LMFDB - Embedded newform 546.2.bq.c.419.19

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			419.19
Character	$\chi$	$=$	546.419
Dual form			546.2.bq.c.503.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.59461 - 0.676184i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.932541 q^{5} +(-1.71906 + 0.211712i) q^{6} +(2.18650 - 1.48970i) q^{7} -1.00000i q^{8} +(2.08555 + 2.15650i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.59461 - 0.676184i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.932541 q^{5} +(-1.71906 + 0.211712i) q^{6} +(2.18650 - 1.48970i) q^{7} -1.00000i q^{8} +(2.08555 + 2.15650i) q^{9} +(0.807604 - 0.466271i) q^{10} +(1.61698 - 0.933562i) q^{11} +(-1.38290 + 1.04288i) q^{12} +(-2.88780 + 2.15885i) q^{13} +(1.14871 - 2.38337i) q^{14} +(-1.48704 - 0.630569i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.86243 - 4.95787i) q^{17} +(2.88439 + 0.824806i) q^{18} +(-0.549800 - 0.317427i) q^{19} +(0.466271 - 0.807604i) q^{20} +(-4.49392 + 0.897017i) q^{21} +(0.933562 - 1.61698i) q^{22} +(5.59098 - 3.22795i) q^{23} +(-0.676184 + 1.59461i) q^{24} -4.13037 q^{25} +(-1.42148 + 3.31352i) q^{26} +(-1.86745 - 4.84898i) q^{27} +(-0.196871 - 2.63842i) q^{28} +(-2.40068 + 1.38603i) q^{29} +(-1.60310 + 0.197430i) q^{30} -0.765404i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.20971 + 0.395292i) q^{33} -5.72486i q^{34} +(2.03900 - 1.38921i) q^{35} +(2.91036 - 0.727891i) q^{36} +(-1.91563 - 3.31796i) q^{37} -0.634855 q^{38} +(6.06468 - 1.48984i) q^{39} -0.932541i q^{40} +(-3.61493 - 6.26124i) q^{41} +(-3.44334 + 3.02380i) q^{42} +(-0.927961 + 1.60728i) q^{43} -1.86712i q^{44} +(1.94486 + 2.01102i) q^{45} +(3.22795 - 5.59098i) q^{46} +10.1886 q^{47} +(0.211712 + 1.71906i) q^{48} +(2.56157 - 6.51447i) q^{49} +(-3.57700 + 2.06518i) q^{50} +(-7.91689 + 5.97034i) q^{51} +(0.425719 + 3.58033i) q^{52} +13.2671i q^{53} +(-4.04175 - 3.26562i) q^{54} +(1.50790 - 0.870585i) q^{55} +(-1.48970 - 2.18650i) q^{56} +(0.662077 + 0.877939i) q^{57} +(-1.38603 + 2.40068i) q^{58} +(-1.01910 + 1.76514i) q^{59} +(-1.28961 + 0.972528i) q^{60} +(1.86152 + 1.07475i) q^{61} +(-0.382702 - 0.662860i) q^{62} +(7.77260 + 1.60833i) q^{63} -1.00000 q^{64} +(-2.69299 + 2.01321i) q^{65} +(-2.58204 + 1.94719i) q^{66} +(7.09567 + 12.2901i) q^{67} +(-2.86243 - 4.95787i) q^{68} +(-11.0981 + 1.36679i) q^{69} +(1.07122 - 2.22259i) q^{70} +(-4.64705 - 2.68298i) q^{71} +(2.15650 - 2.08555i) q^{72} +13.6584i q^{73} +(-3.31796 - 1.91563i) q^{74} +(6.58632 + 2.79289i) q^{75} +(-0.549800 + 0.317427i) q^{76} +(2.14479 - 4.45005i) q^{77} +(4.50725 - 4.32258i) q^{78} -10.4934 q^{79} +(-0.466271 - 0.807604i) q^{80} +(-0.300958 + 8.99497i) q^{81} +(-6.26124 - 3.61493i) q^{82} +8.56844 q^{83} +(-1.47012 + 4.34036i) q^{84} +(2.66933 - 4.62342i) q^{85} +1.85592i q^{86} +(4.76535 - 0.586878i) q^{87} +(-0.933562 - 1.61698i) q^{88} +(1.22221 + 2.11693i) q^{89} +(2.68981 + 0.769165i) q^{90} +(-3.09812 + 9.02228i) q^{91} -6.45591i q^{92} +(-0.517554 + 1.22052i) q^{93} +(8.82358 - 5.09430i) q^{94} +(-0.512711 - 0.296014i) q^{95} +(1.04288 + 1.38290i) q^{96} +(-4.38570 - 2.53208i) q^{97} +(-1.03886 - 6.92248i) q^{98} +(5.38551 + 1.54002i) 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
$3$	−1.59461	−	0.676184i	−0.920647	−	0.390395i
$3$	−1.59461	−	0.676184i	−0.920647	−	0.390395i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.932541			0.417045			0.208523	−	0.978018i	$-0.433135\pi$
$5$	0.932541			0.417045			0.208523	+	0.978018i	$0.433135\pi$
$6$	−1.71906	+	0.211712i	−0.701805	+	0.0864309i
$7$	2.18650	−	1.48970i	0.826419	−	0.563055i
$7$	2.18650	−	1.48970i	0.826419	−	0.563055i
$8$		−	1.00000i		−	0.353553i
$9$	2.08555	+	2.15650i	0.695183	+	0.718832i
$10$	0.807604	−	0.466271i	0.255387	−	0.147448i
$11$	1.61698	−	0.933562i	0.487537	−	0.281480i	−0.236015	−	0.971749i	$-0.575841\pi$
$11$	1.61698	−	0.933562i	0.487537	−	0.281480i	0.723552	+	0.690270i	$0.242508\pi$
$12$	−1.38290	+	1.04288i	−0.399208	+	0.301053i
$13$	−2.88780	+	2.15885i	−0.800931	+	0.598757i
$13$	−2.88780	+	2.15885i	−0.800931	+	0.598757i
$14$	1.14871	−	2.38337i	0.307006	−	0.636983i
$15$	−1.48704	−	0.630569i	−0.383951	−	0.162812i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.86243	−	4.95787i	0.694241	−	1.20246i	−0.276195	−	0.961102i	$-0.589074\pi$
$17$	2.86243	−	4.95787i	0.694241	−	1.20246i	0.970436	−	0.241359i	$-0.0775932\pi$
$18$	2.88439	+	0.824806i	0.679857	+	0.194409i
$19$	−0.549800	−	0.317427i	−0.126133	−	0.0728228i	0.435606	−	0.900137i	$-0.356534\pi$
$19$	−0.549800	−	0.317427i	−0.126133	−	0.0728228i	−0.561739	+	0.827315i	$0.689867\pi$
$20$	0.466271	−	0.807604i	0.104261	−	0.180586i
$21$	−4.49392	+	0.897017i	−0.980655	+	0.195745i
$22$	0.933562	−	1.61698i	0.199036	−	0.344741i
$23$	5.59098	−	3.22795i	1.16580	−	0.673075i	0.213113	−	0.977028i	$-0.431640\pi$
$23$	5.59098	−	3.22795i	1.16580	−	0.673075i	0.952687	+	0.303953i	$0.0983065\pi$
$24$	−0.676184	+	1.59461i	−0.138025	+	0.325498i
$25$	−4.13037			−0.826073
$26$	−1.42148	+	3.31352i	−0.278775	+	0.649834i
$27$	−1.86745	−	4.84898i	−0.359390	−	0.933187i
$28$	−0.196871	−	2.63842i	−0.0372052	−	0.498614i
$29$	−2.40068	+	1.38603i	−0.445794	+	0.257379i	−0.706052	−	0.708160i	$-0.749526\pi$
$29$	−2.40068	+	1.38603i	−0.445794	+	0.257379i	0.260258	+	0.965539i	$0.416192\pi$
$30$	−1.60310	+	0.197430i	−0.292684	+	0.0360456i
$31$		−	0.765404i		−	0.137471i	−0.997635	−	0.0687353i	$-0.978104\pi$
$31$		−	0.765404i		−	0.137471i	0.997635	−	0.0687353i	$-0.0218964\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−3.20971	+	0.395292i	−0.558738	+	0.0688115i
$34$		−	5.72486i		−	0.981805i
$35$	2.03900	−	1.38921i	0.344654	−	0.234819i
$36$	2.91036	−	0.727891i	0.485059	−	0.121315i
$37$	−1.91563	−	3.31796i	−0.314927	−	0.545470i	0.664495	−	0.747293i	$-0.268647\pi$
$37$	−1.91563	−	3.31796i	−0.314927	−	0.545470i	−0.979422	+	0.201823i	$0.935313\pi$
$38$	−0.634855			−0.102987
$39$	6.06468	−	1.48984i	0.971127	−	0.238565i
$40$		−	0.932541i		−	0.147448i
$41$	−3.61493	−	6.26124i	−0.564557	−	0.977842i	−0.997091	−	0.0762239i	$-0.975714\pi$
$41$	−3.61493	−	6.26124i	−0.564557	−	0.977842i	0.432534	−	0.901618i	$-0.357620\pi$
$42$	−3.44334	+	3.02380i	−0.531320	+	0.466583i
$43$	−0.927961	+	1.60728i	−0.141513	+	0.245107i	−0.928066	−	0.372415i	$-0.878530\pi$
$43$	−0.927961	+	1.60728i	−0.141513	+	0.245107i	0.786554	+	0.617522i	$0.211863\pi$
$44$		−	1.86712i		−	0.281480i
$45$	1.94486	+	2.01102i	0.289923	+	0.299785i
$46$	3.22795	−	5.59098i	0.475936	−	0.824345i
$47$	10.1886			1.48616			0.743080	−	0.669203i	$-0.233364\pi$
$47$	10.1886			1.48616			0.743080	+	0.669203i	$0.233364\pi$
$48$	0.211712	+	1.71906i	0.0305579	+	0.248125i
$49$	2.56157	−	6.51447i	0.365938	−	0.930639i
$50$	−3.57700	+	2.06518i	−0.505865	+	0.292061i
$51$	−7.91689	+	5.97034i	−1.10859	+	0.836014i
$52$	0.425719	+	3.58033i	0.0590366	+	0.496502i
$53$			13.2671i			1.82237i	0.411997	+	0.911185i	$0.364831\pi$
$53$			13.2671i			1.82237i	−0.411997	+	0.911185i	$0.635169\pi$
$54$	−4.04175	−	3.26562i	−0.550012	−	0.444394i
$55$	1.50790	−	0.870585i	0.203325	−	0.117390i
$56$	−1.48970	−	2.18650i	−0.199070	−	0.292183i
$57$	0.662077	+	0.877939i	0.0876942	+	0.116286i
$58$	−1.38603	+	2.40068i	−0.181995	+	0.315224i
$59$	−1.01910	+	1.76514i	−0.132676	+	0.229802i	−0.924707	−	0.380679i	$-0.875690\pi$
$59$	−1.01910	+	1.76514i	−0.132676	+	0.229802i	0.792031	+	0.610481i	$0.209024\pi$
$60$	−1.28961	+	0.972528i	−0.166488	+	0.125553i
$61$	1.86152	+	1.07475i	0.238343	+	0.137607i	0.614415	−	0.788983i	$-0.289392\pi$
$61$	1.86152	+	1.07475i	0.238343	+	0.137607i	−0.376072	+	0.926590i	$0.622725\pi$
$62$	−0.382702	−	0.662860i	−0.0486032	−	0.0841833i
$63$	7.77260	+	1.60833i	0.979255	+	0.202630i
$64$	−1.00000			−0.125000
$65$	−2.69299	+	2.01321i	−0.334024	+	0.249709i
$66$	−2.58204	+	1.94719i	−0.317827	+	0.239682i
$67$	7.09567	+	12.2901i	0.866874	+	1.50147i	0.865174	+	0.501472i	$0.167208\pi$
$67$	7.09567	+	12.2901i	0.866874	+	1.50147i	0.00170015	+	0.999999i	$0.499459\pi$
$68$	−2.86243	−	4.95787i	−0.347121	−	0.601230i
$69$	−11.0981	+	1.36679i	−1.33606	+	0.164542i
$70$	1.07122	−	2.22259i	0.128035	−	0.265651i
$71$	−4.64705	−	2.68298i	−0.551503	−	0.318411i	0.198225	−	0.980157i	$-0.436482\pi$
$71$	−4.64705	−	2.68298i	−0.551503	−	0.318411i	−0.749728	+	0.661746i	$0.769816\pi$
$72$	2.15650	−	2.08555i	0.254146	−	0.245784i
$73$			13.6584i			1.59860i	0.600932	+	0.799300i	$0.294796\pi$
$73$			13.6584i			1.59860i	−0.600932	+	0.799300i	$0.705204\pi$
$74$	−3.31796	−	1.91563i	−0.385706	−	0.222687i
$75$	6.58632	+	2.79289i	0.760522	+	0.322495i
$76$	−0.549800	+	0.317427i	−0.0630664	+	0.0364114i
$77$	2.14479	−	4.45005i	0.244421	−	0.507130i
$78$	4.50725	−	4.32258i	0.510346	−	0.489435i
$79$	−10.4934			−1.18060			−0.590301	−	0.807183i	$-0.700991\pi$
$79$	−10.4934			−1.18060			−0.590301	+	0.807183i	$0.700991\pi$
