LMFDB - Embedded newform 546.2.bq.c.419.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(419,546)]

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, 3, 2]))

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

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

chi := DirichletCharacter("546.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bq (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:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			419.4
Character	$\chi$	$=$	546.419
Dual form			546.2.bq.c.503.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.66375 - 0.481611i) q^{3} +(0.500000 - 0.866025i) q^{4} +4.01418 q^{5} +(1.68165 - 0.414785i) q^{6} +(1.77617 - 1.96093i) q^{7} +1.00000i q^{8} +(2.53610 + 1.60256i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.66375 - 0.481611i) q^{3} +(0.500000 - 0.866025i) q^{4} +4.01418 q^{5} +(1.68165 - 0.414785i) q^{6} +(1.77617 - 1.96093i) q^{7} +1.00000i q^{8} +(2.53610 + 1.60256i) q^{9} +(-3.47639 + 2.00709i) q^{10} +(1.96455 - 1.13423i) q^{11} +(-1.24896 + 1.20004i) q^{12} +(0.757550 - 3.52507i) q^{13} +(-0.557740 + 2.58630i) q^{14} +(-6.67858 - 1.93328i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.05976 + 7.03171i) q^{17} +(-2.99761 - 0.119805i) q^{18} +(-4.81117 - 2.77773i) q^{19} +(2.00709 - 3.47639i) q^{20} +(-3.89949 + 2.40706i) q^{21} +(-1.13423 + 1.96455i) q^{22} +(0.855244 - 0.493775i) q^{23} +(0.481611 - 1.66375i) q^{24} +11.1137 q^{25} +(1.10648 + 3.43158i) q^{26} +(-3.44762 - 3.88766i) q^{27} +(-0.810131 - 2.51867i) q^{28} +(6.90171 - 3.98470i) q^{29} +(6.75046 - 1.66503i) q^{30} +3.94262i q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.81476 + 0.940925i) q^{33} -8.11952i q^{34} +(7.12985 - 7.87153i) q^{35} +(2.65591 - 1.39505i) q^{36} +(-2.53038 - 4.38274i) q^{37} +5.55547 q^{38} +(-2.95808 + 5.49998i) q^{39} +4.01418i q^{40} +(0.351799 + 0.609334i) q^{41} +(2.17353 - 4.03433i) q^{42} +(-1.30520 + 2.26067i) q^{43} -2.26846i q^{44} +(10.1804 + 6.43296i) q^{45} +(-0.493775 + 0.855244i) q^{46} +2.33521 q^{47} +(0.414785 + 1.68165i) q^{48} +(-0.690475 - 6.96586i) q^{49} +(-9.62473 + 5.55684i) q^{50} +(10.1410 - 9.74376i) q^{51} +(-2.67402 - 2.41859i) q^{52} +8.39199i q^{53} +(4.92956 + 1.64301i) q^{54} +(7.88605 - 4.55301i) q^{55} +(1.96093 + 1.77617i) q^{56} +(6.66678 + 6.93856i) q^{57} +(-3.98470 + 6.90171i) q^{58} +(4.38840 - 7.60093i) q^{59} +(-5.01356 + 4.81718i) q^{60} +(1.95343 + 1.12781i) q^{61} +(-1.97131 - 3.41441i) q^{62} +(7.64703 - 2.12670i) q^{63} -1.00000 q^{64} +(3.04095 - 14.1503i) q^{65} +(2.83322 - 2.72225i) q^{66} +(-1.70065 - 2.94561i) q^{67} +(4.05976 + 7.03171i) q^{68} +(-1.66072 + 0.409622i) q^{69} +(-2.23887 + 10.3819i) q^{70} +(-0.00678280 - 0.00391605i) q^{71} +(-1.60256 + 2.53610i) q^{72} +6.26312i q^{73} +(4.38274 + 2.53038i) q^{74} +(-18.4903 - 5.35247i) q^{75} +(-4.81117 + 2.77773i) q^{76} +(1.26521 - 5.86691i) q^{77} +(-0.188212 - 6.24216i) q^{78} +6.23858 q^{79} +(-2.00709 - 3.47639i) q^{80} +(3.86362 + 8.12850i) q^{81} +(-0.609334 - 0.351799i) q^{82} -3.69906 q^{83} +(0.134833 + 4.58059i) q^{84} +(-16.2966 + 28.2266i) q^{85} -2.61039i q^{86} +(-13.4018 + 3.30559i) q^{87} +(1.13423 + 1.96455i) q^{88} +(-2.36686 - 4.09953i) q^{89} +(-12.0329 - 0.480919i) q^{90} +(-5.56687 - 7.74661i) q^{91} -0.987551i q^{92} +(1.89881 - 6.55952i) q^{93} +(-2.02235 + 1.16760i) q^{94} +(-19.3129 - 11.1503i) q^{95} +(-1.20004 - 1.24896i) q^{96} +(-4.88472 - 2.82020i) q^{97} +(4.08090 + 5.68738i) q^{98} +(6.79996 + 0.271773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.66375	−	0.481611i	−0.960564	−	0.278058i
$3$	−1.66375	−	0.481611i	−0.960564	−	0.278058i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	4.01418			1.79520			0.897599	−	0.440813i	$-0.145310\pi$
$5$	4.01418			1.79520			0.897599	+	0.440813i	$0.145310\pi$
$6$	1.68165	−	0.414785i	0.686532	−	0.169335i
$7$	1.77617	−	1.96093i	0.671327	−	0.741161i
$7$	1.77617	−	1.96093i	0.671327	−	0.741161i
$8$			1.00000i			0.353553i
$9$	2.53610	+	1.60256i	0.845367	+	0.534186i
$10$	−3.47639	+	2.00709i	−1.09933	+	0.634698i
$11$	1.96455	−	1.13423i	0.592333	−	0.341983i	−0.173687	−	0.984801i	$-0.555568\pi$
$11$	1.96455	−	1.13423i	0.592333	−	0.341983i	0.766019	+	0.642818i	$0.222235\pi$
$12$	−1.24896	+	1.20004i	−0.360544	+	0.346422i
$13$	0.757550	−	3.52507i	0.210107	−	0.977678i
$13$	0.757550	−	3.52507i	0.210107	−	0.977678i
$14$	−0.557740	+	2.58630i	−0.149062	+	0.691217i
$15$	−6.67858	−	1.93328i	−1.72440	−	0.499170i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.05976	+	7.03171i	−0.984637	+	1.70544i	−0.341098	+	0.940028i	$0.610799\pi$
$17$	−4.05976	+	7.03171i	−0.984637	+	1.70544i	−0.643539	+	0.765413i	$0.722535\pi$
$18$	−2.99761	−	0.119805i	−0.706543	−	0.0282383i
$19$	−4.81117	−	2.77773i	−1.10376	−	0.637256i	−0.166553	−	0.986032i	$-0.553264\pi$
$19$	−4.81117	−	2.77773i	−1.10376	−	0.637256i	−0.937206	+	0.348777i	$0.886597\pi$
$20$	2.00709	−	3.47639i	0.448800	−	0.777344i
$21$	−3.89949	+	2.40706i	−0.850939	+	0.525265i
$22$	−1.13423	+	1.96455i	−0.241819	+	0.418842i
$23$	0.855244	−	0.493775i	0.178331	−	0.102959i	−0.408177	−	0.912903i	$-0.633836\pi$
$23$	0.855244	−	0.493775i	0.178331	−	0.102959i	0.586508	+	0.809943i	$0.300502\pi$
$24$	0.481611	−	1.66375i	0.0983085	−	0.339611i
$25$	11.1137			2.22274
$26$	1.10648	+	3.43158i	0.216998	+	0.672987i
$27$	−3.44762	−	3.88766i	−0.663494	−	0.748181i
$28$	−0.810131	−	2.51867i	−0.153100	−	0.475984i
$29$	6.90171	−	3.98470i	1.28162	−	0.739941i	0.304471	−	0.952521i	$-0.401520\pi$
$29$	6.90171	−	3.98470i	1.28162	−	0.739941i	0.977144	+	0.212581i	$0.0681868\pi$
$30$	6.75046	−	1.66503i	1.23246	−	0.303991i
$31$			3.94262i			0.708116i	0.935223	+	0.354058i	$0.115198\pi$
$31$			3.94262i			0.708116i	−0.935223	+	0.354058i	$0.884802\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−3.81476	+	0.940925i	−0.664065	+	0.163794i
$34$		−	8.11952i		−	1.39249i
$35$	7.12985	−	7.87153i	1.20517	−	1.33053i
$36$	2.65591	−	1.39505i	0.442651	−	0.232508i
$37$	−2.53038	−	4.38274i	−0.415992	−	0.720518i	0.579540	−	0.814943i	$-0.303232\pi$
$37$	−2.53038	−	4.38274i	−0.415992	−	0.720518i	−0.995532	+	0.0944250i	$0.969899\pi$
$38$	5.55547			0.901215
$39$	−2.95808	+	5.49998i	−0.473673	+	0.880701i
$40$			4.01418i			0.634698i
$41$	0.351799	+	0.609334i	0.0549418	+	0.0951619i	0.892188	−	0.451664i	$-0.149169\pi$
$41$	0.351799	+	0.609334i	0.0549418	+	0.0951619i	−0.837246	+	0.546826i	$0.815836\pi$
$42$	2.17353	−	4.03433i	0.335383	−	0.622510i
$43$	−1.30520	+	2.26067i	−0.199041	+	0.344749i	−0.948218	−	0.317621i	$-0.897116\pi$
$43$	−1.30520	+	2.26067i	−0.199041	+	0.344749i	0.749177	+	0.662370i	$0.230449\pi$
$44$		−	2.26846i		−	0.341983i
$45$	10.1804	+	6.43296i	1.51760	+	0.958969i
$46$	−0.493775	+	0.855244i	−0.0728032	+	0.126099i
$47$	2.33521			0.340625			0.170312	−	0.985390i	$-0.445522\pi$
$47$	2.33521			0.340625			0.170312	+	0.985390i	$0.445522\pi$
$48$	0.414785	+	1.68165i	0.0598691	+	0.242726i
$49$	−0.690475	−	6.96586i	−0.0986393	−	0.995123i
$50$	−9.62473	+	5.55684i	−1.36114	+	0.785856i
$51$	10.1410	−	9.74376i	1.42002	−	1.36440i
$52$	−2.67402	−	2.41859i	−0.370821	−	0.335398i
$53$			8.39199i			1.15273i	0.817193	+	0.576364i	$0.195529\pi$
$53$			8.39199i			1.15273i	−0.817193	+	0.576364i	$0.804471\pi$
$54$	4.92956	+	1.64301i	0.670828	+	0.223585i
$55$	7.88605	−	4.55301i	1.06335	−	0.613928i
$56$	1.96093	+	1.77617i	0.262040	+	0.237350i
$57$	6.66678	+	6.93856i	0.883037	+	0.919034i
$58$	−3.98470	+	6.90171i	−0.523217	+	0.906239i
$59$	4.38840	−	7.60093i	0.571321	−	0.989557i	−0.425109	−	0.905142i	$-0.639764\pi$
$59$	4.38840	−	7.60093i	0.571321	−	0.989557i	0.996431	−	0.0844154i	$-0.0269023\pi$
$60$	−5.01356	+	4.81718i	−0.647248	+	0.621896i
$61$	1.95343	+	1.12781i	0.250111	+	0.144402i	0.619815	−	0.784748i	$-0.287208\pi$
$61$	1.95343	+	1.12781i	0.250111	+	0.144402i	−0.369704	+	0.929149i	$0.620541\pi$
$62$	−1.97131	−	3.41441i	−0.250357	−	0.433631i
$63$	7.64703	−	2.12670i	0.963436	−	0.267940i
$64$	−1.00000			−0.125000
$65$	3.04095	−	14.1503i	0.377183	−	1.75513i
$66$	2.83322	−	2.72225i	0.348745	−	0.335085i
$67$	−1.70065	−	2.94561i	−0.207767	−	0.359864i	0.743244	−	0.669021i	$-0.233286\pi$
$67$	−1.70065	−	2.94561i	−0.207767	−	0.359864i	−0.951011	+	0.309157i	$0.899953\pi$
$68$	4.05976	+	7.03171i	0.492318	+	0.852721i
$69$	−1.66072	+	0.409622i	−0.199927	+	0.0493127i
$70$	−2.23887	+	10.3819i	−0.267596	+	1.24087i
$71$	−0.00678280	−	0.00391605i	−0.000804971	−	0.000464750i	0.499597	−	0.866258i	$-0.333481\pi$
$71$	−0.00678280	−	0.00391605i	−0.000804971	−	0.000464750i	−0.500402	+	0.865793i	$0.666815\pi$
$72$	−1.60256	+	2.53610i	−0.188863	+	0.298882i
$73$			6.26312i			0.733043i	0.930410	+	0.366522i	$0.119451\pi$
$73$			6.26312i			0.733043i	−0.930410	+	0.366522i	$0.880549\pi$
$74$	4.38274	+	2.53038i	0.509483	+	0.294150i
$75$	−18.4903	−	5.35247i	−2.13508	−	0.618050i
