LMFDB - Embedded newform 546.2.bg.a.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.a.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} +(3.41032 - 1.17036i) 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} +(5.51740 - 2.92546i) 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} +(-2.71872 - 2.36824i) 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} +(2.97761 + 8.67644i) 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} +(-5.29222 - 3.31548i) 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} +(-2.84470 - 9.10537i) 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	0.0814725	−	0.996676i	$-0.474038\pi$
$5$	2.20332	−	1.27209i	0.985355	−	0.568895i	0.903883	+	0.427781i	$0.140704\pi$
$6$	−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	$0.379389\pi$
$11$	−2.05512	+	3.55958i	−0.619643	+	1.07325i	−0.989551	+	0.144184i	$0.953944\pi$
$12$	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	$-0.745296\pi$
$19$	−4.22658	−	7.32066i	−0.969645	−	1.67947i	−0.273064	−	0.961996i	$-0.588037\pi$
$20$			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
$26$	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	$0.809712\pi$
$30$	0.688764	+	4.35248i	0.125751	+	0.794651i
$31$	0.00131550	−	0.00227852i	0.000236271	−	0.000409234i	−0.865907	−	0.500205i	$-0.833258\pi$
$31$	0.00131550	−	0.00227852i	0.000236271	−	0.000409234i	0.866144	+	0.499795i	$0.166591\pi$
$32$	−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	−0.910605	−	0.413277i	$-0.864384\pi$
$37$	−6.13142	+	3.53998i	−1.00800	+	0.581969i	−0.0973943	+	0.995246i	$0.531051\pi$
$38$	−4.22658	+	7.32066i	−0.685642	+	1.18757i
$39$	5.51740	−	2.92546i	0.883491	−	0.468448i
$40$	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	$-0.0628907\pi$
$42$	−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	−0.206451	−	0.978457i	$-0.566191\pi$
$47$	3.68624	−	2.12825i	0.537693	−	0.310437i	0.744143	+	0.668020i	$0.232858\pi$
$48$	−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
$52$	−2.71872	−	2.36824i	−0.377019	−	0.328416i
$53$	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	0.605554	−	0.795805i	$-0.292952\pi$
$59$	1.68327	+	0.971837i	0.219143	+	0.126522i	−0.386410	+	0.922327i	$0.626285\pi$
$60$	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
$65$	2.97761	+	8.67644i	0.369327	+	1.07618i
$66$	−4.47948	−	5.53322i	−0.551386	−	0.681093i
$67$	2.80901	+	1.62178i	0.343175	+	0.198132i	0.661675	−	0.749791i	$-0.269846\pi$
$67$	2.80901	+	1.62178i	0.343175	+	0.198132i	−0.318500	+	0.947923i	$0.603179\pi$
$68$	−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	$-0.629914\pi$
$71$	−6.68865			−0.793797			−0.396899	+	0.917862i	$0.629914\pi$
$72$	−0.624526	+	2.93427i	−0.0736011	+	0.345808i
$73$	1.31969	−	2.28578i	0.154458	−	0.267530i	−0.778403	−	0.627765i	$-0.783970\pi$
$73$	1.31969	−	2.28578i	0.154458	−	0.267530i	0.932862	+	0.360235i	$0.117303\pi$
$74$	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
$78$	−5.29222	−	3.31548i	−0.599226	−	0.375404i
$79$	−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	$0.209168\pi$
$83$			11.1300i			1.22168i	−0.791755	+	0.610839i	$0.790832\pi$
$84$	−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	−0.313698	−	0.949523i	$-0.601568\pi$
$89$	3.31853	−	1.91595i	0.351763	−	0.203091i	0.665462	+	0.746432i	$0.268235\pi$
$90$	5.10869	−	5.67070i	0.538503	−	0.597744i
$91$	−2.84470	−	9.10537i	−0.298205	−	0.954502i
$92$		−	1.30792i		−	0.136360i
$93$	−0.00450102		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	$-0.563654\pi$
$97$	−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	−0.166100	−	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	−0.0114648	−	0.999934i	$-0.503649\pi$
$109$	−9.22052	−	5.32347i	−0.883166	−	0.509896i	−0.871701	+	0.490038i	$0.836983\pi$
