LMFDB - Embedded newform 546.2.z.a.521.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.2
Character	$\chi$	$=$	546.521
Dual form			546.2.z.a.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.54393 + 0.785030i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.890016 - 1.54155i) q^{5} +(0.944570 - 1.45182i) q^{6} +(-1.51727 - 2.16746i) q^{7} +1.00000i q^{8} +(1.76746 - 2.42407i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.54393 + 0.785030i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.890016 - 1.54155i) q^{5} +(0.944570 - 1.45182i) q^{6} +(-1.51727 - 2.16746i) q^{7} +1.00000i q^{8} +(1.76746 - 2.42407i) q^{9} +(1.54155 + 0.890016i) q^{10} +(3.61827 + 2.08901i) q^{11} +(-0.0921101 + 1.72960i) q^{12} -1.00000i q^{13} +(2.39772 + 1.11845i) q^{14} +(2.58429 + 1.68136i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.81268 + 6.60376i) q^{17} +(-0.318627 + 2.98303i) q^{18} +(-2.62640 + 1.51635i) q^{19} -1.78003 q^{20} +(4.04408 + 2.15532i) q^{21} -4.17801 q^{22} +(-6.70577 + 3.87158i) q^{23} +(-0.785030 - 1.54393i) q^{24} +(0.915742 - 1.58611i) q^{25} +(0.500000 + 0.866025i) q^{26} +(-0.825865 + 5.13010i) q^{27} +(-2.63571 + 0.230259i) q^{28} -7.65112i q^{29} +(-3.07874 - 0.163959i) q^{30} +(-1.78918 - 1.03299i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-7.22629 - 0.384837i) q^{33} -7.62536i q^{34} +(-1.99087 + 4.26803i) q^{35} +(-1.21558 - 2.74269i) q^{36} +(3.95462 + 6.84960i) q^{37} +(1.51635 - 2.62640i) q^{38} +(0.785030 + 1.54393i) q^{39} +(1.54155 - 0.890016i) q^{40} -2.69649 q^{41} +(-4.57994 + 0.155480i) q^{42} +0.322841 q^{43} +(3.61827 - 2.08901i) q^{44} +(-5.30989 - 0.567167i) q^{45} +(3.87158 - 6.70577i) q^{46} +(2.04779 + 3.54688i) q^{47} +(1.45182 + 0.944570i) q^{48} +(-2.39581 + 6.57724i) q^{49} +1.83148i q^{50} +(0.702373 - 13.1888i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(-10.2425 - 5.91349i) q^{53} +(-1.84983 - 4.85573i) q^{54} -7.43700i q^{55} +(2.16746 - 1.51727i) q^{56} +(2.86460 - 4.40295i) q^{57} +(3.82556 + 6.62606i) q^{58} +(-6.86324 + 11.8875i) q^{59} +(2.74825 - 1.39738i) q^{60} +(-7.38934 + 4.26624i) q^{61} +2.06597 q^{62} +(-7.93578 - 0.152941i) q^{63} -1.00000 q^{64} +(-1.54155 + 0.890016i) q^{65} +(6.45057 - 3.27987i) q^{66} +(-6.25392 + 10.8321i) q^{67} +(3.81268 + 6.60376i) q^{68} +(7.31395 - 11.2417i) q^{69} +(-0.409868 - 4.69165i) q^{70} +3.91612i q^{71} +(2.42407 + 1.76746i) q^{72} +(1.14565 + 0.661439i) q^{73} +(-6.84960 - 3.95462i) q^{74} +(-0.168698 + 3.16773i) q^{75} +3.03271i q^{76} +(-0.962024 - 11.0120i) q^{77} +(-1.45182 - 0.944570i) q^{78} +(5.64583 + 9.77886i) q^{79} +(-0.890016 + 1.54155i) q^{80} +(-2.75221 - 8.56886i) q^{81} +(2.33523 - 1.34825i) q^{82} +3.38793 q^{83} +(3.88860 - 2.42462i) q^{84} +13.5734 q^{85} +(-0.279589 + 0.161421i) q^{86} +(6.00636 + 11.8128i) q^{87} +(-2.08901 + 3.61827i) q^{88} +(1.23778 + 2.14390i) q^{89} +(4.88209 - 2.16377i) q^{90} +(-2.16746 + 1.51727i) q^{91} +7.74315i q^{92} +(3.57331 + 0.190297i) q^{93} +(-3.54688 - 2.04779i) q^{94} +(4.67508 + 2.69916i) q^{95} +(-1.72960 - 0.0921101i) q^{96} -6.52429i q^{97} +(-1.21379 - 6.89396i) q^{98} +(11.4590 - 5.07869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.54393	+	0.785030i	−0.891390	+	0.453237i
$3$	−1.54393	+	0.785030i	−0.891390	+	0.453237i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.890016	−	1.54155i	−0.398027	−	0.689404i	0.595455	−	0.803389i	$-0.296972\pi$
$5$	−0.890016	−	1.54155i	−0.398027	−	0.689404i	−0.993482	+	0.113985i	$0.963638\pi$
$6$	0.944570	−	1.45182i	0.385619	−	0.592704i
$7$	−1.51727	−	2.16746i	−0.573473	−	0.819225i
$7$	−1.51727	−	2.16746i	−0.573473	−	0.819225i
$8$			1.00000i			0.353553i
$9$	1.76746	−	2.42407i	0.589152	−	0.808022i
$10$	1.54155	+	0.890016i	0.487482	+	0.281448i
$11$	3.61827	+	2.08901i	1.09095	+	0.629859i	0.933829	−	0.357720i	$-0.116446\pi$
$11$	3.61827	+	2.08901i	1.09095	+	0.629859i	0.157119	+	0.987580i	$0.449779\pi$
$12$	−0.0921101	+	1.72960i	−0.0265899	+	0.499292i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	2.39772	+	1.11845i	0.640819	+	0.298917i
$15$	2.58429	+	1.68136i	0.667261	+	0.434127i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.81268	+	6.60376i	−0.924711	+	1.60165i	−0.132686	+	0.991158i	$0.542360\pi$
$17$	−3.81268	+	6.60376i	−0.924711	+	1.60165i	−0.792025	+	0.610489i	$0.790973\pi$
$18$	−0.318627	+	2.98303i	−0.0751012	+	0.703107i
$19$	−2.62640	+	1.51635i	−0.602538	+	0.347875i	−0.770039	−	0.637996i	$-0.779763\pi$
$19$	−2.62640	+	1.51635i	−0.602538	+	0.347875i	0.167502	+	0.985872i	$0.446430\pi$
$20$	−1.78003			−0.398027
$21$	4.04408	+	2.15532i	0.882491	+	0.470329i
$22$	−4.17801			−0.890755
$23$	−6.70577	+	3.87158i	−1.39825	+	0.807279i	−0.994209	−	0.107462i	$-0.965728\pi$
$23$	−6.70577	+	3.87158i	−1.39825	+	0.807279i	−0.404040	+	0.914741i	$0.632394\pi$
$24$	−0.785030	−	1.54393i	−0.160244	−	0.315154i
$25$	0.915742	−	1.58611i	0.183148	−	0.317222i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$	−0.825865	+	5.13010i	−0.158938	+	0.987289i
$28$	−2.63571	+	0.230259i	−0.498103	+	0.0435148i
$29$		−	7.65112i		−	1.42078i	−0.703810	−	0.710388i	$-0.748519\pi$
$29$		−	7.65112i		−	1.42078i	0.703810	−	0.710388i	$-0.251481\pi$
$30$	−3.07874	−	0.163959i	−0.562099	−	0.0299347i
$31$	−1.78918	−	1.03299i	−0.321347	−	0.185530i	0.330646	−	0.943755i	$-0.392733\pi$
$31$	−1.78918	−	1.03299i	−0.321347	−	0.185530i	−0.651993	+	0.758225i	$0.726067\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−7.22629	−	0.384837i	−1.25794	−	0.0669916i
$34$		−	7.62536i		−	1.30774i
$35$	−1.99087	+	4.26803i	−0.336519	+	0.721428i
$36$	−1.21558	−	2.74269i	−0.202596	−	0.457116i
$37$	3.95462	+	6.84960i	0.650135	+	1.12607i	0.983090	+	0.183124i	$0.0586209\pi$
$37$	3.95462	+	6.84960i	0.650135	+	1.12607i	−0.332955	+	0.942943i	$0.608046\pi$
$38$	1.51635	−	2.62640i	0.245985	−	0.426059i
$39$	0.785030	+	1.54393i	0.125705	+	0.247227i
$40$	1.54155	−	0.890016i	0.243741	−	0.140724i
$41$	−2.69649			−0.421121			−0.210561	−	0.977581i	$-0.567529\pi$
$41$	−2.69649			−0.421121			−0.210561	+	0.977581i	$0.567529\pi$
$42$	−4.57994	+	0.155480i	−0.706700	+	0.0239910i
$43$	0.322841			0.0492328			0.0246164	−	0.999697i	$-0.492164\pi$
$43$	0.322841			0.0492328			0.0246164	+	0.999697i	$0.492164\pi$
$44$	3.61827	−	2.08901i	0.545474	−	0.314930i
$45$	−5.30989	−	0.567167i	−0.791552	−	0.0845483i
$46$	3.87158	−	6.70577i	0.570833	−	0.988711i
$47$	2.04779	+	3.54688i	0.298701	+	0.517366i	0.975839	−	0.218490i	$-0.0701132\pi$
$47$	2.04779	+	3.54688i	0.298701	+	0.517366i	−0.677138	+	0.735856i	$0.736780\pi$
$48$	1.45182	+	0.944570i	0.209553	+	0.136337i
$49$	−2.39581	+	6.57724i	−0.342258	+	0.939606i
$50$			1.83148i			0.259011i
$51$	0.702373	−	13.1888i	0.0983519	−	1.84681i
$52$	−0.866025	−	0.500000i	−0.120096	−	0.0693375i
$53$	−10.2425	−	5.91349i	−1.40691	−	0.812281i	−0.411822	−	0.911264i	$-0.635108\pi$
$53$	−10.2425	−	5.91349i	−1.40691	−	0.812281i	−0.995089	+	0.0989835i	$0.968441\pi$
$54$	−1.84983	−	4.85573i	−0.251730	−	0.660781i
$55$		−	7.43700i		−	1.00280i
$56$	2.16746	−	1.51727i	0.289640	−	0.202753i
$57$	2.86460	−	4.40295i	0.379426	−	0.583185i
$58$	3.82556	+	6.62606i	0.502320	+	0.870044i
$59$	−6.86324	+	11.8875i	−0.893517	+	1.54762i	−0.0578885	+	0.998323i	$0.518437\pi$
$59$	−6.86324	+	11.8875i	−0.893517	+	1.54762i	−0.835629	+	0.549294i	$0.814897\pi$
$60$	2.74825	−	1.39738i	0.354798	−	0.180401i
$61$	−7.38934	+	4.26624i	−0.946108	+	0.546236i	−0.891870	−	0.452292i	$-0.850606\pi$
$61$	−7.38934	+	4.26624i	−0.946108	+	0.546236i	−0.0542381	+	0.998528i	$0.517273\pi$
$62$	2.06597			0.262379
$63$	−7.93578	−	0.152941i	−0.999814	−	0.0192688i
$64$	−1.00000			−0.125000
$65$	−1.54155	+	0.890016i	−0.191206	+	0.110393i
$66$	6.45057	−	3.27987i	0.794010	−	0.403724i
$67$	−6.25392	+	10.8321i	−0.764037	+	1.32335i	0.176716	+	0.984262i	$0.443452\pi$
$67$	−6.25392	+	10.8321i	−0.764037	+	1.32335i	−0.940754	+	0.339090i	$0.889881\pi$
$68$	3.81268	+	6.60376i	0.462356	+	0.800823i
$69$	7.31395	−	11.2417i	0.880496	−	1.35334i
$70$	−0.409868	−	4.69165i	−0.0489886	−	0.560760i
$71$			3.91612i			0.464758i	0.972625	+	0.232379i	$0.0746509\pi$
$71$			3.91612i			0.464758i	−0.972625	+	0.232379i	$0.925349\pi$
$72$	2.42407	+	1.76746i	0.285679	+	0.208297i
$73$	1.14565	+	0.661439i	0.134088	+	0.0774155i	0.565543	−	0.824719i	$-0.308667\pi$
$73$	1.14565	+	0.661439i	0.134088	+	0.0774155i	−0.431456	+	0.902134i	$0.642000\pi$
$74$	−6.84960	−	3.95462i	−0.796249	−	0.459715i
$75$	−0.168698	+	3.16773i	−0.0194796	+	0.365778i
$76$			3.03271i			0.347875i
$77$	−0.962024	−	11.0120i	−0.109633	−	1.25494i
$78$	−1.45182	−	0.944570i	−0.164387	−	0.106951i
$79$	5.64583	+	9.77886i	0.635205	+	1.10021i	0.986472	+	0.163932i	$0.0524179\pi$
$79$	5.64583	+	9.77886i	0.635205	+	1.10021i	−0.351266	+	0.936276i	$0.614249\pi$
