LMFDB - Embedded newform 546.2.bg.b.467.1

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			467.1
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.b.311.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.71076 + 0.270722i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.20332 - 1.27209i) q^{5} +(-0.620929 + 1.61693i) q^{6} +(-2.32714 - 1.25873i) q^{7} -1.00000 q^{8} +(2.85342 - 0.926282i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.71076 + 0.270722i) 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} +(2.85342 - 0.926282i) q^{9} +(-2.20332 + 1.27209i) q^{10} +(2.05512 + 3.55958i) q^{11} +(1.08983 + 1.34620i) 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} +(0.624526 - 2.93427i) q^{18} +(-4.22658 + 7.32066i) q^{19} +2.54418i q^{20} +(4.32196 + 1.52338i) q^{21} +4.11024 q^{22} +(1.13269 + 0.653959i) q^{23} +(1.71076 - 0.270722i) q^{24} +(0.736416 + 1.27551i) q^{25} +(-3.41032 - 1.17036i) q^{26} +(-4.63076 + 2.35713i) q^{27} +(0.0734817 + 2.64473i) q^{28} +6.06189i q^{29} +(3.42498 - 2.77273i) q^{30} +(0.00131550 + 0.00227852i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.47948 - 5.53322i) 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} +(2.14113 + 5.86648i) q^{39} +(2.20332 + 1.27209i) q^{40} -2.51379i q^{41} +(3.48026 - 2.98124i) q^{42} +3.31665 q^{43} +(2.05512 - 3.55958i) q^{44} +(-7.46531 - 1.58890i) 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} +(-6.21399 - 7.67576i) q^{51} +(-2.71872 + 2.36824i) q^{52} +(-4.39543 + 2.53770i) q^{53} +(-0.274044 + 5.18892i) 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} +(-0.688764 - 4.35248i) q^{60} +(-3.15576 - 1.82198i) q^{61} +0.00263100 q^{62} +(-7.80626 - 1.43609i) q^{63} +1.00000 q^{64} +(-2.97761 + 8.67644i) q^{65} +(-7.03165 + 1.11273i) 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} +(-2.85342 + 0.926282i) q^{72} +(1.31969 + 2.28578i) q^{73} +(-6.13142 + 3.53998i) q^{74} +(-1.60514 - 1.98273i) 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} +(7.28400 - 5.28614i) q^{81} +(-2.17701 - 1.25689i) q^{82} +11.1300i q^{83} +(-0.841696 - 4.50461i) q^{84} -14.5063i q^{85} +(1.65832 - 2.87230i) q^{86} +(-1.64109 - 10.3705i) q^{87} +(-2.05512 - 3.55958i) q^{88} +(-3.31853 - 1.91595i) q^{89} +(-5.10869 + 5.67070i) q^{90} +(-2.84470 + 9.10537i) q^{91} -1.30792i q^{92} +(-0.00286736 - 0.00354187i) q^{93} +(-3.68624 + 2.12825i) q^{94} +(18.6250 - 10.7532i) q^{95} +(-1.08983 - 1.34620i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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
$3$	−1.71076	+	0.270722i	−0.987709	+	0.156301i
$3$	−1.71076	+	0.270722i	−0.987709	+	0.156301i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.20332	−	1.27209i	−0.985355	−	0.568895i	−0.0814725	−	0.996676i	$-0.525962\pi$
$5$	−2.20332	−	1.27209i	−0.985355	−	0.568895i	−0.903883	+	0.427781i	$0.859296\pi$
$6$	−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
$9$	2.85342	−	0.926282i	0.951140	−	0.308761i
$10$	−2.20332	+	1.27209i	−0.696751	+	0.402270i
$11$	2.05512	+	3.55958i	0.619643	+	1.07325i	0.989551	+	0.144184i	$0.0460558\pi$
$11$	2.05512	+	3.55958i	0.619643	+	1.07325i	−0.369908	+	0.929068i	$0.620611\pi$
$12$	1.08983	+	1.34620i	0.314608	+	0.388615i
$13$	−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	0.971365	+	0.237591i	$0.0763579\pi$
$17$	2.85089	+	4.93789i	0.691443	+	1.19761i	−0.279922	+	0.960023i	$0.590309\pi$
$18$	0.624526	−	2.93427i	0.147202	−	0.691615i
$19$	−4.22658	+	7.32066i	−0.969645	+	1.67947i	−0.273064	+	0.961996i	$0.588037\pi$
$19$	−4.22658	+	7.32066i	−0.969645	+	1.67947i	−0.696581	+	0.717478i	$0.745296\pi$
$20$			2.54418i			0.568895i
$21$	4.32196	+	1.52338i	0.943129	+	0.332428i
$22$	4.11024			0.876307
$23$	1.13269	+	0.653959i	0.236182	+	0.136360i	0.613421	−	0.789756i	$-0.289793\pi$
$23$	1.13269	+	0.653959i	0.236182	+	0.136360i	−0.377238	+	0.926116i	$0.623126\pi$
$24$	1.71076	−	0.270722i	0.349208	−	0.0552609i
$25$	0.736416	+	1.27551i	0.147283	+	0.255102i
$26$	−3.41032	−	1.17036i	−0.668818	−	0.229527i
$27$	−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	$0.809712\pi$
$30$	3.42498	−	2.77273i	0.625313	−	0.506229i
$31$	0.00131550	+	0.00227852i	0.000236271	+	0.000409234i	0.866144	−	0.499795i	$-0.166591\pi$
$31$	0.00131550	+	0.00227852i	0.000236271	+	0.000409234i	−0.865907	+	0.500205i	$0.833258\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−4.47948	−	5.53322i	−0.779778	−	0.963211i
$34$	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	$-0.531051\pi$
$37$	−6.13142	−	3.53998i	−1.00800	−	0.581969i	−0.910605	+	0.413277i	$0.864384\pi$
$38$	4.22658	+	7.32066i	0.685642	+	1.18757i
$39$	2.14113	+	5.86648i	0.342855	+	0.939388i
$40$	2.20332	+	1.27209i	0.348376	+	0.201135i
$41$		−	2.51379i		−	0.392588i	−0.980545	−	0.196294i	$-0.937109\pi$
$41$		−	2.51379i		−	0.392588i	0.980545	−	0.196294i	$-0.0628907\pi$
$42$	3.48026	−	2.98124i	0.537016	−	0.460015i
$43$	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
$45$	−7.46531	−	1.58890i	−1.11286	−	0.236860i
$46$	1.13269	−	0.653959i	0.167006	−	0.0964211i
$47$	−3.68624	−	2.12825i	−0.537693	−	0.310437i	0.206451	−	0.978457i	$-0.433809\pi$
$47$	−3.68624	−	2.12825i	−0.537693	−	0.310437i	−0.744143	+	0.668020i	$0.767142\pi$
$48$	0.620929	−	1.61693i	0.0896234	−	0.233383i
$49$	3.83121	+	5.85849i	0.547315	+	0.836927i
$50$	1.47283			0.208290
$51$	−6.21399	−	7.67576i	−0.870133	−	1.07482i
$52$	−2.71872	+	2.36824i	−0.377019	+	0.328416i
$53$	−4.39543	+	2.53770i	−0.603758	+	0.348580i	−0.770519	−	0.637417i	$-0.780003\pi$
$53$	−4.39543	+	2.53770i	−0.603758	+	0.348580i	0.166760	+	0.985997i	$0.446669\pi$
$54$	−0.274044	+	5.18892i	−0.0372927	+	0.706123i
$55$		−	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	−0.605554	−	0.795805i	$-0.707048\pi$
$59$	−1.68327	+	0.971837i	−0.219143	+	0.126522i	0.386410	+	0.922327i	$0.373715\pi$
$60$	−0.688764	−	4.35248i	−0.0889191	−	0.561903i
$61$	−3.15576	−	1.82198i	−0.404054	−	0.233281i	0.284178	−	0.958772i	$-0.408279\pi$
$61$	−3.15576	−	1.82198i	−0.404054	−	0.233281i	−0.688232	+	0.725491i	$0.741613\pi$
$62$	0.00263100			0.000334138
$63$	−7.80626	−	1.43609i	−0.983496	−	0.180930i
$64$	1.00000			0.125000
$65$	−2.97761	+	8.67644i	−0.369327	+	1.07618i
$66$	−7.03165	+	1.11273i	−0.865537	+	0.136968i
$67$	2.80901	−	1.62178i	0.343175	−	0.198132i	−0.318500	−	0.947923i	$-0.603179\pi$
$67$	2.80901	−	1.62178i	0.343175	−	0.198132i	0.661675	+	0.749791i	$0.269846\pi$
$68$	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	$0.370086\pi$
$72$	−2.85342	+	0.926282i	−0.336279	+	0.109163i
$73$	1.31969	+	2.28578i	0.154458	+	0.267530i	0.932862	−	0.360235i	$-0.117303\pi$
$73$	1.31969	+	2.28578i	0.154458	+	0.267530i	−0.778403	+	0.627765i	$0.783970\pi$
$74$	−6.13142	+	3.53998i	−0.712763	+	0.411514i
$75$	−1.60514	−	1.98273i	−0.185346	−	0.228946i
$76$	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	0.125540	+	0.992088i	$0.459934\pi$
$79$	−7.07859	+	12.2605i	−0.796404	+	1.37941i	−0.921944	+	0.387323i	$0.873400\pi$
$80$	2.20332	−	1.27209i	0.246339	−	0.142224i
