LMFDB - Embedded newform 546.2.bg.b.311.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(311,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 3]))

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

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

chi := DirichletCharacter("546.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bg (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.6
Character	$\chi$	$=$	546.311
Dual form			546.2.bg.b.467.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.08983 - 1.34620i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.20332 + 1.27209i) q^{5} +(0.620929 - 1.61693i) q^{6} +(2.32714 - 1.25873i) q^{7} -1.00000 q^{8} +(-0.624526 + 2.93427i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.08983 - 1.34620i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.20332 + 1.27209i) q^{5} +(0.620929 - 1.61693i) q^{6} +(2.32714 - 1.25873i) q^{7} -1.00000 q^{8} +(-0.624526 + 2.93427i) q^{9} +(-2.20332 - 1.27209i) q^{10} +(2.05512 - 3.55958i) q^{11} +(1.71076 - 0.270722i) q^{12} +(0.691594 + 3.53860i) q^{13} +(2.25366 + 1.38600i) q^{14} +(4.11374 + 1.57975i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.85089 + 4.93789i) q^{17} +(-2.85342 + 0.926282i) q^{18} +(4.22658 + 7.32066i) q^{19} -2.54418i q^{20} +(-4.23070 - 1.76101i) q^{21} +4.11024 q^{22} +(-1.13269 + 0.653959i) q^{23} +(1.08983 + 1.34620i) q^{24} +(0.736416 - 1.27551i) q^{25} +(-2.71872 + 2.36824i) q^{26} +(4.63076 - 2.35713i) q^{27} +(-0.0734817 + 2.64473i) q^{28} +6.06189i q^{29} +(0.688764 + 4.35248i) q^{30} +(-0.00131550 + 0.00227852i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.03165 + 1.11273i) q^{33} -5.70178 q^{34} +(-3.52623 + 5.73372i) q^{35} +(-2.22889 - 2.00799i) q^{36} +(6.13142 - 3.53998i) q^{37} +(-4.22658 + 7.32066i) q^{38} +(4.00995 - 4.78751i) q^{39} +(2.20332 - 1.27209i) q^{40} +2.51379i q^{41} +(-0.590277 - 4.54440i) q^{42} +3.31665 q^{43} +(2.05512 + 3.55958i) q^{44} +(-2.35662 - 7.25960i) q^{45} +(-1.13269 - 0.653959i) q^{46} +(-3.68624 + 2.12825i) q^{47} +(-0.620929 + 1.61693i) q^{48} +(3.83121 - 5.85849i) q^{49} +1.47283 q^{50} +(9.75440 - 1.54360i) q^{51} +(-3.41032 - 1.17036i) q^{52} +(4.39543 + 2.53770i) q^{53} +(4.35672 + 2.83179i) q^{54} +10.4572i q^{55} +(-2.32714 + 1.25873i) q^{56} +(5.24882 - 13.6681i) q^{57} +(-5.24975 + 3.03094i) q^{58} +(-1.68327 - 0.971837i) q^{59} +(-3.42498 + 2.77273i) q^{60} +(-3.15576 + 1.82198i) q^{61} -0.00263100 q^{62} +(2.24009 + 7.61459i) q^{63} +1.00000 q^{64} +(-6.02522 - 6.91691i) q^{65} +(-4.47948 - 5.53322i) q^{66} +(-2.80901 - 1.62178i) q^{67} +(-2.85089 - 4.93789i) q^{68} +(2.11481 + 0.812125i) q^{69} +(-6.72866 - 0.186950i) q^{70} +6.68865 q^{71} +(0.624526 - 2.93427i) q^{72} +(-1.31969 + 2.28578i) q^{73} +(6.13142 + 3.53998i) q^{74} +(-2.51967 + 0.398728i) q^{75} -8.45317 q^{76} +(0.302028 - 10.8705i) q^{77} +(6.15108 + 1.07897i) q^{78} +(-7.07859 - 12.2605i) q^{79} +(2.20332 + 1.27209i) q^{80} +(-8.21993 - 3.66506i) q^{81} +(-2.17701 + 1.25689i) q^{82} -11.1300i q^{83} +(3.64043 - 2.78339i) q^{84} -14.5063i q^{85} +(1.65832 + 2.87230i) q^{86} +(8.16053 - 6.60645i) q^{87} +(-2.05512 + 3.55958i) q^{88} +(-3.31853 + 1.91595i) q^{89} +(5.10869 - 5.67070i) q^{90} +(6.06358 + 7.36431i) q^{91} -1.30792i q^{92} +(0.00450102 - 0.000712270i) q^{93} +(-3.68624 - 2.12825i) q^{94} +(-18.6250 - 10.7532i) q^{95} +(-1.71076 + 0.270722i) q^{96} +3.91287 q^{97} +(6.98920 + 0.388679i) q^{98} +(9.16129 + 8.25334i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9} + 14 q^{15} - 18 q^{16} - 4 q^{18} - 23 q^{21} + 14 q^{25} + 6 q^{26} + 7 q^{30} + 18 q^{32} - 24 q^{33} - 8 q^{36} + 10 q^{39} - 16 q^{42} - 16 q^{43} + 9 q^{45} - 72 q^{47} + 12 q^{49} + 28 q^{50} - 3 q^{51} + 6 q^{52} - 9 q^{54} + 8 q^{57} - 24 q^{59} - 7 q^{60} - 36 q^{61} + 39 q^{63} + 36 q^{64} - 18 q^{65} - 24 q^{66} + 72 q^{71} - 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} + 7 q^{84} - 8 q^{86} - 24 q^{87} + 72 q^{89} - 2 q^{91} + 14 q^{93} - 72 q^{94} + 12 q^{98} - 72 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9 + 14 * q^15 - 18 * q^16 - 4 * q^18 - 23 * q^21 + 14 * q^25 + 6 * q^26 + 7 * q^30 + 18 * q^32 - 24 * q^33 - 8 * q^36 + 10 * q^39 - 16 * q^42 - 16 * q^43 + 9 * q^45 - 72 * q^47 + 12 * q^49 + 28 * q^50 - 3 * q^51 + 6 * q^52 - 9 * q^54 + 8 * q^57 - 24 * q^59 - 7 * q^60 - 36 * q^61 + 39 * q^63 + 36 * q^64 - 18 * q^65 - 24 * q^66 + 72 * q^71 - 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 + 7 * q^84 - 8 * q^86 - 24 * q^87 + 72 * q^89 - 2 * q^91 + 14 * q^93 - 72 * q^94 + 12 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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
$3$	−1.08983	−	1.34620i	−0.629216	−	0.777231i
$3$	−1.08983	−	1.34620i	−0.629216	−	0.777231i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.20332	+	1.27209i	−0.985355	+	0.568895i	−0.903883	−	0.427781i	$-0.859296\pi$
$5$	−2.20332	+	1.27209i	−0.985355	+	0.568895i	−0.0814725	+	0.996676i	$0.525962\pi$
$6$	0.620929	−	1.61693i	0.253493	−	0.660107i
$7$	2.32714	−	1.25873i	0.879578	−	0.475755i
$7$	2.32714	−	1.25873i	0.879578	−	0.475755i
$8$	−1.00000			−0.353553
$9$	−0.624526	+	2.93427i	−0.208175	+	0.978092i
$10$	−2.20332	−	1.27209i	−0.696751	−	0.402270i
$11$	2.05512	−	3.55958i	0.619643	−	1.07325i	−0.369908	−	0.929068i	$-0.620611\pi$
$11$	2.05512	−	3.55958i	0.619643	−	1.07325i	0.989551	−	0.144184i	$-0.0460558\pi$
$12$	1.71076	−	0.270722i	0.493855	−	0.0781507i
$13$	0.691594	+	3.53860i	0.191814	+	0.981431i
$13$	0.691594	+	3.53860i	0.191814	+	0.981431i
$14$	2.25366	+	1.38600i	0.602317	+	0.370425i
$15$	4.11374	+	1.57975i	1.06216	+	0.407891i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.85089	+	4.93789i	−0.691443	+	1.19761i	0.279922	+	0.960023i	$0.409691\pi$
$17$	−2.85089	+	4.93789i	−0.691443	+	1.19761i	−0.971365	+	0.237591i	$0.923642\pi$
$18$	−2.85342	+	0.926282i	−0.672557	+	0.218327i
$19$	4.22658	+	7.32066i	0.969645	+	1.67947i	0.696581	+	0.717478i	$0.254704\pi$
$19$	4.22658	+	7.32066i	0.969645	+	1.67947i	0.273064	+	0.961996i	$0.411963\pi$
$20$		−	2.54418i		−	0.568895i
$21$	−4.23070	−	1.76101i	−0.923215	−	0.384283i
$22$	4.11024			0.876307
$23$	−1.13269	+	0.653959i	−0.236182	+	0.136360i	−0.613421	−	0.789756i	$-0.710207\pi$
$23$	−1.13269	+	0.653959i	−0.236182	+	0.136360i	0.377238	+	0.926116i	$0.376874\pi$
$24$	1.08983	+	1.34620i	0.222461	+	0.274793i
$25$	0.736416	−	1.27551i	0.147283	−	0.255102i
$26$	−2.71872	+	2.36824i	−0.533185	+	0.464450i
$27$	4.63076	−	2.35713i	0.891190	−	0.453630i
$28$	−0.0734817	+	2.64473i	−0.0138867	+	0.499807i
$29$			6.06189i			1.12566i	0.826571	+	0.562832i	$0.190288\pi$
$29$			6.06189i			1.12566i	−0.826571	+	0.562832i	$0.809712\pi$
$30$	0.688764	+	4.35248i	0.125751	+	0.794651i
$31$	−0.00131550	+	0.00227852i	−0.000236271	+	0.000409234i	−0.866144	−	0.499795i	$-0.833409\pi$
$31$	−0.00131550	+	0.00227852i	−0.000236271	+	0.000409234i	0.865907	+	0.500205i	$0.166742\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−7.03165	+	1.11273i	−1.22405	+	0.193702i
$34$	−5.70178			−0.977848
$35$	−3.52623	+	5.73372i	−0.596042	+	0.969175i
$36$	−2.22889	−	2.00799i	−0.371482	−	0.334665i
$37$	6.13142	−	3.53998i	1.00800	−	0.581969i	0.0973943	−	0.995246i	$-0.468949\pi$
$37$	6.13142	−	3.53998i	1.00800	−	0.581969i	0.910605	+	0.413277i	$0.135616\pi$
$38$	−4.22658	+	7.32066i	−0.685642	+	1.18757i
$39$	4.00995	−	4.78751i	0.642106	−	0.766615i
$40$	2.20332	−	1.27209i	0.348376	−	0.201135i
$41$			2.51379i			0.392588i	0.980545	+	0.196294i	$0.0628907\pi$
$41$			2.51379i			0.392588i	−0.980545	+	0.196294i	$0.937109\pi$
$42$	−0.590277	−	4.54440i	−0.0910817	−	0.701216i
$43$	3.31665			0.505784			0.252892	−	0.967494i	$-0.418618\pi$
$43$	3.31665			0.505784			0.252892	+	0.967494i	$0.418618\pi$
$44$	2.05512	+	3.55958i	0.309821	+	0.536626i
$45$	−2.35662	−	7.25960i	−0.351305	−	1.08220i
$46$	−1.13269	−	0.653959i	−0.167006	−	0.0964211i
$47$	−3.68624	+	2.12825i	−0.537693	+	0.310437i	−0.744143	−	0.668020i	$-0.767142\pi$
$47$	−3.68624	+	2.12825i	−0.537693	+	0.310437i	0.206451	+	0.978457i	$0.433809\pi$
$48$	−0.620929	+	1.61693i	−0.0896234	+	0.233383i
$49$	3.83121	−	5.85849i	0.547315	−	0.836927i
$50$	1.47283			0.208290
$51$	9.75440	−	1.54360i	1.36589	−	0.216147i
$52$	−3.41032	−	1.17036i	−0.472926	−	0.162300i
$53$	4.39543	+	2.53770i	0.603758	+	0.348580i	0.770519	−	0.637417i	$-0.219997\pi$
$53$	4.39543	+	2.53770i	0.603758	+	0.348580i	−0.166760	+	0.985997i	$0.553331\pi$
$54$	4.35672	+	2.83179i	0.592874	+	0.385358i
$55$			10.4572i			1.41005i
$56$	−2.32714	+	1.25873i	−0.310978	+	0.168205i
$57$	5.24882	−	13.6681i	0.695223	−	1.81039i
$58$	−5.24975	+	3.03094i	−0.689326	+	0.397982i
$59$	−1.68327	−	0.971837i	−0.219143	−	0.126522i	0.386410	−	0.922327i	$-0.373715\pi$
$59$	−1.68327	−	0.971837i	−0.219143	−	0.126522i	−0.605554	+	0.795805i	$0.707048\pi$
$60$	−3.42498	+	2.77273i	−0.442163	+	0.357958i
$61$	−3.15576	+	1.82198i	−0.404054	+	0.233281i	−0.688232	−	0.725491i	$-0.741613\pi$
$61$	−3.15576	+	1.82198i	−0.404054	+	0.233281i	0.284178	+	0.958772i	$0.408279\pi$
$62$	−0.00263100			−0.000334138
$63$	2.24009	+	7.61459i	0.282225	+	0.959348i