$80$	−0.466271	−	0.807604i	−0.0521306	−	0.0902929i
$81$	−0.300958	+	8.99497i	−0.0334398	+	0.999441i
$82$	−6.26124	−	3.61493i	−0.691439	−	0.399202i
$83$	8.56844			0.940509			0.470254	−	0.882531i	$-0.344162\pi$
$83$	8.56844			0.940509			0.470254	+	0.882531i	$0.344162\pi$
$84$	−1.47012	+	4.34036i	−0.160404	+	0.473572i
$85$	2.66933	−	4.62342i	0.289530	−	0.501480i
$86$			1.85592i			0.200129i
$87$	4.76535	−	0.586878i	0.510899	−	0.0629199i
$88$	−0.933562	−	1.61698i	−0.0995181	−	0.172370i
$89$	1.22221	+	2.11693i	0.129554	+	0.224394i	0.923504	−	0.383589i	$-0.125312\pi$
$89$	1.22221	+	2.11693i	0.129554	+	0.224394i	−0.793950	+	0.607983i	$0.791979\pi$
$90$	2.68981	+	0.769165i	0.283531	+	0.0810771i
$91$	−3.09812	+	9.02228i	−0.324772	+	0.945792i
$92$		−	6.45591i		−	0.673075i
$93$	−0.517554	+	1.22052i	−0.0536679	+	0.126562i
$94$	8.82358	−	5.09430i	0.910083	−	0.525437i
$95$	−0.512711	−	0.296014i	−0.0526031	−	0.0303704i
$96$	1.04288	+	1.38290i	0.106438	+	0.141141i
$97$	−4.38570	−	2.53208i	−0.445300	−	0.257094i	0.260543	−	0.965462i	$-0.416098\pi$
$97$	−4.38570	−	2.53208i	−0.445300	−	0.257094i	−0.705843	+	0.708368i	$0.749432\pi$
$98$	−1.03886	−	6.92248i	−0.104940	−	0.699276i
$99$	5.38551	+	1.54002i	0.541264	+	0.154777i
$100$	−2.06518	+	3.57700i	−0.206518	+	0.357700i
$101$	5.14102	+	8.90451i	0.511551	+	0.886032i	0.999910	+	0.0133896i	$0.00426218\pi$
$101$	5.14102	+	8.90451i	0.511551	+	0.886032i	−0.488359	+	0.872643i	$0.662404\pi$
$102$	−3.87106	+	9.12891i	−0.383292	+	0.903896i
$103$			6.04457i			0.595589i	0.954630	+	0.297795i	$0.0962510\pi$
$103$			6.04457i			0.595589i	−0.954630	+	0.297795i	$0.903749\pi$
$104$	2.15885	+	2.88780i	0.211693	+	0.283172i
$105$	−4.19077	+	0.836506i	−0.408977	+	0.0816346i
$106$	6.63353	+	11.4896i	0.644305	+	1.11597i
$107$	1.85547	−	1.07125i	0.179375	−	0.103562i	−0.407624	−	0.913150i	$-0.633643\pi$
$107$	1.85547	−	1.07125i	0.179375	−	0.103562i	0.586999	+	0.809588i	$0.300309\pi$
$108$	−5.13307	−	0.807235i	−0.493930	−	0.0776762i
$109$	13.2607			1.27014			0.635071	−	0.772454i	$-0.280971\pi$
$109$	13.2607			1.27014			0.635071	+	0.772454i	$0.280971\pi$
$110$	0.870585	−	1.50790i	0.0830070	−	0.143772i
$111$	0.811121	+	6.58617i	0.0769882	+	0.625132i
$112$	−2.38337	−	1.14871i	−0.225207	−	0.108543i
$113$	−7.01777	−	4.05171i	−0.660176	−	0.381153i	0.132168	−	0.991227i	$-0.457806\pi$
$113$	−7.01777	−	4.05171i	−0.660176	−	0.381153i	−0.792344	+	0.610075i	$0.791139\pi$
$114$	1.01234	+	0.429279i	0.0948148	+	0.0402056i
$115$	5.21382	−	3.01020i	0.486191	−	0.280703i
$116$			2.77206i			0.257379i
$117$	−10.6782	−	1.72514i	−0.987200	−	0.159489i
$118$			2.03821i			0.187632i
$119$	−1.12706	−	15.1046i	−0.103317	−	1.38463i
$120$	−0.630569	+	1.48704i	−0.0575628	+	0.135747i
$121$	−3.75692	+	6.50718i	−0.341538	+	0.591562i
$122$	2.14949			0.194606
$123$	1.53065	+	12.4286i	0.138014	+	1.12065i
$124$	−0.662860	−	0.382702i	−0.0595266	−	0.0343677i
$125$	−8.51444			−0.761555
$126$	7.53543	−	2.49345i	0.671310	−	0.222134i
$127$	10.7274	+	18.5804i	0.951901	+	1.64874i	0.741305	+	0.671169i	$0.234207\pi$
$127$	10.7274	+	18.5804i	0.951901	+	1.64874i	0.210597	+	0.977573i	$0.432459\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.56655	−	1.93550i	0.225972	−	0.170411i
$130$	−1.32559	+	3.08999i	−0.116262	+	0.271010i
$131$	6.62905			0.579183			0.289592	−	0.957150i	$-0.406481\pi$
$131$	6.62905			0.579183			0.289592	+	0.957150i	$0.406481\pi$
$132$	−1.26252	+	2.97733i	−0.109888	+	0.259144i
$133$	−1.67501	+	0.124985i	−0.145242	+	0.0108375i
$134$	12.2901	+	7.09567i	1.06170	+	0.612973i
$135$	−1.74147	−	4.52188i	−0.149882	−	0.389181i
$136$	−4.95787	−	2.86243i	−0.425134	−	0.245451i
$137$	−7.21381	−	4.16489i	−0.616317	−	0.355831i	0.159117	−	0.987260i	$-0.449135\pi$
$137$	−7.21381	−	4.16489i	−0.616317	−	0.355831i	−0.775434	+	0.631429i	$0.782469\pi$
$138$	−8.92785	+	6.73273i	−0.759989	+	0.573128i
$139$	−1.81718	−	1.04915i	−0.154131	−	0.0889877i	0.420951	−	0.907083i	$-0.361697\pi$
$139$	−1.81718	−	1.04915i	−0.154131	−	0.0889877i	−0.575082	+	0.818096i	$0.695030\pi$
$140$	−0.183590	−	2.46043i	−0.0155162	−	0.207944i
$141$	−16.2468	−	6.88937i	−1.36823	−	0.580189i
$142$	−5.36595			−0.450301
$143$	−2.65408	+	6.18675i	−0.221946	+	0.517362i
$144$	0.824806	−	2.88439i	0.0687338	−	0.240366i
$145$	−2.23873	+	1.29253i	−0.185916	+	0.107339i
$146$	6.82922	+	11.8286i	0.565190	+	0.978939i
$147$	−8.48968	+	8.65595i	−0.700217	+	0.713930i
$148$	−3.83126			−0.314927
$149$	−8.00992	−	4.62453i	−0.656199	−	0.378856i	0.134628	−	0.990896i	$-0.457016\pi$
$149$	−8.00992	−	4.62453i	−0.656199	−	0.378856i	−0.790827	+	0.612040i	$0.790349\pi$
$150$	7.10036	−	0.874447i	0.579742	−	0.0713983i
$151$	16.3936			1.33409			0.667045	−	0.745017i	$-0.267559\pi$
$151$	16.3936			1.33409			0.667045	+	0.745017i	$0.267559\pi$
$152$	−0.317427	+	0.549800i	−0.0257468	+	0.0445947i
$153$	16.6614	−	4.16707i	1.34699	−	0.336888i
$154$	−0.367583	−	4.92625i	−0.0296207	−	0.396969i
$155$		−	0.713771i		−	0.0573315i
$156$	1.74211	−	5.99709i	0.139480	−	0.480151i
$157$		−	18.6459i		−	1.48811i	−0.668120	−	0.744053i	$-0.732901\pi$
$157$		−	18.6459i		−	1.48811i	0.668120	−	0.744053i	$-0.267099\pi$
$158$	−9.08758	+	5.24671i	−0.722969	+	0.417406i
$159$	8.97097	−	21.1558i	0.711444	−	1.67776i
$160$	−0.807604	−	0.466271i	−0.0638467	−	0.0368619i
$161$	7.41598	−	15.3868i	0.584461	−	1.21265i
$162$	4.23685	+	7.94035i	0.332878	+	0.623853i
$163$	−1.68466	+	2.91792i	−0.131953	+	0.228549i	−0.924429	−	0.381353i	$-0.875458\pi$
$163$	−1.68466	+	2.91792i	−0.131953	+	0.228549i	0.792476	+	0.609903i	$0.208791\pi$
$164$	−7.22986			−0.564557
$165$	−2.99318	+	0.368626i	−0.233019	+	0.0286975i
$166$	7.42049	−	4.28422i	0.575942	−	0.332520i
$167$	−8.79974	−	15.2416i	−0.680944	−	1.17943i	−0.974693	−	0.223547i	$-0.928236\pi$
$167$	−8.79974	−	15.2416i	−0.680944	−	1.17943i	0.293749	−	0.955883i	$-0.405097\pi$
$168$	0.897017	+	4.49392i	0.0692064	+	0.346714i
$169$	3.67875	−	12.4686i	0.282981	−	0.959126i
$170$		−	5.33867i		−	0.409457i
$171$	−0.462105	−	1.84765i	−0.0353381	−	0.141294i
$172$	0.927961	+	1.60728i	0.0707564	+	0.122554i
$173$	−6.17619	+	10.6975i	−0.469567	+	0.813314i	−0.999395	−	0.0347917i	$-0.988923\pi$
$173$	−6.17619	+	10.6975i	−0.469567	+	0.813314i	0.529828	+	0.848105i	$0.322257\pi$
$174$	3.83348	−	2.89093i	0.290615	−	0.219161i
$175$	−9.03105	+	6.15302i	−0.682683	+	0.465125i
$176$	−1.61698	−	0.933562i	−0.121884	−	0.0703699i
$177$	2.81863	−	2.12560i	0.211861	−	0.159770i
$178$	2.11693	+	1.22221i	0.158670	+	0.0916083i
$179$	−2.31419	+	1.33610i	−0.172971	+	0.0998647i	−0.583986	−	0.811764i	$-0.698508\pi$
$179$	−2.31419	+	1.33610i	−0.172971	+	0.0998647i	0.411015	+	0.911629i	$0.365174\pi$
$180$	2.71403	−	0.678788i	0.202292	−	0.0505939i
$181$			22.5269i			1.67441i	0.546891	+	0.837204i	$0.315811\pi$
$181$			22.5269i			1.67441i	−0.546891	+	0.837204i	$0.684189\pi$
$182$	1.82809	+	9.36259i	0.135507	+	0.694001i
$183$	−2.24166	−	2.97253i	−0.165708	−	0.219736i
$184$	−3.22795	−	5.59098i	−0.237968	−	0.412173i
$185$	−1.78640	−	3.09414i	−0.131339	−	0.227486i
$186$	0.162045	+	1.31578i	0.0118817	+	0.0964776i
$187$		−	10.6890i		−	0.781659i
$188$	5.09430	−	8.82358i	0.371540	−	0.643526i
$189$	−11.3067	−	7.82036i	−0.822443	−	0.568847i
$190$	−0.592028			−0.0429502
$191$	5.65445	+	3.26460i	0.409142	+	0.236218i	0.690421	−	0.723408i	$-0.257425\pi$
$191$	5.65445	+	3.26460i	0.409142	+	0.236218i	−0.281279	+	0.959626i	$0.590759\pi$
$192$	1.59461	+	0.676184i	0.115081	+	0.0487994i
$193$	4.77135	+	8.26422i	0.343449	+	0.594872i	0.985071	−	0.172150i	$-0.0550713\pi$
$193$	4.77135	+	8.26422i	0.343449	+	0.594872i	−0.641621	+	0.767021i	$0.721738\pi$
$194$	−5.06417			−0.363586
$195$	5.65557	−	1.38933i	0.405004	−	0.0994922i
$196$	−4.36092	−	5.47562i	−0.311494	−	0.391116i
$197$	−6.56673	+	3.79130i	−0.467860	+	0.270119i	−0.715344	−	0.698773i	$-0.753730\pi$
$197$	−6.56673	+	3.79130i	−0.467860	+	0.270119i	0.247483	+	0.968892i	$0.420396\pi$
$198$	5.43400	−	1.35906i	0.386177	−	0.0965844i
$199$	−17.0996	−	9.87247i	−1.21216	−	0.699841i	−0.248931	−	0.968521i	$-0.580079\pi$
$199$	−17.0996	−	9.87247i	−1.21216	−	0.699841i	−0.963229	+	0.268680i	$0.913413\pi$
$200$			4.13037i			0.292061i
$201$	−3.00447	−	24.3958i	−0.211919	−	1.72075i
$202$	8.90451	+	5.14102i	0.626519	+	0.361721i
$203$	−3.18430	+	6.60685i	−0.223494	+	0.463710i
$204$	1.21202	+	9.84139i	0.0848583	+	0.689035i
$205$	−3.37107	−	5.83887i	−0.235446	−	0.407804i
$206$	3.02228	+	5.23475i	0.210573	+	0.364722i
$207$	18.6213	+	5.32487i	1.29427	+	0.370104i
$208$	3.31352	+	1.42148i	0.229751	+	0.0985620i
$209$	−1.18535			−0.0819926
$210$	−3.21106	+	2.81982i	−0.221584	+	0.194586i
$211$	−12.0796	−	20.9224i	−0.831592	−	1.44036i	−0.896776	−	0.442486i	$-0.854097\pi$
$211$	−12.0796	−	20.9224i	−0.831592	−	1.44036i	0.0651838	−	0.997873i	$-0.479237\pi$
$212$	11.4896	+	6.63353i	0.789110	+	0.455593i