$81$	7.28400	−	5.28614i	0.809334	−	0.587349i
$82$	−2.17701	−	1.25689i	−0.240410	−	0.138801i
$83$			11.1300i			1.22168i	0.791755	+	0.610839i	$0.209168\pi$
$83$			11.1300i			1.22168i	−0.791755	+	0.610839i	$0.790832\pi$
$84$	−0.841696	−	4.50461i	−0.0918366	−	0.491494i
$85$		−	14.5063i		−	1.57343i
$86$	1.65832	−	2.87230i	0.178822	−	0.309728i
$87$	−1.64109	−	10.3705i	−0.175943	−	1.11183i
$88$	−2.05512	−	3.55958i	−0.219077	−	0.379452i
$89$	−3.31853	−	1.91595i	−0.351763	−	0.203091i	0.313698	−	0.949523i	$-0.398432\pi$
$89$	−3.31853	−	1.91595i	−0.351763	−	0.203091i	−0.665462	+	0.746432i	$0.731765\pi$
$90$	−5.10869	+	5.67070i	−0.538503	+	0.597744i
$91$	−2.84470	+	9.10537i	−0.298205	+	0.954502i
$92$		−	1.30792i		−	0.136360i
$93$	−0.00286736	−	0.00354187i	−0.000297331	−	0.000367274i
$94$	−3.68624	+	2.12825i	−0.380206	+	0.219512i
$95$	18.6250	−	10.7532i	1.91089	−	1.10325i
$96$	−1.08983	−	1.34620i	−0.111231	−	0.137396i
$97$	−3.91287			−0.397292			−0.198646	−	0.980071i	$-0.563654\pi$
$97$	−3.91287			−0.397292			−0.198646	+	0.980071i	$0.563654\pi$
$98$	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	−0.937045	−	0.349208i	$-0.886451\pi$
$101$	−7.74790	−	13.4198i	−0.770945	−	1.33532i	0.166100	−	0.986109i	$-0.446883\pi$
$102$	−9.75440	+	1.54360i	−0.965829	+	0.152839i
$103$	−11.5111	−	6.64596i	−1.13423	−	0.654846i	−0.189231	−	0.981933i	$-0.560600\pi$
$103$	−11.5111	−	6.64596i	−1.13423	−	0.654846i	−0.944994	+	0.327087i	$0.893933\pi$
$104$	0.691594	+	3.53860i	0.0678164	+	0.346988i
$105$	−7.58479	−	8.85440i	−0.740200	−	0.864101i
$106$			5.07540i			0.492967i
$107$	12.3570	+	7.13432i	1.19460	+	0.689701i	0.959346	−	0.282234i	$-0.0910754\pi$
$107$	12.3570	+	7.13432i	1.19460	+	0.689701i	0.235251	+	0.971935i	$0.424409\pi$
$108$	4.35672	+	2.83179i	0.419225	+	0.272489i
$109$	−9.22052	+	5.32347i	−0.883166	+	0.509896i	−0.871701	−	0.490038i	$-0.836983\pi$
$109$	−9.22052	+	5.32347i	−0.883166	+	0.509896i	−0.0114648	+	0.999934i	$0.503649\pi$
$110$	−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	$0.987206\pi$
$114$	−9.21254	−	11.3797i	−0.862834	−	1.06580i
$115$	−1.66379	−	2.88177i	−0.155149	−	0.268726i
$116$	5.24975	−	3.03094i	0.487427	−	0.281416i
$117$	−5.25115	−	9.45650i	−0.485469	−	0.874254i
$118$			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
$123$	0.680538	+	4.30050i	0.0613620	+	0.387763i
$124$	0.00131550	−	0.00227852i	0.000118136	−	0.000204617i
$125$			8.97374i			0.802635i
$126$	−5.14682	+	6.04237i	−0.458515	+	0.538297i
$127$	−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
$129$	−5.67400	+	0.897889i	−0.499568	+	0.0790547i
$130$	6.02522	+	6.91691i	0.528446	+	0.606653i
$131$	−8.61673	+	14.9246i	−0.752847	+	1.30397i	0.193591	+	0.981082i	$0.437987\pi$
$131$	−8.61673	+	14.9246i	−0.752847	+	1.30397i	−0.946438	+	0.322887i	$0.895347\pi$
$132$	−2.55217	+	6.64596i	−0.222138	+	0.578456i
$133$	19.0506	−	11.7161i	1.65190	−	1.01592i
$134$		−	3.24356i		−	0.280201i
$135$	13.2015	+	0.697216i	1.13621	+	0.0600068i
$136$	−2.85089	−	4.93789i	−0.244462	−	0.423421i
$137$	−6.52427	−	11.3004i	−0.557406	−	0.965456i	−0.997712	−	0.0676081i	$-0.978463\pi$
$137$	−6.52427	−	11.3004i	−0.557406	−	0.965456i	0.440306	−	0.897848i	$-0.354870\pi$
$138$	−1.76072	+	1.42541i	−0.149883	+	0.121339i
$139$		−	0.623348i		−	0.0528717i	−0.999651	−	0.0264359i	$-0.991584\pi$
$139$		−	0.623348i		−	0.0528717i	0.999651	−	0.0264359i	$-0.00841577\pi$
$140$	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
$143$	11.1746	−	9.73404i	0.934468	−	0.814001i
$144$	−0.624526	+	2.93427i	−0.0520438	+	0.244523i
$145$	7.71125	−	13.3563i	0.640385	−	1.10918i
$146$	2.63939			0.218437
$147$	−8.14031	−	8.98529i	−0.671401	−	0.741094i
$148$			7.07996i			0.581969i
$149$	−0.986187	+	1.70813i	−0.0807916	+	0.139935i	−0.903590	−	0.428398i	$-0.859078\pi$
$149$	−0.986187	+	1.70813i	−0.0807916	+	0.139935i	0.822799	+	0.568333i	$0.192411\pi$
$150$	−2.51967	+	0.398728i	−0.205730	+	0.0325560i
$151$	−8.14145	+	4.70047i	−0.662542	+	0.382519i	−0.793245	−	0.608903i	$-0.791610\pi$
$151$	−8.14145	+	4.70047i	−0.662542	+	0.382519i	0.130703	+	0.991422i	$0.458277\pi$
$152$	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
$156$	4.00995	−	4.78751i	0.321053	−	0.383308i
$157$	6.32327	−	3.65074i	0.504652	−	0.291361i	−0.225980	−	0.974132i	$-0.572559\pi$
$157$	6.32327	−	3.65074i	0.504652	−	0.291361i	0.730633	+	0.682771i	$0.239225\pi$
$158$	7.07859	+	12.2605i	0.563142	+	0.975391i
$159$	6.83252	−	5.53134i	0.541854	−	0.438664i
$160$		−	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	$-0.535219\pi$
$163$	−13.1037	−	7.56540i	−1.02636	−	0.592568i	−0.915939	+	0.401317i	$0.868552\pi$
$164$	−2.17701	+	1.25689i	−0.169996	+	0.0981470i
$165$	2.83099	+	17.8898i	0.220392	+	1.39272i
$166$	9.63888	+	5.56501i	0.748122	+	0.431929i
$167$			24.2735i			1.87834i	0.343458	+	0.939168i	$0.388402\pi$
$167$			24.2735i			1.87834i	−0.343458	+	0.939168i	$0.611598\pi$
$168$	−4.32196	−	1.52338i	−0.333446	−	0.117531i
$169$	−12.0434	+	4.89455i	−0.926415	+	0.376504i
$170$	−12.5629	−	7.25317i	−0.963527	−	0.556293i
$171$	−5.27922	+	24.8039i	−0.403712	+	1.89680i
$172$	−1.65832	−	2.87230i	−0.126446	−	0.219011i
$173$	−0.204681	+	0.354517i	−0.0155616	+	0.0269535i	−0.873701	−	0.486463i	$-0.838287\pi$
$173$	−0.204681	+	0.354517i	−0.0155616	+	0.0269535i	0.858140	+	0.513416i	$0.171620\pi$
$174$	−9.80162	−	3.76400i	−0.743059	−	0.285348i
$175$	−0.108226	−	3.89524i	−0.00818113	−	0.294453i
$176$	−4.11024			−0.309821
$177$	2.61658	−	2.11828i	0.196674	−	0.159220i
$178$	−3.31853	+	1.91595i	−0.248734	+	0.143607i
$179$	−20.4933	+	11.8318i	−1.53174	+	0.884352i	−0.532460	+	0.846455i	$0.678732\pi$
$179$	−20.4933	+	11.8318i	−1.53174	+	0.884352i	−0.999282	+	0.0378964i	$0.987934\pi$
$180$	2.35662	+	7.25960i	0.175652	+	0.541099i
$181$			14.2247i			1.05732i	0.848835	+	0.528658i	$0.177304\pi$
$181$			14.2247i			1.05732i	−0.848835	+	0.528658i	$0.822696\pi$
$182$	6.46313	+	7.01626i	0.479079	+	0.520080i
$183$	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
$186$	−0.00450102		0.000712270i	−0.000330031		5.22262e-5i
$187$	−11.7179	+	20.2959i	−0.856895	+	1.48419i
$188$			4.25650i			0.310437i
$189$	13.7434	+	0.343482i	0.999688	+	0.0249846i
$190$		−	21.5063i		−	1.56023i
$191$	−13.8603	−	8.00228i	−1.00290	−	0.579024i	−0.0937947	−	0.995592i	$-0.529900\pi$
$191$	−13.8603	−	8.00228i	−1.00290	−	0.579024i	−0.909105	+	0.416567i	$0.863233\pi$
$192$	−1.71076	+	0.270722i	−0.123464	+	0.0195377i
$193$	14.6848	−	8.47830i	1.05704	−	0.610281i	0.132427	−	0.991193i	$-0.457723\pi$
$193$	14.6848	−	8.47830i	1.05704	−	0.610281i	0.924611	+	0.380912i	$0.124390\pi$
$194$	−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	$0.470867\pi$
$198$	11.7282	−	3.80724i	0.833490	−	0.270569i
$199$	18.7467	−	10.8234i	1.32892	−	0.767249i	0.343783	−	0.939049i	$-0.388292\pi$
$199$	18.7467	−	10.8234i	1.32892	−	0.767249i	0.985132	+	0.171800i	$0.0549582\pi$
$200$	−0.736416	−	1.27551i	−0.0520725	−	0.0901922i
$201$	−4.36649	+	3.53494i	−0.307988	+	0.249335i
$202$	−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