$64$	1.00000			0.125000
$65$	−6.02522	−	6.91691i	−0.747336	−	0.857937i
$66$	−4.47948	−	5.53322i	−0.551386	−	0.681093i
$67$	−2.80901	−	1.62178i	−0.343175	−	0.198132i	0.318500	−	0.947923i	$-0.396821\pi$
$67$	−2.80901	−	1.62178i	−0.343175	−	0.198132i	−0.661675	+	0.749791i	$0.730154\pi$
$68$	−2.85089	−	4.93789i	−0.345721	−	0.598807i
$69$	2.11481	+	0.812125i	0.254593	+	0.0977684i
$70$	−6.72866	−	0.186950i	−0.804229	−	0.0223448i
$71$	6.68865			0.793797			0.396899	−	0.917862i	$-0.370086\pi$
$71$	6.68865			0.793797			0.396899	+	0.917862i	$0.370086\pi$
$72$	0.624526	−	2.93427i	0.0736011	−	0.345808i
$73$	−1.31969	+	2.28578i	−0.154458	+	0.267530i	−0.932862	−	0.360235i	$-0.882697\pi$
$73$	−1.31969	+	2.28578i	−0.154458	+	0.267530i	0.778403	+	0.627765i	$0.216030\pi$
$74$	6.13142	+	3.53998i	0.712763	+	0.411514i
$75$	−2.51967	+	0.398728i	−0.290946	+	0.0460411i
$76$	−8.45317			−0.969645
$77$	0.302028	−	10.8705i	0.0344192	−	1.23881i
$78$	6.15108	+	1.07897i	0.696473	+	0.122169i
$79$	−7.07859	−	12.2605i	−0.796404	−	1.37941i	−0.921944	−	0.387323i	$-0.873400\pi$
$79$	−7.07859	−	12.2605i	−0.796404	−	1.37941i	0.125540	−	0.992088i	$-0.459934\pi$
$80$	2.20332	+	1.27209i	0.246339	+	0.142224i
$81$	−8.21993	−	3.66506i	−0.913326	−	0.407229i
$82$	−2.17701	+	1.25689i	−0.240410	+	0.138801i
$83$		−	11.1300i		−	1.22168i	−0.791755	−	0.610839i	$-0.790832\pi$
$83$		−	11.1300i		−	1.22168i	0.791755	−	0.610839i	$-0.209168\pi$
$84$	3.64043	−	2.78339i	0.397203	−	0.303693i
$85$		−	14.5063i		−	1.57343i
$86$	1.65832	+	2.87230i	0.178822	+	0.309728i
$87$	8.16053	−	6.60645i	0.874901	−	0.708286i
$88$	−2.05512	+	3.55958i	−0.219077	+	0.379452i
$89$	−3.31853	+	1.91595i	−0.351763	+	0.203091i	−0.665462	−	0.746432i	$-0.731765\pi$
$89$	−3.31853	+	1.91595i	−0.351763	+	0.203091i	0.313698	+	0.949523i	$0.398432\pi$
$90$	5.10869	−	5.67070i	0.538503	−	0.597744i
$91$	6.06358	+	7.36431i	0.635636	+	0.771989i
$92$		−	1.30792i		−	0.136360i
$93$	0.00450102		0.000712270i	0.000466735		7.38590e-5i
$94$	−3.68624	−	2.12825i	−0.380206	−	0.219512i
$95$	−18.6250	−	10.7532i	−1.91089	−	1.10325i
$96$	−1.71076	+	0.270722i	−0.174604	+	0.0276304i
$97$	3.91287			0.397292			0.198646	−	0.980071i	$-0.436346\pi$
$97$	3.91287			0.397292			0.198646	+	0.980071i	$0.436346\pi$
$98$	6.98920	+	0.388679i	0.706016	+	0.0392625i
$99$	9.16129	+	8.25334i	0.920745	+	0.829492i
$100$	0.736416	+	1.27551i	0.0736416	+	0.127551i
$101$	7.74790	−	13.4198i	0.770945	−	1.33532i	−0.166100	−	0.986109i	$-0.553117\pi$
$101$	7.74790	−	13.4198i	0.770945	−	1.33532i	0.937045	−	0.349208i	$-0.113549\pi$
$102$	6.21399	+	7.67576i	0.615277	+	0.760013i
$103$	−11.5111	+	6.64596i	−1.13423	+	0.654846i	−0.944994	−	0.327087i	$-0.893933\pi$
$103$	−11.5111	+	6.64596i	−1.13423	+	0.654846i	−0.189231	+	0.981933i	$0.560600\pi$
$104$	−0.691594	−	3.53860i	−0.0678164	−	0.346988i
$105$	11.5618	−	1.50177i	1.12831	−	0.146558i
$106$			5.07540i			0.492967i
$107$	−12.3570	+	7.13432i	−1.19460	+	0.689701i	−0.959346	−	0.282234i	$-0.908925\pi$
$107$	−12.3570	+	7.13432i	−1.19460	+	0.689701i	−0.235251	+	0.971935i	$0.575591\pi$
$108$	−0.274044	+	5.18892i	−0.0263699	+	0.499304i
$109$	9.22052	+	5.32347i	0.883166	+	0.509896i	0.871701	−	0.490038i	$-0.163017\pi$
$109$	9.22052	+	5.32347i	0.883166	+	0.509896i	0.0114648	+	0.999934i	$0.496351\pi$
$110$	−9.05619	+	5.22859i	−0.863474	+	0.498527i
$111$	−11.4478	−	4.39615i	−1.08657	−	0.417264i
$112$	−2.25366	−	1.38600i	−0.212951	−	0.130965i
$113$			0.854272i			0.0803632i	0.999192	+	0.0401816i	$0.0127936\pi$
$113$			0.854272i			0.0803632i	−0.999192	+	0.0401816i	$0.987206\pi$
$114$	14.4614	−	2.28846i	1.35443	−	0.214334i
$115$	1.66379	−	2.88177i	0.155149	−	0.268726i
$116$	−5.24975	−	3.03094i	−0.487427	−	0.281416i
$117$	−10.8151	−	0.180622i	−0.999861	−	0.0166985i
$118$		−	1.94367i		−	0.178930i
$119$	−0.418977	+	15.0797i	−0.0384075	+	1.38235i
$120$	−4.11374	−	1.57975i	−0.375532	−	0.144211i
$121$	−2.94705	−	5.10444i	−0.267914	−	0.464040i
$122$	−3.15576	−	1.82198i	−0.285709	−	0.164954i
$123$	3.38407	−	2.73961i	0.305131	−	0.247022i
$124$	−0.00131550	−	0.00227852i	−0.000118136	−	0.000204617i
$125$		−	8.97374i		−	0.802635i
$126$	−5.47438	+	5.74727i	−0.487697	+	0.512008i
$127$	−12.0715			−1.07117			−0.535584	−	0.844482i	$-0.679908\pi$
$127$	−12.0715			−1.07117			−0.535584	+	0.844482i	$0.679908\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−3.61459	−	4.46488i	−0.318247	−	0.393111i
$130$	2.97761	−	8.67644i	0.261154	−	0.760974i
$131$	8.61673	+	14.9246i	0.752847	+	1.30397i	0.946438	+	0.322887i	$0.104653\pi$
$131$	8.61673	+	14.9246i	0.752847	+	1.30397i	−0.193591	+	0.981082i	$0.562013\pi$
$132$	2.55217	−	6.64596i	0.222138	−	0.578456i
$133$	19.0506	+	11.7161i	1.65190	+	1.01592i
$134$		−	3.24356i		−	0.280201i
$135$	−7.20457	+	11.0843i	−0.620071	+	0.953980i
$136$	2.85089	−	4.93789i	0.244462	−	0.423421i
$137$	−6.52427	+	11.3004i	−0.557406	+	0.965456i	0.440306	+	0.897848i	$0.354870\pi$
$137$	−6.52427	+	11.3004i	−0.557406	+	0.965456i	−0.997712	+	0.0676081i	$0.978463\pi$
$138$	0.354082	+	2.23754i	0.0301415	+	0.190472i
$139$			0.623348i			0.0528717i	0.999651	+	0.0264359i	$0.00841577\pi$
$139$			0.623348i			0.0528717i	−0.999651	+	0.0264359i	$0.991584\pi$
$140$	−3.20243	−	5.92067i	−0.270654	−	0.500388i
$141$	6.88244	+	2.64299i	0.579606	+	0.222580i
$142$	3.34433	+	5.79254i	0.280650	+	0.486099i
$143$	14.0172	+	4.81047i	1.17218	+	0.402272i
$144$	2.85342	−	0.926282i	0.237785	−	0.0771901i
$145$	−7.71125	−	13.3563i	−0.640385	−	1.10918i
$146$	−2.63939			−0.218437
$147$	−12.0621	+	1.22719i	−0.994864	+	0.101217i
$148$			7.07996i			0.581969i
$149$	−0.986187	−	1.70813i	−0.0807916	−	0.139935i	0.822799	−	0.568333i	$-0.192411\pi$
$149$	−0.986187	−	1.70813i	−0.0807916	−	0.139935i	−0.903590	+	0.428398i	$0.859078\pi$
$150$	−1.60514	−	1.98273i	−0.131059	−	0.161889i
$151$	8.14145	+	4.70047i	0.662542	+	0.382519i	0.793245	−	0.608903i	$-0.208390\pi$
$151$	8.14145	+	4.70047i	0.662542	+	0.382519i	−0.130703	+	0.991422i	$0.541723\pi$
$152$	−4.22658	−	7.32066i	−0.342821	−	0.593784i
$153$	−12.7087	−	11.4491i	−1.02743	−	0.925608i
$154$	9.56513	−	5.17368i	0.770780	−	0.416907i
$155$		−	0.00669374i		−	0.000537654i
$156$	2.14113	+	5.86648i	0.171428	+	0.469694i
$157$	6.32327	+	3.65074i	0.504652	+	0.291361i	0.730633	−	0.682771i	$-0.239225\pi$
$157$	6.32327	+	3.65074i	0.504652	+	0.291361i	−0.225980	+	0.974132i	$0.572559\pi$
$158$	7.07859	−	12.2605i	0.563142	−	0.975391i
$159$	−1.37402	−	8.68281i	−0.108967	−	0.688592i
$160$			2.54418i			0.201135i
$161$	−1.81278	+	2.94761i	−0.142867	+	0.232304i
$162$	−0.935930	−	8.95120i	−0.0735336	−	0.703273i
$163$	13.1037	−	7.56540i	1.02636	−	0.592568i	0.110418	−	0.993885i	$-0.464781\pi$
$163$	13.1037	−	7.56540i	1.02636	−	0.592568i	0.915939	+	0.401317i	$0.131448\pi$
$164$	−2.17701	−	1.25689i	−0.169996	−	0.0981470i
$165$	14.0775	−	11.3966i	1.09593	−	0.887223i
$166$	9.63888	−	5.56501i	0.748122	−	0.431929i
$167$		−	24.2735i		−	1.87834i	−0.343458	−	0.939168i	$-0.611598\pi$
$167$		−	24.2735i		−	1.87834i	0.343458	−	0.939168i	$-0.388402\pi$
$168$	4.23070	+	1.76101i	0.326406	+	0.135865i
$169$	−12.0434	+	4.89455i	−0.926415	+	0.376504i
$170$	12.5629	−	7.25317i	0.963527	−	0.556293i
$171$	−24.1204	+	7.83001i	−1.84454	+	0.598776i
$172$	−1.65832	+	2.87230i	−0.126446	+	0.219011i
$173$	0.204681	+	0.354517i	0.0155616	+	0.0269535i	0.873701	−	0.486463i	$-0.161713\pi$
$173$	0.204681	+	0.354517i	0.0155616	+	0.0269535i	−0.858140	+	0.513416i	$0.828380\pi$
$174$	9.80162	+	3.76400i	0.743059	+	0.285348i
$175$	0.108226	−	3.89524i	0.00818113	−	0.294453i
$176$	−4.11024			−0.309821
$177$	0.526195	+	3.32517i	0.0395512	+	0.249935i
$178$	−3.31853	−	1.91595i	−0.248734	−	0.143607i
$179$	20.4933	+	11.8318i	1.53174	+	0.884352i	0.999282	+	0.0378964i	$0.0120657\pi$
$179$	20.4933	+	11.8318i	1.53174	+	0.884352i	0.532460	+	0.846455i	$0.321268\pi$
$180$	7.46531	+	1.58890i	0.556431	+	0.118430i
$181$		−	14.2247i		−	1.05732i	−0.848835	−	0.528658i	$-0.822696\pi$
$181$		−	14.2247i		−	1.05732i	0.848835	−	0.528658i	$-0.177304\pi$
$182$	−3.34589	+	8.93337i	−0.248014	+	0.662185i
$183$	5.89201	+	2.26264i	0.435550	+	0.167259i
$184$	1.13269	−	0.653959i	0.0835031	−	0.0482105i
$185$	−9.00633	+	15.5994i	−0.662158	+	1.14689i
$186$	0.00286736	+	0.00354187i	0.000210245	+	0.000259702i
$187$	11.7179	+	20.2959i	0.856895	+	1.48419i
$188$		−	4.25650i		−	0.310437i
$189$	7.80946	−	11.3143i	0.568055	−	0.822991i
$190$		−	21.5063i		−	1.56023i
$191$	13.8603	−	8.00228i	1.00290	−	0.579024i	0.0937947	−	0.995592i	$-0.470100\pi$
$191$	13.8603	−	8.00228i	1.00290	−	0.579024i	0.909105	+	0.416567i	$0.136767\pi$
$192$	−1.08983	−	1.34620i	−0.0786520	−	0.0971538i
$193$	−14.6848	−	8.47830i	−1.05704	−	0.610281i	−0.132427	−	0.991193i	$-0.542277\pi$
$193$	−14.6848	−	8.47830i	−1.05704	−	0.610281i	−0.924611	+	0.380912i	$0.875610\pi$
$194$	1.95644	+	3.38865i	0.140464	+	0.243291i
$195$	−2.74508	+	15.6494i	−0.196579	+	1.12068i
$196$	3.15799	+	6.24716i	0.225571	+	0.446226i
$197$	2.56563			0.182794			0.0913969	−	0.995815i	$-0.470867\pi$
$197$	2.56563			0.182794			0.0913969	+	0.995815i	$0.470867\pi$
$198$	−2.56695	+	12.0606i	−0.182426	+	0.857108i
