626464i	$0.784501\pi$
$192$	−4.49998	+	9.13883i	−0.324758	+	0.659538i
$193$	−15.7700	+	15.7700i	−1.13515	+	1.13515i	−0.145842	+	0.989308i	$0.546589\pi$
$193$	−15.7700	+	15.7700i	−1.13515	+	1.13515i	−0.989308	+	0.145842i	$0.953411\pi$
$194$	−0.258526	+	3.38355i	−0.0185611	+	0.242925i
$195$	−16.4789	−	9.77266i	−1.18008	−	0.699834i
$196$	−1.97678	−	0.303853i	−0.141199	−	0.0217038i
$197$			8.59144i			0.612115i	0.952013	+	0.306057i	$0.0990099\pi$
$197$			8.59144i			0.612115i	−0.952013	+	0.306057i	$0.900990\pi$
$198$	8.97074	+	0.685424i	0.637523	+	0.0487110i
$199$		−	9.65879i		−	0.684693i	−0.939574	−	0.342347i	$-0.888778\pi$
$199$		−	9.65879i		−	0.684693i	0.939574	−	0.342347i	$-0.111222\pi$
$200$	−12.3151	−	6.95257i	−0.870809	−	0.491621i
$201$		−	0.427167i		−	0.0301300i
$202$	1.96108	−	25.6663i	0.137981	−	1.80588i
$203$			2.83973i			0.199310i
$204$	4.98220	−	3.65463i	0.348824	−	0.255875i
$205$	−19.4249	−	11.5197i	−1.35669	−	0.804572i
$206$	−14.4223	−	1.10196i	−1.00485	−	0.0767773i
$207$	−2.58569	+	2.58569i	−0.179718	+	0.179718i
$208$	8.08340	−	25.6729i	0.560483	−	1.78010i
$209$		−	15.0132i		−	1.03848i
$210$	3.29685	+	2.31182i	0.227505	+	0.159531i
$211$	−14.9227	−	14.9227i	−1.02732	−	1.02732i	−0.999616	−	0.0277041i	$-0.991180\pi$
$211$	−14.9227	−	14.9227i	−1.02732	−	1.02732i	−0.0277041	−	0.999616i	$-0.508820\pi$
$212$	3.18748	−	20.7369i	0.218917	−	1.42422i
$213$	−1.28197			−0.0878392
$214$	16.2385	+	18.9253i	1.11004	+	1.29371i
$215$	2.77335	+	1.64471i	0.189141	+	0.112168i
$216$	13.3892	−	8.33149i	0.911020	−	0.566886i
$217$	4.33804	−	4.33804i	0.294485	−	0.294485i
$218$	1.63493	−	21.3978i	0.110732	−	1.44924i
$219$	−10.5296	−	10.5296i	−0.711525	−	0.711525i
$220$	20.5388	−	2.01087i	1.38473	−	0.135573i
$221$	−11.5442	+	11.5442i	−0.776548	+	0.776548i
$222$	3.71758	−	3.18981i	0.249508	−	0.214086i
$223$	−20.6951	−	20.6951i	−1.38585	−	1.38585i	−0.833837	−	0.552011i	$-0.813860\pi$
$223$	−20.6951	−	20.6951i	−1.38585	−	1.38585i	−0.552011	−	0.833837i	$-0.686140\pi$
$224$	−2.10503	+	5.25060i	−0.140648	+	0.350821i
$225$	3.30609	+	6.04854i	0.220406	+	0.403236i
$226$	−12.1472	−	0.928127i	−0.808019	−	0.0617381i
$227$			21.7765i			1.44536i	0.691183	+	0.722680i	$0.257090\pi$
$227$			21.7765i			1.44536i	−0.691183	+	0.722680i	$0.742910\pi$
$228$	−4.90057	−	6.68074i	−0.324548	−	0.442443i
$229$	5.84434	−	5.84434i	0.386205	−	0.386205i	−0.487127	−	0.873331i	$-0.661955\pi$
$229$	5.84434	−	5.84434i	0.386205	−	0.386205i	0.873331	+	0.487127i	$0.161955\pi$
$230$	−4.81569	+	6.86758i	−0.317537	+	0.452835i
$231$	−5.87589			−0.386605
$232$	7.82268	+	1.82153i	0.513584	+	0.119589i
$233$	−12.7385	−	12.7385i	−0.834525	−	0.834525i	0.153607	−	0.988132i	$-0.450911\pi$
$233$	−12.7385	−	12.7385i	−0.834525	−	0.834525i	−0.988132	+	0.153607i	$0.950911\pi$
$234$	−9.95633	+	8.54287i	−0.650866	+	0.558465i
$235$	−6.18000	−	24.1915i	−0.403139	−	1.57808i
$236$	5.43233	−	3.98482i	0.353615	−	0.259389i
$237$	−2.51482			−0.163355
$238$	2.60406	−	2.23437i	0.168796	−	0.144833i
$239$	−1.16635			−0.0754448			−0.0377224	−	0.999288i	$-0.512010\pi$
$239$	−1.16635			−0.0754448			−0.0377224	+	0.999288i	$0.512010\pi$
$240$	8.48320	−	7.59904i	0.547588	−	0.490516i
$241$	−17.6599			−1.13757			−0.568787	−	0.822485i	$-0.692587\pi$
$241$	−17.6599			−1.13757			−0.568787	+	0.822485i	$0.692587\pi$
$242$	−11.0486	+	9.48010i	−0.710233	+	0.609404i
$243$	−12.9528			−0.830921
$244$	8.07859	+	11.0132i	0.517179	+	0.705048i
$245$	1.92329	+	1.14059i	0.122875	+	0.0728696i
$246$	13.8028	−	11.8433i	0.880033	−	0.755098i
$247$	15.4799	+	15.4799i	0.984961	+	0.984961i
$248$	−9.16752	−	14.7328i	−0.582138	−	0.935531i
$249$	−2.32705			−0.147471
$250$	9.86910	+	12.3532i	0.624177	+	0.781283i
$251$	6.40087	−	6.40087i	0.404020	−	0.404020i	−0.475627	−	0.879647i	$-0.657779\pi$
$251$	6.40087	−	6.40087i	0.404020	−	0.404020i	0.879647	+	0.475627i	$0.157779\pi$
$252$	2.22324	−	1.63083i	0.140051	−	0.102733i
$253$		−	12.2399i		−	0.769516i
$254$	20.6247	+	1.57586i	1.29411	+	0.0988786i
$255$	−6.69325	+	1.70987i	−0.419148	+	0.107076i
$256$	13.1137	+	9.16678i	0.819609	+	0.572923i
$257$	3.75800	+	3.75800i	0.234418	+	0.234418i	0.814534	−	0.580116i	$-0.196993\pi$
$257$	3.75800	+	3.75800i	0.234418	+	0.234418i	−0.580116	+	0.814534i	$0.696993\pi$
$258$	−1.97067	+	1.69090i	−0.122689	+	0.105271i
$259$	1.92350	−	1.92350i	0.119520	−	0.119520i
$260$	−19.1039	+	23.2506i	−1.18477	+	1.44194i
$261$	−2.76826	−	2.76826i	−0.171351	−	0.171351i
$262$	0.999421	−	13.0803i	0.0617444	−	0.808102i
$263$	14.3792	−	14.3792i	0.886662	−	0.886662i	−0.107538	−	0.994201i	$-0.534297\pi$
$263$	14.3792	−	14.3792i	0.886662	−	0.886662i	0.994201	+	0.107538i	$0.0342969\pi$
$264$	−3.76906	+	16.1865i	−0.231970	+	0.996210i
$265$	−11.9650	+	20.1758i	−0.735006	+	1.23939i
$266$	−2.99611	−	3.49183i	−0.183703	−	0.214098i
$267$	8.01765			0.490672
$268$	−0.663154	−	0.101934i	−0.0405086	−	0.00622661i
$269$	−10.2388	−	10.2388i	−0.624269	−	0.624269i	0.322351	−	0.946620i	$-0.395527\pi$
$269$	−10.2388	−	10.2388i	−0.624269	−	0.624269i	−0.946620	+	0.322351i	$0.895527\pi$
$270$	−17.3653	+	3.04981i	−1.05682	+	0.185606i
$271$			12.8071i			0.777975i	0.921243	+	0.388987i	$0.127175\pi$
$271$			12.8071i			0.777975i	−0.921243	+	0.388987i	$0.872825\pi$
$272$	−4.48472	−	8.60670i	−0.271926	−	0.521858i
$273$	6.05854	−	6.05854i	0.366680	−	0.366680i
$274$	−18.1344	−	1.38559i	−1.09554	−	0.0837066i
$275$	−22.1410	−	6.49097i	−1.33515	−	0.391420i
$276$	−3.99532	−	5.44665i	−0.240490	−	0.327850i
$277$			12.1869i			0.732237i	0.930568	+	0.366119i	$0.119314\pi$
$277$			12.1869i			0.732237i	−0.930568	+	0.366119i	$0.880686\pi$
$278$	0.514109	−	6.72859i	0.0308342	−	0.403554i
$279$			8.45774i			0.506352i
$280$	4.37571	−	4.56653i	0.261498	−	0.272902i
$281$		−	2.33852i		−	0.139504i	−0.997564	−	0.0697522i	$-0.977779\pi$
$281$		−	2.33852i		−	0.139504i	0.997564	−	0.0697522i	$-0.0222209\pi$
$282$	20.0493	+	1.53190i	1.19392	+	0.0912234i
$283$			13.1189i			0.779837i	0.920849	+	0.389919i	$0.127497\pi$
$283$			13.1189i			0.779837i	−0.920849	+	0.389919i	$0.872503\pi$
$284$	−0.305914	+	1.99019i	−0.0181527	+	0.118096i
$285$	2.29280	+	8.97512i	0.135813	+	0.531640i
$286$	3.34546	−	43.7848i	0.197821	−	2.58905i
$287$	7.14163	−	7.14163i	0.421557	−	0.421557i
$288$	−3.06641	−	7.17052i	−0.180690	−	0.422527i
$289$		−	11.1132i		−	0.653720i
$290$	−7.35248	−	5.15571i	−0.431753	−	0.302754i
$291$	2.16047	+	2.16047i	0.126649	+	0.126649i
$292$	−18.8593	+	13.8340i	−1.10366	+	0.809575i
$293$	14.3419			0.837862			0.418931	−	0.908018i	$-0.362405\pi$
$293$	14.3419			0.837862			0.418931	+	0.908018i	$0.362405\pi$
$294$	−1.36664	+	1.17262i	−0.0797041	+	0.0683888i
$295$	−7.29798	+	1.86435i	−0.424905	+	0.108547i
$296$	−4.06490	−	6.53254i	−0.236268	−	0.379696i
$297$	18.1927	−	18.1927i	1.05564	−	1.05564i