$207$	3.83779	+	0.816830i	0.266745	+	0.0567736i
$208$	3.41032	+	1.17036i	0.236463	+	0.0811500i
$209$	−34.7446			−2.40333
$210$	−11.4605	+	2.14142i	−0.790852	+	0.147772i
$211$	−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
$213$	−11.4427	+	1.81076i	−0.784041	+	0.124072i
$214$	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
$219$	−2.87649	−	3.55315i	−0.194375	−	0.240100i
$220$	−9.05619	+	5.22859i	−0.610568	+	0.352512i
$221$	15.5016	−	13.5032i	1.04275	−	0.908322i
$222$	9.53106	−	7.71597i	0.639683	−	0.517862i
$223$	21.1582			1.41686			0.708429	−	0.705782i	$-0.249404\pi$
$223$	21.1582			1.41686			0.708429	+	0.705782i	$0.249404\pi$
$224$	−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	−0.0602614	−	0.998183i	$-0.519193\pi$
$227$	11.6624	−	6.73328i	0.774059	−	0.446903i	0.834321	+	0.551279i	$0.185860\pi$
$228$	−14.4614	+	2.28846i	−0.957727	+	0.151557i
$229$	1.12680	−	1.95167i	0.0744607	−	0.128970i	−0.826391	−	0.563097i	$-0.809610\pi$
$229$	1.12680	−	1.95167i	0.0744607	−	0.128970i	0.900852	+	0.434127i	$0.142943\pi$
$230$	−3.32758			−0.219414
$231$	3.45958	+	18.5151i	0.227623	+	1.21820i
$232$		−	6.06189i		−	0.397982i
$233$	1.12902	+	0.651840i	0.0739645	+	0.0427034i	0.536526	−	0.843884i	$-0.319736\pi$
$233$	1.12902	+	0.651840i	0.0739645	+	0.0427034i	−0.462562	+	0.886587i	$0.653070\pi$
$234$	−10.8151	−	0.180622i	−0.707008	−	0.0118076i
$235$	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	$0.463878\pi$
$240$	−3.42498	+	2.77273i	−0.221081	+	0.178979i
$241$	6.59729	+	11.4268i	0.424969	+	0.736067i	0.996418	−	0.0845704i	$-0.0269518\pi$
$241$	6.59729	+	11.4268i	0.424969	+	0.736067i	−0.571449	+	0.820638i	$0.693618\pi$
$242$	2.94705	+	5.10444i	0.189444	+	0.328126i
$243$	−11.0301	+	11.0153i	−0.707583	+	0.706630i
$244$			3.64396i			0.233281i
$245$	−0.988867	−	17.7818i	−0.0631764	−	1.13603i
$246$	4.06461	+	1.56089i	0.259150	+	0.0995184i
$247$	28.8280	+	9.89327i	1.83428	+	0.629494i
$248$	−0.00131550	−	0.00227852i	−8.35345e−5	−	0.000144686i
$249$	−3.01314	−	19.0408i	−0.190950	−	1.20666i
$250$	7.77148	+	4.48687i	0.491512	+	0.283774i
$251$	28.4357			1.79485			0.897424	−	0.441169i	$-0.145436\pi$
$251$	28.4357			1.79485			0.897424	+	0.441169i	$0.145436\pi$
$252$	2.65944	+	7.47846i	0.167529	+	0.471099i
$253$			5.37586i			0.337978i
$254$	−6.03573	+	10.4542i	−0.378715	+	0.655954i
$255$	3.92718	+	24.8169i	0.245930	+	1.55410i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.54939	−	16.5400i	0.595675	−	1.03174i	−0.397776	−	0.917482i	$-0.630218\pi$
$257$	9.54939	−	16.5400i	0.595675	−	1.03174i	0.993451	−	0.114257i	$-0.0364486\pi$
$258$	−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
$261$	5.61502	+	17.2971i	0.347561	+	1.07066i
$262$	8.61673	+	14.9246i	0.532343	+	0.922045i
$263$	−4.49853	+	2.59723i	−0.277391	+	0.160152i	−0.632242	−	0.774771i	$-0.717865\pi$
$263$	−4.49853	+	2.59723i	−0.277391	+	0.160152i	0.354851	+	0.934923i	$0.384532\pi$
$264$	4.47948	+	5.53322i	0.275693	+	0.340546i
$265$	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	$-0.227235\pi$
$269$	−3.10207	−	5.37294i	−0.189136	−	0.327594i	−0.944963	+	0.327179i	$0.893902\pi$
$270$	7.20457	−	11.0843i	0.438456	−	0.674566i
$271$	12.8489	−	22.2550i	0.780518	−	1.35190i	−0.151123	−	0.988515i	$-0.548289\pi$
$271$	12.8489	−	22.2550i	0.780518	−	1.35190i	0.931640	−	0.363382i	$-0.118378\pi$
$272$	−5.70178			−0.345721
$273$	2.40158	−	16.3472i	0.145350	−	0.989380i
$274$	−13.0485			−0.788292
$275$	−3.02685	+	5.24266i	−0.182526	+	0.316144i
$276$	0.354082	+	2.23754i	0.0213132	+	0.134684i
$277$	−12.1581	−	21.0584i	−0.730507	−	1.26528i	−0.956667	−	0.291186i	$-0.905950\pi$
$277$	−12.1581	−	21.0584i	−0.730507	−	1.26528i	0.226159	−	0.974090i	$-0.427383\pi$
$278$	−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	$0.262966\pi$
$282$	5.73011	−	4.63887i	0.341223	−	0.276241i
$283$	16.6217	−	9.59655i	0.988059	−	0.570456i	0.0833652	−	0.996519i	$-0.473433\pi$
$283$	16.6217	−	9.59655i	0.988059	−	0.570456i	0.904693	+	0.426063i	$0.140100\pi$
$284$	−3.34433	−	5.79254i	−0.198449	−	0.343724i
$285$	−28.9519	+	23.4383i	−1.71496	+	1.38837i
$286$	−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
$291$	6.69399	−	1.05930i	0.392409	−	0.0620972i
$292$	1.31969	−	2.28578i	0.0772292	−	0.133765i
$293$			11.7362i			0.685634i	0.939402	+	0.342817i	$0.111381\pi$
$293$			11.7362i			0.685634i	−0.939402	+	0.342817i	$0.888619\pi$
$294$	−11.8516	+	2.55707i	−0.691202	+	0.149131i
$295$	4.94505			0.287912
$296$	6.13142	+	3.53998i	0.356382	+	0.205757i
$297$	−17.9072	−	11.6393i	−1.03908	−	0.675383i
$298$	0.986187	+	1.70813i	0.0571283	+	0.0989491i
$299$	1.53074	−	4.46042i	0.0885249	−	0.257952i
$300$	−0.914525	+	2.38146i	−0.0528001	+	0.137494i
$301$	−7.71832	−	4.17476i	−0.444877	−	0.240629i
$302$			9.40094i			0.540963i
$303$	16.8879	+	20.8605i	0.970182	+	1.19840i
$304$	−4.22658	−	7.32066i	−0.242411	−	0.419869i
$305$	4.63544	+	8.02882i	0.265425	+	0.459729i
$306$	16.2696	−	5.28146i	0.930070	−	0.301921i
$307$	−27.2408			−1.55471			−0.777357	−	0.629060i	$-0.783440\pi$
$307$	−27.2408			−1.55471			−0.777357	+	0.629060i	$0.783440\pi$
$308$	−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	$-0.193048\pi$
$311$	−1.45991	−	2.52863i	−0.0827837	−	0.143386i	−0.904445	+	0.426591i	$0.859714\pi$
$312$	−2.14113	−	5.86648i	−0.121218	−	0.332124i
$313$	5.81374	+	3.35656i	0.328612	+	0.189724i	0.655225	−	0.755434i	$-0.272574\pi$
$313$	5.81374	+	3.35656i	0.328612	+	0.189724i	−0.326613	+	0.945158i	$0.605907\pi$
$314$		−	7.30149i		−	0.412047i
$315$	15.3729	+	13.0944i	0.866163	+	0.737786i
$316$	14.1572			0.796404
$317$	−7.72251	+	13.3758i	−0.433740	+	0.751259i	−0.997192	−	0.0748897i	$-0.976140\pi$
$317$	−7.72251	+	13.3758i	−0.433740	+	0.751259i	0.563452	+	0.826149i	$0.309473\pi$
$318$	−1.37402	−	8.68281i	−0.0770514	−	0.486908i
$319$	−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
$324$	−8.21993	−	3.66506i	−0.456663	−	0.203615i
$325$	4.00422	−	3.48802i	0.222114	−	0.193480i
$326$	−13.1037	+	7.56540i	−0.725744	+	0.419009i
$327$	14.3329	−	11.6034i	0.792614	−	0.641669i
$328$			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	$-0.291357\pi$
$331$	4.14357	+	2.39229i	0.227751	+	0.131492i	−0.381783	+	0.924252i	$0.624690\pi$
$332$	9.63888	−	5.56501i	0.529002	−	0.305420i
$333$	−20.7745	−	4.42162i	−1.13844	−	0.242303i
$334$	21.0214	+	12.1367i	1.15024	+	0.664092i
$335$	−8.25219			−0.450865
$336$	−3.48026	+	2.98124i	−0.189864	+	0.162640i
$337$	26.6494			1.45169			0.725843	−	0.687860i	$-0.241450\pi$
$337$	26.6494			1.45169			0.725843	+	0.687860i	$0.241450\pi$
$338$	−1.78289	+	12.8772i	−0.0969765	+	0.700425i
$339$	−0.231270	−	1.46146i	−0.0125609	−	0.0793755i
$340$	−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
$345$	3.62650	+	4.47959i	0.195244	+	0.241173i
$346$	0.204681	+	0.354517i	0.0110037	+	0.0190590i
$347$	5.45892	−	3.15171i	0.293050	−	0.169193i	−0.346266	−	0.938136i	$-0.612551\pi$
$347$	5.45892	−	3.15171i	0.293050	−	0.169193i	0.639317	+	0.768944i	$0.279217\pi$
$348$	−8.16053	+	6.60645i	−0.437450	+	0.354143i
$349$	9.52826			0.510036			0.255018	−	0.966936i	$-0.417919\pi$