$199$	18.7467	+	10.8234i	1.32892	+	0.767249i	0.985132	−	0.171800i	$-0.0549582\pi$
$199$	18.7467	+	10.8234i	1.32892	+	0.767249i	0.343783	+	0.939049i	$0.388292\pi$
$200$	−0.736416	+	1.27551i	−0.0520725	+	0.0901922i
$201$	0.878102	+	5.54896i	0.0619366	+	0.391394i
$202$	15.4958			1.09028
$203$	7.63027	+	14.1069i	0.535540	+	0.990110i
$204$	−3.54041	+	9.21936i	−0.247878	+	0.645484i
$205$	−3.19776	−	5.53868i	−0.223341	−	0.386839i
$206$	−11.5111	−	6.64596i	−0.802019	−	0.463046i
$207$	−1.21150	−	3.73204i	−0.0842052	−	0.259395i
$208$	2.71872	−	2.36824i	0.188509	−	0.164208i
$209$	34.7446			2.40333
$210$	7.08145	+	9.26189i	0.488666	+	0.639131i
$211$	−7.00715			−0.482392			−0.241196	−	0.970476i	$-0.577540\pi$
$211$	−7.00715			−0.482392			−0.241196	+	0.970476i	$0.577540\pi$
$212$	−4.39543	+	2.53770i	−0.301879	+	0.174290i
$213$	−7.28952	−	9.00429i	−0.499470	−	0.616964i
$214$	−12.3570	−	7.13432i	−0.844707	−	0.487692i
$215$	−7.30764	+	4.21907i	−0.498377	+	0.287738i
$216$	−4.63076	+	2.35713i	−0.315083	+	0.160382i
$217$	−0.000193331		0.00695830i	−1.31241e−5		0.000472360i
$218$			10.6469i			0.721102i
$219$	4.51536	−	0.714539i	0.305120	−	0.0482841i
$220$	−9.05619	−	5.22859i	−0.610568	−	0.352512i
$221$	−19.4449	−	6.67315i	−1.30800	−	0.448885i
$222$	−1.91670	−	12.1121i	−0.128640	−	0.812913i
$223$	−21.1582			−1.41686			−0.708429	−	0.705782i	$-0.750596\pi$
$223$	−21.1582			−1.41686			−0.708429	+	0.705782i	$0.750596\pi$
$224$	0.0734817	−	2.64473i	0.00490970	−	0.176709i
$225$	3.28279	+	2.95744i	0.218852	+	0.197162i
$226$	−0.739822	+	0.427136i	−0.0492122	+	0.0284127i
$227$	11.6624	+	6.73328i	0.774059	+	0.446903i	0.834321	−	0.551279i	$-0.185860\pi$
$227$	11.6624	+	6.73328i	0.774059	+	0.446903i	−0.0602614	+	0.998183i	$0.519193\pi$
$228$	9.21254	+	11.3797i	0.610116	+	0.753638i
$229$	−1.12680	−	1.95167i	−0.0744607	−	0.128970i	0.826391	−	0.563097i	$-0.190390\pi$
$229$	−1.12680	−	1.95167i	−0.0744607	−	0.128970i	−0.900852	+	0.434127i	$0.857057\pi$
$230$	3.32758			0.219414
$231$	−14.9630	+	11.4404i	−0.984496	+	0.752725i
$232$		−	6.06189i		−	0.397982i
$233$	−1.12902	+	0.651840i	−0.0739645	+	0.0427034i	−0.536526	−	0.843884i	$-0.680264\pi$
$233$	−1.12902	+	0.651840i	−0.0739645	+	0.0427034i	0.462562	+	0.886587i	$0.346930\pi$
$234$	−5.25115	−	9.45650i	−0.343278	−	0.618191i
$235$	5.41464	−	9.37843i	0.353212	−	0.611782i
$236$	1.68327	−	0.971837i	0.109572	−	0.0632612i
$237$	−8.79061	+	22.8911i	−0.571012	+	1.48694i
$238$	−13.2689	+	7.17700i	−0.860093	+	0.465216i
$239$	3.50122			0.226475			0.113238	−	0.993568i	$-0.463878\pi$
$239$	3.50122			0.226475			0.113238	+	0.993568i	$0.463878\pi$
$240$	−0.688764	−	4.35248i	−0.0444595	−	0.280952i
$241$	−6.59729	+	11.4268i	−0.424969	+	0.736067i	−0.996418	−	0.0845704i	$-0.973048\pi$
$241$	−6.59729	+	11.4268i	−0.424969	+	0.736067i	0.571449	+	0.820638i	$0.306382\pi$
$242$	2.94705	−	5.10444i	0.189444	−	0.328126i
$243$	4.02444	+	15.0600i	0.258168	+	0.966100i
$244$		−	3.64396i		−	0.233281i
$245$	−0.988867	+	17.7818i	−0.0631764	+	1.13603i
$246$	4.06461	+	1.56089i	0.259150	+	0.0995184i
$247$	−22.9818	+	20.0191i	−1.46230	+	1.27379i
$248$	0.00131550	−	0.00227852i	8.35345e−5	−	0.000144686i
$249$	−14.9833	+	12.1299i	−0.949526	+	0.768699i
$250$	7.77148	−	4.48687i	0.491512	−	0.283774i
$251$	−28.4357			−1.79485			−0.897424	−	0.441169i	$-0.854564\pi$
$251$	−28.4357			−1.79485			−0.897424	+	0.441169i	$0.854564\pi$
$252$	−7.71447	−	1.86732i	−0.485966	−	0.117630i
$253$			5.37586i			0.337978i
$254$	−6.03573	−	10.4542i	−0.378715	−	0.655954i
$255$	−19.5285	+	15.8095i	−1.22292	+	0.990029i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.54939	−	16.5400i	−0.595675	−	1.03174i	−0.993451	−	0.114257i	$-0.963551\pi$
$257$	−9.54939	−	16.5400i	−0.595675	−	1.03174i	0.397776	−	0.917482i	$-0.369782\pi$
$258$	2.05940	−	5.36277i	0.128213	−	0.333872i
$259$	9.81284	−	15.9558i	0.609740	−	0.991448i
$260$	9.00282	−	1.75954i	0.558331	−	0.109122i
$261$	−17.7872	−	3.78581i	−1.10100	−	0.234336i
$262$	−8.61673	+	14.9246i	−0.532343	+	0.922045i
$263$	4.49853	+	2.59723i	0.277391	+	0.160152i	0.632242	−	0.774771i	$-0.282135\pi$
$263$	4.49853	+	2.59723i	0.277391	+	0.160152i	−0.354851	+	0.934923i	$0.615468\pi$
$264$	7.03165	−	1.11273i	0.432768	−	0.0684840i
$265$	−12.9127			−0.793222
$266$	−0.621153	+	22.3564i	−0.0380853	+	1.37076i
$267$	6.19590	+	2.37934i	0.379183	+	0.145613i
$268$	2.80901	−	1.62178i	0.171587	−	0.0990660i
$269$	3.10207	−	5.37294i	0.189136	−	0.327594i	−0.755826	−	0.654772i	$-0.772765\pi$
$269$	3.10207	−	5.37294i	0.189136	−	0.327594i	0.944963	+	0.327179i	$0.106098\pi$
$270$	−13.2015	−	0.697216i	−0.803419	−	0.0424312i
$271$	−12.8489	−	22.2550i	−0.780518	−	1.35190i	−0.931640	−	0.363382i	$-0.881622\pi$
$271$	−12.8489	−	22.2550i	−0.780518	−	1.35190i	0.151123	−	0.988515i	$-0.451711\pi$
$272$	5.70178			0.345721
$273$	3.30557	−	16.1887i	0.200062	−	0.979783i
$274$	−13.0485			−0.788292
$275$	−3.02685	−	5.24266i	−0.182526	−	0.316144i
$276$	−1.76072	+	1.42541i	−0.105983	+	0.0857998i
$277$	−12.1581	+	21.0584i	−0.730507	+	1.26528i	0.226159	+	0.974090i	$0.427383\pi$
$277$	−12.1581	+	21.0584i	−0.730507	+	1.26528i	−0.956667	+	0.291186i	$0.905950\pi$
$278$	−0.539835	+	0.311674i	−0.0323772	+	0.0186930i
$279$	−0.00586423	−	0.00528304i	−0.000351082	−	0.000316287i
$280$	3.52623	−	5.73372i	0.210733	−	0.342655i
$281$	22.7215			1.35545			0.677724	−	0.735316i	$-0.262966\pi$
$281$	22.7215			1.35545			0.677724	+	0.735316i	$0.262966\pi$
$282$	1.15233	+	7.28186i	0.0686201	+	0.433628i
$283$	16.6217	+	9.59655i	0.988059	+	0.570456i	0.904693	−	0.426063i	$-0.140100\pi$
$283$	16.6217	+	9.59655i	0.988059	+	0.570456i	0.0833652	+	0.996519i	$0.473433\pi$
$284$	−3.34433	+	5.79254i	−0.198449	+	0.343724i
$285$	5.82224	+	36.7923i	0.344880	+	2.17939i
$286$	2.84262	+	14.5445i	0.168088	+	0.860035i
$287$	3.16418	+	5.84995i	0.186775	+	0.345312i
$288$	2.22889	+	2.00799i	0.131339	+	0.118322i
$289$	−7.75517	−	13.4323i	−0.456186	−	0.790138i
$290$	7.71125	−	13.3563i	0.452820	−	0.784308i
$291$	−4.26438	−	5.26752i	−0.249982	−	0.308787i
$292$	−1.31969	−	2.28578i	−0.0772292	−	0.133765i
$293$		−	11.7362i		−	0.685634i	−0.939402	−	0.342817i	$-0.888619\pi$
$293$		−	11.7362i		−	0.685634i	0.939402	−	0.342817i	$-0.111381\pi$
$294$	−7.09382	−	9.83248i	−0.413720	−	0.573442i
$295$	4.94505			0.287912
$296$	−6.13142	+	3.53998i	−0.356382	+	0.205757i
$297$	1.12639	−	21.3277i	0.0653596	−	1.23756i
$298$	0.986187	−	1.70813i	0.0571283	−	0.0989491i
$299$	−3.09746	−	3.55587i	−0.179131	−	0.205641i
$300$	0.914525	−	2.38146i	0.0528001	−	0.137494i
$301$	7.71832	−	4.17476i	0.444877	−	0.240629i
$302$			9.40094i			0.540963i
$303$	−26.5097	+	4.19505i	−1.52294	+	0.241000i
$304$	4.22658	−	7.32066i	0.242411	−	0.419869i
$305$	4.63544	−	8.02882i	0.265425	−	0.459729i
$306$	3.56091	−	16.7306i	0.203564	−	0.956425i
$307$	27.2408			1.55471			0.777357	−	0.629060i	$-0.216560\pi$
$307$	27.2408			1.55471			0.777357	+	0.629060i	$0.216560\pi$
$308$	9.26310	+	5.69681i	0.527814	+	0.324606i
$309$	21.4920	+	8.25334i	1.22264	+	0.469516i
$310$	0.00579695	−	0.00334687i	0.000329245	−	0.000190089i
$311$	1.45991	−	2.52863i	0.0827837	−	0.143386i	−0.821661	−	0.569977i	$-0.806952\pi$
$311$	1.45991	−	2.52863i	0.0827837	−	0.143386i	0.904445	+	0.426591i	$0.140286\pi$
$312$	−4.00995	+	4.78751i	−0.227019	+	0.271039i
$313$	5.81374	−	3.35656i	0.328612	−	0.189724i	−0.326613	−	0.945158i	$-0.605907\pi$
$313$	5.81374	−	3.35656i	0.328612	−	0.189724i	0.655225	+	0.755434i	$0.272574\pi$
$314$			7.30149i			0.412047i
$315$	−14.6221	−	13.9278i	−0.823860	−	0.784742i
$316$	14.1572			0.796404
$317$	−7.72251	−	13.3758i	−0.433740	−	0.751259i	0.563452	−	0.826149i	$-0.309473\pi$
$317$	−7.72251	−	13.3758i	−0.433740	−	0.751259i	−0.997192	+	0.0748897i	$0.976140\pi$
$318$	6.83252	−	5.53134i	0.383149	−	0.310182i
$319$	21.5777	+	12.4579i	1.20812	+	0.697509i
$320$	−2.20332	+	1.27209i	−0.123169	+	0.0711119i
$321$	23.0713	+	8.85982i	1.28772	+	0.494507i
$322$	−3.45909	−	0.0961081i	−0.192768	−	0.00535589i
$323$	−48.1981			−2.68182
$324$	7.28400	−	5.28614i	0.404667	−	0.293674i
$325$	5.02282	+	1.72375i	0.278616	+	0.0956163i
$326$	13.1037	+	7.56540i	0.725744	+	0.419009i
$327$	−2.88236	−	18.2144i	−0.159395	−	1.00726i
$328$		−	2.51379i		−	0.138801i
$329$	−5.89952	+	9.59271i	−0.325251	+	0.528863i
$330$	16.9085	+	6.49317i	0.930781	+	0.357437i
$331$	−4.14357	+	2.39229i	−0.227751	+	0.131492i	−0.609534	−	0.792760i	$-0.708643\pi$
$331$	−4.14357	+	2.39229i	−0.227751	+	0.131492i	0.381783	+	0.924252i	$0.375310\pi$
$332$	9.63888	+	5.56501i	0.529002	+	0.305420i
$333$	6.55804	+	20.2021i	0.359378	+	1.10707i
$334$	21.0214	−	12.1367i	1.15024	−	0.664092i
$335$	8.25219			0.450865
$336$	0.590277	+	4.54440i	0.0322022	+	0.247917i
$337$	26.6494			1.45169			0.725843	−	0.687860i	$-0.241450\pi$
$337$	26.6494			1.45169			0.725843	+	0.687860i	$0.241450\pi$
$338$	−10.2605	−	7.98261i	−0.558098	−	0.434197i
$339$	1.15002	−	0.931015i	0.0624607	−	0.0505658i
$340$	12.5629	+	7.25317i	0.681317	+	0.393358i
$341$	0.00540703	+	0.00936526i	0.000292807	+	0.000507157i
$342$	−18.8412	−	16.9739i	−1.01882	−	0.917843i
$343$	1.54153	−	18.4560i	0.0832347	−	0.996530i
$344$	−3.31665			−0.178822
$345$	−5.69269	+	0.900847i	−0.306484	+	0.0485000i