$80$	−0.890016	+	1.54155i	−0.0995068	+	0.172351i
$81$	−2.75221	−	8.56886i	−0.305801	−	0.952096i
$82$	2.33523	−	1.34825i	0.257883	−	0.148889i
$83$	3.38793			0.371874			0.185937	−	0.982562i	$-0.440468\pi$
$83$	3.38793			0.371874			0.185937	+	0.982562i	$0.440468\pi$
$84$	3.88860	−	2.42462i	0.424281	−	0.264548i
$85$	13.5734			1.47224
$86$	−0.279589	+	0.161421i	−0.0301488	+	0.0174064i
$87$	6.00636	+	11.8128i	0.643949	+	1.26647i
$88$	−2.08901	+	3.61827i	−0.222689	+	0.385708i
$89$	1.23778	+	2.14390i	0.131205	+	0.227253i	0.924141	−	0.382051i	$-0.124782\pi$
$89$	1.23778	+	2.14390i	0.131205	+	0.227253i	−0.792937	+	0.609304i	$0.791449\pi$
$90$	4.88209	−	2.16377i	0.514617	−	0.228081i
$91$	−2.16746	+	1.51727i	−0.227212	+	0.159053i
$92$			7.74315i			0.807279i
$93$	3.57331	+	0.190297i	0.370535	+	0.0197329i
$94$	−3.54688	−	2.04779i	−0.365833	−	0.211214i
$95$	4.67508	+	2.69916i	0.479653	+	0.276928i
$96$	−1.72960	−	0.0921101i	−0.176527	−	0.00940095i
$97$		−	6.52429i		−	0.662442i	−0.943553	−	0.331221i	$-0.892540\pi$
$97$		−	6.52429i		−	0.662442i	0.943553	−	0.331221i	$-0.107460\pi$
$98$	−1.21379	−	6.89396i	−0.122611	−	0.696395i
$99$	11.4590	−	5.07869i	1.15167	−	0.510428i
$100$	−0.915742	−	1.58611i	−0.0915742	−	0.158611i
$101$	0.0989242	−	0.171342i	0.00984333	−	0.0170491i	−0.861062	−	0.508500i	$-0.830200\pi$
$101$	0.0989242	−	0.171342i	0.00984333	−	0.0170491i	0.870905	+	0.491451i	$0.163533\pi$
$102$	5.98614	+	11.7730i	0.592716	+	1.16571i
$103$	5.71582	−	3.30003i	0.563196	−	0.325161i	−0.191231	−	0.981545i	$-0.561248\pi$
$103$	5.71582	−	3.30003i	0.563196	−	0.325161i	0.754427	+	0.656384i	$0.227915\pi$
$104$	1.00000			0.0980581
$105$	−0.276759	−	8.15244i	−0.0270089	−	0.795596i
$106$	11.8270			1.14874
$107$	−9.96012	+	5.75048i	−0.962882	+	0.555920i	−0.897059	−	0.441911i	$-0.854301\pi$
$107$	−9.96012	+	5.75048i	−0.962882	+	0.555920i	−0.0658228	+	0.997831i	$0.520967\pi$
$108$	4.02987	+	3.28027i	0.387774	+	0.315644i
$109$	5.16177	−	8.94045i	0.494408	−	0.856340i	−0.505571	−	0.862785i	$-0.668718\pi$
$109$	5.16177	−	8.94045i	0.494408	−	0.856340i	0.999979	+	0.00644502i	$0.00205153\pi$
$110$	3.71850	+	6.44063i	0.354545	+	0.614090i
$111$	−11.4828	−	7.47082i	−1.08990	−	0.709099i
$112$	−1.11845	+	2.39772i	−0.105683	+	0.226564i
$113$			0.362383i			0.0340901i	0.999855	+	0.0170450i	$0.00542587\pi$
$113$			0.362383i			0.0340901i	−0.999855	+	0.0170450i	$0.994574\pi$
$114$	−0.279343	+	5.24537i	−0.0261629	+	0.491274i
$115$	11.9365	+	6.89153i	1.11308	+	0.642639i
$116$	−6.62606	−	3.82556i	−0.615214	−	0.355194i
$117$	−2.42407	−	1.76746i	−0.224105	−	0.163401i
$118$		−	13.7265i		−	1.26362i
$119$	20.0983	−	1.75581i	1.84241	−	0.160954i
$120$	−1.68136	+	2.58429i	−0.153487	+	0.235912i
$121$	3.22790	+	5.59088i	0.293445	+	0.508262i
$122$	4.26624	−	7.38934i	0.386247	−	0.668999i
$123$	4.16320	−	2.11683i	0.375383	−	0.190868i
$124$	−1.78918	+	1.03299i	−0.160674	+	0.0927649i
$125$	−12.1603			−1.08765
$126$	6.94906	−	3.83544i	0.619071	−	0.341688i
$127$	17.7284			1.57314			0.786572	−	0.617498i	$-0.211854\pi$
$127$	17.7284			1.57314			0.786572	+	0.617498i	$0.211854\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−0.498445	+	0.253440i	−0.0438856	+	0.0223141i
$130$	0.890016	−	1.54155i	0.0780596	−	0.135203i
$131$	−4.34750	−	7.53010i	−0.379843	−	0.657908i	0.611196	−	0.791479i	$-0.290689\pi$
$131$	−4.34750	−	7.53010i	−0.379843	−	0.657908i	−0.991039	+	0.133572i	$0.957355\pi$
$132$	−3.94642	+	6.06573i	−0.343492	+	0.527954i
$133$	7.27159	+	3.39192i	0.630527	+	0.294117i
$134$		−	12.5078i		−	1.08051i
$135$	8.64336	−	3.29276i	0.743902	−	0.283396i
$136$	−6.60376	−	3.81268i	−0.566268	−	0.326935i
$137$	7.42752	+	4.28828i	0.634576	+	0.366373i	0.782522	−	0.622623i	$-0.213933\pi$
$137$	7.42752	+	4.28828i	0.634576	+	0.366373i	−0.147946	+	0.988995i	$0.547266\pi$
$138$	−0.713223	+	13.3926i	−0.0607135	+	1.14005i
$139$		−	0.761522i		−	0.0645915i	−0.999478	−	0.0322957i	$-0.989718\pi$
$139$		−	0.761522i		−	0.0645915i	0.999478	−	0.0322957i	$-0.0102818\pi$
$140$	2.70078	+	3.85816i	0.228258	+	0.326074i
$141$	−5.94606	−	3.86857i	−0.500749	−	0.325792i
$142$	−1.95806	−	3.39146i	−0.164317	−	0.284605i
$143$	2.08901	−	3.61827i	0.174691	−	0.302575i
$144$	−2.98303	−	0.318627i	−0.248586	−	0.0265523i
$145$	−11.7946	+	6.80962i	−0.979489	+	0.565508i
$146$	−1.32288			−0.109482
$147$	−1.46437	−	12.0356i	−0.120779	−	0.992679i
$148$	7.90923			0.650135
$149$	1.22069	−	0.704767i	0.100003	−	0.0577368i	−0.449164	−	0.893449i	$-0.648278\pi$
$149$	1.22069	−	0.704767i	0.100003	−	0.0577368i	0.549167	+	0.835712i	$0.314945\pi$
$150$	−1.43777	−	2.82769i	−0.117393	−	0.230880i
$151$	−7.33631	+	12.7069i	−0.597020	+	1.03407i	0.396238	+	0.918148i	$0.370316\pi$
$151$	−7.33631	+	12.7069i	−0.597020	+	1.03407i	−0.993258	+	0.115922i	$0.963018\pi$
$152$	−1.51635	−	2.62640i	−0.122993	−	0.213029i
$153$	9.26921	+	20.9140i	0.749371	+	1.69080i
$154$	6.33916	+	9.05570i	0.510824	+	0.729729i
$155$			3.67750i			0.295384i
$156$	1.72960	+	0.0921101i	0.138479	+	0.00737471i
$157$	−18.1677	−	10.4891i	−1.44994	−	0.837121i	−0.451459	−	0.892292i	$-0.649096\pi$
$157$	−18.1677	−	10.4891i	−1.44994	−	0.837121i	−0.998477	+	0.0551705i	$0.982430\pi$
$158$	−9.77886	−	5.64583i	−0.777965	−	0.449158i
$159$	20.4560	+	1.08938i	1.62226	+	0.0863938i
$160$		−	1.78003i		−	0.140724i
$161$	18.5659	+	8.66030i	1.46320	+	0.682527i
$162$	6.66791	+	6.04475i	0.523880	+	0.474920i
$163$	−11.4406	−	19.8157i	−0.896095	−	1.55208i	−0.832444	−	0.554109i	$-0.813059\pi$
$163$	−11.4406	−	19.8157i	−0.896095	−	1.55208i	−0.0636510	−	0.997972i	$-0.520274\pi$
$164$	−1.34825	+	2.33523i	−0.105280	+	0.182351i
$165$	5.83827	+	11.4822i	0.454509	+	0.893890i
$166$	−2.93403	+	1.69397i	−0.227725	+	0.131477i
$167$	0.927408			0.0717650			0.0358825	−	0.999356i	$-0.488576\pi$
$167$	0.927408			0.0717650			0.0358825	+	0.999356i	$0.488576\pi$
$168$	−2.15532	+	4.04408i	−0.166287	+	0.312008i
$169$	−1.00000			−0.0769231
$170$	−11.7549	+	6.78670i	−0.901560	+	0.520516i
$171$	−0.966303	+	9.04666i	−0.0738950	+	0.691815i
$172$	0.161421	−	0.279589i	0.0123082	−	0.0213184i
$173$	−1.98619	−	3.44018i	−0.151007	−	0.261552i	0.780591	−	0.625042i	$-0.214918\pi$
$173$	−1.98619	−	3.44018i	−0.151007	−	0.261552i	−0.931598	+	0.363490i	$0.881585\pi$
$174$	−11.1081	−	7.22701i	−0.842100	−	0.547878i
$175$	−4.82727	+	0.421715i	−0.364907	+	0.0318787i
$176$		−	4.17801i		−	0.314930i
$177$	1.26435	−	23.7413i	0.0950342	−	1.78451i
$178$	−2.14390	−	1.23778i	−0.160692	−	0.0927757i
$179$	−12.3345	−	7.12132i	−0.921923	−	0.532273i	−0.0376751	−	0.999290i	$-0.511995\pi$
$179$	−12.3345	−	7.12132i	−0.921923	−	0.532273i	−0.884248	+	0.467017i	$0.845329\pi$
$180$	−3.14613	+	4.31492i	−0.234499	+	0.321615i
$181$		−	8.17371i		−	0.607547i	−0.952744	−	0.303774i	$-0.901753\pi$
$181$		−	8.17371i		−	0.607547i	0.952744	−	0.303774i	$-0.0982467\pi$
$182$	1.11845	−	2.39772i	0.0829048	−	0.177731i
$183$	8.05951	−	12.3876i	0.595776	−	0.915720i
$184$	−3.87158	−	6.70577i	−0.285416	−	0.494356i
$185$	7.03934	−	12.1925i	0.517543	−	0.896411i
$186$	−3.18972	+	1.62185i	−0.233882	+	0.118920i
$187$	−27.5906	+	15.9294i	−2.01762	+	1.16488i
$188$	4.09559			0.298701
$189$	12.3724	−	5.99370i	0.899958	−	0.435977i
$190$	−5.39832			−0.391635
$191$	21.0081	−	12.1290i	1.52009	−	0.877627i	0.520375	−	0.853938i	$-0.325792\pi$
$191$	21.0081	−	12.1290i	1.52009	−	0.877627i	0.999719	−	0.0236888i	$-0.00754109\pi$
$192$	1.54393	−	0.785030i	0.111424	−	0.0566547i
$193$	−9.38887	+	16.2620i	−0.675826	+	1.17056i	0.300401	+	0.953813i	$0.402879\pi$
$193$	−9.38887	+	16.2620i	−0.675826	+	1.17056i	−0.976227	+	0.216751i	$0.930454\pi$
$194$	3.26215	+	5.65020i	0.234208	+	0.405661i
$195$	1.68136	−	2.58429i	0.120405	−	0.185065i
$196$	4.49816	+	5.36345i	0.321297	+	0.383104i
$197$			6.12048i			0.436066i	0.975941	+	0.218033i	$0.0699640\pi$
$197$			6.12048i			0.436066i	−0.975941	+	0.218033i	$0.930036\pi$
$198$	−7.38445	+	10.1278i	−0.524790	+	0.719750i
$199$	−2.20348	−	1.27218i	−0.156200	−	0.0901824i	0.419862	−	0.907588i	$-0.362078\pi$
$199$	−2.20348	−	1.27218i	−0.156200	−	0.0901824i	−0.576063	+	0.817405i	$0.695412\pi$
$200$	1.58611	+	0.915742i	0.112155	+	0.0647527i
$201$	1.15210	−	21.6335i	0.0812627	−	1.52591i
$202$			0.197848i			0.0139206i
$203$	−16.5835	+	11.6088i	−1.16394	+	0.814777i
$204$	−11.0707	−	7.20269i	−0.775102	−	0.504289i
$205$	2.39992	+	4.15679i	0.167618	+	0.290323i
$206$	−3.30003	+	5.71582i	−0.229924	+	0.398240i
$207$	−2.46718	+	23.0981i	−0.171481	+	1.60543i
$208$	−0.866025	+	0.500000i	−0.0600481	+	0.0346688i
$209$	−12.6707			−0.876450
$210$	4.31590	+	6.92184i	0.297825	+	0.477652i
$211$	2.79394			0.192343			0.0961714	−	0.995365i	$-0.469340\pi$
$211$	2.79394			0.192343			0.0961714	+	0.995365i	$0.469340\pi$