$349$	9.52826			0.510036			0.255018	+	0.966936i	$0.417919\pi$
$350$	−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	−0.831172	−	0.556016i	$-0.812329\pi$
$353$	−14.3774	+	8.30082i	−0.765234	+	0.441808i	0.0659376	+	0.997824i	$0.478996\pi$
$354$	−0.526195	−	3.32517i	−0.0279670	−	0.176731i
$355$	−14.7373	−	8.50856i	−0.782172	−	0.451587i
$356$			3.83190i			0.203091i
$357$	4.79917	+	25.6843i	0.253999	+	1.35936i
$358$			23.6636i			1.25066i
$359$	−8.18866	+	14.1832i	−0.432181	+	0.748559i	−0.997061	−	0.0766138i	$-0.975589\pi$
$359$	−8.18866	+	14.1832i	−0.432181	+	0.748559i	0.564880	+	0.825173i	$0.308922\pi$
$360$	7.46531	+	1.58890i	0.393456	+	0.0837426i
$361$	−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
$364$	9.30783	−	2.08910i	0.487863	−	0.109499i
$365$		−	6.71506i		−	0.351482i
$366$	4.90551	−	3.97131i	0.256415	−	0.207584i
$367$	−26.9853	+	15.5800i	−1.40862	+	0.813269i	−0.995256	−	0.0972954i	$-0.968981\pi$
$367$	−26.9853	+	15.5800i	−1.40862	+	0.813269i	−0.413368	+	0.910564i	$0.635648\pi$
$368$	−1.13269	+	0.653959i	−0.0590456	+	0.0340900i
$369$	−2.32848	−	7.17289i	−0.121216	−	0.373406i
$370$	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	0.374948	+	0.927046i	$0.377661\pi$
$373$	−11.8848	+	20.5851i	−0.615372	+	1.06585i	−0.990319	+	0.138809i	$0.955673\pi$
$374$	11.7179	+	20.2959i	0.605916	+	1.04948i
$375$	−2.42939	−	15.3519i	−0.125453	−	0.792771i
$376$	3.68624	+	2.12825i	0.190103	+	0.109756i
$377$	21.4506	−	4.19237i	1.10476	−	0.215918i
$378$	7.16918	−	11.7304i	0.368743	−	0.603348i
$379$		−	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
$381$	20.6514	−	3.26801i	1.05800	−	0.167425i
$382$	−13.8603	+	8.00228i	−0.709157	+	0.409432i
$383$	−12.8839	−	7.43851i	−0.658336	−	0.380090i	0.133307	−	0.991075i	$-0.457440\pi$
$383$	−12.8839	−	7.43851i	−0.658336	−	0.380090i	−0.791643	+	0.610985i	$0.790774\pi$
$384$	−0.620929	+	1.61693i	−0.0316867	+	0.0825134i
$385$	−13.1628	+	24.3354i	−0.670836	+	1.24025i
$386$		−	16.9566i		−	0.863068i
$387$	9.46379	−	3.07215i	0.481071	−	0.156166i
$388$	1.95644	+	3.38865i	0.0993229	+	0.172032i
$389$	−26.8563	+	15.5055i	−1.36167	+	0.786158i	−0.989846	−	0.142146i	$-0.954600\pi$
$389$	−26.8563	+	15.5055i	−1.36167	+	0.786158i	−0.371821	+	0.928305i	$0.621266\pi$
$390$	−12.1803	−	10.2020i	−0.616772	−	0.516600i
$391$			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
$396$	2.56695	−	12.0606i	0.128994	−	0.606067i
$397$	−7.10552	+	12.3071i	−0.356616	+	0.617677i	−0.987393	−	0.158287i	$-0.949403\pi$
$397$	−7.10552	+	12.3071i	−0.356616	+	0.617677i	0.630777	+	0.775964i	$0.282736\pi$
$398$		−	21.6468i		−	1.08505i
$399$	−29.4192	+	25.2009i	−1.47280	+	1.26162i
$400$	−1.47283			−0.0736416
$401$	19.1854	−	33.2301i	0.958073	−	1.65943i	0.230899	−	0.972978i	$-0.425833\pi$
$401$	19.1854	−	33.2301i	0.958073	−	1.65943i	0.727174	−	0.686453i	$-0.240833\pi$
$402$	0.878102	+	5.54896i	0.0437958	+	0.276757i
$403$	0.00715297	−	0.00623085i	0.000356315	−	0.000310381i
$404$	−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
$408$	6.21399	+	7.67576i	0.307639	+	0.380007i
$409$	2.09152	+	3.62262i	0.103419	+	0.179127i	0.913091	−	0.407755i	$-0.133688\pi$
$409$	2.09152	+	3.62262i	0.103419	+	0.179127i	−0.809672	+	0.586882i	$0.800355\pi$
$410$	3.19776	+	5.53868i	0.157926	+	0.273536i
$411$	14.2207	+	17.5660i	0.701457	+	0.866467i
$412$			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
$416$	2.71872	−	2.36824i	0.133296	−	0.116112i
$417$	0.168754	+	1.06640i	0.00826392	+	0.0522219i
$418$	−17.3723	+	30.0897i	−0.849706	+	1.47173i
$419$	−24.4059			−1.19231			−0.596154	−	0.802870i	$-0.703305\pi$
$419$	−24.4059			−1.19231			−0.596154	+	0.802870i	$0.703305\pi$
$420$	−3.87574	+	10.9958i	−0.189117	+	0.536541i
$421$		−	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
$423$	−12.4897	−	2.65829i	−0.607272	−	0.129251i
$424$	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
$429$	−16.4819	+	19.6778i	−0.795753	+	0.950055i
$430$	−7.30764	+	4.21907i	−0.352406	+	0.203462i
$431$	1.83652	+	3.18094i	0.0884620	+	0.153221i	0.906861	−	0.421429i	$-0.138471\pi$
$431$	1.83652	+	3.18094i	0.0884620	+	0.153221i	−0.818399	+	0.574650i	$0.805138\pi$
$432$	0.274044	−	5.18892i	0.0131849	−	0.249652i
$433$			30.9079i			1.48534i	0.669658	+	0.742669i	$0.266441\pi$
$433$			30.9079i			1.48534i	−0.669658	+	0.742669i	$0.733559\pi$
$434$	−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
$438$	−4.51536	+	0.714539i	−0.215752	+	0.0341420i
$439$	31.8737	+	18.4023i	1.52125	+	0.878294i	0.999685	+	0.0250815i	$0.00798452\pi$
$439$	31.8737	+	18.4023i	1.52125	+	0.878294i	0.521564	+	0.853212i	$0.325349\pi$
$440$			10.4572i			0.498527i
$441$	16.3586	+	13.1679i	0.778983	+	0.627045i
$442$	−3.94332	−	20.1763i	−0.187565	−	0.959690i
$443$	−31.8442	−	18.3852i	−1.51296	−	0.873509i	−0.999885	−	0.0151669i	$-0.995172\pi$
$443$	−31.8442	−	18.3852i	−1.51296	−	0.873509i	−0.513077	−	0.858342i	$-0.671495\pi$
$444$	−1.91670	−	12.1121i	−0.0909625	−	0.574816i
$445$	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	$0.529685\pi$
$450$	4.20261	−	1.36426i	0.198113	−	0.0643117i
$451$	8.94802	−	5.16614i	0.421346	−	0.243264i
$452$	0.739822	−	0.427136i	0.0347983	−	0.0200908i
$453$	12.6556	−	10.2455i	0.594611	−	0.481374i
$454$		−	13.4666i		−	0.632017i
$455$	17.8506	−	16.4433i	0.836850	−	0.770876i
$456$	−5.24882	+	13.6681i	−0.245799	+	0.640069i
$457$	−0.843279	−	0.486868i	−0.0394469	−	0.0227747i	0.480147	−	0.877188i	$-0.340583\pi$
$457$	−0.843279	−	0.486868i	−0.0394469	−	0.0227747i	−0.519594	+	0.854413i	$0.673917\pi$
$458$	−1.12680	−	1.95167i	−0.0526517	−	0.0911954i
$459$	−24.8410	−	16.1463i	−1.15948	−	0.753642i
$460$	−1.66379	+	2.88177i	−0.0775745	+	0.134363i
$461$			10.2088i			0.475471i	0.971330	+	0.237736i	$0.0764052\pi$
$461$			10.2088i			0.475471i	−0.971330	+	0.237736i	$0.923595\pi$
$462$	17.7643	+	6.26145i	0.826470	+	0.291309i
$463$		−	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
$465$	0.00181214	+	0.0114514i	8.40360e−5	+	0.000531046i
$466$	1.12902	−	0.651840i	0.0523008	−	0.0301959i
$467$	12.8601	−	22.2744i	0.595097	−	1.03074i	−0.398437	−	0.917196i	$-0.630447\pi$
$467$	12.8601	−	22.2744i	0.595097	−	1.03074i	0.993533	−	0.113542i	$-0.0362196\pi$
$468$	−5.56400	+	9.27588i	−0.257196	+	0.428778i
$469$	−8.57834	+	0.238342i	−0.396111	+	0.0110056i
$470$	10.8293			0.499518
$471$	−9.82929	+	7.95741i	−0.452910	+	0.366658i
$472$	1.68327	−	0.971837i	0.0774789	−	0.0447324i
$473$	6.81612	+	11.8059i	0.313405	+	0.542834i
$474$	−15.4290	−	19.0584i	−0.708676	−	0.875383i
$475$	−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	0.287160	−	0.957883i	$-0.407289\pi$
$479$	27.5828	−	15.9249i	1.26029	−	0.727629i	0.973131	+	0.230254i	$0.0739557\pi$
$480$	0.688764	+	4.35248i	0.0314376	+	0.198663i
$481$	−8.28612	+	24.1449i	−0.377814	+	1.10091i
$482$	13.1946			0.600996
$483$	3.89922	+	4.55190i	0.177420	+	0.207119i
$484$	5.89410			0.267914
$485$	8.62131	+	4.97752i	0.391474	+	0.226017i
$486$	4.02444	+	15.0600i	0.182552	+	0.683136i
$487$	17.8940	−	10.3311i	0.810854	−	0.468147i	−0.0363981	−	0.999337i	$-0.511588\pi$