$213$	5.59604	+	7.42056i	0.383434	+	0.508448i
$214$	1.07125	−	1.85547i	0.0732295	−	0.126837i
$215$	−0.865362	+	1.49885i	−0.0590172	+	0.102221i
$216$	−4.84898	+	1.86745i	−0.329932	+	0.127064i
$217$	−1.14023	−	1.67356i	−0.0774036	−	0.113608i
$218$	11.4841	−	6.63033i	0.777800	−	0.449063i
$219$	9.23562	−	21.7799i	0.624085	−	1.47175i
$220$		−	1.74117i		−	0.117390i
$221$	2.43718	+	20.4969i	0.163942	+	1.37877i
$222$	3.99554	+	5.29823i	0.268163	+	0.355594i
$223$	−11.4883	+	6.63275i	−0.769311	+	0.444162i	−0.832629	−	0.553832i	$-0.813165\pi$
$223$	−11.4883	+	6.63275i	−0.769311	+	0.444162i	0.0633178	+	0.997993i	$0.479832\pi$
$224$	−2.63842	+	0.196871i	−0.176287	+	0.0131540i
$225$	−8.61409	−	8.90712i	−0.574273	−	0.593808i
$226$	−8.10342			−0.539031
$227$	−1.13046	+	1.95801i	−0.0750310	+	0.129958i	−0.901100	−	0.433612i	$-0.857239\pi$
$227$	−1.13046	+	1.95801i	−0.0750310	+	0.129958i	0.826069	+	0.563569i	$0.190572\pi$
$228$	1.09136	−	0.134406i	0.0722768	−	0.00890126i
$229$			16.6285i			1.09885i	0.835545	+	0.549423i	$0.185152\pi$
$229$			16.6285i			1.09885i	−0.835545	+	0.549423i	$0.814848\pi$
$230$	3.01020	−	5.21382i	0.198487	−	0.343789i
$231$	−6.42915	+	5.64582i	−0.423007	+	0.371467i
$232$	1.38603	+	2.40068i	0.0909974	+	0.157612i
$233$		−	10.1593i		−	0.665559i	−0.943005	−	0.332780i	$-0.892013\pi$
$233$		−	10.1593i		−	0.665559i	0.943005	−	0.332780i	$-0.107987\pi$
$234$	−10.1102	+	3.84508i	−0.660922	+	0.251361i
$235$	9.50128			0.619795
$236$	1.01910	+	1.76514i	0.0663380	+	0.114901i
$237$	16.7329	+	7.09549i	1.08692	+	0.460901i
$238$	−8.52834	−	12.5174i	−0.552810	−	0.811383i
$239$			0.687807i			0.0444905i	0.999753	+	0.0222453i	$0.00708147\pi$
$239$			0.687807i			0.0444905i	−0.999753	+	0.0222453i	$0.992919\pi$
$240$	0.197430	+	1.60310i	0.0127440	+	0.103479i
$241$	−7.55703	−	4.36305i	−0.486791	−	0.281049i	0.236451	−	0.971643i	$-0.424016\pi$
$241$	−7.55703	−	4.36305i	−0.486791	−	0.281049i	−0.723242	+	0.690594i	$0.757349\pi$
$242$			7.51385i			0.483008i
$243$	6.56216	−	14.1399i	0.420963	−	0.907078i
$244$	1.86152	−	1.07475i	0.119171	−	0.0688036i
$245$	2.38876	−	6.07502i	0.152613	−	0.388118i
$246$	7.53987	+	9.99815i	0.480725	+	0.637459i
$247$	2.27299	−	0.270270i	0.144627	−	0.0171968i
$248$	−0.765404			−0.0486032
$249$	−13.6633	−	5.79384i	−0.865877	−	0.367170i
$250$	−7.37372	+	4.25722i	−0.466355	+	0.269250i
$251$	9.22814	−	15.9836i	0.582475	−	1.00888i	−0.412710	−	0.910862i	$-0.635418\pi$
$251$	9.22814	−	15.9836i	0.582475	−	1.00888i	0.995185	−	0.0980136i	$-0.0312489\pi$
$252$	5.27915	−	5.92710i	0.332555	−	0.373372i
$253$	6.02699	−	10.4391i	0.378914	−	0.656298i
$254$	18.5804	+	10.7274i	1.16584	+	0.673096i
$255$	−7.38282	+	5.56758i	−0.462330	+	0.348656i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.3551	+	19.6677i	0.708313	+	1.22683i	0.965482	+	0.260468i	$0.0838769\pi$
$257$	11.3551	+	19.6677i	0.708313	+	1.22683i	−0.257169	+	0.966366i	$0.582790\pi$
$258$	1.25494	−	2.95947i	0.0781294	−	0.184248i
$259$	−9.13130	−	4.40101i	−0.567392	−	0.273466i
$260$	0.397000	+	3.33880i	0.0246209	+	0.207064i
$261$	−7.99570	−	2.28641i	−0.494922	−	0.141525i
$262$	5.74093	−	3.31453i	0.354676	−	0.204772i
$263$	18.0623	−	10.4283i	1.11377	−	0.643034i	0.173965	−	0.984752i	$-0.444342\pi$
$263$	18.0623	−	10.4283i	1.11377	−	0.643034i	0.939803	+	0.341717i	$0.111009\pi$
$264$	0.395292	+	3.20971i	0.0243285	+	0.197544i
$265$			12.3721i			0.760011i
$266$	−1.38811	+	0.945746i	−0.0851105	+	0.0579874i
$267$	−0.517511	−	4.20210i	−0.0316712	−	0.257165i
$268$	14.1913			0.866874
$269$	−1.35690	+	2.35022i	−0.0827317	+	0.143296i	−0.904422	−	0.426638i	$-0.859698\pi$
$269$	−1.35690	+	2.35022i	−0.0827317	+	0.143296i	0.821691	+	0.569934i	$0.193031\pi$
$270$	−3.76910	−	3.04532i	−0.229380	−	0.185333i
$271$	−9.52168	+	5.49735i	−0.578401	+	0.333940i	−0.760498	−	0.649341i	$-0.775045\pi$
$271$	−9.52168	+	5.49735i	−0.578401	+	0.333940i	0.182097	+	0.983281i	$0.441712\pi$
$272$	−5.72486			−0.347121
$273$	11.0410	−	12.2921i	0.668233	−	0.743952i
$274$	−8.32979			−0.503221
$275$	−6.67871	+	3.85596i	−0.402741	+	0.232523i
$276$	−4.36538	+	10.2946i	−0.262765	+	0.619665i
$277$	−3.87875	+	6.71819i	−0.233052	+	0.403657i	−0.958705	−	0.284404i	$-0.908204\pi$
$277$	−3.87875	+	6.71819i	−0.233052	+	0.403657i	0.725653	+	0.688061i	$0.241538\pi$
$278$	−2.09830			−0.125848
$279$	1.65059	−	1.59629i	0.0988184	−	0.0955674i
$280$	−1.38921	−	2.03900i	−0.0830212	−	0.121854i
$281$			16.7481i			0.999106i	0.866283	+	0.499553i	$0.166502\pi$
$281$			16.7481i			0.999106i	−0.866283	+	0.499553i	$0.833498\pi$
$282$	−17.5148	+	2.15704i	−1.04299	+	0.128450i
$283$	−3.91036	+	2.25764i	−0.232446	+	0.134203i	−0.611700	−	0.791090i	$-0.709514\pi$
$283$	−3.91036	+	2.25764i	−0.232446	+	0.134203i	0.379254	+	0.925293i	$0.376181\pi$
$284$	−4.64705	+	2.68298i	−0.275752	+	0.159205i
$285$	0.617414	+	0.818714i	0.0365724	+	0.0484964i
$286$	0.794870	+	6.68492i	0.0470017	+	0.395288i
$287$	−17.2314	−	8.30503i	−1.01714	−	0.490231i
$288$	−0.727891	−	2.91036i	−0.0428914	−	0.171494i
$289$	−7.88700	−	13.6607i	−0.463941	−	0.803570i
$290$	−1.29253	+	2.23873i	−0.0759000	+	0.131463i
$291$	5.28131	+	7.00322i	0.309596	+	0.410536i
$292$	11.8286	+	6.82922i	0.692214	+	0.399650i
$293$	−8.52328	+	14.7627i	−0.497935	+	0.862449i	−0.999997	−	0.00238269i	$-0.999242\pi$
$293$	−8.52328	+	14.7627i	−0.497935	+	0.862449i	0.502062	+	0.864832i	$0.332575\pi$
$294$	−3.02430	+	11.7411i	−0.176381	+	0.684755i
$295$	−0.950356	+	1.64606i	−0.0553319	+	0.0958376i
$296$	−3.31796	+	1.91563i	−0.192853	+	0.111344i
$297$	−7.54645	−	6.09732i	−0.437889	−	0.353802i
$298$	−9.24906			−0.535784
$299$	−9.17696	+	21.3918i	−0.530717	+	1.23712i
$300$	5.71187	−	4.30747i	0.329775	−	0.248692i
$301$	0.365378	+	4.89670i	0.0210600	+	0.282241i
$302$	14.1973	−	8.19679i	0.816960	−	0.471672i
$303$	−2.17683	−	17.6755i	−0.125056	−	1.01543i
$304$			0.634855i			0.0364114i
$305$	1.73594	+	1.00225i	0.0993997	+	0.0573884i
$306$	12.3456	−	11.9395i	0.705753	−	0.682535i
$307$			28.0243i			1.59943i	0.600378	+	0.799716i	$0.295017\pi$
$307$			28.0243i			1.59943i	−0.600378	+	0.799716i	$0.704983\pi$
$308$	−2.78146	−	4.08247i	−0.158489	−	0.232620i
$309$	4.08724	−	9.63872i	0.232515	−	0.548328i
$310$	−0.356885	−	0.618144i	−0.0202697	−	0.0351082i
$311$	−22.0267			−1.24902			−0.624509	−	0.781018i	$-0.714701\pi$
$311$	−22.0267			−1.24902			−0.624509	+	0.781018i	$0.714701\pi$
$312$	−1.48984	−	6.06468i	−0.0843453	−	0.343345i
$313$			7.10373i			0.401526i	0.979640	+	0.200763i	$0.0643422\pi$
$313$			7.10373i			0.401526i	−0.979640	+	0.200763i	$0.935658\pi$
$314$	−9.32296	−	16.1478i	−0.526125	−	0.911275i
$315$	7.24827	+	1.49983i	0.408394	+	0.0845060i
$316$	−5.24671	+	9.08758i	−0.295151	+	0.511216i
$317$		−	25.4231i		−	1.42790i	−0.700196	−	0.713951i	$-0.746904\pi$
$317$		−	25.4231i		−	1.42790i	0.700196	−	0.713951i	$-0.253096\pi$
$318$	−2.80879	−	22.8069i	−0.157509	−	1.27895i
$319$	−2.58789	+	4.48236i	−0.144894	+	0.250964i
$320$	−0.932541			−0.0521306
$321$	−3.68311	+	0.453594i	−0.205571	+	0.0253172i
$322$	−1.27098	−	17.0334i	−0.0708291	−	0.949233i
$323$	−3.14753	+	1.81723i	−0.175133	+	0.101113i
$324$	7.63939	+	4.75812i	0.424411	+	0.264340i
$325$	11.9277	−	8.91684i	0.661628	−	0.494617i
$326$			3.36933i			0.186610i
$327$	−21.1456	−	8.96665i	−1.16935	−	0.495857i
$328$	−6.26124	+	3.61493i	−0.345719	+	0.199601i
$329$	22.2774	−	15.1780i	1.22819	−	0.836790i
$330$	−2.40786	+	1.81583i	−0.132548	+	0.0999582i
$331$	8.58446	−	14.8687i	0.471845	−	0.817259i	−0.527637	−	0.849470i	$-0.676922\pi$
$331$	8.58446	−	14.8687i	0.471845	−	0.817259i	0.999481	+	0.0322116i	$0.0102550\pi$
$332$	4.28422	−	7.42049i	0.235127	−	0.407252i
$333$	3.16004	−	11.0508i	0.173169	−	0.605582i
$334$	−15.2416	−	8.79974i	−0.833983	−	0.481500i
$335$	6.61700	+	11.4610i	0.361526	+	0.626181i
$336$	3.02380	+	3.44334i	0.164962	+	0.187850i
$337$	19.6997			1.07311			0.536556	−	0.843865i	$-0.319725\pi$
$337$	19.6997			1.07311			0.536556	+	0.843865i	$0.319725\pi$
$338$	−3.04843	−	12.6375i	−0.165813	−	0.687391i
$339$	8.45089	+	11.2062i	0.458989	+	0.608637i
$340$	−2.66933	−	4.62342i	−0.144765	−	0.250740i
$341$	−0.714553	−	1.23764i	−0.0386952	−	0.0670220i
$342$	−1.32402	−	1.36906i	−0.0715949	−	0.0740304i
$343$	−4.10377	−	18.0599i	−0.221583	−	0.975142i
$344$	1.60728	+	0.927961i	0.0866585	+	0.0500323i
$345$	−10.3494	+	1.27459i	−0.557195	+	0.0686215i
$346$			12.3524i			0.664068i
$347$	−0.489763	−	0.282765i	−0.0262919	−	0.0151796i	0.486796	−	0.873515i	$-0.338165\pi$
$347$	−0.489763	−	0.282765i	−0.0262919	−	0.0151796i	−0.513088	+	0.858336i	$0.671499\pi$
$348$	1.87442	−	4.42035i	0.100480	−	0.236956i
$349$	11.6379	−	6.71913i	0.622961	−	0.359667i	−0.155060	−	0.987905i	$-0.549557\pi$
$349$	11.6379	−	6.71913i	0.622961	−	0.359667i	0.778021	+	0.628239i	$0.216224\pi$
$350$	−4.74461	+	9.84420i	−0.253610	+	0.526195i
$351$	15.8610	+	9.97135i	0.846599	+	0.532231i