$298$	17.4184	+	1.33088i	1.00902	+	0.0770957i
$299$	12.6204	+	12.6204i	0.729856	+	0.729856i
$300$	−11.9713	+	4.33879i	−0.691165	+	0.250500i
$301$	−1.01964	+	1.01964i	−0.0587708	+	0.0587708i
$302$	−2.61849	−	3.05174i	−0.150677	−	0.175608i
$303$	−16.3885	−	16.3885i	−0.941497	−	0.941497i
$304$	−11.5409	+	6.01366i	−0.661917	+	0.344907i
$305$	−3.77968	−	14.7955i	−0.216424	−	0.847188i
$306$	−0.360384	+	4.71666i	−0.0206018	+	0.269633i
$307$			14.7843i			0.843785i	0.906646	+	0.421892i	$0.138634\pi$
$307$			14.7843i			0.843785i	−0.906646	+	0.421892i	$0.861366\pi$
$308$	−1.40215	+	9.12201i	−0.0798950	+	0.519775i
$309$	−9.20896	+	9.20896i	−0.523880	+	0.523880i
$310$	3.35585	+	19.1079i	0.190599	+	1.08525i
$311$	19.2681			1.09259			0.546297	−	0.837592i	$-0.316037\pi$
$311$	19.2681			1.09259			0.546297	+	0.837592i	$0.316037\pi$
$312$	−12.8034	−	20.5759i	−0.724852	−	1.16488i
$313$	12.7097	+	12.7097i	0.718392	+	0.718392i	0.968276	−	0.249884i	$-0.0803923\pi$
$313$	12.7097	+	12.7097i	0.718392	+	0.718392i	−0.249884	+	0.968276i	$0.580392\pi$
$314$	−5.35450	−	6.24043i	−0.302172	−	0.352168i
$315$	−2.98678	+	0.763005i	−0.168286	+	0.0429905i
$316$	−0.600107	+	3.90413i	−0.0337586	+	0.219624i
$317$	32.4711			1.82376			0.911878	−	0.410461i	$-0.134632\pi$
$317$	32.4711			1.82376			0.911878	+	0.410461i	$0.134632\pi$
$318$	−12.3011	−	14.3364i	−0.689810	−	0.803943i
$319$	13.1041			0.733690
$320$	−9.77279	−	14.9831i	−0.546315	−	0.837579i
$321$	22.4529			1.25320
$322$	−2.44266	−	2.84681i	−0.136124	−	0.158647i
$323$	7.89368			0.439216
$324$	0.900477	−	5.85825i	0.0500265	−	0.325458i
$325$	29.5220	−	16.1365i	1.63759	−	0.895094i
$326$	3.77456	+	4.39908i	0.209053	+	0.243642i
$327$	−13.6629	−	13.6629i	−0.755563	−	0.755563i
$328$	−15.0923	−	24.2542i	−0.833333	−	1.33922i
$329$	11.1662			0.615614
$330$	10.6681	−	15.2136i	0.587258	−	0.837480i
$331$	−1.37082	+	1.37082i	−0.0753471	+	0.0753471i	−0.743776	−	0.668429i	$-0.766967\pi$
$331$	−1.37082	+	1.37082i	−0.0753471	+	0.0753471i	0.668429	+	0.743776i	$0.266967\pi$
$332$	−0.555300	+	3.61263i	−0.0304760	+	0.198269i
$333$			3.75018i			0.205509i
$334$	1.34119	−	17.5533i	0.0733865	−	0.960472i
$335$	0.645210	+	0.382635i	0.0352516	+	0.0209056i
$336$	2.35364	+	4.51690i	0.128402	+	0.246417i
$337$	−22.1999	−	22.1999i	−1.20930	−	1.20930i	−0.971253	−	0.238051i	$-0.923491\pi$
$337$	−22.1999	−	22.1999i	−1.20930	−	1.20930i	−0.238051	−	0.971253i	$-0.576509\pi$
$338$	29.7246	+	34.6427i	1.61681	+	1.88432i
$339$	−7.75625	+	7.75625i	−0.421262	+	0.421262i
$340$	1.05728	+	10.7989i	0.0573391	+	0.585655i
$341$	−20.0182	−	20.0182i	−1.08405	−	1.08405i
$342$	6.32467	+	0.483247i	0.341999	+	0.0261310i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	2.15478	+	3.46286i	0.116178	+	0.186705i
$345$	1.86926	+	7.31721i	0.100638	+	0.393945i
$346$	11.1654	−	9.58032i	0.600258	−	0.515041i
$347$	−11.8380			−0.635496			−0.317748	−	0.948175i	$-0.602927\pi$
$347$	−11.8380			−0.635496			−0.317748	+	0.948175i	$0.602927\pi$
$348$	5.83122	−	4.27741i	0.312586	−	0.229293i
$349$	12.3500	+	12.3500i	0.661079	+	0.661079i	0.955634	−	0.294556i	$-0.0951717\pi$
$349$	12.3500	+	12.3500i	0.661079	+	0.661079i	−0.294556	+	0.955634i	$0.595172\pi$
$350$	−6.44503	+	2.90888i	−0.344501	+	0.155486i
$351$			37.5164i			2.00248i
$352$	24.2293	+	9.71382i	1.29143	+	0.517749i
$353$	−11.0354	+	11.0354i	−0.587357	+	0.587357i	−0.936915	−	0.349558i	$-0.886332\pi$
$353$	−11.0354	+	11.0354i	−0.587357	+	0.587357i	0.349558	+	0.936915i	$0.386332\pi$
$354$	0.462136	−	6.04837i	0.0245623	−	0.321467i
$355$	1.14833	−	1.93634i	0.0609468	−	0.102770i
$356$	1.91324	−	12.4470i	0.101401	−	0.659689i
$357$		−	3.08944i		−	0.163511i
$358$	−11.0942	−	0.847668i	−0.586345	−	0.0448007i
$359$		−	31.1792i		−	1.64557i	−0.568350	−	0.822787i	$-0.692418\pi$
$359$		−	31.1792i		−	1.64557i	0.568350	−	0.822787i	$-0.307582\pi$
$360$	0.186021	+	8.71720i	0.00980419	+	0.459437i
$361$			8.41520i			0.442905i
$362$	−0.318707	+	4.17119i	−0.0167509	+	0.219233i
$363$			13.1080i			0.687994i
$364$	−7.95984	−	10.8513i	−0.417209	−	0.568763i
$365$	25.3363	−	6.47243i	1.32616	−	0.338783i
$366$	12.2621	+	0.936908i	0.640951	+	0.0489730i
$367$	2.21993	−	2.21993i	0.115880	−	0.115880i	−0.646789	−	0.762669i	$-0.723889\pi$
$367$	2.21993	−	2.21993i	0.115880	−	0.115880i	0.762669	+	0.646789i	$0.223889\pi$
$368$	−9.40904	+	4.90280i	−0.490480	+	0.255576i
$369$			13.9238i			0.724844i
$370$	1.48799	+	8.47247i	0.0773569	+	0.440463i
$371$	−7.41770	−	7.41770i	−0.385108	−	0.385108i
$372$	−15.4422	−	2.37364i	−0.800642	−	0.123067i
$373$	5.66635			0.293393			0.146696	−	0.989182i	$-0.453136\pi$
$373$	5.66635			0.293393			0.146696	+	0.989182i	$0.453136\pi$
$374$	−10.3107	−	12.0166i	−0.533151	−	0.621364i
$375$	14.2275	+	0.499054i	0.734707	+	0.0257711i
$376$	7.16253	−	30.7600i	0.369379	−	1.58632i
$377$	−13.5115	+	13.5115i	−0.695876	+	0.695876i
$378$	0.600706	−	7.86195i	0.0308970	−	0.404375i
$379$	20.0154	+	20.0154i	1.02812	+	1.02812i	0.999593	+	0.0285302i	$0.00908267\pi$
$379$	20.0154	+	20.0154i	1.02812	+	1.02812i	0.0285302	+	0.999593i	$0.490917\pi$
$380$	14.4805	−	1.41773i	0.742836	−	0.0727280i
$381$	13.1693	−	13.1693i	0.674685	−	0.674685i
$382$	18.5847	−	15.9463i	0.950876	−	0.815884i
$383$	−19.2607	−	19.2607i	−0.984175	−	0.984175i	0.0157017	−	0.999877i	$-0.495002\pi$
$383$	−19.2607	−	19.2607i	−0.984175	−	0.984175i	−0.999877	+	0.0157017i	$0.995002\pi$
$384$	13.9526	−	3.58630i	0.712015	−	0.183012i
$385$	5.26333	−	8.87517i	0.268244	−	0.452321i
$386$	31.4484	+	2.40286i	1.60068	+	0.122303i
$387$		−	1.98795i		−	0.101053i
$388$	3.86957	−	2.83847i	0.196448	−	0.144102i
$389$	2.61826	−	2.61826i	0.132751	−	0.132751i	−0.637609	−	0.770360i	$-0.720076\pi$
$389$	2.61826	−	2.61826i	0.132751	−	0.132751i	0.770360	+	0.637609i	$0.220076\pi$
$390$	4.68680	+	26.6862i	0.237325	+	1.35131i
$391$	6.43553			0.325459
$392$	1.49432	+	2.40146i	0.0754745	+	0.121292i
$393$	−8.35205	−	8.35205i	−0.421305	−	0.421305i
$394$	9.22100	−	7.91193i	0.464547	−	0.398597i
$395$	2.25265	−	3.79848i	0.113343	−	0.191123i
$396$	−7.52558	−	10.2593i	−0.378175	−	0.515550i
$397$	−14.3337			−0.719386			−0.359693	−	0.933071i	$-0.617119\pi$
$397$	−14.3337			−0.719386			−0.359693	+	0.933071i	$0.617119\pi$
$398$	−10.3666	+	8.89487i	−0.519629	+	0.445859i
$399$	−4.14270			−0.207394
$400$	3.87905	+	19.6202i	0.193953	+	0.981011i
$401$	−28.4153			−1.41899			−0.709496	−	0.704710i	$-0.751077\pi$
$401$	−28.4153			−1.41899			−0.709496	+	0.704710i	$0.751077\pi$
$402$	−0.458469	+	0.393382i	−0.0228663	+	0.0196201i
$403$	41.2810			2.05635
$404$	−29.3531	+	21.5316i	−1.46037	+	1.07124i
$405$	−3.38017	+	5.69973i	−0.167962	+	0.283222i
$406$	3.04782	−	2.61513i	0.151261	−	0.129787i
$407$	−8.87612	−	8.87612i	−0.439973	−	0.439973i
$408$	−8.51058	−	1.98171i	−0.421337	−	0.0981092i