$76$	−4.81117	+	2.77773i	−0.551880	+	0.318628i
$77$	1.26521	−	5.86691i	0.144184	−	0.668597i
$78$	−0.188212	−	6.24216i	−0.0213108	−	0.706786i
$79$	6.23858			0.701895			0.350947	−	0.936395i	$-0.385860\pi$
$79$	6.23858			0.701895			0.350947	+	0.936395i	$0.385860\pi$
$80$	−2.00709	−	3.47639i	−0.224400	−	0.388672i
$81$	3.86362	+	8.12850i	0.429291	+	0.903166i
$82$	−0.609334	−	0.351799i	−0.0672896	−	0.0388497i
$83$	−3.69906			−0.406025			−0.203013	−	0.979176i	$-0.565073\pi$
$83$	−3.69906			−0.406025			−0.203013	+	0.979176i	$0.565073\pi$
$84$	0.134833	+	4.58059i	0.0147115	+	0.499784i
$85$	−16.2966	+	28.2266i	−1.76762	+	3.06160i
$86$		−	2.61039i		−	0.281486i
$87$	−13.4018	+	3.30559i	−1.43682	+	0.354397i
$88$	1.13423	+	1.96455i	0.120909	+	0.209421i
$89$	−2.36686	−	4.09953i	−0.250887	−	0.434549i	0.712883	−	0.701283i	$-0.247389\pi$
$89$	−2.36686	−	4.09953i	−0.250887	−	0.434549i	−0.963770	+	0.266734i	$0.914056\pi$
$90$	−12.0329	−	0.480919i	−1.26838	−	0.0506933i
$91$	−5.56687	−	7.74661i	−0.583567	−	0.812065i
$92$		−	0.987551i		−	0.102959i
$93$	1.89881	−	6.55952i	0.196898	−	0.680191i
$94$	−2.02235	+	1.16760i	−0.208589	+	0.120429i
$95$	−19.3129	−	11.1503i	−1.98147	−	1.14400i
$96$	−1.20004	−	1.24896i	−0.122479	−	0.127472i
$97$	−4.88472	−	2.82020i	−0.495969	−	0.286348i	0.231079	−	0.972935i	$-0.425775\pi$
$97$	−4.88472	−	2.82020i	−0.495969	−	0.286348i	−0.727047	+	0.686587i	$0.759108\pi$
$98$	4.08090	+	5.68738i	0.412233	+	0.574512i
$99$	6.79996	+	0.271773i	0.683421	+	0.0273142i
$100$	5.55684	−	9.62473i	0.555684	−	0.962473i
$101$	4.60849	+	7.98213i	0.458562	+	0.794252i	0.998885	−	0.0472054i	$-0.0150315\pi$
$101$	4.60849	+	7.98213i	0.458562	+	0.794252i	−0.540324	+	0.841457i	$0.681698\pi$
$102$	−3.91045	+	13.5088i	−0.387193	+	1.33757i
$103$		−	4.05811i		−	0.399858i	−0.979810	−	0.199929i	$-0.935929\pi$
$103$		−	4.05811i		−	0.399858i	0.979810	−	0.199929i	$-0.0640711\pi$
$104$	3.52507	+	0.757550i	0.345662	+	0.0742839i
$105$	−15.6533	+	9.66240i	−1.52760	+	0.942954i
$106$	−4.19600	−	7.26768i	−0.407551	−	0.705899i
$107$	−9.97005	+	5.75621i	−0.963841	+	0.556474i	−0.897353	−	0.441313i	$-0.854513\pi$
$107$	−9.97005	+	5.75621i	−0.963841	+	0.556474i	−0.0664881	+	0.997787i	$0.521179\pi$
$108$	−5.09062	+	1.04189i	−0.489846	+	0.100256i
$109$	2.34167			0.224292			0.112146	−	0.993692i	$-0.464228\pi$
$109$	2.34167			0.224292			0.112146	+	0.993692i	$0.464228\pi$
$110$	−4.55301	+	7.88605i	−0.434113	+	0.751905i
$111$	2.09913	+	8.51043i	0.199240	+	0.807774i
$112$	−2.58630	−	0.557740i	−0.244382	−	0.0527015i
$113$	−3.95800	−	2.28515i	−0.372337	−	0.214969i	0.302142	−	0.953263i	$-0.402298\pi$
$113$	−3.95800	−	2.28515i	−0.372337	−	0.214969i	−0.674479	+	0.738294i	$0.735632\pi$
$114$	−9.24288	−	2.67557i	−0.865675	−	0.250591i
$115$	3.43311	−	1.98211i	0.320139	−	0.184832i
$116$		−	7.96941i		−	0.739941i
$117$	7.57035	−	7.72592i	0.699879	−	0.714261i
$118$			8.77680i			0.807970i
$119$	6.57788	+	20.4504i	0.602993	+	1.87468i
$120$	1.93328	−	6.67858i	0.176483	−	0.609668i
$121$	−2.92704	+	5.06978i	−0.266095	+	0.460889i
$122$	−2.25562			−0.204215
$123$	−0.291842	−	1.18321i	−0.0263145	−	0.106686i
$124$	3.41441	+	1.97131i	0.306623	+	0.177029i
$125$	24.5414			2.19505
$126$	−5.55917	+	5.66530i	−0.495251	+	0.504705i
$127$	−0.733160	−	1.26987i	−0.0650575	−	0.112683i	0.831662	−	0.555282i	$-0.187390\pi$
$127$	−0.733160	−	1.26987i	−0.0650575	−	0.112683i	−0.896719	+	0.442599i	$0.854056\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	3.26028	−	3.13258i	0.287052	−	0.275808i
$130$	4.44160	+	13.7750i	0.389554	+	1.20815i
$131$	−11.5506			−1.00918			−0.504592	−	0.863358i	$-0.668357\pi$
$131$	−11.5506			−1.00918			−0.504592	+	0.863358i	$0.668357\pi$
$132$	−1.09252	+	3.77414i	−0.0950914	+	0.328497i
$133$	−13.9924	+	4.50065i	−1.21329	+	0.390256i
$134$	2.94561	+	1.70065i	0.254462	+	0.146914i
$135$	−13.8394	−	15.6058i	−1.19110	−	1.34313i
$136$	−7.03171	−	4.05976i	−0.602964	−	0.348122i
$137$	−12.2325	−	7.06243i	−1.04509	−	0.603384i	−0.123821	−	0.992305i	$-0.539515\pi$
$137$	−12.2325	−	7.06243i	−1.04509	−	0.603384i	−0.921271	+	0.388921i	$0.872848\pi$
$138$	1.23341	−	1.18510i	0.104995	−	0.100883i
$139$	12.1047	+	6.98865i	1.02671	+	0.592770i	0.916040	−	0.401088i	$-0.131368\pi$
$139$	12.1047	+	6.98865i	1.02671	+	0.592770i	0.110667	+	0.993857i	$0.464701\pi$
$140$	−3.25201	−	10.1104i	−0.274845	−	0.854485i
$141$	−3.88519	−	1.12466i	−0.327192	−	0.0947135i
$142$	0.00783211			0.000657256
$143$	−2.51000	−	7.78440i	−0.209897	−	0.650964i
$144$	0.119805	−	2.99761i	0.00998374	−	0.249801i
$145$	27.7047	−	15.9953i	2.30075	−	1.32834i
$146$	−3.13156	−	5.42402i	−0.259170	−	0.448895i
$147$	−2.20606	+	11.9220i	−0.181953	+	0.983307i
$148$	−5.06076			−0.415992
$149$	18.4080	+	10.6278i	1.50804	+	0.870667i	0.999956	+	0.00935860i	$0.00297898\pi$
$149$	18.4080	+	10.6278i	1.50804	+	0.870667i	0.508083	+	0.861308i	$0.330354\pi$
$150$	18.6893	−	4.60979i	1.52598	−	0.376388i
$151$	−8.28984			−0.674617			−0.337309	−	0.941394i	$-0.609517\pi$
$151$	−8.28984			−0.674617			−0.337309	+	0.941394i	$0.609517\pi$
$152$	2.77773	−	4.81117i	0.225304	−	0.390238i
$153$	−21.5647	+	11.3271i	−1.74340	+	0.915745i
$154$	1.83775	+	5.71350i	0.148090	+	0.460407i
$155$			15.8264i			1.27121i
$156$	3.28408	+	5.31176i	0.262937	+	0.425282i
$157$			3.16769i			0.252809i	0.991979	+	0.126405i	$0.0403438\pi$
$157$			3.16769i			0.252809i	−0.991979	+	0.126405i	$0.959656\pi$
$158$	−5.40277	+	3.11929i	−0.429821	+	0.248157i
$159$	4.04168	−	13.9621i	0.320526	−	1.10727i
$160$	3.47639	+	2.00709i	0.274832	+	0.158675i
$161$	0.550797	−	2.55410i	0.0434089	−	0.201291i
$162$	−7.41024	−	5.10767i	−0.582203	−	0.401297i
$163$	8.02328	−	13.8967i	0.628432	−	1.08848i	−0.359435	−	0.933170i	$-0.617030\pi$
$163$	8.02328	−	13.8967i	0.628432	−	1.08848i	0.987866	−	0.155306i	$-0.0496363\pi$
$164$	0.703598			0.0549418
$165$	−15.3132	+	3.77705i	−1.19213	+	0.294043i
$166$	3.20348	−	1.84953i	0.248639	−	0.143552i
$167$	3.78574	+	6.55709i	0.292949	+	0.507403i	0.974506	−	0.224362i	$-0.0720299\pi$
$167$	3.78574	+	6.55709i	0.292949	+	0.507403i	−0.681556	+	0.731766i	$0.738697\pi$
$168$	−2.40706	−	3.89949i	−0.185709	−	0.300852i
$169$	−11.8522	−	5.34083i	−0.911710	−	0.410833i
$170$		−	32.5933i		−	2.49979i
$171$	−7.75015	−	14.7548i	−0.592669	−	1.12833i
$172$	1.30520	+	2.26067i	0.0995204	+	0.172374i
$173$	−2.39162	+	4.14242i	−0.181832	+	0.314942i	−0.942504	−	0.334194i	$-0.891536\pi$
$173$	−2.39162	+	4.14242i	−0.181832	+	0.314942i	0.760673	+	0.649136i	$0.224869\pi$
$174$	9.95347	−	9.56361i	0.754571	−	0.725015i
$175$	19.7397	−	21.7931i	1.49218	−	1.64741i
$176$	−1.96455	−	1.13423i	−0.148083	−	0.0854959i
$177$	−10.9619	+	10.5325i	−0.823945	+	0.791673i
$178$	4.09953	+	2.36686i	0.307273	+	0.177404i
$179$	−12.4998	+	7.21674i	−0.934276	+	0.539405i	−0.888161	−	0.459532i	$-0.848017\pi$
$179$	−12.4998	+	7.21674i	−0.934276	+	0.539405i	−0.0461146	+	0.998936i	$0.514684\pi$
$180$	10.6613	−	5.59999i	0.794646	−	0.417398i
$181$		−	13.4675i		−	1.00103i	−0.865727	−	0.500516i	$-0.833144\pi$
$181$		−	13.4675i		−	1.00103i	0.865727	−	0.500516i	$-0.166856\pi$
$182$	8.69436	+	3.92532i	0.644469	+	0.290964i
$183$	−2.70684	−	2.81718i	−0.200095	−	0.208252i
$184$	0.493775	+	0.855244i	0.0364016	+	0.0630494i
$185$	−10.1574	−	17.5931i	−0.746787	−	1.29347i
$186$	1.63534	+	6.63012i	0.119909	+	0.486144i
$187$			18.4188i			1.34692i
$188$	1.16760	−	2.02235i	0.0851562	−	0.147495i
$189$	−13.7470	−	0.144602i	−0.999945	−	0.0105182i
$190$	22.3007			1.61786
$191$	11.8282	+	6.82900i	0.855856	+	0.494129i	0.862622	−	0.505848i	$-0.168820\pi$
$191$	11.8282	+	6.82900i	0.855856	+	0.494129i	−0.00676627	+	0.999977i	$0.502154\pi$
$192$	1.66375	+	0.481611i	0.120071	+	0.0347573i
$193$	7.64881	+	13.2481i	0.550573	+	0.953621i	0.998233	+	0.0594171i	$0.0189242\pi$
$193$	7.64881	+	13.2481i	0.550573	+	0.953621i	−0.447660	+	0.894204i	$0.647742\pi$
$194$	5.64039			0.404957
$195$	−11.8743	+	22.0779i	−0.850336	+	1.58103i
$196$	−6.37785	−	2.88496i	−0.455561	−	0.206069i
$197$	−7.62170	+	4.40039i	−0.543023	+	0.313515i	−0.746303	−	0.665606i	$-0.768173\pi$
$197$	−7.62170	+	4.40039i	−0.543023	+	0.313515i	0.203280	+	0.979121i	$0.434840\pi$
$198$	−6.02482	+	3.16462i	−0.428165	+	0.224899i
$199$	19.7321	+	11.3924i	1.39877	+	0.807583i	0.994264	−	0.106951i	$-0.0341088\pi$
$199$	19.7321	+	11.3924i	1.39877	+	0.807583i	0.404510	+	0.914534i	$0.367442\pi$
$200$			11.1137i			0.785856i
$201$	1.41081	+	5.71980i	0.0995108	+	0.403443i
$202$	−7.98213	−	4.60849i	−0.561621	−	0.324252i
$203$	4.44486	−	20.6112i	0.311968	−	1.44663i
$204$	−3.36786	−	13.6542i	−0.235797	−	0.955986i
$205$	1.41219	+	2.44598i	0.0986313	+	0.170834i
$206$	2.02906	+	3.51443i	0.141371	+	0.244862i
$207$	2.96029	+	0.118313i	0.205754	+	0.00822335i
$208$	−3.43158	+	1.10648i	−0.237937	+	0.0767204i
$209$	−12.6024			−0.871723
$210$	8.72494	−	16.1945i	0.602078	−	1.11753i