$212$	−10.2425	+	5.91349i	−0.703456	+	0.406140i
$213$	−3.07427	−	6.04622i	−0.210646	−	0.414280i
$214$	5.75048	−	9.96012i	0.393095	−	0.680860i
$215$	−0.287334	−	0.497677i	−0.0195960	−	0.0339413i
$216$	−5.13010	−	0.825865i	−0.349059	−	0.0561930i
$217$	0.475708	+	5.44531i	0.0322932	+	0.369652i
$218$			10.3235i			0.699199i
$219$	−2.28805	−	0.121850i	−0.154612	−	0.00823388i
$220$	−6.44063	−	3.71850i	−0.434227	−	0.250701i
$221$	6.60376	+	3.81268i	0.444217	+	0.256469i
$222$	13.6798	+	0.728520i	0.918128	+	0.0488951i
$223$		−	16.6396i		−	1.11427i	−0.830423	−	0.557134i	$-0.811901\pi$
$223$		−	16.6396i		−	1.11427i	0.830423	−	0.557134i	$-0.188099\pi$
$224$	−0.230259	−	2.63571i	−0.0153848	−	0.176106i
$225$	−2.22631	−	5.02320i	−0.148421	−	0.334880i
$226$	−0.181191	−	0.313832i	−0.0120527	−	0.0208758i
$227$	7.37740	−	12.7780i	0.489655	−	0.848108i	−0.510274	−	0.860012i	$-0.670456\pi$
$227$	7.37740	−	12.7780i	0.489655	−	0.848108i	0.999929	+	0.0119039i	$0.00378923\pi$
$228$	−2.38077	−	4.68229i	−0.157670	−	0.310093i
$229$	18.7792	−	10.8422i	1.24097	−	0.716473i	0.271676	−	0.962389i	$-0.412422\pi$
$229$	18.7792	−	10.8422i	1.24097	−	0.716473i	0.969291	+	0.245916i	$0.0790888\pi$
$230$	−13.7831			−0.908828
$231$	10.1301	+	16.2466i	0.666511	+	1.06895i
$232$	7.65112			0.502320
$233$	6.74565	−	3.89460i	0.441922	−	0.255144i	−0.262490	−	0.964935i	$-0.584544\pi$
$233$	6.74565	−	3.89460i	0.441922	−	0.255144i	0.704413	+	0.709791i	$0.251210\pi$
$234$	2.98303	+	0.318627i	0.195007	+	0.0208293i
$235$	3.64514	−	6.31356i	0.237783	−	0.411852i
$236$	6.86324	+	11.8875i	0.446759	+	0.773809i
$237$	−16.3935	−	10.6658i	−1.06487	−	0.692815i
$238$	−16.5277	+	11.5697i	−1.07133	+	0.749953i
$239$			12.0680i			0.780615i	0.920685	+	0.390308i	$0.127631\pi$
$239$			12.0680i			0.780615i	−0.920685	+	0.390308i	$0.872369\pi$
$240$	0.163959	−	3.07874i	0.0105835	−	0.198732i
$241$	13.9929	+	8.07879i	0.901360	+	0.520400i	0.877641	−	0.479318i	$-0.159116\pi$
$241$	13.9929	+	8.07879i	0.901360	+	0.520400i	0.0237187	+	0.999719i	$0.492449\pi$
$242$	−5.59088	−	3.22790i	−0.359395	−	0.207497i
$243$	10.9760	+	11.0692i	0.704113	+	0.710088i
$244$			8.53247i			0.546236i
$245$	12.2715	−	2.16059i	0.783996	−	0.138035i
$246$	−2.54702	+	3.91483i	−0.162392	+	0.249600i
$247$	1.51635	+	2.62640i	0.0964833	+	0.167114i
$248$	1.03299	−	1.78918i	0.0655947	−	0.113613i
$249$	−5.23074	+	2.65963i	−0.331484	+	0.168547i
$250$	10.5311	−	6.08013i	0.666045	−	0.384541i
$251$	0.0295982			0.00186822			0.000934112	−	1.00000i	$-0.499703\pi$
$251$	0.0295982			0.00186822			0.000934112		1.00000i	$0.499703\pi$
$252$	−4.10034	+	6.79612i	−0.258297	+	0.428115i
$253$	−32.3510			−2.03389
$254$	−15.3533	+	8.86422i	−0.963350	+	0.556190i
$255$	−20.9564	+	10.6555i	−1.31234	+	0.667275i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.68113	+	13.3041i	0.479136	+	0.829887i	0.999714	−	0.0239268i	$-0.00761686\pi$
$257$	7.68113	+	13.3041i	0.479136	+	0.829887i	−0.520578	+	0.853814i	$0.674284\pi$
$258$	0.304946	−	0.468708i	0.0189851	−	0.0291805i
$259$	8.84605	−	18.9641i	0.549667	−	1.17837i
$260$			1.78003i			0.110393i
$261$	−18.5468	−	13.5230i	−1.14802	−	0.837053i
$262$	7.53010	+	4.34750i	0.465211	+	0.268590i
$263$	−16.8894	−	9.75108i	−1.04144	−	0.601277i	−0.121201	−	0.992628i	$-0.538675\pi$
$263$	−16.8894	−	9.75108i	−1.04144	−	0.601277i	−0.920242	+	0.391351i	$0.872008\pi$
$264$	0.384837	−	7.22629i	0.0236851	−	0.444747i
$265$			21.0524i			1.29324i
$266$	−7.99334	+	0.698307i	−0.490103	+	0.0428160i
$267$	−3.59408	−	2.33834i	−0.219954	−	0.143104i
$268$	6.25392	+	10.8321i	0.382019	+	0.661676i
$269$	1.69151	−	2.92978i	0.103133	−	0.178632i	−0.809841	−	0.586650i	$-0.800447\pi$
$269$	1.69151	−	2.92978i	0.103133	−	0.178632i	0.912974	+	0.408018i	$0.133780\pi$
$270$	−5.83899	+	7.17329i	−0.355350	+	0.436553i
$271$	−27.5354	+	15.8975i	−1.67265	+	0.965707i	−0.706510	+	0.707703i	$0.749732\pi$
$271$	−27.5354	+	15.8975i	−1.67265	+	0.965707i	−0.966144	+	0.258004i	$0.916935\pi$
$272$	7.62536			0.462356
$273$	2.15532	−	4.04408i	0.130446	−	0.244759i
$274$	−8.57657			−0.518129
$275$	6.62680	−	3.82598i	0.399611	−	0.230715i
$276$	−6.07861	−	11.9549i	−0.365889	−	0.719601i
$277$	−0.205326	+	0.355636i	−0.0123369	+	0.0213681i	−0.872128	−	0.489278i	$-0.837260\pi$
$277$	−0.205326	+	0.355636i	−0.0123369	+	0.0213681i	0.859791	+	0.510646i	$0.170594\pi$
$278$	0.380761	+	0.659498i	0.0228365	+	0.0395540i
$279$	−5.66633	+	2.51135i	−0.339234	+	0.150350i
$280$	−4.26803	−	1.99087i	−0.255063	−	0.118977i
$281$		−	21.7003i		−	1.29453i	−0.762265	−	0.647264i	$-0.775913\pi$
$281$		−	21.7003i		−	1.29453i	0.762265	−	0.647264i	$-0.224087\pi$
$282$	7.08372	+	0.377245i	0.421830	+	0.0224646i
$283$	−9.90407	−	5.71812i	−0.588736	−	0.339907i	0.175861	−	0.984415i	$-0.443729\pi$
$283$	−9.90407	−	5.71812i	−0.588736	−	0.339907i	−0.764598	+	0.644508i	$0.777062\pi$
$284$	3.39146	+	1.95806i	0.201246	+	0.116189i
$285$	−9.33693	−	0.497240i	−0.553072	−	0.0294539i
$286$			4.17801i			0.247051i
$287$	4.09130	+	5.84455i	0.241502	+	0.344993i
$288$	2.74269	−	1.21558i	0.161615	−	0.0716285i
$289$	−20.5731	−	35.6336i	−1.21018	−	2.09610i
$290$	6.80962	−	11.7946i	0.399875	−	0.692603i
$291$	5.12177	+	10.0731i	0.300243	+	0.590494i
$292$	1.14565	−	0.661439i	0.0670438	−	0.0387078i
$293$	−10.6232			−0.620616			−0.310308	−	0.950636i	$-0.600432\pi$
$293$	−10.6232			−0.620616			−0.310308	+	0.950636i	$0.600432\pi$
$294$	7.28598	+	9.69095i	0.424927	+	0.565188i
$295$	24.4336			1.42258
$296$	−6.84960	+	3.95462i	−0.398125	+	0.229857i
$297$	−13.7050	+	16.8368i	−0.795246	+	0.976972i
$298$	−0.704767	+	1.22069i	−0.0408261	+	0.0707128i
$299$	3.87158	+	6.70577i	0.223899	+	0.387804i
$300$	2.65899	+	1.72996i	0.153517	+	0.0998795i
$301$	−0.489836	−	0.699747i	−0.0282337	−	0.0403327i
$302$		−	14.6726i		−	0.844314i
$303$	−0.0182238	+	0.342199i	−0.00104693	+	0.0196588i
$304$	2.62640	+	1.51635i	0.150634	+	0.0869688i
$305$	13.1533	+	7.59404i	0.753154	+	0.434833i
$306$	−18.4844	−	13.4775i	−1.05668	−	0.770457i
$307$			30.4761i			1.73936i	0.493615	+	0.869680i	$0.335675\pi$
$307$			30.4761i			1.73936i	−0.493615	+	0.869680i	$0.664325\pi$
$308$	−10.0177	−	4.67288i	−0.570813	−	0.266262i
$309$	−6.23421	+	9.58211i	−0.354652	+	0.545107i
$310$	−1.83875	−	3.18481i	−0.104434	−	0.180885i
$311$	−3.65935	+	6.33818i	−0.207503	+	0.359405i	−0.950927	−	0.309415i	$-0.899867\pi$
$311$	−3.65935	+	6.33818i	−0.207503	+	0.359405i	0.743425	+	0.668820i	$0.233200\pi$
$312$	−1.54393	+	0.785030i	−0.0874080	+	0.0444436i
$313$	−3.28061	+	1.89406i	−0.185431	+	0.107059i	−0.589842	−	0.807519i	$-0.700810\pi$
$313$	−3.28061	+	1.89406i	−0.185431	+	0.107059i	0.404411	+	0.914577i	$0.367477\pi$
$314$	20.9782			1.18387
$315$	6.82721	+	12.3695i	0.384670	+	0.696945i
$316$	11.2917			0.635205
$317$	−4.69062	+	2.70813i	−0.263452	+	0.152104i	−0.625908	−	0.779897i	$-0.715272\pi$
$317$	−4.69062	+	2.70813i	−0.263452	+	0.152104i	0.362456	+	0.932001i	$0.381938\pi$
$318$	−18.2601	+	9.28454i	−1.02397	+	0.520651i
$319$	15.9832	−	27.6838i	0.894889	−	1.54999i
$320$	0.890016	+	1.54155i	0.0497534	+	0.0861755i
$321$	10.8635	−	16.6974i	0.606339	−	0.931955i
$322$	−20.4087	+	1.78293i	−1.13733	+	0.0993587i
$323$		−	23.1255i		−	1.28674i
$324$	−8.79695	−	1.90095i	−0.488720	−	0.105608i
$325$	−1.58611	−	0.915742i	−0.0879816	−	0.0507962i
$326$	19.8157	+	11.4406i	1.09749	+	0.633635i
$327$	−0.950903	+	17.8556i	−0.0525850	+	0.987417i
$328$		−	2.69649i		−	0.148889i
$329$	4.58069	−	9.82008i	0.252542	−	0.541399i
$330$	−10.7972	−	7.02476i	−0.594366	−	0.386701i
$331$	11.1387	+	19.2928i	0.612237	+	1.06043i	0.990862	+	0.134876i	$0.0430636\pi$
$331$	11.1387	+	19.2928i	0.612237	+	1.06043i	−0.378625	+	0.925550i	$0.623603\pi$
$332$	1.69397	−	2.93403i	0.0929684	−	0.161026i
$333$	23.5935	+	2.52010i	1.29292	+	0.138100i
$334$	−0.803159	+	0.463704i	−0.0439469	+	0.0253728i
$335$	22.2643			1.21643
$336$	−0.155480	−	4.57994i	−0.00848211	−	0.249856i
$337$	−4.55407			−0.248076			−0.124038	−	0.992277i	$-0.539584\pi$
$337$	−4.55407			−0.248076			−0.124038	+	0.992277i	$0.539584\pi$
$338$	0.866025	−	0.500000i	0.0471056	−	0.0271964i
$339$	−0.284481	−	0.559494i	−0.0154509	−	0.0303876i
$340$	6.78670	−	11.7549i	0.368060	−	0.637499i
$341$	−4.31583	−	7.47524i	−0.233715	−	0.404807i
$342$	−3.68649	−	8.31779i	−0.199342	−	0.449775i
$343$	17.8910	−	4.78660i	0.966024	−	0.258452i
$344$			0.322841i			0.0174064i
$345$	−23.8392	−	1.26956i	−1.28346	−	0.0683508i
$346$	3.44018	+	1.98619i	0.184945	+	0.106778i
$347$	−7.46932	−	4.31241i	−0.400974	−	0.231502i	0.285930	−	0.958250i	$-0.407697\pi$
$347$	−7.46932	−	4.31241i	−0.400974	−	0.231502i	−0.686904	+	0.726748i	$0.741031\pi$
$348$	13.2334	+	0.704745i	0.709383	+	0.0377783i
$349$		−	0.237322i		−	0.0127035i	−0.999980	−	0.00635177i	$-0.997978\pi$
$349$		−	0.237322i		−	0.0127035i	0.999980	−	0.00635177i	$-0.00202184\pi$