$110$	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
$117$	−9.95131	−	4.23928i	−0.919999	−	0.391921i
$118$		−	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
$130$	6.02522	−	6.91691i	0.528446	−	0.606653i
$131$	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	$-0.645130\pi$
$137$	6.52427	−	11.3004i	0.557406	−	0.965456i	0.997712	−	0.0676081i	$-0.0215367\pi$
$138$	−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
$143$	−11.1746	−	9.73404i	−0.934468	−	0.814001i
$144$	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	0.903590	−	0.428398i	$-0.140922\pi$
$149$	0.986187	+	1.70813i	0.0807916	+	0.139935i	−0.822799	+	0.568333i	$0.807589\pi$
$150$	1.60514	+	1.98273i	0.131059	+	0.161889i
$151$	−8.14145	−	4.70047i	−0.662542	−	0.382519i	0.130703	−	0.991422i	$-0.458277\pi$
$151$	−8.14145	−	4.70047i	−0.662542	−	0.382519i	−0.793245	+	0.608903i	$0.791610\pi$
$152$	−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
$156$	−0.225177	+	6.24094i	−0.0180286	+	0.499675i
$157$	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	−0.915939	−	0.401317i	$-0.868552\pi$
$163$	−13.1037	+	7.56540i	−1.02636	+	0.592568i	−0.110418	+	0.993885i	$0.535219\pi$
$164$	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	$0.388402\pi$
$167$			24.2735i			1.87834i	−0.343458	+	0.939168i	$0.611598\pi$
$168$	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	$-0.177304\pi$
$182$	−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
$186$	0.00286736	+	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	0.924611	−	0.380912i	$-0.124390\pi$
$193$	14.6848	+	8.47830i	1.05704	+	0.610281i	0.132427	+	0.991193i	$0.457723\pi$
$194$	1.95644	+	3.38865i	0.140464	+	0.243291i
$195$	8.43516	−	13.4643i	0.604054	−	0.964202i
$196$	3.15799	+	6.24716i	0.225571	+	0.446226i
$197$	−2.56563			−0.182794			−0.0913969	−	0.995815i	$-0.529133\pi$
$197$	−2.56563			−0.182794			−0.0913969	+	0.995815i	$0.529133\pi$
$198$	−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
$208$	3.41032	−	1.17036i	0.236463	−	0.0811500i
$209$	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
$221$	−15.5016	−	13.5032i	−1.04275	−	0.908322i
$222$	−1.91670	−	12.1121i	−0.128640	−	0.812913i
$223$	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	$-0.480807\pi$
$227$	−11.6624	−	6.73328i	−0.774059	−	0.446903i	−0.834321	+	0.551279i	$0.814140\pi$
$228$	−9.21254	−	11.3797i	−0.610116	−	0.753638i
$229$	1.12680	+	1.95167i	0.0744607	+	0.128970i	0.900852	−	0.434127i	$-0.142943\pi$
$229$	1.12680	+	1.95167i	0.0744607	+	0.128970i	−0.826391	+	0.563097i	$0.809610\pi$
$230$	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	$0.346930\pi$
$234$	1.30433	+	10.7377i	0.0852669	+	0.701947i
$235$	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	$-0.536122\pi$
$239$	−3.50122			−0.226475			−0.113238	+	0.993568i	$0.536122\pi$
$240$	0.688764	+	4.35248i	0.0444595	+	0.280952i
$241$	6.59729	−	11.4268i	0.424969	−	0.736067i	−0.571449	−	0.820638i	$-0.693618\pi$
$241$	6.59729	−	11.4268i	0.424969	−	0.736067i	0.996418	+	0.0845704i	$0.0269518\pi$
$242$	−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
$247$	28.8280	−	9.89327i	1.83428	−	0.629494i
$248$	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	$0.118378\pi$
$271$	12.8489	+	22.2550i	0.780518	+	1.35190i	−0.151123	+	0.988515i	$0.548289\pi$
$272$	5.70178			0.345721
$273$	−9.15743	+	13.7529i	−0.554233	+	0.832362i
$274$	−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	$-0.737034\pi$
$281$	−22.7215			−1.35545			−0.677724	+	0.735316i	$0.737034\pi$
$282$	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	$0.111381\pi$
$293$			11.7362i			0.685634i	−0.939402	+	0.342817i	$0.888619\pi$
$294$	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
$299$	−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
$303$	−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	$-0.783440\pi$