$352$	−1.86712			−0.0995181
$353$	3.93978	+	6.82391i	0.209694	+	0.363200i	0.951618	−	0.307284i	$-0.0994200\pi$
$353$	3.93978	+	6.82391i	0.209694	+	0.363200i	−0.741924	+	0.670484i	$0.766087\pi$
$354$	1.37820	−	3.25014i	0.0732507	−	0.172743i
$355$	−4.33357	−	2.50199i	−0.230002	−	0.132792i
$356$	2.44442			0.129554
$357$	−8.41624	+	24.8480i	−0.445435	+	1.31509i
$358$	−1.33610	+	2.31419i	−0.0706150	+	0.122309i
$359$		−	6.51246i		−	0.343715i	−0.985122	−	0.171857i	$-0.945023\pi$
$359$		−	6.51246i		−	0.343715i	0.985122	−	0.171857i	$-0.0549768\pi$
$360$	2.01102	−	1.94486i	0.105990	−	0.102503i
$361$	−9.29848	−	16.1054i	−0.489394	−	0.847655i
$362$	11.2634	+	19.5088i	0.591993	+	1.02536i
$363$	10.3909	−	7.83603i	0.545379	−	0.411285i
$364$	6.26447	+	7.19420i	0.328347	+	0.377078i
$365$			12.7371i			0.666688i
$366$	−3.42760	−	1.45345i	−0.179164	−	0.0759732i
$367$	26.3204	−	15.1961i	1.37391	−	0.793229i	0.382494	−	0.923958i	$-0.375065\pi$
$367$	26.3204	−	15.1961i	1.37391	−	0.793229i	0.991418	+	0.130729i	$0.0417319\pi$
$368$	−5.59098	−	3.22795i	−0.291450	−	0.168269i
$369$	5.96323	−	20.8537i	0.310433	−	1.08560i
$370$	−3.09414	−	1.78640i	−0.160857	−	0.0928706i
$371$	19.7640	+	29.0084i	1.02610	+	1.50604i
$372$	0.798224	+	1.05848i	0.0413860	+	0.0548794i
$373$	7.76325	−	13.4463i	0.401966	−	0.696225i	−0.591997	−	0.805940i	$-0.701660\pi$
$373$	7.76325	−	13.4463i	0.401966	−	0.696225i	0.993963	+	0.109715i	$0.0349937\pi$
$374$	−5.34451	−	9.25697i	−0.276358	−	0.478666i
$375$	13.5772	+	5.75733i	0.701124	+	0.297307i
$376$		−	10.1886i		−	0.525437i
$377$	3.94044	−	9.18527i	0.202943	−	0.473066i
$378$	−13.7021	−	1.11927i	−0.704759	−	0.0575690i
$379$	1.15229	+	1.99583i	0.0591894	+	0.102519i	0.894102	−	0.447864i	$-0.147815\pi$
$379$	1.15229	+	1.99583i	0.0591894	+	0.102519i	−0.834912	+	0.550383i	$0.814482\pi$
$380$	−0.512711	+	0.296014i	−0.0263015	+	0.0151852i
$381$	−4.54222	−	36.8821i	−0.232705	−	1.88953i
$382$	6.52920			0.334063
$383$	−2.16495	+	3.74980i	−0.110624	+	0.191606i	−0.916022	−	0.401128i	$-0.868618\pi$
$383$	−2.16495	+	3.74980i	−0.110624	+	0.191606i	0.805398	+	0.592734i	$0.201952\pi$
$384$	1.71906	−	0.211712i	0.0877256	−	0.0108039i
$385$	2.00010	−	4.14986i	0.101935	−	0.211496i
$386$	8.26422	+	4.77135i	0.420638	+	0.242855i
$387$	−5.40139	+	1.35091i	−0.274568	+	0.0686706i
$388$	−4.38570	+	2.53208i	−0.222650	+	0.128547i
$389$		−	9.78199i		−	0.495966i	−0.968764	−	0.247983i	$-0.920232\pi$
$389$		−	9.78199i		−	0.495966i	0.968764	−	0.247983i	$-0.0797678\pi$
$390$	4.20320	−	4.03098i	0.212837	−	0.204117i
$391$		−	36.9592i		−	1.86911i
$392$	−6.51447	−	2.56157i	−0.329031	−	0.129379i
$393$	−10.5707	−	4.48246i	−0.533223	−	0.226110i
$394$	−3.79130	+	6.56673i	−0.191003	+	0.330827i
$395$	−9.78555			−0.492365
$396$	4.02645	−	3.89398i	0.202337	−	0.195680i
$397$	30.5806	+	17.6557i	1.53480	+	0.886116i	0.999131	+	0.0416878i	$0.0132735\pi$
$397$	30.5806	+	17.6557i	1.53480	+	0.886116i	0.535668	+	0.844429i	$0.320060\pi$
$398$	−19.7449			−0.989725
$399$	2.75550	+	0.933314i	0.137948	+	0.0467242i
$400$	2.06518	+	3.57700i	0.103259	+	0.178850i
$401$	−11.3151	+	6.53278i	−0.565050	+	0.326231i	−0.755170	−	0.655529i	$-0.772446\pi$
$401$	−11.3151	+	6.53278i	−0.565050	+	0.326231i	0.190120	+	0.981761i	$0.439112\pi$
$402$	−14.7999	−	19.6252i	−0.738150	−	0.978814i
$403$	1.65239	+	2.21033i	0.0823115	+	0.110105i
$404$	10.2820			0.511551
$405$	−0.280656	+	8.38818i	−0.0139459	+	0.416812i
$406$	0.545739	+	7.31385i	0.0270846	+	0.362980i
$407$	−6.19505	−	3.57672i	−0.307077	−	0.177291i
$408$	5.97034	+	7.91689i	0.295576	+	0.391944i
$409$	−22.7760	−	13.1497i	−1.12620	−	0.650211i	−0.183223	−	0.983071i	$-0.558653\pi$
$409$	−22.7760	−	13.1497i	−1.12620	−	0.650211i	−0.942976	+	0.332860i	$0.891986\pi$
$410$	−5.83887	−	3.37107i	−0.288361	−	0.166485i
$411$	8.68696	+	11.5192i	0.428496	+	0.568202i
$412$	5.23475	+	3.02228i	0.257898	+	0.148897i
$413$	0.401264	+	5.37764i	0.0197449	+	0.264616i
$414$	18.7890	−	4.69920i	0.923429	−	0.230953i
$415$	7.99042			0.392234
$416$	3.58033	−	0.425719i	0.175540	−	0.0208726i
$417$	2.18827	+	2.90173i	0.107160	+	0.142098i
$418$	−1.02655	+	0.592677i	−0.0502100	+	0.0289888i
$419$	−16.4000	−	28.4056i	−0.801193	−	1.38771i	−0.918832	−	0.394650i	$-0.870866\pi$
$419$	−16.4000	−	28.4056i	−0.801193	−	1.38771i	0.117639	−	0.993056i	$-0.462468\pi$
$420$	−1.37095	+	4.04757i	−0.0668955	+	0.197501i
$421$	−38.0625			−1.85505			−0.927526	−	0.373758i	$-0.878069\pi$
$421$	−38.0625			−1.85505			−0.927526	+	0.373758i	$0.878069\pi$
$422$	−20.9224	−	12.0796i	−1.01849	−	0.588024i
$423$	21.2488	+	21.9717i	1.03315	+	1.06830i
$424$	13.2671			0.644305
$425$	−11.8229	+	20.4778i	−0.573494	+	0.993321i
$426$	8.55659	+	3.62837i	0.414568	+	0.175795i
$427$	5.67126	−	0.423173i	0.274452	−	0.0204788i
$428$		−	2.14251i		−	0.103562i
$429$	8.41560	−	8.07079i	0.406309	−	0.389661i
$430$			1.73072i			0.0834629i
$431$	21.5266	−	12.4284i	1.03690	−	0.598653i	0.117945	−	0.993020i	$-0.462369\pi$
$431$	21.5266	−	12.4284i	1.03690	−	0.598653i	0.918953	+	0.394367i	$0.129036\pi$
$432$	−3.26562	+	4.04175i	−0.157117	+	0.194459i
$433$	−0.763740	−	0.440946i	−0.0367030	−	0.0211905i	0.481536	−	0.876426i	$-0.340079\pi$
$433$	−0.763740	−	0.440946i	−0.0367030	−	0.0211905i	−0.518239	+	0.855236i	$0.673412\pi$
$434$	−1.82424	−	0.879230i	−0.0875665	−	0.0422044i
$435$	4.44388	−	0.547288i	0.213068	−	0.0262404i
$436$	6.63033	−	11.4841i	0.317535	−	0.549987i
$437$	−4.09856			−0.196061
$438$	−2.89165	−	23.4797i	−0.138168	−	1.12190i
$439$	15.8314	−	9.14027i	0.755592	−	0.436241i	−0.0721188	−	0.997396i	$-0.522976\pi$
$439$	15.8314	−	9.14027i	0.755592	−	0.436241i	0.827711	+	0.561155i	$0.189643\pi$
$440$	−0.870585	−	1.50790i	−0.0415035	−	0.0718862i
$441$	19.3907	−	8.06226i	0.923368	−	0.383917i
$442$	12.3591	+	16.5322i	0.587862	+	0.786358i
$443$			23.3877i			1.11119i	0.831455	+	0.555593i	$0.187509\pi$
$443$			23.3877i			1.11119i	−0.831455	+	0.555593i	$0.812491\pi$
$444$	6.10935	+	2.59063i	0.289937	+	0.122946i
$445$	1.13976	+	1.97412i	0.0540297	+	0.0935823i
$446$	−6.63275	+	11.4883i	−0.314070	+	0.543985i
$447$	9.64566	+	12.7905i	0.456224	+	0.604970i
$448$	−2.18650	+	1.48970i	−0.103302	+	0.0703819i
$449$	1.52934	+	0.882966i	0.0721741	+	0.0416697i	0.535653	−	0.844438i	$-0.320066\pi$
$449$	1.52934	+	0.882966i	0.0721741	+	0.0416697i	−0.463479	+	0.886108i	$0.653399\pi$
$450$	−11.9136	−	3.40675i	−0.561612	−	0.160596i
$451$	−11.6905	−	6.74952i	−0.550485	−	0.317823i
$452$	−7.01777	+	4.05171i	−0.330088	+	0.190576i
$453$	−26.1413	−	11.0851i	−1.22823	−	0.520822i
$454$			2.26091i			0.106110i
$455$	−2.88913	+	8.41365i	−0.135444	+	0.394438i
$456$	0.877939	−	0.662077i	0.0411132	−	0.0310046i
$457$	10.4432	+	18.0881i	0.488511	+	0.846126i	0.999913	−	0.0132159i	$-0.00420686\pi$
$457$	10.4432	+	18.0881i	0.488511	+	0.846126i	−0.511402	+	0.859342i	$0.670874\pi$
$458$	8.31427	+	14.4007i	0.388500	+	0.672902i
$459$	−29.3861	−	4.62131i	−1.37162	−	0.215704i
$460$		−	6.02040i		−	0.280703i
$461$	−13.0497	+	22.6027i	−0.607784	+	1.05271i	0.383821	+	0.923408i	$0.374608\pi$
$461$	−13.0497	+	22.6027i	−0.607784	+	1.05271i	−0.991605	+	0.129306i	$0.958725\pi$
$462$	−2.74490	+	8.10400i	−0.127704	+	0.377032i
$463$	−11.7557			−0.546334			−0.273167	−	0.961967i	$-0.588071\pi$
$463$	−11.7557			−0.546334			−0.273167	+	0.961967i	$0.588071\pi$
$464$	2.40068	+	1.38603i	0.111449	+	0.0643449i
$465$	−0.482640	+	1.13819i	−0.0223819	+	0.0527821i
$466$	−5.07966	−	8.79823i	−0.235311	−	0.407570i
$467$	−17.1353			−0.792926			−0.396463	−	0.918051i	$-0.629763\pi$
$467$	−17.1353			−0.792926			−0.396463	+	0.918051i	$0.629763\pi$
$468$	−6.83311	+	8.38502i	−0.315861	+	0.387598i
$469$	33.8232	+	16.3018i	1.56181	+	0.752746i
$470$	8.22835	−	4.75064i	0.379546	−	0.219131i
$471$	−12.6081	+	29.7329i	−0.580949	+	1.37002i
$472$	1.76514	+	1.01910i	0.0812471	+	0.0469080i
$473$			3.46524i			0.159332i
$474$	18.0389	−	2.22158i	0.828553	−	0.102041i
$475$	2.27088	+	1.31109i	0.104195	+	0.0601570i
$476$	−13.6445	−	6.57622i	−0.625393	−	0.301420i
$477$	−28.6104	+	27.6691i	−1.30998	+	1.26688i
$478$	0.343904	+	0.595658i	0.0157298	+	0.0272448i
$479$	17.7964	+	30.8242i	0.813137	+	1.40840i	0.910658	+	0.413162i	$0.135576\pi$
$479$	17.7964	+	30.8242i	0.813137	+	1.40840i	−0.0975203	+	0.995234i	$0.531091\pi$
$480$	0.972528	+	1.28961i	0.0443896	+	0.0588623i
$481$	12.6949	+	5.44606i	0.578839	+	0.248319i
$482$	−8.72611			−0.397463
$483$	−22.2299	+	19.5214i	−1.01150	+	0.888254i
$484$	3.75692	+	6.50718i	0.170769	+	0.295781i
$485$	−4.08984	−	2.36127i	−0.185710	−	0.107220i
$486$	−1.38697	−	15.5266i	−0.0629144	−	0.704302i
$487$	−18.0962	+	31.3436i	−0.820018	+	1.42031i	0.0856496	+	0.996325i	$0.472703\pi$
$487$	−18.0962	+	31.3436i	−0.820018	+	1.42031i	−0.905668	+	0.423988i	$0.860630\pi$
$488$	1.07475	−	1.86152i	0.0486515	−	0.0842669i
$489$	4.65943	−	3.51380i	0.210707	−	0.158900i