$409$	−8.75887			−0.433098			−0.216549	−	0.976272i	$-0.569480\pi$
$409$	−8.75887			−0.433098			−0.216549	+	0.976272i	$0.569480\pi$
$410$	5.52466	+	31.4569i	0.272844	+	1.55354i
$411$	−11.5792	+	11.5792i	−0.571161	+	0.571161i
$412$	12.0989	+	16.4940i	0.596071	+	0.812599i
$413$		−	3.36857i		−	0.165756i
$414$	5.15636	+	0.393980i	0.253421	+	0.0193631i
$415$	2.08446	−	3.51487i	0.102322	−	0.172538i
$416$	−34.9983	+	14.9667i	−1.71593	+	0.733802i
$417$	−4.29635	−	4.29635i	−0.210393	−	0.210393i
$418$	−16.1133	+	13.8258i	−0.788129	+	0.676241i
$419$	−5.51336	+	5.51336i	−0.269345	+	0.269345i	−0.828836	−	0.559491i	$-0.810997\pi$
$419$	−5.51336	+	5.51336i	−0.269345	+	0.269345i	0.559491	+	0.828836i	$0.310997\pi$
$420$	−0.554874	−	5.66742i	−0.0270751	−	0.276542i
$421$	8.93086	+	8.93086i	0.435263	+	0.435263i	0.890414	−	0.455151i	$-0.150415\pi$
$421$	8.93086	+	8.93086i	0.435263	+	0.435263i	−0.455151	+	0.890414i	$0.650415\pi$
$422$	−2.27376	+	29.7586i	−0.110685	+	1.44863i
$423$	−10.8852	+	10.8852i	−0.529257	+	0.529257i
$424$	−25.1918	+	15.6757i	−1.22342	+	0.761281i
$425$	3.41284	−	11.6414i	0.165547	−	0.564689i
$426$	1.18058	+	1.37591i	0.0571992	+	0.0666631i
$427$	6.82924			0.330490
$428$	5.35789	−	34.8569i	0.258983	−	1.68487i
$429$	−27.9576	−	27.9576i	−1.34981	−	1.34981i
$430$	−0.788775	−	4.49121i	−0.0380381	−	0.216585i
$431$			36.9828i			1.78140i	0.454591	+	0.890700i	$0.349785\pi$
$431$			36.9828i			1.78140i	−0.454591	+	0.890700i	$0.650215\pi$
$432$	−21.2723	−	6.69780i	−1.02346	−	0.322248i
$433$	3.28725	−	3.28725i	0.157975	−	0.157975i	−0.623694	−	0.781669i	$-0.714369\pi$
$433$	3.28725	−	3.28725i	0.157975	−	0.157975i	0.781669	+	0.623694i	$0.214369\pi$
$434$	−8.65087	−	0.660984i	−0.415255	−	0.0317283i
$435$	−7.83385	+	2.00125i	−0.375604	+	0.0959524i
$436$	−24.4714	+	17.9507i	−1.17197	+	0.859680i
$437$		−	8.62954i		−	0.412807i
$438$	−1.60439	+	20.9980i	−0.0766607	+	1.00332i
$439$		−	14.5348i		−	0.693709i	−0.937919	−	0.346855i	$-0.887250\pi$
$439$		−	14.5348i		−	0.693709i	0.937919	−	0.346855i	$-0.112750\pi$
$440$	−21.0726	−	20.1920i	−1.00460	−	0.962617i
$441$		−	1.37862i		−	0.0656487i
$442$	23.0213	+	1.75898i	1.09501	+	0.0836663i
$443$			6.21102i			0.295094i	0.989055	+	0.147547i	$0.0471378\pi$
$443$			6.21102i			0.295094i	−0.989055	+	0.147547i	$0.952862\pi$
$444$	−6.84711	−	1.05248i	−0.324950	−	0.0499483i
$445$	−7.18183	+	12.1102i	−0.340451	+	0.574078i
$446$	−3.15330	+	41.2700i	−0.149313	+	1.95419i
$447$	11.1220	−	11.1220i	0.526053	−	0.526053i
$448$	7.57390	−	2.57604i	0.357833	−	0.121707i
$449$		−	12.9545i		−	0.611362i	−0.952134	−	0.305681i	$-0.901116\pi$
$449$		−	12.9545i		−	0.611362i	0.952134	−	0.305681i	$-0.0988841\pi$
$450$	3.44716	−	9.11851i	0.162501	−	0.429851i
$451$	−32.9556	−	32.9556i	−1.55182	−	1.55182i
$452$	10.1903	+	13.8920i	0.479312	+	0.653426i
$453$	−3.62057			−0.170109
$454$	23.3723	−	20.0542i	1.09692	−	0.941191i
$455$	3.72412	+	14.5780i	0.174589	+	0.683428i
$456$	−2.65731	+	11.4120i	−0.124440	+	0.534417i
$457$	−13.8025	+	13.8025i	−0.645656	+	0.645656i	−0.951940	−	0.306285i	$-0.900914\pi$
$457$	−13.8025	+	13.8025i	−0.645656	+	0.645656i	0.306285	+	0.951940i	$0.400914\pi$
$458$	−11.6547	−	0.890498i	−0.544589	−	0.0416102i
$459$	9.56539	+	9.56539i	0.446474	+	0.446474i
$460$	11.8056	−	1.15584i	0.550441	−	0.0538914i
$461$	−4.74064	+	4.74064i	−0.220793	+	0.220793i	−0.808833	−	0.588039i	$-0.799900\pi$
$461$	−4.74064	+	4.74064i	−0.220793	+	0.220793i	0.588039	+	0.808833i	$0.299900\pi$
$462$	5.41116	+	6.30646i	0.251750	+	0.293403i
$463$	−17.8769	−	17.8769i	−0.830810	−	0.830810i	0.156818	−	0.987628i	$-0.449876\pi$
$463$	−17.8769	−	17.8769i	−0.830810	−	0.830810i	−0.987628	+	0.156818i	$0.949876\pi$
$464$	−5.24897	−	10.0734i	−0.243677	−	0.467645i
$465$	15.0244	+	8.91005i	0.696738	+	0.413194i
$466$	−1.94095	+	25.4029i	−0.0899128	+	1.17677i
$467$			22.4914i			1.04078i	0.853929	+	0.520389i	$0.174213\pi$
$467$			22.4914i			1.04078i	−0.853929	+	0.520389i	$0.825787\pi$
$468$	18.3377	+	2.81871i	0.847663	+	0.130295i
$469$	−0.237214	+	0.237214i	−0.0109535	+	0.0109535i
$470$	−20.2730	+	28.9111i	−0.935126	+	1.33357i
$471$	−7.40362			−0.341141
$472$	−9.27950	−	2.16075i	−0.427124	−	0.0994567i
$473$	4.70518	+	4.70518i	0.216344	+	0.216344i
$474$	2.31592	+	2.69910i	0.106374	+	0.123974i
$475$	−15.6102	−	4.57635i	−0.716243	−	0.209977i
$476$	−4.79620	−	0.737227i	−0.219833	−	0.0337908i
$477$	14.4621			0.662172
$478$	1.07410	+	1.25182i	0.0491282	+	0.0572568i
$479$	21.3461			0.975327			0.487664	−	0.873032i	$-0.337849\pi$
$479$	21.3461			0.975327			0.487664	+	0.873032i	$0.337849\pi$
$480$	−15.9681	−	2.10681i	−0.728843	−	0.0961623i
$481$	18.3041			0.834594
$482$	16.2631	+	18.9540i	0.740766	+	0.863330i
$483$	−3.37744			−0.153679
$484$	20.3496	+	3.12795i	0.924980	+	0.142179i
$485$	−5.19851	+	1.32802i	−0.236052	+	0.0603021i
$486$	11.9283	+	13.9019i	0.541080	+	0.630605i
$487$	29.4655	+	29.4655i	1.33521	+	1.33521i	0.900638	+	0.434570i	$0.143100\pi$
$487$	29.4655	+	29.4655i	1.33521	+	1.33521i	0.434570	+	0.900638i	$0.356900\pi$
$488$	4.38059	−	18.8127i	0.198300	−	0.851612i
$489$	5.21905			0.236013
$490$	−0.547008	−	3.11461i	−0.0247113	−	0.140704i
$491$	17.4275	−	17.4275i	0.786493	−	0.786493i	−0.194425	−	0.980917i	$-0.562284\pi$
$491$	17.4275	−	17.4275i	0.786493	−	0.786493i	0.980917	+	0.194425i	$0.0622840\pi$
$492$	−25.4222	−	3.90767i	−1.14612	−	0.176171i
$493$			6.88992i			0.310306i
$494$	2.35866	−	30.8698i	0.106121	−	1.38890i
$495$	3.52094	+	13.7827i	0.158255	+	0.619486i
$496$	−7.36989	+	23.4068i	−0.330918	+	1.05100i
$497$	0.711903	+	0.711903i	0.0319332	+	0.0319332i
$498$	2.14300	+	2.49757i	0.0960302	+	0.111919i
$499$	−23.6289	+	23.6289i	−1.05778	+	1.05778i	−0.0595504	+	0.998225i	$0.518967\pi$
$499$	−23.6289	+	23.6289i	−1.05778	+	1.05778i	−0.998225	+	0.0595504i	$0.981033\pi$
$500$	4.16985	−	21.9684i	0.186481	−	0.982459i
$501$	−11.2082	−	11.2082i	−0.500743	−	0.500743i
$502$	−12.7645	−	0.975297i	−0.569709	−	0.0435296i
$503$	−18.0619	+	18.0619i	−0.805339	+	0.805339i	−0.983924	−	0.178585i	$-0.942848\pi$
$503$	−18.0619	+	18.0619i	−0.805339	+	0.805339i	0.178585	+	0.983924i	$0.442848\pi$
$504$	−3.79774	−	0.884312i	−0.169165	−	0.0393904i
$505$	39.4339	−	10.0738i	1.75479	−	0.448280i
$506$	−13.1368	+	11.2718i	−0.584003	+	0.501094i
$507$	41.1000			1.82532
$508$	−17.3021	−	23.5873i	−0.767658	−	1.04652i
$509$	23.4364	+	23.4364i	1.03880	+	1.03880i	0.999216	+	0.0395817i	$0.0126025\pi$
$509$	23.4364	+	23.4364i	1.03880	+	1.03880i	0.0395817	+	0.999216i	$0.487397\pi$
$510$	7.99904	+	5.60909i	0.354203	+	0.248375i
$511$			11.6946i			0.517339i
$512$	−2.23806	−	22.5165i	−0.0989093	−	0.995096i
$513$	12.8264	−	12.8264i	0.566301	−	0.566301i
$514$	0.572604	−	7.49416i	0.0252565	−	0.330553i
$515$	−5.66064	−	22.1585i	−0.249438	−	0.976421i