$487$	17.8940	−	10.3311i	0.810854	−	0.468147i	0.847252	+	0.531190i	$0.178255\pi$
$488$	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	$-0.0657322\pi$
$492$	3.38407	−	2.73961i	0.152566	−	0.123511i
$493$	−29.9329	+	17.2818i	−1.34811	+	0.778332i
$494$	22.9818	−	20.0191i	1.03400	−	0.900703i
$495$	−9.68630	−	29.8387i	−0.435367	−	1.34115i
$496$	−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	$-0.455264\pi$
$499$	−14.4611	−	8.34913i	−0.647368	−	0.373758i	−0.787447	+	0.616382i	$0.788598\pi$
$500$	7.77148	−	4.48687i	0.347551	−	0.200659i
$501$	−6.57135	−	41.5261i	−0.293586	−	1.85525i
$502$	14.2179	−	24.6261i	0.634575	−	1.09912i
$503$	−29.9262			−1.33434			−0.667171	−	0.744904i	$-0.732495\pi$
$503$	−29.9262			−1.33434			−0.667171	+	0.744904i	$0.732495\pi$
$504$	7.80626	+	1.43609i	0.347718	+	0.0639684i
$505$			39.4241i			1.75435i
$506$	4.65564	+	2.68793i	0.206968	+	0.119493i
$507$	19.2783	−	11.6338i	0.856181	−	0.516676i
$508$	6.03573	+	10.4542i	0.267792	+	0.463829i
$509$	29.2792	+	16.9043i	1.29778	+	0.749272i	0.980020	−	0.198900i	$-0.0637369\pi$
$509$	29.2792	+	16.9043i	1.29778	+	0.749272i	0.317757	+	0.948172i	$0.397070\pi$
$510$	23.4557	+	9.00741i	1.03863	+	0.398855i
$511$	−0.193947	−	6.98046i	−0.00857969	−	0.308798i
$512$	−1.00000			−0.0441942
$513$	2.31654	−	43.8628i	0.102278	−	1.93659i
$514$	−9.54939	−	16.5400i	−0.421206	−	0.729550i
$515$	16.9085	+	29.2864i	0.745077	+	1.29051i
$516$	3.61459	+	4.46488i	0.159124	+	0.196556i
$517$		−	17.4952i		−	0.769440i
$518$	18.7246	−	0.520247i	0.822711	−	0.0228583i
$519$	0.254185	−	0.661907i	0.0111575	−	0.0290545i
$520$	2.97761	−	8.67644i	0.130577	−	0.380487i
$521$	−12.3261	−	21.3495i	−0.540017	−	0.935338i	−0.998902	−	0.0468419i	$-0.985084\pi$
$521$	−12.3261	−	21.3495i	−0.540017	−	0.935338i	0.458885	−	0.888496i	$-0.348249\pi$
$522$	17.7872	+	3.78581i	0.778526	+	0.165700i
$523$	−9.97765	−	5.76060i	−0.436292	−	0.251893i	0.265732	−	0.964047i	$-0.414387\pi$
$523$	−9.97765	−	5.76060i	−0.436292	−	0.251893i	−0.702024	+	0.712154i	$0.747720\pi$
$524$	17.2335			0.752847
$525$	1.23968	+	6.63454i	0.0541039	+	0.289555i
$526$			5.19445i			0.226489i
$527$	−0.00750071	+	0.0129916i	−0.000326736	+	0.000565923i
$528$	7.03165	−	1.11273i	0.306013	−	0.0484255i
$529$	−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
$534$	5.15852	−	4.17614i	0.223231	−	0.180719i
$535$	−18.1510	−	31.4384i	−0.784735	−	1.35920i
$536$	−2.80901	+	1.62178i	−0.121331	+	0.0700502i
$537$	31.8561	−	25.7894i	1.37469	−	1.11290i
$538$	−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	$-0.459827\pi$
$541$	−15.5915	−	9.00176i	−0.670331	−	0.387016i	−0.796202	+	0.605031i	$0.793161\pi$
$542$	−12.8489	−	22.2550i	−0.551909	−	0.955935i
$543$	−3.85094	−	24.3351i	−0.165260	−	1.04432i
$544$	−2.85089	+	4.93789i	−0.122231	+	0.211710i
$545$	27.0877			1.16031
$546$	−12.9563	−	10.2535i	−0.554480	−	0.438807i
$547$	−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
$549$	−10.6924	−	2.27575i	−0.456340	−	0.0971266i
$550$	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
$555$	−19.6308	−	24.2487i	−0.833281	−	1.02930i
$556$	−0.539835	+	0.311674i	−0.0228941	+	0.0132179i
$557$	14.7789	+	25.5978i	0.626201	+	1.08461i	0.988307	+	0.152475i	$0.0487244\pi$
$557$	14.7789	+	25.5978i	0.626201	+	1.08461i	−0.362106	+	0.932137i	$0.617942\pi$
$558$	0.00750736	−	0.00243705i	0.000317812	−	0.000103169i
$559$	−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	$-0.329256\pi$
$563$	−11.5996	−	20.0912i	−0.488866	−	0.846741i	−0.999918	+	0.0128088i	$0.995923\pi$
$564$	−1.15233	−	7.28186i	−0.0485217	−	0.306622i
$565$	1.08671	−	1.88224i	0.0457182	−	0.0791863i
$566$		−	19.1931i		−	0.806747i
$567$	−23.6047	+	3.13303i	−0.991306	+	0.131575i
$568$	−6.68865			−0.280650
$569$	15.1314	+	8.73610i	0.634340	+	0.366236i	0.782431	−	0.622738i	$-0.213980\pi$
$569$	15.1314	+	8.73610i	0.634340	+	0.366236i	−0.148091	+	0.988974i	$0.547313\pi$
$570$	5.82224	+	36.7923i	0.243867	+	1.54106i
$571$	4.98953	+	8.64212i	0.208805	+	0.361662i	0.951339	−	0.308148i	$-0.0997091\pi$
$571$	4.98953	+	8.64212i	0.208805	+	0.361662i	−0.742533	+	0.669809i	$0.766376\pi$
$572$	−14.0172	−	4.81047i	−0.586090	−	0.201136i
$573$	25.8782	+	9.93770i	1.08108	+	0.415153i
$574$	3.48412	+	5.66523i	0.145424	+	0.236462i
$575$			1.92634i			0.0803341i
$576$	2.85342	−	0.926282i	0.118892	−	0.0385951i
$577$	−8.91246	−	15.4368i	−0.371031	−	0.642644i	0.618694	−	0.785632i	$-0.287662\pi$
$577$	−8.91246	−	15.4368i	−0.371031	−	0.642644i	−0.989724	+	0.142988i	$0.954329\pi$
$578$	7.75517	+	13.4323i	0.322572	+	0.558712i
$579$	−22.8270	+	18.4799i	−0.948659	+	0.767997i
$580$	−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
$585$	−0.459534	+	27.5156i	−0.0189994	+	1.13763i
$586$	10.1638	+	5.86808i	0.419863	+	0.242408i
$587$		−	47.7903i		−	1.97252i	−0.165206	−	0.986259i	$-0.552829\pi$
$587$		−	47.7903i		−	1.97252i	0.165206	−	0.986259i	$-0.447171\pi$
$588$	−3.71134	+	11.5424i	−0.153053	+	0.475999i
$589$	−0.0222403			−0.000916396
$590$	2.47253	−	4.28254i	0.101792	−	0.176309i
$591$	−4.38919	+	0.694573i	−0.180547	+	0.0285709i
$592$	6.13142	−	3.53998i	0.252000	−	0.145492i
$593$	−8.78037	−	5.06935i	−0.360566	−	0.208173i	0.308763	−	0.951139i	$-0.400085\pi$
$593$	−8.78037	−	5.06935i	−0.360566	−	0.208173i	−0.669329	+	0.742966i	$0.733418\pi$
$594$	−19.0335	+	9.68838i	−0.780956	+	0.397519i
$595$	−18.2595	+	33.7584i	−0.748568	+	1.38396i
$596$	1.97237			0.0807916
$597$	−29.1410	+	23.5914i	−1.19266	+	0.965531i
$598$	−3.09746	−	3.55587i	−0.126665	−	0.145410i
$599$	−10.0365	+	5.79458i	−0.410081	+	0.236760i	−0.690824	−	0.723023i	$-0.742752\pi$
$599$	−10.0365	+	5.79458i	−0.410081	+	0.236760i	0.280744	+	0.959783i	$0.409419\pi$
$600$	1.60514	+	1.98273i	0.0655296	+	0.0809447i
$601$		−	4.44714i		−	0.181403i	−0.995878	−	0.0907013i	$-0.971089\pi$
$601$		−	4.44714i		−	0.181403i	0.995878	−	0.0907013i	$-0.0289109\pi$
$602$	−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
$606$	26.5097	−	4.19505i	1.07688	−	0.170412i
$607$	5.35667	+	3.09268i	0.217421	+	0.125528i	0.604755	−	0.796411i	$-0.293271\pi$
$607$	5.35667	+	3.09268i	0.217421	+	0.125528i	−0.387335	+	0.921939i	$0.626604\pi$
$608$	−8.45317			−0.342821
$609$	−9.23454	+	26.1992i	−0.374202	+	1.06165i
$610$	9.27088			0.375367
$611$	−4.98165	+	14.5160i	−0.201536	+	0.587255i
$612$	3.56091	−	16.7306i	0.143941	−	0.676294i
$613$	19.9940	−	11.5435i	0.807549	−	0.466239i	−0.0385548	−	0.999256i	$-0.512275\pi$
$613$	19.9940	−	11.5435i	0.807549	−	0.466239i	0.846104	+	0.533018i	$0.178942\pi$
$614$	−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	$0.594279\pi$
$618$	17.8936	−	14.4860i	0.719787	−	0.582711i
$619$	11.4323	+	19.8013i	0.459503	+	0.795882i	0.998935	−	0.0461472i	$-0.0146943\pi$
$619$	11.4323	+	19.8013i	0.459503	+	0.795882i	−0.539432	+	0.842029i	$0.681361\pi$
$620$	−0.00579695	+	0.00334687i	−0.000232811	+	0.000134414i
$621$	−6.78669	−	0.358427i	−0.272340	−	0.0143832i
$622$	−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
$627$	59.4397	−	9.40612i	2.37379	−	0.375644i