$350$	3.96968	−	2.77885i	0.212188	−	0.148536i
$351$	5.13010	+	0.825865i	0.273825	+	0.0440814i
$352$	2.08901	+	3.61827i	0.111344	+	0.192854i
$353$	−2.05021	+	3.55106i	−0.109121	+	0.189004i	−0.915415	−	0.402512i	$-0.868137\pi$
$353$	−2.05021	+	3.55106i	−0.109121	+	0.189004i	0.806293	+	0.591516i	$0.201470\pi$
$354$	10.7757	+	21.1928i	0.572722	+	1.12638i
$355$	6.03690	−	3.48541i	0.320406	−	0.184986i
$356$	2.47557			0.131205
$357$	−29.6520	+	18.4886i	−1.56935	+	0.978520i
$358$	14.2426			0.752747
$359$	−5.27567	+	3.04591i	−0.278439	+	0.160757i	−0.632717	−	0.774383i	$-0.718060\pi$
$359$	−5.27567	+	3.04591i	−0.278439	+	0.160757i	0.354277	+	0.935140i	$0.384727\pi$
$360$	0.567167	−	5.30989i	0.0298923	−	0.279856i
$361$	−4.90134	+	8.48938i	−0.257965	+	0.446809i
$362$	4.08686	+	7.07864i	0.214800	+	0.372045i
$363$	−9.37266	−	6.09795i	−0.491937	−	0.320059i
$364$	0.230259	+	2.63571i	0.0120688	+	0.138149i
$365$		−	2.35476i		−	0.123254i
$366$	−0.785927	+	14.7578i	−0.0410811	+	0.771401i
$367$	−18.0027	−	10.3939i	−0.939734	−	0.542556i	−0.0498569	−	0.998756i	$-0.515877\pi$
$367$	−18.0027	−	10.3939i	−0.939734	−	0.542556i	−0.889877	+	0.456201i	$0.849210\pi$
$368$	6.70577	+	3.87158i	0.349562	+	0.201820i
$369$	−4.76593	+	6.53648i	−0.248104	+	0.340275i
$370$			14.0787i			0.731916i
$371$	2.72327	+	31.1725i	0.141385	+	1.61840i
$372$	1.95145	−	2.99943i	0.101178	−	0.155513i
$373$	3.44216	+	5.96200i	0.178228	+	0.308701i	0.941274	−	0.337644i	$-0.109630\pi$
$373$	3.44216	+	5.96200i	0.178228	+	0.308701i	−0.763045	+	0.646345i	$0.776297\pi$
$374$	15.9294	−	27.5906i	0.823691	−	1.42668i
$375$	18.7746	−	9.54618i	0.969518	−	0.492962i
$376$	−3.54688	+	2.04779i	−0.182916	+	0.105607i
$377$	−7.65112			−0.394053
$378$	−7.71794	+	11.3769i	−0.396968	+	0.585164i
$379$	−14.6704			−0.753570			−0.376785	−	0.926301i	$-0.622970\pi$
$379$	−14.6704			−0.753570			−0.376785	+	0.926301i	$0.622970\pi$
$380$	4.67508	−	2.69916i	0.239827	−	0.138464i
$381$	−27.3715	+	13.9174i	−1.40228	+	0.713008i
$382$	−12.1290	+	21.0081i	−0.620576	+	1.07487i
$383$	−10.9702	−	19.0009i	−0.560550	−	0.970900i	−0.997448	−	0.0713898i	$-0.977257\pi$
$383$	−10.9702	−	19.0009i	−0.560550	−	0.970900i	0.436899	−	0.899511i	$-0.356077\pi$
$384$	−0.944570	+	1.45182i	−0.0482024	+	0.0740880i
$385$	−16.1194	+	11.2839i	−0.821522	+	0.575081i
$386$		−	18.7777i		−	0.955762i
$387$	0.570607	−	0.782589i	0.0290056	−	0.0397812i
$388$	−5.65020	−	3.26215i	−0.286846	−	0.165610i
$389$	−19.8429	−	11.4563i	−1.00608	−	0.580858i	−0.0960352	−	0.995378i	$-0.530616\pi$
$389$	−19.8429	−	11.4563i	−1.00608	−	0.580858i	−0.910040	+	0.414520i	$0.863949\pi$
$390$	−0.163959	+	3.07874i	−0.00830239	+	0.155898i
$391$		−	59.0443i		−	2.98600i
$392$	−6.57724	−	2.39581i	−0.332201	−	0.121007i
$393$	12.6236	+	8.21304i	0.636777	+	0.414293i
$394$	−3.06024	−	5.30049i	−0.154173	−	0.267035i
$395$	10.0498	−	17.4067i	0.505658	−	0.875826i
$396$	1.33123	−	12.4631i	0.0668968	−	0.626297i
$397$	−3.67578	+	2.12221i	−0.184482	+	0.106511i	−0.589397	−	0.807844i	$-0.700635\pi$
$397$	−3.67578	+	2.12221i	−0.184482	+	0.106511i	0.404915	+	0.914354i	$0.367301\pi$
$398$	2.54436			0.127537
$399$	−13.8896	+	0.471524i	−0.695350	+	0.0236057i
$400$	−1.83148			−0.0915742
$401$	12.9346	−	7.46782i	0.645925	−	0.372925i	−0.140968	−	0.990014i	$-0.545022\pi$
$401$	12.9346	−	7.46782i	0.645925	−	0.372925i	0.786893	+	0.617089i	$0.211688\pi$
$402$	9.81903	+	19.3112i	0.489729	+	0.963158i
$403$	−1.03299	+	1.78918i	−0.0514567	+	0.0891256i
$404$	−0.0989242	−	0.171342i	−0.00492166	−	0.00852457i
$405$	−10.7598	+	11.8691i	−0.534661	+	0.589780i
$406$	8.55736	−	18.3453i	0.424695	−	0.910460i
$407$			33.0449i			1.63797i
$408$	13.1888	+	0.702373i	0.652944	+	0.0347727i
$409$	28.2564	+	16.3138i	1.39719	+	0.806666i	0.994097	−	0.108494i	$-0.0346028\pi$
$409$	28.2564	+	16.3138i	1.39719	+	0.806666i	0.403090	+	0.915160i	$0.367936\pi$
$410$	−4.15679	−	2.39992i	−0.205289	−	0.118524i
$411$	−14.8340	−	0.789989i	−0.731709	−	0.0389673i
$412$		−	6.60006i		−	0.325161i
$413$	36.1790	−	3.16064i	1.78025	−	0.155525i
$414$	−9.41239	−	21.2371i	−0.462594	−	1.04375i
$415$	−3.01531	−	5.22268i	−0.148016	−	0.256371i
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$	0.597818	+	1.17574i	0.0292753	+	0.0575762i
$418$	10.9731	−	6.33534i	0.536714	−	0.309872i
$419$	−27.4096			−1.33905			−0.669524	−	0.742790i	$-0.733502\pi$
$419$	−27.4096			−1.33905			−0.669524	+	0.742790i	$0.733502\pi$
$420$	−7.19860	−	3.83654i	−0.351256	−	0.187204i
$421$	−18.9065			−0.921447			−0.460724	−	0.887544i	$-0.652410\pi$
$421$	−18.9065			−0.921447			−0.460724	+	0.887544i	$0.652410\pi$
$422$	−2.41962	+	1.39697i	−0.117785	+	0.0680035i
$423$	12.2173	+	1.30497i	0.594024	+	0.0634496i
$424$	5.91349	−	10.2425i	0.287185	−	0.497418i
$425$	6.98287	+	12.0947i	0.338719	+	0.586678i
$426$	5.68551	+	3.69905i	0.275464	+	0.179219i
$427$	20.4585	+	9.54311i	0.990057	+	0.461824i
$428$			11.5010i			0.555920i
$429$	−0.384837	+	7.22629i	−0.0185801	+	0.348889i
$430$	0.497677	+	0.287334i	0.0240001	+	0.0138565i
$431$	−4.24835	−	2.45278i	−0.204636	−	0.118146i	0.394180	−	0.919033i	$-0.371029\pi$
$431$	−4.24835	−	2.45278i	−0.204636	−	0.118146i	−0.598816	+	0.800887i	$0.704362\pi$
$432$	4.85573	−	1.84983i	0.233621	−	0.0890000i
$433$		−	1.02650i		−	0.0493306i	−0.999696	−	0.0246653i	$-0.992148\pi$
$433$		−	1.02650i		−	0.0493306i	0.999696	−	0.0246653i	$-0.00785201\pi$
$434$	−3.13463	−	4.47792i	−0.150467	−	0.214947i
$435$	12.8643	−	19.7727i	0.616797	−	0.948029i
$436$	−5.16177	−	8.94045i	−0.247204	−	0.428170i
$437$	11.7414	−	20.3366i	0.561665	−	0.972833i
$438$	2.04243	−	1.03850i	0.0975912	−	0.0496214i
$439$	1.98357	−	1.14522i	0.0946708	−	0.0546582i	−0.451917	−	0.892060i	$-0.649260\pi$
$439$	1.98357	−	1.14522i	0.0946708	−	0.0546582i	0.546588	+	0.837402i	$0.315926\pi$
$440$	7.43700			0.354545
$441$	11.7092	+	17.4326i	0.557581	+	0.830123i
$442$	−7.62536			−0.362702
$443$	23.5109	−	13.5740i	1.11704	−	0.644922i	0.176395	−	0.984319i	$-0.443556\pi$
$443$	23.5109	−	13.5740i	1.11704	−	0.644922i	0.940643	+	0.339397i	$0.110223\pi$
$444$	−12.2113	+	6.20899i	−0.579524	+	0.294665i
$445$	2.20329	−	3.81622i	0.104446	−	0.180906i
$446$	8.31978	+	14.4103i	0.393953	+	0.682347i
$447$	−1.33140	+	2.04639i	−0.0629732	+	0.0967911i
$448$	1.51727	+	2.16746i	0.0716841	+	0.102403i
$449$			5.17387i			0.244170i	0.992520	+	0.122085i	$0.0389581\pi$
$449$			5.17387i			0.244170i	−0.992520	+	0.122085i	$0.961042\pi$
$450$	4.43964	+	3.23707i	0.209287	+	0.152597i
$451$	−9.75662	−	5.63299i	−0.459421	−	0.265247i
$452$	0.313832	+	0.181191i	0.0147614	+	0.00852252i
$453$	1.35150	−	25.3778i	0.0634989	−	1.19235i
$454$			14.7548i			0.692477i
$455$	4.26803	+	1.99087i	0.200088	+	0.0933335i
$456$	4.40295	+	2.86460i	0.206187	+	0.134147i
$457$	10.9929	+	19.0402i	0.514225	+	0.890664i	0.999864	+	0.0165046i	$0.00525381\pi$
$457$	10.9929	+	19.0402i	0.514225	+	0.890664i	−0.485638	+	0.874160i	$0.661413\pi$
$458$	−10.8422	+	18.7792i	−0.506623	+	0.877496i
$459$	−30.7292	−	25.0133i	−1.43432	−	1.16752i
$460$	11.9365	−	6.89153i	0.556541	−	0.321319i
$461$	11.9652			0.557276			0.278638	−	0.960396i	$-0.410117\pi$
$461$	11.9652			0.557276			0.278638	+	0.960396i	$0.410117\pi$
$462$	−16.8962	−	9.00495i	−0.786084	−	0.418948i
$463$	16.1445			0.750299			0.375150	−	0.926964i	$-0.377591\pi$
$463$	16.1445			0.750299			0.375150	+	0.926964i	$0.377591\pi$
$464$	−6.62606	+	3.82556i	−0.307607	+	0.177597i
$465$	−2.88695	−	5.67781i	−0.133879	−	0.263302i
$466$	−3.89460	+	6.74565i	−0.180414	+	0.312486i
$467$	−12.6840	−	21.9693i	−0.586943	−	1.01662i	−0.994630	−	0.103494i	$-0.966998\pi$
$467$	−12.6840	−	21.9693i	−0.586943	−	1.01662i	0.407687	−	0.913122i	$-0.366336\pi$
$468$	−2.74269	+	1.21558i	−0.126781	+	0.0561900i
$469$	32.9671	−	2.88004i	1.52228	−	0.132988i
$470$			7.29028i			0.336275i
$471$	36.2839	+	1.93230i	1.67187	+	0.0890359i
$472$	−11.8875	−	6.86324i	−0.547165	−	0.315906i
$473$	1.16812	+	0.674417i	0.0537104	+	0.0310097i
$474$	19.5301	+	1.04008i	0.897045	+	0.0477723i
$475$			5.55435i			0.254851i
$476$	8.52856	−	18.2835i	0.390906	−	0.838023i
$477$	−32.4378	+	14.3766i	−1.48523	+	0.658259i
$478$	−6.03401	−	10.4512i	−0.275989	−	0.478027i
$479$	−6.02439	+	10.4346i	−0.275261	+	0.476767i	−0.970201	−	0.242301i	$-0.922098\pi$
$479$	−6.02439	+	10.4346i	−0.275261	+	0.476767i	0.694940	+	0.719068i	$0.255431\pi$
$480$	1.39738	+	2.74825i	0.0637814	+	0.125440i
$481$	6.84960	−	3.95462i	0.312315	−	0.180315i
$482$	−16.1576			−0.735957
$483$	−35.4631	+	1.20390i	−1.61363	+	0.0547794i
$484$	6.45579			0.293445
$485$	−10.0575	+	5.80673i	−0.456690	+	0.263670i
$486$	−15.0401	−	4.09817i	−0.682233	−	0.185897i
$487$	3.26366	−	5.65282i	0.147890	−	0.256154i	−0.782557	−	0.622579i	$-0.786085\pi$