$516$	3.62962	+	0.557911i	0.159785	+	0.0245607i
$517$		−	51.5274i		−	2.26617i
$518$	−3.83581	−	0.293082i	−0.168536	−	0.0128773i
$519$		−	13.2466i		−	0.581462i
$520$	42.5473	−	0.907943i	1.86582	−	0.0398159i
$521$		−	13.3876i		−	0.586520i	−0.956033	−	0.293260i	$-0.905260\pi$
$521$		−	13.3876i		−	0.586520i	0.956033	−	0.293260i	$-0.0947402\pi$
$522$	−0.421798	+	5.52043i	−0.0184616	+	0.241623i
$523$		−	29.1077i		−	1.27279i	−0.771363	−	0.636396i	$-0.780425\pi$
$523$		−	29.1077i		−	1.27279i	0.771363	−	0.636396i	$-0.219575\pi$
$524$	−14.9592	+	10.9731i	−0.653494	+	0.479362i
$525$	−1.79110	+	6.10953i	−0.0781700	+	0.266642i
$526$	−28.6749	−	2.19096i	−1.25029	−	0.0955302i
$527$	10.5252	−	10.5252i	0.458486	−	0.458486i
$528$	20.8436	−	10.8610i	0.907100	−	0.472666i
$529$			15.9645i			0.694110i
$530$	32.6729	−	5.73823i	1.41922	−	0.249253i
$531$	3.28379	+	3.28379i	0.142505	+	0.142505i
$532$	−0.988564	+	6.43132i	−0.0428597	+	0.278833i
$533$	67.9600			2.94368
$534$	−7.38353	−	8.60518i	−0.319517	−	0.372382i
$535$	−20.1122	+	33.9137i	−0.869526	+	1.46622i
$536$	0.501301	+	0.805621i	0.0216529	+	0.0347975i
$537$	−7.08387	+	7.08387i	−0.305692	+	0.305692i
$538$	−1.56008	+	20.4180i	−0.0672596	+	0.880285i
$539$	3.26300	+	3.26300i	0.140547	+	0.140547i
$540$	19.2652	+	15.8292i	0.829041	+	0.681182i
$541$	−32.3520	+	32.3520i	−1.39092	+	1.39092i	−0.567653	+	0.823268i	$0.692148\pi$
$541$	−32.3520	+	32.3520i	−1.39092	+	1.39092i	−0.823268	+	0.567653i	$0.807852\pi$
$542$	13.7456	−	11.7942i	0.590423	−	0.506603i
$543$	2.66340	+	2.66340i	0.114297	+	0.114297i
$544$	−5.10736	+	12.7393i	−0.218976	+	0.546195i
$545$	32.8757	−	8.39845i	1.40824	−	0.359750i
$546$	−12.0819	−	0.923136i	−0.517056	−	0.0395066i
$547$			13.0529i			0.558103i	0.960276	+	0.279052i	$0.0900200\pi$
$547$			13.0529i			0.558103i	−0.960276	+	0.279052i	$0.909980\pi$
$548$	15.2130	+	20.7393i	0.649868	+	0.885938i
$549$	−6.65738	+	6.65738i	−0.284130	+	0.284130i
$550$	13.4232	+	29.7411i	0.572369	+	1.26816i
$551$	9.23884			0.393588
$552$	−2.16645	+	9.30395i	−0.0922101	+	0.396003i
$553$	1.39653	+	1.39653i	0.0593865	+	0.0593865i
$554$	13.0799	−	11.2230i	0.555711	−	0.476819i
$555$	6.66184	+	3.95074i	0.282779	+	0.167699i
$556$	−7.69510	+	5.64464i	−0.326345	+	0.239386i
$557$	−4.90851			−0.207980			−0.103990	−	0.994578i	$-0.533161\pi$
$557$	−4.90851			−0.207980			−0.103990	+	0.994578i	$0.533161\pi$
$558$	9.07751	−	7.78881i	0.384282	−	0.329727i
$559$	−9.70289			−0.410388
$560$	−8.93079	−	0.490992i	−0.377395	−	0.0207482i
$561$	−14.2565			−0.601908
$562$	−2.50988	+	2.15356i	−0.105873	+	0.0908426i
$563$	−31.3073			−1.31945			−0.659724	−	0.751508i	$-0.729327\pi$
$563$	−31.3073			−1.31945			−0.659724	+	0.751508i	$0.729327\pi$
$564$	−16.8194	−	22.9292i	−0.708226	−	0.965495i
$565$	−4.76768	−	18.6630i	−0.200578	−	0.785159i
$566$	14.0802	−	12.0813i	0.591836	−	0.507815i
$567$	−2.09553	−	2.09553i	−0.0880040	−	0.0880040i
$568$	2.41775	−	1.50446i	0.101447	−	0.0631256i
$569$	3.62849			0.152114			0.0760572	−	0.997103i	$-0.475767\pi$
$569$	3.62849			0.152114			0.0760572	+	0.997103i	$0.475767\pi$
$570$	7.52135	−	10.7261i	0.315035	−	0.449266i
$571$	10.5531	−	10.5531i	0.441634	−	0.441634i	−0.450927	−	0.892561i	$-0.648906\pi$
$571$	10.5531	−	10.5531i	0.441634	−	0.441634i	0.892561	+	0.450927i	$0.148906\pi$
$572$	−50.0742	+	36.7312i	−2.09371	+	1.53581i
$573$		−	22.0488i		−	0.921102i
$574$	−14.2417	−	1.08817i	−0.594439	−	0.0454191i
$575$	−12.7266	−	3.73099i	−0.530736	−	0.155593i
$576$	−4.87208	+	9.89451i	−0.203003	+	0.412271i
$577$	14.2057	+	14.2057i	0.591393	+	0.591393i	0.938008	−	0.346615i	$-0.112669\pi$
$577$	14.2057	+	14.2057i	0.591393	+	0.591393i	−0.346615	+	0.938008i	$0.612669\pi$
$578$	−11.9276	+	10.2343i	−0.496123	+	0.425690i
$579$	20.0805	−	20.0805i	0.834516	−	0.834516i
$580$	1.23745	+	12.6392i	0.0513824	+	0.524814i
$581$	1.29226	+	1.29226i	0.0536119	+	0.0536119i
$582$	0.329190	−	4.30839i	0.0136453	−	0.178588i
$583$	−34.2295	+	34.2295i	−1.41764	+	1.41764i
$584$	32.2155	+	7.50145i	1.33309	+	0.310412i
$585$	−17.8415	−	10.5807i	−0.737657	−	0.437460i
$586$	−13.2076	−	15.3928i	−0.545600	−	0.635872i
$587$	−44.9515			−1.85535			−0.927674	−	0.373392i	$-0.878195\pi$
$587$	−44.9515			−1.85535			−0.927674	+	0.373392i	$0.878195\pi$
$588$	2.51710	+	0.386906i	0.103804	+	0.0159557i
$589$	−14.1135	−	14.1135i	−0.581537	−	0.581537i
$590$	8.72174	+	6.11586i	0.359068	+	0.251786i
$591$		−	10.9398i		−	0.450002i
$592$	−3.26783	+	10.3786i	−0.134307	+	0.426560i
$593$	12.4054	−	12.4054i	0.509428	−	0.509428i	−0.404923	−	0.914351i	$-0.632702\pi$
$593$	12.4054	−	12.4054i	0.509428	−	0.509428i	0.914351	+	0.404923i	$0.132702\pi$
$594$	−36.2796	−	2.77200i	−1.48857	−	0.113737i
$595$	4.66641	+	2.76737i	0.191304	+	0.113451i
$596$	−14.6123	−	19.9204i	−0.598544	−	0.815970i
$597$			12.2989i			0.503359i
$598$	1.92296	−	25.1674i	0.0786356	−	1.02917i
$599$			1.06248i			0.0434119i	0.999764	+	0.0217059i	$0.00690976\pi$
$599$			1.06248i			0.0434119i	−0.999764	+	0.0217059i	$0.993090\pi$
$600$	15.6812	+	8.85293i	0.640184	+	0.361419i
$601$			12.1915i			0.497302i	0.968593	+	0.248651i	$0.0799873\pi$
$601$			12.1915i			0.497302i	−0.968593	+	0.248651i	$0.920013\pi$
$602$	2.03334	+	0.155361i	0.0828729	+	0.00633205i
$603$		−	0.462489i		−	0.0188340i
$604$	−0.863969	+	5.62074i	−0.0351544	+	0.228705i
$605$	−19.7989	−	11.7416i	−0.804941	−	0.477362i
$606$	−2.49711	+	32.6818i	−0.101438	+	1.32761i
$607$	−6.15215	+	6.15215i	−0.249708	+	0.249708i	−0.820851	−	0.571143i	$-0.806500\pi$
$607$	−6.15215	+	6.15215i	−0.249708	+	0.249708i	0.571143	+	0.820851i	$0.306500\pi$
$608$	17.0825	+	6.84857i	0.692785	+	0.277746i
$609$		−	3.61592i		−	0.146524i
$610$	−12.3990	+	17.6820i	−0.502019	+	0.715922i
$611$	53.1291	+	53.1291i	2.14937	+	2.14937i
$612$	5.39417	−	3.95682i	0.218046	−	0.159945i
$613$	−13.5179			−0.545982			−0.272991	−	0.962017i	$-0.588013\pi$
$613$	−13.5179			−0.545982			−0.272991	+	0.962017i	$0.588013\pi$
$614$	15.8677	−	13.6150i	0.640367	−	0.549456i
$615$	24.7343	+	14.6684i	0.997383	+	0.591488i
$616$	11.0817	−	6.89564i	0.446495	−	0.277833i
$617$	2.52264	−	2.52264i	0.101558	−	0.101558i	−0.654502	−	0.756060i	$-0.727122\pi$
$617$	2.52264	−	2.52264i	0.101558	−	0.101558i	0.756060	+	0.654502i	$0.227122\pi$
$618$	18.3644	+	1.40316i	0.738724	+	0.0564435i
$619$	−21.6100	−	21.6100i	−0.868577	−	0.868577i	0.123738	−	0.992315i	$-0.460512\pi$
$619$	−21.6100	−	21.6100i	−0.868577	−	0.868577i	−0.992315	+	0.123738i	$0.960512\pi$
$620$	17.4176	−	21.1984i	0.699509	−	0.851346i
$621$	10.4571	−	10.4571i	0.419629	−	0.419629i
$622$	−17.7442	−	20.6800i	−0.711476	−	0.829194i
$623$	−4.45236	−	4.45236i	−0.178380	−	0.178380i
$624$	−10.2929	+	32.6902i	−0.412044	+	1.30865i
$625$	−13.4981	+	21.0428i	−0.539925	+	0.841713i
$626$	1.93656	−	25.3454i	0.0774006	−	1.01301i
$627$			19.1168i			0.763451i