$628$	−6.32327	−	3.65074i	−0.252326	−	0.145681i
$629$		−	40.3684i		−	1.60959i
$630$	19.0265	−	6.76608i	0.758035	−	0.269567i
$631$		−	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
$633$	11.9876	−	1.89699i	0.476463	−	0.0753985i
$634$	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
$637$	18.0812	−	17.6088i	0.716403	−	0.697686i
$638$			24.9158i			0.986427i
$639$	19.0855	−	6.19558i	0.755012	−	0.245093i
$640$	−2.20332	+	1.27209i	−0.0870939	+	0.0502837i
$641$	−24.5592	+	14.1793i	−0.970030	+	0.560047i	−0.899245	−	0.437445i	$-0.855884\pi$
$641$	−24.5592	+	14.1793i	−0.970030	+	0.560047i	−0.0707844	+	0.997492i	$0.522550\pi$
$642$	−19.2085	+	15.5504i	−0.758099	+	0.613727i
$643$	−7.46124			−0.294243			−0.147121	−	0.989118i	$-0.547001\pi$
$643$	−7.46124			−0.294243			−0.147121	+	0.989118i	$0.547001\pi$
$644$	−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	$-0.00267646\pi$
$647$	12.5324	+	21.7068i	0.492701	+	0.853382i	−0.507264	+	0.861791i	$0.669343\pi$
$648$	−7.28400	+	5.28614i	−0.286143	+	0.207659i
$649$	−6.91866	−	3.99449i	−0.271581	−	0.156797i
$650$	−1.01860	−	5.21177i	−0.0399529	−	0.204422i
$651$	0.00221451	+	0.0118517i	8.67933e−5	+	0.000464503i
$652$			15.1308i			0.592568i
$653$	9.06026	+	5.23094i	0.354555	+	0.204703i	0.666690	−	0.745335i	$-0.267711\pi$
$653$	9.06026	+	5.23094i	0.354555	+	0.204703i	−0.312134	+	0.950038i	$0.601044\pi$
$654$	−2.88236	−	18.2144i	−0.112709	−	0.712239i
$655$	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	$0.838931\pi$
$660$	14.0775	−	11.3966i	0.547966	−	0.443612i
$661$	24.9458	+	43.2074i	0.970280	+	1.68057i	0.694706	+	0.719294i	$0.255535\pi$
$661$	24.9458	+	43.2074i	0.970280	+	1.68057i	0.275574	+	0.961280i	$0.411132\pi$
$662$	4.14357	−	2.39229i	0.161044	−	0.0929790i
$663$	−22.8639	+	27.2974i	−0.887960	+	1.06014i
$664$		−	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
$669$	−36.1967	+	5.72799i	−1.39944	+	0.221457i
$670$	−4.12609	+	7.14660i	−0.159405	+	0.276097i
$671$		−	14.9776i		−	0.578203i
$672$	0.841696	+	4.50461i	0.0324691	+	0.173769i
$673$	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
$675$	−6.41671	−	4.17075i	−0.246979	−	0.160532i
$676$	10.2605	+	7.98261i	0.394635	+	0.307023i
$677$	−17.9807	+	31.1435i	−0.691056	+	1.19694i	0.280437	+	0.959873i	$0.409521\pi$
$677$	−17.9807	+	31.1435i	−0.691056	+	1.19694i	−0.971492	+	0.237071i	$0.923813\pi$
$678$	−1.38129	−	0.530443i	−0.0530483	−	0.0203715i
$679$	9.10582	+	4.92524i	0.349449	+	0.189013i
$680$			14.5063i			0.556293i
$681$	−18.1287	+	14.6763i	−0.694694	+	0.562397i
$682$	0.00540703	+	0.00936526i	0.000207046	+	0.000358614i
$683$	13.5825	+	23.5256i	0.519721	+	0.900184i	0.999737	+	0.0229240i	$0.00729756\pi$
$683$	13.5825	+	23.5256i	0.519721	+	0.900184i	−0.480016	+	0.877260i	$0.659369\pi$
$684$	24.1204	−	7.83001i	0.922268	−	0.299388i
$685$			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
$689$	12.0198	+	13.7986i	0.457917	+	0.525685i
$690$	5.69269	−	0.900847i	0.216717	−	0.0342947i
$691$	15.9012	−	27.5418i	0.604912	−	1.04774i	−0.387153	−	0.922015i	$-0.626542\pi$
$691$	15.9012	−	27.5418i	0.604912	−	1.04774i	0.992065	−	0.125723i	$-0.0401251\pi$
$692$	0.409361			0.0155616
$693$	−10.9309	−	30.7383i	−0.415232	−	1.16765i
$694$		−	6.30342i		−	0.239275i
$695$	−0.792954	+	1.37344i	−0.0300785	+	0.0520974i
$696$	1.64109	+	10.3705i	0.0622052	+	0.393091i
$697$	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	$-0.152170\pi$
$702$	18.5510	−	2.61889i	0.700164	−	0.0988438i
$703$	51.8299	−	29.9240i	1.95480	−	1.12861i
$704$	2.05512	+	3.55958i	0.0774553	+	0.134157i
$705$	−11.8021	−	14.5784i	−0.444493	−	0.549055i
$706$			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	$-0.0355613\pi$
$709$	37.1207	+	21.4317i	1.39410	+	0.804883i	0.400332	+	0.916370i	$0.368895\pi$
$710$	−14.7373	+	8.50856i	−0.553079	+	0.319320i
$711$	−8.84153	+	41.5411i	−0.331583	+	1.55791i
$712$	3.31853	+	1.91595i	0.124367	+	0.0718034i
$713$			0.00344114i			0.000128872i
$714$	24.6429	+	8.68596i	0.922236	+	0.325064i
$715$	−37.0038	+	7.23213i	−1.38386	+	0.270466i
$716$	20.4933	+	11.8318i	0.765871	+	0.442176i
$717$	−5.98976	+	0.947857i	−0.223692	+	0.0353984i
$718$	8.18866	+	14.1832i	0.305598	+	0.529311i
$719$	−14.3834	+	24.9128i	−0.536410	+	0.929090i	0.462683	+	0.886524i	$0.346887\pi$
$719$	−14.3834	+	24.9128i	−0.536410	+	0.929090i	−0.999094	+	0.0425664i	$0.986447\pi$
$720$	5.10869	−	5.67070i	0.190390	−	0.211334i
$721$	18.4226	+	29.9555i	0.686094	+	1.11560i
$722$	−52.4560			−1.95221
$723$	−14.3799	−	17.7626i	−0.534794	−	0.660597i
$724$	12.3190	−	7.11236i	0.457831	−	0.264329i
$725$	−7.73200	+	4.46407i	−0.287159	+	0.165791i
$726$	−6.42359	−	7.93466i	−0.238402	−	0.294483i
$727$		−	9.23311i		−	0.342437i	−0.985233	−	0.171219i	$-0.945230\pi$
$727$		−	9.23311i		−	0.342437i	0.985233	−	0.171219i	$-0.0547704\pi$
$728$	2.84470	−	9.10537i	0.105432	−	0.337467i
$729$	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
$732$	−0.986500	−	6.23395i	−0.0364621	−	0.230414i
$733$	19.7916	−	34.2800i	0.731018	−	1.26616i	−0.225431	−	0.974259i	$-0.572379\pi$
$733$	19.7916	−	34.2800i	0.731018	−	1.26616i	0.956449	−	0.291901i	$-0.0942878\pi$
$734$			31.1600i			1.15014i
$735$	6.50563	+	30.1527i	0.239964	+	1.11220i
$736$			1.30792i			0.0482105i
$737$	11.5457	+	6.66591i	0.425291	+	0.245542i
$738$	−7.37615	−	1.56993i	−0.271520	−	0.0577898i
$739$	−25.0159	+	14.4429i	−0.920224	+	0.531291i	−0.883706	−	0.468042i	$-0.844960\pi$
$739$	−25.0159	+	14.4429i	−0.920224	+	0.531291i	−0.0365171	+	0.999333i	$0.511626\pi$
$740$	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	$0.583922\pi$
$744$	0.00286736	+	0.00354187i	0.000105122	+	0.000129851i
$745$	4.34577	−	2.50903i	0.159217	−	0.0919238i
$746$	11.8848	+	20.5851i	0.435133	+	0.753673i
$747$	10.3095	+	31.7586i	0.377206	+	1.16199i
$748$	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	−0.974704	−	0.223498i	$-0.928253\pi$
$751$	−8.05134	+	13.9453i	−0.293798	+	0.508873i	0.680907	+	0.732370i	$0.261586\pi$
$752$	3.68624	−	2.12825i	0.134423	−	0.0776093i
$753$	−48.6468	+	7.69818i	−1.77279	+	0.280537i
$754$	7.09461	−	20.6729i	0.258370	−	0.752864i
$755$	23.9176			0.870452
$756$	−6.57425	−	12.0739i	−0.239103	−	0.439124i
$757$	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
$759$	−1.45536	−	9.19683i	−0.0528264	−	0.333824i
$760$	−18.6250	+	10.7532i	−0.675601	+	0.390059i
$761$	2.32242	+	1.34085i	0.0841876	+	0.0486057i	0.541503	−	0.840699i	$-0.317856\pi$
$761$	2.32242	+	1.34085i	0.0841876	+	0.0486057i	−0.457315	+	0.889305i	$0.651189\pi$
$762$	7.49552	−	19.5186i	0.271534	−	0.707085i
$763$	28.1583	−	0.782355i	1.01940	−	0.0283232i
$764$			16.0046i			0.579024i
$765$	−13.4370	−	41.3927i	−0.485814	−	1.49656i
$766$	−12.8839	+	7.43851i	−0.465514	+	0.268764i
$767$	4.60309	+	5.28431i	0.166208	+	0.190805i
$768$	1.08983	+	1.34620i	0.0393260	+	0.0485769i
$769$	−39.1298			−1.41106			−0.705528	−	0.708682i	$-0.749290\pi$
$769$	−39.1298			−1.41106			−0.705528	+	0.708682i	$0.749290\pi$
$770$	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	−0.000279226	−	1.00000i	$-0.500089\pi$