$211$	6.62975	+	11.4831i	0.456411	+	0.790527i	0.998768	−	0.0496211i	$-0.0158014\pi$
$211$	6.62975	+	11.4831i	0.456411	+	0.790527i	−0.542357	+	0.840148i	$0.682468\pi$
$212$	7.26768	+	4.19600i	0.499146	+	0.288182i
$213$	0.00939885	+	0.00978199i	0.000643998	+	0.000670251i
$214$	5.75621	−	9.97005i	0.393487	−	0.681539i
$215$	−5.23930	+	9.07474i	−0.357318	+	0.618892i
$216$	3.88766	−	3.44762i	0.264522	−	0.234581i
$217$	7.73120	+	7.00275i	0.524828	+	0.475378i
$218$	−2.02795	+	1.17084i	−0.137350	+	0.0792991i
$219$	3.01639	−	10.4202i	0.203829	−	0.704135i
$220$		−	9.10602i		−	0.613928i
$221$	21.7118	+	19.6378i	1.46049	+	1.32098i
$222$	−6.07311	−	6.32068i	−0.407601	−	0.424217i
$223$	7.43387	−	4.29194i	0.497808	−	0.287410i	−0.230000	−	0.973191i	$-0.573872\pi$
$223$	7.43387	−	4.29194i	0.497808	−	0.287410i	0.727808	+	0.685781i	$0.240539\pi$
$224$	2.51867	−	0.810131i	0.168286	−	0.0541291i
$225$	28.1854	+	17.8103i	1.87903	+	1.18735i
$226$	4.57030			0.304012
$227$	−12.2462	+	21.2111i	−0.812812	+	1.40783i	0.0980766	+	0.995179i	$0.468731\pi$
$227$	−12.2462	+	21.2111i	−0.812812	+	1.40783i	−0.910888	+	0.412653i	$0.864602\pi$
$228$	9.34236	−	2.30433i	0.618713	−	0.152608i
$229$		−	14.5320i		−	0.960300i	−0.877186	−	0.480150i	$-0.840582\pi$
$229$		−	14.5320i		−	0.960300i	0.877186	−	0.480150i	$-0.159418\pi$
$230$	−1.98211	+	3.43311i	−0.130696	+	0.226372i
$231$	−4.93056	+	9.15171i	−0.324407	+	0.602138i
$232$	3.98470	+	6.90171i	0.261609	+	0.453119i
$233$			15.4391i			1.01145i	0.862694	+	0.505726i	$0.168775\pi$
$233$			15.4391i			1.01145i	−0.862694	+	0.505726i	$0.831225\pi$
$234$	−2.69316	+	10.4760i	−0.176057	+	0.684839i
$235$	9.37394			0.611489
$236$	−4.38840	−	7.60093i	−0.285661	−	0.494779i
$237$	−10.3794	−	3.00457i	−0.674215	−	0.195168i
$238$	−15.9218	−	14.4216i	−1.03206	−	0.934814i
$239$			10.5191i			0.680426i	0.940348	+	0.340213i	$0.110499\pi$
$239$			10.5191i			0.680426i	−0.940348	+	0.340213i	$0.889501\pi$
$240$	1.66503	+	6.75046i	0.107477	+	0.435740i
$241$	−20.1410	−	11.6284i	−1.29740	−	0.749052i	−0.317443	−	0.948277i	$-0.602824\pi$
$241$	−20.1410	−	11.6284i	−1.29740	−	0.749052i	−0.979954	+	0.199225i	$0.936158\pi$
$242$		−	5.85408i		−	0.376315i
$243$	−2.51330	−	15.3845i	−0.161229	−	0.986917i
$244$	1.95343	−	1.12781i	0.125055	−	0.0722008i
$245$	−2.77170	−	27.9623i	−0.177077	−	1.78644i
$246$	0.844346	+	0.878766i	0.0538335	+	0.0560281i
$247$	−13.4364	+	14.8555i	−0.854938	+	0.945230i
$248$	−3.94262			−0.250357
$249$	6.15430	+	1.78151i	0.390013	+	0.112899i
$250$	−21.2535	+	12.2707i	−1.34419	+	0.776069i
$251$	−5.05812	+	8.76091i	−0.319265	+	0.552984i	−0.980335	−	0.197341i	$-0.936769\pi$
$251$	−5.05812	+	8.76091i	−0.319265	+	0.552984i	0.661070	+	0.750325i	$0.270103\pi$
$252$	1.98174	−	7.68588i	0.124838	−	0.484165i
$253$	1.12011	−	1.94009i	0.0704208	−	0.121972i
$254$	1.26987	+	0.733160i	0.0796788	+	0.0460026i
$255$	40.7077	−	39.1132i	2.54922	−	2.44937i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.289546	+	0.501508i	0.0180614	+	0.0312832i	0.874915	−	0.484277i	$-0.160917\pi$
$257$	0.289546	+	0.501508i	0.0180614	+	0.0312832i	−0.856853	+	0.515560i	$0.827584\pi$
$258$	−1.25720	+	4.34303i	−0.0782696	+	0.270385i
$259$	−13.0886	−	2.82259i	−0.813287	−	0.175387i
$260$	−10.7340	−	9.70868i	−0.665696	−	0.602107i
$261$	23.8891	+	0.954774i	1.47870	+	0.0590990i
$262$	10.0031	−	5.77532i	0.617997	−	0.356801i
$263$	−22.2158	+	12.8263i	−1.36989	+	0.790904i	−0.990913	−	0.134503i	$-0.957056\pi$
$263$	−22.2158	+	12.8263i	−1.36989	+	0.790904i	−0.378974	+	0.925408i	$0.623723\pi$
$264$	−0.940925	−	3.81476i	−0.0579099	−	0.234782i
$265$			33.6870i			2.06938i
$266$	9.86742	−	10.8939i	0.605011	−	0.667946i
$267$	1.96348	+	7.96048i	0.120163	+	0.487173i
$268$	−3.40130			−0.207767
$269$	−0.0405741	+	0.0702764i	−0.00247385	+	0.00428483i	−0.867260	−	0.497856i	$-0.834121\pi$
$269$	−0.0405741	+	0.0702764i	−0.00247385	+	0.00428483i	0.864786	+	0.502141i	$0.167454\pi$
$270$	19.7882	+	6.59533i	1.20427	+	0.401379i
$271$	−17.2401	+	9.95358i	−1.04726	+	0.604637i	−0.921882	−	0.387472i	$-0.873349\pi$
$271$	−17.2401	+	9.95358i	−1.04726	+	0.604637i	−0.125381	+	0.992109i	$0.540015\pi$
$272$	8.11952			0.492318
$273$	5.53101	+	15.5695i	0.334752	+	0.942306i
$274$	14.1249			0.853314
$275$	21.8333	−	12.6055i	1.31660	−	0.760139i
$276$	−0.475616	+	1.64303i	−0.0286287	+	0.0988990i
$277$	−4.37855	+	7.58387i	−0.263082	+	0.455671i	−0.967059	−	0.254551i	$-0.918072\pi$
$277$	−4.37855	+	7.58387i	−0.263082	+	0.455671i	0.703978	+	0.710222i	$0.251406\pi$
$278$	−13.9773			−0.838303
$279$	−6.31828	+	9.99889i	−0.378265	+	0.598618i
$280$	7.87153	+	7.12985i	0.470414	+	0.426090i
$281$		−	17.7331i		−	1.05787i	−0.848664	−	0.528933i	$-0.822592\pi$
$281$		−	17.7331i		−	1.05787i	0.848664	−	0.528933i	$-0.177408\pi$
$282$	3.92700	−	0.968609i	0.233850	−	0.0576798i
$283$	−14.9119	+	8.60942i	−0.886423	+	0.511777i	−0.872771	−	0.488130i	$-0.837679\pi$
$283$	−14.9119	+	8.60942i	−0.886423	+	0.511777i	−0.0136524	+	0.999907i	$0.504346\pi$
$284$	−0.00678280	+	0.00391605i	−0.000402485	+	0.000232375i
$285$	26.7617	+	27.8527i	1.58523	+	1.64985i
$286$	6.06592	+	5.48648i	0.358686	+	0.324423i
$287$	1.81971	+	0.392425i	0.107414	+	0.0231641i
$288$	1.39505	+	2.65591i	0.0822041	+	0.156501i
$289$	−24.4633	−	42.3717i	−1.43902	−	2.49245i
$290$	−15.9953	+	27.7047i	−0.939278	+	1.62688i
$291$	6.76870	+	7.04463i	0.396788	+	0.412963i
$292$	5.42402	+	3.13156i	0.317417	+	0.183261i
$293$	12.8490	−	22.2552i	0.750648	−	1.30016i	−0.196861	−	0.980431i	$-0.563075\pi$
$293$	12.8490	−	22.2552i	0.750648	−	1.30016i	0.947509	−	0.319729i	$-0.103592\pi$
$294$	−4.05048	−	11.4278i	−0.236229	−	0.666480i
$295$	17.6159	−	30.5116i	1.02563	−	1.77645i
$296$	4.38274	−	2.53038i	0.254742	−	0.147075i
$297$	−11.1825	−	3.72710i	−0.648875	−	0.216268i
$298$	−21.2557			−1.23131
$299$	−1.09270	−	3.38886i	−0.0631926	−	0.195983i
$300$	−13.8805	+	13.3369i	−0.801394	+	0.770004i
$301$	2.11476	+	6.57472i	0.121893	+	0.378960i
$302$	7.17921	−	4.14492i	0.413117	−	0.238513i
$303$	−3.82307	−	15.4997i	−0.219629	−	0.890437i
$304$			5.55547i			0.318628i
$305$	7.84142	+	4.52725i	0.448998	+	0.259229i
$306$	13.0120	−	20.5919i	0.743847	−	1.17716i
$307$			5.18537i			0.295945i	0.988991	+	0.147972i	$0.0472747\pi$
$307$			5.18537i			0.295945i	−0.988991	+	0.147972i	$0.952725\pi$
$308$	−4.44829	−	4.02916i	−0.253465	−	0.229583i
$309$	−1.95443	+	6.75167i	−0.111184	+	0.384089i
$310$	−7.91321	−	13.7061i	−0.449440	−	0.778453i
$311$	−0.309481			−0.0175490			−0.00877452	−	0.999962i	$-0.502793\pi$
$311$	−0.309481			−0.0175490			−0.00877452	+	0.999962i	$0.502793\pi$
$312$	−5.49998	−	2.95808i	−0.311375	−	0.167469i
$313$		−	7.71774i		−	0.436233i	−0.975923	−	0.218116i	$-0.930009\pi$
$313$		−	7.71774i		−	0.436233i	0.975923	−	0.218116i	$-0.0699912\pi$
$314$	−1.58385	−	2.74330i	−0.0893815	−	0.154813i
$315$	30.6966	−	8.53698i	1.72956	−	0.481005i
$316$	3.11929	−	5.40277i	0.175474	−	0.303929i
$317$			0.193335i			0.0108588i	0.999985	+	0.00542939i	$0.00172824\pi$
$317$			0.193335i			0.0108588i	−0.999985	+	0.00542939i	$0.998272\pi$
$318$	3.48088	+	14.1124i	0.195198	+	0.791384i
$319$	9.03915	−	15.6563i	0.506095	−	0.876582i
$320$	−4.01418			−0.224400
$321$	19.3599	−	4.77519i	1.08056	−	0.266525i
$322$	0.800045	+	2.48731i	0.0445848	+	0.138613i
$323$	39.0644	−	22.5539i	2.17360	−	1.25493i
$324$	8.97129	+	0.718256i	0.498405	+	0.0399031i
$325$	8.41917	−	39.1765i	0.467012	−	2.17312i
$326$			16.0466i			0.888737i
$327$	−3.89595	−	1.12778i	−0.215447	−	0.0623662i
$328$	−0.609334	+	0.351799i	−0.0336448	+	0.0194248i
$329$	4.14771	−	4.57917i	0.228671	−	0.252458i
$330$	11.3731	−	10.9276i	0.626067	−	0.601545i
$331$	−11.9411	+	20.6826i	−0.656342	+	1.13682i	0.325214	+	0.945640i	$0.394564\pi$
$331$	−11.9411	+	20.6826i	−0.656342	+	1.13682i	−0.981556	+	0.191177i	$0.938770\pi$
$332$	−1.84953	+	3.20348i	−0.101506	+	0.175814i
$333$	0.606303	−	15.1702i	0.0332252	−	0.831319i
$334$	−6.55709	−	3.78574i	−0.358788	−	0.207146i
$335$	−6.82672	−	11.8242i	−0.372983	−	0.646026i
$336$	4.03433	+	2.17353i	0.220090	+	0.118576i
$337$	−28.4627			−1.55046			−0.775232	−	0.631677i	$-0.782367\pi$
$337$	−28.4627			−1.55046			−0.775232	+	0.631677i	$0.782367\pi$
$338$	12.9348	−	1.30082i	0.703558	−	0.0707552i
$339$	5.48455	+	5.70813i	0.297880	+	0.310023i
$340$	16.2966	+	28.2266i	0.883809	+	1.53080i
$341$	4.47184	+	7.74546i	0.242164	+	0.419440i
$342$	14.0892	+	8.90295i	0.761858	+	0.481417i
$343$	−14.8860	−	11.0186i	−0.803766	−	0.594946i
$344$	−2.26067	−	1.30520i	−0.121887	−	0.0703715i
$345$	−6.66642	+	1.64430i	−0.358908	+	0.0885260i
$346$		−	4.78325i		−	0.257149i
$347$	−23.4106	−	13.5161i	−1.25675	−	0.725582i	−0.284305	−	0.958734i	$-0.591763\pi$
$347$	−23.4106	−	13.5161i	−1.25675	−	0.725582i	−0.972440	+	0.233152i	$0.925096\pi$
$348$	−3.83816	+	13.2591i	−0.205747	+	0.710761i
$349$	19.4151	−	11.2093i	1.03927	−	0.600022i	0.119643	−	0.992817i	$-0.461825\pi$