$346$	−0.204681	+	0.354517i	−0.0110037	+	0.0190590i
$347$	−5.45892	−	3.15171i	−0.293050	−	0.169193i	0.346266	−	0.938136i	$-0.387449\pi$
$347$	−5.45892	−	3.15171i	−0.293050	−	0.169193i	−0.639317	+	0.768944i	$0.720783\pi$
$348$	1.64109	+	10.3705i	0.0879714	+	0.555915i
$349$	−9.52826			−0.510036			−0.255018	−	0.966936i	$-0.582081\pi$
$349$	−9.52826			−0.510036			−0.255018	+	0.966936i	$0.582081\pi$
$350$	3.42749	−	1.85390i	0.183207	−	0.0990949i
$351$	11.5436	+	14.7562i	0.616149	+	0.787629i
$352$	−2.05512	−	3.55958i	−0.109538	−	0.189726i
$353$	−14.3774	−	8.30082i	−0.765234	−	0.441808i	0.0659376	−	0.997824i	$-0.478996\pi$
$353$	−14.3774	−	8.30082i	−0.765234	−	0.441808i	−0.831172	+	0.556016i	$0.812329\pi$
$354$	−2.61658	+	2.11828i	−0.139070	+	0.112585i
$355$	−14.7373	+	8.50856i	−0.782172	+	0.451587i
$356$		−	3.83190i		−	0.203091i
$357$	20.7569	−	15.8703i	1.09857	−	0.839946i
$358$			23.6636i			1.25066i
$359$	−8.18866	−	14.1832i	−0.432181	−	0.748559i	0.564880	−	0.825173i	$-0.308922\pi$
$359$	−8.18866	−	14.1832i	−0.432181	−	0.748559i	−0.997061	+	0.0766138i	$0.975589\pi$
$360$	2.35662	+	7.25960i	0.124205	+	0.382615i
$361$	−26.2280	+	45.4283i	−1.38042	+	2.39096i
$362$	12.3190	−	7.11236i	0.647471	−	0.373817i
$363$	−3.65982	+	9.53032i	−0.192091	+	0.500212i
$364$	−9.40947	+	1.56906i	−0.493190	+	0.0822410i
$365$		−	6.71506i		−	0.351482i
$366$	0.986500	+	6.23395i	0.0515652	+	0.325854i
$367$	−26.9853	−	15.5800i	−1.40862	−	0.813269i	−0.413368	−	0.910564i	$-0.635648\pi$
$367$	−26.9853	−	15.5800i	−1.40862	−	0.813269i	−0.995256	+	0.0972954i	$0.968981\pi$
$368$	1.13269	+	0.653959i	0.0590456	+	0.0340900i
$369$	−7.37615	−	1.56993i	−0.383987	−	0.0817271i
$370$	−18.0127			−0.936434
$371$	13.4231	+	0.372949i	0.696891	+	0.0193626i
$372$	−0.00163367	+	0.00425414i	−8.47018e−5	+	0.000220567i
$373$	−11.8848	−	20.5851i	−0.615372	−	1.06585i	−0.990319	−	0.138809i	$-0.955673\pi$
$373$	−11.8848	−	20.5851i	−0.615372	−	1.06585i	0.374948	−	0.927046i	$-0.377661\pi$
$374$	−11.7179	+	20.2959i	−0.605916	+	1.04948i
$375$	−12.0805	+	9.77988i	−0.623833	+	0.505031i
$376$	3.68624	−	2.12825i	0.190103	−	0.109756i
$377$	−21.4506	+	4.19237i	−1.10476	+	0.215918i
$378$	13.7032	+	1.10606i	0.704815	+	0.0568898i
$379$		−	5.87885i		−	0.301976i	−0.988536	−	0.150988i	$-0.951755\pi$
$379$		−	5.87885i		−	0.301976i	0.988536	−	0.150988i	$-0.0482455\pi$
$380$	18.6250	−	10.7532i	0.955445	−	0.551626i
$381$	13.1559	+	16.2506i	0.673996	+	0.832545i
$382$	13.8603	+	8.00228i	0.709157	+	0.409432i
$383$	−12.8839	+	7.43851i	−0.658336	+	0.380090i	−0.791643	−	0.610985i	$-0.790774\pi$
$383$	−12.8839	+	7.43851i	−0.658336	+	0.380090i	0.133307	+	0.991075i	$0.457440\pi$
$384$	0.620929	−	1.61693i	0.0316867	−	0.0825134i
$385$	13.1628	+	24.3354i	0.670836	+	1.24025i
$386$		−	16.9566i		−	0.863068i
$387$	−2.07133	+	9.73196i	−0.105292	+	0.494703i
$388$	−1.95644	+	3.38865i	−0.0993229	+	0.172032i
$389$	26.8563	+	15.5055i	1.36167	+	0.786158i	0.989846	−	0.142146i	$-0.0454004\pi$
$389$	26.8563	+	15.5055i	1.36167	+	0.786158i	0.371821	+	0.928305i	$0.378734\pi$
$390$	−14.9254	+	5.44741i	−0.755775	+	0.275840i
$391$		−	7.45747i		−	0.377140i
$392$	−3.83121	+	5.85849i	−0.193505	+	0.295898i
$393$	10.7008	−	27.8652i	0.539782	−	1.40561i
$394$	1.28282	+	2.22190i	0.0646273	+	0.111938i
$395$	31.1928	+	18.0092i	1.56948	+	0.906140i
$396$	−11.7282	+	3.80724i	−0.589367	+	0.191321i
$397$	7.10552	+	12.3071i	0.356616	+	0.617677i	0.987393	−	0.158287i	$-0.0505972\pi$
$397$	7.10552	+	12.3071i	0.356616	+	0.617677i	−0.630777	+	0.775964i	$0.717264\pi$
$398$			21.6468i			1.08505i
$399$	−4.98971	−	38.4146i	−0.249798	−	1.92313i
$400$	−1.47283			−0.0736416
$401$	19.1854	+	33.2301i	0.958073	+	1.65943i	0.727174	+	0.686453i	$0.240833\pi$
$401$	19.1854	+	33.2301i	0.958073	+	1.65943i	0.230899	+	0.972978i	$0.425833\pi$
$402$	−4.36649	+	3.53494i	−0.217781	+	0.176307i
$403$	−0.00897256	−	0.00307923i	−0.000446955	−	0.000153387i
$404$	7.74790	+	13.4198i	0.385473	+	0.667658i
$405$	22.7734	−	2.38117i	1.13162	−	0.118321i
$406$	−8.40179	+	13.6615i	−0.416974	+	0.678006i
$407$		−	29.1004i		−	1.44245i
$408$	−9.75440	+	1.54360i	−0.482915	+	0.0764195i
$409$	−2.09152	+	3.62262i	−0.103419	+	0.179127i	−0.913091	−	0.407755i	$-0.866312\pi$
$409$	−2.09152	+	3.62262i	−0.103419	+	0.179127i	0.809672	+	0.586882i	$0.199645\pi$
$410$	3.19776	−	5.53868i	0.157926	−	0.273536i
$411$	22.3230	−	3.53253i	1.10111	−	0.174247i
$412$		−	13.2919i		−	0.654846i
$413$	−5.14050	−	0.142824i	−0.252947	−	0.00702793i
$414$	2.62629	−	2.91521i	0.129075	−	0.143275i
$415$	14.1584	+	24.5230i	0.695007	+	1.20379i
$416$	3.41032	+	1.17036i	0.167204	+	0.0573817i
$417$	0.839153	−	0.679346i	0.0410935	−	0.0332677i
$418$	17.3723	+	30.0897i	0.849706	+	1.47173i
$419$	24.4059			1.19231			0.596154	−	0.802870i	$-0.296695\pi$
$419$	24.4059			1.19231			0.596154	+	0.802870i	$0.296695\pi$
$420$	−4.48031	+	10.7637i	−0.218617	+	0.525213i
$421$		−	7.06979i		−	0.344560i	−0.985048	−	0.172280i	$-0.944887\pi$
$421$		−	7.06979i		−	0.344560i	0.985048	−	0.172280i	$-0.0551135\pi$
$422$	−3.50357	−	6.06837i	−0.170551	−	0.295404i
$423$	−3.94272	−	12.1456i	−0.191701	−	0.590538i
$424$	−4.39543	−	2.53770i	−0.213461	−	0.123242i
$425$	4.19888	+	7.27268i	0.203676	+	0.352777i
$426$	4.15318	−	10.8151i	0.201222	−	0.523991i
$427$	−5.05054	+	8.21226i	−0.244413	+	0.397419i
$428$		−	14.2686i		−	0.689701i
$429$	−8.80057	−	24.1127i	−0.424895	−	1.16417i
$430$	−7.30764	−	4.21907i	−0.352406	−	0.203462i
$431$	1.83652	−	3.18094i	0.0884620	−	0.153221i	−0.818399	−	0.574650i	$-0.805138\pi$
$431$	1.83652	−	3.18094i	0.0884620	−	0.153221i	0.906861	+	0.421429i	$0.138471\pi$
$432$	−4.35672	−	2.83179i	−0.209613	−	0.136245i
$433$		−	30.9079i		−	1.48534i	−0.669658	−	0.742669i	$-0.733559\pi$
$433$		−	30.9079i		−	1.48534i	0.669658	−	0.742669i	$-0.266441\pi$
$434$	−0.00612273	+	0.00331172i	−0.000293900	+	0.000158968i
$435$	−9.57629	+	24.9370i	−0.459148	+	1.19564i
$436$	−9.22052	+	5.32347i	−0.441583	+	0.254948i
$437$	−9.57483	−	5.52803i	−0.458026	−	0.264441i
$438$	2.87649	+	3.55315i	0.137444	+	0.169776i
$439$	31.8737	−	18.4023i	1.52125	−	0.878294i	0.521564	−	0.853212i	$-0.325349\pi$
$439$	31.8737	−	18.4023i	1.52125	−	0.878294i	0.999685	−	0.0250815i	$-0.00798452\pi$
$440$		−	10.4572i		−	0.498527i
$441$	14.7977	+	14.9006i	0.704653	+	0.709552i
$442$	−3.94332	−	20.1763i	−0.187565	−	0.959690i
$443$	31.8442	−	18.3852i	1.51296	−	0.873509i	0.513077	−	0.858342i	$-0.328505\pi$
$443$	31.8442	−	18.3852i	1.51296	−	0.873509i	0.999885	−	0.0151669i	$-0.00482798\pi$
$444$	9.53106	−	7.71597i	0.452324	−	0.366184i
$445$	4.87452	−	8.44292i	0.231074	−	0.400233i
$446$	−10.5791	−	18.3235i	−0.500935	−	0.867645i
$447$	−1.22470	+	3.18918i	−0.0579265	+	0.150843i
$448$	2.32714	−	1.25873i	0.109947	−	0.0594693i
$449$	−3.94653			−0.186248			−0.0931240	−	0.995655i	$-0.529685\pi$
$449$	−3.94653			−0.186248			−0.0931240	+	0.995655i	$0.529685\pi$
$450$	−0.919822	+	4.32169i	−0.0433608	+	0.203727i
$451$	8.94802	+	5.16614i	0.421346	+	0.243264i
$452$	−0.739822	−	0.427136i	−0.0347983	−	0.0200908i
$453$	−2.54504	−	16.0828i	−0.119576	−	0.755635i
$454$			13.4666i			0.632017i
$455$	−22.7281	−	8.51253i	−1.06551	−	0.399074i
$456$	−5.24882	+	13.6681i	−0.245799	+	0.640069i
$457$	0.843279	−	0.486868i	0.0394469	−	0.0227747i	−0.480147	−	0.877188i	$-0.659417\pi$
$457$	0.843279	−	0.486868i	0.0394469	−	0.0227747i	0.519594	+	0.854413i	$0.326083\pi$
$458$	1.12680	−	1.95167i	0.0526517	−	0.0911954i
$459$	−1.56254	+	29.5861i	−0.0729331	+	1.38096i
$460$	1.66379	+	2.88177i	0.0775745	+	0.134363i
$461$		−	10.2088i		−	0.475471i	−0.971330	−	0.237736i	$-0.923595\pi$
$461$		−	10.2088i		−	0.475471i	0.971330	−	0.237736i	$-0.0764052\pi$
$462$	−17.3892	−	7.23816i	−0.809020	−	0.336750i
$463$		−	11.4435i		−	0.531824i	−0.963997	−	0.265912i	$-0.914327\pi$
$463$		−	11.4435i		−	0.531824i	0.963997	−	0.265912i	$-0.0856731\pi$
$464$	5.24975	−	3.03094i	0.243713	−	0.140708i
$465$	−0.00901113	+	0.00729506i	−0.000417881	+	0.000338300i
$466$	−1.12902	−	0.651840i	−0.0523008	−	0.0301959i
$467$	−12.8601	−	22.2744i	−0.595097	−	1.03074i	−0.993533	−	0.113542i	$-0.963780\pi$
$467$	−12.8601	−	22.2744i	−0.595097	−	1.03074i	0.398437	−	0.917196i	$-0.369553\pi$
$468$	5.56400	−	9.27588i	0.257196	−	0.428778i
$469$	−8.57834	−	0.238342i	−0.396111	−	0.0110056i
$470$	10.8293			0.499518
$471$	−1.97667	−	12.4911i	−0.0910803	−	0.575560i
$472$	1.68327	+	0.971837i	0.0774789	+	0.0447324i
$473$	6.81612	−	11.8059i	0.313405	−	0.542834i
$474$	−24.2196	+	3.83266i	−1.11244	+	0.176040i
$475$	12.4501			0.571250
$476$	−12.8499	−	7.90269i	−0.588974	−	0.362219i
$477$	−10.1914	+	11.3125i	−0.466631	+	0.517965i
$478$	1.75061	+	3.03215i	0.0800711	+	0.138687i
$479$	27.5828	+	15.9249i	1.26029	+	0.727629i	0.973131	−	0.230254i	$-0.0739557\pi$
$479$	27.5828	+	15.9249i	1.26029	+	0.727629i	0.287160	+	0.957883i	$0.407289\pi$
$480$	3.42498	−	2.77273i	0.156328	−	0.126557i
$481$	16.7670	+	19.2484i	0.764511	+	0.877653i
$482$	−13.1946			−0.600996
$483$	5.94371	−	0.772034i	0.270448	−	0.0351288i
$484$	5.89410			0.267914
$485$	−8.62131	+	4.97752i	−0.391474	+	0.226017i
$486$	−11.0301	+	11.0153i	−0.500337	+	0.499663i