$773$	24.0664	−	13.8947i	0.865607	−	0.499758i	0.865886	+	0.500242i	$0.166756\pi$
$774$	2.07133	−	9.73196i	0.0744526	−	0.349808i
$775$	−0.00193751	+	0.00335587i	−6.95976e−5	+	0.000120547i
$776$	3.91287			0.140464
$777$	−21.1070	−	24.6401i	−0.757211	−	0.883959i
$778$			31.0109i			1.11180i
$779$	18.4026	+	10.6247i	0.659341	+	0.380671i
$780$	−14.9254	+	5.44741i	−0.534413	+	0.195049i
$781$	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
$786$	−18.7816	−	23.1997i	−0.669917	−	0.827507i
$787$	−22.3703	−	38.7465i	−0.797415	−	1.38116i	−0.921294	−	0.388866i	$-0.872867\pi$
$787$	−22.3703	−	38.7465i	−0.797415	−	1.38116i	0.123879	−	0.992297i	$-0.460466\pi$
$788$	−1.28282	−	2.22190i	−0.0456984	−	0.0791520i
$789$	6.99279	−	5.66109i	0.248950	−	0.201540i
$790$		−	36.0184i		−	1.28148i
$791$	1.07530	−	1.98802i	0.0382332	−	0.0706857i
$792$	−9.16129	−	8.25334i	−0.325532	−	0.293270i
$793$	−4.26476	+	12.4271i	−0.151446	+	0.441298i
$794$	7.10552	+	12.3071i	0.252166	+	0.436763i
$795$	−22.0906	+	3.49576i	−0.783473	+	0.123982i
$796$	−18.7467	−	10.8234i	−0.664458	−	0.383625i
$797$	16.6004			0.588016			0.294008	−	0.955803i	$-0.405011\pi$
$797$	16.6004			0.588016			0.294008	+	0.955803i	$0.405011\pi$
$798$	7.11500	+	38.0783i	0.251868	+	1.34796i
$799$		−	24.2696i		−	0.858598i
$800$	−0.736416	+	1.27551i	−0.0260362	+	0.0450961i
$801$	−11.2439	−	2.39312i	−0.397282	−	0.0845569i
$802$	−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
$807$	6.76147	+	8.35202i	0.238015	+	0.294005i
$808$	7.74790	+	13.4198i	0.272570	+	0.472106i
$809$	−11.8831	+	6.86068i	−0.417786	+	0.241209i	−0.694130	−	0.719850i	$-0.744211\pi$
$809$	−11.8831	+	6.86068i	−0.417786	+	0.241209i	0.276344	+	0.961059i	$0.410877\pi$
$810$	−9.32456	+	20.9130i	−0.327632	+	0.734807i
$811$	−27.2852			−0.958114			−0.479057	−	0.877784i	$-0.659021\pi$
$811$	−27.2852			−0.958114			−0.479057	+	0.877784i	$0.659021\pi$
$812$	−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
$816$	9.75440	−	1.54360i	0.341472	−	0.0540367i
$817$	−14.0181	+	24.2800i	−0.490431	+	0.849451i
$818$	4.18304			0.146257
$819$	0.317019	+	28.6164i	0.0110775	+	0.999939i
$820$	6.39552			0.223341
$821$	−25.2745	+	43.7767i	−0.882085	+	1.52782i	−0.0330672	+	0.999453i	$0.510528\pi$
$821$	−25.2745	+	43.7767i	−0.882085	+	1.52782i	−0.849018	+	0.528364i	$0.822806\pi$
$822$	22.3230	−	3.53253i	0.778603	−	0.123211i
$823$	22.1516	+	38.3677i	0.772156	+	1.33741i	0.936379	+	0.350990i	$0.114155\pi$
$823$	22.1516	+	38.3677i	0.772156	+	1.33741i	−0.164224	+	0.986423i	$0.552512\pi$
$824$	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	$0.387471\pi$
$828$	−1.21150	−	3.73204i	−0.0421026	−	0.129697i
$829$	7.87052	−	4.54405i	0.273354	−	0.157821i	−0.357057	−	0.934083i	$-0.616220\pi$
$829$	7.87052	−	4.54405i	0.273354	−	0.157821i	0.630411	+	0.776261i	$0.282886\pi$
$830$	−14.1584	−	24.5230i	−0.491444	−	0.851206i
$831$	26.5005	+	32.7345i	0.919293	+	1.13555i
$832$	−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
$837$	−0.0114625	−	0.00745045i	−0.000396203	−	0.000257525i
$838$	−12.2030	+	21.1362i	−0.421544	+	0.730136i
$839$			27.0968i			0.935486i	0.883865	+	0.467743i	$0.154933\pi$
$839$			27.0968i			0.935486i	−0.883865	+	0.467743i	$0.845067\pi$
$840$	7.58479	+	8.85440i	0.261700	+	0.305506i
$841$	−7.74648			−0.267120
$842$	−6.12262	−	3.53489i	−0.210999	−	0.121821i
$843$	−38.8710	+	6.15120i	−1.33879	+	0.211858i
$844$	3.50357	+	6.06837i	0.120598	+	0.208882i
$845$	32.7618	+	4.53599i	1.12704	+	0.156043i
$846$	−8.54702	+	9.48728i	−0.293853	+	0.326179i
$847$	13.2833	−	8.16924i	0.456420	−	0.280698i
$848$		−	5.07540i		−	0.174290i
$849$	−25.8378	+	20.9173i	−0.886752	+	0.717880i
$850$	4.19888	+	7.27268i	0.144021	+	0.249451i
$851$	−4.63000	−	8.01940i	−0.158715	−	0.274902i
$852$	7.28952	+	9.00429i	0.249735	+	0.308482i
$853$	22.7608			0.779314			0.389657	−	0.920960i	$-0.372594\pi$
$853$	22.7608			0.779314			0.389657	+	0.920960i	$0.372594\pi$
$854$	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	$-0.0248779\pi$
$857$	12.6132	+	21.8466i	0.430857	+	0.746267i	−0.566090	+	0.824343i	$0.691545\pi$
$858$	8.80057	+	24.1127i	0.300446	+	0.823192i
$859$	−30.6299	−	17.6842i	−1.04508	−	0.603377i	−0.123812	−	0.992306i	$-0.539512\pi$
$859$	−30.6299	−	17.6842i	−1.04508	−	0.603377i	−0.921268	+	0.388928i	$0.872845\pi$
$860$			8.43814i			0.287738i
$861$	3.82945	−	10.8645i	0.130507	−	0.370261i
$862$	3.67304			0.125104
$863$	−4.16054	+	7.20627i	−0.141627	+	0.245304i	−0.928109	−	0.372308i	$-0.878567\pi$
$863$	−4.16054	+	7.20627i	−0.141627	+	0.245304i	0.786483	+	0.617612i	$0.211900\pi$
$864$	−4.35672	−	2.83179i	−0.148218	−	0.0963394i
$865$	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
$870$	16.8080	+	20.7618i	0.569843	+	0.703892i
$871$	−7.68152	−	8.81834i	−0.260278	−	0.298798i
$872$	9.22052	−	5.32347i	0.312246	−	0.180275i
$873$	−11.1651	+	3.62442i	−0.377880	+	0.122668i
$874$			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	$-0.370697\pi$
$877$	−6.00709	−	3.46819i	−0.202845	−	0.117113i	−0.597982	+	0.801510i	$0.704031\pi$
$878$	31.8737	−	18.4023i	1.07569	−	0.621047i
$879$	−3.17724	−	20.0778i	−0.107166	−	0.677207i
$880$	9.05619	+	5.22859i	0.305284	+	0.176256i
$881$	10.2056			0.343835			0.171917	−	0.985111i	$-0.445004\pi$
$881$	10.2056			0.343835			0.171917	+	0.985111i	$0.445004\pi$
$882$	19.5831	−	7.58303i	0.659397	−	0.255334i
$883$	−16.1358			−0.543013			−0.271506	−	0.962437i	$-0.587522\pi$
$883$	−16.1358			−0.543013			−0.271506	+	0.962437i	$0.587522\pi$
$884$	−19.4449	−	6.67315i	−0.654002	−	0.224442i
$885$	−8.45981	+	1.33873i	−0.284373	+	0.0450010i
$886$	−31.8442	+	18.3852i	−1.06983	+	0.617664i
$887$	−12.1918	+	21.1167i	−0.409359	+	0.709031i	−0.994818	−	0.101671i	$-0.967581\pi$
$887$	−12.1918	+	21.1167i	−0.409359	+	0.709031i	0.585459	+	0.810702i	$0.300914\pi$
$888$	−11.4478	−	4.39615i	−0.384162	−	0.147525i
$889$	28.0920	+	15.1947i	0.942176	+	0.509613i
$890$	9.74904			0.326789
$891$	33.7859	+	15.0643i	1.13187	+	0.504673i
$892$	−10.5791	−	18.3235i	−0.354214	−	0.613517i
$893$	31.1604	−	17.9904i	1.04274	−	0.602027i
$894$	−2.14956	−	2.65522i	−0.0718920	−	0.0888037i
$895$	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
$900$	0.919822	−	4.32169i	0.0306607	−	0.144056i
$901$	−25.0618	−	14.4694i	−0.834929	−	0.482046i
$902$		−	10.3323i		−	0.344027i
$903$	14.3344	+	5.05251i	0.477020	+	0.168137i
$904$		−	0.854272i		−	0.0284127i
$905$	18.0951	−	31.3416i	0.601501	−	1.04183i
$906$	−2.54504	−	16.0828i	−0.0845533	−	0.534315i
$907$	−9.19556	−	15.9272i	−0.305334	−	0.528853i	0.672002	−	0.740549i	$-0.265435\pi$
$907$	−9.19556	−	15.9272i	−0.305334	−	0.528853i	−0.977336	+	0.211696i	$0.932101\pi$
$908$	−11.6624	−	6.73328i	−0.387030	−	0.223452i
$909$	−34.5385	−	31.1155i	−1.14557	−	1.03204i
$910$	−5.31504	−	23.6808i	−0.176192	−	0.785009i
$911$			29.8085i			0.987598i	0.869576	+	0.493799i	$0.164392\pi$
$911$			29.8085i			0.987598i	−0.869576	+	0.493799i	$0.835608\pi$
$912$	9.21254	+	11.3797i	0.305058	+	0.376819i
$913$	−39.6182	+	22.8736i	−1.31117	+	0.757004i