$490$	−0.968776	−	6.45550i	−0.0437649	−	0.291630i
$491$	−19.8191	+	11.4426i	−0.894423	+	0.516395i	−0.875387	−	0.483423i	$-0.839393\pi$
$491$	−19.8191	+	11.4426i	−0.894423	+	0.516395i	−0.0190364	+	0.999819i	$0.506060\pi$
$492$	11.5288	+	4.88872i	0.519758	+	0.220400i
$493$			15.8697i			0.714734i
$494$	1.83333	−	1.37056i	0.0824855	−	0.0616642i
$495$	5.02221	+	1.43613i	0.225732	+	0.0645491i
$496$	−0.662860	+	0.382702i	−0.0297633	+	0.0171838i
$497$	−14.1576	+	1.05640i	−0.635056	+	0.0473861i
$498$	−14.7297	+	1.81404i	−0.660053	+	0.0812890i
$499$	−29.9963			−1.34282			−0.671408	−	0.741088i	$-0.734310\pi$
$499$	−29.9963			−1.34282			−0.671408	+	0.741088i	$0.734310\pi$
$500$	−4.25722	+	7.37372i	−0.190389	+	0.329763i
$501$	3.72601	+	30.2546i	0.166466	+	1.35168i
$502$		−	18.4563i		−	0.823744i
$503$	16.8113	−	29.1180i	0.749577	−	1.29831i	−0.198448	−	0.980111i	$-0.563590\pi$
$503$	16.8113	−	29.1180i	0.749577	−	1.29831i	0.948025	−	0.318195i	$-0.103077\pi$
$504$	1.60833	−	7.77260i	0.0716406	−	0.346219i
$505$	4.79422	+	8.30382i	0.213340	+	0.369515i
$506$		−	12.0540i		−	0.535865i
$507$	−14.2972	+	17.3951i	−0.634963	+	0.772542i
$508$	21.4548			0.951901
$509$	−6.61627	−	11.4597i	−0.293261	−	0.507943i	0.681318	−	0.731988i	$-0.261407\pi$
$509$	−6.61627	−	11.4597i	−0.293261	−	0.507943i	−0.974579	+	0.224045i	$0.928074\pi$
$510$	−3.60992	+	8.51308i	−0.159850	+	0.376965i
$511$	20.3470	+	29.8642i	0.900100	+	1.32111i
$512$			1.00000i			0.0441942i
$513$	−0.512477	+	3.25875i	−0.0226264	+	0.143877i
$514$	19.6677	+	11.3551i	0.867503	+	0.500853i
$515$			5.63681i			0.248387i
$516$	−0.392920	−	3.19045i	−0.0172973	−	0.140452i
$517$	16.4747	−	9.51169i	0.724558	−	0.418324i
$518$	−10.1084	+	0.754264i	−0.444140	+	0.0331405i
$519$	17.0821	−	12.8820i	0.749819	−	0.565459i
$520$	2.01321	+	2.69299i	0.0882853	+	0.118095i
$521$	14.3778			0.629903			0.314952	−	0.949108i	$-0.398012\pi$
$521$	14.3778			0.629903			0.314952	+	0.949108i	$0.398012\pi$
$522$	−8.06769	+	2.01776i	−0.353113	+	0.0883149i
$523$	−3.40228	+	1.96431i	−0.148772	+	0.0858933i	−0.572538	−	0.819878i	$-0.694041\pi$
$523$	−3.40228	+	1.96431i	−0.148772	+	0.0858933i	0.423766	+	0.905772i	$0.360708\pi$
$524$	3.31453	−	5.74093i	0.144796	−	0.250794i
$525$	18.5616	−	3.70501i	0.810093	−	0.161700i
$526$	10.4283	−	18.0623i	0.454694	−	0.787553i
$527$	−3.79478	−	2.19092i	−0.165303	−	0.0954378i
$528$	1.94719	+	2.58204i	0.0847404	+	0.112369i
$529$	9.33938	−	16.1763i	0.406060	−	0.703316i
$530$	6.18604	+	10.7145i	0.268704	+	0.465410i
$531$	−5.93191	+	1.48359i	−0.257423	+	0.0643825i
$532$	−0.729266	+	1.51309i	−0.0316177	+	0.0656010i
$533$	23.9563	+	10.2771i	1.03766	+	0.445151i
$534$	−2.54923	−	3.38037i	−0.110316	−	0.146283i
$535$	1.73030	−	0.998989i	0.0748074	−	0.0431901i
$536$	12.2901	−	7.09567i	0.530850	−	0.306486i
$537$	4.59368	−	0.565735i	0.198232	−	0.0244133i
$538$			2.71380i			0.117000i
$539$	−1.93967	−	12.9251i	−0.0835477	−	0.556725i
$540$	−4.78680	−	0.752780i	−0.205991	−	0.0323945i
$541$	20.1365			0.865737			0.432868	−	0.901457i	$-0.357501\pi$
$541$	20.1365			0.865737			0.432868	+	0.901457i	$0.357501\pi$
$542$	−5.49735	+	9.52168i	−0.236131	+	0.408991i
$543$	15.2323	−	35.9215i	0.653680	−	1.54154i
$544$	−4.95787	+	2.86243i	−0.212567	+	0.122726i
$545$	12.3661			0.529706
$546$	3.41575	−	16.1658i	0.146181	−	0.691832i
$547$	−20.4953			−0.876316			−0.438158	−	0.898898i	$-0.644369\pi$
$547$	−20.4953			−0.876316			−0.438158	+	0.898898i	$0.644369\pi$
$548$	−7.21381	+	4.16489i	−0.308159	+	0.177915i
$549$	1.56460	+	6.25579i	0.0667754	+	0.266991i
$550$	−3.85596	+	6.67871i	−0.164418	+	0.284781i
$551$	1.75986			0.0749724
$552$	1.36679	+	11.0981i	0.0581745	+	0.472367i
$553$	−22.9439	+	15.6321i	−0.975673	+	0.664744i
$554$			7.75750i			0.329585i
$555$	0.756404	+	6.14187i	0.0321076	+	0.260708i
$556$	−1.81718	+	1.04915i	−0.0770656	+	0.0444938i
$557$	−33.8696	+	19.5546i	−1.43510	+	0.828556i	−0.997504	−	0.0706143i	$-0.977504\pi$
$557$	−33.8696	+	19.5546i	−1.43510	+	0.828556i	−0.437598	+	0.899171i	$0.644171\pi$
$558$	0.631310	−	2.20772i	0.0267255	−	0.0934604i
$559$	−0.790101	−	6.64481i	−0.0334177	−	0.281046i
$560$	−2.22259	−	1.07122i	−0.0939216	−	0.0452674i
$561$	−7.22775	+	17.0448i	−0.305156	+	0.719632i
$562$	8.37403	+	14.5042i	0.353237	+	0.611825i
$563$	22.3303	−	38.6772i	0.941110	−	1.63005i	0.177752	−	0.984075i	$-0.443118\pi$
$563$	22.3303	−	38.6772i	0.941110	−	1.63005i	0.763358	−	0.645975i	$-0.223549\pi$
$564$	−14.0898	+	10.6255i	−0.593287	+	0.447413i
$565$	−6.54436	−	3.77839i	−0.275323	−	0.158958i
$566$	−2.25764	+	3.91036i	−0.0948959	+	0.164364i
$567$	12.7418	+	20.1158i	0.535105	+	0.844786i
$568$	−2.68298	+	4.64705i	−0.112575	+	0.194986i
$569$	18.2120	−	10.5147i	0.763488	−	0.440800i	−0.0670586	−	0.997749i	$-0.521361\pi$
$569$	18.2120	−	10.5147i	0.763488	−	0.440800i	0.830547	+	0.556949i	$0.188028\pi$
$570$	0.944053	+	0.400320i	0.0395420	+	0.0167676i
$571$	−14.3959			−0.602449			−0.301225	−	0.953553i	$-0.597395\pi$
$571$	−14.3959			−0.602449			−0.301225	+	0.953553i	$0.597395\pi$
$572$	4.03084	+	5.39188i	0.168538	+	0.225446i
$573$	−6.80916	−	9.02920i	−0.284457	−	0.377200i
$574$	−19.0754	+	1.42335i	−0.796191	+	0.0594095i
$575$	−23.0928	+	13.3326i	−0.963036	+	0.556009i
$576$	−2.08555	−	2.15650i	−0.0868979	−	0.0898540i
$577$			28.9192i			1.20392i	0.798525	+	0.601961i	$0.205614\pi$
$577$			28.9192i			1.20392i	−0.798525	+	0.601961i	$0.794386\pi$
$578$	−13.6607	−	7.88700i	−0.568210	−	0.328056i
$579$	−2.02030	−	16.4045i	−0.0839608	−	0.681748i
$580$			2.58506i			0.107339i
$581$	18.7349	−	12.7644i	0.777255	−	0.529558i
$582$	8.07536	+	3.42431i	0.334735	+	0.141942i
$583$	12.3856	+	21.4525i	0.512960	+	0.888473i
$584$	13.6584			0.565190
$585$	−9.95786	−	1.60876i	−0.411707	−	0.0665141i
$586$			17.0466i			0.704187i
$587$	16.7716	+	29.0492i	0.692236	+	1.19899i	0.971104	+	0.238659i	$0.0767077\pi$
$587$	16.7716	+	29.0492i	0.692236	+	1.19899i	−0.278867	+	0.960330i	$0.589959\pi$
$588$	3.25143	+	11.6802i	0.134087	+	0.481685i
$589$	−0.242960	+	0.420820i	−0.0100110	+	0.0173396i
$590$			1.90071i			0.0782511i
$591$	13.0350	−	1.60533i	0.536187	−	0.0660343i
$592$	−1.91563	+	3.31796i	−0.0787318	+	0.136368i
$593$	−3.58323			−0.147146			−0.0735728	−	0.997290i	$-0.523440\pi$
$593$	−3.58323			−0.147146			−0.0735728	+	0.997290i	$0.523440\pi$
$594$	−9.58407	−	1.50721i	−0.393239	−	0.0618415i
$595$	−1.05103	−	14.0856i	−0.0430880	−	0.577454i
$596$	−8.00992	+	4.62453i	−0.328099	+	0.189428i
$597$	20.5916	+	27.3052i	0.842758	+	1.11753i
$598$	2.74840	+	23.1143i	0.112391	+	0.945213i
$599$		−	47.1051i		−	1.92466i	−0.271880	−	0.962331i	$-0.587646\pi$
$599$		−	47.1051i		−	1.92466i	0.271880	−	0.962331i	$-0.412354\pi$
$600$	2.79289	−	6.58632i	0.114019	−	0.268885i
$601$	−3.49020	+	2.01507i	−0.142368	+	0.0821962i	−0.569492	−	0.821997i	$-0.692860\pi$
$601$	−3.49020	+	2.01507i	−0.142368	+	0.0821962i	0.427124	+	0.904193i	$0.359527\pi$
$602$	2.76477	+	4.05797i	0.112684	+	0.165391i
$603$	−11.7051	+	40.9333i	−0.476669	+	1.66693i
$604$	8.19679	−	14.1973i	0.333523	−	0.577678i
$605$	−3.50348	+	6.06821i	−0.142437	+	0.246708i
$606$	−10.7229	−	14.2190i	−0.435589	−	0.577608i
$607$	−24.6986	−	14.2598i	−1.00249	−	0.578786i	−0.0935040	−	0.995619i	$-0.529807\pi$
$607$	−24.6986	−	14.2598i	−1.00249	−	0.578786i	−0.908983	+	0.416833i	$0.863140\pi$
$608$	0.317427	+	0.549800i	0.0128734	+	0.0222973i
$609$	9.54516	−	8.38217i	0.386790	−	0.339663i
$610$	2.00449			0.0811595
$611$	−29.4226	+	21.9956i	−1.19031	+	0.889848i
$612$	4.72190	−	16.5127i	0.190871	−	0.667487i
$613$	−8.12169	−	14.0672i	−0.328032	−	0.568168i	0.654089	−	0.756417i	$-0.273052\pi$
$613$	−8.12169	−	14.0672i	−0.328032	−	0.568168i	−0.982121	+	0.188249i	$0.939719\pi$
$614$	14.0122	+	24.2698i	0.565485	+	0.979448i
$615$	1.42739	+	11.5902i	0.0575579	+	0.467361i
$616$	−4.45005	−	2.14479i	−0.179298	−	0.0864160i
$617$	−31.9716	−	18.4588i	−1.28713	−	0.743125i	−0.308988	−	0.951066i	$-0.599990\pi$
$617$	−31.9716	−	18.4588i	−1.28713	−	0.743125i	−0.978141	+	0.207941i	$0.933324\pi$
$618$	−1.27971	−	10.3910i	−0.0514773	−	0.417987i
$619$		−	3.39461i		−	0.136441i	−0.997670	−	0.0682205i	$-0.978268\pi$
$619$		−	3.39461i		−	0.136441i	0.997670	−	0.0682205i	$-0.0217321\pi$
$620$	−0.618144	−	0.356885i	−0.0248253	−	0.0143329i
$621$	−26.0932	−	21.0825i	−1.04708	−	0.846013i
$622$	−19.0756	+	11.0133i	−0.764864	+	0.441594i
$623$	5.82595	+	2.80793i	0.233412	+	0.112497i
$624$	−4.32258	−	4.50725i	−0.173042	−	0.180435i
$625$	12.7118			0.508471
$626$	3.55186	+	6.15201i	0.141961	+	0.245884i
$627$	1.89017	+	0.801517i	0.0754863	+	0.0320095i
$628$	−16.1478	−	9.32296i	−0.644369	−	0.372027i
$629$	−21.9334			−0.874542
$630$	7.02710	−	2.32524i	0.279966	−	0.0926398i
$631$	10.6226	−	18.3990i	0.422881	−	0.732451i	−0.573339	−	0.819318i	$-0.694352\pi$
$631$	10.6226	−	18.3990i	0.422881	−	0.732451i	0.996220	+	0.0868674i	$0.0276856\pi$