$487$	3.26366	−	5.65282i	0.147890	−	0.256154i	0.930448	+	0.366425i	$0.119418\pi$
$488$	−4.26624	−	7.38934i	−0.193123	−	0.334500i
$489$	33.2194	+	21.6128i	1.50223	+	0.977366i
$490$	−9.54712	+	8.00686i	−0.431295	+	0.361713i
$491$			27.9942i			1.26336i	0.775229	+	0.631680i	$0.217634\pi$
$491$			27.9942i			1.26336i	−0.775229	+	0.631680i	$0.782366\pi$
$492$	0.248374	−	4.66385i	0.0111976	−	0.210263i
$493$	50.5261	+	29.1713i	2.27558	+	1.31381i
$494$	−2.62640	−	1.51635i	−0.118167	−	0.0682240i
$495$	−18.0278	−	13.1446i	−0.810289	−	0.590804i
$496$			2.06597i			0.0927649i
$497$	8.48805	−	5.94179i	0.380741	−	0.266526i
$498$	3.20014	−	4.91867i	0.143402	−	0.220411i
$499$	13.3598	+	23.1399i	0.598068	+	1.03588i	0.993106	+	0.117220i	$0.0373982\pi$
$499$	13.3598	+	23.1399i	0.598068	+	1.03588i	−0.395038	+	0.918665i	$0.629268\pi$
$500$	−6.08013	+	10.5311i	−0.271912	+	0.470965i
$501$	−1.43186	+	0.728043i	−0.0639706	+	0.0325266i
$502$	−0.0256328	+	0.0147991i	−0.00114405	+	0.000660517i
$503$	−5.93142			−0.264469			−0.132234	−	0.991218i	$-0.542215\pi$
$503$	−5.93142			−0.264469			−0.132234	+	0.991218i	$0.542215\pi$
$504$	0.152941	−	7.93578i	0.00681254	−	0.353488i
$505$	−0.352177			−0.0156717
$506$	28.0168	−	16.1755i	1.24550	−	0.719088i
$507$	1.54393	−	0.785030i	0.0685684	−	0.0348644i
$508$	8.86422	−	15.3533i	0.393286	−	0.681191i
$509$	−0.579080	−	1.00300i	−0.0256673	−	0.0444570i	0.852906	−	0.522064i	$-0.174838\pi$
$509$	−0.579080	−	1.00300i	−0.0256673	−	0.0444570i	−0.878574	+	0.477607i	$0.841504\pi$
$510$	12.8210	−	19.7062i	0.567724	−	0.872603i
$511$	−0.304604	−	3.48672i	−0.0134749	−	0.154244i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.60999	−	14.7260i	−0.247687	−	0.650169i
$514$	−13.3041	−	7.68113i	−0.586819	−	0.338800i
$515$	−10.1743	−	5.87416i	−0.448335	−	0.258846i
$516$	−0.0297369	+	0.558386i	−0.00130910	+	0.0245816i
$517$			17.1114i			0.752559i
$518$	1.82117	+	20.8465i	0.0800176	+	0.915941i
$519$	5.76719	+	3.75219i	0.253151	+	0.164703i
$520$	−0.890016	−	1.54155i	−0.0390298	−	0.0676016i
$521$	10.8139	−	18.7301i	0.473764	−	0.820583i	−0.525785	−	0.850617i	$-0.676228\pi$
$521$	10.8139	−	18.7301i	0.473764	−	0.820583i	0.999549	+	0.0300347i	$0.00956178\pi$
$522$	22.8235	+	2.43785i	0.998958	+	0.106702i
$523$	7.93704	−	4.58245i	0.347062	−	0.200377i	−0.316328	−	0.948650i	$-0.602450\pi$
$523$	7.93704	−	4.58245i	0.347062	−	0.200377i	0.663391	+	0.748273i	$0.269117\pi$
$524$	−8.69501			−0.379843
$525$	7.12191	−	4.44065i	0.310826	−	0.193806i
$526$	19.5022			0.850334
$527$	13.6432	−	7.87690i	0.594306	−	0.343123i
$528$	3.27987	+	6.45057i	0.142738	+	0.280725i
$529$	18.4782	−	32.0052i	0.803400	−	1.39153i
$530$	−10.5262	−	18.2319i	−0.457229	−	0.791944i
$531$	16.6856	+	37.6475i	0.724092	+	1.63376i
$532$	6.57329	−	4.60142i	0.284988	−	0.199497i
$533$			2.69649i			0.116798i
$534$	4.28174	+	0.228025i	0.185289	+	0.00986759i
$535$	17.7293	+	10.2360i	0.766506	+	0.442543i
$536$	−10.8321	−	6.25392i	−0.467875	−	0.270128i
$537$	24.6341	+	1.31189i	1.06304	+	0.0566123i
$538$			3.38302i			0.145852i
$539$	−22.4086	+	18.7934i	−0.965205	+	0.809487i
$540$	1.47007	−	9.13175i	0.0632616	−	0.392968i
$541$	3.56736	+	6.17885i	0.153373	+	0.265649i	0.932465	−	0.361260i	$-0.117653\pi$
$541$	3.56736	+	6.17885i	0.153373	+	0.265649i	−0.779093	+	0.626909i	$0.784320\pi$
$542$	15.8975	−	27.5354i	0.682858	−	1.18274i
$543$	6.41661	+	12.6197i	0.275363	+	0.541561i
$544$	−6.60376	+	3.81268i	−0.283134	+	0.163467i
$545$	−18.3762			−0.787152
$546$	0.155480	+	4.57994i	0.00665391	+	0.196003i
$547$	−27.2663			−1.16582			−0.582911	−	0.812536i	$-0.698086\pi$
$547$	−27.2663			−1.16582			−0.582911	+	0.812536i	$0.698086\pi$
$548$	7.42752	−	4.28828i	0.317288	−	0.183186i
$549$	−2.71868	+	25.4526i	−0.116030	+	1.08629i
$550$	−3.82598	+	6.62680i	−0.163140	+	0.282568i
$551$	11.6018	+	20.0949i	0.494253	+	0.856072i
$552$	11.2417	+	7.31395i	0.478478	+	0.311302i
$553$	12.6291	−	27.0743i	0.537045	−	1.15132i
$554$		−	0.410653i		−	0.0174470i
$555$	−1.29679	+	24.3505i	−0.0550457	+	1.03362i
$556$	−0.659498	−	0.380761i	−0.0279689	−	0.0161479i
$557$	16.3293	+	9.42770i	0.691893	+	0.399464i	0.804321	−	0.594195i	$-0.202529\pi$
$557$	16.3293	+	9.42770i	0.691893	+	0.399464i	−0.112428	+	0.993660i	$0.535863\pi$
$558$	3.65151	−	5.00806i	0.154581	−	0.212008i
$559$		−	0.322841i		−	0.0136547i
$560$	4.69165	−	0.409868i	0.198259	−	0.0173201i
$561$	30.0929	−	46.2534i	1.27052	−	1.95282i
$562$	10.8501	+	18.7930i	0.457685	+	0.792734i
$563$	17.0233	−	29.4852i	0.717446	−	1.24265i	−0.244562	−	0.969634i	$-0.578644\pi$
$563$	17.0233	−	29.4852i	0.717446	−	1.24265i	0.962008	−	0.273020i	$-0.0880225\pi$
$564$	−6.32331	+	3.21516i	−0.266259	+	0.135383i
$565$	0.558632	−	0.322526i	0.0235018	−	0.0135688i
$566$	11.4362			0.480701
$567$	−14.3969	+	18.9665i	−0.604612	+	0.796520i
$568$	−3.91612			−0.164317
$569$	−9.68078	+	5.58920i	−0.405839	+	0.234311i	−0.689000	−	0.724761i	$-0.741950\pi$
$569$	−9.68078	+	5.58920i	−0.405839	+	0.234311i	0.283161	+	0.959072i	$0.408617\pi$
$570$	8.33464	−	4.23784i	0.349100	−	0.177504i
$571$	−8.44767	+	14.6318i	−0.353524	+	0.612322i	−0.986864	−	0.161552i	$-0.948350\pi$
$571$	−8.44767	+	14.6318i	−0.353524	+	0.612322i	0.633340	+	0.773874i	$0.281683\pi$
$572$	−2.08901	−	3.61827i	−0.0873457	−	0.151287i
$573$	−22.9135	+	35.2184i	−0.957223	+	1.47127i
$574$	−6.46544	−	3.01588i	−0.269862	−	0.125880i
$575$			14.1815i			0.591408i
$576$	−1.76746	+	2.42407i	−0.0736440	+	0.101003i
$577$	5.63256	+	3.25196i	0.234487	+	0.135381i	0.612640	−	0.790362i	$-0.290108\pi$
$577$	5.63256	+	3.25196i	0.234487	+	0.135381i	−0.378154	+	0.925743i	$0.623441\pi$
$578$	35.6336	+	20.5731i	1.48216	+	0.855728i
$579$	1.72962	−	32.4780i	0.0718805	−	1.34974i
$580$			13.6192i			0.565508i
$581$	−5.14039	−	7.34322i	−0.213259	−	0.304648i
$582$	−9.47211	−	6.16265i	−0.392632	−	0.255450i
$583$	−24.7066	−	42.7932i	−1.02324	−	1.77231i
$584$	−0.661439	+	1.14565i	−0.0273705	+	0.0474071i
$585$	−0.567167	+	5.30989i	−0.0234495	+	0.219537i
$586$	9.19999	−	5.31162i	0.380048	−	0.219421i
$587$	22.5985			0.932741			0.466370	−	0.884590i	$-0.345561\pi$
$587$	22.5985			0.932741			0.466370	+	0.884590i	$0.345561\pi$
$588$	−11.1553	−	4.74962i	−0.460038	−	0.195871i
$589$	6.26549			0.258165
$590$	−21.1601	+	12.2168i	−0.871147	+	0.502957i
$591$	−4.80476	−	9.44960i	−0.197641	−	0.388705i
$592$	3.95462	−	6.84960i	0.162534	−	0.281517i
$593$	−15.5467	−	26.9276i	−0.638425	−	1.10578i	−0.985779	−	0.168050i	$-0.946253\pi$
$593$	−15.5467	−	26.9276i	−0.638425	−	1.10578i	0.347354	−	0.937734i	$-0.387080\pi$
$594$	3.45047	−	21.4336i	0.141575	−	0.879433i
$595$	−20.5945	−	29.4199i	−0.844290	−	1.20610i
$596$		−	1.40953i		−	0.0577368i
$597$	4.40072	+	0.234361i	0.180109	+	0.00959176i
$598$	−6.70577	−	3.87158i	−0.274219	−	0.158321i
$599$	−19.9056	−	11.4925i	−0.813321	−	0.469571i	0.0347868	−	0.999395i	$-0.488925\pi$
$599$	−19.9056	−	11.4925i	−0.813321	−	0.469571i	−0.848108	+	0.529824i	$0.822258\pi$
$600$	−3.16773	−	0.168698i	−0.129322	−	0.00688708i
$601$		−	3.44036i		−	0.140335i	−0.997535	−	0.0701675i	$-0.977647\pi$
$601$		−	3.44036i		−	0.140335i	0.997535	−	0.0701675i	$-0.0223534\pi$
$602$	0.774084	+	0.361080i	0.0315493	+	0.0147165i
$603$	15.2042	+	34.3052i	0.619164	+	1.39701i
$604$	7.33631	+	12.7069i	0.298510	+	0.517035i
$605$	5.74576	−	9.95195i	0.233598	−	0.404604i
$606$	−0.155317	−	0.305465i	−0.00630932	−	0.0124086i
$607$	6.79228	−	3.92152i	0.275690	−	0.159170i	−0.355781	−	0.934570i	$-0.615785\pi$
$607$	6.79228	−	3.92152i	0.275690	−	0.159170i	0.631471	+	0.775400i	$0.282452\pi$
$608$	−3.03271			−0.122993
$609$	16.4906	−	30.9417i	0.668233	−	1.25382i
$610$	−15.1881			−0.614947
$611$	3.54688	−	2.04779i	0.143491	−	0.0828448i
$612$	22.7467	+	2.42965i	0.919481	+	0.0982127i
$613$	−3.03080	+	5.24950i	−0.122413	+	0.212025i	−0.920719	−	0.390227i	$-0.872397\pi$
$613$	−3.03080	+	5.24950i	−0.122413	+	0.212025i	0.798306	+	0.602252i	$0.205730\pi$
$614$	−15.2380	−	26.3930i	−0.614957	−	1.06514i
$615$	−6.96852	−	4.53379i	−0.280998	−	0.182820i
$616$	11.0120	−	0.962024i	0.443688	−	0.0387610i
$617$			7.32788i			0.295010i	0.989061	+	0.147505i	$0.0471242\pi$
$617$			7.32788i			0.295010i	−0.989061	+	0.147505i	$0.952876\pi$
$618$	0.607932	−	11.4155i	0.0244546	−	0.459197i
$619$	−14.1166	−	8.15023i	−0.567394	−	0.327585i	0.188714	−	0.982032i	$-0.439568\pi$
$619$	−14.1166	−	8.15023i	−0.567394	−	0.327585i	−0.756108	+	0.654447i	$0.772902\pi$
$620$	3.18481	+	1.83875i	0.127905	+	0.0738459i
$621$	−14.3235	−	37.5987i	−0.574783	−	1.50878i
$622$		−	7.31870i		−	0.293453i
$623$	2.76879	−	5.93572i	0.110929	−	0.237810i
$624$	0.944570	−	1.45182i	0.0378130	−	0.0581194i
$625$	6.24412	+	10.8151i	0.249765	+	0.432606i
$626$	1.89406	−	3.28061i	0.0757020	−	0.131120i
$627$	19.5627	−	9.94687i	0.781259	−	0.397240i