$349$	19.4151	−	11.2093i	1.03927	−	0.600022i	0.919626	+	0.392795i	$0.128492\pi$
$350$	−6.19855	+	28.7433i	−0.331326	+	1.53639i
$351$	−16.3160	+	9.20800i	−0.870885	+	0.491486i
$352$	2.26846			0.120909
$353$	1.64240	+	2.84473i	0.0874164	+	0.151410i	0.906418	−	0.422381i	$-0.138806\pi$
$353$	1.64240	+	2.84473i	0.0874164	+	0.151410i	−0.819002	+	0.573791i	$0.805472\pi$
$354$	4.22701	−	14.6024i	0.224663	−	0.776107i
$355$	−0.0272274	−	0.0157198i	−0.00144508	−	0.000834318i
$356$	−4.73373			−0.250887
$357$	−1.09478	−	37.1922i	−0.0579418	−	1.96842i
$358$	7.21674	−	12.4998i	0.381417	−	0.660633i
$359$			37.0702i			1.95649i	0.207453	+	0.978245i	$0.433483\pi$
$359$			37.0702i			1.95649i	−0.207453	+	0.978245i	$0.566517\pi$
$360$	−6.43296	+	10.1804i	−0.339047	+	0.536553i
$361$	5.93160	+	10.2738i	0.312189	+	0.540728i
$362$	6.73376	+	11.6632i	0.353918	+	0.613005i
$363$	7.31152	−	7.02514i	0.383755	−	0.368724i
$364$	−9.49220	+	0.947750i	−0.497526	+	0.0496756i
$365$			25.1413i			1.31596i
$366$	3.75278	+	1.08633i	0.196161	+	0.0567836i
$367$	−20.1100	+	11.6105i	−1.04973	+	0.606065i	−0.922575	−	0.385817i	$-0.873919\pi$
$367$	−20.1100	+	11.6105i	−1.04973	+	0.606065i	−0.127160	+	0.991882i	$0.540586\pi$
$368$	−0.855244	−	0.493775i	−0.0445827	−	0.0257398i
$369$	−0.0842945	+	2.10911i	−0.00438820	+	0.109796i
$370$	17.5931	+	10.1574i	0.914624	+	0.528058i
$371$	16.4561	+	14.9056i	0.854357	+	0.773858i
$372$	−4.73131	−	4.92418i	−0.245307	−	0.255307i
$373$	2.86944	−	4.97001i	0.148574	−	0.257337i	−0.782127	−	0.623119i	$-0.785865\pi$
$373$	2.86944	−	4.97001i	0.148574	−	0.257337i	0.930701	+	0.365782i	$0.119198\pi$
$374$	−9.20941	−	15.9512i	−0.476207	−	0.824816i
$375$	−40.8307	−	11.8194i	−2.10849	−	0.610353i
$376$			2.33521i			0.120429i
$377$	−8.81797	−	27.3476i	−0.454148	−	1.40847i
$378$	11.9775	−	6.74825i	0.616057	−	0.347093i
$379$	8.32374	+	14.4171i	0.427562	+	0.740559i	0.996656	−	0.0817134i	$-0.0260392\pi$
$379$	8.32374	+	14.4171i	0.427562	+	0.740559i	−0.569094	+	0.822273i	$0.692706\pi$
$380$	−19.3129	+	11.1503i	−0.990733	+	0.572000i
$381$	0.608209	+	2.46584i	0.0311595	+	0.126329i
$382$	−13.6580			−0.698804
$383$	−5.67426	+	9.82810i	−0.289941	+	0.502192i	−0.973795	−	0.227426i	$-0.926969\pi$
$383$	−5.67426	+	9.82810i	−0.289941	+	0.502192i	0.683854	+	0.729619i	$0.260302\pi$
$384$	−1.68165	+	0.414785i	−0.0858164	+	0.0211669i
$385$	5.07880	−	23.5509i	0.258839	−	1.20026i
$386$	−13.2481	−	7.64881i	−0.674312	−	0.389314i
$387$	−6.93296	+	3.64163i	−0.352422	+	0.185114i
$388$	−4.88472	+	2.82020i	−0.247984	+	0.143174i
$389$			1.51415i			0.0767706i	0.999263	+	0.0383853i	$0.0122214\pi$
$389$			1.51415i			0.0767706i	−0.999263	+	0.0383853i	$0.987779\pi$
$390$	−0.755517	−	25.0572i	−0.0382571	−	1.26882i
$391$			8.01844i			0.405510i
$392$	6.96586	−	0.690475i	0.351829	−	0.0348743i
$393$	19.2173	+	5.56292i	0.969386	+	0.280612i
$394$	4.40039	−	7.62170i	0.221688	−	0.383975i
$395$	25.0428			1.26004
$396$	3.63534	−	5.75305i	0.182683	−	0.289102i
$397$	6.67704	+	3.85499i	0.335111	+	0.193476i	0.658108	−	0.752924i	$-0.271357\pi$
$397$	6.67704	+	3.85499i	0.335111	+	0.193476i	−0.322997	+	0.946400i	$0.604690\pi$
$398$	−22.7847			−1.14209
$399$	25.4473	−	0.749059i	1.27396	−	0.0374999i
$400$	−5.55684	−	9.62473i	−0.277842	−	0.481236i
$401$	−22.3081	+	12.8796i	−1.11401	+	0.643177i	−0.939866	−	0.341543i	$-0.889051\pi$
$401$	−22.3081	+	12.8796i	−1.11401	+	0.643177i	−0.174148	+	0.984719i	$0.555717\pi$
$402$	−4.08170	−	4.24809i	−0.203576	−	0.211875i
$403$	13.8980	+	2.98673i	0.692310	+	0.148780i
$404$	9.21697			0.458562
$405$	15.5093	+	32.6293i	0.770662	+	1.62136i
$406$	6.45626	+	20.0723i	0.320419	+	0.996171i
$407$	−9.94208	−	5.74006i	−0.492811	−	0.284524i
$408$	9.74376	+	10.1410i	0.482388	+	0.502053i
$409$	−6.78248	−	3.91587i	−0.335372	−	0.193627i	0.322852	−	0.946450i	$-0.395359\pi$
$409$	−6.78248	−	3.91587i	−0.335372	−	0.193627i	−0.658224	+	0.752822i	$0.728692\pi$
$410$	−2.44598	−	1.41219i	−0.120798	−	0.0697429i
$411$	16.9504	+	17.6414i	0.836102	+	0.870186i
$412$	−3.51443	−	2.02906i	−0.173144	−	0.0999645i
$413$	−7.11036	−	22.1059i	−0.349878	−	1.08776i
$414$	−2.62284	+	1.37768i	−0.128906	+	0.0677094i
$415$	−14.8487			−0.728895
$416$	2.41859	−	2.67402i	0.118581	−	0.131105i
$417$	−16.7733	−	17.4571i	−0.821393	−	0.854878i
$418$	10.9140	−	6.30118i	0.533819	−	0.308201i
$419$	−15.1579	−	26.2543i	−0.740514	−	1.28261i	−0.952262	−	0.305284i	$-0.901249\pi$
$419$	−15.1579	−	26.2543i	−0.740514	−	1.28261i	0.211747	−	0.977324i	$-0.432085\pi$
$420$	0.541244	+	18.3873i	0.0264100	+	0.897210i
$421$	36.0634			1.75762			0.878810	−	0.477171i	$-0.158338\pi$
$421$	36.0634			1.75762			0.878810	+	0.477171i	$0.158338\pi$
$422$	−11.4831	−	6.62975i	−0.558987	−	0.322731i
$423$	5.92232	+	3.74230i	0.287953	+	0.181957i
$424$	−8.39199			−0.407551
$425$	−45.1189	+	78.1482i	−2.18859	+	3.79075i
$426$	−0.0130306	−	0.00377203i	−0.000631336	−	0.000182755i
$427$	5.68117	−	1.82735i	0.274931	−	0.0884317i
$428$			11.5124i			0.556474i
$429$	0.426951	+	14.1601i	0.0206134	+	0.683656i
$430$		−	10.4786i		−	0.505323i
$431$	21.4300	−	12.3726i	1.03225	−	0.595969i	0.114620	−	0.993409i	$-0.463435\pi$
$431$	21.4300	−	12.3726i	1.03225	−	0.595969i	0.917628	+	0.397441i	$0.130102\pi$
$432$	−1.64301	+	4.92956i	−0.0790492	+	0.237173i
$433$	9.26567	+	5.34954i	0.445280	+	0.257082i	0.705835	−	0.708377i	$-0.250572\pi$
$433$	9.26567	+	5.34954i	0.445280	+	0.257082i	−0.260555	+	0.965459i	$0.583905\pi$
$434$	−10.1968	−	2.19896i	−0.489461	−	0.105553i
$435$	−53.7972	+	13.2693i	−2.57938	+	0.636212i
$436$	1.17084	−	2.02795i	0.0560729	−	0.0971211i
$437$	−5.48630			−0.262446
$438$	2.59785	+	10.5324i	0.124130	+	0.503257i
$439$	−16.3694	+	9.45090i	−0.781271	+	0.451067i	−0.836881	−	0.547386i	$-0.815623\pi$
$439$	−16.3694	+	9.45090i	−0.781271	+	0.451067i	0.0556095	+	0.998453i	$0.482290\pi$
$440$	4.55301	+	7.88605i	0.217056	+	0.375953i
$441$	9.41208	−	18.7727i	0.448194	−	0.893936i
$442$	−28.6219	−	6.15095i	−1.36140	−	0.292571i
$443$		−	19.1461i		−	0.909658i	−0.890579	−	0.454829i	$-0.849700\pi$
$443$		−	19.1461i		−	0.909658i	0.890579	−	0.454829i	$-0.150300\pi$
$444$	8.41981	+	2.43732i	0.399587	+	0.115670i
$445$	−9.50102	−	16.4563i	−0.450392	−	0.780101i
$446$	−4.29194	+	7.43387i	−0.203229	+	0.352004i
$447$	−25.5077	−	26.5475i	−1.20647	−	1.25565i
$448$	−1.77617	+	1.96093i	−0.0839159	+	0.0926451i
$449$	−5.69004	−	3.28514i	−0.268529	−	0.155036i	0.359690	−	0.933072i	$-0.382883\pi$
$449$	−5.69004	−	3.28514i	−0.268529	−	0.155036i	−0.628219	+	0.778036i	$0.716216\pi$
$450$	−33.3144	−	1.33147i	−1.57046	−	0.0627663i
$451$	1.38225	+	0.798042i	0.0650876	+	0.0375783i
$452$	−3.95800	+	2.28515i	−0.186169	+	0.107484i
$453$	13.7922	+	3.99248i	0.648013	+	0.187583i
$454$		−	24.4925i		−	1.14949i
$455$	−22.3465	−	31.0963i	−1.04762	−	1.45782i
$456$	−6.93856	+	6.66678i	−0.324928	+	0.312201i
$457$	14.7244	+	25.5034i	0.688779	+	1.19300i	0.972233	+	0.234014i	$0.0751861\pi$
$457$	14.7244	+	25.5034i	0.688779	+	1.19300i	−0.283455	+	0.958986i	$0.591481\pi$
$458$	7.26599	+	12.5851i	0.339517	+	0.588061i
$459$	41.3334	−	8.45968i	1.92928	−	0.394864i
$460$		−	3.96421i		−	0.184832i
$461$	−6.55063	+	11.3460i	−0.305093	+	0.528437i	−0.977282	−	0.211943i	$-0.932021\pi$
$461$	−6.55063	+	11.3460i	−0.305093	+	0.528437i	0.672189	+	0.740380i	$0.265354\pi$
$462$	−0.305863	−	10.3909i	−0.0142300	−	0.483428i
$463$	12.9808			0.603270			0.301635	−	0.953424i	$-0.402468\pi$
$463$	12.9808			0.603270			0.301635	+	0.953424i	$0.402468\pi$
$464$	−6.90171	−	3.98470i	−0.320404	−	0.184985i
$465$	7.62218	−	26.3311i	0.353470	−	1.22108i
$466$	−7.71957	−	13.3707i	−0.357602	−	0.619385i
$467$	−0.410726			−0.0190061			−0.00950306	−	0.999955i	$-0.503025\pi$
$467$	−0.410726			−0.0190061			−0.00950306	+	0.999955i	$0.503025\pi$
$468$	−2.90566	−	10.4191i	−0.134314	−	0.481622i
$469$	−8.79676	−	1.89704i	−0.406197	−	0.0875972i
$470$	−8.11807	+	4.68697i	−0.374459	+	0.216194i
$471$	1.52560	−	5.27023i	0.0702957	−	0.242839i
$472$	7.60093	+	4.38840i	0.349861	+	0.201993i
$473$			5.92158i			0.272275i
$474$	10.4911	−	2.58767i	0.481873	−	0.118856i
$475$	−53.4698	−	30.8708i	−2.45336	−	1.41645i
$476$	20.9995	+	4.52858i	0.962510	+	0.207567i
$477$	−13.4486	+	21.2829i	−0.615771	+	0.974479i
$478$	−5.25957	−	9.10984i	−0.240567	−	0.416674i
$479$	−4.72048	−	8.17611i	−0.215684	−	0.373576i	0.737800	−	0.675020i	$-0.235865\pi$
$479$	−4.72048	−	8.17611i	−0.215684	−	0.373576i	−0.953484	+	0.301443i	$0.902532\pi$
$480$	−4.81718	−	5.01356i	−0.219873	−	0.228837i
$481$	−17.3664	+	5.59961i	−0.791838	+	0.255320i
$482$	23.2568			1.05932
$483$	−2.14647	+	3.98410i	−0.0976677	+	0.181283i
$484$	2.92704	+	5.06978i	0.133047	+	0.230445i
$485$	−19.6082	−	11.3208i	−0.890362	−	0.514051i
$486$	9.86884	+	12.0667i	0.447660	+	0.547358i
$487$	−1.50355	+	2.60422i	−0.0681321	+	0.118008i	−0.898079	−	0.439834i	$-0.855037\pi$