$307$	−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	$-0.806952\pi$
$311$	1.45991	−	2.52863i	0.0827837	−	0.143386i	0.904445	+	0.426591i	$0.140286\pi$
$312$	5.51740	−	2.92546i	0.312361	−	0.165622i
$313$	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	0.997192	−	0.0748897i	$-0.0238605\pi$
$317$	7.72251	+	13.3758i	0.433740	+	0.751259i	−0.563452	+	0.826149i	$0.690527\pi$
$318$	−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
$325$	4.00422	+	3.48802i	0.222114	+	0.193480i
$326$	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	−0.381783	−	0.924252i	$-0.624690\pi$
$331$	4.14357	−	2.39229i	0.227751	−	0.131492i	0.609534	+	0.792760i	$0.291357\pi$
$332$	−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	$0.241450\pi$
$338$	1.78289	+	12.8772i	0.0969765	+	0.700425i
$339$	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	$-0.417919\pi$
$349$	9.52826			0.510036			0.255018	+	0.966936i	$0.417919\pi$
$350$	3.42749	−	1.85390i	0.183207	−	0.0990949i
$351$	5.13834	+	18.0166i	0.274264	+	0.961654i
$352$	−2.05512	−	3.55958i	−0.109538	−	0.189726i
$353$	14.3774	+	8.30082i	0.765234	+	0.441808i	0.831172	−	0.556016i	$-0.187671\pi$
$353$	14.3774	+	8.30082i	0.765234	+	0.441808i	−0.0659376	+	0.997824i	$0.521004\pi$
$354$	−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	0.997061	−	0.0766138i	$-0.0244109\pi$
$359$	8.18866	+	14.1832i	0.432181	+	0.748559i	−0.564880	+	0.825173i	$0.691078\pi$
$360$	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
$364$	9.30783	+	2.08910i	0.487863	+	0.109499i
$365$		−	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	$0.0482455\pi$
$379$			5.87885i			0.301976i	−0.988536	+	0.150988i	$0.951755\pi$
$380$	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	−0.133307	−	0.991075i	$-0.542560\pi$
$383$	12.8839	−	7.43851i	0.658336	−	0.380090i	0.791643	+	0.610985i	$0.209226\pi$
$384$	−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	$0.378734\pi$
$390$	−15.8780	−	0.572890i	−0.804016	−	0.0290094i
$391$		−	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	0.630777	−	0.775964i	$-0.282736\pi$
$397$	−7.10552	−	12.3071i	−0.356616	−	0.617677i	−0.987393	+	0.158287i	$0.949403\pi$
$398$		−	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	$-0.759167\pi$
$401$	−19.1854	−	33.2301i	−0.958073	−	1.65943i	−0.230899	−	0.972978i	$-0.574167\pi$
$402$	−4.36649	+	3.53494i	−0.217781	+	0.176307i
$403$	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
$408$	9.75440	−	1.54360i	0.482915	−	0.0764195i
$409$	2.09152	−	3.62262i	0.103419	−	0.179127i	−0.809672	−	0.586882i	$-0.800355\pi$
$409$	2.09152	−	3.62262i	0.103419	−	0.179127i	0.913091	+	0.407755i	$0.133688\pi$
$410$	−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
$416$	−2.71872	−	2.36824i	−0.133296	−	0.116112i
$417$	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	$0.0551135\pi$
$421$			7.06979i			0.344560i	−0.985048	+	0.172280i	$0.944887\pi$
$422$	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
$429$	−0.925532	+	25.6518i	−0.0446851	+	1.23848i
$430$	−7.30764	−	4.21907i	−0.352406	−	0.203462i
$431$	−1.83652	+	3.18094i	−0.0884620	+	0.153221i	−0.906861	−	0.421429i	$-0.861529\pi$
$431$	−1.83652	+	3.18094i	−0.0884620	+	0.153221i	0.818399	+	0.574650i	$0.194862\pi$
$432$	−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	$-0.470315\pi$
$449$	3.94653			0.186248			0.0931240	+	0.995655i	$0.470315\pi$
$450$	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
$455$	−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	−0.519594	−	0.854413i	$-0.673917\pi$
$457$	−0.843279	+	0.486868i	−0.0394469	+	0.0227747i	0.480147	+	0.877188i	$0.340583\pi$
$458$	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	$0.0764052\pi$
$461$			10.2088i			0.475471i	−0.971330	+	0.237736i	$0.923595\pi$