$628$	−1.76671	+	11.4937i	−0.0704995	+	0.458650i
$629$	4.66691	−	4.66691i	0.186082	−	0.186082i
$630$	3.56947	+	2.50298i	0.142211	+	0.0997213i
$631$	−26.0445			−1.03681			−0.518407	−	0.855134i	$-0.673475\pi$
$631$	−26.0445			−1.03681			−0.518407	+	0.855134i	$0.673475\pi$
$632$	4.74286	−	2.95127i	0.188661	−	0.117395i
$633$	19.0016	+	19.0016i	0.755244	+	0.755244i
$634$	−29.9029	−	34.8505i	−1.18760	−	1.38409i
$635$	8.09503	+	31.6879i	0.321242	+	1.25750i
$636$	−4.05873	+	26.4050i	−0.160939	+	1.04702i
$637$	−6.72886			−0.266607
$638$	−12.0677	−	14.0644i	−0.477765	−	0.556814i
$639$	−1.38797			−0.0549074
$640$	−7.08116	+	24.2870i	−0.279908	+	0.960027i
$641$	−40.6458			−1.60541			−0.802707	−	0.596373i	$-0.796608\pi$
$641$	−40.6458			−1.60541			−0.802707	+	0.596373i	$0.796608\pi$
$642$	−20.6771	−	24.0982i	−0.816059	−	0.951080i
$643$	2.60900			0.102889			0.0514445	−	0.998676i	$-0.483617\pi$
$643$	2.60900			0.102889			0.0514445	+	0.998676i	$0.483617\pi$
$644$	−0.805953	+	5.24331i	−0.0317590	+	0.206615i
$645$	−3.53140	−	2.09426i	−0.139049	−	0.0824615i
$646$	−7.26936	−	8.47211i	−0.286009	−	0.333331i
$647$	−0.747727	−	0.747727i	−0.0293962	−	0.0293962i	0.692256	−	0.721652i	$-0.256617\pi$
$647$	−0.747727	−	0.747727i	−0.0293962	−	0.0293962i	−0.721652	+	0.692256i	$0.756617\pi$
$648$	−7.11679	+	4.42846i	−0.279574	+	0.173966i
$649$	−15.5445			−0.610175
$650$	−44.5061	−	16.8251i	−1.74567	−	0.659933i
$651$	−5.52377	+	5.52377i	−0.216494	+	0.216494i
$652$	1.24541	−	8.10230i	0.0487741	−	0.317311i
$653$		−	35.8180i		−	1.40167i	−0.713325	−	0.700834i	$-0.752811\pi$
$653$		−	35.8180i		−	1.40167i	0.713325	−	0.700834i	$-0.247189\pi$
$654$	−2.08181	+	27.2465i	−0.0814053	+	1.06542i
$655$	20.0966	−	5.13391i	0.785240	−	0.200598i
$656$	−12.1329	+	38.5342i	−0.473710	+	1.50451i
$657$	−11.4003	−	11.4003i	−0.444768	−	0.444768i
$658$	−10.2831	−	11.9845i	−0.400876	−	0.467203i
$659$	9.84609	−	9.84609i	0.383549	−	0.383549i	−0.488830	−	0.872379i	$-0.662576\pi$
$659$	9.84609	−	9.84609i	0.383549	−	0.383549i	0.872379	+	0.488830i	$0.162576\pi$
$660$	−26.1527	+	2.56051i	−1.01799	+	0.0996676i
$661$	17.8149	+	17.8149i	0.692918	+	0.692918i	0.962873	−	0.269955i	$-0.0870089\pi$
$661$	17.8149	+	17.8149i	0.692918	+	0.692918i	−0.269955	+	0.962873i	$0.587009\pi$
$662$	2.73367	+	0.208871i	0.106247	+	0.00811800i
$663$	14.6996	−	14.6996i	0.570886	−	0.570886i
$664$	4.38873	−	2.73091i	0.170316	−	0.105980i
$665$	3.71083	−	6.25730i	0.143900	−	0.242648i
$666$	4.02499	−	3.45358i	0.155965	−	0.133823i
$667$	7.53221			0.291648
$668$	−20.0747	+	14.7255i	−0.776712	+	0.569747i
$669$	26.3518	+	26.3518i	1.01882	+	1.01882i
$670$	−0.183505	−	1.04486i	−0.00708943	−	0.0403665i
$671$		−	31.5140i		−	1.21659i
$672$	2.68041	−	6.68577i	0.103399	−	0.257909i
$673$	−21.5505	+	21.5505i	−0.830709	+	0.830709i	−0.987614	−	0.156905i	$-0.949849\pi$
$673$	−21.5505	+	21.5505i	−0.830709	+	0.830709i	0.156905	+	0.987614i	$0.449849\pi$
$674$	−3.38258	+	44.2707i	−0.130292	+	1.70524i
$675$	−13.3705	−	24.4616i	−0.514632	−	0.941526i
$676$	9.80761	−	63.8056i	0.377216	−	2.45406i
$677$		−	12.4739i		−	0.479411i	−0.970846	−	0.239706i	$-0.922949\pi$
$677$		−	12.4739i		−	0.479411i	0.970846	−	0.239706i	$-0.0770509\pi$
$678$	15.4674	+	1.18181i	0.594022	+	0.0453873i
$679$		−	2.39950i		−	0.0920845i
$680$	10.6166	−	11.0796i	0.407129	−	0.424883i
$681$		−	27.7288i		−	1.06257i
$682$	−3.05016	+	39.9201i	−0.116797	+	1.52862i
$683$			3.46419i			0.132553i	0.997801	+	0.0662767i	$0.0211120\pi$
$683$			3.46419i			0.132553i	−0.997801	+	0.0662767i	$0.978888\pi$
$684$	−5.30579	−	7.23316i	−0.202872	−	0.276567i
$685$	−7.11762	−	27.8618i	−0.271950	−	1.06455i
$686$	1.41010	+	0.107741i	0.0538380	+	0.00411358i
$687$	−7.44179	+	7.44179i	−0.283922	+	0.283922i
$688$	1.73226	−	5.50166i	0.0660417	−	0.209749i
$689$		−	70.5872i		−	2.68916i
$690$	6.13198	−	8.74472i	0.233440	−	0.332906i
$691$	0.942094	+	0.942094i	0.0358389	+	0.0358389i	0.724799	−	0.688960i	$-0.241933\pi$
$691$	0.942094	+	0.942094i	0.0358389	+	0.0358389i	−0.688960	+	0.724799i	$0.741933\pi$
$692$	−20.5647	−	3.16102i	−0.781753	−	0.120164i
$693$	−6.36176			−0.241663
$694$	10.9017	+	12.7054i	0.413823	+	0.482292i
$695$	10.3378	−	2.64092i	0.392137	−	0.100176i
$696$	−9.96088	−	2.31941i	−0.377566	−	0.0879171i
$697$	17.3275	−	17.3275i	0.656325	−	0.656325i
$698$	1.88176	−	24.6281i	0.0712255	−	0.932189i
$699$	16.2203	+	16.2203i	0.613508	+	0.613508i
$700$	9.05733	+	4.23850i	0.342335	+	0.160200i
$701$	22.3178	−	22.3178i	0.842932	−	0.842932i	−0.146307	−	0.989239i	$-0.546739\pi$
$701$	22.3178	−	22.3178i	0.842932	−	0.842932i	0.989239	+	0.146307i	$0.0467388\pi$
$702$	40.2655	−	34.5492i	1.51972	−	1.30397i
$703$	−6.25796	−	6.25796i	−0.236023	−	0.236023i
$704$	−11.8873	−	34.9503i	−0.448021	−	1.31724i
$705$	7.86920	+	30.8039i	0.296371	+	1.16014i
$706$	22.0067	+	1.68146i	0.828234	+	0.0632826i
$707$			18.2017i			0.684547i
$708$	−6.91717	+	5.07400i	−0.259963	+	0.190693i
$709$	−28.7102	+	28.7102i	−1.07823	+	1.07823i	−0.0815667	+	0.996668i	$0.525992\pi$
$709$	−28.7102	+	28.7102i	−1.07823	+	1.07823i	−0.996668	+	0.0815667i	$0.974008\pi$
$710$	−3.13574	+	0.550718i	−0.117682	+	0.0206681i
$711$	−2.72277			−0.102112
$712$	−15.1210	+	9.40911i	−0.566684	+	0.352621i
$713$	−11.5064	−	11.5064i	−0.430919	−	0.430919i
$714$	−3.31583	+	2.84509i	−0.124092	+	0.106475i
$715$	67.2713	−	17.1852i	2.51580	−	0.642690i
$716$	9.30693	+	12.6878i	0.347816	+	0.474164i
$717$	1.48515			0.0554640
$718$	−33.4639	+	28.7132i	−1.24886	+	1.07157i
$719$	23.9587			0.893508			0.446754	−	0.894657i	$-0.352580\pi$
$719$	23.9587			0.893508			0.446754	+	0.894657i	$0.352580\pi$
$720$	9.18467	−	8.22740i	0.342292	−	0.306617i
$721$	10.2278			0.380905
$722$	9.03185	−	7.74963i	0.336131	−	0.288412i
$723$	22.4869			0.836297
$724$	4.77035	−	3.49923i	0.177289	−	0.130048i
$725$	3.99442	−	13.6252i	0.148349	−	0.506027i
$726$	14.0686	−	12.0713i	0.522134	−	0.448009i
$727$	−25.9889	−	25.9889i	−0.963875	−	0.963875i	0.0354953	−	0.999370i	$-0.488699\pi$
$727$	−25.9889	−	25.9889i	−0.963875	−	0.963875i	−0.999370	+	0.0354953i	$0.988699\pi$
$728$	−4.31619	+	18.5362i	−0.159969	+	0.686997i
$729$	25.3838			0.940140
$730$	−30.2791	−	21.2323i	−1.12068	−	0.785844i
$731$	−2.47390	+	2.47390i	−0.0915006	+	0.0915006i
$732$	−10.2867	−	14.0235i	−0.380209	−	0.518323i
$733$		−	21.8954i		−	0.808724i	−0.914599	−	0.404362i	$-0.867494\pi$
$733$		−	21.8954i		−	0.808724i	0.914599	−	0.404362i	$-0.132506\pi$
$734$	−4.42696	−	0.338250i	−0.163402	−	0.0124850i
$735$	−2.44899	−	1.45235i	−0.0903324	−	0.0535708i
$736$	13.9269	+	5.58348i	0.513354	+	0.205810i
$737$	1.09464	+	1.09464i	0.0403216	+	0.0403216i
$738$	14.9441	−	12.8226i	0.550101	−	0.472005i
$739$	17.8596	−	17.8596i	0.656974	−	0.656974i	−0.297689	−	0.954663i	$-0.596216\pi$