$487$	−1.50355	+	2.60422i	−0.0681321	+	0.118008i	0.829947	+	0.557842i	$0.188371\pi$
$488$	−1.12781	+	1.95343i	−0.0510536	+	0.0884275i
$489$	−20.0415	+	19.2565i	−0.906309	+	0.870810i
$490$	16.3815	+	22.8302i	0.740040	+	1.03136i
$491$	−5.01812	+	2.89721i	−0.226465	+	0.130749i	−0.608940	−	0.793216i	$-0.708405\pi$
$491$	−5.01812	+	2.89721i	−0.226465	+	0.130749i	0.382475	+	0.923966i	$0.375072\pi$
$492$	−1.17061	−	0.338861i	−0.0527751	−	0.0152770i
$493$			64.7078i			2.91429i
$494$	4.20854	−	19.5834i	0.189351	−	0.881099i
$495$	27.2963	+	1.09095i	1.22688	+	0.0490344i
$496$	3.41441	−	1.97131i	0.153312	−	0.0885145i
$497$	−0.0197265	+	0.00634503i	−0.000884853	+	0.000284614i
$498$	−6.22054	+	1.53432i	−0.278749	+	0.0687544i
$499$	21.1043			0.944760			0.472380	−	0.881395i	$-0.343395\pi$
$499$	21.1043			0.944760			0.472380	+	0.881395i	$0.343395\pi$
$500$	12.2707	−	21.2535i	0.548763	−	0.950486i
$501$	−3.14054	−	12.7326i	−0.140309	−	0.568850i
$502$		−	10.1162i		−	0.451510i
$503$	15.6330	−	27.0772i	0.697042	−	1.20731i	−0.272445	−	0.962171i	$-0.587832\pi$
$503$	15.6330	−	27.0772i	0.697042	−	1.20731i	0.969487	−	0.245142i	$-0.0788344\pi$
$504$	2.12670	+	7.64703i	0.0947309	+	0.340626i
$505$	18.4993	+	32.0418i	0.823209	+	1.42584i
$506$			2.24022i			0.0995900i
$507$	17.1469	+	14.5940i	0.761521	+	0.648141i
$508$	−1.46632			−0.0650575
$509$	3.80587	+	6.59196i	0.168692	+	0.292183i	0.937960	−	0.346743i	$-0.112712\pi$
$509$	3.80587	+	6.59196i	0.168692	+	0.292183i	−0.769268	+	0.638926i	$0.779379\pi$
$510$	−15.6973	+	54.2269i	−0.695087	+	2.40121i
$511$	12.2815	+	11.1243i	0.543303	+	0.492112i
$512$		−	1.00000i		−	0.0441942i
$513$	5.78820	+	28.2808i	0.255555	+	1.24863i
$514$	−0.501508	−	0.289546i	−0.0221206	−	0.0127713i
$515$		−	16.2900i		−	0.717824i
$516$	−1.08275	−	4.38978i	−0.0476656	−	0.193249i
$517$	4.58762	−	2.64866i	0.201763	−	0.116488i
$518$	12.7464	−	4.09987i	0.560043	−	0.180138i
$519$	5.97409	−	5.74009i	0.262233	−	0.251962i
$520$	14.1503	+	3.04095i	0.620531	+	0.133354i
$521$	−23.2965			−1.02064			−0.510320	−	0.859985i	$-0.670473\pi$
$521$	−23.2965			−1.02064			−0.510320	+	0.859985i	$0.670473\pi$
$522$	−21.1660	+	11.1177i	−0.926410	+	0.486609i
$523$	31.9594	−	18.4517i	1.39748	−	0.806838i	0.403356	−	0.915043i	$-0.367844\pi$
$523$	31.9594	−	18.4517i	1.39748	−	0.806838i	0.994129	+	0.108205i	$0.0345102\pi$
$524$	−5.77532	+	10.0031i	−0.252296	+	0.436990i
$525$	−43.3377	+	26.7513i	−1.89141	+	1.16752i
$526$	12.8263	−	22.2158i	0.559254	−	0.968656i
$527$	−27.7234	−	16.0061i	−1.20765	−	0.697237i
$528$	2.72225	+	2.83322i	0.118471	+	0.123300i
$529$	−11.0124	+	19.0740i	−0.478799	+	0.829304i
$530$	−16.8435	−	29.1738i	−0.731635	−	1.26723i
$531$	23.3104	−	12.2441i	1.01158	−	0.531348i
$532$	−3.09851	+	14.3681i	−0.134337	+	0.622935i
$533$	2.41445	−	0.778515i	0.104581	−	0.0337212i
$534$	−5.68066	−	5.91224i	−0.245826	−	0.255847i
$535$	−40.0216	+	23.1065i	−1.73029	+	0.998981i
$536$	2.94561	−	1.70065i	0.127231	−	0.0734568i
$537$	24.2721	−	5.98680i	1.04742	−	0.258349i
$538$		−	0.0811482i		−	0.00349855i
$539$	−9.25737	−	12.9016i	−0.398743	−	0.555711i
$540$	−20.4347	+	4.18235i	−0.879370	+	0.179980i
$541$	−31.5015			−1.35436			−0.677178	−	0.735820i	$-0.736797\pi$
$541$	−31.5015			−1.35436			−0.677178	+	0.735820i	$0.736797\pi$
$542$	9.95358	−	17.2401i	0.427543	−	0.740526i
$543$	−6.48611	+	22.4065i	−0.278345	+	0.961556i
$544$	−7.03171	+	4.05976i	−0.301482	+	0.174061i
$545$	9.39991			0.402648
$546$	−12.5747	−	10.7180i	−0.538148	−	0.458690i
$547$	−41.0811			−1.75650			−0.878251	−	0.478200i	$-0.841290\pi$
$547$	−41.0811			−1.75650			−0.878251	+	0.478200i	$0.841290\pi$
$548$	−12.2325	+	7.06243i	−0.522546	+	0.301692i
$549$	3.14671	+	5.99072i	0.134298	+	0.255678i
$550$	−12.6055	+	21.8333i	−0.537499	+	0.930976i
$551$	−44.2738			−1.88613
$552$	−0.409622	−	1.66072i	−0.0174347	−	0.0706848i
$553$	11.0807	−	12.2334i	0.471201	−	0.520217i
$554$		−	8.75710i		−	0.372054i
$555$	8.42629	+	34.1624i	0.357676	+	1.45011i
$556$	12.1047	−	6.98865i	0.513354	−	0.296385i
$557$	−1.88989	+	1.09113i	−0.0800770	+	0.0462325i	−0.539504	−	0.841983i	$-0.681388\pi$
$557$	−1.88989	+	1.09113i	−0.0800770	+	0.0462325i	0.459427	+	0.888216i	$0.348055\pi$
$558$	0.472346	−	11.8184i	0.0199960	−	0.500314i
$559$	6.98026	+	6.31348i	0.295234	+	0.267032i
$560$	−10.3819	−	2.23887i	−0.438714	−	0.0946096i
$561$	8.87071	−	30.6443i	0.374522	−	1.29380i
$562$	8.86653	+	15.3573i	0.374012	+	0.647807i
$563$	−4.18060	+	7.24101i	−0.176191	+	0.305172i	−0.940573	−	0.339592i	$-0.889711\pi$
$563$	−4.18060	+	7.24101i	−0.176191	+	0.305172i	0.764382	+	0.644764i	$0.223044\pi$
$564$	−2.91658	+	2.80234i	−0.122810	+	0.118000i
$565$	−15.8881	−	9.17302i	−0.668419	−	0.385912i
$566$	8.60942	−	14.9119i	0.361881	−	0.626796i
$567$	22.8018	+	6.86127i	0.957586	+	0.288146i
$568$	0.00391605	−	0.00678280i	0.000164314	−	0.000284600i
$569$	1.43201	−	0.826770i	0.0600329	−	0.0346600i	−0.469683	−	0.882835i	$-0.655632\pi$
$569$	1.43201	−	0.826770i	0.0600329	−	0.0346600i	0.529716	+	0.848175i	$0.322298\pi$
$570$	−37.1026	−	10.7403i	−1.55406	−	0.449860i
$571$	14.0859			0.589475			0.294738	−	0.955578i	$-0.404768\pi$
$571$	14.0859			0.589475			0.294738	+	0.955578i	$0.404768\pi$
$572$	−7.99649	−	1.71847i	−0.334350	−	0.0718530i
$573$	−16.3901	−	17.0583i	−0.684708	−	0.712620i
$574$	−1.77213	+	0.570006i	−0.0739672	+	0.0237916i
$575$	9.50491	−	5.48766i	0.396382	−	0.228851i
$576$	−2.53610	−	1.60256i	−0.105671	−	0.0667732i
$577$		−	30.4215i		−	1.26647i	−0.773962	−	0.633233i	$-0.781728\pi$
$577$		−	30.4215i		−	1.26647i	0.773962	−	0.633233i	$-0.218272\pi$
$578$	42.3717	+	24.4633i	1.76243	+	1.01754i
$579$	−6.34523	−	25.7253i	−0.263699	−	1.06911i
$580$		−	31.9907i		−	1.32834i
$581$	−6.57015	+	7.25360i	−0.272576	+	0.300930i
$582$	−9.38418	−	2.71648i	−0.388987	−	0.112602i
$583$	9.51845	+	16.4864i	0.394214	+	0.682799i
$584$	−6.26312			−0.259170
$585$	30.3888	−	31.0133i	1.25642	−	1.28224i
$586$			25.6980i			1.06158i
$587$	12.4840	+	21.6229i	0.515269	+	0.892472i	0.999843	+	0.0177214i	$0.00564120\pi$
$587$	12.4840	+	21.6229i	0.515269	+	0.892472i	−0.484574	+	0.874750i	$0.661025\pi$
$588$	9.22169	+	7.87149i	0.380296	+	0.324615i
$589$	10.9516	−	18.9686i	0.451251	−	0.781589i
$590$			35.2317i			1.45047i
$591$	14.7998	−	3.65043i	0.608784	−	0.150159i
$592$	−2.53038	+	4.38274i	−0.103998	+	0.180130i
$593$	38.4298			1.57812			0.789061	−	0.614315i	$-0.210568\pi$
$593$	38.4298			1.57812			0.789061	+	0.614315i	$0.210568\pi$
$594$	11.5479	−	2.36350i	0.473816	−	0.0969754i
$595$	26.4048	+	82.0916i	1.08249	+	3.36543i
$596$	18.4080	−	10.6278i	0.754020	−	0.435333i
$597$	−27.3426	−	28.4572i	−1.11906	−	1.16468i
$598$	2.64074	+	2.38848i	0.107988	+	0.0976724i
$599$		−	13.7876i		−	0.563347i	−0.959510	−	0.281674i	$-0.909110\pi$
$599$		−	13.7876i		−	0.563347i	0.959510	−	0.281674i	$-0.0908896\pi$
$600$	5.35247	−	18.4903i	0.218514	−	0.754865i
$601$	23.4431	−	13.5349i	0.956264	−	0.552099i	0.0612430	−	0.998123i	$-0.480494\pi$
$601$	23.4431	−	13.5349i	0.956264	−	0.552099i	0.895021	+	0.446023i	$0.147160\pi$
$602$	−5.11880	−	4.63649i	−0.208627	−	0.188969i
$603$	0.407492	−	10.1958i	0.0165944	−	0.415203i
$604$	−4.14492	+	7.17921i	−0.168654	+	0.292118i
$605$	−11.7497	+	20.3510i	−0.477693	+	0.827388i
$606$	11.0607	+	11.5116i	0.449312	+	0.467628i
$607$	−2.92294	−	1.68756i	−0.118638	−	0.0684959i	0.439507	−	0.898239i	$-0.355153\pi$
$607$	−2.92294	−	1.68756i	−0.118638	−	0.0684959i	−0.558145	+	0.829744i	$0.688487\pi$
$608$	−2.77773	−	4.81117i	−0.112652	−	0.195119i
$609$	−17.3217	+	32.1512i	−0.701912	+	1.30283i
$610$	−9.05449			−0.366606
$611$	1.76904	−	8.23176i	0.0715675	−	0.333021i
$612$	−0.972759	+	24.3391i	−0.0393214	+	0.983851i
$613$	−11.1134	−	19.2490i	−0.448866	−	0.777459i	0.549446	−	0.835529i	$-0.314839\pi$
$613$	−11.1134	−	19.2490i	−0.448866	−	0.777459i	−0.998313	+	0.0580698i	$0.981505\pi$
$614$	−2.59268	−	4.49066i	−0.104632	−	0.181228i
$615$	−1.17151	−	4.74961i	−0.0472398	−	0.191523i
$616$	5.86691	+	1.26521i	0.236385	+	0.0509769i
$617$	8.08240	+	4.66637i	0.325385	+	0.187861i	0.653790	−	0.756676i	$-0.273178\pi$
$617$	8.08240	+	4.66637i	0.325385	+	0.187861i	−0.328405	+	0.944537i	$0.606511\pi$
$618$	−1.68325	−	6.82434i	−0.0677101	−	0.274515i
$619$		−	0.923782i		−	0.0371299i	−0.999828	−	0.0185650i	$-0.994090\pi$
$619$		−	0.923782i		−	0.0371299i	0.999828	−	0.0185650i	$-0.00590975\pi$
$620$	13.7061	+	7.91321i	0.550449	+	0.317802i
$621$	−4.86819	−	1.62255i	−0.195354	−	0.0651108i
$622$	0.268018	−	0.154740i	0.0107465	−	0.00620452i
$623$	−12.2428	−	2.64019i	−0.490498	−	0.105777i
$624$	6.24216	−	0.188212i	0.249886	−	0.00753450i
$625$	42.9455			1.71782
$626$	3.85887	+	6.68376i	0.154232	+	0.267137i
$627$	20.9671	+	6.06944i	0.837346	+	0.242390i
$628$	2.74330	+	1.58385i	0.109470	+	0.0632023i
$629$	41.0909			1.63840
$630$	−22.3155	+	22.7415i	−0.889073	+	0.906045i