$462$	17.3892	+	7.23816i	0.809020	+	0.336750i
$463$			11.4435i			0.531824i	0.963997	+	0.265912i	$0.0856731\pi$
$463$			11.4435i			0.531824i	−0.963997	+	0.265912i	$0.914327\pi$
$464$	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	$-0.369553\pi$
$468$	8.64697	−	6.49845i	0.399707	−	0.300391i
$469$	−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	−0.287160	−	0.957883i	$-0.592711\pi$
$479$	−27.5828	−	15.9249i	−1.26029	−	0.727629i	−0.973131	+	0.230254i	$0.926044\pi$
$480$	3.42498	−	2.77273i	0.156328	−	0.126557i
$481$	−8.28612	−	24.1449i	−0.377814	−	1.10091i
$482$	−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	0.847252	−	0.531190i	$-0.178255\pi$
$487$	17.8940	+	10.3311i	0.810854	+	0.468147i	−0.0363981	+	0.999337i	$0.511588\pi$
$488$	−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
$494$	−22.9818	−	20.0191i	−1.03400	−	0.900703i
$495$	−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	−0.787447	−	0.616382i	$-0.788598\pi$
$499$	−14.4611	+	8.34913i	−0.647368	+	0.373758i	0.140079	+	0.990140i	$0.455264\pi$
$500$	−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
$507$	6.53623	+	21.5471i	0.290284	+	0.956940i
$508$	6.03573	−	10.4542i	0.267792	−	0.463829i
$509$	−29.2792	+	16.9043i	−1.29778	+	0.749272i	−0.980020	−	0.198900i	$-0.936263\pi$
$509$	−29.2792	+	16.9043i	−1.29778	+	0.749272i	−0.317757	+	0.948172i	$0.602930\pi$
$510$	−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
$520$	2.97761	+	8.67644i	0.130577	+	0.380487i
$521$	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	−0.796202	−	0.605031i	$-0.793161\pi$
$541$	−15.5915	+	9.00176i	−0.670331	+	0.387016i	0.125871	+	0.992047i	$0.459827\pi$
$542$	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
$546$	16.4891	+	1.05413i	0.705666	+	0.0451125i
$547$	−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	$0.382058\pi$
$557$	−14.7789	+	25.5978i	−0.626201	+	1.08461i	−0.988307	+	0.152475i	$0.951276\pi$
$558$	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	$0.0997091\pi$
$572$	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
$576$	−0.624526	+	2.93427i	−0.0260219	+	0.122261i
$577$	−8.91246	+	15.4368i	−0.371031	+	0.642644i	−0.989724	−	0.142988i	$-0.954329\pi$
$577$	−8.91246	+	15.4368i	−0.371031	+	0.642644i	0.618694	+	0.785632i	$0.287662\pi$
$578$	−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
$585$	−27.3187	+	3.31845i	−1.12949	+	0.137201i
$586$	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	$-0.447171\pi$
$588$	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	−0.308763	−	0.951139i	$-0.599915\pi$
$593$	8.78037	−	5.06935i	0.360566	−	0.208173i	0.669329	+	0.742966i	$0.266582\pi$
$594$	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
$598$	−3.09746	+	3.55587i	−0.126665	+	0.145410i
$599$	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
$611$	4.98165	+	14.5160i	0.201536	+	0.587255i
$612$	16.2696	−	5.28146i	0.657659	−	0.213490i
$613$	19.9940	+	11.5435i	0.807549	+	0.466239i	0.846104	−	0.533018i	$-0.178942\pi$
$613$	19.9940	+	11.5435i	0.807549	+	0.466239i	−0.0385548	+	0.999256i	$0.512275\pi$
$614$	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	$-0.405721\pi$
$617$	14.5000			0.583749			0.291874	+	0.956457i	$0.405721\pi$
$618$	−3.59841	−	22.7393i	−0.144749	−	0.914709i
$619$	11.4323	−	19.8013i	0.459503	−	0.795882i	−0.539432	−	0.842029i	$-0.681361\pi$
$619$	11.4323	−	19.8013i	0.459503	−	0.795882i	0.998935	+	0.0461472i	$0.0146943\pi$
$620$	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
$624$	−5.29222	−	3.31548i	−0.211858	−	0.132725i
$625$	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	$0.0649989\pi$
$631$			10.1877i			0.405568i	−0.979224	+	0.202784i	$0.935001\pi$
$632$	−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
$637$	18.0812	+	17.6088i	0.716403	+	0.697686i