$739$	17.8596	−	17.8596i	0.656974	−	0.656974i	0.954663	+	0.297689i	$0.0962157\pi$
$740$	7.72301	−	9.39940i	0.283904	−	0.345529i
$741$	−19.7110	−	19.7110i	−0.724103	−	0.724103i
$742$	−1.13023	+	14.7923i	−0.0414921	+	0.543042i
$743$	−23.5083	+	23.5083i	−0.862434	+	0.862434i	−0.991620	−	0.129186i	$-0.958764\pi$
$743$	−23.5083	+	23.5083i	−0.862434	+	0.862434i	0.129186	+	0.991620i	$0.458764\pi$
$744$	11.6733	+	18.7597i	0.427964	+	0.687764i
$745$	6.83657	+	26.7617i	0.250472	+	0.980472i
$746$	−5.21819	−	6.08157i	−0.191052	−	0.222662i
$747$	−2.51947			−0.0921827
$748$	−3.40199	+	22.1324i	−0.124389	+	0.809241i
$749$	−12.4685	−	12.4685i	−0.455590	−	0.455590i
$750$	−12.5667	−	15.7297i	−0.458869	−	0.574367i
$751$		−	36.4196i		−	1.32897i	−0.747302	−	0.664484i	$-0.768651\pi$
$751$		−	36.4196i		−	1.32897i	0.747302	−	0.664484i	$-0.231349\pi$
$752$	−39.6100	+	20.6397i	−1.44443	+	0.752654i
$753$	−8.15044	+	8.15044i	−0.297019	+	0.297019i
$754$	26.9444	+	2.05873i	0.981257	+	0.0749746i
$755$	3.24313	−	5.46865i	0.118029	−	0.199024i
$756$	−8.99126	+	6.59542i	−0.327009	+	0.239873i
$757$			23.6762i			0.860527i	0.902703	+	0.430264i	$0.141579\pi$
$757$			23.6762i			0.860527i	−0.902703	+	0.430264i	$0.858421\pi$
$758$	3.04974	−	39.9145i	0.110771	−	1.44976i
$759$			15.5855i			0.565717i
$760$	−14.8569	−	14.2360i	−0.538916	−	0.516396i
$761$			24.9638i			0.904937i	0.891780	+	0.452469i	$0.149457\pi$
$761$			24.9638i			0.904937i	−0.891780	+	0.452469i	$0.850543\pi$
$762$	−26.2621	−	2.00660i	−0.951375	−	0.0726915i
$763$			15.1746i			0.549357i
$764$	−34.2296	−	5.26146i	−1.23838	−	0.190353i
$765$	−7.24671	+	1.85125i	−0.262005	+	0.0669322i
$766$	−2.93474	+	38.4094i	−0.106036	+	1.38779i
$767$	16.0277	−	16.0277i	0.578727	−	0.578727i
$768$	−16.6982	−	11.6724i	−0.602543	−	0.421190i
$769$			14.0070i			0.505106i	0.967583	+	0.252553i	$0.0812702\pi$
$769$			14.0070i			0.505106i	−0.967583	+	0.252553i	$0.918730\pi$
$770$	−14.3726	+	2.52421i	−0.517952	+	0.0909661i
$771$	−4.78519	−	4.78519i	−0.172334	−	0.172334i
$772$	−26.3821	−	35.9657i	−0.949514	−	1.29443i
$773$	4.28623			0.154165			0.0770825	−	0.997025i	$-0.475440\pi$
$773$	4.28623			0.154165			0.0770825	+	0.997025i	$0.475440\pi$
$774$	−2.13362	+	1.83072i	−0.0766915	+	0.0658039i
$775$	−26.9162	+	14.7122i	−0.966858	+	0.528478i
$776$	−6.60999	−	1.53915i	−0.237285	−	0.0552523i
$777$	−2.44925	+	2.44925i	−0.0878664	+	0.0878664i
$778$	−5.22130	−	0.398943i	−0.187193	−	0.0143028i
$779$	−23.2348	−	23.2348i	−0.832473	−	0.832473i
$780$	24.3256	−	29.6058i	0.870996	−	1.06006i
$781$	3.28513	−	3.28513i	0.117551	−	0.117551i
$782$	−5.92654	−	6.90711i	−0.211933	−	0.246998i
$783$	11.1954	+	11.1954i	0.400092	+	0.400092i
$784$	1.20130	−	3.81535i	0.0429037	−	0.136262i
$785$	6.63181	−	11.1827i	0.236699	−	0.399129i
$786$	−1.27260	+	16.6555i	−0.0453920	+	0.594084i
$787$		−	5.64585i		−	0.201253i	−0.994924	−	0.100626i	$-0.967915\pi$
$787$		−	5.64585i		−	0.201253i	0.994924	−	0.100626i	$-0.0320847\pi$
$788$	−16.9834	−	2.61053i	−0.605009	−	0.0929964i
$789$	−18.3096	+	18.3096i	−0.651838	+	0.651838i
$790$	−6.15132	+	1.08033i	−0.218854	+	0.0384366i
$791$	8.61440			0.306293
$792$	−4.08072	+	17.5249i	−0.145002	+	0.622722i
$793$	32.4937	+	32.4937i	1.15388	+	1.15388i
$794$	13.2000	+	15.3840i	0.468450	+	0.545958i
$795$	15.2355	−	25.6905i	0.540346	−	0.911146i
$796$	19.0933	+	2.93485i	0.676745	+	0.104023i
$797$	20.8995			0.740298			0.370149	−	0.928972i	$-0.379307\pi$
$797$	20.8995			0.740298			0.370149	+	0.928972i	$0.379307\pi$
$798$	3.81505	+	4.44627i	0.135051	+	0.157396i
$799$	27.0922			0.958453
$800$	17.4857	−	22.2317i	0.618213	−	0.786011i
$801$	8.68063			0.306715
$802$	26.1679	+	30.4975i	0.924020	+	1.07690i
$803$	53.9656			1.90440
$804$	0.844416	+	0.129796i	0.0297803	+	0.00457755i
$805$	3.02535	−	5.10143i	0.106630	−	0.179802i
$806$	−38.0160	−	44.3060i	−1.33906	−	1.56061i
$807$	13.0374	+	13.0374i	0.458937	+	0.458937i
$808$	50.1409	+	11.6754i	1.76395	+	0.410740i
$809$	−21.1336			−0.743018			−0.371509	−	0.928429i	$-0.621159\pi$
$809$	−21.1336			−0.743018			−0.371509	+	0.928429i	$0.621159\pi$
$810$	9.23023	−	1.62107i	0.324317	−	0.0569587i
$811$	−30.2074	+	30.2074i	−1.06072	+	1.06072i	−0.0626906	+	0.998033i	$0.519968\pi$
$811$	−30.2074	+	30.2074i	−1.06072	+	1.06072i	−0.998033	+	0.0626906i	$0.980032\pi$
$812$	−5.61352	−	0.862859i	−0.196996	−	0.0302804i
$813$		−	16.3077i		−	0.571935i
$814$	−1.35245	+	17.7006i	−0.0474033	+	0.620407i
$815$	−4.67497	+	7.88306i	−0.163757	+	0.276131i
$816$	5.71055	+	10.9592i	0.199909	+	0.383649i
$817$	3.31731	+	3.31731i	0.116058	+	0.116058i
$818$	8.06612	+	9.40071i	0.282025	+	0.328688i
$819$	6.55952	−	6.55952i	0.229208	−	0.229208i
$820$	28.6743	−	34.8984i	1.00135	−	1.21871i
$821$	4.12000	+	4.12000i	0.143789	+	0.143789i	0.775337	−	0.631548i	$-0.217580\pi$
$821$	4.12000	+	4.12000i	0.143789	+	0.143789i	−0.631548	+	0.775337i	$0.717580\pi$
$822$	23.0912	+	1.76432i	0.805396	+	0.0615377i
$823$	−0.141649	+	0.141649i	−0.00493757	+	0.00493757i	−0.709571	−	0.704634i	$-0.751111\pi$
$823$	−0.141649	+	0.141649i	−0.00493757	+	0.00493757i	0.704634	+	0.709571i	$0.251111\pi$
$824$	6.56060	−	28.1749i	0.228549	−	0.981521i
$825$	28.1929	+	8.26516i	0.981550	+	0.287756i
$826$	−3.61541	+	3.10215i	−0.125796	+	0.107937i
$827$	−27.5589			−0.958316			−0.479158	−	0.877729i	$-0.659058\pi$
$827$	−27.5589			−0.958316			−0.479158	+	0.877729i	$0.659058\pi$
$828$	−4.32568	−	5.89703i	−0.150328	−	0.204936i
$829$	7.35288	+	7.35288i	0.255376	+	0.255376i	0.823170	−	0.567794i	$-0.192203\pi$
$829$	7.35288	+	7.35288i	0.255376	+	0.255376i	−0.567794	+	0.823170i	$0.692203\pi$
$830$	−5.69203	+	0.999671i	−0.197573	+	0.0346991i
$831$		−	15.5179i		−	0.538311i
$832$	48.2936	+	23.7799i	1.67428	+	0.824420i
$833$	−1.71563	+	1.71563i	−0.0594430	+	0.0594430i
$834$	−0.654632	+	8.56773i	−0.0226681	+	0.296676i
$835$	26.9690	−	6.88952i	0.933299	−	0.238422i
$836$	29.6778	+	4.56180i	1.02643	+	0.157773i
$837$		−	34.2049i		−	1.18229i
$838$	10.9947	+	0.840067i	0.379805	+	0.0290196i
$839$			21.1319i			0.729554i	0.931095	+	0.364777i	$0.118855\pi$
$839$			21.1319i			0.729554i	−0.931095	+	0.364777i	$0.881145\pi$
$840$	−5.57173	+	5.81471i	−0.192243	+	0.200627i
$841$		−	20.9360i		−	0.721930i
$842$	1.36079	−	17.8098i	0.0468959	−	0.613766i
$843$			2.97772i			0.102558i
$844$	34.0332	−	24.9646i	1.17147	−	0.859318i
$845$	−36.8154	+	62.0791i	−1.26649	+	2.13559i
$846$	21.7072	+	1.65857i	0.746308	+	0.0570229i
$847$	7.27916	−	7.27916i	0.250115	−	0.250115i
$848$	40.0238	+	12.6019i	1.37442	+	0.432752i
$849$		−	16.7047i		−	0.573304i
$850$	−15.6373	+	7.05771i	−0.536356	+	0.242078i
$851$	−5.10197	−	5.10197i	−0.174893	−	0.174893i
$852$	0.389530	−	2.53418i	0.0133451	−	0.0868195i
$853$	−9.88276			−0.338379			−0.169190	−	0.985584i	$-0.554115\pi$
$853$	−9.88276			−0.338379			−0.169190	+	0.985584i	$0.554115\pi$