$632$			10.4934i			0.417406i
$633$	5.11477	+	41.5311i	0.203294	+	1.65071i
$634$	−12.7115	−	22.0170i	−0.504840	−	0.874408i
$635$	10.0037	+	17.3270i	0.396986	+	0.687599i
$636$	−13.8359	−	18.3470i	−0.548631	−	0.727505i
$637$	6.66648	+	24.3425i	0.264136	+	0.964486i
$638$			5.17579i			0.204911i
$639$	−3.90583	−	15.6168i	−0.154512	−	0.617792i
$640$	−0.807604	+	0.466271i	−0.0319234	+	0.0184310i
$641$	30.7362	+	17.7455i	1.21401	+	0.700906i	0.963629	−	0.267242i	$-0.0861125\pi$
$641$	30.7362	+	17.7455i	1.21401	+	0.700906i	0.250376	+	0.968149i	$0.419446\pi$
$642$	−2.96287	+	2.23438i	−0.116935	+	0.0881839i
$643$	−22.8799	−	13.2097i	−0.902297	−	0.520941i	−0.0243522	−	0.999703i	$-0.507752\pi$
$643$	−22.8799	−	13.2097i	−0.902297	−	0.520941i	−0.877945	+	0.478762i	$0.841086\pi$
$644$	−9.61739	−	14.1158i	−0.378978	−	0.556242i
$645$	2.39341	−	1.80494i	0.0942405	−	0.0710693i
$646$	−1.81723	+	3.14753i	−0.0714978	+	0.123838i
$647$	8.61293	+	14.9180i	0.338609	+	0.586488i	0.984171	−	0.177219i	$-0.0567102\pi$
$647$	8.61293	+	14.9180i	0.338609	+	0.586488i	−0.645562	+	0.763708i	$0.723377\pi$
$648$	8.99497	+	0.300958i	0.353356	+	0.0118228i
$649$			3.80559i			0.149382i
$650$	5.87124	−	13.6860i	0.230289	−	0.536811i
$651$	0.686581	+	3.43967i	0.0269092	+	0.134811i
$652$	1.68466	+	2.91792i	0.0659765	+	0.114275i
$653$	10.3481	−	5.97447i	0.404952	−	0.233799i	−0.283666	−	0.958923i	$-0.591551\pi$
$653$	10.3481	−	5.97447i	0.404952	−	0.233799i	0.688619	+	0.725124i	$0.258217\pi$
$654$	−22.7959	+	2.80744i	−0.891391	+	0.109779i
$655$	6.18186			0.241545
$656$	−3.61493	+	6.26124i	−0.141139	+	0.244460i
$657$	−29.4544	+	28.4854i	−1.14913	+	1.11132i
$658$	11.7038	−	24.2832i	0.456261	−	0.946658i
$659$	21.4777	+	12.4002i	0.836653	+	0.483042i	0.856125	−	0.516768i	$-0.172865\pi$
$659$	21.4777	+	12.4002i	0.836653	+	0.483042i	−0.0194720	+	0.999810i	$0.506199\pi$
$660$	−1.17735	+	2.77648i	−0.0458283	+	0.108075i
$661$	38.8130	−	22.4087i	1.50965	−	0.871597i	0.509714	−	0.860344i	$-0.329751\pi$
$661$	38.8130	−	22.4087i	1.50965	−	0.871597i	0.999937	−	0.0112531i	$-0.00358205\pi$
$662$		−	17.1689i		−	0.667289i
$663$	9.97332	−	34.3325i	0.387331	−	1.33336i
$664$		−	8.56844i		−	0.332520i
$665$	−1.56202	+	0.116553i	−0.0605724	+	0.00451974i
$666$	−2.78874	−	11.1503i	−0.108061	−	0.432066i
$667$	−8.94809	+	15.4985i	−0.346471	+	0.600106i
$668$	−17.5995			−0.680944
$669$	22.8042	−	2.80846i	0.881663	−	0.108581i
$670$	11.4610	+	6.61700i	0.442777	+	0.255637i
$671$	4.01337			0.154935
$672$	4.34036	+	1.47012i	0.167433	+	0.0567112i
$673$	1.59187	+	2.75719i	0.0613619	+	0.106282i	0.895074	−	0.445917i	$-0.147122\pi$
$673$	1.59187	+	2.75719i	0.0613619	+	0.106282i	−0.833712	+	0.552199i	$0.813789\pi$
$674$	17.0605	−	9.84986i	0.657145	−	0.379403i
$675$	7.71324	+	20.0281i	0.296883	+	0.770881i
$676$	−8.95878	−	9.42021i	−0.344568	−	0.362316i
$677$	7.08945			0.272470			0.136235	−	0.990677i	$-0.456500\pi$
$677$	7.08945			0.272470			0.136235	+	0.990677i	$0.456500\pi$
$678$	12.9218	+	5.47940i	0.496258	+	0.210435i
$679$	−13.3614	+	0.996989i	−0.512763	+	0.0382609i
$680$	−4.62342	−	2.66933i	−0.177300	−	0.102364i
$681$	3.12661	−	2.35786i	0.119812	−	0.0903534i
$682$	−1.23764	−	0.714553i	−0.0473917	−	0.0273616i
$683$	15.2544	+	8.80712i	0.583693	+	0.336995i	0.762599	−	0.646871i	$-0.223923\pi$
$683$	15.2544	+	8.80712i	0.583693	+	0.336995i	−0.178907	+	0.983866i	$0.557256\pi$
$684$	−1.83117	−	0.523632i	−0.0700164	−	0.0200216i
$685$	−6.72717	−	3.88394i	−0.257032	−	0.148398i
$686$	−12.5839	−	13.5884i	−0.480456	−	0.518808i
$687$	11.2440	−	26.5160i	0.428984	−	1.01165i
$688$	1.85592			0.0707564
$689$	−28.6416	−	38.3126i	−1.09116	−	1.45959i
$690$	−8.32559	+	6.27855i	−0.316950	+	0.239020i
$691$	−7.95862	+	4.59491i	−0.302760	+	0.174799i	−0.643682	−	0.765293i	$-0.722594\pi$
$691$	−7.95862	+	4.59491i	−0.302760	+	0.174799i	0.340922	+	0.940092i	$0.389261\pi$
$692$	6.17619	+	10.6975i	0.234783	+	0.406657i
$693$	14.0696	−	4.65557i	0.534460	−	0.176851i
$694$	−0.565530			−0.0214672
$695$	−1.69459	−	0.978375i	−0.0642796	−	0.0371119i
$696$	−0.586878	−	4.76535i	−0.0222455	−	0.180630i
$697$	−41.3899			−1.56776
$698$	6.71913	−	11.6379i	0.254323	−	0.440500i
$699$	−6.86957	+	16.2001i	−0.259831	+	0.612746i
$700$	0.813150	+	10.8976i	0.0307342	+	0.411892i
$701$		−	37.5296i		−	1.41747i	−0.705473	−	0.708737i	$-0.749265\pi$
$701$		−	37.5296i		−	1.41747i	0.705473	−	0.708737i	$-0.250735\pi$
$702$	18.7217	+	0.704924i	0.706606	+	0.0266057i
$703$			2.43229i			0.0917356i
$704$	−1.61698	+	0.933562i	−0.0609421	+	0.0351850i
$705$	−15.1508	−	6.42462i	−0.570613	−	0.241965i
$706$	6.82391	+	3.93978i	0.256821	+	0.148276i
$707$	24.5059	+	11.8111i	0.921641	+	0.444203i
$708$	−0.431512	−	3.50381i	−0.0162172	−	0.131681i
$709$	−1.06909	+	1.85172i	−0.0401506	+	0.0695430i	−0.885402	−	0.464825i	$-0.846117\pi$
$709$	−1.06909	+	1.85172i	−0.0401506	+	0.0695430i	0.845252	+	0.534368i	$0.179450\pi$
$710$	−5.00397			−0.187796
$711$	−21.8846	−	22.6290i	−0.820736	−	0.848656i
$712$	2.11693	−	1.22221i	0.0793351	−	0.0458042i
$713$	−2.47069	−	4.27936i	−0.0925281	−	0.160263i
$714$	5.13530	+	25.7271i	0.192184	+	0.962812i
$715$	−2.47504	+	5.76940i	−0.0925613	+	0.215763i
$716$			2.67220i			0.0998647i
$717$	0.465084	−	1.09678i	0.0173689	−	0.0409601i
$718$	−3.25623	−	5.63996i	−0.121521	−	0.210481i
$719$	−1.05758	+	1.83178i	−0.0394410	+	0.0683137i	−0.885072	−	0.465454i	$-0.845891\pi$
$719$	−1.05758	+	1.83178i	−0.0394410	+	0.0683137i	0.845631	+	0.533768i	$0.179224\pi$
$720$	0.769165	−	2.68981i	0.0286651	−	0.100243i
$721$	9.00462	+	13.2165i	0.335349	+	0.492206i
$722$	−16.1054	−	9.29848i	−0.599382	−	0.346054i
$723$	9.10028	+	12.0673i	0.338443	+	0.448788i
$724$	19.5088	+	11.2634i	0.725040	+	0.418602i
$725$	9.91567	−	5.72482i	0.368259	−	0.212614i
$726$	5.08074	−	11.9816i	0.188564	−	0.444680i
$727$		−	19.1520i		−	0.710310i	−0.934807	−	0.355155i	$-0.884428\pi$
$727$		−	19.1520i		−	0.710310i	0.934807	−	0.355155i	$-0.115572\pi$
$728$	9.02228	+	3.09812i	0.334388	+	0.114824i
$729$	−20.0253	+	18.1104i	−0.741677	+	0.670757i
$730$	6.36853	+	11.0306i	0.235710	+	0.408261i
$731$	5.31245	+	9.20142i	0.196488	+	0.340327i
$732$	−3.69512	+	0.455073i	−0.136575	+	0.0168200i
$733$		−	37.7941i		−	1.39596i	−0.716118	−	0.697979i	$-0.754083\pi$
$733$		−	37.7941i		−	1.39596i	0.716118	−	0.697979i	$-0.245917\pi$
$734$	15.1961	−	26.3204i	0.560897	−	0.971503i
$735$	−7.91697	+	8.07202i	−0.292022	+	0.297741i
$736$	−6.45591			−0.237968
$737$	22.9471	+	13.2485i	0.845267	+	0.488015i
$738$	−5.26255	−	21.0415i	−0.193717	−	0.774547i
$739$	−3.76021	−	6.51288i	−0.138322	−	0.239580i	0.788540	−	0.614984i	$-0.210837\pi$
$739$	−3.76021	−	6.51288i	−0.138322	−	0.239580i	−0.926861	+	0.375404i	$0.877504\pi$
$740$	−3.57280			−0.131339
$741$	−3.80728	−	1.10598i	−0.139864	−	0.0406294i
$742$	31.6203	+	15.2400i	1.16082	+	0.559479i
$743$	38.7762	−	22.3875i	1.42256	−	0.821317i	0.426045	−	0.904702i	$-0.359907\pi$
$743$	38.7762	−	22.3875i	1.42256	−	0.821317i	0.996517	+	0.0833854i	$0.0265733\pi$
$744$	1.22052	+	0.517554i	0.0447464	+	0.0189745i
$745$	−7.46958	−	4.31257i	−0.273664	−	0.158000i
$746$		−	15.5265i		−	0.568466i
$747$	17.8699	+	18.4778i	0.653826	+	0.676068i
$748$	−9.25697	−	5.34451i	−0.338468	−	0.195415i
$749$	2.46113	−	5.10640i	0.0899277	−	0.186584i
$750$	14.6369	−	1.80261i	0.534463	−	0.0658219i
$751$	1.10741	+	1.91808i	0.0404098	+	0.0699918i	0.885523	−	0.464596i	$-0.153800\pi$
$751$	1.10741	+	1.91808i	0.0404098	+	0.0699918i	−0.845113	+	0.534588i	$0.820467\pi$
$752$	−5.09430	−	8.82358i	−0.185770	−	0.321763i
$753$	−25.5231	+	19.2477i	−0.930114	+	0.701424i
$754$	−1.18012	−	9.92490i	−0.0429774	−	0.361443i
$755$	15.2877			0.556376
$756$	−12.4260	+	5.88173i	−0.451929	+	0.213916i
$757$	−6.73982	−	11.6737i	−0.244963	−	0.424288i	0.717158	−	0.696910i	$-0.245442\pi$
$757$	−6.73982	−	11.6737i	−0.244963	−	0.424288i	−0.962121	+	0.272622i	$0.912109\pi$
$758$	1.99583	+	1.15229i	0.0724919	+	0.0418532i
$759$	−16.6694	+	12.5709i	−0.605061	+	0.456293i
$760$	−0.296014	+	0.512711i	−0.0107376	+	0.0185980i
$761$	−3.99567	+	6.92070i	−0.144843	+	0.250875i	−0.929314	−	0.369290i	$-0.879601\pi$
$761$	−3.99567	+	6.92070i	−0.144843	+	0.250875i	0.784471	+	0.620165i	$0.212934\pi$
$762$	−22.3747	−	29.6697i	−0.810551	−	1.07482i
$763$	28.9944	−	19.7545i	1.04967	−	0.715160i
$764$	5.65445	−	3.26460i	0.204571	−	0.118109i
$765$	15.5374	−	3.88597i	0.561757	−	0.140497i
$766$			4.32990i			0.156446i
$767$	−0.867703	−	7.29745i	−0.0313310	−	0.263496i
$768$	1.38290	−	1.04288i	0.0499010	−	0.0376317i
$769$	−17.7222	+	10.2319i	−0.639077	+	0.368972i	−0.784259	−	0.620433i	$-0.786957\pi$
$769$	−17.7222	+	10.2319i	−0.639077	+	0.368972i	0.145182	+	0.989405i	$0.453623\pi$
$770$	−0.342786	−	4.59393i	−0.0123532	−	0.165554i
$771$	−4.80802	−	39.0404i	−0.173157	−	1.40600i
$772$	9.54270			0.343449