$638$			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	$-0.547001\pi$
$643$	−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	$-0.997324\pi$
$647$	−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	$-0.411132\pi$
$661$	24.9458	−	43.2074i	0.970280	−	1.68057i	0.694706	−	0.719294i	$-0.255535\pi$
$662$	−4.14357	−	2.39229i	−0.161044	−	0.0929790i
$663$	−1.28391	+	35.5845i	−0.0498630	+	1.38199i
$664$			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
$676$	10.2605	−	7.98261i	0.394635	−	0.307023i
$677$	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	$0.340631\pi$
$683$	−13.5825	+	23.5256i	−0.519721	+	0.900184i	−0.999737	+	0.0229240i	$0.992702\pi$
$684$	−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
$689$	−12.0198	+	13.7986i	−0.457917	+	0.525685i
$690$	−3.62650	−	4.47959i	−0.138059	−	0.170535i
$691$	15.9012	+	27.5418i	0.604912	+	1.04774i	0.992065	+	0.125723i	$0.0401251\pi$
$691$	15.9012	+	27.5418i	0.604912	+	1.04774i	−0.387153	+	0.922015i	$0.626542\pi$
$692$	−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	$-0.152170\pi$
$702$	13.0337	−	13.4582i	0.491924	−	0.507948i
$703$	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	0.400332	−	0.916370i	$-0.368895\pi$
$709$	37.1207	−	21.4317i	1.39410	−	0.804883i	0.993766	+	0.111487i	$0.0355613\pi$
$710$	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	$0.945230\pi$
$728$	−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
$732$	−4.90551	+	3.97131i	−0.181313	+	0.146784i
$733$	19.7916	+	34.2800i	0.731018	+	1.26616i	0.956449	+	0.291901i	$0.0942878\pi$
$733$	19.7916	+	34.2800i	0.731018	+	1.26616i	−0.225431	+	0.974259i	$0.572379\pi$
$734$			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	−0.0365171	−	0.999333i	$-0.511626\pi$
$739$	−25.0159	−	14.4429i	−0.920224	−	0.531291i	−0.883706	+	0.468042i	$0.844960\pi$
$740$	−9.00633	−	15.5994i	−0.331079	−	0.573446i
$741$	−44.7360	−	28.0263i	−1.64342	−	1.02957i
$742$	6.38855	+	11.8112i	0.234531	+	0.433603i
$743$	14.2072			0.521211			0.260605	−	0.965445i	$-0.416078\pi$
$743$	14.2072			0.521211			0.260605	+	0.965445i	$0.416078\pi$
$744$	−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
$754$	7.09461	+	20.6729i	0.258370	+	0.752864i
$755$	−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	−0.541503	−	0.840699i	$-0.682144\pi$
$761$	−2.32242	+	1.34085i	−0.0841876	+	0.0486057i	0.457315	+	0.889305i	$0.348811\pi$
$762$	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
$767$	−4.60309	+	5.28431i	−0.166208	+	0.190805i
$768$	1.71076	−	0.270722i	0.0617318	−	0.00976883i
$769$	−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	$-0.499911\pi$
$773$	−24.0664	−	13.8947i	−0.865607	−	0.499758i	−0.865886	+	0.500242i	$0.833244\pi$
$774$	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
$780$	7.44288	+	14.0372i	0.266498	+	0.502614i
$781$	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	$0.460466\pi$
$787$	−22.3703	+	38.7465i	−0.797415	+	1.38116i	−0.921294	+	0.388866i	$0.872867\pi$
$788$	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
$793$	−4.26476	−	12.4271i	−0.151446	−	0.441298i
$794$	−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	$-0.659021\pi$
$811$	−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
$816$	−6.21399	−	7.67576i	−0.217533	−	0.268705i
$817$	−14.0181	−	24.2800i	−0.490431	−	0.849451i
$818$	−4.18304			−0.146257
$819$	28.4942	−	2.66058i	0.995669	−	0.0929684i
$820$	6.39552			0.223341
$821$	25.2745	+	43.7767i	0.882085	+	1.52782i	0.849018	+	0.528364i	$0.177194\pi$
$821$	25.2745	+	43.7767i	0.882085	+	1.52782i	0.0330672	+	0.999453i	$0.489472\pi$
$822$	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	$-0.612529\pi$
$827$	−19.9119			−0.692405			−0.346203	+	0.938160i	$0.612529\pi$
$828$	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	$0.154933\pi$