$854$	−6.28911	−	7.32968i	−0.215209	−	0.250816i
$855$	2.48238	+	9.71726i	0.0848957	+	0.332323i
$856$	−42.3453	+	26.3496i	−1.44733	+	0.900610i
$857$	29.1583	−	29.1583i	0.996029	−	0.996029i	−0.00396326	−	0.999992i	$-0.501262\pi$
$857$	29.1583	−	29.1583i	0.996029	−	0.996029i	0.999992	+	0.00396326i	$0.00126155\pi$
$858$	−4.25988	+	55.7527i	−0.145430	+	1.90336i
$859$	−34.0990	−	34.0990i	−1.16344	−	1.16344i	−0.983717	−	0.179726i	$-0.942479\pi$
$859$	−34.0990	−	34.0990i	−1.16344	−	1.16344i	−0.179726	−	0.983717i	$-0.557521\pi$
$860$	−4.09393	+	4.98257i	−0.139602	+	0.169904i
$861$	−9.09367	+	9.09367i	−0.309912	+	0.309912i
$862$	39.6929	−	34.0578i	1.35194	−	1.16001i
$863$	−28.0672	−	28.0672i	−0.955418	−	0.955418i	0.0436294	−	0.999048i	$-0.486108\pi$
$863$	−28.0672	−	28.0672i	−0.955418	−	0.955418i	−0.999048	+	0.0436294i	$0.986108\pi$
$864$	12.4012	+	28.9991i	0.421898	+	0.986570i
$865$	20.0082	+	11.8657i	0.680300	+	0.403445i
$866$	−6.55539	−	0.500876i	−0.222761	−	0.0170205i
$867$			14.1509i			0.480588i
$868$	7.25724	+	9.89349i	0.246327	+	0.335807i
$869$	6.44439	−	6.44439i	0.218611	−	0.218611i
$870$	9.36216	+	6.56494i	0.317407	+	0.222572i
$871$	−2.25734			−0.0764870
$872$	41.8020	+	9.73368i	1.41559	+	0.329624i
$873$	2.33912	+	2.33912i	0.0791672	+	0.0791672i
$874$	−9.26190	+	7.94702i	−0.313288	+	0.268812i
$875$	−7.62370	−	8.17797i	−0.257728	−	0.276466i
$876$	24.0142	−	17.6153i	0.811365	−	0.595166i
$877$	28.8331			0.973623			0.486811	−	0.873507i	$-0.338160\pi$
$877$	28.8331			0.973623			0.486811	+	0.873507i	$0.338160\pi$
$878$	−15.5999	+	13.3852i	−0.526471	+	0.451730i
$879$	−18.2620			−0.615962
$880$	−2.26572	+	41.2118i	−0.0763774	+	1.38925i
$881$	41.1147			1.38519			0.692595	−	0.721327i	$-0.256468\pi$
$881$	41.1147			1.38519			0.692595	+	0.721327i	$0.256468\pi$
$882$	−1.47965	+	1.26959i	−0.0498223	+	0.0427492i
$883$	−23.0096			−0.774336			−0.387168	−	0.922009i	$-0.626547\pi$
$883$	−23.0096			−0.774336			−0.387168	+	0.922009i	$0.626547\pi$
$884$	−19.3127	−	26.3281i	−0.649555	−	0.885511i
$885$	9.29275	−	2.37394i	0.312373	−	0.0797991i
$886$	6.66615	−	5.71978i	0.223954	−	0.192160i
$887$	−12.1772	−	12.1772i	−0.408869	−	0.408869i	0.472475	−	0.881344i	$-0.343361\pi$
$887$	−12.1772	−	12.1772i	−0.408869	−	0.408869i	−0.881344	+	0.472475i	$0.843361\pi$
$888$	5.17597	+	8.31809i	0.173694	+	0.279137i
$889$	−14.6264			−0.490553
$890$	19.6114	−	3.44428i	0.657376	−	0.115453i
$891$	−9.66998	+	9.66998i	−0.323956	+	0.323956i
$892$	47.1981	−	34.6215i	1.58031	−	1.15921i
$893$		−	36.3285i		−	1.21569i
$894$	−22.1794	−	1.69465i	−0.741789	−	0.0566776i
$895$	−4.35437	−	17.0451i	−0.145551	−	0.569756i
$896$	−9.73969	−	5.75660i	−0.325380	−	0.192315i
$897$	−16.0699	−	16.0699i	−0.536560	−	0.536560i
$898$	−13.9038	+	11.9299i	−0.463976	+	0.398107i
$899$	12.3188	−	12.3188i	0.410856	−	0.410856i
$900$	−12.9612	+	4.69756i	−0.432041	+	0.156585i
$901$	−17.9973	−	17.9973i	−0.599577	−	0.599577i
$902$	−5.02142	+	65.7196i	−0.167195	+	2.18822i
$903$	1.29834	−	1.29834i	0.0432059	−	0.0432059i
$904$	5.52566	−	23.7303i	0.183781	−	0.789260i
$905$	−6.40864	+	1.63716i	−0.213031	+	0.0544210i
$906$	3.33421	+	3.88588i	0.110772	+	0.129100i
$907$	−13.1204			−0.435657			−0.217829	−	0.975987i	$-0.569897\pi$
$907$	−13.1204			−0.435657			−0.217829	+	0.975987i	$0.569897\pi$
$908$	−43.0475	−	6.61686i	−1.42858	−	0.219588i
$909$	−17.7437	−	17.7437i	−0.588521	−	0.588521i
$910$	12.2167	−	17.4220i	0.404979	−	0.577535i
$911$			31.5760i			1.04616i	0.852284	+	0.523079i	$0.175217\pi$
$911$			31.5760i			1.04616i	−0.852284	+	0.523079i	$0.824783\pi$
$912$	14.6954	−	7.65740i	0.486614	−	0.253562i
$913$	5.96321	−	5.96321i	0.197354	−	0.197354i
$914$	27.5248	+	2.10308i	0.910441	+	0.0695638i
$915$	4.81279	+	18.8396i	0.159106	+	0.622818i
$916$	9.77717	+	13.3288i	0.323047	+	0.440396i
$917$			9.27611i			0.306324i
$918$	1.45747	−	19.0752i	0.0481037	−	0.629574i
$919$			2.70772i			0.0893194i	0.999002	+	0.0446597i	$0.0142204\pi$
$919$			2.70772i			0.0893194i	−0.999002	+	0.0446597i	$0.985780\pi$
$920$	−12.1125	−	11.6063i	−0.399336	−	0.382649i
$921$		−	18.8253i		−	0.620316i
$922$	9.45372	+	0.722328i	0.311342	+	0.0237886i
$923$			6.77450i			0.222985i
$924$	1.78541	−	11.6154i	0.0587355	−	0.382117i
$925$	−11.9347	+	6.52342i	−0.392410	+	0.214489i
$926$	−2.72389	+	35.6499i	−0.0895126	+	1.17153i
$927$	−9.97044	+	9.97044i	−0.327472	+	0.327472i
$928$	−5.97771	+	14.9103i	−0.196228	+	0.489454i
$929$			19.6925i			0.646091i	0.946383	+	0.323045i	$0.104707\pi$
$929$			19.6925i			0.646091i	−0.946383	+	0.323045i	$0.895293\pi$
$930$	−4.27311	−	24.3307i	−0.140121	−	0.797834i
$931$	2.30052	+	2.30052i	0.0753965	+	0.0753965i
$932$	29.0518	−	21.3106i	0.951624	−	0.698051i
$933$	−24.5347			−0.803230
$934$	24.1396	−	20.7126i	0.789870	−	0.677735i
$935$	12.7702	−	21.5335i	0.417631	−	0.704221i
$936$	−13.8621	−	22.2773i	−0.453098	−	0.728156i
$937$	−9.98966	+	9.98966i	−0.326348	+	0.326348i	−0.851196	−	0.524848i	$-0.824122\pi$
$937$	−9.98966	+	9.98966i	−0.326348	+	0.326348i	0.524848	+	0.851196i	$0.324122\pi$
$938$	0.473049	+	0.0361441i	0.0154456	+	0.00118015i
$939$	−16.1836	−	16.1836i	−0.528133	−	0.528133i
$940$	49.6993	−	4.86585i	1.62101	−	0.158707i
$941$	19.9907	−	19.9907i	0.651679	−	0.651679i	−0.301718	−	0.953397i	$-0.597560\pi$
$941$	19.9907	−	19.9907i	0.651679	−	0.651679i	0.953397	+	0.301718i	$0.0975601\pi$
$942$	6.81806	+	7.94615i	0.222145	+	0.258899i
$943$	−18.9428	−	18.9428i	−0.616862	−	0.616862i
$944$	6.22649	+	11.9493i	0.202655	+	0.388918i
$945$	12.0792	−	3.08576i	0.392935	−	0.100380i
$946$	0.716925	−	9.38301i	0.0233092	−	0.305068i
$947$		−	32.0465i		−	1.04137i	−0.853748	−	0.520686i	$-0.825676\pi$
$947$		−	32.0465i		−	1.04137i	0.853748	−	0.520686i	$-0.174324\pi$
$948$	0.764136	−	4.97126i	0.0248180	−	0.161459i
$949$	−55.6431	+	55.6431i	−1.80625	+	1.80625i
$950$	9.46384	+	20.9684i	0.307047	+	0.680306i
$951$	−41.3465			−1.34075
$952$	3.62561	+	5.82657i	0.117507	+	0.188840i
$953$	19.6279	+	19.6279i	0.635810	+	0.635810i	0.949519	−	0.313710i	$-0.101572\pi$
$953$	19.6279	+	19.6279i	0.635810	+	0.635810i	−0.313710	+	0.949519i	$0.601572\pi$
$954$	−13.3182	−	15.5218i	−0.431194	−	0.502537i
$955$	33.3034	+	19.7502i	1.07767	+	0.639103i
$956$	0.354398	−	2.30562i	0.0114621	−	0.0745691i
$957$	−16.6859			−0.539379
$958$	−19.6578	−	22.9103i	−0.635115	−	0.740198i
$959$	12.8603			0.415282
$960$	12.4440	+	19.0784i	0.401629	+	0.615754i
$961$	−6.63719			−0.214103
$962$	−16.8564	−	19.6454i	−0.543472	−	0.633392i
$963$	24.3095			0.783362
$964$	5.36601	−	34.9098i	0.172827	−	1.12437i
$965$	12.3432	+	48.3174i	0.397343	+	1.55539i
$966$	3.11032	+	3.62494i	0.100073	+	0.116630i
$967$	−17.3151	−	17.3151i	−0.556815	−	0.556815i	0.371584	−	0.928399i	$-0.378815\pi$
$967$	−17.3151	−	17.3151i	−0.556815	−	0.556815i	−0.928399	+	0.371584i	$0.878815\pi$