$914$	−0.843279	+	0.486868i	−0.0278932	+	0.0161041i
$915$	−10.1037	−	12.4805i	−0.334019	−	0.412592i
$916$	−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	−0.755399	−	0.655265i	$-0.772557\pi$
$919$	5.75307	−	9.96461i	0.189776	−	0.328702i	0.945176	+	0.326563i	$0.105890\pi$
$920$	1.66379	+	2.88177i	0.0548535	+	0.0950090i
$921$	46.6025	−	7.37468i	1.53561	−	0.243004i
$922$	8.84108	+	5.10440i	0.291166	+	0.168105i
$923$	−4.62583	−	23.6685i	−0.152261	−	0.779057i
$924$	14.3047	−	12.2536i	0.470591	−	0.403114i
$925$		−	10.4276i		−	0.342857i
$926$	−9.91036	−	5.72175i	−0.325675	−	0.188028i
$927$	−39.0021	−	8.30115i	−1.28100	−	0.272645i
$928$	−5.24975	+	3.03094i	−0.172331	+	0.0994956i
$929$	26.9309	+	15.5486i	0.883576	+	0.510133i	0.871836	−	0.489798i	$-0.162930\pi$
$929$	26.9309	+	15.5486i	0.883576	+	0.510133i	0.0117399	+	0.999931i	$0.496263\pi$
$930$	0.0108233	+	0.00415634i	0.000354909	+	0.000136292i
$931$	−59.0809	+	3.28556i	−1.93630	+	0.107680i
$932$		−	1.30368i		−	0.0427034i
$933$	3.18211	+	3.93066i	0.104178	+	0.128684i
$934$	−12.8601	−	22.2744i	−0.420797	−	0.728842i
$935$	51.6364	−	29.8123i	1.68869	−	0.974966i
$936$	5.25115	+	9.45650i	0.171639	+	0.309095i
$937$			39.5487i			1.29200i	0.763338	+	0.645999i	$0.223559\pi$
$937$			39.5487i			1.29200i	−0.763338	+	0.645999i	$0.776441\pi$
$938$	−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	−0.454553	−	0.890720i	$-0.650201\pi$
$941$	2.74724	−	1.58612i	0.0895573	−	0.0517059i	0.544110	+	0.839014i	$0.316867\pi$
$942$	1.97667	+	12.4911i	0.0644035	+	0.406983i
$943$	1.64392	−	2.84735i	0.0535333	−	0.0927223i
$944$		−	1.94367i		−	0.0632612i
$945$	−29.8443	−	18.2397i	−0.970834	−	0.593336i
$946$	13.6322			0.443222
$947$	4.60358	−	7.97363i	0.149596	−	0.259108i	−0.781482	−	0.623928i	$-0.785536\pi$
$947$	4.60358	−	7.97363i	0.149596	−	0.259108i	0.931078	+	0.364819i	$0.118869\pi$
$948$	−24.2196	+	3.83266i	−0.786615	+	0.124479i
$949$	7.17575	−	6.25070i	0.232935	−	0.202906i
$950$	−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	$0.826737\pi$
$954$	4.70125	+	14.4823i	0.152209	+	0.468880i
$955$	20.3592	+	35.2632i	0.658808	+	1.14109i
$956$	−1.75061	−	3.03215i	−0.0566188	−	0.0980666i
$957$	33.5418	−	27.1541i	1.08425	−	0.877768i
$958$		−	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
$962$	16.7670	+	19.2484i	0.540591	+	0.620594i
$963$	41.8681	+	8.91114i	1.34918	+	0.287157i
$964$	6.59729	−	11.4268i	0.212484	−	0.368034i
$965$	−43.1406			−1.38874
$966$	5.89167	−	1.10087i	0.189561	−	0.0354199i
$967$		−	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
$969$	82.4556	−	13.0483i	2.64885	−	0.419171i
$970$	8.62131	−	4.97752i	0.276814	−	0.159818i
$971$	10.8088	−	18.7213i	0.346870	−	0.600796i	−0.638822	−	0.769355i	$-0.720578\pi$
$971$	10.8088	−	18.7213i	0.346870	−	0.600796i	0.985692	+	0.168559i	$0.0539113\pi$
$972$	15.0546	+	4.04474i	0.482876	+	0.129735i
$973$	−0.784626	+	1.45062i	−0.0251540	+	0.0465048i
$974$		−	20.6622i		−	0.662060i
$975$	−5.90599	+	7.05120i	−0.189143	+	0.225819i
$976$	3.15576	−	1.82198i	0.101014	−	0.0583202i
$977$	22.6382	+	39.2106i	0.724261	+	1.25446i	0.959277	+	0.282466i	$0.0911523\pi$
$977$	22.6382	+	39.2106i	0.724261	+	1.25446i	−0.235016	+	0.971991i	$0.575514\pi$
$978$	20.3691	−	16.4900i	0.651333	−	0.527294i
$979$		−	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	−0.861595	−	0.507596i	$-0.830534\pi$
$983$	−26.7378	+	15.4371i	−0.852802	+	0.492365i	0.00879326	+	0.999961i	$0.497201\pi$
$984$	−0.680538	−	4.30050i	−0.0216947	−	0.137095i
$985$	−5.65291	−	3.26371i	−0.180117	−	0.103990i
$986$			34.5636i			1.10073i
$987$	−12.6896	−	14.8137i	−0.403915	−	0.471526i
$988$	−5.84616	−	29.9124i	−0.185991	−	0.951640i
$989$	3.75674	+	2.16895i	0.119457	+	0.0689687i
$990$	−30.6842	−	6.53079i	−0.975209	−	0.207562i
$991$	8.78463	+	15.2154i	0.279053	+	0.483334i	0.971150	−	0.238471i	$-0.0766462\pi$
$991$	8.78463	+	15.2154i	0.279053	+	0.483334i	−0.692097	+	0.721805i	$0.743313\pi$
$992$	−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
$996$	−14.9833	+	12.1299i	−0.474763	+	0.384350i
$997$	−25.9590	+	14.9874i	−0.822129	+	0.474656i	−0.851150	−	0.524922i	$-0.824094\pi$
$997$	−25.9590	+	14.9874i	−0.822129	+	0.474656i	0.0290211	+	0.999579i	$0.490761\pi$
$998$	−14.4611	+	8.34913i	−0.457759	+	0.264287i
$999$	36.7373	+	1.94022i	1.16232	+	0.0613858i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.1	✓	36	21.17	even	6
546.2.bg.a.311.6	yes	36	91.38	odd	6
546.2.bg.a.467.1	yes	36	13.12	even	2
546.2.bg.a.467.6	yes	36	3.2	odd	2
546.2.bg.b.311.1	yes	36	273.38	even	6	inner
546.2.bg.b.311.6	yes	36	7.3	odd	6	inner
546.2.bg.b.467.1	yes	36	1.1	even	1	trivial
546.2.bg.b.467.6	yes	36	39.38	odd	2	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.71076 + 0.270722i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.20332 - 1.27209i) q^{5} +(-0.620929 + 1.61693i) q^{6} +(-2.32714 - 1.25873i) q^{7} -1.00000 q^{8} +(2.85342 - 0.926282i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.71076 + 0.270722i) 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} +(2.85342 - 0.926282i) q^{9} +(-2.20332 + 1.27209i) q^{10} +(2.05512 + 3.55958i) q^{11} +(1.08983 + 1.34620i) 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} +(0.624526 - 2.93427i) q^{18} +(-4.22658 + 7.32066i) q^{19} +2.54418i q^{20} +(4.32196 + 1.52338i) q^{21} +4.11024 q^{22} +(1.13269 + 0.653959i) q^{23} +(1.71076 - 0.270722i) q^{24} +(0.736416 + 1.27551i) q^{25} +(-3.41032 - 1.17036i) q^{26} +(-4.63076 + 2.35713i) q^{27} +(0.0734817 + 2.64473i) q^{28} +6.06189i q^{29} +(3.42498 - 2.77273i) q^{30} +(0.00131550 + 0.00227852i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.47948 - 5.53322i) 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} +(2.14113 + 5.86648i) q^{39} +(2.20332 + 1.27209i) q^{40} -2.51379i q^{41} +(3.48026 - 2.98124i) q^{42} +3.31665 q^{43} +(2.05512 - 3.55958i) q^{44} +(-7.46531 - 1.58890i) 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} +(-6.21399 - 7.67576i) q^{51} +(-2.71872 + 2.36824i) q^{52} +(-4.39543 + 2.53770i) q^{53} +(-0.274044 + 5.18892i) 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} +(-0.688764 - 4.35248i) q^{60} +(-3.15576 - 1.82198i) q^{61} +0.00263100 q^{62} +(-7.80626 - 1.43609i) q^{63} +1.00000 q^{64} +(-2.97761 + 8.67644i) q^{65} +(-7.03165 + 1.11273i) 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} +(-2.85342 + 0.926282i) q^{72} +(1.31969 + 2.28578i) q^{73} +(-6.13142 + 3.53998i) q^{74} +(-1.60514 - 1.98273i) 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} +(7.28400 - 5.28614i) q^{81} +(-2.17701 - 1.25689i) q^{82} +11.1300i q^{83} +(-0.841696 - 4.50461i) q^{84} -14.5063i q^{85} +(1.65832 - 2.87230i) q^{86} +(-1.64109 - 10.3705i) q^{87} +(-2.05512 - 3.55958i) q^{88} +(-3.31853 - 1.91595i) q^{89} +(-5.10869 + 5.67070i) q^{90} +(-2.84470 + 9.10537i) q^{91} -1.30792i q^{92} +(-0.00286736 - 0.00354187i) q^{93} +(-3.68624 + 2.12825i) q^{94} +(18.6250 - 10.7532i) q^{95} +(-1.08983 - 1.34620i) 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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