$631$	2.64857	−	4.58746i	0.105438	−	0.182624i	−0.808479	−	0.588525i	$-0.799709\pi$
$631$	2.64857	−	4.58746i	0.105438	−	0.182624i	0.913917	+	0.405901i	$0.133042\pi$
$632$			6.23858i			0.248157i
$633$	−5.49985	−	22.2979i	−0.218599	−	0.886261i
$634$	−0.0966675	−	0.167433i	−0.00383916	−	0.00664962i
$635$	−2.94304	−	5.09750i	−0.116791	−	0.202288i
$636$	−10.0707	−	10.4813i	−0.399330	−	0.415609i
$637$	−25.0782	−	2.84302i	−0.993635	−	0.112644i
$638$			18.0783i			0.715726i
$639$	−0.0109262	−	0.0208013i	−0.000432233	−	0.000822888i
$640$	3.47639	−	2.00709i	0.137416	−	0.0793373i
$641$	6.51519	+	3.76155i	0.257335	+	0.148572i	0.623118	−	0.782128i	$-0.285866\pi$
$641$	6.51519	+	3.76155i	0.257335	+	0.148572i	−0.365784	+	0.930700i	$0.619199\pi$
$642$	−14.3786	+	13.8154i	−0.567477	+	0.545249i
$643$	36.7294	+	21.2057i	1.44846	+	0.836271i	0.998390	−	0.0567200i	$-0.0180642\pi$
$643$	36.7294	+	21.2057i	1.44846	+	0.836271i	0.450074	+	0.892991i	$0.351398\pi$
$644$	−1.93652	−	1.75405i	−0.0763094	−	0.0691194i
$645$	13.0874	−	12.5748i	0.515315	−	0.495130i
$646$	−22.5539	+	39.0644i	−0.887370	+	1.53697i
$647$	18.1549	+	31.4452i	0.713742	+	1.23624i	0.963443	+	0.267915i	$0.0863346\pi$
$647$	18.1549	+	31.4452i	0.713742	+	1.23624i	−0.249700	+	0.968323i	$0.580332\pi$
$648$	−8.12850	+	3.86362i	−0.319317	+	0.151777i
$649$		−	19.9098i		−	0.781530i
$650$	12.2970	+	38.1374i	0.482329	+	1.49587i
$651$	−9.49015	−	15.3742i	−0.371948	−	0.602563i
$652$	−8.02328	−	13.8967i	−0.314216	−	0.544238i
$653$	−21.3580	+	12.3310i	−0.835801	+	0.482550i	−0.855835	−	0.517249i	$-0.826956\pi$
$653$	−21.3580	+	12.3310i	−0.835801	+	0.482550i	0.0200335	+	0.999799i	$0.493623\pi$
$654$	3.93788	−	0.971292i	0.153983	−	0.0379805i
$655$	−46.3664			−1.81169
$656$	0.351799	−	0.609334i	0.0137354	−	0.0237905i
$657$	−10.0370	+	15.8839i	−0.391581	+	0.619690i
$658$	−1.30244	+	6.03953i	−0.0507743	+	0.235445i
$659$	25.0769	+	14.4781i	0.976856	+	0.563988i	0.901320	−	0.433155i	$-0.142600\pi$
$659$	25.0769	+	14.4781i	0.976856	+	0.563988i	0.0755368	+	0.997143i	$0.475933\pi$
$660$	−4.38556	+	15.1501i	−0.170708	+	0.589717i
$661$	14.1347	−	8.16065i	0.549775	−	0.317413i	−0.199256	−	0.979947i	$-0.563853\pi$
$661$	14.1347	−	8.16065i	0.549775	−	0.317413i	0.749031	+	0.662535i	$0.230519\pi$
$662$		−	23.8822i		−	0.928207i
$663$	−26.6651	−	43.1290i	−1.03559	−	1.67499i
$664$		−	3.69906i		−	0.143552i
$665$	−56.1680	+	18.0665i	−2.17810	+	0.700587i
$666$	7.06000	+	13.4409i	0.273570	+	0.520824i
$667$	3.93510	−	6.81579i	0.152368	−	0.263908i
$668$	7.57148			0.292949
$669$	−14.4351	+	3.56047i	−0.558094	+	0.137656i
$670$	11.8242	+	6.82672i	0.456810	+	0.263739i
$671$	5.11680			0.197532
$672$	−4.58059	+	0.134833i	−0.176700	+	0.00520129i
$673$	−17.2346	−	29.8511i	−0.664343	−	1.15068i	−0.979463	−	0.201625i	$-0.935378\pi$
$673$	−17.2346	−	29.8511i	−0.664343	−	1.15068i	0.315119	−	0.949052i	$-0.397955\pi$
$674$	24.6494	−	14.2314i	0.949461	−	0.548172i
$675$	−38.3157	−	43.2062i	−1.47477	−	1.66301i
$676$	−10.5514	+	7.59392i	−0.405824	+	0.292074i
$677$	28.7493			1.10493			0.552463	−	0.833537i	$-0.313688\pi$
$677$	28.7493			1.10493			0.552463	+	0.833537i	$0.313688\pi$
$678$	−7.60382	−	2.20111i	−0.292023	−	0.0845331i
$679$	−14.2063	+	4.56946i	−0.545187	+	0.175360i
$680$	−28.2266	−	16.2966i	−1.08244	−	0.624947i
$681$	30.5902	−	29.3920i	1.17222	−	1.12630i
$682$	−7.74546	−	4.47184i	−0.296589	−	0.171236i
$683$	3.43153	+	1.98120i	0.131304	+	0.0758083i	0.564213	−	0.825629i	$-0.309180\pi$
$683$	3.43153	+	1.98120i	0.131304	+	0.0758083i	−0.432909	+	0.901438i	$0.642513\pi$
$684$	−16.6531	−	0.665572i	−0.636747	−	0.0254488i
$685$	−49.1035	−	28.3499i	−1.87615	−	1.08319i
$686$	18.4009	+	2.09937i	0.702549	+	0.0801543i
$687$	−6.99877	+	24.1775i	−0.267020	+	0.922430i
$688$	2.61039			0.0995204
$689$	29.5824	+	6.35735i	1.12700	+	0.242196i
$690$	4.95114	−	4.75722i	0.188487	−	0.181104i
$691$	37.4810	−	21.6396i	1.42584	−	0.823211i	0.429054	−	0.903279i	$-0.358847\pi$
$691$	37.4810	−	21.6396i	1.42584	−	0.823211i	0.996789	+	0.0800680i	$0.0255138\pi$
$692$	2.39162	+	4.14242i	0.0909159	+	0.157471i
$693$	12.6108	−	12.8515i	0.479044	−	0.488188i
$694$	27.0322			1.02613
$695$	48.5905	+	28.0537i	1.84314	+	1.06414i
$696$	−3.30559	−	13.4018i	−0.125298	−	0.507993i
$697$	−5.71288			−0.216391
$698$	−11.2093	+	19.4151i	−0.424280	+	0.734874i
$699$	7.43566	−	25.6868i	0.281243	−	0.971564i
$700$	−9.00353	−	27.9917i	−0.340302	−	1.05799i
$701$		−	39.4517i		−	1.49007i	−0.667025	−	0.745035i	$-0.732433\pi$
$701$		−	39.4517i		−	1.49007i	0.667025	−	0.745035i	$-0.267567\pi$
$702$	9.52610	−	16.1324i	0.359539	−	0.608877i
$703$			28.1149i			1.06037i
$704$	−1.96455	+	1.13423i	−0.0740416	+	0.0427479i
$705$	−15.5959	−	4.51460i	−0.587374	−	0.170030i
$706$	−2.84473	−	1.64240i	−0.107063	−	0.0618127i
$707$	23.8378	+	5.14068i	0.896513	+	0.193335i
$708$	3.64049	+	14.7595i	0.136818	+	0.554697i
$709$	3.91084	−	6.77378i	0.146875	−	0.254395i	−0.783196	−	0.621775i	$-0.786412\pi$
$709$	3.91084	−	6.77378i	0.146875	−	0.254395i	0.930071	+	0.367380i	$0.119745\pi$
$710$	0.0314395			0.00117990
$711$	15.8217	+	9.99768i	0.593359	+	0.374942i
$712$	4.09953	−	2.36686i	0.153636	−	0.0887019i
$713$	1.94677	+	3.37190i	0.0729071	+	0.126279i
$714$	19.5442	+	31.6620i	0.731424	+	1.18492i
$715$	−10.0756	−	31.2480i	−0.376806	−	1.16861i
$716$			14.4335i			0.539405i
$717$	5.06613	−	17.5012i	0.189198	−	0.653593i
$718$	−18.5351	−	32.1037i	−0.691724	−	1.19810i
$719$	2.33583	−	4.04577i	0.0871116	−	0.150882i	−0.819177	−	0.573540i	$-0.805570\pi$
$719$	2.33583	−	4.04577i	0.0871116	−	0.150882i	0.906289	+	0.422658i	$0.138903\pi$
$720$	0.480919	−	12.0329i	0.0179228	−	0.448441i
$721$	−7.95767	−	7.20788i	−0.296359	−	0.268436i
$722$	−10.2738	−	5.93160i	−0.382352	−	0.220751i
$723$	27.9092	+	29.0469i	1.03795	+	1.08026i
$724$	−11.6632	−	6.73376i	−0.433460	−	0.250258i
$725$	76.7034	−	44.2847i	2.84869	−	1.64469i
$726$	−2.81939	+	9.73970i	−0.104637	+	0.361474i
$727$			19.6014i			0.726976i	0.931599	+	0.363488i	$0.118414\pi$
$727$			19.6014i			0.726976i	−0.931599	+	0.363488i	$0.881586\pi$
$728$	7.74661	−	5.56687i	0.287108	−	0.206322i
$729$	−3.22785	+	26.8064i	−0.119550	+	0.992828i
$730$	−12.5707	−	21.7730i	−0.465261	−	0.805856i
$731$	−10.5976	−	18.3555i	−0.391966	−	0.678904i
$732$	−3.79317	+	0.935600i	−0.140200	+	0.0345808i
$733$		−	24.4651i		−	0.903637i	−0.892110	−	0.451819i	$-0.850775\pi$
$733$		−	24.4651i		−	0.903637i	0.892110	−	0.451819i	$-0.149225\pi$
$734$	11.6105	−	20.1100i	0.428552	−	0.742275i
$735$	−8.85554	+	47.8570i	−0.326642	+	1.76523i
$736$	0.987551			0.0364016
$737$	−6.68200	−	3.85786i	−0.246135	−	0.142106i
$738$	−0.981554	−	1.86869i	−0.0361315	−	0.0687874i
$739$	−21.8086	−	37.7737i	−0.802243	−	1.38953i	−0.918136	−	0.396265i	$-0.870306\pi$
$739$	−21.8086	−	37.7737i	−0.802243	−	1.38953i	0.115893	−	0.993262i	$-0.463027\pi$
$740$	−20.3148			−0.746787
$741$	29.5093	−	18.2446i	1.08405	−	0.670231i
$742$	−21.7042	−	4.68055i	−0.796785	−	0.171828i
$743$	−17.4281	+	10.0621i	−0.639376	+	0.369144i	−0.784374	−	0.620288i	$-0.787016\pi$
$743$	−17.4281	+	10.0621i	−0.639376	+	0.369144i	0.144998	+	0.989432i	$0.453682\pi$
$744$	6.55952	+	1.89881i	0.240484	+	0.0696138i
$745$	73.8930	+	42.6621i	2.70723	+	1.56302i
$746$			5.73887i			0.210115i
$747$	−9.38120	−	5.92796i	−0.343240	−	0.216893i
$748$	15.9512	+	9.20941i	0.583233	+	0.336730i
$749$	−6.42094	+	29.7745i	−0.234616	+	1.08794i
$750$	41.2702	−	10.1794i	1.50697	−	0.371700i
$751$	−6.86283	−	11.8868i	−0.250428	−	0.433754i	0.713216	−	0.700945i	$-0.247238\pi$
$751$	−6.86283	−	11.8868i	−0.250428	−	0.433754i	−0.963644	+	0.267190i	$0.913905\pi$
$752$	−1.16760	−	2.02235i	−0.0425781	−	0.0737474i
$753$	12.6348	−	12.1399i	0.460437	−	0.442402i
$754$	21.3104	+	19.2747i	0.776079	+	0.701945i
$755$	−33.2769			−1.21107
$756$	−6.99871	+	11.8329i	−0.254541	+	0.430359i
$757$	26.9905	+	46.7489i	0.980987	+	1.69912i	0.658566	+	0.752523i	$0.271163\pi$
$757$	26.9905	+	46.7489i	0.980987	+	1.69912i	0.322421	+	0.946596i	$0.395503\pi$
$758$	−14.4171	−	8.32374i	−0.523654	−	0.302332i
$759$	−2.79795	+	2.68836i	−0.101559	+	0.0975812i
$760$	11.1503	−	19.3129i	0.404465	−	0.700554i
$761$	9.42194	−	16.3193i	0.341545	−	0.591573i	−0.643175	−	0.765719i	$-0.722383\pi$
$761$	9.42194	−	16.3193i	0.341545	−	0.591573i	0.984720	+	0.174146i	$0.0557165\pi$
$762$	−1.75964	−	1.83138i	−0.0637452	−	0.0663438i
$763$	4.15920	−	4.59185i	0.150573	−	0.166236i
$764$	11.8282	−	6.82900i	0.427928	−	0.247064i
$765$	−86.5647	+	45.4692i	−3.12975	+	1.64394i
$766$		−	11.3485i		−	0.410038i
$767$	−23.4694	−	21.2275i	−0.847431	−	0.766481i
$768$	1.24896	−	1.20004i	0.0450680	−	0.0433027i
$769$	−37.5392	+	21.6733i	−1.35370	+	0.781559i	−0.988765	−	0.149475i	$-0.952242\pi$
$769$	−37.5392	+	21.6733i	−1.35370	+	0.781559i	−0.364934	+	0.931034i	$0.618908\pi$
$770$	7.37707	+	22.9351i	0.265851	+	0.826522i