$773$	13.8300	−	23.9543i	0.497431	−	0.861576i	−0.502565	−	0.864540i	$-0.667610\pi$
$773$	13.8300	−	23.9543i	0.497431	−	0.861576i	0.999996	+	0.00296387i	$0.000943429\pi$
$774$	−4.00229	+	3.87062i	−0.143859	+	0.139127i
$775$			3.16140i			0.113561i
$776$	−2.53208	+	4.38570i	−0.0908965	+	0.157437i
$777$	11.5850	+	13.1923i	0.415608	+	0.473272i
$778$	−4.89099	−	8.47145i	−0.175351	−	0.303716i
$779$			4.58991i			0.164451i
$780$	1.62459	−	5.59253i	0.0581695	−	0.200245i
$781$	−10.0189			−0.358504
$782$	−18.4796	−	32.0076i	−0.660828	−	1.14459i
$783$	11.2040	+	9.05250i	0.400397	+	0.323510i
$784$	−6.92248	+	1.03886i	−0.247232	+	0.0371020i
$785$		−	17.3881i		−	0.620607i
$786$	−11.3958	+	1.40345i	−0.406473	+	0.0500593i
$787$	−33.7892	−	19.5082i	−1.20445	−	0.695392i	−0.242912	−	0.970048i	$-0.578103\pi$
$787$	−33.7892	−	19.5082i	−1.20445	−	0.695392i	−0.961543	+	0.274656i	$0.911436\pi$
$788$			7.58261i			0.270119i
$789$	−35.8537	+	4.41557i	−1.27643	+	0.157198i
$790$	−8.47454	+	4.89278i	−0.301510	+	0.174077i
$791$	−21.3802	+	1.59533i	−0.760192	+	0.0567234i
$792$	1.54002	−	5.38551i	0.0547221	−	0.191366i
$793$	−7.69590	+	0.915080i	−0.273289	+	0.0324955i
$794$	35.3115			1.25316
$795$	8.36580	−	19.7286i	0.296704	−	0.699702i
$796$	−17.0996	+	9.87247i	−0.606080	+	0.349921i
$797$	20.7422	−	35.9266i	0.734727	−	1.27259i	−0.220116	−	0.975474i	$-0.570643\pi$
$797$	20.7422	−	35.9266i	0.734727	−	1.27259i	0.954843	−	0.297111i	$-0.0960232\pi$
$798$	2.85299	−	0.569476i	0.100995	−	0.0201592i
$799$	29.1641	−	50.5138i	1.03175	−	1.78705i
$800$	3.57700	+	2.06518i	0.126466	+	0.0730153i
$801$	−2.01617	+	7.05064i	−0.0712378	+	0.249122i
$802$	−6.53278	+	11.3151i	−0.230681	+	0.399550i
$803$	12.7510	+	22.0854i	0.449973	+	0.779377i
$804$	−22.6296	−	9.59596i	−0.798086	−	0.338423i
$805$	6.91571	−	14.3488i	0.243747	−	0.505730i
$806$	2.53618	+	1.08801i	0.0893331	+	0.0383235i
$807$	3.75291	−	2.83017i	0.132109	−	0.0996266i
$808$	8.90451	−	5.14102i	0.313260	−	0.180861i
$809$	23.1242	−	13.3507i	0.813003	−	0.469387i	−0.0349948	−	0.999387i	$-0.511141\pi$
$809$	23.1242	−	13.3507i	0.813003	−	0.469387i	0.847998	+	0.530000i	$0.177808\pi$
$810$	3.95103	+	7.40470i	0.138825	+	0.260175i
$811$		−	28.3947i		−	0.997075i	−0.866868	−	0.498537i	$-0.833871\pi$
$811$		−	28.3947i		−	0.997075i	0.866868	−	0.498537i	$-0.166129\pi$
$812$	4.12955	+	6.06111i	0.144919	+	0.212703i
$813$	18.9006	−	2.32770i	0.662872	−	0.0816361i
$814$	−7.15343			−0.250728
$815$	−1.57102	+	2.72108i	−0.0550304	+	0.0953154i
$816$	9.12891	+	3.87106i	0.319576	+	0.135514i
$817$	1.02039	−	0.589120i	0.0356988	−	0.0206107i
$818$	−26.2994			−0.919538
$819$	−25.9178	+	12.1353i	−0.905642	+	0.424043i
$820$	−6.74214			−0.235446
$821$	7.65883	−	4.42182i	0.267295	−	0.154323i	−0.360363	−	0.932812i	$-0.617347\pi$
$821$	7.65883	−	4.42182i	0.267295	−	0.154323i	0.627658	+	0.778489i	$0.284014\pi$
$822$	13.2827	+	5.63247i	0.463289	+	0.196455i
$823$	9.49367	−	16.4435i	0.330928	−	0.573185i	−0.651766	−	0.758420i	$-0.725971\pi$
$823$	9.49367	−	16.4435i	0.330928	−	0.573185i	0.982694	+	0.185235i	$0.0593048\pi$
$824$	6.04457			0.210573
$825$	13.2573	−	1.63270i	0.461559	−	0.0568433i
$826$	3.03632	+	4.45654i	0.105647	+	0.155063i
$827$		−	23.0912i		−	0.802959i	−0.915868	−	0.401480i	$-0.868496\pi$
$827$		−	23.0912i		−	0.802959i	0.915868	−	0.401480i	$-0.131504\pi$
$828$	13.9221	−	13.4641i	0.483828	−	0.467911i
$829$	−29.3364	+	16.9374i	−1.01890	+	0.588259i	−0.913784	−	0.406201i	$-0.866853\pi$
$829$	−29.3364	+	16.9374i	−1.01890	+	0.588259i	−0.105111	+	0.994460i	$0.533520\pi$
$830$	6.91991	−	3.99521i	0.240194	−	0.138676i
$831$	10.7278	−	8.09014i	0.372144	−	0.280644i
$832$	2.88780	−	2.15885i	0.100116	−	0.0748446i
$833$	−24.9656	−	31.3471i	−0.865008	−	1.08611i
$834$	3.34596	+	1.41884i	0.115861	+	0.0491303i
$835$	−8.20612	−	14.2134i	−0.283984	−	0.491875i
$836$	−0.592677	+	1.02655i	−0.0204981	+	0.0355038i
$837$	−3.71143	+	1.42935i	−0.128286	+	0.0494056i
$838$	−28.4056	−	16.4000i	−0.981257	−	0.566529i
$839$	7.60788	−	13.1772i	0.262653	−	0.454928i	−0.704293	−	0.709909i	$-0.748736\pi$
$839$	7.60788	−	13.1772i	0.262653	−	0.454928i	0.966946	+	0.254981i	$0.0820692\pi$
$840$	0.836506	+	4.19077i	0.0288622	+	0.144595i
$841$	−10.6578	+	18.4599i	−0.367512	+	0.636549i
$842$	−32.9631	+	19.0313i	−1.13598	+	0.655860i
$843$	11.3248	−	26.7066i	0.390046	−	0.919824i
$844$	−24.1591			−0.831592
$845$	3.43058	−	11.6275i	0.118016	−	0.399999i
$846$	29.3879	+	8.40361i	1.01038	+	0.288922i
$847$	1.47926	+	19.8247i	0.0508280	+	0.681183i
$848$	11.4896	−	6.63353i	0.394555	−	0.227796i
$849$	7.76207	−	0.955939i	0.266393	−	0.0328077i
$850$			23.6458i			0.811043i
$851$	−21.4205	−	12.3671i	−0.734284	−	0.423939i
$852$	9.22441	−	1.13603i	0.316023	−	0.0389199i
$853$			5.66539i			0.193979i	0.995285	+	0.0969896i	$0.0309214\pi$
$853$			5.66539i			0.193979i	−0.995285	+	0.0969896i	$0.969079\pi$
$854$	4.69987	−	3.20211i	0.160826	−	0.109574i
$855$	−0.430932	−	1.72301i	−0.0147376	−	0.0589258i
$856$	−1.07125	−	1.85547i	−0.0366147	−	0.0634186i
$857$	31.0120			1.05935			0.529674	−	0.848201i	$-0.322314\pi$
$857$	31.0120			1.05935			0.529674	+	0.848201i	$0.322314\pi$
$858$	3.25273	−	11.1973i	0.111046	−	0.382270i
$859$			40.0946i			1.36801i	0.729477	+	0.684005i	$0.239763\pi$
$859$			40.0946i			1.36801i	−0.729477	+	0.684005i	$0.760237\pi$
$860$	0.865362	+	1.49885i	0.0295086	+	0.0511104i
$861$	21.8617	+	24.8949i	0.745044	+	0.848416i
$862$	12.4284	−	21.5266i	0.423312	−	0.733198i
$863$			16.3101i			0.555203i	0.960696	+	0.277601i	$0.0895394\pi$
$863$			16.3101i			0.555203i	−0.960696	+	0.277601i	$0.910461\pi$
$864$	−0.807235	+	5.13307i	−0.0274627	+	0.174630i
$865$	−5.75955	+	9.97583i	−0.195831	+	0.339188i
$866$	−0.881891			−0.0299679
$867$	3.33954	+	27.1165i	0.113417	+	0.920925i
$868$	−2.01946	+	0.150686i	−0.0685448	+	0.00511462i
$869$	−16.9676	+	9.79627i	−0.575588	+	0.332316i
$870$	3.57487	−	2.69591i	0.121200	−	0.0913998i
$871$	−47.0232	−	20.1727i	−1.59332	−	0.683527i
$872$		−	13.2607i		−	0.449063i
$873$	−3.68616	−	14.7385i	−0.124758	−	0.498824i
$874$	−3.54946	+	2.04928i	−0.120062	+	0.0693180i
$875$	−18.6168	+	12.6840i	−0.629364	+	0.428797i
$876$	−14.2441	−	18.8882i	−0.481264	−	0.638174i
$877$	5.37456	−	9.30901i	0.181486	−	0.314343i	−0.760901	−	0.648868i	$-0.775243\pi$
$877$	5.37456	−	9.30901i	0.181486	−	0.314343i	0.942387	+	0.334525i	$0.108576\pi$
$878$	9.14027	−	15.8314i	0.308469	−	0.534284i
$879$	23.5736	−	17.7775i	0.795118	−	0.599620i
$880$	−1.50790	−	0.870585i	−0.0508312	−	0.0293474i
$881$	−23.8133	−	41.2459i	−0.802292	−	1.38961i	−0.918104	−	0.396339i	$-0.870281\pi$
$881$	−23.8133	−	41.2459i	−0.802292	−	1.38961i	0.115813	−	0.993271i	$-0.463053\pi$
$882$	12.7617	−	16.6775i	0.429710	−	0.561560i
$883$	−23.8253			−0.801784			−0.400892	−	0.916125i	$-0.631300\pi$
$883$	−23.8253			−0.801784			−0.400892	+	0.916125i	$0.631300\pi$
$884$	18.9694	+	8.13778i	0.638010	+	0.273703i
$885$	2.62849	−	1.98221i	0.0883556	−	0.0666314i
$886$	11.6939	+	20.2544i	0.392863	+	0.680459i
$887$	−12.4042	−	21.4846i	−0.416491	−	0.721384i	0.579093	−	0.815262i	$-0.303407\pi$
$887$	−12.4042	−	21.4846i	−0.416491	−	0.721384i	−0.995584	+	0.0938781i	$0.970074\pi$
$888$	6.58617	−	0.811121i	0.221017	−	0.0272194i
$889$	51.1347	+	24.6454i	1.71500	+	0.826579i
$890$	1.97412	+	1.13976i	0.0661727	+	0.0382048i
$891$	7.91072	+	14.8256i	0.265019	+	0.496677i
$892$			13.2655i			0.444162i
$893$	−5.60169	−	3.23414i	−0.187454	−	0.108226i
$894$	14.7486	+	6.25407i	0.493268	+	0.209167i
$895$	−2.15808	+	1.24597i	−0.0721366	+	0.0416481i
$896$	−1.14871	+	2.38337i	−0.0383758	+	0.0796228i
$897$	29.0984	−	27.9062i	0.971568	−	0.931760i
$898$	1.76593			0.0589299
$899$	1.06087	+	1.83749i	0.0353821	+	0.0612837i
$900$	−12.0208	+	3.00646i	−0.400695	+	0.100215i
$901$	65.7764	+	37.9760i	2.19133	+	1.26516i
$902$	−13.4990			−0.449469
$903$	2.72843	−	8.05537i	0.0907965	−	0.268066i
$904$	−4.05171	+	7.01777i	−0.134758	+	0.233407i
$905$			21.0072i			0.698304i
$906$	−28.1816	+	3.47071i	−0.936271	+	0.115307i
$907$	1.66813	+	2.88929i	0.0553894	+	0.0959373i	0.892391	−	0.451264i	$-0.149027\pi$
$907$	1.66813	+	2.88929i	0.0553894	+	0.0959373i	−0.837001	+	0.547201i	$0.815693\pi$
$908$	1.13046	+	1.95801i	0.0375155	+	0.0649788i
$909$	−8.48069	+	29.6574i	−0.281287	+	0.983674i
$910$	1.70477	+	8.73100i	0.0565125	+	0.289430i
$911$		−	38.6767i		−	1.28142i	−0.767785	−	0.640708i	$-0.778641\pi$
$911$		−	38.6767i		−	1.28142i	0.767785	−	0.640708i	$-0.221359\pi$
$912$	0.429279	−	1.01234i	0.0142148	−	0.0335221i
$913$	13.8550	−	7.99917i	0.458533	−	0.264734i
$914$	18.0881	+	10.4432i	0.598301	+	0.345429i
$915$	−2.09044	−	2.77200i	−0.0691079	−	0.0916396i
$916$	14.4007	+	8.31427i	0.475814	+	0.274711i
$917$	14.4944	−	9.87532i	0.478648	−	0.326112i
$918$	−27.7597	+	10.6909i	−0.916208	+	0.352851i
$919$	5.34270	−	9.25382i	0.176239	−	0.305255i	−0.764350	−	0.644801i	$-0.776940\pi$