$628$	−18.1677	+	10.4891i	−0.724968	+	0.418561i
$629$	−60.3108			−2.40475
$630$	−12.0973	−	7.29874i	−0.481968	−	0.290789i
$631$	2.77879			0.110622			0.0553110	−	0.998469i	$-0.482385\pi$
$631$	2.77879			0.110622			0.0553110	+	0.998469i	$0.482385\pi$
$632$	−9.77886	+	5.64583i	−0.388982	+	0.224579i
$633$	−4.31366	+	2.19333i	−0.171452	+	0.0871770i
$634$	2.70813	−	4.69062i	0.107554	−	0.186288i
$635$	−15.7786	−	27.3293i	−0.626154	−	1.08453i
$636$	11.1714	−	17.1707i	0.442975	−	0.680862i
$637$	6.57724	+	2.39581i	0.260600	+	0.0949253i
$638$			31.9665i			1.26556i
$639$	9.49293	+	6.92156i	0.375535	+	0.273813i
$640$	−1.54155	−	0.890016i	−0.0609352	−	0.0351810i
$641$	11.6157	+	6.70635i	0.458794	+	0.264885i	0.711537	−	0.702648i	$-0.247999\pi$
$641$	11.6157	+	6.70635i	0.458794	+	0.264885i	−0.252743	+	0.967534i	$0.581333\pi$
$642$	−1.05935	+	19.8921i	−0.0418094	+	0.785077i
$643$		−	13.1234i		−	0.517536i	−0.965939	−	0.258768i	$-0.916683\pi$
$643$		−	13.1234i		−	0.517536i	0.965939	−	0.258768i	$-0.0833165\pi$
$644$	16.7830	−	11.7484i	0.661343	−	0.462953i
$645$	0.834315	+	0.542814i	0.0328511	+	0.0213733i
$646$	11.5627	+	20.0273i	0.454930	+	0.787962i
$647$	4.75405	−	8.23425i	0.186901	−	0.323722i	−0.757315	−	0.653050i	$-0.773489\pi$
$647$	4.75405	−	8.23425i	0.186901	−	0.323722i	0.944215	+	0.329328i	$0.106822\pi$
$648$	8.56886	−	2.75221i	0.336617	−	0.108117i
$649$	−49.6660	+	28.6747i	−1.94956	+	1.12558i
$650$	1.83148			0.0718367
$651$	−5.00919	−	8.03375i	−0.196326	−	0.314867i
$652$	−22.8811			−0.896095
$653$	−37.9647	+	21.9189i	−1.48567	+	0.857753i	−0.999867	−	0.0163145i	$-0.994807\pi$
$653$	−37.9647	+	21.9189i	−1.48567	+	0.857753i	−0.485805	+	0.874067i	$0.661473\pi$
$654$	−8.10429	−	15.9389i	−0.316903	−	0.623259i
$655$	−7.73870	+	13.4038i	−0.302376	+	0.523731i
$656$	1.34825	+	2.33523i	0.0526402	+	0.0911754i
$657$	3.62825	−	1.60806i	0.141551	−	0.0627363i
$658$	0.943044	+	10.7948i	0.0367637	+	0.420825i
$659$		−	0.586590i		−	0.0228503i	−0.999935	−	0.0114252i	$-0.996363\pi$
$659$		−	0.586590i		−	0.0228503i	0.999935	−	0.0114252i	$-0.00363682\pi$
$660$	12.8630	+	0.685023i	0.500693	+	0.0266645i
$661$	22.3525	+	12.9052i	0.869412	+	0.501955i	0.867153	−	0.498042i	$-0.165948\pi$
$661$	22.3525	+	12.9052i	0.869412	+	0.501955i	0.00225925	+	0.999997i	$0.499281\pi$
$662$	−19.2928	−	11.1387i	−0.749835	−	0.432917i
$663$	−13.1888	−	0.702373i	−0.512212	−	0.0272779i
$664$			3.38793i			0.131477i
$665$	−1.24301	−	14.2284i	−0.0482018	−	0.551754i
$666$	−21.6926	+	9.61428i	−0.840571	+	0.372546i
$667$	29.6219	+	51.3066i	1.14696	+	1.98660i
$668$	0.463704	−	0.803159i	0.0179412	−	0.0310752i
$669$	13.0626	+	25.6904i	0.505028	+	0.993247i
$670$	−19.2815	+	11.1322i	−0.744909	+	0.430073i
$671$	−35.6488			−1.37621
$672$	2.42462	+	3.88860i	0.0935317	+	0.150006i
$673$	17.9739			0.692842			0.346421	−	0.938079i	$-0.387397\pi$
$673$	17.9739			0.692842			0.346421	+	0.938079i	$0.387397\pi$
$674$	3.94394	−	2.27703i	0.151915	−	0.0877081i
$675$	7.38064	+	6.00776i	0.284081	+	0.231239i
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	1.34288	+	2.32594i	0.0516110	+	0.0893929i	0.890677	−	0.454637i	$-0.150231\pi$
$677$	1.34288	+	2.32594i	0.0516110	+	0.0893929i	−0.839066	+	0.544030i	$0.816898\pi$
$678$	0.526115	+	0.342296i	0.0202053	+	0.0131458i
$679$	−14.1412	+	9.89909i	−0.542688	+	0.379892i
$680$			13.5734i			0.520516i
$681$	−1.35907	+	25.5199i	−0.0520796	+	0.977925i
$682$	7.47524	+	4.31583i	0.286242	+	0.165262i
$683$	−20.6264	−	11.9087i	−0.789249	−	0.455673i	0.0504493	−	0.998727i	$-0.483935\pi$
$683$	−20.6264	−	11.9087i	−0.789249	−	0.455673i	−0.839698	+	0.543054i	$0.817268\pi$
$684$	7.35149	+	5.36017i	0.281091	+	0.204951i
$685$		−	15.2666i		−	0.583306i
$686$	−13.1008	+	13.0908i	−0.500190	+	0.499810i
$687$	−20.4824	+	31.4819i	−0.781453	+	1.20111i
$688$	−0.161421	−	0.279589i	−0.00615410	−	0.0106592i
$689$	−5.91349	+	10.2425i	−0.225286	+	0.390207i
$690$	21.2801	−	10.8201i	0.810120	−	0.411915i
$691$	−19.1284	+	11.0438i	−0.727680	+	0.420126i	−0.817573	−	0.575825i	$-0.804681\pi$
$691$	−19.1284	+	11.0438i	−0.727680	+	0.420126i	0.0898926	+	0.995951i	$0.471348\pi$
$692$	−3.97238			−0.151007
$693$	−28.3943	−	17.1313i	−1.07861	−	0.650763i
$694$	8.62482			0.327394
$695$	−1.17393	+	0.677767i	−0.0445296	+	0.0257092i
$696$	−11.8128	+	6.00636i	−0.447763	+	0.227670i
$697$	10.2809	−	17.8070i	0.389416	−	0.674488i
$698$	0.118661	+	0.205527i	0.00449138	+	0.00777929i
$699$	−7.35745	+	11.3085i	−0.278284	+	0.427729i
$700$	−2.04842	+	4.39139i	−0.0774229	+	0.165979i
$701$			41.6034i			1.57134i	0.618646	+	0.785670i	$0.287682\pi$
$701$			41.6034i			1.57134i	−0.618646	+	0.785670i	$0.712318\pi$
$702$	−4.85573	+	1.84983i	−0.183268	+	0.0698174i
$703$	−20.7728	−	11.9932i	−0.783462	−	0.452332i
$704$	−3.61827	−	2.08901i	−0.136369	−	0.0787324i
$705$	−0.671508	+	12.6093i	−0.0252905	+	0.474892i
$706$		−	4.10041i		−	0.154321i
$707$	−0.521471	+	0.0455563i	−0.0196120	+	0.00171332i
$708$	−19.9284	−	12.9656i	−0.748955	−	0.487278i
$709$	−8.48128	−	14.6900i	−0.318521	−	0.551695i	0.661659	−	0.749805i	$-0.269853\pi$
$709$	−8.48128	−	14.6900i	−0.318521	−	0.551695i	−0.980180	+	0.198111i	$0.936519\pi$
$710$	−3.48541	+	6.03690i	−0.130805	+	0.226561i
$711$	33.6834	+	3.59783i	1.26323	+	0.134929i
$712$	−2.14390	+	1.23778i	−0.0803461	+	0.0463879i
$713$	15.9971			0.599098
$714$	16.4351	−	30.8376i	0.615068	−	1.15407i
$715$	−7.43700			−0.278128
$716$	−12.3345	+	7.12132i	−0.460962	+	0.266136i
$717$	−9.47376	−	18.6322i	−0.353804	−	0.695832i
$718$	3.04591	−	5.27567i	0.113672	−	0.196886i
$719$	16.5688	+	28.6980i	0.617912	+	1.07025i	0.989866	+	0.142003i	$0.0453544\pi$
$719$	16.5688	+	28.6980i	0.617912	+	1.07025i	−0.371954	+	0.928251i	$0.621312\pi$
$720$	2.16377	+	4.88209i	0.0806388	+	0.181945i
$721$	−15.8251	−	7.38181i	−0.589358	−	0.274913i
$722$		−	9.80269i		−	0.364818i
$723$	−27.9461	−	1.48828i	−1.03933	−	0.0553496i
$724$	−7.07864	−	4.08686i	−0.263076	−	0.151887i
$725$	−12.1355	−	7.00645i	−0.450702	−	0.260213i
$726$	11.1659	+	0.594644i	0.414407	+	0.0220693i
$727$			21.4992i			0.797361i	0.917090	+	0.398680i	$0.130532\pi$
$727$			21.4992i			0.797361i	−0.917090	+	0.398680i	$0.869468\pi$
$728$	−1.51727	−	2.16746i	−0.0562336	−	0.0803316i
$729$	−25.6359	−	8.47354i	−0.949478	−	0.313835i
$730$	1.17738	+	2.03929i	0.0435769	+	0.0754774i
$731$	−1.23089	+	2.13196i	−0.0455261	+	0.0788536i
$732$	−6.69825	−	13.1736i	−0.247574	−	0.486909i
$733$	23.1346	−	13.3568i	0.854497	−	0.493344i	−0.00766847	−	0.999971i	$-0.502441\pi$
$733$	23.1346	−	13.3568i	0.854497	−	0.493344i	0.862166	+	0.506626i	$0.169108\pi$
$734$	20.7877			0.767289
$735$	−17.2502	+	12.9693i	−0.636283	+	0.478379i
$736$	−7.74315			−0.285416
$737$	−45.2567	+	26.1289i	−1.66705	+	0.962472i
$738$	0.859176	−	8.04372i	0.0316267	−	0.296093i
$739$	−3.52025	+	6.09726i	−0.129495	+	0.224291i	−0.923481	−	0.383644i	$-0.874669\pi$
$739$	−3.52025	+	6.09726i	−0.129495	+	0.224291i	0.793986	+	0.607936i	$0.208002\pi$
$740$	−7.03934	−	12.1925i	−0.258771	−	0.448205i
$741$	−4.40295	−	2.86460i	−0.161746	−	0.105234i
$742$	−17.9447	−	25.6346i	−0.658770	−	0.941075i
$743$		−	11.1695i		−	0.409770i	−0.978786	−	0.204885i	$-0.934318\pi$
$743$		−	11.1695i		−	0.409770i	0.978786	−	0.204885i	$-0.0656821\pi$
$744$	−0.190297	+	3.57331i	−0.00697662	+	0.131004i
$745$	−2.17287	−	1.25451i	−0.0796079	−	0.0459616i
$746$	−5.96200	−	3.44216i	−0.218284	−	0.126027i
$747$	5.98801	−	8.21257i	0.219090	−	0.300482i
$748$			31.8589i			1.16488i
$749$	27.5761	+	12.8632i	1.00761	+	0.470011i
$750$	−11.4862	+	17.6545i	−0.419417	+	0.644653i
$751$	−20.7730	−	35.9798i	−0.758017	−	1.31292i	−0.943861	−	0.330344i	$-0.892835\pi$
$751$	−20.7730	−	35.9798i	−0.758017	−	1.31292i	0.185844	−	0.982579i	$-0.440498\pi$
$752$	2.04779	−	3.54688i	0.0746753	−	0.129341i
$753$	−0.0456977	+	0.0232355i	−0.00166532	+	0.000846749i
$754$	6.62606	−	3.82556i	0.241307	−	0.139319i
$755$	26.1177			0.950522
$756$	0.995492	−	13.7116i	0.0362057	−	0.498687i
$757$	−26.8239			−0.974933			−0.487466	−	0.873142i	$-0.662079\pi$
$757$	−26.8239			−0.974933			−0.487466	+	0.873142i	$0.662079\pi$
$758$	12.7050	−	7.33522i	0.461465	−	0.266427i
$759$	49.9477	−	25.3965i	1.81299	−	0.921835i
$760$	−2.69916	+	4.67508i	−0.0979088	+	0.169583i
$761$	25.7381	+	44.5797i	0.933006	+	1.61601i	0.778152	+	0.628076i	$0.216157\pi$
$761$	25.7381	+	44.5797i	0.933006	+	1.61601i	0.154853	+	0.987937i	$0.450510\pi$
$762$	16.7457	−	25.7385i	0.606634	−	0.932409i
$763$	−27.2099	+	2.37709i	−0.985064	+	0.0860563i
$764$		−	24.2581i		−	0.877627i
$765$	23.9904	−	32.9028i	0.867374	−	1.18960i
$766$	19.0009	+	10.9702i	0.686530	+	0.396368i
$767$	11.8875	+	6.86324i	0.429232	+	0.247817i
$768$	0.0921101	−	1.72960i	0.00332374	−	0.0624116i
$769$		−	1.33310i		−	0.0480730i	−0.999711	−	0.0240365i	$-0.992348\pi$