$771$	−0.240199	−	0.973830i	−0.00865054	−	0.0350716i
$772$	15.2976			0.550573
$773$	−10.3803	+	17.9793i	−0.373355	+	0.646669i	−0.990079	−	0.140510i	$-0.955126\pi$
$773$	−10.3803	+	17.9793i	−0.373355	+	0.646669i	0.616725	+	0.787179i	$0.288459\pi$
$774$	4.18331	−	6.62023i	0.150366	−	0.237959i
$775$			43.8170i			1.57395i
$776$	2.82020	−	4.88472i	0.101239	−	0.175351i
$777$	20.4167	+	10.9997i	0.732446	+	0.394612i
$778$	−0.757076	−	1.31129i	−0.0271425	−	0.0470122i
$779$		−	3.90881i		−	0.140048i
$780$	13.1829	+	21.3224i	0.472023	+	0.763465i
$781$	−0.0177668			−0.000635747
$782$	−4.00922	−	6.94418i	−0.143369	−	0.248323i
$783$	−39.2856	−	13.0938i	−1.40395	−	0.467934i
$784$	−5.68738	+	4.08090i	−0.203121	+	0.145746i
$785$			12.7157i			0.453843i
$786$	−19.4242	+	4.79104i	−0.692837	+	0.170891i
$787$	30.3582	+	17.5273i	1.08215	+	0.624782i	0.931477	−	0.363801i	$-0.118521\pi$
$787$	30.3582	+	17.5273i	1.08215	+	0.624782i	0.150677	+	0.988583i	$0.451855\pi$
$788$			8.80078i			0.313515i
$789$	43.1388	−	10.6403i	1.53578	−	0.378806i
$790$	−21.6877	+	12.5214i	−0.771614	+	0.445492i
$791$	−11.5111	+	3.70254i	−0.409287	+	0.131647i
$792$	−0.271773	+	6.79996i	−0.00965703	+	0.241626i
$793$	5.45543	−	6.03159i	0.193728	−	0.214188i
$794$	−7.70998			−0.273617
$795$	16.2240	−	56.0466i	0.575407	−	1.98777i
$796$	19.7321	−	11.3924i	0.699387	−	0.403791i
$797$	17.2751	−	29.9213i	0.611914	−	1.05987i	−0.379003	−	0.925395i	$-0.623733\pi$
$797$	17.2751	−	29.9213i	0.611914	−	1.05987i	0.990918	−	0.134471i	$-0.0429335\pi$
$798$	−21.6635	+	13.3724i	−0.766879	+	0.473377i
$799$	−9.48038	+	16.4205i	−0.335392	+	0.580915i
$800$	9.62473	+	5.55684i	0.340286	+	0.196464i
$801$	0.567124	−	14.1898i	0.0200383	−	0.501374i
$802$	12.8796	−	22.3081i	0.454794	−	0.787727i
$803$	7.10383	+	12.3042i	0.250689	+	0.434205i
$804$	5.65890	+	1.63810i	0.199574	+	0.0577714i
$805$	2.21100	−	10.2526i	0.0779275	−	0.361358i
$806$	−13.5294	+	4.36242i	−0.476553	+	0.153660i
$807$	0.101351	−	0.0973811i	0.00356772	−	0.00342798i
$808$	−7.98213	+	4.60849i	−0.280810	+	0.162126i
$809$	16.6054	−	9.58712i	0.583814	−	0.337065i	−0.178834	−	0.983879i	$-0.557232\pi$
$809$	16.6054	−	9.58712i	0.583814	−	0.337065i	0.762648	+	0.646814i	$0.223899\pi$
$810$	−29.7461	−	20.5032i	−1.04517	−	0.720407i
$811$			4.98832i			0.175163i	0.996157	+	0.0875817i	$0.0279139\pi$
$811$			4.98832i			0.175163i	−0.996157	+	0.0875817i	$0.972086\pi$
$812$	−15.6274	−	14.1550i	−0.548415	−	0.496742i
$813$	33.4769	−	8.25720i	1.17409	−	0.289593i
$814$	11.4801			0.402378
$815$	32.2069	−	55.7841i	1.12816	−	1.95403i
$816$	−13.5088	−	3.91045i	−0.472903	−	0.136893i
$817$	12.5591	−	7.25098i	0.439386	−	0.253680i
$818$	7.83174			0.273830
$819$	−1.70377	−	28.5674i	−0.0595345	−	0.998226i
$820$	2.82437			0.0986313
$821$	−24.2403	+	13.9951i	−0.845991	+	0.488433i	−0.859296	−	0.511478i	$-0.829098\pi$
$821$	−24.2403	+	13.9951i	−0.845991	+	0.488433i	0.0133052	+	0.999911i	$0.495765\pi$
$822$	−23.5002	−	6.80269i	−0.819663	−	0.237271i
$823$	22.5407	−	39.0417i	0.785721	−	1.36091i	−0.142847	−	0.989745i	$-0.545626\pi$
$823$	22.5407	−	39.0417i	0.785721	−	1.36091i	0.928568	−	0.371163i	$-0.121041\pi$
$824$	4.05811			0.141371
$825$	−42.3961	+	10.4571i	−1.47604	+	0.364071i
$826$	17.2107	+	15.5891i	0.598836	+	0.542412i
$827$			12.6279i			0.439117i	0.975599	+	0.219558i	$0.0704616\pi$
$827$			12.6279i			0.439117i	−0.975599	+	0.219558i	$0.929538\pi$
$828$	1.58261	−	2.50453i	0.0549994	−	0.0870384i
$829$	−32.2216	+	18.6032i	−1.11910	+	0.646114i	−0.941172	−	0.337929i	$-0.890274\pi$
$829$	−32.2216	+	18.6032i	−1.11910	+	0.646114i	−0.177931	+	0.984043i	$0.556940\pi$
$830$	12.8594	−	7.42436i	0.446355	−	0.257703i
$831$	10.9373	−	10.5089i	0.379410	−	0.364549i
$832$	−0.757550	+	3.52507i	−0.0262633	+	0.122210i
$833$	51.7851	+	23.4245i	1.79425	+	0.811611i
$834$	23.2547	+	6.73163i	0.805244	+	0.233097i
$835$	15.1967	+	26.3214i	0.525902	+	0.910889i
$836$	−6.30118	+	10.9140i	−0.217931	+	0.377467i
$837$	15.3276	−	13.5927i	0.529799	−	0.469831i
$838$	26.2543	+	15.1579i	0.906941	+	0.523622i
$839$	−17.0336	+	29.5030i	−0.588064	+	1.01856i	0.406421	+	0.913686i	$0.366777\pi$
$839$	−17.0336	+	29.5030i	−0.588064	+	1.01856i	−0.994486	+	0.104872i	$0.966557\pi$
$840$	−9.66240	−	15.6533i	−0.333385	−	0.540090i
$841$	17.2557	−	29.8878i	0.595025	−	1.03061i
$842$	−31.2318	+	18.0317i	−1.07632	+	0.621413i
$843$	−8.54044	+	29.5033i	−0.294148	+	1.01615i
$844$	13.2595			0.456411
$845$	−47.5771	−	21.4391i	−1.63670	−	0.737527i
$846$	−7.00003	−	0.279769i	−0.240666	−	0.00961866i
$847$	4.74257	+	14.7445i	0.162957	+	0.506627i
$848$	7.26768	−	4.19600i	0.249573	−	0.144091i
$849$	28.9561	−	7.14212i	0.993770	−	0.245117i
$850$		−	90.2378i		−	3.09513i
$851$	−4.32818	−	2.49888i	−0.148368	−	0.0856604i
$852$	0.0131709	−	0.00324864i	0.000451227	−	0.000111297i
$853$		−	35.7194i		−	1.22301i	−0.791241	−	0.611504i	$-0.790565\pi$
$853$		−	35.7194i		−	1.22301i	0.791241	−	0.611504i	$-0.209435\pi$
$854$	−4.00636	+	4.42311i	−0.137095	+	0.151356i
$855$	−31.1105	−	59.2285i	−1.06396	−	2.02557i
$856$	−5.75621	−	9.97005i	−0.196743	−	0.340769i
$857$	35.3021			1.20590			0.602948	−	0.797781i	$-0.293993\pi$
$857$	35.3021			1.20590			0.602948	+	0.797781i	$0.293993\pi$
$858$	−7.44980	−	12.0495i	−0.254332	−	0.411364i
$859$			9.74087i			0.332354i	0.986096	+	0.166177i	$0.0531423\pi$
$859$			9.74087i			0.332354i	−0.986096	+	0.166177i	$0.946858\pi$
$860$	5.23930	+	9.07474i	0.178659	+	0.309446i
$861$	−2.83854	−	1.52929i	−0.0967373	−	0.0521180i
$862$	−12.3726	+	21.4300i	−0.421413	+	0.729910i
$863$		−	1.89765i		−	0.0645967i	−0.999478	−	0.0322983i	$-0.989717\pi$
$863$		−	1.89765i		−	0.0645967i	0.999478	−	0.0322983i	$-0.0102827\pi$
$864$	−1.04189	−	5.09062i	−0.0354459	−	0.173187i
$865$	−9.60042	+	16.6284i	−0.326424	+	0.565383i
$866$	−10.6991			−0.363569
$867$	20.2941	+	82.2776i	0.689223	+	2.79429i
$868$	9.93016	−	3.19404i	0.337051	−	0.108413i
$869$	12.2560	−	7.07599i	0.415755	−	0.240036i
$870$	39.9551	−	38.3901i	1.35460	−	1.30155i
$871$	−11.6718	+	3.76346i	−0.395484	+	0.127520i
$872$			2.34167i			0.0792991i
$873$	−7.86863	−	14.9804i	−0.266313	−	0.507008i
$874$	4.75128	−	2.74315i	0.160714	−	0.0927885i
$875$	43.5897	−	48.1240i	1.47360	−	1.62689i
$876$	−7.51600	−	7.82239i	−0.253942	−	0.264294i
$877$	0.202737	−	0.351151i	0.00684595	−	0.0118575i	−0.862582	−	0.505917i	$-0.831154\pi$
$877$	0.202737	−	0.351151i	0.00684595	−	0.0118575i	0.869428	+	0.494060i	$0.164488\pi$
$878$	9.45090	−	16.3694i	0.318953	−	0.552442i
$879$	−32.0958	+	30.8387i	−1.08257	+	1.04016i
$880$	−7.88605	−	4.55301i	−0.265839	−	0.153482i
$881$	−7.37246	−	12.7695i	−0.248384	−	0.430214i	0.714693	−	0.699438i	$-0.246566\pi$
$881$	−7.37246	−	12.7695i	−0.248384	−	0.430214i	−0.963078	+	0.269224i	$0.913233\pi$
$882$	1.23523	+	20.9636i	0.0415923	+	0.705882i
$883$	0.0828538			0.00278825			0.00139413	−	0.999999i	$-0.499556\pi$
$883$	0.0828538			0.00278825			0.00139413	+	0.999999i	$0.499556\pi$
$884$	27.8628	−	8.98407i	0.937126	−	0.302167i
$885$	−44.0030	+	42.2795i	−1.47915	+	1.42121i
$886$	9.57304	+	16.5810i	0.321613	+	0.557049i
$887$	5.54881	+	9.61083i	0.186311	+	0.322700i	0.944017	−	0.329895i	$-0.107013\pi$
$887$	5.54881	+	9.61083i	0.186311	+	0.322700i	−0.757707	+	0.652595i	$0.773680\pi$
$888$	−8.51043	+	2.09913i	−0.285591	+	0.0704421i
$889$	−3.79234	−	0.817826i	−0.127191	−	0.0274290i
$890$	16.4563	+	9.50102i	0.551615	+	0.318475i
$891$	16.8098	+	11.5866i	0.563151	+	0.388165i
$892$		−	8.58389i		−	0.287410i
$893$	−11.2351	−	6.48658i	−0.375968	−	0.217065i
$894$	35.3641	+	10.2370i	1.18275	+	0.342376i
$895$	−50.1764	+	28.9693i	−1.67721	+	0.968338i
$896$	0.557740	−	2.58630i	0.0186328	−	0.0864021i
$897$	0.185869	+	6.16445i	0.00620598	+	0.205825i
$898$	6.57029			0.219253
$899$	15.7102	+	27.2108i	0.523964	+	0.907532i
$900$	29.5169	−	15.5041i	0.983896	−	0.516804i
$901$	−59.0101	−	34.0695i	−1.96591	−	1.13502i
$902$	−1.59608			−0.0531438
$903$	−0.351967	−	11.9572i	−0.0117127	−	0.397909i
$904$	2.28515	−	3.95800i	0.0760030	−	0.131641i
$905$		−	54.0611i		−	1.79705i
$906$	−13.9406	+	3.43850i	−0.463146	+	0.114237i
$907$	6.79002	+	11.7607i	0.225459	+	0.390506i	0.956457	−	0.291873i	$-0.0942786\pi$
$907$	6.79002	+	11.7607i	0.225459	+	0.390506i	−0.730998	+	0.682379i	$0.760945\pi$
$908$	12.2462	+	21.2111i	0.406406	+	0.703916i
$909$	−1.10424	+	27.6289i	−0.0366253	+	0.916391i
$910$	34.9008	+	15.7570i	1.15695	+	0.522338i
$911$			2.39193i			0.0792482i	0.999215	+	0.0396241i	$0.0126160\pi$
$911$			2.39193i			0.0792482i	−0.999215	+	0.0396241i	$0.987384\pi$
$912$	2.67557	−	9.24288i	0.0885971	−	0.306062i
$913$	−7.26698	+	4.19559i	−0.240502	+	0.138854i
$914$	−25.5034	−	14.7244i	−0.843578	−	0.487040i
$915$	−10.8658	−	11.3087i	−0.359211	−	0.373854i
$916$	−12.5851	−	7.26599i	−0.415822	−	0.240075i
$917$	−20.5158	+	22.6500i	−0.677493	+	0.747968i
$918$	−31.5660	+	27.9930i	−1.04183	+	0.923907i