$487$	−17.8940	−	10.3311i	−0.810854	−	0.468147i	0.0363981	−	0.999337i	$-0.488412\pi$
$487$	−17.8940	−	10.3311i	−0.810854	−	0.468147i	−0.847252	+	0.531190i	$0.821745\pi$
$488$	3.15576	−	1.82198i	0.142855	−	0.0824772i
$489$	−24.4654	−	9.39516i	−1.10636	−	0.424864i
$490$	−15.8939	+	8.03450i	−0.718013	+	0.362962i
$491$		−	9.08674i		−	0.410079i	−0.978754	−	0.205039i	$-0.934268\pi$
$491$		−	9.08674i		−	0.410079i	0.978754	−	0.205039i	$-0.0657322\pi$
$492$	0.680538	+	4.30050i	0.0306810	+	0.193881i
$493$	−29.9329	−	17.2818i	−1.34811	−	0.778332i
$494$	−28.8280	−	9.89327i	−1.29703	−	0.445119i
$495$	−30.6842	−	6.53079i	−1.37915	−	0.293537i
$496$	0.00263100			0.000118136
$497$	15.5655	−	8.41920i	0.698207	−	0.377653i
$498$	−17.9964	−	6.91096i	−0.806438	−	0.309687i
$499$	14.4611	−	8.34913i	0.647368	−	0.373758i	−0.140079	−	0.990140i	$-0.544736\pi$
$499$	14.4611	−	8.34913i	0.647368	−	0.373758i	0.787447	+	0.616382i	$0.211402\pi$
$500$	7.77148	+	4.48687i	0.347551	+	0.200659i
$501$	−32.6770	+	26.4540i	−1.45990	+	1.18188i
$502$	−14.2179	−	24.6261i	−0.634575	−	1.09912i
$503$	29.9262			1.33434			0.667171	−	0.744904i	$-0.267505\pi$
$503$	29.9262			1.33434			0.667171	+	0.744904i	$0.267505\pi$
$504$	−2.24009	−	7.61459i	−0.0997816	−	0.339181i
$505$			39.4241i			1.75435i
$506$	−4.65564	+	2.68793i	−0.206968	+	0.119493i
$507$	19.7144	+	10.8786i	0.875545	+	0.483136i
$508$	6.03573	−	10.4542i	0.267792	−	0.463829i
$509$	29.2792	−	16.9043i	1.29778	−	0.749272i	0.317757	−	0.948172i	$-0.397070\pi$
$509$	29.2792	−	16.9043i	1.29778	−	0.749272i	0.980020	+	0.198900i	$0.0637369\pi$
$510$	−23.4557	−	9.00741i	−1.03863	−	0.398855i
$511$	−0.193947	+	6.98046i	−0.00857969	+	0.308798i
$512$	−1.00000			−0.0441942
$513$	36.8280	+	23.9376i	1.62600	+	1.05687i
$514$	9.54939	−	16.5400i	0.421206	−	0.729550i
$515$	16.9085	−	29.2864i	0.745077	−	1.29051i
$516$	5.67400	−	0.897889i	0.249784	−	0.0395274i
$517$			17.4952i			0.769440i
$518$	18.7246	+	0.520247i	0.822711	+	0.0228583i
$519$	0.254185	−	0.661907i	0.0111575	−	0.0290545i
$520$	6.02522	+	6.91691i	0.264223	+	0.303326i
$521$	12.3261	−	21.3495i	0.540017	−	0.935338i	−0.458885	−	0.888496i	$-0.651751\pi$
$521$	12.3261	−	21.3495i	0.540017	−	0.935338i	0.998902	−	0.0468419i	$-0.0149157\pi$
$522$	−5.61502	−	17.2971i	−0.245763	−	0.757074i
$523$	−9.97765	+	5.76060i	−0.436292	+	0.251893i	−0.702024	−	0.712154i	$-0.747720\pi$
$523$	−9.97765	+	5.76060i	−0.436292	+	0.251893i	0.265732	+	0.964047i	$0.414387\pi$
$524$	−17.2335			−0.752847
$525$	−5.36174	+	4.09947i	−0.234005	+	0.178916i
$526$			5.19445i			0.226489i
$527$	−0.00750071	−	0.0129916i	−0.000326736	−	0.000565923i
$528$	4.47948	+	5.53322i	0.194944	+	0.240803i
$529$	−10.6447	+	18.4371i	−0.462812	+	0.801614i
$530$	−6.45636	−	11.1827i	−0.280446	−	0.485747i
$531$	3.90288	−	4.33224i	0.169371	−	0.188003i
$532$	−19.6717	+	10.6402i	−0.852878	+	0.461313i
$533$	−8.89530	+	1.73852i	−0.385298	+	0.0753037i
$534$	1.03738	+	6.55548i	0.0448918	+	0.283683i
$535$	18.1510	−	31.4384i	0.784735	−	1.35920i
$536$	2.80901	+	1.62178i	0.121331	+	0.0700502i
$537$	−6.40626	−	40.4829i	−0.276451	−	1.74696i
$538$	6.20413			0.267479
$539$	−12.9801	−	25.6774i	−0.559094	−	1.10600i
$540$	−5.99696	−	11.7815i	−0.258068	−	0.506994i
$541$	15.5915	−	9.00176i	0.670331	−	0.387016i	−0.125871	−	0.992047i	$-0.540173\pi$
$541$	15.5915	−	9.00176i	0.670331	−	0.387016i	0.796202	+	0.605031i	$0.206839\pi$
$542$	12.8489	−	22.2550i	0.551909	−	0.955935i
$543$	−19.1494	+	15.5026i	−0.821778	+	0.665279i
$544$	2.85089	+	4.93789i	0.122231	+	0.211710i
$545$	−27.0877			−1.16031
$546$	15.6726	−	5.23163i	0.670725	−	0.223893i
$547$	−31.6765			−1.35439			−0.677194	−	0.735804i	$-0.736804\pi$
$547$	−31.6765			−1.35439			−0.677194	+	0.735804i	$0.736804\pi$
$548$	−6.52427	−	11.3004i	−0.278703	−	0.482728i
$549$	−3.37534	−	10.3978i	−0.144056	−	0.443765i
$550$	3.02685	−	5.24266i	0.129065	−	0.223548i
$551$	−44.3770	+	25.6211i	−1.89052	+	1.09149i
$552$	−2.11481	−	0.812125i	−0.0900121	−	0.0345663i
$553$	−31.9055	−	19.6219i	−1.35676	−	0.834407i
$554$	−24.3161			−1.03309
$555$	30.8154	−	4.87642i	1.30804	−	0.206992i
$556$	−0.539835	−	0.311674i	−0.0228941	−	0.0132179i
$557$	14.7789	−	25.5978i	0.626201	−	1.08461i	−0.362106	−	0.932137i	$-0.617942\pi$
$557$	14.7789	−	25.5978i	0.626201	−	1.08461i	0.988307	−	0.152475i	$-0.0487244\pi$
$558$	0.00164313	−	0.00772009i	6.95593e−5	−	0.000326817i
$559$	2.29377	+	11.7363i	0.0970163	+	0.496392i
$560$	6.72866	+	0.186950i	0.284338	+	0.00790009i
$561$	14.5519	−	37.8938i	0.614383	−	1.59988i
$562$	11.3607	+	19.6774i	0.479224	+	0.830040i
$563$	11.5996	−	20.0912i	0.488866	−	0.846741i	−0.511052	−	0.859550i	$-0.670744\pi$
$563$	11.5996	−	20.0912i	0.488866	−	0.846741i	0.999918	+	0.0128088i	$0.00407729\pi$
$564$	−5.73011	+	4.63887i	−0.241281	+	0.195332i
$565$	−1.08671	−	1.88224i	−0.0457182	−	0.0791863i
$566$			19.1931i			0.806747i
$567$	−23.7423	+	1.81753i	−0.997083	+	0.0763292i
$568$	−6.68865			−0.280650
$569$	−15.1314	+	8.73610i	−0.634340	+	0.366236i	−0.782431	−	0.622738i	$-0.786020\pi$
$569$	−15.1314	+	8.73610i	−0.634340	+	0.366236i	0.148091	+	0.988974i	$0.452687\pi$
$570$	−28.9519	+	23.4383i	−1.21266	+	0.981724i
$571$	4.98953	−	8.64212i	0.208805	−	0.361662i	−0.742533	−	0.669809i	$-0.766376\pi$
$571$	4.98953	−	8.64212i	0.208805	−	0.361662i	0.951339	+	0.308148i	$0.0997091\pi$
$572$	−11.1746	+	9.73404i	−0.467234	+	0.407001i
$573$	−25.8782	−	9.93770i	−1.08108	−	0.415153i
$574$	−3.48412	+	5.66523i	−0.145424	+	0.236462i
$575$			1.92634i			0.0803341i
$576$	−0.624526	+	2.93427i	−0.0260219	+	0.122261i
$577$	8.91246	−	15.4368i	0.371031	−	0.642644i	−0.618694	−	0.785632i	$-0.712338\pi$
$577$	8.91246	−	15.4368i	0.371031	−	0.642644i	0.989724	+	0.142988i	$0.0456712\pi$
$578$	7.75517	−	13.4323i	0.322572	−	0.558712i
$579$	4.59052	+	29.0087i	0.190776	+	1.20556i
$580$	15.4225			0.640385
$581$	−14.0097	−	25.9012i	−0.581219	−	1.07456i
$582$	2.42962	−	6.32682i	0.100711	−	0.262255i
$583$	18.0663	−	10.4306i	0.748229	−	0.431990i
$584$	1.31969	−	2.28578i	0.0546093	−	0.0945860i
$585$	24.0590	−	13.3598i	0.994717	−	0.552362i
$586$	10.1638	−	5.86808i	0.419863	−	0.242408i
$587$			47.7903i			1.97252i	0.165206	+	0.986259i	$0.447171\pi$
$587$			47.7903i			1.97252i	−0.165206	+	0.986259i	$0.552829\pi$
$588$	4.96826	−	11.0597i	0.204888	−	0.456093i
$589$	−0.0222403			−0.000916396
$590$	2.47253	+	4.28254i	0.101792	+	0.176309i
$591$	−2.79611	−	3.45386i	−0.115017	−	0.142073i
$592$	−6.13142	−	3.53998i	−0.252000	−	0.145492i
$593$	−8.78037	+	5.06935i	−0.360566	+	0.208173i	−0.669329	−	0.742966i	$-0.733418\pi$
$593$	−8.78037	+	5.06935i	−0.360566	+	0.208173i	0.308763	+	0.951139i	$0.400085\pi$
$594$	19.0335	−	9.68838i	0.780956	−	0.397519i
$595$	−18.2595	−	33.7584i	−0.748568	−	1.38396i
$596$	1.97237			0.0807916
$597$	−5.86025	−	37.0325i	−0.239844	−	1.51564i
$598$	1.53074	−	4.46042i	0.0625966	−	0.182400i
$599$	10.0365	+	5.79458i	0.410081	+	0.236760i	0.690824	−	0.723023i	$-0.257248\pi$
$599$	10.0365	+	5.79458i	0.410081	+	0.236760i	−0.280744	+	0.959783i	$0.590581\pi$
$600$	2.51967	−	0.398728i	0.102865	−	0.0162780i
$601$			4.44714i			0.181403i	0.995878	+	0.0907013i	$0.0289109\pi$
$601$			4.44714i			0.181403i	−0.995878	+	0.0907013i	$0.971089\pi$
$602$	7.47461	+	4.59688i	0.304642	+	0.187355i
$603$	6.51304	−	7.22955i	0.265232	−	0.294410i
$604$	−8.14145	+	4.70047i	−0.331271	+	0.191259i
$605$	12.9866	+	7.49782i	0.527981	+	0.304830i
$606$	−16.8879	−	20.8605i	−0.686022	−	0.847400i
$607$	5.35667	−	3.09268i	0.217421	−	0.125528i	−0.387335	−	0.921939i	$-0.626604\pi$
$607$	5.35667	−	3.09268i	0.217421	−	0.125528i	0.604755	+	0.796411i	$0.293271\pi$
$608$	8.45317			0.342821
$609$	10.6750	−	25.6461i	0.432574	−	1.03923i
$610$	9.27088			0.375367
$611$	−10.0804	−	11.5722i	−0.407810	−	0.468162i
$612$	16.2696	−	5.28146i	0.657659	−	0.213490i
$613$	−19.9940	−	11.5435i	−0.807549	−	0.466239i	0.0385548	−	0.999256i	$-0.487725\pi$
$613$	−19.9940	−	11.5435i	−0.807549	−	0.466239i	−0.846104	+	0.533018i	$0.821058\pi$
$614$	13.6204	+	23.5912i	0.549674	+	0.952064i
$615$	−3.97117	+	10.3411i	−0.160133	+	0.416993i
$616$	−0.302028	+	10.8705i	−0.0121690	+	0.437984i
$617$	−14.5000			−0.583749			−0.291874	−	0.956457i	$-0.594279\pi$
$617$	−14.5000			−0.583749			−0.291874	+	0.956457i	$0.594279\pi$
$618$	3.59841	+	22.7393i	0.144749	+	0.914709i
$619$	−11.4323	+	19.8013i	−0.459503	+	0.795882i	−0.998935	−	0.0461472i	$-0.985306\pi$
$619$	−11.4323	+	19.8013i	−0.459503	+	0.795882i	0.539432	+	0.842029i	$0.318639\pi$
$620$	0.00579695	+	0.00334687i	0.000232811	+	0.000134414i
$621$	−3.70375	+	5.69823i	−0.148626	+	0.228662i
$622$	2.91981			0.117074
$623$	−5.31103	+	8.63582i	−0.212782	+	0.345987i
$624$	−6.15108	−	1.07897i	−0.246240	−	0.0431932i
$625$	15.0975	+	26.1496i	0.603899	+	1.04598i
$626$	5.81374	+	3.35656i	0.232364	+	0.134155i
$627$	−37.8658	−	46.7733i	−1.51221	−	1.86794i
$628$	−6.32327	+	3.65074i	−0.252326	+	0.145681i
$629$			40.3684i			1.60959i
$630$	4.75079	−	19.6270i	0.189276	−	0.781958i
$631$		−	10.1877i		−	0.405568i	−0.979224	−	0.202784i	$-0.935001\pi$
$631$		−	10.1877i		−	0.405568i	0.979224	−	0.202784i	$-0.0649989\pi$
$632$	7.07859	+	12.2605i	0.281571	+	0.487696i