$769$		−	1.33310i		−	0.0480730i	0.999711	−	0.0240365i	$-0.00765179\pi$
$770$	8.31789	−	17.8319i	0.299756	−	0.642616i
$771$	−22.3033	−	14.5107i	−0.803233	−	0.522591i
$772$	9.38887	+	16.2620i	0.337913	+	0.585282i
$773$	0.945780	−	1.63814i	0.0340173	−	0.0589198i	−0.848516	−	0.529171i	$-0.822503\pi$
$773$	0.945780	−	1.63814i	0.0340173	−	0.0589198i	0.882533	+	0.470251i	$0.155837\pi$
$774$	−0.102866	+	0.963045i	−0.00369744	+	0.0346159i
$775$	−3.27686	+	1.89190i	−0.117708	+	0.0679590i
$776$	6.52429			0.234208
$777$	1.22972	+	36.2238i	0.0441161	+	1.29952i
$778$	22.9126			0.821457
$779$	7.08207	−	4.08884i	0.253741	−	0.146498i
$780$	−1.39738	−	2.74825i	−0.0500342	−	0.0984031i
$781$	−8.18080	+	14.1696i	−0.292732	+	0.507026i
$782$	29.5222	+	51.1339i	1.05571	+	1.82854i
$783$	39.2510	+	6.31879i	1.40272	+	0.225815i
$784$	6.89396	−	1.21379i	0.246213	−	0.0433497i
$785$			37.3419i			1.33279i
$786$	−15.0389	−	0.800898i	−0.536419	−	0.0285671i
$787$	−20.5239	−	11.8495i	−0.731598	−	0.422388i	0.0874084	−	0.996173i	$-0.472141\pi$
$787$	−20.5239	−	11.8495i	−0.731598	−	0.422388i	−0.819007	+	0.573784i	$0.805475\pi$
$788$	5.30049	+	3.06024i	0.188822	+	0.109016i
$789$	33.7309	+	1.79635i	1.20085	+	0.0639516i
$790$			20.0995i			0.715109i
$791$	0.785451	−	0.549831i	0.0279274	−	0.0195497i
$792$	5.07869	+	11.4590i	0.180464	+	0.407178i
$793$	4.26624	+	7.38934i	0.151498	+	0.262403i
$794$	2.12221	−	3.67578i	0.0753145	−	0.130449i
$795$	−16.5268	−	32.5035i	−0.586145	−	1.15278i
$796$	−2.20348	+	1.27218i	−0.0781002	+	0.0450912i
$797$	37.0409			1.31205			0.656027	−	0.754737i	$-0.272236\pi$
$797$	37.0409			1.31205			0.656027	+	0.754737i	$0.272236\pi$
$798$	11.7930	−	7.35316i	0.417467	−	0.260299i
$799$	−31.2303			−1.10485
$800$	1.58611	−	0.915742i	0.0560775	−	0.0323764i
$801$	7.38469	+	0.788783i	0.260925	+	0.0278703i
$802$	−7.46782	+	12.9346i	−0.263698	+	0.456738i
$803$	2.76350	+	4.78652i	0.0975218	+	0.168913i
$804$	−18.1592	−	11.8145i	−0.640424	−	0.416666i
$805$	−3.17367	−	36.3282i	−0.111857	−	1.28040i
$806$		−	2.06597i		−	0.0727708i
$807$	−0.311611	+	5.85127i	−0.0109692	+	0.205975i
$808$	0.171342	+	0.0989242i	0.00602778	+	0.00348014i
$809$	−32.3735	−	18.6908i	−1.13819	−	0.657135i	−0.192209	−	0.981354i	$-0.561565\pi$
$809$	−32.3735	−	18.6908i	−1.13819	−	0.657135i	−0.945982	+	0.324219i	$0.894898\pi$
$810$	3.38375	−	15.6589i	0.118893	−	0.550196i
$811$		−	45.1640i		−	1.58592i	−0.609272	−	0.792961i	$-0.708538\pi$
$811$		−	45.1640i		−	1.58592i	0.609272	−	0.792961i	$-0.291462\pi$
$812$	1.76174	+	20.1661i	0.0618248	+	0.707693i
$813$	30.0327	−	46.1608i	1.05329	−	1.61893i
$814$	−16.5224	−	28.6177i	−0.579111	−	1.00305i
$815$	−20.3646	+	35.2725i	−0.713341	+	1.23554i
$816$	−11.7730	+	5.98614i	−0.412139	+	0.209557i
$817$	−0.847910	+	0.489541i	−0.0296646	+	0.0171269i
$818$	−32.6276			−1.14080
$819$	−0.152941	+	7.93578i	−0.00534419	+	0.277299i
$820$	4.79984			0.167618
$821$	−6.52016	+	3.76442i	−0.227555	+	0.131379i	−0.609444	−	0.792829i	$-0.708607\pi$
$821$	−6.52016	+	3.76442i	−0.227555	+	0.131379i	0.381889	+	0.924208i	$0.375274\pi$
$822$	13.2416	−	6.73286i	0.461855	−	0.234836i
$823$	−5.65277	+	9.79088i	−0.197043	+	0.341289i	−0.947568	−	0.319553i	$-0.896467\pi$
$823$	−5.65277	+	9.79088i	−0.197043	+	0.341289i	0.750525	+	0.660842i	$0.229801\pi$
$824$	3.30003	+	5.71582i	0.114962	+	0.199120i
$825$	−7.22781	+	11.1093i	−0.251640	+	0.386776i
$826$	−29.7516	+	20.8267i	−1.03519	+	0.724654i
$827$		−	16.4328i		−	0.571426i	−0.958315	−	0.285713i	$-0.907770\pi$
$827$		−	16.4328i		−	0.571426i	0.958315	−	0.285713i	$-0.0922304\pi$
$828$	18.7699	+	13.6857i	0.652300	+	0.475610i
$829$	−9.26281	−	5.34789i	−0.321711	−	0.185740i	0.330444	−	0.943826i	$-0.392801\pi$
$829$	−9.26281	−	5.34789i	−0.321711	−	0.185740i	−0.652155	+	0.758086i	$0.726135\pi$
$830$	5.22268	+	3.01531i	0.181282	+	0.104663i
$831$	0.0378253	−	0.710265i	0.00131214	−	0.0246388i
$832$			1.00000i			0.0346688i
$833$	−34.3001	−	40.8983i	−1.18843	−	1.41704i
$834$	−1.10560	−	0.719311i	−0.0382836	−	0.0249077i
$835$	−0.825408	−	1.42965i	−0.0285644	−	0.0494750i
$836$	−6.33534	+	10.9731i	−0.219112	+	0.379514i
$837$	6.77695	−	8.32559i	0.234246	−	0.287775i
$838$	23.7375	−	13.7048i	0.819997	−	0.473425i
$839$	37.6696			1.30050			0.650250	−	0.759721i	$-0.274664\pi$
$839$	37.6696			1.30050			0.650250	+	0.759721i	$0.274664\pi$
$840$	8.15244	−	0.276759i	0.281286	−	0.00954908i
$841$	−29.5396			−1.01861
$842$	16.3735	−	9.45326i	0.564269	−	0.325781i
$843$	17.0354	+	33.5037i	0.586729	+	1.15393i
$844$	1.39697	−	2.41962i	0.0480857	−	0.0832869i
$845$	0.890016	+	1.54155i	0.0306175	+	0.0530310i
$846$	−11.2329	+	4.97850i	−0.386196	+	0.171164i
$847$	7.22046	−	15.4792i	0.248098	−	0.531872i
$848$			11.8270i			0.406140i
$849$	19.7801	+	1.05339i	0.678852	+	0.0361524i
$850$	−12.0947	−	6.98287i	−0.414844	−	0.239510i
$851$	−53.0375	−	30.6212i	−1.81810	−	1.04968i
$852$	−6.77332	−	0.360714i	−0.232050	−	0.0123579i
$853$			20.1209i			0.688926i	0.938800	+	0.344463i	$0.111939\pi$
$853$			20.1209i			0.688926i	−0.938800	+	0.344463i	$0.888061\pi$
$854$	−22.4891	+	1.96468i	−0.769563	+	0.0672298i
$855$	14.8059	−	6.56207i	0.506352	−	0.224418i
$856$	−5.75048	−	9.96012i	−0.196547	−	0.340430i
$857$	−18.8978	+	32.7320i	−0.645538	+	1.11810i	0.338639	+	0.940916i	$0.390033\pi$
$857$	−18.8978	+	32.7320i	−0.645538	+	1.11810i	−0.984177	+	0.177188i	$0.943300\pi$
$858$	−3.27987	−	6.45057i	−0.111973	−	0.220219i
$859$	3.63139	−	2.09658i	0.123901	−	0.0715345i	−0.436768	−	0.899574i	$-0.643877\pi$
$859$	3.63139	−	2.09658i	0.123901	−	0.0715345i	0.560670	+	0.828040i	$0.310544\pi$
$860$	−0.574668			−0.0195960
$861$	−10.9048	−	5.81180i	−0.371636	−	0.198066i
$862$	4.90557			0.167084
$863$	17.3613	−	10.0235i	0.590984	−	0.341205i	−0.174503	−	0.984657i	$-0.555832\pi$
$863$	17.3613	−	10.0235i	0.590984	−	0.341205i	0.765486	+	0.643452i	$0.222498\pi$
$864$	−3.28027	+	4.02987i	−0.111597	+	0.137099i
$865$	−3.53548	+	6.12363i	−0.120210	+	0.208210i
$866$	0.513252	+	0.888979i	0.0174410	+	0.0302087i
$867$	59.7369	+	38.8654i	2.02877	+	1.31994i
$868$	4.95363	+	2.31068i	0.168137	+	0.0784296i
$869$			47.1767i			1.60036i
$870$	−1.25447	+	23.5558i	−0.0425305	+	0.798617i
$871$	10.8321	+	6.25392i	0.367032	+	0.211906i
$872$	8.94045	+	5.16177i	0.302762	+	0.174800i
$873$	−15.8153	−	11.5314i	−0.535268	−	0.390279i
$874$			23.4827i			0.794315i
$875$	18.4504	+	26.3569i	0.623736	+	0.891027i
$876$	−1.24955	+	1.92058i	−0.0422184	+	0.0648905i
$877$	4.12611	+	7.14663i	0.139329	+	0.241325i	0.927243	−	0.374461i	$-0.122172\pi$
$877$	4.12611	+	7.14663i	0.139329	+	0.241325i	−0.787914	+	0.615785i	$0.788839\pi$
$878$	−1.14522	+	1.98357i	−0.0386492	+	0.0669423i
$879$	16.4016	−	8.33956i	0.553211	−	0.281286i
$880$	−6.44063	+	3.71850i	−0.217114	+	0.125351i
$881$	20.8084			0.701052			0.350526	−	0.936553i	$-0.386003\pi$
$881$	20.8084			0.701052			0.350526	+	0.936553i	$0.386003\pi$
$882$	−18.8567	−	9.24246i	−0.634940	−	0.311210i
$883$	3.29418			0.110858			0.0554289	−	0.998463i	$-0.482347\pi$
$883$	3.29418			0.110858			0.0554289	+	0.998463i	$0.482347\pi$
$884$	6.60376	−	3.81268i	0.222108	−	0.128234i
$885$	−37.7238	+	19.1811i	−1.26807	+	0.644765i
$886$	−13.5740	+	23.5109i	−0.456029	+	0.789865i
$887$	8.46183	+	14.6563i	0.284120	+	0.492111i	0.972396	−	0.233339i	$-0.0749651\pi$
$887$	8.46183	+	14.6563i	0.284120	+	0.492111i	−0.688275	+	0.725450i	$0.741632\pi$
$888$	7.47082	−	11.4828i	0.250704	−	0.385338i
$889$	−26.8988	−	38.4258i	−0.902155	−	1.28876i
$890$			4.40659i			0.147709i
$891$	7.94220	−	36.7538i	0.266074	−	1.23130i
$892$	−14.4103	−	8.31978i	−0.482492	−	0.278567i
$893$	−10.7567	−	6.21036i	−0.359958	−	0.207822i
$894$	0.129832	−	2.43793i	0.00434224	−	0.0815366i
$895$			25.3524i			0.847436i
$896$	−2.39772	−	1.11845i	−0.0801023	−	0.0373647i
$897$	−11.2417	−	7.31395i	−0.375349	−	0.244206i
$898$	−2.58694	−	4.48070i	−0.0863272	−	0.149523i
$899$	−7.90350	+	13.6893i	−0.263596	+	0.456562i
$900$	−5.46337	−	0.583561i	−0.182112	−	0.0194520i
$901$	78.1026	−	45.0925i	2.60197	−	1.50225i
$902$	11.2660			0.375116
$903$	1.30560	+	0.695826i	0.0434475	+	0.0231556i
$904$	−0.362383			−0.0120527
$905$	−12.6002	+	7.27474i	−0.418845	+	0.241820i
$906$	11.5185	+	22.6535i	0.382675	+	0.752613i
$907$	13.6532	−	23.6481i	0.453349	−	0.785223i	−0.545243	−	0.838278i	$-0.683563\pi$
$907$	13.6532	−	23.6481i	0.453349	−	0.785223i	0.998592	+	0.0530552i	$0.0168959\pi$
$908$	−7.37740	−	12.7780i	−0.244828	−	0.424054i
$909$	−0.240500	−	0.542638i	−0.00797688	−	0.0179982i
$910$	−4.69165	+	0.409868i	−0.155527	+	0.0135870i
$911$			44.0421i			1.45918i	0.683884	+	0.729591i	$0.260289\pi$
$911$			44.0421i			1.45918i	−0.683884	+	0.729591i	$0.739711\pi$
$912$	−5.24537	−	0.279343i	−0.173692	−	0.00924997i
$913$	12.2584	+	7.07741i	0.405695	+	0.234228i