$919$	5.34270	−	9.25382i	0.176239	−	0.305255i	0.940589	+	0.339546i	$0.110273\pi$
$920$	−3.01020	−	5.21382i	−0.0992433	−	0.171895i
$921$	18.9496	−	44.6878i	0.624410	−	1.47251i
$922$			26.0994i			0.859537i
$923$	19.2119	−	2.28439i	0.632367	−	0.0751915i
$924$	1.67484	+	8.39072i	0.0550983	+	0.276034i
$925$	7.91225	+	13.7044i	0.260153	+	0.450598i
$926$	−10.1807	+	5.87785i	−0.334560	+	0.193158i
$927$	−13.0351	+	12.6063i	−0.428129	+	0.414044i
$928$	2.77206			0.0909974
$929$	−25.9483	+	44.9437i	−0.851335	+	1.47456i	0.0286680	+	0.999589i	$0.490873\pi$
$929$	−25.9483	+	44.9437i	−0.851335	+	1.47456i	−0.880003	+	0.474967i	$0.842460\pi$
$930$	0.151114	+	1.22702i	0.00495521	+	0.0402355i
$931$	−3.47622	+	2.76855i	−0.113929	+	0.0907355i
$932$	−8.79823	−	5.07966i	−0.288196	−	0.166390i
$933$	35.1239	+	14.8941i	1.14990	+	0.487610i
$934$	−14.8396	+	8.56764i	−0.485566	+	0.280342i
$935$		−	9.96795i		−	0.325987i
$936$	−1.72514	+	10.6782i	−0.0563879	+	0.349028i
$937$		−	38.4373i		−	1.25569i	−0.778337	−	0.627846i	$-0.783937\pi$
$937$		−	38.4373i		−	1.25569i	0.778337	−	0.627846i	$-0.216063\pi$
$938$	37.4427	−	2.79387i	1.22255	−	0.0912230i
$939$	4.80343	−	11.3277i	0.156754	−	0.369664i
$940$	4.75064	−	8.22835i	0.154949	−	0.268379i
$941$	−37.6578			−1.22761			−0.613805	−	0.789458i	$-0.710362\pi$
$941$	−37.6578			−1.22761			−0.613805	+	0.789458i	$0.710362\pi$
$942$	3.94756	+	32.0535i	0.128618	+	1.04436i
$943$	−40.4220	−	23.3377i	−1.31632	−	0.759979i
$944$	2.03821			0.0663380
$945$	−10.5440	−	7.29281i	−0.342996	−	0.237235i
$946$	1.73262	+	3.00098i	0.0563323	+	0.0975704i
$947$	−50.4878	+	29.1492i	−1.64063	+	0.947221i	−0.660026	+	0.751243i	$0.729455\pi$
$947$	−50.4878	+	29.1492i	−1.64063	+	0.947221i	−0.980608	+	0.195978i	$0.937212\pi$
$948$	14.5113	−	10.9434i	0.471306	−	0.355424i
$949$	−29.4865	−	39.4428i	−0.957173	−	1.28037i
$950$	2.62218			0.0850749
$951$	−17.1907	+	40.5398i	−0.557446	+	1.31459i
$952$	−15.1046	+	1.12706i	−0.489542	+	0.0365282i
$953$	40.5605	+	23.4176i	1.31388	+	0.758570i	0.982737	−	0.185010i	$-0.0592316\pi$
$953$	40.5605	+	23.4176i	1.31388	+	0.758570i	0.331145	+	0.943580i	$0.392565\pi$
$954$	−10.9427	+	38.2673i	−0.354285	+	1.23895i
$955$	5.27301	+	3.04437i	0.170630	+	0.0985135i
$956$	0.595658	+	0.343904i	0.0192650	+	0.0111226i
$957$	7.15758	−	5.39772i	0.231372	−	0.174483i
$958$	30.8242	+	17.7964i	0.995886	+	0.574975i
$959$	−21.9775	+	1.63990i	−0.709689	+	0.0529550i
$960$	1.48704	+	0.630569i	0.0479939	+	0.0203515i
$961$	30.4142			0.981102
$962$	13.7172	−	1.63104i	0.442259	−	0.0525868i
$963$	6.17983	+	1.76715i	0.199142	+	0.0569458i
$964$	−7.55703	+	4.36305i	−0.243396	+	0.140525i
$965$	4.44948	+	7.70672i	0.143234	+	0.248088i
$966$	−9.49098	+	28.0210i	−0.305367	+	0.901560i
$967$	4.42081			0.142164			0.0710818	−	0.997470i	$-0.477355\pi$
$967$	4.42081			0.142164			0.0710818	+	0.997470i	$0.477355\pi$
$968$	6.50718	+	3.75692i	0.209149	+	0.120752i
$969$	6.24786	−	0.769456i	0.200710	−	0.0247185i
$970$	−4.72254			−0.151632
$971$	−14.1427	+	24.4959i	−0.453862	+	0.786112i	−0.998622	−	0.0524802i	$-0.983287\pi$
$971$	−14.1427	+	24.4959i	−0.453862	+	0.786112i	0.544760	+	0.838592i	$0.316621\pi$
$972$	−8.96447	−	12.7530i	−0.287535	−	0.409052i
$973$	−5.53619	+	0.413095i	−0.177482	+	0.0132432i
$974$			36.1924i			1.15968i
$975$	−25.0494	+	6.15357i	−0.802222	+	0.197072i
$976$		−	2.14949i		−	0.0688036i
$977$	−29.5206	+	17.0437i	−0.944448	+	0.545277i	−0.891352	−	0.453312i	$-0.850242\pi$
$977$	−29.5206	+	17.0437i	−0.944448	+	0.545277i	−0.0530962	+	0.998589i	$0.516909\pi$
$978$	2.27829	−	5.37276i	0.0728515	−	0.171802i
$979$	3.95256	+	2.28201i	0.126324	+	0.0729335i
$980$	−4.06673	−	5.10624i	−0.129907	−	0.163113i
$981$	27.6558	+	28.5966i	0.882981	+	0.913019i
$982$	−11.4426	+	19.8191i	−0.365147	+	0.632453i
$983$	2.45554			0.0783195			0.0391598	−	0.999233i	$-0.487532\pi$
$983$	2.45554			0.0783195			0.0391598	+	0.999233i	$0.487532\pi$
$984$	12.4286	−	1.53065i	0.396209	−	0.0487952i
$985$	−6.12375	+	3.53555i	−0.195119	+	0.112652i
$986$	7.93483	+	13.7435i	0.252696	+	0.437683i
$987$	−45.7868	+	9.13935i	−1.45741	+	0.290909i
$988$	0.902434	−	2.10360i	0.0287103	−	0.0669245i
$989$			11.9817i			0.380995i
$990$	5.06743	−	1.26738i	0.161053	−	0.0402801i
$991$	−7.47304	−	12.9437i	−0.237389	−	0.411169i	0.722575	−	0.691292i	$-0.242958\pi$
$991$	−7.47304	−	12.9437i	−0.237389	−	0.411169i	−0.959964	+	0.280123i	$0.909625\pi$
$992$	−0.382702	+	0.662860i	−0.0121508	+	0.0210458i
$993$	−23.7428	+	17.9051i	−0.753456	+	0.568201i
$994$	−11.7327	+	7.99368i	−0.372137	+	0.253544i
$995$	−15.9461	−	9.20649i	−0.505525	−	0.291865i
$996$	−11.8493	+	8.93585i	−0.375458	+	0.283143i
$997$	−7.28444	−	4.20567i	−0.230700	−	0.133195i	0.380195	−	0.924906i	$-0.375857\pi$
$997$	−7.28444	−	4.20567i	−0.230700	−	0.133195i	−0.610895	+	0.791711i	$0.709190\pi$
$998$	−25.9775	+	14.9981i	−0.822304	+	0.474757i
$999$	−12.5114	+	15.4850i	−0.395844	+	0.489923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bq.c.419.19	yes	64
3.2	odd	2	inner	546.2.bq.c.419.8	✓	64
7.6	odd	2	inner	546.2.bq.c.419.30	yes	64
13.9	even	3	inner	546.2.bq.c.503.9	yes	64
21.20	even	2	inner	546.2.bq.c.419.9	yes	64
39.35	odd	6	inner	546.2.bq.c.503.30	yes	64
91.48	odd	6	inner	546.2.bq.c.503.8	yes	64
273.230	even	6	inner	546.2.bq.c.503.19	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bq.c.419.8	✓	64	3.2	odd	2	inner
546.2.bq.c.419.9	yes	64	21.20	even	2	inner
546.2.bq.c.419.19	yes	64	1.1	even	1	trivial
546.2.bq.c.419.30	yes	64	7.6	odd	2	inner
546.2.bq.c.503.8	yes	64	91.48	odd	6	inner
546.2.bq.c.503.9	yes	64	13.9	even	3	inner
546.2.bq.c.503.19	yes	64	273.230	even	6	inner
546.2.bq.c.503.30	yes	64	39.35	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.59461 - 0.676184i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.932541 q^{5} +(-1.71906 + 0.211712i) q^{6} +(2.18650 - 1.48970i) q^{7} -1.00000i q^{8} +(2.08555 + 2.15650i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.59461 - 0.676184i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.932541 q^{5} +(-1.71906 + 0.211712i) q^{6} +(2.18650 - 1.48970i) q^{7} -1.00000i q^{8} +(2.08555 + 2.15650i) q^{9} +(0.807604 - 0.466271i) q^{10} +(1.61698 - 0.933562i) q^{11} +(-1.38290 + 1.04288i) q^{12} +(-2.88780 + 2.15885i) q^{13} +(1.14871 - 2.38337i) q^{14} +(-1.48704 - 0.630569i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.86243 - 4.95787i) q^{17} +(2.88439 + 0.824806i) q^{18} +(-0.549800 - 0.317427i) q^{19} +(0.466271 - 0.807604i) q^{20} +(-4.49392 + 0.897017i) q^{21} +(0.933562 - 1.61698i) q^{22} +(5.59098 - 3.22795i) q^{23} +(-0.676184 + 1.59461i) q^{24} -4.13037 q^{25} +(-1.42148 + 3.31352i) q^{26} +(-1.86745 - 4.84898i) q^{27} +(-0.196871 - 2.63842i) q^{28} +(-2.40068 + 1.38603i) q^{29} +(-1.60310 + 0.197430i) q^{30} -0.765404i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.20971 + 0.395292i) q^{33} -5.72486i q^{34} +(2.03900 - 1.38921i) q^{35} +(2.91036 - 0.727891i) q^{36} +(-1.91563 - 3.31796i) q^{37} -0.634855 q^{38} +(6.06468 - 1.48984i) q^{39} -0.932541i q^{40} +(-3.61493 - 6.26124i) q^{41} +(-3.44334 + 3.02380i) q^{42} +(-0.927961 + 1.60728i) q^{43} -1.86712i q^{44} +(1.94486 + 2.01102i) q^{45} +(3.22795 - 5.59098i) q^{46} +10.1886 q^{47} +(0.211712 + 1.71906i) q^{48} +(2.56157 - 6.51447i) q^{49} +(-3.57700 + 2.06518i) q^{50} +(-7.91689 + 5.97034i) q^{51} +(0.425719 + 3.58033i) q^{52} +13.2671i q^{53} +(-4.04175 - 3.26562i) q^{54} +(1.50790 - 0.870585i) q^{55} +(-1.48970 - 2.18650i) q^{56} +(0.662077 + 0.877939i) q^{57} +(-1.38603 + 2.40068i) q^{58} +(-1.01910 + 1.76514i) q^{59} +(-1.28961 + 0.972528i) q^{60} +(1.86152 + 1.07475i) q^{61} +(-0.382702 - 0.662860i) q^{62} +(7.77260 + 1.60833i) q^{63} -1.00000 q^{64} +(-2.69299 + 2.01321i) q^{65} +(-2.58204 + 1.94719i) q^{66} +(7.09567 + 12.2901i) q^{67} +(-2.86243 - 4.95787i) q^{68} +(-11.0981 + 1.36679i) q^{69} +(1.07122 - 2.22259i) q^{70} +(-4.64705 - 2.68298i) q^{71} +(2.15650 - 2.08555i) q^{72} +13.6584i q^{73} +(-3.31796 - 1.91563i) q^{74} +(6.58632 + 2.79289i) q^{75} +(-0.549800 + 0.317427i) q^{76} +(2.14479 - 4.45005i) q^{77} +(4.50725 - 4.32258i) q^{78} -10.4934 q^{79} +(-0.466271 - 0.807604i) q^{80} +(-0.300958 + 8.99497i) q^{81} +(-6.26124 - 3.61493i) q^{82} +8.56844 q^{83} +(-1.47012 + 4.34036i) q^{84} +(2.66933 - 4.62342i) q^{85} +1.85592i q^{86} +(4.76535 - 0.586878i) q^{87} +(-0.933562 - 1.61698i) q^{88} +(1.22221 + 2.11693i) q^{89} +(2.68981 + 0.769165i) q^{90} +(-3.09812 + 9.02228i) q^{91} -6.45591i q^{92} +(-0.517554 + 1.22052i) q^{93} +(8.82358 - 5.09430i) q^{94} +(-0.512711 - 0.296014i) q^{95} +(1.04288 + 1.38290i) q^{96} +(-4.38570 - 2.53208i) q^{97} +(-1.03886 - 6.92248i) q^{98} +(5.38551 + 1.54002i) 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

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