$633$	7.63662	+	9.43304i	0.303529	+	0.374930i
$634$	7.72251	−	13.3758i	0.306700	−	0.531220i
$635$	26.5973	−	15.3559i	1.05548	−	0.609382i
$636$	8.20655	+	3.15147i	0.325411	+	0.124964i
$637$	23.3805	+	9.50541i	0.926369	+	0.376618i
$638$			24.9158i			0.986427i
$639$	−4.17724	+	19.6263i	−0.165249	+	0.776406i
$640$	−2.20332	−	1.27209i	−0.0870939	−	0.0502837i
$641$	24.5592	+	14.1793i	0.970030	+	0.560047i	0.899245	−	0.437445i	$-0.144116\pi$
$641$	24.5592	+	14.1793i	0.970030	+	0.560047i	0.0707844	+	0.997492i	$0.477450\pi$
$642$	3.86283	+	24.4103i	0.152454	+	0.963396i
$643$	7.46124			0.294243			0.147121	−	0.989118i	$-0.452999\pi$
$643$	7.46124			0.294243			0.147121	+	0.989118i	$0.452999\pi$
$644$	−1.64631	−	3.04372i	−0.0648739	−	0.119939i
$645$	13.6438	+	5.23949i	0.537226	+	0.206305i
$646$	−24.0991	−	41.7408i	−0.948165	−	1.64227i
$647$	−12.5324	+	21.7068i	−0.492701	+	0.853382i	−0.999965	−	0.00840826i	$-0.997324\pi$
$647$	−12.5324	+	21.7068i	−0.492701	+	0.853382i	0.507264	+	0.861791i	$0.330657\pi$
$648$	8.21993	+	3.66506i	0.322910	+	0.143977i
$649$	−6.91866	+	3.99449i	−0.271581	+	0.156797i
$650$	1.01860	+	5.21177i	0.0399529	+	0.204422i
$651$	0.00957798	−	0.00732312i	0.000375391	−	0.000287016i
$652$			15.1308i			0.592568i
$653$	−9.06026	+	5.23094i	−0.354555	+	0.204703i	−0.666690	−	0.745335i	$-0.732289\pi$
$653$	−9.06026	+	5.23094i	−0.354555	+	0.204703i	0.312134	+	0.950038i	$0.398956\pi$
$654$	14.3329	−	11.6034i	0.560463	−	0.453729i
$655$	−37.9708	−	21.9225i	−1.48364	−	0.856582i
$656$	2.17701	−	1.25689i	0.0849978	−	0.0490735i
$657$	−5.88291	−	5.29987i	−0.229514	−	0.206768i
$658$	−11.2573	−	0.312775i	−0.438855	−	0.0121932i
$659$			24.8852i			0.969389i	0.874684	+	0.484694i	$0.161069\pi$
$659$			24.8852i			0.969389i	−0.874684	+	0.484694i	$0.838931\pi$
$660$	2.83099	+	17.8898i	0.110196	+	0.696358i
$661$	−24.9458	+	43.2074i	−0.970280	+	1.68057i	−0.275574	+	0.961280i	$0.588868\pi$
$661$	−24.9458	+	43.2074i	−0.970280	+	1.68057i	−0.694706	+	0.719294i	$0.744465\pi$
$662$	−4.14357	−	2.39229i	−0.161044	−	0.0929790i
$663$	12.2083	+	33.4494i	0.474130	+	1.29907i
$664$			11.1300i			0.431929i
$665$	−56.8785	−	1.58032i	−2.20565	−	0.0612823i
$666$	−14.2165	+	15.7805i	−0.550878	+	0.611481i
$667$	−3.96423	−	6.86624i	−0.153496	−	0.265862i
$668$	21.0214	+	12.1367i	0.813343	+	0.469584i
$669$	23.0589	+	28.4832i	0.891509	+	1.10123i
$670$	4.12609	+	7.14660i	0.159405	+	0.276097i
$671$			14.9776i			0.578203i
$672$	−3.64043	+	2.78339i	−0.140433	+	0.107372i
$673$	14.9301			0.575513			0.287756	−	0.957704i	$-0.407091\pi$
$673$	14.9301			0.575513			0.287756	+	0.957704i	$0.407091\pi$
$674$	13.3247	+	23.0791i	0.513249	+	0.888973i
$675$	0.403621	−	7.64241i	0.0155354	−	0.294156i
$676$	1.78289	−	12.8772i	0.0685728	−	0.495275i
$677$	17.9807	+	31.1435i	0.691056	+	1.19694i	0.971492	+	0.237071i	$0.0761874\pi$
$677$	17.9807	+	31.1435i	0.691056	+	1.19694i	−0.280437	+	0.959873i	$0.590479\pi$
$678$	1.38129	+	0.530443i	0.0530483	+	0.0203715i
$679$	9.10582	−	4.92524i	0.349449	−	0.189013i
$680$			14.5063i			0.556293i
$681$	−3.64569	−	23.0381i	−0.139703	−	0.882821i
$682$	−0.00540703	+	0.00936526i	−0.000207046	+	0.000358614i
$683$	13.5825	−	23.5256i	0.519721	−	0.900184i	−0.480016	−	0.877260i	$-0.659369\pi$
$683$	13.5825	−	23.5256i	0.519721	−	0.900184i	0.999737	−	0.0229240i	$-0.00729756\pi$
$684$	5.27922	−	24.8039i	0.201856	−	0.948401i
$685$		−	33.1978i		−	1.26842i
$686$	16.7541	−	7.89299i	0.639675	−	0.301356i
$687$	−1.39932	+	3.64389i	−0.0533874	+	0.139023i
$688$	−1.65832	−	2.87230i	−0.0632230	−	0.109505i
$689$	−5.94006	+	17.3087i	−0.226298	+	0.659410i
$690$	−3.62650	−	4.47959i	−0.138059	−	0.170535i
$691$	−15.9012	−	27.5418i	−0.604912	−	1.04774i	−0.992065	−	0.125723i	$-0.959875\pi$
$691$	−15.9012	−	27.5418i	−0.604912	−	1.04774i	0.387153	−	0.922015i	$-0.373458\pi$
$692$	−0.409361			−0.0155616
$693$	31.7084	+	7.67514i	1.20450	+	0.291554i
$694$		−	6.30342i		−	0.239275i
$695$	−0.792954	−	1.37344i	−0.0300785	−	0.0520974i
$696$	−8.16053	+	6.60645i	−0.309324	+	0.250417i
$697$	−12.4128	−	7.16654i	−0.470169	−	0.271452i
$698$	−4.76413	−	8.25172i	−0.180325	−	0.312332i
$699$	2.10795	+	0.809493i	0.0797301	+	0.0306178i
$700$	3.31927	+	2.04135i	0.125457	+	0.0771557i
$701$		−	24.3611i		−	0.920107i	−0.887891	−	0.460053i	$-0.847830\pi$
$701$		−	24.3611i		−	0.920107i	0.887891	−	0.460053i	$-0.152170\pi$
$702$	−7.00749	+	17.3751i	−0.264481	+	0.655782i
$703$	51.8299	+	29.9240i	1.95480	+	1.12861i
$704$	2.05512	−	3.55958i	0.0774553	−	0.134157i
$705$	−18.5263	+	2.93172i	−0.697742	+	0.110415i
$706$		−	16.6016i		−	0.624811i
$707$	1.13866	−	40.9822i	0.0428236	−	1.54130i
$708$	−3.14278	−	1.20688i	−0.118113	−	0.0453575i
$709$	−37.1207	+	21.4317i	−1.39410	+	0.804883i	−0.993766	−	0.111487i	$-0.964439\pi$
$709$	−37.1207	+	21.4317i	−1.39410	+	0.804883i	−0.400332	+	0.916370i	$0.631105\pi$
$710$	−14.7373	−	8.50856i	−0.553079	−	0.319320i
$711$	40.3964	−	13.1135i	1.51498	−	0.491796i
$712$	3.31853	−	1.91595i	0.124367	−	0.0718034i
$713$		−	0.00344114i		−	0.000128872i
$714$	24.1226	+	10.0409i	0.902764	+	0.375770i
$715$	−37.0038	+	7.23213i	−1.38386	+	0.270466i
$716$	−20.4933	+	11.8318i	−0.765871	+	0.442176i
$717$	−3.81575	−	4.71336i	−0.142502	−	0.176023i
$718$	8.18866	−	14.1832i	0.305598	−	0.529311i
$719$	14.3834	+	24.9128i	0.536410	+	0.929090i	0.999094	+	0.0425664i	$0.0135534\pi$
$719$	14.3834	+	24.9128i	0.536410	+	0.929090i	−0.462683	+	0.886524i	$0.653113\pi$
$720$	−5.10869	+	5.67070i	−0.190390	+	0.211334i
$721$	−18.4226	+	29.9555i	−0.686094	+	1.11560i
$722$	−52.4560			−1.95221
$723$	22.5728	−	3.57206i	0.839491	−	0.132846i
$724$	12.3190	+	7.11236i	0.457831	+	0.264329i
$725$	7.73200	+	4.46407i	0.287159	+	0.165791i
$726$	−10.0834	+	1.59566i	−0.374231	+	0.0592206i
$727$			9.23311i			0.342437i	0.985233	+	0.171219i	$0.0547704\pi$
$727$			9.23311i			0.342437i	−0.985233	+	0.171219i	$0.945230\pi$
$728$	−6.06358	−	7.36431i	−0.224731	−	0.272939i
$729$	15.8879	−	21.8306i	0.588439	−	0.808541i
$730$	5.81541	−	3.35753i	0.215238	−	0.124268i
$731$	−9.45541	+	16.3772i	−0.349721	+	0.605734i
$732$	−4.90551	+	3.97131i	−0.181313	+	0.146784i
$733$	−19.7916	−	34.2800i	−0.731018	−	1.26616i	−0.956449	−	0.291901i	$-0.905712\pi$
$733$	−19.7916	−	34.2800i	−0.731018	−	1.26616i	0.225431	−	0.974259i	$-0.427621\pi$
$734$		−	31.1600i		−	1.15014i
$735$	25.0156	−	18.0479i	0.922713	−	0.665708i
$736$			1.30792i			0.0482105i
$737$	−11.5457	+	6.66591i	−0.425291	+	0.245542i
$738$	−2.32848	−	7.17289i	−0.0857124	−	0.264038i
$739$	25.0159	+	14.4429i	0.920224	+	0.531291i	0.883706	−	0.468042i	$-0.155040\pi$
$739$	25.0159	+	14.4429i	0.920224	+	0.531291i	0.0365171	+	0.999333i	$0.488374\pi$
$740$	−9.00633	−	15.5994i	−0.331079	−	0.573446i
$741$	51.9961	+	9.12068i	1.91013	+	0.335056i
$742$	6.38855	+	11.8112i	0.234531	+	0.433603i
$743$	−14.2072			−0.521211			−0.260605	−	0.965445i	$-0.583922\pi$
$743$	−14.2072			−0.521211			−0.260605	+	0.965445i	$0.583922\pi$
$744$	−0.00450102		0.000712270i	−0.000165016		2.61131e-5i
$745$	4.34577	+	2.50903i	0.159217	+	0.0919238i
$746$	11.8848	−	20.5851i	0.435133	−	0.753673i
$747$	32.6585	+	6.95099i	1.19491	+	0.254323i
$748$	−23.4357			−0.856895
$749$	−19.7764	+	32.1567i	−0.722613	+	1.17498i
$750$	−14.5099	−	5.57206i	−0.529825	−	0.203463i
$751$	−8.05134	−	13.9453i	−0.293798	−	0.508873i	0.680907	−	0.732370i	$-0.261586\pi$
$751$	−8.05134	−	13.9453i	−0.293798	−	0.508873i	−0.974704	+	0.223498i	$0.928253\pi$
$752$	3.68624	+	2.12825i	0.134423	+	0.0776093i
$753$	30.9902	+	38.2803i	1.12935	+	1.39501i
$754$	−14.3560	−	16.4806i	−0.522815	−	0.600187i
$755$	−23.9176			−0.870452
$756$	5.89370	+	12.4203i	0.214352	+	0.451723i
$757$	24.7260			0.898684			0.449342	−	0.893360i	$-0.351659\pi$
$757$	24.7260			0.898684			0.449342	+	0.893360i	$0.351659\pi$
$758$	5.09123	−	2.93942i	0.184922	−	0.106765i
$759$	7.23701	−	5.85880i	0.262687	−	0.212661i
$760$	18.6250	+	10.7532i	0.675601	+	0.390059i
$761$	2.32242	−	1.34085i	0.0841876	−	0.0486057i	−0.457315	−	0.889305i	$-0.651189\pi$
$761$	2.32242	−	1.34085i	0.0841876	−	0.0486057i	0.541503	+	0.840699i	$0.317856\pi$
$762$	−7.49552	+	19.5186i	−0.271534	+	0.707085i
$763$	28.1583	+	0.782355i	1.01940	+	0.0283232i
$764$			16.0046i			0.579024i
$765$	42.5656	+	9.05959i	1.53896	+	0.327550i
$766$	−12.8839	−	7.43851i	−0.465514	−	0.268764i
$767$	2.27480	−	6.62854i	0.0821384	−	0.239343i
$768$	1.71076	−	0.270722i	0.0617318	−	0.00976883i
$769$	39.1298			1.41106			0.705528	−	0.708682i	$-0.250710\pi$
$769$	39.1298			1.41106			0.705528	+	0.708682i	$0.250710\pi$
$770$	−14.4937	+	23.5670i	−0.522316	+	0.849295i
$771$	−11.8590	+	30.8813i	−0.427091	+	1.11216i
$772$	14.6848	−	8.47830i	0.528519	−	0.305141i
$773$	24.0664	+	13.8947i	0.865607	+	0.499758i	0.865886	−	0.500242i	$-0.166756\pi$
$773$	24.0664	+	13.8947i	0.865607	+	0.499758i	−0.000279226		1.00000i	$0.500089\pi$
$774$	−9.46379	+	3.07215i	−0.340169	+	0.110426i
$775$	0.00193751	+	0.00335587i	6.95976e−5	+	0.000120547i
$776$	−3.91287			−0.140464
$777$	−32.1742	+	4.17913i	−1.15424	+	0.149926i
$778$			31.0109i			1.11180i
$779$	−18.4026	+	10.6247i	−0.659341	+	0.380671i
$780$	−12.1803	−	10.2020i	−0.436124	−	0.365291i