$919$	5.36950	−	9.30025i	0.177124	−	0.306787i	−0.763771	−	0.645488i	$-0.776654\pi$
$919$	5.36950	−	9.30025i	0.177124	−	0.306787i	0.940894	+	0.338701i	$0.109987\pi$
$920$	1.98211	+	3.43311i	0.0653481	+	0.113186i
$921$	2.49733	−	8.62714i	0.0822899	−	0.284274i
$922$		−	13.1013i		−	0.431467i
$923$	−0.0189427	+	0.0209432i	−0.000623506	+	0.000689355i
$924$	5.46033	+	8.84585i	0.179632	+	0.291007i
$925$	−28.1218	−	48.7084i	−0.924639	−	1.60152i
$926$	−11.2417	+	6.49041i	−0.369426	+	0.213288i
$927$	6.50336	−	10.2918i	0.213598	−	0.338027i
$928$	7.96941			0.261609
$929$	14.6024	−	25.2921i	0.479089	−	0.829806i	−0.520623	−	0.853786i	$-0.674300\pi$
$929$	14.6024	−	25.2921i	0.479089	−	0.829806i	0.999712	+	0.0239800i	$0.00763380\pi$
$930$	6.56457	+	26.6145i	0.215261	+	0.872725i
$931$	−16.0273	+	35.4319i	−0.525274	+	1.16123i
$932$	13.3707	+	7.71957i	0.437971	+	0.252863i
$933$	0.514897	+	0.149049i	0.0168570	+	0.00487966i
$934$	0.355699	−	0.205363i	0.0116388	−	0.00671968i
$935$			73.9366i			2.41798i
$936$	7.72592	+	7.57035i	0.252529	+	0.247445i
$937$			5.17099i			0.168929i	0.996426	+	0.0844644i	$0.0269179\pi$
$937$			5.17099i			0.168929i	−0.996426	+	0.0844644i	$0.973082\pi$
$938$	8.56674	−	2.75550i	0.279714	−	0.0899701i
$939$	−3.71695	+	12.8404i	−0.121298	+	0.419029i
$940$	4.68697	−	8.11807i	0.152872	−	0.264782i
$941$	−31.2867			−1.01992			−0.509958	−	0.860199i	$-0.670339\pi$
$941$	−31.2867			−1.01992			−0.509958	+	0.860199i	$0.670339\pi$
$942$	1.31391	+	5.32695i	0.0428096	+	0.173561i
$943$	0.601748	+	0.347419i	0.0195956	+	0.0113135i
$944$	−8.77680			−0.285661
$945$	−55.1829	−	0.580457i	−1.79510	−	0.0188823i
$946$	−2.96079	−	5.12824i	−0.0962636	−	0.166733i
$947$	52.1128	−	30.0873i	1.69344	−	0.977707i	0.741731	−	0.670697i	$-0.234005\pi$
$947$	52.1128	−	30.0873i	1.69344	−	0.977707i	0.951706	−	0.307010i	$-0.0993284\pi$
$948$	−7.79174	+	7.48655i	−0.253064	+	0.243152i
$949$	22.0779	+	4.74463i	0.716680	+	0.154017i
$950$	61.7417			2.00316
$951$	0.0931123	−	0.321660i	0.00301937	−	0.0104306i
$952$	−20.4504	+	6.57788i	−0.662801	+	0.213190i
$953$	−7.04934	−	4.06994i	−0.228351	−	0.131838i	0.381460	−	0.924385i	$-0.375421\pi$
$953$	−7.04934	−	4.06994i	−0.228351	−	0.131838i	−0.609811	+	0.792547i	$0.708755\pi$
$954$	1.00540	−	25.1559i	0.0325511	−	0.814452i
$955$	47.4805	+	27.4129i	1.53643	+	0.887059i
$956$	9.10984	+	5.25957i	0.294633	+	0.170107i
$957$	−22.5791	+	21.6947i	−0.729878	+	0.701290i
$958$	8.17611	+	4.72048i	0.264158	+	0.152512i
$959$	−35.5758	+	11.4430i	−1.14880	+	0.369513i
$960$	6.67858	+	1.93328i	0.215550	+	0.0623962i
$961$	15.4557			0.498572
$962$	12.2399	−	13.5326i	0.394630	−	0.436308i
$963$	−34.5097	−	1.37924i	−1.11206	−	0.0444455i
$964$	−20.1410	+	11.6284i	−0.648698	+	0.374526i
$965$	30.7037	+	53.1804i	0.988388	+	1.71194i
$966$	−0.133154	−	4.52357i	−0.00428417	−	0.145543i
$967$	−30.3473			−0.975903			−0.487951	−	0.872871i	$-0.662256\pi$
$967$	−30.3473			−0.975903			−0.487951	+	0.872871i	$0.662256\pi$
$968$	−5.06978	−	2.92704i	−0.162949	−	0.0940787i
$969$	−75.8555	+	18.7100i	−2.43683	+	0.601053i
$970$	22.6416			0.726977
$971$	−8.97759	+	15.5496i	−0.288105	+	0.499012i	−0.973357	−	0.229294i	$-0.926358\pi$
$971$	−8.97759	+	15.5496i	−0.288105	+	0.499012i	0.685253	+	0.728305i	$0.259692\pi$
$972$	−14.5800	−	5.51567i	−0.467655	−	0.176915i
$973$	35.2042	−	11.3234i	1.12859	−	0.363013i
$974$		−	3.00709i		−	0.0963534i
$975$	−32.8752	+	61.1250i	−1.05285	+	1.95757i
$976$		−	2.25562i		−	0.0722008i
$977$	0.709702	−	0.409747i	0.0227054	−	0.0131090i	−0.488604	−	0.872505i	$-0.662494\pi$
$977$	0.709702	−	0.409747i	0.0227054	−	0.0131090i	0.511310	+	0.859397i	$0.329161\pi$
$978$	7.72821	−	26.6974i	0.247121	−	0.853689i
$979$	−9.29962	−	5.36914i	−0.297217	−	0.171598i
$980$	−25.6019	−	11.5808i	−0.817822	−	0.369934i
$981$	5.93872	+	3.75267i	0.189609	+	0.119813i
$982$	2.89721	−	5.01812i	0.0924538	−	0.160135i
$983$	−27.5273			−0.877983			−0.438991	−	0.898491i	$-0.644664\pi$
$983$	−27.5273			−0.877983			−0.438991	+	0.898491i	$0.644664\pi$
$984$	1.18321	−	0.291842i	0.0377193	−	0.00930359i
$985$	−30.5949	+	17.6640i	−0.974834	+	0.562821i
$986$	−32.3539	−	56.0386i	−1.03036	−	1.78463i
$987$	−9.10611	+	5.62099i	−0.289851	+	0.178918i
$988$	6.14700	+	19.0640i	0.195562	+	0.606507i
$989$			2.57790i			0.0819724i
$990$	−24.1847	+	12.7034i	−0.768642	+	0.403739i
$991$	−26.3473	−	45.6349i	−0.836951	−	1.44964i	−0.892432	−	0.451182i	$-0.851003\pi$
$991$	−26.3473	−	45.6349i	−0.836951	−	1.44964i	0.0554809	−	0.998460i	$-0.482331\pi$
$992$	−1.97131	+	3.41441i	−0.0625892	+	0.108408i
$993$	29.8279	−	28.6596i	0.946560	−	0.909485i
$994$	0.0139111	−	0.0153582i	0.000441234	−	0.000487132i
$995$	79.2084	+	45.7310i	2.51108	+	1.44977i
$996$	4.61999	−	4.43903i	0.146390	−	0.140656i
$997$	−36.5103	−	21.0792i	−1.15629	−	0.667586i	−0.205880	−	0.978577i	$-0.566006\pi$
$997$	−36.5103	−	21.0792i	−1.15629	−	0.667586i	−0.950413	+	0.310991i	$0.899339\pi$
$998$	−18.2769	+	10.5522i	−0.578545	+	0.334023i
$999$	−8.31485	+	24.9473i	−0.263070	+	0.789297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bq.c.419.4	✓	64
3.2	odd	2	inner	546.2.bq.c.419.24	yes	64
7.6	odd	2	inner	546.2.bq.c.419.13	yes	64
13.9	even	3	inner	546.2.bq.c.503.25	yes	64
21.20	even	2	inner	546.2.bq.c.419.25	yes	64
39.35	odd	6	inner	546.2.bq.c.503.13	yes	64
91.48	odd	6	inner	546.2.bq.c.503.24	yes	64
273.230	even	6	inner	546.2.bq.c.503.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bq.c.419.4	✓	64	1.1	even	1	trivial
546.2.bq.c.419.13	yes	64	7.6	odd	2	inner
546.2.bq.c.419.24	yes	64	3.2	odd	2	inner
546.2.bq.c.419.25	yes	64	21.20	even	2	inner
546.2.bq.c.503.4	yes	64	273.230	even	6	inner
546.2.bq.c.503.13	yes	64	39.35	odd	6	inner
546.2.bq.c.503.24	yes	64	91.48	odd	6	inner
546.2.bq.c.503.25	yes	64	13.9	even	3	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.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.66375 - 0.481611i) q^{3} +(0.500000 - 0.866025i) q^{4} +4.01418 q^{5} +(1.68165 - 0.414785i) q^{6} +(1.77617 - 1.96093i) q^{7} +1.00000i q^{8} +(2.53610 + 1.60256i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.66375 - 0.481611i) q^{3} +(0.500000 - 0.866025i) q^{4} +4.01418 q^{5} +(1.68165 - 0.414785i) q^{6} +(1.77617 - 1.96093i) q^{7} +1.00000i q^{8} +(2.53610 + 1.60256i) q^{9} +(-3.47639 + 2.00709i) q^{10} +(1.96455 - 1.13423i) q^{11} +(-1.24896 + 1.20004i) q^{12} +(0.757550 - 3.52507i) q^{13} +(-0.557740 + 2.58630i) q^{14} +(-6.67858 - 1.93328i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.05976 + 7.03171i) q^{17} +(-2.99761 - 0.119805i) q^{18} +(-4.81117 - 2.77773i) q^{19} +(2.00709 - 3.47639i) q^{20} +(-3.89949 + 2.40706i) q^{21} +(-1.13423 + 1.96455i) q^{22} +(0.855244 - 0.493775i) q^{23} +(0.481611 - 1.66375i) q^{24} +11.1137 q^{25} +(1.10648 + 3.43158i) q^{26} +(-3.44762 - 3.88766i) q^{27} +(-0.810131 - 2.51867i) q^{28} +(6.90171 - 3.98470i) q^{29} +(6.75046 - 1.66503i) q^{30} +3.94262i q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.81476 + 0.940925i) q^{33} -8.11952i q^{34} +(7.12985 - 7.87153i) q^{35} +(2.65591 - 1.39505i) q^{36} +(-2.53038 - 4.38274i) q^{37} +5.55547 q^{38} +(-2.95808 + 5.49998i) q^{39} +4.01418i q^{40} +(0.351799 + 0.609334i) q^{41} +(2.17353 - 4.03433i) q^{42} +(-1.30520 + 2.26067i) q^{43} -2.26846i q^{44} +(10.1804 + 6.43296i) q^{45} +(-0.493775 + 0.855244i) q^{46} +2.33521 q^{47} +(0.414785 + 1.68165i) q^{48} +(-0.690475 - 6.96586i) q^{49} +(-9.62473 + 5.55684i) q^{50} +(10.1410 - 9.74376i) q^{51} +(-2.67402 - 2.41859i) q^{52} +8.39199i q^{53} +(4.92956 + 1.64301i) q^{54} +(7.88605 - 4.55301i) q^{55} +(1.96093 + 1.77617i) q^{56} +(6.66678 + 6.93856i) q^{57} +(-3.98470 + 6.90171i) q^{58} +(4.38840 - 7.60093i) q^{59} +(-5.01356 + 4.81718i) q^{60} +(1.95343 + 1.12781i) q^{61} +(-1.97131 - 3.41441i) q^{62} +(7.64703 - 2.12670i) q^{63} -1.00000 q^{64} +(3.04095 - 14.1503i) q^{65} +(2.83322 - 2.72225i) q^{66} +(-1.70065 - 2.94561i) q^{67} +(4.05976 + 7.03171i) q^{68} +(-1.66072 + 0.409622i) q^{69} +(-2.23887 + 10.3819i) q^{70} +(-0.00678280 - 0.00391605i) q^{71} +(-1.60256 + 2.53610i) q^{72} +6.26312i q^{73} +(4.38274 + 2.53038i) q^{74} +(-18.4903 - 5.35247i) q^{75} +(-4.81117 + 2.77773i) q^{76} +(1.26521 - 5.86691i) q^{77} +(-0.188212 - 6.24216i) q^{78} +6.23858 q^{79} +(-2.00709 - 3.47639i) q^{80} +(3.86362 + 8.12850i) q^{81} +(-0.609334 - 0.351799i) q^{82} -3.69906 q^{83} +(0.134833 + 4.58059i) q^{84} +(-16.2966 + 28.2266i) q^{85} -2.61039i q^{86} +(-13.4018 + 3.30559i) q^{87} +(1.13423 + 1.96455i) q^{88} +(-2.36686 - 4.09953i) q^{89} +(-12.0329 - 0.480919i) q^{90} +(-5.56687 - 7.74661i) q^{91} -0.987551i q^{92} +(1.89881 - 6.55952i) q^{93} +(-2.02235 + 1.16760i) q^{94} +(-19.3129 - 11.1503i) q^{95} +(-1.20004 - 1.24896i) q^{96} +(-4.88472 - 2.82020i) q^{97} +(4.08090 + 5.68738i) q^{98} +(6.79996 + 0.271773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more