$914$	−19.0402	−	10.9929i	−0.629795	−	0.363612i
$915$	−26.2693	−	1.39898i	−0.868436	−	0.0462487i
$916$		−	21.6844i		−	0.716473i
$917$	−9.72490	+	20.8482i	−0.321145	+	0.688469i
$918$	39.1189	+	6.29752i	1.29112	+	0.207849i
$919$	20.5810	+	35.6474i	0.678906	+	1.17590i	0.975311	+	0.220837i	$0.0708790\pi$
$919$	20.5810	+	35.6474i	0.678906	+	1.17590i	−0.296405	+	0.955062i	$0.595788\pi$
$920$	−6.89153	+	11.9365i	−0.227207	+	0.393534i
$921$	−23.9246	−	47.0530i	−0.788343	−	1.55045i
$922$	−10.3622	+	5.98261i	−0.341260	+	0.197027i
$923$	3.91612			0.128901
$924$	19.1350	−	0.649596i	0.629497	−	0.0213701i
$925$	14.4856			0.476285
$926$	−13.9816	+	8.07226i	−0.459463	+	0.265271i
$927$	2.10296	−	19.6882i	0.0690702	−	0.646645i
$928$	3.82556	−	6.62606i	0.125580	−	0.217511i
$929$	12.9117	+	22.3637i	0.423619	+	0.733730i	0.996290	−	0.0860551i	$-0.0274261\pi$
$929$	12.9117	+	22.3637i	0.423619	+	0.733730i	−0.572671	+	0.819785i	$0.694093\pi$
$930$	5.33907	+	3.47365i	0.175075	+	0.113906i
$931$	−3.68107	−	20.9074i	−0.120642	−	0.685211i
$932$		−	7.78921i		−	0.255144i
$933$	0.674126	−	12.6584i	0.0220699	−	0.414418i
$934$	21.9693	+	12.6840i	0.718856	+	0.415032i
$935$	49.1121	+	28.3549i	1.60614	+	0.927305i
$936$	1.76746	−	2.42407i	0.0577711	−	0.0792331i
$937$			34.6955i			1.13345i	0.823906	+	0.566726i	$0.191790\pi$
$937$			34.6955i			1.13345i	−0.823906	+	0.566726i	$0.808210\pi$
$938$	−27.1103	+	18.9777i	−0.885182	+	0.619644i
$939$	3.57815	−	5.49968i	0.116768	−	0.179475i
$940$	−3.64514	−	6.31356i	−0.118891	−	0.205926i
$941$	11.7288	−	20.3148i	0.382347	−	0.662245i	−0.609050	−	0.793132i	$-0.708449\pi$
$941$	11.7288	−	20.3148i	0.382347	−	0.662245i	0.991397	+	0.130887i	$0.0417824\pi$
$942$	−32.3889	+	16.4685i	−1.05529	+	0.536573i
$943$	18.0820	−	10.4397i	0.588832	−	0.339963i
$944$	13.7265			0.446759
$945$	−20.2512	−	13.7382i	−0.658772	−	0.446903i
$946$	−1.34883			−0.0438544
$947$	−21.8287	+	12.6028i	−0.709337	+	0.409536i	−0.810815	−	0.585302i	$-0.800976\pi$
$947$	−21.8287	+	12.6028i	−0.709337	+	0.409536i	0.101479	+	0.994838i	$0.467643\pi$
$948$	−17.4336	+	8.86429i	−0.566216	+	0.287899i
$949$	0.661439	−	1.14565i	0.0214712	−	0.0371892i
$950$	−2.77718	−	4.81021i	−0.0901035	−	0.156064i
$951$	5.11604	−	7.86346i	0.165899	−	0.254990i
$952$	1.75581	+	20.0983i	0.0569060	+	0.651389i
$953$			41.9411i			1.35861i	0.733858	+	0.679303i	$0.237718\pi$
$953$			41.9411i			1.35861i	−0.733858	+	0.679303i	$0.762282\pi$
$954$	20.9037	−	28.6694i	0.676781	−	0.928206i
$955$	−37.3951	−	21.5901i	−1.21008	−	0.698639i
$956$	10.4512	+	6.03401i	0.338016	+	0.195154i
$957$	−2.94443	+	55.2892i	−0.0951800	+	1.78725i
$958$		−	12.0488i		−	0.389279i
$959$	−1.97483	−	22.6054i	−0.0637706	−	0.729965i
$960$	−2.58429	−	1.68136i	−0.0834076	−	0.0542658i
$961$	−13.3659	−	23.1504i	−0.431157	−	0.746786i
$962$	−3.95462	+	6.84960i	−0.127502	+	0.220840i
$963$	−3.66452	+	34.3077i	−0.118087	+	1.10555i
$964$	13.9929	−	8.07879i	0.450680	−	0.260200i
$965$	33.4250			1.07599
$966$	30.1100	−	18.7742i	0.968775	−	0.604049i
$967$	−48.4673			−1.55860			−0.779301	−	0.626649i	$-0.784426\pi$
$967$	−48.4673			−1.55860			−0.779301	+	0.626649i	$0.784426\pi$
$968$	−5.59088	+	3.22790i	−0.179698	+	0.103749i
$969$	18.1542	+	35.7042i	0.583197	+	1.14698i
$970$	5.80673	−	10.0575i	0.186443	−	0.322928i
$971$	−16.5100	−	28.5961i	−0.529830	−	0.917692i	−0.999395	−	0.0347938i	$-0.988923\pi$
$971$	−16.5100	−	28.5961i	−0.529830	−	0.917692i	0.469565	−	0.882898i	$-0.344411\pi$
$972$	15.0742	−	3.97094i	0.483505	−	0.127368i
$973$	−1.65057	+	1.15543i	−0.0529149	+	0.0370414i
$974$			6.52731i			0.209149i
$975$	3.16773	+	0.168698i	0.101449	+	0.00540267i
$976$	7.38934	+	4.26624i	0.236527	+	0.136559i
$977$	−6.63023	−	3.82796i	−0.212120	−	0.122467i	0.390176	−	0.920740i	$-0.372414\pi$
$977$	−6.63023	−	3.82796i	−0.212120	−	0.122467i	−0.602296	+	0.798273i	$0.705747\pi$
$978$	−39.5752	−	2.10758i	−1.26548	−	0.0673931i
$979$			10.3429i			0.330562i
$980$	4.26461	−	11.7077i	0.136228	−	0.373989i
$981$	−12.5491	−	28.3143i	−0.400661	−	0.904007i
$982$	−13.9971	−	24.2437i	−0.446665	−	0.773647i
$983$	21.1296	−	36.5976i	0.673931	−	1.16728i	−0.302850	−	0.953038i	$-0.597938\pi$
$983$	21.1296	−	36.5976i	0.673931	−	1.16728i	0.976780	−	0.214244i	$-0.0687287\pi$
$984$	2.11683	+	4.16320i	0.0674820	+	0.132718i
$985$	9.43504	−	5.44732i	0.300625	−	0.173566i
$986$	−58.3425			−1.85801
$987$	0.636780	+	18.7575i	0.0202689	+	0.597059i
$988$	3.03271			0.0964833
$989$	−2.16490	+	1.24990i	−0.0688397	+	0.0397446i
$990$	22.1848	+	2.36963i	0.705079	+	0.0753118i
$991$	−6.94512	+	12.0293i	−0.220619	+	0.382124i	−0.954996	−	0.296618i	$-0.904141\pi$
$991$	−6.94512	+	12.0293i	−0.220619	+	0.382124i	0.734377	+	0.678742i	$0.237474\pi$
$992$	−1.03299	−	1.78918i	−0.0327973	−	0.0568067i
$993$	−32.3428	−	21.0425i	−1.02637	−	0.667764i
$994$	−4.37997	+	9.38977i	−0.138924	+	0.297825i
$995$			4.52904i			0.143580i
$996$	−0.312063	+	5.85976i	−0.00988808	+	0.185674i
$997$	38.9188	+	22.4698i	1.23257	+	0.711626i	0.967565	−	0.252621i	$-0.0812925\pi$
$997$	38.9188	+	22.4698i	1.23257	+	0.711626i	0.265007	+	0.964247i	$0.414626\pi$
$998$	−23.1399	−	13.3598i	−0.732481	−	0.422898i
$999$	−38.4051	+	14.6307i	−1.21508	+	0.462896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.a.521.2	yes	32
3.2	odd	2		546.2.z.b.521.12	yes	32
7.5	odd	6		546.2.z.b.131.12	yes	32
21.5	even	6	inner	546.2.z.a.131.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.2	✓	32	21.5	even	6	inner
546.2.z.a.521.2	yes	32	1.1	even	1	trivial
546.2.z.b.131.12	yes	32	7.5	odd	6
546.2.z.b.521.12	yes	32	3.2	odd	2

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.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.54393 + 0.785030i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.890016 - 1.54155i) q^{5} +(0.944570 - 1.45182i) q^{6} +(-1.51727 - 2.16746i) q^{7} +1.00000i q^{8} +(1.76746 - 2.42407i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.54393 + 0.785030i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.890016 - 1.54155i) q^{5} +(0.944570 - 1.45182i) q^{6} +(-1.51727 - 2.16746i) q^{7} +1.00000i q^{8} +(1.76746 - 2.42407i) q^{9} +(1.54155 + 0.890016i) q^{10} +(3.61827 + 2.08901i) q^{11} +(-0.0921101 + 1.72960i) q^{12} -1.00000i q^{13} +(2.39772 + 1.11845i) q^{14} +(2.58429 + 1.68136i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.81268 + 6.60376i) q^{17} +(-0.318627 + 2.98303i) q^{18} +(-2.62640 + 1.51635i) q^{19} -1.78003 q^{20} +(4.04408 + 2.15532i) q^{21} -4.17801 q^{22} +(-6.70577 + 3.87158i) q^{23} +(-0.785030 - 1.54393i) q^{24} +(0.915742 - 1.58611i) q^{25} +(0.500000 + 0.866025i) q^{26} +(-0.825865 + 5.13010i) q^{27} +(-2.63571 + 0.230259i) q^{28} -7.65112i q^{29} +(-3.07874 - 0.163959i) q^{30} +(-1.78918 - 1.03299i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-7.22629 - 0.384837i) q^{33} -7.62536i q^{34} +(-1.99087 + 4.26803i) q^{35} +(-1.21558 - 2.74269i) q^{36} +(3.95462 + 6.84960i) q^{37} +(1.51635 - 2.62640i) q^{38} +(0.785030 + 1.54393i) q^{39} +(1.54155 - 0.890016i) q^{40} -2.69649 q^{41} +(-4.57994 + 0.155480i) q^{42} +0.322841 q^{43} +(3.61827 - 2.08901i) q^{44} +(-5.30989 - 0.567167i) q^{45} +(3.87158 - 6.70577i) q^{46} +(2.04779 + 3.54688i) q^{47} +(1.45182 + 0.944570i) q^{48} +(-2.39581 + 6.57724i) q^{49} +1.83148i q^{50} +(0.702373 - 13.1888i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(-10.2425 - 5.91349i) q^{53} +(-1.84983 - 4.85573i) q^{54} -7.43700i q^{55} +(2.16746 - 1.51727i) q^{56} +(2.86460 - 4.40295i) q^{57} +(3.82556 + 6.62606i) q^{58} +(-6.86324 + 11.8875i) q^{59} +(2.74825 - 1.39738i) q^{60} +(-7.38934 + 4.26624i) q^{61} +2.06597 q^{62} +(-7.93578 - 0.152941i) q^{63} -1.00000 q^{64} +(-1.54155 + 0.890016i) q^{65} +(6.45057 - 3.27987i) q^{66} +(-6.25392 + 10.8321i) q^{67} +(3.81268 + 6.60376i) q^{68} +(7.31395 - 11.2417i) q^{69} +(-0.409868 - 4.69165i) q^{70} +3.91612i q^{71} +(2.42407 + 1.76746i) q^{72} +(1.14565 + 0.661439i) q^{73} +(-6.84960 - 3.95462i) q^{74} +(-0.168698 + 3.16773i) q^{75} +3.03271i q^{76} +(-0.962024 - 11.0120i) q^{77} +(-1.45182 - 0.944570i) q^{78} +(5.64583 + 9.77886i) q^{79} +(-0.890016 + 1.54155i) q^{80} +(-2.75221 - 8.56886i) q^{81} +(2.33523 - 1.34825i) q^{82} +3.38793 q^{83} +(3.88860 - 2.42462i) q^{84} +13.5734 q^{85} +(-0.279589 + 0.161421i) q^{86} +(6.00636 + 11.8128i) q^{87} +(-2.08901 + 3.61827i) q^{88} +(1.23778 + 2.14390i) q^{89} +(4.88209 - 2.16377i) q^{90} +(-2.16746 + 1.51727i) q^{91} +7.74315i q^{92} +(3.57331 + 0.190297i) q^{93} +(-3.54688 - 2.04779i) q^{94} +(4.67508 + 2.69916i) q^{95} +(-1.72960 - 0.0921101i) q^{96} -6.52429i q^{97} +(-1.21379 - 6.89396i) q^{98} +(11.4590 - 5.07869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

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