$781$	13.7460	−	23.8088i	0.491870	−	0.851945i
$782$	6.45836	−	3.72873i	0.230950	−	0.133339i
$783$	14.2887	+	28.0711i	0.510635	+	1.00318i
$784$	−6.98920	−	0.388679i	−0.249614	−	0.0138814i
$785$	−18.5763			−0.663016
$786$	29.4824	−	4.66547i	1.05160	−	0.166412i
$787$	22.3703	−	38.7465i	0.797415	−	1.38116i	−0.123879	−	0.992297i	$-0.539534\pi$
$787$	22.3703	−	38.7465i	0.797415	−	1.38116i	0.921294	−	0.388866i	$-0.127133\pi$
$788$	−1.28282	+	2.22190i	−0.0456984	+	0.0791520i
$789$	−1.40625	−	8.88647i	−0.0500639	−	0.316367i
$790$			36.0184i			1.28148i
$791$	1.07530	+	1.98802i	0.0382332	+	0.0706857i
$792$	−9.16129	−	8.25334i	−0.325532	−	0.293270i
$793$	−8.62977	−	9.90692i	−0.306452	−	0.351805i
$794$	−7.10552	+	12.3071i	−0.252166	+	0.436763i
$795$	14.0727	+	17.3831i	0.499108	+	0.616517i
$796$	−18.7467	+	10.8234i	−0.664458	+	0.383625i
$797$	−16.6004			−0.588016			−0.294008	−	0.955803i	$-0.594989\pi$
$797$	−16.6004			−0.588016			−0.294008	+	0.955803i	$0.594989\pi$
$798$	30.7731	−	23.5285i	1.08936	−	0.832900i
$799$		−	24.2696i		−	0.858598i
$800$	−0.736416	−	1.27551i	−0.0260362	−	0.0450961i
$801$	−3.54942	−	10.9340i	−0.125413	−	0.386335i
$802$	−19.1854	+	33.2301i	−0.677460	+	1.17339i
$803$	5.42426	+	9.39509i	0.191418	+	0.331546i
$804$	−5.24459	−	2.01402i	−0.184963	−	0.0710291i
$805$	0.244516	−	8.80054i	0.00861805	−	0.310178i
$806$	−0.00181959	−	0.00931008i	−6.40922e−5	−	0.000327933i
$807$	−10.6138	+	1.67959i	−0.373623	+	0.0591245i
$808$	−7.74790	+	13.4198i	−0.272570	+	0.472106i
$809$	11.8831	+	6.86068i	0.417786	+	0.241209i	0.694130	−	0.719850i	$-0.255789\pi$
$809$	11.8831	+	6.86068i	0.417786	+	0.241209i	−0.276344	+	0.961059i	$0.589123\pi$
$810$	13.4489	+	18.5318i	0.472545	+	0.651141i
$811$	27.2852			0.958114			0.479057	−	0.877784i	$-0.340979\pi$
$811$	27.2852			0.958114			0.479057	+	0.877784i	$0.340979\pi$
$812$	−16.0321	−	0.445438i	−0.562615	−	0.0156318i
$813$	−15.9566	+	41.5516i	−0.559622	+	1.45728i
$814$	25.2016	−	14.5502i	0.883317	−	0.509983i
$815$	−19.2477	+	33.3380i	−0.674218	+	1.16778i
$816$	−6.21399	−	7.67576i	−0.217533	−	0.268705i
$817$	14.0181	+	24.2800i	0.490431	+	0.849451i
$818$	−4.18304			−0.146257
$819$	−25.3958	+	13.1930i	−0.887400	+	0.461001i
$820$	6.39552			0.223341
$821$	−25.2745	−	43.7767i	−0.882085	−	1.52782i	−0.849018	−	0.528364i	$-0.822806\pi$
$821$	−25.2745	−	43.7767i	−0.882085	−	1.52782i	−0.0330672	−	0.999453i	$-0.510528\pi$
$822$	14.2207	+	17.5660i	0.496005	+	0.612684i
$823$	22.1516	−	38.3677i	0.772156	−	1.33741i	−0.164224	−	0.986423i	$-0.552512\pi$
$823$	22.1516	−	38.3677i	0.772156	−	1.33741i	0.936379	−	0.350990i	$-0.114155\pi$
$824$	11.5111	−	6.64596i	0.401009	−	0.231523i
$825$	−3.75892	+	9.78838i	−0.130869	+	0.340788i
$826$	−2.44656	−	4.52321i	−0.0851266	−	0.157383i
$827$	19.9119			0.692405			0.346203	−	0.938160i	$-0.387471\pi$
$827$	19.9119			0.692405			0.346203	+	0.938160i	$0.387471\pi$
$828$	3.83779	+	0.816830i	0.133373	+	0.0283868i
$829$	7.87052	+	4.54405i	0.273354	+	0.157821i	0.630411	−	0.776261i	$-0.282886\pi$
$829$	7.87052	+	4.54405i	0.273354	+	0.157821i	−0.357057	+	0.934083i	$0.616220\pi$
$830$	−14.1584	+	24.5230i	−0.491444	+	0.851206i
$831$	41.5991	−	6.58291i	1.44306	−	0.228359i
$832$	0.691594	+	3.53860i	0.0239767	+	0.122679i
$833$	18.0062	+	35.6200i	0.623878	+	1.23416i
$834$	1.00791	+	0.387055i	0.0349010	+	0.0134026i
$835$	30.8780	+	53.4822i	1.06858	+	1.85083i
$836$	−17.3723	+	30.0897i	−0.600833	+	1.04067i
$837$	−0.000721011		0.0136521i	−2.49218e−5		0.000471885i
$838$	12.2030	+	21.1362i	0.421544	+	0.730136i
$839$		−	27.0968i		−	0.935486i	−0.883865	−	0.467743i	$-0.845067\pi$
$839$		−	27.0968i		−	0.935486i	0.883865	−	0.467743i	$-0.154933\pi$
$840$	−11.5618	+	1.50177i	−0.398918	+	0.0518159i
$841$	−7.74648			−0.267120
$842$	6.12262	−	3.53489i	0.210999	−	0.121821i
$843$	−24.7626	−	30.5877i	−0.852870	−	1.05350i
$844$	3.50357	−	6.06837i	0.120598	−	0.208882i
$845$	20.3092	−	26.1045i	0.698657	−	0.898023i
$846$	8.54702	−	9.48728i	0.293853	−	0.326179i
$847$	−13.2833	−	8.16924i	−0.456420	−	0.280698i
$848$		−	5.07540i		−	0.174290i
$849$	−5.19599	−	32.8349i	−0.178326	−	1.12689i
$850$	−4.19888	+	7.27268i	−0.144021	+	0.249451i
$851$	−4.63000	+	8.01940i	−0.158715	+	0.274902i
$852$	11.4427	−	1.81076i	0.392020	−	0.0620358i
$853$	−22.7608			−0.779314			−0.389657	−	0.920960i	$-0.627406\pi$
$853$	−22.7608			−0.779314			−0.389657	+	0.920960i	$0.627406\pi$
$854$	−9.63730	−	0.267764i	−0.329782	−	0.00916271i
$855$	43.1846	−	47.9353i	1.47688	−	1.63935i
$856$	12.3570	−	7.13432i	0.422354	−	0.243846i
$857$	−12.6132	+	21.8466i	−0.430857	+	0.746267i	−0.996947	−	0.0780766i	$-0.975122\pi$
$857$	−12.6132	+	21.8466i	−0.430857	+	0.746267i	0.566090	+	0.824343i	$0.308455\pi$
$858$	16.4819	−	19.6778i	0.562682	−	0.671790i
$859$	−30.6299	+	17.6842i	−1.04508	+	0.603377i	−0.921268	−	0.388928i	$-0.872845\pi$
$859$	−30.6299	+	17.6842i	−1.04508	+	0.603377i	−0.123812	+	0.992306i	$0.539512\pi$
$860$		−	8.43814i		−	0.287738i
$861$	4.42680	−	10.6351i	0.150865	−	0.362443i
$862$	3.67304			0.125104
$863$	−4.16054	−	7.20627i	−0.141627	−	0.245304i	0.786483	−	0.617612i	$-0.211900\pi$
$863$	−4.16054	−	7.20627i	−0.141627	−	0.245304i	−0.928109	+	0.372308i	$0.878567\pi$
$864$	0.274044	−	5.18892i	0.00932317	−	0.176531i
$865$	−0.901955	−	0.520744i	−0.0306674	−	0.0177058i
$866$	26.7670	−	15.4540i	0.909581	−	0.525147i
$867$	−9.63082	+	25.0790i	−0.327080	+	0.851729i
$868$	−0.00592940	−	0.00364658i	−0.000201257	−	0.000123773i
$869$	−58.1895			−1.97394
$870$	−26.3843	+	4.17521i	−0.894510	+	0.141553i
$871$	3.79614	−	11.0616i	0.128627	−	0.374807i
$872$	−9.22052	−	5.32347i	−0.312246	−	0.180275i
$873$	−2.44369	+	11.4814i	−0.0827064	+	0.388588i
$874$		−	11.0561i		−	0.373977i
$875$	−11.2955	−	20.8832i	−0.381857	−	0.705980i
$876$	−1.63887	+	4.26769i	−0.0553724	+	0.144192i
$877$	6.00709	−	3.46819i	0.202845	−	0.117113i	−0.395137	−	0.918622i	$-0.629303\pi$
$877$	6.00709	−	3.46819i	0.202845	−	0.117113i	0.597982	+	0.801510i	$0.295969\pi$
$878$	31.8737	+	18.4023i	1.07569	+	0.621047i
$879$	−15.7993	+	12.7905i	−0.532896	+	0.431412i
$880$	9.05619	−	5.22859i	0.305284	−	0.176256i
$881$	−10.2056			−0.343835			−0.171917	−	0.985111i	$-0.554996\pi$
$881$	−10.2056			−0.343835			−0.171917	+	0.985111i	$0.554996\pi$
$882$	−5.50543	+	20.2655i	−0.185377	+	0.682375i
$883$	−16.1358			−0.543013			−0.271506	−	0.962437i	$-0.587522\pi$
$883$	−16.1358			−0.543013			−0.271506	+	0.962437i	$0.587522\pi$
$884$	15.5016	−	13.5032i	0.521374	−	0.454161i
$885$	−5.38928	−	6.65704i	−0.181159	−	0.223774i
$886$	31.8442	+	18.3852i	1.06983	+	0.617664i
$887$	12.1918	+	21.1167i	0.409359	+	0.709031i	0.994818	−	0.101671i	$-0.0324190\pi$
$887$	12.1918	+	21.1167i	0.409359	+	0.709031i	−0.585459	+	0.810702i	$0.699086\pi$
$888$	11.4478	+	4.39615i	0.384162	+	0.147525i
$889$	−28.0920	+	15.1947i	−0.942176	+	0.509613i
$890$	9.74904			0.326789
$891$	−29.9390	+	21.7273i	−1.00300	+	0.727893i
$892$	10.5791	−	18.3235i	0.354214	−	0.613517i
$893$	−31.1604	−	17.9904i	−1.04274	−	0.602027i
$894$	−3.37426	+	0.533965i	−0.112852	+	0.0178584i
$895$	−60.2045			−2.01241
$896$	2.25366	+	1.38600i	0.0752896	+	0.0463031i
$897$	−1.41120	+	8.04512i	−0.0471186	+	0.268619i
$898$	−1.97326	−	3.41779i	−0.0658486	−	0.114053i
$899$	−0.0138121	−	0.00797443i	−0.000460660	−	0.000265962i
$900$	−4.20261	+	1.36426i	−0.140087	+	0.0454752i
$901$	−25.0618	+	14.4694i	−0.834929	+	0.482046i
$902$			10.3323i			0.344027i
$903$	−14.0318	−	5.84064i	−0.466948	−	0.194364i
$904$		−	0.854272i		−	0.0284127i
$905$	18.0951	+	31.3416i	0.601501	+	1.04183i
$906$	12.6556	−	10.2455i	0.420453	−	0.340383i
$907$	−9.19556	+	15.9272i	−0.305334	+	0.528853i	−0.977336	−	0.211696i	$-0.932101\pi$
$907$	−9.19556	+	15.9272i	−0.305334	+	0.528853i	0.672002	+	0.740549i	$0.265435\pi$
$908$	−11.6624	+	6.73328i	−0.387030	+	0.223452i
$909$	34.5385	+	31.1155i	1.14557	+	1.03204i
$910$	−3.99196	−	23.9393i	−0.132332	−	0.793581i
$911$			29.8085i			0.987598i	0.869576	+	0.493799i	$0.164392\pi$
$911$			29.8085i			0.987598i	−0.869576	+	0.493799i	$0.835608\pi$
$912$	−14.4614	+	2.28846i	−0.478864	+	0.0757784i
$913$	−39.6182	−	22.8736i	−1.31117	−	0.757004i
$914$	0.843279	+	0.486868i	0.0278932	+	0.0161041i
$915$	−15.8603	+	2.50983i	−0.524325	+	0.0829724i
$916$	2.25359			0.0744607
$917$	38.8384	+	23.8856i	1.28256	+	0.788772i
$918$	−26.4036	+	13.4399i	−0.871448	+	0.443581i
$919$	5.75307	+	9.96461i	0.189776	+	0.328702i	0.945176	−	0.326563i	$-0.105890\pi$
$919$	5.75307	+	9.96461i	0.189776	+	0.328702i	−0.755399	+	0.655265i	$0.772557\pi$
$920$	−1.66379	+	2.88177i	−0.0548535	+	0.0950090i
$921$	−29.6879	−	36.6716i	−0.978250	−	1.20837i
$922$	8.84108	−	5.10440i	0.291166	−	0.168105i
$923$	4.62583	+	23.6685i	0.152261	+	0.779057i
$924$	−2.42618	−	18.6786i	−0.0798155	−	0.614481i
$925$		−	10.4276i		−	0.342857i
$926$	9.91036	−	5.72175i	0.325675	−	0.188028i
$927$	−12.3121	−	37.9274i	−0.404381	−	1.24570i
$928$	5.24975	+	3.03094i	0.172331	+	0.0994956i
$929$	26.9309	−	15.5486i	0.883576	−	0.510133i	0.0117399	−	0.999931i	$-0.496263\pi$
$929$	26.9309	−	15.5486i	0.883576	−	0.510133i	0.871836	+	0.489798i	$0.162930\pi$
$930$	−0.0108233	−	0.00415634i	−0.000354909	−	0.000136292i