$968$	−15.3829	−	24.7213i	−0.494427	−	0.794573i
$969$	−10.0513			−0.322894
$970$	6.21269	+	4.35646i	0.199477	+	0.139878i
$971$	−4.02234	+	4.02234i	−0.129083	+	0.129083i	−0.768697	−	0.639614i	$-0.779094\pi$
$971$	−4.02234	+	4.02234i	−0.129083	+	0.129083i	0.639614	+	0.768697i	$0.279094\pi$
$972$	3.93574	−	25.6048i	0.126239	−	0.821276i
$973$			4.77170i			0.152974i
$974$	4.48963	−	58.7597i	0.143857	−	1.88278i
$975$	−37.5914	+	20.5472i	−1.20389	+	0.658037i
$976$	−24.2254	+	12.6232i	−0.775437	+	0.404060i
$977$	−12.6876	−	12.6876i	−0.405913	−	0.405913i	0.474398	−	0.880311i	$-0.342666\pi$
$977$	−12.6876	−	12.6876i	−0.405913	−	0.405913i	−0.880311	+	0.474398i	$0.842666\pi$
$978$	−4.80627	−	5.60149i	−0.153687	−	0.179116i
$979$	−20.5457	+	20.5457i	−0.656645	+	0.656645i
$980$	−2.83910	+	3.45536i	−0.0906916	+	0.110377i
$981$	−14.7927	−	14.7927i	−0.472295	−	0.472295i
$982$	−34.7537	−	2.65542i	−1.10904	−	0.0847378i
$983$	−16.9846	+	16.9846i	−0.541726	+	0.541726i	−0.924035	−	0.382309i	$-0.875129\pi$
$983$	−16.9846	+	16.9846i	−0.541726	+	0.541726i	0.382309	+	0.924035i	$0.375129\pi$
$984$	19.2175	+	30.8837i	0.612633	+	0.984537i
$985$	16.5239	+	9.79931i	0.526494	+	0.312232i
$986$	7.39480	−	6.34499i	0.235499	−	0.202066i
$987$	−14.2183			−0.452574
$988$	−35.3040	+	25.8968i	−1.12317	+	0.823886i
$989$	2.70453	+	2.70453i	0.0859989	+	0.0859989i
$990$	11.5502	−	16.4716i	0.367090	−	0.523501i
$991$		−	23.8194i		−	0.756648i	−0.925673	−	0.378324i	$-0.876501\pi$
$991$		−	23.8194i		−	0.756648i	0.925673	−	0.378324i	$-0.123499\pi$
$992$	31.9090	−	13.6456i	1.01311	−	0.433249i
$993$	1.74551	−	1.74551i	0.0553921	−	0.0553921i
$994$	0.108472	−	1.41967i	0.00344053	−	0.0450292i
$995$	−18.5767	−	11.0167i	−0.588920	−	0.349253i
$996$	0.707081	−	4.60008i	0.0224047	−	0.145759i
$997$			24.7382i			0.783465i	0.920079	+	0.391733i	$0.128124\pi$
$997$			24.7382i			0.783465i	−0.920079	+	0.391733i	$0.871876\pi$
$998$	47.1205	+	3.60032i	1.49157	+	0.113966i
$999$		−	15.1665i		−	0.479848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bl.a.267.20	yes	144
5.3	odd	4		560.2.t.a.43.18	✓	144
16.3	odd	4		560.2.t.a.547.18	yes	144
80.3	even	4	inner	560.2.bl.a.323.20	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.18	✓	144	5.3	odd	4
560.2.t.a.547.18	yes	144	16.3	odd	4
560.2.bl.a.267.20	yes	144	1.1	even	1	trivial
560.2.bl.a.323.20	yes	144	80.3	even	4	inner

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.920909 - 1.07328i) q^{2} -1.27333 q^{3} +(-0.303853 + 1.97678i) q^{4} +(1.14059 - 1.92329i) q^{5} +(1.17262 + 1.36664i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.40146 - 1.49432i) q^{8} -1.37862 q^{9} +O(q^{10})\)	\(q+(-0.920909 - 1.07328i) q^{2} -1.27333 q^{3} +(-0.303853 + 1.97678i) q^{4} +(1.14059 - 1.92329i) q^{5} +(1.17262 + 1.36664i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.40146 - 1.49432i) q^{8} -1.37862 q^{9} +(-3.11461 + 0.547008i) q^{10} +(3.26300 - 3.26300i) q^{11} +(0.386906 - 2.51710i) q^{12} +6.72886i q^{13} +(0.107741 - 1.41010i) q^{14} +(-1.45235 + 2.44899i) q^{15} +(-3.81535 - 1.20130i) q^{16} +(1.71563 + 1.71563i) q^{17} +(1.26959 + 1.47965i) q^{18} +(2.30052 - 2.30052i) q^{19} +(3.45536 + 2.83910i) q^{20} +(-0.900382 - 0.900382i) q^{21} +(-6.50703 - 0.497180i) q^{22} +(1.87556 - 1.87556i) q^{23} +(-3.05786 + 1.90277i) q^{24} +(-2.39811 - 4.38738i) q^{25} +(7.22194 - 6.19666i) q^{26} +5.57545 q^{27} +(-1.61265 + 1.18294i) q^{28} +(2.00799 + 2.00799i) q^{29} +(3.96593 - 0.696523i) q^{30} -6.13492i q^{31} +(2.22425 + 5.20122i) q^{32} +(-4.15488 + 4.15488i) q^{33} +(0.261409 - 3.42128i) q^{34} +(2.16649 - 0.553455i) q^{35} +(0.418899 - 2.72524i) q^{36} -2.72024i q^{37} +(-4.58767 - 0.350529i) q^{38} -8.56807i q^{39} +(-0.134933 - 6.32312i) q^{40} -10.0998i q^{41} +(-0.137191 + 1.79553i) q^{42} +1.44198i q^{43} +(5.45877 + 7.44171i) q^{44} +(-1.57244 + 2.65150i) q^{45} +(-3.74022 - 0.285778i) q^{46} +(7.89571 - 7.89571i) q^{47} +(4.85821 + 1.52966i) q^{48} +1.00000i q^{49} +(-2.50043 + 6.61421i) q^{50} +(-2.18456 - 2.18456i) q^{51} +(-13.3015 - 2.04458i) q^{52} -10.4902 q^{53} +(-5.13448 - 5.98400i) q^{54} +(-2.55396 - 9.99744i) q^{55} +(2.75473 + 0.641445i) q^{56} +(-2.92933 + 2.92933i) q^{57} +(0.305956 - 4.00431i) q^{58} +(-2.38194 - 2.38194i) q^{59} +(-4.39983 - 3.61512i) q^{60} +(4.82900 - 4.82900i) q^{61} +(-6.58447 + 5.64970i) q^{62} +(-0.974834 - 0.974834i) q^{63} +(3.53402 - 7.17710i) q^{64} +(12.9416 + 7.67486i) q^{65} +(8.28561 + 0.633076i) q^{66} +0.335471i q^{67} +(-3.91272 + 2.87013i) q^{68} +(-2.38821 + 2.38821i) q^{69} +(-2.58915 - 1.81557i) q^{70} +1.00678 q^{71} +(-3.31071 + 2.06010i) q^{72} +(8.26933 + 8.26933i) q^{73} +(-2.91957 + 2.50509i) q^{74} +(3.05359 + 5.58659i) q^{75} +(3.84861 + 5.24665i) q^{76} +4.61457 q^{77} +(-9.19593 + 7.89042i) q^{78} +1.97499 q^{79} +(-6.66220 + 5.96784i) q^{80} -2.96353 q^{81} +(-10.8399 + 9.30099i) q^{82} +1.82753 q^{83} +(2.05344 - 1.50628i) q^{84} +(5.25648 - 1.34283i) q^{85} +(1.54765 - 1.32793i) q^{86} +(-2.55684 - 2.55684i) q^{87} +(2.96000 - 12.7119i) q^{88} -6.29659 q^{89} +(4.29387 - 0.754117i) q^{90} +(-4.75802 + 4.75802i) q^{91} +(3.13768 + 4.27747i) q^{92} +7.81179i q^{93} +(-15.7455 - 1.20306i) q^{94} +(-1.80063 - 7.04853i) q^{95} +(-2.83222 - 6.62288i) q^{96} +(-1.69671 - 1.69671i) q^{97} +(1.07328 - 0.920909i) q^{98} +(-4.49844 + 4.49844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 8 q^{4} + 144 q^{9}+O(q^{10}) \) 144 * q - 8 * q^4 + 144 * q^9	\( 144 q - 8 q^{4} + 144 q^{9} - 16 q^{12} + 8 q^{16} + 28 q^{18} + 16 q^{19} - 36 q^{22} + 32 q^{26} - 36 q^{30} - 40 q^{32} - 32 q^{34} - 32 q^{36} - 56 q^{38} - 48 q^{40} + 20 q^{42} + 56 q^{44} - 32 q^{46} - 24 q^{48} + 8 q^{50} - 16 q^{51} - 16 q^{52} - 32 q^{54} - 24 q^{56} - 52 q^{58} - 32 q^{60} - 32 q^{61} + 40 q^{62} - 32 q^{64} + 32 q^{66} + 80 q^{68} + 32 q^{69} + 40 q^{72} + 16 q^{73} + 32 q^{74} - 24 q^{75} - 28 q^{78} + 72 q^{80} + 144 q^{81} + 24 q^{82} - 80 q^{83} + 32 q^{86} - 112 q^{87} + 40 q^{88} + 32 q^{90} - 16 q^{92} + 8 q^{94} - 80 q^{95} + 32 q^{96} - 64 q^{99}+O(q^{100}) \) 144 * q - 8 * q^4 + 144 * q^9 - 16 * q^12 + 8 * q^16 + 28 * q^18 + 16 * q^19 - 36 * q^22 + 32 * q^26 - 36 * q^30 - 40 * q^32 - 32 * q^34 - 32 * q^36 - 56 * q^38 - 48 * q^40 + 20 * q^42 + 56 * q^44 - 32 * q^46 - 24 * q^48 + 8 * q^50 - 16 * q^51 - 16 * q^52 - 32 * q^54 - 24 * q^56 - 52 * q^58 - 32 * q^60 - 32 * q^61 + 40 * q^62 - 32 * q^64 + 32 * q^66 + 80 * q^68 + 32 * q^69 + 40 * q^72 + 16 * q^73 + 32 * q^74 - 24 * q^75 - 28 * q^78 + 72 * q^80 + 144 * q^81 + 24 * q^82 - 80 * q^83 + 32 * q^86 - 112 * q^87 + 40 * q^88 + 32 * q^90 - 16 * q^92 + 8 * q^94 - 80 * q^95 + 32 * q^96 - 64 * q^99

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