$839$			27.0968i			0.935486i	−0.883865	+	0.467743i	$0.845067\pi$
$840$	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
$845$	−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
$849$	−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	$-0.372594\pi$
$853$	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	$-0.975122\pi$
$857$	−12.6132	+	21.8466i	−0.430857	+	0.746267i	0.566090	+	0.824343i	$0.308455\pi$
$858$	22.6779	−	12.0244i	0.774209	−	0.410505i
$859$	−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	0.928109	−	0.372308i	$-0.121433\pi$
$863$	4.16054	+	7.20627i	0.141627	+	0.245304i	−0.786483	+	0.617612i	$0.788100\pi$
$864$	−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
$871$	−7.68152	+	8.81834i	−0.260278	+	0.298798i
$872$	−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	−0.597982	−	0.801510i	$-0.704031\pi$
$877$	−6.00709	+	3.46819i	−0.202845	+	0.117113i	0.395137	+	0.918622i	$0.370697\pi$
$878$	−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	$0.587522\pi$
$884$	19.4449	−	6.67315i	0.654002	−	0.224442i
$885$	−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
$897$	−4.33638	+	6.92180i	−0.144787	+	0.231112i
$898$	−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
$910$	−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	$0.835608\pi$
$912$	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	−0.871836	−	0.489798i	$-0.837070\pi$
$929$	−26.9309	+	15.5486i	−0.883576	+	0.510133i	−0.0117399	+	0.999931i	$0.503737\pi$
$930$	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
$936$	−9.95131	−	4.23928i	−0.325269	−	0.138565i
$937$		−	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	0.454553	−	0.890720i	$-0.349799\pi$
$941$	−2.74724	−	1.58612i	−0.0895573	−	0.0517059i	−0.544110	+	0.839014i	$0.683133\pi$
$942$	−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	0.781482	−	0.623928i	$-0.214464\pi$
$947$	−4.60358	−	7.97363i	−0.149596	−	0.259108i	−0.931078	+	0.364819i	$0.881131\pi$
$948$	−15.4290	−	19.0584i	−0.501110	−	0.618989i
$949$	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	$0.826737\pi$
$954$	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
$962$	−16.7670	+	19.2484i	−0.540591	+	0.620594i
$963$	−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	$0.0456661\pi$
$967$			8.89193i			0.285945i	−0.989727	+	0.142973i	$0.954334\pi$
$968$	−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
$975$	0.331648	−	9.19185i	0.0106212	−	0.294375i
$976$	3.15576	+	1.82198i	0.101014	+	0.0583202i
$977$	−22.6382	+	39.2106i	−0.724261	+	1.25446i	0.235016	+	0.971991i	$0.424486\pi$
$977$	−22.6382	+	39.2106i	−0.724261	+	1.25446i	−0.959277	+	0.282466i	$0.908848\pi$
$978$	−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	0.861595	−	0.507596i	$-0.169466\pi$
$983$	26.7378	+	15.4371i	0.852802	+	0.492365i	−0.00879326	+	0.999961i	$0.502799\pi$
$984$	−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.a.311.6	yes	36
3.2	odd	2		546.2.bg.b.311.1	yes	36
7.5	odd	6	inner	546.2.bg.a.467.1	yes	36
13.12	even	2		546.2.bg.b.311.6	yes	36
21.5	even	6		546.2.bg.b.467.6	yes	36
39.38	odd	2	inner	546.2.bg.a.311.1	✓	36
91.12	odd	6		546.2.bg.b.467.1	yes	36
273.194	even	6	inner	546.2.bg.a.467.6	yes	36

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
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} +(3.41032 - 1.17036i) 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} +(5.51740 - 2.92546i) 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} +(-2.71872 - 2.36824i) 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} +(2.97761 + 8.67644i) 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} +(-5.29222 - 3.31548i) 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} +(-2.84470 - 9.10537i) 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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