$931$	59.0809	+	3.28556i	1.93630	+	0.107680i
$932$		−	1.30368i		−	0.0427034i
$933$	−4.99511	+	0.790457i	−0.163532	+	0.0258784i
$934$	12.8601	−	22.2744i	0.420797	−	0.728842i
$935$	−51.6364	−	29.8123i	−1.68869	−	0.974966i
$936$	10.8151	+	0.180622i	0.353504	+	0.00590381i
$937$		−	39.5487i		−	1.29200i	−0.763338	−	0.645999i	$-0.776441\pi$
$937$		−	39.5487i		−	1.29200i	0.763338	−	0.645999i	$-0.223559\pi$
$938$	−4.08276	−	7.54823i	−0.133307	−	0.246459i
$939$	−10.8546	−	4.16838i	−0.354227	−	0.136030i
$940$	5.41464	+	9.37843i	0.176606	+	0.305891i
$941$	2.74724	+	1.58612i	0.0895573	+	0.0517059i	0.544110	−	0.839014i	$-0.316867\pi$
$941$	2.74724	+	1.58612i	0.0895573	+	0.0517059i	−0.454553	+	0.890720i	$0.650201\pi$
$942$	9.82929	−	7.95741i	0.320255	−	0.259266i
$943$	−1.64392	−	2.84735i	−0.0535333	−	0.0927223i
$944$			1.94367i			0.0632612i
$945$	−2.81402	+	34.8633i	−0.0915401	+	1.13410i
$946$	13.6322			0.443222
$947$	4.60358	+	7.97363i	0.149596	+	0.259108i	0.931078	−	0.364819i	$-0.118869\pi$
$947$	4.60358	+	7.97363i	0.149596	+	0.259108i	−0.781482	+	0.623928i	$0.785536\pi$
$948$	−15.4290	−	19.0584i	−0.501110	−	0.618989i
$949$	−9.00114	−	3.08904i	−0.292189	−	0.100274i
$950$	6.22505	+	10.7821i	0.201967	+	0.349817i
$951$	−9.59027	+	24.9734i	−0.310986	+	0.809820i
$952$	0.418977	−	15.0797i	0.0135791	−	0.488735i
$953$			31.9720i			1.03567i	0.855479	+	0.517837i	$0.173263\pi$
$953$			31.9720i			1.03567i	−0.855479	+	0.517837i	$0.826737\pi$
$954$	−14.8926	−	3.16972i	−0.482167	−	0.102624i
$955$	−20.3592	+	35.2632i	−0.658808	+	1.14109i
$956$	−1.75061	+	3.03215i	−0.0566188	+	0.0980666i
$957$	−6.74526	−	42.6251i	−0.218043	−	1.37787i
$958$			31.8499i			1.02902i
$959$	−0.958829	+	34.5099i	−0.0309622	+	1.11438i
$960$	4.11374	+	1.57975i	0.132770	+	0.0509863i
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	−8.28612	+	24.1449i	−0.267155	+	0.778462i
$963$	−13.2168	−	40.7144i	−0.425905	−	1.31200i
$964$	−6.59729	−	11.4268i	−0.212484	−	0.368034i
$965$	43.1406			1.38874
$966$	3.64045	+	4.76138i	0.117130	+	0.153195i
$967$		−	8.89193i		−	0.285945i	−0.989727	−	0.142973i	$-0.954334\pi$
$967$		−	8.89193i		−	0.285945i	0.989727	−	0.142973i	$-0.0456661\pi$
$968$	2.94705	+	5.10444i	0.0947218	+	0.164063i
$969$	52.5279	+	64.8845i	1.68744	+	2.08439i
$970$	−8.62131	−	4.97752i	−0.276814	−	0.159818i
$971$	−10.8088	−	18.7213i	−0.346870	−	0.600796i	0.638822	−	0.769355i	$-0.279422\pi$
$971$	−10.8088	−	18.7213i	−0.346870	−	0.600796i	−0.985692	+	0.168559i	$0.946089\pi$
$972$	−15.0546	−	4.04474i	−0.482876	−	0.129735i
$973$	0.784626	+	1.45062i	0.0251540	+	0.0465048i
$974$		−	20.6622i		−	0.662060i
$975$	−3.15353	−	8.64034i	−0.100994	−	0.276712i
$976$	3.15576	+	1.82198i	0.101014	+	0.0583202i
$977$	22.6382	−	39.2106i	0.724261	−	1.25446i	−0.235016	−	0.971991i	$-0.575514\pi$
$977$	22.6382	−	39.2106i	0.724261	−	1.25446i	0.959277	−	0.282466i	$-0.0911523\pi$
$978$	−4.09624	−	25.8852i	−0.130983	−	0.827718i
$979$			15.7501i			0.503374i
$980$	−14.9050	−	9.74726i	−0.476123	−	0.311365i
$981$	−21.3790	+	23.7309i	−0.682578	+	0.757669i
$982$	7.86934	−	4.54337i	0.251121	−	0.144985i
$983$	−26.7378	−	15.4371i	−0.852802	−	0.492365i	0.00879326	−	0.999961i	$-0.497201\pi$
$983$	−26.7378	−	15.4371i	−0.852802	−	0.492365i	−0.861595	+	0.507596i	$0.830534\pi$
$984$	−3.38407	+	2.73961i	−0.107880	+	0.0873356i
$985$	−5.65291	+	3.26371i	−0.180117	+	0.103990i
$986$		−	34.5636i		−	1.10073i
$987$	19.3432	−	2.51251i	0.615702	−	0.0799741i
$988$	−5.84616	−	29.9124i	−0.185991	−	0.951640i
$989$	−3.75674	+	2.16895i	−0.119457	+	0.0689687i
$990$	−9.68630	−	29.8387i	−0.307851	−	0.948337i
$991$	8.78463	−	15.2154i	0.279053	−	0.483334i	−0.692097	−	0.721805i	$-0.743313\pi$
$991$	8.78463	−	15.2154i	0.279053	−	0.483334i	0.971150	+	0.238471i	$0.0766462\pi$
$992$	0.00131550	+	0.00227852i	4.17672e−5	+	7.23430e-5i
$993$	7.73631	+	2.97089i	0.245504	+	0.0942782i
$994$	15.0740	+	9.27049i	0.478117	+	0.294042i
$995$	−55.0732			−1.74594
$996$	−3.01314	−	19.0408i	−0.0954750	−	0.603332i
$997$	−25.9590	−	14.9874i	−0.822129	−	0.474656i	0.0290211	−	0.999579i	$-0.490761\pi$
$997$	−25.9590	−	14.9874i	−0.822129	−	0.474656i	−0.851150	+	0.524922i	$0.824094\pi$
$998$	14.4611	+	8.34913i	0.457759	+	0.264287i
$999$	20.0489	−	30.8454i	0.634321	−	0.975904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bg.b.311.6	yes	36
3.2	odd	2		546.2.bg.a.311.1	✓	36
7.5	odd	6	inner	546.2.bg.b.467.1	yes	36
13.12	even	2		546.2.bg.a.311.6	yes	36
21.5	even	6		546.2.bg.a.467.6	yes	36
39.38	odd	2	inner	546.2.bg.b.311.1	yes	36
91.12	odd	6		546.2.bg.a.467.1	yes	36
273.194	even	6	inner	546.2.bg.b.467.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.1	✓	36	3.2	odd	2
546.2.bg.a.311.6	yes	36	13.12	even	2
546.2.bg.a.467.1	yes	36	91.12	odd	6
546.2.bg.a.467.6	yes	36	21.5	even	6
546.2.bg.b.311.1	yes	36	39.38	odd	2	inner
546.2.bg.b.311.6	yes	36	1.1	even	1	trivial
546.2.bg.b.467.1	yes	36	7.5	odd	6	inner
546.2.bg.b.467.6	yes	36	273.194	even	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.08983 - 1.34620i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.20332 + 1.27209i) q^{5} +(0.620929 - 1.61693i) q^{6} +(2.32714 - 1.25873i) q^{7} -1.00000 q^{8} +(-0.624526 + 2.93427i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.08983 - 1.34620i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.20332 + 1.27209i) q^{5} +(0.620929 - 1.61693i) q^{6} +(2.32714 - 1.25873i) q^{7} -1.00000 q^{8} +(-0.624526 + 2.93427i) q^{9} +(-2.20332 - 1.27209i) q^{10} +(2.05512 - 3.55958i) q^{11} +(1.71076 - 0.270722i) q^{12} +(0.691594 + 3.53860i) q^{13} +(2.25366 + 1.38600i) q^{14} +(4.11374 + 1.57975i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.85089 + 4.93789i) q^{17} +(-2.85342 + 0.926282i) q^{18} +(4.22658 + 7.32066i) q^{19} -2.54418i q^{20} +(-4.23070 - 1.76101i) q^{21} +4.11024 q^{22} +(-1.13269 + 0.653959i) q^{23} +(1.08983 + 1.34620i) q^{24} +(0.736416 - 1.27551i) q^{25} +(-2.71872 + 2.36824i) q^{26} +(4.63076 - 2.35713i) q^{27} +(-0.0734817 + 2.64473i) q^{28} +6.06189i q^{29} +(0.688764 + 4.35248i) q^{30} +(-0.00131550 + 0.00227852i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.03165 + 1.11273i) q^{33} -5.70178 q^{34} +(-3.52623 + 5.73372i) q^{35} +(-2.22889 - 2.00799i) q^{36} +(6.13142 - 3.53998i) q^{37} +(-4.22658 + 7.32066i) q^{38} +(4.00995 - 4.78751i) q^{39} +(2.20332 - 1.27209i) q^{40} +2.51379i q^{41} +(-0.590277 - 4.54440i) q^{42} +3.31665 q^{43} +(2.05512 + 3.55958i) q^{44} +(-2.35662 - 7.25960i) q^{45} +(-1.13269 - 0.653959i) q^{46} +(-3.68624 + 2.12825i) q^{47} +(-0.620929 + 1.61693i) q^{48} +(3.83121 - 5.85849i) q^{49} +1.47283 q^{50} +(9.75440 - 1.54360i) q^{51} +(-3.41032 - 1.17036i) q^{52} +(4.39543 + 2.53770i) q^{53} +(4.35672 + 2.83179i) q^{54} +10.4572i q^{55} +(-2.32714 + 1.25873i) q^{56} +(5.24882 - 13.6681i) q^{57} +(-5.24975 + 3.03094i) q^{58} +(-1.68327 - 0.971837i) q^{59} +(-3.42498 + 2.77273i) q^{60} +(-3.15576 + 1.82198i) q^{61} -0.00263100 q^{62} +(2.24009 + 7.61459i) q^{63} +1.00000 q^{64} +(-6.02522 - 6.91691i) q^{65} +(-4.47948 - 5.53322i) q^{66} +(-2.80901 - 1.62178i) q^{67} +(-2.85089 - 4.93789i) q^{68} +(2.11481 + 0.812125i) q^{69} +(-6.72866 - 0.186950i) q^{70} +6.68865 q^{71} +(0.624526 - 2.93427i) q^{72} +(-1.31969 + 2.28578i) q^{73} +(6.13142 + 3.53998i) q^{74} +(-2.51967 + 0.398728i) q^{75} -8.45317 q^{76} +(0.302028 - 10.8705i) q^{77} +(6.15108 + 1.07897i) q^{78} +(-7.07859 - 12.2605i) q^{79} +(2.20332 + 1.27209i) q^{80} +(-8.21993 - 3.66506i) q^{81} +(-2.17701 + 1.25689i) q^{82} -11.1300i q^{83} +(3.64043 - 2.78339i) q^{84} -14.5063i q^{85} +(1.65832 + 2.87230i) q^{86} +(8.16053 - 6.60645i) q^{87} +(-2.05512 + 3.55958i) q^{88} +(-3.31853 + 1.91595i) q^{89} +(5.10869 - 5.67070i) q^{90} +(6.06358 + 7.36431i) q^{91} -1.30792i q^{92} +(0.00450102 - 0.000712270i) q^{93} +(-3.68624 - 2.12825i) q^{94} +(-18.6250 - 10.7532i) q^{95} +(-1.71076 + 0.270722i) q^{96} +3.91287 q^{97} +(6.98920 + 0.388679i) q^{98} +(9.16129 + 8.25334i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9} + 14 q^{15} - 18 q^{16} - 4 q^{18} - 23 q^{21} + 14 q^{25} + 6 q^{26} + 7 q^{30} + 18 q^{32} - 24 q^{33} - 8 q^{36} + 10 q^{39} - 16 q^{42} - 16 q^{43} + 9 q^{45} - 72 q^{47} + 12 q^{49} + 28 q^{50} - 3 q^{51} + 6 q^{52} - 9 q^{54} + 8 q^{57} - 24 q^{59} - 7 q^{60} - 36 q^{61} + 39 q^{63} + 36 q^{64} - 18 q^{65} - 24 q^{66} + 72 q^{71} - 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} + 7 q^{84} - 8 q^{86} - 24 q^{87} + 72 q^{89} - 2 q^{91} + 14 q^{93} - 72 q^{94} + 12 q^{98} - 72 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9 + 14 * q^15 - 18 * q^16 - 4 * q^18 - 23 * q^21 + 14 * q^25 + 6 * q^26 + 7 * q^30 + 18 * q^32 - 24 * q^33 - 8 * q^36 + 10 * q^39 - 16 * q^42 - 16 * q^43 + 9 * q^45 - 72 * q^47 + 12 * q^49 + 28 * q^50 - 3 * q^51 + 6 * q^52 - 9 * q^54 + 8 * q^57 - 24 * q^59 - 7 * q^60 - 36 * q^61 + 39 * q^63 + 36 * q^64 - 18 * q^65 - 24 * q^66 + 72 * q^71 - 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 + 7 * q^84 - 8 * q^86 - 24 * q^87 + 72 * q^89 - 2 * q^91 + 14 * q^93 - 72 * q^94 + 12 * q^98 - 72 * q^99

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